Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-2.20360\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.09722 | 0.937905 | 0.468953 | − | 0.883223i | \(-0.344632\pi\) | ||||
0.468953 | + | 0.883223i | \(0.344632\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.0373018 | −0.0140987 | −0.00704937 | − | 0.999975i | \(-0.502244\pi\) | ||||
−0.00704937 | + | 0.999975i | \(0.502244\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.09722 | −0.663199 | ||||||||
\(11\) | −3.17762 | −0.958090 | −0.479045 | − | 0.877790i | \(-0.659017\pi\) | ||||
−0.479045 | + | 0.877790i | \(0.659017\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.0373018 | 0.00996931 | ||||||||
\(15\) | 2.09722 | 0.541500 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.38289 | −0.577935 | −0.288967 | − | 0.957339i | \(-0.593312\pi\) | ||||
−0.288967 | + | 0.957339i | \(0.593312\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.91209 | 0.668078 | 0.334039 | − | 0.942559i | \(-0.391588\pi\) | ||||
0.334039 | + | 0.942559i | \(0.391588\pi\) | |||||||
\(20\) | 2.09722 | 0.468953 | ||||||||
\(21\) | −0.0373018 | −0.00813991 | ||||||||
\(22\) | 3.17762 | 0.677472 | ||||||||
\(23\) | 3.99261 | 0.832518 | 0.416259 | − | 0.909246i | \(-0.363341\pi\) | ||||
0.416259 | + | 0.909246i | \(0.363341\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −0.601670 | −0.120334 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.0373018 | −0.00704937 | ||||||||
\(29\) | −2.46598 | −0.457921 | −0.228960 | − | 0.973436i | \(-0.573533\pi\) | ||||
−0.228960 | + | 0.973436i | \(0.573533\pi\) | |||||||
\(30\) | −2.09722 | −0.382898 | ||||||||
\(31\) | 0.760072 | 0.136513 | 0.0682564 | − | 0.997668i | \(-0.478256\pi\) | ||||
0.0682564 | + | 0.997668i | \(0.478256\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.17762 | −0.553153 | ||||||||
\(34\) | 2.38289 | 0.408661 | ||||||||
\(35\) | −0.0782300 | −0.0132233 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.84213 | −1.45364 | −0.726818 | − | 0.686830i | \(-0.759002\pi\) | ||||
−0.726818 | + | 0.686830i | \(0.759002\pi\) | |||||||
\(38\) | −2.91209 | −0.472403 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.09722 | −0.331600 | ||||||||
\(41\) | −9.70721 | −1.51601 | −0.758006 | − | 0.652248i | \(-0.773826\pi\) | ||||
−0.758006 | + | 0.652248i | \(0.773826\pi\) | |||||||
\(42\) | 0.0373018 | 0.00575579 | ||||||||
\(43\) | −10.8256 | −1.65089 | −0.825447 | − | 0.564480i | \(-0.809077\pi\) | ||||
−0.825447 | + | 0.564480i | \(0.809077\pi\) | |||||||
\(44\) | −3.17762 | −0.479045 | ||||||||
\(45\) | 2.09722 | 0.312635 | ||||||||
\(46\) | −3.99261 | −0.588679 | ||||||||
\(47\) | −5.29982 | −0.773058 | −0.386529 | − | 0.922277i | \(-0.626326\pi\) | ||||
−0.386529 | + | 0.922277i | \(0.626326\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.99861 | −0.999801 | ||||||||
\(50\) | 0.601670 | 0.0850890 | ||||||||
\(51\) | −2.38289 | −0.333671 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −10.7397 | −1.47521 | −0.737604 | − | 0.675234i | \(-0.764043\pi\) | ||||
−0.737604 | + | 0.675234i | \(0.764043\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −6.66417 | −0.898597 | ||||||||
\(56\) | 0.0373018 | 0.00498466 | ||||||||
\(57\) | 2.91209 | 0.385715 | ||||||||
\(58\) | 2.46598 | 0.323799 | ||||||||
\(59\) | 4.58591 | 0.597034 | 0.298517 | − | 0.954404i | \(-0.403508\pi\) | ||||
0.298517 | + | 0.954404i | \(0.403508\pi\) | |||||||
\(60\) | 2.09722 | 0.270750 | ||||||||
\(61\) | −1.68161 | −0.215308 | −0.107654 | − | 0.994188i | \(-0.534334\pi\) | ||||
−0.107654 | + | 0.994188i | \(0.534334\pi\) | |||||||
\(62\) | −0.760072 | −0.0965292 | ||||||||
\(63\) | −0.0373018 | −0.00469958 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.09722 | 0.260128 | ||||||||
\(66\) | 3.17762 | 0.391138 | ||||||||
\(67\) | 7.20145 | 0.879797 | 0.439899 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439899 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(68\) | −2.38289 | −0.288967 | ||||||||
\(69\) | 3.99261 | 0.480654 | ||||||||
\(70\) | 0.0782300 | 0.00935027 | ||||||||
\(71\) | −14.3856 | −1.70726 | −0.853628 | − | 0.520882i | \(-0.825603\pi\) | ||||
−0.853628 | + | 0.520882i | \(0.825603\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 15.2846 | 1.78893 | 0.894463 | − | 0.447141i | \(-0.147558\pi\) | ||||
0.894463 | + | 0.447141i | \(0.147558\pi\) | |||||||
\(74\) | 8.84213 | 1.02788 | ||||||||
\(75\) | −0.601670 | −0.0694749 | ||||||||
\(76\) | 2.91209 | 0.334039 | ||||||||
\(77\) | 0.118531 | 0.0135079 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 6.39400 | 0.719381 | 0.359691 | − | 0.933072i | \(-0.382882\pi\) | ||||
0.359691 | + | 0.933072i | \(0.382882\pi\) | |||||||
\(80\) | 2.09722 | 0.234476 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.70721 | 1.07198 | ||||||||
\(83\) | −5.88671 | −0.646151 | −0.323075 | − | 0.946373i | \(-0.604717\pi\) | ||||
−0.323075 | + | 0.946373i | \(0.604717\pi\) | |||||||
\(84\) | −0.0373018 | −0.00406996 | ||||||||
\(85\) | −4.99743 | −0.542048 | ||||||||
\(86\) | 10.8256 | 1.16736 | ||||||||
\(87\) | −2.46598 | −0.264381 | ||||||||
\(88\) | 3.17762 | 0.338736 | ||||||||
\(89\) | 2.63980 | 0.279818 | 0.139909 | − | 0.990164i | \(-0.455319\pi\) | ||||
0.139909 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(90\) | −2.09722 | −0.221066 | ||||||||
\(91\) | −0.0373018 | −0.00391029 | ||||||||
\(92\) | 3.99261 | 0.416259 | ||||||||
\(93\) | 0.760072 | 0.0788158 | ||||||||
\(94\) | 5.29982 | 0.546635 | ||||||||
\(95\) | 6.10728 | 0.626594 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.73678 | −0.277878 | −0.138939 | − | 0.990301i | \(-0.544369\pi\) | ||||
−0.138939 | + | 0.990301i | \(0.544369\pi\) | |||||||
\(98\) | 6.99861 | 0.706966 | ||||||||
\(99\) | −3.17762 | −0.319363 | ||||||||
\(100\) | −0.601670 | −0.0601670 | ||||||||
\(101\) | 17.7613 | 1.76731 | 0.883656 | − | 0.468137i | \(-0.155075\pi\) | ||||
0.883656 | + | 0.468137i | \(0.155075\pi\) | |||||||
\(102\) | 2.38289 | 0.235941 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −0.0782300 | −0.00763446 | ||||||||
\(106\) | 10.7397 | 1.04313 | ||||||||
\(107\) | 7.44643 | 0.719873 | 0.359937 | − | 0.932977i | \(-0.382798\pi\) | ||||
0.359937 | + | 0.932977i | \(0.382798\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.30101 | −0.316180 | −0.158090 | − | 0.987425i | \(-0.550534\pi\) | ||||
−0.158090 | + | 0.987425i | \(0.550534\pi\) | |||||||
\(110\) | 6.66417 | 0.635404 | ||||||||
\(111\) | −8.84213 | −0.839257 | ||||||||
\(112\) | −0.0373018 | −0.00352468 | ||||||||
\(113\) | −6.21481 | −0.584640 | −0.292320 | − | 0.956321i | \(-0.594427\pi\) | ||||
−0.292320 | + | 0.956321i | \(0.594427\pi\) | |||||||
\(114\) | −2.91209 | −0.272742 | ||||||||
\(115\) | 8.37339 | 0.780823 | ||||||||
\(116\) | −2.46598 | −0.228960 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −4.58591 | −0.422167 | ||||||||
\(119\) | 0.0888858 | 0.00814815 | ||||||||
\(120\) | −2.09722 | −0.191449 | ||||||||
\(121\) | −0.902708 | −0.0820644 | ||||||||
\(122\) | 1.68161 | 0.152246 | ||||||||
\(123\) | −9.70721 | −0.875270 | ||||||||
\(124\) | 0.760072 | 0.0682564 | ||||||||
\(125\) | −11.7479 | −1.05077 | ||||||||
\(126\) | 0.0373018 | 0.00332310 | ||||||||
\(127\) | 4.59734 | 0.407948 | 0.203974 | − | 0.978976i | \(-0.434614\pi\) | ||||
0.203974 | + | 0.978976i | \(0.434614\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.8256 | −0.953144 | ||||||||
\(130\) | −2.09722 | −0.183938 | ||||||||
\(131\) | −17.3267 | −1.51385 | −0.756923 | − | 0.653505i | \(-0.773298\pi\) | ||||
−0.756923 | + | 0.653505i | \(0.773298\pi\) | |||||||
\(132\) | −3.17762 | −0.276577 | ||||||||
\(133\) | −0.108626 | −0.00941906 | ||||||||
\(134\) | −7.20145 | −0.622111 | ||||||||
\(135\) | 2.09722 | 0.180500 | ||||||||
\(136\) | 2.38289 | 0.204331 | ||||||||
\(137\) | −14.5720 | −1.24497 | −0.622485 | − | 0.782632i | \(-0.713877\pi\) | ||||
−0.622485 | + | 0.782632i | \(0.713877\pi\) | |||||||
\(138\) | −3.99261 | −0.339874 | ||||||||
\(139\) | −15.9341 | −1.35152 | −0.675758 | − | 0.737124i | \(-0.736183\pi\) | ||||
−0.675758 | + | 0.737124i | \(0.736183\pi\) | |||||||
\(140\) | −0.0782300 | −0.00661164 | ||||||||
\(141\) | −5.29982 | −0.446325 | ||||||||
\(142\) | 14.3856 | 1.20721 | ||||||||
\(143\) | −3.17762 | −0.265726 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.17170 | −0.429486 | ||||||||
\(146\) | −15.2846 | −1.26496 | ||||||||
\(147\) | −6.99861 | −0.577236 | ||||||||
\(148\) | −8.84213 | −0.726818 | ||||||||
\(149\) | −12.4885 | −1.02310 | −0.511548 | − | 0.859255i | \(-0.670928\pi\) | ||||
−0.511548 | + | 0.859255i | \(0.670928\pi\) | |||||||
\(150\) | 0.601670 | 0.0491262 | ||||||||
\(151\) | 11.6943 | 0.951669 | 0.475834 | − | 0.879535i | \(-0.342146\pi\) | ||||
0.475834 | + | 0.879535i | \(0.342146\pi\) | |||||||
\(152\) | −2.91209 | −0.236201 | ||||||||
\(153\) | −2.38289 | −0.192645 | ||||||||
\(154\) | −0.118531 | −0.00955150 | ||||||||
\(155\) | 1.59404 | 0.128036 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −11.0964 | −0.885592 | −0.442796 | − | 0.896622i | \(-0.646013\pi\) | ||||
−0.442796 | + | 0.896622i | \(0.646013\pi\) | |||||||
\(158\) | −6.39400 | −0.508680 | ||||||||
\(159\) | −10.7397 | −0.851712 | ||||||||
\(160\) | −2.09722 | −0.165800 | ||||||||
\(161\) | −0.148932 | −0.0117374 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 5.69850 | 0.446341 | 0.223170 | − | 0.974779i | \(-0.428359\pi\) | ||||
0.223170 | + | 0.974779i | \(0.428359\pi\) | |||||||
\(164\) | −9.70721 | −0.758006 | ||||||||
\(165\) | −6.66417 | −0.518805 | ||||||||
\(166\) | 5.88671 | 0.456898 | ||||||||
\(167\) | 19.9987 | 1.54755 | 0.773773 | − | 0.633464i | \(-0.218367\pi\) | ||||
0.773773 | + | 0.633464i | \(0.218367\pi\) | |||||||
\(168\) | 0.0373018 | 0.00287789 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.99743 | 0.383286 | ||||||||
\(171\) | 2.91209 | 0.222693 | ||||||||
\(172\) | −10.8256 | −0.825447 | ||||||||
\(173\) | 7.43256 | 0.565087 | 0.282544 | − | 0.959254i | \(-0.408822\pi\) | ||||
0.282544 | + | 0.959254i | \(0.408822\pi\) | |||||||
\(174\) | 2.46598 | 0.186945 | ||||||||
\(175\) | 0.0224434 | 0.00169656 | ||||||||
\(176\) | −3.17762 | −0.239522 | ||||||||
\(177\) | 4.58591 | 0.344698 | ||||||||
\(178\) | −2.63980 | −0.197861 | ||||||||
\(179\) | 24.5685 | 1.83634 | 0.918170 | − | 0.396188i | \(-0.129667\pi\) | ||||
0.918170 | + | 0.396188i | \(0.129667\pi\) | |||||||
\(180\) | 2.09722 | 0.156318 | ||||||||
\(181\) | −6.64229 | −0.493718 | −0.246859 | − | 0.969051i | \(-0.579398\pi\) | ||||
−0.246859 | + | 0.969051i | \(0.579398\pi\) | |||||||
\(182\) | 0.0373018 | 0.00276499 | ||||||||
\(183\) | −1.68161 | −0.124308 | ||||||||
\(184\) | −3.99261 | −0.294339 | ||||||||
\(185\) | −18.5439 | −1.36337 | ||||||||
\(186\) | −0.760072 | −0.0557312 | ||||||||
\(187\) | 7.57191 | 0.553713 | ||||||||
\(188\) | −5.29982 | −0.386529 | ||||||||
\(189\) | −0.0373018 | −0.00271330 | ||||||||
\(190\) | −6.10728 | −0.443069 | ||||||||
\(191\) | −12.5288 | −0.906550 | −0.453275 | − | 0.891371i | \(-0.649745\pi\) | ||||
−0.453275 | + | 0.891371i | \(0.649745\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 4.59720 | 0.330914 | 0.165457 | − | 0.986217i | \(-0.447090\pi\) | ||||
0.165457 | + | 0.986217i | \(0.447090\pi\) | |||||||
\(194\) | 2.73678 | 0.196489 | ||||||||
\(195\) | 2.09722 | 0.150185 | ||||||||
\(196\) | −6.99861 | −0.499901 | ||||||||
\(197\) | 15.5509 | 1.10796 | 0.553978 | − | 0.832532i | \(-0.313109\pi\) | ||||
0.553978 | + | 0.832532i | \(0.313109\pi\) | |||||||
\(198\) | 3.17762 | 0.225824 | ||||||||
\(199\) | −9.66523 | −0.685150 | −0.342575 | − | 0.939491i | \(-0.611299\pi\) | ||||
−0.342575 | + | 0.939491i | \(0.611299\pi\) | |||||||
\(200\) | 0.601670 | 0.0425445 | ||||||||
\(201\) | 7.20145 | 0.507951 | ||||||||
\(202\) | −17.7613 | −1.24968 | ||||||||
\(203\) | 0.0919853 | 0.00645610 | ||||||||
\(204\) | −2.38289 | −0.166835 | ||||||||
\(205\) | −20.3582 | −1.42188 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 3.99261 | 0.277506 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −9.25351 | −0.640079 | ||||||||
\(210\) | 0.0782300 | 0.00539838 | ||||||||
\(211\) | −3.17494 | −0.218572 | −0.109286 | − | 0.994010i | \(-0.534856\pi\) | ||||
−0.109286 | + | 0.994010i | \(0.534856\pi\) | |||||||
\(212\) | −10.7397 | −0.737604 | ||||||||
\(213\) | −14.3856 | −0.985685 | ||||||||
\(214\) | −7.44643 | −0.509027 | ||||||||
\(215\) | −22.7037 | −1.54838 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.0283520 | −0.00192466 | ||||||||
\(218\) | 3.30101 | 0.223573 | ||||||||
\(219\) | 15.2846 | 1.03284 | ||||||||
\(220\) | −6.66417 | −0.449299 | ||||||||
\(221\) | −2.38289 | −0.160290 | ||||||||
\(222\) | 8.84213 | 0.593445 | ||||||||
\(223\) | −1.36542 | −0.0914350 | −0.0457175 | − | 0.998954i | \(-0.514557\pi\) | ||||
−0.0457175 | + | 0.998954i | \(0.514557\pi\) | |||||||
\(224\) | 0.0373018 | 0.00249233 | ||||||||
\(225\) | −0.601670 | −0.0401114 | ||||||||
\(226\) | 6.21481 | 0.413403 | ||||||||
\(227\) | −10.1984 | −0.676892 | −0.338446 | − | 0.940986i | \(-0.609901\pi\) | ||||
−0.338446 | + | 0.940986i | \(0.609901\pi\) | |||||||
\(228\) | 2.91209 | 0.192858 | ||||||||
\(229\) | 20.1236 | 1.32980 | 0.664902 | − | 0.746931i | \(-0.268473\pi\) | ||||
0.664902 | + | 0.746931i | \(0.268473\pi\) | |||||||
\(230\) | −8.37339 | −0.552125 | ||||||||
\(231\) | 0.118531 | 0.00779876 | ||||||||
\(232\) | 2.46598 | 0.161899 | ||||||||
\(233\) | −20.9544 | −1.37277 | −0.686383 | − | 0.727240i | \(-0.740803\pi\) | ||||
−0.686383 | + | 0.727240i | \(0.740803\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −11.1149 | −0.725055 | ||||||||
\(236\) | 4.58591 | 0.298517 | ||||||||
\(237\) | 6.39400 | 0.415335 | ||||||||
\(238\) | −0.0888858 | −0.00576161 | ||||||||
\(239\) | −22.3195 | −1.44373 | −0.721865 | − | 0.692034i | \(-0.756715\pi\) | ||||
−0.721865 | + | 0.692034i | \(0.756715\pi\) | |||||||
\(240\) | 2.09722 | 0.135375 | ||||||||
\(241\) | 26.3016 | 1.69424 | 0.847118 | − | 0.531405i | \(-0.178336\pi\) | ||||
0.847118 | + | 0.531405i | \(0.178336\pi\) | |||||||
\(242\) | 0.902708 | 0.0580283 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.68161 | −0.107654 | ||||||||
\(245\) | −14.6776 | −0.937719 | ||||||||
\(246\) | 9.70721 | 0.618909 | ||||||||
\(247\) | 2.91209 | 0.185292 | ||||||||
\(248\) | −0.760072 | −0.0482646 | ||||||||
\(249\) | −5.88671 | −0.373055 | ||||||||
\(250\) | 11.7479 | 0.743004 | ||||||||
\(251\) | 14.0004 | 0.883696 | 0.441848 | − | 0.897090i | \(-0.354323\pi\) | ||||
0.441848 | + | 0.897090i | \(0.354323\pi\) | |||||||
\(252\) | −0.0373018 | −0.00234979 | ||||||||
\(253\) | −12.6870 | −0.797627 | ||||||||
\(254\) | −4.59734 | −0.288463 | ||||||||
\(255\) | −4.99743 | −0.312951 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.7882 | 0.735330 | 0.367665 | − | 0.929958i | \(-0.380157\pi\) | ||||
0.367665 | + | 0.929958i | \(0.380157\pi\) | |||||||
\(258\) | 10.8256 | 0.673974 | ||||||||
\(259\) | 0.329827 | 0.0204944 | ||||||||
\(260\) | 2.09722 | 0.130064 | ||||||||
\(261\) | −2.46598 | −0.152640 | ||||||||
\(262\) | 17.3267 | 1.07045 | ||||||||
\(263\) | −3.34403 | −0.206201 | −0.103101 | − | 0.994671i | \(-0.532876\pi\) | ||||
−0.103101 | + | 0.994671i | \(0.532876\pi\) | |||||||
\(264\) | 3.17762 | 0.195569 | ||||||||
\(265\) | −22.5235 | −1.38361 | ||||||||
\(266\) | 0.108626 | 0.00666028 | ||||||||
\(267\) | 2.63980 | 0.161553 | ||||||||
\(268\) | 7.20145 | 0.439899 | ||||||||
\(269\) | 16.1066 | 0.982037 | 0.491019 | − | 0.871149i | \(-0.336625\pi\) | ||||
0.491019 | + | 0.871149i | \(0.336625\pi\) | |||||||
\(270\) | −2.09722 | −0.127633 | ||||||||
\(271\) | −9.09091 | −0.552234 | −0.276117 | − | 0.961124i | \(-0.589048\pi\) | ||||
−0.276117 | + | 0.961124i | \(0.589048\pi\) | |||||||
\(272\) | −2.38289 | −0.144484 | ||||||||
\(273\) | −0.0373018 | −0.00225760 | ||||||||
\(274\) | 14.5720 | 0.880327 | ||||||||
\(275\) | 1.91188 | 0.115291 | ||||||||
\(276\) | 3.99261 | 0.240327 | ||||||||
\(277\) | 20.2183 | 1.21480 | 0.607401 | − | 0.794396i | \(-0.292212\pi\) | ||||
0.607401 | + | 0.794396i | \(0.292212\pi\) | |||||||
\(278\) | 15.9341 | 0.955666 | ||||||||
\(279\) | 0.760072 | 0.0455043 | ||||||||
\(280\) | 0.0782300 | 0.00467513 | ||||||||
\(281\) | 10.4908 | 0.625827 | 0.312913 | − | 0.949782i | \(-0.398695\pi\) | ||||
0.312913 | + | 0.949782i | \(0.398695\pi\) | |||||||
\(282\) | 5.29982 | 0.315600 | ||||||||
\(283\) | −20.5499 | −1.22157 | −0.610783 | − | 0.791798i | \(-0.709145\pi\) | ||||
−0.610783 | + | 0.791798i | \(0.709145\pi\) | |||||||
\(284\) | −14.3856 | −0.853628 | ||||||||
\(285\) | 6.10728 | 0.361764 | ||||||||
\(286\) | 3.17762 | 0.187897 | ||||||||
\(287\) | 0.362096 | 0.0213739 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −11.3219 | −0.665992 | ||||||||
\(290\) | 5.17170 | 0.303693 | ||||||||
\(291\) | −2.73678 | −0.160433 | ||||||||
\(292\) | 15.2846 | 0.894463 | ||||||||
\(293\) | −2.35918 | −0.137825 | −0.0689124 | − | 0.997623i | \(-0.521953\pi\) | ||||
−0.0689124 | + | 0.997623i | \(0.521953\pi\) | |||||||
\(294\) | 6.99861 | 0.408167 | ||||||||
\(295\) | 9.61765 | 0.559961 | ||||||||
\(296\) | 8.84213 | 0.513938 | ||||||||
\(297\) | −3.17762 | −0.184384 | ||||||||
\(298\) | 12.4885 | 0.723438 | ||||||||
\(299\) | 3.99261 | 0.230899 | ||||||||
\(300\) | −0.601670 | −0.0347375 | ||||||||
\(301\) | 0.403815 | 0.0232755 | ||||||||
\(302\) | −11.6943 | −0.672931 | ||||||||
\(303\) | 17.7613 | 1.02036 | ||||||||
\(304\) | 2.91209 | 0.167020 | ||||||||
\(305\) | −3.52671 | −0.201939 | ||||||||
\(306\) | 2.38289 | 0.136220 | ||||||||
\(307\) | −23.9915 | −1.36927 | −0.684633 | − | 0.728888i | \(-0.740038\pi\) | ||||
−0.684633 | + | 0.728888i | \(0.740038\pi\) | |||||||
\(308\) | 0.118531 | 0.00675393 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −1.59404 | −0.0905352 | ||||||||
\(311\) | −9.06740 | −0.514165 | −0.257083 | − | 0.966389i | \(-0.582761\pi\) | ||||
−0.257083 | + | 0.966389i | \(0.582761\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 27.0568 | 1.52934 | 0.764670 | − | 0.644422i | \(-0.222902\pi\) | ||||
0.764670 | + | 0.644422i | \(0.222902\pi\) | |||||||
\(314\) | 11.0964 | 0.626208 | ||||||||
\(315\) | −0.0782300 | −0.00440776 | ||||||||
\(316\) | 6.39400 | 0.359691 | ||||||||
\(317\) | 25.3558 | 1.42412 | 0.712062 | − | 0.702116i | \(-0.247761\pi\) | ||||
0.712062 | + | 0.702116i | \(0.247761\pi\) | |||||||
\(318\) | 10.7397 | 0.602251 | ||||||||
\(319\) | 7.83595 | 0.438729 | ||||||||
\(320\) | 2.09722 | 0.117238 | ||||||||
\(321\) | 7.44643 | 0.415619 | ||||||||
\(322\) | 0.148932 | 0.00829963 | ||||||||
\(323\) | −6.93916 | −0.386105 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.601670 | −0.0333747 | ||||||||
\(326\) | −5.69850 | −0.315610 | ||||||||
\(327\) | −3.30101 | −0.182546 | ||||||||
\(328\) | 9.70721 | 0.535991 | ||||||||
\(329\) | 0.197693 | 0.0108991 | ||||||||
\(330\) | 6.66417 | 0.366851 | ||||||||
\(331\) | −13.8421 | −0.760829 | −0.380414 | − | 0.924816i | \(-0.624219\pi\) | ||||
−0.380414 | + | 0.924816i | \(0.624219\pi\) | |||||||
\(332\) | −5.88671 | −0.323075 | ||||||||
\(333\) | −8.84213 | −0.484545 | ||||||||
\(334\) | −19.9987 | −1.09428 | ||||||||
\(335\) | 15.1030 | 0.825166 | ||||||||
\(336\) | −0.0373018 | −0.00203498 | ||||||||
\(337\) | −0.107575 | −0.00585998 | −0.00292999 | − | 0.999996i | \(-0.500933\pi\) | ||||
−0.00292999 | + | 0.999996i | \(0.500933\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −6.21481 | −0.337542 | ||||||||
\(340\) | −4.99743 | −0.271024 | ||||||||
\(341\) | −2.41522 | −0.130792 | ||||||||
\(342\) | −2.91209 | −0.157468 | ||||||||
\(343\) | 0.522173 | 0.0281947 | ||||||||
\(344\) | 10.8256 | 0.583679 | ||||||||
\(345\) | 8.37339 | 0.450808 | ||||||||
\(346\) | −7.43256 | −0.399577 | ||||||||
\(347\) | −33.6802 | −1.80805 | −0.904025 | − | 0.427481i | \(-0.859401\pi\) | ||||
−0.904025 | + | 0.427481i | \(0.859401\pi\) | |||||||
\(348\) | −2.46598 | −0.132190 | ||||||||
\(349\) | −14.2268 | −0.761543 | −0.380771 | − | 0.924669i | \(-0.624342\pi\) | ||||
−0.380771 | + | 0.924669i | \(0.624342\pi\) | |||||||
\(350\) | −0.0224434 | −0.00119965 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 3.17762 | 0.169368 | ||||||||
\(353\) | 2.62388 | 0.139655 | 0.0698274 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698274 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(354\) | −4.58591 | −0.243738 | ||||||||
\(355\) | −30.1698 | −1.60124 | ||||||||
\(356\) | 2.63980 | 0.139909 | ||||||||
\(357\) | 0.0888858 | 0.00470434 | ||||||||
\(358\) | −24.5685 | −1.29849 | ||||||||
\(359\) | −15.8065 | −0.834234 | −0.417117 | − | 0.908853i | \(-0.636959\pi\) | ||||
−0.417117 | + | 0.908853i | \(0.636959\pi\) | |||||||
\(360\) | −2.09722 | −0.110533 | ||||||||
\(361\) | −10.5198 | −0.553672 | ||||||||
\(362\) | 6.64229 | 0.349111 | ||||||||
\(363\) | −0.902708 | −0.0473799 | ||||||||
\(364\) | −0.0373018 | −0.00195514 | ||||||||
\(365\) | 32.0552 | 1.67784 | ||||||||
\(366\) | 1.68161 | 0.0878993 | ||||||||
\(367\) | 11.4273 | 0.596500 | 0.298250 | − | 0.954488i | \(-0.403597\pi\) | ||||
0.298250 | + | 0.954488i | \(0.403597\pi\) | |||||||
