Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 2.47214 | 0.745377 | 0.372689 | − | 0.927957i | \(-0.378436\pi\) | ||||
0.372689 | + | 0.927957i | \(0.378436\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.47214 | 0.567147 | 0.283573 | − | 0.958951i | \(-0.408480\pi\) | ||||
0.283573 | + | 0.958951i | \(0.408480\pi\) | |||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.47214 | −0.527061 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | −2.47214 | −0.430344 | ||||||||
\(34\) | 4.47214 | 0.766965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.47214 | 0.735215 | 0.367607 | − | 0.929981i | \(-0.380177\pi\) | ||||
0.367607 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(38\) | −2.47214 | −0.401033 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | −6.00000 | −0.948683 | ||||||||
\(41\) | 6.94427 | 1.08451 | 0.542257 | − | 0.840213i | \(-0.317570\pi\) | ||||
0.542257 | + | 0.840213i | \(0.317570\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47214 | −0.376997 | −0.188499 | − | 0.982073i | \(-0.560362\pi\) | ||||
−0.188499 | + | 0.982073i | \(0.560362\pi\) | |||||||
\(44\) | −2.47214 | −0.372689 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −4.94427 | −0.721196 | −0.360598 | − | 0.932721i | \(-0.617427\pi\) | ||||
−0.360598 | + | 0.932721i | \(0.617427\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.47214 | 0.626224 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −4.94427 | −0.666685 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.47214 | −0.327442 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | −3.52786 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 2.47214 | 0.304299 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 4.47214 | 0.542326 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | 6.94427 | 0.812766 | 0.406383 | − | 0.913703i | \(-0.366790\pi\) | ||||
0.406383 | + | 0.913703i | \(0.366790\pi\) | |||||||
\(74\) | −4.47214 | −0.519875 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.47214 | −0.283573 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | 1.52786 | 0.171898 | 0.0859491 | − | 0.996300i | \(-0.472608\pi\) | ||||
0.0859491 | + | 0.996300i | \(0.472608\pi\) | |||||||
\(80\) | 2.00000 | 0.223607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.94427 | −0.766867 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.94427 | 0.970143 | ||||||||
\(86\) | 2.47214 | 0.266577 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 7.41641 | 0.790592 | ||||||||
\(89\) | 13.4164 | 1.42214 | 0.711068 | − | 0.703123i | \(-0.248212\pi\) | ||||
0.711068 | + | 0.703123i | \(0.248212\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 8.00000 | 0.829561 | ||||||||
\(94\) | 4.94427 | 0.509963 | ||||||||
\(95\) | −4.94427 | −0.507272 | ||||||||
\(96\) | 5.00000 | 0.510310 | ||||||||
\(97\) | −9.41641 | −0.956091 | −0.478046 | − | 0.878335i | \(-0.658655\pi\) | ||||
−0.478046 | + | 0.878335i | \(0.658655\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | 2.47214 | 0.248459 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.9443 | 1.88503 | 0.942513 | − | 0.334170i | \(-0.108456\pi\) | ||||
0.942513 | + | 0.334170i | \(0.108456\pi\) | |||||||
\(102\) | −4.47214 | −0.442807 | ||||||||
\(103\) | −12.9443 | −1.27544 | −0.637719 | − | 0.770270i | \(-0.720122\pi\) | ||||
−0.637719 | + | 0.770270i | \(0.720122\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | −0.944272 | −0.0912862 | −0.0456431 | − | 0.998958i | \(-0.514534\pi\) | ||||
−0.0456431 | + | 0.998958i | \(0.514534\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.9443 | 1.04827 | 0.524136 | − | 0.851635i | \(-0.324389\pi\) | ||||
0.524136 | + | 0.851635i | \(0.324389\pi\) | |||||||
\(110\) | 4.94427 | 0.471418 | ||||||||
\(111\) | −4.47214 | −0.424476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.47214 | 0.796992 | 0.398496 | − | 0.917170i | \(-0.369532\pi\) | ||||
0.398496 | + | 0.917170i | \(0.369532\pi\) | |||||||
\(114\) | 2.47214 | 0.231537 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.00000 | 0.547723 | ||||||||
\(121\) | −4.88854 | −0.444413 | ||||||||
\(122\) | 3.52786 | 0.319398 | ||||||||
\(123\) | −6.94427 | −0.626144 | ||||||||
\(124\) | 8.00000 | 0.718421 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8885 | 1.58735 | 0.793676 | − | 0.608341i | \(-0.208165\pi\) | ||||
0.793676 | + | 0.608341i | \(0.208165\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 2.47214 | 0.217659 | ||||||||
\(130\) | −4.00000 | −0.350823 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 2.47214 | 0.215172 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 2.00000 | 0.172133 | ||||||||
\(136\) | −13.4164 | −1.15045 | ||||||||
\(137\) | 3.52786 | 0.301406 | 0.150703 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150703 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −0.944272 | −0.0800921 | −0.0400460 | − | 0.999198i | \(-0.512750\pi\) | ||||
−0.0400460 | + | 0.999198i | \(0.512750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.94427 | 0.416383 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | −4.94427 | −0.413461 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | −6.94427 | −0.574712 | ||||||||
\(147\) | 7.00000 | 0.577350 | ||||||||
\(148\) | −4.47214 | −0.367607 | ||||||||
\(149\) | 10.9443 | 0.896590 | 0.448295 | − | 0.893886i | \(-0.352031\pi\) | ||||
0.448295 | + | 0.893886i | \(0.352031\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 20.9443 | 1.70442 | 0.852210 | − | 0.523199i | \(-0.175262\pi\) | ||||
0.852210 | + | 0.523199i | \(0.175262\pi\) | |||||||
\(152\) | 7.41641 | 0.601550 | ||||||||
\(153\) | −4.47214 | −0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | 1.28515 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | −3.52786 | −0.281554 | −0.140777 | − | 0.990041i | \(-0.544960\pi\) | ||||
−0.140777 | + | 0.990041i | \(0.544960\pi\) | |||||||
