Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,3,Mod(1601,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.1601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.l (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(78.4743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1601.4 | ||
Root | \(-1.58114 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.1601 |
Dual form | 2880.3.l.c.1601.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.837722 | −0.119675 | −0.0598373 | − | 0.998208i | \(-0.519058\pi\) | ||||
−0.0598373 | + | 0.998208i | \(0.519058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.3716i | 1.30651i | 0.757137 | + | 0.653256i | \(0.226597\pi\) | ||||
−0.757137 | + | 0.653256i | \(0.773403\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.8114 | 1.67780 | 0.838900 | − | 0.544286i | \(-0.183199\pi\) | ||||
0.838900 | + | 0.544286i | \(0.183199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.5454i | 1.38502i | 0.721407 | + | 0.692512i | \(0.243496\pi\) | ||||
−0.721407 | + | 0.692512i | \(0.756504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.32456 | −0.332871 | −0.166436 | − | 0.986052i | \(-0.553226\pi\) | ||||
−0.166436 | + | 0.986052i | \(0.553226\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 38.8723i | 1.69010i | 0.534689 | + | 0.845049i | \(0.320429\pi\) | ||||
−0.534689 | + | 0.845049i | \(0.679571\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.266737i | 0.00919784i | 0.999989 | + | 0.00459892i | \(0.00146389\pi\) | ||||
−0.999989 | + | 0.00459892i | \(0.998536\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −30.2719 | −0.976512 | −0.488256 | − | 0.872700i | \(-0.662367\pi\) | ||||
−0.488256 | + | 0.872700i | \(0.662367\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.87320i | − 0.0535201i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.53950 | −0.257824 | −0.128912 | − | 0.991656i | \(-0.541149\pi\) | ||||
−0.128912 | + | 0.991656i | \(0.541149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 19.3028i | − 0.470799i | −0.971899 | − | 0.235399i | \(-0.924360\pi\) | ||||
0.971899 | − | 0.235399i | \(-0.0756398\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.6228 | 0.456344 | 0.228172 | − | 0.973621i | \(-0.426725\pi\) | ||||
0.228172 | + | 0.973621i | \(0.426725\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 22.1684i | − 0.471669i | −0.971793 | − | 0.235834i | \(-0.924218\pi\) | ||||
0.971793 | − | 0.235834i | \(-0.0757823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.2982 | −0.985678 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 49.0012i | − 0.924552i | −0.886736 | − | 0.462276i | \(-0.847033\pi\) | ||||
0.886736 | − | 0.462276i | \(-0.152967\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −32.1359 | −0.584290 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 73.2351i | − 1.24127i | −0.784098 | − | 0.620637i | \(-0.786874\pi\) | ||||
0.784098 | − | 0.620637i | \(-0.213126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.3246 | 0.792206 | 0.396103 | − | 0.918206i | \(-0.370362\pi\) | ||||
0.396103 | + | 0.918206i | \(0.370362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 48.7717i | 0.750335i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 77.2982 | 1.15370 | 0.576852 | − | 0.816848i | \(-0.304281\pi\) | ||||
0.576852 | + | 0.816848i | \(0.304281\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 104.044i | 1.46541i | 0.680548 | + | 0.732703i | \(0.261742\pi\) | ||||
−0.680548 | + | 0.732703i | \(0.738258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.6754 | 0.653088 | 0.326544 | − | 0.945182i | \(-0.394116\pi\) | ||||
0.326544 | + | 0.945182i | \(0.394116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 12.0394i | − 0.156356i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −68.2192 | −0.863534 | −0.431767 | − | 0.901985i | \(-0.642110\pi\) | ||||
−0.431767 | + | 0.901985i | \(0.642110\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28.2098i | 0.339877i | 0.985455 | + | 0.169938i | \(0.0543569\pi\) | ||||
−0.985455 | + | 0.169938i | \(0.945643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −52.6491 | −0.619401 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 53.7774i | − 0.604240i | −0.953270 | − | 0.302120i | \(-0.902306\pi\) | ||||
0.953270 | − | 0.302120i | \(-0.0976943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.2719 | −0.200790 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 14.1421i | − 0.148865i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114.921 | −1.18475 | −0.592376 | − | 0.805661i | \(-0.701810\pi\) | ||||
−0.592376 | + | 0.805661i | \(0.701810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 17.5473i | − 0.173736i | −0.996220 | − | 0.0868679i | \(-0.972314\pi\) | ||||
0.996220 | − | 0.0868679i | \(-0.0276858\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 71.5395 | 0.694558 | 0.347279 | − | 0.937762i | \(-0.387106\pi\) | ||||
0.347279 | + | 0.937762i | \(0.387106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 76.3675i | 0.713715i | 0.934159 | + | 0.356858i | \(0.116152\pi\) | ||||
−0.934159 | + | 0.356858i | \(0.883848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 126.921 | 1.16441 | 0.582206 | − | 0.813041i | \(-0.302190\pi\) | ||||
0.582206 | + | 0.813041i | \(0.302190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0601i | 0.133275i | 0.997777 | + | 0.0666377i | \(0.0212272\pi\) | ||||
−0.997777 | + | 0.0666377i | \(0.978773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −86.9210 | −0.755835 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 19.7245i | − 0.165752i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.5438 | −0.706973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.1803i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −158.031 | −1.24434 | −0.622168 | − | 0.782884i | \(-0.713748\pi\) | ||||
−0.622168 | + | 0.782884i | \(0.713748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 211.220i | 1.61237i | 0.591665 | + | 0.806184i | \(0.298471\pi\) | ||||
−0.591665 | + | 0.806184i | \(0.701529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.29822 | 0.0398363 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 69.2592i | 0.505542i | 0.967526 | + | 0.252771i | \(0.0813419\pi\) | ||||
−0.967526 | + | 0.252771i | \(0.918658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −159.842 | −1.14994 | −0.574971 | − | 0.818174i | \(-0.694987\pi\) | ||||
−0.574971 | + | 0.818174i | \(0.694987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 313.465i | 2.19206i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.596443 | −0.00411340 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 9.81897i | − 0.0658991i | −0.999457 | − | 0.0329496i | \(-0.989510\pi\) | ||||
0.999457 | − | 0.0329496i | \(-0.0104901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −210.649 | −1.39503 | −0.697514 | − | 0.716572i | \(-0.745710\pi\) | ||||
−0.697514 | + | 0.716572i | \(0.745710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 67.6900i | − 0.436710i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −211.276 | −1.34571 | −0.672854 | − | 0.739775i | \(-0.734932\pi\) | ||||
−0.672854 | + | 0.739775i | \(0.734932\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 32.5642i | − 0.202262i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −222.763 | −1.36664 | −0.683322 | − | 0.730117i | \(-0.739465\pi\) | ||||
−0.683322 | + | 0.730117i | \(0.739465\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 33.3644i | − 0.199787i | −0.994998 | − | 0.0998933i | \(-0.968150\pi\) | ||||
0.994998 | − | 0.0998933i | \(-0.0318501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 306.737 | 1.81501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 29.8102i | − 0.172313i | −0.996282 | − | 0.0861567i | \(-0.972541\pi\) | ||||
0.996282 | − | 0.0861567i | \(-0.0274586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.18861 | 0.0239349 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 111.841i | 0.624808i | 0.949949 | + | 0.312404i | \(0.101134\pi\) | ||||
−0.949949 | + | 0.312404i | \(0.898866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 49.0790 | 0.271155 | 0.135577 | − | 0.990767i | \(-0.456711\pi\) | ||||
0.135577 | + | 0.990767i | \(0.456711\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 21.3310i | − 0.115303i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −338.386 | −1.80955 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 278.947i | − 1.46046i | −0.683203 | − | 0.730229i | \(-0.739414\pi\) | ||||
0.683203 | − | 0.730229i | \(-0.260586\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 89.8947 | 0.465775 | 0.232888 | − | 0.972504i | \(-0.425183\pi\) | ||||
0.232888 | + | 0.972504i | \(0.425183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 212.709i | 1.07974i | 0.841748 | + | 0.539870i | \(0.181527\pi\) | ||||
−0.841748 | + | 0.539870i | \(0.818473\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −96.4911 | −0.484880 | −0.242440 | − | 0.970166i | \(-0.577948\pi\) | ||||
−0.242440 | + | 0.970166i | \(0.577948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.223452i | − 0.00110075i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 43.1623 | 0.210548 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 90.8942i | − 0.434900i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −65.7893 | −0.311798 | −0.155899 | − | 0.987773i | \(-0.549827\pi\) | ||||
−0.155899 | + | 0.987773i | \(0.549827\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 43.8779i | 0.204083i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.3594 | 0.116864 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 513.558i | 2.32379i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −102.302 | −0.458756 | −0.229378 | − | 0.973337i | \(-0.573669\pi\) | ||||
−0.229378 | + | 0.973337i | \(0.573669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.5296i | − 0.0551966i | −0.999619 | − | 0.0275983i | \(-0.991214\pi\) | ||||
0.999619 | − | 0.0275983i | \(-0.00878593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.2982 | −0.101739 | −0.0508695 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508695 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 356.382i | 1.52954i | 0.644306 | + | 0.764768i | \(0.277146\pi\) | ||||
−0.644306 | + | 0.764768i | \(0.722854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 49.5701 | 0.210937 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 175.524i | 0.734408i | 0.930140 | + | 0.367204i | \(0.119685\pi\) | ||||
