Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.89122\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89122 | −1.33729 | −0.668647 | − | 0.743580i | \(-0.733126\pi\) | ||||
−0.668647 | + | 0.743580i | \(0.733126\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.57671 | 0.788356 | ||||||||
\(5\) | 1.57671 | 0.705127 | 0.352564 | − | 0.935788i | \(-0.385310\pi\) | ||||
0.352564 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(6\) | −1.89122 | −0.772087 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.800530 | 0.283030 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.98191 | −0.942963 | ||||||||
\(11\) | 1.66740 | 0.502741 | 0.251370 | − | 0.967891i | \(-0.419119\pi\) | ||||
0.251370 | + | 0.967891i | \(0.419119\pi\) | |||||||
\(12\) | 1.57671 | 0.455158 | ||||||||
\(13\) | 5.04464 | 1.39913 | 0.699566 | − | 0.714568i | \(-0.253377\pi\) | ||||
0.699566 | + | 0.714568i | \(0.253377\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.57671 | 0.407105 | ||||||||
\(16\) | −4.66740 | −1.16685 | ||||||||
\(17\) | −6.35915 | −1.54232 | −0.771160 | − | 0.636641i | \(-0.780323\pi\) | ||||
−0.771160 | + | 0.636641i | \(0.780323\pi\) | |||||||
\(18\) | −1.89122 | −0.445765 | ||||||||
\(19\) | −0.691750 | −0.158698 | −0.0793491 | − | 0.996847i | \(-0.525284\pi\) | ||||
−0.0793491 | + | 0.996847i | \(0.525284\pi\) | |||||||
\(20\) | 2.48602 | 0.555891 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.15343 | −0.672312 | ||||||||
\(23\) | 8.82708 | 1.84057 | 0.920287 | − | 0.391244i | \(-0.127955\pi\) | ||||
0.920287 | + | 0.391244i | \(0.127955\pi\) | |||||||
\(24\) | 0.800530 | 0.163407 | ||||||||
\(25\) | −2.51398 | −0.502796 | ||||||||
\(26\) | −9.54053 | −1.87105 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.64931 | −1.23475 | −0.617373 | − | 0.786670i | \(-0.711803\pi\) | ||||
−0.617373 | + | 0.786670i | \(0.711803\pi\) | |||||||
\(30\) | −2.98191 | −0.544420 | ||||||||
\(31\) | −2.35915 | −0.423716 | −0.211858 | − | 0.977300i | \(-0.567951\pi\) | ||||
−0.211858 | + | 0.977300i | \(0.567951\pi\) | |||||||
\(32\) | 7.22603 | 1.27739 | ||||||||
\(33\) | 1.66740 | 0.290258 | ||||||||
\(34\) | 12.0266 | 2.06254 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.57671 | 0.262785 | ||||||||
\(37\) | 9.02655 | 1.48396 | 0.741978 | − | 0.670424i | \(-0.233888\pi\) | ||||
0.741978 | + | 0.670424i | \(0.233888\pi\) | |||||||
\(38\) | 1.30825 | 0.212226 | ||||||||
\(39\) | 5.04464 | 0.807790 | ||||||||
\(40\) | 1.26221 | 0.199572 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.96021 | −1.51892 | −0.759459 | − | 0.650555i | \(-0.774536\pi\) | ||||
−0.759459 | + | 0.650555i | \(0.774536\pi\) | |||||||
\(44\) | 2.62901 | 0.396339 | ||||||||
\(45\) | 1.57671 | 0.235042 | ||||||||
\(46\) | −16.6940 | −2.46139 | ||||||||
\(47\) | 1.33621 | 0.194906 | 0.0974528 | − | 0.995240i | \(-0.468930\pi\) | ||||
0.0974528 | + | 0.995240i | \(0.468930\pi\) | |||||||
\(48\) | −4.66740 | −0.673682 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.75448 | 0.672386 | ||||||||
\(51\) | −6.35915 | −0.890459 | ||||||||
\(52\) | 7.95395 | 1.10302 | ||||||||
\(53\) | 1.66115 | 0.228176 | 0.114088 | − | 0.993471i | \(-0.463605\pi\) | ||||
0.114088 | + | 0.993471i | \(0.463605\pi\) | |||||||
\(54\) | −1.89122 | −0.257362 | ||||||||
\(55\) | 2.62901 | 0.354496 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.691750 | −0.0916245 | ||||||||
\(58\) | 12.5753 | 1.65122 | ||||||||
\(59\) | 12.0266 | 1.56572 | 0.782862 | − | 0.622195i | \(-0.213759\pi\) | ||||
0.782862 | + | 0.622195i | \(0.213759\pi\) | |||||||
\(60\) | 2.48602 | 0.320944 | ||||||||
\(61\) | 11.9602 | 1.53135 | 0.765674 | − | 0.643229i | \(-0.222406\pi\) | ||||
0.765674 | + | 0.643229i | \(0.222406\pi\) | |||||||
\(62\) | 4.46168 | 0.566633 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.33120 | −0.541400 | ||||||||
\(65\) | 7.95395 | 0.986567 | ||||||||
\(66\) | −3.15343 | −0.388160 | ||||||||
\(67\) | −0.870922 | −0.106400 | −0.0532000 | − | 0.998584i | \(-0.516942\pi\) | ||||
−0.0532000 | + | 0.998584i | \(0.516942\pi\) | |||||||
\(68\) | −10.0266 | −1.21590 | ||||||||
\(69\) | 8.82708 | 1.06266 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8961 | −1.29313 | −0.646563 | − | 0.762860i | \(-0.723794\pi\) | ||||
−0.646563 | + | 0.762860i | \(0.723794\pi\) | |||||||
\(72\) | 0.800530 | 0.0943433 | ||||||||
\(73\) | 2.79427 | 0.327045 | 0.163522 | − | 0.986540i | \(-0.447714\pi\) | ||||
0.163522 | + | 0.986540i | \(0.447714\pi\) | |||||||
\(74\) | −17.0712 | −1.98449 | ||||||||
\(75\) | −2.51398 | −0.290289 | ||||||||
\(76\) | −1.09069 | −0.125111 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.54053 | −1.08025 | ||||||||
\(79\) | 12.2463 | 1.37782 | 0.688910 | − | 0.724847i | \(-0.258090\pi\) | ||||
0.688910 | + | 0.724847i | \(0.258090\pi\) | |||||||
\(80\) | −7.35915 | −0.822778 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.89122 | −0.208850 | ||||||||
\(83\) | 2.62901 | 0.288572 | 0.144286 | − | 0.989536i | \(-0.453911\pi\) | ||||
0.144286 | + | 0.989536i | \(0.453911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0266 | −1.08753 | ||||||||
\(86\) | 18.8369 | 2.03124 | ||||||||
\(87\) | −6.64931 | −0.712881 | ||||||||
\(88\) | 1.33481 | 0.142291 | ||||||||
\(89\) | 12.7183 | 1.34814 | 0.674069 | − | 0.738669i | \(-0.264545\pi\) | ||||
0.674069 | + | 0.738669i | \(0.264545\pi\) | |||||||
\(90\) | −2.98191 | −0.314321 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.9178 | 1.45103 | ||||||||
\(93\) | −2.35915 | −0.244633 | ||||||||
\(94\) | −2.52706 | −0.260646 | ||||||||
\(95\) | −1.09069 | −0.111902 | ||||||||
\(96\) | 7.22603 | 0.737503 | ||||||||
\(97\) | 3.21198 | 0.326128 | 0.163064 | − | 0.986616i | \(-0.447862\pi\) | ||||
0.163064 | + | 0.986616i | \(0.447862\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.66740 | 0.167580 | ||||||||
\(100\) | −3.96382 | −0.396382 | ||||||||
\(101\) | 7.97425 | 0.793468 | 0.396734 | − | 0.917934i | \(-0.370144\pi\) | ||||
0.396734 | + | 0.917934i | \(0.370144\pi\) | |||||||
\(102\) | 12.0266 | 1.19081 | ||||||||
\(103\) | 6.34246 | 0.624941 | 0.312471 | − | 0.949927i | \(-0.398843\pi\) | ||||
0.312471 | + | 0.949927i | \(0.398843\pi\) | |||||||
\(104\) | 4.03839 | 0.395997 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.14159 | −0.305138 | ||||||||
\(107\) | −11.2401 | −1.08662 | −0.543309 | − | 0.839533i | \(-0.682829\pi\) | ||||
−0.543309 | + | 0.839533i | \(0.682829\pi\) | |||||||
\(108\) | 1.57671 | 0.151719 | ||||||||
\(109\) | −7.48963 | −0.717377 | −0.358688 | − | 0.933457i | \(-0.616776\pi\) | ||||
−0.358688 | + | 0.933457i | \(0.616776\pi\) | |||||||
\(110\) | −4.97204 | −0.474066 | ||||||||
\(111\) | 9.02655 | 0.856763 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.3348 | 1.44258 | 0.721289 | − | 0.692635i | \(-0.243550\pi\) | ||||
0.721289 | + | 0.692635i | \(0.243550\pi\) | |||||||
\(114\) | 1.30825 | 0.122529 | ||||||||
\(115\) | 13.9178 | 1.29784 | ||||||||
\(116\) | −10.4841 | −0.973420 | ||||||||
\(117\) | 5.04464 | 0.466378 | ||||||||
\(118\) | −22.7449 | −2.09383 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.26221 | 0.115223 | ||||||||
\(121\) | −8.21977 | −0.747252 | ||||||||
\(122\) | −22.6194 | −2.04786 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −3.71970 | −0.334039 | ||||||||
\(125\) | −11.8474 | −1.05966 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4241 | −1.36867 | −0.684334 | − | 0.729169i | \(-0.739907\pi\) | ||||
−0.684334 | + | 0.729169i | \(0.739907\pi\) | |||||||
\(128\) | −6.26080 | −0.553382 | ||||||||
\(129\) | −9.96021 | −0.876948 | ||||||||
\(130\) | −15.0427 | −1.31933 | ||||||||
\(131\) | 15.9345 | 1.39220 | 0.696100 | − | 0.717945i | \(-0.254917\pi\) | ||||
0.696100 | + | 0.717945i | \(0.254917\pi\) | |||||||
\(132\) | 2.62901 | 0.228826 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.64710 | 0.142288 | ||||||||
\(135\) | 1.57671 | 0.135702 | ||||||||
\(136\) | −5.09069 | −0.436523 | ||||||||
\(137\) | 3.13313 | 0.267681 | 0.133841 | − | 0.991003i | \(-0.457269\pi\) | ||||
0.133841 | + | 0.991003i | \(0.457269\pi\) | |||||||
\(138\) | −16.6940 | −1.42108 | ||||||||
\(139\) | 12.9192 | 1.09579 | 0.547895 | − | 0.836547i | \(-0.315429\pi\) | ||||
0.547895 | + | 0.836547i | \(0.315429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.33621 | 0.112529 | ||||||||
\(142\) | 20.6069 | 1.72929 | ||||||||
\(143\) | 8.41145 | 0.703401 | ||||||||
\(144\) | −4.66740 | −0.388950 | ||||||||
\(145\) | −10.4841 | −0.870653 | ||||||||
\(146\) | −5.28458 | −0.437355 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.2323 | 1.16989 | ||||||||
\(149\) | 17.0545 | 1.39716 | 0.698580 | − | 0.715532i | \(-0.253816\pi\) | ||||
0.698580 | + | 0.715532i | \(0.253816\pi\) | |||||||
\(150\) | 4.75448 | 0.388202 | ||||||||
\(151\) | −4.62901 | −0.376704 | −0.188352 | − | 0.982102i | \(-0.560315\pi\) | ||||
−0.188352 | + | 0.982102i | \(0.560315\pi\) | |||||||
\(152\) | −0.553766 | −0.0449164 | ||||||||
\(153\) | −6.35915 | −0.514107 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.71970 | −0.298774 | ||||||||
\(156\) | 7.95395 | 0.636826 | ||||||||
\(157\) | −18.4380 | −1.47151 | −0.735757 | − | 0.677246i | \(-0.763173\pi\) | ||||
−0.735757 | + | 0.677246i | \(0.763173\pi\) | |||||||
\(158\) | −23.1605 | −1.84255 | ||||||||
\(159\) | 1.66115 | 0.131737 | ||||||||
\(160\) | 11.3934 | 0.900725 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.89122 | −0.148588 | ||||||||
\(163\) | −17.6019 | −1.37868 | −0.689342 | − | 0.724436i | \(-0.742100\pi\) | ||||
−0.689342 | + | 0.724436i | \(0.742100\pi\) | |||||||
\(164\) | 1.57671 | 0.123121 | ||||||||
\(165\) | 2.62901 | 0.204669 | ||||||||
\(166\) | −4.97204 | −0.385906 | ||||||||
\(167\) | 0.255948 | 0.0198059 | 0.00990294 | − | 0.999951i | \(-0.496848\pi\) | ||||
0.00990294 | + | 0.999951i | \(0.496848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4484 | 0.957572 | ||||||||
\(170\) | 18.9624 | 1.45435 | ||||||||
\(171\) | −0.691750 | −0.0528994 | ||||||||
\(172\) | −15.7044 | −1.19745 | ||||||||
\(173\) | −21.9173 | −1.66634 | −0.833172 | − | 0.553014i | \(-0.813478\pi\) | ||||
−0.833172 | + | 0.553014i | \(0.813478\pi\) | |||||||
\(174\) | 12.5753 | 0.953332 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.78244 | −0.586623 | ||||||||
\(177\) | 12.0266 | 0.903971 | ||||||||
\(178\) | −24.0531 | −1.80286 | ||||||||
\(179\) | 15.5685 | 1.16364 | 0.581822 | − | 0.813316i | \(-0.302340\pi\) | ||||
0.581822 | + | 0.813316i | \(0.302340\pi\) | |||||||
\(180\) | 2.48602 | 0.185297 | ||||||||
\(181\) | 22.5707 | 1.67767 | 0.838833 | − | 0.544388i | \(-0.183238\pi\) | ||||
0.838833 | + | 0.544388i | \(0.183238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9602 | 0.884124 | ||||||||
\(184\) | 7.06634 | 0.520938 | ||||||||
\(185\) | 14.2323 | 1.04638 | ||||||||
\(186\) | 4.46168 | 0.327146 | ||||||||
\(187\) | −10.6033 | −0.775388 | ||||||||
\(188\) | 2.10681 | 0.153655 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.06273 | 0.149647 | ||||||||
\(191\) | 20.0797 | 1.45291 | 0.726457 | − | 0.687212i | \(-0.241166\pi\) | ||||
0.726457 | + | 0.687212i | \(0.241166\pi\) | |||||||
\(192\) | −4.33120 | −0.312577 | ||||||||
\(193\) | 2.56628 | 0.184725 | 0.0923624 | − | 0.995725i | \(-0.470558\pi\) | ||||
0.0923624 | + | 0.995725i | \(0.470558\pi\) | |||||||
\(194\) | −6.07457 | −0.436129 | ||||||||
\(195\) | 7.95395 | 0.569595 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.4241 | 1.81139 | 0.905696 | − | 0.423928i | \(-0.139349\pi\) | ||||
0.905696 | + | 0.423928i | \(0.139349\pi\) | |||||||
\(198\) | −3.15343 | −0.224104 | ||||||||
\(199\) | −15.8215 | −1.12156 | −0.560778 | − | 0.827966i | \(-0.689498\pi\) | ||||
−0.560778 | + | 0.827966i | \(0.689498\pi\) | |||||||
\(200\) | −2.01251 | −0.142306 | ||||||||
\(201\) | −0.870922 | −0.0614301 | ||||||||
\(202\) | −15.0811 | −1.06110 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.0266 | −0.701999 | ||||||||
\(205\) | 1.57671 | 0.110122 | ||||||||
\(206\) | −11.9950 | −0.835731 | ||||||||
\(207\) | 8.82708 | 0.613525 | ||||||||
\(208\) | −23.5454 | −1.63258 | ||||||||
\(209\) | −1.15343 | −0.0797841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.63262 | 0.387766 | 0.193883 | − | 0.981025i | \(-0.437892\pi\) | ||||
0.193883 | + | 0.981025i | \(0.437892\pi\) | |||||||
\(212\) | 2.61915 | 0.179884 | ||||||||
\(213\) | −10.8961 | −0.746587 | ||||||||
\(214\) | 21.2574 | 1.45313 | ||||||||
\(215\) | −15.7044 | −1.07103 | ||||||||
\(216\) | 0.800530 | 0.0544691 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.1645 | 0.959344 | ||||||||
\(219\) | 2.79427 | 0.188819 | ||||||||
\(220\) | 4.14520 | 0.279469 | ||||||||
\(221\) | −32.0797 | −2.15791 | ||||||||
\(222\) | −17.0712 | −1.14574 | ||||||||
\(223\) | 14.7909 | 0.990472 | 0.495236 | − | 0.868758i | \(-0.335082\pi\) | ||||
0.495236 | + | 0.868758i | \(0.335082\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.51398 | −0.167599 | ||||||||
\(226\) | −29.0015 | −1.92915 | ||||||||
\(227\) | 5.41298 | 0.359272 | 0.179636 | − | 0.983733i | \(-0.442508\pi\) | ||||
0.179636 | + | 0.983733i | \(0.442508\pi\) | |||||||
\(228\) | −1.09069 | −0.0722327 | ||||||||
\(229\) | −0.527059 | −0.0348290 | −0.0174145 | − | 0.999848i | \(-0.505543\pi\) | ||||
−0.0174145 | + | 0.999848i | \(0.505543\pi\) | |||||||
\(230\) | −26.3216 | −1.73559 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.32297 | −0.349470 | ||||||||
\(233\) | −16.7449 | −1.09699 | −0.548496 | − | 0.836153i | \(-0.684799\pi\) | ||||
−0.548496 | + | 0.836153i | \(0.684799\pi\) | |||||||
\(234\) | −9.54053 | −0.623684 | ||||||||
\(235\) | 2.10681 | 0.137433 | ||||||||
\(236\) | 18.9624 | 1.23435 | ||||||||
\(237\) | 12.2463 | 0.795484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.42690 | 0.0922982 | 0.0461491 | − | 0.998935i | \(-0.485305\pi\) | ||||
0.0461491 | + | 0.998935i | \(0.485305\pi\) | |||||||
\(240\) | −7.35915 | −0.475031 | ||||||||
\(241\) | −12.8767 | −0.829464 | −0.414732 | − | 0.909944i | \(-0.636125\pi\) | ||||
−0.414732 | + | 0.909944i | \(0.636125\pi\) | |||||||
\(242\) | 15.5454 | 0.999295 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 18.8578 | 1.20725 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.89122 | −0.120580 | ||||||||
\(247\) | −3.48963 | −0.222040 | ||||||||
\(248\) | −1.88857 | −0.119924 | ||||||||
\(249\) | 2.62901 | 0.166607 | ||||||||
\(250\) | 22.4060 | 1.41708 | ||||||||
\(251\) | 20.8104 | 1.31354 | 0.656770 | − | 0.754091i | \(-0.271922\pi\) | ||||
0.656770 | + | 0.754091i | \(0.271922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7183 | 0.925332 | ||||||||
\(254\) | 29.1704 | 1.83031 | ||||||||
\(255\) | −10.0266 | −0.627887 | ||||||||
\(256\) | 20.5030 | 1.28143 | ||||||||
\(257\) | 24.4388 | 1.52445 | 0.762226 | − | 0.647311i | \(-0.224107\pi\) | ||||
0.762226 | + | 0.647311i | \(0.224107\pi\) | |||||||
\(258\) | 18.8369 | 1.17274 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.5411 | 0.777766 | ||||||||
\(261\) | −6.64931 | −0.411582 | ||||||||
\(262\) | −30.1356 | −1.86178 | ||||||||
\(263\) | −15.0147 | −0.925847 | −0.462924 | − | 0.886398i | \(-0.653200\pi\) | ||||
−0.462924 | + | 0.886398i | \(0.653200\pi\) | |||||||
\(264\) | 1.33481 | 0.0821516 | ||||||||
\(265\) | 2.61915 | 0.160893 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.7183 | 0.778348 | ||||||||
\(268\) | −1.37319 | −0.0838811 | ||||||||
\(269\) | −4.84598 | −0.295465 | −0.147732 | − | 0.989027i | \(-0.547197\pi\) | ||||
−0.147732 | + | 0.989027i | \(0.547197\pi\) | |||||||
\(270\) | −2.98191 | −0.181473 | ||||||||
\(271\) | −15.3411 | −0.931903 | −0.465952 | − | 0.884810i | \(-0.654288\pi\) | ||||
−0.465952 | + | 0.884810i | \(0.654288\pi\) | |||||||
\(272\) | 29.6807 | 1.79966 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.92543 | −0.357968 | ||||||||
\(275\) | −4.19181 | −0.252776 | ||||||||
\(276\) | 13.9178 | 0.837752 | ||||||||
\(277\) | −4.75741 | −0.285845 | −0.142923 | − | 0.989734i | \(-0.545650\pi\) | ||||
−0.142923 | + | 0.989734i | \(0.545650\pi\) | |||||||
\(278\) | −24.4330 | −1.46539 | ||||||||
\(279\) | −2.35915 | −0.141239 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.6242 | −1.76723 | −0.883617 | − | 0.468210i | \(-0.844899\pi\) | ||||
−0.883617 | + | 0.468210i | \(0.844899\pi\) | |||||||
\(282\) | −2.52706 | −0.150484 | ||||||||
\(283\) | 4.78176 | 0.284246 | 0.142123 | − | 0.989849i | \(-0.454607\pi\) | ||||
0.142123 | + | 0.989849i | \(0.454607\pi\) | |||||||
\(284\) | −17.1800 | −1.01944 | ||||||||
\(285\) | −1.09069 | −0.0646069 | ||||||||
\(286\) | −15.9079 | −0.940654 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.22603 | 0.425798 | ||||||||
\(289\) | 23.4388 | 1.37875 | ||||||||
\(290\) | 19.8277 | 1.16432 | ||||||||
\(291\) | 3.21198 | 0.188290 | ||||||||
\(292\) | 4.40576 | 0.257828 | ||||||||
\(293\) | −15.6380 | −0.913584 | −0.456792 | − | 0.889573i | \(-0.651002\pi\) | ||||
−0.456792 | + | 0.889573i | \(0.651002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.9624 | 1.10403 | ||||||||
\(296\) | 7.22603 | 0.420004 | ||||||||
\(297\) | 1.66740 | 0.0967525 | ||||||||
\(298\) | −32.2538 | −1.86841 | ||||||||
\(299\) | 44.5295 | 2.57521 | ||||||||
\(300\) | −3.96382 | −0.228851 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.75448 | 0.503764 | ||||||||
\(303\) | 7.97425 | 0.458109 | ||||||||
\(304\) | 3.22867 | 0.185177 | ||||||||
\(305\) | 18.8578 | 1.07980 | ||||||||
\(306\) | 12.0266 | 0.687512 | ||||||||
\(307\) | 21.2711 | 1.21401 | 0.607003 | − | 0.794699i | \(-0.292372\pi\) | ||||
0.607003 | + | 0.794699i | \(0.292372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.34246 | 0.360810 | ||||||||
\(310\) | 7.03478 | 0.399549 | ||||||||
\(311\) | −2.85031 | −0.161626 | −0.0808131 | − | 0.996729i | \(-0.525752\pi\) | ||||
−0.0808131 | + | 0.996729i | \(0.525752\pi\) | |||||||
\(312\) | 4.03839 | 0.228629 | ||||||||
\(313\) | 13.3306 | 0.753492 | 0.376746 | − | 0.926317i | \(-0.377043\pi\) | ||||
0.376746 | + | 0.926317i | \(0.377043\pi\) | |||||||
\(314\) | 34.8703 | 1.96785 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.3089 | 1.08621 | ||||||||
\(317\) | 8.50980 | 0.477958 | 0.238979 | − | 0.971025i | \(-0.423187\pi\) | ||||
0.238979 | + | 0.971025i | \(0.423187\pi\) | |||||||
\(318\) | −3.14159 | −0.176172 | ||||||||
\(319\) | −11.0871 | −0.620757 | ||||||||
\(320\) | −6.82905 | −0.381756 | ||||||||
\(321\) | −11.2401 | −0.627359 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.39894 | 0.244764 | ||||||||
\(324\) | 1.57671 | 0.0875951 | ||||||||
\(325\) | −12.6821 | −0.703478 | ||||||||
\(326\) | 33.2890 | 1.84371 | ||||||||
\(327\) | −7.48963 | −0.414178 | ||||||||
\(328\) | 0.800530 | 0.0442019 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.97204 | −0.273702 | ||||||||
\(331\) | −29.9173 | −1.64441 | −0.822203 | − | 0.569195i | \(-0.807255\pi\) | ||||
−0.822203 | + | 0.569195i | \(0.807255\pi\) | |||||||
\(332\) | 4.14520 | 0.227497 | ||||||||
\(333\) | 9.02655 | 0.494652 | ||||||||
\(334\) | −0.484055 | −0.0264863 | ||||||||
\(335\) | −1.37319 | −0.0750256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.71161 | −0.365605 | −0.182802 | − | 0.983150i | \(-0.558517\pi\) | ||||
−0.182802 | + | 0.983150i | \(0.558517\pi\) | |||||||
\(338\) | −23.5427 | −1.28056 | ||||||||
\(339\) | 15.3348 | 0.832872 | ||||||||
\(340\) | −15.8090 | −0.857363 | ||||||||
\(341\) | −3.93366 | −0.213019 | ||||||||
\(342\) | 1.30825 | 0.0707421 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.97345 | −0.429899 | ||||||||
\(345\) | 13.9178 | 0.749308 | ||||||||
\(346\) | 41.4505 | 2.22839 | ||||||||
\(347\) | 34.5656 | 1.85558 | 0.927788 | − | 0.373107i | \(-0.121708\pi\) | ||||
0.927788 | + | 0.373107i | \(0.121708\pi\) | |||||||
\(348\) | −10.4841 | −0.562004 | ||||||||
\(349\) | −9.95211 | −0.532724 | −0.266362 | − | 0.963873i | \(-0.585822\pi\) | ||||
−0.266362 | + | 0.963873i | \(0.585822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.04464 | 0.269263 | ||||||||
\(352\) | 12.0487 | 0.642198 | ||||||||
\(353\) | 7.57739 | 0.403304 | 0.201652 | − | 0.979457i | \(-0.435369\pi\) | ||||
0.201652 | + | 0.979457i | \(0.435369\pi\) | |||||||
\(354\) | −22.7449 | −1.20888 | ||||||||
\(355\) | −17.1800 | −0.911819 | ||||||||
\(356\) | 20.0531 | 1.06281 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.4434 | −1.55613 | ||||||||
\(359\) | −6.47307 | −0.341635 | −0.170818 | − | 0.985303i | \(-0.554641\pi\) | ||||
−0.170818 | + | 0.985303i | \(0.554641\pi\) | |||||||
\(360\) | 1.26221 | 0.0665241 | ||||||||
\(361\) | −18.5215 | −0.974815 | ||||||||
\(362\) | −42.6861 | −2.24353 | ||||||||
\(363\) | −8.21977 | −0.431426 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.40576 | 0.230608 | ||||||||
\(366\) | −22.6194 | −1.18233 | ||||||||
\(367\) | 11.1250 | 0.580722 | 0.290361 | − | 0.956917i | \(-0.406225\pi\) | ||||
0.290361 | + | 0.956917i | \(0.406225\pi\) | |||||||
\(368\) | −41.1996 | −2.14768 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −26.9164 | −1.39932 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.71970 | −0.192858 | ||||||||
\(373\) | −25.1437 | −1.30189 | −0.650945 | − | 0.759125i | \(-0.725627\pi\) | ||||
−0.650945 | + | 0.759125i | \(0.725627\pi\) | |||||||
\(374\) | 20.0531 | 1.03692 | ||||||||
\(375\) | −11.8474 | −0.611796 | ||||||||
\(376\) | 1.06967 | 0.0551641 | ||||||||
\(377\) | −33.5434 | −1.72757 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.8289 | −1.27537 | −0.637686 | − | 0.770296i | \(-0.720108\pi\) | ||||
−0.637686 | + | 0.770296i | \(0.720108\pi\) | |||||||
\(380\) | −1.71970 | −0.0882190 | ||||||||
\(381\) | −15.4241 | −0.790200 | ||||||||
\(382\) | −37.9751 | −1.94297 | ||||||||
\(383\) | 18.1410 | 0.926962 | 0.463481 | − | 0.886107i | \(-0.346600\pi\) | ||||
0.463481 | + | 0.886107i | \(0.346600\pi\) | |||||||
\(384\) | −6.26080 | −0.319495 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.85340 | −0.247032 | ||||||||
\(387\) | −9.96021 | −0.506306 | ||||||||
\(388\) | 5.06438 | 0.257105 | ||||||||
\(389\) | −28.8703 | −1.46378 | −0.731892 | − | 0.681421i | \(-0.761362\pi\) | ||||
−0.731892 | + | 0.681421i | \(0.761362\pi\) | |||||||
\(390\) | −15.0427 | −0.761716 | ||||||||
\(391\) | −56.1328 | −2.83876 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.9345 | 0.803787 | ||||||||
\(394\) | −48.0826 | −2.42236 | ||||||||
\(395\) | 19.3089 | 0.971538 | ||||||||
\(396\) | 2.62901 | 0.132113 | ||||||||
\(397\) | −26.5988 | −1.33495 | −0.667477 | − | 0.744630i | \(-0.732626\pi\) | ||||
−0.667477 | + | 0.744630i | \(0.732626\pi\) | |||||||
\(398\) | 29.9220 | 1.49985 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.7337 | 0.586687 | ||||||||
\(401\) | 7.07665 | 0.353391 | 0.176695 | − | 0.984266i | \(-0.443459\pi\) | ||||
0.176695 | + | 0.984266i | \(0.443459\pi\) | |||||||
\(402\) | 1.64710 | 0.0821501 | ||||||||
\(403\) | −11.9011 | −0.592835 | ||||||||
\(404\) | 12.5731 | 0.625535 | ||||||||
\(405\) | 1.57671 | 0.0783475 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0509 | 0.746046 | ||||||||
\(408\) | −5.09069 | −0.252027 | ||||||||
\(409\) | 9.14019 | 0.451953 | 0.225977 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225977 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(410\) | −2.98191 | −0.147266 | ||||||||
\(411\) | 3.13313 | 0.154546 | ||||||||
\(412\) | 10.0002 | 0.492676 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −16.6940 | −0.820463 | ||||||||
\(415\) | 4.14520 | 0.203480 | ||||||||
\(416\) | 36.4527 | 1.78724 | ||||||||
\(417\) | 12.9192 | 0.632655 | ||||||||
\(418\) | 2.18138 | 0.106695 | ||||||||
\(419\) | 23.3208 | 1.13929 | 0.569647 | − | 0.821890i | \(-0.307080\pi\) | ||||
0.569647 | + | 0.821890i | \(0.307080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.23309 | −0.352519 | −0.176260 | − | 0.984344i | \(-0.556400\pi\) | ||||
−0.176260 | + | 0.984344i | \(0.556400\pi\) | |||||||
\(422\) | −10.6525 | −0.518557 | ||||||||
\(423\) | 1.33621 | 0.0649685 | ||||||||
\(424\) | 1.32980 | 0.0645806 | ||||||||
\(425\) | 15.9868 | 0.775472 | ||||||||
\(426\) | 20.6069 | 0.998406 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17.7224 | −0.856642 | ||||||||
\(429\) | 8.41145 | 0.406109 | ||||||||
\(430\) | 29.7005 | 1.43228 | ||||||||
\(431\) | 9.75308 | 0.469790 | 0.234895 | − | 0.972021i | \(-0.424525\pi\) | ||||
0.234895 | + | 0.972021i | \(0.424525\pi\) | |||||||
\(432\) | −4.66740 | −0.224561 | ||||||||
\(433\) | −14.8459 | −0.713446 | −0.356723 | − | 0.934210i | \(-0.616106\pi\) | ||||
−0.356723 | + | 0.934210i | \(0.616106\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4841 | −0.502672 | ||||||||
\(436\) | −11.8090 | −0.565548 | ||||||||
\(437\) | −6.10613 | −0.292096 | ||||||||
\(438\) | −5.28458 | −0.252507 | ||||||||
\(439\) | 0.686453 | 0.0327626 | 0.0163813 | − | 0.999866i | \(-0.494785\pi\) | ||||
0.0163813 | + | 0.999866i | \(0.494785\pi\) | |||||||
\(440\) | 2.10460 | 0.100333 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 60.6697 | 2.88576 | ||||||||
\(443\) | 14.2413 | 0.676625 | 0.338313 | − | 0.941034i | \(-0.390144\pi\) | ||||
0.338313 | + | 0.941034i | \(0.390144\pi\) | |||||||
\(444\) | 14.2323 | 0.675434 | ||||||||
\(445\) | 20.0531 | 0.950609 | ||||||||
\(446\) | −27.9729 | −1.32455 | ||||||||
\(447\) | 17.0545 | 0.806651 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.0517 | 0.993492 | 0.496746 | − | 0.867896i | \(-0.334528\pi\) | ||||
0.496746 | + | 0.867896i | \(0.334528\pi\) | |||||||
\(450\) | 4.75448 | 0.224129 | ||||||||
\(451\) | 1.66740 | 0.0785149 | ||||||||
\(452\) | 24.1786 | 1.13726 | ||||||||
\(453\) | −4.62901 | −0.217490 | ||||||||
\(454\) | −10.2371 | −0.480453 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.553766 | −0.0259325 | ||||||||
\(457\) | −29.4366 | −1.37699 | −0.688493 | − | 0.725243i | \(-0.741728\pi\) | ||||
−0.688493 | + | 0.725243i | \(0.741728\pi\) | |||||||
\(458\) | 0.996784 | 0.0465767 | ||||||||
\(459\) | −6.35915 | −0.296820 | ||||||||
\(460\) | 21.9443 | 1.02316 | ||||||||
\(461\) | −12.8388 | −0.597961 | −0.298980 | − | 0.954259i | \(-0.596647\pi\) | ||||
−0.298980 | + | 0.954259i | \(0.596647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2308 | −0.568411 | −0.284206 | − | 0.958763i | \(-0.591730\pi\) | ||||
−0.284206 | + | 0.958763i | \(0.591730\pi\) | |||||||
\(464\) | 31.0350 | 1.44076 | ||||||||
\(465\) | −3.71970 | −0.172497 | ||||||||
\(466\) | 31.6682 | 1.46700 | ||||||||
\(467\) | 22.4867 | 1.04056 | 0.520280 | − | 0.853996i | \(-0.325827\pi\) | ||||
0.520280 | + | 0.853996i | \(0.325827\pi\) | |||||||
\(468\) | 7.95395 | 0.367672 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.98445 | −0.183789 | ||||||||
\(471\) | −18.4380 | −0.849579 | ||||||||
\(472\) | 9.62761 | 0.443147 | ||||||||
\(473\) | −16.6077 | −0.763622 | ||||||||
\(474\) | −23.1605 | −1.06380 | ||||||||
\(475\) | 1.73904 | 0.0797928 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.66115 | 0.0760586 | ||||||||
\(478\) | −2.69857 | −0.123430 | ||||||||
\(479\) | −0.0510288 | −0.00233156 | −0.00116578 | − | 0.999999i | \(-0.500371\pi\) | ||||
−0.00116578 | + | 0.999999i | \(0.500371\pi\) | |||||||
\(480\) | 11.3934 | 0.520034 | ||||||||
\(481\) | 45.5358 | 2.07625 | ||||||||
\(482\) | 24.3527 | 1.10924 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.9602 | −0.589101 | ||||||||
\(485\) | 5.06438 | 0.229961 | ||||||||
\(486\) | −1.89122 | −0.0857875 | ||||||||
\(487\) | 21.9309 | 0.993782 | 0.496891 | − | 0.867813i | \(-0.334475\pi\) | ||||
0.496891 | + | 0.867813i | \(0.334475\pi\) | |||||||
\(488\) | 9.57450 | 0.433417 | ||||||||
\(489\) | −17.6019 | −0.795984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.7657 | −1.02740 | −0.513701 | − | 0.857969i | \(-0.671726\pi\) | ||||
−0.513701 | + | 0.857969i | \(0.671726\pi\) | |||||||
\(492\) | 1.57671 | 0.0710837 | ||||||||
\(493\) | 42.2840 | 1.90438 | ||||||||
\(494\) | 6.59966 | 0.296933 | ||||||||
\(495\) | 2.62901 | 0.118165 | ||||||||
\(496\) | 11.0111 | 0.494414 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.97204 | −0.222803 | ||||||||
\(499\) | 25.0730 | 1.12242 | 0.561210 | − | 0.827673i | \(-0.310336\pi\) | ||||
0.561210 | + | 0.827673i | \(0.310336\pi\) | |||||||
\(500\) | −18.6799 | −0.835391 | ||||||||
\(501\) | 0.255948 | 0.0114349 | ||||||||
\(502\) | −39.3570 | −1.75659 | ||||||||
\(503\) | 29.4448 | 1.31288 | 0.656440 | − | 0.754378i | \(-0.272061\pi\) | ||||
0.656440 | + | 0.754378i | \(0.272061\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.5731 | 0.559496 | ||||||||
\(506\) | −27.8355 | −1.23744 | ||||||||
\(507\) | 12.4484 | 0.552855 | ||||||||
\(508\) | −24.3194 | −1.07900 | ||||||||
\(509\) | −8.94477 | −0.396470 | −0.198235 | − | 0.980155i | \(-0.563521\pi\) | ||||
−0.198235 | + | 0.980155i | \(0.563521\pi\) | |||||||
\(510\) | 18.9624 | 0.839670 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −26.2540 | −1.16027 | ||||||||
\(513\) | −0.691750 | −0.0305415 | ||||||||
\(514\) | −46.2192 | −2.03864 | ||||||||
\(515\) | 10.0002 | 0.440663 | ||||||||
\(516\) | −15.7044 | −0.691347 | ||||||||
\(517\) | 2.22799 | 0.0979870 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.9173 | −0.962064 | ||||||||
\(520\) | 6.36738 | 0.279228 | ||||||||
\(521\) | 1.13578 | 0.0497592 | 0.0248796 | − | 0.999690i | \(-0.492080\pi\) | ||||
0.0248796 | + | 0.999690i | \(0.492080\pi\) | |||||||
\(522\) | 12.5753 | 0.550406 | ||||||||
\(523\) | −24.2249 | −1.05928 | −0.529640 | − | 0.848223i | \(-0.677673\pi\) | ||||
−0.529640 | + | 0.848223i | \(0.677673\pi\) | |||||||
\(524\) | 25.1241 | 1.09755 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.3961 | 1.23813 | ||||||||
\(527\) | 15.0022 | 0.653506 | ||||||||
\(528\) | −7.78244 | −0.338687 | ||||||||
\(529\) | 54.9174 | 2.38771 | ||||||||
\(530\) | −4.95339 | −0.215161 | ||||||||
\(531\) | 12.0266 | 0.521908 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.04464 | 0.218508 | ||||||||
\(534\) | −24.0531 | −1.04088 | ||||||||
\(535\) | −17.7224 | −0.766204 | ||||||||
\(536\) | −0.697199 | −0.0301144 | ||||||||
\(537\) | 15.5685 | 0.671830 | ||||||||
\(538\) | 9.16482 | 0.395123 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.48602 | 0.106981 | ||||||||
\(541\) | 15.5016 | 0.666464 | 0.333232 | − | 0.942845i | \(-0.391861\pi\) | ||||
0.333232 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(542\) | 29.0133 | 1.24623 | ||||||||
\(543\) | 22.5707 | 0.968601 | ||||||||
\(544\) | −45.9514 | −1.97015 | ||||||||
\(545\) | −11.8090 | −0.505842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.5952 | 1.43643 | 0.718213 | − | 0.695823i | \(-0.244960\pi\) | ||||
0.718213 | + | 0.695823i | \(0.244960\pi\) | |||||||
\(548\) | 4.94004 | 0.211028 | ||||||||
\(549\) | 11.9602 | 0.510449 | ||||||||
\(550\) | 7.92764 | 0.338036 | ||||||||
\(551\) | 4.59966 | 0.195952 | ||||||||
\(552\) | 7.06634 | 0.300764 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.99731 | 0.382259 | ||||||||
\(555\) | 14.2323 | 0.604127 | ||||||||
\(556\) | 20.3698 | 0.863873 | ||||||||
\(557\) | 12.7050 | 0.538327 | 0.269164 | − | 0.963094i | \(-0.413253\pi\) | ||||
0.269164 | + | 0.963094i | \(0.413253\pi\) | |||||||
\(558\) | 4.46168 | 0.188878 | ||||||||
\(559\) | −50.2457 | −2.12517 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6033 | −0.447670 | ||||||||
\(562\) | 56.0260 | 2.36331 | ||||||||
\(563\) | 17.0531 | 0.718703 | 0.359351 | − | 0.933202i | \(-0.382998\pi\) | ||||
0.359351 | + | 0.933202i | \(0.382998\pi\) | |||||||
\(564\) | 2.10681 | 0.0887128 | ||||||||
\(565\) | 24.1786 | 1.01720 | ||||||||
\(566\) | −9.04336 | −0.380121 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.72263 | −0.365994 | ||||||||
\(569\) | 28.0319 | 1.17516 | 0.587578 | − | 0.809167i | \(-0.300081\pi\) | ||||
0.587578 | + | 0.809167i | \(0.300081\pi\) | |||||||
\(570\) | 2.06273 | 0.0863985 | ||||||||
\(571\) | −30.4034 | −1.27234 | −0.636170 | − | 0.771549i | \(-0.719482\pi\) | ||||
−0.636170 | + | 0.771549i | \(0.719482\pi\) | |||||||
\(572\) | 13.2624 | 0.554531 | ||||||||
\(573\) | 20.0797 | 0.838840 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.1911 | −0.925433 | ||||||||
\(576\) | −4.33120 | −0.180467 | ||||||||
\(577\) | −32.6653 | −1.35987 | −0.679937 | − | 0.733271i | \(-0.737993\pi\) | ||||
−0.679937 | + | 0.733271i | \(0.737993\pi\) | |||||||
\(578\) | −44.3280 | −1.84380 | ||||||||
\(579\) | 2.56628 | 0.106651 | ||||||||
\(580\) | −16.5303 | −0.686385 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.07457 | −0.251799 | ||||||||
\(583\) | 2.76980 | 0.114713 | ||||||||
\(584\) | 2.23690 | 0.0925635 | ||||||||
\(585\) | 7.95395 | 0.328856 | ||||||||
\(586\) | 29.5750 | 1.22173 | ||||||||
\(587\) | −4.70346 | −0.194132 | −0.0970662 | − | 0.995278i | \(-0.530946\pi\) | ||||
−0.0970662 | + | 0.995278i | \(0.530946\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.63194 | 0.0672430 | ||||||||
\(590\) | −35.8621 | −1.47642 | ||||||||
\(591\) | 25.4241 | 1.04581 | ||||||||
\(592\) | −42.1306 | −1.73156 | ||||||||
\(593\) | −22.8333 | −0.937653 | −0.468826 | − | 0.883290i | \(-0.655323\pi\) | ||||
−0.468826 | + | 0.883290i | \(0.655323\pi\) | |||||||
\(594\) | −3.15343 | −0.129387 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.8901 | 1.10146 | ||||||||
\(597\) | −15.8215 | −0.647531 | ||||||||
\(598\) | −84.2151 | −3.44381 | ||||||||
\(599\) | −28.2078 | −1.15254 | −0.576269 | − | 0.817260i | \(-0.695492\pi\) | ||||
−0.576269 | + | 0.817260i | \(0.695492\pi\) | |||||||
\(600\) | −2.01251 | −0.0821605 | ||||||||
\(601\) | 46.0212 | 1.87724 | 0.938622 | − | 0.344948i | \(-0.112103\pi\) | ||||
0.938622 | + | 0.344948i | \(0.112103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.870922 | −0.0354667 | ||||||||
\(604\) | −7.29863 | −0.296977 | ||||||||
\(605\) | −12.9602 | −0.526908 | ||||||||
\(606\) | −15.0811 | −0.612626 | ||||||||
\(607\) | 48.3754 | 1.96350 | 0.981748 | − | 0.190188i | \(-0.0609098\pi\) | ||||
0.981748 | + | 0.190188i | \(0.0609098\pi\) | |||||||
\(608\) | −4.99860 | −0.202720 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −35.6643 | −1.44400 | ||||||||
\(611\) | 6.74068 | 0.272699 | ||||||||
\(612\) | −10.0266 | −0.405299 | ||||||||
\(613\) | 30.5767 | 1.23498 | 0.617490 | − | 0.786579i | \(-0.288150\pi\) | ||||
0.617490 | + | 0.786579i | \(0.288150\pi\) | |||||||
\(614\) | −40.2283 | −1.62348 | ||||||||
\(615\) | 1.57671 | 0.0635792 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.6874 | 1.55750 | 0.778748 | − | 0.627336i | \(-0.215855\pi\) | ||||
0.778748 | + | 0.627336i | \(0.215855\pi\) | |||||||
\(618\) | −11.9950 | −0.482509 | ||||||||
\(619\) | −0.413942 | −0.0166377 | −0.00831886 | − | 0.999965i | \(-0.502648\pi\) | ||||
−0.00831886 | + | 0.999965i | \(0.502648\pi\) | |||||||
\(620\) | −5.86491 | −0.235540 | ||||||||
\(621\) | 8.82708 | 0.354219 | ||||||||
\(622\) | 5.39056 | 0.216142 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.5454 | −0.942570 | ||||||||
\(625\) | −6.11003 | −0.244401 | ||||||||
\(626\) | −25.2112 | −1.00764 | ||||||||
\(627\) | −1.15343 | −0.0460634 | ||||||||
\(628\) | −29.0714 | −1.16008 | ||||||||
\(629\) | −57.4012 | −2.28874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.84144 | 0.113116 | 0.0565580 | − | 0.998399i | \(-0.481987\pi\) | ||||
0.0565580 | + | 0.998399i | \(0.481987\pi\) | |||||||
\(632\) | 9.80355 | 0.389964 | ||||||||
\(633\) | 5.63262 | 0.223877 | ||||||||
\(634\) | −16.0939 | −0.639171 | ||||||||
\(635\) | −24.3194 | −0.965085 | ||||||||
\(636\) | 2.61915 | 0.103856 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.9681 | 0.830135 | ||||||||
\(639\) | −10.8961 | −0.431042 | ||||||||
\(640\) | −9.87149 | −0.390205 | ||||||||
\(641\) | −9.25354 | −0.365493 | −0.182746 | − | 0.983160i | \(-0.558499\pi\) | ||||
−0.182746 | + | 0.983160i | \(0.558499\pi\) | |||||||
\(642\) | 21.2574 | 0.838964 | ||||||||
\(643\) | −8.80165 | −0.347103 | −0.173552 | − | 0.984825i | \(-0.555524\pi\) | ||||
−0.173552 | + | 0.984825i | \(0.555524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.7044 | −0.618360 | ||||||||
\(646\) | −8.31936 | −0.327321 | ||||||||
\(647\) | 30.1439 | 1.18508 | 0.592540 | − | 0.805541i | \(-0.298125\pi\) | ||||
0.592540 | + | 0.805541i | \(0.298125\pi\) | |||||||
\(648\) | 0.800530 | 0.0314478 | ||||||||
\(649\) | 20.0531 | 0.787153 | ||||||||
\(650\) | 23.9847 | 0.940757 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.7531 | −1.08689 | ||||||||
\(653\) | 3.42858 | 0.134171 | 0.0670854 | − | 0.997747i | \(-0.478630\pi\) | ||||
0.0670854 | + | 0.997747i | \(0.478630\pi\) | |||||||
\(654\) | 14.1645 | 0.553877 | ||||||||
\(655\) | 25.1241 | 0.981679 | ||||||||
\(656\) | −4.66740 | −0.182231 | ||||||||
\(657\) | 2.79427 | 0.109015 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.84806 | 0.227808 | 0.113904 | − | 0.993492i | \(-0.463664\pi\) | ||||
0.113904 | + | 0.993492i | \(0.463664\pi\) | |||||||
\(660\) | 4.14520 | 0.161352 | ||||||||
\(661\) | 10.8716 | 0.422856 | 0.211428 | − | 0.977394i | \(-0.432189\pi\) | ||||
0.211428 | + | 0.977394i | \(0.432189\pi\) | |||||||
\(662\) | 56.5803 | 2.19905 | ||||||||
\(663\) | −32.0797 | −1.24587 | ||||||||
\(664\) | 2.10460 | 0.0816745 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −17.0712 | −0.661496 | ||||||||
\(667\) | −58.6940 | −2.27264 | ||||||||
\(668\) | 0.403557 | 0.0156141 | ||||||||
\(669\) | 14.7909 | 0.571849 | ||||||||
\(670\) | 2.59701 | 0.100331 | ||||||||
\(671\) | 19.9425 | 0.769871 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.8775 | 0.881865 | 0.440932 | − | 0.897540i | \(-0.354648\pi\) | ||||
0.440932 | + | 0.897540i | \(0.354648\pi\) | |||||||
\(674\) | 12.6931 | 0.488921 | ||||||||
\(675\) | −2.51398 | −0.0967630 | ||||||||
\(676\) | 19.6276 | 0.754908 | ||||||||
\(677\) | 16.2635 | 0.625055 | 0.312528 | − | 0.949909i | \(-0.398824\pi\) | ||||
0.312528 | + | 0.949909i | \(0.398824\pi\) | |||||||
\(678\) | −29.0015 | −1.11380 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.02655 | −0.307804 | ||||||||
\(681\) | 5.41298 | 0.207426 | ||||||||
\(682\) | 7.43941 | 0.284870 | ||||||||
\(683\) | 7.01794 | 0.268534 | 0.134267 | − | 0.990945i | \(-0.457132\pi\) | ||||
0.134267 | + | 0.990945i | \(0.457132\pi\) | |||||||
\(684\) | −1.09069 | −0.0417036 | ||||||||
\(685\) | 4.94004 | 0.188749 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.527059 | −0.0201085 | ||||||||
\(688\) | 46.4883 | 1.77235 | ||||||||
\(689\) | 8.37989 | 0.319248 | ||||||||
\(690\) | −26.3216 | −1.00205 | ||||||||
\(691\) | −47.3364 | −1.80076 | −0.900381 | − | 0.435102i | \(-0.856712\pi\) | ||||
−0.900381 | + | 0.435102i | \(0.856712\pi\) | |||||||
\(692\) | −34.5573 | −1.31367 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −65.3711 | −2.48145 | ||||||||
\(695\) | 20.3698 | 0.772672 | ||||||||
\(696\) | −5.32297 | −0.201767 | ||||||||
\(697\) | −6.35915 | −0.240870 | ||||||||
\(698\) | 18.8216 | 0.712409 | ||||||||
\(699\) | −16.7449 | −0.633349 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.65268 | 0.100190 | 0.0500952 | − | 0.998744i | \(-0.484048\pi\) | ||||
0.0500952 | + | 0.998744i | \(0.484048\pi\) | |||||||
\(702\) | −9.54053 | −0.360084 | ||||||||
\(703\) | −6.24412 | −0.235501 | ||||||||
\(704\) | −7.22185 | −0.272184 | ||||||||
\(705\) | 2.10681 | 0.0793471 | ||||||||
\(706\) | −14.3305 | −0.539336 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.9624 | 0.712651 | ||||||||
\(709\) | −28.8201 | −1.08236 | −0.541181 | − | 0.840906i | \(-0.682023\pi\) | ||||
−0.541181 | + | 0.840906i | \(0.682023\pi\) | |||||||
\(710\) | 32.4911 | 1.21937 | ||||||||
\(711\) | 12.2463 | 0.459273 | ||||||||
\(712\) | 10.1814 | 0.381563 | ||||||||
\(713\) | −20.8244 | −0.779881 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.2624 | 0.495987 | ||||||||
\(716\) | 24.5470 | 0.917366 | ||||||||
\(717\) | 1.42690 | 0.0532884 | ||||||||
\(718\) | 12.2420 | 0.456867 | ||||||||
\(719\) | −23.3900 | −0.872300 | −0.436150 | − | 0.899874i | \(-0.643658\pi\) | ||||
−0.436150 | + | 0.899874i | \(0.643658\pi\) | |||||||
\(720\) | −7.35915 | −0.274259 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 35.0282 | 1.30361 | ||||||||
\(723\) | −12.8767 | −0.478891 | ||||||||
\(724\) | 35.5875 | 1.32260 | ||||||||
\(725\) | 16.7162 | 0.620825 | ||||||||
\(726\) | 15.5454 | 0.576943 | ||||||||
\(727\) | −24.6218 | −0.913172 | −0.456586 | − | 0.889679i | \(-0.650928\pi\) | ||||
−0.456586 | + | 0.889679i | \(0.650928\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.33227 | −0.308391 | ||||||||
\(731\) | 63.3385 | 2.34266 | ||||||||
\(732\) | 18.8578 | 0.697005 | ||||||||
\(733\) | 47.1181 | 1.74035 | 0.870174 | − | 0.492744i | \(-0.164006\pi\) | ||||
0.870174 | + | 0.492744i | \(0.164006\pi\) | |||||||
\(734\) | −21.0399 | −0.776596 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 63.7847 | 2.35114 | ||||||||
\(737\) | −1.45218 | −0.0534916 | ||||||||
\(738\) | −1.89122 | −0.0696168 | ||||||||
\(739\) | −2.83767 | −0.104385 | −0.0521927 | − | 0.998637i | \(-0.516621\pi\) | ||||
−0.0521927 | + | 0.998637i | \(0.516621\pi\) | |||||||
\(740\) | 22.4402 | 0.824919 | ||||||||
\(741\) | −3.48963 | −0.128195 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.6763 | −0.575108 | −0.287554 | − | 0.957764i | \(-0.592842\pi\) | ||||
−0.287554 | + | 0.957764i | \(0.592842\pi\) | |||||||
\(744\) | −1.88857 | −0.0692384 | ||||||||
\(745\) | 26.8901 | 0.985176 | ||||||||
\(746\) | 47.5522 | 1.74101 | ||||||||
\(747\) | 2.62901 | 0.0961906 | ||||||||
\(748\) | −16.7183 | −0.611282 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 22.4060 | 0.818152 | ||||||||
\(751\) | −26.2001 | −0.956056 | −0.478028 | − | 0.878345i | \(-0.658648\pi\) | ||||
−0.478028 | + | 0.878345i | \(0.658648\pi\) | |||||||
\(752\) | −6.23661 | −0.227426 | ||||||||
\(753\) | 20.8104 | 0.758373 | ||||||||
\(754\) | 63.4380 | 2.31028 | ||||||||
\(755\) | −7.29863 | −0.265624 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9359 | 1.34246 | 0.671228 | − | 0.741251i | \(-0.265767\pi\) | ||||
0.671228 | + | 0.741251i | \(0.265767\pi\) | |||||||
\(758\) | 46.9568 | 1.70555 | ||||||||
\(759\) | 14.7183 | 0.534241 | ||||||||
\(760\) | −0.873130 | −0.0316717 | ||||||||
\(761\) | 4.64085 | 0.168231 | 0.0841153 | − | 0.996456i | \(-0.473194\pi\) | ||||
0.0841153 | + | 0.996456i | \(0.473194\pi\) | |||||||
\(762\) | 29.1704 | 1.05673 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 31.6599 | 1.14541 | ||||||||
\(765\) | −10.0266 | −0.362511 | ||||||||
\(766\) | −34.3086 | −1.23962 | ||||||||
\(767\) | 60.6697 | 2.19066 | ||||||||
\(768\) | 20.5030 | 0.739837 | ||||||||
\(769\) | 37.9759 | 1.36944 | 0.684722 | − | 0.728804i | \(-0.259923\pi\) | ||||
0.684722 | + | 0.728804i | \(0.259923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.4388 | 0.880142 | ||||||||
\(772\) | 4.04629 | 0.145629 | ||||||||
\(773\) | 35.0191 | 1.25955 | 0.629775 | − | 0.776777i | \(-0.283147\pi\) | ||||
0.629775 | + | 0.776777i | \(0.283147\pi\) | |||||||
\(774\) | 18.8369 | 0.677080 | ||||||||
\(775\) | 5.93086 | 0.213043 | ||||||||
\(776\) | 2.57129 | 0.0923039 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 54.6001 | 1.95751 | ||||||||
\(779\) | −0.691750 | −0.0247845 | ||||||||
\(780\) | 12.5411 | 0.449043 | ||||||||
\(781\) | −18.1681 | −0.650107 | ||||||||
\(782\) | 106.159 | 3.79625 | ||||||||
\(783\) | −6.64931 | −0.237627 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.0714 | −1.03760 | ||||||||
\(786\) | −30.1356 | −1.07490 | ||||||||
\(787\) | −30.4583 | −1.08572 | −0.542861 | − | 0.839823i | \(-0.682659\pi\) | ||||
−0.542861 | + | 0.839823i | \(0.682659\pi\) | |||||||
\(788\) | 40.0865 | 1.42802 | ||||||||
\(789\) | −15.0147 | −0.534538 | ||||||||
\(790\) | −36.5174 | −1.29923 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.33481 | 0.0474302 | ||||||||
\(793\) | 60.3350 | 2.14256 | ||||||||
\(794\) | 50.3041 | 1.78523 | ||||||||
\(795\) | 2.61915 | 0.0928917 | ||||||||
\(796\) | −24.9460 | −0.884186 | ||||||||
\(797\) | −14.9234 | −0.528612 | −0.264306 | − | 0.964439i | \(-0.585143\pi\) | ||||
−0.264306 | + | 0.964439i | \(0.585143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.49714 | −0.300607 | ||||||||
\(800\) | −18.1661 | −0.642267 | ||||||||
\(801\) | 12.7183 | 0.449379 | ||||||||
\(802\) | −13.3835 | −0.472588 | ||||||||
\(803\) | 4.65918 | 0.164419 | ||||||||
\(804\) | −1.37319 | −0.0484288 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.5076 | 0.792795 | ||||||||
\(807\) | −4.84598 | −0.170587 | ||||||||
\(808\) | 6.38363 | 0.224575 | ||||||||
\(809\) | 40.8287 | 1.43546 | 0.717730 | − | 0.696321i | \(-0.245181\pi\) | ||||
0.717730 | + | 0.696321i | \(0.245181\pi\) | |||||||
\(810\) | −2.98191 | −0.104774 | ||||||||
\(811\) | −11.4066 | −0.400540 | −0.200270 | − | 0.979741i | \(-0.564182\pi\) | ||||
−0.200270 | + | 0.979741i | \(0.564182\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.3411 | −0.538035 | ||||||||
\(814\) | −28.4646 | −0.997682 | ||||||||
\(815\) | −27.7531 | −0.972148 | ||||||||
\(816\) | 29.6807 | 1.03903 | ||||||||
\(817\) | 6.88997 | 0.241050 | ||||||||
\(818\) | −17.2861 | −0.604395 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.48602 | 0.0868157 | ||||||||
\(821\) | 42.0952 | 1.46913 | 0.734567 | − | 0.678536i | \(-0.237385\pi\) | ||||
0.734567 | + | 0.678536i | \(0.237385\pi\) | |||||||
\(822\) | −5.92543 | −0.206673 | ||||||||
\(823\) | −17.7641 | −0.619217 | −0.309608 | − | 0.950864i | \(-0.600198\pi\) | ||||
−0.309608 | + | 0.950864i | \(0.600198\pi\) | |||||||
\(824\) | 5.07733 | 0.176877 | ||||||||
\(825\) | −4.19181 | −0.145940 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.3092 | −0.845313 | −0.422657 | − | 0.906290i | \(-0.638902\pi\) | ||||
−0.422657 | + | 0.906290i | \(0.638902\pi\) | |||||||
\(828\) | 13.9178 | 0.483676 | ||||||||
\(829\) | −20.3379 | −0.706364 | −0.353182 | − | 0.935555i | \(-0.614900\pi\) | ||||
−0.353182 | + | 0.935555i | \(0.614900\pi\) | |||||||
\(830\) | −7.83949 | −0.272113 | ||||||||
\(831\) | −4.75741 | −0.165033 | ||||||||
\(832\) | −21.8494 | −0.757490 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −24.4330 | −0.846046 | ||||||||
\(835\) | 0.403557 | 0.0139657 | ||||||||
\(836\) | −1.81862 | −0.0628983 | ||||||||
\(837\) | −2.35915 | −0.0815442 | ||||||||
\(838\) | −44.1047 | −1.52357 | ||||||||
\(839\) | −7.52649 | −0.259843 | −0.129922 | − | 0.991524i | \(-0.541473\pi\) | ||||
−0.129922 | + | 0.991524i | \(0.541473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.2134 | 0.524599 | ||||||||
\(842\) | 13.6794 | 0.471422 | ||||||||
\(843\) | −29.6242 | −1.02031 | ||||||||
\(844\) | 8.88103 | 0.305698 | ||||||||
\(845\) | 19.6276 | 0.675210 | ||||||||
\(846\) | −2.52706 | −0.0868821 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.75324 | −0.266247 | ||||||||
\(849\) | 4.78176 | 0.164110 | ||||||||
\(850\) | −30.2345 | −1.03703 | ||||||||
\(851\) | 79.6782 | 2.73133 | ||||||||
\(852\) | −17.1800 | −0.588576 | ||||||||
\(853\) | 30.5664 | 1.04657 | 0.523286 | − | 0.852157i | \(-0.324706\pi\) | ||||
0.523286 | + | 0.852157i | \(0.324706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.09069 | −0.0373008 | ||||||||
\(856\) | −8.99801 | −0.307546 | ||||||||
\(857\) | −23.2562 | −0.794415 | −0.397208 | − | 0.917729i | \(-0.630021\pi\) | ||||
−0.397208 | + | 0.917729i | \(0.630021\pi\) | |||||||
\(858\) | −15.9079 | −0.543087 | ||||||||
\(859\) | 15.2284 | 0.519585 | 0.259792 | − | 0.965664i | \(-0.416346\pi\) | ||||
0.259792 | + | 0.965664i | \(0.416346\pi\) | |||||||
\(860\) | −24.7613 | −0.844354 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.4452 | −0.628247 | ||||||||
\(863\) | −31.1449 | −1.06019 | −0.530093 | − | 0.847940i | \(-0.677843\pi\) | ||||
−0.530093 | + | 0.847940i | \(0.677843\pi\) | |||||||
\(864\) | 7.22603 | 0.245834 | ||||||||
\(865\) | −34.5573 | −1.17498 | ||||||||
\(866\) | 28.0768 | 0.954088 | ||||||||
\(867\) | 23.4388 | 0.796024 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.4196 | 0.692686 | ||||||||
\(870\) | 19.8277 | 0.672220 | ||||||||
\(871\) | −4.39349 | −0.148868 | ||||||||
\(872\) | −5.99567 | −0.203039 | ||||||||
\(873\) | 3.21198 | 0.108709 | ||||||||
\(874\) | 11.5480 | 0.390618 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.40576 | 0.148857 | ||||||||
\(877\) | 11.7539 | 0.396901 | 0.198450 | − | 0.980111i | \(-0.436409\pi\) | ||||
0.198450 | + | 0.980111i | \(0.436409\pi\) | |||||||
\(878\) | −1.29823 | −0.0438132 | ||||||||
\(879\) | −15.6380 | −0.527458 | ||||||||
\(880\) | −12.2707 | −0.413644 | ||||||||
\(881\) | 47.4654 | 1.59915 | 0.799575 | − | 0.600567i | \(-0.205058\pi\) | ||||
0.799575 | + | 0.600567i | \(0.205058\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.4218 | 0.350720 | 0.175360 | − | 0.984504i | \(-0.443891\pi\) | ||||
0.175360 | + | 0.984504i | \(0.443891\pi\) | |||||||
\(884\) | −50.5804 | −1.70120 | ||||||||
\(885\) | 18.9624 | 0.637415 | ||||||||
\(886\) | −26.9335 | −0.904847 | ||||||||
\(887\) | 4.31114 | 0.144754 | 0.0723769 | − | 0.997377i | \(-0.476942\pi\) | ||||
0.0723769 | + | 0.997377i | \(0.476942\pi\) | |||||||
\(888\) | 7.22603 | 0.242490 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −37.9248 | −1.27124 | ||||||||
\(891\) | 1.66740 | 0.0558601 | ||||||||
\(892\) | 23.3210 | 0.780845 | ||||||||
\(893\) | −0.924320 | −0.0309312 | ||||||||
\(894\) | −32.2538 | −1.07873 | ||||||||
\(895\) | 24.5470 | 0.820517 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.5295 | 1.48680 | ||||||||
\(898\) | −39.8134 | −1.32859 | ||||||||
\(899\) | 15.6867 | 0.523182 | ||||||||
\(900\) | −3.96382 | −0.132127 | ||||||||
\(901\) | −10.5635 | −0.351921 | ||||||||
\(902\) | −3.15343 | −0.104998 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.2760 | 0.408293 | ||||||||
\(905\) | 35.5875 | 1.18297 | ||||||||
\(906\) | 8.75448 | 0.290848 | ||||||||
\(907\) | −7.31924 | −0.243031 | −0.121516 | − | 0.992590i | \(-0.538775\pi\) | ||||
−0.121516 | + | 0.992590i | \(0.538775\pi\) | |||||||
\(908\) | 8.53472 | 0.283235 | ||||||||
\(909\) | 7.97425 | 0.264489 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5987 | −0.450543 | −0.225272 | − | 0.974296i | \(-0.572327\pi\) | ||||
−0.225272 | + | 0.974296i | \(0.572327\pi\) | |||||||
\(912\) | 3.22867 | 0.106912 | ||||||||
\(913\) | 4.38363 | 0.145077 | ||||||||
\(914\) | 55.6711 | 1.84144 | ||||||||
\(915\) | 18.8578 | 0.623420 | ||||||||
\(916\) | −0.831020 | −0.0274577 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.0266 | 0.396935 | ||||||||
\(919\) | −21.2143 | −0.699797 | −0.349898 | − | 0.936788i | \(-0.613784\pi\) | ||||
−0.349898 | + | 0.936788i | \(0.613784\pi\) | |||||||
\(920\) | 11.1416 | 0.367327 | ||||||||
\(921\) | 21.2711 | 0.700907 | ||||||||
\(922\) | 24.2809 | 0.799650 | ||||||||
\(923\) | −54.9668 | −1.80926 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.6926 | −0.746127 | ||||||||
\(926\) | 23.1310 | 0.760133 | ||||||||
\(927\) | 6.34246 | 0.208314 | ||||||||
\(928\) | −48.0481 | −1.57726 | ||||||||
\(929\) | −30.5044 | −1.00082 | −0.500408 | − | 0.865790i | \(-0.666817\pi\) | ||||
−0.500408 | + | 0.865790i | \(0.666817\pi\) | |||||||
\(930\) | 7.03478 | 0.230680 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −26.4018 | −0.864821 | ||||||||
\(933\) | −2.85031 | −0.0933150 | ||||||||
\(934\) | −42.5273 | −1.39154 | ||||||||
\(935\) | −16.7183 | −0.546747 | ||||||||
\(936\) | 4.03839 | 0.131999 | ||||||||
\(937\) | 21.5636 | 0.704452 | 0.352226 | − | 0.935915i | \(-0.385425\pi\) | ||||
0.352226 | + | 0.935915i | \(0.385425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.3306 | 0.435029 | ||||||||
\(940\) | 3.32184 | 0.108346 | ||||||||
\(941\) | −21.3467 | −0.695883 | −0.347942 | − | 0.937516i | \(-0.613119\pi\) | ||||
−0.347942 | + | 0.937516i | \(0.613119\pi\) | |||||||
\(942\) | 34.8703 | 1.13614 | ||||||||
\(943\) | 8.82708 | 0.287449 | ||||||||
\(944\) | −56.1328 | −1.82697 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.4088 | 1.02119 | ||||||||
\(947\) | 40.6083 | 1.31959 | 0.659795 | − | 0.751445i | \(-0.270643\pi\) | ||||
0.659795 | + | 0.751445i | \(0.270643\pi\) | |||||||
\(948\) | 19.3089 | 0.627125 | ||||||||
\(949\) | 14.0961 | 0.457579 | ||||||||
\(950\) | −3.28891 | −0.106706 | ||||||||
\(951\) | 8.50980 | 0.275949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.4968 | 0.437206 | 0.218603 | − | 0.975814i | \(-0.429850\pi\) | ||||
0.218603 | + | 0.975814i | \(0.429850\pi\) | |||||||
\(954\) | −3.14159 | −0.101713 | ||||||||
\(955\) | 31.6599 | 1.02449 | ||||||||
\(956\) | 2.24980 | 0.0727639 | ||||||||
\(957\) | −11.0871 | −0.358394 | ||||||||
\(958\) | 0.0965066 | 0.00311799 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.82905 | −0.220407 | ||||||||
\(961\) | −25.4344 | −0.820465 | ||||||||
\(962\) | −86.1181 | −2.77656 | ||||||||
\(963\) | −11.2401 | −0.362206 | ||||||||
\(964\) | −20.3029 | −0.653913 | ||||||||
\(965\) | 4.04629 | 0.130255 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7592 | −0.860517 | −0.430259 | − | 0.902706i | \(-0.641578\pi\) | ||||
−0.430259 | + | 0.902706i | \(0.641578\pi\) | |||||||
\(968\) | −6.58017 | −0.211495 | ||||||||
\(969\) | 4.39894 | 0.141314 | ||||||||
\(970\) | −9.57785 | −0.307526 | ||||||||
\(971\) | −37.6519 | −1.20831 | −0.604153 | − | 0.796868i | \(-0.706489\pi\) | ||||
−0.604153 | + | 0.796868i | \(0.706489\pi\) | |||||||
\(972\) | 1.57671 | 0.0505731 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −41.4761 | −1.32898 | ||||||||
\(975\) | −12.6821 | −0.406153 | ||||||||
\(976\) | −55.8231 | −1.78685 | ||||||||
\(977\) | 48.0278 | 1.53654 | 0.768272 | − | 0.640124i | \(-0.221117\pi\) | ||||
0.768272 | + | 0.640124i | \(0.221117\pi\) | |||||||
\(978\) | 33.2890 | 1.06446 | ||||||||
\(979\) | 21.2065 | 0.677764 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.48963 | −0.239126 | ||||||||
\(982\) | 43.0550 | 1.37394 | ||||||||
\(983\) | −21.5525 | −0.687417 | −0.343708 | − | 0.939076i | \(-0.611683\pi\) | ||||
−0.343708 | + | 0.939076i | \(0.611683\pi\) | |||||||
\(984\) | 0.800530 | 0.0255200 | ||||||||
\(985\) | 40.0865 | 1.27726 | ||||||||
\(986\) | −79.9683 | −2.54671 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.50214 | −0.175047 | ||||||||
\(989\) | −87.9196 | −2.79568 | ||||||||
\(990\) | −4.97204 | −0.158022 | ||||||||
\(991\) | 3.92823 | 0.124784 | 0.0623922 | − | 0.998052i | \(-0.480127\pi\) | ||||
0.0623922 | + | 0.998052i | \(0.480127\pi\) | |||||||
\(992\) | −17.0473 | −0.541252 | ||||||||
\(993\) | −29.9173 | −0.949398 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.9460 | −0.790840 | ||||||||
\(996\) | 4.14520 | 0.131346 | ||||||||
\(997\) | −51.0675 | −1.61732 | −0.808662 | − | 0.588273i | \(-0.799808\pi\) | ||||
−0.808662 | + | 0.588273i | \(0.799808\pi\) | |||||||
\(998\) | −47.4185 | −1.50101 | ||||||||
\(999\) | 9.02655 | 0.285588 |
(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 | 6027.2.a.u.1.1 | 4 | ||
7.6 | odd | 2 | 861.2.a.i.1.1 | ✓ | 4 | ||
21.20 | even | 2 | 2583.2.a.o.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.i.1.1 | ✓ | 4 | 7.6 | odd | 2 | ||
2583.2.a.o.1.4 | 4 | 21.20 | even | 2 | |||
6027.2.a.u.1.1 | 4 | 1.1 | even | 1 | trivial |