Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.78078\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(5\) | −2.78078 | −1.24360 | −0.621800 | − | 0.783176i | \(-0.713598\pi\) | ||||
−0.621800 | + | 0.783176i | \(0.713598\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.42043 | 1.29280 | 0.646400 | − | 0.762999i | \(-0.276274\pi\) | ||||
0.646400 | + | 0.762999i | \(0.276274\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.78078 | 0.879358 | ||||||||
\(11\) | −6.40684 | −1.93173 | −0.965867 | − | 0.259038i | \(-0.916595\pi\) | ||||
−0.965867 | + | 0.259038i | \(0.916595\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.09916 | −0.304851 | −0.152425 | − | 0.988315i | \(-0.548708\pi\) | ||||
−0.152425 | + | 0.988315i | \(0.548708\pi\) | |||||||
\(14\) | −3.42043 | −0.914147 | ||||||||
\(15\) | 2.78078 | 0.717993 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.34964 | 1.45671 | 0.728354 | − | 0.685201i | \(-0.240286\pi\) | ||||
0.728354 | + | 0.685201i | \(0.240286\pi\) | |||||||
\(20\) | −2.78078 | −0.621800 | ||||||||
\(21\) | −3.42043 | −0.746398 | ||||||||
\(22\) | 6.40684 | 1.36594 | ||||||||
\(23\) | −0.0945846 | −0.0197223 | −0.00986113 | − | 0.999951i | \(-0.503139\pi\) | ||||
−0.00986113 | + | 0.999951i | \(0.503139\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.73271 | 0.546543 | ||||||||
\(26\) | 1.09916 | 0.215562 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.42043 | 0.646400 | ||||||||
\(29\) | −3.02228 | −0.561223 | −0.280612 | − | 0.959821i | \(-0.590537\pi\) | ||||
−0.280612 | + | 0.959821i | \(0.590537\pi\) | |||||||
\(30\) | −2.78078 | −0.507698 | ||||||||
\(31\) | −2.51109 | −0.451006 | −0.225503 | − | 0.974243i | \(-0.572402\pi\) | ||||
−0.225503 | + | 0.974243i | \(0.572402\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.40684 | 1.11529 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −9.51144 | −1.60773 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.03293 | −0.663010 | −0.331505 | − | 0.943453i | \(-0.607556\pi\) | ||||
−0.331505 | + | 0.943453i | \(0.607556\pi\) | |||||||
\(38\) | −6.34964 | −1.03005 | ||||||||
\(39\) | 1.09916 | 0.176006 | ||||||||
\(40\) | 2.78078 | 0.439679 | ||||||||
\(41\) | 3.94277 | 0.615757 | 0.307879 | − | 0.951426i | \(-0.400381\pi\) | ||||
0.307879 | + | 0.951426i | \(0.400381\pi\) | |||||||
\(42\) | 3.42043 | 0.527783 | ||||||||
\(43\) | −4.15125 | −0.633060 | −0.316530 | − | 0.948583i | \(-0.602518\pi\) | ||||
−0.316530 | + | 0.948583i | \(0.602518\pi\) | |||||||
\(44\) | −6.40684 | −0.965867 | ||||||||
\(45\) | −2.78078 | −0.414534 | ||||||||
\(46\) | 0.0945846 | 0.0139457 | ||||||||
\(47\) | 3.44949 | 0.503159 | 0.251580 | − | 0.967837i | \(-0.419050\pi\) | ||||
0.251580 | + | 0.967837i | \(0.419050\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.69932 | 0.671331 | ||||||||
\(50\) | −2.73271 | −0.386464 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −1.09916 | −0.152425 | ||||||||
\(53\) | 0.825282 | 0.113361 | 0.0566806 | − | 0.998392i | \(-0.481948\pi\) | ||||
0.0566806 | + | 0.998392i | \(0.481948\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 17.8160 | 2.40231 | ||||||||
\(56\) | −3.42043 | −0.457074 | ||||||||
\(57\) | −6.34964 | −0.841031 | ||||||||
\(58\) | 3.02228 | 0.396845 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 2.78078 | 0.358997 | ||||||||
\(61\) | −1.88013 | −0.240726 | −0.120363 | − | 0.992730i | \(-0.538406\pi\) | ||||
−0.120363 | + | 0.992730i | \(0.538406\pi\) | |||||||
\(62\) | 2.51109 | 0.318909 | ||||||||
\(63\) | 3.42043 | 0.430933 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.05651 | 0.379113 | ||||||||
\(66\) | −6.40684 | −0.788627 | ||||||||
\(67\) | −6.99934 | −0.855106 | −0.427553 | − | 0.903990i | \(-0.640624\pi\) | ||||
−0.427553 | + | 0.903990i | \(0.640624\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 0.0945846 | 0.0113866 | ||||||||
\(70\) | 9.51144 | 1.13683 | ||||||||
\(71\) | −8.64966 | −1.02653 | −0.513263 | − | 0.858231i | \(-0.671563\pi\) | ||||
−0.513263 | + | 0.858231i | \(0.671563\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 6.87094 | 0.804183 | 0.402091 | − | 0.915600i | \(-0.368283\pi\) | ||||
0.402091 | + | 0.915600i | \(0.368283\pi\) | |||||||
\(74\) | 4.03293 | 0.468819 | ||||||||
\(75\) | −2.73271 | −0.315547 | ||||||||
\(76\) | 6.34964 | 0.728354 | ||||||||
\(77\) | −21.9141 | −2.49735 | ||||||||
\(78\) | −1.09916 | −0.124455 | ||||||||
\(79\) | 6.85217 | 0.770930 | 0.385465 | − | 0.922723i | \(-0.374041\pi\) | ||||
0.385465 | + | 0.922723i | \(0.374041\pi\) | |||||||
\(80\) | −2.78078 | −0.310900 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.94277 | −0.435406 | ||||||||
\(83\) | −0.152814 | −0.0167735 | −0.00838677 | − | 0.999965i | \(-0.502670\pi\) | ||||
−0.00838677 | + | 0.999965i | \(0.502670\pi\) | |||||||
\(84\) | −3.42043 | −0.373199 | ||||||||
\(85\) | −2.78078 | −0.301617 | ||||||||
\(86\) | 4.15125 | 0.447641 | ||||||||
\(87\) | 3.02228 | 0.324022 | ||||||||
\(88\) | 6.40684 | 0.682971 | ||||||||
\(89\) | −9.59621 | −1.01720 | −0.508598 | − | 0.861004i | \(-0.669836\pi\) | ||||
−0.508598 | + | 0.861004i | \(0.669836\pi\) | |||||||
\(90\) | 2.78078 | 0.293119 | ||||||||
\(91\) | −3.75958 | −0.394111 | ||||||||
\(92\) | −0.0945846 | −0.00986113 | ||||||||
\(93\) | 2.51109 | 0.260388 | ||||||||
\(94\) | −3.44949 | −0.355787 | ||||||||
\(95\) | −17.6569 | −1.81156 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.52877 | 0.155223 | 0.0776114 | − | 0.996984i | \(-0.475271\pi\) | ||||
0.0776114 | + | 0.996984i | \(0.475271\pi\) | |||||||
\(98\) | −4.69932 | −0.474703 | ||||||||
\(99\) | −6.40684 | −0.643911 | ||||||||
\(100\) | 2.73271 | 0.273271 | ||||||||
\(101\) | 7.28219 | 0.724605 | 0.362302 | − | 0.932061i | \(-0.381991\pi\) | ||||
0.362302 | + | 0.932061i | \(0.381991\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −3.54082 | −0.348887 | −0.174444 | − | 0.984667i | \(-0.555813\pi\) | ||||
−0.174444 | + | 0.984667i | \(0.555813\pi\) | |||||||
\(104\) | 1.09916 | 0.107781 | ||||||||
\(105\) | 9.51144 | 0.928221 | ||||||||
\(106\) | −0.825282 | −0.0801585 | ||||||||
\(107\) | 7.81413 | 0.755420 | 0.377710 | − | 0.925924i | \(-0.376712\pi\) | ||||
0.377710 | + | 0.925924i | \(0.376712\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −5.99899 | −0.574599 | −0.287300 | − | 0.957841i | \(-0.592758\pi\) | ||||
−0.287300 | + | 0.957841i | \(0.592758\pi\) | |||||||
\(110\) | −17.8160 | −1.69869 | ||||||||
\(111\) | 4.03293 | 0.382789 | ||||||||
\(112\) | 3.42043 | 0.323200 | ||||||||
\(113\) | −5.66954 | −0.533346 | −0.266673 | − | 0.963787i | \(-0.585924\pi\) | ||||
−0.266673 | + | 0.963787i | \(0.585924\pi\) | |||||||
\(114\) | 6.34964 | 0.594698 | ||||||||
\(115\) | 0.263019 | 0.0245266 | ||||||||
\(116\) | −3.02228 | −0.280612 | ||||||||
\(117\) | −1.09916 | −0.101617 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 3.42043 | 0.313550 | ||||||||
\(120\) | −2.78078 | −0.253849 | ||||||||
\(121\) | 30.0476 | 2.73160 | ||||||||
\(122\) | 1.88013 | 0.170219 | ||||||||
\(123\) | −3.94277 | −0.355508 | ||||||||
\(124\) | −2.51109 | −0.225503 | ||||||||
\(125\) | 6.30482 | 0.563920 | ||||||||
\(126\) | −3.42043 | −0.304716 | ||||||||
\(127\) | −8.88937 | −0.788804 | −0.394402 | − | 0.918938i | \(-0.629048\pi\) | ||||
−0.394402 | + | 0.918938i | \(0.629048\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.15125 | 0.365497 | ||||||||
\(130\) | −3.05651 | −0.268073 | ||||||||
\(131\) | 3.04262 | 0.265835 | 0.132917 | − | 0.991127i | \(-0.457566\pi\) | ||||
0.132917 | + | 0.991127i | \(0.457566\pi\) | |||||||
\(132\) | 6.40684 | 0.557644 | ||||||||
\(133\) | 21.7185 | 1.88323 | ||||||||
\(134\) | 6.99934 | 0.604651 | ||||||||
\(135\) | 2.78078 | 0.239331 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 0.484042 | 0.0413545 | 0.0206772 | − | 0.999786i | \(-0.493418\pi\) | ||||
0.0206772 | + | 0.999786i | \(0.493418\pi\) | |||||||
\(138\) | −0.0945846 | −0.00805158 | ||||||||
\(139\) | −0.179257 | −0.0152044 | −0.00760221 | − | 0.999971i | \(-0.502420\pi\) | ||||
−0.00760221 | + | 0.999971i | \(0.502420\pi\) | |||||||
\(140\) | −9.51144 | −0.803863 | ||||||||
\(141\) | −3.44949 | −0.290499 | ||||||||
\(142\) | 8.64966 | 0.725864 | ||||||||
\(143\) | 7.04211 | 0.588891 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.40428 | 0.697938 | ||||||||
\(146\) | −6.87094 | −0.568643 | ||||||||
\(147\) | −4.69932 | −0.387593 | ||||||||
\(148\) | −4.03293 | −0.331505 | ||||||||
\(149\) | −8.32811 | −0.682265 | −0.341133 | − | 0.940015i | \(-0.610811\pi\) | ||||
−0.341133 | + | 0.940015i | \(0.610811\pi\) | |||||||
\(150\) | 2.73271 | 0.223125 | ||||||||
\(151\) | 7.36479 | 0.599338 | 0.299669 | − | 0.954043i | \(-0.403124\pi\) | ||||
0.299669 | + | 0.954043i | \(0.403124\pi\) | |||||||
\(152\) | −6.34964 | −0.515024 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 21.9141 | 1.76589 | ||||||||
\(155\) | 6.98279 | 0.560871 | ||||||||
\(156\) | 1.09916 | 0.0880029 | ||||||||
\(157\) | 9.87753 | 0.788313 | 0.394156 | − | 0.919043i | \(-0.371037\pi\) | ||||
0.394156 | + | 0.919043i | \(0.371037\pi\) | |||||||
\(158\) | −6.85217 | −0.545130 | ||||||||
\(159\) | −0.825282 | −0.0654491 | ||||||||
\(160\) | 2.78078 | 0.219840 | ||||||||
\(161\) | −0.323520 | −0.0254969 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −21.8700 | −1.71299 | −0.856494 | − | 0.516156i | \(-0.827362\pi\) | ||||
−0.856494 | + | 0.516156i | \(0.827362\pi\) | |||||||
\(164\) | 3.94277 | 0.307879 | ||||||||
\(165\) | −17.8160 | −1.38697 | ||||||||
\(166\) | 0.152814 | 0.0118607 | ||||||||
\(167\) | 21.1311 | 1.63517 | 0.817587 | − | 0.575806i | \(-0.195312\pi\) | ||||
0.817587 | + | 0.575806i | \(0.195312\pi\) | |||||||
\(168\) | 3.42043 | 0.263892 | ||||||||
\(169\) | −11.7919 | −0.907066 | ||||||||
\(170\) | 2.78078 | 0.213276 | ||||||||
\(171\) | 6.34964 | 0.485569 | ||||||||
\(172\) | −4.15125 | −0.316530 | ||||||||
\(173\) | 11.2828 | 0.857813 | 0.428906 | − | 0.903349i | \(-0.358899\pi\) | ||||
0.428906 | + | 0.903349i | \(0.358899\pi\) | |||||||
\(174\) | −3.02228 | −0.229118 | ||||||||
\(175\) | 9.34705 | 0.706570 | ||||||||
\(176\) | −6.40684 | −0.482934 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 9.59621 | 0.719266 | ||||||||
\(179\) | 2.55732 | 0.191143 | 0.0955716 | − | 0.995423i | \(-0.469532\pi\) | ||||
0.0955716 | + | 0.995423i | \(0.469532\pi\) | |||||||
\(180\) | −2.78078 | −0.207267 | ||||||||
\(181\) | 2.69513 | 0.200327 | 0.100164 | − | 0.994971i | \(-0.468063\pi\) | ||||
0.100164 | + | 0.994971i | \(0.468063\pi\) | |||||||
\(182\) | 3.75958 | 0.278679 | ||||||||
\(183\) | 1.88013 | 0.138983 | ||||||||
\(184\) | 0.0945846 | 0.00697287 | ||||||||
\(185\) | 11.2147 | 0.824520 | ||||||||
\(186\) | −2.51109 | −0.184122 | ||||||||
\(187\) | −6.40684 | −0.468514 | ||||||||
\(188\) | 3.44949 | 0.251580 | ||||||||
\(189\) | −3.42043 | −0.248799 | ||||||||
\(190\) | 17.6569 | 1.28097 | ||||||||
\(191\) | 10.1874 | 0.737131 | 0.368566 | − | 0.929602i | \(-0.379849\pi\) | ||||
0.368566 | + | 0.929602i | \(0.379849\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −18.6070 | −1.33936 | −0.669681 | − | 0.742649i | \(-0.733569\pi\) | ||||
−0.669681 | + | 0.742649i | \(0.733569\pi\) | |||||||
\(194\) | −1.52877 | −0.109759 | ||||||||
\(195\) | −3.05651 | −0.218881 | ||||||||
\(196\) | 4.69932 | 0.335666 | ||||||||
\(197\) | −24.3322 | −1.73359 | −0.866797 | − | 0.498661i | \(-0.833825\pi\) | ||||
−0.866797 | + | 0.498661i | \(0.833825\pi\) | |||||||
\(198\) | 6.40684 | 0.455314 | ||||||||
\(199\) | −3.70805 | −0.262857 | −0.131428 | − | 0.991326i | \(-0.541956\pi\) | ||||
−0.131428 | + | 0.991326i | \(0.541956\pi\) | |||||||
\(200\) | −2.73271 | −0.193232 | ||||||||
\(201\) | 6.99934 | 0.493695 | ||||||||
\(202\) | −7.28219 | −0.512373 | ||||||||
\(203\) | −10.3375 | −0.725549 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −10.9640 | −0.765756 | ||||||||
\(206\) | 3.54082 | 0.246700 | ||||||||
\(207\) | −0.0945846 | −0.00657409 | ||||||||
\(208\) | −1.09916 | −0.0762127 | ||||||||
\(209\) | −40.6811 | −2.81397 | ||||||||
\(210\) | −9.51144 | −0.656352 | ||||||||
\(211\) | −5.01235 | −0.345064 | −0.172532 | − | 0.985004i | \(-0.555195\pi\) | ||||
−0.172532 | + | 0.985004i | \(0.555195\pi\) | |||||||
\(212\) | 0.825282 | 0.0566806 | ||||||||
\(213\) | 8.64966 | 0.592665 | ||||||||
\(214\) | −7.81413 | −0.534163 | ||||||||
\(215\) | 11.5437 | 0.787273 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.58901 | −0.583060 | ||||||||
\(218\) | 5.99899 | 0.406303 | ||||||||
\(219\) | −6.87094 | −0.464295 | ||||||||
\(220\) | 17.8160 | 1.20115 | ||||||||
\(221\) | −1.09916 | −0.0739372 | ||||||||
\(222\) | −4.03293 | −0.270673 | ||||||||
\(223\) | 1.38896 | 0.0930118 | 0.0465059 | − | 0.998918i | \(-0.485191\pi\) | ||||
0.0465059 | + | 0.998918i | \(0.485191\pi\) | |||||||
\(224\) | −3.42043 | −0.228537 | ||||||||
\(225\) | 2.73271 | 0.182181 | ||||||||
\(226\) | 5.66954 | 0.377132 | ||||||||
\(227\) | −8.74677 | −0.580544 | −0.290272 | − | 0.956944i | \(-0.593746\pi\) | ||||
−0.290272 | + | 0.956944i | \(0.593746\pi\) | |||||||
\(228\) | −6.34964 | −0.420515 | ||||||||
\(229\) | 13.4870 | 0.891244 | 0.445622 | − | 0.895221i | \(-0.352982\pi\) | ||||
0.445622 | + | 0.895221i | \(0.352982\pi\) | |||||||
\(230\) | −0.263019 | −0.0173429 | ||||||||
\(231\) | 21.9141 | 1.44184 | ||||||||
\(232\) | 3.02228 | 0.198422 | ||||||||
\(233\) | −6.74729 | −0.442030 | −0.221015 | − | 0.975270i | \(-0.570937\pi\) | ||||
−0.221015 | + | 0.975270i | \(0.570937\pi\) | |||||||
\(234\) | 1.09916 | 0.0718541 | ||||||||
\(235\) | −9.59225 | −0.625730 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | −6.85217 | −0.445096 | ||||||||
\(238\) | −3.42043 | −0.221713 | ||||||||
\(239\) | −3.39472 | −0.219586 | −0.109793 | − | 0.993954i | \(-0.535019\pi\) | ||||
−0.109793 | + | 0.993954i | \(0.535019\pi\) | |||||||
\(240\) | 2.78078 | 0.179498 | ||||||||
\(241\) | 13.6691 | 0.880507 | 0.440254 | − | 0.897874i | \(-0.354889\pi\) | ||||
0.440254 | + | 0.897874i | \(0.354889\pi\) | |||||||
\(242\) | −30.0476 | −1.93153 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.88013 | −0.120363 | ||||||||
\(245\) | −13.0678 | −0.834868 | ||||||||
\(246\) | 3.94277 | 0.251382 | ||||||||
\(247\) | −6.97925 | −0.444079 | ||||||||
\(248\) | 2.51109 | 0.159455 | ||||||||
\(249\) | 0.152814 | 0.00968421 | ||||||||
\(250\) | −6.30482 | −0.398752 | ||||||||
\(251\) | 17.2811 | 1.09077 | 0.545385 | − | 0.838185i | \(-0.316383\pi\) | ||||
0.545385 | + | 0.838185i | \(0.316383\pi\) | |||||||
\(252\) | 3.42043 | 0.215467 | ||||||||
\(253\) | 0.605988 | 0.0380982 | ||||||||
\(254\) | 8.88937 | 0.557768 | ||||||||
\(255\) | 2.78078 | 0.174139 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.6761 | 1.85115 | 0.925573 | − | 0.378570i | \(-0.123584\pi\) | ||||
0.925573 | + | 0.378570i | \(0.123584\pi\) | |||||||
\(258\) | −4.15125 | −0.258446 | ||||||||
\(259\) | −13.7944 | −0.857139 | ||||||||
\(260\) | 3.05651 | 0.189556 | ||||||||
\(261\) | −3.02228 | −0.187074 | ||||||||
\(262\) | −3.04262 | −0.187973 | ||||||||
\(263\) | 21.9414 | 1.35297 | 0.676484 | − | 0.736458i | \(-0.263503\pi\) | ||||
0.676484 | + | 0.736458i | \(0.263503\pi\) | |||||||
\(264\) | −6.40684 | −0.394314 | ||||||||
\(265\) | −2.29492 | −0.140976 | ||||||||
\(266\) | −21.7185 | −1.33165 | ||||||||
\(267\) | 9.59621 | 0.587279 | ||||||||
\(268\) | −6.99934 | −0.427553 | ||||||||
\(269\) | −1.06146 | −0.0647184 | −0.0323592 | − | 0.999476i | \(-0.510302\pi\) | ||||
−0.0323592 | + | 0.999476i | \(0.510302\pi\) | |||||||
\(270\) | −2.78078 | −0.169233 | ||||||||
\(271\) | −4.15826 | −0.252597 | −0.126298 | − | 0.991992i | \(-0.540310\pi\) | ||||
−0.126298 | + | 0.991992i | \(0.540310\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 3.75958 | 0.227540 | ||||||||
\(274\) | −0.484042 | −0.0292420 | ||||||||
\(275\) | −17.5081 | −1.05578 | ||||||||
\(276\) | 0.0945846 | 0.00569332 | ||||||||
\(277\) | −0.918785 | −0.0552045 | −0.0276022 | − | 0.999619i | \(-0.508787\pi\) | ||||
−0.0276022 | + | 0.999619i | \(0.508787\pi\) | |||||||
\(278\) | 0.179257 | 0.0107511 | ||||||||
\(279\) | −2.51109 | −0.150335 | ||||||||
\(280\) | 9.51144 | 0.568417 | ||||||||
\(281\) | 20.3440 | 1.21362 | 0.606811 | − | 0.794846i | \(-0.292448\pi\) | ||||
0.606811 | + | 0.794846i | \(0.292448\pi\) | |||||||
\(282\) | 3.44949 | 0.205414 | ||||||||
\(283\) | −28.9503 | −1.72092 | −0.860459 | − | 0.509519i | \(-0.829823\pi\) | ||||
−0.860459 | + | 0.509519i | \(0.829823\pi\) | |||||||
\(284\) | −8.64966 | −0.513263 | ||||||||
\(285\) | 17.6569 | 1.04591 | ||||||||
\(286\) | −7.04211 | −0.416409 | ||||||||
\(287\) | 13.4860 | 0.796051 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.40428 | −0.493516 | ||||||||
\(291\) | −1.52877 | −0.0896180 | ||||||||
\(292\) | 6.87094 | 0.402091 | ||||||||
\(293\) | −21.5847 | −1.26099 | −0.630497 | − | 0.776192i | \(-0.717149\pi\) | ||||
−0.630497 | + | 0.776192i | \(0.717149\pi\) | |||||||
\(294\) | 4.69932 | 0.274070 | ||||||||
\(295\) | 2.78078 | 0.161903 | ||||||||
\(296\) | 4.03293 | 0.234410 | ||||||||
\(297\) | 6.40684 | 0.371762 | ||||||||
\(298\) | 8.32811 | 0.482435 | ||||||||
\(299\) | 0.103963 | 0.00601235 | ||||||||
\(300\) | −2.73271 | −0.157773 | ||||||||
\(301\) | −14.1990 | −0.818419 | ||||||||
\(302\) | −7.36479 | −0.423796 | ||||||||
\(303\) | −7.28219 | −0.418351 | ||||||||
\(304\) | 6.34964 | 0.364177 | ||||||||
\(305\) | 5.22821 | 0.299367 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 13.7268 | 0.783429 | 0.391714 | − | 0.920087i | \(-0.371882\pi\) | ||||
0.391714 | + | 0.920087i | \(0.371882\pi\) | |||||||
\(308\) | −21.9141 | −1.24867 | ||||||||
\(309\) | 3.54082 | 0.201430 | ||||||||
\(310\) | −6.98279 | −0.396596 | ||||||||
\(311\) | −13.7718 | −0.780926 | −0.390463 | − | 0.920619i | \(-0.627685\pi\) | ||||
−0.390463 | + | 0.920619i | \(0.627685\pi\) | |||||||
\(312\) | −1.09916 | −0.0622274 | ||||||||
\(313\) | 19.3987 | 1.09648 | 0.548239 | − | 0.836321i | \(-0.315298\pi\) | ||||
0.548239 | + | 0.836321i | \(0.315298\pi\) | |||||||
\(314\) | −9.87753 | −0.557421 | ||||||||
\(315\) | −9.51144 | −0.535909 | ||||||||
\(316\) | 6.85217 | 0.385465 | ||||||||
\(317\) | 21.2894 | 1.19573 | 0.597866 | − | 0.801596i | \(-0.296016\pi\) | ||||
0.597866 | + | 0.801596i | \(0.296016\pi\) | |||||||
\(318\) | 0.825282 | 0.0462795 | ||||||||
\(319\) | 19.3633 | 1.08413 | ||||||||
\(320\) | −2.78078 | −0.155450 | ||||||||
\(321\) | −7.81413 | −0.436142 | ||||||||
\(322\) | 0.323520 | 0.0180291 | ||||||||
\(323\) | 6.34964 | 0.353304 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.00368 | −0.166614 | ||||||||
\(326\) | 21.8700 | 1.21127 | ||||||||
\(327\) | 5.99899 | 0.331745 | ||||||||
\(328\) | −3.94277 | −0.217703 | ||||||||
\(329\) | 11.7987 | 0.650484 | ||||||||
\(330\) | 17.8160 | 0.980737 | ||||||||
\(331\) | 10.7517 | 0.590964 | 0.295482 | − | 0.955348i | \(-0.404520\pi\) | ||||
0.295482 | + | 0.955348i | \(0.404520\pi\) | |||||||
\(332\) | −0.152814 | −0.00838677 | ||||||||
\(333\) | −4.03293 | −0.221003 | ||||||||
\(334\) | −21.1311 | −1.15624 | ||||||||
\(335\) | 19.4636 | 1.06341 | ||||||||
\(336\) | −3.42043 | −0.186600 | ||||||||
\(337\) | 27.6531 | 1.50636 | 0.753181 | − | 0.657813i | \(-0.228518\pi\) | ||||
0.753181 | + | 0.657813i | \(0.228518\pi\) | |||||||
\(338\) | 11.7919 | 0.641392 | ||||||||
\(339\) | 5.66954 | 0.307927 | ||||||||
\(340\) | −2.78078 | −0.150809 | ||||||||
\(341\) | 16.0882 | 0.871223 | ||||||||
\(342\) | −6.34964 | −0.343349 | ||||||||
\(343\) | −7.86931 | −0.424903 | ||||||||
\(344\) | 4.15125 | 0.223820 | ||||||||
\(345\) | −0.263019 | −0.0141604 | ||||||||
\(346\) | −11.2828 | −0.606565 | ||||||||
\(347\) | 17.0845 | 0.917147 | 0.458573 | − | 0.888657i | \(-0.348361\pi\) | ||||
0.458573 | + | 0.888657i | \(0.348361\pi\) | |||||||
\(348\) | 3.02228 | 0.162011 | ||||||||
\(349\) | 12.8542 | 0.688072 | 0.344036 | − | 0.938957i | \(-0.388206\pi\) | ||||
0.344036 | + | 0.938957i | \(0.388206\pi\) | |||||||
\(350\) | −9.34705 | −0.499621 | ||||||||
\(351\) | 1.09916 | 0.0586686 | ||||||||
\(352\) | 6.40684 | 0.341486 | ||||||||
\(353\) | 24.7686 | 1.31830 | 0.659149 | − | 0.752012i | \(-0.270916\pi\) | ||||
0.659149 | + | 0.752012i | \(0.270916\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 24.0528 | 1.27659 | ||||||||
\(356\) | −9.59621 | −0.508598 | ||||||||
\(357\) | −3.42043 | −0.181028 | ||||||||
\(358\) | −2.55732 | −0.135159 | ||||||||
\(359\) | 6.82217 | 0.360061 | 0.180030 | − | 0.983661i | \(-0.442380\pi\) | ||||
0.180030 | + | 0.983661i | \(0.442380\pi\) | |||||||
\(360\) | 2.78078 | 0.146560 | ||||||||
\(361\) | 21.3179 | 1.12200 | ||||||||
\(362\) | −2.69513 | −0.141653 | ||||||||
\(363\) | −30.0476 | −1.57709 | ||||||||
\(364\) | −3.75958 | −0.197056 | ||||||||
\(365\) | −19.1065 | −1.00008 | ||||||||
\(366\) | −1.88013 | −0.0982759 | ||||||||
\(367\) | 32.6009 | 1.70175 | 0.850877 | − | 0.525365i | \(-0.176071\pi\) | ||||
0.850877 | + | 0.525365i | \(0.176071\pi\) | |||||||
\(368\) | −0.0945846 | −0.00493056 | ||||||||
\(369\) | 3.94277 | 0.205252 | ||||||||
\(370\) | −11.2147 | −0.583024 | ||||||||
\(371\) | 2.82282 | 0.146553 | ||||||||
\(372\) | 2.51109 | 0.130194 | ||||||||
\(373\) | 12.2917 | 0.636438 | 0.318219 | − | 0.948017i | \(-0.396915\pi\) | ||||
0.318219 | + | 0.948017i | \(0.396915\pi\) | |||||||
\(374\) | 6.40684 | 0.331290 | ||||||||
\(375\) | −6.30482 | −0.325579 | ||||||||
\(376\) | −3.44949 | −0.177894 | ||||||||
\(377\) | 3.32196 | 0.171089 | ||||||||
\(378\) | 3.42043 | 0.175928 | ||||||||
\(379\) | 6.21412 | 0.319198 | 0.159599 | − | 0.987182i | \(-0.448980\pi\) | ||||
0.159599 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(380\) | −17.6569 | −0.905781 | ||||||||
\(381\) | 8.88937 | 0.455416 | ||||||||
\(382\) | −10.1874 | −0.521231 | ||||||||
\(383\) | −24.5786 | −1.25591 | −0.627953 | − | 0.778251i | \(-0.716107\pi\) | ||||
−0.627953 | + | 0.778251i | \(0.716107\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 60.9383 | 3.10570 | ||||||||
\(386\) | 18.6070 | 0.947071 | ||||||||
\(387\) | −4.15125 | −0.211020 | ||||||||
\(388\) | 1.52877 | 0.0776114 | ||||||||
\(389\) | 19.3063 | 0.978869 | 0.489434 | − | 0.872040i | \(-0.337203\pi\) | ||||
0.489434 | + | 0.872040i | \(0.337203\pi\) | |||||||
\(390\) | 3.05651 | 0.154772 | ||||||||
\(391\) | −0.0945846 | −0.00478335 | ||||||||
\(392\) | −4.69932 | −0.237351 | ||||||||
\(393\) | −3.04262 | −0.153480 | ||||||||
\(394\) | 24.3322 | 1.22584 | ||||||||
\(395\) | −19.0544 | −0.958729 | ||||||||
\(396\) | −6.40684 | −0.321956 | ||||||||
\(397\) | −23.0737 | −1.15803 | −0.579017 | − | 0.815316i | \(-0.696563\pi\) | ||||
−0.579017 | + | 0.815316i | \(0.696563\pi\) | |||||||
\(398\) | 3.70805 | 0.185868 | ||||||||
\(399\) | −21.7185 | −1.08728 | ||||||||
\(400\) | 2.73271 | 0.136636 | ||||||||
\(401\) | 6.62545 | 0.330859 | 0.165429 | − | 0.986222i | \(-0.447099\pi\) | ||||
0.165429 | + | 0.986222i | \(0.447099\pi\) | |||||||
\(402\) | −6.99934 | −0.349095 | ||||||||
\(403\) | 2.76008 | 0.137490 | ||||||||
\(404\) | 7.28219 | 0.362302 | ||||||||
\(405\) | −2.78078 | −0.138178 | ||||||||
\(406\) | 10.3375 | 0.513041 | ||||||||
\(407\) | 25.8384 | 1.28076 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 4.87099 | 0.240855 | 0.120427 | − | 0.992722i | \(-0.461573\pi\) | ||||
0.120427 | + | 0.992722i | \(0.461573\pi\) | |||||||
\(410\) | 10.9640 | 0.541471 | ||||||||
\(411\) | −0.484042 | −0.0238760 | ||||||||
\(412\) | −3.54082 | −0.174444 | ||||||||
\(413\) | −3.42043 | −0.168308 | ||||||||
\(414\) | 0.0945846 | 0.00464858 | ||||||||
\(415\) | 0.424942 | 0.0208596 | ||||||||
\(416\) | 1.09916 | 0.0538906 | ||||||||
\(417\) | 0.179257 | 0.00877827 | ||||||||
\(418\) | 40.6811 | 1.98978 | ||||||||
\(419\) | −13.5440 | −0.661669 | −0.330834 | − | 0.943689i | \(-0.607330\pi\) | ||||
−0.330834 | + | 0.943689i | \(0.607330\pi\) | |||||||
\(420\) | 9.51144 | 0.464111 | ||||||||
\(421\) | 16.4086 | 0.799709 | 0.399854 | − | 0.916579i | \(-0.369061\pi\) | ||||
0.399854 | + | 0.916579i | \(0.369061\pi\) | |||||||
\(422\) | 5.01235 | 0.243997 | ||||||||
\(423\) | 3.44949 | 0.167720 | ||||||||
\(424\) | −0.825282 | −0.0400792 | ||||||||
\(425\) | 2.73271 | 0.132556 | ||||||||
\(426\) | −8.64966 | −0.419078 | ||||||||
\(427\) | −6.43084 | −0.311210 | ||||||||
\(428\) | 7.81413 | 0.377710 | ||||||||
\(429\) | −7.04211 | −0.339996 | ||||||||
\(430\) | −11.5437 | −0.556686 | ||||||||
\(431\) | 5.11972 | 0.246608 | 0.123304 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123304 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −26.7697 | −1.28647 | −0.643234 | − | 0.765670i | \(-0.722408\pi\) | ||||
−0.643234 | + | 0.765670i | \(0.722408\pi\) | |||||||
\(434\) | 8.58901 | 0.412286 | ||||||||
\(435\) | −8.40428 | −0.402954 | ||||||||
\(436\) | −5.99899 | −0.287300 | ||||||||
\(437\) | −0.600578 | −0.0287296 | ||||||||
\(438\) | 6.87094 | 0.328306 | ||||||||
\(439\) | 25.7731 | 1.23008 | 0.615042 | − | 0.788495i | \(-0.289139\pi\) | ||||
0.615042 | + | 0.788495i | \(0.289139\pi\) | |||||||
\(440\) | −17.8160 | −0.849343 | ||||||||
\(441\) | 4.69932 | 0.223777 | ||||||||
\(442\) | 1.09916 | 0.0522815 | ||||||||
\(443\) | 6.33359 | 0.300918 | 0.150459 | − | 0.988616i | \(-0.451925\pi\) | ||||
0.150459 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(444\) | 4.03293 | 0.191395 | ||||||||
\(445\) | 26.6849 | 1.26499 | ||||||||
\(446\) | −1.38896 | −0.0657693 | ||||||||
\(447\) | 8.32811 | 0.393906 | ||||||||
\(448\) | 3.42043 | 0.161600 | ||||||||
\(449\) | −6.05616 | −0.285808 | −0.142904 | − | 0.989737i | \(-0.545644\pi\) | ||||
−0.142904 | + | 0.989737i | \(0.545644\pi\) | |||||||
\(450\) | −2.73271 | −0.128821 | ||||||||
\(451\) | −25.2607 | −1.18948 | ||||||||
\(452\) | −5.66954 | −0.266673 | ||||||||
\(453\) | −7.36479 | −0.346028 | ||||||||
\(454\) | 8.74677 | 0.410506 | ||||||||
\(455\) | 10.4546 | 0.490117 | ||||||||
\(456\) | 6.34964 | 0.297349 | ||||||||
\(457\) | 24.5777 | 1.14970 | 0.574849 | − | 0.818259i | \(-0.305061\pi\) | ||||
0.574849 | + | 0.818259i | \(0.305061\pi\) | |||||||
\(458\) | −13.4870 | −0.630205 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0.263019 | 0.0122633 | ||||||||
\(461\) | 23.1601 | 1.07867 | 0.539336 | − | 0.842090i | \(-0.318675\pi\) | ||||
0.539336 | + | 0.842090i | \(0.318675\pi\) | |||||||
\(462\) | −21.9141 | −1.01954 | ||||||||
\(463\) | −6.15000 | −0.285815 | −0.142907 | − | 0.989736i | \(-0.545645\pi\) | ||||
−0.142907 | + | 0.989736i | \(0.545645\pi\) | |||||||
\(464\) | −3.02228 | −0.140306 | ||||||||
\(465\) | −6.98279 | −0.323819 | ||||||||
\(466\) | 6.74729 | 0.312562 | ||||||||
\(467\) | 38.5003 | 1.78158 | 0.890791 | − | 0.454413i | \(-0.150151\pi\) | ||||
0.890791 | + | 0.454413i | \(0.150151\pi\) | |||||||
\(468\) | −1.09916 | −0.0508085 | ||||||||
\(469\) | −23.9407 | −1.10548 | ||||||||
\(470\) | 9.59225 | 0.442458 | ||||||||
\(471\) | −9.87753 | −0.455132 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 26.5964 | 1.22290 | ||||||||
\(474\) | 6.85217 | 0.314731 | ||||||||
\(475\) | 17.3518 | 0.796153 | ||||||||
\(476\) | 3.42043 | 0.156775 | ||||||||
\(477\) | 0.825282 | 0.0377871 | ||||||||
\(478\) | 3.39472 | 0.155271 | ||||||||
\(479\) | 3.10423 | 0.141836 | 0.0709180 | − | 0.997482i | \(-0.477407\pi\) | ||||
0.0709180 | + | 0.997482i | \(0.477407\pi\) | |||||||
\(480\) | −2.78078 | −0.126924 | ||||||||
\(481\) | 4.43282 | 0.202119 | ||||||||
\(482\) | −13.6691 | −0.622612 | ||||||||
\(483\) | 0.323520 | 0.0147207 | ||||||||
\(484\) | 30.0476 | 1.36580 | ||||||||
\(485\) | −4.25116 | −0.193035 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 28.9801 | 1.31321 | 0.656606 | − | 0.754234i | \(-0.271991\pi\) | ||||
0.656606 | + | 0.754234i | \(0.271991\pi\) | |||||||
\(488\) | 1.88013 | 0.0851094 | ||||||||
\(489\) | 21.8700 | 0.988994 | ||||||||
\(490\) | 13.0678 | 0.590341 | ||||||||
\(491\) | 41.1935 | 1.85904 | 0.929519 | − | 0.368775i | \(-0.120223\pi\) | ||||
0.929519 | + | 0.368775i | \(0.120223\pi\) | |||||||
\(492\) | −3.94277 | −0.177754 | ||||||||
\(493\) | −3.02228 | −0.136117 | ||||||||
\(494\) | 6.97925 | 0.314011 | ||||||||
\(495\) | 17.8160 | 0.800769 | ||||||||
\(496\) | −2.51109 | −0.112751 | ||||||||
\(497\) | −29.5855 | −1.32709 | ||||||||
\(498\) | −0.152814 | −0.00684777 | ||||||||
\(499\) | −16.5558 | −0.741141 | −0.370570 | − | 0.928804i | \(-0.620838\pi\) | ||||
−0.370570 | + | 0.928804i | \(0.620838\pi\) | |||||||
\(500\) | 6.30482 | 0.281960 | ||||||||
\(501\) | −21.1311 | −0.944068 | ||||||||
\(502\) | −17.2811 | −0.771291 | ||||||||
\(503\) | 8.40763 | 0.374878 | 0.187439 | − | 0.982276i | \(-0.439981\pi\) | ||||
0.187439 | + | 0.982276i | \(0.439981\pi\) | |||||||
\(504\) | −3.42043 | −0.152358 | ||||||||
\(505\) | −20.2501 | −0.901119 | ||||||||
\(506\) | −0.605988 | −0.0269395 | ||||||||
\(507\) | 11.7919 | 0.523695 | ||||||||
\(508\) | −8.88937 | −0.394402 | ||||||||
\(509\) | 14.7215 | 0.652517 | 0.326258 | − | 0.945281i | \(-0.394212\pi\) | ||||
0.326258 | + | 0.945281i | \(0.394212\pi\) | |||||||
\(510\) | −2.78078 | −0.123135 | ||||||||
\(511\) | 23.5015 | 1.03965 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.34964 | −0.280344 | ||||||||
\(514\) | −29.6761 | −1.30896 | ||||||||
\(515\) | 9.84622 | 0.433876 | ||||||||
\(516\) | 4.15125 | 0.182749 | ||||||||
\(517\) | −22.1003 | −0.971970 | ||||||||
\(518\) | 13.7944 | 0.606089 | ||||||||
\(519\) | −11.2828 | −0.495258 | ||||||||
\(520\) | −3.05651 | −0.134037 | ||||||||
\(521\) | 4.13825 | 0.181300 | 0.0906500 | − | 0.995883i | \(-0.471106\pi\) | ||||
0.0906500 | + | 0.995883i | \(0.471106\pi\) | |||||||
\(522\) | 3.02228 | 0.132282 | ||||||||
\(523\) | 20.0157 | 0.875227 | 0.437614 | − | 0.899163i | \(-0.355824\pi\) | ||||
0.437614 | + | 0.899163i | \(0.355824\pi\) | |||||||
\(524\) | 3.04262 | 0.132917 | ||||||||
\(525\) | −9.34705 | −0.407939 | ||||||||
\(526\) | −21.9414 | −0.956693 | ||||||||
\(527\) | −2.51109 | −0.109385 | ||||||||
\(528\) | 6.40684 | 0.278822 | ||||||||
\(529\) | −22.9911 | −0.999611 | ||||||||
\(530\) | 2.29492 | 0.0996852 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 21.7185 | 0.941616 | ||||||||
\(533\) | −4.33372 | −0.187714 | ||||||||
\(534\) | −9.59621 | −0.415269 | ||||||||
\(535\) | −21.7293 | −0.939441 | ||||||||
\(536\) | 6.99934 | 0.302325 | ||||||||
\(537\) | −2.55732 | −0.110357 | ||||||||
\(538\) | 1.06146 | 0.0457628 | ||||||||
\(539\) | −30.1078 | −1.29683 | ||||||||
\(540\) | 2.78078 | 0.119666 | ||||||||
\(541\) | 6.61115 | 0.284236 | 0.142118 | − | 0.989850i | \(-0.454609\pi\) | ||||
0.142118 | + | 0.989850i | \(0.454609\pi\) | |||||||
\(542\) | 4.15826 | 0.178613 | ||||||||
\(543\) | −2.69513 | −0.115659 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 16.6819 | 0.714572 | ||||||||
\(546\) | −3.75958 | −0.160895 | ||||||||
\(547\) | 4.21646 | 0.180283 | 0.0901414 | − | 0.995929i | \(-0.471268\pi\) | ||||
0.0901414 | + | 0.995929i | \(0.471268\pi\) | |||||||
\(548\) | 0.484042 | 0.0206772 | ||||||||
\(549\) | −1.88013 | −0.0802419 | ||||||||
\(550\) | 17.5081 | 0.746546 | ||||||||
\(551\) | −19.1904 | −0.817538 | ||||||||
\(552\) | −0.0945846 | −0.00402579 | ||||||||
\(553\) | 23.4374 | 0.996658 | ||||||||
\(554\) | 0.918785 | 0.0390355 | ||||||||
\(555\) | −11.2147 | −0.476037 | ||||||||
\(556\) | −0.179257 | −0.00760221 | ||||||||
\(557\) | 39.5624 | 1.67631 | 0.838155 | − | 0.545432i | \(-0.183634\pi\) | ||||
0.838155 | + | 0.545432i | \(0.183634\pi\) | |||||||
\(558\) | 2.51109 | 0.106303 | ||||||||
\(559\) | 4.56287 | 0.192989 | ||||||||
\(560\) | −9.51144 | −0.401932 | ||||||||
\(561\) | 6.40684 | 0.270497 | ||||||||
\(562\) | −20.3440 | −0.858160 | ||||||||
\(563\) | −25.9702 | −1.09452 | −0.547258 | − | 0.836964i | \(-0.684328\pi\) | ||||
−0.547258 | + | 0.836964i | \(0.684328\pi\) | |||||||
\(564\) | −3.44949 | −0.145250 | ||||||||
\(565\) | 15.7657 | 0.663269 | ||||||||
\(566\) | 28.9503 | 1.21687 | ||||||||
\(567\) | 3.42043 | 0.143644 | ||||||||
\(568\) | 8.64966 | 0.362932 | ||||||||
\(569\) | −26.7710 | −1.12230 | −0.561149 | − | 0.827715i | \(-0.689640\pi\) | ||||
−0.561149 | + | 0.827715i | \(0.689640\pi\) | |||||||
\(570\) | −17.6569 | −0.739567 | ||||||||
\(571\) | 17.2078 | 0.720124 | 0.360062 | − | 0.932928i | \(-0.382756\pi\) | ||||
0.360062 | + | 0.932928i | \(0.382756\pi\) | |||||||
\(572\) | 7.04211 | 0.294446 | ||||||||
\(573\) | −10.1874 | −0.425583 | ||||||||
\(574\) | −13.4860 | −0.562893 | ||||||||
\(575\) | −0.258473 | −0.0107791 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 24.0676 | 1.00195 | 0.500973 | − | 0.865463i | \(-0.332976\pi\) | ||||
0.500973 | + | 0.865463i | \(0.332976\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 18.6070 | 0.773280 | ||||||||
\(580\) | 8.40428 | 0.348969 | ||||||||
\(581\) | −0.522690 | −0.0216848 | ||||||||
\(582\) | 1.52877 | 0.0633695 | ||||||||
\(583\) | −5.28745 | −0.218984 | ||||||||
\(584\) | −6.87094 | −0.284321 | ||||||||
\(585\) | 3.05651 | 0.126371 | ||||||||
\(586\) | 21.5847 | 0.891657 | ||||||||
\(587\) | 25.2960 | 1.04408 | 0.522039 | − | 0.852922i | \(-0.325172\pi\) | ||||
0.522039 | + | 0.852922i | \(0.325172\pi\) | |||||||
\(588\) | −4.69932 | −0.193797 | ||||||||
\(589\) | −15.9445 | −0.656983 | ||||||||
\(590\) | −2.78078 | −0.114483 | ||||||||
\(591\) | 24.3322 | 1.00089 | ||||||||
\(592\) | −4.03293 | −0.165753 | ||||||||
\(593\) | 16.3906 | 0.673082 | 0.336541 | − | 0.941669i | \(-0.390743\pi\) | ||||
0.336541 | + | 0.941669i | \(0.390743\pi\) | |||||||
\(594\) | −6.40684 | −0.262876 | ||||||||
\(595\) | −9.51144 | −0.389931 | ||||||||
\(596\) | −8.32811 | −0.341133 | ||||||||
\(597\) | 3.70805 | 0.151760 | ||||||||
\(598\) | −0.103963 | −0.00425137 | ||||||||
\(599\) | 27.7346 | 1.13321 | 0.566603 | − | 0.823991i | \(-0.308257\pi\) | ||||
0.566603 | + | 0.823991i | \(0.308257\pi\) | |||||||
\(600\) | 2.73271 | 0.111563 | ||||||||
\(601\) | −27.9576 | −1.14042 | −0.570208 | − | 0.821501i | \(-0.693137\pi\) | ||||
−0.570208 | + | 0.821501i | \(0.693137\pi\) | |||||||
\(602\) | 14.1990 | 0.578710 | ||||||||
\(603\) | −6.99934 | −0.285035 | ||||||||
\(604\) | 7.36479 | 0.299669 | ||||||||
\(605\) | −83.5556 | −3.39702 | ||||||||
\(606\) | 7.28219 | 0.295819 | ||||||||
\(607\) | −6.68756 | −0.271440 | −0.135720 | − | 0.990747i | \(-0.543335\pi\) | ||||
−0.135720 | + | 0.990747i | \(0.543335\pi\) | |||||||
\(608\) | −6.34964 | −0.257512 | ||||||||
\(609\) | 10.3375 | 0.418896 | ||||||||
\(610\) | −5.22821 | −0.211684 | ||||||||
\(611\) | −3.79152 | −0.153389 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −13.7819 | −0.556644 | −0.278322 | − | 0.960488i | \(-0.589778\pi\) | ||||
−0.278322 | + | 0.960488i | \(0.589778\pi\) | |||||||
\(614\) | −13.7268 | −0.553968 | ||||||||
\(615\) | 10.9640 | 0.442109 | ||||||||
\(616\) | 21.9141 | 0.882945 | ||||||||
\(617\) | −19.6056 | −0.789290 | −0.394645 | − | 0.918834i | \(-0.629132\pi\) | ||||
−0.394645 | + | 0.918834i | \(0.629132\pi\) | |||||||
\(618\) | −3.54082 | −0.142433 | ||||||||
\(619\) | 32.6087 | 1.31065 | 0.655327 | − | 0.755345i | \(-0.272531\pi\) | ||||
0.655327 | + | 0.755345i | \(0.272531\pi\) | |||||||
\(620\) | 6.98279 | 0.280436 | ||||||||
\(621\) | 0.0945846 | 0.00379555 | ||||||||
\(622\) | 13.7718 | 0.552198 | ||||||||
\(623\) | −32.8231 | −1.31503 | ||||||||
\(624\) | 1.09916 | 0.0440015 | ||||||||
\(625\) | −31.1958 | −1.24783 | ||||||||
\(626\) | −19.3987 | −0.775328 | ||||||||
\(627\) | 40.6811 | 1.62465 | ||||||||
\(628\) | 9.87753 | 0.394156 | ||||||||
\(629\) | −4.03293 | −0.160804 | ||||||||
\(630\) | 9.51144 | 0.378945 | ||||||||
\(631\) | 14.7811 | 0.588427 | 0.294213 | − | 0.955740i | \(-0.404942\pi\) | ||||
0.294213 | + | 0.955740i | \(0.404942\pi\) | |||||||
\(632\) | −6.85217 | −0.272565 | ||||||||
\(633\) | 5.01235 | 0.199223 | ||||||||
\(634\) | −21.2894 | −0.845510 | ||||||||
\(635\) | 24.7193 | 0.980957 | ||||||||
\(636\) | −0.825282 | −0.0327246 | ||||||||
\(637\) | −5.16528 | −0.204656 | ||||||||
\(638\) | −19.3633 | −0.766599 | ||||||||
\(639\) | −8.64966 | −0.342175 | ||||||||
\(640\) | 2.78078 | 0.109920 | ||||||||
\(641\) | −7.44836 | −0.294192 | −0.147096 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147096 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(642\) | 7.81413 | 0.308399 | ||||||||
\(643\) | 34.2894 | 1.35224 | 0.676121 | − | 0.736791i | \(-0.263660\pi\) | ||||
0.676121 | + | 0.736791i | \(0.263660\pi\) | |||||||
\(644\) | −0.323520 | −0.0127485 | ||||||||
\(645\) | −11.5437 | −0.454533 | ||||||||
\(646\) | −6.34964 | −0.249823 | ||||||||
\(647\) | 17.0872 | 0.671767 | 0.335884 | − | 0.941904i | \(-0.390965\pi\) | ||||
0.335884 | + | 0.941904i | \(0.390965\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 6.40684 | 0.251490 | ||||||||
\(650\) | 3.00368 | 0.117814 | ||||||||
\(651\) | 8.58901 | 0.336630 | ||||||||
\(652\) | −21.8700 | −0.856494 | ||||||||
\(653\) | −25.2629 | −0.988615 | −0.494307 | − | 0.869287i | \(-0.664578\pi\) | ||||
−0.494307 | + | 0.869287i | \(0.664578\pi\) | |||||||
\(654\) | −5.99899 | −0.234579 | ||||||||
\(655\) | −8.46083 | −0.330592 | ||||||||
\(656\) | 3.94277 | 0.153939 | ||||||||
\(657\) | 6.87094 | 0.268061 | ||||||||
\(658\) | −11.7987 | −0.459962 | ||||||||
\(659\) | −35.6885 | −1.39023 | −0.695113 | − | 0.718900i | \(-0.744646\pi\) | ||||
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(660\) | −17.8160 | −0.693486 | ||||||||
\(661\) | −17.9778 | −0.699257 | −0.349628 | − | 0.936889i | \(-0.613692\pi\) | ||||
−0.349628 | + | 0.936889i | \(0.613692\pi\) | |||||||
\(662\) | −10.7517 | −0.417875 | ||||||||
\(663\) | 1.09916 | 0.0426877 | ||||||||
\(664\) | 0.152814 | 0.00593034 | ||||||||
\(665\) | −60.3942 | −2.34199 | ||||||||
\(666\) | 4.03293 | 0.156273 | ||||||||
\(667\) | 0.285861 | 0.0110686 | ||||||||
\(668\) | 21.1311 | 0.817587 | ||||||||
\(669\) | −1.38896 | −0.0537004 | ||||||||
\(670\) | −19.4636 | −0.751944 | ||||||||
\(671\) | 12.0457 | 0.465018 | ||||||||
\(672\) | 3.42043 | 0.131946 | ||||||||
\(673\) | 35.5902 | 1.37190 | 0.685950 | − | 0.727649i | \(-0.259387\pi\) | ||||
0.685950 | + | 0.727649i | \(0.259387\pi\) | |||||||
\(674\) | −27.6531 | −1.06516 | ||||||||
\(675\) | −2.73271 | −0.105182 | ||||||||
\(676\) | −11.7919 | −0.453533 | ||||||||
\(677\) | 44.9411 | 1.72723 | 0.863614 | − | 0.504153i | \(-0.168195\pi\) | ||||
0.863614 | + | 0.504153i | \(0.168195\pi\) | |||||||
\(678\) | −5.66954 | −0.217737 | ||||||||
\(679\) | 5.22904 | 0.200672 | ||||||||
\(680\) | 2.78078 | 0.106638 | ||||||||
\(681\) | 8.74677 | 0.335177 | ||||||||
\(682\) | −16.0882 | −0.616048 | ||||||||
\(683\) | −27.0493 | −1.03501 | −0.517507 | − | 0.855679i | \(-0.673140\pi\) | ||||
−0.517507 | + | 0.855679i | \(0.673140\pi\) | |||||||
\(684\) | 6.34964 | 0.242785 | ||||||||
\(685\) | −1.34601 | −0.0514285 | ||||||||
\(686\) | 7.86931 | 0.300452 | ||||||||
\(687\) | −13.4870 | −0.514560 | ||||||||
\(688\) | −4.15125 | −0.158265 | ||||||||
\(689\) | −0.907114 | −0.0345583 | ||||||||
\(690\) | 0.263019 | 0.0100129 | ||||||||
\(691\) | 27.0426 | 1.02875 | 0.514374 | − | 0.857566i | \(-0.328024\pi\) | ||||
0.514374 | + | 0.857566i | \(0.328024\pi\) | |||||||
\(692\) | 11.2828 | 0.428906 | ||||||||
\(693\) | −21.9141 | −0.832449 | ||||||||
\(694\) | −17.0845 | −0.648521 | ||||||||
\(695\) | 0.498475 | 0.0189082 | ||||||||
\(696\) | −3.02228 | −0.114559 | ||||||||
\(697\) | 3.94277 | 0.149343 | ||||||||
\(698\) | −12.8542 | −0.486540 | ||||||||
\(699\) | 6.74729 | 0.255206 | ||||||||
\(700\) | 9.34705 | 0.353285 | ||||||||
\(701\) | 33.6517 | 1.27101 | 0.635504 | − | 0.772098i | \(-0.280793\pi\) | ||||
0.635504 | + | 0.772098i | \(0.280793\pi\) | |||||||
\(702\) | −1.09916 | −0.0414850 | ||||||||
\(703\) | −25.6077 | −0.965812 | ||||||||
\(704\) | −6.40684 | −0.241467 | ||||||||
\(705\) | 9.59225 | 0.361265 | ||||||||
\(706\) | −24.7686 | −0.932178 | ||||||||
\(707\) | 24.9082 | 0.936769 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −20.0642 | −0.753526 | −0.376763 | − | 0.926310i | \(-0.622963\pi\) | ||||
−0.376763 | + | 0.926310i | \(0.622963\pi\) | |||||||
\(710\) | −24.0528 | −0.902684 | ||||||||
\(711\) | 6.85217 | 0.256977 | ||||||||
\(712\) | 9.59621 | 0.359633 | ||||||||
\(713\) | 0.237511 | 0.00889485 | ||||||||
\(714\) | 3.42043 | 0.128006 | ||||||||
\(715\) | −19.5825 | −0.732345 | ||||||||
\(716\) | 2.55732 | 0.0955716 | ||||||||
\(717\) | 3.39472 | 0.126778 | ||||||||
\(718\) | −6.82217 | −0.254601 | ||||||||
\(719\) | 21.6002 | 0.805550 | 0.402775 | − | 0.915299i | \(-0.368046\pi\) | ||||
0.402775 | + | 0.915299i | \(0.368046\pi\) | |||||||
\(720\) | −2.78078 | −0.103633 | ||||||||
\(721\) | −12.1111 | −0.451041 | ||||||||
\(722\) | −21.3179 | −0.793372 | ||||||||
\(723\) | −13.6691 | −0.508361 | ||||||||
\(724\) | 2.69513 | 0.100164 | ||||||||
\(725\) | −8.25902 | −0.306732 | ||||||||
\(726\) | 30.0476 | 1.11517 | ||||||||
\(727\) | −14.9641 | −0.554988 | −0.277494 | − | 0.960727i | \(-0.589504\pi\) | ||||
−0.277494 | + | 0.960727i | \(0.589504\pi\) | |||||||
\(728\) | 3.75958 | 0.139339 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.1065 | 0.707165 | ||||||||
\(731\) | −4.15125 | −0.153540 | ||||||||
\(732\) | 1.88013 | 0.0694915 | ||||||||
\(733\) | −13.9674 | −0.515898 | −0.257949 | − | 0.966158i | \(-0.583047\pi\) | ||||
−0.257949 | + | 0.966158i | \(0.583047\pi\) | |||||||
\(734\) | −32.6009 | −1.20332 | ||||||||
\(735\) | 13.0678 | 0.482011 | ||||||||
\(736\) | 0.0945846 | 0.00348644 | ||||||||
\(737\) | 44.8436 | 1.65184 | ||||||||
\(738\) | −3.94277 | −0.145135 | ||||||||
\(739\) | −7.23539 | −0.266158 | −0.133079 | − | 0.991105i | \(-0.542486\pi\) | ||||
−0.133079 | + | 0.991105i | \(0.542486\pi\) | |||||||
\(740\) | 11.2147 | 0.412260 | ||||||||
\(741\) | 6.97925 | 0.256389 | ||||||||
\(742\) | −2.82282 | −0.103629 | ||||||||
\(743\) | 41.5093 | 1.52283 | 0.761414 | − | 0.648265i | \(-0.224505\pi\) | ||||
0.761414 | + | 0.648265i | \(0.224505\pi\) | |||||||
\(744\) | −2.51109 | −0.0920612 | ||||||||
\(745\) | 23.1586 | 0.848466 | ||||||||
\(746\) | −12.2917 | −0.450030 | ||||||||
\(747\) | −0.152814 | −0.00559118 | ||||||||
\(748\) | −6.40684 | −0.234257 | ||||||||
\(749\) | 26.7276 | 0.976607 | ||||||||
\(750\) | 6.30482 | 0.230219 | ||||||||
\(751\) | −17.8437 | −0.651125 | −0.325562 | − | 0.945521i | \(-0.605554\pi\) | ||||
−0.325562 | + | 0.945521i | \(0.605554\pi\) | |||||||
\(752\) | 3.44949 | 0.125790 | ||||||||
\(753\) | −17.2811 | −0.629757 | ||||||||
\(754\) | −3.32196 | −0.120979 | ||||||||
\(755\) | −20.4798 | −0.745337 | ||||||||
\(756\) | −3.42043 | −0.124400 | ||||||||
\(757\) | −13.5549 | −0.492662 | −0.246331 | − | 0.969186i | \(-0.579225\pi\) | ||||
−0.246331 | + | 0.969186i | \(0.579225\pi\) | |||||||
\(758\) | −6.21412 | −0.225707 | ||||||||
\(759\) | −0.605988 | −0.0219960 | ||||||||
\(760\) | 17.6569 | 0.640484 | ||||||||
\(761\) | 5.51582 | 0.199948 | 0.0999742 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999742 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(762\) | −8.88937 | −0.322028 | ||||||||
\(763\) | −20.5191 | −0.742842 | ||||||||
\(764\) | 10.1874 | 0.368566 | ||||||||
\(765\) | −2.78078 | −0.100539 | ||||||||
\(766\) | 24.5786 | 0.888060 | ||||||||
\(767\) | 1.09916 | 0.0396882 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −26.9607 | −0.972229 | −0.486115 | − | 0.873895i | \(-0.661586\pi\) | ||||
−0.486115 | + | 0.873895i | \(0.661586\pi\) | |||||||
\(770\) | −60.9383 | −2.19606 | ||||||||
\(771\) | −29.6761 | −1.06876 | ||||||||
\(772\) | −18.6070 | −0.669681 | ||||||||
\(773\) | 19.2940 | 0.693957 | 0.346979 | − | 0.937873i | \(-0.387208\pi\) | ||||
0.346979 | + | 0.937873i | \(0.387208\pi\) | |||||||
\(774\) | 4.15125 | 0.149214 | ||||||||
\(775\) | −6.86210 | −0.246494 | ||||||||
\(776\) | −1.52877 | −0.0548796 | ||||||||
\(777\) | 13.7944 | 0.494870 | ||||||||
\(778\) | −19.3063 | −0.692165 | ||||||||
\(779\) | 25.0352 | 0.896978 | ||||||||
\(780\) | −3.05651 | −0.109440 | ||||||||
\(781\) | 55.4170 | 1.98298 | ||||||||
\(782\) | 0.0945846 | 0.00338234 | ||||||||
\(783\) | 3.02228 | 0.108007 | ||||||||
\(784\) | 4.69932 | 0.167833 | ||||||||
\(785\) | −27.4672 | −0.980346 | ||||||||
\(786\) | 3.04262 | 0.108527 | ||||||||
\(787\) | −41.7477 | −1.48814 | −0.744072 | − | 0.668099i | \(-0.767108\pi\) | ||||
−0.744072 | + | 0.668099i | \(0.767108\pi\) | |||||||
\(788\) | −24.3322 | −0.866797 | ||||||||
\(789\) | −21.9414 | −0.781136 | ||||||||
\(790\) | 19.0544 | 0.677924 | ||||||||
\(791\) | −19.3923 | −0.689509 | ||||||||
\(792\) | 6.40684 | 0.227657 | ||||||||
\(793\) | 2.06655 | 0.0733855 | ||||||||
\(794\) | 23.0737 | 0.818853 | ||||||||
\(795\) | 2.29492 | 0.0813926 | ||||||||
\(796\) | −3.70805 | −0.131428 | ||||||||
\(797\) | −36.1574 | −1.28076 | −0.640381 | − | 0.768058i | \(-0.721223\pi\) | ||||
−0.640381 | + | 0.768058i | \(0.721223\pi\) | |||||||
\(798\) | 21.7185 | 0.768826 | ||||||||
\(799\) | 3.44949 | 0.122034 | ||||||||
\(800\) | −2.73271 | −0.0966160 | ||||||||
\(801\) | −9.59621 | −0.339065 | ||||||||
\(802\) | −6.62545 | −0.233953 | ||||||||
\(803\) | −44.0210 | −1.55347 | ||||||||
\(804\) | 6.99934 | 0.246848 | ||||||||
\(805\) | 0.899636 | 0.0317080 | ||||||||
\(806\) | −2.76008 | −0.0972198 | ||||||||
\(807\) | 1.06146 | 0.0373652 | ||||||||
\(808\) | −7.28219 | −0.256186 | ||||||||
\(809\) | 14.9124 | 0.524292 | 0.262146 | − | 0.965028i | \(-0.415570\pi\) | ||||
0.262146 | + | 0.965028i | \(0.415570\pi\) | |||||||
\(810\) | 2.78078 | 0.0977065 | ||||||||
\(811\) | 21.2737 | 0.747021 | 0.373510 | − | 0.927626i | \(-0.378154\pi\) | ||||
0.373510 | + | 0.927626i | \(0.378154\pi\) | |||||||
\(812\) | −10.3375 | −0.362775 | ||||||||
\(813\) | 4.15826 | 0.145837 | ||||||||
\(814\) | −25.8384 | −0.905634 | ||||||||
\(815\) | 60.8155 | 2.13027 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −26.3589 | −0.922183 | ||||||||
\(818\) | −4.87099 | −0.170310 | ||||||||
\(819\) | −3.75958 | −0.131370 | ||||||||
\(820\) | −10.9640 | −0.382878 | ||||||||
\(821\) | −42.2690 | −1.47520 | −0.737598 | − | 0.675240i | \(-0.764040\pi\) | ||||
−0.737598 | + | 0.675240i | \(0.764040\pi\) | |||||||
\(822\) | 0.484042 | 0.0168829 | ||||||||
\(823\) | −4.16450 | −0.145166 | −0.0725828 | − | 0.997362i | \(-0.523124\pi\) | ||||
−0.0725828 | + | 0.997362i | \(0.523124\pi\) | |||||||
\(824\) | 3.54082 | 0.123350 | ||||||||
\(825\) | 17.5081 | 0.609552 | ||||||||
\(826\) | 3.42043 | 0.119012 | ||||||||
\(827\) | 6.91461 | 0.240445 | 0.120222 | − | 0.992747i | \(-0.461639\pi\) | ||||
0.120222 | + | 0.992747i | \(0.461639\pi\) | |||||||
\(828\) | −0.0945846 | −0.00328704 | ||||||||
\(829\) | 25.1055 | 0.871949 | 0.435974 | − | 0.899959i | \(-0.356404\pi\) | ||||
0.435974 | + | 0.899959i | \(0.356404\pi\) | |||||||
\(830\) | −0.424942 | −0.0147500 | ||||||||
\(831\) | 0.918785 | 0.0318723 | ||||||||
\(832\) | −1.09916 | −0.0381064 | ||||||||
\(833\) | 4.69932 | 0.162822 | ||||||||
\(834\) | −0.179257 | −0.00620717 | ||||||||
\(835\) | −58.7608 | −2.03350 | ||||||||
\(836\) | −40.6811 | −1.40699 | ||||||||
\(837\) | 2.51109 | 0.0867961 | ||||||||
\(838\) | 13.5440 | 0.467871 | ||||||||
\(839\) | −18.4359 | −0.636478 | −0.318239 | − | 0.948010i | \(-0.603092\pi\) | ||||
−0.318239 | + | 0.948010i | \(0.603092\pi\) | |||||||
\(840\) | −9.51144 | −0.328176 | ||||||||
\(841\) | −19.8658 | −0.685028 | ||||||||
\(842\) | −16.4086 | −0.565479 | ||||||||
\(843\) | −20.3440 | −0.700685 | ||||||||
\(844\) | −5.01235 | −0.172532 | ||||||||
\(845\) | 32.7905 | 1.12803 | ||||||||
\(846\) | −3.44949 | −0.118596 | ||||||||
\(847\) | 102.776 | 3.53141 | ||||||||
\(848\) | 0.825282 | 0.0283403 | ||||||||
\(849\) | 28.9503 | 0.993573 | ||||||||
\(850\) | −2.73271 | −0.0937313 | ||||||||
\(851\) | 0.381453 | 0.0130761 | ||||||||
\(852\) | 8.64966 | 0.296333 | ||||||||
\(853\) | 28.3342 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(854\) | 6.43084 | 0.220059 | ||||||||
\(855\) | −17.6569 | −0.603854 | ||||||||
\(856\) | −7.81413 | −0.267081 | ||||||||
\(857\) | −54.2781 | −1.85411 | −0.927053 | − | 0.374931i | \(-0.877666\pi\) | ||||
−0.927053 | + | 0.374931i | \(0.877666\pi\) | |||||||
\(858\) | 7.04211 | 0.240414 | ||||||||
\(859\) | −20.7844 | −0.709154 | −0.354577 | − | 0.935027i | \(-0.615375\pi\) | ||||
−0.354577 | + | 0.935027i | \(0.615375\pi\) | |||||||
\(860\) | 11.5437 | 0.393637 | ||||||||
\(861\) | −13.4860 | −0.459600 | ||||||||
\(862\) | −5.11972 | −0.174378 | ||||||||
\(863\) | 16.8653 | 0.574102 | 0.287051 | − | 0.957915i | \(-0.407325\pi\) | ||||
0.287051 | + | 0.957915i | \(0.407325\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −31.3748 | −1.06678 | ||||||||
\(866\) | 26.7697 | 0.909670 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −8.58901 | −0.291530 | ||||||||
\(869\) | −43.9008 | −1.48923 | ||||||||
\(870\) | 8.40428 | 0.284932 | ||||||||
\(871\) | 7.69337 | 0.260680 | ||||||||
\(872\) | 5.99899 | 0.203152 | ||||||||
\(873\) | 1.52877 | 0.0517410 | ||||||||
\(874\) | 0.600578 | 0.0203149 | ||||||||
\(875\) | 21.5652 | 0.729035 | ||||||||
\(876\) | −6.87094 | −0.232148 | ||||||||
\(877\) | −7.45399 | −0.251704 | −0.125852 | − | 0.992049i | \(-0.540166\pi\) | ||||
−0.125852 | + | 0.992049i | \(0.540166\pi\) | |||||||
\(878\) | −25.7731 | −0.869800 | ||||||||
\(879\) | 21.5847 | 0.728035 | ||||||||
\(880\) | 17.8160 | 0.600577 | ||||||||
\(881\) | −14.9966 | −0.505247 | −0.252623 | − | 0.967565i | \(-0.581293\pi\) | ||||
−0.252623 | + | 0.967565i | \(0.581293\pi\) | |||||||
\(882\) | −4.69932 | −0.158234 | ||||||||
\(883\) | 45.1455 | 1.51927 | 0.759634 | − | 0.650351i | \(-0.225378\pi\) | ||||
0.759634 | + | 0.650351i | \(0.225378\pi\) | |||||||
\(884\) | −1.09916 | −0.0369686 | ||||||||
\(885\) | −2.78078 | −0.0934748 | ||||||||
\(886\) | −6.33359 | −0.212781 | ||||||||
\(887\) | −19.1800 | −0.644001 | −0.322001 | − | 0.946739i | \(-0.604355\pi\) | ||||
−0.322001 | + | 0.946739i | \(0.604355\pi\) | |||||||
\(888\) | −4.03293 | −0.135336 | ||||||||
\(889\) | −30.4054 | −1.01977 | ||||||||
\(890\) | −26.6849 | −0.894480 | ||||||||
\(891\) | −6.40684 | −0.214637 | ||||||||
\(892\) | 1.38896 | 0.0465059 | ||||||||
\(893\) | 21.9030 | 0.732956 | ||||||||
\(894\) | −8.32811 | −0.278534 | ||||||||
\(895\) | −7.11134 | −0.237706 | ||||||||
\(896\) | −3.42043 | −0.114268 | ||||||||
\(897\) | −0.103963 | −0.00347123 | ||||||||
\(898\) | 6.05616 | 0.202097 | ||||||||
\(899\) | 7.58923 | 0.253115 | ||||||||
\(900\) | 2.73271 | 0.0910905 | ||||||||
\(901\) | 0.825282 | 0.0274941 | ||||||||
\(902\) | 25.2607 | 0.841089 | ||||||||
\(903\) | 14.1990 | 0.472515 | ||||||||
\(904\) | 5.66954 | 0.188566 | ||||||||
\(905\) | −7.49455 | −0.249127 | ||||||||
\(906\) | 7.36479 | 0.244679 | ||||||||
\(907\) | 48.8641 | 1.62250 | 0.811252 | − | 0.584697i | \(-0.198786\pi\) | ||||
0.811252 | + | 0.584697i | \(0.198786\pi\) | |||||||
\(908\) | −8.74677 | −0.290272 | ||||||||
\(909\) | 7.28219 | 0.241535 | ||||||||
\(910\) | −10.4546 | −0.346565 | ||||||||
\(911\) | −52.1806 | −1.72882 | −0.864410 | − | 0.502788i | \(-0.832308\pi\) | ||||
−0.864410 | + | 0.502788i | \(0.832308\pi\) | |||||||
\(912\) | −6.34964 | −0.210258 | ||||||||
\(913\) | 0.979056 | 0.0324020 | ||||||||
\(914\) | −24.5777 | −0.812959 | ||||||||
\(915\) | −5.22821 | −0.172839 | ||||||||
\(916\) | 13.4870 | 0.445622 | ||||||||
\(917\) | 10.4070 | 0.343671 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 27.8217 | 0.917752 | 0.458876 | − | 0.888500i | \(-0.348252\pi\) | ||||
0.458876 | + | 0.888500i | \(0.348252\pi\) | |||||||
\(920\) | −0.263019 | −0.00867147 | ||||||||
\(921\) | −13.7268 | −0.452313 | ||||||||
\(922\) | −23.1601 | −0.762737 | ||||||||
\(923\) | 9.50733 | 0.312938 | ||||||||
\(924\) | 21.9141 | 0.720922 | ||||||||
\(925\) | −11.0209 | −0.362363 | ||||||||
\(926\) | 6.15000 | 0.202102 | ||||||||
\(927\) | −3.54082 | −0.116296 | ||||||||
\(928\) | 3.02228 | 0.0992112 | ||||||||
\(929\) | −5.64580 | −0.185233 | −0.0926164 | − | 0.995702i | \(-0.529523\pi\) | ||||
−0.0926164 | + | 0.995702i | \(0.529523\pi\) | |||||||
\(930\) | 6.98279 | 0.228975 | ||||||||
\(931\) | 29.8390 | 0.977933 | ||||||||
\(932\) | −6.74729 | −0.221015 | ||||||||
\(933\) | 13.7718 | 0.450868 | ||||||||
\(934\) | −38.5003 | −1.25977 | ||||||||
\(935\) | 17.8160 | 0.582645 | ||||||||
\(936\) | 1.09916 | 0.0359270 | ||||||||
\(937\) | −41.9119 | −1.36920 | −0.684601 | − | 0.728918i | \(-0.740024\pi\) | ||||
−0.684601 | + | 0.728918i | \(0.740024\pi\) | |||||||
\(938\) | 23.9407 | 0.781693 | ||||||||
\(939\) | −19.3987 | −0.633052 | ||||||||
\(940\) | −9.59225 | −0.312865 | ||||||||
\(941\) | −5.59293 | −0.182324 | −0.0911621 | − | 0.995836i | \(-0.529058\pi\) | ||||
−0.0911621 | + | 0.995836i | \(0.529058\pi\) | |||||||
\(942\) | 9.87753 | 0.321827 | ||||||||
\(943\) | −0.372925 | −0.0121441 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 9.51144 | 0.309407 | ||||||||
\(946\) | −26.5964 | −0.864723 | ||||||||
\(947\) | 36.5743 | 1.18851 | 0.594253 | − | 0.804278i | \(-0.297448\pi\) | ||||
0.594253 | + | 0.804278i | \(0.297448\pi\) | |||||||
\(948\) | −6.85217 | −0.222548 | ||||||||
\(949\) | −7.55223 | −0.245156 | ||||||||
\(950\) | −17.3518 | −0.562965 | ||||||||
\(951\) | −21.2894 | −0.690356 | ||||||||
\(952\) | −3.42043 | −0.110857 | ||||||||
\(953\) | 26.3468 | 0.853457 | 0.426728 | − | 0.904380i | \(-0.359666\pi\) | ||||
0.426728 | + | 0.904380i | \(0.359666\pi\) | |||||||
\(954\) | −0.825282 | −0.0267195 | ||||||||
\(955\) | −28.3288 | −0.916697 | ||||||||
\(956\) | −3.39472 | −0.109793 | ||||||||
\(957\) | −19.3633 | −0.625925 | ||||||||
\(958\) | −3.10423 | −0.100293 | ||||||||
\(959\) | 1.65563 | 0.0534631 | ||||||||
\(960\) | 2.78078 | 0.0897492 | ||||||||
\(961\) | −24.6944 | −0.796594 | ||||||||
\(962\) | −4.43282 | −0.142920 | ||||||||
\(963\) | 7.81413 | 0.251807 | ||||||||
\(964\) | 13.6691 | 0.440254 | ||||||||
\(965\) | 51.7419 | 1.66563 | ||||||||
\(966\) | −0.323520 | −0.0104091 | ||||||||
\(967\) | −26.9030 | −0.865141 | −0.432570 | − | 0.901600i | \(-0.642393\pi\) | ||||
−0.432570 | + | 0.901600i | \(0.642393\pi\) | |||||||
\(968\) | −30.0476 | −0.965765 | ||||||||
\(969\) | −6.34964 | −0.203980 | ||||||||
\(970\) | 4.25116 | 0.136497 | ||||||||
\(971\) | −36.5952 | −1.17440 | −0.587199 | − | 0.809443i | \(-0.699769\pi\) | ||||
−0.587199 | + | 0.809443i | \(0.699769\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −0.613137 | −0.0196563 | ||||||||
\(974\) | −28.9801 | −0.928581 | ||||||||
\(975\) | 3.00368 | 0.0961947 | ||||||||
\(976\) | −1.88013 | −0.0601814 | ||||||||
\(977\) | 13.5085 | 0.432176 | 0.216088 | − | 0.976374i | \(-0.430670\pi\) | ||||
0.216088 | + | 0.976374i | \(0.430670\pi\) | |||||||
\(978\) | −21.8700 | −0.699325 | ||||||||
\(979\) | 61.4814 | 1.96495 | ||||||||
\(980\) | −13.0678 | −0.417434 | ||||||||
\(981\) | −5.99899 | −0.191533 | ||||||||
\(982\) | −41.1935 | −1.31454 | ||||||||
\(983\) | 25.3590 | 0.808827 | 0.404413 | − | 0.914576i | \(-0.367476\pi\) | ||||
0.404413 | + | 0.914576i | \(0.367476\pi\) | |||||||
\(984\) | 3.94277 | 0.125691 | ||||||||
\(985\) | 67.6623 | 2.15590 | ||||||||
\(986\) | 3.02228 | 0.0962490 | ||||||||
\(987\) | −11.7987 | −0.375557 | ||||||||
\(988\) | −6.97925 | −0.222039 | ||||||||
\(989\) | 0.392644 | 0.0124854 | ||||||||
\(990\) | −17.8160 | −0.566229 | ||||||||
\(991\) | −38.2337 | −1.21453 | −0.607267 | − | 0.794498i | \(-0.707734\pi\) | ||||
−0.607267 | + | 0.794498i | \(0.707734\pi\) | |||||||
\(992\) | 2.51109 | 0.0797273 | ||||||||
\(993\) | −10.7517 | −0.341193 | ||||||||
\(994\) | 29.5855 | 0.938396 | ||||||||
\(995\) | 10.3113 | 0.326889 | ||||||||
\(996\) | 0.152814 | 0.00484210 | ||||||||
\(997\) | −10.8817 | −0.344628 | −0.172314 | − | 0.985042i | \(-0.555124\pi\) | ||||
−0.172314 | + | 0.985042i | \(0.555124\pi\) | |||||||
\(998\) | 16.5558 | 0.524066 | ||||||||
\(999\) | 4.03293 | 0.127596 |
(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 | 6018.2.a.x.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.x.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial |