Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.49412 | −1.43998 | −0.719990 | − | 0.693985i | \(-0.755854\pi\) | ||||
−0.719990 | + | 0.693985i | \(0.755854\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.01405 | 0.900712 | 0.450356 | − | 0.892849i | \(-0.351297\pi\) | ||||
0.450356 | + | 0.892849i | \(0.351297\pi\) | |||||||
\(6\) | −2.49412 | −1.01822 | ||||||||
\(7\) | 2.26153 | 0.854778 | 0.427389 | − | 0.904068i | \(-0.359433\pi\) | ||||
0.427389 | + | 0.904068i | \(0.359433\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.22062 | 1.07354 | ||||||||
\(10\) | 2.01405 | 0.636899 | ||||||||
\(11\) | −3.70387 | −1.11676 | −0.558380 | − | 0.829585i | \(-0.688577\pi\) | ||||
−0.558380 | + | 0.829585i | \(0.688577\pi\) | |||||||
\(12\) | −2.49412 | −0.719990 | ||||||||
\(13\) | −3.55865 | −0.986991 | −0.493496 | − | 0.869748i | \(-0.664281\pi\) | ||||
−0.493496 | + | 0.869748i | \(0.664281\pi\) | |||||||
\(14\) | 2.26153 | 0.604419 | ||||||||
\(15\) | −5.02328 | −1.29701 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.88697 | 1.67034 | 0.835168 | − | 0.549995i | \(-0.185370\pi\) | ||||
0.835168 | + | 0.549995i | \(0.185370\pi\) | |||||||
\(18\) | 3.22062 | 0.759108 | ||||||||
\(19\) | 2.37414 | 0.544665 | 0.272333 | − | 0.962203i | \(-0.412205\pi\) | ||||
0.272333 | + | 0.962203i | \(0.412205\pi\) | |||||||
\(20\) | 2.01405 | 0.450356 | ||||||||
\(21\) | −5.64052 | −1.23086 | ||||||||
\(22\) | −3.70387 | −0.789669 | ||||||||
\(23\) | −2.90483 | −0.605698 | −0.302849 | − | 0.953038i | \(-0.597938\pi\) | ||||
−0.302849 | + | 0.953038i | \(0.597938\pi\) | |||||||
\(24\) | −2.49412 | −0.509110 | ||||||||
\(25\) | −0.943592 | −0.188718 | ||||||||
\(26\) | −3.55865 | −0.697908 | ||||||||
\(27\) | −0.550262 | −0.105898 | ||||||||
\(28\) | 2.26153 | 0.427389 | ||||||||
\(29\) | 5.51423 | 1.02397 | 0.511983 | − | 0.858995i | \(-0.328911\pi\) | ||||
0.511983 | + | 0.858995i | \(0.328911\pi\) | |||||||
\(30\) | −5.02328 | −0.917122 | ||||||||
\(31\) | −6.05211 | −1.08699 | −0.543495 | − | 0.839412i | \(-0.682899\pi\) | ||||
−0.543495 | + | 0.839412i | \(0.682899\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 9.23790 | 1.60811 | ||||||||
\(34\) | 6.88697 | 1.18111 | ||||||||
\(35\) | 4.55484 | 0.769909 | ||||||||
\(36\) | 3.22062 | 0.536771 | ||||||||
\(37\) | 4.05981 | 0.667428 | 0.333714 | − | 0.942674i | \(-0.391698\pi\) | ||||
0.333714 | + | 0.942674i | \(0.391698\pi\) | |||||||
\(38\) | 2.37414 | 0.385136 | ||||||||
\(39\) | 8.87569 | 1.42125 | ||||||||
\(40\) | 2.01405 | 0.318450 | ||||||||
\(41\) | 5.33998 | 0.833964 | 0.416982 | − | 0.908915i | \(-0.363088\pi\) | ||||
0.416982 | + | 0.908915i | \(0.363088\pi\) | |||||||
\(42\) | −5.64052 | −0.870351 | ||||||||
\(43\) | −1.25313 | −0.191101 | −0.0955505 | − | 0.995425i | \(-0.530461\pi\) | ||||
−0.0955505 | + | 0.995425i | \(0.530461\pi\) | |||||||
\(44\) | −3.70387 | −0.558380 | ||||||||
\(45\) | 6.48651 | 0.966951 | ||||||||
\(46\) | −2.90483 | −0.428293 | ||||||||
\(47\) | 6.32993 | 0.923315 | 0.461658 | − | 0.887058i | \(-0.347255\pi\) | ||||
0.461658 | + | 0.887058i | \(0.347255\pi\) | |||||||
\(48\) | −2.49412 | −0.359995 | ||||||||
\(49\) | −1.88548 | −0.269355 | ||||||||
\(50\) | −0.943592 | −0.133444 | ||||||||
\(51\) | −17.1769 | −2.40525 | ||||||||
\(52\) | −3.55865 | −0.493496 | ||||||||
\(53\) | 12.2322 | 1.68023 | 0.840114 | − | 0.542410i | \(-0.182488\pi\) | ||||
0.840114 | + | 0.542410i | \(0.182488\pi\) | |||||||
\(54\) | −0.550262 | −0.0748811 | ||||||||
\(55\) | −7.45980 | −1.00588 | ||||||||
\(56\) | 2.26153 | 0.302210 | ||||||||
\(57\) | −5.92139 | −0.784307 | ||||||||
\(58\) | 5.51423 | 0.724054 | ||||||||
\(59\) | −4.09159 | −0.532679 | −0.266340 | − | 0.963879i | \(-0.585814\pi\) | ||||
−0.266340 | + | 0.963879i | \(0.585814\pi\) | |||||||
\(60\) | −5.02328 | −0.648503 | ||||||||
\(61\) | 2.55932 | 0.327687 | 0.163843 | − | 0.986486i | \(-0.447611\pi\) | ||||
0.163843 | + | 0.986486i | \(0.447611\pi\) | |||||||
\(62\) | −6.05211 | −0.768618 | ||||||||
\(63\) | 7.28354 | 0.917639 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.16730 | −0.888994 | ||||||||
\(66\) | 9.23790 | 1.13711 | ||||||||
\(67\) | 15.7411 | 1.92308 | 0.961540 | − | 0.274665i | \(-0.0885668\pi\) | ||||
0.961540 | + | 0.274665i | \(0.0885668\pi\) | |||||||
\(68\) | 6.88697 | 0.835168 | ||||||||
\(69\) | 7.24498 | 0.872193 | ||||||||
\(70\) | 4.55484 | 0.544408 | ||||||||
\(71\) | 0.641025 | 0.0760757 | 0.0380379 | − | 0.999276i | \(-0.487889\pi\) | ||||
0.0380379 | + | 0.999276i | \(0.487889\pi\) | |||||||
\(72\) | 3.22062 | 0.379554 | ||||||||
\(73\) | −8.54143 | −0.999699 | −0.499849 | − | 0.866112i | \(-0.666611\pi\) | ||||
−0.499849 | + | 0.866112i | \(0.666611\pi\) | |||||||
\(74\) | 4.05981 | 0.471943 | ||||||||
\(75\) | 2.35343 | 0.271751 | ||||||||
\(76\) | 2.37414 | 0.272333 | ||||||||
\(77\) | −8.37642 | −0.954582 | ||||||||
\(78\) | 8.87569 | 1.00497 | ||||||||
\(79\) | 2.47415 | 0.278363 | 0.139182 | − | 0.990267i | \(-0.455553\pi\) | ||||
0.139182 | + | 0.990267i | \(0.455553\pi\) | |||||||
\(80\) | 2.01405 | 0.225178 | ||||||||
\(81\) | −8.28945 | −0.921050 | ||||||||
\(82\) | 5.33998 | 0.589702 | ||||||||
\(83\) | 5.59401 | 0.614022 | 0.307011 | − | 0.951706i | \(-0.400671\pi\) | ||||
0.307011 | + | 0.951706i | \(0.400671\pi\) | |||||||
\(84\) | −5.64052 | −0.615431 | ||||||||
\(85\) | 13.8707 | 1.50449 | ||||||||
\(86\) | −1.25313 | −0.135129 | ||||||||
\(87\) | −13.7531 | −1.47449 | ||||||||
\(88\) | −3.70387 | −0.394834 | ||||||||
\(89\) | 8.40142 | 0.890549 | 0.445275 | − | 0.895394i | \(-0.353106\pi\) | ||||
0.445275 | + | 0.895394i | \(0.353106\pi\) | |||||||
\(90\) | 6.48651 | 0.683738 | ||||||||
\(91\) | −8.04799 | −0.843658 | ||||||||
\(92\) | −2.90483 | −0.302849 | ||||||||
\(93\) | 15.0947 | 1.56524 | ||||||||
\(94\) | 6.32993 | 0.652882 | ||||||||
\(95\) | 4.78164 | 0.490586 | ||||||||
\(96\) | −2.49412 | −0.254555 | ||||||||
\(97\) | −7.21256 | −0.732324 | −0.366162 | − | 0.930551i | \(-0.619328\pi\) | ||||
−0.366162 | + | 0.930551i | \(0.619328\pi\) | |||||||
\(98\) | −1.88548 | −0.190462 | ||||||||
\(99\) | −11.9288 | −1.19889 | ||||||||
\(100\) | −0.943592 | −0.0943592 | ||||||||
\(101\) | −6.35568 | −0.632414 | −0.316207 | − | 0.948690i | \(-0.602409\pi\) | ||||
−0.316207 | + | 0.948690i | \(0.602409\pi\) | |||||||
\(102\) | −17.1769 | −1.70077 | ||||||||
\(103\) | −11.2162 | −1.10516 | −0.552582 | − | 0.833459i | \(-0.686357\pi\) | ||||
−0.552582 | + | 0.833459i | \(0.686357\pi\) | |||||||
\(104\) | −3.55865 | −0.348954 | ||||||||
\(105\) | −11.3603 | −1.10865 | ||||||||
\(106\) | 12.2322 | 1.18810 | ||||||||
\(107\) | −13.6183 | −1.31653 | −0.658267 | − | 0.752785i | \(-0.728710\pi\) | ||||
−0.658267 | + | 0.752785i | \(0.728710\pi\) | |||||||
\(108\) | −0.550262 | −0.0529490 | ||||||||
\(109\) | 0.0239725 | 0.00229615 | 0.00114807 | − | 0.999999i | \(-0.499635\pi\) | ||||
0.00114807 | + | 0.999999i | \(0.499635\pi\) | |||||||
\(110\) | −7.45980 | −0.711264 | ||||||||
\(111\) | −10.1256 | −0.961083 | ||||||||
\(112\) | 2.26153 | 0.213694 | ||||||||
\(113\) | 20.2362 | 1.90366 | 0.951831 | − | 0.306624i | \(-0.0991994\pi\) | ||||
0.951831 | + | 0.306624i | \(0.0991994\pi\) | |||||||
\(114\) | −5.92139 | −0.554589 | ||||||||
\(115\) | −5.85048 | −0.545560 | ||||||||
\(116\) | 5.51423 | 0.511983 | ||||||||
\(117\) | −11.4611 | −1.05958 | ||||||||
\(118\) | −4.09159 | −0.376661 | ||||||||
\(119\) | 15.5751 | 1.42777 | ||||||||
\(120\) | −5.02328 | −0.458561 | ||||||||
\(121\) | 2.71868 | 0.247153 | ||||||||
\(122\) | 2.55932 | 0.231710 | ||||||||
\(123\) | −13.3185 | −1.20089 | ||||||||
\(124\) | −6.05211 | −0.543495 | ||||||||
\(125\) | −11.9707 | −1.07069 | ||||||||
\(126\) | 7.28354 | 0.648869 | ||||||||
\(127\) | −15.7777 | −1.40004 | −0.700022 | − | 0.714121i | \(-0.746826\pi\) | ||||
−0.700022 | + | 0.714121i | \(0.746826\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.12546 | 0.275182 | ||||||||
\(130\) | −7.16730 | −0.628614 | ||||||||
\(131\) | −5.27108 | −0.460536 | −0.230268 | − | 0.973127i | \(-0.573960\pi\) | ||||
−0.230268 | + | 0.973127i | \(0.573960\pi\) | |||||||
\(132\) | 9.23790 | 0.804056 | ||||||||
\(133\) | 5.36919 | 0.465568 | ||||||||
\(134\) | 15.7411 | 1.35982 | ||||||||
\(135\) | −1.10826 | −0.0953835 | ||||||||
\(136\) | 6.88697 | 0.590553 | ||||||||
\(137\) | 14.6575 | 1.25228 | 0.626138 | − | 0.779712i | \(-0.284635\pi\) | ||||
0.626138 | + | 0.779712i | \(0.284635\pi\) | |||||||
\(138\) | 7.24498 | 0.616734 | ||||||||
\(139\) | 21.7180 | 1.84210 | 0.921048 | − | 0.389448i | \(-0.127334\pi\) | ||||
0.921048 | + | 0.389448i | \(0.127334\pi\) | |||||||
\(140\) | 4.55484 | 0.384954 | ||||||||
\(141\) | −15.7876 | −1.32956 | ||||||||
\(142\) | 0.641025 | 0.0537937 | ||||||||
\(143\) | 13.1808 | 1.10223 | ||||||||
\(144\) | 3.22062 | 0.268385 | ||||||||
\(145\) | 11.1059 | 0.922299 | ||||||||
\(146\) | −8.54143 | −0.706894 | ||||||||
\(147\) | 4.70261 | 0.387865 | ||||||||
\(148\) | 4.05981 | 0.333714 | ||||||||
\(149\) | 19.8344 | 1.62490 | 0.812449 | − | 0.583032i | \(-0.198134\pi\) | ||||
0.812449 | + | 0.583032i | \(0.198134\pi\) | |||||||
\(150\) | 2.35343 | 0.192157 | ||||||||
\(151\) | −4.66734 | −0.379823 | −0.189911 | − | 0.981801i | \(-0.560820\pi\) | ||||
−0.189911 | + | 0.981801i | \(0.560820\pi\) | |||||||
\(152\) | 2.37414 | 0.192568 | ||||||||
\(153\) | 22.1803 | 1.79317 | ||||||||
\(154\) | −8.37642 | −0.674991 | ||||||||
\(155\) | −12.1893 | −0.979065 | ||||||||
\(156\) | 8.87569 | 0.710624 | ||||||||
\(157\) | 21.6430 | 1.72730 | 0.863652 | − | 0.504089i | \(-0.168172\pi\) | ||||
0.863652 | + | 0.504089i | \(0.168172\pi\) | |||||||
\(158\) | 2.47415 | 0.196833 | ||||||||
\(159\) | −30.5087 | −2.41949 | ||||||||
\(160\) | 2.01405 | 0.159225 | ||||||||
\(161\) | −6.56935 | −0.517738 | ||||||||
\(162\) | −8.28945 | −0.651281 | ||||||||
\(163\) | 10.8339 | 0.848576 | 0.424288 | − | 0.905527i | \(-0.360524\pi\) | ||||
0.424288 | + | 0.905527i | \(0.360524\pi\) | |||||||
\(164\) | 5.33998 | 0.416982 | ||||||||
\(165\) | 18.6056 | 1.44845 | ||||||||
\(166\) | 5.59401 | 0.434179 | ||||||||
\(167\) | 13.3377 | 1.03211 | 0.516053 | − | 0.856557i | \(-0.327401\pi\) | ||||
0.516053 | + | 0.856557i | \(0.327401\pi\) | |||||||
\(168\) | −5.64052 | −0.435176 | ||||||||
\(169\) | −0.336031 | −0.0258485 | ||||||||
\(170\) | 13.8707 | 1.06384 | ||||||||
\(171\) | 7.64621 | 0.584721 | ||||||||
\(172\) | −1.25313 | −0.0955505 | ||||||||
\(173\) | −22.9937 | −1.74818 | −0.874088 | − | 0.485767i | \(-0.838540\pi\) | ||||
−0.874088 | + | 0.485767i | \(0.838540\pi\) | |||||||
\(174\) | −13.7531 | −1.04262 | ||||||||
\(175\) | −2.13396 | −0.161312 | ||||||||
\(176\) | −3.70387 | −0.279190 | ||||||||
\(177\) | 10.2049 | 0.767047 | ||||||||
\(178\) | 8.40142 | 0.629713 | ||||||||
\(179\) | 0.526188 | 0.0393292 | 0.0196646 | − | 0.999807i | \(-0.493740\pi\) | ||||
0.0196646 | + | 0.999807i | \(0.493740\pi\) | |||||||
\(180\) | 6.48651 | 0.483476 | ||||||||
\(181\) | 22.4799 | 1.67092 | 0.835460 | − | 0.549551i | \(-0.185201\pi\) | ||||
0.835460 | + | 0.549551i | \(0.185201\pi\) | |||||||
\(182\) | −8.04799 | −0.596556 | ||||||||
\(183\) | −6.38323 | −0.471862 | ||||||||
\(184\) | −2.90483 | −0.214147 | ||||||||
\(185\) | 8.17666 | 0.601160 | ||||||||
\(186\) | 15.0947 | 1.10679 | ||||||||
\(187\) | −25.5085 | −1.86536 | ||||||||
\(188\) | 6.32993 | 0.461658 | ||||||||
\(189\) | −1.24443 | −0.0905192 | ||||||||
\(190\) | 4.78164 | 0.346897 | ||||||||
\(191\) | 11.3651 | 0.822349 | 0.411175 | − | 0.911557i | \(-0.365119\pi\) | ||||
0.411175 | + | 0.911557i | \(0.365119\pi\) | |||||||
\(192\) | −2.49412 | −0.179997 | ||||||||
\(193\) | −6.87508 | −0.494879 | −0.247440 | − | 0.968903i | \(-0.579589\pi\) | ||||
−0.247440 | + | 0.968903i | \(0.579589\pi\) | |||||||
\(194\) | −7.21256 | −0.517832 | ||||||||
\(195\) | 17.8761 | 1.28013 | ||||||||
\(196\) | −1.88548 | −0.134677 | ||||||||
\(197\) | 19.5956 | 1.39613 | 0.698064 | − | 0.716035i | \(-0.254045\pi\) | ||||
0.698064 | + | 0.716035i | \(0.254045\pi\) | |||||||
\(198\) | −11.9288 | −0.847742 | ||||||||
\(199\) | 21.9514 | 1.55609 | 0.778045 | − | 0.628208i | \(-0.216211\pi\) | ||||
0.778045 | + | 0.628208i | \(0.216211\pi\) | |||||||
\(200\) | −0.943592 | −0.0667220 | ||||||||
\(201\) | −39.2601 | −2.76920 | ||||||||
\(202\) | −6.35568 | −0.447184 | ||||||||
\(203\) | 12.4706 | 0.875264 | ||||||||
\(204\) | −17.1769 | −1.20262 | ||||||||
\(205\) | 10.7550 | 0.751162 | ||||||||
\(206\) | −11.2162 | −0.781469 | ||||||||
\(207\) | −9.35536 | −0.650242 | ||||||||
\(208\) | −3.55865 | −0.246748 | ||||||||
\(209\) | −8.79352 | −0.608260 | ||||||||
\(210\) | −11.3603 | −0.783936 | ||||||||
\(211\) | 2.41930 | 0.166551 | 0.0832757 | − | 0.996527i | \(-0.473462\pi\) | ||||
0.0832757 | + | 0.996527i | \(0.473462\pi\) | |||||||
\(212\) | 12.2322 | 0.840114 | ||||||||
\(213\) | −1.59879 | −0.109547 | ||||||||
\(214\) | −13.6183 | −0.930930 | ||||||||
\(215\) | −2.52388 | −0.172127 | ||||||||
\(216\) | −0.550262 | −0.0374406 | ||||||||
\(217\) | −13.6870 | −0.929135 | ||||||||
\(218\) | 0.0239725 | 0.00162362 | ||||||||
\(219\) | 21.3033 | 1.43955 | ||||||||
\(220\) | −7.45980 | −0.502939 | ||||||||
\(221\) | −24.5083 | −1.64861 | ||||||||
\(222\) | −10.1256 | −0.679588 | ||||||||
\(223\) | 23.7336 | 1.58932 | 0.794660 | − | 0.607055i | \(-0.207649\pi\) | ||||
0.794660 | + | 0.607055i | \(0.207649\pi\) | |||||||
\(224\) | 2.26153 | 0.151105 | ||||||||
\(225\) | −3.03895 | −0.202597 | ||||||||
\(226\) | 20.2362 | 1.34609 | ||||||||
\(227\) | 3.74598 | 0.248629 | 0.124315 | − | 0.992243i | \(-0.460327\pi\) | ||||
0.124315 | + | 0.992243i | \(0.460327\pi\) | |||||||
\(228\) | −5.92139 | −0.392153 | ||||||||
\(229\) | −6.05569 | −0.400171 | −0.200085 | − | 0.979778i | \(-0.564122\pi\) | ||||
−0.200085 | + | 0.979778i | \(0.564122\pi\) | |||||||
\(230\) | −5.85048 | −0.385769 | ||||||||
\(231\) | 20.8918 | 1.37458 | ||||||||
\(232\) | 5.51423 | 0.362027 | ||||||||
\(233\) | −4.78829 | −0.313691 | −0.156846 | − | 0.987623i | \(-0.550133\pi\) | ||||
−0.156846 | + | 0.987623i | \(0.550133\pi\) | |||||||
\(234\) | −11.4611 | −0.749233 | ||||||||
\(235\) | 12.7488 | 0.831641 | ||||||||
\(236\) | −4.09159 | −0.266340 | ||||||||
\(237\) | −6.17081 | −0.400837 | ||||||||
\(238\) | 15.5751 | 1.00958 | ||||||||
\(239\) | −23.7507 | −1.53630 | −0.768151 | − | 0.640268i | \(-0.778823\pi\) | ||||
−0.768151 | + | 0.640268i | \(0.778823\pi\) | |||||||
\(240\) | −5.02328 | −0.324252 | ||||||||
\(241\) | 14.2155 | 0.915700 | 0.457850 | − | 0.889029i | \(-0.348620\pi\) | ||||
0.457850 | + | 0.889029i | \(0.348620\pi\) | |||||||
\(242\) | 2.71868 | 0.174764 | ||||||||
\(243\) | 22.3257 | 1.43219 | ||||||||
\(244\) | 2.55932 | 0.163843 | ||||||||
\(245\) | −3.79746 | −0.242611 | ||||||||
\(246\) | −13.3185 | −0.849159 | ||||||||
\(247\) | −8.44873 | −0.537580 | ||||||||
\(248\) | −6.05211 | −0.384309 | ||||||||
\(249\) | −13.9521 | −0.884179 | ||||||||
\(250\) | −11.9707 | −0.757094 | ||||||||
\(251\) | −0.0817027 | −0.00515703 | −0.00257852 | − | 0.999997i | \(-0.500821\pi\) | ||||
−0.00257852 | + | 0.999997i | \(0.500821\pi\) | |||||||
\(252\) | 7.28354 | 0.458820 | ||||||||
\(253\) | 10.7591 | 0.676420 | ||||||||
\(254\) | −15.7777 | −0.989980 | ||||||||
\(255\) | −34.5952 | −2.16644 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.34170 | −0.520341 | −0.260171 | − | 0.965563i | \(-0.583779\pi\) | ||||
−0.260171 | + | 0.965563i | \(0.583779\pi\) | |||||||
\(258\) | 3.12546 | 0.194583 | ||||||||
\(259\) | 9.18137 | 0.570503 | ||||||||
\(260\) | −7.16730 | −0.444497 | ||||||||
\(261\) | 17.7593 | 1.09927 | ||||||||
\(262\) | −5.27108 | −0.325648 | ||||||||
\(263\) | −5.21436 | −0.321531 | −0.160766 | − | 0.986993i | \(-0.551396\pi\) | ||||
−0.160766 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(264\) | 9.23790 | 0.568553 | ||||||||
\(265\) | 24.6364 | 1.51340 | ||||||||
\(266\) | 5.36919 | 0.329206 | ||||||||
\(267\) | −20.9541 | −1.28237 | ||||||||
\(268\) | 15.7411 | 0.961540 | ||||||||
\(269\) | −8.22161 | −0.501280 | −0.250640 | − | 0.968080i | \(-0.580641\pi\) | ||||
−0.250640 | + | 0.968080i | \(0.580641\pi\) | |||||||
\(270\) | −1.10826 | −0.0674463 | ||||||||
\(271\) | −15.5448 | −0.944279 | −0.472140 | − | 0.881524i | \(-0.656518\pi\) | ||||
−0.472140 | + | 0.881524i | \(0.656518\pi\) | |||||||
\(272\) | 6.88697 | 0.417584 | ||||||||
\(273\) | 20.0726 | 1.21485 | ||||||||
\(274\) | 14.6575 | 0.885493 | ||||||||
\(275\) | 3.49494 | 0.210753 | ||||||||
\(276\) | 7.24498 | 0.436097 | ||||||||
\(277\) | −12.3455 | −0.741768 | −0.370884 | − | 0.928679i | \(-0.620945\pi\) | ||||
−0.370884 | + | 0.928679i | \(0.620945\pi\) | |||||||
\(278\) | 21.7180 | 1.30256 | ||||||||
\(279\) | −19.4916 | −1.16693 | ||||||||
\(280\) | 4.55484 | 0.272204 | ||||||||
\(281\) | 10.2175 | 0.609523 | 0.304761 | − | 0.952429i | \(-0.401423\pi\) | ||||
0.304761 | + | 0.952429i | \(0.401423\pi\) | |||||||
\(282\) | −15.7876 | −0.940137 | ||||||||
\(283\) | 17.1257 | 1.01802 | 0.509010 | − | 0.860761i | \(-0.330012\pi\) | ||||
0.509010 | + | 0.860761i | \(0.330012\pi\) | |||||||
\(284\) | 0.641025 | 0.0380379 | ||||||||
\(285\) | −11.9260 | −0.706434 | ||||||||
\(286\) | 13.1808 | 0.779396 | ||||||||
\(287\) | 12.0765 | 0.712854 | ||||||||
\(288\) | 3.22062 | 0.189777 | ||||||||
\(289\) | 30.4304 | 1.79002 | ||||||||
\(290\) | 11.1059 | 0.652164 | ||||||||
\(291\) | 17.9890 | 1.05453 | ||||||||
\(292\) | −8.54143 | −0.499849 | ||||||||
\(293\) | −1.28713 | −0.0751952 | −0.0375976 | − | 0.999293i | \(-0.511971\pi\) | ||||
−0.0375976 | + | 0.999293i | \(0.511971\pi\) | |||||||
\(294\) | 4.70261 | 0.274262 | ||||||||
\(295\) | −8.24067 | −0.479790 | ||||||||
\(296\) | 4.05981 | 0.235971 | ||||||||
\(297\) | 2.03810 | 0.118263 | ||||||||
\(298\) | 19.8344 | 1.14898 | ||||||||
\(299\) | 10.3373 | 0.597819 | ||||||||
\(300\) | 2.35343 | 0.135875 | ||||||||
\(301\) | −2.83400 | −0.163349 | ||||||||
\(302\) | −4.66734 | −0.268575 | ||||||||
\(303\) | 15.8518 | 0.910663 | ||||||||
\(304\) | 2.37414 | 0.136166 | ||||||||
\(305\) | 5.15460 | 0.295151 | ||||||||
\(306\) | 22.1803 | 1.26797 | ||||||||
\(307\) | −2.79331 | −0.159423 | −0.0797113 | − | 0.996818i | \(-0.525400\pi\) | ||||
−0.0797113 | + | 0.996818i | \(0.525400\pi\) | |||||||
\(308\) | −8.37642 | −0.477291 | ||||||||
\(309\) | 27.9745 | 1.59141 | ||||||||
\(310\) | −12.1893 | −0.692304 | ||||||||
\(311\) | −23.6621 | −1.34175 | −0.670877 | − | 0.741569i | \(-0.734082\pi\) | ||||
−0.670877 | + | 0.741569i | \(0.734082\pi\) | |||||||
\(312\) | 8.87569 | 0.502487 | ||||||||
\(313\) | 18.7782 | 1.06140 | 0.530702 | − | 0.847558i | \(-0.321928\pi\) | ||||
0.530702 | + | 0.847558i | \(0.321928\pi\) | |||||||
\(314\) | 21.6430 | 1.22139 | ||||||||
\(315\) | 14.6694 | 0.826529 | ||||||||
\(316\) | 2.47415 | 0.139182 | ||||||||
\(317\) | 22.9427 | 1.28859 | 0.644295 | − | 0.764777i | \(-0.277151\pi\) | ||||
0.644295 | + | 0.764777i | \(0.277151\pi\) | |||||||
\(318\) | −30.5087 | −1.71084 | ||||||||
\(319\) | −20.4240 | −1.14353 | ||||||||
\(320\) | 2.01405 | 0.112589 | ||||||||
\(321\) | 33.9657 | 1.89578 | ||||||||
\(322\) | −6.56935 | −0.366096 | ||||||||
\(323\) | 16.3506 | 0.909774 | ||||||||
\(324\) | −8.28945 | −0.460525 | ||||||||
\(325\) | 3.35791 | 0.186263 | ||||||||
\(326\) | 10.8339 | 0.600034 | ||||||||
\(327\) | −0.0597902 | −0.00330641 | ||||||||
\(328\) | 5.33998 | 0.294851 | ||||||||
\(329\) | 14.3153 | 0.789230 | ||||||||
\(330\) | 18.6056 | 1.02421 | ||||||||
\(331\) | 1.57418 | 0.0865249 | 0.0432625 | − | 0.999064i | \(-0.486225\pi\) | ||||
0.0432625 | + | 0.999064i | \(0.486225\pi\) | |||||||
\(332\) | 5.59401 | 0.307011 | ||||||||
\(333\) | 13.0751 | 0.716511 | ||||||||
\(334\) | 13.3377 | 0.729809 | ||||||||
\(335\) | 31.7034 | 1.73214 | ||||||||
\(336\) | −5.64052 | −0.307716 | ||||||||
\(337\) | −0.477872 | −0.0260313 | −0.0130157 | − | 0.999915i | \(-0.504143\pi\) | ||||
−0.0130157 | + | 0.999915i | \(0.504143\pi\) | |||||||
\(338\) | −0.336031 | −0.0182777 | ||||||||
\(339\) | −50.4715 | −2.74123 | ||||||||
\(340\) | 13.8707 | 0.752246 | ||||||||
\(341\) | 22.4162 | 1.21391 | ||||||||
\(342\) | 7.64621 | 0.413460 | ||||||||
\(343\) | −20.0948 | −1.08502 | ||||||||
\(344\) | −1.25313 | −0.0675644 | ||||||||
\(345\) | 14.5918 | 0.785595 | ||||||||
\(346\) | −22.9937 | −1.23615 | ||||||||
\(347\) | −20.1302 | −1.08064 | −0.540322 | − | 0.841458i | \(-0.681698\pi\) | ||||
−0.540322 | + | 0.841458i | \(0.681698\pi\) | |||||||
\(348\) | −13.7531 | −0.737246 | ||||||||
\(349\) | 15.7844 | 0.844920 | 0.422460 | − | 0.906382i | \(-0.361167\pi\) | ||||
0.422460 | + | 0.906382i | \(0.361167\pi\) | |||||||
\(350\) | −2.13396 | −0.114065 | ||||||||
\(351\) | 1.95819 | 0.104520 | ||||||||
\(352\) | −3.70387 | −0.197417 | ||||||||
\(353\) | 16.6971 | 0.888696 | 0.444348 | − | 0.895854i | \(-0.353435\pi\) | ||||
0.444348 | + | 0.895854i | \(0.353435\pi\) | |||||||
\(354\) | 10.2049 | 0.542384 | ||||||||
\(355\) | 1.29106 | 0.0685223 | ||||||||
\(356\) | 8.40142 | 0.445275 | ||||||||
\(357\) | −38.8461 | −2.05595 | ||||||||
\(358\) | 0.526188 | 0.0278099 | ||||||||
\(359\) | −28.5977 | −1.50933 | −0.754663 | − | 0.656112i | \(-0.772200\pi\) | ||||
−0.754663 | + | 0.656112i | \(0.772200\pi\) | |||||||
\(360\) | 6.48651 | 0.341869 | ||||||||
\(361\) | −13.3635 | −0.703340 | ||||||||
\(362\) | 22.4799 | 1.18152 | ||||||||
\(363\) | −6.78071 | −0.355895 | ||||||||
\(364\) | −8.04799 | −0.421829 | ||||||||
\(365\) | −17.2029 | −0.900441 | ||||||||
\(366\) | −6.38323 | −0.333657 | ||||||||
\(367\) | 1.18623 | 0.0619208 | 0.0309604 | − | 0.999521i | \(-0.490143\pi\) | ||||
0.0309604 | + | 0.999521i | \(0.490143\pi\) | |||||||
\(368\) | −2.90483 | −0.151425 | ||||||||
\(369\) | 17.1981 | 0.895295 | ||||||||
\(370\) | 8.17666 | 0.425084 | ||||||||
\(371\) | 27.6636 | 1.43622 | ||||||||
\(372\) | 15.0947 | 0.782622 | ||||||||
\(373\) | −2.98533 | −0.154574 | −0.0772872 | − | 0.997009i | \(-0.524626\pi\) | ||||
−0.0772872 | + | 0.997009i | \(0.524626\pi\) | |||||||
\(374\) | −25.5085 | −1.31901 | ||||||||
\(375\) | 29.8564 | 1.54178 | ||||||||
\(376\) | 6.32993 | 0.326441 | ||||||||
\(377\) | −19.6232 | −1.01065 | ||||||||
\(378\) | −1.24443 | −0.0640067 | ||||||||
\(379\) | 3.12466 | 0.160503 | 0.0802516 | − | 0.996775i | \(-0.474428\pi\) | ||||
0.0802516 | + | 0.996775i | \(0.474428\pi\) | |||||||
\(380\) | 4.78164 | 0.245293 | ||||||||
\(381\) | 39.3514 | 2.01603 | ||||||||
\(382\) | 11.3651 | 0.581489 | ||||||||
\(383\) | −9.08236 | −0.464087 | −0.232044 | − | 0.972705i | \(-0.574541\pi\) | ||||
−0.232044 | + | 0.972705i | \(0.574541\pi\) | |||||||
\(384\) | −2.49412 | −0.127277 | ||||||||
\(385\) | −16.8706 | −0.859803 | ||||||||
\(386\) | −6.87508 | −0.349932 | ||||||||
\(387\) | −4.03587 | −0.205155 | ||||||||
\(388\) | −7.21256 | −0.366162 | ||||||||
\(389\) | −28.3345 | −1.43661 | −0.718307 | − | 0.695726i | \(-0.755083\pi\) | ||||
−0.718307 | + | 0.695726i | \(0.755083\pi\) | |||||||
\(390\) | 17.8761 | 0.905191 | ||||||||
\(391\) | −20.0055 | −1.01172 | ||||||||
\(392\) | −1.88548 | −0.0952312 | ||||||||
\(393\) | 13.1467 | 0.663163 | ||||||||
\(394\) | 19.5956 | 0.987212 | ||||||||
\(395\) | 4.98306 | 0.250725 | ||||||||
\(396\) | −11.9288 | −0.599444 | ||||||||
\(397\) | 18.5496 | 0.930976 | 0.465488 | − | 0.885054i | \(-0.345879\pi\) | ||||
0.465488 | + | 0.885054i | \(0.345879\pi\) | |||||||
\(398\) | 21.9514 | 1.10032 | ||||||||
\(399\) | −13.3914 | −0.670408 | ||||||||
\(400\) | −0.943592 | −0.0471796 | ||||||||
\(401\) | −0.135001 | −0.00674164 | −0.00337082 | − | 0.999994i | \(-0.501073\pi\) | ||||
−0.00337082 | + | 0.999994i | \(0.501073\pi\) | |||||||
\(402\) | −39.2601 | −1.95812 | ||||||||
\(403\) | 21.5373 | 1.07285 | ||||||||
\(404\) | −6.35568 | −0.316207 | ||||||||
\(405\) | −16.6954 | −0.829601 | ||||||||
\(406\) | 12.4706 | 0.618905 | ||||||||
\(407\) | −15.0370 | −0.745357 | ||||||||
\(408\) | −17.1769 | −0.850384 | ||||||||
\(409\) | 25.1046 | 1.24134 | 0.620672 | − | 0.784070i | \(-0.286860\pi\) | ||||
0.620672 | + | 0.784070i | \(0.286860\pi\) | |||||||
\(410\) | 10.7550 | 0.531151 | ||||||||
\(411\) | −36.5576 | −1.80325 | ||||||||
\(412\) | −11.2162 | −0.552582 | ||||||||
\(413\) | −9.25325 | −0.455322 | ||||||||
\(414\) | −9.35536 | −0.459791 | ||||||||
\(415\) | 11.2666 | 0.553057 | ||||||||
\(416\) | −3.55865 | −0.174477 | ||||||||
\(417\) | −54.1672 | −2.65258 | ||||||||
\(418\) | −8.79352 | −0.430105 | ||||||||
\(419\) | 27.8624 | 1.36117 | 0.680585 | − | 0.732669i | \(-0.261726\pi\) | ||||
0.680585 | + | 0.732669i | \(0.261726\pi\) | |||||||
\(420\) | −11.3603 | −0.554326 | ||||||||
\(421\) | 20.2765 | 0.988215 | 0.494107 | − | 0.869401i | \(-0.335495\pi\) | ||||
0.494107 | + | 0.869401i | \(0.335495\pi\) | |||||||
\(422\) | 2.41930 | 0.117770 | ||||||||
\(423\) | 20.3863 | 0.991217 | ||||||||
\(424\) | 12.2322 | 0.594050 | ||||||||
\(425\) | −6.49849 | −0.315223 | ||||||||
\(426\) | −1.59879 | −0.0774618 | ||||||||
\(427\) | 5.78797 | 0.280099 | ||||||||
\(428\) | −13.6183 | −0.658267 | ||||||||
\(429\) | −32.8744 | −1.58719 | ||||||||
\(430\) | −2.52388 | −0.121712 | ||||||||
\(431\) | 17.8164 | 0.858183 | 0.429092 | − | 0.903261i | \(-0.358834\pi\) | ||||
0.429092 | + | 0.903261i | \(0.358834\pi\) | |||||||
\(432\) | −0.550262 | −0.0264745 | ||||||||
\(433\) | −36.7403 | −1.76563 | −0.882814 | − | 0.469722i | \(-0.844354\pi\) | ||||
−0.882814 | + | 0.469722i | \(0.844354\pi\) | |||||||
\(434\) | −13.6870 | −0.656998 | ||||||||
\(435\) | −27.6995 | −1.32809 | ||||||||
\(436\) | 0.0239725 | 0.00114807 | ||||||||
\(437\) | −6.89647 | −0.329903 | ||||||||
\(438\) | 21.3033 | 1.01791 | ||||||||
\(439\) | −27.3337 | −1.30456 | −0.652282 | − | 0.757976i | \(-0.726188\pi\) | ||||
−0.652282 | + | 0.757976i | \(0.726188\pi\) | |||||||
\(440\) | −7.45980 | −0.355632 | ||||||||
\(441\) | −6.07243 | −0.289163 | ||||||||
\(442\) | −24.5083 | −1.16574 | ||||||||
\(443\) | 11.9975 | 0.570020 | 0.285010 | − | 0.958524i | \(-0.408003\pi\) | ||||
0.285010 | + | 0.958524i | \(0.408003\pi\) | |||||||
\(444\) | −10.1256 | −0.480541 | ||||||||
\(445\) | 16.9209 | 0.802128 | ||||||||
\(446\) | 23.7336 | 1.12382 | ||||||||
\(447\) | −49.4694 | −2.33982 | ||||||||
\(448\) | 2.26153 | 0.106847 | ||||||||
\(449\) | −31.4885 | −1.48603 | −0.743017 | − | 0.669272i | \(-0.766606\pi\) | ||||
−0.743017 | + | 0.669272i | \(0.766606\pi\) | |||||||
\(450\) | −3.03895 | −0.143258 | ||||||||
\(451\) | −19.7786 | −0.931338 | ||||||||
\(452\) | 20.2362 | 0.951831 | ||||||||
\(453\) | 11.6409 | 0.546937 | ||||||||
\(454\) | 3.74598 | 0.175808 | ||||||||
\(455\) | −16.2091 | −0.759893 | ||||||||
\(456\) | −5.92139 | −0.277294 | ||||||||
\(457\) | −5.43642 | −0.254305 | −0.127153 | − | 0.991883i | \(-0.540584\pi\) | ||||
−0.127153 | + | 0.991883i | \(0.540584\pi\) | |||||||
\(458\) | −6.05569 | −0.282964 | ||||||||
\(459\) | −3.78964 | −0.176885 | ||||||||
\(460\) | −5.85048 | −0.272780 | ||||||||
\(461\) | −0.418075 | −0.0194717 | −0.00973585 | − | 0.999953i | \(-0.503099\pi\) | ||||
−0.00973585 | + | 0.999953i | \(0.503099\pi\) | |||||||
\(462\) | 20.8918 | 0.971974 | ||||||||
\(463\) | 2.04479 | 0.0950296 | 0.0475148 | − | 0.998871i | \(-0.484870\pi\) | ||||
0.0475148 | + | 0.998871i | \(0.484870\pi\) | |||||||
\(464\) | 5.51423 | 0.255992 | ||||||||
\(465\) | 30.4015 | 1.40983 | ||||||||
\(466\) | −4.78829 | −0.221813 | ||||||||
\(467\) | −35.7920 | −1.65626 | −0.828129 | − | 0.560538i | \(-0.810594\pi\) | ||||
−0.828129 | + | 0.560538i | \(0.810594\pi\) | |||||||
\(468\) | −11.4611 | −0.529788 | ||||||||
\(469\) | 35.5989 | 1.64381 | ||||||||
\(470\) | 12.7488 | 0.588059 | ||||||||
\(471\) | −53.9803 | −2.48728 | ||||||||
\(472\) | −4.09159 | −0.188331 | ||||||||
\(473\) | 4.64145 | 0.213414 | ||||||||
\(474\) | −6.17081 | −0.283435 | ||||||||
\(475\) | −2.24022 | −0.102788 | ||||||||
\(476\) | 15.5751 | 0.713883 | ||||||||
\(477\) | 39.3955 | 1.80379 | ||||||||
\(478\) | −23.7507 | −1.08633 | ||||||||
\(479\) | 4.99316 | 0.228143 | 0.114072 | − | 0.993473i | \(-0.463611\pi\) | ||||
0.114072 | + | 0.993473i | \(0.463611\pi\) | |||||||
\(480\) | −5.02328 | −0.229281 | ||||||||
\(481\) | −14.4474 | −0.658745 | ||||||||
\(482\) | 14.2155 | 0.647498 | ||||||||
\(483\) | 16.3847 | 0.745532 | ||||||||
\(484\) | 2.71868 | 0.123576 | ||||||||
\(485\) | −14.5265 | −0.659613 | ||||||||
\(486\) | 22.3257 | 1.01271 | ||||||||
\(487\) | −9.48550 | −0.429829 | −0.214915 | − | 0.976633i | \(-0.568947\pi\) | ||||
−0.214915 | + | 0.976633i | \(0.568947\pi\) | |||||||
\(488\) | 2.55932 | 0.115855 | ||||||||
\(489\) | −27.0210 | −1.22193 | ||||||||
\(490\) | −3.79746 | −0.171552 | ||||||||
\(491\) | 33.4510 | 1.50962 | 0.754811 | − | 0.655942i | \(-0.227729\pi\) | ||||
0.754811 | + | 0.655942i | \(0.227729\pi\) | |||||||
\(492\) | −13.3185 | −0.600446 | ||||||||
\(493\) | 37.9763 | 1.71037 | ||||||||
\(494\) | −8.44873 | −0.380126 | ||||||||
\(495\) | −24.0252 | −1.07985 | ||||||||
\(496\) | −6.05211 | −0.271748 | ||||||||
\(497\) | 1.44970 | 0.0650278 | ||||||||
\(498\) | −13.9521 | −0.625209 | ||||||||
\(499\) | 26.4188 | 1.18267 | 0.591334 | − | 0.806426i | \(-0.298601\pi\) | ||||
0.591334 | + | 0.806426i | \(0.298601\pi\) | |||||||
\(500\) | −11.9707 | −0.535346 | ||||||||
\(501\) | −33.2659 | −1.48621 | ||||||||
\(502\) | −0.0817027 | −0.00364657 | ||||||||
\(503\) | −34.0270 | −1.51719 | −0.758594 | − | 0.651564i | \(-0.774113\pi\) | ||||
−0.758594 | + | 0.651564i | \(0.774113\pi\) | |||||||
\(504\) | 7.28354 | 0.324435 | ||||||||
\(505\) | −12.8007 | −0.569623 | ||||||||
\(506\) | 10.7591 | 0.478301 | ||||||||
\(507\) | 0.838101 | 0.0372214 | ||||||||
\(508\) | −15.7777 | −0.700022 | ||||||||
\(509\) | 26.3595 | 1.16836 | 0.584182 | − | 0.811623i | \(-0.301415\pi\) | ||||
0.584182 | + | 0.811623i | \(0.301415\pi\) | |||||||
\(510\) | −34.5952 | −1.53190 | ||||||||
\(511\) | −19.3167 | −0.854521 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.30640 | −0.0576789 | ||||||||
\(514\) | −8.34170 | −0.367937 | ||||||||
\(515\) | −22.5900 | −0.995434 | ||||||||
\(516\) | 3.12546 | 0.137591 | ||||||||
\(517\) | −23.4453 | −1.03112 | ||||||||
\(518\) | 9.18137 | 0.403406 | ||||||||
\(519\) | 57.3489 | 2.51734 | ||||||||
\(520\) | −7.16730 | −0.314307 | ||||||||
\(521\) | −43.5700 | −1.90883 | −0.954417 | − | 0.298476i | \(-0.903522\pi\) | ||||
−0.954417 | + | 0.298476i | \(0.903522\pi\) | |||||||
\(522\) | 17.7593 | 0.777302 | ||||||||
\(523\) | −26.7780 | −1.17092 | −0.585461 | − | 0.810701i | \(-0.699086\pi\) | ||||
−0.585461 | + | 0.810701i | \(0.699086\pi\) | |||||||
\(524\) | −5.27108 | −0.230268 | ||||||||
\(525\) | 5.32235 | 0.232286 | ||||||||
\(526\) | −5.21436 | −0.227357 | ||||||||
\(527\) | −41.6807 | −1.81564 | ||||||||
\(528\) | 9.23790 | 0.402028 | ||||||||
\(529\) | −14.5620 | −0.633129 | ||||||||
\(530\) | 24.6364 | 1.07014 | ||||||||
\(531\) | −13.1775 | −0.571853 | ||||||||
\(532\) | 5.36919 | 0.232784 | ||||||||
\(533\) | −19.0031 | −0.823116 | ||||||||
\(534\) | −20.9541 | −0.906774 | ||||||||
\(535\) | −27.4280 | −1.18582 | ||||||||
\(536\) | 15.7411 | 0.679912 | ||||||||
\(537\) | −1.31238 | −0.0566332 | ||||||||
\(538\) | −8.22161 | −0.354459 | ||||||||
\(539\) | 6.98359 | 0.300804 | ||||||||
\(540\) | −1.10826 | −0.0476917 | ||||||||
\(541\) | −27.6992 | −1.19088 | −0.595441 | − | 0.803399i | \(-0.703023\pi\) | ||||
−0.595441 | + | 0.803399i | \(0.703023\pi\) | |||||||
\(542\) | −15.5448 | −0.667706 | ||||||||
\(543\) | −56.0676 | −2.40609 | ||||||||
\(544\) | 6.88697 | 0.295276 | ||||||||
\(545\) | 0.0482819 | 0.00206817 | ||||||||
\(546\) | 20.0726 | 0.859029 | ||||||||
\(547\) | −2.36790 | −0.101244 | −0.0506222 | − | 0.998718i | \(-0.516120\pi\) | ||||
−0.0506222 | + | 0.998718i | \(0.516120\pi\) | |||||||
\(548\) | 14.6575 | 0.626138 | ||||||||
\(549\) | 8.24259 | 0.351785 | ||||||||
\(550\) | 3.49494 | 0.149025 | ||||||||
\(551\) | 13.0916 | 0.557719 | ||||||||
\(552\) | 7.24498 | 0.308367 | ||||||||
\(553\) | 5.59536 | 0.237939 | ||||||||
\(554\) | −12.3455 | −0.524509 | ||||||||
\(555\) | −20.3936 | −0.865658 | ||||||||
\(556\) | 21.7180 | 0.921048 | ||||||||
\(557\) | −23.7533 | −1.00646 | −0.503231 | − | 0.864152i | \(-0.667855\pi\) | ||||
−0.503231 | + | 0.864152i | \(0.667855\pi\) | |||||||
\(558\) | −19.4916 | −0.825143 | ||||||||
\(559\) | 4.45946 | 0.188615 | ||||||||
\(560\) | 4.55484 | 0.192477 | ||||||||
\(561\) | 63.6211 | 2.68609 | ||||||||
\(562\) | 10.2175 | 0.430998 | ||||||||
\(563\) | −15.8021 | −0.665980 | −0.332990 | − | 0.942930i | \(-0.608058\pi\) | ||||
−0.332990 | + | 0.942930i | \(0.608058\pi\) | |||||||
\(564\) | −15.7876 | −0.664778 | ||||||||
\(565\) | 40.7568 | 1.71465 | ||||||||
\(566\) | 17.1257 | 0.719848 | ||||||||
\(567\) | −18.7468 | −0.787294 | ||||||||
\(568\) | 0.641025 | 0.0268968 | ||||||||
\(569\) | −9.81604 | −0.411510 | −0.205755 | − | 0.978604i | \(-0.565965\pi\) | ||||
−0.205755 | + | 0.978604i | \(0.565965\pi\) | |||||||
\(570\) | −11.9260 | −0.499525 | ||||||||
\(571\) | −23.6515 | −0.989785 | −0.494892 | − | 0.868954i | \(-0.664792\pi\) | ||||
−0.494892 | + | 0.868954i | \(0.664792\pi\) | |||||||
\(572\) | 13.1808 | 0.551116 | ||||||||
\(573\) | −28.3459 | −1.18417 | ||||||||
\(574\) | 12.0765 | 0.504064 | ||||||||
\(575\) | 2.74097 | 0.114306 | ||||||||
\(576\) | 3.22062 | 0.134193 | ||||||||
\(577\) | −12.9868 | −0.540646 | −0.270323 | − | 0.962770i | \(-0.587130\pi\) | ||||
−0.270323 | + | 0.962770i | \(0.587130\pi\) | |||||||
\(578\) | 30.4304 | 1.26574 | ||||||||
\(579\) | 17.1473 | 0.712616 | ||||||||
\(580\) | 11.1059 | 0.461149 | ||||||||
\(581\) | 12.6510 | 0.524852 | ||||||||
\(582\) | 17.9890 | 0.745667 | ||||||||
\(583\) | −45.3067 | −1.87641 | ||||||||
\(584\) | −8.54143 | −0.353447 | ||||||||
\(585\) | −23.0832 | −0.954372 | ||||||||
\(586\) | −1.28713 | −0.0531710 | ||||||||
\(587\) | 35.9740 | 1.48480 | 0.742402 | − | 0.669955i | \(-0.233686\pi\) | ||||
0.742402 | + | 0.669955i | \(0.233686\pi\) | |||||||
\(588\) | 4.70261 | 0.193933 | ||||||||
\(589\) | −14.3686 | −0.592046 | ||||||||
\(590\) | −8.24067 | −0.339263 | ||||||||
\(591\) | −48.8737 | −2.01040 | ||||||||
\(592\) | 4.05981 | 0.166857 | ||||||||
\(593\) | −6.08419 | −0.249848 | −0.124924 | − | 0.992166i | \(-0.539869\pi\) | ||||
−0.124924 | + | 0.992166i | \(0.539869\pi\) | |||||||
\(594\) | 2.03810 | 0.0836243 | ||||||||
\(595\) | 31.3691 | 1.28601 | ||||||||
\(596\) | 19.8344 | 0.812449 | ||||||||
\(597\) | −54.7493 | −2.24074 | ||||||||
\(598\) | 10.3373 | 0.422722 | ||||||||
\(599\) | 4.09711 | 0.167403 | 0.0837016 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0837016 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(600\) | 2.35343 | 0.0960783 | ||||||||
\(601\) | 40.1134 | 1.63626 | 0.818130 | − | 0.575033i | \(-0.195011\pi\) | ||||
0.818130 | + | 0.575033i | \(0.195011\pi\) | |||||||
\(602\) | −2.83400 | −0.115505 | ||||||||
\(603\) | 50.6961 | 2.06451 | ||||||||
\(604\) | −4.66734 | −0.189911 | ||||||||
\(605\) | 5.47557 | 0.222614 | ||||||||
\(606\) | 15.8518 | 0.643936 | ||||||||
\(607\) | −43.2460 | −1.75530 | −0.877652 | − | 0.479299i | \(-0.840891\pi\) | ||||
−0.877652 | + | 0.479299i | \(0.840891\pi\) | |||||||
\(608\) | 2.37414 | 0.0962841 | ||||||||
\(609\) | −31.1031 | −1.26036 | ||||||||
\(610\) | 5.15460 | 0.208704 | ||||||||
\(611\) | −22.5260 | −0.911304 | ||||||||
\(612\) | 22.1803 | 0.896587 | ||||||||
\(613\) | 20.9795 | 0.847356 | 0.423678 | − | 0.905813i | \(-0.360739\pi\) | ||||
0.423678 | + | 0.905813i | \(0.360739\pi\) | |||||||
\(614\) | −2.79331 | −0.112729 | ||||||||
\(615\) | −26.8242 | −1.08166 | ||||||||
\(616\) | −8.37642 | −0.337496 | ||||||||
\(617\) | 41.0688 | 1.65337 | 0.826684 | − | 0.562666i | \(-0.190224\pi\) | ||||
0.826684 | + | 0.562666i | \(0.190224\pi\) | |||||||
\(618\) | 27.9745 | 1.12530 | ||||||||
\(619\) | 35.2143 | 1.41538 | 0.707691 | − | 0.706522i | \(-0.249737\pi\) | ||||
0.707691 | + | 0.706522i | \(0.249737\pi\) | |||||||
\(620\) | −12.1893 | −0.489533 | ||||||||
\(621\) | 1.59842 | 0.0641422 | ||||||||
\(622\) | −23.6621 | −0.948763 | ||||||||
\(623\) | 19.0001 | 0.761222 | ||||||||
\(624\) | 8.87569 | 0.355312 | ||||||||
\(625\) | −19.3917 | −0.775667 | ||||||||
\(626\) | 18.7782 | 0.750526 | ||||||||
\(627\) | 21.9321 | 0.875882 | ||||||||
\(628\) | 21.6430 | 0.863652 | ||||||||
\(629\) | 27.9598 | 1.11483 | ||||||||
\(630\) | 14.6694 | 0.584444 | ||||||||
\(631\) | −19.4169 | −0.772975 | −0.386488 | − | 0.922295i | \(-0.626312\pi\) | ||||
−0.386488 | + | 0.922295i | \(0.626312\pi\) | |||||||
\(632\) | 2.47415 | 0.0984163 | ||||||||
\(633\) | −6.03401 | −0.239830 | ||||||||
\(634\) | 22.9427 | 0.911171 | ||||||||
\(635\) | −31.7771 | −1.26104 | ||||||||
\(636\) | −30.5087 | −1.20975 | ||||||||
\(637\) | 6.70977 | 0.265851 | ||||||||
\(638\) | −20.4240 | −0.808594 | ||||||||
\(639\) | 2.06450 | 0.0816704 | ||||||||
\(640\) | 2.01405 | 0.0796124 | ||||||||
\(641\) | 2.74610 | 0.108464 | 0.0542322 | − | 0.998528i | \(-0.482729\pi\) | ||||
0.0542322 | + | 0.998528i | \(0.482729\pi\) | |||||||
\(642\) | 33.9657 | 1.34052 | ||||||||
\(643\) | 20.4085 | 0.804833 | 0.402417 | − | 0.915457i | \(-0.368170\pi\) | ||||
0.402417 | + | 0.915457i | \(0.368170\pi\) | |||||||
\(644\) | −6.56935 | −0.258869 | ||||||||
\(645\) | 6.29485 | 0.247859 | ||||||||
\(646\) | 16.3506 | 0.643307 | ||||||||
\(647\) | −15.2695 | −0.600305 | −0.300152 | − | 0.953891i | \(-0.597038\pi\) | ||||
−0.300152 | + | 0.953891i | \(0.597038\pi\) | |||||||
\(648\) | −8.28945 | −0.325641 | ||||||||
\(649\) | 15.1547 | 0.594875 | ||||||||
\(650\) | 3.35791 | 0.131708 | ||||||||
\(651\) | 34.1370 | 1.33794 | ||||||||
\(652\) | 10.8339 | 0.424288 | ||||||||
\(653\) | −45.6646 | −1.78699 | −0.893497 | − | 0.449070i | \(-0.851755\pi\) | ||||
−0.893497 | + | 0.449070i | \(0.851755\pi\) | |||||||
\(654\) | −0.0597902 | −0.00233798 | ||||||||
\(655\) | −10.6162 | −0.414810 | ||||||||
\(656\) | 5.33998 | 0.208491 | ||||||||
\(657\) | −27.5087 | −1.07322 | ||||||||
\(658\) | 14.3153 | 0.558070 | ||||||||
\(659\) | 13.9482 | 0.543344 | 0.271672 | − | 0.962390i | \(-0.412423\pi\) | ||||
0.271672 | + | 0.962390i | \(0.412423\pi\) | |||||||
\(660\) | 18.6056 | 0.724223 | ||||||||
\(661\) | 30.9262 | 1.20289 | 0.601445 | − | 0.798914i | \(-0.294592\pi\) | ||||
0.601445 | + | 0.798914i | \(0.294592\pi\) | |||||||
\(662\) | 1.57418 | 0.0611824 | ||||||||
\(663\) | 61.1266 | 2.37396 | ||||||||
\(664\) | 5.59401 | 0.217090 | ||||||||
\(665\) | 10.8138 | 0.419342 | ||||||||
\(666\) | 13.0751 | 0.506650 | ||||||||
\(667\) | −16.0179 | −0.620215 | ||||||||
\(668\) | 13.3377 | 0.516053 | ||||||||
\(669\) | −59.1944 | −2.28859 | ||||||||
\(670\) | 31.7034 | 1.22481 | ||||||||
\(671\) | −9.47938 | −0.365947 | ||||||||
\(672\) | −5.64052 | −0.217588 | ||||||||
\(673\) | −9.57022 | −0.368905 | −0.184452 | − | 0.982841i | \(-0.559051\pi\) | ||||
−0.184452 | + | 0.982841i | \(0.559051\pi\) | |||||||
\(674\) | −0.477872 | −0.0184069 | ||||||||
\(675\) | 0.519222 | 0.0199849 | ||||||||
\(676\) | −0.336031 | −0.0129243 | ||||||||
\(677\) | −25.9543 | −0.997506 | −0.498753 | − | 0.866744i | \(-0.666209\pi\) | ||||
−0.498753 | + | 0.866744i | \(0.666209\pi\) | |||||||
\(678\) | −50.4715 | −1.93834 | ||||||||
\(679\) | −16.3114 | −0.625975 | ||||||||
\(680\) | 13.8707 | 0.531918 | ||||||||
\(681\) | −9.34291 | −0.358021 | ||||||||
\(682\) | 22.4162 | 0.858362 | ||||||||
\(683\) | −13.8477 | −0.529869 | −0.264935 | − | 0.964266i | \(-0.585350\pi\) | ||||
−0.264935 | + | 0.964266i | \(0.585350\pi\) | |||||||
\(684\) | 7.64621 | 0.292360 | ||||||||
\(685\) | 29.5210 | 1.12794 | ||||||||
\(686\) | −20.0948 | −0.767222 | ||||||||
\(687\) | 15.1036 | 0.576238 | ||||||||
\(688\) | −1.25313 | −0.0477753 | ||||||||
\(689\) | −43.5302 | −1.65837 | ||||||||
\(690\) | 14.5918 | 0.555499 | ||||||||
\(691\) | −31.2996 | −1.19069 | −0.595347 | − | 0.803469i | \(-0.702985\pi\) | ||||
−0.595347 | + | 0.803469i | \(0.702985\pi\) | |||||||
\(692\) | −22.9937 | −0.874088 | ||||||||
\(693\) | −26.9773 | −1.02478 | ||||||||
\(694\) | −20.1302 | −0.764131 | ||||||||
\(695\) | 43.7412 | 1.65920 | ||||||||
\(696\) | −13.7531 | −0.521311 | ||||||||
\(697\) | 36.7763 | 1.39300 | ||||||||
\(698\) | 15.7844 | 0.597449 | ||||||||
\(699\) | 11.9426 | 0.451709 | ||||||||
\(700\) | −2.13396 | −0.0806561 | ||||||||
\(701\) | −32.9107 | −1.24302 | −0.621510 | − | 0.783407i | \(-0.713480\pi\) | ||||
−0.621510 | + | 0.783407i | \(0.713480\pi\) | |||||||
\(702\) | 1.95819 | 0.0739070 | ||||||||
\(703\) | 9.63855 | 0.363525 | ||||||||
\(704\) | −3.70387 | −0.139595 | ||||||||
\(705\) | −31.7970 | −1.19755 | ||||||||
\(706\) | 16.6971 | 0.628403 | ||||||||
\(707\) | −14.3736 | −0.540574 | ||||||||
\(708\) | 10.2049 | 0.383524 | ||||||||
\(709\) | −16.5984 | −0.623366 | −0.311683 | − | 0.950186i | \(-0.600893\pi\) | ||||
−0.311683 | + | 0.950186i | \(0.600893\pi\) | |||||||
\(710\) | 1.29106 | 0.0484526 | ||||||||
\(711\) | 7.96830 | 0.298834 | ||||||||
\(712\) | 8.40142 | 0.314857 | ||||||||
\(713\) | 17.5803 | 0.658388 | ||||||||
\(714\) | −38.8461 | −1.45378 | ||||||||
\(715\) | 26.5468 | 0.992794 | ||||||||
\(716\) | 0.526188 | 0.0196646 | ||||||||
\(717\) | 59.2369 | 2.21224 | ||||||||
\(718\) | −28.5977 | −1.06726 | ||||||||
\(719\) | −46.7763 | −1.74446 | −0.872231 | − | 0.489094i | \(-0.837328\pi\) | ||||
−0.872231 | + | 0.489094i | \(0.837328\pi\) | |||||||
\(720\) | 6.48651 | 0.241738 | ||||||||
\(721\) | −25.3657 | −0.944669 | ||||||||
\(722\) | −13.3635 | −0.497336 | ||||||||
\(723\) | −35.4551 | −1.31859 | ||||||||
\(724\) | 22.4799 | 0.835460 | ||||||||
\(725\) | −5.20318 | −0.193241 | ||||||||
\(726\) | −6.78071 | −0.251656 | ||||||||
\(727\) | 9.39673 | 0.348505 | 0.174253 | − | 0.984701i | \(-0.444249\pi\) | ||||
0.174253 | + | 0.984701i | \(0.444249\pi\) | |||||||
\(728\) | −8.04799 | −0.298278 | ||||||||
\(729\) | −30.8145 | −1.14128 | ||||||||
\(730\) | −17.2029 | −0.636708 | ||||||||
\(731\) | −8.63029 | −0.319203 | ||||||||
\(732\) | −6.38323 | −0.235931 | ||||||||
\(733\) | 15.7585 | 0.582052 | 0.291026 | − | 0.956715i | \(-0.406003\pi\) | ||||
0.291026 | + | 0.956715i | \(0.406003\pi\) | |||||||
\(734\) | 1.18623 | 0.0437846 | ||||||||
\(735\) | 9.47131 | 0.349355 | ||||||||
\(736\) | −2.90483 | −0.107073 | ||||||||
\(737\) | −58.3030 | −2.14762 | ||||||||
\(738\) | 17.1981 | 0.633069 | ||||||||
\(739\) | 26.5556 | 0.976862 | 0.488431 | − | 0.872603i | \(-0.337569\pi\) | ||||
0.488431 | + | 0.872603i | \(0.337569\pi\) | |||||||
\(740\) | 8.17666 | 0.300580 | ||||||||
\(741\) | 21.0721 | 0.774104 | ||||||||
\(742\) | 27.6636 | 1.01556 | ||||||||
\(743\) | −26.2022 | −0.961267 | −0.480633 | − | 0.876922i | \(-0.659593\pi\) | ||||
−0.480633 | + | 0.876922i | \(0.659593\pi\) | |||||||
\(744\) | 15.0947 | 0.553397 | ||||||||
\(745\) | 39.9476 | 1.46357 | ||||||||
\(746\) | −2.98533 | −0.109301 | ||||||||
\(747\) | 18.0162 | 0.659178 | ||||||||
\(748\) | −25.5085 | −0.932682 | ||||||||
\(749\) | −30.7983 | −1.12534 | ||||||||
\(750\) | 29.8564 | 1.09020 | ||||||||
\(751\) | −28.1226 | −1.02621 | −0.513104 | − | 0.858326i | \(-0.671505\pi\) | ||||
−0.513104 | + | 0.858326i | \(0.671505\pi\) | |||||||
\(752\) | 6.32993 | 0.230829 | ||||||||
\(753\) | 0.203776 | 0.00742602 | ||||||||
\(754\) | −19.6232 | −0.714635 | ||||||||
\(755\) | −9.40027 | −0.342111 | ||||||||
\(756\) | −1.24443 | −0.0452596 | ||||||||
\(757\) | −31.8928 | −1.15916 | −0.579582 | − | 0.814914i | \(-0.696784\pi\) | ||||
−0.579582 | + | 0.814914i | \(0.696784\pi\) | |||||||
\(758\) | 3.12466 | 0.113493 | ||||||||
\(759\) | −26.8345 | −0.974031 | ||||||||
\(760\) | 4.78164 | 0.173448 | ||||||||
\(761\) | 8.87040 | 0.321552 | 0.160776 | − | 0.986991i | \(-0.448600\pi\) | ||||
0.160776 | + | 0.986991i | \(0.448600\pi\) | |||||||
\(762\) | 39.3514 | 1.42555 | ||||||||
\(763\) | 0.0542145 | 0.00196270 | ||||||||
\(764\) | 11.3651 | 0.411175 | ||||||||
\(765\) | 44.6724 | 1.61513 | ||||||||
\(766\) | −9.08236 | −0.328159 | ||||||||
\(767\) | 14.5605 | 0.525750 | ||||||||
\(768\) | −2.49412 | −0.0899987 | ||||||||
\(769\) | 0.145034 | 0.00523005 | 0.00261503 | − | 0.999997i | \(-0.499168\pi\) | ||||
0.00261503 | + | 0.999997i | \(0.499168\pi\) | |||||||
\(770\) | −16.8706 | −0.607973 | ||||||||
\(771\) | 20.8052 | 0.749280 | ||||||||
\(772\) | −6.87508 | −0.247440 | ||||||||
\(773\) | −28.1788 | −1.01352 | −0.506761 | − | 0.862086i | \(-0.669157\pi\) | ||||
−0.506761 | + | 0.862086i | \(0.669157\pi\) | |||||||
\(774\) | −4.03587 | −0.145066 | ||||||||
\(775\) | 5.71072 | 0.205135 | ||||||||
\(776\) | −7.21256 | −0.258916 | ||||||||
\(777\) | −22.8994 | −0.821512 | ||||||||
\(778\) | −28.3345 | −1.01584 | ||||||||
\(779\) | 12.6779 | 0.454231 | ||||||||
\(780\) | 17.8761 | 0.640067 | ||||||||
\(781\) | −2.37428 | −0.0849583 | ||||||||
\(782\) | −20.0055 | −0.715394 | ||||||||
\(783\) | −3.03427 | −0.108436 | ||||||||
\(784\) | −1.88548 | −0.0673386 | ||||||||
\(785\) | 43.5902 | 1.55580 | ||||||||
\(786\) | 13.1467 | 0.468927 | ||||||||
\(787\) | −4.62878 | −0.164998 | −0.0824990 | − | 0.996591i | \(-0.526290\pi\) | ||||
−0.0824990 | + | 0.996591i | \(0.526290\pi\) | |||||||
\(788\) | 19.5956 | 0.698064 | ||||||||
\(789\) | 13.0052 | 0.462998 | ||||||||
\(790\) | 4.98306 | 0.177289 | ||||||||
\(791\) | 45.7648 | 1.62721 | ||||||||
\(792\) | −11.9288 | −0.423871 | ||||||||
\(793\) | −9.10770 | −0.323424 | ||||||||
\(794\) | 18.5496 | 0.658299 | ||||||||
\(795\) | −61.4460 | −2.17927 | ||||||||
\(796\) | 21.9514 | 0.778045 | ||||||||
\(797\) | 23.3111 | 0.825721 | 0.412861 | − | 0.910794i | \(-0.364530\pi\) | ||||
0.412861 | + | 0.910794i | \(0.364530\pi\) | |||||||
\(798\) | −13.3914 | −0.474050 | ||||||||
\(799\) | 43.5941 | 1.54225 | ||||||||
\(800\) | −0.943592 | −0.0333610 | ||||||||
\(801\) | 27.0578 | 0.956041 | ||||||||
\(802\) | −0.135001 | −0.00476706 | ||||||||
\(803\) | 31.6364 | 1.11642 | ||||||||
\(804\) | −39.2601 | −1.38460 | ||||||||
\(805\) | −13.2310 | −0.466332 | ||||||||
\(806\) | 21.5373 | 0.758619 | ||||||||
\(807\) | 20.5057 | 0.721833 | ||||||||
\(808\) | −6.35568 | −0.223592 | ||||||||
\(809\) | 3.93721 | 0.138425 | 0.0692125 | − | 0.997602i | \(-0.477951\pi\) | ||||
0.0692125 | + | 0.997602i | \(0.477951\pi\) | |||||||
\(810\) | −16.6954 | −0.586616 | ||||||||
\(811\) | −8.77345 | −0.308077 | −0.154039 | − | 0.988065i | \(-0.549228\pi\) | ||||
−0.154039 | + | 0.988065i | \(0.549228\pi\) | |||||||
\(812\) | 12.4706 | 0.437632 | ||||||||
\(813\) | 38.7706 | 1.35974 | ||||||||
\(814\) | −15.0370 | −0.527047 | ||||||||
\(815\) | 21.8200 | 0.764322 | ||||||||
\(816\) | −17.1769 | −0.601312 | ||||||||
\(817\) | −2.97511 | −0.104086 | ||||||||
\(818\) | 25.1046 | 0.877763 | ||||||||
\(819\) | −25.9195 | −0.905702 | ||||||||
\(820\) | 10.7550 | 0.375581 | ||||||||
\(821\) | 0.517055 | 0.0180453 | 0.00902267 | − | 0.999959i | \(-0.497128\pi\) | ||||
0.00902267 | + | 0.999959i | \(0.497128\pi\) | |||||||
\(822\) | −36.5576 | −1.27509 | ||||||||
\(823\) | 16.0261 | 0.558636 | 0.279318 | − | 0.960199i | \(-0.409892\pi\) | ||||
0.279318 | + | 0.960199i | \(0.409892\pi\) | |||||||
\(824\) | −11.2162 | −0.390734 | ||||||||
\(825\) | −8.71680 | −0.303480 | ||||||||
\(826\) | −9.25325 | −0.321962 | ||||||||
\(827\) | −49.1062 | −1.70759 | −0.853795 | − | 0.520609i | \(-0.825705\pi\) | ||||
−0.853795 | + | 0.520609i | \(0.825705\pi\) | |||||||
\(828\) | −9.35536 | −0.325121 | ||||||||
\(829\) | −33.7931 | −1.17368 | −0.586841 | − | 0.809702i | \(-0.699629\pi\) | ||||
−0.586841 | + | 0.809702i | \(0.699629\pi\) | |||||||
\(830\) | 11.2666 | 0.391070 | ||||||||
\(831\) | 30.7911 | 1.06813 | ||||||||
\(832\) | −3.55865 | −0.123374 | ||||||||
\(833\) | −12.9853 | −0.449913 | ||||||||
\(834\) | −54.1672 | −1.87566 | ||||||||
\(835\) | 26.8629 | 0.929630 | ||||||||
\(836\) | −8.79352 | −0.304130 | ||||||||
\(837\) | 3.33024 | 0.115110 | ||||||||
\(838\) | 27.8624 | 0.962492 | ||||||||
\(839\) | 47.4779 | 1.63912 | 0.819559 | − | 0.572994i | \(-0.194218\pi\) | ||||
0.819559 | + | 0.572994i | \(0.194218\pi\) | |||||||
\(840\) | −11.3603 | −0.391968 | ||||||||
\(841\) | 1.40673 | 0.0485078 | ||||||||
\(842\) | 20.2765 | 0.698773 | ||||||||
\(843\) | −25.4836 | −0.877700 | ||||||||
\(844\) | 2.41930 | 0.0832757 | ||||||||
\(845\) | −0.676784 | −0.0232821 | ||||||||
\(846\) | 20.3863 | 0.700896 | ||||||||
\(847\) | 6.14838 | 0.211261 | ||||||||
\(848\) | 12.2322 | 0.420057 | ||||||||
\(849\) | −42.7136 | −1.46593 | ||||||||
\(850\) | −6.49849 | −0.222896 | ||||||||
\(851\) | −11.7930 | −0.404260 | ||||||||
\(852\) | −1.59879 | −0.0547737 | ||||||||
\(853\) | −32.2823 | −1.10533 | −0.552663 | − | 0.833405i | \(-0.686388\pi\) | ||||
−0.552663 | + | 0.833405i | \(0.686388\pi\) | |||||||
\(854\) | 5.78797 | 0.198060 | ||||||||
\(855\) | 15.3999 | 0.526665 | ||||||||
\(856\) | −13.6183 | −0.465465 | ||||||||
\(857\) | −8.60550 | −0.293958 | −0.146979 | − | 0.989140i | \(-0.546955\pi\) | ||||
−0.146979 | + | 0.989140i | \(0.546955\pi\) | |||||||
\(858\) | −32.8744 | −1.12231 | ||||||||
\(859\) | −34.7924 | −1.18710 | −0.593551 | − | 0.804797i | \(-0.702274\pi\) | ||||
−0.593551 | + | 0.804797i | \(0.702274\pi\) | |||||||
\(860\) | −2.52388 | −0.0860635 | ||||||||
\(861\) | −30.1203 | −1.02650 | ||||||||
\(862\) | 17.8164 | 0.606827 | ||||||||
\(863\) | 1.13842 | 0.0387522 | 0.0193761 | − | 0.999812i | \(-0.493832\pi\) | ||||
0.0193761 | + | 0.999812i | \(0.493832\pi\) | |||||||
\(864\) | −0.550262 | −0.0187203 | ||||||||
\(865\) | −46.3105 | −1.57460 | ||||||||
\(866\) | −36.7403 | −1.24849 | ||||||||
\(867\) | −75.8970 | −2.57760 | ||||||||
\(868\) | −13.6870 | −0.464568 | ||||||||
\(869\) | −9.16393 | −0.310865 | ||||||||
\(870\) | −27.6995 | −0.939103 | ||||||||
\(871\) | −56.0170 | −1.89806 | ||||||||
\(872\) | 0.0239725 | 0.000811811 0 | ||||||||
\(873\) | −23.2289 | −0.786180 | ||||||||
\(874\) | −6.89647 | −0.233277 | ||||||||
\(875\) | −27.0721 | −0.915204 | ||||||||
\(876\) | 21.3033 | 0.719773 | ||||||||
\(877\) | 31.2059 | 1.05375 | 0.526874 | − | 0.849943i | \(-0.323364\pi\) | ||||
0.526874 | + | 0.849943i | \(0.323364\pi\) | |||||||
\(878\) | −27.3337 | −0.922466 | ||||||||
\(879\) | 3.21026 | 0.108280 | ||||||||
\(880\) | −7.45980 | −0.251470 | ||||||||
\(881\) | 25.7583 | 0.867820 | 0.433910 | − | 0.900956i | \(-0.357134\pi\) | ||||
0.433910 | + | 0.900956i | \(0.357134\pi\) | |||||||
\(882\) | −6.07243 | −0.204469 | ||||||||
\(883\) | −45.0254 | −1.51523 | −0.757613 | − | 0.652704i | \(-0.773635\pi\) | ||||
−0.757613 | + | 0.652704i | \(0.773635\pi\) | |||||||
\(884\) | −24.5083 | −0.824303 | ||||||||
\(885\) | 20.5532 | 0.690888 | ||||||||
\(886\) | 11.9975 | 0.403065 | ||||||||
\(887\) | 0.401785 | 0.0134906 | 0.00674530 | − | 0.999977i | \(-0.497853\pi\) | ||||
0.00674530 | + | 0.999977i | \(0.497853\pi\) | |||||||
\(888\) | −10.1256 | −0.339794 | ||||||||
\(889\) | −35.6817 | −1.19673 | ||||||||
\(890\) | 16.9209 | 0.567190 | ||||||||
\(891\) | 30.7031 | 1.02859 | ||||||||
\(892\) | 23.7336 | 0.794660 | ||||||||
\(893\) | 15.0281 | 0.502898 | ||||||||
\(894\) | −49.4694 | −1.65450 | ||||||||
\(895\) | 1.05977 | 0.0354242 | ||||||||
\(896\) | 2.26153 | 0.0755524 | ||||||||
\(897\) | −25.7823 | −0.860847 | ||||||||
\(898\) | −31.4885 | −1.05079 | ||||||||
\(899\) | −33.3727 | −1.11304 | ||||||||
\(900\) | −3.03895 | −0.101298 | ||||||||
\(901\) | 84.2431 | 2.80655 | ||||||||
\(902\) | −19.7786 | −0.658556 | ||||||||
\(903\) | 7.06833 | 0.235219 | ||||||||
\(904\) | 20.2362 | 0.673046 | ||||||||
\(905\) | 45.2758 | 1.50502 | ||||||||
\(906\) | 11.6409 | 0.386743 | ||||||||
\(907\) | −46.5912 | −1.54704 | −0.773518 | − | 0.633775i | \(-0.781505\pi\) | ||||
−0.773518 | + | 0.633775i | \(0.781505\pi\) | |||||||
\(908\) | 3.74598 | 0.124315 | ||||||||
\(909\) | −20.4693 | −0.678923 | ||||||||
\(910\) | −16.2091 | −0.537325 | ||||||||
\(911\) | 21.6758 | 0.718152 | 0.359076 | − | 0.933308i | \(-0.383092\pi\) | ||||
0.359076 | + | 0.933308i | \(0.383092\pi\) | |||||||
\(912\) | −5.92139 | −0.196077 | ||||||||
\(913\) | −20.7195 | −0.685715 | ||||||||
\(914\) | −5.43642 | −0.179821 | ||||||||
\(915\) | −12.8562 | −0.425012 | ||||||||
\(916\) | −6.05569 | −0.200085 | ||||||||
\(917\) | −11.9207 | −0.393656 | ||||||||
\(918\) | −3.78964 | −0.125077 | ||||||||
\(919\) | −28.2429 | −0.931646 | −0.465823 | − | 0.884878i | \(-0.654242\pi\) | ||||
−0.465823 | + | 0.884878i | \(0.654242\pi\) | |||||||
\(920\) | −5.85048 | −0.192884 | ||||||||
\(921\) | 6.96684 | 0.229565 | ||||||||
\(922\) | −0.418075 | −0.0137686 | ||||||||
\(923\) | −2.28118 | −0.0750861 | ||||||||
\(924\) | 20.8918 | 0.687289 | ||||||||
\(925\) | −3.83080 | −0.125956 | ||||||||
\(926\) | 2.04479 | 0.0671960 | ||||||||
\(927\) | −36.1231 | −1.18644 | ||||||||
\(928\) | 5.51423 | 0.181013 | ||||||||
\(929\) | 42.2378 | 1.38578 | 0.692888 | − | 0.721045i | \(-0.256338\pi\) | ||||
0.692888 | + | 0.721045i | \(0.256338\pi\) | |||||||
\(930\) | 30.4015 | 0.996903 | ||||||||
\(931\) | −4.47640 | −0.146708 | ||||||||
\(932\) | −4.78829 | −0.156846 | ||||||||
\(933\) | 59.0160 | 1.93210 | ||||||||
\(934\) | −35.7920 | −1.17115 | ||||||||
\(935\) | −51.3754 | −1.68016 | ||||||||
\(936\) | −11.4611 | −0.374617 | ||||||||
\(937\) | 13.3743 | 0.436918 | 0.218459 | − | 0.975846i | \(-0.429897\pi\) | ||||
0.218459 | + | 0.975846i | \(0.429897\pi\) | |||||||
\(938\) | 35.5989 | 1.16235 | ||||||||
\(939\) | −46.8349 | −1.52840 | ||||||||
\(940\) | 12.7488 | 0.415820 | ||||||||
\(941\) | −5.34684 | −0.174302 | −0.0871510 | − | 0.996195i | \(-0.527776\pi\) | ||||
−0.0871510 | + | 0.996195i | \(0.527776\pi\) | |||||||
\(942\) | −53.9803 | −1.75877 | ||||||||
\(943\) | −15.5117 | −0.505131 | ||||||||
\(944\) | −4.09159 | −0.133170 | ||||||||
\(945\) | −2.50635 | −0.0815317 | ||||||||
\(946\) | 4.64145 | 0.150906 | ||||||||
\(947\) | −47.3436 | −1.53846 | −0.769231 | − | 0.638971i | \(-0.779360\pi\) | ||||
−0.769231 | + | 0.638971i | \(0.779360\pi\) | |||||||
\(948\) | −6.17081 | −0.200419 | ||||||||
\(949\) | 30.3959 | 0.986694 | ||||||||
\(950\) | −2.24022 | −0.0726823 | ||||||||
\(951\) | −57.2218 | −1.85554 | ||||||||
\(952\) | 15.5751 | 0.504792 | ||||||||
\(953\) | −25.1830 | −0.815757 | −0.407879 | − | 0.913036i | \(-0.633731\pi\) | ||||
−0.407879 | + | 0.913036i | \(0.633731\pi\) | |||||||
\(954\) | 39.3955 | 1.27547 | ||||||||
\(955\) | 22.8899 | 0.740700 | ||||||||
\(956\) | −23.7507 | −0.768151 | ||||||||
\(957\) | 50.9399 | 1.64665 | ||||||||
\(958\) | 4.99316 | 0.161322 | ||||||||
\(959\) | 33.1484 | 1.07042 | ||||||||
\(960\) | −5.02328 | −0.162126 | ||||||||
\(961\) | 5.62799 | 0.181548 | ||||||||
\(962\) | −14.4474 | −0.465803 | ||||||||
\(963\) | −43.8595 | −1.41335 | ||||||||
\(964\) | 14.2155 | 0.457850 | ||||||||
\(965\) | −13.8468 | −0.445743 | ||||||||
\(966\) | 16.3847 | 0.527171 | ||||||||
\(967\) | −18.1464 | −0.583549 | −0.291775 | − | 0.956487i | \(-0.594246\pi\) | ||||
−0.291775 | + | 0.956487i | \(0.594246\pi\) | |||||||
\(968\) | 2.71868 | 0.0873818 | ||||||||
\(969\) | −40.7804 | −1.31006 | ||||||||
\(970\) | −14.5265 | −0.466417 | ||||||||
\(971\) | −21.7629 | −0.698406 | −0.349203 | − | 0.937047i | \(-0.613548\pi\) | ||||
−0.349203 | + | 0.937047i | \(0.613548\pi\) | |||||||
\(972\) | 22.3257 | 0.716096 | ||||||||
\(973\) | 49.1159 | 1.57458 | ||||||||
\(974\) | −9.48550 | −0.303935 | ||||||||
\(975\) | −8.37502 | −0.268215 | ||||||||
\(976\) | 2.55932 | 0.0819217 | ||||||||
\(977\) | 2.63198 | 0.0842045 | 0.0421023 | − | 0.999113i | \(-0.486594\pi\) | ||||
0.0421023 | + | 0.999113i | \(0.486594\pi\) | |||||||
\(978\) | −27.0210 | −0.864036 | ||||||||
\(979\) | −31.1178 | −0.994530 | ||||||||
\(980\) | −3.79746 | −0.121305 | ||||||||
\(981\) | 0.0772064 | 0.00246501 | ||||||||
\(982\) | 33.4510 | 1.06746 | ||||||||
\(983\) | 48.1572 | 1.53598 | 0.767988 | − | 0.640464i | \(-0.221258\pi\) | ||||
0.767988 | + | 0.640464i | \(0.221258\pi\) | |||||||
\(984\) | −13.3185 | −0.424579 | ||||||||
\(985\) | 39.4666 | 1.25751 | ||||||||
\(986\) | 37.9763 | 1.20941 | ||||||||
\(987\) | −35.7041 | −1.13647 | ||||||||
\(988\) | −8.44873 | −0.268790 | ||||||||
\(989\) | 3.64014 | 0.115750 | ||||||||
\(990\) | −24.0252 | −0.763571 | ||||||||
\(991\) | −0.147273 | −0.00467829 | −0.00233914 | − | 0.999997i | \(-0.500745\pi\) | ||||
−0.00233914 | + | 0.999997i | \(0.500745\pi\) | |||||||
\(992\) | −6.05211 | −0.192155 | ||||||||
\(993\) | −3.92620 | −0.124594 | ||||||||
\(994\) | 1.44970 | 0.0459816 | ||||||||
\(995\) | 44.2112 | 1.40159 | ||||||||
\(996\) | −13.9521 | −0.442089 | ||||||||
\(997\) | −26.1014 | −0.826639 | −0.413319 | − | 0.910586i | \(-0.635631\pi\) | ||||
−0.413319 | + | 0.910586i | \(0.635631\pi\) | |||||||
\(998\) | 26.4188 | 0.836273 | ||||||||
\(999\) | −2.23396 | −0.0706792 |
(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 | 4034.2.a.d.1.8 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.d.1.8 | ✓ | 52 | 1.1 | even | 1 | trivial |