Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(361,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.q (of order \(3\), degree \(2\), 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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 721.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.721 |
Dual form | 1080.2.q.c.361.1 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.72474 | + | 2.98735i | −0.651892 | + | 1.12911i | 0.330771 | + | 0.943711i | \(0.392691\pi\) |
−0.982663 | + | 0.185399i | \(0.940642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.89898 | −1.58273 | −0.791367 | − | 0.611341i | \(-0.790630\pi\) | ||||
−0.791367 | + | 0.611341i | \(0.790630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.72474 | − | 6.45145i | −0.776663 | − | 1.34522i | −0.933855 | − | 0.357652i | \(-0.883578\pi\) |
0.157192 | − | 0.987568i | \(-0.449756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.949490 | + | 1.64456i | −0.176316 | + | 0.305388i | −0.940616 | − | 0.339473i | \(-0.889751\pi\) |
0.764300 | + | 0.644861i | \(0.223085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.550510 | − | 0.953512i | −0.0988746 | − | 0.171256i | 0.812345 | − | 0.583178i | \(-0.198191\pi\) |
−0.911219 | + | 0.411922i | \(0.864858\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.44949 | 0.583070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.94949 | − | 8.57277i | −0.772980 | − | 1.33884i | −0.935923 | − | 0.352206i | \(-0.885432\pi\) |
0.162942 | − | 0.986636i | \(-0.447902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.89898 | + | 10.2173i | −0.899586 | + | 1.55813i | −0.0715617 | + | 0.997436i | \(0.522798\pi\) |
−0.828024 | + | 0.560692i | \(0.810535\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.72474 | + | 8.18350i | −0.689175 | + | 1.19369i | 0.282930 | + | 0.959140i | \(0.408693\pi\) |
−0.972105 | + | 0.234545i | \(0.924640\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.44949 | − | 4.24264i | −0.349927 | − | 0.606092i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79796 | −1.07113 | −0.535566 | − | 0.844493i | \(-0.679902\pi\) | ||||
−0.535566 | + | 0.844493i | \(0.679902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.550510 | − | 0.953512i | −0.0716703 | − | 0.124137i | 0.827963 | − | 0.560783i | \(-0.189500\pi\) |
−0.899633 | + | 0.436646i | \(0.856166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.50000 | − | 2.59808i | 0.192055 | − | 0.332650i | −0.753876 | − | 0.657017i | \(-0.771818\pi\) |
0.945931 | + | 0.324367i | \(0.105151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.62372 | + | 11.4726i | 0.809217 | + | 1.40160i | 0.913407 | + | 0.407047i | \(0.133442\pi\) |
−0.104190 | + | 0.994557i | \(0.533225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.79796 | −1.16280 | −0.581402 | − | 0.813617i | \(-0.697496\pi\) | ||||
−0.581402 | + | 0.813617i | \(0.697496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7980 | 1.61493 | 0.807464 | − | 0.589916i | \(-0.200839\pi\) | ||||
0.807464 | + | 0.589916i | \(0.200839\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.44949 | − | 5.97469i | 0.388098 | − | 0.672205i | −0.604096 | − | 0.796912i | \(-0.706466\pi\) |
0.992194 | + | 0.124706i | \(0.0397989\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.72474 | + | 4.71940i | −0.299080 | + | 0.518021i | −0.975926 | − | 0.218104i | \(-0.930013\pi\) |
0.676846 | + | 0.736125i | \(0.263346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 1.73205i | −0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.79796 | −0.296583 | −0.148292 | − | 0.988944i | \(-0.547377\pi\) | ||||
−0.148292 | + | 0.988944i | \(0.547377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.44949 | + | 5.97469i | 0.353910 | + | 0.612990i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00000 | − | 8.66025i | −0.492665 | − | 0.853320i | 0.507300 | − | 0.861770i | \(-0.330644\pi\) |
−0.999964 | + | 0.00844953i | \(0.997310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.3485 | 1.19377 | 0.596886 | − | 0.802326i | \(-0.296405\pi\) | ||||
0.596886 | + | 0.802326i | \(0.296405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7980 | −1.03426 | −0.517128 | − | 0.855908i | \(-0.672999\pi\) | ||||
−0.517128 | + | 0.855908i | \(0.672999\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.89898 | − | 8.48528i | −0.460857 | − | 0.798228i | 0.538147 | − | 0.842851i | \(-0.319125\pi\) |
−0.999004 | + | 0.0446231i | \(0.985791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.72474 | + | 6.45145i | −0.347334 | + | 0.601601i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.44949 | + | 5.97469i | −0.316214 | + | 0.547699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.348469 | 0.0309216 | 0.0154608 | − | 0.999880i | \(-0.495078\pi\) | ||||
0.0154608 | + | 0.999880i | \(0.495078\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.44949 | + | 2.51059i | 0.126643 | + | 0.219351i | 0.922374 | − | 0.386299i | \(-0.126247\pi\) |
−0.795731 | + | 0.605650i | \(0.792913\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.8990 | − | 20.6096i | 1.03177 | − | 1.78708i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.79796 | − | 16.9706i | 0.837096 | − | 1.44989i | −0.0552162 | − | 0.998474i | \(-0.517585\pi\) |
0.892312 | − | 0.451419i | \(-0.149082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.79796 | − | 16.9706i | −0.831052 | − | 1.43942i | −0.897205 | − | 0.441615i | \(-0.854406\pi\) |
0.0661527 | − | 0.997810i | \(-0.478928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.89898 | 0.157702 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5000 | − | 18.1865i | −0.860194 | − | 1.48990i | −0.871742 | − | 0.489966i | \(-0.837009\pi\) |
0.0115483 | − | 0.999933i | \(-0.496324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.550510 | + | 0.953512i | −0.0442180 | + | 0.0765879i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8990 | + | 20.6096i | 0.949642 | + | 1.64483i | 0.746179 | + | 0.665745i | \(0.231886\pi\) |
0.203463 | + | 0.979083i | \(0.434780\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.6969 | 2.02520 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.79796 | −0.610783 | −0.305392 | − | 0.952227i | \(-0.598787\pi\) | ||||
−0.305392 | + | 0.952227i | \(0.598787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.17423 | + | 7.22999i | 0.323012 | + | 0.559473i | 0.981108 | − | 0.193461i | \(-0.0619713\pi\) |
−0.658096 | + | 0.752934i | \(0.728638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.50000 | − | 11.2583i | 0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | + | 10.3923i | −0.456172 | + | 0.790112i | −0.998755 | − | 0.0498898i | \(-0.984113\pi\) |
0.542583 | + | 0.840002i | \(0.317446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.72474 | − | 2.98735i | −0.130378 | − | 0.225822i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7980 | 1.03131 | 0.515654 | − | 0.856797i | \(-0.327549\pi\) | ||||
0.515654 | + | 0.856797i | \(0.327549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.69694 | −0.720768 | −0.360384 | − | 0.932804i | \(-0.617354\pi\) | ||||
−0.360384 | + | 0.932804i | \(0.617354\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.44949 | + | 12.9029i | −0.539026 | + | 0.933621i | 0.459931 | + | 0.887955i | \(0.347874\pi\) |
−0.998957 | + | 0.0456658i | \(0.985459\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.10102 | + | 1.90702i | 0.0792532 | + | 0.137271i | 0.902928 | − | 0.429792i | \(-0.141413\pi\) |
−0.823675 | + | 0.567063i | \(0.808080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5959 | 1.11116 | 0.555582 | − | 0.831462i | \(-0.312496\pi\) | ||||
0.555582 | + | 0.831462i | \(0.312496\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.8990 | 1.62327 | 0.811633 | − | 0.584168i | \(-0.198579\pi\) | ||||
0.811633 | + | 0.584168i | \(0.198579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.27526 | − | 5.67291i | −0.229878 | − | 0.398160i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.94949 | + | 8.57277i | −0.345687 | + | 0.598748i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | − | 10.3923i | −0.413057 | − | 0.715436i | 0.582165 | − | 0.813070i | \(-0.302206\pi\) |
−0.995222 | + | 0.0976347i | \(0.968872\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.7980 | 0.804614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.79796 | 0.257822 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.72474 | + | 4.71940i | −0.182462 | + | 0.316034i | −0.942718 | − | 0.333589i | \(-0.891740\pi\) |
0.760256 | + | 0.649623i | \(0.225073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.10102 | + | 7.10318i | −0.272194 | + | 0.471454i | −0.969423 | − | 0.245394i | \(-0.921083\pi\) |
0.697229 | + | 0.716848i | \(0.254416\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.05051 | + | 3.55159i | 0.135502 | + | 0.234696i | 0.925789 | − | 0.378041i | \(-0.123402\pi\) |
−0.790287 | + | 0.612736i | \(0.790069\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.7980 | 1.29701 | 0.648504 | − | 0.761211i | \(-0.275395\pi\) | ||||
0.648504 | + | 0.761211i | \(0.275395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.44949 | 0.616417 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.10102 | + | 1.90702i | 0.0712191 | + | 0.123355i | 0.899436 | − | 0.437053i | \(-0.143978\pi\) |
−0.828217 | + | 0.560408i | \(0.810644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.84847 | − | 3.20164i | 0.119070 | − | 0.206236i | −0.800329 | − | 0.599561i | \(-0.795342\pi\) |
0.919400 | + | 0.393325i | \(0.128675\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.44949 | + | 4.24264i | −0.156492 | + | 0.271052i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.89898 | −0.182982 | −0.0914910 | − | 0.995806i | \(-0.529163\pi\) | ||||
−0.0914910 | + | 0.995806i | \(0.529163\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.8990 | + | 24.0737i | 0.866995 | + | 1.50168i | 0.865053 | + | 0.501680i | \(0.167285\pi\) |
0.00194150 | + | 0.999998i | \(0.499382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.3485 | − | 17.9241i | 0.643023 | − | 1.11375i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | − | 15.5885i | 0.554964 | − | 0.961225i | −0.442943 | − | 0.896550i | \(-0.646065\pi\) |
0.997906 | − | 0.0646755i | \(-0.0206012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.89898 | + | 6.75323i | 0.239512 | + | 0.414848i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5959 | −1.37770 | −0.688849 | − | 0.724905i | \(-0.741884\pi\) | ||||
−0.688849 | + | 0.724905i | \(0.741884\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.8990 | 1.87698 | 0.938490 | − | 0.345307i | \(-0.112225\pi\) | ||||
0.938490 | + | 0.345307i | \(0.112225\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00000 | − | 12.1244i | 0.420589 | − | 0.728482i | −0.575408 | − | 0.817867i | \(-0.695157\pi\) |
0.995997 | + | 0.0893846i | \(0.0284900\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.05051 | + | 7.01569i | −0.241633 | + | 0.418521i | −0.961180 | − | 0.275923i | \(-0.911016\pi\) |
0.719546 | + | 0.694444i | \(0.244350\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.82577 | + | 3.16232i | 0.108530 | + | 0.187980i | 0.915175 | − | 0.403056i | \(-0.132052\pi\) |
−0.806645 | + | 0.591037i | \(0.798719\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.1464 | 2.01560 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.79796 | + | 15.2385i | 0.513982 | + | 0.890243i | 0.999868 | + | 0.0162213i | \(0.00516362\pi\) |
−0.485886 | + | 0.874022i | \(0.661503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.550510 | + | 0.953512i | −0.0320519 | + | 0.0555156i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.3485 | − | 35.2446i | −1.17287 | − | 2.03146i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00000 | −0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.75255 | −0.271242 | −0.135621 | − | 0.990761i | \(-0.543303\pi\) | ||||
−0.135621 | + | 0.990761i | \(0.543303\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.44949 | − | 5.97469i | −0.195603 | − | 0.338794i | 0.751495 | − | 0.659738i | \(-0.229333\pi\) |
−0.947098 | + | 0.320945i | \(0.896000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.79796 | − | 13.5065i | 0.440767 | − | 0.763430i | −0.556980 | − | 0.830526i | \(-0.688040\pi\) |
0.997747 | + | 0.0670957i | \(0.0213733\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.8990 | + | 22.3417i | −0.724479 | + | 1.25483i | 0.234709 | + | 0.972066i | \(0.424586\pi\) |
−0.959188 | + | 0.282769i | \(0.908747\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.7980 | −0.767739 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.2980 | − | 28.2289i | −0.898536 | − | 1.55631i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.44949 | − | 5.97469i | 0.189601 | − | 0.328399i | −0.755516 | − | 0.655130i | \(-0.772614\pi\) |
0.945117 | + | 0.326731i | \(0.105947\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.62372 | − | 11.4726i | 0.361893 | − | 0.626817i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8990 | + | 25.8058i | 0.811599 | + | 1.40573i | 0.911744 | + | 0.410758i | \(0.134736\pi\) |
−0.100145 | + | 0.994973i | \(0.531931\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.24745 | −0.391325 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7980 | − | 22.1667i | −0.687030 | − | 1.18997i | −0.972794 | − | 0.231671i | \(-0.925581\pi\) |
0.285764 | − | 0.958300i | \(-0.407753\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.15153 | − | 1.99451i | 0.0616400 | − | 0.106764i | −0.833559 | − | 0.552431i | \(-0.813700\pi\) |
0.895199 | + | 0.445667i | \(0.147034\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.89898 | + | 8.48528i | 0.260011 | + | 0.450352i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.6969 | −1.51457 | −0.757283 | − | 0.653087i | \(-0.773474\pi\) | ||||
−0.757283 | + | 0.653087i | \(0.773474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.5959 | 1.50505 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.89898 | − | 11.9494i | −0.361109 | − | 0.625459i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0000 | + | 19.0526i | −0.574195 | + | 0.994535i | 0.421933 | + | 0.906627i | \(0.361352\pi\) |
−0.996129 | + | 0.0879086i | \(0.971982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.4495 | − | 23.2952i | 0.698263 | − | 1.20943i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7980 | − | 18.7026i | −0.559097 | − | 0.968385i | −0.997572 | − | 0.0696412i | \(-0.977815\pi\) |
0.438475 | − | 0.898743i | \(-0.355519\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8990 | 1.38171 | 0.690854 | − | 0.722994i | \(-0.257235\pi\) | ||||
0.690854 | + | 0.722994i | \(0.257235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.00000 | + | 1.73205i | 0.0510976 | + | 0.0885037i | 0.890443 | − | 0.455095i | \(-0.150395\pi\) |
−0.839345 | + | 0.543599i | \(0.817061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.29796 | + | 14.3725i | −0.420723 | + | 0.728714i | −0.996010 | − | 0.0892375i | \(-0.971557\pi\) |
0.575287 | + | 0.817952i | \(0.304890\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.44949 | − | 12.9029i | −0.376737 | − | 0.652527i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.89898 | −0.347125 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7980 | + | 22.1667i | 0.639100 | + | 1.10695i | 0.985631 | + | 0.168914i | \(0.0540262\pi\) |
−0.346531 | + | 0.938038i | \(0.612641\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.79796 | + | 8.31031i | 0.237244 | + | 0.410918i | 0.959922 | − | 0.280266i | \(-0.0904226\pi\) |
−0.722679 | + | 0.691184i | \(0.757089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.79796 | 0.186885 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.44949 | 0.267505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0000 | + | 17.3205i | 0.488532 | + | 0.846162i | 0.999913 | − | 0.0131919i | \(-0.00419923\pi\) |
−0.511381 | + | 0.859354i | \(0.670866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.7980 | + | 22.1667i | −0.623734 | + | 1.08034i | 0.365050 | + | 0.930988i | \(0.381052\pi\) |
−0.988784 | + | 0.149352i | \(0.952281\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.17423 | + | 8.96204i | 0.250399 | + | 0.433703i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8990 | −0.717659 | −0.358829 | − | 0.933403i | \(-0.616824\pi\) | ||||
−0.358829 | + | 0.933403i | \(0.616824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7980 | −0.566974 | −0.283487 | − | 0.958976i | \(-0.591491\pi\) | ||||
−0.283487 | + | 0.958976i | \(0.591491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.6969 | + | 44.5084i | 1.22925 | + | 2.12913i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.89898 | − | 15.4135i | 0.424725 | − | 0.735645i | −0.571670 | − | 0.820484i | \(-0.693704\pi\) |
0.996395 | + | 0.0848384i | \(0.0270374\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.07321 | + | 7.05501i | −0.193524 | + | 0.335194i | −0.946416 | − | 0.322951i | \(-0.895325\pi\) |
0.752892 | + | 0.658145i | \(0.228658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.39898 | + | 2.42310i | 0.0663180 | + | 0.114866i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.5959 | −1.01917 | −0.509587 | − | 0.860419i | \(-0.670202\pi\) | ||||
−0.509587 | + | 0.860419i | \(0.670202\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.79796 | + | 15.2385i | −0.411551 | + | 0.712828i | −0.995060 | − | 0.0992796i | \(-0.968346\pi\) |
0.583508 | + | 0.812107i | \(0.301680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.05051 | − | 10.4798i | 0.281800 | − | 0.488093i | −0.690028 | − | 0.723783i | \(-0.742402\pi\) |
0.971828 | + | 0.235690i | \(0.0757351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.10102 | − | 10.5673i | −0.283538 | − | 0.491103i | 0.688715 | − | 0.725032i | \(-0.258175\pi\) |
−0.972254 | + | 0.233929i | \(0.924842\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.79796 | −0.360847 | −0.180423 | − | 0.983589i | \(-0.557747\pi\) | ||||
−0.180423 | + | 0.983589i | \(0.557747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.6969 | −2.11009 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.44949 | − | 5.97469i | 0.158273 | − | 0.274138i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.2474 | − | 26.4094i | 0.696674 | − | 1.20667i | −0.272939 | − | 0.962031i | \(-0.587996\pi\) |
0.969613 | − | 0.244643i | \(-0.0786708\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5959 | −0.616090 | −0.308045 | − | 0.951372i | \(-0.599675\pi\) | ||||
−0.308045 | + | 0.951372i | \(0.599675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.89898 | − | 11.9494i | −0.311347 | − | 0.539268i | 0.667308 | − | 0.744782i | \(-0.267447\pi\) |
−0.978654 | + | 0.205514i | \(0.934113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.89898 | + | 3.28913i | −0.0855257 | + | 0.148135i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.8990 | − | 29.2699i | 0.758023 | − | 1.31293i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | + | 24.2487i | 0.626726 | + | 1.08552i | 0.988204 | + | 0.153141i | \(0.0489388\pi\) |
−0.361478 | + | 0.932381i | \(0.617728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.0454 | −1.11672 | −0.558360 | − | 0.829599i | \(-0.688569\pi\) | ||||
−0.558360 | + | 0.829599i | \(0.688569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.05051 | − | 3.55159i | −0.0908873 | − | 0.157421i | 0.816997 | − | 0.576641i | \(-0.195637\pi\) |
−0.907885 | + | 0.419220i | \(0.862304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.7980 | + | 41.2193i | −1.05276 | + | 1.82343i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.00000 | + | 8.66025i | −0.220326 | + | 0.381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.20204 | −0.403149 | −0.201574 | − | 0.979473i | \(-0.564606\pi\) | ||||
−0.201574 | + | 0.979473i | \(0.564606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.3485 | −1.50195 | −0.750977 | − | 0.660329i | \(-0.770417\pi\) | ||||
−0.750977 | + | 0.660329i | \(0.770417\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.10102 | − | 1.90702i | −0.0479612 | − | 0.0830712i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2474 | + | 28.1414i | −0.706411 | + | 1.22354i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.17423 | − | 10.6941i | −0.266935 | − | 0.462346i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1010 | 0.520264 | 0.260132 | − | 0.965573i | \(-0.416234\pi\) | ||||
0.260132 | + | 0.965573i | \(0.416234\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.39898 | + | 9.35131i | 0.231267 | + | 0.400566i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.37628 | − | 14.5081i | 0.358144 | − | 0.620323i | −0.629507 | − | 0.776995i | \(-0.716743\pi\) |
0.987651 | + | 0.156672i | \(0.0500765\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.55051 | − | 11.3458i | 0.279061 | − | 0.483348i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8990 | + | 20.6096i | 0.505996 | + | 0.876411i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.7980 | −1.85578 | −0.927890 | − | 0.372855i | \(-0.878379\pi\) | ||||
−0.927890 | + | 0.372855i | \(0.878379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.17423 | − | 8.96204i | −0.218068 | − | 0.377705i | 0.736149 | − | 0.676819i | \(-0.236642\pi\) |
−0.954217 | + | 0.299114i | \(0.903309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.89898 | + | 8.48528i | −0.206102 | + | 0.356978i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.00000 | − | 8.66025i | 0.209611 | − | 0.363057i | −0.741981 | − | 0.670421i | \(-0.766114\pi\) |
0.951592 | + | 0.307364i | \(0.0994469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.8990 | − | 22.3417i | −0.539805 | − | 0.934971i | −0.998914 | − | 0.0465904i | \(-0.985164\pi\) |
0.459109 | − | 0.888380i | \(-0.348169\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.44949 | 0.310665 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0000 | −1.08239 | −0.541197 | − | 0.840896i | \(-0.682029\pi\) | ||||
−0.541197 | + | 0.840896i | \(0.682029\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.39898 | − | 16.2795i | −0.389935 | − | 0.675388i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.82577 | − | 6.62642i | 0.157906 | − | 0.273502i | −0.776207 | − | 0.630478i | \(-0.782859\pi\) |
0.934113 | + | 0.356976i | \(0.116192\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.79796 | + | 6.57826i | 0.156492 | + | 0.271052i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.3939 | 1.28919 | 0.644596 | − | 0.764523i | \(-0.277026\pi\) | ||||
0.644596 | + | 0.764523i | \(0.277026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.89898 | 0.282831 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.3485 | − | 21.3882i | −0.504545 | − | 0.873897i | −0.999986 | − | 0.00525583i | \(-0.998327\pi\) |
0.495441 | − | 0.868641i | \(-0.335006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | + | 12.1244i | −0.285536 | + | 0.494563i | −0.972739 | − | 0.231903i | \(-0.925505\pi\) |
0.687203 | + | 0.726465i | \(0.258838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.50000 | − | 9.52628i | 0.223607 | − | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.07321 | − | 1.85886i | −0.0435604 | − | 0.0754489i | 0.843423 | − | 0.537250i | \(-0.180537\pi\) |
−0.886984 | + | 0.461801i | \(0.847203\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5959 | −1.19537 | −0.597684 | − | 0.801732i | \(-0.703912\pi\) | ||||
−0.597684 | + | 0.801732i | \(0.703912\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.5959 | − | 30.4770i | −0.708385 | − | 1.22696i | −0.965456 | − | 0.260566i | \(-0.916091\pi\) |
0.257071 | − | 0.966393i | \(-0.417243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.3485 | − | 21.3882i | 0.496327 | − | 0.859663i | −0.503664 | − | 0.863900i | \(-0.668015\pi\) |
0.999991 | + | 0.00423617i | \(0.00134842\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.82577 | − | 8.35847i | 0.193340 | − | 0.334875i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5959 | −0.620864 | −0.310432 | − | 0.950596i | \(-0.600474\pi\) | ||||
−0.310432 | + | 0.950596i | \(0.600474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.174235 | − | 0.301783i | −0.00691429 | − | 0.0119759i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.94949 | + | 12.0369i | −0.274488 | + | 0.475428i | −0.970006 | − | 0.243081i | \(-0.921842\pi\) |
0.695518 | + | 0.718509i | \(0.255175\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0732 | + | 17.4473i | 0.397249 | + | 0.688055i | 0.993385 | − | 0.114828i | \(-0.0366317\pi\) |
−0.596137 | + | 0.802883i | \(0.703298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.55051 | −0.257527 | −0.128764 | − | 0.991675i | \(-0.541101\pi\) | ||||
−0.128764 | + | 0.991675i | \(0.541101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.8990 | + | 24.0737i | 0.543909 | + | 0.942078i | 0.998675 | + | 0.0514670i | \(0.0163897\pi\) |
−0.454766 | + | 0.890611i | \(0.650277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.44949 | − | 2.51059i | 0.0566363 | − | 0.0980969i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.10102 | − | 8.83523i | 0.198708 | − | 0.344172i | −0.749402 | − | 0.662115i | \(-0.769659\pi\) |
0.948110 | + | 0.317944i | \(0.102992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00000 | − | 8.66025i | −0.194477 | − | 0.336845i | 0.752252 | − | 0.658876i | \(-0.228968\pi\) |
−0.946729 | + | 0.322031i | \(0.895634\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.7980 | −0.922845 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1464 | 0.547752 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | − | 13.8564i | 0.308377 | − | 0.534125i | −0.669630 | − | 0.742695i | \(-0.733547\pi\) |
0.978008 | + | 0.208569i | \(0.0668807\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.10102 | − | 12.2993i | 0.272914 | − | 0.472702i | −0.696692 | − | 0.717370i | \(-0.745346\pi\) |
0.969607 | + | 0.244668i | \(0.0786791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.44949 | − | 5.97469i | −0.132379 | − | 0.229288i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.3939 | −0.895142 | −0.447571 | − | 0.894248i | \(-0.647711\pi\) | ||||
−0.447571 | + | 0.894248i | \(0.647711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5959 | −0.748722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.4495 | + | 33.6875i | −0.739893 | + | 1.28153i | 0.212649 | + | 0.977129i | \(0.431791\pi\) |
−0.952543 | + | 0.304404i | \(0.901543\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.79796 | + | 16.9706i | −0.371658 | + | 0.643730i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.89898 | − | 17.1455i | −0.374951 | − | 0.649433i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.3939 | −1.14796 | −0.573980 | − | 0.818869i | \(-0.694601\pi\) | ||||
−0.573980 | + | 0.818869i | \(0.694601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.3939 | 1.56120 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.44949 | − | 5.97469i | −0.129731 | − | 0.224701i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.84847 | + | 8.39780i | −0.182088 | + | 0.315386i | −0.942591 | − | 0.333948i | \(-0.891619\pi\) |
0.760503 | + | 0.649334i | \(0.224952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.10102 | + | 7.10318i | −0.153584 | + | 0.266016i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.2929 | 1.05515 | 0.527573 | − | 0.849510i | \(-0.323102\pi\) | ||||
0.527573 | + | 0.849510i | \(0.323102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.4949 | 1.28466 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.949490 | − | 1.64456i | −0.0352632 | − | 0.0610776i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.6237 | − | 27.0611i | 0.579452 | − | 1.00364i | −0.416090 | − | 0.909323i | \(-0.636600\pi\) |
0.995542 | − | 0.0943168i | \(-0.0300667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.7980 | + | 20.4347i | −0.436363 | + | 0.755803i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7980 | + | 25.6308i | 0.546575 | + | 0.946696i | 0.998506 | + | 0.0546429i | \(0.0174020\pi\) |
−0.451931 | + | 0.892053i | \(0.649265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.1010 | −1.21764 | −0.608820 | − | 0.793308i | \(-0.708357\pi\) | ||||
−0.608820 | + | 0.793308i | \(0.708357\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.52270 | − | 6.10150i | −0.129235 | − | 0.223842i | 0.794145 | − | 0.607728i | \(-0.207919\pi\) |
−0.923381 | + | 0.383886i | \(0.874586\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5000 | + | 18.1865i | −0.384690 | + | 0.666303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.2980 | + | 36.8891i | −0.778210 | + | 1.34790i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1010 | − | 22.6916i | −0.478063 | − | 0.828029i | 0.521621 | − | 0.853177i | \(-0.325328\pi\) |
−0.999684 | + | 0.0251480i | \(0.991994\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.5959 | 1.14837 | 0.574187 | − | 0.818724i | \(-0.305318\pi\) | ||||
0.574187 | + | 0.818724i | \(0.305318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.5000 | + | 30.3109i | 0.634375 | + | 1.09877i | 0.986647 | + | 0.162872i | \(0.0520756\pi\) |
−0.352273 | + | 0.935897i | \(0.614591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.6237 | − | 32.2572i | 0.674224 | − | 1.16779i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.60102 | + | 4.50510i | 0.0937952 | + | 0.162458i | 0.909105 | − | 0.416567i | \(-0.136767\pi\) |
−0.815310 | + | 0.579025i | \(0.803433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.20204 | −0.223072 | −0.111536 | − | 0.993760i | \(-0.535577\pi\) | ||||
−0.111536 | + | 0.993760i | \(0.535577\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.10102 | 0.0395498 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.1464 | + | 59.1433i | 1.22342 | + | 2.11903i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8990 | − | 20.6096i | 0.424693 | − | 0.735589i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.7980 | + | 42.9513i | 0.883952 | + | 1.53105i | 0.846910 | + | 0.531736i | \(0.178460\pi\) |
0.0370414 | + | 0.999314i | \(0.488207\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.7980 | 1.20172 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.00000 | − | 6.92820i | −0.141687 | − | 0.245410i | 0.786445 | − | 0.617661i | \(-0.211919\pi\) |
−0.928132 | + | 0.372251i | \(0.878586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.44949 | + | 16.3670i | −0.334299 | + | 0.579023i | ||||
\(800\) | 0 |