\(158\) | −1.52786 | −0.121550 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 10.0000 | 0.790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.944272 | −0.0739611 | −0.0369805 | − | 0.999316i | \(-0.511774\pi\) | ||||
−0.0369805 | + | 0.999316i | \(0.511774\pi\) | |||||||
\(164\) | −6.94427 | −0.542257 | ||||||||
\(165\) | 4.94427 | 0.384911 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 20.9443 | 1.62072 | 0.810358 | − | 0.585935i | \(-0.199273\pi\) | ||||
0.810358 | + | 0.585935i | \(0.199273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −8.94427 | −0.685994 | ||||||||
\(171\) | 2.47214 | 0.189049 | ||||||||
\(172\) | 2.47214 | 0.188499 | ||||||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.47214 | −0.186344 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | −13.4164 | −1.00560 | ||||||||
\(179\) | −8.94427 | −0.668526 | −0.334263 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334263 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(180\) | 2.00000 | 0.149071 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.52786 | 0.260787 | ||||||||
\(184\) | −3.00000 | −0.221163 | ||||||||
\(185\) | −8.94427 | −0.657596 | ||||||||
\(186\) | −8.00000 | −0.586588 | ||||||||
\(187\) | −11.0557 | −0.808475 | ||||||||
\(188\) | 4.94427 | 0.360598 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.94427 | 0.358695 | ||||||||
\(191\) | −6.47214 | −0.468307 | −0.234154 | − | 0.972200i | \(-0.575232\pi\) | ||||
−0.234154 | + | 0.972200i | \(0.575232\pi\) | |||||||
\(192\) | −7.00000 | −0.505181 | ||||||||
\(193\) | 5.05573 | 0.363919 | 0.181960 | − | 0.983306i | \(-0.441756\pi\) | ||||
0.181960 | + | 0.983306i | \(0.441756\pi\) | |||||||
\(194\) | 9.41641 | 0.676059 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | −2.47214 | −0.175687 | ||||||||
\(199\) | −12.9443 | −0.917595 | −0.458798 | − | 0.888541i | \(-0.651720\pi\) | ||||
−0.458798 | + | 0.888541i | \(0.651720\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | −18.9443 | −1.33291 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.47214 | −0.313112 | ||||||||
\(205\) | −13.8885 | −0.970018 | ||||||||
\(206\) | 12.9443 | 0.901870 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 6.11146 | 0.422738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9443 | −1.16649 | −0.583246 | − | 0.812296i | \(-0.698218\pi\) | ||||
−0.583246 | + | 0.812296i | \(0.698218\pi\) | |||||||
\(212\) | 2.00000 | 0.137361 | ||||||||
\(213\) | −8.00000 | −0.548151 | ||||||||
\(214\) | 0.944272 | 0.0645491 | ||||||||
\(215\) | 4.94427 | 0.337197 | ||||||||
\(216\) | −3.00000 | −0.204124 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.9443 | −0.741240 | ||||||||
\(219\) | −6.94427 | −0.469250 | ||||||||
\(220\) | 4.94427 | 0.333343 | ||||||||
\(221\) | 8.94427 | 0.601657 | ||||||||
\(222\) | 4.47214 | 0.300150 | ||||||||
\(223\) | 25.8885 | 1.73363 | 0.866813 | − | 0.498634i | \(-0.166165\pi\) | ||||
0.866813 | + | 0.498634i | \(0.166165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −8.47214 | −0.563558 | ||||||||
\(227\) | −21.8885 | −1.45279 | −0.726397 | − | 0.687276i | \(-0.758807\pi\) | ||||
−0.726397 | + | 0.687276i | \(0.758807\pi\) | |||||||
\(228\) | 2.47214 | 0.163721 | ||||||||
\(229\) | 17.4164 | 1.15091 | 0.575454 | − | 0.817834i | \(-0.304825\pi\) | ||||
0.575454 | + | 0.817834i | \(0.304825\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 19.8885 | 1.30294 | 0.651471 | − | 0.758674i | \(-0.274152\pi\) | ||||
0.651471 | + | 0.758674i | \(0.274152\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | 9.88854 | 0.645057 | ||||||||
\(236\) | 4.00000 | 0.260378 | ||||||||
\(237\) | −1.52786 | −0.0992454 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.9443 | 0.837295 | 0.418648 | − | 0.908149i | \(-0.362504\pi\) | ||||
0.418648 | + | 0.908149i | \(0.362504\pi\) | |||||||
\(240\) | −2.00000 | −0.129099 | ||||||||
\(241\) | −26.9443 | −1.73563 | −0.867817 | − | 0.496885i | \(-0.834477\pi\) | ||||
−0.867817 | + | 0.496885i | \(0.834477\pi\) | |||||||
\(242\) | 4.88854 | 0.314247 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.52786 | 0.225848 | ||||||||
\(245\) | 14.0000 | 0.894427 | ||||||||
\(246\) | 6.94427 | 0.442751 | ||||||||
\(247\) | −4.94427 | −0.314596 | ||||||||
\(248\) | −24.0000 | −1.52400 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | −12.0000 | −0.758947 | ||||||||
\(251\) | 28.3607 | 1.79011 | 0.895055 | − | 0.445956i | \(-0.147136\pi\) | ||||
0.895055 | + | 0.445956i | \(0.147136\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.47214 | −0.155422 | ||||||||
\(254\) | −17.8885 | −1.12243 | ||||||||
\(255\) | −8.94427 | −0.560112 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −23.8885 | −1.49013 | −0.745063 | − | 0.666994i | \(-0.767581\pi\) | ||||
−0.745063 | + | 0.666994i | \(0.767581\pi\) | |||||||
\(258\) | −2.47214 | −0.153908 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −12.0000 | −0.741362 | ||||||||
\(263\) | 1.52786 | 0.0942121 | 0.0471061 | − | 0.998890i | \(-0.485000\pi\) | ||||
0.0471061 | + | 0.998890i | \(0.485000\pi\) | |||||||
\(264\) | −7.41641 | −0.456448 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.4164 | −0.821071 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | 17.8885 | 1.08665 | 0.543326 | − | 0.839522i | \(-0.317165\pi\) | ||||
0.543326 | + | 0.839522i | \(0.317165\pi\) | |||||||
\(272\) | 4.47214 | 0.271163 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.52786 | −0.213126 | ||||||||
\(275\) | −2.47214 | −0.149075 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 15.8885 | 0.954650 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(278\) | 0.944272 | 0.0566337 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.9443 | 1.84598 | 0.922990 | − | 0.384823i | \(-0.125738\pi\) | ||||
0.922990 | + | 0.384823i | \(0.125738\pi\) | |||||||
\(282\) | −4.94427 | −0.294427 | ||||||||
\(283\) | 16.9443 | 1.00723 | 0.503616 | − | 0.863927i | \(-0.332003\pi\) | ||||