−0.930140 | + | 0.367204i | \(0.880315\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 104.438 | 0.433355 | 0.216677 | − | 0.976243i | \(-0.430478\pi\) | ||||
0.216677 | + | 0.976243i | \(0.430478\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 107.998i | − 0.440809i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −137.947 | −0.558491 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 130.945i | 0.521694i | 0.965380 | + | 0.260847i | \(0.0840018\pi\) | ||||
−0.965380 | + | 0.260847i | \(0.915998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −558.658 | −2.20813 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 425.641i | − 1.65619i | −0.560587 | − | 0.828095i | \(-0.689425\pi\) | ||||
0.560587 | − | 0.828095i | \(-0.310575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.99145 | 0.0308550 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 74.5004i | − 0.283271i | −0.989919 | − | 0.141636i | \(-0.954764\pi\) | ||||
0.989919 | − | 0.141636i | \(-0.0452362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 109.570 | 0.413472 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 205.067i | − 0.762331i | −0.924507 | − | 0.381165i | \(-0.875523\pi\) | ||||
0.924507 | − | 0.381165i | \(-0.124477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 233.351 | 0.861073 | 0.430537 | − | 0.902573i | \(-0.358324\pi\) | ||||
0.430537 | + | 0.902573i | \(0.358324\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 71.8582i | − 0.261302i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 423.715 | 1.52966 | 0.764828 | − | 0.644235i | \(-0.222824\pi\) | ||||
0.764828 | + | 0.644235i | \(0.222824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 402.604i | − 1.43275i | −0.697713 | − | 0.716377i | \(-0.745799\pi\) | ||||
0.697713 | − | 0.716377i | \(-0.254201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −272.333 | −0.962308 | −0.481154 | − | 0.876636i | \(-0.659782\pi\) | ||||
−0.481154 | + | 0.876636i | \(0.659782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.1704i | 0.0563427i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −265.386 | −0.918290 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 443.188i | − 1.51259i | −0.654232 | − | 0.756294i | \(-0.727008\pi\) | ||||
0.654232 | − | 0.756294i | \(-0.272992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 163.759 | 0.555114 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 847.858i | 2.83564i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.4384 | −0.0546128 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 108.057i | 0.354285i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −390.824 | −1.27304 | −0.636522 | − | 0.771259i | \(-0.719627\pi\) | ||||
−0.636522 | + | 0.771259i | \(0.719627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.97739i | − 0.00957362i | −0.999989 | − | 0.00478681i | \(-0.998476\pi\) | ||||
0.999989 | − | 0.00478681i | \(-0.00152369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 130.105 | 0.415672 | 0.207836 | − | 0.978164i | \(-0.433358\pi\) | ||||
0.207836 | + | 0.978164i | \(0.433358\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 131.677i | 0.415384i | 0.978194 | + | 0.207692i | \(0.0665953\pi\) | ||||
−0.978194 | + | 0.207692i | \(0.933405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.83345 | −0.0120171 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 148.914i | − 0.461035i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −109.057 | −0.335560 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.5710i | 0.0564468i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 160.483 | 0.484842 | 0.242421 | − | 0.970171i | \(-0.422059\pi\) | ||||
0.242421 | + | 0.970171i | \(0.422059\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 172.844i | 0.515952i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −128.114 | −0.380160 | −0.190080 | − | 0.981769i | \(-0.560875\pi\) | ||||
−0.190080 | + | 0.981769i | \(0.560875\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 435.056i | − 1.27583i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 81.5089 | 0.237635 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 219.637i | 0.632959i | 0.948599 | + | 0.316480i | \(0.102501\pi\) | ||||
−0.948599 | + | 0.316480i | \(0.897499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −403.465 | −1.15606 | −0.578030 | − | 0.816016i | \(-0.696178\pi\) | ||||
−0.578030 | + | 0.816016i | \(0.696178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 54.8192i | − 0.155295i | −0.996981 | − | 0.0776475i | \(-0.975259\pi\) | ||||
0.996981 | − | 0.0776475i | \(-0.0247409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −232.649 | −0.655350 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 480.460i | 1.33833i | 0.743114 | + | 0.669165i | \(0.233348\pi\) | ||||
−0.743114 | + | 0.669165i | \(0.766652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −321.000 | −0.889197 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 106.606i | 0.292070i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −522.364 | −1.42333 | −0.711667 | − | 0.702517i | \(-0.752060\pi\) | ||||
−0.711667 | + | 0.702517i | \(0.752060\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 41.0494i | 0.110645i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 233.285 | 0.625428 | 0.312714 | − | 0.949847i | \(-0.398762\pi\) | ||||
0.312714 | + | 0.949847i | \(0.398762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.81791i | 0.0154321i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 248.596 | 0.655927 | 0.327964 | − | 0.944690i | \(-0.393638\pi\) | ||||
0.327964 | + | 0.944690i | \(0.393638\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 468.291i | 1.22269i | 0.791364 | + | 0.611346i | \(0.209372\pi\) | ||||
−0.791364 | + | 0.611346i | \(0.790628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.9210 | 0.0699247 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 484.238i | 1.24483i | 0.782688 | + | 0.622414i | \(0.213848\pi\) | ||||
−0.782688 | + | 0.622414i | \(0.786152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −915.263 | −2.34083 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 152.543i | − 0.386184i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 298.943 | 0.753005 | 0.376503 | − | 0.926416i | \(-0.377127\pi\) | ||||
0.376503 | + | 0.926416i | \(0.377127\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 467.509i | 1.16586i | 0.812523 | + | 0.582929i | \(0.198093\pi\) | ||||
−0.812523 | + | 0.582929i | \(0.801907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −660.272 | −1.63839 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 137.098i | − 0.336851i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −184.158 | −0.450264 | −0.225132 | − | 0.974328i | \(-0.572281\pi\) | ||||
−0.225132 | + | 0.974328i | \(0.572281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 61.3507i | 0.148549i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −63.0790 | −0.151998 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 429.840i | 1.02587i | 0.858427 | + | 0.512936i | \(0.171442\pi\) | ||||
−0.858427 | + | 0.512936i | \(0.828558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 305.035 | 0.724548 | 0.362274 | − | 0.932072i | \(-0.382000\pi\) | ||||
0.362274 | + | 0.932072i | \(0.382000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 117.727i | − 0.277005i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.4826 | −0.0948069 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 128.880i | − 0.299025i | −0.988760 | − | 0.149512i | \(-0.952230\pi\) | ||||
0.988760 | − | 0.149512i | \(-0.0477704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 243.886 | 0.563247 | 0.281624 | − | 0.959525i | \(-0.409127\pi\) | ||||
0.281624 | + | 0.959525i | \(0.409127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 245.850i | − 0.562585i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 259.614 | 0.591376 | 0.295688 | − | 0.955285i | \(-0.404451\pi\) | ||||
0.295688 | + | 0.955285i | \(0.404451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 541.011i | − 1.22124i | −0.791923 | − | 0.610622i | \(-0.790920\pi\) | ||||
0.791923 | − | 0.610622i | \(-0.209080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 120.250 | 0.270224 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 791.947i | 1.76380i | 0.471436 | + | 0.881900i | \(0.343736\pi\) | ||||
−0.471436 | + | 0.881900i | \(0.656264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 277.412 | 0.615104 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 40.8572i | − 0.0897960i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 611.359 | 1.33777 | 0.668883 | − | 0.743367i | \(-0.266773\pi\) | ||||
0.668883 | + | 0.743367i | \(0.266773\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 586.991i | 1.27330i | 0.771153 | + | 0.636650i | \(0.219680\pi\) | ||||
−0.771153 | + | 0.636650i | \(0.780320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −195.285 | −0.421781 | −0.210891 | − | 0.977510i | \(-0.567636\pi\) | ||||
−0.210891 | + | 0.977510i | \(0.567636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 753.763i | − 1.61405i | −0.590515 | − | 0.807027i | \(-0.701075\pi\) | ||||
0.590515 | − | 0.807027i | \(-0.298925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.7544 | −0.138069 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 282.011i | 0.596218i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.6228 | 0.0665743 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 614.848i | 1.28361i | 0.766869 | + | 0.641803i | \(0.221814\pi\) | ||||
−0.766869 | + | 0.641803i | \(0.778186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −208.070 | −0.432577 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 256.971i | − 0.529837i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −478.197 | −0.981924 | −0.490962 | − | 0.871181i | \(-0.663355\pi\) | ||||
−0.490962 | + | 0.871181i | \(0.663355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 617.223i | 1.25707i | 0.777780 | + | 0.628537i | \(0.216346\pi\) | ||||
−0.777780 | + | 0.628537i | \(0.783654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.28043 | −0.0127392 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 87.1599i | − 0.175372i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 783.096 | 1.56933 | 0.784665 | − | 0.619919i | \(-0.212835\pi\) | ||||
0.784665 | + | 0.619919i | \(0.212835\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 369.395i | 0.734383i | 0.930145 | + | 0.367191i | \(0.119681\pi\) | ||||
