Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5610,2,Mod(1,5610)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5610.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5610.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: | \(44.7960755339\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1284160.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 7x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.11852\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5610.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.25889 | 0.853782 | 0.426891 | − | 0.904303i | \(-0.359609\pi\) | ||||
0.426891 | + | 0.904303i | \(0.359609\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.258895 | −0.0718044 | −0.0359022 | − | 0.999355i | \(-0.511430\pi\) | ||||
−0.0359022 | + | 0.999355i | \(0.511430\pi\) | |||||||
\(14\) | 2.25889 | 0.603715 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.14701 | −0.951389 | −0.475694 | − | 0.879611i | \(-0.657803\pi\) | ||||
−0.475694 | + | 0.879611i | \(0.657803\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.25889 | 0.492931 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.76174 | −1.20141 | −0.600703 | − | 0.799472i | \(-0.705113\pi\) | ||||
−0.600703 | + | 0.799472i | \(0.705113\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.258895 | −0.0507734 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.25889 | 0.426891 | ||||||||
\(29\) | 10.4741 | 1.94499 | 0.972493 | − | 0.232932i | \(-0.0748319\pi\) | ||||
0.972493 | + | 0.232932i | \(0.0748319\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −1.28266 | −0.230373 | −0.115186 | − | 0.993344i | \(-0.536747\pi\) | ||||
−0.115186 | + | 0.993344i | \(0.536747\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 2.25889 | 0.381823 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.71734 | 0.775526 | 0.387763 | − | 0.921759i | \(-0.373248\pi\) | ||||
0.387763 | + | 0.921759i | \(0.373248\pi\) | |||||||
\(38\) | −4.14701 | −0.672733 | ||||||||
\(39\) | −0.258895 | −0.0414563 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 12.5860 | 1.96560 | 0.982798 | − | 0.184683i | \(-0.0591258\pi\) | ||||
0.982798 | + | 0.184683i | \(0.0591258\pi\) | |||||||
\(42\) | 2.25889 | 0.348555 | ||||||||
\(43\) | −3.54156 | −0.540082 | −0.270041 | − | 0.962849i | \(-0.587037\pi\) | ||||
−0.270041 | + | 0.962849i | \(0.587037\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −5.76174 | −0.849522 | ||||||||
\(47\) | 1.43468 | 0.209269 | 0.104635 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104635 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.89740 | −0.271056 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.258895 | −0.0359022 | ||||||||
\(53\) | −9.04440 | −1.24234 | −0.621172 | − | 0.783674i | \(-0.713343\pi\) | ||||
−0.621172 | + | 0.783674i | \(0.713343\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.25889 | 0.301857 | ||||||||
\(57\) | −4.14701 | −0.549285 | ||||||||
\(58\) | 10.4741 | 1.37531 | ||||||||
\(59\) | 12.9325 | 1.68367 | 0.841835 | − | 0.539735i | \(-0.181476\pi\) | ||||
0.841835 | + | 0.539735i | \(0.181476\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 14.8061 | 1.89573 | 0.947866 | − | 0.318668i | \(-0.103236\pi\) | ||||
0.947866 | + | 0.318668i | \(0.103236\pi\) | |||||||
\(62\) | −1.28266 | −0.162898 | ||||||||
\(63\) | 2.25889 | 0.284594 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.258895 | −0.0321119 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −9.30330 | −1.13658 | −0.568289 | − | 0.822829i | \(-0.692395\pi\) | ||||
−0.568289 | + | 0.822829i | \(0.692395\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −5.76174 | −0.693632 | ||||||||
\(70\) | 2.25889 | 0.269990 | ||||||||
\(71\) | 7.83557 | 0.929911 | 0.464956 | − | 0.885334i | \(-0.346070\pi\) | ||||
0.464956 | + | 0.885334i | \(0.346070\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 15.4503 | 1.80832 | 0.904161 | − | 0.427193i | \(-0.140497\pi\) | ||||
0.904161 | + | 0.427193i | \(0.140497\pi\) | |||||||
\(74\) | 4.71734 | 0.548380 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −4.14701 | −0.475694 | ||||||||
\(77\) | 2.25889 | 0.257425 | ||||||||
\(78\) | −0.258895 | −0.0293140 | ||||||||
\(79\) | −11.3384 | −1.27567 | −0.637836 | − | 0.770172i | \(-0.720170\pi\) | ||||
−0.637836 | + | 0.770172i | \(0.720170\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.5860 | 1.38989 | ||||||||
\(83\) | −11.7092 | −1.28525 | −0.642626 | − | 0.766180i | \(-0.722155\pi\) | ||||
−0.642626 | + | 0.766180i | \(0.722155\pi\) | |||||||
\(84\) | 2.25889 | 0.246466 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | −3.54156 | −0.381896 | ||||||||
\(87\) | 10.4741 | 1.12294 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −5.08311 | −0.538809 | −0.269404 | − | 0.963027i | \(-0.586827\pi\) | ||||
−0.269404 | + | 0.963027i | \(0.586827\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −0.584816 | −0.0613053 | ||||||||
\(92\) | −5.76174 | −0.600703 | ||||||||
\(93\) | −1.28266 | −0.133006 | ||||||||
\(94\) | 1.43468 | 0.147976 | ||||||||
\(95\) | −4.14701 | −0.425474 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.68856 | 0.983724 | 0.491862 | − | 0.870673i | \(-0.336316\pi\) | ||||
0.491862 | + | 0.870673i | \(0.336316\pi\) | |||||||
\(98\) | −1.89740 | −0.191666 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.84058 | −0.979174 | −0.489587 | − | 0.871954i | \(-0.662853\pi\) | ||||
−0.489587 | + | 0.871954i | \(0.662853\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 2.89740 | 0.285489 | 0.142744 | − | 0.989760i | \(-0.454407\pi\) | ||||
0.142744 | + | 0.989760i | \(0.454407\pi\) | |||||||
\(104\) | −0.258895 | −0.0253867 | ||||||||
\(105\) | 2.25889 | 0.220446 | ||||||||
\(106\) | −9.04440 | −0.878470 | ||||||||
\(107\) | −4.18006 | −0.404101 | −0.202051 | − | 0.979375i | \(-0.564761\pi\) | ||||
−0.202051 | + | 0.979375i | \(0.564761\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 3.28266 | 0.314422 | 0.157211 | − | 0.987565i | \(-0.449750\pi\) | ||||
0.157211 | + | 0.987565i | \(0.449750\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 4.71734 | 0.447750 | ||||||||
\(112\) | 2.25889 | 0.213445 | ||||||||
\(113\) | −5.38214 | −0.506309 | −0.253154 | − | 0.967426i | \(-0.581468\pi\) | ||||
−0.253154 | + | 0.967426i | \(0.581468\pi\) | |||||||
\(114\) | −4.14701 | −0.388403 | ||||||||
\(115\) | −5.76174 | −0.537285 | ||||||||
\(116\) | 10.4741 | 0.972493 | ||||||||
\(117\) | −0.258895 | −0.0239348 | ||||||||
\(118\) | 12.9325 | 1.19053 | ||||||||
\(119\) | 2.25889 | 0.207073 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 14.8061 | 1.34049 | ||||||||
\(123\) | 12.5860 | 1.13484 | ||||||||
\(124\) | −1.28266 | −0.115186 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.25889 | 0.201238 | ||||||||
\(127\) | 3.08311 | 0.273582 | 0.136791 | − | 0.990600i | \(-0.456321\pi\) | ||||
