Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.618034 | 0.437016 | 0.218508 | − | 0.975835i | \(-0.429881\pi\) | ||||
0.218508 | + | 0.975835i | \(0.429881\pi\) | |||||||
\(3\) | 0.381966 | 0.220528 | 0.110264 | − | 0.993902i | \(-0.464830\pi\) | ||||
0.110264 | + | 0.993902i | \(0.464830\pi\) | |||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 1.61803 | 0.723607 | 0.361803 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361803 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(6\) | 0.236068 | 0.0963743 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.23607 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.618034 | 0.159576 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −1.47214 | −0.357045 | −0.178523 | − | 0.983936i | \(-0.557132\pi\) | ||||
−0.178523 | + | 0.983936i | \(0.557132\pi\) | |||||||
\(18\) | −1.76393 | −0.415763 | ||||||||
\(19\) | 4.85410 | 1.11361 | 0.556804 | − | 0.830644i | \(-0.312028\pi\) | ||||
0.556804 | + | 0.830644i | \(0.312028\pi\) | |||||||
\(20\) | −2.61803 | −0.585410 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.38197 | −0.294636 | ||||||||
\(23\) | 0.381966 | 0.0796454 | 0.0398227 | − | 0.999207i | \(-0.487321\pi\) | ||||
0.0398227 | + | 0.999207i | \(0.487321\pi\) | |||||||
\(24\) | −0.854102 | −0.174343 | ||||||||
\(25\) | −2.38197 | −0.476393 | ||||||||
\(26\) | 1.85410 | 0.363619 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.85410 | 1.45847 | 0.729235 | − | 0.684263i | \(-0.239876\pi\) | ||||
0.729235 | + | 0.684263i | \(0.239876\pi\) | |||||||
\(30\) | 0.381966 | 0.0697371 | ||||||||
\(31\) | 9.61803 | 1.72745 | 0.863725 | − | 0.503964i | \(-0.168125\pi\) | ||||
0.863725 | + | 0.503964i | \(0.168125\pi\) | |||||||
\(32\) | 5.61803 | 0.993137 | ||||||||
\(33\) | −0.854102 | −0.148680 | ||||||||
\(34\) | −0.909830 | −0.156035 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.61803 | 0.769672 | ||||||||
\(37\) | 7.70820 | 1.26722 | 0.633610 | − | 0.773652i | \(-0.281572\pi\) | ||||
0.633610 | + | 0.773652i | \(0.281572\pi\) | |||||||
\(38\) | 3.00000 | 0.486664 | ||||||||
\(39\) | 1.14590 | 0.183491 | ||||||||
\(40\) | −3.61803 | −0.572061 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.94427 | 1.21149 | 0.605745 | − | 0.795659i | \(-0.292875\pi\) | ||||
0.605745 | + | 0.795659i | \(0.292875\pi\) | |||||||
\(44\) | 3.61803 | 0.545439 | ||||||||
\(45\) | −4.61803 | −0.688416 | ||||||||
\(46\) | 0.236068 | 0.0348063 | ||||||||
\(47\) | 3.23607 | 0.472029 | 0.236015 | − | 0.971750i | \(-0.424159\pi\) | ||||
0.236015 | + | 0.971750i | \(0.424159\pi\) | |||||||
\(48\) | 0.708204 | 0.102220 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.47214 | −0.208191 | ||||||||
\(51\) | −0.562306 | −0.0787386 | ||||||||
\(52\) | −4.85410 | −0.673143 | ||||||||
\(53\) | −14.0902 | −1.93543 | −0.967717 | − | 0.252040i | \(-0.918899\pi\) | ||||
−0.967717 | + | 0.252040i | \(0.918899\pi\) | |||||||
\(54\) | −1.38197 | −0.188062 | ||||||||
\(55\) | −3.61803 | −0.487856 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.85410 | 0.245582 | ||||||||
\(58\) | 4.85410 | 0.637375 | ||||||||
\(59\) | −7.61803 | −0.991784 | −0.495892 | − | 0.868384i | \(-0.665159\pi\) | ||||
−0.495892 | + | 0.868384i | \(0.665159\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 11.0000 | 1.40841 | 0.704203 | − | 0.709999i | \(-0.251305\pi\) | ||||
0.704203 | + | 0.709999i | \(0.251305\pi\) | |||||||
\(62\) | 5.94427 | 0.754923 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 4.85410 | 0.602077 | ||||||||
\(66\) | −0.527864 | −0.0649756 | ||||||||
\(67\) | 4.38197 | 0.535342 | 0.267671 | − | 0.963510i | \(-0.413746\pi\) | ||||
0.267671 | + | 0.963510i | \(0.413746\pi\) | |||||||
\(68\) | 2.38197 | 0.288856 | ||||||||
\(69\) | 0.145898 | 0.0175641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.236068 | 0.0280161 | 0.0140081 | − | 0.999902i | \(-0.495541\pi\) | ||||
0.0140081 | + | 0.999902i | \(0.495541\pi\) | |||||||
\(72\) | 6.38197 | 0.752122 | ||||||||
\(73\) | 15.0000 | 1.75562 | 0.877809 | − | 0.479012i | \(-0.159005\pi\) | ||||
0.877809 | + | 0.479012i | \(0.159005\pi\) | |||||||
\(74\) | 4.76393 | 0.553796 | ||||||||
\(75\) | −0.909830 | −0.105058 | ||||||||
\(76\) | −7.85410 | −0.900927 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.708204 | 0.0801883 | ||||||||
\(79\) | −7.70820 | −0.867241 | −0.433620 | − | 0.901096i | \(-0.642764\pi\) | ||||
−0.433620 | + | 0.901096i | \(0.642764\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | −0.618034 | −0.0682504 | ||||||||
\(83\) | −11.9443 | −1.31105 | −0.655527 | − | 0.755172i | \(-0.727553\pi\) | ||||
−0.655527 | + | 0.755172i | \(0.727553\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.38197 | −0.258360 | ||||||||
\(86\) | 4.90983 | 0.529441 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 14.5623 | 1.54360 | 0.771801 | − | 0.635865i | \(-0.219356\pi\) | ||||
0.771801 | + | 0.635865i | \(0.219356\pi\) | |||||||
\(90\) | −2.85410 | −0.300849 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.618034 | −0.0644345 | ||||||||
\(93\) | 3.67376 | 0.380951 | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | 7.85410 | 0.805814 | ||||||||
\(96\) | 2.14590 | 0.219015 | ||||||||
\(97\) | 5.14590 | 0.522487 | 0.261243 | − | 0.965273i | \(-0.415867\pi\) | ||||
0.261243 | + | 0.965273i | \(0.415867\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.38197 | 0.641412 | ||||||||
\(100\) | 3.85410 | 0.385410 | ||||||||
\(101\) | −1.76393 | −0.175518 | −0.0877589 | − | 0.996142i | \(-0.527971\pi\) | ||||
−0.0877589 | + | 0.996142i | \(0.527971\pi\) | |||||||
\(102\) | −0.347524 | −0.0344100 | ||||||||
\(103\) | −3.56231 | −0.351004 | −0.175502 | − | 0.984479i | \(-0.556155\pi\) | ||||
−0.175502 | + | 0.984479i | \(0.556155\pi\) | |||||||
\(104\) | −6.70820 | −0.657794 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.70820 | −0.845816 | ||||||||
\(107\) | 9.70820 | 0.938527 | 0.469264 | − | 0.883058i | \(-0.344519\pi\) | ||||
0.469264 | + | 0.883058i | \(0.344519\pi\) | |||||||
\(108\) | 3.61803 | 0.348145 | ||||||||
\(109\) | −6.94427 | −0.665141 | −0.332570 | − | 0.943078i | \(-0.607916\pi\) | ||||
−0.332570 | + | 0.943078i | \(0.607916\pi\) | |||||||
\(110\) | −2.23607 | −0.213201 | ||||||||
\(111\) | 2.94427 | 0.279458 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.94427 | −0.935478 | −0.467739 | − | 0.883867i | \(-0.654931\pi\) | ||||
−0.467739 | + | 0.883867i | \(0.654931\pi\) | |||||||
\(114\) | 1.14590 | 0.107323 | ||||||||
\(115\) | 0.618034 | 0.0576320 | ||||||||
\(116\) | −12.7082 | −1.17993 | ||||||||
\(117\) | −8.56231 | −0.791585 | ||||||||
\(118\) | −4.70820 | −0.433425 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.38197 | −0.126156 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 6.79837 | 0.615496 | ||||||||
\(123\) | −0.381966 | −0.0344407 | ||||||||
\(124\) | −15.5623 | −1.39754 | ||||||||
\(125\) | −11.9443 | −1.06833 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6525 | −1.03399 | −0.516995 | − | 0.855988i | \(-0.672949\pi\) | ||||
−0.516995 | + | 0.855988i | \(0.672949\pi\) | |||||||
\(128\) | −11.3820 | −1.00603 | ||||||||
\(129\) | 3.03444 | 0.267168 | ||||||||
\(130\) | 3.00000 | 0.263117 | ||||||||
\(131\) | 8.38197 | 0.732336 | 0.366168 | − | 0.930549i | \(-0.380670\pi\) | ||||
0.366168 | + | 0.930549i | \(0.380670\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.70820 | 0.233953 | ||||||||
\(135\) | −3.61803 | −0.311391 | ||||||||
\(136\) | 3.29180 | 0.282269 | ||||||||
\(137\) | −9.61803 | −0.821724 | −0.410862 | − | 0.911698i | \(-0.634772\pi\) | ||||
−0.410862 | + | 0.911698i | \(0.634772\pi\) | |||||||
\(138\) | 0.0901699 | 0.00767578 | ||||||||
\(139\) | 18.4164 | 1.56206 | 0.781030 | − | 0.624494i | \(-0.214695\pi\) | ||||
0.781030 | + | 0.624494i | \(0.214695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.23607 | 0.104096 | ||||||||
\(142\) | 0.145898 | 0.0122435 | ||||||||
\(143\) | −6.70820 | −0.560968 | ||||||||
\(144\) | −5.29180 | −0.440983 | ||||||||
\(145\) | 12.7082 | 1.05536 | ||||||||
\(146\) | 9.27051 | 0.767233 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.4721 | −1.02520 | ||||||||
\(149\) | 19.8885 | 1.62933 | 0.814666 | − | 0.579930i | \(-0.196920\pi\) | ||||
0.814666 | + | 0.579930i | \(0.196920\pi\) | |||||||
\(150\) | −0.562306 | −0.0459121 | ||||||||
\(151\) | 17.6525 | 1.43654 | 0.718269 | − | 0.695765i | \(-0.244935\pi\) | ||||
0.718269 | + | 0.695765i | \(0.244935\pi\) | |||||||
\(152\) | −10.8541 | −0.880384 | ||||||||
\(153\) | 4.20163 | 0.339681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.5623 | 1.24999 | ||||||||
\(156\) | −1.85410 | −0.148447 | ||||||||
\(157\) | 7.41641 | 0.591894 | 0.295947 | − | 0.955204i | \(-0.404365\pi\) | ||||
0.295947 | + | 0.955204i | \(0.404365\pi\) | |||||||
\(158\) | −4.76393 | −0.378998 | ||||||||
\(159\) | −5.38197 | −0.426818 | ||||||||
\(160\) | 9.09017 | 0.718641 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.76393 | 0.374290 | ||||||||
\(163\) | 5.52786 | 0.432976 | 0.216488 | − | 0.976285i | \(-0.430540\pi\) | ||||
0.216488 | + | 0.976285i | \(0.430540\pi\) | |||||||
\(164\) | 1.61803 | 0.126347 | ||||||||
\(165\) | −1.38197 | −0.107586 | ||||||||
\(166\) | −7.38197 | −0.572952 | ||||||||
\(167\) | −6.70820 | −0.519096 | −0.259548 | − | 0.965730i | \(-0.583574\pi\) | ||||
−0.259548 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | −1.47214 | −0.112908 | ||||||||
\(171\) | −13.8541 | −1.05945 | ||||||||
\(172\) | −12.8541 | −0.980116 | ||||||||
\(173\) | 0.708204 | 0.0538437 | 0.0269219 | − | 0.999638i | \(-0.491429\pi\) | ||||
0.0269219 | + | 0.999638i | \(0.491429\pi\) | |||||||
\(174\) | 1.85410 | 0.140559 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.14590 | −0.312509 | ||||||||
\(177\) | −2.90983 | −0.218716 | ||||||||
\(178\) | 9.00000 | 0.674579 | ||||||||
\(179\) | 4.67376 | 0.349333 | 0.174667 | − | 0.984628i | \(-0.444115\pi\) | ||||
0.174667 | + | 0.984628i | \(0.444115\pi\) | |||||||
\(180\) | 7.47214 | 0.556940 | ||||||||
\(181\) | 5.41641 | 0.402598 | 0.201299 | − | 0.979530i | \(-0.435484\pi\) | ||||
0.201299 | + | 0.979530i | \(0.435484\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.20163 | 0.310593 | ||||||||
\(184\) | −0.854102 | −0.0629652 | ||||||||
\(185\) | 12.4721 | 0.916970 | ||||||||
\(186\) | 2.27051 | 0.166482 | ||||||||
\(187\) | 3.29180 | 0.240720 | ||||||||
\(188\) | −5.23607 | −0.381880 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.85410 | 0.352154 | ||||||||
\(191\) | −3.05573 | −0.221105 | −0.110552 | − | 0.993870i | \(-0.535262\pi\) | ||||
−0.110552 | + | 0.993870i | \(0.535262\pi\) | |||||||
\(192\) | −0.0901699 | −0.00650746 | ||||||||
\(193\) | −14.4164 | −1.03772 | −0.518858 | − | 0.854861i | \(-0.673643\pi\) | ||||
−0.518858 | + | 0.854861i | \(0.673643\pi\) | |||||||
\(194\) | 3.18034 | 0.228335 | ||||||||
\(195\) | 1.85410 | 0.132775 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.09017 | −0.291413 | −0.145706 | − | 0.989328i | \(-0.546545\pi\) | ||||
−0.145706 | + | 0.989328i | \(0.546545\pi\) | |||||||
\(198\) | 3.94427 | 0.280307 | ||||||||
\(199\) | −0.708204 | −0.0502032 | −0.0251016 | − | 0.999685i | \(-0.507991\pi\) | ||||
−0.0251016 | + | 0.999685i | \(0.507991\pi\) | |||||||
\(200\) | 5.32624 | 0.376622 | ||||||||
\(201\) | 1.67376 | 0.118058 | ||||||||
\(202\) | −1.09017 | −0.0767041 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.909830 | 0.0637008 | ||||||||
\(205\) | −1.61803 | −0.113008 | ||||||||
\(206\) | −2.20163 | −0.153395 | ||||||||
\(207\) | −1.09017 | −0.0757720 | ||||||||
\(208\) | 5.56231 | 0.385677 | ||||||||
\(209\) | −10.8541 | −0.750794 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.85410 | 0.127642 | 0.0638208 | − | 0.997961i | \(-0.479671\pi\) | ||||
0.0638208 | + | 0.997961i | \(0.479671\pi\) | |||||||
\(212\) | 22.7984 | 1.56580 | ||||||||
\(213\) | 0.0901699 | 0.00617834 | ||||||||
\(214\) | 6.00000 | 0.410152 | ||||||||
\(215\) | 12.8541 | 0.876642 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.29180 | −0.290677 | ||||||||
\(219\) | 5.72949 | 0.387163 | ||||||||
\(220\) | 5.85410 | 0.394683 | ||||||||
\(221\) | −4.41641 | −0.297080 | ||||||||
\(222\) | 1.81966 | 0.122128 | ||||||||
\(223\) | 5.14590 | 0.344595 | 0.172297 | − | 0.985045i | \(-0.444881\pi\) | ||||
0.172297 | + | 0.985045i | \(0.444881\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.79837 | 0.453225 | ||||||||
\(226\) | −6.14590 | −0.408819 | ||||||||
\(227\) | −0.527864 | −0.0350356 | −0.0175178 | − | 0.999847i | \(-0.505576\pi\) | ||||
−0.0175178 | + | 0.999847i | \(0.505576\pi\) | |||||||
\(228\) | −3.00000 | −0.198680 | ||||||||
\(229\) | −15.7082 | −1.03803 | −0.519014 | − | 0.854766i | \(-0.673701\pi\) | ||||
−0.519014 | + | 0.854766i | \(0.673701\pi\) | |||||||
\(230\) | 0.381966 | 0.0251861 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.5623 | −1.15302 | ||||||||
\(233\) | 1.85410 | 0.121466 | 0.0607331 | − | 0.998154i | \(-0.480656\pi\) | ||||
0.0607331 | + | 0.998154i | \(0.480656\pi\) | |||||||
\(234\) | −5.29180 | −0.345936 | ||||||||
\(235\) | 5.23607 | 0.341563 | ||||||||
\(236\) | 12.3262 | 0.802370 | ||||||||
\(237\) | −2.94427 | −0.191251 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.5623 | 1.52412 | 0.762059 | − | 0.647507i | \(-0.224188\pi\) | ||||
0.762059 | + | 0.647507i | \(0.224188\pi\) | |||||||
\(240\) | 1.14590 | 0.0739674 | ||||||||
\(241\) | −13.7082 | −0.883023 | −0.441512 | − | 0.897256i | \(-0.645558\pi\) | ||||
−0.441512 | + | 0.897256i | \(0.645558\pi\) | |||||||
\(242\) | −3.70820 | −0.238372 | ||||||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | −17.7984 | −1.13942 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.236068 | −0.0150511 | ||||||||
\(247\) | 14.5623 | 0.926577 | ||||||||
\(248\) | −21.5066 | −1.36567 | ||||||||
\(249\) | −4.56231 | −0.289124 | ||||||||
\(250\) | −7.38197 | −0.466877 | ||||||||
\(251\) | 19.3607 | 1.22204 | 0.611018 | − | 0.791617i | \(-0.290760\pi\) | ||||
0.611018 | + | 0.791617i | \(0.290760\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.854102 | −0.0536969 | ||||||||
\(254\) | −7.20163 | −0.451870 | ||||||||
\(255\) | −0.909830 | −0.0569758 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −3.00000 | −0.187135 | −0.0935674 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935674 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(258\) | 1.87539 | 0.116757 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.85410 | −0.487091 | ||||||||
\(261\) | −22.4164 | −1.38754 | ||||||||
\(262\) | 5.18034 | 0.320042 | ||||||||
\(263\) | −4.41641 | −0.272327 | −0.136164 | − | 0.990686i | \(-0.543477\pi\) | ||||
−0.136164 | + | 0.990686i | \(0.543477\pi\) | |||||||
\(264\) | 1.90983 | 0.117542 | ||||||||
\(265\) | −22.7984 | −1.40049 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.56231 | 0.340408 | ||||||||
\(268\) | −7.09017 | −0.433101 | ||||||||
\(269\) | −20.5066 | −1.25031 | −0.625154 | − | 0.780501i | \(-0.714964\pi\) | ||||
−0.625154 | + | 0.780501i | \(0.714964\pi\) | |||||||
\(270\) | −2.23607 | −0.136083 | ||||||||
\(271\) | −29.6525 | −1.80126 | −0.900630 | − | 0.434587i | \(-0.856894\pi\) | ||||
−0.900630 | + | 0.434587i | \(0.856894\pi\) | |||||||
\(272\) | −2.72949 | −0.165500 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.94427 | −0.359107 | ||||||||
\(275\) | 5.32624 | 0.321184 | ||||||||
\(276\) | −0.236068 | −0.0142096 | ||||||||
\(277\) | 4.70820 | 0.282889 | 0.141444 | − | 0.989946i | \(-0.454825\pi\) | ||||
0.141444 | + | 0.989946i | \(0.454825\pi\) | |||||||
\(278\) | 11.3820 | 0.682645 | ||||||||
\(279\) | −27.4508 | −1.64344 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0000 | 1.61068 | 0.805342 | − | 0.592810i | \(-0.201981\pi\) | ||||
0.805342 | + | 0.592810i | \(0.201981\pi\) | |||||||
\(282\) | 0.763932 | 0.0454915 | ||||||||
\(283\) | 9.88854 | 0.587813 | 0.293906 | − | 0.955834i | \(-0.405045\pi\) | ||||
0.293906 | + | 0.955834i | \(0.405045\pi\) | |||||||
\(284\) | −0.381966 | −0.0226655 | ||||||||
\(285\) | 3.00000 | 0.177705 | ||||||||
\(286\) | −4.14590 | −0.245152 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.0344 | −0.944839 | ||||||||
\(289\) | −14.8328 | −0.872519 | ||||||||
\(290\) | 7.85410 | 0.461209 | ||||||||
\(291\) | 1.96556 | 0.115223 | ||||||||
\(292\) | −24.2705 | −1.42032 | ||||||||
\(293\) | 0.0557281 | 0.00325567 | 0.00162783 | − | 0.999999i | \(-0.499482\pi\) | ||||
0.00162783 | + | 0.999999i | \(0.499482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.3262 | −0.717661 | ||||||||
\(296\) | −17.2361 | −1.00183 | ||||||||
\(297\) | 5.00000 | 0.290129 | ||||||||
\(298\) | 12.2918 | 0.712045 | ||||||||
\(299\) | 1.14590 | 0.0662690 | ||||||||
\(300\) | 1.47214 | 0.0849938 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.9098 | 0.627790 | ||||||||
\(303\) | −0.673762 | −0.0387066 | ||||||||
\(304\) | 9.00000 | 0.516185 | ||||||||
\(305\) | 17.7984 | 1.01913 | ||||||||
\(306\) | 2.59675 | 0.148446 | ||||||||
\(307\) | 19.8885 | 1.13510 | 0.567550 | − | 0.823339i | \(-0.307892\pi\) | ||||
0.567550 | + | 0.823339i | \(0.307892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.36068 | −0.0774064 | ||||||||
\(310\) | 9.61803 | 0.546268 | ||||||||
\(311\) | −18.0344 | −1.02264 | −0.511320 | − | 0.859391i | \(-0.670843\pi\) | ||||
−0.511320 | + | 0.859391i | \(0.670843\pi\) | |||||||
\(312\) | −2.56231 | −0.145062 | ||||||||
\(313\) | −14.1246 | −0.798370 | −0.399185 | − | 0.916870i | \(-0.630707\pi\) | ||||
−0.399185 | + | 0.916870i | \(0.630707\pi\) | |||||||
\(314\) | 4.58359 | 0.258667 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.4721 | 0.701612 | ||||||||
\(317\) | −1.58359 | −0.0889434 | −0.0444717 | − | 0.999011i | \(-0.514160\pi\) | ||||
−0.0444717 | + | 0.999011i | \(0.514160\pi\) | |||||||
\(318\) | −3.32624 | −0.186526 | ||||||||
\(319\) | −17.5623 | −0.983300 | ||||||||
\(320\) | −0.381966 | −0.0213525 | ||||||||
\(321\) | 3.70820 | 0.206972 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.14590 | −0.397608 | ||||||||
\(324\) | −12.4721 | −0.692896 | ||||||||
\(325\) | −7.14590 | −0.396383 | ||||||||
\(326\) | 3.41641 | 0.189217 | ||||||||
\(327\) | −2.65248 | −0.146682 | ||||||||
\(328\) | 2.23607 | 0.123466 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.854102 | −0.0470168 | ||||||||
\(331\) | 9.88854 | 0.543524 | 0.271762 | − | 0.962365i | \(-0.412394\pi\) | ||||
0.271762 | + | 0.962365i | \(0.412394\pi\) | |||||||
\(332\) | 19.3262 | 1.06067 | ||||||||
\(333\) | −22.0000 | −1.20559 | ||||||||
\(334\) | −4.14590 | −0.226853 | ||||||||
\(335\) | 7.09017 | 0.387377 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.05573 | −0.275403 | −0.137702 | − | 0.990474i | \(-0.543971\pi\) | ||||
−0.137702 | + | 0.990474i | \(0.543971\pi\) | |||||||
\(338\) | −2.47214 | −0.134466 | ||||||||
\(339\) | −3.79837 | −0.206299 | ||||||||
\(340\) | 3.85410 | 0.209018 | ||||||||
\(341\) | −21.5066 | −1.16465 | ||||||||
\(342\) | −8.56231 | −0.462996 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.7639 | −0.957767 | ||||||||
\(345\) | 0.236068 | 0.0127095 | ||||||||
\(346\) | 0.437694 | 0.0235306 | ||||||||
\(347\) | 35.1246 | 1.88559 | 0.942794 | − | 0.333376i | \(-0.108188\pi\) | ||||
0.942794 | + | 0.333376i | \(0.108188\pi\) | |||||||
\(348\) | −4.85410 | −0.260207 | ||||||||
\(349\) | −2.70820 | −0.144967 | −0.0724834 | − | 0.997370i | \(-0.523092\pi\) | ||||
−0.0724834 | + | 0.997370i | \(0.523092\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.70820 | −0.358057 | ||||||||
\(352\) | −12.5623 | −0.669573 | ||||||||
\(353\) | 11.8885 | 0.632763 | 0.316382 | − | 0.948632i | \(-0.397532\pi\) | ||||
0.316382 | + | 0.948632i | \(0.397532\pi\) | |||||||
\(354\) | −1.79837 | −0.0955825 | ||||||||
\(355\) | 0.381966 | 0.0202727 | ||||||||
\(356\) | −23.5623 | −1.24880 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.88854 | 0.152664 | ||||||||
\(359\) | −6.76393 | −0.356987 | −0.178493 | − | 0.983941i | \(-0.557122\pi\) | ||||
−0.178493 | + | 0.983941i | \(0.557122\pi\) | |||||||
\(360\) | 10.3262 | 0.544241 | ||||||||
\(361\) | 4.56231 | 0.240121 | ||||||||
\(362\) | 3.34752 | 0.175942 | ||||||||
\(363\) | −2.29180 | −0.120288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.2705 | 1.27038 | ||||||||
\(366\) | 2.59675 | 0.135734 | ||||||||
\(367\) | −33.4508 | −1.74612 | −0.873060 | − | 0.487613i | \(-0.837868\pi\) | ||||
−0.873060 | + | 0.487613i | \(0.837868\pi\) | |||||||
\(368\) | 0.708204 | 0.0369177 | ||||||||
\(369\) | 2.85410 | 0.148579 | ||||||||
\(370\) | 7.70820 | 0.400730 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.94427 | −0.308196 | ||||||||
\(373\) | −9.50658 | −0.492232 | −0.246116 | − | 0.969240i | \(-0.579154\pi\) | ||||
−0.246116 | + | 0.969240i | \(0.579154\pi\) | |||||||
\(374\) | 2.03444 | 0.105198 | ||||||||
\(375\) | −4.56231 | −0.235596 | ||||||||
\(376\) | −7.23607 | −0.373172 | ||||||||
\(377\) | 23.5623 | 1.21352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.2361 | −0.988090 | −0.494045 | − | 0.869436i | \(-0.664482\pi\) | ||||
−0.494045 | + | 0.869436i | \(0.664482\pi\) | |||||||
\(380\) | −12.7082 | −0.651917 | ||||||||
\(381\) | −4.45085 | −0.228024 | ||||||||
\(382\) | −1.88854 | −0.0966263 | ||||||||
\(383\) | 4.52786 | 0.231363 | 0.115682 | − | 0.993286i | \(-0.463095\pi\) | ||||
0.115682 | + | 0.993286i | \(0.463095\pi\) | |||||||
\(384\) | −4.34752 | −0.221859 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.90983 | −0.453498 | ||||||||
\(387\) | −22.6738 | −1.15257 | ||||||||
\(388\) | −8.32624 | −0.422701 | ||||||||
\(389\) | −6.32624 | −0.320753 | −0.160376 | − | 0.987056i | \(-0.551271\pi\) | ||||
−0.160376 | + | 0.987056i | \(0.551271\pi\) | |||||||
\(390\) | 1.14590 | 0.0580248 | ||||||||
\(391\) | −0.562306 | −0.0284370 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.20163 | 0.161501 | ||||||||
\(394\) | −2.52786 | −0.127352 | ||||||||
\(395\) | −12.4721 | −0.627541 | ||||||||
\(396\) | −10.3262 | −0.518913 | ||||||||
\(397\) | 30.7426 | 1.54293 | 0.771465 | − | 0.636272i | \(-0.219525\pi\) | ||||
0.771465 | + | 0.636272i | \(0.219525\pi\) | |||||||
\(398\) | −0.437694 | −0.0219396 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.41641 | −0.220820 | ||||||||
\(401\) | −38.1803 | −1.90664 | −0.953318 | − | 0.301969i | \(-0.902356\pi\) | ||||
−0.953318 | + | 0.301969i | \(0.902356\pi\) | |||||||
\(402\) | 1.03444 | 0.0515933 | ||||||||
\(403\) | 28.8541 | 1.43733 | ||||||||
\(404\) | 2.85410 | 0.141997 | ||||||||
\(405\) | 12.4721 | 0.619745 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.2361 | −0.854360 | ||||||||
\(408\) | 1.25735 | 0.0622483 | ||||||||
\(409\) | −26.5967 | −1.31512 | −0.657562 | − | 0.753400i | \(-0.728412\pi\) | ||||
−0.657562 | + | 0.753400i | \(0.728412\pi\) | |||||||
\(410\) | −1.00000 | −0.0493865 | ||||||||
\(411\) | −3.67376 | −0.181213 | ||||||||
\(412\) | 5.76393 | 0.283969 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.673762 | −0.0331136 | ||||||||
\(415\) | −19.3262 | −0.948688 | ||||||||
\(416\) | 16.8541 | 0.826340 | ||||||||
\(417\) | 7.03444 | 0.344478 | ||||||||
\(418\) | −6.70820 | −0.328109 | ||||||||
\(419\) | 17.5623 | 0.857975 | 0.428987 | − | 0.903310i | \(-0.358870\pi\) | ||||
0.428987 | + | 0.903310i | \(0.358870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5279 | 0.561834 | 0.280917 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280917 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(422\) | 1.14590 | 0.0557814 | ||||||||
\(423\) | −9.23607 | −0.449073 | ||||||||
\(424\) | 31.5066 | 1.53009 | ||||||||
\(425\) | 3.50658 | 0.170094 | ||||||||
\(426\) | 0.0557281 | 0.00270003 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −15.7082 | −0.759285 | ||||||||
\(429\) | −2.56231 | −0.123709 | ||||||||
\(430\) | 7.94427 | 0.383107 | ||||||||
\(431\) | −14.0557 | −0.677041 | −0.338520 | − | 0.940959i | \(-0.609926\pi\) | ||||
−0.338520 | + | 0.940959i | \(0.609926\pi\) | |||||||
\(432\) | −4.14590 | −0.199470 | ||||||||
\(433\) | 37.5066 | 1.80245 | 0.901226 | − | 0.433350i | \(-0.142669\pi\) | ||||
0.901226 | + | 0.433350i | \(0.142669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.85410 | 0.232736 | ||||||||
\(436\) | 11.2361 | 0.538110 | ||||||||
\(437\) | 1.85410 | 0.0886937 | ||||||||
\(438\) | 3.54102 | 0.169196 | ||||||||
\(439\) | −19.7639 | −0.943281 | −0.471641 | − | 0.881791i | \(-0.656338\pi\) | ||||
−0.471641 | + | 0.881791i | \(0.656338\pi\) | |||||||
\(440\) | 8.09017 | 0.385684 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.72949 | −0.129829 | ||||||||
\(443\) | −33.6180 | −1.59724 | −0.798620 | − | 0.601835i | \(-0.794437\pi\) | ||||
−0.798620 | + | 0.601835i | \(0.794437\pi\) | |||||||
\(444\) | −4.76393 | −0.226086 | ||||||||
\(445\) | 23.5623 | 1.11696 | ||||||||
\(446\) | 3.18034 | 0.150593 | ||||||||
\(447\) | 7.59675 | 0.359314 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.8885 | −1.31614 | −0.658071 | − | 0.752956i | \(-0.728627\pi\) | ||||
−0.658071 | + | 0.752956i | \(0.728627\pi\) | |||||||
\(450\) | 4.20163 | 0.198067 | ||||||||
\(451\) | 2.23607 | 0.105292 | ||||||||
\(452\) | 16.0902 | 0.756818 | ||||||||
\(453\) | 6.74265 | 0.316797 | ||||||||
\(454\) | −0.326238 | −0.0153111 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.14590 | −0.194149 | ||||||||
\(457\) | −20.7082 | −0.968689 | −0.484344 | − | 0.874877i | \(-0.660942\pi\) | ||||
−0.484344 | + | 0.874877i | \(0.660942\pi\) | |||||||
\(458\) | −9.70820 | −0.453635 | ||||||||
\(459\) | 3.29180 | 0.153648 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | 8.81966 | 0.410773 | 0.205386 | − | 0.978681i | \(-0.434155\pi\) | ||||
0.205386 | + | 0.978681i | \(0.434155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.6869 | −1.79793 | −0.898967 | − | 0.438017i | \(-0.855681\pi\) | ||||
−0.898967 | + | 0.438017i | \(0.855681\pi\) | |||||||
\(464\) | 14.5623 | 0.676038 | ||||||||
\(465\) | 5.94427 | 0.275659 | ||||||||
\(466\) | 1.14590 | 0.0530827 | ||||||||
\(467\) | 18.5967 | 0.860555 | 0.430277 | − | 0.902697i | \(-0.358416\pi\) | ||||
0.430277 | + | 0.902697i | \(0.358416\pi\) | |||||||
\(468\) | 13.8541 | 0.640406 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.23607 | 0.149269 | ||||||||
\(471\) | 2.83282 | 0.130529 | ||||||||
\(472\) | 17.0344 | 0.784074 | ||||||||
\(473\) | −17.7639 | −0.816786 | ||||||||
\(474\) | −1.81966 | −0.0835798 | ||||||||
\(475\) | −11.5623 | −0.530515 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 40.2148 | 1.84131 | ||||||||
\(478\) | 14.5623 | 0.666064 | ||||||||
\(479\) | 1.03444 | 0.0472649 | 0.0236324 | − | 0.999721i | \(-0.492477\pi\) | ||||
0.0236324 | + | 0.999721i | \(0.492477\pi\) | |||||||
\(480\) | 3.47214 | 0.158481 | ||||||||
\(481\) | 23.1246 | 1.05439 | ||||||||
\(482\) | −8.47214 | −0.385895 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.70820 | 0.441282 | ||||||||
\(485\) | 8.32624 | 0.378075 | ||||||||
\(486\) | 5.96556 | 0.270603 | ||||||||
\(487\) | 20.2918 | 0.919509 | 0.459755 | − | 0.888046i | \(-0.347937\pi\) | ||||
0.459755 | + | 0.888046i | \(0.347937\pi\) | |||||||
\(488\) | −24.5967 | −1.11344 | ||||||||
\(489\) | 2.11146 | 0.0954833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.1591 | 1.76722 | 0.883612 | − | 0.468220i | \(-0.155105\pi\) | ||||
0.883612 | + | 0.468220i | \(0.155105\pi\) | |||||||
\(492\) | 0.618034 | 0.0278631 | ||||||||
\(493\) | −11.5623 | −0.520740 | ||||||||
\(494\) | 9.00000 | 0.404929 | ||||||||
\(495\) | 10.3262 | 0.464130 | ||||||||
\(496\) | 17.8328 | 0.800717 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.81966 | −0.126352 | ||||||||
\(499\) | −1.23607 | −0.0553340 | −0.0276670 | − | 0.999617i | \(-0.508808\pi\) | ||||
−0.0276670 | + | 0.999617i | \(0.508808\pi\) | |||||||
\(500\) | 19.3262 | 0.864296 | ||||||||
\(501\) | −2.56231 | −0.114475 | ||||||||
\(502\) | 11.9656 | 0.534049 | ||||||||
\(503\) | −1.38197 | −0.0616188 | −0.0308094 | − | 0.999525i | \(-0.509808\pi\) | ||||
−0.0308094 | + | 0.999525i | \(0.509808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.85410 | −0.127006 | ||||||||
\(506\) | −0.527864 | −0.0234664 | ||||||||
\(507\) | −1.52786 | −0.0678548 | ||||||||
\(508\) | 18.8541 | 0.836516 | ||||||||
\(509\) | −37.0902 | −1.64399 | −0.821996 | − | 0.569493i | \(-0.807140\pi\) | ||||
−0.821996 | + | 0.569493i | \(0.807140\pi\) | |||||||
\(510\) | −0.562306 | −0.0248993 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.7082 | 0.826794 | ||||||||
\(513\) | −10.8541 | −0.479220 | ||||||||
\(514\) | −1.85410 | −0.0817809 | ||||||||
\(515\) | −5.76393 | −0.253989 | ||||||||
\(516\) | −4.90983 | −0.216143 | ||||||||
\(517\) | −7.23607 | −0.318242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.270510 | 0.0118741 | ||||||||
\(520\) | −10.8541 | −0.475984 | ||||||||
\(521\) | −15.4377 | −0.676338 | −0.338169 | − | 0.941085i | \(-0.609807\pi\) | ||||
−0.338169 | + | 0.941085i | \(0.609807\pi\) | |||||||
\(522\) | −13.8541 | −0.606378 | ||||||||
\(523\) | 13.8328 | 0.604867 | 0.302433 | − | 0.953171i | \(-0.402201\pi\) | ||||
0.302433 | + | 0.953171i | \(0.402201\pi\) | |||||||
\(524\) | −13.5623 | −0.592472 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.72949 | −0.119011 | ||||||||
\(527\) | −14.1591 | −0.616778 | ||||||||
\(528\) | −1.58359 | −0.0689170 | ||||||||
\(529\) | −22.8541 | −0.993657 | ||||||||
\(530\) | −14.0902 | −0.612038 | ||||||||
\(531\) | 21.7426 | 0.943550 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.00000 | −0.129944 | ||||||||
\(534\) | 3.43769 | 0.148764 | ||||||||
\(535\) | 15.7082 | 0.679125 | ||||||||
\(536\) | −9.79837 | −0.423225 | ||||||||
\(537\) | 1.78522 | 0.0770379 | ||||||||
\(538\) | −12.6738 | −0.546405 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.85410 | 0.251920 | ||||||||
\(541\) | −8.20163 | −0.352615 | −0.176308 | − | 0.984335i | \(-0.556415\pi\) | ||||
−0.176308 | + | 0.984335i | \(0.556415\pi\) | |||||||
\(542\) | −18.3262 | −0.787179 | ||||||||
\(543\) | 2.06888 | 0.0887843 | ||||||||
\(544\) | −8.27051 | −0.354595 | ||||||||
\(545\) | −11.2361 | −0.481300 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.1803 | 0.649064 | 0.324532 | − | 0.945875i | \(-0.394793\pi\) | ||||
0.324532 | + | 0.945875i | \(0.394793\pi\) | |||||||
\(548\) | 15.5623 | 0.664789 | ||||||||
\(549\) | −31.3951 | −1.33991 | ||||||||
\(550\) | 3.29180 | 0.140363 | ||||||||
\(551\) | 38.1246 | 1.62416 | ||||||||
\(552\) | −0.326238 | −0.0138856 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.90983 | 0.123627 | ||||||||
\(555\) | 4.76393 | 0.202218 | ||||||||
\(556\) | −29.7984 | −1.26373 | ||||||||
\(557\) | −41.5623 | −1.76105 | −0.880526 | − | 0.473998i | \(-0.842810\pi\) | ||||
−0.880526 | + | 0.473998i | \(0.842810\pi\) | |||||||
\(558\) | −16.9656 | −0.718209 | ||||||||
\(559\) | 23.8328 | 1.00802 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.25735 | 0.0530855 | ||||||||
\(562\) | 16.6869 | 0.703895 | ||||||||
\(563\) | 29.1803 | 1.22980 | 0.614902 | − | 0.788603i | \(-0.289195\pi\) | ||||
0.614902 | + | 0.788603i | \(0.289195\pi\) | |||||||
\(564\) | −2.00000 | −0.0842152 | ||||||||
\(565\) | −16.0902 | −0.676919 | ||||||||
\(566\) | 6.11146 | 0.256884 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.527864 | −0.0221487 | ||||||||
\(569\) | 18.2705 | 0.765940 | 0.382970 | − | 0.923761i | \(-0.374901\pi\) | ||||
0.382970 | + | 0.923761i | \(0.374901\pi\) | |||||||
\(570\) | 1.85410 | 0.0776598 | ||||||||
\(571\) | 36.8328 | 1.54141 | 0.770703 | − | 0.637195i | \(-0.219905\pi\) | ||||
0.770703 | + | 0.637195i | \(0.219905\pi\) | |||||||
\(572\) | 10.8541 | 0.453833 | ||||||||
\(573\) | −1.16718 | −0.0487598 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.909830 | −0.0379425 | ||||||||
\(576\) | 0.673762 | 0.0280734 | ||||||||
\(577\) | 10.8885 | 0.453296 | 0.226648 | − | 0.973977i | \(-0.427223\pi\) | ||||
0.226648 | + | 0.973977i | \(0.427223\pi\) | |||||||
\(578\) | −9.16718 | −0.381305 | ||||||||
\(579\) | −5.50658 | −0.228846 | ||||||||
\(580\) | −20.5623 | −0.853803 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.21478 | 0.0503543 | ||||||||
\(583\) | 31.5066 | 1.30487 | ||||||||
\(584\) | −33.5410 | −1.38794 | ||||||||
\(585\) | −13.8541 | −0.572797 | ||||||||
\(586\) | 0.0344419 | 0.00142278 | ||||||||
\(587\) | 8.52786 | 0.351983 | 0.175991 | − | 0.984392i | \(-0.443687\pi\) | ||||
0.175991 | + | 0.984392i | \(0.443687\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.6869 | 1.92370 | ||||||||
\(590\) | −7.61803 | −0.313629 | ||||||||
\(591\) | −1.56231 | −0.0642647 | ||||||||
\(592\) | 14.2918 | 0.587389 | ||||||||
\(593\) | −36.0000 | −1.47834 | −0.739171 | − | 0.673517i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(594\) | 3.09017 | 0.126791 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32.1803 | −1.31816 | ||||||||
\(597\) | −0.270510 | −0.0110712 | ||||||||
\(598\) | 0.708204 | 0.0289606 | ||||||||
\(599\) | −5.12461 | −0.209386 | −0.104693 | − | 0.994505i | \(-0.533386\pi\) | ||||
−0.104693 | + | 0.994505i | \(0.533386\pi\) | |||||||
\(600\) | 2.03444 | 0.0830557 | ||||||||
\(601\) | 23.5623 | 0.961127 | 0.480563 | − | 0.876960i | \(-0.340432\pi\) | ||||
0.480563 | + | 0.876960i | \(0.340432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.5066 | −0.509307 | ||||||||
\(604\) | −28.5623 | −1.16218 | ||||||||
\(605\) | −9.70820 | −0.394695 | ||||||||
\(606\) | −0.416408 | −0.0169154 | ||||||||
\(607\) | −11.5836 | −0.470164 | −0.235082 | − | 0.971976i | \(-0.575536\pi\) | ||||
−0.235082 | + | 0.971976i | \(0.575536\pi\) | |||||||
\(608\) | 27.2705 | 1.10597 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.0000 | 0.445377 | ||||||||
\(611\) | 9.70820 | 0.392752 | ||||||||
\(612\) | −6.79837 | −0.274808 | ||||||||
\(613\) | 43.3951 | 1.75271 | 0.876356 | − | 0.481664i | \(-0.159967\pi\) | ||||
0.876356 | + | 0.481664i | \(0.159967\pi\) | |||||||
\(614\) | 12.2918 | 0.496057 | ||||||||
\(615\) | −0.618034 | −0.0249215 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7639 | 0.795666 | 0.397833 | − | 0.917458i | \(-0.369762\pi\) | ||||
0.397833 | + | 0.917458i | \(0.369762\pi\) | |||||||
\(618\) | −0.840946 | −0.0338278 | ||||||||
\(619\) | −9.09017 | −0.365365 | −0.182682 | − | 0.983172i | \(-0.558478\pi\) | ||||
−0.182682 | + | 0.983172i | \(0.558478\pi\) | |||||||
\(620\) | −25.1803 | −1.01127 | ||||||||
\(621\) | −0.854102 | −0.0342739 | ||||||||
\(622\) | −11.1459 | −0.446910 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.12461 | 0.0850525 | ||||||||
\(625\) | −7.41641 | −0.296656 | ||||||||
\(626\) | −8.72949 | −0.348901 | ||||||||
\(627\) | −4.14590 | −0.165571 | ||||||||
\(628\) | −12.0000 | −0.478852 | ||||||||
\(629\) | −11.3475 | −0.452455 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7082 | 0.903999 | 0.452000 | − | 0.892018i | \(-0.350711\pi\) | ||||
0.452000 | + | 0.892018i | \(0.350711\pi\) | |||||||
\(632\) | 17.2361 | 0.685614 | ||||||||
\(633\) | 0.708204 | 0.0281486 | ||||||||
\(634\) | −0.978714 | −0.0388697 | ||||||||
\(635\) | −18.8541 | −0.748202 | ||||||||
\(636\) | 8.70820 | 0.345303 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.8541 | −0.429718 | ||||||||
\(639\) | −0.673762 | −0.0266536 | ||||||||
\(640\) | −18.4164 | −0.727972 | ||||||||
\(641\) | −8.05573 | −0.318182 | −0.159091 | − | 0.987264i | \(-0.550856\pi\) | ||||
−0.159091 | + | 0.987264i | \(0.550856\pi\) | |||||||
\(642\) | 2.29180 | 0.0904500 | ||||||||
\(643\) | −19.4508 | −0.767067 | −0.383533 | − | 0.923527i | \(-0.625293\pi\) | ||||
−0.383533 | + | 0.923527i | \(0.625293\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.90983 | 0.193324 | ||||||||
\(646\) | −4.41641 | −0.173761 | ||||||||
\(647\) | 39.7214 | 1.56161 | 0.780804 | − | 0.624776i | \(-0.214810\pi\) | ||||
0.780804 | + | 0.624776i | \(0.214810\pi\) | |||||||
\(648\) | −17.2361 | −0.677097 | ||||||||
\(649\) | 17.0344 | 0.668660 | ||||||||
\(650\) | −4.41641 | −0.173226 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.94427 | −0.350285 | ||||||||
\(653\) | −31.6869 | −1.24000 | −0.620002 | − | 0.784600i | \(-0.712868\pi\) | ||||
−0.620002 | + | 0.784600i | \(0.712868\pi\) | |||||||
\(654\) | −1.63932 | −0.0641025 | ||||||||
\(655\) | 13.5623 | 0.529923 | ||||||||
\(656\) | −1.85410 | −0.0723905 | ||||||||
\(657\) | −42.8115 | −1.67024 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.0000 | −1.28550 | −0.642749 | − | 0.766077i | \(-0.722206\pi\) | ||||
−0.642749 | + | 0.766077i | \(0.722206\pi\) | |||||||
\(660\) | 2.23607 | 0.0870388 | ||||||||
\(661\) | 40.6525 | 1.58120 | 0.790599 | − | 0.612334i | \(-0.209769\pi\) | ||||
0.790599 | + | 0.612334i | \(0.209769\pi\) | |||||||
\(662\) | 6.11146 | 0.237528 | ||||||||
\(663\) | −1.68692 | −0.0655145 | ||||||||
\(664\) | 26.7082 | 1.03648 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.5967 | −0.526863 | ||||||||
\(667\) | 3.00000 | 0.116160 | ||||||||
\(668\) | 10.8541 | 0.419958 | ||||||||
\(669\) | 1.96556 | 0.0759929 | ||||||||
\(670\) | 4.38197 | 0.169290 | ||||||||
\(671\) | −24.5967 | −0.949547 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.7082 | −1.49209 | −0.746046 | − | 0.665895i | \(-0.768050\pi\) | ||||
−0.746046 | + | 0.665895i | \(0.768050\pi\) | |||||||
\(674\) | −3.12461 | −0.120356 | ||||||||
\(675\) | 5.32624 | 0.205007 | ||||||||
\(676\) | 6.47214 | 0.248928 | ||||||||
\(677\) | 31.3262 | 1.20397 | 0.601983 | − | 0.798509i | \(-0.294378\pi\) | ||||
0.601983 | + | 0.798509i | \(0.294378\pi\) | |||||||
\(678\) | −2.34752 | −0.0901561 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.32624 | 0.204252 | ||||||||
\(681\) | −0.201626 | −0.00772633 | ||||||||
\(682\) | −13.2918 | −0.508969 | ||||||||
\(683\) | 3.87539 | 0.148288 | 0.0741438 | − | 0.997248i | \(-0.476378\pi\) | ||||
0.0741438 | + | 0.997248i | \(0.476378\pi\) | |||||||
\(684\) | 22.4164 | 0.857113 | ||||||||
\(685\) | −15.5623 | −0.594605 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.00000 | −0.228914 | ||||||||
\(688\) | 14.7295 | 0.561557 | ||||||||
\(689\) | −42.2705 | −1.61038 | ||||||||
\(690\) | 0.145898 | 0.00555424 | ||||||||
\(691\) | −46.5066 | −1.76919 | −0.884597 | − | 0.466357i | \(-0.845566\pi\) | ||||
−0.884597 | + | 0.466357i | \(0.845566\pi\) | |||||||
\(692\) | −1.14590 | −0.0435605 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.7082 | 0.824032 | ||||||||
\(695\) | 29.7984 | 1.13032 | ||||||||
\(696\) | −6.70820 | −0.254274 | ||||||||
\(697\) | 1.47214 | 0.0557611 | ||||||||
\(698\) | −1.67376 | −0.0633528 | ||||||||
\(699\) | 0.708204 | 0.0267867 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2016 | 0.460849 | 0.230425 | − | 0.973090i | \(-0.425989\pi\) | ||||
0.230425 | + | 0.973090i | \(0.425989\pi\) | |||||||
\(702\) | −4.14590 | −0.156477 | ||||||||
\(703\) | 37.4164 | 1.41119 | ||||||||
\(704\) | 0.527864 | 0.0198946 | ||||||||
\(705\) | 2.00000 | 0.0753244 | ||||||||
\(706\) | 7.34752 | 0.276528 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.70820 | 0.176945 | ||||||||
\(709\) | −22.5410 | −0.846546 | −0.423273 | − | 0.906002i | \(-0.639119\pi\) | ||||
−0.423273 | + | 0.906002i | \(0.639119\pi\) | |||||||
\(710\) | 0.236068 | 0.00885947 | ||||||||
\(711\) | 22.0000 | 0.825064 | ||||||||
\(712\) | −32.5623 | −1.22032 | ||||||||
\(713\) | 3.67376 | 0.137583 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8541 | −0.405920 | ||||||||
\(716\) | −7.56231 | −0.282617 | ||||||||
\(717\) | 9.00000 | 0.336111 | ||||||||
\(718\) | −4.18034 | −0.156009 | ||||||||
\(719\) | −11.3607 | −0.423682 | −0.211841 | − | 0.977304i | \(-0.567946\pi\) | ||||
−0.211841 | + | 0.977304i | \(0.567946\pi\) | |||||||
\(720\) | −8.56231 | −0.319098 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.81966 | 0.104937 | ||||||||
\(723\) | −5.23607 | −0.194731 | ||||||||
\(724\) | −8.76393 | −0.325709 | ||||||||
\(725\) | −18.7082 | −0.694805 | ||||||||
\(726\) | −1.41641 | −0.0525678 | ||||||||
\(727\) | 36.9787 | 1.37146 | 0.685732 | − | 0.727854i | \(-0.259482\pi\) | ||||
0.685732 | + | 0.727854i | \(0.259482\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 15.0000 | 0.555175 | ||||||||
\(731\) | −11.6950 | −0.432557 | ||||||||
\(732\) | −6.79837 | −0.251275 | ||||||||
\(733\) | 28.4164 | 1.04958 | 0.524792 | − | 0.851231i | \(-0.324143\pi\) | ||||
0.524792 | + | 0.851231i | \(0.324143\pi\) | |||||||
\(734\) | −20.6738 | −0.763082 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.14590 | 0.0790989 | ||||||||
\(737\) | −9.79837 | −0.360928 | ||||||||
\(738\) | 1.76393 | 0.0649312 | ||||||||
\(739\) | 2.14590 | 0.0789381 | 0.0394691 | − | 0.999221i | \(-0.487433\pi\) | ||||
0.0394691 | + | 0.999221i | \(0.487433\pi\) | |||||||
\(740\) | −20.1803 | −0.741844 | ||||||||
\(741\) | 5.56231 | 0.204336 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.4377 | 0.896532 | 0.448266 | − | 0.893900i | \(-0.352042\pi\) | ||||
0.448266 | + | 0.893900i | \(0.352042\pi\) | |||||||
\(744\) | −8.21478 | −0.301169 | ||||||||
\(745\) | 32.1803 | 1.17900 | ||||||||
\(746\) | −5.87539 | −0.215113 | ||||||||
\(747\) | 34.0902 | 1.24729 | ||||||||
\(748\) | −5.32624 | −0.194747 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.81966 | −0.102959 | ||||||||
\(751\) | 33.9443 | 1.23864 | 0.619322 | − | 0.785137i | \(-0.287408\pi\) | ||||
0.619322 | + | 0.785137i | \(0.287408\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | 7.39512 | 0.269493 | ||||||||
\(754\) | 14.5623 | 0.530328 | ||||||||
\(755\) | 28.5623 | 1.03949 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.70820 | 0.134777 | 0.0673885 | − | 0.997727i | \(-0.478533\pi\) | ||||
0.0673885 | + | 0.997727i | \(0.478533\pi\) | |||||||
\(758\) | −11.8885 | −0.431811 | ||||||||
\(759\) | −0.326238 | −0.0118417 | ||||||||
\(760\) | −17.5623 | −0.637052 | ||||||||
\(761\) | 38.4721 | 1.39461 | 0.697307 | − | 0.716773i | \(-0.254381\pi\) | ||||
0.697307 | + | 0.716773i | \(0.254381\pi\) | |||||||
\(762\) | −2.75078 | −0.0996501 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.94427 | 0.178877 | ||||||||
\(765\) | 6.79837 | 0.245796 | ||||||||
\(766\) | 2.79837 | 0.101109 | ||||||||
\(767\) | −22.8541 | −0.825214 | ||||||||
\(768\) | −2.50658 | −0.0904483 | ||||||||
\(769\) | 7.34752 | 0.264958 | 0.132479 | − | 0.991186i | \(-0.457706\pi\) | ||||
0.132479 | + | 0.991186i | \(0.457706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.14590 | −0.0412685 | ||||||||
\(772\) | 23.3262 | 0.839530 | ||||||||
\(773\) | −21.9443 | −0.789281 | −0.394640 | − | 0.918836i | \(-0.629131\pi\) | ||||
−0.394640 | + | 0.918836i | \(0.629131\pi\) | |||||||
\(774\) | −14.0132 | −0.503692 | ||||||||
\(775\) | −22.9098 | −0.822945 | ||||||||
\(776\) | −11.5066 | −0.413062 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.90983 | −0.140174 | ||||||||
\(779\) | −4.85410 | −0.173916 | ||||||||
\(780\) | −3.00000 | −0.107417 | ||||||||
\(781\) | −0.527864 | −0.0188885 | ||||||||
\(782\) | −0.347524 | −0.0124274 | ||||||||
\(783\) | −17.5623 | −0.627626 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0000 | 0.428298 | ||||||||
\(786\) | 1.97871 | 0.0705784 | ||||||||
\(787\) | −27.7082 | −0.987691 | −0.493845 | − | 0.869550i | \(-0.664409\pi\) | ||||
−0.493845 | + | 0.869550i | \(0.664409\pi\) | |||||||
\(788\) | 6.61803 | 0.235758 | ||||||||
\(789\) | −1.68692 | −0.0600559 | ||||||||
\(790\) | −7.70820 | −0.274246 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.2705 | −0.507080 | ||||||||
\(793\) | 33.0000 | 1.17186 | ||||||||
\(794\) | 19.0000 | 0.674285 | ||||||||
\(795\) | −8.70820 | −0.308848 | ||||||||
\(796\) | 1.14590 | 0.0406153 | ||||||||
\(797\) | −6.52786 | −0.231229 | −0.115614 | − | 0.993294i | \(-0.536884\pi\) | ||||
−0.115614 | + | 0.993294i | \(0.536884\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.76393 | −0.168536 | ||||||||
\(800\) | −13.3820 | −0.473124 | ||||||||
\(801\) | −41.5623 | −1.46853 | ||||||||
\(802\) | −23.5967 | −0.833230 | ||||||||
\(803\) | −33.5410 | −1.18364 | ||||||||
\(804\) | −2.70820 | −0.0955110 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.8328 | 0.628134 | ||||||||
\(807\) | −7.83282 | −0.275728 | ||||||||
\(808\) | 3.94427 | 0.138759 | ||||||||
\(809\) | −12.9656 | −0.455845 | −0.227922 | − | 0.973679i | \(-0.573193\pi\) | ||||
−0.227922 | + | 0.973679i | \(0.573193\pi\) | |||||||
\(810\) | 7.70820 | 0.270839 | ||||||||
\(811\) | 40.2361 | 1.41288 | 0.706440 | − | 0.707773i | \(-0.250300\pi\) | ||||
0.706440 | + | 0.707773i | \(0.250300\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3262 | −0.397229 | ||||||||
\(814\) | −10.6525 | −0.373369 | ||||||||
\(815\) | 8.94427 | 0.313304 | ||||||||
\(816\) | −1.04257 | −0.0364973 | ||||||||
\(817\) | 38.5623 | 1.34912 | ||||||||
\(818\) | −16.4377 | −0.574730 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.61803 | 0.0914257 | ||||||||
\(821\) | −0.0557281 | −0.00194492 | −0.000972462 | − | 1.00000i | \(-0.500310\pi\) | ||||
−0.000972462 | 1.00000i | \(0.500310\pi\) | ||||||||
\(822\) | −2.27051 | −0.0791931 | ||||||||
\(823\) | 4.50658 | 0.157089 | 0.0785447 | − | 0.996911i | \(-0.474973\pi\) | ||||
0.0785447 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(824\) | 7.96556 | 0.277493 | ||||||||
\(825\) | 2.03444 | 0.0708302 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.1246 | −1.74300 | −0.871502 | − | 0.490392i | \(-0.836853\pi\) | ||||
−0.871502 | + | 0.490392i | \(0.836853\pi\) | |||||||
\(828\) | 1.76393 | 0.0613009 | ||||||||
\(829\) | −12.3050 | −0.427369 | −0.213684 | − | 0.976903i | \(-0.568546\pi\) | ||||
−0.213684 | + | 0.976903i | \(0.568546\pi\) | |||||||
\(830\) | −11.9443 | −0.414592 | ||||||||
\(831\) | 1.79837 | 0.0623849 | ||||||||
\(832\) | −0.708204 | −0.0245526 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.34752 | 0.150542 | ||||||||
\(835\) | −10.8541 | −0.375622 | ||||||||
\(836\) | 17.5623 | 0.607405 | ||||||||
\(837\) | −21.5066 | −0.743376 | ||||||||
\(838\) | 10.8541 | 0.374949 | ||||||||
\(839\) | −27.5967 | −0.952746 | −0.476373 | − | 0.879243i | \(-0.658049\pi\) | ||||
−0.476373 | + | 0.879243i | \(0.658049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.6869 | 1.12714 | ||||||||
\(842\) | 7.12461 | 0.245530 | ||||||||
\(843\) | 10.3131 | 0.355201 | ||||||||
\(844\) | −3.00000 | −0.103264 | ||||||||
\(845\) | −6.47214 | −0.222648 | ||||||||
\(846\) | −5.70820 | −0.196252 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −26.1246 | −0.897123 | ||||||||
\(849\) | 3.77709 | 0.129629 | ||||||||
\(850\) | 2.16718 | 0.0743338 | ||||||||
\(851\) | 2.94427 | 0.100928 | ||||||||
\(852\) | −0.145898 | −0.00499838 | ||||||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.4164 | −0.766625 | ||||||||
\(856\) | −21.7082 | −0.741971 | ||||||||
\(857\) | 11.0902 | 0.378833 | 0.189416 | − | 0.981897i | \(-0.439340\pi\) | ||||
0.189416 | + | 0.981897i | \(0.439340\pi\) | |||||||
\(858\) | −1.58359 | −0.0540629 | ||||||||
\(859\) | 22.3820 | 0.763663 | 0.381831 | − | 0.924232i | \(-0.375293\pi\) | ||||
0.381831 | + | 0.924232i | \(0.375293\pi\) | |||||||
\(860\) | −20.7984 | −0.709219 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.68692 | −0.295878 | ||||||||
\(863\) | −9.87539 | −0.336162 | −0.168081 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168081 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(864\) | −12.5623 | −0.427378 | ||||||||
\(865\) | 1.14590 | 0.0389617 | ||||||||
\(866\) | 23.1803 | 0.787700 | ||||||||
\(867\) | −5.66563 | −0.192415 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.2361 | 0.584694 | ||||||||
\(870\) | 3.00000 | 0.101710 | ||||||||
\(871\) | 13.1459 | 0.445432 | ||||||||
\(872\) | 15.5279 | 0.525840 | ||||||||
\(873\) | −14.6869 | −0.497077 | ||||||||
\(874\) | 1.14590 | 0.0387606 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.27051 | −0.313222 | ||||||||
\(877\) | 32.9787 | 1.11361 | 0.556806 | − | 0.830643i | \(-0.312027\pi\) | ||||
0.556806 | + | 0.830643i | \(0.312027\pi\) | |||||||
\(878\) | −12.2148 | −0.412229 | ||||||||
\(879\) | 0.0212862 | 0.000717967 0 | ||||||||
\(880\) | −6.70820 | −0.226134 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.5623 | 0.691977 | 0.345988 | − | 0.938239i | \(-0.387544\pi\) | ||||
0.345988 | + | 0.938239i | \(0.387544\pi\) | |||||||
\(884\) | 7.14590 | 0.240343 | ||||||||
\(885\) | −4.70820 | −0.158265 | ||||||||
\(886\) | −20.7771 | −0.698020 | ||||||||
\(887\) | 41.3050 | 1.38688 | 0.693442 | − | 0.720512i | \(-0.256093\pi\) | ||||
0.693442 | + | 0.720512i | \(0.256093\pi\) | |||||||
\(888\) | −6.58359 | −0.220931 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.5623 | 0.488130 | ||||||||
\(891\) | −17.2361 | −0.577430 | ||||||||
\(892\) | −8.32624 | −0.278783 | ||||||||
\(893\) | 15.7082 | 0.525655 | ||||||||
\(894\) | 4.69505 | 0.157026 | ||||||||
\(895\) | 7.56231 | 0.252780 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.437694 | 0.0146142 | ||||||||
\(898\) | −17.2361 | −0.575175 | ||||||||
\(899\) | 75.5410 | 2.51943 | ||||||||
\(900\) | −11.0000 | −0.366667 | ||||||||
\(901\) | 20.7426 | 0.691038 | ||||||||
\(902\) | 1.38197 | 0.0460144 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.2361 | 0.739561 | ||||||||
\(905\) | 8.76393 | 0.291323 | ||||||||
\(906\) | 4.16718 | 0.138445 | ||||||||
\(907\) | −2.54915 | −0.0846431 | −0.0423216 | − | 0.999104i | \(-0.513475\pi\) | ||||
−0.0423216 | + | 0.999104i | \(0.513475\pi\) | |||||||
\(908\) | 0.854102 | 0.0283444 | ||||||||
\(909\) | 5.03444 | 0.166982 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.3050 | −0.705865 | −0.352932 | − | 0.935649i | \(-0.614815\pi\) | ||||
−0.352932 | + | 0.935649i | \(0.614815\pi\) | |||||||
\(912\) | 3.43769 | 0.113833 | ||||||||
\(913\) | 26.7082 | 0.883913 | ||||||||
\(914\) | −12.7984 | −0.423333 | ||||||||
\(915\) | 6.79837 | 0.224747 | ||||||||
\(916\) | 25.4164 | 0.839782 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.03444 | 0.0671466 | ||||||||
\(919\) | −7.56231 | −0.249457 | −0.124729 | − | 0.992191i | \(-0.539806\pi\) | ||||
−0.124729 | + | 0.992191i | \(0.539806\pi\) | |||||||
\(920\) | −1.38197 | −0.0455621 | ||||||||
\(921\) | 7.59675 | 0.250321 | ||||||||
\(922\) | 5.45085 | 0.179514 | ||||||||
\(923\) | 0.708204 | 0.0233108 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.3607 | −0.603695 | ||||||||
\(926\) | −23.9098 | −0.785726 | ||||||||
\(927\) | 10.1672 | 0.333934 | ||||||||
\(928\) | 44.1246 | 1.44846 | ||||||||
\(929\) | 16.6869 | 0.547480 | 0.273740 | − | 0.961804i | \(-0.411739\pi\) | ||||
0.273740 | + | 0.961804i | \(0.411739\pi\) | |||||||
\(930\) | 3.67376 | 0.120467 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.00000 | −0.0982683 | ||||||||
\(933\) | −6.88854 | −0.225521 | ||||||||
\(934\) | 11.4934 | 0.376076 | ||||||||
\(935\) | 5.32624 | 0.174187 | ||||||||
\(936\) | 19.1459 | 0.625803 | ||||||||
\(937\) | −16.5967 | −0.542192 | −0.271096 | − | 0.962552i | \(-0.587386\pi\) | ||||
−0.271096 | + | 0.962552i | \(0.587386\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.39512 | −0.176063 | ||||||||
\(940\) | −8.47214 | −0.276331 | ||||||||
\(941\) | −2.49342 | −0.0812832 | −0.0406416 | − | 0.999174i | \(-0.512940\pi\) | ||||
−0.0406416 | + | 0.999174i | \(0.512940\pi\) | |||||||
\(942\) | 1.75078 | 0.0570434 | ||||||||
\(943\) | −0.381966 | −0.0124385 | ||||||||
\(944\) | −14.1246 | −0.459717 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.9787 | −0.356949 | ||||||||
\(947\) | 19.0902 | 0.620347 | 0.310174 | − | 0.950680i | \(-0.399613\pi\) | ||||
0.310174 | + | 0.950680i | \(0.399613\pi\) | |||||||
\(948\) | 4.76393 | 0.154725 | ||||||||
\(949\) | 45.0000 | 1.46076 | ||||||||
\(950\) | −7.14590 | −0.231844 | ||||||||
\(951\) | −0.604878 | −0.0196145 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.32624 | 0.204927 | 0.102463 | − | 0.994737i | \(-0.467328\pi\) | ||||
0.102463 | + | 0.994737i | \(0.467328\pi\) | |||||||
\(954\) | 24.8541 | 0.804681 | ||||||||
\(955\) | −4.94427 | −0.159993 | ||||||||
\(956\) | −38.1246 | −1.23304 | ||||||||
\(957\) | −6.70820 | −0.216845 | ||||||||
\(958\) | 0.639320 | 0.0206555 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.145898 | −0.00470884 | ||||||||
\(961\) | 61.5066 | 1.98408 | ||||||||
\(962\) | 14.2918 | 0.460786 | ||||||||
\(963\) | −27.7082 | −0.892884 | ||||||||
\(964\) | 22.1803 | 0.714381 | ||||||||
\(965\) | −23.3262 | −0.750898 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.2492 | 1.48727 | 0.743637 | − | 0.668583i | \(-0.233099\pi\) | ||||
0.743637 | + | 0.668583i | \(0.233099\pi\) | |||||||
\(968\) | 13.4164 | 0.431220 | ||||||||
\(969\) | −2.72949 | −0.0876839 | ||||||||
\(970\) | 5.14590 | 0.165225 | ||||||||
\(971\) | −43.9443 | −1.41024 | −0.705119 | − | 0.709089i | \(-0.749107\pi\) | ||||
−0.705119 | + | 0.709089i | \(0.749107\pi\) | |||||||
\(972\) | −15.6180 | −0.500949 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.5410 | 0.401840 | ||||||||
\(975\) | −2.72949 | −0.0874136 | ||||||||
\(976\) | 20.3951 | 0.652832 | ||||||||
\(977\) | 8.32624 | 0.266380 | 0.133190 | − | 0.991091i | \(-0.457478\pi\) | ||||
0.133190 | + | 0.991091i | \(0.457478\pi\) | |||||||
\(978\) | 1.30495 | 0.0417278 | ||||||||
\(979\) | −32.5623 | −1.04070 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.8197 | 0.632793 | ||||||||
\(982\) | 24.2016 | 0.772305 | ||||||||
\(983\) | 34.3050 | 1.09416 | 0.547079 | − | 0.837081i | \(-0.315740\pi\) | ||||
0.547079 | + | 0.837081i | \(0.315740\pi\) | |||||||
\(984\) | 0.854102 | 0.0272278 | ||||||||
\(985\) | −6.61803 | −0.210868 | ||||||||
\(986\) | −7.14590 | −0.227572 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.5623 | −0.749617 | ||||||||
\(989\) | 3.03444 | 0.0964896 | ||||||||
\(990\) | 6.38197 | 0.202832 | ||||||||
\(991\) | 1.58359 | 0.0503045 | 0.0251522 | − | 0.999684i | \(-0.491993\pi\) | ||||
0.0251522 | + | 0.999684i | \(0.491993\pi\) | |||||||
\(992\) | 54.0344 | 1.71560 | ||||||||
\(993\) | 3.77709 | 0.119862 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.14590 | −0.0363274 | ||||||||
\(996\) | 7.38197 | 0.233907 | ||||||||
\(997\) | 8.32624 | 0.263695 | 0.131847 | − | 0.991270i | \(-0.457909\pi\) | ||||
0.131847 | + | 0.991270i | \(0.457909\pi\) | |||||||
\(998\) | −0.763932 | −0.0241818 | ||||||||
\(999\) | −17.2361 | −0.545325 |
(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 | 2009.2.a.b.1.2 | 2 | ||
7.6 | odd | 2 | 287.2.a.a.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 2583.2.a.h.1.1 | 2 | |||
28.27 | even | 2 | 4592.2.a.p.1.1 | 2 | |||
35.34 | odd | 2 | 7175.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.a.a.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
2009.2.a.b.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2583.2.a.h.1.1 | 2 | 21.20 | even | 2 | |||
4592.2.a.p.1.1 | 2 | 28.27 | even | 2 | |||
7175.2.a.h.1.1 | 2 | 35.34 | odd | 2 |