−0.930145 | + | 0.367191i | \(0.880319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.2370 | 0.0776970 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 225.635i | 0.443291i | 0.975127 | + | 0.221645i | \(0.0711427\pi\) | ||||
−0.975127 | + | 0.221645i | \(0.928857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.9388 | −0.0781581 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 159.967i | 0.310616i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 318.596 | 0.616241 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1007.73i | − 1.93422i | −0.254367 | − | 0.967108i | \(-0.581867\pi\) | ||||
0.254367 | − | 0.967108i | \(-0.418133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 935.517 | 1.78875 | 0.894376 | − | 0.447316i | \(-0.147620\pi\) | ||||
0.894376 | + | 0.447316i | \(0.147620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 712.764i | − 1.35249i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −982.052 | −1.85643 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 421.020i | − 0.789906i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −170.763 | −0.319183 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 694.124i | − 1.28780i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 399.149 | 0.737798 | 0.368899 | − | 0.929469i | \(-0.379735\pi\) | ||||
0.368899 | + | 0.929469i | \(0.379735\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 283.804i | 0.520741i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 480.833 | 0.879036 | 0.439518 | − | 0.898234i | \(-0.355149\pi\) | ||||
0.439518 | + | 0.898234i | \(0.355149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.68699i | − 0.00306170i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 57.1488 | 0.103343 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 751.542i | − 1.34927i | −0.738152 | − | 0.674634i | \(-0.764301\pi\) | ||||
0.738152 | − | 0.674634i | \(-0.235699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 428.000 | 0.765653 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 670.820i | 1.19151i | 0.803166 | + | 0.595755i | \(0.203147\pi\) | ||||
−0.803166 | + | 0.595755i | \(0.796853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.6754 | −0.0596026 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 275.325i | − 0.483875i | −0.970292 | − | 0.241937i | \(-0.922217\pi\) | ||||
0.970292 | − | 0.241937i | \(-0.0777829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −900.289 | −1.57669 | −0.788344 | − | 0.615235i | \(-0.789061\pi\) | ||||
−0.788344 | + | 0.615235i | \(0.789061\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 194.361i | − 0.338020i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −596.236 | −1.03334 | −0.516669 | − | 0.856185i | \(-0.672828\pi\) | ||||
−0.516669 | + | 0.856185i | \(0.672828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 23.6320i | − 0.0406746i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 704.228 | 1.20794 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 497.431i | − 0.847412i | −0.905800 | − | 0.423706i | \(-0.860729\pi\) | ||||
0.905800 | − | 0.423706i | \(-0.139271\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 191.456 | 0.325053 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 898.856i | 1.51578i | 0.652384 | + | 0.757889i | \(0.273769\pi\) | ||||
−0.652384 | + | 0.757889i | \(0.726231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 44.1053 | 0.0741266 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.5701i | 0.0476964i | 0.999716 | + | 0.0238482i | \(0.00759183\pi\) | ||||
−0.999716 | + | 0.0238482i | \(0.992408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2107 | −0.0336284 | −0.0168142 | − | 0.999859i | \(-0.505352\pi\) | ||||
−0.0168142 | + | 0.999859i | \(0.505352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 191.282i | − 0.316168i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 713.626 | 1.17566 | 0.587831 | − | 0.808984i | \(-0.299982\pi\) | ||||
0.587831 | + | 0.808984i | \(0.299982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 483.524i | − 0.791365i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 76.1530 | 0.124230 | 0.0621150 | − | 0.998069i | \(-0.480215\pi\) | ||||
0.0621150 | + | 0.998069i | \(0.480215\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 201.599i | − 0.326741i | −0.986565 | − | 0.163371i | \(-0.947763\pi\) | ||||
0.986565 | − | 0.163371i | \(-0.0522367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −204.263 | −0.329989 | −0.164995 | − | 0.986294i | \(-0.552761\pi\) | ||||
−0.164995 | + | 0.986294i | \(0.552761\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.0505i | 0.0723122i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 224.611i | − 0.357093i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 639.903 | 1.01411 | 0.507055 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507055 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 353.367i | − 0.556484i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1053.45 | −1.65377 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 570.709i | 0.890342i | 0.895446 | + | 0.445171i | \(0.146857\pi\) | ||||
−0.895446 | + | 0.445171i | \(0.853143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 453.693 | 0.705587 | 0.352794 | − | 0.935701i | \(-0.385232\pi\) | ||||
0.352794 | + | 0.935701i | \(0.385232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 983.536i | − 1.52015i | −0.649837 | − | 0.760074i | \(-0.725163\pi\) | ||||
0.649837 | − | 0.760074i | \(-0.274837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1052.51 | 1.62174 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 544.478i | 0.833811i | 0.908950 | + | 0.416905i | \(0.136885\pi\) | ||||
−0.908950 | + | 0.416905i | \(0.863115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −472.302 | −0.721073 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 107.933i | 0.163783i | 0.996641 | + | 0.0818916i | \(0.0260961\pi\) | ||||
−0.996641 | + | 0.0818916i | \(0.973904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −345.728 | −0.523038 | −0.261519 | − | 0.965198i | \(-0.584223\pi\) | ||||
−0.261519 | + | 0.965198i | \(0.584223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.8472i | 0.0178153i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3687 | −0.0155452 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 694.503i | 1.03503i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1204.78 | −1.79016 | −0.895082 | − | 0.445902i | \(-0.852883\pi\) | ||||
−0.895082 | + | 0.445902i | \(0.852883\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 574.598i | 0.848742i | 0.905488 | + | 0.424371i | \(0.139505\pi\) | ||||
−0.905488 | + | 0.424371i | \(0.860495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 96.2719 | 0.141785 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 334.387i | − 0.489585i | −0.969575 | − | 0.244792i | \(-0.921280\pi\) | ||||
0.969575 | − | 0.244792i | \(-0.0787198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −154.868 | −0.226085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1068.79i | − 1.55121i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 901.149 | 1.30412 | 0.652061 | − | 0.758166i | \(-0.273904\pi\) | ||||
0.652061 | + | 0.758166i | \(0.273904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 357.418i | − 0.514270i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 454.491 | 0.652068 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 887.934i | − 1.26667i | −0.773879 | − | 0.633334i | \(-0.781686\pi\) | ||||
0.773879 | − | 0.633334i | \(-0.218314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.3331 | 0.0858223 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.6998i | 0.0207918i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1026.35 | 1.44760 | 0.723801 | − | 0.690008i | \(-0.242393\pi\) | ||||
0.723801 | + | 0.690008i | \(0.242393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1176.74i | − 1.65040i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −700.930 | −0.980321 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 740.080i | − 1.02932i | −0.857395 | − | 0.514659i | \(-0.827919\pi\) | ||||
0.857395 | − | 0.514659i | \(-0.172081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.9302 | −0.0831210 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.33369i | − 0.00183957i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1063.75 | −1.46321 | −0.731603 | − | 0.681731i | \(-0.761227\pi\) | ||||
−0.731603 | + | 0.681731i | \(0.761227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 462.026i | 0.632047i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −134.749 | −0.183833 | −0.0919164 | − | 0.995767i | \(-0.529299\pi\) | ||||
−0.0919164 | + | 0.995767i | \(0.529299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1110.90i | 1.50733i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −711.429 | −0.962692 | −0.481346 | − | 0.876531i | \(-0.659852\pi\) | ||||
−0.481346 | + | 0.876531i | \(0.659852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 466.330i | 0.627631i | 0.949484 | + | 0.313816i | \(0.101607\pi\) | ||||
−0.949484 | + | 0.313816i | \(0.898393\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.9559 | 0.0294710 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 63.9748i | − 0.0854136i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −227.359 | −0.302742 | −0.151371 | − | 0.988477i | \(-0.548369\pi\) | ||||
−0.151371 | + | 0.988477i | \(0.548369\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 471.026i | − 0.623875i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 552.258 | 0.729535 | 0.364768 | − | 0.931099i | \(-0.381148\pi\) | ||||
0.364768 | + | 0.931099i | \(0.381148\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 303.051i | 0.398228i | 0.979976 | + | 0.199114i | \(0.0638064\pi\) | ||||
−0.979976 | + | 0.199114i | \(0.936194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −106.325 | −0.139351 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1597.36i | − 2.08261i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 739.684 | 0.961878 | 0.480939 | − | 0.876754i | \(-0.340296\pi\) | ||||
0.480939 | + | 0.876754i | \(0.340296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 603.479i | 0.780697i | 0.920667 | + | 0.390348i | \(0.127645\pi\) | ||||
−0.920667 | + | 0.390348i | \(0.872355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 151.359 | 0.195302 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 122.081i | 0.156715i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1495.28 | −1.91457 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 472.428i | − 0.601819i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −660.483 | −0.839241 | −0.419620 | − | 0.907700i | \(-0.637837\pi\) | ||||
−0.419620 | + | 0.907700i | \(0.637837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 12.6162i | − 0.0159497i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1054.03 | 1.32916 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 634.969i | 0.796699i | 0.917234 | + | 0.398349i | \(0.130417\pi\) | ||||
−0.917234 | + | 0.398349i | \(0.869583\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 521.964 | 0.653272 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 685.174i | 0.853268i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 72.8157 | 0.0904542 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 405.048i | − 0.500677i | −0.968158 | − | 0.250339i | \(-0.919458\pi\) | ||||
0.968158 | − | 0.250339i | \(-0.0805419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 406.034 | 0.500659 | 0.250329 | − | 0.968161i | \(-0.419461\pi\) | ||||
0.250329 | + | 0.968161i | \(0.419461\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 498.113i | − 0.611182i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −124.105 | −0.151904 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 550.073i | 0.670003i | 0.942218 | + | 0.335002i | \(0.108737\pi\) | ||||
−0.942218 | + | 0.335002i | \(0.891263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1472.51 | 1.78920 | 0.894600 | − | 0.446868i | \(-0.147460\pi\) | ||||
0.894600 | + | 0.446868i | \(0.147460\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1510.47i | − 1.82644i | −0.407466 | − | 0.913220i | \(-0.633587\pi\) | ||||
0.407466 | − | 0.913220i | \(-0.366413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −712.692 | −0.859701 | −0.429850 | − | 0.902900i | \(-0.641434\pi\) | ||||
−0.429850 | + | 0.902900i | \(0.641434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1137.20i | − 1.36519i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 74.6050 | 0.0893473 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 530.579i | 0.632394i | 0.948694 | + | 0.316197i | \(0.102406\pi\) | ||||
−0.948694 | + | 0.316197i | \(0.897594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.929 | 0.999915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 685.884i | 0.811697i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 71.6619 | 0.0846068 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 370.822i | − 0.435748i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −215.232 | −0.252324 | −0.126162 | − | 0.992010i | \(-0.540266\pi\) | ||||
−0.126162 | + | 0.992010i | \(0.540266\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.97441i | 0.00580445i | 0.999996 | + | 0.00290222i | \(0.000923808\pi\) | ||||
−0.999996 | + | 0.00290222i | \(0.999076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1652.28 | 1.92349 | 0.961746 | − | 0.273941i | \(-0.0883273\pi\) | ||||
0.961746 | + | 0.273941i | \(0.0883273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 379.077i | − 0.439255i | −0.975584 | − | 0.219627i | \(-0.929516\pi\) | ||||
0.975584 | − | 0.219627i | \(-0.0704841\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 66.6577 | 0.0770609 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 980.421i | − 1.12822i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1685.98 | 1.93568 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.36602i | 0.0107040i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1101.60 | −1.25610 | −0.628051 | − | 0.778173i | \(-0.716147\pi\) | ||||
−0.628051 | + | 0.778173i | \(0.716147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 184.877i | 0.209850i | 0.994480 | + | 0.104925i | \(0.0334602\pi\) | ||||
−0.994480 | + | 0.104925i | \(0.966540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 978.236 | 1.10786 | 0.553928 | − | 0.832565i | \(-0.313128\pi\) | ||||
0.553928 | + | 0.832565i | \(0.313128\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 667.937i | 0.753029i | 0.926411 | + | 0.376514i | \(0.122877\pi\) | ||||
−0.926411 | + | 0.376514i | \(0.877123\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 132.386 | 0.148915 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 140.205i | 0.157005i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −250.083 | −0.279423 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 8.07464i | − 0.00898180i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1153.75 | 1.28053 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 109.744i | 0.121264i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −832.622 | −0.917996 | −0.458998 | − | 0.888437i | \(-0.651791\pi\) | ||||
−0.458998 | + | 0.888437i | \(0.651791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 565.263i | − 0.620486i | −0.950657 | − | 0.310243i | \(-0.899590\pi\) | ||||
0.950657 | − | 0.310243i | \(-0.100410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −405.421 | −0.444053 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 176.944i | − 0.192959i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1185.75 | 1.29026 | 0.645128 | − | 0.764075i | \(-0.276804\pi\) | ||||
0.645128 | + | 0.764075i | \(0.276804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2269.34i | 2.45866i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.6975 | 0.0515649 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 942.995i | 1.01506i | 0.861633 | + | 0.507532i | \(0.169442\pi\) | ||||
−0.861633 | + | 0.507532i | \(0.830558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 305.465 | 0.328104 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 756.654i | − 0.809255i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −531.281 | −0.567002 | −0.283501 | − | 0.958972i | \(-0.591496\pi\) | ||||
−0.283501 | + | 0.958972i | \(0.591496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 595.650i | 0.632996i | 0.948593 | + | 0.316498i | \(0.102507\pi\) | ||||
−0.948593 | + | 0.316498i | \(0.897493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 750.342 | 0.795696 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 782.246i | − 0.826026i | −0.910725 | − | 0.413013i | \(-0.864476\pi\) | ||||
0.910725 | − | 0.413013i | \(-0.135524\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1039.87 | 1.09575 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 426.708i | 0.447752i | 0.974618 | + | 0.223876i | \(0.0718711\pi\) | ||||
−0.974618 | + | 0.223876i | \(0.928129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 623.745 | 0.653136 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 58.0200i | − 0.0605005i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.6128 | −0.0464234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 201.011i | 0.208301i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1210.91 | 1.25223 | 0.626116 | − | 0.779730i | \(-0.284644\pi\) | ||||
0.626116 | + | 0.779730i | \(0.284644\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1193.69i | − 1.22934i | −0.788784 | − | 0.614670i | \(-0.789289\pi\) | ||||
0.788784 | − | 0.614670i | \(-0.210711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 133.903 | 0.137619 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 909.475i | 0.930886i | 0.885078 | + | 0.465443i | \(0.154105\pi\) | ||||
−0.885078 | + | 0.465443i | \(0.845895\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 772.868 | 0.789447 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1560.88i | − 1.58788i | −0.607999 | − | 0.793938i | \(-0.708028\pi\) | ||||
0.607999 | − | 0.793938i | \(-0.291972\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −475.631 | −0.482874 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 762.782i | 0.771265i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1692.63 | 1.70800 | 0.854001 | − | 0.520271i | \(-0.174169\pi\) | ||||
0.854001 | + | 0.520271i | \(0.174169\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 215.761i | − 0.216845i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.5744 | −0.0166243 | −0.00831213 | − | 0.999965i | \(-0.502646\pi\) | ||||
−0.00831213 | + | 0.999965i | \(0.502646\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2880.3.l.c.1601.4 | 4 | ||
3.2 | odd | 2 | inner | 2880.3.l.c.1601.2 | 4 | ||
4.3 | odd | 2 | 2880.3.l.g.1601.3 | 4 | |||
8.3 | odd | 2 | 45.3.c.a.26.2 | ✓ | 4 | ||
8.5 | even | 2 | 720.3.l.a.161.2 | 4 | |||
12.11 | even | 2 | 2880.3.l.g.1601.1 | 4 | |||
24.5 | odd | 2 | 720.3.l.a.161.4 | 4 | |||
24.11 | even | 2 | 45.3.c.a.26.3 | yes | 4 | ||
40.3 | even | 4 | 225.3.d.b.224.3 | 8 | |||
40.13 | odd | 4 | 3600.3.c.i.449.5 | 8 | |||
40.19 | odd | 2 | 225.3.c.c.26.3 | 4 | |||
40.27 | even | 4 | 225.3.d.b.224.6 | 8 | |||
40.29 | even | 2 | 3600.3.l.v.1601.1 | 4 | |||
40.37 | odd | 4 | 3600.3.c.i.449.3 | 8 | |||
72.11 | even | 6 | 405.3.i.d.296.3 | 8 | |||
72.43 | odd | 6 | 405.3.i.d.296.2 | 8 | |||
72.59 | even | 6 | 405.3.i.d.26.2 | 8 | |||
72.67 | odd | 6 | 405.3.i.d.26.3 | 8 | |||
120.29 | odd | 2 | 3600.3.l.v.1601.2 | 4 | |||
120.53 | even | 4 | 3600.3.c.i.449.6 | 8 | |||
120.59 | even | 2 | 225.3.c.c.26.2 | 4 | |||
120.77 | even | 4 | 3600.3.c.i.449.4 | 8 | |||
120.83 | odd | 4 | 225.3.d.b.224.5 | 8 | |||
120.107 | odd | 4 | 225.3.d.b.224.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.c.a.26.2 | ✓ | 4 | 8.3 | odd | 2 | ||
45.3.c.a.26.3 | yes | 4 | 24.11 | even | 2 | ||
225.3.c.c.26.2 | 4 | 120.59 | even | 2 | |||
225.3.c.c.26.3 | 4 | 40.19 | odd | 2 | |||
225.3.d.b.224.3 | 8 | 40.3 | even | 4 | |||
225.3.d.b.224.4 | 8 | 120.107 | odd | 4 | |||
225.3.d.b.224.5 | 8 | 120.83 | odd | 4 | |||
225.3.d.b.224.6 | 8 | 40.27 | even | 4 | |||
405.3.i.d.26.2 | 8 | 72.59 | even | 6 | |||
405.3.i.d.26.3 | 8 | 72.67 | odd | 6 | |||
405.3.i.d.296.2 | 8 | 72.43 | odd | 6 | |||
405.3.i.d.296.3 | 8 | 72.11 | even | 6 | |||
720.3.l.a.161.2 | 4 | 8.5 | even | 2 | |||
720.3.l.a.161.4 | 4 | 24.5 | odd | 2 | |||
2880.3.l.c.1601.2 | 4 | 3.2 | odd | 2 | inner | ||
2880.3.l.c.1601.4 | 4 | 1.1 | even | 1 | trivial | ||
2880.3.l.g.1601.1 | 4 | 12.11 | even | 2 | |||
2880.3.l.g.1601.3 | 4 | 4.3 | odd | 2 | |||
3600.3.c.i.449.3 | 8 | 40.37 | odd | 4 | |||
3600.3.c.i.449.4 | 8 | 120.77 | even | 4 | |||
3600.3.c.i.449.5 | 8 | 40.13 | odd | 4 | |||
3600.3.c.i.449.6 | 8 | 120.53 | even | 4 | |||
3600.3.l.v.1601.1 | 4 | 40.29 | even | 2 | |||
3600.3.l.v.1601.2 | 4 | 120.29 | odd | 2 |