0.136791 | + | 0.990600i | \(0.456321\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.54156 | −0.311817 | ||||||||
\(130\) | −0.258895 | −0.0227066 | ||||||||
\(131\) | −13.2389 | −1.15669 | −0.578346 | − | 0.815792i | \(-0.696302\pi\) | ||||
−0.578346 | + | 0.815792i | \(0.696302\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −9.36765 | −0.812278 | ||||||||
\(134\) | −9.30330 | −0.803682 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 14.6598 | 1.25247 | 0.626235 | − | 0.779634i | \(-0.284595\pi\) | ||||
0.626235 | + | 0.779634i | \(0.284595\pi\) | |||||||
\(138\) | −5.76174 | −0.490472 | ||||||||
\(139\) | 7.03939 | 0.597073 | 0.298537 | − | 0.954398i | \(-0.403501\pi\) | ||||
0.298537 | + | 0.954398i | \(0.403501\pi\) | |||||||
\(140\) | 2.25889 | 0.190911 | ||||||||
\(141\) | 1.43468 | 0.120822 | ||||||||
\(142\) | 7.83557 | 0.657546 | ||||||||
\(143\) | −0.258895 | −0.0216499 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.4741 | 0.869824 | ||||||||
\(146\) | 15.4503 | 1.27868 | ||||||||
\(147\) | −1.89740 | −0.156495 | ||||||||
\(148\) | 4.71734 | 0.387763 | ||||||||
\(149\) | −4.81539 | −0.394492 | −0.197246 | − | 0.980354i | \(-0.563200\pi\) | ||||
−0.197246 | + | 0.980354i | \(0.563200\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −3.23513 | −0.263271 | −0.131636 | − | 0.991298i | \(-0.542023\pi\) | ||||
−0.131636 | + | 0.991298i | \(0.542023\pi\) | |||||||
\(152\) | −4.14701 | −0.336367 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 2.25889 | 0.182027 | ||||||||
\(155\) | −1.28266 | −0.103026 | ||||||||
\(156\) | −0.258895 | −0.0207282 | ||||||||
\(157\) | −15.2652 | −1.21830 | −0.609149 | − | 0.793056i | \(-0.708489\pi\) | ||||
−0.609149 | + | 0.793056i | \(0.708489\pi\) | |||||||
\(158\) | −11.3384 | −0.902036 | ||||||||
\(159\) | −9.04440 | −0.717268 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −13.0152 | −1.02574 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −21.8650 | −1.71260 | −0.856301 | − | 0.516478i | \(-0.827243\pi\) | ||||
−0.856301 | + | 0.516478i | \(0.827243\pi\) | |||||||
\(164\) | 12.5860 | 0.982798 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | −11.7092 | −0.908810 | ||||||||
\(167\) | −14.4265 | −1.11636 | −0.558180 | − | 0.829720i | \(-0.688500\pi\) | ||||
−0.558180 | + | 0.829720i | \(0.688500\pi\) | |||||||
\(168\) | 2.25889 | 0.174278 | ||||||||
\(169\) | −12.9330 | −0.994844 | ||||||||
\(170\) | 1.00000 | 0.0766965 | ||||||||
\(171\) | −4.14701 | −0.317130 | ||||||||
\(172\) | −3.54156 | −0.270041 | ||||||||
\(173\) | 6.10830 | 0.464405 | 0.232203 | − | 0.972667i | \(-0.425407\pi\) | ||||
0.232203 | + | 0.972667i | \(0.425407\pi\) | |||||||
\(174\) | 10.4741 | 0.794037 | ||||||||
\(175\) | 2.25889 | 0.170756 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 12.9325 | 0.972067 | ||||||||
\(178\) | −5.08311 | −0.380995 | ||||||||
\(179\) | −11.0707 | −0.827463 | −0.413731 | − | 0.910399i | \(-0.635775\pi\) | ||||
−0.413731 | + | 0.910399i | \(0.635775\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −12.3828 | −0.920408 | −0.460204 | − | 0.887813i | \(-0.652224\pi\) | ||||
−0.460204 | + | 0.887813i | \(0.652224\pi\) | |||||||
\(182\) | −0.584816 | −0.0433494 | ||||||||
\(183\) | 14.8061 | 1.09450 | ||||||||
\(184\) | −5.76174 | −0.424761 | ||||||||
\(185\) | 4.71734 | 0.346826 | ||||||||
\(186\) | −1.28266 | −0.0940492 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 1.43468 | 0.104635 | ||||||||
\(189\) | 2.25889 | 0.164310 | ||||||||
\(190\) | −4.14701 | −0.300856 | ||||||||
\(191\) | −19.4798 | −1.40951 | −0.704753 | − | 0.709453i | \(-0.748942\pi\) | ||||
−0.704753 | + | 0.709453i | \(0.748942\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 6.17330 | 0.444364 | 0.222182 | − | 0.975005i | \(-0.428682\pi\) | ||||
0.222182 | + | 0.975005i | \(0.428682\pi\) | |||||||
\(194\) | 9.68856 | 0.695598 | ||||||||
\(195\) | −0.258895 | −0.0185398 | ||||||||
\(196\) | −1.89740 | −0.135528 | ||||||||
\(197\) | 3.23894 | 0.230765 | 0.115383 | − | 0.993321i | \(-0.463191\pi\) | ||||
0.115383 | + | 0.993321i | \(0.463191\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 6.71734 | 0.476180 | 0.238090 | − | 0.971243i | \(-0.423479\pi\) | ||||
0.238090 | + | 0.971243i | \(0.423479\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −9.30330 | −0.656204 | ||||||||
\(202\) | −9.84058 | −0.692381 | ||||||||
\(203\) | 23.6598 | 1.66059 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 12.5860 | 0.879041 | ||||||||
\(206\) | 2.89740 | 0.201871 | ||||||||
\(207\) | −5.76174 | −0.400469 | ||||||||
\(208\) | −0.258895 | −0.0179511 | ||||||||
\(209\) | −4.14701 | −0.286854 | ||||||||
\(210\) | 2.25889 | 0.155879 | ||||||||
\(211\) | 22.7206 | 1.56415 | 0.782074 | − | 0.623186i | \(-0.214162\pi\) | ||||
0.782074 | + | 0.623186i | \(0.214162\pi\) | |||||||
\(212\) | −9.04440 | −0.621172 | ||||||||
\(213\) | 7.83557 | 0.536884 | ||||||||
\(214\) | −4.18006 | −0.285743 | ||||||||
\(215\) | −3.54156 | −0.241532 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −2.89740 | −0.196688 | ||||||||
\(218\) | 3.28266 | 0.222330 | ||||||||
\(219\) | 15.4503 | 1.04403 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −0.258895 | −0.0174151 | ||||||||
\(222\) | 4.71734 | 0.316607 | ||||||||
\(223\) | 11.1914 | 0.749432 | 0.374716 | − | 0.927140i | \(-0.377740\pi\) | ||||
0.374716 | + | 0.927140i | \(0.377740\pi\) | |||||||
\(224\) | 2.25889 | 0.150929 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −5.38214 | −0.358014 | ||||||||
\(227\) | −8.87317 | −0.588933 | −0.294467 | − | 0.955662i | \(-0.595142\pi\) | ||||
−0.294467 | + | 0.955662i | \(0.595142\pi\) | |||||||
\(228\) | −4.14701 | −0.274642 | ||||||||
\(229\) | 28.4209 | 1.87810 | 0.939052 | − | 0.343774i | \(-0.111706\pi\) | ||||
0.939052 | + | 0.343774i | \(0.111706\pi\) | |||||||
\(230\) | −5.76174 | −0.379918 | ||||||||
\(231\) | 2.25889 | 0.148624 | ||||||||
\(232\) | 10.4741 | 0.687656 | ||||||||
\(233\) | −17.8949 | −1.17233 | −0.586167 | − | 0.810190i | \(-0.699364\pi\) | ||||
−0.586167 | + | 0.810190i | \(0.699364\pi\) | |||||||
\(234\) | −0.258895 | −0.0169245 | ||||||||
\(235\) | 1.43468 | 0.0935881 | ||||||||
\(236\) | 12.9325 | 0.841835 | ||||||||
\(237\) | −11.3384 | −0.736509 | ||||||||
\(238\) | 2.25889 | 0.146422 | ||||||||
\(239\) | −8.29401 | −0.536495 | −0.268248 | − | 0.963350i | \(-0.586445\pi\) | ||||
−0.268248 | + | 0.963350i | \(0.586445\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −14.2657 | −0.918934 | −0.459467 | − | 0.888195i | \(-0.651960\pi\) | ||||
−0.459467 | + | 0.888195i | \(0.651960\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.8061 | 0.947866 | ||||||||
\(245\) | −1.89740 | −0.121220 | ||||||||
\(246\) | 12.5860 | 0.802451 | ||||||||
\(247\) | 1.07364 | 0.0683139 | ||||||||
\(248\) | −1.28266 | −0.0814490 | ||||||||
