Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.327392 | −0.231501 | −0.115751 | − | 0.993278i | \(-0.536927\pi\) | ||||
−0.115751 | + | 0.993278i | \(0.536927\pi\) | |||||||
\(3\) | −2.36457 | −1.36518 | −0.682592 | − | 0.730799i | \(-0.739148\pi\) | ||||
−0.682592 | + | 0.730799i | \(0.739148\pi\) | |||||||
\(4\) | −1.89281 | −0.946407 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.774141 | 0.316042 | ||||||||
\(7\) | 2.46288 | 0.930881 | 0.465440 | − | 0.885079i | \(-0.345896\pi\) | ||||
0.465440 | + | 0.885079i | \(0.345896\pi\) | |||||||
\(8\) | 1.27448 | 0.450595 | ||||||||
\(9\) | 2.59119 | 0.863729 | ||||||||
\(10\) | −0.327392 | −0.103530 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 4.47569 | 1.29202 | ||||||||
\(13\) | −0.641298 | −0.177864 | −0.0889321 | − | 0.996038i | \(-0.528345\pi\) | ||||
−0.0889321 | + | 0.996038i | \(0.528345\pi\) | |||||||
\(14\) | −0.806327 | −0.215500 | ||||||||
\(15\) | −2.36457 | −0.610529 | ||||||||
\(16\) | 3.36838 | 0.842094 | ||||||||
\(17\) | −6.07665 | −1.47380 | −0.736902 | − | 0.675999i | \(-0.763712\pi\) | ||||
−0.736902 | + | 0.675999i | \(0.763712\pi\) | |||||||
\(18\) | −0.848334 | −0.199954 | ||||||||
\(19\) | 8.35139 | 1.91594 | 0.957970 | − | 0.286869i | \(-0.0926144\pi\) | ||||
0.957970 | + | 0.286869i | \(0.0926144\pi\) | |||||||
\(20\) | −1.89281 | −0.423246 | ||||||||
\(21\) | −5.82365 | −1.27082 | ||||||||
\(22\) | −0.327392 | −0.0698002 | ||||||||
\(23\) | 2.42427 | 0.505495 | 0.252748 | − | 0.967532i | \(-0.418666\pi\) | ||||
0.252748 | + | 0.967532i | \(0.418666\pi\) | |||||||
\(24\) | −3.01359 | −0.615146 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.209956 | 0.0411757 | ||||||||
\(27\) | 0.966665 | 0.186035 | ||||||||
\(28\) | −4.66177 | −0.880992 | ||||||||
\(29\) | 5.36357 | 0.995991 | 0.497995 | − | 0.867180i | \(-0.334070\pi\) | ||||
0.497995 | + | 0.867180i | \(0.334070\pi\) | |||||||
\(30\) | 0.774141 | 0.141338 | ||||||||
\(31\) | 7.23441 | 1.29934 | 0.649669 | − | 0.760217i | \(-0.274907\pi\) | ||||
0.649669 | + | 0.760217i | \(0.274907\pi\) | |||||||
\(32\) | −3.65173 | −0.645541 | ||||||||
\(33\) | −2.36457 | −0.411619 | ||||||||
\(34\) | 1.98945 | 0.341187 | ||||||||
\(35\) | 2.46288 | 0.416302 | ||||||||
\(36\) | −4.90464 | −0.817440 | ||||||||
\(37\) | −5.09224 | −0.837159 | −0.418579 | − | 0.908180i | \(-0.637472\pi\) | ||||
−0.418579 | + | 0.908180i | \(0.637472\pi\) | |||||||
\(38\) | −2.73418 | −0.443542 | ||||||||
\(39\) | 1.51639 | 0.242817 | ||||||||
\(40\) | 1.27448 | 0.201512 | ||||||||
\(41\) | −0.993086 | −0.155094 | −0.0775470 | − | 0.996989i | \(-0.524709\pi\) | ||||
−0.0775470 | + | 0.996989i | \(0.524709\pi\) | |||||||
\(42\) | 1.90662 | 0.294197 | ||||||||
\(43\) | 5.57472 | 0.850136 | 0.425068 | − | 0.905161i | \(-0.360250\pi\) | ||||
0.425068 | + | 0.905161i | \(0.360250\pi\) | |||||||
\(44\) | −1.89281 | −0.285353 | ||||||||
\(45\) | 2.59119 | 0.386271 | ||||||||
\(46\) | −0.793687 | −0.117023 | ||||||||
\(47\) | 3.08560 | 0.450081 | 0.225040 | − | 0.974349i | \(-0.427749\pi\) | ||||
0.225040 | + | 0.974349i | \(0.427749\pi\) | |||||||
\(48\) | −7.96476 | −1.14961 | ||||||||
\(49\) | −0.934228 | −0.133461 | ||||||||
\(50\) | −0.327392 | −0.0463002 | ||||||||
\(51\) | 14.3687 | 2.01202 | ||||||||
\(52\) | 1.21386 | 0.168332 | ||||||||
\(53\) | 3.89942 | 0.535626 | 0.267813 | − | 0.963471i | \(-0.413699\pi\) | ||||
0.267813 | + | 0.963471i | \(0.413699\pi\) | |||||||
\(54\) | −0.316478 | −0.0430672 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 3.13888 | 0.419451 | ||||||||
\(57\) | −19.7474 | −2.61561 | ||||||||
\(58\) | −1.75599 | −0.230573 | ||||||||
\(59\) | −0.200959 | −0.0261627 | −0.0130813 | − | 0.999914i | \(-0.504164\pi\) | ||||
−0.0130813 | + | 0.999914i | \(0.504164\pi\) | |||||||
\(60\) | 4.47569 | 0.577809 | ||||||||
\(61\) | −10.9562 | −1.40280 | −0.701400 | − | 0.712768i | \(-0.747441\pi\) | ||||
−0.701400 | + | 0.712768i | \(0.747441\pi\) | |||||||
\(62\) | −2.36849 | −0.300798 | ||||||||
\(63\) | 6.38178 | 0.804029 | ||||||||
\(64\) | −5.54120 | −0.692651 | ||||||||
\(65\) | −0.641298 | −0.0795432 | ||||||||
\(66\) | 0.774141 | 0.0952902 | ||||||||
\(67\) | −10.6466 | −1.30069 | −0.650347 | − | 0.759637i | \(-0.725376\pi\) | ||||
−0.650347 | + | 0.759637i | \(0.725376\pi\) | |||||||
\(68\) | 11.5020 | 1.39482 | ||||||||
\(69\) | −5.73236 | −0.690095 | ||||||||
\(70\) | −0.806327 | −0.0963745 | ||||||||
\(71\) | −0.323595 | −0.0384037 | −0.0192018 | − | 0.999816i | \(-0.506113\pi\) | ||||
−0.0192018 | + | 0.999816i | \(0.506113\pi\) | |||||||
\(72\) | 3.30241 | 0.389192 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 1.66716 | 0.193803 | ||||||||
\(75\) | −2.36457 | −0.273037 | ||||||||
\(76\) | −15.8076 | −1.81326 | ||||||||
\(77\) | 2.46288 | 0.280671 | ||||||||
\(78\) | −0.496455 | −0.0562125 | ||||||||
\(79\) | −10.7550 | −1.21003 | −0.605014 | − | 0.796215i | \(-0.706832\pi\) | ||||
−0.605014 | + | 0.796215i | \(0.706832\pi\) | |||||||
\(80\) | 3.36838 | 0.376596 | ||||||||
\(81\) | −10.0593 | −1.11770 | ||||||||
\(82\) | 0.325128 | 0.0359044 | ||||||||
\(83\) | 13.1546 | 1.44391 | 0.721954 | − | 0.691941i | \(-0.243244\pi\) | ||||
0.721954 | + | 0.691941i | \(0.243244\pi\) | |||||||
\(84\) | 11.0231 | 1.20272 | ||||||||
\(85\) | −6.07665 | −0.659106 | ||||||||
\(86\) | −1.82512 | −0.196807 | ||||||||
\(87\) | −12.6825 | −1.35971 | ||||||||
\(88\) | 1.27448 | 0.135860 | ||||||||
\(89\) | 8.38454 | 0.888760 | 0.444380 | − | 0.895838i | \(-0.353424\pi\) | ||||
0.444380 | + | 0.895838i | \(0.353424\pi\) | |||||||
\(90\) | −0.848334 | −0.0894223 | ||||||||
\(91\) | −1.57944 | −0.165570 | ||||||||
\(92\) | −4.58869 | −0.478405 | ||||||||
\(93\) | −17.1063 | −1.77384 | ||||||||
\(94\) | −1.01020 | −0.104194 | ||||||||
\(95\) | 8.35139 | 0.856834 | ||||||||
\(96\) | 8.63477 | 0.881283 | ||||||||
\(97\) | −1.74254 | −0.176928 | −0.0884638 | − | 0.996079i | \(-0.528196\pi\) | ||||
−0.0884638 | + | 0.996079i | \(0.528196\pi\) | |||||||
\(98\) | 0.305859 | 0.0308964 | ||||||||
\(99\) | 2.59119 | 0.260424 | ||||||||
\(100\) | −1.89281 | −0.189281 | ||||||||
\(101\) | −3.45766 | −0.344050 | −0.172025 | − | 0.985093i | \(-0.555031\pi\) | ||||
−0.172025 | + | 0.985093i | \(0.555031\pi\) | |||||||
\(102\) | −4.70419 | −0.465784 | ||||||||
\(103\) | −15.8333 | −1.56010 | −0.780051 | − | 0.625716i | \(-0.784807\pi\) | ||||
−0.780051 | + | 0.625716i | \(0.784807\pi\) | |||||||
\(104\) | −0.817319 | −0.0801447 | ||||||||
\(105\) | −5.82365 | −0.568330 | ||||||||
\(106\) | −1.27664 | −0.123998 | ||||||||
\(107\) | −6.58676 | −0.636767 | −0.318383 | − | 0.947962i | \(-0.603140\pi\) | ||||
−0.318383 | + | 0.947962i | \(0.603140\pi\) | |||||||
\(108\) | −1.82972 | −0.176065 | ||||||||
\(109\) | 11.4360 | 1.09537 | 0.547687 | − | 0.836683i | \(-0.315509\pi\) | ||||
0.547687 | + | 0.836683i | \(0.315509\pi\) | |||||||
\(110\) | −0.327392 | −0.0312156 | ||||||||
\(111\) | 12.0409 | 1.14288 | ||||||||
\(112\) | 8.29590 | 0.783889 | ||||||||
\(113\) | 2.18592 | 0.205634 | 0.102817 | − | 0.994700i | \(-0.467214\pi\) | ||||
0.102817 | + | 0.994700i | \(0.467214\pi\) | |||||||
\(114\) | 6.46515 | 0.605517 | ||||||||
\(115\) | 2.42427 | 0.226064 | ||||||||
\(116\) | −10.1522 | −0.942613 | ||||||||
\(117\) | −1.66172 | −0.153626 | ||||||||
\(118\) | 0.0657924 | 0.00605669 | ||||||||
\(119\) | −14.9661 | −1.37194 | ||||||||
\(120\) | −3.01359 | −0.275102 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.58698 | 0.324750 | ||||||||
\(123\) | 2.34822 | 0.211732 | ||||||||
\(124\) | −13.6934 | −1.22970 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.08934 | −0.186134 | ||||||||
\(127\) | 2.14448 | 0.190292 | 0.0951459 | − | 0.995463i | \(-0.469668\pi\) | ||||
0.0951459 | + | 0.995463i | \(0.469668\pi\) | |||||||
\(128\) | 9.11761 | 0.805890 | ||||||||
\(129\) | −13.1818 | −1.16059 | ||||||||
\(130\) | 0.209956 | 0.0184143 | ||||||||
\(131\) | 13.2584 | 1.15839 | 0.579195 | − | 0.815189i | \(-0.303367\pi\) | ||||
0.579195 | + | 0.815189i | \(0.303367\pi\) | |||||||
\(132\) | 4.47569 | 0.389559 | ||||||||
\(133\) | 20.5685 | 1.78351 | ||||||||
\(134\) | 3.48562 | 0.301112 | ||||||||
\(135\) | 0.966665 | 0.0831973 | ||||||||
\(136\) | −7.74455 | −0.664090 | ||||||||
\(137\) | 4.52897 | 0.386936 | 0.193468 | − | 0.981107i | \(-0.438026\pi\) | ||||
0.193468 | + | 0.981107i | \(0.438026\pi\) | |||||||
\(138\) | 1.87673 | 0.159758 | ||||||||
\(139\) | −18.8654 | −1.60015 | −0.800073 | − | 0.599903i | \(-0.795206\pi\) | ||||
−0.800073 | + | 0.599903i | \(0.795206\pi\) | |||||||
\(140\) | −4.66177 | −0.393992 | ||||||||
\(141\) | −7.29611 | −0.614443 | ||||||||
\(142\) | 0.105942 | 0.00889049 | ||||||||
\(143\) | −0.641298 | −0.0536280 | ||||||||
\(144\) | 8.72809 | 0.727341 | ||||||||
\(145\) | 5.36357 | 0.445420 | ||||||||
\(146\) | −0.327392 | −0.0270952 | ||||||||
\(147\) | 2.20905 | 0.182199 | ||||||||
\(148\) | 9.63866 | 0.792293 | ||||||||
\(149\) | 12.7596 | 1.04531 | 0.522653 | − | 0.852545i | \(-0.324942\pi\) | ||||
0.522653 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(150\) | 0.774141 | 0.0632083 | ||||||||
\(151\) | 14.4526 | 1.17613 | 0.588066 | − | 0.808813i | \(-0.299889\pi\) | ||||
0.588066 | + | 0.808813i | \(0.299889\pi\) | |||||||
\(152\) | 10.6436 | 0.863314 | ||||||||
\(153\) | −15.7457 | −1.27297 | ||||||||
\(154\) | −0.806327 | −0.0649757 | ||||||||
\(155\) | 7.23441 | 0.581082 | ||||||||
\(156\) | −2.87025 | −0.229804 | ||||||||
\(157\) | 1.71958 | 0.137237 | 0.0686187 | − | 0.997643i | \(-0.478141\pi\) | ||||
0.0686187 | + | 0.997643i | \(0.478141\pi\) | |||||||
\(158\) | 3.52109 | 0.280123 | ||||||||
\(159\) | −9.22044 | −0.731228 | ||||||||
\(160\) | −3.65173 | −0.288695 | ||||||||
\(161\) | 5.97068 | 0.470556 | ||||||||
\(162\) | 3.29334 | 0.258749 | ||||||||
\(163\) | 10.3229 | 0.808549 | 0.404275 | − | 0.914638i | \(-0.367524\pi\) | ||||
0.404275 | + | 0.914638i | \(0.367524\pi\) | |||||||
\(164\) | 1.87973 | 0.146782 | ||||||||
\(165\) | −2.36457 | −0.184081 | ||||||||
\(166\) | −4.30672 | −0.334266 | ||||||||
\(167\) | −19.0750 | −1.47607 | −0.738033 | − | 0.674765i | \(-0.764245\pi\) | ||||
−0.738033 | + | 0.674765i | \(0.764245\pi\) | |||||||
\(168\) | −7.42210 | −0.572627 | ||||||||
\(169\) | −12.5887 | −0.968364 | ||||||||
\(170\) | 1.98945 | 0.152584 | ||||||||
\(171\) | 21.6400 | 1.65485 | ||||||||
\(172\) | −10.5519 | −0.804575 | ||||||||
\(173\) | 4.87923 | 0.370961 | 0.185480 | − | 0.982648i | \(-0.440616\pi\) | ||||
0.185480 | + | 0.982648i | \(0.440616\pi\) | |||||||
\(174\) | 4.15216 | 0.314775 | ||||||||
\(175\) | 2.46288 | 0.186176 | ||||||||
\(176\) | 3.36838 | 0.253901 | ||||||||
\(177\) | 0.475182 | 0.0357169 | ||||||||
\(178\) | −2.74503 | −0.205749 | ||||||||
\(179\) | 7.09888 | 0.530595 | 0.265298 | − | 0.964167i | \(-0.414530\pi\) | ||||
0.265298 | + | 0.964167i | \(0.414530\pi\) | |||||||
\(180\) | −4.90464 | −0.365570 | ||||||||
\(181\) | 4.60092 | 0.341984 | 0.170992 | − | 0.985272i | \(-0.445303\pi\) | ||||
0.170992 | + | 0.985272i | \(0.445303\pi\) | |||||||
\(182\) | 0.517096 | 0.0383297 | ||||||||
\(183\) | 25.9067 | 1.91508 | ||||||||
\(184\) | 3.08968 | 0.227774 | ||||||||
\(185\) | −5.09224 | −0.374389 | ||||||||
\(186\) | 5.60045 | 0.410645 | ||||||||
\(187\) | −6.07665 | −0.444369 | ||||||||
\(188\) | −5.84047 | −0.425960 | ||||||||
\(189\) | 2.38078 | 0.173176 | ||||||||
\(190\) | −2.73418 | −0.198358 | ||||||||
\(191\) | −7.01107 | −0.507303 | −0.253652 | − | 0.967296i | \(-0.581632\pi\) | ||||
−0.253652 | + | 0.967296i | \(0.581632\pi\) | |||||||
\(192\) | 13.1026 | 0.945596 | ||||||||
\(193\) | 10.9203 | 0.786061 | 0.393030 | − | 0.919525i | \(-0.371427\pi\) | ||||
0.393030 | + | 0.919525i | \(0.371427\pi\) | |||||||
\(194\) | 0.570492 | 0.0409589 | ||||||||
\(195\) | 1.51639 | 0.108591 | ||||||||
\(196\) | 1.76832 | 0.126309 | ||||||||
\(197\) | −5.70336 | −0.406348 | −0.203174 | − | 0.979143i | \(-0.565126\pi\) | ||||
−0.203174 | + | 0.979143i | \(0.565126\pi\) | |||||||
\(198\) | −0.848334 | −0.0602885 | ||||||||
\(199\) | 17.4143 | 1.23447 | 0.617233 | − | 0.786780i | \(-0.288253\pi\) | ||||
0.617233 | + | 0.786780i | \(0.288253\pi\) | |||||||
\(200\) | 1.27448 | 0.0901191 | ||||||||
\(201\) | 25.1747 | 1.77569 | ||||||||
\(202\) | 1.13201 | 0.0796480 | ||||||||
\(203\) | 13.2098 | 0.927148 | ||||||||
\(204\) | −27.1972 | −1.90419 | ||||||||
\(205\) | −0.993086 | −0.0693601 | ||||||||
\(206\) | 5.18369 | 0.361165 | ||||||||
\(207\) | 6.28174 | 0.436611 | ||||||||
\(208\) | −2.16013 | −0.149778 | ||||||||
\(209\) | 8.35139 | 0.577678 | ||||||||
\(210\) | 1.90662 | 0.131569 | ||||||||
\(211\) | 26.0862 | 1.79585 | 0.897924 | − | 0.440151i | \(-0.145075\pi\) | ||||
0.897924 | + | 0.440151i | \(0.145075\pi\) | |||||||
\(212\) | −7.38087 | −0.506920 | ||||||||
\(213\) | 0.765163 | 0.0524281 | ||||||||
\(214\) | 2.15645 | 0.147412 | ||||||||
\(215\) | 5.57472 | 0.380192 | ||||||||
\(216\) | 1.23199 | 0.0838264 | ||||||||
\(217\) | 17.8175 | 1.20953 | ||||||||
\(218\) | −3.74407 | −0.253580 | ||||||||
\(219\) | −2.36457 | −0.159783 | ||||||||
\(220\) | −1.89281 | −0.127614 | ||||||||
\(221\) | 3.89695 | 0.262137 | ||||||||
\(222\) | −3.94211 | −0.264577 | ||||||||
\(223\) | −15.1221 | −1.01265 | −0.506326 | − | 0.862342i | \(-0.668997\pi\) | ||||
−0.506326 | + | 0.862342i | \(0.668997\pi\) | |||||||
\(224\) | −8.99377 | −0.600922 | ||||||||
\(225\) | 2.59119 | 0.172746 | ||||||||
\(226\) | −0.715652 | −0.0476045 | ||||||||
\(227\) | −15.3772 | −1.02062 | −0.510309 | − | 0.859991i | \(-0.670469\pi\) | ||||
−0.510309 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(228\) | 37.3782 | 2.47543 | ||||||||
\(229\) | 28.8247 | 1.90479 | 0.952394 | − | 0.304871i | \(-0.0986134\pi\) | ||||
0.952394 | + | 0.304871i | \(0.0986134\pi\) | |||||||
\(230\) | −0.793687 | −0.0523342 | ||||||||
\(231\) | −5.82365 | −0.383168 | ||||||||
\(232\) | 6.83575 | 0.448789 | ||||||||
\(233\) | 21.3999 | 1.40195 | 0.700977 | − | 0.713183i | \(-0.252747\pi\) | ||||
0.700977 | + | 0.713183i | \(0.252747\pi\) | |||||||
\(234\) | 0.544035 | 0.0355647 | ||||||||
\(235\) | 3.08560 | 0.201282 | ||||||||
\(236\) | 0.380379 | 0.0247605 | ||||||||
\(237\) | 25.4308 | 1.65191 | ||||||||
\(238\) | 4.89977 | 0.317605 | ||||||||
\(239\) | −23.2103 | −1.50135 | −0.750676 | − | 0.660670i | \(-0.770272\pi\) | ||||
−0.750676 | + | 0.660670i | \(0.770272\pi\) | |||||||
\(240\) | −7.96476 | −0.514123 | ||||||||
\(241\) | 15.7636 | 1.01543 | 0.507713 | − | 0.861526i | \(-0.330491\pi\) | ||||
0.507713 | + | 0.861526i | \(0.330491\pi\) | |||||||
\(242\) | −0.327392 | −0.0210456 | ||||||||
\(243\) | 20.8859 | 1.33983 | ||||||||
\(244\) | 20.7381 | 1.32762 | ||||||||
\(245\) | −0.934228 | −0.0596857 | ||||||||
\(246\) | −0.768788 | −0.0490161 | ||||||||
\(247\) | −5.35573 | −0.340777 | ||||||||
\(248\) | 9.22008 | 0.585476 | ||||||||
\(249\) | −31.1050 | −1.97120 | ||||||||
\(250\) | −0.327392 | −0.0207061 | ||||||||
\(251\) | 4.88454 | 0.308309 | 0.154155 | − | 0.988047i | \(-0.450735\pi\) | ||||
0.154155 | + | 0.988047i | \(0.450735\pi\) | |||||||
\(252\) | −12.0795 | −0.760939 | ||||||||
\(253\) | 2.42427 | 0.152413 | ||||||||
\(254\) | −0.702085 | −0.0440527 | ||||||||
\(255\) | 14.3687 | 0.899801 | ||||||||
\(256\) | 8.09738 | 0.506086 | ||||||||
\(257\) | 15.0578 | 0.939283 | 0.469641 | − | 0.882857i | \(-0.344383\pi\) | ||||
0.469641 | + | 0.882857i | \(0.344383\pi\) | |||||||
\(258\) | 4.31562 | 0.268678 | ||||||||
\(259\) | −12.5416 | −0.779295 | ||||||||
\(260\) | 1.21386 | 0.0752803 | ||||||||
\(261\) | 13.8980 | 0.860266 | ||||||||
\(262\) | −4.34068 | −0.268168 | ||||||||
\(263\) | 16.2991 | 1.00505 | 0.502524 | − | 0.864563i | \(-0.332405\pi\) | ||||
0.502524 | + | 0.864563i | \(0.332405\pi\) | |||||||
\(264\) | −3.01359 | −0.185473 | ||||||||
\(265\) | 3.89942 | 0.239539 | ||||||||
\(266\) | −6.73395 | −0.412885 | ||||||||
\(267\) | −19.8258 | −1.21332 | ||||||||
\(268\) | 20.1521 | 1.23099 | ||||||||
\(269\) | 23.9598 | 1.46085 | 0.730426 | − | 0.682992i | \(-0.239322\pi\) | ||||
0.730426 | + | 0.682992i | \(0.239322\pi\) | |||||||
\(270\) | −0.316478 | −0.0192603 | ||||||||
\(271\) | 13.9318 | 0.846295 | 0.423148 | − | 0.906061i | \(-0.360925\pi\) | ||||
0.423148 | + | 0.906061i | \(0.360925\pi\) | |||||||
\(272\) | −20.4685 | −1.24108 | ||||||||
\(273\) | 3.73469 | 0.226034 | ||||||||
\(274\) | −1.48275 | −0.0895762 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 10.8503 | 0.653111 | ||||||||
\(277\) | −11.7456 | −0.705723 | −0.352861 | − | 0.935676i | \(-0.614791\pi\) | ||||
−0.352861 | + | 0.935676i | \(0.614791\pi\) | |||||||
\(278\) | 6.17639 | 0.370435 | ||||||||
\(279\) | 18.7457 | 1.12228 | ||||||||
\(280\) | 3.13888 | 0.187584 | ||||||||
\(281\) | −4.89579 | −0.292058 | −0.146029 | − | 0.989280i | \(-0.546649\pi\) | ||||
−0.146029 | + | 0.989280i | \(0.546649\pi\) | |||||||
\(282\) | 2.38869 | 0.142244 | ||||||||
\(283\) | −6.09546 | −0.362338 | −0.181169 | − | 0.983452i | \(-0.557988\pi\) | ||||
−0.181169 | + | 0.983452i | \(0.557988\pi\) | |||||||
\(284\) | 0.612505 | 0.0363455 | ||||||||
\(285\) | −19.7474 | −1.16974 | ||||||||
\(286\) | 0.209956 | 0.0124150 | ||||||||
\(287\) | −2.44585 | −0.144374 | ||||||||
\(288\) | −9.46232 | −0.557573 | ||||||||
\(289\) | 19.9257 | 1.17210 | ||||||||
\(290\) | −1.75599 | −0.103115 | ||||||||
\(291\) | 4.12035 | 0.241539 | ||||||||
\(292\) | −1.89281 | −0.110769 | ||||||||
\(293\) | −2.88854 | −0.168750 | −0.0843750 | − | 0.996434i | \(-0.526889\pi\) | ||||
−0.0843750 | + | 0.996434i | \(0.526889\pi\) | |||||||
\(294\) | −0.723224 | −0.0421793 | ||||||||
\(295\) | −0.200959 | −0.0117003 | ||||||||
\(296\) | −6.48993 | −0.377220 | ||||||||
\(297\) | 0.966665 | 0.0560916 | ||||||||
\(298\) | −4.17739 | −0.241990 | ||||||||
\(299\) | −1.55468 | −0.0899095 | ||||||||
\(300\) | 4.47569 | 0.258404 | ||||||||
\(301\) | 13.7298 | 0.791375 | ||||||||
\(302\) | −4.73165 | −0.272276 | ||||||||
\(303\) | 8.17588 | 0.469692 | ||||||||
\(304\) | 28.1306 | 1.61340 | ||||||||
\(305\) | −10.9562 | −0.627351 | ||||||||
\(306\) | 5.15503 | 0.294694 | ||||||||
\(307\) | −12.1863 | −0.695511 | −0.347756 | − | 0.937585i | \(-0.613056\pi\) | ||||
−0.347756 | + | 0.937585i | \(0.613056\pi\) | |||||||
\(308\) | −4.66177 | −0.265629 | ||||||||
\(309\) | 37.4389 | 2.12983 | ||||||||
\(310\) | −2.36849 | −0.134521 | ||||||||
\(311\) | 2.83566 | 0.160795 | 0.0803977 | − | 0.996763i | \(-0.474381\pi\) | ||||
0.0803977 | + | 0.996763i | \(0.474381\pi\) | |||||||
\(312\) | 1.93261 | 0.109412 | ||||||||
\(313\) | −8.16184 | −0.461334 | −0.230667 | − | 0.973033i | \(-0.574091\pi\) | ||||
−0.230667 | + | 0.973033i | \(0.574091\pi\) | |||||||
\(314\) | −0.562976 | −0.0317706 | ||||||||
\(315\) | 6.38178 | 0.359573 | ||||||||
\(316\) | 20.3571 | 1.14518 | ||||||||
\(317\) | −6.90411 | −0.387773 | −0.193887 | − | 0.981024i | \(-0.562109\pi\) | ||||
−0.193887 | + | 0.981024i | \(0.562109\pi\) | |||||||
\(318\) | 3.01870 | 0.169280 | ||||||||
\(319\) | 5.36357 | 0.300302 | ||||||||
\(320\) | −5.54120 | −0.309763 | ||||||||
\(321\) | 15.5749 | 0.869304 | ||||||||
\(322\) | −1.95475 | −0.108934 | ||||||||
\(323\) | −50.7485 | −2.82372 | ||||||||
\(324\) | 19.0404 | 1.05780 | ||||||||
\(325\) | −0.641298 | −0.0355728 | ||||||||
\(326\) | −3.37962 | −0.187180 | ||||||||
\(327\) | −27.0413 | −1.49539 | ||||||||
\(328\) | −1.26566 | −0.0698846 | ||||||||
\(329\) | 7.59945 | 0.418971 | ||||||||
\(330\) | 0.774141 | 0.0426151 | ||||||||
\(331\) | −22.3558 | −1.22878 | −0.614392 | − | 0.789001i | \(-0.710599\pi\) | ||||
−0.614392 | + | 0.789001i | \(0.710599\pi\) | |||||||
\(332\) | −24.8993 | −1.36652 | ||||||||
\(333\) | −13.1949 | −0.723078 | ||||||||
\(334\) | 6.24499 | 0.341711 | ||||||||
\(335\) | −10.6466 | −0.581688 | ||||||||
\(336\) | −19.6162 | −1.07015 | ||||||||
\(337\) | −10.0892 | −0.549595 | −0.274797 | − | 0.961502i | \(-0.588611\pi\) | ||||
−0.274797 | + | 0.961502i | \(0.588611\pi\) | |||||||
\(338\) | 4.12145 | 0.224177 | ||||||||
\(339\) | −5.16876 | −0.280728 | ||||||||
\(340\) | 11.5020 | 0.623782 | ||||||||
\(341\) | 7.23441 | 0.391765 | ||||||||
\(342\) | −7.08477 | −0.383100 | ||||||||
\(343\) | −19.5410 | −1.05512 | ||||||||
\(344\) | 7.10484 | 0.383067 | ||||||||
\(345\) | −5.73236 | −0.308620 | ||||||||
\(346\) | −1.59742 | −0.0858778 | ||||||||
\(347\) | 25.6422 | 1.37655 | 0.688274 | − | 0.725451i | \(-0.258369\pi\) | ||||
0.688274 | + | 0.725451i | \(0.258369\pi\) | |||||||
\(348\) | 24.0057 | 1.28684 | ||||||||
\(349\) | −24.9774 | −1.33701 | −0.668505 | − | 0.743707i | \(-0.733066\pi\) | ||||
−0.668505 | + | 0.743707i | \(0.733066\pi\) | |||||||
\(350\) | −0.806327 | −0.0431000 | ||||||||
\(351\) | −0.619920 | −0.0330889 | ||||||||
\(352\) | −3.65173 | −0.194638 | ||||||||
\(353\) | 7.78170 | 0.414178 | 0.207089 | − | 0.978322i | \(-0.433601\pi\) | ||||
0.207089 | + | 0.978322i | \(0.433601\pi\) | |||||||
\(354\) | −0.155571 | −0.00826849 | ||||||||
\(355\) | −0.323595 | −0.0171746 | ||||||||
\(356\) | −15.8704 | −0.841129 | ||||||||
\(357\) | 35.3883 | 1.87295 | ||||||||
\(358\) | −2.32412 | −0.122833 | ||||||||
\(359\) | 30.4828 | 1.60882 | 0.804411 | − | 0.594073i | \(-0.202481\pi\) | ||||
0.804411 | + | 0.594073i | \(0.202481\pi\) | |||||||
\(360\) | 3.30241 | 0.174052 | ||||||||
\(361\) | 50.7457 | 2.67083 | ||||||||
\(362\) | −1.50630 | −0.0791696 | ||||||||
\(363\) | −2.36457 | −0.124108 | ||||||||
\(364\) | 2.98959 | 0.156697 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −8.48166 | −0.443343 | ||||||||
\(367\) | 2.96163 | 0.154596 | 0.0772980 | − | 0.997008i | \(-0.475371\pi\) | ||||
0.0772980 | + | 0.997008i | \(0.475371\pi\) | |||||||
\(368\) | 8.16586 | 0.425675 | ||||||||
\(369\) | −2.57327 | −0.133959 | ||||||||
\(370\) | 1.66716 | 0.0866714 | ||||||||
\(371\) | 9.60379 | 0.498604 | ||||||||
\(372\) | 32.3790 | 1.67877 | ||||||||
\(373\) | −0.746015 | −0.0386272 | −0.0193136 | − | 0.999813i | \(-0.506148\pi\) | ||||
−0.0193136 | + | 0.999813i | \(0.506148\pi\) | |||||||
\(374\) | 1.98945 | 0.102872 | ||||||||
\(375\) | −2.36457 | −0.122106 | ||||||||
\(376\) | 3.93252 | 0.202804 | ||||||||
\(377\) | −3.43965 | −0.177151 | ||||||||
\(378\) | −0.779448 | −0.0400905 | ||||||||
\(379\) | 6.58248 | 0.338119 | 0.169060 | − | 0.985606i | \(-0.445927\pi\) | ||||
0.169060 | + | 0.985606i | \(0.445927\pi\) | |||||||
\(380\) | −15.8076 | −0.810914 | ||||||||
\(381\) | −5.07077 | −0.259783 | ||||||||
\(382\) | 2.29537 | 0.117441 | ||||||||
\(383\) | 26.6271 | 1.36058 | 0.680290 | − | 0.732943i | \(-0.261854\pi\) | ||||
0.680290 | + | 0.732943i | \(0.261854\pi\) | |||||||
\(384\) | −21.5592 | −1.10019 | ||||||||
\(385\) | 2.46288 | 0.125520 | ||||||||
\(386\) | −3.57522 | −0.181974 | ||||||||
\(387\) | 14.4451 | 0.734287 | ||||||||
\(388\) | 3.29830 | 0.167446 | ||||||||
\(389\) | −27.7437 | −1.40666 | −0.703330 | − | 0.710864i | \(-0.748304\pi\) | ||||
−0.703330 | + | 0.710864i | \(0.748304\pi\) | |||||||
\(390\) | −0.496455 | −0.0251390 | ||||||||
\(391\) | −14.7315 | −0.745002 | ||||||||
\(392\) | −1.19065 | −0.0601370 | ||||||||
\(393\) | −31.3503 | −1.58142 | ||||||||
\(394\) | 1.86723 | 0.0940699 | ||||||||
\(395\) | −10.7550 | −0.541141 | ||||||||
\(396\) | −4.90464 | −0.246467 | ||||||||
\(397\) | −0.366934 | −0.0184159 | −0.00920794 | − | 0.999958i | \(-0.502931\pi\) | ||||
−0.00920794 | + | 0.999958i | \(0.502931\pi\) | |||||||
\(398\) | −5.70130 | −0.285780 | ||||||||
\(399\) | −48.6355 | −2.43482 | ||||||||
\(400\) | 3.36838 | 0.168419 | ||||||||
\(401\) | 27.6164 | 1.37909 | 0.689547 | − | 0.724240i | \(-0.257809\pi\) | ||||
0.689547 | + | 0.724240i | \(0.257809\pi\) | |||||||
\(402\) | −8.24200 | −0.411073 | ||||||||
\(403\) | −4.63941 | −0.231106 | ||||||||
\(404\) | 6.54471 | 0.325612 | ||||||||
\(405\) | −10.0593 | −0.499851 | ||||||||
\(406\) | −4.32479 | −0.214636 | ||||||||
\(407\) | −5.09224 | −0.252413 | ||||||||
\(408\) | 18.3125 | 0.906605 | ||||||||
\(409\) | 23.3264 | 1.15342 | 0.576709 | − | 0.816950i | \(-0.304337\pi\) | ||||
0.576709 | + | 0.816950i | \(0.304337\pi\) | |||||||
\(410\) | 0.325128 | 0.0160569 | ||||||||
\(411\) | −10.7091 | −0.528240 | ||||||||
\(412\) | 29.9695 | 1.47649 | ||||||||
\(413\) | −0.494938 | −0.0243543 | ||||||||
\(414\) | −2.05659 | −0.101076 | ||||||||
\(415\) | 13.1546 | 0.645735 | ||||||||
\(416\) | 2.34185 | 0.114819 | ||||||||
\(417\) | 44.6086 | 2.18449 | ||||||||
\(418\) | −2.73418 | −0.133733 | ||||||||
\(419\) | −28.2163 | −1.37846 | −0.689229 | − | 0.724543i | \(-0.742051\pi\) | ||||
−0.689229 | + | 0.724543i | \(0.742051\pi\) | |||||||
\(420\) | 11.0231 | 0.537871 | ||||||||
\(421\) | 10.3554 | 0.504691 | 0.252346 | − | 0.967637i | \(-0.418798\pi\) | ||||
0.252346 | + | 0.967637i | \(0.418798\pi\) | |||||||
\(422\) | −8.54041 | −0.415741 | ||||||||
\(423\) | 7.99536 | 0.388748 | ||||||||
\(424\) | 4.96971 | 0.241351 | ||||||||
\(425\) | −6.07665 | −0.294761 | ||||||||
\(426\) | −0.250508 | −0.0121372 | ||||||||
\(427\) | −26.9838 | −1.30584 | ||||||||
\(428\) | 12.4675 | 0.602640 | ||||||||
\(429\) | 1.51639 | 0.0732122 | ||||||||
\(430\) | −1.82512 | −0.0880150 | ||||||||
\(431\) | 11.9710 | 0.576625 | 0.288312 | − | 0.957536i | \(-0.406906\pi\) | ||||
0.288312 | + | 0.957536i | \(0.406906\pi\) | |||||||
\(432\) | 3.25609 | 0.156659 | ||||||||
\(433\) | 20.1829 | 0.969927 | 0.484963 | − | 0.874534i | \(-0.338833\pi\) | ||||
0.484963 | + | 0.874534i | \(0.338833\pi\) | |||||||
\(434\) | −5.83330 | −0.280007 | ||||||||
\(435\) | −12.6825 | −0.608081 | ||||||||
\(436\) | −21.6463 | −1.03667 | ||||||||
\(437\) | 20.2460 | 0.968499 | ||||||||
\(438\) | 0.774141 | 0.0369899 | ||||||||
\(439\) | 0.532483 | 0.0254140 | 0.0127070 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127070 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(440\) | 1.27448 | 0.0607583 | ||||||||
\(441\) | −2.42076 | −0.115274 | ||||||||
\(442\) | −1.27583 | −0.0606850 | ||||||||
\(443\) | 25.8413 | 1.22776 | 0.613879 | − | 0.789400i | \(-0.289608\pi\) | ||||
0.613879 | + | 0.789400i | \(0.289608\pi\) | |||||||
\(444\) | −22.7913 | −1.08163 | ||||||||
\(445\) | 8.38454 | 0.397465 | ||||||||
\(446\) | 4.95086 | 0.234430 | ||||||||
\(447\) | −30.1710 | −1.42704 | ||||||||
\(448\) | −13.6473 | −0.644775 | ||||||||
\(449\) | 25.4548 | 1.20129 | 0.600643 | − | 0.799518i | \(-0.294911\pi\) | ||||
0.600643 | + | 0.799518i | \(0.294911\pi\) | |||||||
\(450\) | −0.848334 | −0.0399908 | ||||||||
\(451\) | −0.993086 | −0.0467626 | ||||||||
\(452\) | −4.13754 | −0.194613 | ||||||||
\(453\) | −34.1741 | −1.60564 | ||||||||
\(454\) | 5.03436 | 0.236274 | ||||||||
\(455\) | −1.57944 | −0.0740453 | ||||||||
\(456\) | −25.1676 | −1.17858 | ||||||||
\(457\) | −20.7494 | −0.970617 | −0.485309 | − | 0.874343i | \(-0.661293\pi\) | ||||
−0.485309 | + | 0.874343i | \(0.661293\pi\) | |||||||
\(458\) | −9.43696 | −0.440960 | ||||||||
\(459\) | −5.87409 | −0.274179 | ||||||||
\(460\) | −4.58869 | −0.213949 | ||||||||
\(461\) | 14.7332 | 0.686196 | 0.343098 | − | 0.939300i | \(-0.388524\pi\) | ||||
0.343098 | + | 0.939300i | \(0.388524\pi\) | |||||||
\(462\) | 1.90662 | 0.0887038 | ||||||||
\(463\) | −36.0823 | −1.67689 | −0.838443 | − | 0.544989i | \(-0.816534\pi\) | ||||
−0.838443 | + | 0.544989i | \(0.816534\pi\) | |||||||
\(464\) | 18.0665 | 0.838718 | ||||||||
\(465\) | −17.1063 | −0.793284 | ||||||||
\(466\) | −7.00616 | −0.324554 | ||||||||
\(467\) | 7.80516 | 0.361180 | 0.180590 | − | 0.983558i | \(-0.442199\pi\) | ||||
0.180590 | + | 0.983558i | \(0.442199\pi\) | |||||||
\(468\) | 3.14534 | 0.145393 | ||||||||
\(469\) | −26.2214 | −1.21079 | ||||||||
\(470\) | −1.01020 | −0.0465971 | ||||||||
\(471\) | −4.06606 | −0.187354 | ||||||||
\(472\) | −0.256118 | −0.0117888 | ||||||||
\(473\) | 5.57472 | 0.256326 | ||||||||
\(474\) | −8.32586 | −0.382419 | ||||||||
\(475\) | 8.35139 | 0.383188 | ||||||||
\(476\) | 28.3280 | 1.29841 | ||||||||
\(477\) | 10.1041 | 0.462636 | ||||||||
\(478\) | 7.59888 | 0.347565 | ||||||||
\(479\) | 38.3255 | 1.75114 | 0.875569 | − | 0.483094i | \(-0.160487\pi\) | ||||
0.875569 | + | 0.483094i | \(0.160487\pi\) | |||||||
\(480\) | 8.63477 | 0.394122 | ||||||||
\(481\) | 3.26564 | 0.148900 | ||||||||
\(482\) | −5.16089 | −0.235072 | ||||||||
\(483\) | −14.1181 | −0.642396 | ||||||||
\(484\) | −1.89281 | −0.0860370 | ||||||||
\(485\) | −1.74254 | −0.0791245 | ||||||||
\(486\) | −6.83789 | −0.310173 | ||||||||
\(487\) | 1.75485 | 0.0795197 | 0.0397598 | − | 0.999209i | \(-0.487341\pi\) | ||||
0.0397598 | + | 0.999209i | \(0.487341\pi\) | |||||||
\(488\) | −13.9634 | −0.632095 | ||||||||
\(489\) | −24.4091 | −1.10382 | ||||||||
\(490\) | 0.305859 | 0.0138173 | ||||||||
\(491\) | −26.6477 | −1.20259 | −0.601297 | − | 0.799026i | \(-0.705349\pi\) | ||||
−0.601297 | + | 0.799026i | \(0.705349\pi\) | |||||||
\(492\) | −4.44474 | −0.200385 | ||||||||
\(493\) | −32.5926 | −1.46790 | ||||||||
\(494\) | 1.75342 | 0.0788902 | ||||||||
\(495\) | 2.59119 | 0.116465 | ||||||||
\(496\) | 24.3682 | 1.09417 | ||||||||
\(497\) | −0.796975 | −0.0357492 | ||||||||
\(498\) | 10.1835 | 0.456335 | ||||||||
\(499\) | −28.4960 | −1.27566 | −0.637829 | − | 0.770178i | \(-0.720167\pi\) | ||||
−0.637829 | + | 0.770178i | \(0.720167\pi\) | |||||||
\(500\) | −1.89281 | −0.0846492 | ||||||||
\(501\) | 45.1041 | 2.01510 | ||||||||
\(502\) | −1.59916 | −0.0713740 | ||||||||
\(503\) | −4.60256 | −0.205218 | −0.102609 | − | 0.994722i | \(-0.532719\pi\) | ||||
−0.102609 | + | 0.994722i | \(0.532719\pi\) | |||||||
\(504\) | 8.13343 | 0.362292 | ||||||||
\(505\) | −3.45766 | −0.153864 | ||||||||
\(506\) | −0.793687 | −0.0352837 | ||||||||
\(507\) | 29.7669 | 1.32200 | ||||||||
\(508\) | −4.05910 | −0.180093 | ||||||||
\(509\) | 6.95620 | 0.308328 | 0.154164 | − | 0.988045i | \(-0.450732\pi\) | ||||
0.154164 | + | 0.988045i | \(0.450732\pi\) | |||||||
\(510\) | −4.70419 | −0.208305 | ||||||||
\(511\) | 2.46288 | 0.108951 | ||||||||
\(512\) | −20.8862 | −0.923050 | ||||||||
\(513\) | 8.07299 | 0.356431 | ||||||||
\(514\) | −4.92982 | −0.217445 | ||||||||
\(515\) | −15.8333 | −0.697699 | ||||||||
\(516\) | 24.9507 | 1.09839 | ||||||||
\(517\) | 3.08560 | 0.135704 | ||||||||
\(518\) | 4.10601 | 0.180408 | ||||||||
\(519\) | −11.5373 | −0.506430 | ||||||||
\(520\) | −0.817319 | −0.0358418 | ||||||||
\(521\) | −8.91754 | −0.390685 | −0.195342 | − | 0.980735i | \(-0.562582\pi\) | ||||
−0.195342 | + | 0.980735i | \(0.562582\pi\) | |||||||
\(522\) | −4.55010 | −0.199153 | ||||||||
\(523\) | −17.4525 | −0.763144 | −0.381572 | − | 0.924339i | \(-0.624617\pi\) | ||||
−0.381572 | + | 0.924339i | \(0.624617\pi\) | |||||||
\(524\) | −25.0956 | −1.09631 | ||||||||
\(525\) | −5.82365 | −0.254165 | ||||||||
\(526\) | −5.33621 | −0.232670 | ||||||||
\(527\) | −43.9610 | −1.91497 | ||||||||
\(528\) | −7.96476 | −0.346622 | ||||||||
\(529\) | −17.1229 | −0.744474 | ||||||||
\(530\) | −1.27664 | −0.0554536 | ||||||||
\(531\) | −0.520723 | −0.0225975 | ||||||||
\(532\) | −38.9323 | −1.68793 | ||||||||
\(533\) | 0.636864 | 0.0275856 | ||||||||
\(534\) | 6.49082 | 0.280885 | ||||||||
\(535\) | −6.58676 | −0.284771 | ||||||||
\(536\) | −13.5689 | −0.586087 | ||||||||
\(537\) | −16.7858 | −0.724361 | ||||||||
\(538\) | −7.84423 | −0.338189 | ||||||||
\(539\) | −0.934228 | −0.0402401 | ||||||||
\(540\) | −1.82972 | −0.0787385 | ||||||||
\(541\) | −29.6284 | −1.27382 | −0.636911 | − | 0.770937i | \(-0.719788\pi\) | ||||
−0.636911 | + | 0.770937i | \(0.719788\pi\) | |||||||
\(542\) | −4.56115 | −0.195918 | ||||||||
\(543\) | −10.8792 | −0.466871 | ||||||||
\(544\) | 22.1903 | 0.951402 | ||||||||
\(545\) | 11.4360 | 0.489866 | ||||||||
\(546\) | −1.22271 | −0.0523271 | ||||||||
\(547\) | 5.42820 | 0.232093 | 0.116046 | − | 0.993244i | \(-0.462978\pi\) | ||||
0.116046 | + | 0.993244i | \(0.462978\pi\) | |||||||
\(548\) | −8.57251 | −0.366199 | ||||||||
\(549\) | −28.3896 | −1.21164 | ||||||||
\(550\) | −0.327392 | −0.0139600 | ||||||||
\(551\) | 44.7933 | 1.90826 | ||||||||
\(552\) | −7.30575 | −0.310953 | ||||||||
\(553\) | −26.4882 | −1.12639 | ||||||||
\(554\) | 3.84541 | 0.163376 | ||||||||
\(555\) | 12.0409 | 0.511110 | ||||||||
\(556\) | 35.7088 | 1.51439 | ||||||||
\(557\) | −43.3884 | −1.83842 | −0.919212 | − | 0.393762i | \(-0.871173\pi\) | ||||
−0.919212 | + | 0.393762i | \(0.871173\pi\) | |||||||
\(558\) | −6.13720 | −0.259808 | ||||||||
\(559\) | −3.57505 | −0.151209 | ||||||||
\(560\) | 8.29590 | 0.350566 | ||||||||
\(561\) | 14.3687 | 0.606646 | ||||||||
\(562\) | 1.60284 | 0.0676118 | ||||||||
\(563\) | −32.9000 | −1.38657 | −0.693284 | − | 0.720665i | \(-0.743837\pi\) | ||||
−0.693284 | + | 0.720665i | \(0.743837\pi\) | |||||||
\(564\) | 13.8102 | 0.581514 | ||||||||
\(565\) | 2.18592 | 0.0919623 | ||||||||
\(566\) | 1.99561 | 0.0838816 | ||||||||
\(567\) | −24.7749 | −1.04045 | ||||||||
\(568\) | −0.412414 | −0.0173045 | ||||||||
\(569\) | −24.0786 | −1.00943 | −0.504714 | − | 0.863287i | \(-0.668402\pi\) | ||||
−0.504714 | + | 0.863287i | \(0.668402\pi\) | |||||||
\(570\) | 6.46515 | 0.270795 | ||||||||
\(571\) | 26.4741 | 1.10791 | 0.553953 | − | 0.832548i | \(-0.313119\pi\) | ||||
0.553953 | + | 0.832548i | \(0.313119\pi\) | |||||||
\(572\) | 1.21386 | 0.0507540 | ||||||||
\(573\) | 16.5782 | 0.692563 | ||||||||
\(574\) | 0.800751 | 0.0334227 | ||||||||
\(575\) | 2.42427 | 0.101099 | ||||||||
\(576\) | −14.3583 | −0.598263 | ||||||||
\(577\) | 34.5156 | 1.43690 | 0.718452 | − | 0.695577i | \(-0.244851\pi\) | ||||
0.718452 | + | 0.695577i | \(0.244851\pi\) | |||||||
\(578\) | −6.52352 | −0.271343 | ||||||||
\(579\) | −25.8218 | −1.07312 | ||||||||
\(580\) | −10.1522 | −0.421549 | ||||||||
\(581\) | 32.3983 | 1.34411 | ||||||||
\(582\) | −1.34897 | −0.0559165 | ||||||||
\(583\) | 3.89942 | 0.161497 | ||||||||
\(584\) | 1.27448 | 0.0527382 | ||||||||
\(585\) | −1.66172 | −0.0687038 | ||||||||
\(586\) | 0.945683 | 0.0390658 | ||||||||
\(587\) | 37.2797 | 1.53870 | 0.769350 | − | 0.638828i | \(-0.220580\pi\) | ||||
0.769350 | + | 0.638828i | \(0.220580\pi\) | |||||||
\(588\) | −4.18132 | −0.172435 | ||||||||
\(589\) | 60.4174 | 2.48945 | ||||||||
\(590\) | 0.0657924 | 0.00270863 | ||||||||
\(591\) | 13.4860 | 0.554739 | ||||||||
\(592\) | −17.1526 | −0.704966 | ||||||||
\(593\) | 26.6379 | 1.09389 | 0.546944 | − | 0.837169i | \(-0.315791\pi\) | ||||
0.546944 | + | 0.837169i | \(0.315791\pi\) | |||||||
\(594\) | −0.316478 | −0.0129853 | ||||||||
\(595\) | −14.9661 | −0.613549 | ||||||||
\(596\) | −24.1516 | −0.989286 | ||||||||
\(597\) | −41.1773 | −1.68527 | ||||||||
\(598\) | 0.508990 | 0.0208141 | ||||||||
\(599\) | 43.8011 | 1.78966 | 0.894832 | − | 0.446404i | \(-0.147296\pi\) | ||||
0.894832 | + | 0.446404i | \(0.147296\pi\) | |||||||
\(600\) | −3.01359 | −0.123029 | ||||||||
\(601\) | −47.8903 | −1.95349 | −0.976743 | − | 0.214412i | \(-0.931217\pi\) | ||||
−0.976743 | + | 0.214412i | \(0.931217\pi\) | |||||||
\(602\) | −4.49504 | −0.183204 | ||||||||
\(603\) | −27.5874 | −1.12345 | ||||||||
\(604\) | −27.3560 | −1.11310 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −2.67672 | −0.108734 | ||||||||
\(607\) | −0.500138 | −0.0203000 | −0.0101500 | − | 0.999948i | \(-0.503231\pi\) | ||||
−0.0101500 | + | 0.999948i | \(0.503231\pi\) | |||||||
\(608\) | −30.4970 | −1.23682 | ||||||||
\(609\) | −31.2356 | −1.26573 | ||||||||
\(610\) | 3.58698 | 0.145232 | ||||||||
\(611\) | −1.97879 | −0.0800532 | ||||||||
\(612\) | 29.8038 | 1.20475 | ||||||||
\(613\) | 31.3670 | 1.26690 | 0.633450 | − | 0.773784i | \(-0.281638\pi\) | ||||
0.633450 | + | 0.773784i | \(0.281638\pi\) | |||||||
\(614\) | 3.98971 | 0.161012 | ||||||||
\(615\) | 2.34822 | 0.0946893 | ||||||||
\(616\) | 3.13888 | 0.126469 | ||||||||
\(617\) | −27.1936 | −1.09477 | −0.547386 | − | 0.836880i | \(-0.684377\pi\) | ||||
−0.547386 | + | 0.836880i | \(0.684377\pi\) | |||||||
\(618\) | −12.2572 | −0.493057 | ||||||||
\(619\) | 42.6195 | 1.71302 | 0.856511 | − | 0.516130i | \(-0.172628\pi\) | ||||
0.856511 | + | 0.516130i | \(0.172628\pi\) | |||||||
\(620\) | −13.6934 | −0.549940 | ||||||||
\(621\) | 2.34346 | 0.0940397 | ||||||||
\(622\) | −0.928371 | −0.0372243 | ||||||||
\(623\) | 20.6501 | 0.827329 | ||||||||
\(624\) | 5.10778 | 0.204475 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.67212 | 0.106799 | ||||||||
\(627\) | −19.7474 | −0.788637 | ||||||||
\(628\) | −3.25484 | −0.129882 | ||||||||
\(629\) | 30.9438 | 1.23381 | ||||||||
\(630\) | −2.08934 | −0.0832414 | ||||||||
\(631\) | −14.5786 | −0.580366 | −0.290183 | − | 0.956971i | \(-0.593716\pi\) | ||||
−0.290183 | + | 0.956971i | \(0.593716\pi\) | |||||||
\(632\) | −13.7069 | −0.545233 | ||||||||
\(633\) | −61.6826 | −2.45166 | ||||||||
\(634\) | 2.26035 | 0.0897699 | ||||||||
\(635\) | 2.14448 | 0.0851010 | ||||||||
\(636\) | 17.4526 | 0.692040 | ||||||||
\(637\) | 0.599119 | 0.0237380 | ||||||||
\(638\) | −1.75599 | −0.0695203 | ||||||||
\(639\) | −0.838495 | −0.0331704 | ||||||||
\(640\) | 9.11761 | 0.360405 | ||||||||
\(641\) | 39.1527 | 1.54644 | 0.773219 | − | 0.634139i | \(-0.218645\pi\) | ||||
0.773219 | + | 0.634139i | \(0.218645\pi\) | |||||||
\(642\) | −5.09908 | −0.201245 | ||||||||
\(643\) | 25.0115 | 0.986358 | 0.493179 | − | 0.869928i | \(-0.335835\pi\) | ||||
0.493179 | + | 0.869928i | \(0.335835\pi\) | |||||||
\(644\) | −11.3014 | −0.445338 | ||||||||
\(645\) | −13.1818 | −0.519033 | ||||||||
\(646\) | 16.6146 | 0.653695 | ||||||||
\(647\) | −12.8263 | −0.504253 | −0.252127 | − | 0.967694i | \(-0.581130\pi\) | ||||
−0.252127 | + | 0.967694i | \(0.581130\pi\) | |||||||
\(648\) | −12.8203 | −0.503631 | ||||||||
\(649\) | −0.200959 | −0.00788834 | ||||||||
\(650\) | 0.209956 | 0.00823515 | ||||||||
\(651\) | −42.1307 | −1.65123 | ||||||||
\(652\) | −19.5393 | −0.765217 | ||||||||
\(653\) | −29.0871 | −1.13827 | −0.569133 | − | 0.822245i | \(-0.692721\pi\) | ||||
−0.569133 | + | 0.822245i | \(0.692721\pi\) | |||||||
\(654\) | 8.85310 | 0.346184 | ||||||||
\(655\) | 13.2584 | 0.518047 | ||||||||
\(656\) | −3.34509 | −0.130604 | ||||||||
\(657\) | 2.59119 | 0.101092 | ||||||||
\(658\) | −2.48800 | −0.0969923 | ||||||||
\(659\) | −23.4984 | −0.915366 | −0.457683 | − | 0.889115i | \(-0.651321\pi\) | ||||
−0.457683 | + | 0.889115i | \(0.651321\pi\) | |||||||
\(660\) | 4.47569 | 0.174216 | ||||||||
\(661\) | 18.5339 | 0.720886 | 0.360443 | − | 0.932781i | \(-0.382626\pi\) | ||||
0.360443 | + | 0.932781i | \(0.382626\pi\) | |||||||
\(662\) | 7.31910 | 0.284465 | ||||||||
\(663\) | −9.21460 | −0.357865 | ||||||||
\(664\) | 16.7653 | 0.650618 | ||||||||
\(665\) | 20.5685 | 0.797610 | ||||||||
\(666\) | 4.31992 | 0.167393 | ||||||||
\(667\) | 13.0028 | 0.503469 | ||||||||
\(668\) | 36.1054 | 1.39696 | ||||||||
\(669\) | 35.7573 | 1.38246 | ||||||||
\(670\) | 3.48562 | 0.134661 | ||||||||
\(671\) | −10.9562 | −0.422960 | ||||||||
\(672\) | 21.2664 | 0.820369 | ||||||||
\(673\) | −15.2624 | −0.588321 | −0.294160 | − | 0.955756i | \(-0.595040\pi\) | ||||
−0.294160 | + | 0.955756i | \(0.595040\pi\) | |||||||
\(674\) | 3.30313 | 0.127232 | ||||||||
\(675\) | 0.966665 | 0.0372070 | ||||||||
\(676\) | 23.8281 | 0.916467 | ||||||||
\(677\) | −36.4187 | −1.39969 | −0.699843 | − | 0.714297i | \(-0.746747\pi\) | ||||
−0.699843 | + | 0.714297i | \(0.746747\pi\) | |||||||
\(678\) | 1.69221 | 0.0649889 | ||||||||
\(679\) | −4.29165 | −0.164699 | ||||||||
\(680\) | −7.74455 | −0.296990 | ||||||||
\(681\) | 36.3603 | 1.39333 | ||||||||
\(682\) | −2.36849 | −0.0906941 | ||||||||
\(683\) | 1.68988 | 0.0646615 | 0.0323307 | − | 0.999477i | \(-0.489707\pi\) | ||||
0.0323307 | + | 0.999477i | \(0.489707\pi\) | |||||||
\(684\) | −40.9605 | −1.56617 | ||||||||
\(685\) | 4.52897 | 0.173043 | ||||||||
\(686\) | 6.39758 | 0.244261 | ||||||||
\(687\) | −68.1579 | −2.60039 | ||||||||
\(688\) | 18.7777 | 0.715895 | ||||||||
\(689\) | −2.50069 | −0.0952686 | ||||||||
\(690\) | 1.87673 | 0.0714458 | ||||||||
\(691\) | −8.73047 | −0.332123 | −0.166061 | − | 0.986115i | \(-0.553105\pi\) | ||||
−0.166061 | + | 0.986115i | \(0.553105\pi\) | |||||||
\(692\) | −9.23547 | −0.351080 | ||||||||
\(693\) | 6.38178 | 0.242424 | ||||||||
\(694\) | −8.39506 | −0.318672 | ||||||||
\(695\) | −18.8654 | −0.715607 | ||||||||
\(696\) | −16.1636 | −0.612679 | ||||||||
\(697\) | 6.03464 | 0.228578 | ||||||||
\(698\) | 8.17741 | 0.309519 | ||||||||
\(699\) | −50.6016 | −1.91393 | ||||||||
\(700\) | −4.66177 | −0.176198 | ||||||||
\(701\) | −26.8542 | −1.01427 | −0.507135 | − | 0.861867i | \(-0.669295\pi\) | ||||
−0.507135 | + | 0.861867i | \(0.669295\pi\) | |||||||
\(702\) | 0.202957 | 0.00766012 | ||||||||
\(703\) | −42.5272 | −1.60395 | ||||||||
\(704\) | −5.54120 | −0.208842 | ||||||||
\(705\) | −7.29611 | −0.274787 | ||||||||
\(706\) | −2.54767 | −0.0958827 | ||||||||
\(707\) | −8.51580 | −0.320270 | ||||||||
\(708\) | −0.899432 | −0.0338027 | ||||||||
\(709\) | 35.9422 | 1.34984 | 0.674919 | − | 0.737892i | \(-0.264178\pi\) | ||||
0.674919 | + | 0.737892i | \(0.264178\pi\) | |||||||
\(710\) | 0.105942 | 0.00397595 | ||||||||
\(711\) | −27.8681 | −1.04514 | ||||||||
\(712\) | 10.6859 | 0.400471 | ||||||||
\(713\) | 17.5382 | 0.656810 | ||||||||
\(714\) | −11.5858 | −0.433589 | ||||||||
\(715\) | −0.641298 | −0.0239832 | ||||||||
\(716\) | −13.4369 | −0.502159 | ||||||||
\(717\) | 54.8825 | 2.04962 | ||||||||
\(718\) | −9.97984 | −0.372444 | ||||||||
\(719\) | 32.7152 | 1.22007 | 0.610036 | − | 0.792374i | \(-0.291155\pi\) | ||||
0.610036 | + | 0.792374i | \(0.291155\pi\) | |||||||
\(720\) | 8.72809 | 0.325277 | ||||||||
\(721\) | −38.9955 | −1.45227 | ||||||||
\(722\) | −16.6137 | −0.618299 | ||||||||
\(723\) | −37.2742 | −1.38624 | ||||||||
\(724\) | −8.70869 | −0.323656 | ||||||||
\(725\) | 5.36357 | 0.199198 | ||||||||
\(726\) | 0.774141 | 0.0287311 | ||||||||
\(727\) | −17.9525 | −0.665820 | −0.332910 | − | 0.942959i | \(-0.608031\pi\) | ||||
−0.332910 | + | 0.942959i | \(0.608031\pi\) | |||||||
\(728\) | −2.01296 | −0.0746052 | ||||||||
\(729\) | −19.2083 | −0.711419 | ||||||||
\(730\) | −0.327392 | −0.0121173 | ||||||||
\(731\) | −33.8756 | −1.25293 | ||||||||
\(732\) | −49.0366 | −1.81245 | ||||||||
\(733\) | 41.1438 | 1.51968 | 0.759840 | − | 0.650110i | \(-0.225277\pi\) | ||||
0.759840 | + | 0.650110i | \(0.225277\pi\) | |||||||
\(734\) | −0.969614 | −0.0357891 | ||||||||
\(735\) | 2.20905 | 0.0814819 | ||||||||
\(736\) | −8.85279 | −0.326318 | ||||||||
\(737\) | −10.6466 | −0.392174 | ||||||||
\(738\) | 0.842468 | 0.0310117 | ||||||||
\(739\) | 11.4091 | 0.419692 | 0.209846 | − | 0.977734i | \(-0.432704\pi\) | ||||
0.209846 | + | 0.977734i | \(0.432704\pi\) | |||||||
\(740\) | 9.63866 | 0.354324 | ||||||||
\(741\) | 12.6640 | 0.465223 | ||||||||
\(742\) | −3.14420 | −0.115427 | ||||||||
\(743\) | 10.8685 | 0.398725 | 0.199362 | − | 0.979926i | \(-0.436113\pi\) | ||||
0.199362 | + | 0.979926i | \(0.436113\pi\) | |||||||
\(744\) | −21.8015 | −0.799283 | ||||||||
\(745\) | 12.7596 | 0.467475 | ||||||||
\(746\) | 0.244239 | 0.00894224 | ||||||||
\(747\) | 34.0861 | 1.24715 | ||||||||
\(748\) | 11.5020 | 0.420554 | ||||||||
\(749\) | −16.2224 | −0.592754 | ||||||||
\(750\) | 0.774141 | 0.0282676 | ||||||||
\(751\) | −14.7036 | −0.536541 | −0.268271 | − | 0.963344i | \(-0.586452\pi\) | ||||
−0.268271 | + | 0.963344i | \(0.586452\pi\) | |||||||
\(752\) | 10.3935 | 0.379010 | ||||||||
\(753\) | −11.5498 | −0.420899 | ||||||||
\(754\) | 1.12611 | 0.0410106 | ||||||||
\(755\) | 14.4526 | 0.525983 | ||||||||
\(756\) | −4.50637 | −0.163895 | ||||||||
\(757\) | 12.3967 | 0.450565 | 0.225282 | − | 0.974294i | \(-0.427670\pi\) | ||||
0.225282 | + | 0.974294i | \(0.427670\pi\) | |||||||
\(758\) | −2.15505 | −0.0782750 | ||||||||
\(759\) | −5.73236 | −0.208071 | ||||||||
\(760\) | 10.6436 | 0.386086 | ||||||||
\(761\) | 25.8774 | 0.938053 | 0.469027 | − | 0.883184i | \(-0.344605\pi\) | ||||
0.469027 | + | 0.883184i | \(0.344605\pi\) | |||||||
\(762\) | 1.66013 | 0.0601401 | ||||||||
\(763\) | 28.1656 | 1.01966 | ||||||||
\(764\) | 13.2707 | 0.480116 | ||||||||
\(765\) | −15.7457 | −0.569289 | ||||||||
\(766\) | −8.71749 | −0.314976 | ||||||||
\(767\) | 0.128875 | 0.00465340 | ||||||||
\(768\) | −19.1468 | −0.690901 | ||||||||
\(769\) | −36.7336 | −1.32465 | −0.662323 | − | 0.749218i | \(-0.730429\pi\) | ||||
−0.662323 | + | 0.749218i | \(0.730429\pi\) | |||||||
\(770\) | −0.806327 | −0.0290580 | ||||||||
\(771\) | −35.6053 | −1.28229 | ||||||||
\(772\) | −20.6701 | −0.743934 | ||||||||
\(773\) | −50.3884 | −1.81235 | −0.906173 | − | 0.422907i | \(-0.861010\pi\) | ||||
−0.906173 | + | 0.422907i | \(0.861010\pi\) | |||||||
\(774\) | −4.72922 | −0.169988 | ||||||||
\(775\) | 7.23441 | 0.259868 | ||||||||
\(776\) | −2.22082 | −0.0797228 | ||||||||
\(777\) | 29.6554 | 1.06388 | ||||||||
\(778\) | 9.08305 | 0.325643 | ||||||||
\(779\) | −8.29364 | −0.297151 | ||||||||
\(780\) | −2.87025 | −0.102772 | ||||||||
\(781\) | −0.323595 | −0.0115791 | ||||||||
\(782\) | 4.82296 | 0.172469 | ||||||||
\(783\) | 5.18478 | 0.185289 | ||||||||
\(784\) | −3.14683 | −0.112387 | ||||||||
\(785\) | 1.71958 | 0.0613744 | ||||||||
\(786\) | 10.2638 | 0.366099 | ||||||||
\(787\) | 36.6300 | 1.30572 | 0.652859 | − | 0.757479i | \(-0.273569\pi\) | ||||
0.652859 | + | 0.757479i | \(0.273569\pi\) | |||||||
\(788\) | 10.7954 | 0.384570 | ||||||||
\(789\) | −38.5405 | −1.37208 | ||||||||
\(790\) | 3.52109 | 0.125275 | ||||||||
\(791\) | 5.38365 | 0.191421 | ||||||||
\(792\) | 3.30241 | 0.117346 | ||||||||
\(793\) | 7.02620 | 0.249508 | ||||||||
\(794\) | 0.120131 | 0.00426329 | ||||||||
\(795\) | −9.22044 | −0.327015 | ||||||||
\(796\) | −32.9620 | −1.16831 | ||||||||
\(797\) | 26.3137 | 0.932080 | 0.466040 | − | 0.884764i | \(-0.345680\pi\) | ||||
0.466040 | + | 0.884764i | \(0.345680\pi\) | |||||||
\(798\) | 15.9229 | 0.563664 | ||||||||
\(799\) | −18.7501 | −0.663331 | ||||||||
\(800\) | −3.65173 | −0.129108 | ||||||||
\(801\) | 21.7259 | 0.767648 | ||||||||
\(802\) | −9.04137 | −0.319262 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −47.6511 | −1.68052 | ||||||||
\(805\) | 5.97068 | 0.210439 | ||||||||
\(806\) | 1.51891 | 0.0535012 | ||||||||
\(807\) | −56.6545 | −1.99433 | ||||||||
\(808\) | −4.40671 | −0.155027 | ||||||||
\(809\) | 39.1233 | 1.37550 | 0.687751 | − | 0.725947i | \(-0.258598\pi\) | ||||
0.687751 | + | 0.725947i | \(0.258598\pi\) | |||||||
\(810\) | 3.29334 | 0.115716 | ||||||||
\(811\) | 5.79807 | 0.203598 | 0.101799 | − | 0.994805i | \(-0.467540\pi\) | ||||
0.101799 | + | 0.994805i | \(0.467540\pi\) | |||||||
\(812\) | −25.0038 | −0.877460 | ||||||||
\(813\) | −32.9427 | −1.15535 | ||||||||
\(814\) | 1.66716 | 0.0584338 | ||||||||
\(815\) | 10.3229 | 0.361594 | ||||||||
\(816\) | 48.3991 | 1.69431 | ||||||||
\(817\) | 46.5566 | 1.62881 | ||||||||
\(818\) | −7.63689 | −0.267018 | ||||||||
\(819\) | −4.09262 | −0.143008 | ||||||||
\(820\) | 1.87973 | 0.0656429 | ||||||||
\(821\) | −3.76985 | −0.131569 | −0.0657843 | − | 0.997834i | \(-0.520955\pi\) | ||||
−0.0657843 | + | 0.997834i | \(0.520955\pi\) | |||||||
\(822\) | 3.50606 | 0.122288 | ||||||||
\(823\) | −21.5281 | −0.750421 | −0.375210 | − | 0.926940i | \(-0.622430\pi\) | ||||
−0.375210 | + | 0.926940i | \(0.622430\pi\) | |||||||
\(824\) | −20.1792 | −0.702974 | ||||||||
\(825\) | −2.36457 | −0.0823237 | ||||||||
\(826\) | 0.162039 | 0.00563805 | ||||||||
\(827\) | 9.66591 | 0.336117 | 0.168058 | − | 0.985777i | \(-0.446250\pi\) | ||||
0.168058 | + | 0.985777i | \(0.446250\pi\) | |||||||
\(828\) | −11.8902 | −0.413212 | ||||||||
\(829\) | 17.5613 | 0.609929 | 0.304965 | − | 0.952364i | \(-0.401355\pi\) | ||||
0.304965 | + | 0.952364i | \(0.401355\pi\) | |||||||
\(830\) | −4.30672 | −0.149488 | ||||||||
\(831\) | 27.7732 | 0.963442 | ||||||||
\(832\) | 3.55356 | 0.123198 | ||||||||
\(833\) | 5.67698 | 0.196696 | ||||||||
\(834\) | −14.6045 | −0.505713 | ||||||||
\(835\) | −19.0750 | −0.660117 | ||||||||
\(836\) | −15.8076 | −0.546718 | ||||||||
\(837\) | 6.99325 | 0.241722 | ||||||||
\(838\) | 9.23780 | 0.319115 | ||||||||
\(839\) | −14.8219 | −0.511708 | −0.255854 | − | 0.966715i | \(-0.582357\pi\) | ||||
−0.255854 | + | 0.966715i | \(0.582357\pi\) | |||||||
\(840\) | −7.42210 | −0.256087 | ||||||||
\(841\) | −0.232084 | −0.00800289 | ||||||||
\(842\) | −3.39027 | −0.116837 | ||||||||
\(843\) | 11.5764 | 0.398714 | ||||||||
\(844\) | −49.3763 | −1.69960 | ||||||||
\(845\) | −12.5887 | −0.433066 | ||||||||
\(846\) | −2.61762 | −0.0899956 | ||||||||
\(847\) | 2.46288 | 0.0846255 | ||||||||
\(848\) | 13.1347 | 0.451047 | ||||||||
\(849\) | 14.4131 | 0.494658 | ||||||||
\(850\) | 1.98945 | 0.0682375 | ||||||||
\(851\) | −12.3450 | −0.423180 | ||||||||
\(852\) | −1.44831 | −0.0496183 | ||||||||
\(853\) | −17.0110 | −0.582445 | −0.291223 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291223 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(854\) | 8.83429 | 0.302303 | ||||||||
\(855\) | 21.6400 | 0.740073 | ||||||||
\(856\) | −8.39467 | −0.286924 | ||||||||
\(857\) | 34.9627 | 1.19430 | 0.597152 | − | 0.802128i | \(-0.296299\pi\) | ||||
0.597152 | + | 0.802128i | \(0.296299\pi\) | |||||||
\(858\) | −0.496455 | −0.0169487 | ||||||||
\(859\) | 35.1109 | 1.19797 | 0.598985 | − | 0.800760i | \(-0.295571\pi\) | ||||
0.598985 | + | 0.800760i | \(0.295571\pi\) | |||||||
\(860\) | −10.5519 | −0.359817 | ||||||||
\(861\) | 5.78338 | 0.197097 | ||||||||
\(862\) | −3.91922 | −0.133489 | ||||||||
\(863\) | 31.4924 | 1.07201 | 0.536006 | − | 0.844214i | \(-0.319932\pi\) | ||||
0.536006 | + | 0.844214i | \(0.319932\pi\) | |||||||
\(864\) | −3.53000 | −0.120093 | ||||||||
\(865\) | 4.87923 | 0.165899 | ||||||||
\(866\) | −6.60771 | −0.224539 | ||||||||
\(867\) | −47.1157 | −1.60013 | ||||||||
\(868\) | −33.7252 | −1.14471 | ||||||||
\(869\) | −10.7550 | −0.364837 | ||||||||
\(870\) | 4.15216 | 0.140771 | ||||||||
\(871\) | 6.82767 | 0.231347 | ||||||||
\(872\) | 14.5750 | 0.493570 | ||||||||
\(873\) | −4.51524 | −0.152818 | ||||||||
\(874\) | −6.62839 | −0.224208 | ||||||||
\(875\) | 2.46288 | 0.0832605 | ||||||||
\(876\) | 4.47569 | 0.151220 | ||||||||
\(877\) | −12.9989 | −0.438941 | −0.219471 | − | 0.975619i | \(-0.570433\pi\) | ||||
−0.219471 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(878\) | −0.174331 | −0.00588338 | ||||||||
\(879\) | 6.83014 | 0.230375 | ||||||||
\(880\) | 3.36838 | 0.113548 | ||||||||
\(881\) | 18.5787 | 0.625933 | 0.312966 | − | 0.949764i | \(-0.398677\pi\) | ||||
0.312966 | + | 0.949764i | \(0.398677\pi\) | |||||||
\(882\) | 0.792538 | 0.0266861 | ||||||||
\(883\) | −37.9881 | −1.27840 | −0.639201 | − | 0.769040i | \(-0.720735\pi\) | ||||
−0.639201 | + | 0.769040i | \(0.720735\pi\) | |||||||
\(884\) | −7.37620 | −0.248088 | ||||||||
\(885\) | 0.475182 | 0.0159731 | ||||||||
\(886\) | −8.46023 | −0.284227 | ||||||||
\(887\) | 14.5261 | 0.487738 | 0.243869 | − | 0.969808i | \(-0.421583\pi\) | ||||
0.243869 | + | 0.969808i | \(0.421583\pi\) | |||||||
\(888\) | 15.3459 | 0.514975 | ||||||||
\(889\) | 5.28159 | 0.177139 | ||||||||
\(890\) | −2.74503 | −0.0920137 | ||||||||
\(891\) | −10.0593 | −0.337000 | ||||||||
\(892\) | 28.6234 | 0.958381 | ||||||||
\(893\) | 25.7690 | 0.862328 | ||||||||
\(894\) | 9.87773 | 0.330361 | ||||||||
\(895\) | 7.09888 | 0.237289 | ||||||||
\(896\) | 22.4556 | 0.750188 | ||||||||
\(897\) | 3.67615 | 0.122743 | ||||||||
\(898\) | −8.33369 | −0.278099 | ||||||||
\(899\) | 38.8023 | 1.29413 | ||||||||
\(900\) | −4.90464 | −0.163488 | ||||||||
\(901\) | −23.6954 | −0.789408 | ||||||||
\(902\) | 0.325128 | 0.0108256 | ||||||||
\(903\) | −32.4652 | −1.08037 | ||||||||
\(904\) | 2.78590 | 0.0926577 | ||||||||
\(905\) | 4.60092 | 0.152940 | ||||||||
\(906\) | 11.1883 | 0.371707 | ||||||||
\(907\) | −43.7140 | −1.45150 | −0.725750 | − | 0.687959i | \(-0.758507\pi\) | ||||
−0.725750 | + | 0.687959i | \(0.758507\pi\) | |||||||
\(908\) | 29.1061 | 0.965920 | ||||||||
\(909\) | −8.95945 | −0.297166 | ||||||||
\(910\) | 0.517096 | 0.0171416 | ||||||||
\(911\) | −22.0078 | −0.729152 | −0.364576 | − | 0.931174i | \(-0.618786\pi\) | ||||
−0.364576 | + | 0.931174i | \(0.618786\pi\) | |||||||
\(912\) | −66.5168 | −2.20259 | ||||||||
\(913\) | 13.1546 | 0.435355 | ||||||||
\(914\) | 6.79319 | 0.224699 | ||||||||
\(915\) | 25.9067 | 0.856450 | ||||||||
\(916\) | −54.5597 | −1.80270 | ||||||||
\(917\) | 32.6538 | 1.07832 | ||||||||
\(918\) | 1.92313 | 0.0634727 | ||||||||
\(919\) | −37.4451 | −1.23520 | −0.617600 | − | 0.786492i | \(-0.711895\pi\) | ||||
−0.617600 | + | 0.786492i | \(0.711895\pi\) | |||||||
\(920\) | 3.08968 | 0.101864 | ||||||||
\(921\) | 28.8154 | 0.949501 | ||||||||
\(922\) | −4.82355 | −0.158855 | ||||||||
\(923\) | 0.207521 | 0.00683063 | ||||||||
\(924\) | 11.0231 | 0.362633 | ||||||||
\(925\) | −5.09224 | −0.167432 | ||||||||
\(926\) | 11.8130 | 0.388201 | ||||||||
\(927\) | −41.0271 | −1.34751 | ||||||||
\(928\) | −19.5863 | −0.642953 | ||||||||
\(929\) | −26.9397 | −0.883863 | −0.441932 | − | 0.897049i | \(-0.645707\pi\) | ||||
−0.441932 | + | 0.897049i | \(0.645707\pi\) | |||||||
\(930\) | 5.60045 | 0.183646 | ||||||||
\(931\) | −7.80210 | −0.255704 | ||||||||
\(932\) | −40.5061 | −1.32682 | ||||||||
\(933\) | −6.70511 | −0.219515 | ||||||||
\(934\) | −2.55535 | −0.0836135 | ||||||||
\(935\) | −6.07665 | −0.198728 | ||||||||
\(936\) | −2.11783 | −0.0692234 | ||||||||
\(937\) | −0.290083 | −0.00947661 | −0.00473831 | − | 0.999989i | \(-0.501508\pi\) | ||||
−0.00473831 | + | 0.999989i | \(0.501508\pi\) | |||||||
\(938\) | 8.58467 | 0.280299 | ||||||||
\(939\) | 19.2992 | 0.629806 | ||||||||
\(940\) | −5.84047 | −0.190495 | ||||||||
\(941\) | 12.8927 | 0.420292 | 0.210146 | − | 0.977670i | \(-0.432606\pi\) | ||||
0.210146 | + | 0.977670i | \(0.432606\pi\) | |||||||
\(942\) | 1.33120 | 0.0433727 | ||||||||
\(943\) | −2.40751 | −0.0783993 | ||||||||
\(944\) | −0.676906 | −0.0220314 | ||||||||
\(945\) | 2.38078 | 0.0774467 | ||||||||
\(946\) | −1.82512 | −0.0593397 | ||||||||
\(947\) | −14.2277 | −0.462337 | −0.231168 | − | 0.972914i | \(-0.574255\pi\) | ||||
−0.231168 | + | 0.972914i | \(0.574255\pi\) | |||||||
\(948\) | −48.1359 | −1.56338 | ||||||||
\(949\) | −0.641298 | −0.0208174 | ||||||||
\(950\) | −2.73418 | −0.0887084 | ||||||||
\(951\) | 16.3252 | 0.529382 | ||||||||
\(952\) | −19.0739 | −0.618188 | ||||||||
\(953\) | 26.5061 | 0.858618 | 0.429309 | − | 0.903158i | \(-0.358757\pi\) | ||||
0.429309 | + | 0.903158i | \(0.358757\pi\) | |||||||
\(954\) | −3.30801 | −0.107101 | ||||||||
\(955\) | −7.01107 | −0.226873 | ||||||||
\(956\) | 43.9329 | 1.42089 | ||||||||
\(957\) | −12.6825 | −0.409968 | ||||||||
\(958\) | −12.5475 | −0.405390 | ||||||||
\(959\) | 11.1543 | 0.360192 | ||||||||
\(960\) | 13.1026 | 0.422883 | ||||||||
\(961\) | 21.3367 | 0.688280 | ||||||||
\(962\) | −1.06915 | −0.0344706 | ||||||||
\(963\) | −17.0675 | −0.549994 | ||||||||
\(964\) | −29.8377 | −0.961006 | ||||||||
\(965\) | 10.9203 | 0.351537 | ||||||||
\(966\) | 4.62215 | 0.148715 | ||||||||
\(967\) | 34.5708 | 1.11172 | 0.555861 | − | 0.831275i | \(-0.312389\pi\) | ||||
0.555861 | + | 0.831275i | \(0.312389\pi\) | |||||||
\(968\) | 1.27448 | 0.0409632 | ||||||||
\(969\) | 119.998 | 3.85490 | ||||||||
\(970\) | 0.570492 | 0.0183174 | ||||||||
\(971\) | −19.9766 | −0.641080 | −0.320540 | − | 0.947235i | \(-0.603864\pi\) | ||||
−0.320540 | + | 0.947235i | \(0.603864\pi\) | |||||||
\(972\) | −39.5332 | −1.26803 | ||||||||
\(973\) | −46.4633 | −1.48954 | ||||||||
\(974\) | −0.574523 | −0.0184089 | ||||||||
\(975\) | 1.51639 | 0.0485635 | ||||||||
\(976\) | −36.9047 | −1.18129 | ||||||||
\(977\) | 13.4085 | 0.428975 | 0.214488 | − | 0.976727i | \(-0.431192\pi\) | ||||
0.214488 | + | 0.976727i | \(0.431192\pi\) | |||||||
\(978\) | 7.99135 | 0.255535 | ||||||||
\(979\) | 8.38454 | 0.267971 | ||||||||
\(980\) | 1.76832 | 0.0564869 | ||||||||
\(981\) | 29.6329 | 0.946106 | ||||||||
\(982\) | 8.72424 | 0.278402 | ||||||||
\(983\) | 14.5455 | 0.463928 | 0.231964 | − | 0.972724i | \(-0.425485\pi\) | ||||
0.231964 | + | 0.972724i | \(0.425485\pi\) | |||||||
\(984\) | 2.99275 | 0.0954054 | ||||||||
\(985\) | −5.70336 | −0.181724 | ||||||||
\(986\) | 10.6705 | 0.339819 | ||||||||
\(987\) | −17.9694 | −0.571973 | ||||||||
\(988\) | 10.1374 | 0.322514 | ||||||||
\(989\) | 13.5146 | 0.429740 | ||||||||
\(990\) | −0.848334 | −0.0269618 | ||||||||
\(991\) | 34.9445 | 1.11005 | 0.555024 | − | 0.831834i | \(-0.312709\pi\) | ||||
0.555024 | + | 0.831834i | \(0.312709\pi\) | |||||||
\(992\) | −26.4181 | −0.838776 | ||||||||
\(993\) | 52.8618 | 1.67752 | ||||||||
\(994\) | 0.260923 | 0.00827598 | ||||||||
\(995\) | 17.4143 | 0.552070 | ||||||||
\(996\) | 58.8760 | 1.86556 | ||||||||
\(997\) | −14.0164 | −0.443903 | −0.221952 | − | 0.975058i | \(-0.571243\pi\) | ||||
−0.221952 | + | 0.975058i | \(0.571243\pi\) | |||||||
\(998\) | 9.32937 | 0.295316 | ||||||||
\(999\) | −4.92249 | −0.155741 |
(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 | 4015.2.a.h.1.17 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.17 | ✓ | 37 | 1.1 | even | 1 | trivial |