\(368\) | 3.99261 | 0.208129 | ||||||||
\(369\) | −9.70721 | −0.505337 | ||||||||
\(370\) | 18.5439 | 0.964050 | ||||||||
\(371\) | 0.400609 | 0.0207986 | ||||||||
\(372\) | 0.760072 | 0.0394079 | ||||||||
\(373\) | −5.05968 | −0.261980 | −0.130990 | − | 0.991384i | \(-0.541816\pi\) | ||||
−0.130990 | + | 0.991384i | \(0.541816\pi\) | |||||||
\(374\) | −7.57191 | −0.391534 | ||||||||
\(375\) | −11.7479 | −0.606661 | ||||||||
\(376\) | 5.29982 | 0.273317 | ||||||||
\(377\) | −2.46598 | −0.127004 | ||||||||
\(378\) | 0.0373018 | 0.00191860 | ||||||||
\(379\) | 12.8369 | 0.659389 | 0.329695 | − | 0.944088i | \(-0.393054\pi\) | ||||
0.329695 | + | 0.944088i | \(0.393054\pi\) | |||||||
\(380\) | 6.10728 | 0.313297 | ||||||||
\(381\) | 4.59734 | 0.235529 | ||||||||
\(382\) | 12.5288 | 0.641028 | ||||||||
\(383\) | −19.1538 | −0.978715 | −0.489357 | − | 0.872083i | \(-0.662769\pi\) | ||||
−0.489357 | + | 0.872083i | \(0.662769\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0.248585 | 0.0126691 | ||||||||
\(386\) | −4.59720 | −0.233991 | ||||||||
\(387\) | −10.8256 | −0.550298 | ||||||||
\(388\) | −2.73678 | −0.138939 | ||||||||
\(389\) | 11.7164 | 0.594045 | 0.297022 | − | 0.954870i | \(-0.404006\pi\) | ||||
0.297022 | + | 0.954870i | \(0.404006\pi\) | |||||||
\(390\) | −2.09722 | −0.106197 | ||||||||
\(391\) | −9.51394 | −0.481141 | ||||||||
\(392\) | 6.99861 | 0.353483 | ||||||||
\(393\) | −17.3267 | −0.874019 | ||||||||
\(394\) | −15.5509 | −0.783443 | ||||||||
\(395\) | 13.4096 | 0.674712 | ||||||||
\(396\) | −3.17762 | −0.159682 | ||||||||
\(397\) | 23.4133 | 1.17508 | 0.587540 | − | 0.809195i | \(-0.300097\pi\) | ||||
0.587540 | + | 0.809195i | \(0.300097\pi\) | |||||||
\(398\) | 9.66523 | 0.484474 | ||||||||
\(399\) | −0.108626 | −0.00543810 | ||||||||
\(400\) | −0.601670 | −0.0300835 | ||||||||
\(401\) | 28.4310 | 1.41978 | 0.709889 | − | 0.704314i | \(-0.248745\pi\) | ||||
0.709889 | + | 0.704314i | \(0.248745\pi\) | |||||||
\(402\) | −7.20145 | −0.359176 | ||||||||
\(403\) | 0.760072 | 0.0378619 | ||||||||
\(404\) | 17.7613 | 0.883656 | ||||||||
\(405\) | 2.09722 | 0.104212 | ||||||||
\(406\) | −0.0919853 | −0.00456515 | ||||||||
\(407\) | 28.0969 | 1.39271 | ||||||||
\(408\) | 2.38289 | 0.117970 | ||||||||
\(409\) | −5.14846 | −0.254575 | −0.127287 | − | 0.991866i | \(-0.540627\pi\) | ||||
−0.127287 | + | 0.991866i | \(0.540627\pi\) | |||||||
\(410\) | 20.3582 | 1.00542 | ||||||||
\(411\) | −14.5720 | −0.718784 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −0.171062 | −0.00841743 | ||||||||
\(414\) | −3.99261 | −0.196226 | ||||||||
\(415\) | −12.3457 | −0.606028 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −15.9341 | −0.780298 | ||||||||
\(418\) | 9.25351 | 0.452604 | ||||||||
\(419\) | −15.5597 | −0.760143 | −0.380072 | − | 0.924957i | \(-0.624101\pi\) | ||||
−0.380072 | + | 0.924957i | \(0.624101\pi\) | |||||||
\(420\) | −0.0782300 | −0.00381723 | ||||||||
\(421\) | 19.2163 | 0.936547 | 0.468274 | − | 0.883584i | \(-0.344876\pi\) | ||||
0.468274 | + | 0.883584i | \(0.344876\pi\) | |||||||
\(422\) | 3.17494 | 0.154554 | ||||||||
\(423\) | −5.29982 | −0.257686 | ||||||||
\(424\) | 10.7397 | 0.521565 | ||||||||
\(425\) | 1.43371 | 0.0695452 | ||||||||
\(426\) | 14.3856 | 0.696985 | ||||||||
\(427\) | 0.0627271 | 0.00303558 | ||||||||
\(428\) | 7.44643 | 0.359937 | ||||||||
\(429\) | −3.17762 | −0.153417 | ||||||||
\(430\) | 22.7037 | 1.09487 | ||||||||
\(431\) | −24.8965 | −1.19922 | −0.599611 | − | 0.800292i | \(-0.704678\pi\) | ||||
−0.599611 | + | 0.800292i | \(0.704678\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 29.0280 | 1.39500 | 0.697498 | − | 0.716586i | \(-0.254296\pi\) | ||||
0.697498 | + | 0.716586i | \(0.254296\pi\) | |||||||
\(434\) | 0.0283520 | 0.00136094 | ||||||||
\(435\) | −5.17170 | −0.247964 | ||||||||
\(436\) | −3.30101 | −0.158090 | ||||||||
\(437\) | 11.6268 | 0.556187 | ||||||||
\(438\) | −15.2846 | −0.730326 | ||||||||
\(439\) | −12.1657 | −0.580636 | −0.290318 | − | 0.956930i | \(-0.593761\pi\) | ||||
−0.290318 | + | 0.956930i | \(0.593761\pi\) | |||||||
\(440\) | 6.66417 | 0.317702 | ||||||||
\(441\) | −6.99861 | −0.333267 | ||||||||
\(442\) | 2.38289 | 0.113342 | ||||||||
\(443\) | −26.0682 | −1.23854 | −0.619269 | − | 0.785179i | \(-0.712571\pi\) | ||||
−0.619269 | + | 0.785179i | \(0.712571\pi\) | |||||||
\(444\) | −8.84213 | −0.419629 | ||||||||
\(445\) | 5.53623 | 0.262443 | ||||||||
\(446\) | 1.36542 | 0.0646543 | ||||||||
\(447\) | −12.4885 | −0.590685 | ||||||||
\(448\) | −0.0373018 | −0.00176234 | ||||||||
\(449\) | −17.1631 | −0.809977 | −0.404988 | − | 0.914322i | \(-0.632724\pi\) | ||||
−0.404988 | + | 0.914322i | \(0.632724\pi\) | |||||||
\(450\) | 0.601670 | 0.0283630 | ||||||||
\(451\) | 30.8459 | 1.45248 | ||||||||
\(452\) | −6.21481 | −0.292320 | ||||||||
\(453\) | 11.6943 | 0.549446 | ||||||||
\(454\) | 10.1984 | 0.478635 | ||||||||
\(455\) | −0.0782300 | −0.00366748 | ||||||||
\(456\) | −2.91209 | −0.136371 | ||||||||
\(457\) | 1.04913 | 0.0490760 | 0.0245380 | − | 0.999699i | \(-0.492189\pi\) | ||||
0.0245380 | + | 0.999699i | \(0.492189\pi\) | |||||||
\(458\) | −20.1236 | −0.940313 | ||||||||
\(459\) | −2.38289 | −0.111224 | ||||||||
\(460\) | 8.37339 | 0.390411 | ||||||||
\(461\) | 1.36203 | 0.0634362 | 0.0317181 | − | 0.999497i | \(-0.489902\pi\) | ||||
0.0317181 | + | 0.999497i | \(0.489902\pi\) | |||||||
\(462\) | −0.118531 | −0.00551456 | ||||||||
\(463\) | −17.9663 | −0.834963 | −0.417482 | − | 0.908685i | \(-0.637087\pi\) | ||||
−0.417482 | + | 0.908685i | \(0.637087\pi\) | |||||||
\(464\) | −2.46598 | −0.114480 | ||||||||
\(465\) | 1.59404 | 0.0739217 | ||||||||
\(466\) | 20.9544 | 0.970692 | ||||||||
\(467\) | −12.2355 | −0.566194 | −0.283097 | − | 0.959091i | \(-0.591362\pi\) | ||||
−0.283097 | + | 0.959091i | \(0.591362\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −0.268627 | −0.0124040 | ||||||||
\(470\) | 11.1149 | 0.512691 | ||||||||
\(471\) | −11.0964 | −0.511297 | ||||||||
\(472\) | −4.58591 | −0.211083 | ||||||||
\(473\) | 34.3998 | 1.58170 | ||||||||
\(474\) | −6.39400 | −0.293686 | ||||||||
\(475\) | −1.75212 | −0.0803926 | ||||||||
\(476\) | 0.0888858 | 0.00407407 | ||||||||
\(477\) | −10.7397 | −0.491736 | ||||||||
\(478\) | 22.3195 | 1.02087 | ||||||||
\(479\) | 18.4397 | 0.842531 | 0.421265 | − | 0.906937i | \(-0.361586\pi\) | ||||
0.421265 | + | 0.906937i | \(0.361586\pi\) | |||||||
\(480\) | −2.09722 | −0.0957245 | ||||||||
\(481\) | −8.84213 | −0.403166 | ||||||||
\(482\) | −26.3016 | −1.19801 | ||||||||
\(483\) | −0.148932 | −0.00677662 | ||||||||
\(484\) | −0.902708 | −0.0410322 | ||||||||
\(485\) | −5.73963 | −0.260623 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 24.9829 | 1.13208 | 0.566041 | − | 0.824377i | \(-0.308474\pi\) | ||||
0.566041 | + | 0.824377i | \(0.308474\pi\) | |||||||
\(488\) | 1.68161 | 0.0761230 | ||||||||
\(489\) | 5.69850 | 0.257695 | ||||||||
\(490\) | 14.6776 | 0.663067 | ||||||||
\(491\) | −21.6861 | −0.978679 | −0.489339 | − | 0.872093i | \(-0.662762\pi\) | ||||
−0.489339 | + | 0.872093i | \(0.662762\pi\) | |||||||
\(492\) | −9.70721 | −0.437635 | ||||||||
\(493\) | 5.87614 | 0.264648 | ||||||||
\(494\) | −2.91209 | −0.131021 | ||||||||
\(495\) | −6.66417 | −0.299532 | ||||||||
\(496\) | 0.760072 | 0.0341282 | ||||||||
\(497\) | 0.536608 | 0.0240702 | ||||||||
\(498\) | 5.88671 | 0.263790 | ||||||||
\(499\) | 28.2202 | 1.26331 | 0.631654 | − | 0.775250i | \(-0.282376\pi\) | ||||
0.631654 | + | 0.775250i | \(0.282376\pi\) | |||||||
\(500\) | −11.7479 | −0.525384 | ||||||||
\(501\) | 19.9987 | 0.893476 | ||||||||
\(502\) | −14.0004 | −0.624868 | ||||||||
\(503\) | −15.1995 | −0.677713 | −0.338856 | − | 0.940838i | \(-0.610040\pi\) | ||||
−0.338856 | + | 0.940838i | \(0.610040\pi\) | |||||||
\(504\) | 0.0373018 | 0.00166155 | ||||||||
\(505\) | 37.2493 | 1.65757 | ||||||||
\(506\) | 12.6870 | 0.564007 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 4.59734 | 0.203974 | ||||||||
\(509\) | −27.6342 | −1.22487 | −0.612433 | − | 0.790522i | \(-0.709809\pi\) | ||||
−0.612433 | + | 0.790522i | \(0.709809\pi\) | |||||||
\(510\) | 4.99743 | 0.221290 | ||||||||
\(511\) | −0.570142 | −0.0252216 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.91209 | 0.128572 | ||||||||
\(514\) | −11.7882 | −0.519957 | ||||||||
\(515\) | −2.09722 | −0.0924145 | ||||||||
\(516\) | −10.8256 | −0.476572 | ||||||||
\(517\) | 16.8408 | 0.740659 | ||||||||
\(518\) | −0.329827 | −0.0144918 | ||||||||
\(519\) | 7.43256 | 0.326253 | ||||||||
\(520\) | −2.09722 | −0.0919692 | ||||||||
\(521\) | −40.7700 | −1.78616 | −0.893082 | − | 0.449893i | \(-0.851462\pi\) | ||||
−0.893082 | + | 0.449893i | \(0.851462\pi\) | |||||||
\(522\) | 2.46598 | 0.107933 | ||||||||
\(523\) | 9.57148 | 0.418532 | 0.209266 | − | 0.977859i | \(-0.432893\pi\) | ||||
0.209266 | + | 0.977859i | \(0.432893\pi\) | |||||||
\(524\) | −17.3267 | −0.756923 | ||||||||
\(525\) | 0.0224434 | 0.000979509 0 | ||||||||
\(526\) | 3.34403 | 0.145806 | ||||||||
\(527\) | −1.81116 | −0.0788955 | ||||||||
\(528\) | −3.17762 | −0.138288 | ||||||||
\(529\) | −7.05903 | −0.306914 | ||||||||
\(530\) | 22.5235 | 0.978357 | ||||||||
\(531\) | 4.58591 | 0.199011 | ||||||||
\(532\) | −0.108626 | −0.00470953 | ||||||||
\(533\) | −9.70721 | −0.420466 | ||||||||
\(534\) | −2.63980 | −0.114235 | ||||||||
\(535\) | 15.6168 | 0.675173 | ||||||||
\(536\) | −7.20145 | −0.311055 | ||||||||
\(537\) | 24.5685 | 1.06021 | ||||||||
\(538\) | −16.1066 | −0.694405 | ||||||||
\(539\) | 22.2389 | 0.957899 | ||||||||
\(540\) | 2.09722 | 0.0902500 | ||||||||
\(541\) | 41.1381 | 1.76867 | 0.884333 | − | 0.466857i | \(-0.154614\pi\) | ||||
0.884333 | + | 0.466857i | \(0.154614\pi\) | |||||||
\(542\) | 9.09091 | 0.390488 | ||||||||
\(543\) | −6.64229 | −0.285048 | ||||||||
\(544\) | 2.38289 | 0.102165 | ||||||||
\(545\) | −6.92295 | −0.296547 | ||||||||
\(546\) | 0.0373018 | 0.00159637 | ||||||||
\(547\) | 18.1876 | 0.777644 | 0.388822 | − | 0.921313i | \(-0.372882\pi\) | ||||
0.388822 | + | 0.921313i | \(0.372882\pi\) | |||||||
\(548\) | −14.5720 | −0.622485 | ||||||||
\(549\) | −1.68161 | −0.0717695 | ||||||||
\(550\) | −1.91188 | −0.0815229 | ||||||||
\(551\) | −7.18114 | −0.305927 | ||||||||
\(552\) | −3.99261 | −0.169937 | ||||||||
\(553\) | −0.238508 | −0.0101424 | ||||||||
\(554\) | −20.2183 | −0.858994 | ||||||||
\(555\) | −18.5439 | −0.787144 | ||||||||
\(556\) | −15.9341 | −0.675758 | ||||||||
\(557\) | 6.12099 | 0.259355 | 0.129677 | − | 0.991556i | \(-0.458606\pi\) | ||||
0.129677 | + | 0.991556i | \(0.458606\pi\) | |||||||
\(558\) | −0.760072 | −0.0321764 | ||||||||
\(559\) | −10.8256 | −0.457875 | ||||||||
\(560\) | −0.0782300 | −0.00330582 | ||||||||
\(561\) | 7.57191 | 0.319686 | ||||||||
\(562\) | −10.4908 | −0.442526 | ||||||||
\(563\) | −46.7197 | −1.96900 | −0.984501 | − | 0.175382i | \(-0.943884\pi\) | ||||
−0.984501 | + | 0.175382i | \(0.943884\pi\) | |||||||
\(564\) | −5.29982 | −0.223163 | ||||||||
\(565\) | −13.0338 | −0.548337 | ||||||||
\(566\) | 20.5499 | 0.863778 | ||||||||
\(567\) | −0.0373018 | −0.00156653 | ||||||||
\(568\) | 14.3856 | 0.603606 | ||||||||
\(569\) | −13.9598 | −0.585224 | −0.292612 | − | 0.956231i | \(-0.594524\pi\) | ||||
−0.292612 | + | 0.956231i | \(0.594524\pi\) | |||||||
\(570\) | −6.10728 | −0.255806 | ||||||||
\(571\) | 1.97131 | 0.0824968 | 0.0412484 | − | 0.999149i | \(-0.486866\pi\) | ||||
0.0412484 | + | 0.999149i | \(0.486866\pi\) | |||||||
\(572\) | −3.17762 | −0.132863 | ||||||||
\(573\) | −12.5288 | −0.523397 | ||||||||
\(574\) | −0.362096 | −0.0151136 | ||||||||
\(575\) | −2.40224 | −0.100180 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.8428 | 0.867697 | 0.433849 | − | 0.900986i | \(-0.357155\pi\) | ||||
0.433849 | + | 0.900986i | \(0.357155\pi\) | |||||||
\(578\) | 11.3219 | 0.470927 | ||||||||
\(579\) | 4.59720 | 0.191053 | ||||||||
\(580\) | −5.17170 | −0.214743 | ||||||||
\(581\) | 0.219585 | 0.00910991 | ||||||||
\(582\) | 2.73678 | 0.113443 | ||||||||
\(583\) | 34.1267 | 1.41338 | ||||||||
\(584\) | −15.2846 | −0.632481 | ||||||||
\(585\) | 2.09722 | 0.0867094 | ||||||||
\(586\) | 2.35918 | 0.0974569 | ||||||||
\(587\) | −34.8380 | −1.43792 | −0.718958 | − | 0.695053i | \(-0.755381\pi\) | ||||
−0.718958 | + | 0.695053i | \(0.755381\pi\) | |||||||
\(588\) | −6.99861 | −0.288618 | ||||||||
\(589\) | 2.21339 | 0.0912013 | ||||||||
\(590\) | −9.61765 | −0.395953 | ||||||||
\(591\) | 15.5509 | 0.639678 | ||||||||
\(592\) | −8.84213 | −0.363409 | ||||||||
\(593\) | −2.11731 | −0.0869477 | −0.0434738 | − | 0.999055i | \(-0.513843\pi\) | ||||
−0.0434738 | + | 0.999055i | \(0.513843\pi\) | |||||||
\(594\) | 3.17762 | 0.130379 | ||||||||
\(595\) | 0.186413 | 0.00764219 | ||||||||
\(596\) | −12.4885 | −0.511548 | ||||||||
\(597\) | −9.66523 | −0.395571 | ||||||||
\(598\) | −3.99261 | −0.163270 | ||||||||
\(599\) | 35.5037 | 1.45064 | 0.725320 | − | 0.688411i | \(-0.241692\pi\) | ||||
0.725320 | + | 0.688411i | \(0.241692\pi\) | |||||||
\(600\) | 0.601670 | 0.0245631 | ||||||||
\(601\) | 16.5908 | 0.676752 | 0.338376 | − | 0.941011i | \(-0.390123\pi\) | ||||
0.338376 | + | 0.941011i | \(0.390123\pi\) | |||||||
\(602\) | −0.403815 | −0.0164583 | ||||||||
\(603\) | 7.20145 | 0.293266 | ||||||||
\(604\) | 11.6943 | 0.475834 | ||||||||
\(605\) | −1.89318 | −0.0769686 | ||||||||
\(606\) | −17.7613 | −0.721502 | ||||||||
\(607\) | −40.3761 | −1.63882 | −0.819408 | − | 0.573210i | \(-0.805698\pi\) | ||||
−0.819408 | + | 0.573210i | \(0.805698\pi\) | |||||||
\(608\) | −2.91209 | −0.118101 | ||||||||
\(609\) | 0.0919853 | 0.00372743 | ||||||||
\(610\) | 3.52671 | 0.142792 | ||||||||
\(611\) | −5.29982 | −0.214408 | ||||||||
\(612\) | −2.38289 | −0.0963224 | ||||||||
\(613\) | −14.6447 | −0.591493 | −0.295747 | − | 0.955266i | \(-0.595568\pi\) | ||||
−0.295747 | + | 0.955266i | \(0.595568\pi\) | |||||||
\(614\) | 23.9915 | 0.968218 | ||||||||
\(615\) | −20.3582 | −0.820920 | ||||||||
\(616\) | −0.118531 | −0.00477575 | ||||||||
\(617\) | 14.9516 | 0.601927 | 0.300963 | − | 0.953636i | \(-0.402692\pi\) | ||||
0.300963 | + | 0.953636i | \(0.402692\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 18.1481 | 0.729435 | 0.364717 | − | 0.931118i | \(-0.381166\pi\) | ||||
0.364717 | + | 0.931118i | \(0.381166\pi\) | |||||||
\(620\) | 1.59404 | 0.0640181 | ||||||||
\(621\) | 3.99261 | 0.160218 | ||||||||
\(622\) | 9.06740 | 0.363570 | ||||||||
\(623\) | −0.0984690 | −0.00394508 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −21.6296 | −0.865186 | ||||||||
\(626\) | −27.0568 | −1.08141 | ||||||||
\(627\) | −9.25351 | −0.369550 | ||||||||
\(628\) | −11.0964 | −0.442796 | ||||||||
\(629\) | 21.0698 | 0.840107 | ||||||||
\(630\) | 0.0782300 | 0.00311676 | ||||||||
\(631\) | 12.3163 | 0.490305 | 0.245153 | − | 0.969485i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969485i | \(0.421162\pi\) | |||||||
\(632\) | −6.39400 | −0.254340 | ||||||||
\(633\) | −3.17494 | −0.126193 | ||||||||
\(634\) | −25.3558 | −1.00701 | ||||||||
\(635\) | 9.64162 | 0.382616 | ||||||||
\(636\) | −10.7397 | −0.425856 | ||||||||
\(637\) | −6.99861 | −0.277295 | ||||||||
\(638\) | −7.83595 | −0.310228 | ||||||||
\(639\) | −14.3856 | −0.569086 | ||||||||
\(640\) | −2.09722 | −0.0828999 | ||||||||
\(641\) | 9.98898 | 0.394541 | 0.197270 | − | 0.980349i | \(-0.436792\pi\) | ||||
0.197270 | + | 0.980349i | \(0.436792\pi\) | |||||||
\(642\) | −7.44643 | −0.293887 | ||||||||
\(643\) | 6.16171 | 0.242994 | 0.121497 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121497 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(644\) | −0.148932 | −0.00586872 | ||||||||
\(645\) | −22.7037 | −0.893958 | ||||||||
\(646\) | 6.93916 | 0.273018 | ||||||||
\(647\) | 27.2248 | 1.07032 | 0.535159 | − | 0.844751i | \(-0.320252\pi\) | ||||
0.535159 | + | 0.844751i | \(0.320252\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −14.5723 | −0.572012 | ||||||||
\(650\) | 0.601670 | 0.0235995 | ||||||||
\(651\) | −0.0283520 | −0.00111120 | ||||||||
\(652\) | 5.69850 | 0.223170 | ||||||||
\(653\) | 27.1892 | 1.06400 | 0.531998 | − | 0.846745i | \(-0.321441\pi\) | ||||
0.531998 | + | 0.846745i | \(0.321441\pi\) | |||||||
\(654\) | 3.30101 | 0.129080 | ||||||||
\(655\) | −36.3380 | −1.41984 | ||||||||
\(656\) | −9.70721 | −0.379003 | ||||||||
\(657\) | 15.2846 | 0.596309 | ||||||||
\(658\) | −0.197693 | −0.00770686 | ||||||||
\(659\) | 13.5823 | 0.529093 | 0.264546 | − | 0.964373i | \(-0.414778\pi\) | ||||
0.264546 | + | 0.964373i | \(0.414778\pi\) | |||||||
\(660\) | −6.66417 | −0.259403 | ||||||||
\(661\) | −31.9323 | −1.24202 | −0.621010 | − | 0.783802i | \(-0.713278\pi\) | ||||
−0.621010 | + | 0.783802i | \(0.713278\pi\) | |||||||
\(662\) | 13.8421 | 0.537987 | ||||||||
\(663\) | −2.38289 | −0.0925436 | ||||||||
\(664\) | 5.88671 | 0.228449 | ||||||||
\(665\) | −0.227812 | −0.00883418 | ||||||||
\(666\) | 8.84213 | 0.342625 | ||||||||
\(667\) | −9.84570 | −0.381227 | ||||||||
\(668\) | 19.9987 | 0.773773 | ||||||||
\(669\) | −1.36542 | −0.0527900 | ||||||||
\(670\) | −15.1030 | −0.583481 | ||||||||
\(671\) | 5.34353 | 0.206285 | ||||||||
\(672\) | 0.0373018 | 0.00143895 | ||||||||
\(673\) | 23.8672 | 0.920012 | 0.460006 | − | 0.887916i | \(-0.347847\pi\) | ||||
0.460006 | + | 0.887916i | \(0.347847\pi\) | |||||||
\(674\) | 0.107575 | 0.00414363 | ||||||||
\(675\) | −0.601670 | −0.0231583 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −51.5593 | −1.98158 | −0.990792 | − | 0.135390i | \(-0.956771\pi\) | ||||
−0.990792 | + | 0.135390i | \(0.956771\pi\) | |||||||
\(678\) | 6.21481 | 0.238678 | ||||||||
\(679\) | 0.102087 | 0.00391773 | ||||||||
\(680\) | 4.99743 | 0.191643 | ||||||||
\(681\) | −10.1984 | −0.390804 | ||||||||
\(682\) | 2.41522 | 0.0924836 | ||||||||
\(683\) | 11.2269 | 0.429586 | 0.214793 | − | 0.976660i | \(-0.431092\pi\) | ||||
0.214793 | + | 0.976660i | \(0.431092\pi\) | |||||||
\(684\) | 2.91209 | 0.111346 | ||||||||
\(685\) | −30.5607 | −1.16766 | ||||||||
\(686\) | −0.522173 | −0.0199366 | ||||||||
\(687\) | 20.1236 | 0.767763 | ||||||||
\(688\) | −10.8256 | −0.412723 | ||||||||
\(689\) | −10.7397 | −0.409149 | ||||||||
\(690\) | −8.37339 | −0.318769 | ||||||||
\(691\) | −34.2987 | −1.30478 | −0.652392 | − | 0.757881i | \(-0.726235\pi\) | ||||
−0.652392 | + | 0.757881i | \(0.726235\pi\) | |||||||
\(692\) | 7.43256 | 0.282544 | ||||||||
\(693\) | 0.118531 | 0.00450262 | ||||||||
\(694\) | 33.6802 | 1.27848 | ||||||||
\(695\) | −33.4174 | −1.26759 | ||||||||
\(696\) | 2.46598 | 0.0934727 | ||||||||
\(697\) | 23.1312 | 0.876156 | ||||||||
\(698\) | 14.2268 | 0.538492 | ||||||||
\(699\) | −20.9544 | −0.792567 | ||||||||
\(700\) | 0.0224434 | 0.000848279 0 | ||||||||
\(701\) | −8.77197 | −0.331313 | −0.165656 | − | 0.986184i | \(-0.552974\pi\) | ||||
−0.165656 | + | 0.986184i | \(0.552974\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −25.7490 | −0.971143 | ||||||||
\(704\) | −3.17762 | −0.119761 | ||||||||
\(705\) | −11.1149 | −0.418611 | ||||||||
\(706\) | −2.62388 | −0.0987509 | ||||||||
\(707\) | −0.662526 | −0.0249169 | ||||||||
\(708\) | 4.58591 | 0.172349 | ||||||||
\(709\) | 25.0019 | 0.938967 | 0.469484 | − | 0.882941i | \(-0.344440\pi\) | ||||
0.469484 | + | 0.882941i | \(0.344440\pi\) | |||||||
\(710\) | 30.1698 | 1.13225 | ||||||||
\(711\) | 6.39400 | 0.239794 | ||||||||
\(712\) | −2.63980 | −0.0989305 | ||||||||
\(713\) | 3.03467 | 0.113649 | ||||||||
\(714\) | −0.0888858 | −0.00332647 | ||||||||
\(715\) | −6.66417 | −0.249226 | ||||||||
\(716\) | 24.5685 | 0.918170 | ||||||||
\(717\) | −22.3195 | −0.833538 | ||||||||
\(718\) | 15.8065 | 0.589892 | ||||||||
\(719\) | −39.3676 | −1.46816 | −0.734081 | − | 0.679061i | \(-0.762387\pi\) | ||||
−0.734081 | + | 0.679061i | \(0.762387\pi\) | |||||||
\(720\) | 2.09722 | 0.0781588 | ||||||||
\(721\) | 0.0373018 | 0.00138919 | ||||||||
\(722\) | 10.5198 | 0.391505 | ||||||||
\(723\) | 26.3016 | 0.978168 | ||||||||
\(724\) | −6.64229 | −0.246859 | ||||||||
\(725\) | 1.48371 | 0.0551035 | ||||||||
\(726\) | 0.902708 | 0.0335026 | ||||||||
\(727\) | −5.79125 | −0.214786 | −0.107393 | − | 0.994217i | \(-0.534250\pi\) | ||||
−0.107393 | + | 0.994217i | \(0.534250\pi\) | |||||||
\(728\) | 0.0373018 | 0.00138250 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −32.0552 | −1.18641 | ||||||||
\(731\) | 25.7962 | 0.954108 | ||||||||
\(732\) | −1.68161 | −0.0621542 | ||||||||
\(733\) | 24.9648 | 0.922098 | 0.461049 | − | 0.887375i | \(-0.347473\pi\) | ||||
0.461049 | + | 0.887375i | \(0.347473\pi\) | |||||||
\(734\) | −11.4273 | −0.421789 | ||||||||
\(735\) | −14.6776 | −0.541392 | ||||||||
\(736\) | −3.99261 | −0.147170 | ||||||||
\(737\) | −22.8835 | −0.842925 | ||||||||
\(738\) | 9.70721 | 0.357327 | ||||||||
\(739\) | 16.6930 | 0.614061 | 0.307031 | − | 0.951700i | \(-0.400665\pi\) | ||||
0.307031 | + | 0.951700i | \(0.400665\pi\) | |||||||
\(740\) | −18.5439 | −0.681687 | ||||||||
\(741\) | 2.91209 | 0.106978 | ||||||||
\(742\) | −0.400609 | −0.0147068 | ||||||||
\(743\) | −37.9447 | −1.39206 | −0.696028 | − | 0.718014i | \(-0.745051\pi\) | ||||
−0.696028 | + | 0.718014i | \(0.745051\pi\) | |||||||
\(744\) | −0.760072 | −0.0278656 | ||||||||
\(745\) | −26.1911 | −0.959567 | ||||||||
\(746\) | 5.05968 | 0.185248 | ||||||||
\(747\) | −5.88671 | −0.215384 | ||||||||
\(748\) | 7.57191 | 0.276857 | ||||||||
\(749\) | −0.277765 | −0.0101493 | ||||||||
\(750\) | 11.7479 | 0.428974 | ||||||||
\(751\) | 29.4524 | 1.07474 | 0.537368 | − | 0.843348i | \(-0.319419\pi\) | ||||
0.537368 | + | 0.843348i | \(0.319419\pi\) | |||||||
\(752\) | −5.29982 | −0.193264 | ||||||||
\(753\) | 14.0004 | 0.510202 | ||||||||
\(754\) | 2.46598 | 0.0898056 | ||||||||
\(755\) | 24.5255 | 0.892575 | ||||||||
\(756\) | −0.0373018 | −0.00135665 | ||||||||
\(757\) | 8.22118 | 0.298804 | 0.149402 | − | 0.988777i | \(-0.452265\pi\) | ||||
0.149402 | + | 0.988777i | \(0.452265\pi\) | |||||||
\(758\) | −12.8369 | −0.466259 | ||||||||
\(759\) | −12.6870 | −0.460510 | ||||||||
\(760\) | −6.10728 | −0.221534 | ||||||||
\(761\) | −28.5972 | −1.03665 | −0.518324 | − | 0.855185i | \(-0.673444\pi\) | ||||
−0.518324 | + | 0.855185i | \(0.673444\pi\) | |||||||
\(762\) | −4.59734 | −0.166544 | ||||||||
\(763\) | 0.123134 | 0.00445773 | ||||||||
\(764\) | −12.5288 | −0.453275 | ||||||||
\(765\) | −4.99743 | −0.180683 | ||||||||
\(766\) | 19.1538 | 0.692056 | ||||||||
\(767\) | 4.58591 | 0.165588 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 38.8323 | 1.40033 | 0.700165 | − | 0.713981i | \(-0.253110\pi\) | ||||
0.700165 | + | 0.713981i | \(0.253110\pi\) | |||||||
\(770\) | −0.248585 | −0.00895840 | ||||||||
\(771\) | 11.7882 | 0.424543 | ||||||||
\(772\) | 4.59720 | 0.165457 | ||||||||
\(773\) | −36.2728 | −1.30464 | −0.652320 | − | 0.757943i | \(-0.726204\pi\) | ||||
−0.652320 | + | 0.757943i | \(0.726204\pi\) | |||||||
\(774\) | 10.8256 | 0.389119 | ||||||||
\(775\) | −0.457313 | −0.0164272 | ||||||||
\(776\) | 2.73678 | 0.0982447 | ||||||||
\(777\) | 0.329827 | 0.0118325 | ||||||||
\(778\) | −11.7164 | −0.420053 | ||||||||
\(779\) | −28.2682 | −1.01281 | ||||||||
\(780\) | 2.09722 | 0.0750925 | ||||||||
\(781\) | 45.7120 | 1.63570 | ||||||||
\(782\) | 9.51394 | 0.340218 | ||||||||
\(783\) | −2.46598 | −0.0881269 | ||||||||
\(784\) | −6.99861 | −0.249950 | ||||||||
\(785\) | −23.2717 | −0.830601 | ||||||||
\(786\) | 17.3267 | 0.618025 | ||||||||
\(787\) | −44.7173 | −1.59400 | −0.797000 | − | 0.603979i | \(-0.793581\pi\) | ||||
−0.797000 | + | 0.603979i | \(0.793581\pi\) | |||||||
\(788\) | 15.5509 | 0.553978 | ||||||||
\(789\) | −3.34403 | −0.119050 | ||||||||
\(790\) | −13.4096 | −0.477093 | ||||||||
\(791\) | 0.231823 | 0.00824269 | ||||||||
\(792\) | 3.17762 | 0.112912 | ||||||||
\(793\) | −1.68161 | −0.0597158 | ||||||||
\(794\) | −23.4133 | −0.830907 | ||||||||
\(795\) | −22.5235 | −0.798825 | ||||||||
\(796\) | −9.66523 | −0.342575 | ||||||||
\(797\) | 49.2580 | 1.74481 | 0.872403 | − | 0.488787i | \(-0.162560\pi\) | ||||
0.872403 | + | 0.488787i | \(0.162560\pi\) | |||||||
\(798\) | 0.108626 | 0.00384531 | ||||||||
\(799\) | 12.6289 | 0.446777 | ||||||||
\(800\) | 0.601670 | 0.0212723 | ||||||||
\(801\) | 2.63980 | 0.0932726 | ||||||||
\(802\) | −28.4310 | −1.00393 | ||||||||
\(803\) | −48.5687 | −1.71395 | ||||||||
\(804\) | 7.20145 | 0.253976 | ||||||||
\(805\) | −0.312342 | −0.0110086 | ||||||||
\(806\) | −0.760072 | −0.0267724 | ||||||||
\(807\) | 16.1066 | 0.566979 | ||||||||
\(808\) | −17.7613 | −0.624839 | ||||||||
\(809\) | −33.0157 | −1.16077 | −0.580384 | − | 0.814343i | \(-0.697098\pi\) | ||||
−0.580384 | + | 0.814343i | \(0.697098\pi\) | |||||||
\(810\) | −2.09722 | −0.0736888 | ||||||||
\(811\) | 11.8002 | 0.414360 | 0.207180 | − | 0.978303i | \(-0.433571\pi\) | ||||
0.207180 | + | 0.978303i | \(0.433571\pi\) | |||||||
\(812\) | 0.0919853 | 0.00322805 | ||||||||
\(813\) | −9.09091 | −0.318832 | ||||||||
\(814\) | −28.0969 | −0.984797 | ||||||||
\(815\) | 11.9510 | 0.418625 | ||||||||
\(816\) | −2.38289 | −0.0834177 | ||||||||
\(817\) | −31.5252 | −1.10293 | ||||||||
\(818\) | 5.14846 | 0.180012 | ||||||||
\(819\) | −0.0373018 | −0.00130343 | ||||||||
\(820\) | −20.3582 | −0.710938 | ||||||||
\(821\) | −16.4095 | −0.572695 | −0.286348 | − | 0.958126i | \(-0.592441\pi\) | ||||
−0.286348 | + | 0.958126i | \(0.592441\pi\) | |||||||
\(822\) | 14.5720 | 0.508257 | ||||||||
\(823\) | −12.2205 | −0.425979 | −0.212989 | − | 0.977055i | \(-0.568320\pi\) | ||||
−0.212989 | + | 0.977055i | \(0.568320\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 1.91188 | 0.0665632 | ||||||||
\(826\) | 0.171062 | 0.00595202 | ||||||||
\(827\) | −38.8199 | −1.34990 | −0.674951 | − | 0.737863i | \(-0.735835\pi\) | ||||
−0.674951 | + | 0.737863i | \(0.735835\pi\) | |||||||
\(828\) | 3.99261 | 0.138753 | ||||||||
\(829\) | 41.0684 | 1.42637 | 0.713183 | − | 0.700978i | \(-0.247253\pi\) | ||||
0.713183 | + | 0.700978i | \(0.247253\pi\) | |||||||
\(830\) | 12.3457 | 0.428527 | ||||||||
\(831\) | 20.2183 | 0.701366 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 16.6769 | 0.577820 | ||||||||
\(834\) | 15.9341 | 0.551754 | ||||||||
\(835\) | 41.9416 | 1.45145 | ||||||||
\(836\) | −9.25351 | −0.320039 | ||||||||
\(837\) | 0.760072 | 0.0262719 | ||||||||
\(838\) | 15.5597 | 0.537502 | ||||||||
\(839\) | 38.0471 | 1.31353 | 0.656766 | − | 0.754094i | \(-0.271924\pi\) | ||||
0.656766 | + | 0.754094i | \(0.271924\pi\) | |||||||
\(840\) | 0.0782300 | 0.00269919 | ||||||||
\(841\) | −22.9190 | −0.790309 | ||||||||
\(842\) | −19.2163 | −0.662239 | ||||||||
\(843\) | 10.4908 | 0.361321 | ||||||||
\(844\) | −3.17494 | −0.109286 | ||||||||
\(845\) | 2.09722 | 0.0721465 | ||||||||
\(846\) | 5.29982 | 0.182212 | ||||||||
\(847\) | 0.0336726 | 0.00115700 | ||||||||
\(848\) | −10.7397 | −0.368802 | ||||||||
\(849\) | −20.5499 | −0.705272 | ||||||||
\(850\) | −1.43371 | −0.0491759 | ||||||||
\(851\) | −35.3032 | −1.21018 | ||||||||
\(852\) | −14.3856 | −0.492843 | ||||||||
\(853\) | −3.25026 | −0.111287 | −0.0556434 | − | 0.998451i | \(-0.517721\pi\) | ||||
−0.0556434 | + | 0.998451i | \(0.517721\pi\) | |||||||
\(854\) | −0.0627271 | −0.00214648 | ||||||||
\(855\) | 6.10728 | 0.208865 | ||||||||
\(856\) | −7.44643 | −0.254514 | ||||||||
\(857\) | 5.18334 | 0.177059 | 0.0885297 | − | 0.996074i | \(-0.471783\pi\) | ||||
0.0885297 | + | 0.996074i | \(0.471783\pi\) | |||||||
\(858\) | 3.17762 | 0.108482 | ||||||||
\(859\) | −12.7539 | −0.435159 | −0.217580 | − | 0.976043i | \(-0.569816\pi\) | ||||
−0.217580 | + | 0.976043i | \(0.569816\pi\) | |||||||
\(860\) | −22.7037 | −0.774191 | ||||||||
\(861\) | 0.362096 | 0.0123402 | ||||||||
\(862\) | 24.8965 | 0.847977 | ||||||||
\(863\) | 23.8338 | 0.811312 | 0.405656 | − | 0.914026i | \(-0.367043\pi\) | ||||
0.405656 | + | 0.914026i | \(0.367043\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 15.5877 | 0.529998 | ||||||||
\(866\) | −29.0280 | −0.986412 | ||||||||
\(867\) | −11.3219 | −0.384510 | ||||||||
\(868\) | −0.0283520 | −0.000962330 0 | ||||||||
\(869\) | −20.3177 | −0.689232 | ||||||||
\(870\) | 5.17170 | 0.175337 | ||||||||
\(871\) | 7.20145 | 0.244012 | ||||||||
\(872\) | 3.30101 | 0.111786 | ||||||||
\(873\) | −2.73678 | −0.0926260 | ||||||||
\(874\) | −11.6268 | −0.393284 | ||||||||
\(875\) | 0.438219 | 0.0148145 | ||||||||
\(876\) | 15.2846 | 0.516419 | ||||||||
\(877\) | −38.2283 | −1.29088 | −0.645438 | − | 0.763812i | \(-0.723325\pi\) | ||||
−0.645438 | + | 0.763812i | \(0.723325\pi\) | |||||||
\(878\) | 12.1657 | 0.410571 | ||||||||
\(879\) | −2.35918 | −0.0795732 | ||||||||
\(880\) | −6.66417 | −0.224649 | ||||||||
\(881\) | 8.71342 | 0.293562 | 0.146781 | − | 0.989169i | \(-0.453109\pi\) | ||||
0.146781 | + | 0.989169i | \(0.453109\pi\) | |||||||
\(882\) | 6.99861 | 0.235655 | ||||||||
\(883\) | 31.4124 | 1.05711 | 0.528555 | − | 0.848899i | \(-0.322734\pi\) | ||||
0.528555 | + | 0.848899i | \(0.322734\pi\) | |||||||
\(884\) | −2.38289 | −0.0801451 | ||||||||
\(885\) | 9.61765 | 0.323294 | ||||||||
\(886\) | 26.0682 | 0.875779 | ||||||||
\(887\) | −33.5550 | −1.12667 | −0.563334 | − | 0.826229i | \(-0.690482\pi\) | ||||
−0.563334 | + | 0.826229i | \(0.690482\pi\) | |||||||
\(888\) | 8.84213 | 0.296722 | ||||||||
\(889\) | −0.171489 | −0.00575155 | ||||||||
\(890\) | −5.53623 | −0.185575 | ||||||||
\(891\) | −3.17762 | −0.106454 | ||||||||
\(892\) | −1.36542 | −0.0457175 | ||||||||
\(893\) | −15.4335 | −0.516463 | ||||||||
\(894\) | 12.4885 | 0.417677 | ||||||||
\(895\) | 51.5256 | 1.72231 | ||||||||
\(896\) | 0.0373018 | 0.00124616 | ||||||||
\(897\) | 3.99261 | 0.133310 | ||||||||
\(898\) | 17.1631 | 0.572740 | ||||||||
\(899\) | −1.87432 | −0.0625121 | ||||||||
\(900\) | −0.601670 | −0.0200557 | ||||||||
\(901\) | 25.5914 | 0.852574 | ||||||||
\(902\) | −30.8459 | −1.02705 | ||||||||
\(903\) | 0.403815 | 0.0134381 | ||||||||
\(904\) | 6.21481 | 0.206701 | ||||||||
\(905\) | −13.9303 | −0.463060 | ||||||||
\(906\) | −11.6943 | −0.388517 | ||||||||
\(907\) | −8.26058 | −0.274288 | −0.137144 | − | 0.990551i | \(-0.543792\pi\) | ||||
−0.137144 | + | 0.990551i | \(0.543792\pi\) | |||||||
\(908\) | −10.1984 | −0.338446 | ||||||||
\(909\) | 17.7613 | 0.589104 | ||||||||
\(910\) | 0.0782300 | 0.00259330 | ||||||||
\(911\) | 18.2362 | 0.604191 | 0.302095 | − | 0.953278i | \(-0.402314\pi\) | ||||
0.302095 | + | 0.953278i | \(0.402314\pi\) | |||||||
\(912\) | 2.91209 | 0.0964288 | ||||||||
\(913\) | 18.7058 | 0.619070 | ||||||||
\(914\) | −1.04913 | −0.0347020 | ||||||||
\(915\) | −3.52671 | −0.116589 | ||||||||
\(916\) | 20.1236 | 0.664902 | ||||||||
\(917\) | 0.646318 | 0.0213433 | ||||||||
\(918\) | 2.38289 | 0.0786469 | ||||||||
\(919\) | −50.2704 | −1.65827 | −0.829133 | − | 0.559051i | \(-0.811165\pi\) | ||||
−0.829133 | + | 0.559051i | \(0.811165\pi\) | |||||||
\(920\) | −8.37339 | −0.276062 | ||||||||
\(921\) | −23.9915 | −0.790547 | ||||||||
\(922\) | −1.36203 | −0.0448562 | ||||||||
\(923\) | −14.3856 | −0.473508 | ||||||||
\(924\) | 0.118531 | 0.00389938 | ||||||||
\(925\) | 5.32004 | 0.174922 | ||||||||
\(926\) | 17.9663 | 0.590408 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 2.46598 | 0.0809497 | ||||||||
\(929\) | −26.0641 | −0.855137 | −0.427568 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427568 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(930\) | −1.59404 | −0.0522705 | ||||||||
\(931\) | −20.3805 | −0.667945 | ||||||||
\(932\) | −20.9544 | −0.686383 | ||||||||
\(933\) | −9.06740 | −0.296853 | ||||||||
\(934\) | 12.2355 | 0.400359 | ||||||||
\(935\) | 15.8800 | 0.519330 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 50.1578 | 1.63858 | 0.819292 | − | 0.573376i | \(-0.194367\pi\) | ||||
0.819292 | + | 0.573376i | \(0.194367\pi\) | |||||||
\(938\) | 0.268627 | 0.00877097 | ||||||||
\(939\) | 27.0568 | 0.882965 | ||||||||
\(940\) | −11.1149 | −0.362528 | ||||||||
\(941\) | 52.6830 | 1.71742 | 0.858708 | − | 0.512466i | \(-0.171268\pi\) | ||||
0.858708 | + | 0.512466i | \(0.171268\pi\) | |||||||
\(942\) | 11.0964 | 0.361542 | ||||||||
\(943\) | −38.7572 | −1.26211 | ||||||||
\(944\) | 4.58591 | 0.149259 | ||||||||
\(945\) | −0.0782300 | −0.00254482 | ||||||||
\(946\) | −34.3998 | −1.11843 | ||||||||
\(947\) | 14.4382 | 0.469180 | 0.234590 | − | 0.972094i | \(-0.424625\pi\) | ||||
0.234590 | + | 0.972094i | \(0.424625\pi\) | |||||||
\(948\) | 6.39400 | 0.207668 | ||||||||
\(949\) | 15.2846 | 0.496159 | ||||||||
\(950\) | 1.75212 | 0.0568461 | ||||||||
\(951\) | 25.3558 | 0.822219 | ||||||||
\(952\) | −0.0888858 | −0.00288081 | ||||||||
\(953\) | −54.7392 | −1.77318 | −0.886588 | − | 0.462561i | \(-0.846931\pi\) | ||||
−0.886588 | + | 0.462561i | \(0.846931\pi\) | |||||||
\(954\) | 10.7397 | 0.347710 | ||||||||
\(955\) | −26.2756 | −0.850258 | ||||||||
\(956\) | −22.3195 | −0.721865 | ||||||||
\(957\) | 7.83595 | 0.253300 | ||||||||
\(958\) | −18.4397 | −0.595759 | ||||||||
\(959\) | 0.543561 | 0.0175525 | ||||||||
\(960\) | 2.09722 | 0.0676875 | ||||||||
\(961\) | −30.4223 | −0.981364 | ||||||||
\(962\) | 8.84213 | 0.285082 | ||||||||
\(963\) | 7.44643 | 0.239958 | ||||||||
\(964\) | 26.3016 | 0.847118 | ||||||||
\(965\) | 9.64134 | 0.310366 | ||||||||
\(966\) | 0.148932 | 0.00479179 | ||||||||
\(967\) | 1.08880 | 0.0350135 | 0.0175068 | − | 0.999847i | \(-0.494427\pi\) | ||||
0.0175068 | + | 0.999847i | \(0.494427\pi\) | |||||||
\(968\) | 0.902708 | 0.0290141 | ||||||||
\(969\) | −6.93916 | −0.222918 | ||||||||
\(970\) | 5.73963 | 0.184288 | ||||||||
\(971\) | −32.3608 | −1.03851 | −0.519254 | − | 0.854620i | \(-0.673790\pi\) | ||||
−0.519254 | + | 0.854620i | \(0.673790\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0.594371 | 0.0190547 | ||||||||
\(974\) | −24.9829 | −0.800504 | ||||||||
\(975\) | −0.601670 | −0.0192689 | ||||||||
\(976\) | −1.68161 | −0.0538271 | ||||||||
\(977\) | 32.4148 | 1.03704 | 0.518521 | − | 0.855065i | \(-0.326483\pi\) | ||||
0.518521 | + | 0.855065i | \(0.326483\pi\) | |||||||
\(978\) | −5.69850 | −0.182218 | ||||||||
\(979\) | −8.38828 | −0.268091 | ||||||||
\(980\) | −14.6776 | −0.468859 | ||||||||
\(981\) | −3.30101 | −0.105393 | ||||||||
\(982\) | 21.6861 | 0.692030 | ||||||||
\(983\) | 52.2186 | 1.66552 | 0.832758 | − | 0.553638i | \(-0.186761\pi\) | ||||
0.832758 | + | 0.553638i | \(0.186761\pi\) | |||||||
\(984\) | 9.70721 | 0.309455 | ||||||||
\(985\) | 32.6136 | 1.03916 | ||||||||
\(986\) | −5.87614 | −0.187135 | ||||||||
\(987\) | 0.197693 | 0.00629262 | ||||||||
\(988\) | 2.91209 | 0.0926458 | ||||||||
\(989\) | −43.2226 | −1.37440 | ||||||||
\(990\) | 6.66417 | 0.211801 | ||||||||
\(991\) | −26.0290 | −0.826838 | −0.413419 | − | 0.910541i | \(-0.635665\pi\) | ||||
−0.413419 | + | 0.910541i | \(0.635665\pi\) | |||||||
\(992\) | −0.760072 | −0.0241323 | ||||||||
\(993\) | −13.8421 | −0.439265 | ||||||||
\(994\) | −0.536608 | −0.0170202 | ||||||||
\(995\) | −20.2701 | −0.642606 | ||||||||
\(996\) | −5.88671 | −0.186528 | ||||||||
\(997\) | 26.7927 | 0.848534 | 0.424267 | − | 0.905537i | \(-0.360532\pi\) | ||||
0.424267 | + | 0.905537i | \(0.360532\pi\) | |||||||
\(998\) | −28.2202 | −0.893294 | ||||||||
\(999\) | −8.84213 | −0.279752 |
(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 | 8034.2.a.w.1.10 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.w.1.10 | ✓ | 12 | 1.1 | even | 1 | trivial |