0.503616 | + | 0.863927i | \(0.332003\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | 4.94427 | 0.292873 | ||||||||
\(286\) | 4.94427 | 0.292361 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.00000 | −0.294628 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 2.00000 | 0.117444 | ||||||||
\(291\) | 9.41641 | 0.552000 | ||||||||
\(292\) | −6.94427 | −0.406383 | ||||||||
\(293\) | −13.4164 | −0.783795 | −0.391897 | − | 0.920009i | \(-0.628181\pi\) | ||||
−0.391897 | + | 0.920009i | \(0.628181\pi\) | |||||||
\(294\) | −7.00000 | −0.408248 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 13.4164 | 0.779813 | ||||||||
\(297\) | −2.47214 | −0.143448 | ||||||||
\(298\) | −10.9443 | −0.633985 | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.9443 | −1.20521 | ||||||||
\(303\) | −18.9443 | −1.08832 | ||||||||
\(304\) | −2.47214 | −0.141787 | ||||||||
\(305\) | 7.05573 | 0.404010 | ||||||||
\(306\) | 4.47214 | 0.255655 | ||||||||
\(307\) | −7.05573 | −0.402692 | −0.201346 | − | 0.979520i | \(-0.564532\pi\) | ||||
−0.201346 | + | 0.979520i | \(0.564532\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9443 | 0.736374 | ||||||||
\(310\) | −16.0000 | −0.908739 | ||||||||
\(311\) | −12.9443 | −0.734002 | −0.367001 | − | 0.930220i | \(-0.619615\pi\) | ||||
−0.367001 | + | 0.930220i | \(0.619615\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | 22.9443 | 1.29689 | 0.648443 | − | 0.761263i | \(-0.275420\pi\) | ||||
0.648443 | + | 0.761263i | \(0.275420\pi\) | |||||||
\(314\) | 3.52786 | 0.199089 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.52786 | −0.0859491 | ||||||||
\(317\) | −2.00000 | −0.112331 | −0.0561656 | − | 0.998421i | \(-0.517887\pi\) | ||||
−0.0561656 | + | 0.998421i | \(0.517887\pi\) | |||||||
\(318\) | −2.00000 | −0.112154 | ||||||||
\(319\) | 2.47214 | 0.138413 | ||||||||
\(320\) | −14.0000 | −0.782624 | ||||||||
\(321\) | 0.944272 | 0.0527041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.0557 | −0.615157 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0.944272 | 0.0522984 | ||||||||
\(327\) | −10.9443 | −0.605220 | ||||||||
\(328\) | 20.8328 | 1.15030 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.94427 | −0.272173 | ||||||||
\(331\) | 29.8885 | 1.64282 | 0.821411 | − | 0.570336i | \(-0.193187\pi\) | ||||
0.821411 | + | 0.570336i | \(0.193187\pi\) | |||||||
\(332\) | −4.00000 | −0.219529 | ||||||||
\(333\) | 4.47214 | 0.245072 | ||||||||
\(334\) | −20.9443 | −1.14602 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.472136 | 0.0257189 | 0.0128594 | − | 0.999917i | \(-0.495907\pi\) | ||||
0.0128594 | + | 0.999917i | \(0.495907\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | −8.47214 | −0.460143 | ||||||||
\(340\) | −8.94427 | −0.485071 | ||||||||
\(341\) | −19.7771 | −1.07099 | ||||||||
\(342\) | −2.47214 | −0.133678 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.41641 | −0.399866 | ||||||||
\(345\) | −2.00000 | −0.107676 | ||||||||
\(346\) | 2.00000 | 0.107521 | ||||||||
\(347\) | 5.88854 | 0.316114 | 0.158057 | − | 0.987430i | \(-0.449477\pi\) | ||||
0.158057 | + | 0.987430i | \(0.449477\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | −27.8885 | −1.49284 | −0.746420 | − | 0.665475i | \(-0.768229\pi\) | ||||
−0.746420 | + | 0.665475i | \(0.768229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | −12.3607 | −0.658826 | ||||||||
\(353\) | 2.00000 | 0.106449 | 0.0532246 | − | 0.998583i | \(-0.483050\pi\) | ||||
0.0532246 | + | 0.998583i | \(0.483050\pi\) | |||||||
\(354\) | −4.00000 | −0.212598 | ||||||||
\(355\) | −16.0000 | −0.849192 | ||||||||
\(356\) | −13.4164 | −0.711068 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.94427 | 0.472719 | ||||||||
\(359\) | 30.4721 | 1.60826 | 0.804129 | − | 0.594455i | \(-0.202632\pi\) | ||||
0.804129 | + | 0.594455i | \(0.202632\pi\) | |||||||
\(360\) | −6.00000 | −0.316228 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 10.0000 | 0.525588 | ||||||||
\(363\) | 4.88854 | 0.256582 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.8885 | −0.726960 | ||||||||
\(366\) | −3.52786 | −0.184404 | ||||||||
\(367\) | 1.52786 | 0.0797539 | 0.0398769 | − | 0.999205i | \(-0.487303\pi\) | ||||
0.0398769 | + | 0.999205i | \(0.487303\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 6.94427 | 0.361504 | ||||||||
\(370\) | 8.94427 | 0.464991 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.00000 | −0.414781 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 11.0557 | 0.571678 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | −14.8328 | −0.764944 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4721 | 0.537917 | 0.268959 | − | 0.963152i | \(-0.413320\pi\) | ||||
0.268959 | + | 0.963152i | \(0.413320\pi\) | |||||||
\(380\) | 4.94427 | 0.253636 | ||||||||
\(381\) | −17.8885 | −0.916458 | ||||||||
\(382\) | 6.47214 | 0.331143 | ||||||||
\(383\) | 19.0557 | 0.973702 | 0.486851 | − | 0.873485i | \(-0.338145\pi\) | ||||
0.486851 | + | 0.873485i | \(0.338145\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.05573 | −0.257330 | ||||||||
\(387\) | −2.47214 | −0.125666 | ||||||||
\(388\) | 9.41641 | 0.478046 | ||||||||
\(389\) | −13.4164 | −0.680239 | −0.340119 | − | 0.940382i | \(-0.610468\pi\) | ||||
−0.340119 | + | 0.940382i | \(0.610468\pi\) | |||||||
\(390\) | 4.00000 | 0.202548 | ||||||||
\(391\) | 4.47214 | 0.226166 | ||||||||
\(392\) | −21.0000 | −1.06066 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 10.0000 | 0.503793 | ||||||||
\(395\) | −3.05573 | −0.153750 | ||||||||
\(396\) | −2.47214 | −0.124230 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 12.9443 | 0.648838 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 6.94427 | 0.346780 | 0.173390 | − | 0.984853i | \(-0.444528\pi\) | ||||
0.173390 | + | 0.984853i | \(0.444528\pi\) | |||||||
\(402\) | −4.00000 | −0.199502 | ||||||||
\(403\) | 16.0000 | 0.797017 | ||||||||
\(404\) | −18.9443 | −0.942513 | ||||||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0557 | 0.548012 | ||||||||
\(408\) | 13.4164 | 0.664211 | ||||||||
\(409\) | −9.05573 | −0.447777 | −0.223888 | − | 0.974615i | \(-0.571875\pi\) | ||||
−0.223888 | + | 0.974615i | \(0.571875\pi\) | |||||||
\(410\) | 13.8885 | 0.685906 | ||||||||
\(411\) | −3.52786 | −0.174017 | ||||||||
\(412\) | 12.9443 | 0.637719 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 10.0000 | 0.490290 | ||||||||
\(417\) | 0.944272 | 0.0462412 | ||||||||
\(418\) | −6.11146 | −0.298921 | ||||||||
\(419\) | −21.8885 | −1.06933 | −0.534663 | − | 0.845066i | \(-0.679561\pi\) | ||||
−0.534663 | + | 0.845066i | \(0.679561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5279 | −0.561834 | −0.280917 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280917 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(422\) | 16.9443 | 0.824834 | ||||||||
\(423\) | −4.94427 | −0.240399 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 4.47214 | 0.216930 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.944272 | 0.0456431 | ||||||||
\(429\) | 4.94427 | 0.238712 | ||||||||
\(430\) | −4.94427 | −0.238434 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −6.36068 | −0.305675 | −0.152837 | − | 0.988251i | \(-0.548841\pi\) | ||||
−0.152837 | + | 0.988251i | \(0.548841\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | −10.9443 | −0.524136 | ||||||||
\(437\) | −2.47214 | −0.118258 | ||||||||
\(438\) | 6.94427 | 0.331810 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | −14.8328 | −0.707127 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | −8.94427 | −0.425436 | ||||||||
\(443\) | 26.8328 | 1.27487 | 0.637433 | − | 0.770506i | \(-0.279996\pi\) | ||||
0.637433 | + | 0.770506i | \(0.279996\pi\) | |||||||
\(444\) | 4.47214 | 0.212238 | ||||||||
\(445\) | −26.8328 | −1.27200 | ||||||||
\(446\) | −25.8885 | −1.22586 | ||||||||
\(447\) | −10.9443 | −0.517646 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.9443 | −1.27158 | −0.635789 | − | 0.771863i | \(-0.719325\pi\) | ||||
−0.635789 | + | 0.771863i | \(0.719325\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 17.1672 | 0.808371 | ||||||||
\(452\) | −8.47214 | −0.398496 | ||||||||
\(453\) | −20.9443 | −0.984048 | ||||||||
\(454\) | 21.8885 | 1.02728 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.41641 | −0.347305 | ||||||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | −17.4164 | −0.813815 | ||||||||
\(459\) | 4.47214 | 0.208741 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9443 | 0.601571 | 0.300786 | − | 0.953692i | \(-0.402751\pi\) | ||||
0.300786 | + | 0.953692i | \(0.402751\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −16.0000 | −0.741982 | ||||||||
\(466\) | −19.8885 | −0.921319 | ||||||||
\(467\) | −34.4721 | −1.59518 | −0.797590 | − | 0.603200i | \(-0.793892\pi\) | ||||
−0.797590 | + | 0.603200i | \(0.793892\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.88854 | −0.456125 | ||||||||
\(471\) | 3.52786 | 0.162555 | ||||||||
\(472\) | −12.0000 | −0.552345 | ||||||||
\(473\) | −6.11146 | −0.281005 | ||||||||
\(474\) | 1.52786 | 0.0701771 | ||||||||
\(475\) | −2.47214 | −0.113429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | −12.9443 | −0.592057 | ||||||||
\(479\) | 42.2492 | 1.93042 | 0.965208 | − | 0.261483i | \(-0.0842115\pi\) | ||||
0.965208 | + | 0.261483i | \(0.0842115\pi\) | |||||||
\(480\) | −10.0000 | −0.456435 | ||||||||
\(481\) | −8.94427 | −0.407824 | ||||||||
\(482\) | 26.9443 | 1.22728 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.88854 | 0.222207 | ||||||||
\(485\) | 18.8328 | 0.855154 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −11.0557 | −0.500983 | −0.250491 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250491 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(488\) | −10.5836 | −0.479097 | ||||||||
\(489\) | 0.944272 | 0.0427015 | ||||||||
\(490\) | −14.0000 | −0.632456 | ||||||||
\(491\) | −2.11146 | −0.0952887 | −0.0476443 | − | 0.998864i | \(-0.515171\pi\) | ||||
−0.0476443 | + | 0.998864i | \(0.515171\pi\) | |||||||
\(492\) | 6.94427 | 0.313072 | ||||||||
\(493\) | −4.47214 | −0.201415 | ||||||||
\(494\) | 4.94427 | 0.222453 | ||||||||
\(495\) | −4.94427 | −0.222228 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.00000 | 0.179244 | ||||||||
\(499\) | 32.9443 | 1.47479 | 0.737394 | − | 0.675463i | \(-0.236056\pi\) | ||||
0.737394 | + | 0.675463i | \(0.236056\pi\) | |||||||
\(500\) | −12.0000 | −0.536656 | ||||||||
\(501\) | −20.9443 | −0.935721 | ||||||||
\(502\) | −28.3607 | −1.26580 | ||||||||
\(503\) | 17.5279 | 0.781529 | 0.390764 | − | 0.920491i | \(-0.372211\pi\) | ||||
0.390764 | + | 0.920491i | \(0.372211\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.8885 | −1.68602 | ||||||||
\(506\) | 2.47214 | 0.109900 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | −17.8885 | −0.793676 | ||||||||
\(509\) | 33.7771 | 1.49714 | 0.748572 | − | 0.663054i | \(-0.230740\pi\) | ||||
0.748572 | + | 0.663054i | \(0.230740\pi\) | |||||||
\(510\) | 8.94427 | 0.396059 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | −2.47214 | −0.109147 | ||||||||
\(514\) | 23.8885 | 1.05368 | ||||||||
\(515\) | 25.8885 | 1.14079 | ||||||||
\(516\) | −2.47214 | −0.108830 | ||||||||
\(517\) | −12.2229 | −0.537563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 12.0000 | 0.526235 | ||||||||
\(521\) | −10.9443 | −0.479477 | −0.239739 | − | 0.970837i | \(-0.577062\pi\) | ||||
−0.239739 | + | 0.970837i | \(0.577062\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | 13.8885 | 0.607304 | 0.303652 | − | 0.952783i | \(-0.401794\pi\) | ||||
0.303652 | + | 0.952783i | \(0.401794\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.52786 | −0.0666180 | ||||||||
\(527\) | 35.7771 | 1.55847 | ||||||||
\(528\) | 2.47214 | 0.107586 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.00000 | −0.173749 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.8885 | −0.601580 | ||||||||
