Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 22x^{7} + 20x^{6} + 129x^{5} - 106x^{4} - 126x^{3} + 48x^{2} + 24x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.44979\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.44979 | 0.648367 | 0.324184 | − | 0.945994i | \(-0.394910\pi\) | ||||
0.324184 | + | 0.945994i | \(0.394910\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.37806 | 1.65475 | 0.827375 | − | 0.561650i | \(-0.189833\pi\) | ||||
0.827375 | + | 0.561650i | \(0.189833\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.44979 | −0.458465 | ||||||||
\(11\) | 5.18439 | 1.56315 | 0.781576 | − | 0.623810i | \(-0.214416\pi\) | ||||
0.781576 | + | 0.623810i | \(0.214416\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.77261 | −0.491634 | −0.245817 | − | 0.969316i | \(-0.579056\pi\) | ||||
−0.245817 | + | 0.969316i | \(0.579056\pi\) | |||||||
\(14\) | −4.37806 | −1.17008 | ||||||||
\(15\) | 1.44979 | 0.374335 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.63563 | 0.375240 | 0.187620 | − | 0.982242i | \(-0.439923\pi\) | ||||
0.187620 | + | 0.982242i | \(0.439923\pi\) | |||||||
\(20\) | 1.44979 | 0.324184 | ||||||||
\(21\) | 4.37806 | 0.955370 | ||||||||
\(22\) | −5.18439 | −1.10532 | ||||||||
\(23\) | 0.245496 | 0.0511895 | 0.0255948 | − | 0.999672i | \(-0.491852\pi\) | ||||
0.0255948 | + | 0.999672i | \(0.491852\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.89810 | −0.579620 | ||||||||
\(26\) | 1.77261 | 0.347638 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.37806 | 0.827375 | ||||||||
\(29\) | 4.12193 | 0.765423 | 0.382711 | − | 0.923868i | \(-0.374990\pi\) | ||||
0.382711 | + | 0.923868i | \(0.374990\pi\) | |||||||
\(30\) | −1.44979 | −0.264695 | ||||||||
\(31\) | −4.83360 | −0.868140 | −0.434070 | − | 0.900879i | \(-0.642923\pi\) | ||||
−0.434070 | + | 0.900879i | \(0.642923\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.18439 | 0.902486 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 6.34728 | 1.07289 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.94495 | 1.30614 | 0.653071 | − | 0.757297i | \(-0.273480\pi\) | ||||
0.653071 | + | 0.757297i | \(0.273480\pi\) | |||||||
\(38\) | −1.63563 | −0.265335 | ||||||||
\(39\) | −1.77261 | −0.283845 | ||||||||
\(40\) | −1.44979 | −0.229232 | ||||||||
\(41\) | −9.26927 | −1.44762 | −0.723809 | − | 0.690001i | \(-0.757610\pi\) | ||||
−0.723809 | + | 0.690001i | \(0.757610\pi\) | |||||||
\(42\) | −4.37806 | −0.675549 | ||||||||
\(43\) | −1.10770 | −0.168923 | −0.0844614 | − | 0.996427i | \(-0.526917\pi\) | ||||
−0.0844614 | + | 0.996427i | \(0.526917\pi\) | |||||||
\(44\) | 5.18439 | 0.781576 | ||||||||
\(45\) | 1.44979 | 0.216122 | ||||||||
\(46\) | −0.245496 | −0.0361965 | ||||||||
\(47\) | 4.83205 | 0.704827 | 0.352414 | − | 0.935844i | \(-0.385361\pi\) | ||||
0.352414 | + | 0.935844i | \(0.385361\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 12.1674 | 1.73820 | ||||||||
\(50\) | 2.89810 | 0.409853 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −1.77261 | −0.245817 | ||||||||
\(53\) | −6.02547 | −0.827662 | −0.413831 | − | 0.910354i | \(-0.635809\pi\) | ||||
−0.413831 | + | 0.910354i | \(0.635809\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 7.51629 | 1.01350 | ||||||||
\(56\) | −4.37806 | −0.585042 | ||||||||
\(57\) | 1.63563 | 0.216645 | ||||||||
\(58\) | −4.12193 | −0.541236 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 1.44979 | 0.187168 | ||||||||
\(61\) | 12.3248 | 1.57802 | 0.789012 | − | 0.614377i | \(-0.210593\pi\) | ||||
0.789012 | + | 0.614377i | \(0.210593\pi\) | |||||||
\(62\) | 4.83360 | 0.613868 | ||||||||
\(63\) | 4.37806 | 0.551583 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.56992 | −0.318760 | ||||||||
\(66\) | −5.18439 | −0.638154 | ||||||||
\(67\) | 1.78528 | 0.218107 | 0.109053 | − | 0.994036i | \(-0.465218\pi\) | ||||
0.109053 | + | 0.994036i | \(0.465218\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 0.245496 | 0.0295543 | ||||||||
\(70\) | −6.34728 | −0.758645 | ||||||||
\(71\) | 1.68929 | 0.200482 | 0.100241 | − | 0.994963i | \(-0.468039\pi\) | ||||
0.100241 | + | 0.994963i | \(0.468039\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −3.63143 | −0.425026 | −0.212513 | − | 0.977158i | \(-0.568165\pi\) | ||||
−0.212513 | + | 0.977158i | \(0.568165\pi\) | |||||||
\(74\) | −7.94495 | −0.923582 | ||||||||
\(75\) | −2.89810 | −0.334644 | ||||||||
\(76\) | 1.63563 | 0.187620 | ||||||||
\(77\) | 22.6975 | 2.58663 | ||||||||
\(78\) | 1.77261 | 0.200709 | ||||||||
\(79\) | −8.59258 | −0.966741 | −0.483371 | − | 0.875416i | \(-0.660588\pi\) | ||||
−0.483371 | + | 0.875416i | \(0.660588\pi\) | |||||||
\(80\) | 1.44979 | 0.162092 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.26927 | 1.02362 | ||||||||
\(83\) | 1.43522 | 0.157536 | 0.0787678 | − | 0.996893i | \(-0.474901\pi\) | ||||
0.0787678 | + | 0.996893i | \(0.474901\pi\) | |||||||
\(84\) | 4.37806 | 0.477685 | ||||||||
\(85\) | 1.44979 | 0.157252 | ||||||||
\(86\) | 1.10770 | 0.119446 | ||||||||
\(87\) | 4.12193 | 0.441917 | ||||||||
\(88\) | −5.18439 | −0.552658 | ||||||||
\(89\) | 3.26823 | 0.346432 | 0.173216 | − | 0.984884i | \(-0.444584\pi\) | ||||
0.173216 | + | 0.984884i | \(0.444584\pi\) | |||||||
\(90\) | −1.44979 | −0.152822 | ||||||||
\(91\) | −7.76060 | −0.813532 | ||||||||
\(92\) | 0.245496 | 0.0255948 | ||||||||
\(93\) | −4.83360 | −0.501221 | ||||||||
\(94\) | −4.83205 | −0.498388 | ||||||||
\(95\) | 2.37133 | 0.243294 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −4.03329 | −0.409519 | −0.204759 | − | 0.978812i | \(-0.565641\pi\) | ||||
−0.204759 | + | 0.978812i | \(0.565641\pi\) | |||||||
\(98\) | −12.1674 | −1.22909 | ||||||||
\(99\) | 5.18439 | 0.521051 | ||||||||
\(100\) | −2.89810 | −0.289810 | ||||||||
\(101\) | −2.07672 | −0.206641 | −0.103321 | − | 0.994648i | \(-0.532947\pi\) | ||||
−0.103321 | + | 0.994648i | \(0.532947\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −6.47581 | −0.638080 | −0.319040 | − | 0.947741i | \(-0.603360\pi\) | ||||
−0.319040 | + | 0.947741i | \(0.603360\pi\) | |||||||
\(104\) | 1.77261 | 0.173819 | ||||||||
\(105\) | 6.34728 | 0.619431 | ||||||||
\(106\) | 6.02547 | 0.585245 | ||||||||
\(107\) | 16.8654 | 1.63044 | 0.815221 | − | 0.579150i | \(-0.196615\pi\) | ||||
0.815221 | + | 0.579150i | \(0.196615\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −2.54545 | −0.243810 | −0.121905 | − | 0.992542i | \(-0.538900\pi\) | ||||
−0.121905 | + | 0.992542i | \(0.538900\pi\) | |||||||
\(110\) | −7.51629 | −0.716651 | ||||||||
\(111\) | 7.94495 | 0.754101 | ||||||||
\(112\) | 4.37806 | 0.413687 | ||||||||
\(113\) | −0.191265 | −0.0179927 | −0.00899635 | − | 0.999960i | \(-0.502864\pi\) | ||||
−0.00899635 | + | 0.999960i | \(0.502864\pi\) | |||||||
\(114\) | −1.63563 | −0.153191 | ||||||||
\(115\) | 0.355919 | 0.0331896 | ||||||||
\(116\) | 4.12193 | 0.382711 | ||||||||
\(117\) | −1.77261 | −0.163878 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 4.37806 | 0.401336 | ||||||||
\(120\) | −1.44979 | −0.132347 | ||||||||
\(121\) | 15.8779 | 1.44345 | ||||||||
\(122\) | −12.3248 | −1.11583 | ||||||||
\(123\) | −9.26927 | −0.835782 | ||||||||
\(124\) | −4.83360 | −0.434070 | ||||||||
\(125\) | −11.4506 | −1.02417 | ||||||||
\(126\) | −4.37806 | −0.390028 | ||||||||
\(127\) | −16.0068 | −1.42038 | −0.710189 | − | 0.704011i | \(-0.751390\pi\) | ||||
−0.710189 | + | 0.704011i | \(0.751390\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.10770 | −0.0975276 | ||||||||
\(130\) | 2.56992 | 0.225397 | ||||||||
\(131\) | 14.9695 | 1.30789 | 0.653945 | − | 0.756542i | \(-0.273113\pi\) | ||||
0.653945 | + | 0.756542i | \(0.273113\pi\) | |||||||
\(132\) | 5.18439 | 0.451243 | ||||||||
\(133\) | 7.16090 | 0.620929 | ||||||||
\(134\) | −1.78528 | −0.154225 | ||||||||
\(135\) | 1.44979 | 0.124778 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 0.381874 | 0.0326257 | 0.0163128 | − | 0.999867i | \(-0.494807\pi\) | ||||
0.0163128 | + | 0.999867i | \(0.494807\pi\) | |||||||
\(138\) | −0.245496 | −0.0208980 | ||||||||
\(139\) | 3.65947 | 0.310392 | 0.155196 | − | 0.987884i | \(-0.450399\pi\) | ||||
0.155196 | + | 0.987884i | \(0.450399\pi\) | |||||||
\(140\) | 6.34728 | 0.536443 | ||||||||
\(141\) | 4.83205 | 0.406932 | ||||||||
\(142\) | −1.68929 | −0.141762 | ||||||||
\(143\) | −9.18992 | −0.768500 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.97594 | 0.496275 | ||||||||
\(146\) | 3.63143 | 0.300539 | ||||||||
\(147\) | 12.1674 | 1.00355 | ||||||||
\(148\) | 7.94495 | 0.653071 | ||||||||
\(149\) | 13.6599 | 1.11906 | 0.559531 | − | 0.828809i | \(-0.310981\pi\) | ||||
0.559531 | + | 0.828809i | \(0.310981\pi\) | |||||||
\(150\) | 2.89810 | 0.236629 | ||||||||
\(151\) | −19.2914 | −1.56991 | −0.784955 | − | 0.619553i | \(-0.787314\pi\) | ||||
−0.784955 | + | 0.619553i | \(0.787314\pi\) | |||||||
\(152\) | −1.63563 | −0.132667 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −22.6975 | −1.82902 | ||||||||
\(155\) | −7.00772 | −0.562874 | ||||||||
\(156\) | −1.77261 | −0.141923 | ||||||||
\(157\) | 10.3290 | 0.824342 | 0.412171 | − | 0.911106i | \(-0.364771\pi\) | ||||
0.412171 | + | 0.911106i | \(0.364771\pi\) | |||||||
\(158\) | 8.59258 | 0.683589 | ||||||||
\(159\) | −6.02547 | −0.477851 | ||||||||
\(160\) | −1.44979 | −0.114616 | ||||||||
\(161\) | 1.07480 | 0.0847058 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.7369 | −0.919306 | −0.459653 | − | 0.888099i | \(-0.652026\pi\) | ||||
−0.459653 | + | 0.888099i | \(0.652026\pi\) | |||||||
\(164\) | −9.26927 | −0.723809 | ||||||||
\(165\) | 7.51629 | 0.585143 | ||||||||
\(166\) | −1.43522 | −0.111394 | ||||||||
\(167\) | 0.647953 | 0.0501401 | 0.0250701 | − | 0.999686i | \(-0.492019\pi\) | ||||
0.0250701 | + | 0.999686i | \(0.492019\pi\) | |||||||
\(168\) | −4.37806 | −0.337774 | ||||||||
\(169\) | −9.85784 | −0.758296 | ||||||||
\(170\) | −1.44979 | −0.111194 | ||||||||
\(171\) | 1.63563 | 0.125080 | ||||||||
\(172\) | −1.10770 | −0.0844614 | ||||||||
\(173\) | −2.21096 | −0.168097 | −0.0840483 | − | 0.996462i | \(-0.526785\pi\) | ||||
−0.0840483 | + | 0.996462i | \(0.526785\pi\) | |||||||
\(174\) | −4.12193 | −0.312483 | ||||||||
\(175\) | −12.6880 | −0.959125 | ||||||||
\(176\) | 5.18439 | 0.390788 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | −3.26823 | −0.244964 | ||||||||
\(179\) | −2.20048 | −0.164472 | −0.0822359 | − | 0.996613i | \(-0.526206\pi\) | ||||
−0.0822359 | + | 0.996613i | \(0.526206\pi\) | |||||||
\(180\) | 1.44979 | 0.108061 | ||||||||
\(181\) | −16.8381 | −1.25156 | −0.625781 | − | 0.779999i | \(-0.715220\pi\) | ||||
−0.625781 | + | 0.779999i | \(0.715220\pi\) | |||||||
\(182\) | 7.76060 | 0.575254 | ||||||||
\(183\) | 12.3248 | 0.911073 | ||||||||
\(184\) | −0.245496 | −0.0180982 | ||||||||
\(185\) | 11.5185 | 0.846860 | ||||||||
\(186\) | 4.83360 | 0.354417 | ||||||||
\(187\) | 5.18439 | 0.379120 | ||||||||
\(188\) | 4.83205 | 0.352414 | ||||||||
\(189\) | 4.37806 | 0.318457 | ||||||||
\(190\) | −2.37133 | −0.172035 | ||||||||
\(191\) | 7.42739 | 0.537427 | 0.268713 | − | 0.963220i | \(-0.413402\pi\) | ||||
0.268713 | + | 0.963220i | \(0.413402\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −4.61155 | −0.331947 | −0.165973 | − | 0.986130i | \(-0.553077\pi\) | ||||
−0.165973 | + | 0.986130i | \(0.553077\pi\) | |||||||
\(194\) | 4.03329 | 0.289573 | ||||||||
\(195\) | −2.56992 | −0.184036 | ||||||||
\(196\) | 12.1674 | 0.869098 | ||||||||
\(197\) | −0.0799799 | −0.00569834 | −0.00284917 | − | 0.999996i | \(-0.500907\pi\) | ||||
−0.00284917 | + | 0.999996i | \(0.500907\pi\) | |||||||
\(198\) | −5.18439 | −0.368439 | ||||||||
\(199\) | −14.5150 | −1.02894 | −0.514472 | − | 0.857507i | \(-0.672012\pi\) | ||||
−0.514472 | + | 0.857507i | \(0.672012\pi\) | |||||||
\(200\) | 2.89810 | 0.204927 | ||||||||
\(201\) | 1.78528 | 0.125924 | ||||||||
\(202\) | 2.07672 | 0.146118 | ||||||||
\(203\) | 18.0460 | 1.26658 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −13.4385 | −0.938588 | ||||||||
\(206\) | 6.47581 | 0.451191 | ||||||||
\(207\) | 0.245496 | 0.0170632 | ||||||||
\(208\) | −1.77261 | −0.122909 | ||||||||
\(209\) | 8.47977 | 0.586558 | ||||||||
\(210\) | −6.34728 | −0.438004 | ||||||||
\(211\) | −20.9886 | −1.44491 | −0.722456 | − | 0.691417i | \(-0.756987\pi\) | ||||
−0.722456 | + | 0.691417i | \(0.756987\pi\) | |||||||
\(212\) | −6.02547 | −0.413831 | ||||||||
\(213\) | 1.68929 | 0.115748 | ||||||||
\(214\) | −16.8654 | −1.15290 | ||||||||
\(215\) | −1.60594 | −0.109524 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −21.1618 | −1.43655 | ||||||||
\(218\) | 2.54545 | 0.172400 | ||||||||
\(219\) | −3.63143 | −0.245389 | ||||||||
\(220\) | 7.51629 | 0.506748 | ||||||||
\(221\) | −1.77261 | −0.119239 | ||||||||
\(222\) | −7.94495 | −0.533230 | ||||||||
\(223\) | −5.05973 | −0.338824 | −0.169412 | − | 0.985545i | \(-0.554187\pi\) | ||||
−0.169412 | + | 0.985545i | \(0.554187\pi\) | |||||||
\(224\) | −4.37806 | −0.292521 | ||||||||
\(225\) | −2.89810 | −0.193207 | ||||||||
\(226\) | 0.191265 | 0.0127228 | ||||||||
\(227\) | −12.6609 | −0.840332 | −0.420166 | − | 0.907447i | \(-0.638028\pi\) | ||||
−0.420166 | + | 0.907447i | \(0.638028\pi\) | |||||||
\(228\) | 1.63563 | 0.108323 | ||||||||
\(229\) | 1.68676 | 0.111464 | 0.0557320 | − | 0.998446i | \(-0.482251\pi\) | ||||
0.0557320 | + | 0.998446i | \(0.482251\pi\) | |||||||
\(230\) | −0.355919 | −0.0234686 | ||||||||
\(231\) | 22.6975 | 1.49339 | ||||||||
\(232\) | −4.12193 | −0.270618 | ||||||||
\(233\) | 12.5530 | 0.822376 | 0.411188 | − | 0.911551i | \(-0.365114\pi\) | ||||
0.411188 | + | 0.911551i | \(0.365114\pi\) | |||||||
\(234\) | 1.77261 | 0.115879 | ||||||||
\(235\) | 7.00548 | 0.456987 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −8.59258 | −0.558148 | ||||||||
\(238\) | −4.37806 | −0.283787 | ||||||||
\(239\) | 10.9851 | 0.710565 | 0.355283 | − | 0.934759i | \(-0.384385\pi\) | ||||
0.355283 | + | 0.934759i | \(0.384385\pi\) | |||||||
\(240\) | 1.44979 | 0.0935838 | ||||||||
\(241\) | −10.7798 | −0.694386 | −0.347193 | − | 0.937794i | \(-0.612865\pi\) | ||||
−0.347193 | + | 0.937794i | \(0.612865\pi\) | |||||||
\(242\) | −15.8779 | −1.02067 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.3248 | 0.789012 | ||||||||
\(245\) | 17.6402 | 1.12699 | ||||||||
\(246\) | 9.26927 | 0.590987 | ||||||||
\(247\) | −2.89935 | −0.184481 | ||||||||
\(248\) | 4.83360 | 0.306934 | ||||||||
\(249\) | 1.43522 | 0.0909532 | ||||||||
\(250\) | 11.4506 | 0.724200 | ||||||||
\(251\) | −10.3017 | −0.650238 | −0.325119 | − | 0.945673i | \(-0.605404\pi\) | ||||
−0.325119 | + | 0.945673i | \(0.605404\pi\) | |||||||
\(252\) | 4.37806 | 0.275792 | ||||||||
\(253\) | 1.27275 | 0.0800170 | ||||||||
\(254\) | 16.0068 | 1.00436 | ||||||||
\(255\) | 1.44979 | 0.0907896 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.2138 | 0.949014 | 0.474507 | − | 0.880252i | \(-0.342626\pi\) | ||||
0.474507 | + | 0.880252i | \(0.342626\pi\) | |||||||
\(258\) | 1.10770 | 0.0689624 | ||||||||
\(259\) | 34.7834 | 2.16134 | ||||||||
\(260\) | −2.56992 | −0.159380 | ||||||||
\(261\) | 4.12193 | 0.255141 | ||||||||
\(262\) | −14.9695 | −0.924818 | ||||||||
\(263\) | −24.4168 | −1.50560 | −0.752802 | − | 0.658247i | \(-0.771298\pi\) | ||||
−0.752802 | + | 0.658247i | \(0.771298\pi\) | |||||||
\(264\) | −5.18439 | −0.319077 | ||||||||
\(265\) | −8.73568 | −0.536629 | ||||||||
\(266\) | −7.16090 | −0.439063 | ||||||||
\(267\) | 3.26823 | 0.200013 | ||||||||
\(268\) | 1.78528 | 0.109053 | ||||||||
\(269\) | 11.1815 | 0.681750 | 0.340875 | − | 0.940109i | \(-0.389277\pi\) | ||||
0.340875 | + | 0.940109i | \(0.389277\pi\) | |||||||
\(270\) | −1.44979 | −0.0882316 | ||||||||
\(271\) | 7.52070 | 0.456850 | 0.228425 | − | 0.973562i | \(-0.426642\pi\) | ||||
0.228425 | + | 0.973562i | \(0.426642\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −7.76060 | −0.469693 | ||||||||
\(274\) | −0.381874 | −0.0230698 | ||||||||
\(275\) | −15.0249 | −0.906034 | ||||||||
\(276\) | 0.245496 | 0.0147771 | ||||||||
\(277\) | 6.39054 | 0.383970 | 0.191985 | − | 0.981398i | \(-0.438507\pi\) | ||||
0.191985 | + | 0.981398i | \(0.438507\pi\) | |||||||
\(278\) | −3.65947 | −0.219481 | ||||||||
\(279\) | −4.83360 | −0.289380 | ||||||||
\(280\) | −6.34728 | −0.379322 | ||||||||
\(281\) | −10.8901 | −0.649646 | −0.324823 | − | 0.945775i | \(-0.605305\pi\) | ||||
−0.324823 | + | 0.945775i | \(0.605305\pi\) | |||||||
\(282\) | −4.83205 | −0.287745 | ||||||||
\(283\) | 5.70075 | 0.338874 | 0.169437 | − | 0.985541i | \(-0.445805\pi\) | ||||
0.169437 | + | 0.985541i | \(0.445805\pi\) | |||||||
\(284\) | 1.68929 | 0.100241 | ||||||||
\(285\) | 2.37133 | 0.140466 | ||||||||
\(286\) | 9.18992 | 0.543411 | ||||||||
\(287\) | −40.5814 | −2.39544 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.97594 | −0.350920 | ||||||||
\(291\) | −4.03329 | −0.236436 | ||||||||
\(292\) | −3.63143 | −0.212513 | ||||||||
\(293\) | 1.45272 | 0.0848690 | 0.0424345 | − | 0.999099i | \(-0.486489\pi\) | ||||
0.0424345 | + | 0.999099i | \(0.486489\pi\) | |||||||
\(294\) | −12.1674 | −0.709615 | ||||||||
\(295\) | 1.44979 | 0.0844102 | ||||||||
\(296\) | −7.94495 | −0.461791 | ||||||||
\(297\) | 5.18439 | 0.300829 | ||||||||
\(298\) | −13.6599 | −0.791296 | ||||||||
\(299\) | −0.435170 | −0.0251665 | ||||||||
\(300\) | −2.89810 | −0.167322 | ||||||||
\(301\) | −4.84957 | −0.279525 | ||||||||
\(302\) | 19.2914 | 1.11009 | ||||||||
\(303\) | −2.07672 | −0.119304 | ||||||||
\(304\) | 1.63563 | 0.0938101 | ||||||||
\(305\) | 17.8684 | 1.02314 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −24.5574 | −1.40156 | −0.700781 | − | 0.713376i | \(-0.747165\pi\) | ||||
−0.700781 | + | 0.713376i | \(0.747165\pi\) | |||||||
\(308\) | 22.6975 | 1.29331 | ||||||||
\(309\) | −6.47581 | −0.368396 | ||||||||
\(310\) | 7.00772 | 0.398012 | ||||||||
\(311\) | −4.47009 | −0.253475 | −0.126738 | − | 0.991936i | \(-0.540451\pi\) | ||||
−0.126738 | + | 0.991936i | \(0.540451\pi\) | |||||||
\(312\) | 1.77261 | 0.100354 | ||||||||
\(313\) | 31.5641 | 1.78411 | 0.892055 | − | 0.451927i | \(-0.149263\pi\) | ||||
0.892055 | + | 0.451927i | \(0.149263\pi\) | |||||||
\(314\) | −10.3290 | −0.582898 | ||||||||
\(315\) | 6.34728 | 0.357629 | ||||||||
\(316\) | −8.59258 | −0.483371 | ||||||||
\(317\) | 16.7785 | 0.942375 | 0.471187 | − | 0.882033i | \(-0.343826\pi\) | ||||
0.471187 | + | 0.882033i | \(0.343826\pi\) | |||||||
\(318\) | 6.02547 | 0.337891 | ||||||||
\(319\) | 21.3697 | 1.19647 | ||||||||
\(320\) | 1.44979 | 0.0810459 | ||||||||
\(321\) | 16.8654 | 0.941337 | ||||||||
\(322\) | −1.07480 | −0.0598961 | ||||||||
\(323\) | 1.63563 | 0.0910091 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.13721 | 0.284961 | ||||||||
\(326\) | 11.7369 | 0.650048 | ||||||||
\(327\) | −2.54545 | −0.140764 | ||||||||
\(328\) | 9.26927 | 0.511810 | ||||||||
\(329\) | 21.1550 | 1.16631 | ||||||||
\(330\) | −7.51629 | −0.413758 | ||||||||
\(331\) | 8.17673 | 0.449434 | 0.224717 | − | 0.974424i | \(-0.427854\pi\) | ||||
0.224717 | + | 0.974424i | \(0.427854\pi\) | |||||||
\(332\) | 1.43522 | 0.0787678 | ||||||||
\(333\) | 7.94495 | 0.435381 | ||||||||
\(334\) | −0.647953 | −0.0354544 | ||||||||
\(335\) | 2.58829 | 0.141413 | ||||||||
\(336\) | 4.37806 | 0.238843 | ||||||||
\(337\) | 6.57262 | 0.358033 | 0.179017 | − | 0.983846i | \(-0.442708\pi\) | ||||
0.179017 | + | 0.983846i | \(0.442708\pi\) | |||||||
\(338\) | 9.85784 | 0.536196 | ||||||||
\(339\) | −0.191265 | −0.0103881 | ||||||||
\(340\) | 1.44979 | 0.0786261 | ||||||||
\(341\) | −25.0593 | −1.35704 | ||||||||
\(342\) | −1.63563 | −0.0884450 | ||||||||
\(343\) | 22.6230 | 1.22153 | ||||||||
\(344\) | 1.10770 | 0.0597232 | ||||||||
\(345\) | 0.355919 | 0.0191620 | ||||||||
\(346\) | 2.21096 | 0.118862 | ||||||||
\(347\) | 12.2280 | 0.656432 | 0.328216 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328216 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(348\) | 4.12193 | 0.220959 | ||||||||
\(349\) | 3.69015 | 0.197529 | 0.0987645 | − | 0.995111i | \(-0.468511\pi\) | ||||
0.0987645 | + | 0.995111i | \(0.468511\pi\) | |||||||
\(350\) | 12.6880 | 0.678204 | ||||||||
\(351\) | −1.77261 | −0.0946151 | ||||||||
\(352\) | −5.18439 | −0.276329 | ||||||||
\(353\) | −10.4464 | −0.556007 | −0.278004 | − | 0.960580i | \(-0.589673\pi\) | ||||
−0.278004 | + | 0.960580i | \(0.589673\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 2.44912 | 0.129986 | ||||||||
\(356\) | 3.26823 | 0.173216 | ||||||||
\(357\) | 4.37806 | 0.231711 | ||||||||
\(358\) | 2.20048 | 0.116299 | ||||||||
\(359\) | −27.4693 | −1.44977 | −0.724887 | − | 0.688867i | \(-0.758108\pi\) | ||||
−0.724887 | + | 0.688867i | \(0.758108\pi\) | |||||||
\(360\) | −1.44979 | −0.0764108 | ||||||||
\(361\) | −16.3247 | −0.859195 | ||||||||
\(362\) | 16.8381 | 0.884988 | ||||||||
\(363\) | 15.8779 | 0.833373 | ||||||||
\(364\) | −7.76060 | −0.406766 | ||||||||
\(365\) | −5.26482 | −0.275573 | ||||||||
\(366\) | −12.3248 | −0.644226 | ||||||||
\(367\) | −23.1923 | −1.21063 | −0.605315 | − | 0.795986i | \(-0.706953\pi\) | ||||
−0.605315 | + | 0.795986i | \(0.706953\pi\) | |||||||
\(368\) | 0.245496 | 0.0127974 | ||||||||
\(369\) | −9.26927 | −0.482539 | ||||||||
\(370\) | −11.5185 | −0.598820 | ||||||||
\(371\) | −26.3798 | −1.36957 | ||||||||
\(372\) | −4.83360 | −0.250610 | ||||||||
\(373\) | −7.72058 | −0.399757 | −0.199878 | − | 0.979821i | \(-0.564055\pi\) | ||||
−0.199878 | + | 0.979821i | \(0.564055\pi\) | |||||||
\(374\) | −5.18439 | −0.268078 | ||||||||
\(375\) | −11.4506 | −0.591307 | ||||||||
\(376\) | −4.83205 | −0.249194 | ||||||||
\(377\) | −7.30658 | −0.376308 | ||||||||
\(378\) | −4.37806 | −0.225183 | ||||||||
\(379\) | −8.20322 | −0.421371 | −0.210686 | − | 0.977554i | \(-0.567570\pi\) | ||||
−0.210686 | + | 0.977554i | \(0.567570\pi\) | |||||||
\(380\) | 2.37133 | 0.121647 | ||||||||
\(381\) | −16.0068 | −0.820055 | ||||||||
\(382\) | −7.42739 | −0.380018 | ||||||||
\(383\) | 22.7157 | 1.16072 | 0.580359 | − | 0.814361i | \(-0.302912\pi\) | ||||
0.580359 | + | 0.814361i | \(0.302912\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 32.9068 | 1.67708 | ||||||||
\(386\) | 4.61155 | 0.234722 | ||||||||
\(387\) | −1.10770 | −0.0563076 | ||||||||
\(388\) | −4.03329 | −0.204759 | ||||||||
\(389\) | −3.21475 | −0.162994 | −0.0814972 | − | 0.996674i | \(-0.525970\pi\) | ||||
−0.0814972 | + | 0.996674i | \(0.525970\pi\) | |||||||
\(390\) | 2.56992 | 0.130133 | ||||||||
\(391\) | 0.245496 | 0.0124153 | ||||||||
\(392\) | −12.1674 | −0.614545 | ||||||||
\(393\) | 14.9695 | 0.755111 | ||||||||
\(394\) | 0.0799799 | 0.00402933 | ||||||||
\(395\) | −12.4575 | −0.626803 | ||||||||
\(396\) | 5.18439 | 0.260525 | ||||||||
\(397\) | 36.4680 | 1.83027 | 0.915137 | − | 0.403143i | \(-0.132082\pi\) | ||||
0.915137 | + | 0.403143i | \(0.132082\pi\) | |||||||
\(398\) | 14.5150 | 0.727573 | ||||||||
\(399\) | 7.16090 | 0.358493 | ||||||||
\(400\) | −2.89810 | −0.144905 | ||||||||
\(401\) | 1.86893 | 0.0933299 | 0.0466650 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466650 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(402\) | −1.78528 | −0.0890418 | ||||||||
\(403\) | 8.56810 | 0.426808 | ||||||||
\(404\) | −2.07672 | −0.103321 | ||||||||
\(405\) | 1.44979 | 0.0720408 | ||||||||
\(406\) | −18.0460 | −0.895609 | ||||||||
\(407\) | 41.1897 | 2.04170 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −25.4421 | −1.25803 | −0.629016 | − | 0.777392i | \(-0.716542\pi\) | ||||
−0.629016 | + | 0.777392i | \(0.716542\pi\) | |||||||
\(410\) | 13.4385 | 0.663682 | ||||||||
\(411\) | 0.381874 | 0.0188364 | ||||||||
\(412\) | −6.47581 | −0.319040 | ||||||||
\(413\) | 4.37806 | 0.215430 | ||||||||
\(414\) | −0.245496 | −0.0120655 | ||||||||
\(415\) | 2.08077 | 0.102141 | ||||||||
\(416\) | 1.77261 | 0.0869095 | ||||||||
\(417\) | 3.65947 | 0.179205 | ||||||||
\(418\) | −8.47977 | −0.414759 | ||||||||
\(419\) | −16.7336 | −0.817491 | −0.408746 | − | 0.912648i | \(-0.634034\pi\) | ||||
−0.408746 | + | 0.912648i | \(0.634034\pi\) | |||||||
\(420\) | 6.34728 | 0.309715 | ||||||||
\(421\) | 3.56961 | 0.173972 | 0.0869861 | − | 0.996210i | \(-0.472276\pi\) | ||||
0.0869861 | + | 0.996210i | \(0.472276\pi\) | |||||||
\(422\) | 20.9886 | 1.02171 | ||||||||
\(423\) | 4.83205 | 0.234942 | ||||||||
\(424\) | 6.02547 | 0.292623 | ||||||||
\(425\) | −2.89810 | −0.140578 | ||||||||
\(426\) | −1.68929 | −0.0818464 | ||||||||
\(427\) | 53.9585 | 2.61124 | ||||||||
\(428\) | 16.8654 | 0.815221 | ||||||||
\(429\) | −9.18992 | −0.443693 | ||||||||
\(430\) | 1.60594 | 0.0774452 | ||||||||
\(431\) | −12.8508 | −0.619000 | −0.309500 | − | 0.950899i | \(-0.600162\pi\) | ||||
−0.309500 | + | 0.950899i | \(0.600162\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −7.89068 | −0.379202 | −0.189601 | − | 0.981861i | \(-0.560719\pi\) | ||||
−0.189601 | + | 0.981861i | \(0.560719\pi\) | |||||||
\(434\) | 21.1618 | 1.01580 | ||||||||
\(435\) | 5.97594 | 0.286525 | ||||||||
\(436\) | −2.54545 | −0.121905 | ||||||||
\(437\) | 0.401542 | 0.0192084 | ||||||||
\(438\) | 3.63143 | 0.173516 | ||||||||
\(439\) | −0.241284 | −0.0115159 | −0.00575793 | − | 0.999983i | \(-0.501833\pi\) | ||||
−0.00575793 | + | 0.999983i | \(0.501833\pi\) | |||||||
\(440\) | −7.51629 | −0.358325 | ||||||||
\(441\) | 12.1674 | 0.579399 | ||||||||
\(442\) | 1.77261 | 0.0843146 | ||||||||
\(443\) | −11.3111 | −0.537406 | −0.268703 | − | 0.963223i | \(-0.586595\pi\) | ||||
−0.268703 | + | 0.963223i | \(0.586595\pi\) | |||||||
\(444\) | 7.94495 | 0.377051 | ||||||||
\(445\) | 4.73826 | 0.224615 | ||||||||
\(446\) | 5.05973 | 0.239585 | ||||||||
\(447\) | 13.6599 | 0.646091 | ||||||||
\(448\) | 4.37806 | 0.206844 | ||||||||
\(449\) | −2.53121 | −0.119455 | −0.0597277 | − | 0.998215i | \(-0.519023\pi\) | ||||
−0.0597277 | + | 0.998215i | \(0.519023\pi\) | |||||||
\(450\) | 2.89810 | 0.136618 | ||||||||
\(451\) | −48.0555 | −2.26285 | ||||||||
\(452\) | −0.191265 | −0.00899635 | ||||||||
\(453\) | −19.2914 | −0.906388 | ||||||||
\(454\) | 12.6609 | 0.594204 | ||||||||
\(455\) | −11.2513 | −0.527468 | ||||||||
\(456\) | −1.63563 | −0.0765956 | ||||||||
\(457\) | −30.7641 | −1.43909 | −0.719543 | − | 0.694448i | \(-0.755649\pi\) | ||||
−0.719543 | + | 0.694448i | \(0.755649\pi\) | |||||||
\(458\) | −1.68676 | −0.0788169 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0.355919 | 0.0165948 | ||||||||
\(461\) | −17.1603 | −0.799233 | −0.399617 | − | 0.916682i | \(-0.630857\pi\) | ||||
−0.399617 | + | 0.916682i | \(0.630857\pi\) | |||||||
\(462\) | −22.6975 | −1.05599 | ||||||||
\(463\) | 8.00799 | 0.372163 | 0.186081 | − | 0.982534i | \(-0.440421\pi\) | ||||
0.186081 | + | 0.982534i | \(0.440421\pi\) | |||||||
\(464\) | 4.12193 | 0.191356 | ||||||||
\(465\) | −7.00772 | −0.324975 | ||||||||
\(466\) | −12.5530 | −0.581507 | ||||||||
\(467\) | 20.3714 | 0.942676 | 0.471338 | − | 0.881953i | \(-0.343771\pi\) | ||||
0.471338 | + | 0.881953i | \(0.343771\pi\) | |||||||
\(468\) | −1.77261 | −0.0819391 | ||||||||
\(469\) | 7.81607 | 0.360912 | ||||||||
\(470\) | −7.00548 | −0.323139 | ||||||||
\(471\) | 10.3290 | 0.475934 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −5.74275 | −0.264052 | ||||||||
\(474\) | 8.59258 | 0.394670 | ||||||||
\(475\) | −4.74023 | −0.217497 | ||||||||
\(476\) | 4.37806 | 0.200668 | ||||||||
\(477\) | −6.02547 | −0.275887 | ||||||||
\(478\) | −10.9851 | −0.502446 | ||||||||
\(479\) | 41.9139 | 1.91509 | 0.957547 | − | 0.288278i | \(-0.0930827\pi\) | ||||
0.957547 | + | 0.288278i | \(0.0930827\pi\) | |||||||
\(480\) | −1.44979 | −0.0661737 | ||||||||
\(481\) | −14.0833 | −0.642144 | ||||||||
\(482\) | 10.7798 | 0.491005 | ||||||||
\(483\) | 1.07480 | 0.0489049 | ||||||||
\(484\) | 15.8779 | 0.721723 | ||||||||
\(485\) | −5.84744 | −0.265519 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −17.0648 | −0.773280 | −0.386640 | − | 0.922231i | \(-0.626364\pi\) | ||||
−0.386640 | + | 0.922231i | \(0.626364\pi\) | |||||||
\(488\) | −12.3248 | −0.557916 | ||||||||
\(489\) | −11.7369 | −0.530762 | ||||||||
\(490\) | −17.6402 | −0.796902 | ||||||||
\(491\) | 29.0665 | 1.31175 | 0.655877 | − | 0.754868i | \(-0.272299\pi\) | ||||
0.655877 | + | 0.754868i | \(0.272299\pi\) | |||||||
\(492\) | −9.26927 | −0.417891 | ||||||||
\(493\) | 4.12193 | 0.185642 | ||||||||
\(494\) | 2.89935 | 0.130448 | ||||||||
\(495\) | 7.51629 | 0.337832 | ||||||||
\(496\) | −4.83360 | −0.217035 | ||||||||
\(497\) | 7.39581 | 0.331748 | ||||||||
\(498\) | −1.43522 | −0.0643136 | ||||||||
\(499\) | 13.3167 | 0.596137 | 0.298069 | − | 0.954544i | \(-0.403658\pi\) | ||||
0.298069 | + | 0.954544i | \(0.403658\pi\) | |||||||
\(500\) | −11.4506 | −0.512087 | ||||||||
\(501\) | 0.647953 | 0.0289484 | ||||||||
\(502\) | 10.3017 | 0.459788 | ||||||||
\(503\) | −1.86807 | −0.0832932 | −0.0416466 | − | 0.999132i | \(-0.513260\pi\) | ||||
−0.0416466 | + | 0.999132i | \(0.513260\pi\) | |||||||
\(504\) | −4.37806 | −0.195014 | ||||||||
\(505\) | −3.01082 | −0.133980 | ||||||||
\(506\) | −1.27275 | −0.0565806 | ||||||||
\(507\) | −9.85784 | −0.437802 | ||||||||
\(508\) | −16.0068 | −0.710189 | ||||||||
\(509\) | 23.2264 | 1.02949 | 0.514746 | − | 0.857342i | \(-0.327886\pi\) | ||||
0.514746 | + | 0.857342i | \(0.327886\pi\) | |||||||
\(510\) | −1.44979 | −0.0641979 | ||||||||
\(511\) | −15.8986 | −0.703312 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.63563 | 0.0722150 | ||||||||
\(514\) | −15.2138 | −0.671054 | ||||||||
\(515\) | −9.38858 | −0.413710 | ||||||||
\(516\) | −1.10770 | −0.0487638 | ||||||||
\(517\) | 25.0512 | 1.10175 | ||||||||
\(518\) | −34.7834 | −1.52830 | ||||||||
\(519\) | −2.21096 | −0.0970506 | ||||||||
\(520\) | 2.56992 | 0.112699 | ||||||||
\(521\) | 33.7971 | 1.48068 | 0.740339 | − | 0.672234i | \(-0.234665\pi\) | ||||
0.740339 | + | 0.672234i | \(0.234665\pi\) | |||||||
\(522\) | −4.12193 | −0.180412 | ||||||||
\(523\) | −28.9913 | −1.26770 | −0.633851 | − | 0.773455i | \(-0.718527\pi\) | ||||
−0.633851 | + | 0.773455i | \(0.718527\pi\) | |||||||
\(524\) | 14.9695 | 0.653945 | ||||||||
\(525\) | −12.6880 | −0.553751 | ||||||||
\(526\) | 24.4168 | 1.06462 | ||||||||
\(527\) | −4.83360 | −0.210555 | ||||||||
\(528\) | 5.18439 | 0.225622 | ||||||||
\(529\) | −22.9397 | −0.997380 | ||||||||
\(530\) | 8.73568 | 0.379454 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 7.16090 | 0.310464 | ||||||||
\(533\) | 16.4308 | 0.711698 | ||||||||
\(534\) | −3.26823 | −0.141430 | ||||||||
\(535\) | 24.4514 | 1.05713 | ||||||||
\(536\) | −1.78528 | −0.0771125 | ||||||||
\(537\) | −2.20048 | −0.0949579 | ||||||||
\(538\) | −11.1815 | −0.482070 | ||||||||
\(539\) | 63.0804 | 2.71706 | ||||||||
\(540\) | 1.44979 | 0.0623892 | ||||||||
\(541\) | 40.4523 | 1.73918 | 0.869590 | − | 0.493774i | \(-0.164383\pi\) | ||||
0.869590 | + | 0.493774i | \(0.164383\pi\) | |||||||
\(542\) | −7.52070 | −0.323042 | ||||||||
\(543\) | −16.8381 | −0.722590 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −3.69038 | −0.158079 | ||||||||
\(546\) | 7.76060 | 0.332123 | ||||||||
\(547\) | 37.6258 | 1.60876 | 0.804381 | − | 0.594114i | \(-0.202497\pi\) | ||||
0.804381 | + | 0.594114i | \(0.202497\pi\) | |||||||
\(548\) | 0.381874 | 0.0163128 | ||||||||
\(549\) | 12.3248 | 0.526008 | ||||||||
\(550\) | 15.0249 | 0.640663 | ||||||||
\(551\) | 6.74197 | 0.287217 | ||||||||
\(552\) | −0.245496 | −0.0104490 | ||||||||
\(553\) | −37.6188 | −1.59971 | ||||||||
\(554\) | −6.39054 | −0.271508 | ||||||||
\(555\) | 11.5185 | 0.488935 | ||||||||
\(556\) | 3.65947 | 0.155196 | ||||||||
\(557\) | 30.0412 | 1.27289 | 0.636443 | − | 0.771324i | \(-0.280405\pi\) | ||||
0.636443 | + | 0.771324i | \(0.280405\pi\) | |||||||
\(558\) | 4.83360 | 0.204623 | ||||||||
\(559\) | 1.96352 | 0.0830482 | ||||||||
\(560\) | 6.34728 | 0.268221 | ||||||||
\(561\) | 5.18439 | 0.218885 | ||||||||
\(562\) | 10.8901 | 0.459369 | ||||||||
\(563\) | 2.98074 | 0.125623 | 0.0628116 | − | 0.998025i | \(-0.479993\pi\) | ||||
0.0628116 | + | 0.998025i | \(0.479993\pi\) | |||||||
\(564\) | 4.83205 | 0.203466 | ||||||||
\(565\) | −0.277295 | −0.0116659 | ||||||||
\(566\) | −5.70075 | −0.239620 | ||||||||
\(567\) | 4.37806 | 0.183861 | ||||||||
\(568\) | −1.68929 | −0.0708811 | ||||||||
\(569\) | 9.68369 | 0.405962 | 0.202981 | − | 0.979183i | \(-0.434937\pi\) | ||||
0.202981 | + | 0.979183i | \(0.434937\pi\) | |||||||
\(570\) | −2.37133 | −0.0993242 | ||||||||
\(571\) | −7.37647 | −0.308696 | −0.154348 | − | 0.988017i | \(-0.549328\pi\) | ||||
−0.154348 | + | 0.988017i | \(0.549328\pi\) | |||||||
\(572\) | −9.18992 | −0.384250 | ||||||||
\(573\) | 7.42739 | 0.310284 | ||||||||
\(574\) | 40.5814 | 1.69383 | ||||||||
\(575\) | −0.711473 | −0.0296705 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 38.6927 | 1.61080 | 0.805400 | − | 0.592732i | \(-0.201950\pi\) | ||||
0.805400 | + | 0.592732i | \(0.201950\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −4.61155 | −0.191650 | ||||||||
\(580\) | 5.97594 | 0.248138 | ||||||||
\(581\) | 6.28346 | 0.260682 | ||||||||
\(582\) | 4.03329 | 0.167185 | ||||||||
\(583\) | −31.2384 | −1.29376 | ||||||||
\(584\) | 3.63143 | 0.150269 | ||||||||
\(585\) | −2.56992 | −0.106253 | ||||||||
\(586\) | −1.45272 | −0.0600114 | ||||||||
\(587\) | −20.2520 | −0.835891 | −0.417946 | − | 0.908472i | \(-0.637250\pi\) | ||||
−0.417946 | + | 0.908472i | \(0.637250\pi\) | |||||||
\(588\) | 12.1674 | 0.501774 | ||||||||
\(589\) | −7.90600 | −0.325761 | ||||||||
\(590\) | −1.44979 | −0.0596871 | ||||||||
\(591\) | −0.0799799 | −0.00328994 | ||||||||
\(592\) | 7.94495 | 0.326535 | ||||||||
\(593\) | 7.92828 | 0.325576 | 0.162788 | − | 0.986661i | \(-0.447951\pi\) | ||||
0.162788 | + | 0.986661i | \(0.447951\pi\) | |||||||
\(594\) | −5.18439 | −0.212718 | ||||||||
\(595\) | 6.34728 | 0.260213 | ||||||||
\(596\) | 13.6599 | 0.559531 | ||||||||
\(597\) | −14.5150 | −0.594061 | ||||||||
\(598\) | 0.435170 | 0.0177954 | ||||||||
\(599\) | 12.5467 | 0.512646 | 0.256323 | − | 0.966591i | \(-0.417489\pi\) | ||||
0.256323 | + | 0.966591i | \(0.417489\pi\) | |||||||
\(600\) | 2.89810 | 0.118314 | ||||||||
\(601\) | 9.91921 | 0.404613 | 0.202307 | − | 0.979322i | \(-0.435156\pi\) | ||||
0.202307 | + | 0.979322i | \(0.435156\pi\) | |||||||
\(602\) | 4.84957 | 0.197654 | ||||||||
\(603\) | 1.78528 | 0.0727023 | ||||||||
\(604\) | −19.2914 | −0.784955 | ||||||||
\(605\) | 23.0197 | 0.935883 | ||||||||
\(606\) | 2.07672 | 0.0843610 | ||||||||
\(607\) | −29.9474 | −1.21553 | −0.607763 | − | 0.794119i | \(-0.707933\pi\) | ||||
−0.607763 | + | 0.794119i | \(0.707933\pi\) | |||||||
\(608\) | −1.63563 | −0.0663337 | ||||||||
\(609\) | 18.0460 | 0.731262 | ||||||||
\(610\) | −17.8684 | −0.723469 | ||||||||
\(611\) | −8.56536 | −0.346517 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 4.40182 | 0.177788 | 0.0888939 | − | 0.996041i | \(-0.471667\pi\) | ||||
0.0888939 | + | 0.996041i | \(0.471667\pi\) | |||||||
\(614\) | 24.5574 | 0.991054 | ||||||||
\(615\) | −13.4385 | −0.541894 | ||||||||
\(616\) | −22.6975 | −0.914510 | ||||||||
\(617\) | −33.9438 | −1.36653 | −0.683263 | − | 0.730172i | \(-0.739440\pi\) | ||||
−0.683263 | + | 0.730172i | \(0.739440\pi\) | |||||||
\(618\) | 6.47581 | 0.260495 | ||||||||
\(619\) | 30.0777 | 1.20892 | 0.604462 | − | 0.796634i | \(-0.293388\pi\) | ||||
0.604462 | + | 0.796634i | \(0.293388\pi\) | |||||||
\(620\) | −7.00772 | −0.281437 | ||||||||
\(621\) | 0.245496 | 0.00985143 | ||||||||
\(622\) | 4.47009 | 0.179234 | ||||||||
\(623\) | 14.3085 | 0.573258 | ||||||||
\(624\) | −1.77261 | −0.0709613 | ||||||||
\(625\) | −2.11053 | −0.0844212 | ||||||||
\(626\) | −31.5641 | −1.26156 | ||||||||
\(627\) | 8.47977 | 0.338649 | ||||||||
\(628\) | 10.3290 | 0.412171 | ||||||||
\(629\) | 7.94495 | 0.316786 | ||||||||
\(630\) | −6.34728 | −0.252882 | ||||||||
\(631\) | 17.1407 | 0.682362 | 0.341181 | − | 0.939998i | \(-0.389173\pi\) | ||||
0.341181 | + | 0.939998i | \(0.389173\pi\) | |||||||
\(632\) | 8.59258 | 0.341795 | ||||||||
\(633\) | −20.9886 | −0.834221 | ||||||||
\(634\) | −16.7785 | −0.666360 | ||||||||
\(635\) | −23.2066 | −0.920927 | ||||||||
\(636\) | −6.02547 | −0.238925 | ||||||||
\(637\) | −21.5680 | −0.854557 | ||||||||
\(638\) | −21.3697 | −0.846034 | ||||||||
\(639\) | 1.68929 | 0.0668273 | ||||||||
\(640\) | −1.44979 | −0.0573081 | ||||||||
\(641\) | −17.7927 | −0.702769 | −0.351385 | − | 0.936231i | \(-0.614289\pi\) | ||||
−0.351385 | + | 0.936231i | \(0.614289\pi\) | |||||||
\(642\) | −16.8654 | −0.665625 | ||||||||
\(643\) | 9.89663 | 0.390285 | 0.195142 | − | 0.980775i | \(-0.437483\pi\) | ||||
0.195142 | + | 0.980775i | \(0.437483\pi\) | |||||||
\(644\) | 1.07480 | 0.0423529 | ||||||||
\(645\) | −1.60594 | −0.0632337 | ||||||||
\(646\) | −1.63563 | −0.0643532 | ||||||||
\(647\) | −31.6652 | −1.24489 | −0.622443 | − | 0.782665i | \(-0.713860\pi\) | ||||
−0.622443 | + | 0.782665i | \(0.713860\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 5.18439 | 0.203505 | ||||||||
\(650\) | −5.13721 | −0.201498 | ||||||||
\(651\) | −21.1618 | −0.829395 | ||||||||
\(652\) | −11.7369 | −0.459653 | ||||||||
\(653\) | −26.7297 | −1.04601 | −0.523007 | − | 0.852328i | \(-0.675190\pi\) | ||||
−0.523007 | + | 0.852328i | \(0.675190\pi\) | |||||||
\(654\) | 2.54545 | 0.0995351 | ||||||||
\(655\) | 21.7027 | 0.847993 | ||||||||
\(656\) | −9.26927 | −0.361904 | ||||||||
\(657\) | −3.63143 | −0.141675 | ||||||||
\(658\) | −21.1550 | −0.824708 | ||||||||
\(659\) | −9.01170 | −0.351046 | −0.175523 | − | 0.984475i | \(-0.556162\pi\) | ||||
−0.175523 | + | 0.984475i | \(0.556162\pi\) | |||||||
\(660\) | 7.51629 | 0.292571 | ||||||||
\(661\) | −28.0363 | −1.09049 | −0.545244 | − | 0.838278i | \(-0.683563\pi\) | ||||
−0.545244 | + | 0.838278i | \(0.683563\pi\) | |||||||
\(662\) | −8.17673 | −0.317798 | ||||||||
\(663\) | −1.77261 | −0.0688426 | ||||||||
\(664\) | −1.43522 | −0.0556972 | ||||||||
\(665\) | 10.3818 | 0.402590 | ||||||||
\(666\) | −7.94495 | −0.307861 | ||||||||
\(667\) | 1.01192 | 0.0391816 | ||||||||
\(668\) | 0.647953 | 0.0250701 | ||||||||
\(669\) | −5.05973 | −0.195620 | ||||||||
\(670\) | −2.58829 | −0.0999944 | ||||||||
\(671\) | 63.8964 | 2.46669 | ||||||||
\(672\) | −4.37806 | −0.168887 | ||||||||
\(673\) | 36.1961 | 1.39526 | 0.697628 | − | 0.716461i | \(-0.254239\pi\) | ||||
0.697628 | + | 0.716461i | \(0.254239\pi\) | |||||||
\(674\) | −6.57262 | −0.253168 | ||||||||
\(675\) | −2.89810 | −0.111548 | ||||||||
\(676\) | −9.85784 | −0.379148 | ||||||||
\(677\) | 28.7139 | 1.10356 | 0.551782 | − | 0.833988i | \(-0.313948\pi\) | ||||
0.551782 | + | 0.833988i | \(0.313948\pi\) | |||||||
\(678\) | 0.191265 | 0.00734549 | ||||||||
\(679\) | −17.6580 | −0.677651 | ||||||||
\(680\) | −1.44979 | −0.0555970 | ||||||||
\(681\) | −12.6609 | −0.485166 | ||||||||
\(682\) | 25.0593 | 0.959569 | ||||||||
\(683\) | 12.7428 | 0.487589 | 0.243795 | − | 0.969827i | \(-0.421608\pi\) | ||||
0.243795 | + | 0.969827i | \(0.421608\pi\) | |||||||
\(684\) | 1.63563 | 0.0625400 | ||||||||
\(685\) | 0.553638 | 0.0211534 | ||||||||
\(686\) | −22.6230 | −0.863752 | ||||||||
\(687\) | 1.68676 | 0.0643538 | ||||||||
\(688\) | −1.10770 | −0.0422307 | ||||||||
\(689\) | 10.6808 | 0.406907 | ||||||||
\(690\) | −0.355919 | −0.0135496 | ||||||||
\(691\) | −14.4289 | −0.548900 | −0.274450 | − | 0.961601i | \(-0.588496\pi\) | ||||
−0.274450 | + | 0.961601i | \(0.588496\pi\) | |||||||
\(692\) | −2.21096 | −0.0840483 | ||||||||
\(693\) | 22.6975 | 0.862208 | ||||||||
\(694\) | −12.2280 | −0.464167 | ||||||||
\(695\) | 5.30548 | 0.201248 | ||||||||
\(696\) | −4.12193 | −0.156241 | ||||||||
\(697\) | −9.26927 | −0.351099 | ||||||||
\(698\) | −3.69015 | −0.139674 | ||||||||
\(699\) | 12.5530 | 0.474799 | ||||||||
\(700\) | −12.6880 | −0.479563 | ||||||||
\(701\) | −24.4740 | −0.924371 | −0.462186 | − | 0.886783i | \(-0.652935\pi\) | ||||
−0.462186 | + | 0.886783i | \(0.652935\pi\) | |||||||
\(702\) | 1.77261 | 0.0669030 | ||||||||
\(703\) | 12.9950 | 0.490117 | ||||||||
\(704\) | 5.18439 | 0.195394 | ||||||||
\(705\) | 7.00548 | 0.263842 | ||||||||
\(706\) | 10.4464 | 0.393156 | ||||||||
\(707\) | −9.09200 | −0.341940 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −36.4391 | −1.36850 | −0.684249 | − | 0.729248i | \(-0.739870\pi\) | ||||
−0.684249 | + | 0.729248i | \(0.739870\pi\) | |||||||
\(710\) | −2.44912 | −0.0919140 | ||||||||
\(711\) | −8.59258 | −0.322247 | ||||||||
\(712\) | −3.26823 | −0.122482 | ||||||||
\(713\) | −1.18663 | −0.0444397 | ||||||||
\(714\) | −4.37806 | −0.163845 | ||||||||
\(715\) | −13.3235 | −0.498270 | ||||||||
\(716\) | −2.20048 | −0.0822359 | ||||||||
\(717\) | 10.9851 | 0.410245 | ||||||||
\(718\) | 27.4693 | 1.02515 | ||||||||
\(719\) | −40.9091 | −1.52565 | −0.762826 | − | 0.646604i | \(-0.776188\pi\) | ||||
−0.762826 | + | 0.646604i | \(0.776188\pi\) | |||||||
\(720\) | 1.44979 | 0.0540306 | ||||||||
\(721\) | −28.3514 | −1.05586 | ||||||||
\(722\) | 16.3247 | 0.607542 | ||||||||
\(723\) | −10.7798 | −0.400904 | ||||||||
\(724\) | −16.8381 | −0.625781 | ||||||||
\(725\) | −11.9458 | −0.443654 | ||||||||
\(726\) | −15.8779 | −0.589284 | ||||||||
\(727\) | 6.40377 | 0.237503 | 0.118751 | − | 0.992924i | \(-0.462111\pi\) | ||||
0.118751 | + | 0.992924i | \(0.462111\pi\) | |||||||
\(728\) | 7.76060 | 0.287627 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.26482 | 0.194860 | ||||||||
\(731\) | −1.10770 | −0.0409698 | ||||||||
\(732\) | 12.3248 | 0.455537 | ||||||||
\(733\) | −33.1848 | −1.22571 | −0.612854 | − | 0.790196i | \(-0.709979\pi\) | ||||
−0.612854 | + | 0.790196i | \(0.709979\pi\) | |||||||
\(734\) | 23.1923 | 0.856045 | ||||||||
\(735\) | 17.6402 | 0.650668 | ||||||||
\(736\) | −0.245496 | −0.00904912 | ||||||||
\(737\) | 9.25560 | 0.340934 | ||||||||
\(738\) | 9.26927 | 0.341207 | ||||||||
\(739\) | 8.59928 | 0.316329 | 0.158165 | − | 0.987413i | \(-0.449442\pi\) | ||||
0.158165 | + | 0.987413i | \(0.449442\pi\) | |||||||
\(740\) | 11.5185 | 0.423430 | ||||||||
\(741\) | −2.89935 | −0.106510 | ||||||||
\(742\) | 26.3798 | 0.968434 | ||||||||
\(743\) | 35.4072 | 1.29896 | 0.649482 | − | 0.760377i | \(-0.274986\pi\) | ||||
0.649482 | + | 0.760377i | \(0.274986\pi\) | |||||||
\(744\) | 4.83360 | 0.177208 | ||||||||
\(745\) | 19.8040 | 0.725563 | ||||||||
\(746\) | 7.72058 | 0.282671 | ||||||||
\(747\) | 1.43522 | 0.0525119 | ||||||||
\(748\) | 5.18439 | 0.189560 | ||||||||
\(749\) | 73.8378 | 2.69797 | ||||||||
\(750\) | 11.4506 | 0.418117 | ||||||||
\(751\) | 14.3082 | 0.522113 | 0.261056 | − | 0.965324i | \(-0.415929\pi\) | ||||
0.261056 | + | 0.965324i | \(0.415929\pi\) | |||||||
\(752\) | 4.83205 | 0.176207 | ||||||||
\(753\) | −10.3017 | −0.375415 | ||||||||
\(754\) | 7.30658 | 0.266090 | ||||||||
\(755\) | −27.9685 | −1.01788 | ||||||||
\(756\) | 4.37806 | 0.159228 | ||||||||
\(757\) | 24.2300 | 0.880654 | 0.440327 | − | 0.897837i | \(-0.354863\pi\) | ||||
0.440327 | + | 0.897837i | \(0.354863\pi\) | |||||||
\(758\) | 8.20322 | 0.297954 | ||||||||
\(759\) | 1.27275 | 0.0461979 | ||||||||
\(760\) | −2.37133 | −0.0860173 | ||||||||
\(761\) | 1.99312 | 0.0722507 | 0.0361253 | − | 0.999347i | \(-0.488498\pi\) | ||||
0.0361253 | + | 0.999347i | \(0.488498\pi\) | |||||||
\(762\) | 16.0068 | 0.579867 | ||||||||
\(763\) | −11.1441 | −0.403445 | ||||||||
\(764\) | 7.42739 | 0.268713 | ||||||||
\(765\) | 1.44979 | 0.0524174 | ||||||||
\(766\) | −22.7157 | −0.820752 | ||||||||
\(767\) | −1.77261 | −0.0640054 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −29.2753 | −1.05570 | −0.527848 | − | 0.849339i | \(-0.677001\pi\) | ||||
−0.527848 | + | 0.849339i | \(0.677001\pi\) | |||||||
\(770\) | −32.9068 | −1.18588 | ||||||||
\(771\) | 15.2138 | 0.547913 | ||||||||
\(772\) | −4.61155 | −0.165973 | ||||||||
\(773\) | −40.5864 | −1.45979 | −0.729896 | − | 0.683559i | \(-0.760431\pi\) | ||||
−0.729896 | + | 0.683559i | \(0.760431\pi\) | |||||||
\(774\) | 1.10770 | 0.0398155 | ||||||||
\(775\) | 14.0082 | 0.503191 | ||||||||
\(776\) | 4.03329 | 0.144787 | ||||||||
\(777\) | 34.7834 | 1.24785 | ||||||||
\(778\) | 3.21475 | 0.115255 | ||||||||
\(779\) | −15.1611 | −0.543204 | ||||||||
\(780\) | −2.56992 | −0.0920180 | ||||||||
\(781\) | 8.75795 | 0.313384 | ||||||||
\(782\) | −0.245496 | −0.00877893 | ||||||||
\(783\) | 4.12193 | 0.147306 | ||||||||
\(784\) | 12.1674 | 0.434549 | ||||||||
\(785\) | 14.9749 | 0.534477 | ||||||||
\(786\) | −14.9695 | −0.533944 | ||||||||
\(787\) | 12.9698 | 0.462324 | 0.231162 | − | 0.972915i | \(-0.425747\pi\) | ||||
0.231162 | + | 0.972915i | \(0.425747\pi\) | |||||||
\(788\) | −0.0799799 | −0.00284917 | ||||||||
\(789\) | −24.4168 | −0.869261 | ||||||||
\(790\) | 12.4575 | 0.443217 | ||||||||
\(791\) | −0.837369 | −0.0297734 | ||||||||
\(792\) | −5.18439 | −0.184219 | ||||||||
\(793\) | −21.8470 | −0.775811 | ||||||||
\(794\) | −36.4680 | −1.29420 | ||||||||
\(795\) | −8.73568 | −0.309823 | ||||||||
\(796\) | −14.5150 | −0.514472 | ||||||||
\(797\) | 4.50661 | 0.159632 | 0.0798161 | − | 0.996810i | \(-0.474567\pi\) | ||||
0.0798161 | + | 0.996810i | \(0.474567\pi\) | |||||||
\(798\) | −7.16090 | −0.253493 | ||||||||
\(799\) | 4.83205 | 0.170946 | ||||||||
\(800\) | 2.89810 | 0.102463 | ||||||||
\(801\) | 3.26823 | 0.115477 | ||||||||
\(802\) | −1.86893 | −0.0659942 | ||||||||
\(803\) | −18.8267 | −0.664381 | ||||||||
\(804\) | 1.78528 | 0.0629621 | ||||||||
\(805\) | 1.55823 | 0.0549205 | ||||||||
\(806\) | −8.56810 | −0.301798 | ||||||||
\(807\) | 11.1815 | 0.393609 | ||||||||
\(808\) | 2.07672 | 0.0730588 | ||||||||
\(809\) | −7.80597 | −0.274443 | −0.137222 | − | 0.990540i | \(-0.543817\pi\) | ||||
−0.137222 | + | 0.990540i | \(0.543817\pi\) | |||||||
\(810\) | −1.44979 | −0.0509406 | ||||||||
\(811\) | 20.5255 | 0.720748 | 0.360374 | − | 0.932808i | \(-0.382649\pi\) | ||||
0.360374 | + | 0.932808i | \(0.382649\pi\) | |||||||
\(812\) | 18.0460 | 0.633291 | ||||||||
\(813\) | 7.52070 | 0.263762 | ||||||||
\(814\) | −41.1897 | −1.44370 | ||||||||
\(815\) | −17.0161 | −0.596048 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −1.81179 | −0.0633866 | ||||||||
\(818\) | 25.4421 | 0.889563 | ||||||||
\(819\) | −7.76060 | −0.271177 | ||||||||
\(820\) | −13.4385 | −0.469294 | ||||||||
\(821\) | 17.0975 | 0.596707 | 0.298354 | − | 0.954455i | \(-0.403563\pi\) | ||||
0.298354 | + | 0.954455i | \(0.403563\pi\) | |||||||
\(822\) | −0.381874 | −0.0133194 | ||||||||
\(823\) | 51.5166 | 1.79576 | 0.897878 | − | 0.440244i | \(-0.145108\pi\) | ||||
0.897878 | + | 0.440244i | \(0.145108\pi\) | |||||||
\(824\) | 6.47581 | 0.225595 | ||||||||
\(825\) | −15.0249 | −0.523099 | ||||||||
\(826\) | −4.37806 | −0.152332 | ||||||||
\(827\) | 25.4308 | 0.884316 | 0.442158 | − | 0.896937i | \(-0.354213\pi\) | ||||
0.442158 | + | 0.896937i | \(0.354213\pi\) | |||||||
\(828\) | 0.245496 | 0.00853159 | ||||||||
\(829\) | −6.78146 | −0.235530 | −0.117765 | − | 0.993042i | \(-0.537573\pi\) | ||||
−0.117765 | + | 0.993042i | \(0.537573\pi\) | |||||||
\(830\) | −2.08077 | −0.0722245 | ||||||||
\(831\) | 6.39054 | 0.221685 | ||||||||
\(832\) | −1.77261 | −0.0614543 | ||||||||
\(833\) | 12.1674 | 0.421574 | ||||||||
\(834\) | −3.65947 | −0.126717 | ||||||||
\(835\) | 0.939398 | 0.0325092 | ||||||||
\(836\) | 8.47977 | 0.293279 | ||||||||
\(837\) | −4.83360 | −0.167074 | ||||||||
\(838\) | 16.7336 | 0.578053 | ||||||||
\(839\) | 41.9267 | 1.44747 | 0.723736 | − | 0.690077i | \(-0.242423\pi\) | ||||
0.723736 | + | 0.690077i | \(0.242423\pi\) | |||||||
\(840\) | −6.34728 | −0.219002 | ||||||||
\(841\) | −12.0097 | −0.414128 | ||||||||
\(842\) | −3.56961 | −0.123017 | ||||||||
\(843\) | −10.8901 | −0.375073 | ||||||||
\(844\) | −20.9886 | −0.722456 | ||||||||
\(845\) | −14.2918 | −0.491654 | ||||||||
\(846\) | −4.83205 | −0.166129 | ||||||||
\(847\) | 69.5143 | 2.38854 | ||||||||
\(848\) | −6.02547 | −0.206915 | ||||||||
\(849\) | 5.70075 | 0.195649 | ||||||||
\(850\) | 2.89810 | 0.0994040 | ||||||||
\(851\) | 1.95046 | 0.0668608 | ||||||||
\(852\) | 1.68929 | 0.0578742 | ||||||||
\(853\) | −34.0677 | −1.16646 | −0.583228 | − | 0.812309i | \(-0.698211\pi\) | ||||
−0.583228 | + | 0.812309i | \(0.698211\pi\) | |||||||
\(854\) | −53.9585 | −1.84642 | ||||||||
\(855\) | 2.37133 | 0.0810979 | ||||||||
\(856\) | −16.8654 | −0.576449 | ||||||||
\(857\) | −14.9956 | −0.512239 | −0.256119 | − | 0.966645i | \(-0.582444\pi\) | ||||
−0.256119 | + | 0.966645i | \(0.582444\pi\) | |||||||
\(858\) | 9.18992 | 0.313739 | ||||||||
\(859\) | 40.9152 | 1.39601 | 0.698004 | − | 0.716094i | \(-0.254072\pi\) | ||||
0.698004 | + | 0.716094i | \(0.254072\pi\) | |||||||
\(860\) | −1.60594 | −0.0547620 | ||||||||
\(861\) | −40.5814 | −1.38301 | ||||||||
\(862\) | 12.8508 | 0.437699 | ||||||||
\(863\) | 43.3752 | 1.47651 | 0.738255 | − | 0.674522i | \(-0.235650\pi\) | ||||
0.738255 | + | 0.674522i | \(0.235650\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −3.20544 | −0.108988 | ||||||||
\(866\) | 7.89068 | 0.268136 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −21.1618 | −0.718277 | ||||||||
\(869\) | −44.5473 | −1.51116 | ||||||||
\(870\) | −5.97594 | −0.202603 | ||||||||
\(871\) | −3.16462 | −0.107229 | ||||||||
\(872\) | 2.54545 | 0.0861999 | ||||||||
\(873\) | −4.03329 | −0.136506 | ||||||||
\(874\) | −0.401542 | −0.0135824 | ||||||||
\(875\) | −50.1314 | −1.69475 | ||||||||
\(876\) | −3.63143 | −0.122694 | ||||||||
\(877\) | 13.5089 | 0.456162 | 0.228081 | − | 0.973642i | \(-0.426755\pi\) | ||||
0.228081 | + | 0.973642i | \(0.426755\pi\) | |||||||
\(878\) | 0.241284 | 0.00814294 | ||||||||
\(879\) | 1.45272 | 0.0489991 | ||||||||
\(880\) | 7.51629 | 0.253374 | ||||||||
\(881\) | 0.499198 | 0.0168184 | 0.00840921 | − | 0.999965i | \(-0.497323\pi\) | ||||
0.00840921 | + | 0.999965i | \(0.497323\pi\) | |||||||
\(882\) | −12.1674 | −0.409697 | ||||||||
\(883\) | −26.2013 | −0.881744 | −0.440872 | − | 0.897570i | \(-0.645331\pi\) | ||||
−0.440872 | + | 0.897570i | \(0.645331\pi\) | |||||||
\(884\) | −1.77261 | −0.0596194 | ||||||||
\(885\) | 1.44979 | 0.0487343 | ||||||||
\(886\) | 11.3111 | 0.380003 | ||||||||
\(887\) | 23.0467 | 0.773832 | 0.386916 | − | 0.922115i | \(-0.373540\pi\) | ||||
0.386916 | + | 0.922115i | \(0.373540\pi\) | |||||||
\(888\) | −7.94495 | −0.266615 | ||||||||
\(889\) | −70.0788 | −2.35037 | ||||||||
\(890\) | −4.73826 | −0.158827 | ||||||||
\(891\) | 5.18439 | 0.173684 | ||||||||
\(892\) | −5.05973 | −0.169412 | ||||||||
\(893\) | 7.90347 | 0.264480 | ||||||||
\(894\) | −13.6599 | −0.456855 | ||||||||
\(895\) | −3.19025 | −0.106638 | ||||||||
\(896\) | −4.37806 | −0.146261 | ||||||||
\(897\) | −0.435170 | −0.0145299 | ||||||||
\(898\) | 2.53121 | 0.0844677 | ||||||||
\(899\) | −19.9237 | −0.664494 | ||||||||
\(900\) | −2.89810 | −0.0966033 | ||||||||
\(901\) | −6.02547 | −0.200737 | ||||||||
\(902\) | 48.0555 | 1.60007 | ||||||||
\(903\) | −4.84957 | −0.161384 | ||||||||
\(904\) | 0.191265 | 0.00636138 | ||||||||
\(905\) | −24.4117 | −0.811472 | ||||||||
\(906\) | 19.2914 | 0.640913 | ||||||||
\(907\) | 27.7324 | 0.920838 | 0.460419 | − | 0.887702i | \(-0.347699\pi\) | ||||
0.460419 | + | 0.887702i | \(0.347699\pi\) | |||||||
\(908\) | −12.6609 | −0.420166 | ||||||||
\(909\) | −2.07672 | −0.0688805 | ||||||||
\(910\) | 11.2513 | 0.372976 | ||||||||
\(911\) | 10.8254 | 0.358660 | 0.179330 | − | 0.983789i | \(-0.442607\pi\) | ||||
0.179330 | + | 0.983789i | \(0.442607\pi\) | |||||||
\(912\) | 1.63563 | 0.0541613 | ||||||||
\(913\) | 7.44073 | 0.246252 | ||||||||
\(914\) | 30.7641 | 1.01759 | ||||||||
\(915\) | 17.8684 | 0.590710 | ||||||||
\(916\) | 1.68676 | 0.0557320 | ||||||||
\(917\) | 65.5373 | 2.16423 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 51.7151 | 1.70592 | 0.852961 | − | 0.521974i | \(-0.174804\pi\) | ||||
0.852961 | + | 0.521974i | \(0.174804\pi\) | |||||||
\(920\) | −0.355919 | −0.0117343 | ||||||||
\(921\) | −24.5574 | −0.809192 | ||||||||
\(922\) | 17.1603 | 0.565143 | ||||||||
\(923\) | −2.99446 | −0.0985639 | ||||||||
\(924\) | 22.6975 | 0.746694 | ||||||||
\(925\) | −23.0252 | −0.757065 | ||||||||
\(926\) | −8.00799 | −0.263159 | ||||||||
\(927\) | −6.47581 | −0.212693 | ||||||||
\(928\) | −4.12193 | −0.135309 | ||||||||
\(929\) | −34.4693 | −1.13090 | −0.565450 | − | 0.824782i | \(-0.691298\pi\) | ||||
−0.565450 | + | 0.824782i | \(0.691298\pi\) | |||||||
\(930\) | 7.00772 | 0.229792 | ||||||||
\(931\) | 19.9014 | 0.652241 | ||||||||
\(932\) | 12.5530 | 0.411188 | ||||||||
\(933\) | −4.47009 | −0.146344 | ||||||||
\(934\) | −20.3714 | −0.666573 | ||||||||
\(935\) | 7.51629 | 0.245809 | ||||||||
\(936\) | 1.77261 | 0.0579397 | ||||||||
\(937\) | −51.0063 | −1.66630 | −0.833151 | − | 0.553045i | \(-0.813466\pi\) | ||||
−0.833151 | + | 0.553045i | \(0.813466\pi\) | |||||||
\(938\) | −7.81607 | −0.255204 | ||||||||
\(939\) | 31.5641 | 1.03006 | ||||||||
\(940\) | 7.00548 | 0.228494 | ||||||||
\(941\) | 49.2787 | 1.60644 | 0.803219 | − | 0.595683i | \(-0.203119\pi\) | ||||
0.803219 | + | 0.595683i | \(0.203119\pi\) | |||||||
\(942\) | −10.3290 | −0.336536 | ||||||||
\(943\) | −2.27557 | −0.0741028 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 6.34728 | 0.206477 | ||||||||
\(946\) | 5.74275 | 0.186713 | ||||||||
\(947\) | 30.2193 | 0.981997 | 0.490998 | − | 0.871160i | \(-0.336632\pi\) | ||||
0.490998 | + | 0.871160i | \(0.336632\pi\) | |||||||
\(948\) | −8.59258 | −0.279074 | ||||||||
\(949\) | 6.43711 | 0.208958 | ||||||||
\(950\) | 4.74023 | 0.153793 | ||||||||
\(951\) | 16.7785 | 0.544080 | ||||||||
\(952\) | −4.37806 | −0.141894 | ||||||||
\(953\) | 17.2028 | 0.557254 | 0.278627 | − | 0.960399i | \(-0.410121\pi\) | ||||
0.278627 | + | 0.960399i | \(0.410121\pi\) | |||||||
\(954\) | 6.02547 | 0.195082 | ||||||||
\(955\) | 10.7682 | 0.348450 | ||||||||
\(956\) | 10.9851 | 0.355283 | ||||||||
\(957\) | 21.3697 | 0.690784 | ||||||||
\(958\) | −41.9139 | −1.35418 | ||||||||
\(959\) | 1.67186 | 0.0539873 | ||||||||
\(960\) | 1.44979 | 0.0467919 | ||||||||
\(961\) | −7.63632 | −0.246333 | ||||||||
\(962\) | 14.0833 | 0.454065 | ||||||||
\(963\) | 16.8654 | 0.543481 | ||||||||
\(964\) | −10.7798 | −0.347193 | ||||||||
\(965\) | −6.68580 | −0.215223 | ||||||||
\(966\) | −1.07480 | −0.0345810 | ||||||||
\(967\) | 4.96745 | 0.159743 | 0.0798713 | − | 0.996805i | \(-0.474549\pi\) | ||||
0.0798713 | + | 0.996805i | \(0.474549\pi\) | |||||||
\(968\) | −15.8779 | −0.510335 | ||||||||
\(969\) | 1.63563 | 0.0525441 | ||||||||
\(970\) | 5.84744 | 0.187750 | ||||||||
\(971\) | −40.7526 | −1.30781 | −0.653906 | − | 0.756576i | \(-0.726871\pi\) | ||||
−0.653906 | + | 0.756576i | \(0.726871\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 16.0214 | 0.513622 | ||||||||
\(974\) | 17.0648 | 0.546792 | ||||||||
\(975\) | 5.13721 | 0.164522 | ||||||||
\(976\) | 12.3248 | 0.394506 | ||||||||
\(977\) | −42.7449 | −1.36753 | −0.683765 | − | 0.729703i | \(-0.739659\pi\) | ||||
−0.683765 | + | 0.729703i | \(0.739659\pi\) | |||||||
\(978\) | 11.7369 | 0.375305 | ||||||||
\(979\) | 16.9438 | 0.541526 | ||||||||
\(980\) | 17.6402 | 0.563495 | ||||||||
\(981\) | −2.54545 | −0.0812700 | ||||||||
\(982\) | −29.0665 | −0.927550 | ||||||||
\(983\) | 1.37125 | 0.0437359 | 0.0218680 | − | 0.999761i | \(-0.493039\pi\) | ||||
0.0218680 | + | 0.999761i | \(0.493039\pi\) | |||||||
\(984\) | 9.26927 | 0.295494 | ||||||||
\(985\) | −0.115954 | −0.00369461 | ||||||||
\(986\) | −4.12193 | −0.131269 | ||||||||
\(987\) | 21.1550 | 0.673371 | ||||||||
\(988\) | −2.89935 | −0.0922405 | ||||||||
\(989\) | −0.271936 | −0.00864707 | ||||||||
\(990\) | −7.51629 | −0.238884 | ||||||||
\(991\) | 4.24426 | 0.134823 | 0.0674117 | − | 0.997725i | \(-0.478526\pi\) | ||||
0.0674117 | + | 0.997725i | \(0.478526\pi\) | |||||||
\(992\) | 4.83360 | 0.153467 | ||||||||
\(993\) | 8.17673 | 0.259481 | ||||||||
\(994\) | −7.39581 | −0.234581 | ||||||||
\(995\) | −21.0438 | −0.667134 | ||||||||
\(996\) | 1.43522 | 0.0454766 | ||||||||
\(997\) | 52.8359 | 1.67333 | 0.836664 | − | 0.547716i | \(-0.184503\pi\) | ||||
0.836664 | + | 0.547716i | \(0.184503\pi\) | |||||||
\(998\) | −13.3167 | −0.421533 | ||||||||
\(999\) | 7.94495 | 0.251367 |
(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 | 6018.2.a.w.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.w.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial |