Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0648705 | −0.0458704 | −0.0229352 | − | 0.999737i | \(-0.507301\pi\) | ||||
−0.0229352 | + | 0.999737i | \(0.507301\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.99579 | −0.997896 | ||||||||
\(5\) | 0.118616 | 0.0530467 | 0.0265233 | − | 0.999648i | \(-0.491556\pi\) | ||||
0.0265233 | + | 0.999648i | \(0.491556\pi\) | |||||||
\(6\) | 0.0648705 | 0.0264833 | ||||||||
\(7\) | −4.97378 | −1.87991 | −0.939956 | − | 0.341297i | \(-0.889134\pi\) | ||||
−0.939956 | + | 0.341297i | \(0.889134\pi\) | |||||||
\(8\) | 0.259209 | 0.0916443 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.00769468 | −0.00243327 | ||||||||
\(11\) | −4.34142 | −1.30899 | −0.654494 | − | 0.756067i | \(-0.727118\pi\) | ||||
−0.654494 | + | 0.756067i | \(0.727118\pi\) | |||||||
\(12\) | 1.99579 | 0.576135 | ||||||||
\(13\) | 3.46263 | 0.960360 | 0.480180 | − | 0.877170i | \(-0.340571\pi\) | ||||
0.480180 | + | 0.877170i | \(0.340571\pi\) | |||||||
\(14\) | 0.322652 | 0.0862323 | ||||||||
\(15\) | −0.118616 | −0.0306265 | ||||||||
\(16\) | 3.97477 | 0.993692 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.0648705 | −0.0152901 | ||||||||
\(19\) | −0.806909 | −0.185118 | −0.0925588 | − | 0.995707i | \(-0.529505\pi\) | ||||
−0.0925588 | + | 0.995707i | \(0.529505\pi\) | |||||||
\(20\) | −0.236733 | −0.0529350 | ||||||||
\(21\) | 4.97378 | 1.08537 | ||||||||
\(22\) | 0.281631 | 0.0600438 | ||||||||
\(23\) | 5.73717 | 1.19628 | 0.598141 | − | 0.801391i | \(-0.295906\pi\) | ||||
0.598141 | + | 0.801391i | \(0.295906\pi\) | |||||||
\(24\) | −0.259209 | −0.0529109 | ||||||||
\(25\) | −4.98593 | −0.997186 | ||||||||
\(26\) | −0.224623 | −0.0440521 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 9.92662 | 1.87596 | ||||||||
\(29\) | −6.51973 | −1.21068 | −0.605342 | − | 0.795965i | \(-0.706964\pi\) | ||||
−0.605342 | + | 0.795965i | \(0.706964\pi\) | |||||||
\(30\) | 0.00769468 | 0.00140485 | ||||||||
\(31\) | −2.26114 | −0.406113 | −0.203056 | − | 0.979167i | \(-0.565087\pi\) | ||||
−0.203056 | + | 0.979167i | \(0.565087\pi\) | |||||||
\(32\) | −0.776264 | −0.137225 | ||||||||
\(33\) | 4.34142 | 0.755745 | ||||||||
\(34\) | 0.0648705 | 0.0111252 | ||||||||
\(35\) | −0.589969 | −0.0997230 | ||||||||
\(36\) | −1.99579 | −0.332632 | ||||||||
\(37\) | −2.01285 | −0.330910 | −0.165455 | − | 0.986217i | \(-0.552909\pi\) | ||||
−0.165455 | + | 0.986217i | \(0.552909\pi\) | |||||||
\(38\) | 0.0523446 | 0.00849142 | ||||||||
\(39\) | −3.46263 | −0.554464 | ||||||||
\(40\) | 0.0307463 | 0.00486142 | ||||||||
\(41\) | 6.33093 | 0.988725 | 0.494363 | − | 0.869256i | \(-0.335401\pi\) | ||||
0.494363 | + | 0.869256i | \(0.335401\pi\) | |||||||
\(42\) | −0.322652 | −0.0497862 | ||||||||
\(43\) | 3.21798 | 0.490738 | 0.245369 | − | 0.969430i | \(-0.421091\pi\) | ||||
0.245369 | + | 0.969430i | \(0.421091\pi\) | |||||||
\(44\) | 8.66458 | 1.30623 | ||||||||
\(45\) | 0.118616 | 0.0176822 | ||||||||
\(46\) | −0.372173 | −0.0548740 | ||||||||
\(47\) | 9.60026 | 1.40034 | 0.700171 | − | 0.713975i | \(-0.253107\pi\) | ||||
0.700171 | + | 0.713975i | \(0.253107\pi\) | |||||||
\(48\) | −3.97477 | −0.573708 | ||||||||
\(49\) | 17.7385 | 2.53407 | ||||||||
\(50\) | 0.323440 | 0.0457413 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −6.91069 | −0.958340 | ||||||||
\(53\) | −10.1285 | −1.39125 | −0.695627 | − | 0.718403i | \(-0.744873\pi\) | ||||
−0.695627 | + | 0.718403i | \(0.744873\pi\) | |||||||
\(54\) | 0.0648705 | 0.00882776 | ||||||||
\(55\) | −0.514962 | −0.0694375 | ||||||||
\(56\) | −1.28925 | −0.172283 | ||||||||
\(57\) | 0.806909 | 0.106878 | ||||||||
\(58\) | 0.422939 | 0.0555346 | ||||||||
\(59\) | 2.31048 | 0.300799 | 0.150399 | − | 0.988625i | \(-0.451944\pi\) | ||||
0.150399 | + | 0.988625i | \(0.451944\pi\) | |||||||
\(60\) | 0.236733 | 0.0305621 | ||||||||
\(61\) | −7.66422 | −0.981303 | −0.490652 | − | 0.871356i | \(-0.663241\pi\) | ||||
−0.490652 | + | 0.871356i | \(0.663241\pi\) | |||||||
\(62\) | 0.146681 | 0.0186286 | ||||||||
\(63\) | −4.97378 | −0.626637 | ||||||||
\(64\) | −7.89918 | −0.987398 | ||||||||
\(65\) | 0.410723 | 0.0509439 | ||||||||
\(66\) | −0.281631 | −0.0346663 | ||||||||
\(67\) | 8.05732 | 0.984358 | 0.492179 | − | 0.870494i | \(-0.336200\pi\) | ||||
0.492179 | + | 0.870494i | \(0.336200\pi\) | |||||||
\(68\) | 1.99579 | 0.242025 | ||||||||
\(69\) | −5.73717 | −0.690674 | ||||||||
\(70\) | 0.0382716 | 0.00457433 | ||||||||
\(71\) | 11.9634 | 1.41979 | 0.709897 | − | 0.704305i | \(-0.248741\pi\) | ||||
0.709897 | + | 0.704305i | \(0.248741\pi\) | |||||||
\(72\) | 0.259209 | 0.0305481 | ||||||||
\(73\) | 5.38589 | 0.630371 | 0.315185 | − | 0.949030i | \(-0.397933\pi\) | ||||
0.315185 | + | 0.949030i | \(0.397933\pi\) | |||||||
\(74\) | 0.130575 | 0.0151790 | ||||||||
\(75\) | 4.98593 | 0.575726 | ||||||||
\(76\) | 1.61042 | 0.184728 | ||||||||
\(77\) | 21.5933 | 2.46078 | ||||||||
\(78\) | 0.224623 | 0.0254335 | ||||||||
\(79\) | 9.95475 | 1.12000 | 0.559998 | − | 0.828494i | \(-0.310802\pi\) | ||||
0.559998 | + | 0.828494i | \(0.310802\pi\) | |||||||
\(80\) | 0.471471 | 0.0527120 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.410691 | −0.0453532 | ||||||||
\(83\) | 11.4537 | 1.25721 | 0.628603 | − | 0.777726i | \(-0.283627\pi\) | ||||
0.628603 | + | 0.777726i | \(0.283627\pi\) | |||||||
\(84\) | −9.92662 | −1.08308 | ||||||||
\(85\) | −0.118616 | −0.0128657 | ||||||||
\(86\) | −0.208752 | −0.0225103 | ||||||||
\(87\) | 6.51973 | 0.698989 | ||||||||
\(88\) | −1.12534 | −0.119961 | ||||||||
\(89\) | −10.1718 | −1.07821 | −0.539103 | − | 0.842240i | \(-0.681237\pi\) | ||||
−0.539103 | + | 0.842240i | \(0.681237\pi\) | |||||||
\(90\) | −0.00769468 | −0.000811090 0 | ||||||||
\(91\) | −17.2223 | −1.80539 | ||||||||
\(92\) | −11.4502 | −1.19377 | ||||||||
\(93\) | 2.26114 | 0.234469 | ||||||||
\(94\) | −0.622774 | −0.0642342 | ||||||||
\(95\) | −0.0957122 | −0.00981987 | ||||||||
\(96\) | 0.776264 | 0.0792271 | ||||||||
\(97\) | −8.31464 | −0.844224 | −0.422112 | − | 0.906544i | \(-0.638711\pi\) | ||||
−0.422112 | + | 0.906544i | \(0.638711\pi\) | |||||||
\(98\) | −1.15070 | −0.116239 | ||||||||
\(99\) | −4.34142 | −0.436330 | ||||||||
\(100\) | 9.95088 | 0.995088 | ||||||||
\(101\) | 7.93840 | 0.789900 | 0.394950 | − | 0.918703i | \(-0.370762\pi\) | ||||
0.394950 | + | 0.918703i | \(0.370762\pi\) | |||||||
\(102\) | −0.0648705 | −0.00642314 | ||||||||
\(103\) | 12.0039 | 1.18277 | 0.591387 | − | 0.806388i | \(-0.298580\pi\) | ||||
0.591387 | + | 0.806388i | \(0.298580\pi\) | |||||||
\(104\) | 0.897545 | 0.0880115 | ||||||||
\(105\) | 0.589969 | 0.0575751 | ||||||||
\(106\) | 0.657040 | 0.0638174 | ||||||||
\(107\) | −4.01437 | −0.388084 | −0.194042 | − | 0.980993i | \(-0.562160\pi\) | ||||
−0.194042 | + | 0.980993i | \(0.562160\pi\) | |||||||
\(108\) | 1.99579 | 0.192045 | ||||||||
\(109\) | 6.05499 | 0.579963 | 0.289982 | − | 0.957032i | \(-0.406351\pi\) | ||||
0.289982 | + | 0.957032i | \(0.406351\pi\) | |||||||
\(110\) | 0.0334059 | 0.00318512 | ||||||||
\(111\) | 2.01285 | 0.191051 | ||||||||
\(112\) | −19.7696 | −1.86805 | ||||||||
\(113\) | −2.48475 | −0.233745 | −0.116873 | − | 0.993147i | \(-0.537287\pi\) | ||||
−0.116873 | + | 0.993147i | \(0.537287\pi\) | |||||||
\(114\) | −0.0523446 | −0.00490252 | ||||||||
\(115\) | 0.680520 | 0.0634588 | ||||||||
\(116\) | 13.0120 | 1.20814 | ||||||||
\(117\) | 3.46263 | 0.320120 | ||||||||
\(118\) | −0.149882 | −0.0137977 | ||||||||
\(119\) | 4.97378 | 0.455945 | ||||||||
\(120\) | −0.0307463 | −0.00280674 | ||||||||
\(121\) | 7.84797 | 0.713451 | ||||||||
\(122\) | 0.497182 | 0.0450128 | ||||||||
\(123\) | −6.33093 | −0.570841 | ||||||||
\(124\) | 4.51277 | 0.405258 | ||||||||
\(125\) | −1.18449 | −0.105944 | ||||||||
\(126\) | 0.322652 | 0.0287441 | ||||||||
\(127\) | 4.37521 | 0.388237 | 0.194119 | − | 0.980978i | \(-0.437815\pi\) | ||||
0.194119 | + | 0.980978i | \(0.437815\pi\) | |||||||
\(128\) | 2.06495 | 0.182518 | ||||||||
\(129\) | −3.21798 | −0.283328 | ||||||||
\(130\) | −0.0266438 | −0.00233682 | ||||||||
\(131\) | 1.76672 | 0.154359 | 0.0771796 | − | 0.997017i | \(-0.475409\pi\) | ||||
0.0771796 | + | 0.997017i | \(0.475409\pi\) | |||||||
\(132\) | −8.66458 | −0.754155 | ||||||||
\(133\) | 4.01338 | 0.348005 | ||||||||
\(134\) | −0.522683 | −0.0451529 | ||||||||
\(135\) | −0.118616 | −0.0102088 | ||||||||
\(136\) | −0.259209 | −0.0222270 | ||||||||
\(137\) | −1.71579 | −0.146590 | −0.0732950 | − | 0.997310i | \(-0.523351\pi\) | ||||
−0.0732950 | + | 0.997310i | \(0.523351\pi\) | |||||||
\(138\) | 0.372173 | 0.0316815 | ||||||||
\(139\) | 15.5724 | 1.32083 | 0.660417 | − | 0.750899i | \(-0.270380\pi\) | ||||
0.660417 | + | 0.750899i | \(0.270380\pi\) | |||||||
\(140\) | 1.17746 | 0.0995132 | ||||||||
\(141\) | −9.60026 | −0.808488 | ||||||||
\(142\) | −0.776072 | −0.0651265 | ||||||||
\(143\) | −15.0327 | −1.25710 | ||||||||
\(144\) | 3.97477 | 0.331231 | ||||||||
\(145\) | −0.773344 | −0.0642228 | ||||||||
\(146\) | −0.349385 | −0.0289153 | ||||||||
\(147\) | −17.7385 | −1.46304 | ||||||||
\(148\) | 4.01723 | 0.330214 | ||||||||
\(149\) | 5.85511 | 0.479669 | 0.239834 | − | 0.970814i | \(-0.422907\pi\) | ||||
0.239834 | + | 0.970814i | \(0.422907\pi\) | |||||||
\(150\) | −0.323440 | −0.0264088 | ||||||||
\(151\) | 9.72038 | 0.791033 | 0.395517 | − | 0.918459i | \(-0.370566\pi\) | ||||
0.395517 | + | 0.918459i | \(0.370566\pi\) | |||||||
\(152\) | −0.209158 | −0.0169650 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −1.40077 | −0.112877 | ||||||||
\(155\) | −0.268207 | −0.0215429 | ||||||||
\(156\) | 6.91069 | 0.553298 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −0.645770 | −0.0513747 | ||||||||
\(159\) | 10.1285 | 0.803241 | ||||||||
\(160\) | −0.0920772 | −0.00727935 | ||||||||
\(161\) | −28.5354 | −2.24891 | ||||||||
\(162\) | −0.0648705 | −0.00509671 | ||||||||
\(163\) | 8.84608 | 0.692879 | 0.346439 | − | 0.938072i | \(-0.387391\pi\) | ||||
0.346439 | + | 0.938072i | \(0.387391\pi\) | |||||||
\(164\) | −12.6352 | −0.986645 | ||||||||
\(165\) | 0.514962 | 0.0400897 | ||||||||
\(166\) | −0.743007 | −0.0576685 | ||||||||
\(167\) | −18.1414 | −1.40383 | −0.701913 | − | 0.712263i | \(-0.747670\pi\) | ||||
−0.701913 | + | 0.712263i | \(0.747670\pi\) | |||||||
\(168\) | 1.28925 | 0.0994677 | ||||||||
\(169\) | −1.01020 | −0.0777078 | ||||||||
\(170\) | 0.00769468 | 0.000590155 0 | ||||||||
\(171\) | −0.806909 | −0.0617059 | ||||||||
\(172\) | −6.42242 | −0.489705 | ||||||||
\(173\) | 15.4822 | 1.17709 | 0.588546 | − | 0.808464i | \(-0.299701\pi\) | ||||
0.588546 | + | 0.808464i | \(0.299701\pi\) | |||||||
\(174\) | −0.422939 | −0.0320629 | ||||||||
\(175\) | 24.7989 | 1.87462 | ||||||||
\(176\) | −17.2562 | −1.30073 | ||||||||
\(177\) | −2.31048 | −0.173666 | ||||||||
\(178\) | 0.659849 | 0.0494578 | ||||||||
\(179\) | −3.74689 | −0.280055 | −0.140028 | − | 0.990148i | \(-0.544719\pi\) | ||||
−0.140028 | + | 0.990148i | \(0.544719\pi\) | |||||||
\(180\) | −0.236733 | −0.0176450 | ||||||||
\(181\) | −11.7797 | −0.875580 | −0.437790 | − | 0.899077i | \(-0.644239\pi\) | ||||
−0.437790 | + | 0.899077i | \(0.644239\pi\) | |||||||
\(182\) | 1.11722 | 0.0828141 | ||||||||
\(183\) | 7.66422 | 0.566556 | ||||||||
\(184\) | 1.48713 | 0.109632 | ||||||||
\(185\) | −0.238756 | −0.0175537 | ||||||||
\(186\) | −0.146681 | −0.0107552 | ||||||||
\(187\) | 4.34142 | 0.317476 | ||||||||
\(188\) | −19.1601 | −1.39740 | ||||||||
\(189\) | 4.97378 | 0.361789 | ||||||||
\(190\) | 0.00620890 | 0.000450441 0 | ||||||||
\(191\) | −22.8104 | −1.65050 | −0.825251 | − | 0.564765i | \(-0.808967\pi\) | ||||
−0.825251 | + | 0.564765i | \(0.808967\pi\) | |||||||
\(192\) | 7.89918 | 0.570074 | ||||||||
\(193\) | −7.13856 | −0.513845 | −0.256922 | − | 0.966432i | \(-0.582708\pi\) | ||||
−0.256922 | + | 0.966432i | \(0.582708\pi\) | |||||||
\(194\) | 0.539375 | 0.0387249 | ||||||||
\(195\) | −0.410723 | −0.0294125 | ||||||||
\(196\) | −35.4023 | −2.52873 | ||||||||
\(197\) | 1.71391 | 0.122111 | 0.0610556 | − | 0.998134i | \(-0.480553\pi\) | ||||
0.0610556 | + | 0.998134i | \(0.480553\pi\) | |||||||
\(198\) | 0.281631 | 0.0200146 | ||||||||
\(199\) | −2.59523 | −0.183971 | −0.0919853 | − | 0.995760i | \(-0.529321\pi\) | ||||
−0.0919853 | + | 0.995760i | \(0.529321\pi\) | |||||||
\(200\) | −1.29240 | −0.0913864 | ||||||||
\(201\) | −8.05732 | −0.568320 | ||||||||
\(202\) | −0.514968 | −0.0362330 | ||||||||
\(203\) | 32.4277 | 2.27598 | ||||||||
\(204\) | −1.99579 | −0.139733 | ||||||||
\(205\) | 0.750949 | 0.0524486 | ||||||||
\(206\) | −0.778696 | −0.0542543 | ||||||||
\(207\) | 5.73717 | 0.398761 | ||||||||
\(208\) | 13.7631 | 0.954303 | ||||||||
\(209\) | 3.50313 | 0.242317 | ||||||||
\(210\) | −0.0382716 | −0.00264099 | ||||||||
\(211\) | −13.2324 | −0.910958 | −0.455479 | − | 0.890247i | \(-0.650532\pi\) | ||||
−0.455479 | + | 0.890247i | \(0.650532\pi\) | |||||||
\(212\) | 20.2143 | 1.38833 | ||||||||
\(213\) | −11.9634 | −0.819719 | ||||||||
\(214\) | 0.260415 | 0.0178016 | ||||||||
\(215\) | 0.381704 | 0.0260320 | ||||||||
\(216\) | −0.259209 | −0.0176370 | ||||||||
\(217\) | 11.2464 | 0.763456 | ||||||||
\(218\) | −0.392791 | −0.0266031 | ||||||||
\(219\) | −5.38589 | −0.363945 | ||||||||
\(220\) | 1.02776 | 0.0692914 | ||||||||
\(221\) | −3.46263 | −0.232922 | ||||||||
\(222\) | −0.130575 | −0.00876359 | ||||||||
\(223\) | −2.45175 | −0.164181 | −0.0820905 | − | 0.996625i | \(-0.526160\pi\) | ||||
−0.0820905 | + | 0.996625i | \(0.526160\pi\) | |||||||
\(224\) | 3.86096 | 0.257971 | ||||||||
\(225\) | −4.98593 | −0.332395 | ||||||||
\(226\) | 0.161187 | 0.0107220 | ||||||||
\(227\) | −16.6359 | −1.10416 | −0.552082 | − | 0.833790i | \(-0.686167\pi\) | ||||
−0.552082 | + | 0.833790i | \(0.686167\pi\) | |||||||
\(228\) | −1.61042 | −0.106653 | ||||||||
\(229\) | −17.1990 | −1.13654 | −0.568270 | − | 0.822842i | \(-0.692387\pi\) | ||||
−0.568270 | + | 0.822842i | \(0.692387\pi\) | |||||||
\(230\) | −0.0441457 | −0.00291088 | ||||||||
\(231\) | −21.5933 | −1.42073 | ||||||||
\(232\) | −1.68997 | −0.110952 | ||||||||
\(233\) | −3.83870 | −0.251482 | −0.125741 | − | 0.992063i | \(-0.540131\pi\) | ||||
−0.125741 | + | 0.992063i | \(0.540131\pi\) | |||||||
\(234\) | −0.224623 | −0.0146840 | ||||||||
\(235\) | 1.13874 | 0.0742835 | ||||||||
\(236\) | −4.61123 | −0.300166 | ||||||||
\(237\) | −9.95475 | −0.646630 | ||||||||
\(238\) | −0.322652 | −0.0209144 | ||||||||
\(239\) | 7.17770 | 0.464286 | 0.232143 | − | 0.972682i | \(-0.425426\pi\) | ||||
0.232143 | + | 0.972682i | \(0.425426\pi\) | |||||||
\(240\) | −0.471471 | −0.0304333 | ||||||||
\(241\) | −23.1575 | −1.49171 | −0.745853 | − | 0.666110i | \(-0.767958\pi\) | ||||
−0.745853 | + | 0.666110i | \(0.767958\pi\) | |||||||
\(242\) | −0.509102 | −0.0327263 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 15.2962 | 0.979239 | ||||||||
\(245\) | 2.10406 | 0.134424 | ||||||||
\(246\) | 0.410691 | 0.0261847 | ||||||||
\(247\) | −2.79403 | −0.177780 | ||||||||
\(248\) | −0.586108 | −0.0372179 | ||||||||
\(249\) | −11.4537 | −0.725848 | ||||||||
\(250\) | 0.0768385 | 0.00485970 | ||||||||
\(251\) | 21.1381 | 1.33422 | 0.667112 | − | 0.744957i | \(-0.267530\pi\) | ||||
0.667112 | + | 0.744957i | \(0.267530\pi\) | |||||||
\(252\) | 9.92662 | 0.625319 | ||||||||
\(253\) | −24.9075 | −1.56592 | ||||||||
\(254\) | −0.283822 | −0.0178086 | ||||||||
\(255\) | 0.118616 | 0.00742802 | ||||||||
\(256\) | 15.6644 | 0.979025 | ||||||||
\(257\) | −13.3372 | −0.831950 | −0.415975 | − | 0.909376i | \(-0.636560\pi\) | ||||
−0.415975 | + | 0.909376i | \(0.636560\pi\) | |||||||
\(258\) | 0.208752 | 0.0129963 | ||||||||
\(259\) | 10.0115 | 0.622082 | ||||||||
\(260\) | −0.819717 | −0.0508367 | ||||||||
\(261\) | −6.51973 | −0.403561 | ||||||||
\(262\) | −0.114608 | −0.00708052 | ||||||||
\(263\) | −22.0305 | −1.35846 | −0.679228 | − | 0.733927i | \(-0.737685\pi\) | ||||
−0.679228 | + | 0.733927i | \(0.737685\pi\) | |||||||
\(264\) | 1.12534 | 0.0692597 | ||||||||
\(265\) | −1.20140 | −0.0738014 | ||||||||
\(266\) | −0.260350 | −0.0159631 | ||||||||
\(267\) | 10.1718 | 0.622503 | ||||||||
\(268\) | −16.0807 | −0.982287 | ||||||||
\(269\) | −7.05221 | −0.429981 | −0.214990 | − | 0.976616i | \(-0.568972\pi\) | ||||
−0.214990 | + | 0.976616i | \(0.568972\pi\) | |||||||
\(270\) | 0.00769468 | 0.000468283 0 | ||||||||
\(271\) | −11.5716 | −0.702926 | −0.351463 | − | 0.936202i | \(-0.614316\pi\) | ||||
−0.351463 | + | 0.936202i | \(0.614316\pi\) | |||||||
\(272\) | −3.97477 | −0.241006 | ||||||||
\(273\) | 17.2223 | 1.04234 | ||||||||
\(274\) | 0.111304 | 0.00672414 | ||||||||
\(275\) | 21.6460 | 1.30531 | ||||||||
\(276\) | 11.4502 | 0.689221 | ||||||||
\(277\) | 8.51107 | 0.511381 | 0.255690 | − | 0.966759i | \(-0.417697\pi\) | ||||
0.255690 | + | 0.966759i | \(0.417697\pi\) | |||||||
\(278\) | −1.01019 | −0.0605871 | ||||||||
\(279\) | −2.26114 | −0.135371 | ||||||||
\(280\) | −0.152925 | −0.00913904 | ||||||||
\(281\) | −17.8087 | −1.06238 | −0.531189 | − | 0.847254i | \(-0.678254\pi\) | ||||
−0.531189 | + | 0.847254i | \(0.678254\pi\) | |||||||
\(282\) | 0.622774 | 0.0370857 | ||||||||
\(283\) | −21.5937 | −1.28361 | −0.641805 | − | 0.766868i | \(-0.721814\pi\) | ||||
−0.641805 | + | 0.766868i | \(0.721814\pi\) | |||||||
\(284\) | −23.8765 | −1.41681 | ||||||||
\(285\) | 0.0957122 | 0.00566950 | ||||||||
\(286\) | 0.975182 | 0.0576637 | ||||||||
\(287\) | −31.4886 | −1.85872 | ||||||||
\(288\) | −0.776264 | −0.0457418 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.0501673 | 0.00294592 | ||||||||
\(291\) | 8.31464 | 0.487413 | ||||||||
\(292\) | −10.7491 | −0.629044 | ||||||||
\(293\) | −18.1737 | −1.06172 | −0.530860 | − | 0.847460i | \(-0.678131\pi\) | ||||
−0.530860 | + | 0.847460i | \(0.678131\pi\) | |||||||
\(294\) | 1.15070 | 0.0671104 | ||||||||
\(295\) | 0.274059 | 0.0159564 | ||||||||
\(296\) | −0.521749 | −0.0303260 | ||||||||
\(297\) | 4.34142 | 0.251915 | ||||||||
\(298\) | −0.379824 | −0.0220026 | ||||||||
\(299\) | 19.8657 | 1.14886 | ||||||||
\(300\) | −9.95088 | −0.574514 | ||||||||
\(301\) | −16.0055 | −0.922543 | ||||||||
\(302\) | −0.630566 | −0.0362850 | ||||||||
\(303\) | −7.93840 | −0.456049 | ||||||||
\(304\) | −3.20728 | −0.183950 | ||||||||
\(305\) | −0.909099 | −0.0520549 | ||||||||
\(306\) | 0.0648705 | 0.00370840 | ||||||||
\(307\) | −3.61718 | −0.206443 | −0.103222 | − | 0.994658i | \(-0.532915\pi\) | ||||
−0.103222 | + | 0.994658i | \(0.532915\pi\) | |||||||
\(308\) | −43.0957 | −2.45560 | ||||||||
\(309\) | −12.0039 | −0.682875 | ||||||||
\(310\) | 0.0173988 | 0.000988183 0 | ||||||||
\(311\) | −22.1185 | −1.25423 | −0.627113 | − | 0.778929i | \(-0.715763\pi\) | ||||
−0.627113 | + | 0.778929i | \(0.715763\pi\) | |||||||
\(312\) | −0.897545 | −0.0508135 | ||||||||
\(313\) | 11.2934 | 0.638338 | 0.319169 | − | 0.947698i | \(-0.396596\pi\) | ||||
0.319169 | + | 0.947698i | \(0.396596\pi\) | |||||||
\(314\) | 0.0648705 | 0.00366086 | ||||||||
\(315\) | −0.589969 | −0.0332410 | ||||||||
\(316\) | −19.8676 | −1.11764 | ||||||||
\(317\) | −7.17556 | −0.403019 | −0.201510 | − | 0.979487i | \(-0.564585\pi\) | ||||
−0.201510 | + | 0.979487i | \(0.564585\pi\) | |||||||
\(318\) | −0.657040 | −0.0368450 | ||||||||
\(319\) | 28.3049 | 1.58477 | ||||||||
\(320\) | −0.936969 | −0.0523781 | ||||||||
\(321\) | 4.01437 | 0.224060 | ||||||||
\(322\) | 1.85111 | 0.103158 | ||||||||
\(323\) | 0.806909 | 0.0448976 | ||||||||
\(324\) | −1.99579 | −0.110877 | ||||||||
\(325\) | −17.2644 | −0.957658 | ||||||||
\(326\) | −0.573850 | −0.0317826 | ||||||||
\(327\) | −6.05499 | −0.334842 | ||||||||
\(328\) | 1.64104 | 0.0906110 | ||||||||
\(329\) | −47.7496 | −2.63252 | ||||||||
\(330\) | −0.0334059 | −0.00183893 | ||||||||
\(331\) | 19.5660 | 1.07544 | 0.537722 | − | 0.843122i | \(-0.319285\pi\) | ||||
0.537722 | + | 0.843122i | \(0.319285\pi\) | |||||||
\(332\) | −22.8592 | −1.25456 | ||||||||
\(333\) | −2.01285 | −0.110303 | ||||||||
\(334\) | 1.17684 | 0.0643940 | ||||||||
\(335\) | 0.955726 | 0.0522169 | ||||||||
\(336\) | 19.7696 | 1.07852 | ||||||||
\(337\) | 26.5021 | 1.44366 | 0.721831 | − | 0.692070i | \(-0.243301\pi\) | ||||
0.721831 | + | 0.692070i | \(0.243301\pi\) | |||||||
\(338\) | 0.0655323 | 0.00356449 | ||||||||
\(339\) | 2.48475 | 0.134953 | ||||||||
\(340\) | 0.236733 | 0.0128386 | ||||||||
\(341\) | 9.81657 | 0.531597 | ||||||||
\(342\) | 0.0523446 | 0.00283047 | ||||||||
\(343\) | −53.4107 | −2.88391 | ||||||||
\(344\) | 0.834130 | 0.0449733 | ||||||||
\(345\) | −0.680520 | −0.0366380 | ||||||||
\(346\) | −1.00434 | −0.0539937 | ||||||||
\(347\) | 16.9944 | 0.912306 | 0.456153 | − | 0.889901i | \(-0.349227\pi\) | ||||
0.456153 | + | 0.889901i | \(0.349227\pi\) | |||||||
\(348\) | −13.0120 | −0.697518 | ||||||||
\(349\) | 26.6567 | 1.42690 | 0.713451 | − | 0.700705i | \(-0.247131\pi\) | ||||
0.713451 | + | 0.700705i | \(0.247131\pi\) | |||||||
\(350\) | −1.60872 | −0.0859896 | ||||||||
\(351\) | −3.46263 | −0.184821 | ||||||||
\(352\) | 3.37009 | 0.179626 | ||||||||
\(353\) | 14.5904 | 0.776566 | 0.388283 | − | 0.921540i | \(-0.373068\pi\) | ||||
0.388283 | + | 0.921540i | \(0.373068\pi\) | |||||||
\(354\) | 0.149882 | 0.00796613 | ||||||||
\(355\) | 1.41905 | 0.0753153 | ||||||||
\(356\) | 20.3008 | 1.07594 | ||||||||
\(357\) | −4.97378 | −0.263240 | ||||||||
\(358\) | 0.243062 | 0.0128463 | ||||||||
\(359\) | −15.3922 | −0.812368 | −0.406184 | − | 0.913791i | \(-0.633141\pi\) | ||||
−0.406184 | + | 0.913791i | \(0.633141\pi\) | |||||||
\(360\) | 0.0307463 | 0.00162047 | ||||||||
\(361\) | −18.3489 | −0.965731 | ||||||||
\(362\) | 0.764157 | 0.0401632 | ||||||||
\(363\) | −7.84797 | −0.411911 | ||||||||
\(364\) | 34.3722 | 1.80159 | ||||||||
\(365\) | 0.638852 | 0.0334391 | ||||||||
\(366\) | −0.497182 | −0.0259881 | ||||||||
\(367\) | −12.3531 | −0.644829 | −0.322415 | − | 0.946599i | \(-0.604494\pi\) | ||||
−0.322415 | + | 0.946599i | \(0.604494\pi\) | |||||||
\(368\) | 22.8039 | 1.18874 | ||||||||
\(369\) | 6.33093 | 0.329575 | ||||||||
\(370\) | 0.0154882 | 0.000805195 0 | ||||||||
\(371\) | 50.3768 | 2.61543 | ||||||||
\(372\) | −4.51277 | −0.233976 | ||||||||
\(373\) | 15.3806 | 0.796378 | 0.398189 | − | 0.917303i | \(-0.369639\pi\) | ||||
0.398189 | + | 0.917303i | \(0.369639\pi\) | |||||||
\(374\) | −0.281631 | −0.0145628 | ||||||||
\(375\) | 1.18449 | 0.0611668 | ||||||||
\(376\) | 2.48848 | 0.128333 | ||||||||
\(377\) | −22.5754 | −1.16269 | ||||||||
\(378\) | −0.322652 | −0.0165954 | ||||||||
\(379\) | −25.3664 | −1.30299 | −0.651493 | − | 0.758655i | \(-0.725857\pi\) | ||||
−0.651493 | + | 0.758655i | \(0.725857\pi\) | |||||||
\(380\) | 0.191022 | 0.00979921 | ||||||||
\(381\) | −4.37521 | −0.224149 | ||||||||
\(382\) | 1.47972 | 0.0757092 | ||||||||
\(383\) | 25.1142 | 1.28328 | 0.641638 | − | 0.767008i | \(-0.278255\pi\) | ||||
0.641638 | + | 0.767008i | \(0.278255\pi\) | |||||||
\(384\) | −2.06495 | −0.105377 | ||||||||
\(385\) | 2.56131 | 0.130536 | ||||||||
\(386\) | 0.463082 | 0.0235703 | ||||||||
\(387\) | 3.21798 | 0.163579 | ||||||||
\(388\) | 16.5943 | 0.842448 | ||||||||
\(389\) | −13.9009 | −0.704805 | −0.352402 | − | 0.935849i | \(-0.614635\pi\) | ||||
−0.352402 | + | 0.935849i | \(0.614635\pi\) | |||||||
\(390\) | 0.0266438 | 0.00134916 | ||||||||
\(391\) | −5.73717 | −0.290141 | ||||||||
\(392\) | 4.59797 | 0.232233 | ||||||||
\(393\) | −1.76672 | −0.0891193 | ||||||||
\(394\) | −0.111182 | −0.00560129 | ||||||||
\(395\) | 1.18079 | 0.0594121 | ||||||||
\(396\) | 8.66458 | 0.435411 | ||||||||
\(397\) | 33.7127 | 1.69199 | 0.845996 | − | 0.533190i | \(-0.179007\pi\) | ||||
0.845996 | + | 0.533190i | \(0.179007\pi\) | |||||||
\(398\) | 0.168354 | 0.00843881 | ||||||||
\(399\) | −4.01338 | −0.200921 | ||||||||
\(400\) | −19.8179 | −0.990896 | ||||||||
\(401\) | −8.36903 | −0.417929 | −0.208965 | − | 0.977923i | \(-0.567009\pi\) | ||||
−0.208965 | + | 0.977923i | \(0.567009\pi\) | |||||||
\(402\) | 0.522683 | 0.0260690 | ||||||||
\(403\) | −7.82949 | −0.390015 | ||||||||
\(404\) | −15.8434 | −0.788238 | ||||||||
\(405\) | 0.118616 | 0.00589407 | ||||||||
\(406\) | −2.10360 | −0.104400 | ||||||||
\(407\) | 8.73863 | 0.433158 | ||||||||
\(408\) | 0.259209 | 0.0128328 | ||||||||
\(409\) | 2.67132 | 0.132089 | 0.0660443 | − | 0.997817i | \(-0.478962\pi\) | ||||
0.0660443 | + | 0.997817i | \(0.478962\pi\) | |||||||
\(410\) | −0.0487145 | −0.00240584 | ||||||||
\(411\) | 1.71579 | 0.0846338 | ||||||||
\(412\) | −23.9572 | −1.18029 | ||||||||
\(413\) | −11.4918 | −0.565475 | ||||||||
\(414\) | −0.372173 | −0.0182913 | ||||||||
\(415\) | 1.35859 | 0.0666906 | ||||||||
\(416\) | −2.68791 | −0.131786 | ||||||||
\(417\) | −15.5724 | −0.762583 | ||||||||
\(418\) | −0.227250 | −0.0111152 | ||||||||
\(419\) | 31.8284 | 1.55492 | 0.777460 | − | 0.628932i | \(-0.216508\pi\) | ||||
0.777460 | + | 0.628932i | \(0.216508\pi\) | |||||||
\(420\) | −1.17746 | −0.0574540 | ||||||||
\(421\) | −5.03737 | −0.245506 | −0.122753 | − | 0.992437i | \(-0.539172\pi\) | ||||
−0.122753 | + | 0.992437i | \(0.539172\pi\) | |||||||
\(422\) | 0.858394 | 0.0417860 | ||||||||
\(423\) | 9.60026 | 0.466781 | ||||||||
\(424\) | −2.62539 | −0.127500 | ||||||||
\(425\) | 4.98593 | 0.241853 | ||||||||
\(426\) | 0.776072 | 0.0376008 | ||||||||
\(427\) | 38.1201 | 1.84476 | ||||||||
\(428\) | 8.01185 | 0.387268 | ||||||||
\(429\) | 15.0327 | 0.725788 | ||||||||
\(430\) | −0.0247613 | −0.00119410 | ||||||||
\(431\) | 16.2108 | 0.780849 | 0.390425 | − | 0.920635i | \(-0.372328\pi\) | ||||
0.390425 | + | 0.920635i | \(0.372328\pi\) | |||||||
\(432\) | −3.97477 | −0.191236 | ||||||||
\(433\) | 19.9519 | 0.958829 | 0.479414 | − | 0.877589i | \(-0.340849\pi\) | ||||
0.479414 | + | 0.877589i | \(0.340849\pi\) | |||||||
\(434\) | −0.729561 | −0.0350200 | ||||||||
\(435\) | 0.773344 | 0.0370790 | ||||||||
\(436\) | −12.0845 | −0.578743 | ||||||||
\(437\) | −4.62937 | −0.221453 | ||||||||
\(438\) | 0.349385 | 0.0166943 | ||||||||
\(439\) | −7.04627 | −0.336300 | −0.168150 | − | 0.985761i | \(-0.553779\pi\) | ||||
−0.168150 | + | 0.985761i | \(0.553779\pi\) | |||||||
\(440\) | −0.133483 | −0.00636355 | ||||||||
\(441\) | 17.7385 | 0.844689 | ||||||||
\(442\) | 0.224623 | 0.0106842 | ||||||||
\(443\) | 30.8886 | 1.46756 | 0.733782 | − | 0.679385i | \(-0.237753\pi\) | ||||
0.733782 | + | 0.679385i | \(0.237753\pi\) | |||||||
\(444\) | −4.01723 | −0.190649 | ||||||||
\(445\) | −1.20654 | −0.0571953 | ||||||||
\(446\) | 0.159046 | 0.00753105 | ||||||||
\(447\) | −5.85511 | −0.276937 | ||||||||
\(448\) | 39.2888 | 1.85622 | ||||||||
\(449\) | 6.88966 | 0.325143 | 0.162572 | − | 0.986697i | \(-0.448021\pi\) | ||||
0.162572 | + | 0.986697i | \(0.448021\pi\) | |||||||
\(450\) | 0.323440 | 0.0152471 | ||||||||
\(451\) | −27.4853 | −1.29423 | ||||||||
\(452\) | 4.95903 | 0.233253 | ||||||||
\(453\) | −9.72038 | −0.456703 | ||||||||
\(454\) | 1.07918 | 0.0506485 | ||||||||
\(455\) | −2.04284 | −0.0957700 | ||||||||
\(456\) | 0.209158 | 0.00979473 | ||||||||
\(457\) | −8.68547 | −0.406289 | −0.203145 | − | 0.979149i | \(-0.565116\pi\) | ||||
−0.203145 | + | 0.979149i | \(0.565116\pi\) | |||||||
\(458\) | 1.11571 | 0.0521336 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −1.35818 | −0.0633253 | ||||||||
\(461\) | −13.6759 | −0.636952 | −0.318476 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318476 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(462\) | 1.40077 | 0.0651696 | ||||||||
\(463\) | 1.94603 | 0.0904395 | 0.0452197 | − | 0.998977i | \(-0.485601\pi\) | ||||
0.0452197 | + | 0.998977i | \(0.485601\pi\) | |||||||
\(464\) | −25.9144 | −1.20305 | ||||||||
\(465\) | 0.268207 | 0.0124378 | ||||||||
\(466\) | 0.249019 | 0.0115356 | ||||||||
\(467\) | 12.0677 | 0.558427 | 0.279214 | − | 0.960229i | \(-0.409926\pi\) | ||||
0.279214 | + | 0.960229i | \(0.409926\pi\) | |||||||
\(468\) | −6.91069 | −0.319447 | ||||||||
\(469\) | −40.0753 | −1.85051 | ||||||||
\(470\) | −0.0738709 | −0.00340741 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 0.598897 | 0.0275665 | ||||||||
\(473\) | −13.9706 | −0.642370 | ||||||||
\(474\) | 0.645770 | 0.0296612 | ||||||||
\(475\) | 4.02319 | 0.184597 | ||||||||
\(476\) | −9.92662 | −0.454986 | ||||||||
\(477\) | −10.1285 | −0.463751 | ||||||||
\(478\) | −0.465621 | −0.0212970 | ||||||||
\(479\) | 16.5252 | 0.755056 | 0.377528 | − | 0.925998i | \(-0.376774\pi\) | ||||
0.377528 | + | 0.925998i | \(0.376774\pi\) | |||||||
\(480\) | 0.0920772 | 0.00420273 | ||||||||
\(481\) | −6.96975 | −0.317793 | ||||||||
\(482\) | 1.50224 | 0.0684252 | ||||||||
\(483\) | 28.5354 | 1.29841 | ||||||||
\(484\) | −15.6629 | −0.711950 | ||||||||
\(485\) | −0.986249 | −0.0447833 | ||||||||
\(486\) | 0.0648705 | 0.00294259 | ||||||||
\(487\) | −13.4957 | −0.611549 | −0.305774 | − | 0.952104i | \(-0.598915\pi\) | ||||
−0.305774 | + | 0.952104i | \(0.598915\pi\) | |||||||
\(488\) | −1.98664 | −0.0899308 | ||||||||
\(489\) | −8.84608 | −0.400034 | ||||||||
\(490\) | −0.136492 | −0.00616607 | ||||||||
\(491\) | −0.838904 | −0.0378592 | −0.0189296 | − | 0.999821i | \(-0.506026\pi\) | ||||
−0.0189296 | + | 0.999821i | \(0.506026\pi\) | |||||||
\(492\) | 12.6352 | 0.569640 | ||||||||
\(493\) | 6.51973 | 0.293634 | ||||||||
\(494\) | 0.181250 | 0.00815482 | ||||||||
\(495\) | −0.514962 | −0.0231458 | ||||||||
\(496\) | −8.98751 | −0.403551 | ||||||||
\(497\) | −59.5033 | −2.66909 | ||||||||
\(498\) | 0.743007 | 0.0332949 | ||||||||
\(499\) | 20.7838 | 0.930411 | 0.465206 | − | 0.885203i | \(-0.345980\pi\) | ||||
0.465206 | + | 0.885203i | \(0.345980\pi\) | |||||||
\(500\) | 2.36400 | 0.105721 | ||||||||
\(501\) | 18.1414 | 0.810499 | ||||||||
\(502\) | −1.37124 | −0.0612014 | ||||||||
\(503\) | −22.3605 | −0.997005 | −0.498502 | − | 0.866888i | \(-0.666116\pi\) | ||||
−0.498502 | + | 0.866888i | \(0.666116\pi\) | |||||||
\(504\) | −1.28925 | −0.0574277 | ||||||||
\(505\) | 0.941620 | 0.0419016 | ||||||||
\(506\) | 1.61576 | 0.0718294 | ||||||||
\(507\) | 1.01020 | 0.0448646 | ||||||||
\(508\) | −8.73201 | −0.387420 | ||||||||
\(509\) | −35.2943 | −1.56439 | −0.782196 | − | 0.623032i | \(-0.785901\pi\) | ||||
−0.782196 | + | 0.623032i | \(0.785901\pi\) | |||||||
\(510\) | −0.00769468 | −0.000340726 0 | ||||||||
\(511\) | −26.7882 | −1.18504 | ||||||||
\(512\) | −5.14606 | −0.227426 | ||||||||
\(513\) | 0.806909 | 0.0356259 | ||||||||
\(514\) | 0.865190 | 0.0381619 | ||||||||
\(515\) | 1.42385 | 0.0627422 | ||||||||
\(516\) | 6.42242 | 0.282731 | ||||||||
\(517\) | −41.6788 | −1.83303 | ||||||||
\(518\) | −0.649449 | −0.0285352 | ||||||||
\(519\) | −15.4822 | −0.679594 | ||||||||
\(520\) | 0.106463 | 0.00466872 | ||||||||
\(521\) | −29.4016 | −1.28811 | −0.644055 | − | 0.764979i | \(-0.722749\pi\) | ||||
−0.644055 | + | 0.764979i | \(0.722749\pi\) | |||||||
\(522\) | 0.422939 | 0.0185115 | ||||||||
\(523\) | −14.3280 | −0.626522 | −0.313261 | − | 0.949667i | \(-0.601421\pi\) | ||||
−0.313261 | + | 0.949667i | \(0.601421\pi\) | |||||||
\(524\) | −3.52601 | −0.154034 | ||||||||
\(525\) | −24.7989 | −1.08231 | ||||||||
\(526\) | 1.42913 | 0.0623130 | ||||||||
\(527\) | 2.26114 | 0.0984968 | ||||||||
\(528\) | 17.2562 | 0.750978 | ||||||||
\(529\) | 9.91513 | 0.431093 | ||||||||
\(530\) | 0.0779354 | 0.00338530 | ||||||||
\(531\) | 2.31048 | 0.100266 | ||||||||
\(532\) | −8.00988 | −0.347272 | ||||||||
\(533\) | 21.9217 | 0.949533 | ||||||||
\(534\) | −0.659849 | −0.0285545 | ||||||||
\(535\) | −0.476169 | −0.0205866 | ||||||||
\(536\) | 2.08853 | 0.0902108 | ||||||||
\(537\) | 3.74689 | 0.161690 | ||||||||
\(538\) | 0.457480 | 0.0197234 | ||||||||
\(539\) | −77.0102 | −3.31706 | ||||||||
\(540\) | 0.236733 | 0.0101874 | ||||||||
\(541\) | −23.4474 | −1.00808 | −0.504042 | − | 0.863679i | \(-0.668154\pi\) | ||||
−0.504042 | + | 0.863679i | \(0.668154\pi\) | |||||||
\(542\) | 0.750657 | 0.0322435 | ||||||||
\(543\) | 11.7797 | 0.505516 | ||||||||
\(544\) | 0.776264 | 0.0332820 | ||||||||
\(545\) | 0.718219 | 0.0307651 | ||||||||
\(546\) | −1.11722 | −0.0478127 | ||||||||
\(547\) | −35.2307 | −1.50636 | −0.753178 | − | 0.657817i | \(-0.771480\pi\) | ||||
−0.753178 | + | 0.657817i | \(0.771480\pi\) | |||||||
\(548\) | 3.42436 | 0.146282 | ||||||||
\(549\) | −7.66422 | −0.327101 | ||||||||
\(550\) | −1.40419 | −0.0598749 | ||||||||
\(551\) | 5.26083 | 0.224119 | ||||||||
\(552\) | −1.48713 | −0.0632963 | ||||||||
\(553\) | −49.5127 | −2.10549 | ||||||||
\(554\) | −0.552118 | −0.0234572 | ||||||||
\(555\) | 0.238756 | 0.0101346 | ||||||||
\(556\) | −31.0793 | −1.31805 | ||||||||
\(557\) | 2.37181 | 0.100497 | 0.0502484 | − | 0.998737i | \(-0.483999\pi\) | ||||
0.0502484 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(558\) | 0.146681 | 0.00620952 | ||||||||
\(559\) | 11.1427 | 0.471285 | ||||||||
\(560\) | −2.34499 | −0.0990940 | ||||||||
\(561\) | −4.34142 | −0.183295 | ||||||||
\(562\) | 1.15526 | 0.0487317 | ||||||||
\(563\) | 16.2262 | 0.683854 | 0.341927 | − | 0.939727i | \(-0.388920\pi\) | ||||
0.341927 | + | 0.939727i | \(0.388920\pi\) | |||||||
\(564\) | 19.1601 | 0.806787 | ||||||||
\(565\) | −0.294730 | −0.0123994 | ||||||||
\(566\) | 1.40079 | 0.0588797 | ||||||||
\(567\) | −4.97378 | −0.208879 | ||||||||
\(568\) | 3.10102 | 0.130116 | ||||||||
\(569\) | 36.0438 | 1.51104 | 0.755518 | − | 0.655128i | \(-0.227385\pi\) | ||||
0.755518 | + | 0.655128i | \(0.227385\pi\) | |||||||
\(570\) | −0.00620890 | −0.000260062 0 | ||||||||
\(571\) | 38.1300 | 1.59569 | 0.797845 | − | 0.602862i | \(-0.205973\pi\) | ||||
0.797845 | + | 0.602862i | \(0.205973\pi\) | |||||||
\(572\) | 30.0022 | 1.25446 | ||||||||
\(573\) | 22.8104 | 0.952918 | ||||||||
\(574\) | 2.04269 | 0.0852600 | ||||||||
\(575\) | −28.6051 | −1.19292 | ||||||||
\(576\) | −7.89918 | −0.329133 | ||||||||
\(577\) | −0.446766 | −0.0185991 | −0.00929956 | − | 0.999957i | \(-0.502960\pi\) | ||||
−0.00929956 | + | 0.999957i | \(0.502960\pi\) | |||||||
\(578\) | −0.0648705 | −0.00269826 | ||||||||
\(579\) | 7.13856 | 0.296668 | ||||||||
\(580\) | 1.54343 | 0.0640876 | ||||||||
\(581\) | −56.9681 | −2.36344 | ||||||||
\(582\) | −0.539375 | −0.0223578 | ||||||||
\(583\) | 43.9720 | 1.82114 | ||||||||
\(584\) | 1.39607 | 0.0577699 | ||||||||
\(585\) | 0.410723 | 0.0169813 | ||||||||
\(586\) | 1.17894 | 0.0487015 | ||||||||
\(587\) | 24.5870 | 1.01481 | 0.507406 | − | 0.861707i | \(-0.330604\pi\) | ||||
0.507406 | + | 0.861707i | \(0.330604\pi\) | |||||||
\(588\) | 35.4023 | 1.45997 | ||||||||
\(589\) | 1.82453 | 0.0751786 | ||||||||
\(590\) | −0.0177784 | −0.000731924 0 | ||||||||
\(591\) | −1.71391 | −0.0705009 | ||||||||
\(592\) | −8.00061 | −0.328823 | ||||||||
\(593\) | −11.0526 | −0.453877 | −0.226938 | − | 0.973909i | \(-0.572872\pi\) | ||||
−0.226938 | + | 0.973909i | \(0.572872\pi\) | |||||||
\(594\) | −0.281631 | −0.0115554 | ||||||||
\(595\) | 0.589969 | 0.0241864 | ||||||||
\(596\) | −11.6856 | −0.478660 | ||||||||
\(597\) | 2.59523 | 0.106215 | ||||||||
\(598\) | −1.28870 | −0.0526988 | ||||||||
\(599\) | 35.2735 | 1.44124 | 0.720618 | − | 0.693332i | \(-0.243858\pi\) | ||||
0.720618 | + | 0.693332i | \(0.243858\pi\) | |||||||
\(600\) | 1.29240 | 0.0527620 | ||||||||
\(601\) | −42.5574 | −1.73595 | −0.867976 | − | 0.496606i | \(-0.834579\pi\) | ||||
−0.867976 | + | 0.496606i | \(0.834579\pi\) | |||||||
\(602\) | 1.03829 | 0.0423174 | ||||||||
\(603\) | 8.05732 | 0.328119 | ||||||||
\(604\) | −19.3998 | −0.789369 | ||||||||
\(605\) | 0.930894 | 0.0378462 | ||||||||
\(606\) | 0.514968 | 0.0209191 | ||||||||
\(607\) | −7.52398 | −0.305389 | −0.152694 | − | 0.988273i | \(-0.548795\pi\) | ||||
−0.152694 | + | 0.988273i | \(0.548795\pi\) | |||||||
\(608\) | 0.626374 | 0.0254028 | ||||||||
\(609\) | −32.4277 | −1.31404 | ||||||||
\(610\) | 0.0589737 | 0.00238778 | ||||||||
\(611\) | 33.2421 | 1.34483 | ||||||||
\(612\) | 1.99579 | 0.0806751 | ||||||||
\(613\) | 48.7096 | 1.96736 | 0.983680 | − | 0.179924i | \(-0.0575853\pi\) | ||||
0.983680 | + | 0.179924i | \(0.0575853\pi\) | |||||||
\(614\) | 0.234648 | 0.00946964 | ||||||||
\(615\) | −0.750949 | −0.0302812 | ||||||||
\(616\) | 5.59718 | 0.225517 | ||||||||
\(617\) | −46.3020 | −1.86405 | −0.932024 | − | 0.362397i | \(-0.881959\pi\) | ||||
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(618\) | 0.778696 | 0.0313238 | ||||||||
\(619\) | −2.14850 | −0.0863555 | −0.0431777 | − | 0.999067i | \(-0.513748\pi\) | ||||
−0.0431777 | + | 0.999067i | \(0.513748\pi\) | |||||||
\(620\) | 0.535286 | 0.0214976 | ||||||||
\(621\) | −5.73717 | −0.230225 | ||||||||
\(622\) | 1.43484 | 0.0575318 | ||||||||
\(623\) | 50.5922 | 2.02693 | ||||||||
\(624\) | −13.7631 | −0.550967 | ||||||||
\(625\) | 24.7892 | 0.991566 | ||||||||
\(626\) | −0.732606 | −0.0292808 | ||||||||
\(627\) | −3.50313 | −0.139902 | ||||||||
\(628\) | 1.99579 | 0.0796408 | ||||||||
\(629\) | 2.01285 | 0.0802576 | ||||||||
\(630\) | 0.0382716 | 0.00152478 | ||||||||
\(631\) | 30.3936 | 1.20995 | 0.604975 | − | 0.796244i | \(-0.293183\pi\) | ||||
0.604975 | + | 0.796244i | \(0.293183\pi\) | |||||||
\(632\) | 2.58036 | 0.102641 | ||||||||
\(633\) | 13.2324 | 0.525942 | ||||||||
\(634\) | 0.465482 | 0.0184867 | ||||||||
\(635\) | 0.518970 | 0.0205947 | ||||||||
\(636\) | −20.2143 | −0.801551 | ||||||||
\(637\) | 61.4217 | 2.43362 | ||||||||
\(638\) | −1.83616 | −0.0726941 | ||||||||
\(639\) | 11.9634 | 0.473265 | ||||||||
\(640\) | 0.244936 | 0.00968195 | ||||||||
\(641\) | 24.6608 | 0.974044 | 0.487022 | − | 0.873390i | \(-0.338083\pi\) | ||||
0.487022 | + | 0.873390i | \(0.338083\pi\) | |||||||
\(642\) | −0.260415 | −0.0102777 | ||||||||
\(643\) | −43.5581 | −1.71776 | −0.858882 | − | 0.512173i | \(-0.828841\pi\) | ||||
−0.858882 | + | 0.512173i | \(0.828841\pi\) | |||||||
\(644\) | 56.9507 | 2.24417 | ||||||||
\(645\) | −0.381704 | −0.0150296 | ||||||||
\(646\) | −0.0523446 | −0.00205947 | ||||||||
\(647\) | 10.6798 | 0.419867 | 0.209934 | − | 0.977716i | \(-0.432675\pi\) | ||||
0.209934 | + | 0.977716i | \(0.432675\pi\) | |||||||
\(648\) | 0.259209 | 0.0101827 | ||||||||
\(649\) | −10.0308 | −0.393742 | ||||||||
\(650\) | 1.11995 | 0.0439282 | ||||||||
\(651\) | −11.2464 | −0.440782 | ||||||||
\(652\) | −17.6549 | −0.691421 | ||||||||
\(653\) | −10.7084 | −0.419052 | −0.209526 | − | 0.977803i | \(-0.567192\pi\) | ||||
−0.209526 | + | 0.977803i | \(0.567192\pi\) | |||||||
\(654\) | 0.392791 | 0.0153593 | ||||||||
\(655\) | 0.209561 | 0.00818824 | ||||||||
\(656\) | 25.1640 | 0.982489 | ||||||||
\(657\) | 5.38589 | 0.210124 | ||||||||
\(658\) | 3.09754 | 0.120755 | ||||||||
\(659\) | −6.67168 | −0.259892 | −0.129946 | − | 0.991521i | \(-0.541480\pi\) | ||||
−0.129946 | + | 0.991521i | \(0.541480\pi\) | |||||||
\(660\) | −1.02776 | −0.0400054 | ||||||||
\(661\) | 13.4694 | 0.523899 | 0.261949 | − | 0.965082i | \(-0.415635\pi\) | ||||
0.261949 | + | 0.965082i | \(0.415635\pi\) | |||||||
\(662\) | −1.26926 | −0.0493311 | ||||||||
\(663\) | 3.46263 | 0.134477 | ||||||||
\(664\) | 2.96890 | 0.115216 | ||||||||
\(665\) | 0.476051 | 0.0184605 | ||||||||
\(666\) | 0.130575 | 0.00505966 | ||||||||
\(667\) | −37.4048 | −1.44832 | ||||||||
\(668\) | 36.2065 | 1.40087 | ||||||||
\(669\) | 2.45175 | 0.0947900 | ||||||||
\(670\) | −0.0619985 | −0.00239521 | ||||||||
\(671\) | 33.2737 | 1.28452 | ||||||||
\(672\) | −3.86096 | −0.148940 | ||||||||
\(673\) | −24.5621 | −0.946798 | −0.473399 | − | 0.880848i | \(-0.656973\pi\) | ||||
−0.473399 | + | 0.880848i | \(0.656973\pi\) | |||||||
\(674\) | −1.71921 | −0.0662213 | ||||||||
\(675\) | 4.98593 | 0.191909 | ||||||||
\(676\) | 2.01615 | 0.0775443 | ||||||||
\(677\) | 32.6567 | 1.25510 | 0.627549 | − | 0.778577i | \(-0.284058\pi\) | ||||
0.627549 | + | 0.778577i | \(0.284058\pi\) | |||||||
\(678\) | −0.161187 | −0.00619034 | ||||||||
\(679\) | 41.3552 | 1.58707 | ||||||||
\(680\) | −0.0307463 | −0.00117907 | ||||||||
\(681\) | 16.6359 | 0.637490 | ||||||||
\(682\) | −0.636806 | −0.0243846 | ||||||||
\(683\) | 21.1801 | 0.810435 | 0.405218 | − | 0.914220i | \(-0.367196\pi\) | ||||
0.405218 | + | 0.914220i | \(0.367196\pi\) | |||||||
\(684\) | 1.61042 | 0.0615760 | ||||||||
\(685\) | −0.203520 | −0.00777611 | ||||||||
\(686\) | 3.46478 | 0.132286 | ||||||||
\(687\) | 17.1990 | 0.656182 | ||||||||
\(688\) | 12.7907 | 0.487642 | ||||||||
\(689\) | −35.0712 | −1.33611 | ||||||||
\(690\) | 0.0441457 | 0.00168060 | ||||||||
\(691\) | −40.0266 | −1.52268 | −0.761341 | − | 0.648351i | \(-0.775459\pi\) | ||||
−0.761341 | + | 0.648351i | \(0.775459\pi\) | |||||||
\(692\) | −30.8993 | −1.17462 | ||||||||
\(693\) | 21.5933 | 0.820261 | ||||||||
\(694\) | −1.10243 | −0.0418478 | ||||||||
\(695\) | 1.84713 | 0.0700658 | ||||||||
\(696\) | 1.68997 | 0.0640583 | ||||||||
\(697\) | −6.33093 | −0.239801 | ||||||||
\(698\) | −1.72924 | −0.0654526 | ||||||||
\(699\) | 3.83870 | 0.145193 | ||||||||
\(700\) | −49.4935 | −1.87068 | ||||||||
\(701\) | −15.2192 | −0.574819 | −0.287410 | − | 0.957808i | \(-0.592794\pi\) | ||||
−0.287410 | + | 0.957808i | \(0.592794\pi\) | |||||||
\(702\) | 0.224623 | 0.00847783 | ||||||||
\(703\) | 1.62419 | 0.0612573 | ||||||||
\(704\) | 34.2937 | 1.29249 | ||||||||
\(705\) | −1.13874 | −0.0428876 | ||||||||
\(706\) | −0.946484 | −0.0356214 | ||||||||
\(707\) | −39.4838 | −1.48494 | ||||||||
\(708\) | 4.61123 | 0.173301 | ||||||||
\(709\) | 42.8476 | 1.60917 | 0.804587 | − | 0.593834i | \(-0.202387\pi\) | ||||
0.804587 | + | 0.593834i | \(0.202387\pi\) | |||||||
\(710\) | −0.0920545 | −0.00345474 | ||||||||
\(711\) | 9.95475 | 0.373332 | ||||||||
\(712\) | −2.63662 | −0.0988115 | ||||||||
\(713\) | −12.9725 | −0.485826 | ||||||||
\(714\) | 0.322652 | 0.0120749 | ||||||||
\(715\) | −1.78312 | −0.0666850 | ||||||||
\(716\) | 7.47800 | 0.279466 | ||||||||
\(717\) | −7.17770 | −0.268056 | ||||||||
\(718\) | 0.998499 | 0.0372637 | ||||||||
\(719\) | 10.8590 | 0.404972 | 0.202486 | − | 0.979285i | \(-0.435098\pi\) | ||||
0.202486 | + | 0.979285i | \(0.435098\pi\) | |||||||
\(720\) | 0.471471 | 0.0175707 | ||||||||
\(721\) | −59.7045 | −2.22351 | ||||||||
\(722\) | 1.19030 | 0.0442985 | ||||||||
\(723\) | 23.1575 | 0.861237 | ||||||||
\(724\) | 23.5099 | 0.873738 | ||||||||
\(725\) | 32.5069 | 1.20728 | ||||||||
\(726\) | 0.509102 | 0.0188945 | ||||||||
\(727\) | −22.6353 | −0.839497 | −0.419748 | − | 0.907640i | \(-0.637882\pi\) | ||||
−0.419748 | + | 0.907640i | \(0.637882\pi\) | |||||||
\(728\) | −4.46419 | −0.165454 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.0414427 | −0.00153386 | ||||||||
\(731\) | −3.21798 | −0.119021 | ||||||||
\(732\) | −15.2962 | −0.565364 | ||||||||
\(733\) | 27.3952 | 1.01186 | 0.505932 | − | 0.862573i | \(-0.331149\pi\) | ||||
0.505932 | + | 0.862573i | \(0.331149\pi\) | |||||||
\(734\) | 0.801355 | 0.0295786 | ||||||||
\(735\) | −2.10406 | −0.0776096 | ||||||||
\(736\) | −4.45356 | −0.164160 | ||||||||
\(737\) | −34.9802 | −1.28851 | ||||||||
\(738\) | −0.410691 | −0.0151177 | ||||||||
\(739\) | −40.0980 | −1.47503 | −0.737514 | − | 0.675332i | \(-0.764000\pi\) | ||||
−0.737514 | + | 0.675332i | \(0.764000\pi\) | |||||||
\(740\) | 0.476507 | 0.0175168 | ||||||||
\(741\) | 2.79403 | 0.102641 | ||||||||
\(742\) | −3.26797 | −0.119971 | ||||||||
\(743\) | −5.27356 | −0.193468 | −0.0967341 | − | 0.995310i | \(-0.530840\pi\) | ||||
−0.0967341 | + | 0.995310i | \(0.530840\pi\) | |||||||
\(744\) | 0.586108 | 0.0214878 | ||||||||
\(745\) | 0.694509 | 0.0254448 | ||||||||
\(746\) | −0.997749 | −0.0365302 | ||||||||
\(747\) | 11.4537 | 0.419069 | ||||||||
\(748\) | −8.66458 | −0.316808 | ||||||||
\(749\) | 19.9666 | 0.729564 | ||||||||
\(750\) | −0.0768385 | −0.00280575 | ||||||||
\(751\) | −21.2154 | −0.774161 | −0.387080 | − | 0.922046i | \(-0.626516\pi\) | ||||
−0.387080 | + | 0.922046i | \(0.626516\pi\) | |||||||
\(752\) | 38.1588 | 1.39151 | ||||||||
\(753\) | −21.1381 | −0.770315 | ||||||||
\(754\) | 1.46448 | 0.0533332 | ||||||||
\(755\) | 1.15299 | 0.0419617 | ||||||||
\(756\) | −9.92662 | −0.361028 | ||||||||
\(757\) | −15.5366 | −0.564688 | −0.282344 | − | 0.959313i | \(-0.591112\pi\) | ||||
−0.282344 | + | 0.959313i | \(0.591112\pi\) | |||||||
\(758\) | 1.64553 | 0.0597685 | ||||||||
\(759\) | 24.9075 | 0.904085 | ||||||||
\(760\) | −0.0248095 | −0.000899935 0 | ||||||||
\(761\) | 23.2789 | 0.843858 | 0.421929 | − | 0.906629i | \(-0.361353\pi\) | ||||
0.421929 | + | 0.906629i | \(0.361353\pi\) | |||||||
\(762\) | 0.283822 | 0.0102818 | ||||||||
\(763\) | −30.1162 | −1.09028 | ||||||||
\(764\) | 45.5248 | 1.64703 | ||||||||
\(765\) | −0.118616 | −0.00428857 | ||||||||
\(766\) | −1.62917 | −0.0588644 | ||||||||
\(767\) | 8.00033 | 0.288875 | ||||||||
\(768\) | −15.6644 | −0.565241 | ||||||||
\(769\) | −39.8062 | −1.43545 | −0.717724 | − | 0.696328i | \(-0.754816\pi\) | ||||
−0.717724 | + | 0.696328i | \(0.754816\pi\) | |||||||
\(770\) | −0.166153 | −0.00598775 | ||||||||
\(771\) | 13.3372 | 0.480327 | ||||||||
\(772\) | 14.2471 | 0.512763 | ||||||||
\(773\) | 0.618675 | 0.0222522 | 0.0111261 | − | 0.999938i | \(-0.496458\pi\) | ||||
0.0111261 | + | 0.999938i | \(0.496458\pi\) | |||||||
\(774\) | −0.208752 | −0.00750344 | ||||||||
\(775\) | 11.2739 | 0.404970 | ||||||||
\(776\) | −2.15523 | −0.0773683 | ||||||||
\(777\) | −10.0115 | −0.359159 | ||||||||
\(778\) | 0.901760 | 0.0323297 | ||||||||
\(779\) | −5.10848 | −0.183030 | ||||||||
\(780\) | 0.819717 | 0.0293506 | ||||||||
\(781\) | −51.9382 | −1.85849 | ||||||||
\(782\) | 0.372173 | 0.0133089 | ||||||||
\(783\) | 6.51973 | 0.232996 | ||||||||
\(784\) | 70.5063 | 2.51808 | ||||||||
\(785\) | −0.118616 | −0.00423358 | ||||||||
\(786\) | 0.114608 | 0.00408794 | ||||||||
\(787\) | −30.6959 | −1.09419 | −0.547096 | − | 0.837070i | \(-0.684267\pi\) | ||||
−0.547096 | + | 0.837070i | \(0.684267\pi\) | |||||||
\(788\) | −3.42061 | −0.121854 | ||||||||
\(789\) | 22.0305 | 0.784305 | ||||||||
\(790\) | −0.0765986 | −0.00272526 | ||||||||
\(791\) | 12.3586 | 0.439420 | ||||||||
\(792\) | −1.12534 | −0.0399871 | ||||||||
\(793\) | −26.5384 | −0.942405 | ||||||||
\(794\) | −2.18696 | −0.0776123 | ||||||||
\(795\) | 1.20140 | 0.0426092 | ||||||||
\(796\) | 5.17953 | 0.183584 | ||||||||
\(797\) | 9.23042 | 0.326958 | 0.163479 | − | 0.986547i | \(-0.447728\pi\) | ||||
0.163479 | + | 0.986547i | \(0.447728\pi\) | |||||||
\(798\) | 0.260350 | 0.00921631 | ||||||||
\(799\) | −9.60026 | −0.339633 | ||||||||
\(800\) | 3.87040 | 0.136839 | ||||||||
\(801\) | −10.1718 | −0.359402 | ||||||||
\(802\) | 0.542903 | 0.0191706 | ||||||||
\(803\) | −23.3824 | −0.825148 | ||||||||
\(804\) | 16.0807 | 0.567124 | ||||||||
\(805\) | −3.38475 | −0.119297 | ||||||||
\(806\) | 0.507903 | 0.0178901 | ||||||||
\(807\) | 7.05221 | 0.248249 | ||||||||
\(808\) | 2.05771 | 0.0723898 | ||||||||
\(809\) | −3.92763 | −0.138088 | −0.0690440 | − | 0.997614i | \(-0.521995\pi\) | ||||
−0.0690440 | + | 0.997614i | \(0.521995\pi\) | |||||||
\(810\) | −0.00769468 | −0.000270363 0 | ||||||||
\(811\) | −36.1806 | −1.27047 | −0.635236 | − | 0.772318i | \(-0.719097\pi\) | ||||
−0.635236 | + | 0.772318i | \(0.719097\pi\) | |||||||
\(812\) | −64.7189 | −2.27119 | ||||||||
\(813\) | 11.5716 | 0.405835 | ||||||||
\(814\) | −0.566880 | −0.0198691 | ||||||||
\(815\) | 1.04929 | 0.0367549 | ||||||||
\(816\) | 3.97477 | 0.139145 | ||||||||
\(817\) | −2.59662 | −0.0908442 | ||||||||
\(818\) | −0.173290 | −0.00605895 | ||||||||
\(819\) | −17.2223 | −0.601797 | ||||||||
\(820\) | −1.49874 | −0.0523382 | ||||||||
\(821\) | −21.1093 | −0.736720 | −0.368360 | − | 0.929683i | \(-0.620081\pi\) | ||||
−0.368360 | + | 0.929683i | \(0.620081\pi\) | |||||||
\(822\) | −0.111304 | −0.00388218 | ||||||||
\(823\) | −31.6091 | −1.10182 | −0.550912 | − | 0.834563i | \(-0.685720\pi\) | ||||
−0.550912 | + | 0.834563i | \(0.685720\pi\) | |||||||
\(824\) | 3.11151 | 0.108395 | ||||||||
\(825\) | −21.6460 | −0.753618 | ||||||||
\(826\) | 0.745479 | 0.0259385 | ||||||||
\(827\) | −20.8886 | −0.726367 | −0.363183 | − | 0.931718i | \(-0.618310\pi\) | ||||
−0.363183 | + | 0.931718i | \(0.618310\pi\) | |||||||
\(828\) | −11.4502 | −0.397922 | ||||||||
\(829\) | −31.4468 | −1.09219 | −0.546096 | − | 0.837723i | \(-0.683887\pi\) | ||||
−0.546096 | + | 0.837723i | \(0.683887\pi\) | |||||||
\(830\) | −0.0881325 | −0.00305912 | ||||||||
\(831\) | −8.51107 | −0.295246 | ||||||||
\(832\) | −27.3519 | −0.948258 | ||||||||
\(833\) | −17.7385 | −0.614601 | ||||||||
\(834\) | 1.01019 | 0.0349800 | ||||||||
\(835\) | −2.15186 | −0.0744682 | ||||||||
\(836\) | −6.99153 | −0.241807 | ||||||||
\(837\) | 2.26114 | 0.0781564 | ||||||||
\(838\) | −2.06473 | −0.0713248 | ||||||||
\(839\) | 23.1505 | 0.799245 | 0.399622 | − | 0.916680i | \(-0.369141\pi\) | ||||
0.399622 | + | 0.916680i | \(0.369141\pi\) | |||||||
\(840\) | 0.152925 | 0.00527643 | ||||||||
\(841\) | 13.5069 | 0.465756 | ||||||||
\(842\) | 0.326777 | 0.0112615 | ||||||||
\(843\) | 17.8087 | 0.613364 | ||||||||
\(844\) | 26.4092 | 0.909041 | ||||||||
\(845\) | −0.119826 | −0.00412214 | ||||||||
\(846\) | −0.622774 | −0.0214114 | ||||||||
\(847\) | −39.0340 | −1.34123 | ||||||||
\(848\) | −40.2584 | −1.38248 | ||||||||
\(849\) | 21.5937 | 0.741093 | ||||||||
\(850\) | −0.323440 | −0.0110939 | ||||||||
\(851\) | −11.5481 | −0.395862 | ||||||||
\(852\) | 23.8765 | 0.817994 | ||||||||
\(853\) | −54.9840 | −1.88262 | −0.941308 | − | 0.337548i | \(-0.890403\pi\) | ||||
−0.941308 | + | 0.337548i | \(0.890403\pi\) | |||||||
\(854\) | −2.47287 | −0.0846200 | ||||||||
\(855\) | −0.0957122 | −0.00327329 | ||||||||
\(856\) | −1.04056 | −0.0355657 | ||||||||
\(857\) | 32.0628 | 1.09524 | 0.547622 | − | 0.836726i | \(-0.315533\pi\) | ||||
0.547622 | + | 0.836726i | \(0.315533\pi\) | |||||||
\(858\) | −0.975182 | −0.0332922 | ||||||||
\(859\) | −35.0132 | −1.19463 | −0.597317 | − | 0.802005i | \(-0.703767\pi\) | ||||
−0.597317 | + | 0.802005i | \(0.703767\pi\) | |||||||
\(860\) | −0.761802 | −0.0259772 | ||||||||
\(861\) | 31.4886 | 1.07313 | ||||||||
\(862\) | −1.05161 | −0.0358179 | ||||||||
\(863\) | 23.9360 | 0.814793 | 0.407396 | − | 0.913251i | \(-0.366437\pi\) | ||||
0.407396 | + | 0.913251i | \(0.366437\pi\) | |||||||
\(864\) | 0.776264 | 0.0264090 | ||||||||
\(865\) | 1.83644 | 0.0624408 | ||||||||
\(866\) | −1.29429 | −0.0439818 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −22.4455 | −0.761850 | ||||||||
\(869\) | −43.2178 | −1.46606 | ||||||||
\(870\) | −0.0501673 | −0.00170083 | ||||||||
\(871\) | 27.8995 | 0.945339 | ||||||||
\(872\) | 1.56951 | 0.0531503 | ||||||||
\(873\) | −8.31464 | −0.281408 | ||||||||
\(874\) | 0.300310 | 0.0101581 | ||||||||
\(875\) | 5.89139 | 0.199165 | ||||||||
\(876\) | 10.7491 | 0.363179 | ||||||||
\(877\) | 8.94810 | 0.302156 | 0.151078 | − | 0.988522i | \(-0.451726\pi\) | ||||
0.151078 | + | 0.988522i | \(0.451726\pi\) | |||||||
\(878\) | 0.457096 | 0.0154262 | ||||||||
\(879\) | 18.1737 | 0.612984 | ||||||||
\(880\) | −2.04686 | −0.0689995 | ||||||||
\(881\) | 40.0704 | 1.35001 | 0.675004 | − | 0.737814i | \(-0.264142\pi\) | ||||
0.675004 | + | 0.737814i | \(0.264142\pi\) | |||||||
\(882\) | −1.15070 | −0.0387462 | ||||||||
\(883\) | 41.9711 | 1.41244 | 0.706221 | − | 0.707992i | \(-0.250399\pi\) | ||||
0.706221 | + | 0.707992i | \(0.250399\pi\) | |||||||
\(884\) | 6.91069 | 0.232432 | ||||||||
\(885\) | −0.274059 | −0.00921241 | ||||||||
\(886\) | −2.00376 | −0.0673177 | ||||||||
\(887\) | −12.5179 | −0.420309 | −0.210154 | − | 0.977668i | \(-0.567397\pi\) | ||||
−0.210154 | + | 0.977668i | \(0.567397\pi\) | |||||||
\(888\) | 0.521749 | 0.0175087 | ||||||||
\(889\) | −21.7613 | −0.729851 | ||||||||
\(890\) | 0.0782686 | 0.00262357 | ||||||||
\(891\) | −4.34142 | −0.145443 | ||||||||
\(892\) | 4.89318 | 0.163836 | ||||||||
\(893\) | −7.74654 | −0.259228 | ||||||||
\(894\) | 0.379824 | 0.0127032 | ||||||||
\(895\) | −0.444440 | −0.0148560 | ||||||||
\(896\) | −10.2706 | −0.343117 | ||||||||
\(897\) | −19.8657 | −0.663296 | ||||||||
\(898\) | −0.446936 | −0.0149144 | ||||||||
\(899\) | 14.7420 | 0.491674 | ||||||||
\(900\) | 9.95088 | 0.331696 | ||||||||
\(901\) | 10.1285 | 0.337429 | ||||||||
\(902\) | 1.78298 | 0.0593669 | ||||||||
\(903\) | 16.0055 | 0.532631 | ||||||||
\(904\) | −0.644069 | −0.0214214 | ||||||||
\(905\) | −1.39726 | −0.0464466 | ||||||||
\(906\) | 0.630566 | 0.0209492 | ||||||||
\(907\) | 25.4570 | 0.845287 | 0.422644 | − | 0.906296i | \(-0.361102\pi\) | ||||
0.422644 | + | 0.906296i | \(0.361102\pi\) | |||||||
\(908\) | 33.2018 | 1.10184 | ||||||||
\(909\) | 7.93840 | 0.263300 | ||||||||
\(910\) | 0.132520 | 0.00439301 | ||||||||
\(911\) | −28.7376 | −0.952118 | −0.476059 | − | 0.879413i | \(-0.657935\pi\) | ||||
−0.476059 | + | 0.879413i | \(0.657935\pi\) | |||||||
\(912\) | 3.20728 | 0.106204 | ||||||||
\(913\) | −49.7253 | −1.64567 | ||||||||
\(914\) | 0.563431 | 0.0186366 | ||||||||
\(915\) | 0.909099 | 0.0300539 | ||||||||
\(916\) | 34.3256 | 1.13415 | ||||||||
\(917\) | −8.78728 | −0.290182 | ||||||||
\(918\) | −0.0648705 | −0.00214105 | ||||||||
\(919\) | 34.9113 | 1.15162 | 0.575809 | − | 0.817584i | \(-0.304687\pi\) | ||||
0.575809 | + | 0.817584i | \(0.304687\pi\) | |||||||
\(920\) | 0.176397 | 0.00581564 | ||||||||
\(921\) | 3.61718 | 0.119190 | ||||||||
\(922\) | 0.887165 | 0.0292172 | ||||||||
\(923\) | 41.4248 | 1.36351 | ||||||||
\(924\) | 43.0957 | 1.41774 | ||||||||
\(925\) | 10.0359 | 0.329979 | ||||||||
\(926\) | −0.126240 | −0.00414850 | ||||||||
\(927\) | 12.0039 | 0.394258 | ||||||||
\(928\) | 5.06103 | 0.166137 | ||||||||
\(929\) | 41.1661 | 1.35062 | 0.675308 | − | 0.737536i | \(-0.264011\pi\) | ||||
0.675308 | + | 0.737536i | \(0.264011\pi\) | |||||||
\(930\) | −0.0173988 | −0.000570528 0 | ||||||||
\(931\) | −14.3133 | −0.469100 | ||||||||
\(932\) | 7.66125 | 0.250953 | ||||||||
\(933\) | 22.1185 | 0.724127 | ||||||||
\(934\) | −0.782839 | −0.0256153 | ||||||||
\(935\) | 0.514962 | 0.0168411 | ||||||||
\(936\) | 0.897545 | 0.0293372 | ||||||||
\(937\) | −32.2313 | −1.05295 | −0.526475 | − | 0.850191i | \(-0.676487\pi\) | ||||
−0.526475 | + | 0.850191i | \(0.676487\pi\) | |||||||
\(938\) | 2.59971 | 0.0848834 | ||||||||
\(939\) | −11.2934 | −0.368545 | ||||||||
\(940\) | −2.27270 | −0.0741272 | ||||||||
\(941\) | −9.17313 | −0.299035 | −0.149518 | − | 0.988759i | \(-0.547772\pi\) | ||||
−0.149518 | + | 0.988759i | \(0.547772\pi\) | |||||||
\(942\) | −0.0648705 | −0.00211360 | ||||||||
\(943\) | 36.3216 | 1.18280 | ||||||||
\(944\) | 9.18361 | 0.298901 | ||||||||
\(945\) | 0.589969 | 0.0191917 | ||||||||
\(946\) | 0.906282 | 0.0294658 | ||||||||
\(947\) | −28.3405 | −0.920944 | −0.460472 | − | 0.887674i | \(-0.652320\pi\) | ||||
−0.460472 | + | 0.887674i | \(0.652320\pi\) | |||||||
\(948\) | 19.8676 | 0.645270 | ||||||||
\(949\) | 18.6493 | 0.605383 | ||||||||
\(950\) | −0.260987 | −0.00846752 | ||||||||
\(951\) | 7.17556 | 0.232683 | ||||||||
\(952\) | 1.28925 | 0.0417848 | ||||||||
\(953\) | 7.59226 | 0.245937 | 0.122969 | − | 0.992411i | \(-0.460759\pi\) | ||||
0.122969 | + | 0.992411i | \(0.460759\pi\) | |||||||
\(954\) | 0.657040 | 0.0212725 | ||||||||
\(955\) | −2.70568 | −0.0875537 | ||||||||
\(956\) | −14.3252 | −0.463310 | ||||||||
\(957\) | −28.3049 | −0.914969 | ||||||||
\(958\) | −1.07200 | −0.0346347 | ||||||||
\(959\) | 8.53397 | 0.275576 | ||||||||
\(960\) | 0.936969 | 0.0302405 | ||||||||
\(961\) | −25.8872 | −0.835072 | ||||||||
\(962\) | 0.452131 | 0.0145773 | ||||||||
\(963\) | −4.01437 | −0.129361 | ||||||||
\(964\) | 46.2176 | 1.48857 | ||||||||
\(965\) | −0.846747 | −0.0272577 | ||||||||
\(966\) | −1.85111 | −0.0595584 | ||||||||
\(967\) | −14.0558 | −0.452005 | −0.226002 | − | 0.974127i | \(-0.572566\pi\) | ||||
−0.226002 | + | 0.974127i | \(0.572566\pi\) | |||||||
\(968\) | 2.03426 | 0.0653837 | ||||||||
\(969\) | −0.806909 | −0.0259216 | ||||||||
\(970\) | 0.0639785 | 0.00205423 | ||||||||
\(971\) | −19.6087 | −0.629273 | −0.314636 | − | 0.949212i | \(-0.601883\pi\) | ||||
−0.314636 | + | 0.949212i | \(0.601883\pi\) | |||||||
\(972\) | 1.99579 | 0.0640151 | ||||||||
\(973\) | −77.4536 | −2.48305 | ||||||||
\(974\) | 0.875474 | 0.0280520 | ||||||||
\(975\) | 17.2644 | 0.552904 | ||||||||
\(976\) | −30.4635 | −0.975113 | ||||||||
\(977\) | 33.3842 | 1.06806 | 0.534028 | − | 0.845467i | \(-0.320678\pi\) | ||||
0.534028 | + | 0.845467i | \(0.320678\pi\) | |||||||
\(978\) | 0.573850 | 0.0183497 | ||||||||
\(979\) | 44.1600 | 1.41136 | ||||||||
\(980\) | −4.19927 | −0.134141 | ||||||||
\(981\) | 6.05499 | 0.193321 | ||||||||
\(982\) | 0.0544201 | 0.00173662 | ||||||||
\(983\) | −55.2412 | −1.76192 | −0.880960 | − | 0.473190i | \(-0.843102\pi\) | ||||
−0.880960 | + | 0.473190i | \(0.843102\pi\) | |||||||
\(984\) | −1.64104 | −0.0523143 | ||||||||
\(985\) | 0.203297 | 0.00647759 | ||||||||
\(986\) | −0.422939 | −0.0134691 | ||||||||
\(987\) | 47.7496 | 1.51989 | ||||||||
\(988\) | 5.57629 | 0.177406 | ||||||||
\(989\) | 18.4621 | 0.587061 | ||||||||
\(990\) | 0.0334059 | 0.00106171 | ||||||||
\(991\) | −21.6242 | −0.686916 | −0.343458 | − | 0.939168i | \(-0.611598\pi\) | ||||
−0.343458 | + | 0.939168i | \(0.611598\pi\) | |||||||
\(992\) | 1.75524 | 0.0557290 | ||||||||
\(993\) | −19.5660 | −0.620908 | ||||||||
\(994\) | 3.86001 | 0.122432 | ||||||||
\(995\) | −0.307835 | −0.00975903 | ||||||||
\(996\) | 22.8592 | 0.724321 | ||||||||
\(997\) | −34.0508 | −1.07840 | −0.539200 | − | 0.842178i | \(-0.681273\pi\) | ||||
−0.539200 | + | 0.842178i | \(0.681273\pi\) | |||||||
\(998\) | −1.34826 | −0.0426783 | ||||||||
\(999\) | 2.01285 | 0.0636837 |
(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 | 8007.2.a.f.1.24 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.24 | ✓ | 48 | 1.1 | even | 1 | trivial |