\(534\) | 13.4164 | 0.580585 | ||||||||
\(535\) | 1.88854 | 0.0816489 | ||||||||
\(536\) | −12.0000 | −0.518321 | ||||||||
\(537\) | 8.94427 | 0.385974 | ||||||||
\(538\) | −14.0000 | −0.603583 | ||||||||
\(539\) | −17.3050 | −0.745377 | ||||||||
\(540\) | −2.00000 | −0.0860663 | ||||||||
\(541\) | −8.83282 | −0.379752 | −0.189876 | − | 0.981808i | \(-0.560809\pi\) | ||||
−0.189876 | + | 0.981808i | \(0.560809\pi\) | |||||||
\(542\) | −17.8885 | −0.768379 | ||||||||
\(543\) | 10.0000 | 0.429141 | ||||||||
\(544\) | 22.3607 | 0.958706 | ||||||||
\(545\) | −21.8885 | −0.937602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.88854 | −0.251776 | −0.125888 | − | 0.992044i | \(-0.540178\pi\) | ||||
−0.125888 | + | 0.992044i | \(0.540178\pi\) | |||||||
\(548\) | −3.52786 | −0.150703 | ||||||||
\(549\) | −3.52786 | −0.150566 | ||||||||
\(550\) | 2.47214 | 0.105412 | ||||||||
\(551\) | 2.47214 | 0.105317 | ||||||||
\(552\) | 3.00000 | 0.127688 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.8885 | −0.675040 | ||||||||
\(555\) | 8.94427 | 0.379663 | ||||||||
\(556\) | 0.944272 | 0.0400460 | ||||||||
\(557\) | 15.8885 | 0.673219 | 0.336610 | − | 0.941644i | \(-0.390720\pi\) | ||||
0.336610 | + | 0.941644i | \(0.390720\pi\) | |||||||
\(558\) | 8.00000 | 0.338667 | ||||||||
\(559\) | 4.94427 | 0.209120 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.0557 | 0.466773 | ||||||||
\(562\) | −30.9443 | −1.30531 | ||||||||
\(563\) | 7.41641 | 0.312564 | 0.156282 | − | 0.987712i | \(-0.450049\pi\) | ||||
0.156282 | + | 0.987712i | \(0.450049\pi\) | |||||||
\(564\) | −4.94427 | −0.208191 | ||||||||
\(565\) | −16.9443 | −0.712851 | ||||||||
\(566\) | −16.9443 | −0.712221 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.0000 | 1.00702 | ||||||||
\(569\) | 32.4721 | 1.36130 | 0.680651 | − | 0.732607i | \(-0.261697\pi\) | ||||
0.680651 | + | 0.732607i | \(0.261697\pi\) | |||||||
\(570\) | −4.94427 | −0.207093 | ||||||||
\(571\) | −24.9443 | −1.04389 | −0.521943 | − | 0.852981i | \(-0.674793\pi\) | ||||
−0.521943 | + | 0.852981i | \(0.674793\pi\) | |||||||
\(572\) | 4.94427 | 0.206730 | ||||||||
\(573\) | 6.47214 | 0.270377 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | −26.9443 | −1.12170 | −0.560852 | − | 0.827916i | \(-0.689526\pi\) | ||||
−0.560852 | + | 0.827916i | \(0.689526\pi\) | |||||||
\(578\) | −3.00000 | −0.124784 | ||||||||
\(579\) | −5.05573 | −0.210109 | ||||||||
\(580\) | 2.00000 | 0.0830455 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.41641 | −0.390323 | ||||||||
\(583\) | −4.94427 | −0.204771 | ||||||||
\(584\) | 20.8328 | 0.862068 | ||||||||
\(585\) | 4.00000 | 0.165380 | ||||||||
\(586\) | 13.4164 | 0.554227 | ||||||||
\(587\) | 8.94427 | 0.369170 | 0.184585 | − | 0.982817i | \(-0.440906\pi\) | ||||
0.184585 | + | 0.982817i | \(0.440906\pi\) | |||||||
\(588\) | −7.00000 | −0.288675 | ||||||||
\(589\) | −19.7771 | −0.814901 | ||||||||
\(590\) | −8.00000 | −0.329355 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | −4.47214 | −0.183804 | ||||||||
\(593\) | −23.8885 | −0.980985 | −0.490492 | − | 0.871445i | \(-0.663183\pi\) | ||||
−0.490492 | + | 0.871445i | \(0.663183\pi\) | |||||||
\(594\) | 2.47214 | 0.101433 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.9443 | −0.448295 | ||||||||
\(597\) | 12.9443 | 0.529774 | ||||||||
\(598\) | −2.00000 | −0.0817861 | ||||||||
\(599\) | −3.05573 | −0.124854 | −0.0624268 | − | 0.998050i | \(-0.519884\pi\) | ||||
−0.0624268 | + | 0.998050i | \(0.519884\pi\) | |||||||
\(600\) | 3.00000 | 0.122474 | ||||||||
\(601\) | −2.94427 | −0.120099 | −0.0600497 | − | 0.998195i | \(-0.519126\pi\) | ||||
−0.0600497 | + | 0.998195i | \(0.519126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | −20.9443 | −0.852210 | ||||||||
\(605\) | 9.77709 | 0.397495 | ||||||||
\(606\) | 18.9443 | 0.769558 | ||||||||
\(607\) | −30.8328 | −1.25147 | −0.625733 | − | 0.780038i | \(-0.715200\pi\) | ||||
−0.625733 | + | 0.780038i | \(0.715200\pi\) | |||||||
\(608\) | −12.3607 | −0.501292 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.05573 | −0.285678 | ||||||||
\(611\) | 9.88854 | 0.400048 | ||||||||
\(612\) | 4.47214 | 0.180775 | ||||||||
\(613\) | 44.8328 | 1.81078 | 0.905390 | − | 0.424581i | \(-0.139578\pi\) | ||||
0.905390 | + | 0.424581i | \(0.139578\pi\) | |||||||
\(614\) | 7.05573 | 0.284746 | ||||||||
\(615\) | 13.8885 | 0.560040 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.472136 | 0.0190075 | 0.00950374 | − | 0.999955i | \(-0.496975\pi\) | ||||
0.00950374 | + | 0.999955i | \(0.496975\pi\) | |||||||
\(618\) | −12.9443 | −0.520695 | ||||||||
\(619\) | 0.583592 | 0.0234565 | 0.0117283 | − | 0.999931i | \(-0.496267\pi\) | ||||
0.0117283 | + | 0.999931i | \(0.496267\pi\) | |||||||
\(620\) | −16.0000 | −0.642575 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 12.9443 | 0.519018 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −22.9443 | −0.917038 | ||||||||
\(627\) | −6.11146 | −0.244068 | ||||||||
\(628\) | 3.52786 | 0.140777 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0557 | 0.758597 | 0.379298 | − | 0.925274i | \(-0.376165\pi\) | ||||
0.379298 | + | 0.925274i | \(0.376165\pi\) | |||||||
\(632\) | 4.58359 | 0.182326 | ||||||||
\(633\) | 16.9443 | 0.673474 | ||||||||
\(634\) | 2.00000 | 0.0794301 | ||||||||
\(635\) | −35.7771 | −1.41977 | ||||||||
\(636\) | −2.00000 | −0.0793052 | ||||||||
\(637\) | 14.0000 | 0.554700 | ||||||||
\(638\) | −2.47214 | −0.0978728 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | −6.00000 | −0.237171 | ||||||||
\(641\) | −23.5279 | −0.929295 | −0.464647 | − | 0.885496i | \(-0.653819\pi\) | ||||
−0.464647 | + | 0.885496i | \(0.653819\pi\) | |||||||
\(642\) | −0.944272 | −0.0372674 | ||||||||
\(643\) | −13.8885 | −0.547711 | −0.273855 | − | 0.961771i | \(-0.588299\pi\) | ||||
−0.273855 | + | 0.961771i | \(0.588299\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.94427 | −0.194681 | ||||||||
\(646\) | 11.0557 | 0.434982 | ||||||||
\(647\) | −27.7771 | −1.09203 | −0.546015 | − | 0.837775i | \(-0.683856\pi\) | ||||
−0.546015 | + | 0.837775i | \(0.683856\pi\) | |||||||
\(648\) | 3.00000 | 0.117851 | ||||||||
\(649\) | −9.88854 | −0.388159 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.944272 | 0.0369805 | ||||||||
\(653\) | −30.9443 | −1.21094 | −0.605471 | − | 0.795867i | \(-0.707015\pi\) | ||||
−0.605471 | + | 0.795867i | \(0.707015\pi\) | |||||||
\(654\) | 10.9443 | 0.427955 | ||||||||
\(655\) | −24.0000 | −0.937758 | ||||||||
\(656\) | −6.94427 | −0.271128 | ||||||||
\(657\) | 6.94427 | 0.270922 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.58359 | −0.334369 | −0.167185 | − | 0.985926i | \(-0.553468\pi\) | ||||
−0.167185 | + | 0.985926i | \(0.553468\pi\) | |||||||
\(660\) | −4.94427 | −0.192456 | ||||||||
\(661\) | 34.9443 | 1.35917 | 0.679587 | − | 0.733595i | \(-0.262159\pi\) | ||||
0.679587 | + | 0.733595i | \(0.262159\pi\) | |||||||
\(662\) | −29.8885 | −1.16165 | ||||||||
\(663\) | −8.94427 | −0.347367 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.47214 | −0.173292 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −20.9443 | −0.810358 | ||||||||
\(669\) | −25.8885 | −1.00091 | ||||||||
\(670\) | −8.00000 | −0.309067 | ||||||||
\(671\) | −8.72136 | −0.336684 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | −0.472136 | −0.0181860 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | 28.4721 | 1.09427 | 0.547137 | − | 0.837043i | \(-0.315718\pi\) | ||||
0.547137 | + | 0.837043i | \(0.315718\pi\) | |||||||
\(678\) | 8.47214 | 0.325370 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 26.8328 | 1.02899 | ||||||||
\(681\) | 21.8885 | 0.838771 | ||||||||
\(682\) | 19.7771 | 0.757304 | ||||||||
\(683\) | 15.0557 | 0.576091 | 0.288046 | − | 0.957617i | \(-0.406994\pi\) | ||||
0.288046 | + | 0.957617i | \(0.406994\pi\) | |||||||
\(684\) | −2.47214 | −0.0945245 | ||||||||
\(685\) | −7.05573 | −0.269586 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.4164 | −0.664477 | ||||||||
\(688\) | 2.47214 | 0.0942493 | ||||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 2.00000 | 0.0761387 | ||||||||
\(691\) | 10.8328 | 0.412100 | 0.206050 | − | 0.978541i | \(-0.433939\pi\) | ||||
0.206050 | + | 0.978541i | \(0.433939\pi\) | |||||||
\(692\) | 2.00000 | 0.0760286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.88854 | −0.223526 | ||||||||
\(695\) | 1.88854 | 0.0716366 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | −31.0557 | −1.17632 | ||||||||
\(698\) | 27.8885 | 1.05560 | ||||||||
\(699\) | −19.8885 | −0.752254 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.0557 | 0.946342 | 0.473171 | − | 0.880971i | \(-0.343109\pi\) | ||||
0.473171 | + | 0.880971i | \(0.343109\pi\) | |||||||
\(702\) | −2.00000 | −0.0754851 | ||||||||
\(703\) | 11.0557 | 0.416975 | ||||||||
\(704\) | 17.3050 | 0.652205 | ||||||||
\(705\) | −9.88854 | −0.372424 | ||||||||
\(706\) | −2.00000 | −0.0752710 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | −0.111456 | −0.00418582 | −0.00209291 | − | 0.999998i | \(-0.500666\pi\) | ||||
−0.00209291 | + | 0.999998i | \(0.500666\pi\) | |||||||
\(710\) | 16.0000 | 0.600469 | ||||||||
\(711\) | 1.52786 | 0.0572994 | ||||||||
\(712\) | 40.2492 | 1.50840 | ||||||||
\(713\) | 8.00000 | 0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.88854 | 0.369811 | ||||||||
\(716\) | 8.94427 | 0.334263 | ||||||||
\(717\) | −12.9443 | −0.483413 | ||||||||
\(718\) | −30.4721 | −1.13721 | ||||||||
\(719\) | −28.9443 | −1.07944 | −0.539720 | − | 0.841845i | \(-0.681470\pi\) | ||||
−0.539720 | + | 0.841845i | \(0.681470\pi\) | |||||||
\(720\) | 2.00000 | 0.0745356 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.8885 | 0.479662 | ||||||||
\(723\) | 26.9443 | 1.00207 | ||||||||
\(724\) | 10.0000 | 0.371647 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | −4.88854 | −0.181431 | ||||||||
\(727\) | 48.3607 | 1.79360 | 0.896799 | − | 0.442438i | \(-0.145886\pi\) | ||||
0.896799 | + | 0.442438i | \(0.145886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.8885 | 0.514038 | ||||||||
\(731\) | 11.0557 | 0.408911 | ||||||||
\(732\) | −3.52786 | −0.130394 | ||||||||
\(733\) | −42.3607 | −1.56463 | −0.782314 | − | 0.622885i | \(-0.785961\pi\) | ||||
−0.782314 | + | 0.622885i | \(0.785961\pi\) | |||||||
\(734\) | −1.52786 | −0.0563945 | ||||||||
\(735\) | −14.0000 | −0.516398 | ||||||||
\(736\) | 5.00000 | 0.184302 | ||||||||
\(737\) | −9.88854 | −0.364249 | ||||||||
\(738\) | −6.94427 | −0.255622 | ||||||||
\(739\) | 31.0557 | 1.14240 | 0.571202 | − | 0.820810i | \(-0.306477\pi\) | ||||
0.571202 | + | 0.820810i | \(0.306477\pi\) | |||||||
\(740\) | 8.94427 | 0.328798 | ||||||||
\(741\) | 4.94427 | 0.181632 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.2492 | −1.25648 | −0.628241 | − | 0.778019i | \(-0.716225\pi\) | ||||
−0.628241 | + | 0.778019i | \(0.716225\pi\) | |||||||
\(744\) | 24.0000 | 0.879883 | ||||||||
\(745\) | −21.8885 | −0.801934 | ||||||||
\(746\) | −6.00000 | −0.219676 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 11.0557 | 0.404237 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.0000 | 0.438178 | ||||||||
\(751\) | 33.5279 | 1.22345 | 0.611725 | − | 0.791071i | \(-0.290476\pi\) | ||||
0.611725 | + | 0.791071i | \(0.290476\pi\) | |||||||
\(752\) | 4.94427 | 0.180299 | ||||||||
\(753\) | −28.3607 | −1.03352 | ||||||||
\(754\) | 2.00000 | 0.0728357 | ||||||||
\(755\) | −41.8885 | −1.52448 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4721 | −0.889455 | −0.444727 | − | 0.895666i | \(-0.646699\pi\) | ||||
−0.444727 | + | 0.895666i | \(0.646699\pi\) | |||||||
\(758\) | −10.4721 | −0.380365 | ||||||||
\(759\) | 2.47214 | 0.0897329 | ||||||||
\(760\) | −14.8328 | −0.538043 | ||||||||
\(761\) | 45.7771 | 1.65942 | 0.829709 | − | 0.558196i | \(-0.188506\pi\) | ||||
0.829709 | + | 0.558196i | \(0.188506\pi\) | |||||||
\(762\) | 17.8885 | 0.648034 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.47214 | 0.234154 | ||||||||
\(765\) | 8.94427 | 0.323381 | ||||||||
\(766\) | −19.0557 | −0.688511 | ||||||||
\(767\) | 8.00000 | 0.288863 | ||||||||
\(768\) | 17.0000 | 0.613435 | ||||||||
\(769\) | 23.3050 | 0.840398 | 0.420199 | − | 0.907432i | \(-0.361960\pi\) | ||||
0.420199 | + | 0.907432i | \(0.361960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8885 | 0.860325 | ||||||||
\(772\) | −5.05573 | −0.181960 | ||||||||
\(773\) | −6.58359 | −0.236795 | −0.118398 | − | 0.992966i | \(-0.537776\pi\) | ||||
−0.118398 | + | 0.992966i | \(0.537776\pi\) | |||||||
\(774\) | 2.47214 | 0.0888591 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | −28.2492 | −1.01409 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.4164 | 0.481002 | ||||||||
\(779\) | 17.1672 | 0.615078 | ||||||||
\(780\) | 4.00000 | 0.143223 | ||||||||
\(781\) | 19.7771 | 0.707680 | ||||||||
\(782\) | −4.47214 | −0.159923 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | 7.05573 | 0.251830 | ||||||||
\(786\) | 12.0000 | 0.428026 | ||||||||
\(787\) | −10.1115 | −0.360434 | −0.180217 | − | 0.983627i | \(-0.557680\pi\) | ||||
−0.180217 | + | 0.983627i | \(0.557680\pi\) | |||||||
\(788\) | 10.0000 | 0.356235 | ||||||||
\(789\) | −1.52786 | −0.0543934 | ||||||||
\(790\) | 3.05573 | 0.108718 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.41641 | 0.263531 | ||||||||
\(793\) | 7.05573 | 0.250556 | ||||||||
\(794\) | 2.00000 | 0.0709773 | ||||||||
\(795\) | −4.00000 | −0.141865 | ||||||||
\(796\) | 12.9443 | 0.458798 | ||||||||
\(797\) | −50.3607 | −1.78387 | −0.891933 | − | 0.452167i | \(-0.850651\pi\) | ||||
−0.891933 | + | 0.452167i | \(0.850651\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.1115 | 0.782247 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | 13.4164 | 0.474045 | ||||||||
\(802\) | −6.94427 | −0.245211 | ||||||||
\(803\) | 17.1672 | 0.605817 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.0000 | −0.563576 | ||||||||
\(807\) | −14.0000 | −0.492823 | ||||||||
\(808\) | 56.8328 | 1.99937 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 2.00000 | 0.0702728 | ||||||||
\(811\) | 12.0000 | 0.421377 | 0.210688 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210688 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.8885 | −0.627379 | ||||||||
\(814\) | −11.0557 | −0.387503 | ||||||||
\(815\) | 1.88854 | 0.0661528 | ||||||||
\(816\) | −4.47214 | −0.156556 | ||||||||
\(817\) | −6.11146 | −0.213813 | ||||||||
\(818\) | 9.05573 | 0.316626 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.8885 | 0.485009 | ||||||||
\(821\) | 31.8885 | 1.11292 | 0.556459 | − | 0.830875i | \(-0.312160\pi\) | ||||
0.556459 | + | 0.830875i | \(0.312160\pi\) | |||||||
\(822\) | 3.52786 | 0.123048 | ||||||||
\(823\) | 44.9443 | 1.56666 | 0.783329 | − | 0.621607i | \(-0.213520\pi\) | ||||
0.783329 | + | 0.621607i | \(0.213520\pi\) | |||||||
\(824\) | −38.8328 | −1.35281 | ||||||||
\(825\) | 2.47214 | 0.0860687 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.2492 | −1.05187 | −0.525934 | − | 0.850525i | \(-0.676284\pi\) | ||||
−0.525934 | + | 0.850525i | \(0.676284\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −14.9443 | −0.519036 | −0.259518 | − | 0.965738i | \(-0.583564\pi\) | ||||
−0.259518 | + | 0.965738i | \(0.583564\pi\) | |||||||
\(830\) | 8.00000 | 0.277684 | ||||||||
\(831\) | −15.8885 | −0.551167 | ||||||||
\(832\) | −14.0000 | −0.485363 | ||||||||
\(833\) | 31.3050 | 1.08465 | ||||||||
\(834\) | −0.944272 | −0.0326975 | ||||||||
\(835\) | −41.8885 | −1.44961 | ||||||||
\(836\) | −6.11146 | −0.211369 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 21.8885 | 0.756127 | ||||||||
\(839\) | 40.3607 | 1.39341 | 0.696703 | − | 0.717360i | \(-0.254650\pi\) | ||||
0.696703 | + | 0.717360i | \(0.254650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 11.5279 | 0.397276 | ||||||||
\(843\) | −30.9443 | −1.06578 | ||||||||
\(844\) | 16.9443 | 0.583246 | ||||||||
\(845\) | 18.0000 | 0.619219 | ||||||||
\(846\) | 4.94427 | 0.169988 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | −16.9443 | −0.581526 | ||||||||
\(850\) | −4.47214 | −0.153393 | ||||||||
\(851\) | −4.47214 | −0.153303 | ||||||||
\(852\) | 8.00000 | 0.274075 | ||||||||
\(853\) | −45.7771 | −1.56738 | −0.783689 | − | 0.621154i | \(-0.786664\pi\) | ||||
−0.783689 | + | 0.621154i | \(0.786664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.94427 | −0.169091 | ||||||||
\(856\) | −2.83282 | −0.0968236 | ||||||||
\(857\) | −41.7771 | −1.42708 | −0.713539 | − | 0.700615i | \(-0.752909\pi\) | ||||
−0.713539 | + | 0.700615i | \(0.752909\pi\) | |||||||
\(858\) | −4.94427 | −0.168795 | ||||||||
\(859\) | −2.11146 | −0.0720420 | −0.0360210 | − | 0.999351i | \(-0.511468\pi\) | ||||
−0.0360210 | + | 0.999351i | \(0.511468\pi\) | |||||||
\(860\) | −4.94427 | −0.168598 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.8328 | 0.777238 | 0.388619 | − | 0.921399i | \(-0.372952\pi\) | ||||
0.388619 | + | 0.921399i | \(0.372952\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 4.00000 | 0.136004 | ||||||||
\(866\) | 6.36068 | 0.216145 | ||||||||
\(867\) | −3.00000 | −0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.77709 | 0.128129 | ||||||||
\(870\) | −2.00000 | −0.0678064 | ||||||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 32.8328 | 1.11186 | ||||||||
\(873\) | −9.41641 | −0.318697 | ||||||||
\(874\) | 2.47214 | 0.0836212 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.94427 | 0.234625 | ||||||||
\(877\) | 4.11146 | 0.138834 | 0.0694170 | − | 0.997588i | \(-0.477886\pi\) | ||||
0.0694170 | + | 0.997588i | \(0.477886\pi\) | |||||||
\(878\) | −8.00000 | −0.269987 | ||||||||
\(879\) | 13.4164 | 0.452524 | ||||||||
\(880\) | 4.94427 | 0.166671 | ||||||||
\(881\) | 11.5279 | 0.388384 | 0.194192 | − | 0.980964i | \(-0.437792\pi\) | ||||
0.194192 | + | 0.980964i | \(0.437792\pi\) | |||||||
\(882\) | 7.00000 | 0.235702 | ||||||||
\(883\) | 0.944272 | 0.0317773 | 0.0158886 | − | 0.999874i | \(-0.494942\pi\) | ||||
0.0158886 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(884\) | −8.94427 | −0.300828 | ||||||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | −26.8328 | −0.901466 | ||||||||
\(887\) | 9.88854 | 0.332025 | 0.166012 | − | 0.986124i | \(-0.446911\pi\) | ||||
0.166012 | + | 0.986124i | \(0.446911\pi\) | |||||||
\(888\) | −13.4164 | −0.450225 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 26.8328 | 0.899438 | ||||||||
\(891\) | 2.47214 | 0.0828197 | ||||||||
\(892\) | −25.8885 | −0.866813 | ||||||||
\(893\) | −12.2229 | −0.409024 | ||||||||
\(894\) | 10.9443 | 0.366031 | ||||||||
\(895\) | 17.8885 | 0.597948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 26.9443 | 0.899142 | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 8.94427 | 0.297977 | ||||||||
\(902\) | −17.1672 | −0.571605 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.4164 | 0.845337 | ||||||||
\(905\) | 20.0000 | 0.664822 | ||||||||
\(906\) | 20.9443 | 0.695827 | ||||||||
\(907\) | −34.4721 | −1.14463 | −0.572314 | − | 0.820034i | \(-0.693954\pi\) | ||||
−0.572314 | + | 0.820034i | \(0.693954\pi\) | |||||||
\(908\) | 21.8885 | 0.726397 | ||||||||
\(909\) | 18.9443 | 0.628342 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.3607 | −0.542054 | −0.271027 | − | 0.962572i | \(-0.587363\pi\) | ||||
−0.271027 | + | 0.962572i | \(0.587363\pi\) | |||||||
\(912\) | 2.47214 | 0.0818606 | ||||||||
\(913\) | 9.88854 | 0.327263 | ||||||||
\(914\) | 6.00000 | 0.198462 | ||||||||
\(915\) | −7.05573 | −0.233255 | ||||||||
\(916\) | −17.4164 | −0.575454 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.47214 | −0.147602 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 6.00000 | 0.197814 | ||||||||
\(921\) | 7.05573 | 0.232494 | ||||||||
\(922\) | 18.0000 | 0.592798 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.47214 | −0.147043 | ||||||||
\(926\) | −12.9443 | −0.425375 | ||||||||
\(927\) | −12.9443 | −0.425146 | ||||||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | −33.7771 | −1.10819 | −0.554095 | − | 0.832453i | \(-0.686936\pi\) | ||||
−0.554095 | + | 0.832453i | \(0.686936\pi\) | |||||||
\(930\) | 16.0000 | 0.524661 | ||||||||
\(931\) | −17.3050 | −0.567147 | ||||||||
\(932\) | −19.8885 | −0.651471 | ||||||||
\(933\) | 12.9443 | 0.423776 | ||||||||
\(934\) | 34.4721 | 1.12796 | ||||||||
\(935\) | 22.1115 | 0.723122 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 35.8885 | 1.17243 | 0.586214 | − | 0.810156i | \(-0.300618\pi\) | ||||
0.586214 | + | 0.810156i | \(0.300618\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.9443 | −0.748758 | ||||||||
\(940\) | −9.88854 | −0.322529 | ||||||||
\(941\) | 6.00000 | 0.195594 | 0.0977972 | − | 0.995206i | \(-0.468820\pi\) | ||||
0.0977972 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(942\) | −3.52786 | −0.114944 | ||||||||
\(943\) | −6.94427 | −0.226137 | ||||||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.11146 | 0.198701 | ||||||||
\(947\) | −10.1115 | −0.328578 | −0.164289 | − | 0.986412i | \(-0.552533\pi\) | ||||
−0.164289 | + | 0.986412i | \(0.552533\pi\) | |||||||
\(948\) | 1.52786 | 0.0496227 | ||||||||
\(949\) | −13.8885 | −0.450841 | ||||||||
\(950\) | 2.47214 | 0.0802067 | ||||||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.8328 | 1.32270 | 0.661352 | − | 0.750075i | \(-0.269983\pi\) | ||||
0.661352 | + | 0.750075i | \(0.269983\pi\) | |||||||
\(954\) | 2.00000 | 0.0647524 | ||||||||
\(955\) | 12.9443 | 0.418867 | ||||||||
\(956\) | −12.9443 | −0.418648 | ||||||||
\(957\) | −2.47214 | −0.0799128 | ||||||||
\(958\) | −42.2492 | −1.36501 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 14.0000 | 0.451848 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 8.94427 | 0.288375 | ||||||||
\(963\) | −0.944272 | −0.0304287 | ||||||||
\(964\) | 26.9443 | 0.867817 | ||||||||
\(965\) | −10.1115 | −0.325499 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.7214 | 1.05225 | 0.526124 | − | 0.850408i | \(-0.323645\pi\) | ||||
0.526124 | + | 0.850408i | \(0.323645\pi\) | |||||||
\(968\) | −14.6656 | −0.471371 | ||||||||
\(969\) | 11.0557 | 0.355161 | ||||||||
\(970\) | −18.8328 | −0.604685 | ||||||||
\(971\) | −36.3607 | −1.16687 | −0.583435 | − | 0.812160i | \(-0.698292\pi\) | ||||
−0.583435 | + | 0.812160i | \(0.698292\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.0557 | 0.354248 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 3.52786 | 0.112924 | ||||||||
\(977\) | 0.111456 | 0.00356580 | 0.00178290 | − | 0.999998i | \(-0.499432\pi\) | ||||
0.00178290 | + | 0.999998i | \(0.499432\pi\) | |||||||
\(978\) | −0.944272 | −0.0301945 | ||||||||
\(979\) | 33.1672 | 1.06003 | ||||||||
\(980\) | −14.0000 | −0.447214 | ||||||||
\(981\) | 10.9443 | 0.349424 | ||||||||
\(982\) | 2.11146 | 0.0673793 | ||||||||
\(983\) | 8.36068 | 0.266664 | 0.133332 | − | 0.991071i | \(-0.457432\pi\) | ||||
0.133332 | + | 0.991071i | \(0.457432\pi\) | |||||||
\(984\) | −20.8328 | −0.664126 | ||||||||
\(985\) | 20.0000 | 0.637253 | ||||||||
\(986\) | 4.47214 | 0.142422 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.94427 | 0.157298 | ||||||||
\(989\) | 2.47214 | 0.0786094 | ||||||||
\(990\) | 4.94427 | 0.157139 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 40.0000 | 1.27000 | ||||||||
\(993\) | −29.8885 | −0.948484 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.8885 | 0.820722 | ||||||||
\(996\) | 4.00000 | 0.126745 | ||||||||
\(997\) | 18.9443 | 0.599971 | 0.299986 | − | 0.953944i | \(-0.403018\pi\) | ||||
0.299986 | + | 0.953944i | \(0.403018\pi\) | |||||||
\(998\) | −32.9443 | −1.04283 | ||||||||
\(999\) | −4.47214 | −0.141492 |
(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 | 2001.2.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6003.2.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6003.2.a.f.1.1 | 2 | 3.2 | odd | 2 |