Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73828 | −1.22915 | −0.614575 | − | 0.788859i | \(-0.710672\pi\) | ||||
−0.614575 | + | 0.788859i | \(0.710672\pi\) | |||||||
\(3\) | 2.71256 | 1.56610 | 0.783048 | − | 0.621962i | \(-0.213664\pi\) | ||||
0.783048 | + | 0.621962i | \(0.213664\pi\) | |||||||
\(4\) | 1.02162 | 0.510808 | ||||||||
\(5\) | −1.00305 | −0.448576 | −0.224288 | − | 0.974523i | \(-0.572006\pi\) | ||||
−0.224288 | + | 0.974523i | \(0.572006\pi\) | |||||||
\(6\) | −4.71518 | −1.92496 | ||||||||
\(7\) | 1.91856 | 0.725149 | 0.362574 | − | 0.931955i | \(-0.381898\pi\) | ||||
0.362574 | + | 0.931955i | \(0.381898\pi\) | |||||||
\(8\) | 1.70071 | 0.601290 | ||||||||
\(9\) | 4.35796 | 1.45265 | ||||||||
\(10\) | 1.74357 | 0.551366 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.77119 | 0.799974 | ||||||||
\(13\) | 6.51880 | 1.80799 | 0.903995 | − | 0.427543i | \(-0.140621\pi\) | ||||
0.903995 | + | 0.427543i | \(0.140621\pi\) | |||||||
\(14\) | −3.33500 | −0.891316 | ||||||||
\(15\) | −2.72082 | −0.702512 | ||||||||
\(16\) | −4.99953 | −1.24988 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −7.57536 | −1.78553 | ||||||||
\(19\) | −0.645703 | −0.148135 | −0.0740673 | − | 0.997253i | \(-0.523598\pi\) | ||||
−0.0740673 | + | 0.997253i | \(0.523598\pi\) | |||||||
\(20\) | −1.02473 | −0.229136 | ||||||||
\(21\) | 5.20421 | 1.13565 | ||||||||
\(22\) | −1.73828 | −0.370602 | ||||||||
\(23\) | 4.75758 | 0.992024 | 0.496012 | − | 0.868316i | \(-0.334797\pi\) | ||||
0.496012 | + | 0.868316i | \(0.334797\pi\) | |||||||
\(24\) | 4.61326 | 0.941678 | ||||||||
\(25\) | −3.99390 | −0.798780 | ||||||||
\(26\) | −11.3315 | −2.22229 | ||||||||
\(27\) | 3.68355 | 0.708900 | ||||||||
\(28\) | 1.96003 | 0.370411 | ||||||||
\(29\) | 6.97508 | 1.29524 | 0.647620 | − | 0.761964i | \(-0.275765\pi\) | ||||
0.647620 | + | 0.761964i | \(0.275765\pi\) | |||||||
\(30\) | 4.72954 | 0.863492 | ||||||||
\(31\) | 5.23359 | 0.939980 | 0.469990 | − | 0.882672i | \(-0.344257\pi\) | ||||
0.469990 | + | 0.882672i | \(0.344257\pi\) | |||||||
\(32\) | 5.28917 | 0.935003 | ||||||||
\(33\) | 2.71256 | 0.472195 | ||||||||
\(34\) | −1.73828 | −0.298112 | ||||||||
\(35\) | −1.92441 | −0.325284 | ||||||||
\(36\) | 4.45216 | 0.742027 | ||||||||
\(37\) | −0.654072 | −0.107529 | −0.0537644 | − | 0.998554i | \(-0.517122\pi\) | ||||
−0.0537644 | + | 0.998554i | \(0.517122\pi\) | |||||||
\(38\) | 1.12241 | 0.182079 | ||||||||
\(39\) | 17.6826 | 2.83149 | ||||||||
\(40\) | −1.70589 | −0.269724 | ||||||||
\(41\) | 9.47139 | 1.47918 | 0.739591 | − | 0.673056i | \(-0.235019\pi\) | ||||
0.739591 | + | 0.673056i | \(0.235019\pi\) | |||||||
\(42\) | −9.04637 | −1.39589 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.02162 | 0.154014 | ||||||||
\(45\) | −4.37124 | −0.651625 | ||||||||
\(46\) | −8.27000 | −1.21935 | ||||||||
\(47\) | 1.37344 | 0.200336 | 0.100168 | − | 0.994971i | \(-0.468062\pi\) | ||||
0.100168 | + | 0.994971i | \(0.468062\pi\) | |||||||
\(48\) | −13.5615 | −1.95744 | ||||||||
\(49\) | −3.31912 | −0.474160 | ||||||||
\(50\) | 6.94251 | 0.981820 | ||||||||
\(51\) | 2.71256 | 0.379834 | ||||||||
\(52\) | 6.65971 | 0.923535 | ||||||||
\(53\) | −3.32487 | −0.456706 | −0.228353 | − | 0.973578i | \(-0.573334\pi\) | ||||
−0.228353 | + | 0.973578i | \(0.573334\pi\) | |||||||
\(54\) | −6.40304 | −0.871344 | ||||||||
\(55\) | −1.00305 | −0.135251 | ||||||||
\(56\) | 3.26291 | 0.436025 | ||||||||
\(57\) | −1.75151 | −0.231993 | ||||||||
\(58\) | −12.1246 | −1.59204 | ||||||||
\(59\) | −6.00887 | −0.782288 | −0.391144 | − | 0.920330i | \(-0.627921\pi\) | ||||
−0.391144 | + | 0.920330i | \(0.627921\pi\) | |||||||
\(60\) | −2.77963 | −0.358849 | ||||||||
\(61\) | −0.664019 | −0.0850189 | −0.0425095 | − | 0.999096i | \(-0.513535\pi\) | ||||
−0.0425095 | + | 0.999096i | \(0.513535\pi\) | |||||||
\(62\) | −9.09744 | −1.15538 | ||||||||
\(63\) | 8.36103 | 1.05339 | ||||||||
\(64\) | 0.805005 | 0.100626 | ||||||||
\(65\) | −6.53865 | −0.811020 | ||||||||
\(66\) | −4.71518 | −0.580399 | ||||||||
\(67\) | 12.9481 | 1.58186 | 0.790931 | − | 0.611906i | \(-0.209597\pi\) | ||||
0.790931 | + | 0.611906i | \(0.209597\pi\) | |||||||
\(68\) | 1.02162 | 0.123889 | ||||||||
\(69\) | 12.9052 | 1.55360 | ||||||||
\(70\) | 3.34515 | 0.399822 | ||||||||
\(71\) | −12.9188 | −1.53318 | −0.766588 | − | 0.642140i | \(-0.778047\pi\) | ||||
−0.766588 | + | 0.642140i | \(0.778047\pi\) | |||||||
\(72\) | 7.41161 | 0.873467 | ||||||||
\(73\) | 1.15650 | 0.135358 | 0.0676788 | − | 0.997707i | \(-0.478441\pi\) | ||||
0.0676788 | + | 0.997707i | \(0.478441\pi\) | |||||||
\(74\) | 1.13696 | 0.132169 | ||||||||
\(75\) | −10.8337 | −1.25097 | ||||||||
\(76\) | −0.659660 | −0.0756682 | ||||||||
\(77\) | 1.91856 | 0.218641 | ||||||||
\(78\) | −30.7373 | −3.48032 | ||||||||
\(79\) | 10.1389 | 1.14071 | 0.570356 | − | 0.821398i | \(-0.306805\pi\) | ||||
0.570356 | + | 0.821398i | \(0.306805\pi\) | |||||||
\(80\) | 5.01476 | 0.560667 | ||||||||
\(81\) | −3.08204 | −0.342449 | ||||||||
\(82\) | −16.4639 | −1.81814 | ||||||||
\(83\) | −15.9249 | −1.74799 | −0.873994 | − | 0.485938i | \(-0.838478\pi\) | ||||
−0.873994 | + | 0.485938i | \(0.838478\pi\) | |||||||
\(84\) | 5.31670 | 0.580100 | ||||||||
\(85\) | −1.00305 | −0.108796 | ||||||||
\(86\) | −1.73828 | −0.187443 | ||||||||
\(87\) | 18.9203 | 2.02847 | ||||||||
\(88\) | 1.70071 | 0.181296 | ||||||||
\(89\) | 12.1599 | 1.28895 | 0.644475 | − | 0.764625i | \(-0.277076\pi\) | ||||
0.644475 | + | 0.764625i | \(0.277076\pi\) | |||||||
\(90\) | 7.59843 | 0.800945 | ||||||||
\(91\) | 12.5067 | 1.31106 | ||||||||
\(92\) | 4.86042 | 0.506734 | ||||||||
\(93\) | 14.1964 | 1.47210 | ||||||||
\(94\) | −2.38742 | −0.246243 | ||||||||
\(95\) | 0.647670 | 0.0664495 | ||||||||
\(96\) | 14.3472 | 1.46430 | ||||||||
\(97\) | −2.72699 | −0.276884 | −0.138442 | − | 0.990371i | \(-0.544209\pi\) | ||||
−0.138442 | + | 0.990371i | \(0.544209\pi\) | |||||||
\(98\) | 5.76955 | 0.582813 | ||||||||
\(99\) | 4.35796 | 0.437992 | ||||||||
\(100\) | −4.08023 | −0.408023 | ||||||||
\(101\) | −8.59300 | −0.855035 | −0.427518 | − | 0.904007i | \(-0.640612\pi\) | ||||
−0.427518 | + | 0.904007i | \(0.640612\pi\) | |||||||
\(102\) | −4.71518 | −0.466873 | ||||||||
\(103\) | −13.5679 | −1.33688 | −0.668440 | − | 0.743766i | \(-0.733038\pi\) | ||||
−0.668440 | + | 0.743766i | \(0.733038\pi\) | |||||||
\(104\) | 11.0866 | 1.08713 | ||||||||
\(105\) | −5.22006 | −0.509426 | ||||||||
\(106\) | 5.77955 | 0.561360 | ||||||||
\(107\) | 7.34589 | 0.710154 | 0.355077 | − | 0.934837i | \(-0.384455\pi\) | ||||
0.355077 | + | 0.934837i | \(0.384455\pi\) | |||||||
\(108\) | 3.76317 | 0.362112 | ||||||||
\(109\) | −13.4662 | −1.28983 | −0.644916 | − | 0.764254i | \(-0.723108\pi\) | ||||
−0.644916 | + | 0.764254i | \(0.723108\pi\) | |||||||
\(110\) | 1.74357 | 0.166243 | ||||||||
\(111\) | −1.77421 | −0.168400 | ||||||||
\(112\) | −9.59192 | −0.906351 | ||||||||
\(113\) | 19.2657 | 1.81237 | 0.906185 | − | 0.422882i | \(-0.138982\pi\) | ||||
0.906185 | + | 0.422882i | \(0.138982\pi\) | |||||||
\(114\) | 3.04461 | 0.285154 | ||||||||
\(115\) | −4.77207 | −0.444998 | ||||||||
\(116\) | 7.12585 | 0.661618 | ||||||||
\(117\) | 28.4087 | 2.62639 | ||||||||
\(118\) | 10.4451 | 0.961548 | ||||||||
\(119\) | 1.91856 | 0.175874 | ||||||||
\(120\) | −4.62731 | −0.422414 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.15425 | 0.104501 | ||||||||
\(123\) | 25.6917 | 2.31654 | ||||||||
\(124\) | 5.34672 | 0.480149 | ||||||||
\(125\) | 9.02129 | 0.806889 | ||||||||
\(126\) | −14.5338 | −1.29477 | ||||||||
\(127\) | 3.91481 | 0.347383 | 0.173692 | − | 0.984800i | \(-0.444430\pi\) | ||||
0.173692 | + | 0.984800i | \(0.444430\pi\) | |||||||
\(128\) | −11.9777 | −1.05869 | ||||||||
\(129\) | 2.71256 | 0.238827 | ||||||||
\(130\) | 11.3660 | 0.996865 | ||||||||
\(131\) | −8.42384 | −0.735994 | −0.367997 | − | 0.929827i | \(-0.619956\pi\) | ||||
−0.367997 | + | 0.929827i | \(0.619956\pi\) | |||||||
\(132\) | 2.77119 | 0.241201 | ||||||||
\(133\) | −1.23882 | −0.107420 | ||||||||
\(134\) | −22.5074 | −1.94434 | ||||||||
\(135\) | −3.69477 | −0.317995 | ||||||||
\(136\) | 1.70071 | 0.145834 | ||||||||
\(137\) | 16.7671 | 1.43251 | 0.716253 | − | 0.697841i | \(-0.245856\pi\) | ||||
0.716253 | + | 0.697841i | \(0.245856\pi\) | |||||||
\(138\) | −22.4329 | −1.90961 | ||||||||
\(139\) | 18.7394 | 1.58945 | 0.794726 | − | 0.606968i | \(-0.207615\pi\) | ||||
0.794726 | + | 0.606968i | \(0.207615\pi\) | |||||||
\(140\) | −1.96600 | −0.166158 | ||||||||
\(141\) | 3.72552 | 0.313746 | ||||||||
\(142\) | 22.4564 | 1.88450 | ||||||||
\(143\) | 6.51880 | 0.545130 | ||||||||
\(144\) | −21.7878 | −1.81565 | ||||||||
\(145\) | −6.99632 | −0.581013 | ||||||||
\(146\) | −2.01031 | −0.166375 | ||||||||
\(147\) | −9.00329 | −0.742579 | ||||||||
\(148\) | −0.668210 | −0.0549265 | ||||||||
\(149\) | −13.6632 | −1.11933 | −0.559665 | − | 0.828719i | \(-0.689070\pi\) | ||||
−0.559665 | + | 0.828719i | \(0.689070\pi\) | |||||||
\(150\) | 18.8320 | 1.53762 | ||||||||
\(151\) | 5.01324 | 0.407972 | 0.203986 | − | 0.978974i | \(-0.434610\pi\) | ||||
0.203986 | + | 0.978974i | \(0.434610\pi\) | |||||||
\(152\) | −1.09815 | −0.0890718 | ||||||||
\(153\) | 4.35796 | 0.352320 | ||||||||
\(154\) | −3.33500 | −0.268742 | ||||||||
\(155\) | −5.24953 | −0.421652 | ||||||||
\(156\) | 18.0648 | 1.44634 | ||||||||
\(157\) | −22.6278 | −1.80589 | −0.902946 | − | 0.429753i | \(-0.858601\pi\) | ||||
−0.902946 | + | 0.429753i | \(0.858601\pi\) | |||||||
\(158\) | −17.6242 | −1.40211 | ||||||||
\(159\) | −9.01890 | −0.715245 | ||||||||
\(160\) | −5.30528 | −0.419419 | ||||||||
\(161\) | 9.12772 | 0.719365 | ||||||||
\(162\) | 5.35746 | 0.420921 | ||||||||
\(163\) | −17.2810 | −1.35355 | −0.676777 | − | 0.736188i | \(-0.736624\pi\) | ||||
−0.676777 | + | 0.736188i | \(0.736624\pi\) | |||||||
\(164\) | 9.67612 | 0.755578 | ||||||||
\(165\) | −2.72082 | −0.211815 | ||||||||
\(166\) | 27.6820 | 2.14854 | ||||||||
\(167\) | −13.1928 | −1.02089 | −0.510444 | − | 0.859911i | \(-0.670519\pi\) | ||||
−0.510444 | + | 0.859911i | \(0.670519\pi\) | |||||||
\(168\) | 8.85083 | 0.682856 | ||||||||
\(169\) | 29.4948 | 2.26883 | ||||||||
\(170\) | 1.74357 | 0.133726 | ||||||||
\(171\) | −2.81395 | −0.215188 | ||||||||
\(172\) | 1.02162 | 0.0778974 | ||||||||
\(173\) | −2.00093 | −0.152128 | −0.0760638 | − | 0.997103i | \(-0.524235\pi\) | ||||
−0.0760638 | + | 0.997103i | \(0.524235\pi\) | |||||||
\(174\) | −32.8888 | −2.49329 | ||||||||
\(175\) | −7.66255 | −0.579234 | ||||||||
\(176\) | −4.99953 | −0.376854 | ||||||||
\(177\) | −16.2994 | −1.22514 | ||||||||
\(178\) | −21.1374 | −1.58431 | ||||||||
\(179\) | 3.38728 | 0.253177 | 0.126589 | − | 0.991955i | \(-0.459597\pi\) | ||||
0.126589 | + | 0.991955i | \(0.459597\pi\) | |||||||
\(180\) | −4.46572 | −0.332855 | ||||||||
\(181\) | −2.97143 | −0.220865 | −0.110432 | − | 0.993884i | \(-0.535224\pi\) | ||||
−0.110432 | + | 0.993884i | \(0.535224\pi\) | |||||||
\(182\) | −21.7402 | −1.61149 | ||||||||
\(183\) | −1.80119 | −0.133148 | ||||||||
\(184\) | 8.09125 | 0.596495 | ||||||||
\(185\) | 0.656064 | 0.0482348 | ||||||||
\(186\) | −24.6773 | −1.80943 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 1.40312 | 0.102333 | ||||||||
\(189\) | 7.06713 | 0.514058 | ||||||||
\(190\) | −1.12583 | −0.0816764 | ||||||||
\(191\) | 26.6453 | 1.92799 | 0.963993 | − | 0.265928i | \(-0.0856782\pi\) | ||||
0.963993 | + | 0.265928i | \(0.0856782\pi\) | |||||||
\(192\) | 2.18362 | 0.157589 | ||||||||
\(193\) | −4.80106 | −0.345588 | −0.172794 | − | 0.984958i | \(-0.555279\pi\) | ||||
−0.172794 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(194\) | 4.74028 | 0.340332 | ||||||||
\(195\) | −17.7365 | −1.27014 | ||||||||
\(196\) | −3.39086 | −0.242204 | ||||||||
\(197\) | −6.94457 | −0.494780 | −0.247390 | − | 0.968916i | \(-0.579573\pi\) | ||||
−0.247390 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(198\) | −7.57536 | −0.538357 | ||||||||
\(199\) | −15.0763 | −1.06873 | −0.534366 | − | 0.845253i | \(-0.679449\pi\) | ||||
−0.534366 | + | 0.845253i | \(0.679449\pi\) | |||||||
\(200\) | −6.79245 | −0.480299 | ||||||||
\(201\) | 35.1224 | 2.47735 | ||||||||
\(202\) | 14.9370 | 1.05097 | ||||||||
\(203\) | 13.3821 | 0.939241 | ||||||||
\(204\) | 2.77119 | 0.194022 | ||||||||
\(205\) | −9.50023 | −0.663525 | ||||||||
\(206\) | 23.5847 | 1.64323 | ||||||||
\(207\) | 20.7334 | 1.44107 | ||||||||
\(208\) | −32.5910 | −2.25978 | ||||||||
\(209\) | −0.645703 | −0.0446642 | ||||||||
\(210\) | 9.07392 | 0.626160 | ||||||||
\(211\) | −20.5176 | −1.41249 | −0.706245 | − | 0.707967i | \(-0.749613\pi\) | ||||
−0.706245 | + | 0.707967i | \(0.749613\pi\) | |||||||
\(212\) | −3.39674 | −0.233289 | ||||||||
\(213\) | −35.0429 | −2.40110 | ||||||||
\(214\) | −12.7692 | −0.872885 | ||||||||
\(215\) | −1.00305 | −0.0684071 | ||||||||
\(216\) | 6.26464 | 0.426255 | ||||||||
\(217\) | 10.0410 | 0.681625 | ||||||||
\(218\) | 23.4081 | 1.58540 | ||||||||
\(219\) | 3.13706 | 0.211983 | ||||||||
\(220\) | −1.02473 | −0.0690871 | ||||||||
\(221\) | 6.51880 | 0.438502 | ||||||||
\(222\) | 3.08407 | 0.206989 | ||||||||
\(223\) | 16.6898 | 1.11763 | 0.558815 | − | 0.829292i | \(-0.311256\pi\) | ||||
0.558815 | + | 0.829292i | \(0.311256\pi\) | |||||||
\(224\) | 10.1476 | 0.678016 | ||||||||
\(225\) | −17.4053 | −1.16035 | ||||||||
\(226\) | −33.4893 | −2.22767 | ||||||||
\(227\) | −5.94499 | −0.394583 | −0.197291 | − | 0.980345i | \(-0.563214\pi\) | ||||
−0.197291 | + | 0.980345i | \(0.563214\pi\) | |||||||
\(228\) | −1.78937 | −0.118504 | ||||||||
\(229\) | −25.5371 | −1.68754 | −0.843768 | − | 0.536708i | \(-0.819668\pi\) | ||||
−0.843768 | + | 0.536708i | \(0.819668\pi\) | |||||||
\(230\) | 8.29519 | 0.546969 | ||||||||
\(231\) | 5.20421 | 0.342412 | ||||||||
\(232\) | 11.8626 | 0.778815 | ||||||||
\(233\) | 18.3218 | 1.20030 | 0.600150 | − | 0.799888i | \(-0.295108\pi\) | ||||
0.600150 | + | 0.799888i | \(0.295108\pi\) | |||||||
\(234\) | −49.3823 | −3.22822 | ||||||||
\(235\) | −1.37762 | −0.0898659 | ||||||||
\(236\) | −6.13875 | −0.399599 | ||||||||
\(237\) | 27.5023 | 1.78646 | ||||||||
\(238\) | −3.33500 | −0.216176 | ||||||||
\(239\) | −1.51527 | −0.0980149 | −0.0490074 | − | 0.998798i | \(-0.515606\pi\) | ||||
−0.0490074 | + | 0.998798i | \(0.515606\pi\) | |||||||
\(240\) | 13.6028 | 0.878058 | ||||||||
\(241\) | −6.25007 | −0.402602 | −0.201301 | − | 0.979529i | \(-0.564517\pi\) | ||||
−0.201301 | + | 0.979529i | \(0.564517\pi\) | |||||||
\(242\) | −1.73828 | −0.111741 | ||||||||
\(243\) | −19.4109 | −1.24521 | ||||||||
\(244\) | −0.678372 | −0.0434283 | ||||||||
\(245\) | 3.32923 | 0.212696 | ||||||||
\(246\) | −44.6593 | −2.84737 | ||||||||
\(247\) | −4.20921 | −0.267826 | ||||||||
\(248\) | 8.90080 | 0.565201 | ||||||||
\(249\) | −43.1972 | −2.73751 | ||||||||
\(250\) | −15.6815 | −0.991787 | ||||||||
\(251\) | −14.2921 | −0.902107 | −0.451053 | − | 0.892497i | \(-0.648952\pi\) | ||||
−0.451053 | + | 0.892497i | \(0.648952\pi\) | |||||||
\(252\) | 8.54175 | 0.538080 | ||||||||
\(253\) | 4.75758 | 0.299107 | ||||||||
\(254\) | −6.80503 | −0.426986 | ||||||||
\(255\) | −2.72082 | −0.170384 | ||||||||
\(256\) | 19.2105 | 1.20066 | ||||||||
\(257\) | −19.6832 | −1.22781 | −0.613903 | − | 0.789382i | \(-0.710401\pi\) | ||||
−0.613903 | + | 0.789382i | \(0.710401\pi\) | |||||||
\(258\) | −4.71518 | −0.293554 | ||||||||
\(259\) | −1.25488 | −0.0779743 | ||||||||
\(260\) | −6.67999 | −0.414275 | ||||||||
\(261\) | 30.3971 | 1.88154 | ||||||||
\(262\) | 14.6430 | 0.904647 | ||||||||
\(263\) | −18.1031 | −1.11629 | −0.558143 | − | 0.829745i | \(-0.688486\pi\) | ||||
−0.558143 | + | 0.829745i | \(0.688486\pi\) | |||||||
\(264\) | 4.61326 | 0.283927 | ||||||||
\(265\) | 3.33500 | 0.204867 | ||||||||
\(266\) | 2.15342 | 0.132035 | ||||||||
\(267\) | 32.9845 | 2.01862 | ||||||||
\(268\) | 13.2280 | 0.808027 | ||||||||
\(269\) | 1.47461 | 0.0899086 | 0.0449543 | − | 0.998989i | \(-0.485686\pi\) | ||||
0.0449543 | + | 0.998989i | \(0.485686\pi\) | |||||||
\(270\) | 6.42254 | 0.390864 | ||||||||
\(271\) | −8.97382 | −0.545121 | −0.272560 | − | 0.962139i | \(-0.587870\pi\) | ||||
−0.272560 | + | 0.962139i | \(0.587870\pi\) | |||||||
\(272\) | −4.99953 | −0.303141 | ||||||||
\(273\) | 33.9252 | 2.05325 | ||||||||
\(274\) | −29.1458 | −1.76076 | ||||||||
\(275\) | −3.99390 | −0.240841 | ||||||||
\(276\) | 13.1842 | 0.793593 | ||||||||
\(277\) | 14.9936 | 0.900879 | 0.450439 | − | 0.892807i | \(-0.351267\pi\) | ||||
0.450439 | + | 0.892807i | \(0.351267\pi\) | |||||||
\(278\) | −32.5742 | −1.95367 | ||||||||
\(279\) | 22.8078 | 1.36547 | ||||||||
\(280\) | −3.27285 | −0.195590 | ||||||||
\(281\) | 20.9991 | 1.25270 | 0.626349 | − | 0.779542i | \(-0.284548\pi\) | ||||
0.626349 | + | 0.779542i | \(0.284548\pi\) | |||||||
\(282\) | −6.47600 | −0.385640 | ||||||||
\(283\) | 12.6634 | 0.752762 | 0.376381 | − | 0.926465i | \(-0.377168\pi\) | ||||
0.376381 | + | 0.926465i | \(0.377168\pi\) | |||||||
\(284\) | −13.1980 | −0.783158 | ||||||||
\(285\) | 1.75684 | 0.104066 | ||||||||
\(286\) | −11.3315 | −0.670046 | ||||||||
\(287\) | 18.1715 | 1.07263 | ||||||||
\(288\) | 23.0500 | 1.35824 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 12.1616 | 0.714151 | ||||||||
\(291\) | −7.39712 | −0.433627 | ||||||||
\(292\) | 1.18149 | 0.0691417 | ||||||||
\(293\) | −16.8401 | −0.983809 | −0.491904 | − | 0.870649i | \(-0.663699\pi\) | ||||
−0.491904 | + | 0.870649i | \(0.663699\pi\) | |||||||
\(294\) | 15.6502 | 0.912740 | ||||||||
\(295\) | 6.02717 | 0.350915 | ||||||||
\(296\) | −1.11238 | −0.0646560 | ||||||||
\(297\) | 3.68355 | 0.213741 | ||||||||
\(298\) | 23.7504 | 1.37582 | ||||||||
\(299\) | 31.0137 | 1.79357 | ||||||||
\(300\) | −11.0679 | −0.639003 | ||||||||
\(301\) | 1.91856 | 0.110584 | ||||||||
\(302\) | −8.71441 | −0.501458 | ||||||||
\(303\) | −23.3090 | −1.33907 | ||||||||
\(304\) | 3.22821 | 0.185151 | ||||||||
\(305\) | 0.666041 | 0.0381374 | ||||||||
\(306\) | −7.57536 | −0.433054 | ||||||||
\(307\) | −11.2413 | −0.641578 | −0.320789 | − | 0.947151i | \(-0.603948\pi\) | ||||
−0.320789 | + | 0.947151i | \(0.603948\pi\) | |||||||
\(308\) | 1.96003 | 0.111683 | ||||||||
\(309\) | −36.8036 | −2.09368 | ||||||||
\(310\) | 9.12515 | 0.518274 | ||||||||
\(311\) | 5.57659 | 0.316219 | 0.158110 | − | 0.987422i | \(-0.449460\pi\) | ||||
0.158110 | + | 0.987422i | \(0.449460\pi\) | |||||||
\(312\) | 30.0729 | 1.70254 | ||||||||
\(313\) | −27.9294 | −1.57866 | −0.789331 | − | 0.613967i | \(-0.789573\pi\) | ||||
−0.789331 | + | 0.613967i | \(0.789573\pi\) | |||||||
\(314\) | 39.3334 | 2.21971 | ||||||||
\(315\) | −8.38649 | −0.472525 | ||||||||
\(316\) | 10.3580 | 0.582684 | ||||||||
\(317\) | 34.2628 | 1.92439 | 0.962194 | − | 0.272364i | \(-0.0878055\pi\) | ||||
0.962194 | + | 0.272364i | \(0.0878055\pi\) | |||||||
\(318\) | 15.6774 | 0.879143 | ||||||||
\(319\) | 6.97508 | 0.390529 | ||||||||
\(320\) | −0.807456 | −0.0451382 | ||||||||
\(321\) | 19.9261 | 1.11217 | ||||||||
\(322\) | −15.8665 | −0.884207 | ||||||||
\(323\) | −0.645703 | −0.0359279 | ||||||||
\(324\) | −3.14866 | −0.174926 | ||||||||
\(325\) | −26.0354 | −1.44419 | ||||||||
\(326\) | 30.0392 | 1.66372 | ||||||||
\(327\) | −36.5279 | −2.02000 | ||||||||
\(328\) | 16.1080 | 0.889418 | ||||||||
\(329\) | 2.63502 | 0.145274 | ||||||||
\(330\) | 4.72954 | 0.260353 | ||||||||
\(331\) | 3.43714 | 0.188922 | 0.0944610 | − | 0.995529i | \(-0.469887\pi\) | ||||
0.0944610 | + | 0.995529i | \(0.469887\pi\) | |||||||
\(332\) | −16.2691 | −0.892885 | ||||||||
\(333\) | −2.85042 | −0.156202 | ||||||||
\(334\) | 22.9327 | 1.25482 | ||||||||
\(335\) | −12.9875 | −0.709584 | ||||||||
\(336\) | −26.0186 | −1.41943 | ||||||||
\(337\) | −0.346351 | −0.0188669 | −0.00943346 | − | 0.999956i | \(-0.503003\pi\) | ||||
−0.00943346 | + | 0.999956i | \(0.503003\pi\) | |||||||
\(338\) | −51.2702 | −2.78873 | ||||||||
\(339\) | 52.2594 | 2.83834 | ||||||||
\(340\) | −1.02473 | −0.0555736 | ||||||||
\(341\) | 5.23359 | 0.283415 | ||||||||
\(342\) | 4.89143 | 0.264498 | ||||||||
\(343\) | −19.7979 | −1.06898 | ||||||||
\(344\) | 1.70071 | 0.0916959 | ||||||||
\(345\) | −12.9445 | −0.696909 | ||||||||
\(346\) | 3.47817 | 0.186988 | ||||||||
\(347\) | 35.3760 | 1.89908 | 0.949542 | − | 0.313640i | \(-0.101549\pi\) | ||||
0.949542 | + | 0.313640i | \(0.101549\pi\) | |||||||
\(348\) | 19.3293 | 1.03616 | ||||||||
\(349\) | −8.72306 | −0.466934 | −0.233467 | − | 0.972365i | \(-0.575007\pi\) | ||||
−0.233467 | + | 0.972365i | \(0.575007\pi\) | |||||||
\(350\) | 13.3196 | 0.711965 | ||||||||
\(351\) | 24.0123 | 1.28168 | ||||||||
\(352\) | 5.28917 | 0.281914 | ||||||||
\(353\) | 7.34047 | 0.390694 | 0.195347 | − | 0.980734i | \(-0.437417\pi\) | ||||
0.195347 | + | 0.980734i | \(0.437417\pi\) | |||||||
\(354\) | 28.3329 | 1.50588 | ||||||||
\(355\) | 12.9581 | 0.687745 | ||||||||
\(356\) | 12.4228 | 0.658406 | ||||||||
\(357\) | 5.20421 | 0.275436 | ||||||||
\(358\) | −5.88804 | −0.311193 | ||||||||
\(359\) | −3.09087 | −0.163130 | −0.0815650 | − | 0.996668i | \(-0.525992\pi\) | ||||
−0.0815650 | + | 0.996668i | \(0.525992\pi\) | |||||||
\(360\) | −7.43419 | −0.391816 | ||||||||
\(361\) | −18.5831 | −0.978056 | ||||||||
\(362\) | 5.16518 | 0.271476 | ||||||||
\(363\) | 2.71256 | 0.142372 | ||||||||
\(364\) | 12.7771 | 0.669700 | ||||||||
\(365\) | −1.16002 | −0.0607182 | ||||||||
\(366\) | 3.13097 | 0.163658 | ||||||||
\(367\) | 26.5980 | 1.38840 | 0.694201 | − | 0.719781i | \(-0.255758\pi\) | ||||
0.694201 | + | 0.719781i | \(0.255758\pi\) | |||||||
\(368\) | −23.7857 | −1.23991 | ||||||||
\(369\) | 41.2760 | 2.14874 | ||||||||
\(370\) | −1.14042 | −0.0592877 | ||||||||
\(371\) | −6.37897 | −0.331180 | ||||||||
\(372\) | 14.5033 | 0.751959 | ||||||||
\(373\) | −37.6039 | −1.94706 | −0.973529 | − | 0.228565i | \(-0.926597\pi\) | ||||
−0.973529 | + | 0.228565i | \(0.926597\pi\) | |||||||
\(374\) | −1.73828 | −0.0898843 | ||||||||
\(375\) | 24.4708 | 1.26366 | ||||||||
\(376\) | 2.33581 | 0.120460 | ||||||||
\(377\) | 45.4692 | 2.34178 | ||||||||
\(378\) | −12.2846 | −0.631854 | ||||||||
\(379\) | 7.62421 | 0.391629 | 0.195815 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195815 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(380\) | 0.661669 | 0.0339429 | ||||||||
\(381\) | 10.6191 | 0.544035 | ||||||||
\(382\) | −46.3170 | −2.36978 | ||||||||
\(383\) | 33.7237 | 1.72320 | 0.861601 | − | 0.507586i | \(-0.169462\pi\) | ||||
0.861601 | + | 0.507586i | \(0.169462\pi\) | |||||||
\(384\) | −32.4901 | −1.65800 | ||||||||
\(385\) | −1.92441 | −0.0980768 | ||||||||
\(386\) | 8.34559 | 0.424779 | ||||||||
\(387\) | 4.35796 | 0.221528 | ||||||||
\(388\) | −2.78594 | −0.141435 | ||||||||
\(389\) | 24.4515 | 1.23974 | 0.619871 | − | 0.784704i | \(-0.287185\pi\) | ||||
0.619871 | + | 0.784704i | \(0.287185\pi\) | |||||||
\(390\) | 30.8309 | 1.56119 | ||||||||
\(391\) | 4.75758 | 0.240601 | ||||||||
\(392\) | −5.64484 | −0.285108 | ||||||||
\(393\) | −22.8501 | −1.15264 | ||||||||
\(394\) | 12.0716 | 0.608159 | ||||||||
\(395\) | −10.1697 | −0.511696 | ||||||||
\(396\) | 4.45216 | 0.223730 | ||||||||
\(397\) | 0.404617 | 0.0203072 | 0.0101536 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101536 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(398\) | 26.2068 | 1.31363 | ||||||||
\(399\) | −3.36038 | −0.168229 | ||||||||
\(400\) | 19.9676 | 0.998382 | ||||||||
\(401\) | 23.5867 | 1.17786 | 0.588931 | − | 0.808184i | \(-0.299549\pi\) | ||||
0.588931 | + | 0.808184i | \(0.299549\pi\) | |||||||
\(402\) | −61.0526 | −3.04503 | ||||||||
\(403\) | 34.1167 | 1.69948 | ||||||||
\(404\) | −8.77874 | −0.436759 | ||||||||
\(405\) | 3.09143 | 0.153614 | ||||||||
\(406\) | −23.2619 | −1.15447 | ||||||||
\(407\) | −0.654072 | −0.0324211 | ||||||||
\(408\) | 4.61326 | 0.228390 | ||||||||
\(409\) | 18.7932 | 0.929265 | 0.464633 | − | 0.885504i | \(-0.346186\pi\) | ||||
0.464633 | + | 0.885504i | \(0.346186\pi\) | |||||||
\(410\) | 16.5141 | 0.815571 | ||||||||
\(411\) | 45.4816 | 2.24344 | ||||||||
\(412\) | −13.8611 | −0.682889 | ||||||||
\(413\) | −11.5284 | −0.567275 | ||||||||
\(414\) | −36.0404 | −1.77129 | ||||||||
\(415\) | 15.9734 | 0.784104 | ||||||||
\(416\) | 34.4791 | 1.69048 | ||||||||
\(417\) | 50.8316 | 2.48923 | ||||||||
\(418\) | 1.12241 | 0.0548990 | ||||||||
\(419\) | −4.88463 | −0.238630 | −0.119315 | − | 0.992856i | \(-0.538070\pi\) | ||||
−0.119315 | + | 0.992856i | \(0.538070\pi\) | |||||||
\(420\) | −5.33289 | −0.260219 | ||||||||
\(421\) | −16.4314 | −0.800815 | −0.400408 | − | 0.916337i | \(-0.631131\pi\) | ||||
−0.400408 | + | 0.916337i | \(0.631131\pi\) | |||||||
\(422\) | 35.6654 | 1.73616 | ||||||||
\(423\) | 5.98538 | 0.291019 | ||||||||
\(424\) | −5.65463 | −0.274613 | ||||||||
\(425\) | −3.99390 | −0.193733 | ||||||||
\(426\) | 60.9143 | 2.95131 | ||||||||
\(427\) | −1.27396 | −0.0616513 | ||||||||
\(428\) | 7.50468 | 0.362752 | ||||||||
\(429\) | 17.6826 | 0.853725 | ||||||||
\(430\) | 1.74357 | 0.0840826 | ||||||||
\(431\) | 37.8404 | 1.82271 | 0.911354 | − | 0.411623i | \(-0.135038\pi\) | ||||
0.911354 | + | 0.411623i | \(0.135038\pi\) | |||||||
\(432\) | −18.4160 | −0.886042 | ||||||||
\(433\) | −16.3296 | −0.784751 | −0.392375 | − | 0.919805i | \(-0.628347\pi\) | ||||
−0.392375 | + | 0.919805i | \(0.628347\pi\) | |||||||
\(434\) | −17.4540 | −0.837819 | ||||||||
\(435\) | −18.9779 | −0.909921 | ||||||||
\(436\) | −13.7573 | −0.658856 | ||||||||
\(437\) | −3.07199 | −0.146953 | ||||||||
\(438\) | −5.45309 | −0.260559 | ||||||||
\(439\) | −13.7765 | −0.657514 | −0.328757 | − | 0.944414i | \(-0.606630\pi\) | ||||
−0.328757 | + | 0.944414i | \(0.606630\pi\) | |||||||
\(440\) | −1.70589 | −0.0813249 | ||||||||
\(441\) | −14.4646 | −0.688790 | ||||||||
\(442\) | −11.3315 | −0.538984 | ||||||||
\(443\) | 7.54597 | 0.358520 | 0.179260 | − | 0.983802i | \(-0.442630\pi\) | ||||
0.179260 | + | 0.983802i | \(0.442630\pi\) | |||||||
\(444\) | −1.81256 | −0.0860201 | ||||||||
\(445\) | −12.1970 | −0.578191 | ||||||||
\(446\) | −29.0115 | −1.37373 | ||||||||
\(447\) | −37.0621 | −1.75298 | ||||||||
\(448\) | 1.54445 | 0.0729685 | ||||||||
\(449\) | 10.0748 | 0.475461 | 0.237730 | − | 0.971331i | \(-0.423597\pi\) | ||||
0.237730 | + | 0.971331i | \(0.423597\pi\) | |||||||
\(450\) | 30.2552 | 1.42624 | ||||||||
\(451\) | 9.47139 | 0.445990 | ||||||||
\(452\) | 19.6822 | 0.925772 | ||||||||
\(453\) | 13.5987 | 0.638922 | ||||||||
\(454\) | 10.3340 | 0.485001 | ||||||||
\(455\) | −12.5448 | −0.588110 | ||||||||
\(456\) | −2.97880 | −0.139495 | ||||||||
\(457\) | 14.8430 | 0.694327 | 0.347163 | − | 0.937805i | \(-0.387145\pi\) | ||||
0.347163 | + | 0.937805i | \(0.387145\pi\) | |||||||
\(458\) | 44.3905 | 2.07423 | ||||||||
\(459\) | 3.68355 | 0.171934 | ||||||||
\(460\) | −4.87522 | −0.227308 | ||||||||
\(461\) | 3.00223 | 0.139828 | 0.0699139 | − | 0.997553i | \(-0.477728\pi\) | ||||
0.0699139 | + | 0.997553i | \(0.477728\pi\) | |||||||
\(462\) | −9.04637 | −0.420875 | ||||||||
\(463\) | −7.04016 | −0.327184 | −0.163592 | − | 0.986528i | \(-0.552308\pi\) | ||||
−0.163592 | + | 0.986528i | \(0.552308\pi\) | |||||||
\(464\) | −34.8721 | −1.61890 | ||||||||
\(465\) | −14.2396 | −0.660348 | ||||||||
\(466\) | −31.8484 | −1.47535 | ||||||||
\(467\) | −32.8334 | −1.51935 | −0.759675 | − | 0.650303i | \(-0.774642\pi\) | ||||
−0.759675 | + | 0.650303i | \(0.774642\pi\) | |||||||
\(468\) | 29.0228 | 1.34158 | ||||||||
\(469\) | 24.8417 | 1.14708 | ||||||||
\(470\) | 2.39469 | 0.110459 | ||||||||
\(471\) | −61.3791 | −2.82820 | ||||||||
\(472\) | −10.2193 | −0.470382 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −47.8066 | −2.19583 | ||||||||
\(475\) | 2.57887 | 0.118327 | ||||||||
\(476\) | 1.96003 | 0.0898380 | ||||||||
\(477\) | −14.4897 | −0.663436 | ||||||||
\(478\) | 2.63397 | 0.120475 | ||||||||
\(479\) | −34.1397 | −1.55988 | −0.779942 | − | 0.625851i | \(-0.784752\pi\) | ||||
−0.779942 | + | 0.625851i | \(0.784752\pi\) | |||||||
\(480\) | −14.3909 | −0.656851 | ||||||||
\(481\) | −4.26376 | −0.194411 | ||||||||
\(482\) | 10.8644 | 0.494858 | ||||||||
\(483\) | 24.7594 | 1.12659 | ||||||||
\(484\) | 1.02162 | 0.0464371 | ||||||||
\(485\) | 2.73530 | 0.124203 | ||||||||
\(486\) | 33.7415 | 1.53055 | ||||||||
\(487\) | 28.1357 | 1.27495 | 0.637476 | − | 0.770471i | \(-0.279979\pi\) | ||||
0.637476 | + | 0.770471i | \(0.279979\pi\) | |||||||
\(488\) | −1.12930 | −0.0511211 | ||||||||
\(489\) | −46.8758 | −2.11980 | ||||||||
\(490\) | −5.78712 | −0.261436 | ||||||||
\(491\) | −30.6172 | −1.38174 | −0.690868 | − | 0.722981i | \(-0.742772\pi\) | ||||
−0.690868 | + | 0.722981i | \(0.742772\pi\) | |||||||
\(492\) | 26.2470 | 1.18331 | ||||||||
\(493\) | 6.97508 | 0.314142 | ||||||||
\(494\) | 7.31679 | 0.329198 | ||||||||
\(495\) | −4.37124 | −0.196472 | ||||||||
\(496\) | −26.1655 | −1.17487 | ||||||||
\(497\) | −24.7855 | −1.11178 | ||||||||
\(498\) | 75.0889 | 3.36481 | ||||||||
\(499\) | −10.2086 | −0.457001 | −0.228501 | − | 0.973544i | \(-0.573382\pi\) | ||||
−0.228501 | + | 0.973544i | \(0.573382\pi\) | |||||||
\(500\) | 9.21629 | 0.412165 | ||||||||
\(501\) | −35.7862 | −1.59881 | ||||||||
\(502\) | 24.8436 | 1.10882 | ||||||||
\(503\) | 35.4049 | 1.57863 | 0.789313 | − | 0.613991i | \(-0.210437\pi\) | ||||
0.789313 | + | 0.613991i | \(0.210437\pi\) | |||||||
\(504\) | 14.2196 | 0.633393 | ||||||||
\(505\) | 8.61917 | 0.383548 | ||||||||
\(506\) | −8.27000 | −0.367647 | ||||||||
\(507\) | 80.0062 | 3.55320 | ||||||||
\(508\) | 3.99943 | 0.177446 | ||||||||
\(509\) | 0.0822089 | 0.00364384 | 0.00182192 | − | 0.999998i | \(-0.499420\pi\) | ||||
0.00182192 | + | 0.999998i | \(0.499420\pi\) | |||||||
\(510\) | 4.72954 | 0.209428 | ||||||||
\(511\) | 2.21881 | 0.0981544 | ||||||||
\(512\) | −9.43793 | −0.417101 | ||||||||
\(513\) | −2.37848 | −0.105013 | ||||||||
\(514\) | 34.2149 | 1.50916 | ||||||||
\(515\) | 13.6092 | 0.599692 | ||||||||
\(516\) | 2.77119 | 0.121995 | ||||||||
\(517\) | 1.37344 | 0.0604036 | ||||||||
\(518\) | 2.18133 | 0.0958421 | ||||||||
\(519\) | −5.42763 | −0.238246 | ||||||||
\(520\) | −11.1203 | −0.487659 | ||||||||
\(521\) | −25.0397 | −1.09701 | −0.548504 | − | 0.836148i | \(-0.684803\pi\) | ||||
−0.548504 | + | 0.836148i | \(0.684803\pi\) | |||||||
\(522\) | −52.8387 | −2.31269 | ||||||||
\(523\) | 7.13145 | 0.311837 | 0.155918 | − | 0.987770i | \(-0.450166\pi\) | ||||
0.155918 | + | 0.987770i | \(0.450166\pi\) | |||||||
\(524\) | −8.60592 | −0.375951 | ||||||||
\(525\) | −20.7851 | −0.907136 | ||||||||
\(526\) | 31.4683 | 1.37208 | ||||||||
\(527\) | 5.23359 | 0.227979 | ||||||||
\(528\) | −13.5615 | −0.590189 | ||||||||
\(529\) | −0.365427 | −0.0158881 | ||||||||
\(530\) | −5.79715 | −0.251812 | ||||||||
\(531\) | −26.1864 | −1.13639 | ||||||||
\(532\) | −1.26560 | −0.0548707 | ||||||||
\(533\) | 61.7421 | 2.67435 | ||||||||
\(534\) | −57.3363 | −2.48118 | ||||||||
\(535\) | −7.36826 | −0.318558 | ||||||||
\(536\) | 22.0209 | 0.951158 | ||||||||
\(537\) | 9.18820 | 0.396500 | ||||||||
\(538\) | −2.56329 | −0.110511 | ||||||||
\(539\) | −3.31912 | −0.142964 | ||||||||
\(540\) | −3.77463 | −0.162434 | ||||||||
\(541\) | −2.08035 | −0.0894413 | −0.0447207 | − | 0.999000i | \(-0.514240\pi\) | ||||
−0.0447207 | + | 0.999000i | \(0.514240\pi\) | |||||||
\(542\) | 15.5990 | 0.670035 | ||||||||
\(543\) | −8.06017 | −0.345895 | ||||||||
\(544\) | 5.28917 | 0.226771 | ||||||||
\(545\) | 13.5072 | 0.578587 | ||||||||
\(546\) | −58.9715 | −2.52375 | ||||||||
\(547\) | 12.6144 | 0.539351 | 0.269675 | − | 0.962951i | \(-0.413084\pi\) | ||||
0.269675 | + | 0.962951i | \(0.413084\pi\) | |||||||
\(548\) | 17.1295 | 0.731735 | ||||||||
\(549\) | −2.89377 | −0.123503 | ||||||||
\(550\) | 6.94251 | 0.296030 | ||||||||
\(551\) | −4.50383 | −0.191870 | ||||||||
\(552\) | 21.9480 | 0.934167 | ||||||||
\(553\) | 19.4521 | 0.827186 | ||||||||
\(554\) | −26.0631 | −1.10731 | ||||||||
\(555\) | 1.77961 | 0.0755402 | ||||||||
\(556\) | 19.1444 | 0.811904 | ||||||||
\(557\) | −29.4322 | −1.24708 | −0.623542 | − | 0.781790i | \(-0.714307\pi\) | ||||
−0.623542 | + | 0.781790i | \(0.714307\pi\) | |||||||
\(558\) | −39.6463 | −1.67836 | ||||||||
\(559\) | 6.51880 | 0.275716 | ||||||||
\(560\) | 9.62113 | 0.406567 | ||||||||
\(561\) | 2.71256 | 0.114524 | ||||||||
\(562\) | −36.5022 | −1.53975 | ||||||||
\(563\) | 7.86597 | 0.331511 | 0.165756 | − | 0.986167i | \(-0.446994\pi\) | ||||
0.165756 | + | 0.986167i | \(0.446994\pi\) | |||||||
\(564\) | 3.80605 | 0.160264 | ||||||||
\(565\) | −19.3244 | −0.812985 | ||||||||
\(566\) | −22.0126 | −0.925257 | ||||||||
\(567\) | −5.91310 | −0.248327 | ||||||||
\(568\) | −21.9710 | −0.921884 | ||||||||
\(569\) | −30.0944 | −1.26162 | −0.630811 | − | 0.775936i | \(-0.717278\pi\) | ||||
−0.630811 | + | 0.775936i | \(0.717278\pi\) | |||||||
\(570\) | −3.05388 | −0.127913 | ||||||||
\(571\) | −3.99271 | −0.167090 | −0.0835449 | − | 0.996504i | \(-0.526624\pi\) | ||||
−0.0835449 | + | 0.996504i | \(0.526624\pi\) | |||||||
\(572\) | 6.65971 | 0.278456 | ||||||||
\(573\) | 72.2769 | 3.01941 | ||||||||
\(574\) | −31.5871 | −1.31842 | ||||||||
\(575\) | −19.0013 | −0.792409 | ||||||||
\(576\) | 3.50818 | 0.146174 | ||||||||
\(577\) | −20.9039 | −0.870241 | −0.435120 | − | 0.900372i | \(-0.643294\pi\) | ||||
−0.435120 | + | 0.900372i | \(0.643294\pi\) | |||||||
\(578\) | −1.73828 | −0.0723029 | ||||||||
\(579\) | −13.0232 | −0.541224 | ||||||||
\(580\) | −7.14755 | −0.296786 | ||||||||
\(581\) | −30.5530 | −1.26755 | ||||||||
\(582\) | 12.8583 | 0.532992 | ||||||||
\(583\) | −3.32487 | −0.137702 | ||||||||
\(584\) | 1.96686 | 0.0813893 | ||||||||
\(585\) | −28.4952 | −1.17813 | ||||||||
\(586\) | 29.2728 | 1.20925 | ||||||||
\(587\) | 38.0186 | 1.56920 | 0.784598 | − | 0.620004i | \(-0.212869\pi\) | ||||
0.784598 | + | 0.620004i | \(0.212869\pi\) | |||||||
\(588\) | −9.19790 | −0.379315 | ||||||||
\(589\) | −3.37935 | −0.139244 | ||||||||
\(590\) | −10.4769 | −0.431327 | ||||||||
\(591\) | −18.8375 | −0.774873 | ||||||||
\(592\) | 3.27005 | 0.134398 | ||||||||
\(593\) | −36.3283 | −1.49182 | −0.745911 | − | 0.666045i | \(-0.767986\pi\) | ||||
−0.745911 | + | 0.666045i | \(0.767986\pi\) | |||||||
\(594\) | −6.40304 | −0.262720 | ||||||||
\(595\) | −1.92441 | −0.0788929 | ||||||||
\(596\) | −13.9585 | −0.571763 | ||||||||
\(597\) | −40.8953 | −1.67374 | ||||||||
\(598\) | −53.9105 | −2.20457 | ||||||||
\(599\) | 25.9606 | 1.06072 | 0.530362 | − | 0.847772i | \(-0.322056\pi\) | ||||
0.530362 | + | 0.847772i | \(0.322056\pi\) | |||||||
\(600\) | −18.4249 | −0.752193 | ||||||||
\(601\) | −1.84844 | −0.0753993 | −0.0376996 | − | 0.999289i | \(-0.512003\pi\) | ||||
−0.0376996 | + | 0.999289i | \(0.512003\pi\) | |||||||
\(602\) | −3.33500 | −0.135924 | ||||||||
\(603\) | 56.4273 | 2.29790 | ||||||||
\(604\) | 5.12160 | 0.208395 | ||||||||
\(605\) | −1.00305 | −0.0407796 | ||||||||
\(606\) | 40.5175 | 1.64591 | ||||||||
\(607\) | 35.5192 | 1.44168 | 0.720840 | − | 0.693102i | \(-0.243756\pi\) | ||||
0.720840 | + | 0.693102i | \(0.243756\pi\) | |||||||
\(608\) | −3.41524 | −0.138506 | ||||||||
\(609\) | 36.2998 | 1.47094 | ||||||||
\(610\) | −1.15777 | −0.0468766 | ||||||||
\(611\) | 8.95315 | 0.362206 | ||||||||
\(612\) | 4.45216 | 0.179968 | ||||||||
\(613\) | 20.0787 | 0.810973 | 0.405486 | − | 0.914101i | \(-0.367102\pi\) | ||||
0.405486 | + | 0.914101i | \(0.367102\pi\) | |||||||
\(614\) | 19.5406 | 0.788595 | ||||||||
\(615\) | −25.7699 | −1.03914 | ||||||||
\(616\) | 3.26291 | 0.131466 | ||||||||
\(617\) | 46.1262 | 1.85697 | 0.928484 | − | 0.371371i | \(-0.121112\pi\) | ||||
0.928484 | + | 0.371371i | \(0.121112\pi\) | |||||||
\(618\) | 63.9749 | 2.57345 | ||||||||
\(619\) | −37.7568 | −1.51757 | −0.758787 | − | 0.651339i | \(-0.774208\pi\) | ||||
−0.758787 | + | 0.651339i | \(0.774208\pi\) | |||||||
\(620\) | −5.36300 | −0.215383 | ||||||||
\(621\) | 17.5248 | 0.703246 | ||||||||
\(622\) | −9.69367 | −0.388681 | ||||||||
\(623\) | 23.3296 | 0.934680 | ||||||||
\(624\) | −88.4048 | −3.53903 | ||||||||
\(625\) | 10.9207 | 0.436829 | ||||||||
\(626\) | 48.5491 | 1.94041 | ||||||||
\(627\) | −1.75151 | −0.0699484 | ||||||||
\(628\) | −23.1169 | −0.922464 | ||||||||
\(629\) | −0.654072 | −0.0260796 | ||||||||
\(630\) | 14.5781 | 0.580804 | ||||||||
\(631\) | 1.49485 | 0.0595092 | 0.0297546 | − | 0.999557i | \(-0.490527\pi\) | ||||
0.0297546 | + | 0.999557i | \(0.490527\pi\) | |||||||
\(632\) | 17.2432 | 0.685899 | ||||||||
\(633\) | −55.6552 | −2.21210 | ||||||||
\(634\) | −59.5583 | −2.36536 | ||||||||
\(635\) | −3.92673 | −0.155828 | ||||||||
\(636\) | −9.21385 | −0.365353 | ||||||||
\(637\) | −21.6367 | −0.857276 | ||||||||
\(638\) | −12.1246 | −0.480019 | ||||||||
\(639\) | −56.2995 | −2.22717 | ||||||||
\(640\) | 12.0141 | 0.474901 | ||||||||
\(641\) | 41.7650 | 1.64962 | 0.824809 | − | 0.565411i | \(-0.191283\pi\) | ||||
0.824809 | + | 0.565411i | \(0.191283\pi\) | |||||||
\(642\) | −34.6372 | −1.36702 | ||||||||
\(643\) | −2.01265 | −0.0793710 | −0.0396855 | − | 0.999212i | \(-0.512636\pi\) | ||||
−0.0396855 | + | 0.999212i | \(0.512636\pi\) | |||||||
\(644\) | 9.32502 | 0.367457 | ||||||||
\(645\) | −2.72082 | −0.107132 | ||||||||
\(646\) | 1.12241 | 0.0441607 | ||||||||
\(647\) | −10.5484 | −0.414701 | −0.207351 | − | 0.978267i | \(-0.566484\pi\) | ||||
−0.207351 | + | 0.978267i | \(0.566484\pi\) | |||||||
\(648\) | −5.24165 | −0.205912 | ||||||||
\(649\) | −6.00887 | −0.235869 | ||||||||
\(650\) | 45.2569 | 1.77512 | ||||||||
\(651\) | 27.2367 | 1.06749 | ||||||||
\(652\) | −17.6546 | −0.691406 | ||||||||
\(653\) | 32.3630 | 1.26646 | 0.633230 | − | 0.773963i | \(-0.281729\pi\) | ||||
0.633230 | + | 0.773963i | \(0.281729\pi\) | |||||||
\(654\) | 63.4957 | 2.48288 | ||||||||
\(655\) | 8.44949 | 0.330149 | ||||||||
\(656\) | −47.3525 | −1.84881 | ||||||||
\(657\) | 5.03997 | 0.196628 | ||||||||
\(658\) | −4.58041 | −0.178563 | ||||||||
\(659\) | 22.0220 | 0.857855 | 0.428927 | − | 0.903339i | \(-0.358892\pi\) | ||||
0.428927 | + | 0.903339i | \(0.358892\pi\) | |||||||
\(660\) | −2.77963 | −0.108197 | ||||||||
\(661\) | −23.5021 | −0.914127 | −0.457063 | − | 0.889434i | \(-0.651099\pi\) | ||||
−0.457063 | + | 0.889434i | \(0.651099\pi\) | |||||||
\(662\) | −5.97470 | −0.232213 | ||||||||
\(663\) | 17.6826 | 0.686736 | ||||||||
\(664\) | −27.0836 | −1.05105 | ||||||||
\(665\) | 1.24260 | 0.0481858 | ||||||||
\(666\) | 4.95483 | 0.191996 | ||||||||
\(667\) | 33.1845 | 1.28491 | ||||||||
\(668\) | −13.4780 | −0.521478 | ||||||||
\(669\) | 45.2720 | 1.75032 | ||||||||
\(670\) | 22.5759 | 0.872185 | ||||||||
\(671\) | −0.664019 | −0.0256342 | ||||||||
\(672\) | 27.5260 | 1.06184 | ||||||||
\(673\) | −9.40321 | −0.362467 | −0.181234 | − | 0.983440i | \(-0.558009\pi\) | ||||
−0.181234 | + | 0.983440i | \(0.558009\pi\) | |||||||
\(674\) | 0.602054 | 0.0231903 | ||||||||
\(675\) | −14.7117 | −0.566255 | ||||||||
\(676\) | 30.1323 | 1.15894 | ||||||||
\(677\) | 34.4457 | 1.32386 | 0.661929 | − | 0.749567i | \(-0.269738\pi\) | ||||
0.661929 | + | 0.749567i | \(0.269738\pi\) | |||||||
\(678\) | −90.8415 | −3.48875 | ||||||||
\(679\) | −5.23191 | −0.200782 | ||||||||
\(680\) | −1.70589 | −0.0654177 | ||||||||
\(681\) | −16.1261 | −0.617954 | ||||||||
\(682\) | −9.09744 | −0.348359 | ||||||||
\(683\) | 18.5880 | 0.711249 | 0.355624 | − | 0.934629i | \(-0.384268\pi\) | ||||
0.355624 | + | 0.934629i | \(0.384268\pi\) | |||||||
\(684\) | −2.87478 | −0.109920 | ||||||||
\(685\) | −16.8181 | −0.642587 | ||||||||
\(686\) | 34.4142 | 1.31394 | ||||||||
\(687\) | −69.2707 | −2.64284 | ||||||||
\(688\) | −4.99953 | −0.190605 | ||||||||
\(689\) | −21.6742 | −0.825720 | ||||||||
\(690\) | 22.5012 | 0.856605 | ||||||||
\(691\) | −14.8211 | −0.563822 | −0.281911 | − | 0.959441i | \(-0.590968\pi\) | ||||
−0.281911 | + | 0.959441i | \(0.590968\pi\) | |||||||
\(692\) | −2.04418 | −0.0777080 | ||||||||
\(693\) | 8.36103 | 0.317609 | ||||||||
\(694\) | −61.4934 | −2.33426 | ||||||||
\(695\) | −18.7964 | −0.712989 | ||||||||
\(696\) | 32.1779 | 1.21970 | ||||||||
\(697\) | 9.47139 | 0.358754 | ||||||||
\(698\) | 15.1631 | 0.573932 | ||||||||
\(699\) | 49.6989 | 1.87978 | ||||||||
\(700\) | −7.82818 | −0.295877 | ||||||||
\(701\) | 6.34593 | 0.239682 | 0.119841 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119841 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(702\) | −41.7402 | −1.57538 | ||||||||
\(703\) | 0.422336 | 0.0159287 | ||||||||
\(704\) | 0.805005 | 0.0303397 | ||||||||
\(705\) | −3.73687 | −0.140739 | ||||||||
\(706\) | −12.7598 | −0.480221 | ||||||||
\(707\) | −16.4862 | −0.620028 | ||||||||
\(708\) | −16.6517 | −0.625810 | ||||||||
\(709\) | 10.1001 | 0.379318 | 0.189659 | − | 0.981850i | \(-0.439262\pi\) | ||||
0.189659 | + | 0.981850i | \(0.439262\pi\) | |||||||
\(710\) | −22.5248 | −0.845341 | ||||||||
\(711\) | 44.1848 | 1.65706 | ||||||||
\(712\) | 20.6805 | 0.775033 | ||||||||
\(713\) | 24.8992 | 0.932483 | ||||||||
\(714\) | −9.04637 | −0.338552 | ||||||||
\(715\) | −6.53865 | −0.244532 | ||||||||
\(716\) | 3.46050 | 0.129325 | ||||||||
\(717\) | −4.11026 | −0.153501 | ||||||||
\(718\) | 5.37280 | 0.200511 | ||||||||
\(719\) | 22.9728 | 0.856739 | 0.428370 | − | 0.903604i | \(-0.359088\pi\) | ||||
0.428370 | + | 0.903604i | \(0.359088\pi\) | |||||||
\(720\) | 21.8541 | 0.814456 | ||||||||
\(721\) | −26.0308 | −0.969437 | ||||||||
\(722\) | 32.3026 | 1.20218 | ||||||||
\(723\) | −16.9537 | −0.630514 | ||||||||
\(724\) | −3.03566 | −0.112819 | ||||||||
\(725\) | −27.8578 | −1.03461 | ||||||||
\(726\) | −4.71518 | −0.174997 | ||||||||
\(727\) | 11.7756 | 0.436735 | 0.218367 | − | 0.975867i | \(-0.429927\pi\) | ||||
0.218367 | + | 0.975867i | \(0.429927\pi\) | |||||||
\(728\) | 21.2703 | 0.788329 | ||||||||
\(729\) | −43.4070 | −1.60767 | ||||||||
\(730\) | 2.01644 | 0.0746317 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −1.84012 | −0.0680129 | ||||||||
\(733\) | −5.16842 | −0.190900 | −0.0954500 | − | 0.995434i | \(-0.530429\pi\) | ||||
−0.0954500 | + | 0.995434i | \(0.530429\pi\) | |||||||
\(734\) | −46.2347 | −1.70655 | ||||||||
\(735\) | 9.03071 | 0.333103 | ||||||||
\(736\) | 25.1637 | 0.927545 | ||||||||
\(737\) | 12.9481 | 0.476949 | ||||||||
\(738\) | −71.7492 | −2.64112 | ||||||||
\(739\) | −41.0301 | −1.50932 | −0.754659 | − | 0.656117i | \(-0.772198\pi\) | ||||
−0.754659 | + | 0.656117i | \(0.772198\pi\) | |||||||
\(740\) | 0.670245 | 0.0246387 | ||||||||
\(741\) | −11.4177 | −0.419441 | ||||||||
\(742\) | 11.0884 | 0.407069 | ||||||||
\(743\) | 24.1532 | 0.886096 | 0.443048 | − | 0.896498i | \(-0.353897\pi\) | ||||
0.443048 | + | 0.896498i | \(0.353897\pi\) | |||||||
\(744\) | 24.1439 | 0.885159 | ||||||||
\(745\) | 13.7048 | 0.502104 | ||||||||
\(746\) | 65.3661 | 2.39322 | ||||||||
\(747\) | −69.4002 | −2.53922 | ||||||||
\(748\) | 1.02162 | 0.0373540 | ||||||||
\(749\) | 14.0936 | 0.514967 | ||||||||
\(750\) | −42.5370 | −1.55323 | ||||||||
\(751\) | −1.22172 | −0.0445811 | −0.0222906 | − | 0.999752i | \(-0.507096\pi\) | ||||
−0.0222906 | + | 0.999752i | \(0.507096\pi\) | |||||||
\(752\) | −6.86654 | −0.250397 | ||||||||
\(753\) | −38.7680 | −1.41279 | ||||||||
\(754\) | −79.0381 | −2.87840 | ||||||||
\(755\) | −5.02851 | −0.183006 | ||||||||
\(756\) | 7.21989 | 0.262585 | ||||||||
\(757\) | 30.2803 | 1.10056 | 0.550278 | − | 0.834982i | \(-0.314522\pi\) | ||||
0.550278 | + | 0.834982i | \(0.314522\pi\) | |||||||
\(758\) | −13.2530 | −0.481371 | ||||||||
\(759\) | 12.9052 | 0.468429 | ||||||||
\(760\) | 1.10150 | 0.0399555 | ||||||||
\(761\) | −54.4394 | −1.97343 | −0.986713 | − | 0.162471i | \(-0.948054\pi\) | ||||
−0.986713 | + | 0.162471i | \(0.948054\pi\) | |||||||
\(762\) | −18.4590 | −0.668700 | ||||||||
\(763\) | −25.8358 | −0.935319 | ||||||||
\(764\) | 27.2212 | 0.984830 | ||||||||
\(765\) | −4.37124 | −0.158042 | ||||||||
\(766\) | −58.6213 | −2.11807 | ||||||||
\(767\) | −39.1706 | −1.41437 | ||||||||
\(768\) | 52.1096 | 1.88034 | ||||||||
\(769\) | 2.75387 | 0.0993070 | 0.0496535 | − | 0.998767i | \(-0.484188\pi\) | ||||
0.0496535 | + | 0.998767i | \(0.484188\pi\) | |||||||
\(770\) | 3.34515 | 0.120551 | ||||||||
\(771\) | −53.3918 | −1.92286 | ||||||||
\(772\) | −4.90484 | −0.176529 | ||||||||
\(773\) | −9.54228 | −0.343212 | −0.171606 | − | 0.985166i | \(-0.554896\pi\) | ||||
−0.171606 | + | 0.985166i | \(0.554896\pi\) | |||||||
\(774\) | −7.57536 | −0.272291 | ||||||||
\(775\) | −20.9024 | −0.750837 | ||||||||
\(776\) | −4.63781 | −0.166488 | ||||||||
\(777\) | −3.40393 | −0.122115 | ||||||||
\(778\) | −42.5036 | −1.52383 | ||||||||
\(779\) | −6.11571 | −0.219118 | ||||||||
\(780\) | −18.1199 | −0.648795 | ||||||||
\(781\) | −12.9188 | −0.462270 | ||||||||
\(782\) | −8.27000 | −0.295735 | ||||||||
\(783\) | 25.6931 | 0.918195 | ||||||||
\(784\) | 16.5940 | 0.592644 | ||||||||
\(785\) | 22.6967 | 0.810079 | ||||||||
\(786\) | 39.7199 | 1.41676 | ||||||||
\(787\) | −45.7605 | −1.63119 | −0.815593 | − | 0.578625i | \(-0.803589\pi\) | ||||
−0.815593 | + | 0.578625i | \(0.803589\pi\) | |||||||
\(788\) | −7.09468 | −0.252738 | ||||||||
\(789\) | −49.1057 | −1.74821 | ||||||||
\(790\) | 17.6779 | 0.628950 | ||||||||
\(791\) | 36.9626 | 1.31424 | ||||||||
\(792\) | 7.41161 | 0.263360 | ||||||||
\(793\) | −4.32861 | −0.153713 | ||||||||
\(794\) | −0.703338 | −0.0249605 | ||||||||
\(795\) | 9.04636 | 0.320842 | ||||||||
\(796\) | −15.4022 | −0.545916 | ||||||||
\(797\) | 37.3345 | 1.32246 | 0.661229 | − | 0.750184i | \(-0.270035\pi\) | ||||
0.661229 | + | 0.750184i | \(0.270035\pi\) | |||||||
\(798\) | 5.84127 | 0.206779 | ||||||||
\(799\) | 1.37344 | 0.0485887 | ||||||||
\(800\) | −21.1244 | −0.746861 | ||||||||
\(801\) | 52.9925 | 1.87240 | ||||||||
\(802\) | −41.0002 | −1.44777 | ||||||||
\(803\) | 1.15650 | 0.0408119 | ||||||||
\(804\) | 35.8816 | 1.26545 | ||||||||
\(805\) | −9.15552 | −0.322690 | ||||||||
\(806\) | −59.3044 | −2.08891 | ||||||||
\(807\) | 3.99997 | 0.140805 | ||||||||
\(808\) | −14.6142 | −0.514124 | ||||||||
\(809\) | 0.383409 | 0.0134799 | 0.00673996 | − | 0.999977i | \(-0.497855\pi\) | ||||
0.00673996 | + | 0.999977i | \(0.497855\pi\) | |||||||
\(810\) | −5.37377 | −0.188815 | ||||||||
\(811\) | 6.83317 | 0.239945 | 0.119973 | − | 0.992777i | \(-0.461719\pi\) | ||||
0.119973 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(812\) | 13.6714 | 0.479772 | ||||||||
\(813\) | −24.3420 | −0.853711 | ||||||||
\(814\) | 1.13696 | 0.0398504 | ||||||||
\(815\) | 17.3337 | 0.607171 | ||||||||
\(816\) | −13.5615 | −0.474748 | ||||||||
\(817\) | −0.645703 | −0.0225903 | ||||||||
\(818\) | −32.6679 | −1.14221 | ||||||||
\(819\) | 54.5039 | 1.90452 | ||||||||
\(820\) | −9.70559 | −0.338934 | ||||||||
\(821\) | −38.7817 | −1.35349 | −0.676746 | − | 0.736217i | \(-0.736610\pi\) | ||||
−0.676746 | + | 0.736217i | \(0.736610\pi\) | |||||||
\(822\) | −79.0597 | −2.75752 | ||||||||
\(823\) | 7.00732 | 0.244260 | 0.122130 | − | 0.992514i | \(-0.461028\pi\) | ||||
0.122130 | + | 0.992514i | \(0.461028\pi\) | |||||||
\(824\) | −23.0749 | −0.803853 | ||||||||
\(825\) | −10.8337 | −0.377180 | ||||||||
\(826\) | 20.0396 | 0.697265 | ||||||||
\(827\) | 13.5718 | 0.471937 | 0.235968 | − | 0.971761i | \(-0.424174\pi\) | ||||
0.235968 | + | 0.971761i | \(0.424174\pi\) | |||||||
\(828\) | 21.1815 | 0.736109 | ||||||||
\(829\) | −38.3815 | −1.33304 | −0.666521 | − | 0.745486i | \(-0.732218\pi\) | ||||
−0.666521 | + | 0.745486i | \(0.732218\pi\) | |||||||
\(830\) | −27.7663 | −0.963781 | ||||||||
\(831\) | 40.6710 | 1.41086 | ||||||||
\(832\) | 5.24766 | 0.181930 | ||||||||
\(833\) | −3.31912 | −0.115001 | ||||||||
\(834\) | −88.3595 | −3.05964 | ||||||||
\(835\) | 13.2330 | 0.457946 | ||||||||
\(836\) | −0.659660 | −0.0228148 | ||||||||
\(837\) | 19.2782 | 0.666352 | ||||||||
\(838\) | 8.49084 | 0.293311 | ||||||||
\(839\) | −8.30321 | −0.286659 | −0.143329 | − | 0.989675i | \(-0.545781\pi\) | ||||
−0.143329 | + | 0.989675i | \(0.545781\pi\) | |||||||
\(840\) | −8.87779 | −0.306313 | ||||||||
\(841\) | 19.6517 | 0.677646 | ||||||||
\(842\) | 28.5623 | 0.984322 | ||||||||
\(843\) | 56.9611 | 1.96185 | ||||||||
\(844\) | −20.9611 | −0.721511 | ||||||||
\(845\) | −29.5846 | −1.01774 | ||||||||
\(846\) | −10.4043 | −0.357706 | ||||||||
\(847\) | 1.91856 | 0.0659226 | ||||||||
\(848\) | 16.6228 | 0.570829 | ||||||||
\(849\) | 34.3502 | 1.17890 | ||||||||
\(850\) | 6.94251 | 0.238126 | ||||||||
\(851\) | −3.11180 | −0.106671 | ||||||||
\(852\) | −35.8004 | −1.22650 | ||||||||
\(853\) | −19.3929 | −0.663999 | −0.331999 | − | 0.943280i | \(-0.607723\pi\) | ||||
−0.331999 | + | 0.943280i | \(0.607723\pi\) | |||||||
\(854\) | 2.21450 | 0.0757787 | ||||||||
\(855\) | 2.82252 | 0.0965282 | ||||||||
\(856\) | 12.4932 | 0.427009 | ||||||||
\(857\) | 39.6359 | 1.35394 | 0.676969 | − | 0.736012i | \(-0.263293\pi\) | ||||
0.676969 | + | 0.736012i | \(0.263293\pi\) | |||||||
\(858\) | −30.7373 | −1.04936 | ||||||||
\(859\) | 31.1168 | 1.06169 | 0.530846 | − | 0.847468i | \(-0.321874\pi\) | ||||
0.530846 | + | 0.847468i | \(0.321874\pi\) | |||||||
\(860\) | −1.02473 | −0.0349429 | ||||||||
\(861\) | 49.2911 | 1.67984 | ||||||||
\(862\) | −65.7772 | −2.24038 | ||||||||
\(863\) | −17.1350 | −0.583282 | −0.291641 | − | 0.956528i | \(-0.594201\pi\) | ||||
−0.291641 | + | 0.956528i | \(0.594201\pi\) | |||||||
\(864\) | 19.4829 | 0.662823 | ||||||||
\(865\) | 2.00702 | 0.0682407 | ||||||||
\(866\) | 28.3854 | 0.964576 | ||||||||
\(867\) | 2.71256 | 0.0921233 | ||||||||
\(868\) | 10.2580 | 0.348180 | ||||||||
\(869\) | 10.1389 | 0.343938 | ||||||||
\(870\) | 32.9889 | 1.11843 | ||||||||
\(871\) | 84.4060 | 2.85999 | ||||||||
\(872\) | −22.9021 | −0.775563 | ||||||||
\(873\) | −11.8841 | −0.402217 | ||||||||
\(874\) | 5.33997 | 0.180627 | ||||||||
\(875\) | 17.3079 | 0.585114 | ||||||||
\(876\) | 3.20487 | 0.108283 | ||||||||
\(877\) | 39.4066 | 1.33067 | 0.665333 | − | 0.746546i | \(-0.268289\pi\) | ||||
0.665333 | + | 0.746546i | \(0.268289\pi\) | |||||||
\(878\) | 23.9473 | 0.808183 | ||||||||
\(879\) | −45.6797 | −1.54074 | ||||||||
\(880\) | 5.01476 | 0.169047 | ||||||||
\(881\) | −29.4027 | −0.990602 | −0.495301 | − | 0.868721i | \(-0.664942\pi\) | ||||
−0.495301 | + | 0.868721i | \(0.664942\pi\) | |||||||
\(882\) | 25.1435 | 0.846626 | ||||||||
\(883\) | 34.3859 | 1.15718 | 0.578588 | − | 0.815620i | \(-0.303604\pi\) | ||||
0.578588 | + | 0.815620i | \(0.303604\pi\) | |||||||
\(884\) | 6.65971 | 0.223990 | ||||||||
\(885\) | 16.3490 | 0.549567 | ||||||||
\(886\) | −13.1170 | −0.440675 | ||||||||
\(887\) | −12.2822 | −0.412398 | −0.206199 | − | 0.978510i | \(-0.566109\pi\) | ||||
−0.206199 | + | 0.978510i | \(0.566109\pi\) | |||||||
\(888\) | −3.01740 | −0.101257 | ||||||||
\(889\) | 7.51080 | 0.251904 | ||||||||
\(890\) | 21.2017 | 0.710684 | ||||||||
\(891\) | −3.08204 | −0.103252 | ||||||||
\(892\) | 17.0505 | 0.570894 | ||||||||
\(893\) | −0.886832 | −0.0296767 | ||||||||
\(894\) | 64.4243 | 2.15467 | ||||||||
\(895\) | −3.39760 | −0.113569 | ||||||||
\(896\) | −22.9799 | −0.767705 | ||||||||
\(897\) | 84.1265 | 2.80890 | ||||||||
\(898\) | −17.5129 | −0.584412 | ||||||||
\(899\) | 36.5047 | 1.21750 | ||||||||
\(900\) | −17.7815 | −0.592716 | ||||||||
\(901\) | −3.32487 | −0.110767 | ||||||||
\(902\) | −16.4639 | −0.548189 | ||||||||
\(903\) | 5.20421 | 0.173185 | ||||||||
\(904\) | 32.7654 | 1.08976 | ||||||||
\(905\) | 2.98048 | 0.0990745 | ||||||||
\(906\) | −23.6383 | −0.785331 | ||||||||
\(907\) | −30.4473 | −1.01099 | −0.505494 | − | 0.862830i | \(-0.668690\pi\) | ||||
−0.505494 | + | 0.862830i | \(0.668690\pi\) | |||||||
\(908\) | −6.07349 | −0.201556 | ||||||||
\(909\) | −37.4480 | −1.24207 | ||||||||
\(910\) | 21.8064 | 0.722875 | ||||||||
\(911\) | −20.4981 | −0.679133 | −0.339566 | − | 0.940582i | \(-0.610280\pi\) | ||||
−0.339566 | + | 0.940582i | \(0.610280\pi\) | |||||||
\(912\) | 8.75672 | 0.289964 | ||||||||
\(913\) | −15.9249 | −0.527038 | ||||||||
\(914\) | −25.8013 | −0.853431 | ||||||||
\(915\) | 1.80667 | 0.0597268 | ||||||||
\(916\) | −26.0890 | −0.862006 | ||||||||
\(917\) | −16.1617 | −0.533705 | ||||||||
\(918\) | −6.40304 | −0.211332 | ||||||||
\(919\) | 46.1231 | 1.52146 | 0.760730 | − | 0.649068i | \(-0.224841\pi\) | ||||
0.760730 | + | 0.649068i | \(0.224841\pi\) | |||||||
\(920\) | −8.11589 | −0.267573 | ||||||||
\(921\) | −30.4928 | −1.00477 | ||||||||
\(922\) | −5.21871 | −0.171869 | ||||||||
\(923\) | −84.2149 | −2.77197 | ||||||||
\(924\) | 5.31670 | 0.174907 | ||||||||
\(925\) | 2.61230 | 0.0858918 | ||||||||
\(926\) | 12.2378 | 0.402158 | ||||||||
\(927\) | −59.1282 | −1.94203 | ||||||||
\(928\) | 36.8924 | 1.21105 | ||||||||
\(929\) | 17.3747 | 0.570046 | 0.285023 | − | 0.958521i | \(-0.407999\pi\) | ||||
0.285023 | + | 0.958521i | \(0.407999\pi\) | |||||||
\(930\) | 24.7525 | 0.811666 | ||||||||
\(931\) | 2.14316 | 0.0702394 | ||||||||
\(932\) | 18.7178 | 0.613122 | ||||||||
\(933\) | 15.1268 | 0.495230 | ||||||||
\(934\) | 57.0737 | 1.86751 | ||||||||
\(935\) | −1.00305 | −0.0328031 | ||||||||
\(936\) | 48.3148 | 1.57922 | ||||||||
\(937\) | 10.2370 | 0.334427 | 0.167213 | − | 0.985921i | \(-0.446523\pi\) | ||||
0.167213 | + | 0.985921i | \(0.446523\pi\) | |||||||
\(938\) | −43.1819 | −1.40994 | ||||||||
\(939\) | −75.7601 | −2.47234 | ||||||||
\(940\) | −1.40740 | −0.0459042 | ||||||||
\(941\) | 34.1405 | 1.11295 | 0.556475 | − | 0.830865i | \(-0.312154\pi\) | ||||
0.556475 | + | 0.830865i | \(0.312154\pi\) | |||||||
\(942\) | 106.694 | 3.47628 | ||||||||
\(943\) | 45.0609 | 1.46738 | ||||||||
\(944\) | 30.0415 | 0.977768 | ||||||||
\(945\) | −7.08865 | −0.230594 | ||||||||
\(946\) | −1.73828 | −0.0565163 | ||||||||
\(947\) | −6.07427 | −0.197387 | −0.0986936 | − | 0.995118i | \(-0.531466\pi\) | ||||
−0.0986936 | + | 0.995118i | \(0.531466\pi\) | |||||||
\(948\) | 28.0967 | 0.912539 | ||||||||
\(949\) | 7.53897 | 0.244725 | ||||||||
\(950\) | −4.48280 | −0.145441 | ||||||||
\(951\) | 92.9397 | 3.01378 | ||||||||
\(952\) | 3.26291 | 0.105752 | ||||||||
\(953\) | −37.4663 | −1.21365 | −0.606825 | − | 0.794835i | \(-0.707557\pi\) | ||||
−0.606825 | + | 0.794835i | \(0.707557\pi\) | |||||||
\(954\) | 25.1871 | 0.815462 | ||||||||
\(955\) | −26.7264 | −0.864847 | ||||||||
\(956\) | −1.54803 | −0.0500668 | ||||||||
\(957\) | 18.9203 | 0.611606 | ||||||||
\(958\) | 59.3444 | 1.91733 | ||||||||
\(959\) | 32.1686 | 1.03878 | ||||||||
\(960\) | −2.19027 | −0.0706907 | ||||||||
\(961\) | −3.60954 | −0.116437 | ||||||||
\(962\) | 7.41161 | 0.238960 | ||||||||
\(963\) | 32.0131 | 1.03161 | ||||||||
\(964\) | −6.38517 | −0.205652 | ||||||||
\(965\) | 4.81568 | 0.155022 | ||||||||
\(966\) | −43.0388 | −1.38475 | ||||||||
\(967\) | −24.4207 | −0.785317 | −0.392659 | − | 0.919684i | \(-0.628445\pi\) | ||||
−0.392659 | + | 0.919684i | \(0.628445\pi\) | |||||||
\(968\) | 1.70071 | 0.0546628 | ||||||||
\(969\) | −1.75151 | −0.0562665 | ||||||||
\(970\) | −4.75471 | −0.152665 | ||||||||
\(971\) | −49.7852 | −1.59768 | −0.798841 | − | 0.601542i | \(-0.794553\pi\) | ||||
−0.798841 | + | 0.601542i | \(0.794553\pi\) | |||||||
\(972\) | −19.8305 | −0.636062 | ||||||||
\(973\) | 35.9526 | 1.15259 | ||||||||
\(974\) | −48.9077 | −1.56710 | ||||||||
\(975\) | −70.6226 | −2.26173 | ||||||||
\(976\) | 3.31978 | 0.106264 | ||||||||
\(977\) | 23.9893 | 0.767485 | 0.383743 | − | 0.923440i | \(-0.374635\pi\) | ||||
0.383743 | + | 0.923440i | \(0.374635\pi\) | |||||||
\(978\) | 81.4832 | 2.60554 | ||||||||
\(979\) | 12.1599 | 0.388633 | ||||||||
\(980\) | 3.40119 | 0.108647 | ||||||||
\(981\) | −58.6854 | −1.87368 | ||||||||
\(982\) | 53.2213 | 1.69836 | ||||||||
\(983\) | −48.8932 | −1.55945 | −0.779726 | − | 0.626121i | \(-0.784642\pi\) | ||||
−0.779726 | + | 0.626121i | \(0.784642\pi\) | |||||||
\(984\) | 43.6940 | 1.39291 | ||||||||
\(985\) | 6.96572 | 0.221946 | ||||||||
\(986\) | −12.1246 | −0.386127 | ||||||||
\(987\) | 7.14765 | 0.227512 | ||||||||
\(988\) | −4.30020 | −0.136807 | ||||||||
\(989\) | 4.75758 | 0.151282 | ||||||||
\(990\) | 7.59843 | 0.241494 | ||||||||
\(991\) | 18.6807 | 0.593412 | 0.296706 | − | 0.954969i | \(-0.404112\pi\) | ||||
0.296706 | + | 0.954969i | \(0.404112\pi\) | |||||||
\(992\) | 27.6814 | 0.878884 | ||||||||
\(993\) | 9.32342 | 0.295870 | ||||||||
\(994\) | 43.0841 | 1.36654 | ||||||||
\(995\) | 15.1222 | 0.479407 | ||||||||
\(996\) | −44.1310 | −1.39834 | ||||||||
\(997\) | −18.5437 | −0.587286 | −0.293643 | − | 0.955915i | \(-0.594868\pi\) | ||||
−0.293643 | + | 0.955915i | \(0.594868\pi\) | |||||||
\(998\) | 17.7455 | 0.561723 | ||||||||
\(999\) | −2.40931 | −0.0762271 |
(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 | 8041.2.a.j.1.17 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.17 | ✓ | 82 | 1.1 | even | 1 | trivial |