\(249\) | −11.7092 | −0.742040 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 18.6892 | 1.17965 | 0.589827 | − | 0.807529i | \(-0.299196\pi\) | ||||
0.589827 | + | 0.807529i | \(0.299196\pi\) | |||||||
\(252\) | 2.25889 | 0.142297 | ||||||||
\(253\) | −5.76174 | −0.362238 | ||||||||
\(254\) | 3.08311 | 0.193452 | ||||||||
\(255\) | 1.00000 | 0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.6204 | 0.911997 | 0.455999 | − | 0.889980i | \(-0.349282\pi\) | ||||
0.455999 | + | 0.889980i | \(0.349282\pi\) | |||||||
\(258\) | −3.54156 | −0.220488 | ||||||||
\(259\) | 10.6560 | 0.662130 | ||||||||
\(260\) | −0.258895 | −0.0160560 | ||||||||
\(261\) | 10.4741 | 0.648329 | ||||||||
\(262\) | −13.2389 | −0.817905 | ||||||||
\(263\) | 11.1914 | 0.690092 | 0.345046 | − | 0.938586i | \(-0.387863\pi\) | ||||
0.345046 | + | 0.938586i | \(0.387863\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −9.04440 | −0.555593 | ||||||||
\(266\) | −9.36765 | −0.574368 | ||||||||
\(267\) | −5.08311 | −0.311081 | ||||||||
\(268\) | −9.30330 | −0.568289 | ||||||||
\(269\) | −8.13818 | −0.496194 | −0.248097 | − | 0.968735i | \(-0.579805\pi\) | ||||
−0.248097 | + | 0.968735i | \(0.579805\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 3.19707 | 0.194208 | 0.0971041 | − | 0.995274i | \(-0.469042\pi\) | ||||
0.0971041 | + | 0.995274i | \(0.469042\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −0.584816 | −0.0353946 | ||||||||
\(274\) | 14.6598 | 0.885630 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −5.76174 | −0.346816 | ||||||||
\(277\) | 11.9087 | 0.715527 | 0.357764 | − | 0.933812i | \(-0.383539\pi\) | ||||
0.357764 | + | 0.933812i | \(0.383539\pi\) | |||||||
\(278\) | 7.03939 | 0.422195 | ||||||||
\(279\) | −1.28266 | −0.0767909 | ||||||||
\(280\) | 2.25889 | 0.134995 | ||||||||
\(281\) | −24.3126 | −1.45037 | −0.725183 | − | 0.688556i | \(-0.758245\pi\) | ||||
−0.725183 | + | 0.688556i | \(0.758245\pi\) | |||||||
\(282\) | 1.43468 | 0.0854339 | ||||||||
\(283\) | 6.42654 | 0.382018 | 0.191009 | − | 0.981588i | \(-0.438824\pi\) | ||||
0.191009 | + | 0.981588i | \(0.438824\pi\) | |||||||
\(284\) | 7.83557 | 0.464956 | ||||||||
\(285\) | −4.14701 | −0.245648 | ||||||||
\(286\) | −0.258895 | −0.0153088 | ||||||||
\(287\) | 28.4304 | 1.67819 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 10.4741 | 0.615059 | ||||||||
\(291\) | 9.68856 | 0.567954 | ||||||||
\(292\) | 15.4503 | 0.904161 | ||||||||
\(293\) | −6.75921 | −0.394877 | −0.197439 | − | 0.980315i | \(-0.563262\pi\) | ||||
−0.197439 | + | 0.980315i | \(0.563262\pi\) | |||||||
\(294\) | −1.89740 | −0.110658 | ||||||||
\(295\) | 12.9325 | 0.752960 | ||||||||
\(296\) | 4.71734 | 0.274190 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −4.81539 | −0.278948 | ||||||||
\(299\) | 1.49168 | 0.0862663 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | −3.23513 | −0.186161 | ||||||||
\(303\) | −9.84058 | −0.565327 | ||||||||
\(304\) | −4.14701 | −0.237847 | ||||||||
\(305\) | 14.8061 | 0.847797 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −14.4009 | −0.821902 | −0.410951 | − | 0.911657i | \(-0.634803\pi\) | ||||
−0.410951 | + | 0.911657i | \(0.634803\pi\) | |||||||
\(308\) | 2.25889 | 0.128712 | ||||||||
\(309\) | 2.89740 | 0.164827 | ||||||||
\(310\) | −1.28266 | −0.0728502 | ||||||||
\(311\) | 15.8768 | 0.900293 | 0.450147 | − | 0.892955i | \(-0.351372\pi\) | ||||
0.450147 | + | 0.892955i | \(0.351372\pi\) | |||||||
\(312\) | −0.258895 | −0.0146570 | ||||||||
\(313\) | −11.6587 | −0.658987 | −0.329494 | − | 0.944158i | \(-0.606878\pi\) | ||||
−0.329494 | + | 0.944158i | \(0.606878\pi\) | |||||||
\(314\) | −15.2652 | −0.861467 | ||||||||
\(315\) | 2.25889 | 0.127274 | ||||||||
\(316\) | −11.3384 | −0.637836 | ||||||||
\(317\) | −8.08881 | −0.454313 | −0.227156 | − | 0.973858i | \(-0.572943\pi\) | ||||
−0.227156 | + | 0.973858i | \(0.572943\pi\) | |||||||
\(318\) | −9.04440 | −0.507185 | ||||||||
\(319\) | 10.4741 | 0.586435 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.18006 | −0.233308 | ||||||||
\(322\) | −13.0152 | −0.725307 | ||||||||
\(323\) | −4.14701 | −0.230746 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.258895 | −0.0143609 | ||||||||
\(326\) | −21.8650 | −1.21099 | ||||||||
\(327\) | 3.28266 | 0.181532 | ||||||||
\(328\) | 12.5860 | 0.694943 | ||||||||
\(329\) | 3.24079 | 0.178670 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 16.1363 | 0.886933 | 0.443467 | − | 0.896291i | \(-0.353748\pi\) | ||||
0.443467 | + | 0.896291i | \(0.353748\pi\) | |||||||
\(332\) | −11.7092 | −0.642626 | ||||||||
\(333\) | 4.71734 | 0.258509 | ||||||||
\(334\) | −14.4265 | −0.789385 | ||||||||
\(335\) | −9.30330 | −0.508293 | ||||||||
\(336\) | 2.25889 | 0.123233 | ||||||||
\(337\) | 16.4859 | 0.898043 | 0.449022 | − | 0.893521i | \(-0.351773\pi\) | ||||
0.449022 | + | 0.893521i | \(0.351773\pi\) | |||||||
\(338\) | −12.9330 | −0.703461 | ||||||||
\(339\) | −5.38214 | −0.292317 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | −1.28266 | −0.0694600 | ||||||||
\(342\) | −4.14701 | −0.224244 | ||||||||
\(343\) | −20.0983 | −1.08521 | ||||||||
\(344\) | −3.54156 | −0.190948 | ||||||||
\(345\) | −5.76174 | −0.310202 | ||||||||
\(346\) | 6.10830 | 0.328384 | ||||||||
\(347\) | 7.71486 | 0.414155 | 0.207078 | − | 0.978325i | \(-0.433605\pi\) | ||||
0.207078 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(348\) | 10.4741 | 0.561469 | ||||||||
\(349\) | 5.47720 | 0.293188 | 0.146594 | − | 0.989197i | \(-0.453169\pi\) | ||||
0.146594 | + | 0.989197i | \(0.453169\pi\) | |||||||
\(350\) | 2.25889 | 0.120743 | ||||||||
\(351\) | −0.258895 | −0.0138188 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 11.4190 | 0.607772 | 0.303886 | − | 0.952708i | \(-0.401716\pi\) | ||||
0.303886 | + | 0.952708i | \(0.401716\pi\) | |||||||
\(354\) | 12.9325 | 0.687355 | ||||||||
\(355\) | 7.83557 | 0.415869 | ||||||||
\(356\) | −5.08311 | −0.269404 | ||||||||
\(357\) | 2.25889 | 0.119553 | ||||||||
\(358\) | −11.0707 | −0.585105 | ||||||||
\(359\) | −29.4659 | −1.55515 | −0.777576 | − | 0.628789i | \(-0.783551\pi\) | ||||
−0.777576 | + | 0.628789i | \(0.783551\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −1.80233 | −0.0948595 | ||||||||
\(362\) | −12.3828 | −0.650827 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −0.584816 | −0.0306527 | ||||||||
\(365\) | 15.4503 | 0.808706 | ||||||||
\(366\) | 14.8061 | 0.773930 | ||||||||
\(367\) | 10.0068 | 0.522351 | 0.261175 | − | 0.965291i | \(-0.415890\pi\) | ||||
0.261175 | + | 0.965291i | \(0.415890\pi\) | |||||||
\(368\) | −5.76174 | −0.300352 | ||||||||
\(369\) | 12.5860 | 0.655199 | ||||||||
\(370\) | 4.71734 | 0.245243 | ||||||||
\(371\) | −20.4304 | −1.06069 | ||||||||
\(372\) | −1.28266 | −0.0665029 | ||||||||
\(373\) | −15.9681 | −0.826797 | −0.413398 | − | 0.910550i | \(-0.635658\pi\) | ||||
−0.413398 | + | 0.910550i | \(0.635658\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 1.43468 | 0.0739879 | ||||||||
\(377\) | −2.71168 | −0.139659 | ||||||||
\(378\) | 2.25889 | 0.116185 | ||||||||
\(379\) | 13.9191 | 0.714978 | 0.357489 | − | 0.933917i | \(-0.383633\pi\) | ||||
0.357489 | + | 0.933917i | \(0.383633\pi\) | |||||||
\(380\) | −4.14701 | −0.212737 | ||||||||
\(381\) | 3.08311 | 0.157953 | ||||||||
\(382\) | −19.4798 | −0.996671 | ||||||||
\(383\) | −35.2997 | −1.80373 | −0.901865 | − | 0.432017i | \(-0.857802\pi\) | ||||
−0.901865 | + | 0.432017i | \(0.857802\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.25889 | 0.115124 | ||||||||
\(386\) | 6.17330 | 0.314213 | ||||||||
\(387\) | −3.54156 | −0.180027 | ||||||||
\(388\) | 9.68856 | 0.491862 | ||||||||
\(389\) | −3.88310 | −0.196881 | −0.0984405 | − | 0.995143i | \(-0.531385\pi\) | ||||
−0.0984405 | + | 0.995143i | \(0.531385\pi\) | |||||||
\(390\) | −0.258895 | −0.0131096 | ||||||||
\(391\) | −5.76174 | −0.291384 | ||||||||
\(392\) | −1.89740 | −0.0958329 | ||||||||
\(393\) | −13.2389 | −0.667816 | ||||||||
\(394\) | 3.23894 | 0.163176 | ||||||||
\(395\) | −11.3384 | −0.570498 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −17.3334 | −0.869939 | −0.434969 | − | 0.900445i | \(-0.643241\pi\) | ||||
−0.434969 | + | 0.900445i | \(0.643241\pi\) | |||||||
\(398\) | 6.71734 | 0.336710 | ||||||||
\(399\) | −9.36765 | −0.468969 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.63221 | 0.481009 | 0.240505 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240505 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(402\) | −9.30330 | −0.464006 | ||||||||
\(403\) | 0.332074 | 0.0165418 | ||||||||
\(404\) | −9.84058 | −0.489587 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 23.6598 | 1.17422 | ||||||||
\(407\) | 4.71734 | 0.233830 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −25.8075 | −1.27610 | −0.638049 | − | 0.769996i | \(-0.720258\pi\) | ||||
−0.638049 | + | 0.769996i | \(0.720258\pi\) | |||||||
\(410\) | 12.5860 | 0.621576 | ||||||||
\(411\) | 14.6598 | 0.723114 | ||||||||
\(412\) | 2.89740 | 0.142744 | ||||||||
\(413\) | 29.2132 | 1.43749 | ||||||||
\(414\) | −5.76174 | −0.283174 | ||||||||
\(415\) | −11.7092 | −0.574782 | ||||||||
\(416\) | −0.258895 | −0.0126934 | ||||||||
\(417\) | 7.03939 | 0.344721 | ||||||||
\(418\) | −4.14701 | −0.202837 | ||||||||
\(419\) | 11.0057 | 0.537663 | 0.268832 | − | 0.963187i | \(-0.413362\pi\) | ||||
0.268832 | + | 0.963187i | \(0.413362\pi\) | |||||||
\(420\) | 2.25889 | 0.110223 | ||||||||
\(421\) | −30.5210 | −1.48750 | −0.743751 | − | 0.668456i | \(-0.766955\pi\) | ||||
−0.743751 | + | 0.668456i | \(0.766955\pi\) | |||||||
\(422\) | 22.7206 | 1.10602 | ||||||||
\(423\) | 1.43468 | 0.0697565 | ||||||||
\(424\) | −9.04440 | −0.439235 | ||||||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | 7.83557 | 0.379635 | ||||||||
\(427\) | 33.4455 | 1.61854 | ||||||||
\(428\) | −4.18006 | −0.202051 | ||||||||
\(429\) | −0.258895 | −0.0124995 | ||||||||
\(430\) | −3.54156 | −0.170789 | ||||||||
\(431\) | −19.8406 | −0.955687 | −0.477844 | − | 0.878445i | \(-0.658581\pi\) | ||||
−0.477844 | + | 0.878445i | \(0.658581\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 7.84738 | 0.377121 | 0.188561 | − | 0.982062i | \(-0.439618\pi\) | ||||
0.188561 | + | 0.982062i | \(0.439618\pi\) | |||||||
\(434\) | −2.89740 | −0.139079 | ||||||||
\(435\) | 10.4741 | 0.502193 | ||||||||
\(436\) | 3.28266 | 0.157211 | ||||||||
\(437\) | 23.8940 | 1.14300 | ||||||||
\(438\) | 15.4503 | 0.738244 | ||||||||
\(439\) | 20.3840 | 0.972876 | 0.486438 | − | 0.873715i | \(-0.338296\pi\) | ||||
0.486438 | + | 0.873715i | \(0.338296\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | −1.89740 | −0.0903522 | ||||||||
\(442\) | −0.258895 | −0.0123144 | ||||||||
\(443\) | −14.1889 | −0.674134 | −0.337067 | − | 0.941481i | \(-0.609435\pi\) | ||||
−0.337067 | + | 0.941481i | \(0.609435\pi\) | |||||||
\(444\) | 4.71734 | 0.223875 | ||||||||
\(445\) | −5.08311 | −0.240963 | ||||||||
\(446\) | 11.1914 | 0.529929 | ||||||||
\(447\) | −4.81539 | −0.227760 | ||||||||
\(448\) | 2.25889 | 0.106723 | ||||||||
\(449\) | −24.7330 | −1.16722 | −0.583610 | − | 0.812034i | \(-0.698360\pi\) | ||||
−0.583610 | + | 0.812034i | \(0.698360\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 12.5860 | 0.592650 | ||||||||
\(452\) | −5.38214 | −0.253154 | ||||||||
\(453\) | −3.23513 | −0.152000 | ||||||||
\(454\) | −8.87317 | −0.416439 | ||||||||
\(455\) | −0.584816 | −0.0274166 | ||||||||
\(456\) | −4.14701 | −0.194201 | ||||||||
\(457\) | −23.1002 | −1.08058 | −0.540290 | − | 0.841479i | \(-0.681685\pi\) | ||||
−0.540290 | + | 0.841479i | \(0.681685\pi\) | |||||||
\(458\) | 28.4209 | 1.32802 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −5.76174 | −0.268643 | ||||||||
\(461\) | −24.9237 | −1.16081 | −0.580406 | − | 0.814327i | \(-0.697106\pi\) | ||||
−0.580406 | + | 0.814327i | \(0.697106\pi\) | |||||||
\(462\) | 2.25889 | 0.105093 | ||||||||
\(463\) | 29.1751 | 1.35588 | 0.677942 | − | 0.735116i | \(-0.262872\pi\) | ||||
0.677942 | + | 0.735116i | \(0.262872\pi\) | |||||||
\(464\) | 10.4741 | 0.486247 | ||||||||
\(465\) | −1.28266 | −0.0594820 | ||||||||
\(466\) | −17.8949 | −0.828966 | ||||||||
\(467\) | −2.33654 | −0.108122 | −0.0540610 | − | 0.998538i | \(-0.517217\pi\) | ||||
−0.0540610 | + | 0.998538i | \(0.517217\pi\) | |||||||
\(468\) | −0.258895 | −0.0119674 | ||||||||
\(469\) | −21.0152 | −0.970390 | ||||||||
\(470\) | 1.43468 | 0.0661768 | ||||||||
\(471\) | −15.2652 | −0.703385 | ||||||||
\(472\) | 12.9325 | 0.595267 | ||||||||
\(473\) | −3.54156 | −0.162841 | ||||||||
\(474\) | −11.3384 | −0.520791 | ||||||||
\(475\) | −4.14701 | −0.190278 | ||||||||
\(476\) | 2.25889 | 0.103536 | ||||||||
\(477\) | −9.04440 | −0.414115 | ||||||||
\(478\) | −8.29401 | −0.379359 | ||||||||
\(479\) | −15.6549 | −0.715289 | −0.357645 | − | 0.933858i | \(-0.616420\pi\) | ||||
−0.357645 | + | 0.933858i | \(0.616420\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −1.22129 | −0.0556862 | ||||||||
\(482\) | −14.2657 | −0.649785 | ||||||||
\(483\) | −13.0152 | −0.592211 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 9.68856 | 0.439935 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 31.1787 | 1.41284 | 0.706421 | − | 0.707792i | \(-0.250308\pi\) | ||||
0.706421 | + | 0.707792i | \(0.250308\pi\) | |||||||
\(488\) | 14.8061 | 0.670243 | ||||||||
\(489\) | −21.8650 | −0.988771 | ||||||||
\(490\) | −1.89740 | −0.0857156 | ||||||||
\(491\) | 39.3953 | 1.77789 | 0.888943 | − | 0.458018i | \(-0.151441\pi\) | ||||
0.888943 | + | 0.458018i | \(0.151441\pi\) | |||||||
\(492\) | 12.5860 | 0.567419 | ||||||||
\(493\) | 10.4741 | 0.471728 | ||||||||
\(494\) | 1.07364 | 0.0483052 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | −1.28266 | −0.0575932 | ||||||||
\(497\) | 17.6997 | 0.793941 | ||||||||
\(498\) | −11.7092 | −0.524702 | ||||||||
\(499\) | 17.2859 | 0.773822 | 0.386911 | − | 0.922117i | \(-0.373542\pi\) | ||||
0.386911 | + | 0.922117i | \(0.373542\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −14.4265 | −0.644530 | ||||||||
\(502\) | 18.6892 | 0.834142 | ||||||||
\(503\) | −20.8342 | −0.928950 | −0.464475 | − | 0.885586i | \(-0.653757\pi\) | ||||
−0.464475 | + | 0.885586i | \(0.653757\pi\) | |||||||
\(504\) | 2.25889 | 0.100619 | ||||||||
\(505\) | −9.84058 | −0.437900 | ||||||||
\(506\) | −5.76174 | −0.256141 | ||||||||
\(507\) | −12.9330 | −0.574374 | ||||||||
\(508\) | 3.08311 | 0.136791 | ||||||||
\(509\) | −4.63469 | −0.205429 | −0.102714 | − | 0.994711i | \(-0.532753\pi\) | ||||
−0.102714 | + | 0.994711i | \(0.532753\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | 34.9006 | 1.54391 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.14701 | −0.183095 | ||||||||
\(514\) | 14.6204 | 0.644879 | ||||||||
\(515\) | 2.89740 | 0.127674 | ||||||||
\(516\) | −3.54156 | −0.155908 | ||||||||
\(517\) | 1.43468 | 0.0630971 | ||||||||
\(518\) | 10.6560 | 0.468197 | ||||||||
\(519\) | 6.10830 | 0.268125 | ||||||||
\(520\) | −0.258895 | −0.0113533 | ||||||||
\(521\) | 23.8337 | 1.04417 | 0.522087 | − | 0.852892i | \(-0.325154\pi\) | ||||
0.522087 | + | 0.852892i | \(0.325154\pi\) | |||||||
\(522\) | 10.4741 | 0.458438 | ||||||||
\(523\) | −29.4066 | −1.28586 | −0.642930 | − | 0.765925i | \(-0.722281\pi\) | ||||
−0.642930 | + | 0.765925i | \(0.722281\pi\) | |||||||
\(524\) | −13.2389 | −0.578346 | ||||||||
\(525\) | 2.25889 | 0.0985862 | ||||||||
\(526\) | 11.1914 | 0.487969 | ||||||||
\(527\) | −1.28266 | −0.0558736 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 10.1977 | 0.443377 | ||||||||
\(530\) | −9.04440 | −0.392864 | ||||||||
\(531\) | 12.9325 | 0.561223 | ||||||||
\(532\) | −9.36765 | −0.406139 | ||||||||
\(533\) | −3.25844 | −0.141139 | ||||||||
\(534\) | −5.08311 | −0.219968 | ||||||||
\(535\) | −4.18006 | −0.180720 | ||||||||
\(536\) | −9.30330 | −0.401841 | ||||||||
\(537\) | −11.0707 | −0.477736 | ||||||||
\(538\) | −8.13818 | −0.350862 | ||||||||
\(539\) | −1.89740 | −0.0817266 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 33.2560 | 1.42979 | 0.714893 | − | 0.699234i | \(-0.246475\pi\) | ||||
0.714893 | + | 0.699234i | \(0.246475\pi\) | |||||||
\(542\) | 3.19707 | 0.137326 | ||||||||
\(543\) | −12.3828 | −0.531398 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 3.28266 | 0.140614 | ||||||||
\(546\) | −0.584816 | −0.0250278 | ||||||||
\(547\) | −3.96667 | −0.169603 | −0.0848013 | − | 0.996398i | \(-0.527026\pi\) | ||||
−0.0848013 | + | 0.996398i | \(0.527026\pi\) | |||||||
\(548\) | 14.6598 | 0.626235 | ||||||||
\(549\) | 14.8061 | 0.631911 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −43.4360 | −1.85044 | ||||||||
\(552\) | −5.76174 | −0.245236 | ||||||||
\(553\) | −25.6123 | −1.08915 | ||||||||
\(554\) | 11.9087 | 0.505954 | ||||||||
\(555\) | 4.71734 | 0.200240 | ||||||||
\(556\) | 7.03939 | 0.298537 | ||||||||
\(557\) | −2.53544 | −0.107430 | −0.0537150 | − | 0.998556i | \(-0.517106\pi\) | ||||
−0.0537150 | + | 0.998556i | \(0.517106\pi\) | |||||||
\(558\) | −1.28266 | −0.0542994 | ||||||||
\(559\) | 0.916889 | 0.0387803 | ||||||||
\(560\) | 2.25889 | 0.0954557 | ||||||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | −24.3126 | −1.02556 | ||||||||
\(563\) | −8.55585 | −0.360586 | −0.180293 | − | 0.983613i | \(-0.557705\pi\) | ||||
−0.180293 | + | 0.983613i | \(0.557705\pi\) | |||||||
\(564\) | 1.43468 | 0.0604109 | ||||||||
\(565\) | −5.38214 | −0.226428 | ||||||||
\(566\) | 6.42654 | 0.270128 | ||||||||
\(567\) | 2.25889 | 0.0948647 | ||||||||
\(568\) | 7.83557 | 0.328773 | ||||||||
\(569\) | 5.20273 | 0.218110 | 0.109055 | − | 0.994036i | \(-0.465218\pi\) | ||||
0.109055 | + | 0.994036i | \(0.465218\pi\) | |||||||
\(570\) | −4.14701 | −0.173699 | ||||||||
\(571\) | −24.8732 | −1.04091 | −0.520455 | − | 0.853889i | \(-0.674238\pi\) | ||||
−0.520455 | + | 0.853889i | \(0.674238\pi\) | |||||||
\(572\) | −0.258895 | −0.0108249 | ||||||||
\(573\) | −19.4798 | −0.813779 | ||||||||
\(574\) | 28.4304 | 1.18666 | ||||||||
\(575\) | −5.76174 | −0.240281 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −13.0057 | −0.541434 | −0.270717 | − | 0.962659i | \(-0.587261\pi\) | ||||
−0.270717 | + | 0.962659i | \(0.587261\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 6.17330 | 0.256554 | ||||||||
\(580\) | 10.4741 | 0.434912 | ||||||||
\(581\) | −26.4498 | −1.09732 | ||||||||
\(582\) | 9.68856 | 0.401604 | ||||||||
\(583\) | −9.04440 | −0.374581 | ||||||||
\(584\) | 15.4503 | 0.639338 | ||||||||
\(585\) | −0.258895 | −0.0107040 | ||||||||
\(586\) | −6.75921 | −0.279220 | ||||||||
\(587\) | 4.95315 | 0.204438 | 0.102219 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102219 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(588\) | −1.89740 | −0.0782473 | ||||||||
\(589\) | 5.31920 | 0.219174 | ||||||||
\(590\) | 12.9325 | 0.532423 | ||||||||
\(591\) | 3.23894 | 0.133232 | ||||||||
\(592\) | 4.71734 | 0.193881 | ||||||||
\(593\) | −33.8175 | −1.38872 | −0.694359 | − | 0.719629i | \(-0.744312\pi\) | ||||
−0.694359 | + | 0.719629i | \(0.744312\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 2.25889 | 0.0926056 | ||||||||
\(596\) | −4.81539 | −0.197246 | ||||||||
\(597\) | 6.71734 | 0.274922 | ||||||||
\(598\) | 1.49168 | 0.0609995 | ||||||||
\(599\) | 36.4873 | 1.49083 | 0.745415 | − | 0.666600i | \(-0.232251\pi\) | ||||
0.745415 | + | 0.666600i | \(0.232251\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −40.1307 | −1.63697 | −0.818483 | − | 0.574530i | \(-0.805185\pi\) | ||||
−0.818483 | + | 0.574530i | \(0.805185\pi\) | |||||||
\(602\) | −8.00000 | −0.326056 | ||||||||
\(603\) | −9.30330 | −0.378860 | ||||||||
\(604\) | −3.23513 | −0.131636 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −9.84058 | −0.399746 | ||||||||
\(607\) | −19.7525 | −0.801729 | −0.400865 | − | 0.916137i | \(-0.631290\pi\) | ||||
−0.400865 | + | 0.916137i | \(0.631290\pi\) | |||||||
\(608\) | −4.14701 | −0.168183 | ||||||||
\(609\) | 23.6598 | 0.958744 | ||||||||
\(610\) | 14.8061 | 0.599483 | ||||||||
\(611\) | −0.371431 | −0.0150265 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 39.0588 | 1.57757 | 0.788786 | − | 0.614668i | \(-0.210710\pi\) | ||||
0.788786 | + | 0.614668i | \(0.210710\pi\) | |||||||
\(614\) | −14.4009 | −0.581173 | ||||||||
\(615\) | 12.5860 | 0.507515 | ||||||||
\(616\) | 2.25889 | 0.0910135 | ||||||||
\(617\) | −24.2827 | −0.977586 | −0.488793 | − | 0.872400i | \(-0.662563\pi\) | ||||
−0.488793 | + | 0.872400i | \(0.662563\pi\) | |||||||
\(618\) | 2.89740 | 0.116550 | ||||||||
\(619\) | −28.5547 | −1.14771 | −0.573855 | − | 0.818957i | \(-0.694553\pi\) | ||||
−0.573855 | + | 0.818957i | \(0.694553\pi\) | |||||||
\(620\) | −1.28266 | −0.0515129 | ||||||||
\(621\) | −5.76174 | −0.231211 | ||||||||
\(622\) | 15.8768 | 0.636603 | ||||||||
\(623\) | −11.4822 | −0.460025 | ||||||||
\(624\) | −0.258895 | −0.0103641 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.6587 | −0.465975 | ||||||||
\(627\) | −4.14701 | −0.165616 | ||||||||
\(628\) | −15.2652 | −0.609149 | ||||||||
\(629\) | 4.71734 | 0.188093 | ||||||||
\(630\) | 2.25889 | 0.0899965 | ||||||||
\(631\) | −6.46024 | −0.257178 | −0.128589 | − | 0.991698i | \(-0.541045\pi\) | ||||
−0.128589 | + | 0.991698i | \(0.541045\pi\) | |||||||
\(632\) | −11.3384 | −0.451018 | ||||||||
\(633\) | 22.7206 | 0.903061 | ||||||||
\(634\) | −8.08881 | −0.321247 | ||||||||
\(635\) | 3.08311 | 0.122350 | ||||||||
\(636\) | −9.04440 | −0.358634 | ||||||||
\(637\) | 0.491225 | 0.0194631 | ||||||||
\(638\) | 10.4741 | 0.414672 | ||||||||
\(639\) | 7.83557 | 0.309970 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 34.4536 | 1.36083 | 0.680417 | − | 0.732825i | \(-0.261799\pi\) | ||||
0.680417 | + | 0.732825i | \(0.261799\pi\) | |||||||
\(642\) | −4.18006 | −0.164974 | ||||||||
\(643\) | 8.13634 | 0.320866 | 0.160433 | − | 0.987047i | \(-0.448711\pi\) | ||||
0.160433 | + | 0.987047i | \(0.448711\pi\) | |||||||
\(644\) | −13.0152 | −0.512869 | ||||||||
\(645\) | −3.54156 | −0.139449 | ||||||||
\(646\) | −4.14701 | −0.163162 | ||||||||
\(647\) | 16.3529 | 0.642900 | 0.321450 | − | 0.946927i | \(-0.395830\pi\) | ||||
0.321450 | + | 0.946927i | \(0.395830\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 12.9325 | 0.507646 | ||||||||
\(650\) | −0.258895 | −0.0101547 | ||||||||
\(651\) | −2.89740 | −0.113558 | ||||||||
\(652\) | −21.8650 | −0.856301 | ||||||||
\(653\) | 28.3828 | 1.11071 | 0.555353 | − | 0.831615i | \(-0.312583\pi\) | ||||
0.555353 | + | 0.831615i | \(0.312583\pi\) | |||||||
\(654\) | 3.28266 | 0.128362 | ||||||||
\(655\) | −13.2389 | −0.517288 | ||||||||
\(656\) | 12.5860 | 0.491399 | ||||||||
\(657\) | 15.4503 | 0.602774 | ||||||||
\(658\) | 3.24079 | 0.126339 | ||||||||
\(659\) | −21.3703 | −0.832470 | −0.416235 | − | 0.909257i | \(-0.636651\pi\) | ||||
−0.416235 | + | 0.909257i | \(0.636651\pi\) | |||||||
\(660\) | 1.00000 | 0.0389249 | ||||||||
\(661\) | −9.32775 | −0.362807 | −0.181404 | − | 0.983409i | \(-0.558064\pi\) | ||||
−0.181404 | + | 0.983409i | \(0.558064\pi\) | |||||||
\(662\) | 16.1363 | 0.627157 | ||||||||
\(663\) | −0.258895 | −0.0100546 | ||||||||
\(664\) | −11.7092 | −0.454405 | ||||||||
\(665\) | −9.36765 | −0.363262 | ||||||||
\(666\) | 4.71734 | 0.182793 | ||||||||
\(667\) | −60.3489 | −2.33672 | ||||||||
\(668\) | −14.4265 | −0.558180 | ||||||||
\(669\) | 11.1914 | 0.432685 | ||||||||
\(670\) | −9.30330 | −0.359418 | ||||||||
\(671\) | 14.8061 | 0.571585 | ||||||||
\(672\) | 2.25889 | 0.0871388 | ||||||||
\(673\) | 48.5171 | 1.87020 | 0.935099 | − | 0.354386i | \(-0.115310\pi\) | ||||
0.935099 | + | 0.354386i | \(0.115310\pi\) | |||||||
\(674\) | 16.4859 | 0.635012 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −12.9330 | −0.497422 | ||||||||
\(677\) | −1.77623 | −0.0682659 | −0.0341329 | − | 0.999417i | \(-0.510867\pi\) | ||||
−0.0341329 | + | 0.999417i | \(0.510867\pi\) | |||||||
\(678\) | −5.38214 | −0.206700 | ||||||||
\(679\) | 21.8854 | 0.839886 | ||||||||
\(680\) | 1.00000 | 0.0383482 | ||||||||
\(681\) | −8.87317 | −0.340021 | ||||||||
\(682\) | −1.28266 | −0.0491156 | ||||||||
\(683\) | 23.8455 | 0.912424 | 0.456212 | − | 0.889871i | \(-0.349206\pi\) | ||||
0.456212 | + | 0.889871i | \(0.349206\pi\) | |||||||
\(684\) | −4.14701 | −0.158565 | ||||||||
\(685\) | 14.6598 | 0.560122 | ||||||||
\(686\) | −20.0983 | −0.767356 | ||||||||
\(687\) | 28.4209 | 1.08432 | ||||||||
\(688\) | −3.54156 | −0.135021 | ||||||||
\(689\) | 2.34155 | 0.0892058 | ||||||||
\(690\) | −5.76174 | −0.219346 | ||||||||
\(691\) | −18.7309 | −0.712559 | −0.356279 | − | 0.934379i | \(-0.615955\pi\) | ||||
−0.356279 | + | 0.934379i | \(0.615955\pi\) | |||||||
\(692\) | 6.10830 | 0.232203 | ||||||||
\(693\) | 2.25889 | 0.0858083 | ||||||||
\(694\) | 7.71486 | 0.292852 | ||||||||
\(695\) | 7.03939 | 0.267019 | ||||||||
\(696\) | 10.4741 | 0.397019 | ||||||||
\(697\) | 12.5860 | 0.476727 | ||||||||
\(698\) | 5.47720 | 0.207315 | ||||||||
\(699\) | −17.8949 | −0.676848 | ||||||||
\(700\) | 2.25889 | 0.0853782 | ||||||||
\(701\) | 5.24253 | 0.198008 | 0.0990038 | − | 0.995087i | \(-0.468434\pi\) | ||||
0.0990038 | + | 0.995087i | \(0.468434\pi\) | |||||||
\(702\) | −0.258895 | −0.00977135 | ||||||||
\(703\) | −19.5628 | −0.737826 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 1.43468 | 0.0540331 | ||||||||
\(706\) | 11.4190 | 0.429760 | ||||||||
\(707\) | −22.2288 | −0.836001 | ||||||||
\(708\) | 12.9325 | 0.486034 | ||||||||
\(709\) | 21.2295 | 0.797289 | 0.398645 | − | 0.917105i | \(-0.369481\pi\) | ||||
0.398645 | + | 0.917105i | \(0.369481\pi\) | |||||||
\(710\) | 7.83557 | 0.294064 | ||||||||
\(711\) | −11.3384 | −0.425224 | ||||||||
\(712\) | −5.08311 | −0.190498 | ||||||||
\(713\) | 7.39036 | 0.276771 | ||||||||
\(714\) | 2.25889 | 0.0845370 | ||||||||
\(715\) | −0.258895 | −0.00968211 | ||||||||
\(716\) | −11.0707 | −0.413731 | ||||||||
\(717\) | −8.29401 | −0.309746 | ||||||||
\(718\) | −29.4659 | −1.09966 | ||||||||
\(719\) | 40.8611 | 1.52386 | 0.761931 | − | 0.647658i | \(-0.224251\pi\) | ||||
0.761931 | + | 0.647658i | \(0.224251\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 6.54491 | 0.243745 | ||||||||
\(722\) | −1.80233 | −0.0670758 | ||||||||
\(723\) | −14.2657 | −0.530547 | ||||||||
\(724\) | −12.3828 | −0.460204 | ||||||||
\(725\) | 10.4741 | 0.388997 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −26.0712 | −0.966926 | −0.483463 | − | 0.875365i | \(-0.660621\pi\) | ||||
−0.483463 | + | 0.875365i | \(0.660621\pi\) | |||||||
\(728\) | −0.584816 | −0.0216747 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.4503 | 0.571841 | ||||||||
\(731\) | −3.54156 | −0.130989 | ||||||||
\(732\) | 14.8061 | 0.547251 | ||||||||
\(733\) | −52.8492 | −1.95203 | −0.976015 | − | 0.217703i | \(-0.930144\pi\) | ||||
−0.976015 | + | 0.217703i | \(0.930144\pi\) | |||||||
\(734\) | 10.0068 | 0.369358 | ||||||||
\(735\) | −1.89740 | −0.0699865 | ||||||||
\(736\) | −5.76174 | −0.212381 | ||||||||
\(737\) | −9.30330 | −0.342691 | ||||||||
\(738\) | 12.5860 | 0.463296 | ||||||||
\(739\) | 15.3252 | 0.563746 | 0.281873 | − | 0.959452i | \(-0.409044\pi\) | ||||
0.281873 | + | 0.959452i | \(0.409044\pi\) | |||||||
\(740\) | 4.71734 | 0.173413 | ||||||||
\(741\) | 1.07364 | 0.0394411 | ||||||||
\(742\) | −20.4304 | −0.750022 | ||||||||
\(743\) | −26.5316 | −0.973351 | −0.486675 | − | 0.873583i | \(-0.661791\pi\) | ||||
−0.486675 | + | 0.873583i | \(0.661791\pi\) | |||||||
\(744\) | −1.28266 | −0.0470246 | ||||||||
\(745\) | −4.81539 | −0.176422 | ||||||||
\(746\) | −15.9681 | −0.584633 | ||||||||
\(747\) | −11.7092 | −0.428417 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −9.44231 | −0.345014 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 11.6346 | 0.424552 | 0.212276 | − | 0.977210i | \(-0.431912\pi\) | ||||
0.212276 | + | 0.977210i | \(0.431912\pi\) | |||||||
\(752\) | 1.43468 | 0.0523173 | ||||||||
\(753\) | 18.6892 | 0.681074 | ||||||||
\(754\) | −2.71168 | −0.0987536 | ||||||||
\(755\) | −3.23513 | −0.117738 | ||||||||
\(756\) | 2.25889 | 0.0821552 | ||||||||
\(757\) | 15.0402 | 0.546644 | 0.273322 | − | 0.961923i | \(-0.411878\pi\) | ||||
0.273322 | + | 0.961923i | \(0.411878\pi\) | |||||||
\(758\) | 13.9191 | 0.505566 | ||||||||
\(759\) | −5.76174 | −0.209138 | ||||||||
\(760\) | −4.14701 | −0.150428 | ||||||||
\(761\) | −43.2979 | −1.56955 | −0.784773 | − | 0.619783i | \(-0.787221\pi\) | ||||
−0.784773 | + | 0.619783i | \(0.787221\pi\) | |||||||
\(762\) | 3.08311 | 0.111689 | ||||||||
\(763\) | 7.41518 | 0.268448 | ||||||||
\(764\) | −19.4798 | −0.704753 | ||||||||
\(765\) | 1.00000 | 0.0361551 | ||||||||
\(766\) | −35.2997 | −1.27543 | ||||||||
\(767\) | −3.34816 | −0.120895 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 9.69596 | 0.349645 | 0.174823 | − | 0.984600i | \(-0.444065\pi\) | ||||
0.174823 | + | 0.984600i | \(0.444065\pi\) | |||||||
\(770\) | 2.25889 | 0.0814049 | ||||||||
\(771\) | 14.6204 | 0.526542 | ||||||||
\(772\) | 6.17330 | 0.222182 | ||||||||
\(773\) | −36.2358 | −1.30331 | −0.651656 | − | 0.758515i | \(-0.725925\pi\) | ||||
−0.651656 | + | 0.758515i | \(0.725925\pi\) | |||||||
\(774\) | −3.54156 | −0.127299 | ||||||||
\(775\) | −1.28266 | −0.0460745 | ||||||||
\(776\) | 9.68856 | 0.347799 | ||||||||
\(777\) | 10.6560 | 0.382281 | ||||||||
\(778\) | −3.88310 | −0.139216 | ||||||||
\(779\) | −52.1941 | −1.87005 | ||||||||
\(780\) | −0.258895 | −0.00926991 | ||||||||
\(781\) | 7.83557 | 0.280379 | ||||||||
\(782\) | −5.76174 | −0.206039 | ||||||||
\(783\) | 10.4741 | 0.374313 | ||||||||
\(784\) | −1.89740 | −0.0677641 | ||||||||
\(785\) | −15.2652 | −0.544840 | ||||||||
\(786\) | −13.2389 | −0.472217 | ||||||||
\(787\) | −48.9076 | −1.74337 | −0.871684 | − | 0.490068i | \(-0.836972\pi\) | ||||
−0.871684 | + | 0.490068i | \(0.836972\pi\) | |||||||
\(788\) | 3.23894 | 0.115383 | ||||||||
\(789\) | 11.1914 | 0.398425 | ||||||||
\(790\) | −11.3384 | −0.403403 | ||||||||
\(791\) | −12.1577 | −0.432277 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −3.83323 | −0.136122 | ||||||||
\(794\) | −17.3334 | −0.615140 | ||||||||
\(795\) | −9.04440 | −0.320772 | ||||||||
\(796\) | 6.71734 | 0.238090 | ||||||||
\(797\) | −17.7892 | −0.630125 | −0.315063 | − | 0.949071i | \(-0.602025\pi\) | ||||
−0.315063 | + | 0.949071i | \(0.602025\pi\) | |||||||
\(798\) | −9.36765 | −0.331611 | ||||||||
\(799\) | 1.43468 | 0.0507553 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −5.08311 | −0.179603 | ||||||||
\(802\) | 9.63221 | 0.340125 | ||||||||
\(803\) | 15.4503 | 0.545229 | ||||||||
\(804\) | −9.30330 | −0.328102 | ||||||||
\(805\) | −13.0152 | −0.458724 | ||||||||
\(806\) | 0.332074 | 0.0116968 | ||||||||
\(807\) | −8.13818 | −0.286478 | ||||||||
\(808\) | −9.84058 | −0.346190 | ||||||||
\(809\) | 9.63918 | 0.338896 | 0.169448 | − | 0.985539i | \(-0.445802\pi\) | ||||
0.169448 | + | 0.985539i | \(0.445802\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −32.3577 | −1.13623 | −0.568116 | − | 0.822949i | \(-0.692327\pi\) | ||||
−0.568116 | + | 0.822949i | \(0.692327\pi\) | |||||||
\(812\) | 23.6598 | 0.830297 | ||||||||
\(813\) | 3.19707 | 0.112126 | ||||||||
\(814\) | 4.71734 | 0.165343 | ||||||||
\(815\) | −21.8650 | −0.765899 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 14.6869 | 0.513828 | ||||||||
\(818\) | −25.8075 | −0.902337 | ||||||||
\(819\) | −0.584816 | −0.0204351 | ||||||||
\(820\) | 12.5860 | 0.439521 | ||||||||
\(821\) | −46.5153 | −1.62340 | −0.811698 | − | 0.584077i | \(-0.801457\pi\) | ||||
−0.811698 | + | 0.584077i | \(0.801457\pi\) | |||||||
\(822\) | 14.6598 | 0.511319 | ||||||||
\(823\) | −7.09487 | −0.247312 | −0.123656 | − | 0.992325i | \(-0.539462\pi\) | ||||
−0.123656 | + | 0.992325i | \(0.539462\pi\) | |||||||
\(824\) | 2.89740 | 0.100936 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 29.2132 | 1.01646 | ||||||||
\(827\) | 19.5011 | 0.678120 | 0.339060 | − | 0.940765i | \(-0.389891\pi\) | ||||
0.339060 | + | 0.940765i | \(0.389891\pi\) | |||||||
\(828\) | −5.76174 | −0.200234 | ||||||||
\(829\) | 9.43283 | 0.327616 | 0.163808 | − | 0.986492i | \(-0.447622\pi\) | ||||
0.163808 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(830\) | −11.7092 | −0.406432 | ||||||||
\(831\) | 11.9087 | 0.413110 | ||||||||
\(832\) | −0.258895 | −0.00897555 | ||||||||
\(833\) | −1.89740 | −0.0657409 | ||||||||
\(834\) | 7.03939 | 0.243754 | ||||||||
\(835\) | −14.4265 | −0.499251 | ||||||||
\(836\) | −4.14701 | −0.143427 | ||||||||
\(837\) | −1.28266 | −0.0443352 | ||||||||
\(838\) | 11.0057 | 0.380185 | ||||||||
\(839\) | −24.5771 | −0.848497 | −0.424248 | − | 0.905546i | \(-0.639462\pi\) | ||||
−0.424248 | + | 0.905546i | \(0.639462\pi\) | |||||||
\(840\) | 2.25889 | 0.0779393 | ||||||||
\(841\) | 80.7062 | 2.78297 | ||||||||
\(842\) | −30.5210 | −1.05182 | ||||||||
\(843\) | −24.3126 | −0.837370 | ||||||||
\(844\) | 22.7206 | 0.782074 | ||||||||
\(845\) | −12.9330 | −0.444908 | ||||||||
\(846\) | 1.43468 | 0.0493253 | ||||||||
\(847\) | 2.25889 | 0.0776165 | ||||||||
\(848\) | −9.04440 | −0.310586 | ||||||||
\(849\) | 6.42654 | 0.220558 | ||||||||
\(850\) | 1.00000 | 0.0342997 | ||||||||
\(851\) | −27.1801 | −0.931722 | ||||||||
\(852\) | 7.83557 | 0.268442 | ||||||||
\(853\) | −2.25747 | −0.0772944 | −0.0386472 | − | 0.999253i | \(-0.512305\pi\) | ||||
−0.0386472 | + | 0.999253i | \(0.512305\pi\) | |||||||
\(854\) | 33.4455 | 1.14448 | ||||||||
\(855\) | −4.14701 | −0.141825 | ||||||||
\(856\) | −4.18006 | −0.142871 | ||||||||
\(857\) | 28.3158 | 0.967249 | 0.483625 | − | 0.875276i | \(-0.339320\pi\) | ||||
0.483625 | + | 0.875276i | \(0.339320\pi\) | |||||||
\(858\) | −0.258895 | −0.00883852 | ||||||||
\(859\) | 6.02988 | 0.205737 | 0.102868 | − | 0.994695i | \(-0.467198\pi\) | ||||
0.102868 | + | 0.994695i | \(0.467198\pi\) | |||||||
\(860\) | −3.54156 | −0.120766 | ||||||||
\(861\) | 28.4304 | 0.968904 | ||||||||
\(862\) | −19.8406 | −0.675773 | ||||||||
\(863\) | −32.2550 | −1.09797 | −0.548987 | − | 0.835831i | \(-0.684986\pi\) | ||||
−0.548987 | + | 0.835831i | \(0.684986\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 6.10830 | 0.207688 | ||||||||
\(866\) | 7.84738 | 0.266665 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −2.89740 | −0.0983440 | ||||||||
\(869\) | −11.3384 | −0.384629 | ||||||||
\(870\) | 10.4741 | 0.355104 | ||||||||
\(871\) | 2.40857 | 0.0816114 | ||||||||
\(872\) | 3.28266 | 0.111165 | ||||||||
\(873\) | 9.68856 | 0.327908 | ||||||||
\(874\) | 23.8940 | 0.808226 | ||||||||
\(875\) | 2.25889 | 0.0763646 | ||||||||
\(876\) | 15.4503 | 0.522017 | ||||||||
\(877\) | 19.1105 | 0.645317 | 0.322659 | − | 0.946515i | \(-0.395423\pi\) | ||||
0.322659 | + | 0.946515i | \(0.395423\pi\) | |||||||
\(878\) | 20.3840 | 0.687927 | ||||||||
\(879\) | −6.75921 | −0.227983 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 11.7767 | 0.396768 | 0.198384 | − | 0.980124i | \(-0.436431\pi\) | ||||
0.198384 | + | 0.980124i | \(0.436431\pi\) | |||||||
\(882\) | −1.89740 | −0.0638886 | ||||||||
\(883\) | −31.1887 | −1.04958 | −0.524792 | − | 0.851230i | \(-0.675857\pi\) | ||||
−0.524792 | + | 0.851230i | \(0.675857\pi\) | |||||||
\(884\) | −0.258895 | −0.00870757 | ||||||||
\(885\) | 12.9325 | 0.434722 | ||||||||
\(886\) | −14.1889 | −0.476685 | ||||||||
\(887\) | −26.8782 | −0.902483 | −0.451241 | − | 0.892402i | \(-0.649019\pi\) | ||||
−0.451241 | + | 0.892402i | \(0.649019\pi\) | |||||||
\(888\) | 4.71734 | 0.158304 | ||||||||
\(889\) | 6.96442 | 0.233579 | ||||||||
\(890\) | −5.08311 | −0.170386 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 11.1914 | 0.374716 | ||||||||
\(893\) | −5.94962 | −0.199097 | ||||||||
\(894\) | −4.81539 | −0.161051 | ||||||||
\(895\) | −11.0707 | −0.370053 | ||||||||
\(896\) | 2.25889 | 0.0754644 | ||||||||
\(897\) | 1.49168 | 0.0498059 | ||||||||
\(898\) | −24.7330 | −0.825350 | ||||||||
\(899\) | −13.4347 | −0.448072 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −9.04440 | −0.301313 | ||||||||
\(902\) | 12.5860 | 0.419067 | ||||||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | −5.38214 | −0.179007 | ||||||||
\(905\) | −12.3828 | −0.411619 | ||||||||
\(906\) | −3.23513 | −0.107480 | ||||||||
\(907\) | 38.8906 | 1.29134 | 0.645670 | − | 0.763616i | \(-0.276578\pi\) | ||||
0.645670 | + | 0.763616i | \(0.276578\pi\) | |||||||
\(908\) | −8.87317 | −0.294467 | ||||||||
\(909\) | −9.84058 | −0.326391 | ||||||||
\(910\) | −0.584816 | −0.0193864 | ||||||||
\(911\) | −29.3889 | −0.973699 | −0.486849 | − | 0.873486i | \(-0.661854\pi\) | ||||
−0.486849 | + | 0.873486i | \(0.661854\pi\) | |||||||
\(912\) | −4.14701 | −0.137321 | ||||||||
\(913\) | −11.7092 | −0.387518 | ||||||||
\(914\) | −23.1002 | −0.764085 | ||||||||
\(915\) | 14.8061 | 0.489476 | ||||||||
\(916\) | 28.4209 | 0.939052 | ||||||||
\(917\) | −29.9054 | −0.987562 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 4.64214 | 0.153130 | 0.0765650 | − | 0.997065i | \(-0.475605\pi\) | ||||
0.0765650 | + | 0.997065i | \(0.475605\pi\) | |||||||
\(920\) | −5.76174 | −0.189959 | ||||||||
\(921\) | −14.4009 | −0.474525 | ||||||||
\(922\) | −24.9237 | −0.820818 | ||||||||
\(923\) | −2.02859 | −0.0667717 | ||||||||
\(924\) | 2.25889 | 0.0743122 | ||||||||
\(925\) | 4.71734 | 0.155105 | ||||||||
\(926\) | 29.1751 | 0.958754 | ||||||||
\(927\) | 2.89740 | 0.0951629 | ||||||||
\(928\) | 10.4741 | 0.343828 | ||||||||
\(929\) | 31.5810 | 1.03614 | 0.518069 | − | 0.855339i | \(-0.326651\pi\) | ||||
0.518069 | + | 0.855339i | \(0.326651\pi\) | |||||||
\(930\) | −1.28266 | −0.0420601 | ||||||||
\(931\) | 7.86851 | 0.257880 | ||||||||
\(932\) | −17.8949 | −0.586167 | ||||||||
\(933\) | 15.8768 | 0.519784 | ||||||||
\(934\) | −2.33654 | −0.0764538 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | −0.258895 | −0.00846223 | ||||||||
\(937\) | 52.8673 | 1.72710 | 0.863549 | − | 0.504264i | \(-0.168236\pi\) | ||||
0.863549 | + | 0.504264i | \(0.168236\pi\) | |||||||
\(938\) | −21.0152 | −0.686170 | ||||||||
\(939\) | −11.6587 | −0.380467 | ||||||||
\(940\) | 1.43468 | 0.0467941 | ||||||||
\(941\) | −39.3343 | −1.28226 | −0.641131 | − | 0.767431i | \(-0.721535\pi\) | ||||
−0.641131 | + | 0.767431i | \(0.721535\pi\) | |||||||
\(942\) | −15.2652 | −0.497368 | ||||||||
\(943\) | −72.5170 | −2.36148 | ||||||||
\(944\) | 12.9325 | 0.420918 | ||||||||
\(945\) | 2.25889 | 0.0734818 | ||||||||
\(946\) | −3.54156 | −0.115146 | ||||||||
\(947\) | 9.96009 | 0.323660 | 0.161830 | − | 0.986819i | \(-0.448260\pi\) | ||||
0.161830 | + | 0.986819i | \(0.448260\pi\) | |||||||
\(948\) | −11.3384 | −0.368255 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | −4.14701 | −0.134547 | ||||||||
\(951\) | −8.08881 | −0.262297 | ||||||||
\(952\) | 2.25889 | 0.0732112 | ||||||||
\(953\) | 2.07612 | 0.0672521 | 0.0336260 | − | 0.999434i | \(-0.489294\pi\) | ||||
0.0336260 | + | 0.999434i | \(0.489294\pi\) | |||||||
\(954\) | −9.04440 | −0.292823 | ||||||||
\(955\) | −19.4798 | −0.630350 | ||||||||
\(956\) | −8.29401 | −0.268248 | ||||||||
\(957\) | 10.4741 | 0.338579 | ||||||||
\(958\) | −15.6549 | −0.505786 | ||||||||
\(959\) | 33.1149 | 1.06934 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −29.3548 | −0.946928 | ||||||||
\(962\) | −1.22129 | −0.0393761 | ||||||||
\(963\) | −4.18006 | −0.134700 | ||||||||
\(964\) | −14.2657 | −0.459467 | ||||||||
\(965\) | 6.17330 | 0.198726 | ||||||||
\(966\) | −13.0152 | −0.418756 | ||||||||
\(967\) | 41.1471 | 1.32320 | 0.661601 | − | 0.749856i | \(-0.269877\pi\) | ||||
0.661601 | + | 0.749856i | \(0.269877\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −4.14701 | −0.133221 | ||||||||
\(970\) | 9.68856 | 0.311081 | ||||||||
\(971\) | −45.9187 | −1.47360 | −0.736801 | − | 0.676110i | \(-0.763664\pi\) | ||||
−0.736801 | + | 0.676110i | \(0.763664\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 15.9012 | 0.509770 | ||||||||
\(974\) | 31.1787 | 0.999031 | ||||||||
\(975\) | −0.258895 | −0.00829126 | ||||||||
\(976\) | 14.8061 | 0.473933 | ||||||||
\(977\) | 4.18190 | 0.133791 | 0.0668954 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668954 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(978\) | −21.8650 | −0.699167 | ||||||||
\(979\) | −5.08311 | −0.162457 | ||||||||
\(980\) | −1.89740 | −0.0606101 | ||||||||
\(981\) | 3.28266 | 0.104807 | ||||||||
\(982\) | 39.3953 | 1.25716 | ||||||||
\(983\) | −16.4951 | −0.526113 | −0.263056 | − | 0.964780i | \(-0.584731\pi\) | ||||
−0.263056 | + | 0.964780i | \(0.584731\pi\) | |||||||
\(984\) | 12.5860 | 0.401226 | ||||||||
\(985\) | 3.23894 | 0.103201 | ||||||||
\(986\) | 10.4741 | 0.333562 | ||||||||
\(987\) | 3.24079 | 0.103155 | ||||||||
\(988\) | 1.07364 | 0.0341570 | ||||||||
\(989\) | 20.4055 | 0.648858 | ||||||||
\(990\) | 1.00000 | 0.0317821 | ||||||||
\(991\) | 6.06321 | 0.192604 | 0.0963022 | − | 0.995352i | \(-0.469298\pi\) | ||||
0.0963022 | + | 0.995352i | \(0.469298\pi\) | |||||||
\(992\) | −1.28266 | −0.0407245 | ||||||||
\(993\) | 16.1363 | 0.512071 | ||||||||
\(994\) | 17.6997 | 0.561401 | ||||||||
\(995\) | 6.71734 | 0.212954 | ||||||||
\(996\) | −11.7092 | −0.371020 | ||||||||
\(997\) | 43.2759 | 1.37056 | 0.685280 | − | 0.728280i | \(-0.259680\pi\) | ||||
0.685280 | + | 0.728280i | \(0.259680\pi\) | |||||||
\(998\) | 17.2859 | 0.547175 | ||||||||
\(999\) | 4.71734 | 0.149250 |
(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 | 5610.2.a.cj.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5610.2.a.cj.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial |