Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8670,2,Mod(1,8670)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8670, 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("8670.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8670.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: | \(69.2302985525\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 510) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8670.1 |
$q$-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 | ||||||||
\(7\) | 1.08239 | 0.409106 | 0.204553 | − | 0.978856i | \(-0.434426\pi\) | ||||
0.204553 | + | 0.978856i | \(0.434426\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.152241 | −0.0422240 | −0.0211120 | − | 0.999777i | \(-0.506721\pi\) | ||||
−0.0211120 | + | 0.999777i | \(0.506721\pi\) | |||||||
\(14\) | −1.08239 | −0.289281 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.08239 | −0.236197 | ||||||||
\(22\) | −1.41421 | −0.301511 | ||||||||
\(23\) | −6.67619 | −1.39208 | −0.696041 | − | 0.718002i | \(-0.745057\pi\) | ||||
−0.696041 | + | 0.718002i | \(0.745057\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.152241 | 0.0298569 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.08239 | 0.204553 | ||||||||
\(29\) | 1.81204 | 0.336487 | 0.168244 | − | 0.985745i | \(-0.446191\pi\) | ||||
0.168244 | + | 0.985745i | \(0.446191\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 10.2069 | 1.83322 | 0.916608 | − | 0.399786i | \(-0.130916\pi\) | ||||
0.916608 | + | 0.399786i | \(0.130916\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.41421 | −0.246183 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.08239 | 0.182958 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.39104 | −1.21508 | −0.607539 | − | 0.794290i | \(-0.707843\pi\) | ||||
−0.607539 | + | 0.794290i | \(0.707843\pi\) | |||||||
\(38\) | −2.82843 | −0.458831 | ||||||||
\(39\) | 0.152241 | 0.0243781 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.83938 | −0.911958 | −0.455979 | − | 0.889991i | \(-0.650711\pi\) | ||||
−0.455979 | + | 0.889991i | \(0.650711\pi\) | |||||||
\(42\) | 1.08239 | 0.167017 | ||||||||
\(43\) | −11.0353 | −1.68287 | −0.841437 | − | 0.540355i | \(-0.818290\pi\) | ||||
−0.841437 | + | 0.540355i | \(0.818290\pi\) | |||||||
\(44\) | 1.41421 | 0.213201 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 6.67619 | 0.984350 | ||||||||
\(47\) | −5.39104 | −0.786363 | −0.393182 | − | 0.919461i | \(-0.628626\pi\) | ||||
−0.393182 | + | 0.919461i | \(0.628626\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.82843 | −0.832632 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.152241 | −0.0211120 | ||||||||
\(53\) | −6.35916 | −0.873498 | −0.436749 | − | 0.899583i | \(-0.643870\pi\) | ||||
−0.436749 | + | 0.899583i | \(0.643870\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.41421 | 0.190693 | ||||||||
\(56\) | −1.08239 | −0.144641 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | −1.81204 | −0.237932 | ||||||||
\(59\) | 1.86550 | 0.242867 | 0.121434 | − | 0.992600i | \(-0.461251\pi\) | ||||
0.121434 | + | 0.992600i | \(0.461251\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 5.53073 | 0.708138 | 0.354069 | − | 0.935219i | \(-0.384798\pi\) | ||||
0.354069 | + | 0.935219i | \(0.384798\pi\) | |||||||
\(62\) | −10.2069 | −1.29628 | ||||||||
\(63\) | 1.08239 | 0.136369 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.152241 | −0.0188832 | ||||||||
\(66\) | 1.41421 | 0.174078 | ||||||||
\(67\) | 4.69711 | 0.573843 | 0.286922 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286922 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.67619 | 0.803718 | ||||||||
\(70\) | −1.08239 | −0.129371 | ||||||||
\(71\) | −3.24718 | −0.385369 | −0.192684 | − | 0.981261i | \(-0.561719\pi\) | ||||
−0.192684 | + | 0.981261i | \(0.561719\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 10.1985 | 1.19365 | 0.596824 | − | 0.802372i | \(-0.296429\pi\) | ||||
0.596824 | + | 0.802372i | \(0.296429\pi\) | |||||||
\(74\) | 7.39104 | 0.859191 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.82843 | 0.324443 | ||||||||
\(77\) | 1.53073 | 0.174443 | ||||||||
\(78\) | −0.152241 | −0.0172379 | ||||||||
\(79\) | −16.6417 | −1.87234 | −0.936168 | − | 0.351553i | \(-0.885654\pi\) | ||||
−0.936168 | + | 0.351553i | \(0.885654\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.83938 | 0.644851 | ||||||||
\(83\) | −1.80562 | −0.198193 | −0.0990965 | − | 0.995078i | \(-0.531595\pi\) | ||||
−0.0990965 | + | 0.995078i | \(0.531595\pi\) | |||||||
\(84\) | −1.08239 | −0.118099 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.0353 | 1.18997 | ||||||||
\(87\) | −1.81204 | −0.194271 | ||||||||
\(88\) | −1.41421 | −0.150756 | ||||||||
\(89\) | −4.60127 | −0.487734 | −0.243867 | − | 0.969809i | \(-0.578416\pi\) | ||||
−0.243867 | + | 0.969809i | \(0.578416\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −0.164784 | −0.0172741 | ||||||||
\(92\) | −6.67619 | −0.696041 | ||||||||
\(93\) | −10.2069 | −1.05841 | ||||||||
\(94\) | 5.39104 | 0.556043 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.91082 | −0.194014 | −0.0970072 | − | 0.995284i | \(-0.530927\pi\) | ||||
−0.0970072 | + | 0.995284i | \(0.530927\pi\) | |||||||
\(98\) | 5.82843 | 0.588760 | ||||||||
\(99\) | 1.41421 | 0.142134 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 6.27836 | 0.624720 | 0.312360 | − | 0.949964i | \(-0.398880\pi\) | ||||
0.312360 | + | 0.949964i | \(0.398880\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.58541 | 0.550347 | 0.275174 | − | 0.961395i | \(-0.411265\pi\) | ||||
0.275174 | + | 0.961395i | \(0.411265\pi\) | |||||||
\(104\) | 0.152241 | 0.0149285 | ||||||||
\(105\) | −1.08239 | −0.105631 | ||||||||
\(106\) | 6.35916 | 0.617656 | ||||||||
\(107\) | 3.45929 | 0.334422 | 0.167211 | − | 0.985921i | \(-0.446524\pi\) | ||||
0.167211 | + | 0.985921i | \(0.446524\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.89668 | −0.277452 | −0.138726 | − | 0.990331i | \(-0.544301\pi\) | ||||
−0.138726 | + | 0.990331i | \(0.544301\pi\) | |||||||
\(110\) | −1.41421 | −0.134840 | ||||||||
\(111\) | 7.39104 | 0.701526 | ||||||||
\(112\) | 1.08239 | 0.102276 | ||||||||
\(113\) | −9.46767 | −0.890644 | −0.445322 | − | 0.895371i | \(-0.646911\pi\) | ||||
−0.445322 | + | 0.895371i | \(0.646911\pi\) | |||||||
\(114\) | 2.82843 | 0.264906 | ||||||||
\(115\) | −6.67619 | −0.622558 | ||||||||
\(116\) | 1.81204 | 0.168244 | ||||||||
\(117\) | −0.152241 | −0.0140747 | ||||||||
\(118\) | −1.86550 | −0.171733 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | −5.53073 | −0.500729 | ||||||||
\(123\) | 5.83938 | 0.526519 | ||||||||
\(124\) | 10.2069 | 0.916608 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.08239 | −0.0964272 | ||||||||
\(127\) | −16.6501 | −1.47745 | −0.738727 | − | 0.674005i | \(-0.764573\pi\) | ||||
−0.738727 | + | 0.674005i | \(0.764573\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.0353 | 0.971608 | ||||||||
\(130\) | 0.152241 | 0.0133524 | ||||||||
\(131\) | −16.9378 | −1.47986 | −0.739931 | − | 0.672683i | \(-0.765142\pi\) | ||||
−0.739931 | + | 0.672683i | \(0.765142\pi\) | |||||||
\(132\) | −1.41421 | −0.123091 | ||||||||
\(133\) | 3.06147 | 0.265463 | ||||||||
\(134\) | −4.69711 | −0.405769 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.8303 | 1.09617 | 0.548085 | − | 0.836423i | \(-0.315357\pi\) | ||||
0.548085 | + | 0.836423i | \(0.315357\pi\) | |||||||
\(138\) | −6.67619 | −0.568315 | ||||||||
\(139\) | −2.38425 | −0.202229 | −0.101115 | − | 0.994875i | \(-0.532241\pi\) | ||||
−0.101115 | + | 0.994875i | \(0.532241\pi\) | |||||||
\(140\) | 1.08239 | 0.0914788 | ||||||||
\(141\) | 5.39104 | 0.454007 | ||||||||
\(142\) | 3.24718 | 0.272497 | ||||||||
\(143\) | −0.215301 | −0.0180044 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.81204 | 0.150482 | ||||||||
\(146\) | −10.1985 | −0.844037 | ||||||||
\(147\) | 5.82843 | 0.480721 | ||||||||
\(148\) | −7.39104 | −0.607539 | ||||||||
\(149\) | −3.36075 | −0.275324 | −0.137662 | − | 0.990479i | \(-0.543959\pi\) | ||||
−0.137662 | + | 0.990479i | \(0.543959\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −4.74150 | −0.385858 | −0.192929 | − | 0.981213i | \(-0.561799\pi\) | ||||
−0.192929 | + | 0.981213i | \(0.561799\pi\) | |||||||
\(152\) | −2.82843 | −0.229416 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.53073 | −0.123350 | ||||||||
\(155\) | 10.2069 | 0.819840 | ||||||||
\(156\) | 0.152241 | 0.0121890 | ||||||||
\(157\) | −9.67112 | −0.771840 | −0.385920 | − | 0.922532i | \(-0.626116\pi\) | ||||
−0.385920 | + | 0.922532i | \(0.626116\pi\) | |||||||
\(158\) | 16.6417 | 1.32394 | ||||||||
\(159\) | 6.35916 | 0.504314 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −7.22625 | −0.569508 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −1.44381 | −0.113088 | −0.0565438 | − | 0.998400i | \(-0.518008\pi\) | ||||
−0.0565438 | + | 0.998400i | \(0.518008\pi\) | |||||||
\(164\) | −5.83938 | −0.455979 | ||||||||
\(165\) | −1.41421 | −0.110096 | ||||||||
\(166\) | 1.80562 | 0.140144 | ||||||||
\(167\) | −0.211830 | −0.0163919 | −0.00819593 | − | 0.999966i | \(-0.502609\pi\) | ||||
−0.00819593 | + | 0.999966i | \(0.502609\pi\) | |||||||
\(168\) | 1.08239 | 0.0835084 | ||||||||
\(169\) | −12.9768 | −0.998217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | −11.0353 | −0.841437 | ||||||||
\(173\) | −23.5230 | −1.78842 | −0.894212 | − | 0.447644i | \(-0.852263\pi\) | ||||
−0.894212 | + | 0.447644i | \(0.852263\pi\) | |||||||
\(174\) | 1.81204 | 0.137370 | ||||||||
\(175\) | 1.08239 | 0.0818212 | ||||||||
\(176\) | 1.41421 | 0.106600 | ||||||||
\(177\) | −1.86550 | −0.140219 | ||||||||
\(178\) | 4.60127 | 0.344880 | ||||||||
\(179\) | −17.2388 | −1.28849 | −0.644244 | − | 0.764820i | \(-0.722828\pi\) | ||||
−0.644244 | + | 0.764820i | \(0.722828\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 14.4557 | 1.07448 | 0.537241 | − | 0.843428i | \(-0.319466\pi\) | ||||
0.537241 | + | 0.843428i | \(0.319466\pi\) | |||||||
\(182\) | 0.164784 | 0.0122146 | ||||||||
\(183\) | −5.53073 | −0.408844 | ||||||||
\(184\) | 6.67619 | 0.492175 | ||||||||
\(185\) | −7.39104 | −0.543400 | ||||||||
\(186\) | 10.2069 | 0.748408 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.39104 | −0.393182 | ||||||||
\(189\) | −1.08239 | −0.0787324 | ||||||||
\(190\) | −2.82843 | −0.205196 | ||||||||
\(191\) | 9.44572 | 0.683468 | 0.341734 | − | 0.939797i | \(-0.388986\pi\) | ||||
0.341734 | + | 0.939797i | \(0.388986\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 10.0177 | 0.721093 | 0.360546 | − | 0.932741i | \(-0.382590\pi\) | ||||
0.360546 | + | 0.932741i | \(0.382590\pi\) | |||||||
\(194\) | 1.91082 | 0.137189 | ||||||||
\(195\) | 0.152241 | 0.0109022 | ||||||||
\(196\) | −5.82843 | −0.416316 | ||||||||
\(197\) | −1.47605 | −0.105165 | −0.0525823 | − | 0.998617i | \(-0.516745\pi\) | ||||
−0.0525823 | + | 0.998617i | \(0.516745\pi\) | |||||||
\(198\) | −1.41421 | −0.100504 | ||||||||
\(199\) | 20.6239 | 1.46199 | 0.730996 | − | 0.682381i | \(-0.239056\pi\) | ||||
0.730996 | + | 0.682381i | \(0.239056\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.69711 | −0.331309 | ||||||||
\(202\) | −6.27836 | −0.441744 | ||||||||
\(203\) | 1.96134 | 0.137659 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.83938 | −0.407840 | ||||||||
\(206\) | −5.58541 | −0.389154 | ||||||||
\(207\) | −6.67619 | −0.464027 | ||||||||
\(208\) | −0.152241 | −0.0105560 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 1.08239 | 0.0746922 | ||||||||
\(211\) | 5.90666 | 0.406631 | 0.203316 | − | 0.979113i | \(-0.434828\pi\) | ||||
0.203316 | + | 0.979113i | \(0.434828\pi\) | |||||||
\(212\) | −6.35916 | −0.436749 | ||||||||
\(213\) | 3.24718 | 0.222493 | ||||||||
\(214\) | −3.45929 | −0.236472 | ||||||||
\(215\) | −11.0353 | −0.752604 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 11.0479 | 0.749980 | ||||||||
\(218\) | 2.89668 | 0.196188 | ||||||||
\(219\) | −10.1985 | −0.689153 | ||||||||
\(220\) | 1.41421 | 0.0953463 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.39104 | −0.496054 | ||||||||
\(223\) | 13.5854 | 0.909747 | 0.454873 | − | 0.890556i | \(-0.349685\pi\) | ||||
0.454873 | + | 0.890556i | \(0.349685\pi\) | |||||||
\(224\) | −1.08239 | −0.0723204 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 9.46767 | 0.629780 | ||||||||
\(227\) | 6.87992 | 0.456636 | 0.228318 | − | 0.973587i | \(-0.426677\pi\) | ||||
0.228318 | + | 0.973587i | \(0.426677\pi\) | |||||||
\(228\) | −2.82843 | −0.187317 | ||||||||
\(229\) | −8.59539 | −0.567999 | −0.284000 | − | 0.958824i | \(-0.591661\pi\) | ||||
−0.284000 | + | 0.958824i | \(0.591661\pi\) | |||||||
\(230\) | 6.67619 | 0.440215 | ||||||||
\(231\) | −1.53073 | −0.100715 | ||||||||
\(232\) | −1.81204 | −0.118966 | ||||||||
\(233\) | 19.6945 | 1.29023 | 0.645114 | − | 0.764086i | \(-0.276810\pi\) | ||||
0.645114 | + | 0.764086i | \(0.276810\pi\) | |||||||
\(234\) | 0.152241 | 0.00995230 | ||||||||
\(235\) | −5.39104 | −0.351672 | ||||||||
\(236\) | 1.86550 | 0.121434 | ||||||||
\(237\) | 16.6417 | 1.08099 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.32638 | −0.538589 | −0.269294 | − | 0.963058i | \(-0.586790\pi\) | ||||
−0.269294 | + | 0.963058i | \(0.586790\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 8.33476 | 0.536889 | 0.268445 | − | 0.963295i | \(-0.413490\pi\) | ||||
0.268445 | + | 0.963295i | \(0.413490\pi\) | |||||||
\(242\) | 9.00000 | 0.578542 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.53073 | 0.354069 | ||||||||
\(245\) | −5.82843 | −0.372365 | ||||||||
\(246\) | −5.83938 | −0.372305 | ||||||||
\(247\) | −0.430602 | −0.0273986 | ||||||||
\(248\) | −10.2069 | −0.648140 | ||||||||
\(249\) | 1.80562 | 0.114427 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −21.2043 | −1.33840 | −0.669202 | − | 0.743081i | \(-0.733364\pi\) | ||||
−0.669202 | + | 0.743081i | \(0.733364\pi\) | |||||||
\(252\) | 1.08239 | 0.0681843 | ||||||||
\(253\) | −9.44155 | −0.593585 | ||||||||
\(254\) | 16.6501 | 1.04472 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.56224 | 0.471719 | 0.235860 | − | 0.971787i | \(-0.424209\pi\) | ||||
0.235860 | + | 0.971787i | \(0.424209\pi\) | |||||||
\(258\) | −11.0353 | −0.687031 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | −0.152241 | −0.00944158 | ||||||||
\(261\) | 1.81204 | 0.112162 | ||||||||
\(262\) | 16.9378 | 1.04642 | ||||||||
\(263\) | 11.2417 | 0.693195 | 0.346598 | − | 0.938014i | \(-0.387337\pi\) | ||||
0.346598 | + | 0.938014i | \(0.387337\pi\) | |||||||
\(264\) | 1.41421 | 0.0870388 | ||||||||
\(265\) | −6.35916 | −0.390640 | ||||||||
\(266\) | −3.06147 | −0.187711 | ||||||||
\(267\) | 4.60127 | 0.281593 | ||||||||
\(268\) | 4.69711 | 0.286922 | ||||||||
\(269\) | 29.1380 | 1.77658 | 0.888289 | − | 0.459285i | \(-0.151894\pi\) | ||||
0.888289 | + | 0.459285i | \(0.151894\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 21.4908 | 1.30547 | 0.652736 | − | 0.757585i | \(-0.273621\pi\) | ||||
0.652736 | + | 0.757585i | \(0.273621\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.164784 | 0.00997321 | ||||||||
\(274\) | −12.8303 | −0.775109 | ||||||||
\(275\) | 1.41421 | 0.0852803 | ||||||||
\(276\) | 6.67619 | 0.401859 | ||||||||
\(277\) | 6.87669 | 0.413180 | 0.206590 | − | 0.978428i | \(-0.433763\pi\) | ||||
0.206590 | + | 0.978428i | \(0.433763\pi\) | |||||||
\(278\) | 2.38425 | 0.142998 | ||||||||
\(279\) | 10.2069 | 0.611072 | ||||||||
\(280\) | −1.08239 | −0.0646853 | ||||||||
\(281\) | −7.11933 | −0.424704 | −0.212352 | − | 0.977193i | \(-0.568112\pi\) | ||||
−0.212352 | + | 0.977193i | \(0.568112\pi\) | |||||||
\(282\) | −5.39104 | −0.321032 | ||||||||
\(283\) | 25.8473 | 1.53646 | 0.768230 | − | 0.640174i | \(-0.221138\pi\) | ||||
0.768230 | + | 0.640174i | \(0.221138\pi\) | |||||||
\(284\) | −3.24718 | −0.192684 | ||||||||
\(285\) | −2.82843 | −0.167542 | ||||||||
\(286\) | 0.215301 | 0.0127310 | ||||||||
\(287\) | −6.32050 | −0.373087 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1.81204 | −0.106407 | ||||||||
\(291\) | 1.91082 | 0.112014 | ||||||||
\(292\) | 10.1985 | 0.596824 | ||||||||
\(293\) | −17.7251 | −1.03551 | −0.517756 | − | 0.855528i | \(-0.673232\pi\) | ||||
−0.517756 | + | 0.855528i | \(0.673232\pi\) | |||||||
\(294\) | −5.82843 | −0.339921 | ||||||||
\(295\) | 1.86550 | 0.108614 | ||||||||
\(296\) | 7.39104 | 0.429595 | ||||||||
\(297\) | −1.41421 | −0.0820610 | ||||||||
\(298\) | 3.36075 | 0.194683 | ||||||||
\(299\) | 1.01639 | 0.0587793 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −11.9446 | −0.688474 | ||||||||
\(302\) | 4.74150 | 0.272843 | ||||||||
\(303\) | −6.27836 | −0.360682 | ||||||||
\(304\) | 2.82843 | 0.162221 | ||||||||
\(305\) | 5.53073 | 0.316689 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.2348 | 1.04071 | 0.520357 | − | 0.853949i | \(-0.325799\pi\) | ||||
0.520357 | + | 0.853949i | \(0.325799\pi\) | |||||||
\(308\) | 1.53073 | 0.0872216 | ||||||||
\(309\) | −5.58541 | −0.317743 | ||||||||
\(310\) | −10.2069 | −0.579714 | ||||||||
\(311\) | 31.7112 | 1.79818 | 0.899088 | − | 0.437767i | \(-0.144231\pi\) | ||||
0.899088 | + | 0.437767i | \(0.144231\pi\) | |||||||
\(312\) | −0.152241 | −0.00861895 | ||||||||
\(313\) | −19.1144 | −1.08041 | −0.540206 | − | 0.841533i | \(-0.681654\pi\) | ||||
−0.540206 | + | 0.841533i | \(0.681654\pi\) | |||||||
\(314\) | 9.67112 | 0.545773 | ||||||||
\(315\) | 1.08239 | 0.0609859 | ||||||||
\(316\) | −16.6417 | −0.936168 | ||||||||
\(317\) | −21.9195 | −1.23112 | −0.615561 | − | 0.788090i | \(-0.711070\pi\) | ||||
−0.615561 | + | 0.788090i | \(0.711070\pi\) | |||||||
\(318\) | −6.35916 | −0.356604 | ||||||||
\(319\) | 2.56261 | 0.143479 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.45929 | −0.193079 | ||||||||
\(322\) | 7.22625 | 0.402703 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.152241 | −0.00844481 | ||||||||
\(326\) | 1.44381 | 0.0799650 | ||||||||
\(327\) | 2.89668 | 0.160187 | ||||||||
\(328\) | 5.83938 | 0.322426 | ||||||||
\(329\) | −5.83522 | −0.321706 | ||||||||
\(330\) | 1.41421 | 0.0778499 | ||||||||
\(331\) | −18.7402 | −1.03006 | −0.515028 | − | 0.857173i | \(-0.672218\pi\) | ||||
−0.515028 | + | 0.857173i | \(0.672218\pi\) | |||||||
\(332\) | −1.80562 | −0.0990965 | ||||||||
\(333\) | −7.39104 | −0.405026 | ||||||||
\(334\) | 0.211830 | 0.0115908 | ||||||||
\(335\) | 4.69711 | 0.256631 | ||||||||
\(336\) | −1.08239 | −0.0590493 | ||||||||
\(337\) | 28.8782 | 1.57310 | 0.786548 | − | 0.617529i | \(-0.211866\pi\) | ||||
0.786548 | + | 0.617529i | \(0.211866\pi\) | |||||||
\(338\) | 12.9768 | 0.705846 | ||||||||
\(339\) | 9.46767 | 0.514213 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.4348 | 0.781686 | ||||||||
\(342\) | −2.82843 | −0.152944 | ||||||||
\(343\) | −13.8854 | −0.749741 | ||||||||
\(344\) | 11.0353 | 0.594986 | ||||||||
\(345\) | 6.67619 | 0.359434 | ||||||||
\(346\) | 23.5230 | 1.26461 | ||||||||
\(347\) | −14.9346 | −0.801731 | −0.400866 | − | 0.916137i | \(-0.631291\pi\) | ||||
−0.400866 | + | 0.916137i | \(0.631291\pi\) | |||||||
\(348\) | −1.81204 | −0.0971354 | ||||||||
\(349\) | −3.07054 | −0.164362 | −0.0821811 | − | 0.996617i | \(-0.526189\pi\) | ||||
−0.0821811 | + | 0.996617i | \(0.526189\pi\) | |||||||
\(350\) | −1.08239 | −0.0578563 | ||||||||
\(351\) | 0.152241 | 0.00812602 | ||||||||
\(352\) | −1.41421 | −0.0753778 | ||||||||
\(353\) | −30.8058 | −1.63963 | −0.819813 | − | 0.572631i | \(-0.805923\pi\) | ||||
−0.819813 | + | 0.572631i | \(0.805923\pi\) | |||||||
\(354\) | 1.86550 | 0.0991501 | ||||||||
\(355\) | −3.24718 | −0.172342 | ||||||||
\(356\) | −4.60127 | −0.243867 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.2388 | 0.911099 | ||||||||
\(359\) | −30.8117 | −1.62618 | −0.813089 | − | 0.582140i | \(-0.802216\pi\) | ||||
−0.813089 | + | 0.582140i | \(0.802216\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −14.4557 | −0.759774 | ||||||||
\(363\) | 9.00000 | 0.472377 | ||||||||
\(364\) | −0.164784 | −0.00863705 | ||||||||
\(365\) | 10.1985 | 0.533816 | ||||||||
\(366\) | 5.53073 | 0.289096 | ||||||||
\(367\) | 9.89480 | 0.516505 | 0.258252 | − | 0.966078i | \(-0.416853\pi\) | ||||
0.258252 | + | 0.966078i | \(0.416853\pi\) | |||||||
\(368\) | −6.67619 | −0.348020 | ||||||||
\(369\) | −5.83938 | −0.303986 | ||||||||
\(370\) | 7.39104 | 0.384242 | ||||||||
\(371\) | −6.88311 | −0.357353 | ||||||||
\(372\) | −10.2069 | −0.529204 | ||||||||
\(373\) | −20.9089 | −1.08262 | −0.541310 | − | 0.840823i | \(-0.682072\pi\) | ||||
−0.541310 | + | 0.840823i | \(0.682072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 5.39104 | 0.278021 | ||||||||
\(377\) | −0.275866 | −0.0142078 | ||||||||
\(378\) | 1.08239 | 0.0556722 | ||||||||
\(379\) | 16.9663 | 0.871501 | 0.435751 | − | 0.900067i | \(-0.356483\pi\) | ||||
0.435751 | + | 0.900067i | \(0.356483\pi\) | |||||||
\(380\) | 2.82843 | 0.145095 | ||||||||
\(381\) | 16.6501 | 0.853009 | ||||||||
\(382\) | −9.44572 | −0.483285 | ||||||||
\(383\) | −17.9736 | −0.918410 | −0.459205 | − | 0.888330i | \(-0.651866\pi\) | ||||
−0.459205 | + | 0.888330i | \(0.651866\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.53073 | 0.0780134 | ||||||||
\(386\) | −10.0177 | −0.509889 | ||||||||
\(387\) | −11.0353 | −0.560958 | ||||||||
\(388\) | −1.91082 | −0.0970072 | ||||||||
\(389\) | −8.78948 | −0.445644 | −0.222822 | − | 0.974859i | \(-0.571527\pi\) | ||||
−0.222822 | + | 0.974859i | \(0.571527\pi\) | |||||||
\(390\) | −0.152241 | −0.00770902 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.82843 | 0.294380 | ||||||||
\(393\) | 16.9378 | 0.854398 | ||||||||
\(394\) | 1.47605 | 0.0743626 | ||||||||
\(395\) | −16.6417 | −0.837334 | ||||||||
\(396\) | 1.41421 | 0.0710669 | ||||||||
\(397\) | −20.1158 | −1.00958 | −0.504791 | − | 0.863242i | \(-0.668430\pi\) | ||||
−0.504791 | + | 0.863242i | \(0.668430\pi\) | |||||||
\(398\) | −20.6239 | −1.03378 | ||||||||
\(399\) | −3.06147 | −0.153265 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 0.338236 | 0.0168907 | 0.00844535 | − | 0.999964i | \(-0.497312\pi\) | ||||
0.00844535 | + | 0.999964i | \(0.497312\pi\) | |||||||
\(402\) | 4.69711 | 0.234271 | ||||||||
\(403\) | −1.55391 | −0.0774058 | ||||||||
\(404\) | 6.27836 | 0.312360 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −1.96134 | −0.0973395 | ||||||||
\(407\) | −10.4525 | −0.518111 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.8307 | −0.782778 | −0.391389 | − | 0.920225i | \(-0.628005\pi\) | ||||
−0.391389 | + | 0.920225i | \(0.628005\pi\) | |||||||
\(410\) | 5.83938 | 0.288386 | ||||||||
\(411\) | −12.8303 | −0.632874 | ||||||||
\(412\) | 5.58541 | 0.275174 | ||||||||
\(413\) | 2.01920 | 0.0993584 | ||||||||
\(414\) | 6.67619 | 0.328117 | ||||||||
\(415\) | −1.80562 | −0.0886346 | ||||||||
\(416\) | 0.152241 | 0.00746423 | ||||||||
\(417\) | 2.38425 | 0.116757 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | 23.5134 | 1.14871 | 0.574353 | − | 0.818607i | \(-0.305254\pi\) | ||||
0.574353 | + | 0.818607i | \(0.305254\pi\) | |||||||
\(420\) | −1.08239 | −0.0528153 | ||||||||
\(421\) | −12.0648 | −0.588003 | −0.294001 | − | 0.955805i | \(-0.594987\pi\) | ||||
−0.294001 | + | 0.955805i | \(0.594987\pi\) | |||||||
\(422\) | −5.90666 | −0.287532 | ||||||||
\(423\) | −5.39104 | −0.262121 | ||||||||
\(424\) | 6.35916 | 0.308828 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.24718 | −0.157326 | ||||||||
\(427\) | 5.98642 | 0.289703 | ||||||||
\(428\) | 3.45929 | 0.167211 | ||||||||
\(429\) | 0.215301 | 0.0103948 | ||||||||
\(430\) | 11.0353 | 0.532172 | ||||||||
\(431\) | 6.35744 | 0.306227 | 0.153113 | − | 0.988209i | \(-0.451070\pi\) | ||||
0.153113 | + | 0.988209i | \(0.451070\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −35.0402 | −1.68392 | −0.841962 | − | 0.539536i | \(-0.818600\pi\) | ||||
−0.841962 | + | 0.539536i | \(0.818600\pi\) | |||||||
\(434\) | −11.0479 | −0.530316 | ||||||||
\(435\) | −1.81204 | −0.0868806 | ||||||||
\(436\) | −2.89668 | −0.138726 | ||||||||
\(437\) | −18.8831 | −0.903301 | ||||||||
\(438\) | 10.1985 | 0.487305 | ||||||||
\(439\) | 7.38340 | 0.352391 | 0.176195 | − | 0.984355i | \(-0.443621\pi\) | ||||
0.176195 | + | 0.984355i | \(0.443621\pi\) | |||||||
\(440\) | −1.41421 | −0.0674200 | ||||||||
\(441\) | −5.82843 | −0.277544 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.0539 | 1.04781 | 0.523907 | − | 0.851776i | \(-0.324474\pi\) | ||||
0.523907 | + | 0.851776i | \(0.324474\pi\) | |||||||
\(444\) | 7.39104 | 0.350763 | ||||||||
\(445\) | −4.60127 | −0.218121 | ||||||||
\(446\) | −13.5854 | −0.643288 | ||||||||
\(447\) | 3.36075 | 0.158958 | ||||||||
\(448\) | 1.08239 | 0.0511382 | ||||||||
\(449\) | −37.9191 | −1.78952 | −0.894758 | − | 0.446552i | \(-0.852652\pi\) | ||||
−0.894758 | + | 0.446552i | \(0.852652\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −8.25813 | −0.388860 | ||||||||
\(452\) | −9.46767 | −0.445322 | ||||||||
\(453\) | 4.74150 | 0.222775 | ||||||||
\(454\) | −6.87992 | −0.322891 | ||||||||
\(455\) | −0.164784 | −0.00772521 | ||||||||
\(456\) | 2.82843 | 0.132453 | ||||||||
\(457\) | −6.09785 | −0.285245 | −0.142623 | − | 0.989777i | \(-0.545554\pi\) | ||||
−0.142623 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(458\) | 8.59539 | 0.401636 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.67619 | −0.311279 | ||||||||
\(461\) | 19.1647 | 0.892587 | 0.446293 | − | 0.894887i | \(-0.352744\pi\) | ||||
0.446293 | + | 0.894887i | \(0.352744\pi\) | |||||||
\(462\) | 1.53073 | 0.0712162 | ||||||||
\(463\) | 11.9896 | 0.557204 | 0.278602 | − | 0.960407i | \(-0.410129\pi\) | ||||
0.278602 | + | 0.960407i | \(0.410129\pi\) | |||||||
\(464\) | 1.81204 | 0.0841218 | ||||||||
\(465\) | −10.2069 | −0.473335 | ||||||||
\(466\) | −19.6945 | −0.912329 | ||||||||
\(467\) | −31.3388 | −1.45019 | −0.725093 | − | 0.688651i | \(-0.758203\pi\) | ||||
−0.725093 | + | 0.688651i | \(0.758203\pi\) | |||||||
\(468\) | −0.152241 | −0.00703734 | ||||||||
\(469\) | 5.08412 | 0.234763 | ||||||||
\(470\) | 5.39104 | 0.248670 | ||||||||
\(471\) | 9.67112 | 0.445622 | ||||||||
\(472\) | −1.86550 | −0.0858665 | ||||||||
\(473\) | −15.6063 | −0.717580 | ||||||||
\(474\) | −16.6417 | −0.764378 | ||||||||
\(475\) | 2.82843 | 0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.35916 | −0.291166 | ||||||||
\(478\) | 8.32638 | 0.380840 | ||||||||
\(479\) | −18.4111 | −0.841223 | −0.420611 | − | 0.907241i | \(-0.638184\pi\) | ||||
−0.420611 | + | 0.907241i | \(0.638184\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 1.12522 | 0.0513055 | ||||||||
\(482\) | −8.33476 | −0.379638 | ||||||||
\(483\) | 7.22625 | 0.328806 | ||||||||
\(484\) | −9.00000 | −0.409091 | ||||||||
\(485\) | −1.91082 | −0.0867658 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 15.1280 | 0.685515 | 0.342758 | − | 0.939424i | \(-0.388639\pi\) | ||||
0.342758 | + | 0.939424i | \(0.388639\pi\) | |||||||
\(488\) | −5.53073 | −0.250365 | ||||||||
\(489\) | 1.44381 | 0.0652911 | ||||||||
\(490\) | 5.82843 | 0.263301 | ||||||||
\(491\) | 13.6457 | 0.615821 | 0.307911 | − | 0.951415i | \(-0.400370\pi\) | ||||
0.307911 | + | 0.951415i | \(0.400370\pi\) | |||||||
\(492\) | 5.83938 | 0.263259 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0.430602 | 0.0193737 | ||||||||
\(495\) | 1.41421 | 0.0635642 | ||||||||
\(496\) | 10.2069 | 0.458304 | ||||||||
\(497\) | −3.51472 | −0.157657 | ||||||||
\(498\) | −1.80562 | −0.0809119 | ||||||||
\(499\) | 31.3433 | 1.40312 | 0.701559 | − | 0.712611i | \(-0.252487\pi\) | ||||
0.701559 | + | 0.712611i | \(0.252487\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0.211830 | 0.00946385 | ||||||||
\(502\) | 21.2043 | 0.946394 | ||||||||
\(503\) | −13.0075 | −0.579975 | −0.289987 | − | 0.957030i | \(-0.593651\pi\) | ||||
−0.289987 | + | 0.957030i | \(0.593651\pi\) | |||||||
\(504\) | −1.08239 | −0.0482136 | ||||||||
\(505\) | 6.27836 | 0.279383 | ||||||||
\(506\) | 9.44155 | 0.419728 | ||||||||
\(507\) | 12.9768 | 0.576321 | ||||||||
\(508\) | −16.6501 | −0.738727 | ||||||||
\(509\) | 21.0441 | 0.932762 | 0.466381 | − | 0.884584i | \(-0.345558\pi\) | ||||
0.466381 | + | 0.884584i | \(0.345558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0388 | 0.488329 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | −7.56224 | −0.333556 | ||||||||
\(515\) | 5.58541 | 0.246123 | ||||||||
\(516\) | 11.0353 | 0.485804 | ||||||||
\(517\) | −7.62408 | −0.335307 | ||||||||
\(518\) | 8.00000 | 0.351500 | ||||||||
\(519\) | 23.5230 | 1.03255 | ||||||||
\(520\) | 0.152241 | 0.00667621 | ||||||||
\(521\) | 1.91671 | 0.0839724 | 0.0419862 | − | 0.999118i | \(-0.486631\pi\) | ||||
0.0419862 | + | 0.999118i | \(0.486631\pi\) | |||||||
\(522\) | −1.81204 | −0.0793108 | ||||||||
\(523\) | 37.8410 | 1.65467 | 0.827337 | − | 0.561706i | \(-0.189855\pi\) | ||||
0.827337 | + | 0.561706i | \(0.189855\pi\) | |||||||
\(524\) | −16.9378 | −0.739931 | ||||||||
\(525\) | −1.08239 | −0.0472395 | ||||||||
\(526\) | −11.2417 | −0.490163 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.41421 | −0.0615457 | ||||||||
\(529\) | 21.5715 | 0.937890 | ||||||||
\(530\) | 6.35916 | 0.276224 | ||||||||
\(531\) | 1.86550 | 0.0809557 | ||||||||
\(532\) | 3.06147 | 0.132731 | ||||||||
\(533\) | 0.888992 | 0.0385065 | ||||||||
\(534\) | −4.60127 | −0.199117 | ||||||||
\(535\) | 3.45929 | 0.149558 | ||||||||
\(536\) | −4.69711 | −0.202884 | ||||||||
\(537\) | 17.2388 | 0.743909 | ||||||||
\(538\) | −29.1380 | −1.25623 | ||||||||
\(539\) | −8.24264 | −0.355036 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −4.53752 | −0.195083 | −0.0975417 | − | 0.995231i | \(-0.531098\pi\) | ||||
−0.0975417 | + | 0.995231i | \(0.531098\pi\) | |||||||
\(542\) | −21.4908 | −0.923109 | ||||||||
\(543\) | −14.4557 | −0.620353 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.89668 | −0.124080 | ||||||||
\(546\) | −0.164784 | −0.00705212 | ||||||||
\(547\) | −30.3635 | −1.29825 | −0.649125 | − | 0.760682i | \(-0.724865\pi\) | ||||
−0.649125 | + | 0.760682i | \(0.724865\pi\) | |||||||
\(548\) | 12.8303 | 0.548085 | ||||||||
\(549\) | 5.53073 | 0.236046 | ||||||||
\(550\) | −1.41421 | −0.0603023 | ||||||||
\(551\) | 5.12522 | 0.218342 | ||||||||
\(552\) | −6.67619 | −0.284157 | ||||||||
\(553\) | −18.0128 | −0.765983 | ||||||||
\(554\) | −6.87669 | −0.292163 | ||||||||
\(555\) | 7.39104 | 0.313732 | ||||||||
\(556\) | −2.38425 | −0.101115 | ||||||||
\(557\) | −37.5324 | −1.59030 | −0.795150 | − | 0.606413i | \(-0.792608\pi\) | ||||
−0.795150 | + | 0.606413i | \(0.792608\pi\) | |||||||
\(558\) | −10.2069 | −0.432093 | ||||||||
\(559\) | 1.68003 | 0.0710578 | ||||||||
\(560\) | 1.08239 | 0.0457394 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.11933 | 0.300311 | ||||||||
\(563\) | 4.07388 | 0.171694 | 0.0858468 | − | 0.996308i | \(-0.472640\pi\) | ||||
0.0858468 | + | 0.996308i | \(0.472640\pi\) | |||||||
\(564\) | 5.39104 | 0.227004 | ||||||||
\(565\) | −9.46767 | −0.398308 | ||||||||
\(566\) | −25.8473 | −1.08644 | ||||||||
\(567\) | 1.08239 | 0.0454562 | ||||||||
\(568\) | 3.24718 | 0.136249 | ||||||||
\(569\) | 28.0950 | 1.17781 | 0.588903 | − | 0.808204i | \(-0.299560\pi\) | ||||
0.588903 | + | 0.808204i | \(0.299560\pi\) | |||||||
\(570\) | 2.82843 | 0.118470 | ||||||||
\(571\) | −13.3698 | −0.559507 | −0.279754 | − | 0.960072i | \(-0.590253\pi\) | ||||
−0.279754 | + | 0.960072i | \(0.590253\pi\) | |||||||
\(572\) | −0.215301 | −0.00900220 | ||||||||
\(573\) | −9.44572 | −0.394600 | ||||||||
\(574\) | 6.32050 | 0.263812 | ||||||||
\(575\) | −6.67619 | −0.278416 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 14.8471 | 0.618095 | 0.309047 | − | 0.951047i | \(-0.399990\pi\) | ||||
0.309047 | + | 0.951047i | \(0.399990\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0177 | −0.416323 | ||||||||
\(580\) | 1.81204 | 0.0752408 | ||||||||
\(581\) | −1.95439 | −0.0810819 | ||||||||
\(582\) | −1.91082 | −0.0792060 | ||||||||
\(583\) | −8.99321 | −0.372461 | ||||||||
\(584\) | −10.1985 | −0.422019 | ||||||||
\(585\) | −0.152241 | −0.00629439 | ||||||||
\(586\) | 17.7251 | 0.732218 | ||||||||
\(587\) | 3.95815 | 0.163370 | 0.0816852 | − | 0.996658i | \(-0.473970\pi\) | ||||
0.0816852 | + | 0.996658i | \(0.473970\pi\) | |||||||
\(588\) | 5.82843 | 0.240360 | ||||||||
\(589\) | 28.8695 | 1.18955 | ||||||||
\(590\) | −1.86550 | −0.0768013 | ||||||||
\(591\) | 1.47605 | 0.0607168 | ||||||||
\(592\) | −7.39104 | −0.303770 | ||||||||
\(593\) | −40.3160 | −1.65558 | −0.827790 | − | 0.561039i | \(-0.810402\pi\) | ||||
−0.827790 | + | 0.561039i | \(0.810402\pi\) | |||||||
\(594\) | 1.41421 | 0.0580259 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.36075 | −0.137662 | ||||||||
\(597\) | −20.6239 | −0.844082 | ||||||||
\(598\) | −1.01639 | −0.0415632 | ||||||||
\(599\) | −33.5081 | −1.36910 | −0.684552 | − | 0.728964i | \(-0.740002\pi\) | ||||
−0.684552 | + | 0.728964i | \(0.740002\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 36.5668 | 1.49159 | 0.745795 | − | 0.666175i | \(-0.232070\pi\) | ||||
0.745795 | + | 0.666175i | \(0.232070\pi\) | |||||||
\(602\) | 11.9446 | 0.486824 | ||||||||
\(603\) | 4.69711 | 0.191281 | ||||||||
\(604\) | −4.74150 | −0.192929 | ||||||||
\(605\) | −9.00000 | −0.365902 | ||||||||
\(606\) | 6.27836 | 0.255041 | ||||||||
\(607\) | 27.4408 | 1.11379 | 0.556894 | − | 0.830584i | \(-0.311993\pi\) | ||||
0.556894 | + | 0.830584i | \(0.311993\pi\) | |||||||
\(608\) | −2.82843 | −0.114708 | ||||||||
\(609\) | −1.96134 | −0.0794774 | ||||||||
\(610\) | −5.53073 | −0.223933 | ||||||||
\(611\) | 0.820736 | 0.0332034 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6321 | −0.550596 | −0.275298 | − | 0.961359i | \(-0.588777\pi\) | ||||
−0.275298 | + | 0.961359i | \(0.588777\pi\) | |||||||
\(614\) | −18.2348 | −0.735896 | ||||||||
\(615\) | 5.83938 | 0.235466 | ||||||||
\(616\) | −1.53073 | −0.0616750 | ||||||||
\(617\) | −22.6954 | −0.913682 | −0.456841 | − | 0.889548i | \(-0.651019\pi\) | ||||
−0.456841 | + | 0.889548i | \(0.651019\pi\) | |||||||
\(618\) | 5.58541 | 0.224678 | ||||||||
\(619\) | 35.8492 | 1.44090 | 0.720450 | − | 0.693507i | \(-0.243935\pi\) | ||||
0.720450 | + | 0.693507i | \(0.243935\pi\) | |||||||
\(620\) | 10.2069 | 0.409920 | ||||||||
\(621\) | 6.67619 | 0.267906 | ||||||||
\(622\) | −31.7112 | −1.27150 | ||||||||
\(623\) | −4.98038 | −0.199535 | ||||||||
\(624\) | 0.152241 | 0.00609451 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.1144 | 0.763966 | ||||||||
\(627\) | −4.00000 | −0.159745 | ||||||||
\(628\) | −9.67112 | −0.385920 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.08239 | −0.0431235 | ||||||||
\(631\) | −1.55980 | −0.0620945 | −0.0310473 | − | 0.999518i | \(-0.509884\pi\) | ||||
−0.0310473 | + | 0.999518i | \(0.509884\pi\) | |||||||
\(632\) | 16.6417 | 0.661971 | ||||||||
\(633\) | −5.90666 | −0.234769 | ||||||||
\(634\) | 21.9195 | 0.870534 | ||||||||
\(635\) | −16.6501 | −0.660738 | ||||||||
\(636\) | 6.35916 | 0.252157 | ||||||||
\(637\) | 0.887325 | 0.0351571 | ||||||||
\(638\) | −2.56261 | −0.101455 | ||||||||
\(639\) | −3.24718 | −0.128456 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −14.4233 | −0.569684 | −0.284842 | − | 0.958574i | \(-0.591941\pi\) | ||||
−0.284842 | + | 0.958574i | \(0.591941\pi\) | |||||||
\(642\) | 3.45929 | 0.136527 | ||||||||
\(643\) | −3.92983 | −0.154978 | −0.0774888 | − | 0.996993i | \(-0.524690\pi\) | ||||
−0.0774888 | + | 0.996993i | \(0.524690\pi\) | |||||||
\(644\) | −7.22625 | −0.284754 | ||||||||
\(645\) | 11.0353 | 0.434516 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.4461 | −0.725191 | −0.362595 | − | 0.931947i | \(-0.618109\pi\) | ||||
−0.362595 | + | 0.931947i | \(0.618109\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 2.63821 | 0.103559 | ||||||||
\(650\) | 0.152241 | 0.00597138 | ||||||||
\(651\) | −11.0479 | −0.433001 | ||||||||
\(652\) | −1.44381 | −0.0565438 | ||||||||
\(653\) | −42.0867 | −1.64698 | −0.823490 | − | 0.567331i | \(-0.807976\pi\) | ||||
−0.823490 | + | 0.567331i | \(0.807976\pi\) | |||||||
\(654\) | −2.89668 | −0.113269 | ||||||||
\(655\) | −16.9378 | −0.661814 | ||||||||
\(656\) | −5.83938 | −0.227989 | ||||||||
\(657\) | 10.1985 | 0.397883 | ||||||||
\(658\) | 5.83522 | 0.227480 | ||||||||
\(659\) | −19.0740 | −0.743018 | −0.371509 | − | 0.928429i | \(-0.621160\pi\) | ||||
−0.371509 | + | 0.928429i | \(0.621160\pi\) | |||||||
\(660\) | −1.41421 | −0.0550482 | ||||||||
\(661\) | 16.3766 | 0.636974 | 0.318487 | − | 0.947927i | \(-0.396825\pi\) | ||||
0.318487 | + | 0.947927i | \(0.396825\pi\) | |||||||
\(662\) | 18.7402 | 0.728359 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.80562 | 0.0700718 | ||||||||
\(665\) | 3.06147 | 0.118719 | ||||||||
\(666\) | 7.39104 | 0.286397 | ||||||||
\(667\) | −12.0975 | −0.468417 | ||||||||
\(668\) | −0.211830 | −0.00819593 | ||||||||
\(669\) | −13.5854 | −0.525242 | ||||||||
\(670\) | −4.69711 | −0.181465 | ||||||||
\(671\) | 7.82164 | 0.301951 | ||||||||
\(672\) | 1.08239 | 0.0417542 | ||||||||
\(673\) | −44.4052 | −1.71169 | −0.855847 | − | 0.517229i | \(-0.826963\pi\) | ||||
−0.855847 | + | 0.517229i | \(0.826963\pi\) | |||||||
\(674\) | −28.8782 | −1.11235 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −12.9768 | −0.499109 | ||||||||
\(677\) | 42.2529 | 1.62391 | 0.811955 | − | 0.583720i | \(-0.198403\pi\) | ||||
0.811955 | + | 0.583720i | \(0.198403\pi\) | |||||||
\(678\) | −9.46767 | −0.363604 | ||||||||
\(679\) | −2.06826 | −0.0793724 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.87992 | −0.263639 | ||||||||
\(682\) | −14.4348 | −0.552736 | ||||||||
\(683\) | −3.32803 | −0.127344 | −0.0636718 | − | 0.997971i | \(-0.520281\pi\) | ||||
−0.0636718 | + | 0.997971i | \(0.520281\pi\) | |||||||
\(684\) | 2.82843 | 0.108148 | ||||||||
\(685\) | 12.8303 | 0.490222 | ||||||||
\(686\) | 13.8854 | 0.530147 | ||||||||
\(687\) | 8.59539 | 0.327934 | ||||||||
\(688\) | −11.0353 | −0.420719 | ||||||||
\(689\) | 0.968125 | 0.0368826 | ||||||||
\(690\) | −6.67619 | −0.254158 | ||||||||
\(691\) | 46.7736 | 1.77935 | 0.889676 | − | 0.456592i | \(-0.150930\pi\) | ||||
0.889676 | + | 0.456592i | \(0.150930\pi\) | |||||||
\(692\) | −23.5230 | −0.894212 | ||||||||
\(693\) | 1.53073 | 0.0581478 | ||||||||
\(694\) | 14.9346 | 0.566910 | ||||||||
\(695\) | −2.38425 | −0.0904397 | ||||||||
\(696\) | 1.81204 | 0.0686851 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.07054 | 0.116222 | ||||||||
\(699\) | −19.6945 | −0.744914 | ||||||||
\(700\) | 1.08239 | 0.0409106 | ||||||||
\(701\) | 18.0508 | 0.681769 | 0.340885 | − | 0.940105i | \(-0.389273\pi\) | ||||
0.340885 | + | 0.940105i | \(0.389273\pi\) | |||||||
\(702\) | −0.152241 | −0.00574596 | ||||||||
\(703\) | −20.9050 | −0.788447 | ||||||||
\(704\) | 1.41421 | 0.0533002 | ||||||||
\(705\) | 5.39104 | 0.203038 | ||||||||
\(706\) | 30.8058 | 1.15939 | ||||||||
\(707\) | 6.79565 | 0.255577 | ||||||||
\(708\) | −1.86550 | −0.0701097 | ||||||||
\(709\) | 22.9796 | 0.863018 | 0.431509 | − | 0.902109i | \(-0.357981\pi\) | ||||
0.431509 | + | 0.902109i | \(0.357981\pi\) | |||||||
\(710\) | 3.24718 | 0.121864 | ||||||||
\(711\) | −16.6417 | −0.624112 | ||||||||
\(712\) | 4.60127 | 0.172440 | ||||||||
\(713\) | −68.1433 | −2.55199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.215301 | −0.00805181 | ||||||||
\(716\) | −17.2388 | −0.644244 | ||||||||
\(717\) | 8.32638 | 0.310954 | ||||||||
\(718\) | 30.8117 | 1.14988 | ||||||||
\(719\) | −11.4112 | −0.425566 | −0.212783 | − | 0.977099i | \(-0.568253\pi\) | ||||
−0.212783 | + | 0.977099i | \(0.568253\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 6.04561 | 0.225150 | ||||||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | −8.33476 | −0.309973 | ||||||||
\(724\) | 14.4557 | 0.537241 | ||||||||
\(725\) | 1.81204 | 0.0672974 | ||||||||
\(726\) | −9.00000 | −0.334021 | ||||||||
\(727\) | 36.5894 | 1.35703 | 0.678513 | − | 0.734589i | \(-0.262625\pi\) | ||||
0.678513 | + | 0.734589i | \(0.262625\pi\) | |||||||
\(728\) | 0.164784 | 0.00610732 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.1985 | −0.377465 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5.53073 | −0.204422 | ||||||||
\(733\) | 3.53837 | 0.130693 | 0.0653463 | − | 0.997863i | \(-0.479185\pi\) | ||||
0.0653463 | + | 0.997863i | \(0.479185\pi\) | |||||||
\(734\) | −9.89480 | −0.365224 | ||||||||
\(735\) | 5.82843 | 0.214985 | ||||||||
\(736\) | 6.67619 | 0.246087 | ||||||||
\(737\) | 6.64272 | 0.244688 | ||||||||
\(738\) | 5.83938 | 0.214950 | ||||||||
\(739\) | 14.5253 | 0.534323 | 0.267161 | − | 0.963652i | \(-0.413914\pi\) | ||||
0.267161 | + | 0.963652i | \(0.413914\pi\) | |||||||
\(740\) | −7.39104 | −0.271700 | ||||||||
\(741\) | 0.430602 | 0.0158186 | ||||||||
\(742\) | 6.88311 | 0.252687 | ||||||||
\(743\) | −32.0335 | −1.17519 | −0.587597 | − | 0.809154i | \(-0.699926\pi\) | ||||
−0.587597 | + | 0.809154i | \(0.699926\pi\) | |||||||
\(744\) | 10.2069 | 0.374204 | ||||||||
\(745\) | −3.36075 | −0.123128 | ||||||||
\(746\) | 20.9089 | 0.765529 | ||||||||
\(747\) | −1.80562 | −0.0660643 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.74431 | 0.136814 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −32.2682 | −1.17748 | −0.588742 | − | 0.808321i | \(-0.700376\pi\) | ||||
−0.588742 | + | 0.808321i | \(0.700376\pi\) | |||||||
\(752\) | −5.39104 | −0.196591 | ||||||||
\(753\) | 21.2043 | 0.772727 | ||||||||
\(754\) | 0.275866 | 0.0100465 | ||||||||
\(755\) | −4.74150 | −0.172561 | ||||||||
\(756\) | −1.08239 | −0.0393662 | ||||||||
\(757\) | −48.9409 | −1.77879 | −0.889394 | − | 0.457142i | \(-0.848873\pi\) | ||||
−0.889394 | + | 0.457142i | \(0.848873\pi\) | |||||||
\(758\) | −16.9663 | −0.616244 | ||||||||
\(759\) | 9.44155 | 0.342707 | ||||||||
\(760\) | −2.82843 | −0.102598 | ||||||||
\(761\) | −51.5087 | −1.86719 | −0.933595 | − | 0.358331i | \(-0.883346\pi\) | ||||
−0.933595 | + | 0.358331i | \(0.883346\pi\) | |||||||
\(762\) | −16.6501 | −0.603168 | ||||||||
\(763\) | −3.13535 | −0.113507 | ||||||||
\(764\) | 9.44572 | 0.341734 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.9736 | 0.649414 | ||||||||
\(767\) | −0.284005 | −0.0102548 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −27.8446 | −1.00410 | −0.502051 | − | 0.864838i | \(-0.667421\pi\) | ||||
−0.502051 | + | 0.864838i | \(0.667421\pi\) | |||||||
\(770\) | −1.53073 | −0.0551638 | ||||||||
\(771\) | −7.56224 | −0.272347 | ||||||||
\(772\) | 10.0177 | 0.360546 | ||||||||
\(773\) | 22.1995 | 0.798461 | 0.399231 | − | 0.916851i | \(-0.369277\pi\) | ||||
0.399231 | + | 0.916851i | \(0.369277\pi\) | |||||||
\(774\) | 11.0353 | 0.396657 | ||||||||
\(775\) | 10.2069 | 0.366643 | ||||||||
\(776\) | 1.91082 | 0.0685944 | ||||||||
\(777\) | 8.00000 | 0.286998 | ||||||||
\(778\) | 8.78948 | 0.315118 | ||||||||
\(779\) | −16.5163 | −0.591756 | ||||||||
\(780\) | 0.152241 | 0.00545110 | ||||||||
\(781\) | −4.59220 | −0.164322 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.81204 | −0.0647570 | ||||||||
\(784\) | −5.82843 | −0.208158 | ||||||||
\(785\) | −9.67112 | −0.345177 | ||||||||
\(786\) | −16.9378 | −0.604151 | ||||||||
\(787\) | −36.8914 | −1.31504 | −0.657519 | − | 0.753438i | \(-0.728394\pi\) | ||||
−0.657519 | + | 0.753438i | \(0.728394\pi\) | |||||||
\(788\) | −1.47605 | −0.0525823 | ||||||||
\(789\) | −11.2417 | −0.400216 | ||||||||
\(790\) | 16.6417 | 0.592085 | ||||||||
\(791\) | −10.2477 | −0.364368 | ||||||||
\(792\) | −1.41421 | −0.0502519 | ||||||||
\(793\) | −0.842004 | −0.0299004 | ||||||||
\(794\) | 20.1158 | 0.713882 | ||||||||
\(795\) | 6.35916 | 0.225536 | ||||||||
\(796\) | 20.6239 | 0.730996 | ||||||||
\(797\) | 37.7481 | 1.33711 | 0.668554 | − | 0.743664i | \(-0.266914\pi\) | ||||
0.668554 | + | 0.743664i | \(0.266914\pi\) | |||||||
\(798\) | 3.06147 | 0.108375 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −4.60127 | −0.162578 | ||||||||
\(802\) | −0.338236 | −0.0119435 | ||||||||
\(803\) | 14.4229 | 0.508973 | ||||||||
\(804\) | −4.69711 | −0.165654 | ||||||||
\(805\) | −7.22625 | −0.254692 | ||||||||
\(806\) | 1.55391 | 0.0547342 | ||||||||
\(807\) | −29.1380 | −1.02571 | ||||||||
\(808\) | −6.27836 | −0.220872 | ||||||||
\(809\) | 7.84707 | 0.275888 | 0.137944 | − | 0.990440i | \(-0.455951\pi\) | ||||
0.137944 | + | 0.990440i | \(0.455951\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −22.0296 | −0.773564 | −0.386782 | − | 0.922171i | \(-0.626413\pi\) | ||||
−0.386782 | + | 0.922171i | \(0.626413\pi\) | |||||||
\(812\) | 1.96134 | 0.0688294 | ||||||||
\(813\) | −21.4908 | −0.753715 | ||||||||
\(814\) | 10.4525 | 0.366360 | ||||||||
\(815\) | −1.44381 | −0.0505743 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.2127 | −1.09199 | ||||||||
\(818\) | 15.8307 | 0.553508 | ||||||||
\(819\) | −0.164784 | −0.00575803 | ||||||||
\(820\) | −5.83938 | −0.203920 | ||||||||
\(821\) | −30.6042 | −1.06810 | −0.534048 | − | 0.845454i | \(-0.679330\pi\) | ||||
−0.534048 | + | 0.845454i | \(0.679330\pi\) | |||||||
\(822\) | 12.8303 | 0.447509 | ||||||||
\(823\) | −25.5722 | −0.891390 | −0.445695 | − | 0.895185i | \(-0.647043\pi\) | ||||
−0.445695 | + | 0.895185i | \(0.647043\pi\) | |||||||
\(824\) | −5.58541 | −0.194577 | ||||||||
\(825\) | −1.41421 | −0.0492366 | ||||||||
\(826\) | −2.01920 | −0.0702570 | ||||||||
\(827\) | −49.4829 | −1.72069 | −0.860344 | − | 0.509713i | \(-0.829751\pi\) | ||||
−0.860344 | + | 0.509713i | \(0.829751\pi\) | |||||||
\(828\) | −6.67619 | −0.232014 | ||||||||
\(829\) | −14.5735 | −0.506158 | −0.253079 | − | 0.967446i | \(-0.581443\pi\) | ||||
−0.253079 | + | 0.967446i | \(0.581443\pi\) | |||||||
\(830\) | 1.80562 | 0.0626741 | ||||||||
\(831\) | −6.87669 | −0.238550 | ||||||||
\(832\) | −0.152241 | −0.00527800 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.38425 | −0.0825597 | ||||||||
\(835\) | −0.211830 | −0.00733066 | ||||||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | −10.2069 | −0.352803 | ||||||||
\(838\) | −23.5134 | −0.812258 | ||||||||
\(839\) | −41.1582 | −1.42094 | −0.710470 | − | 0.703728i | \(-0.751518\pi\) | ||||
−0.710470 | + | 0.703728i | \(0.751518\pi\) | |||||||
\(840\) | 1.08239 | 0.0373461 | ||||||||
\(841\) | −25.7165 | −0.886776 | ||||||||
\(842\) | 12.0648 | 0.415781 | ||||||||
\(843\) | 7.11933 | 0.245203 | ||||||||
\(844\) | 5.90666 | 0.203316 | ||||||||
\(845\) | −12.9768 | −0.446416 | ||||||||
\(846\) | 5.39104 | 0.185348 | ||||||||
\(847\) | −9.74153 | −0.334723 | ||||||||
\(848\) | −6.35916 | −0.218374 | ||||||||
\(849\) | −25.8473 | −0.887075 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49.3439 | 1.69149 | ||||||||
\(852\) | 3.24718 | 0.111246 | ||||||||
\(853\) | −27.1881 | −0.930903 | −0.465452 | − | 0.885073i | \(-0.654108\pi\) | ||||
−0.465452 | + | 0.885073i | \(0.654108\pi\) | |||||||
\(854\) | −5.98642 | −0.204851 | ||||||||
\(855\) | 2.82843 | 0.0967302 | ||||||||
\(856\) | −3.45929 | −0.118236 | ||||||||
\(857\) | 15.3112 | 0.523021 | 0.261511 | − | 0.965201i | \(-0.415779\pi\) | ||||
0.261511 | + | 0.965201i | \(0.415779\pi\) | |||||||
\(858\) | −0.215301 | −0.00735026 | ||||||||
\(859\) | −38.2717 | −1.30581 | −0.652907 | − | 0.757438i | \(-0.726451\pi\) | ||||
−0.652907 | + | 0.757438i | \(0.726451\pi\) | |||||||
\(860\) | −11.0353 | −0.376302 | ||||||||
\(861\) | 6.32050 | 0.215402 | ||||||||
\(862\) | −6.35744 | −0.216535 | ||||||||
\(863\) | 12.3789 | 0.421382 | 0.210691 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210691 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −23.5230 | −0.799807 | ||||||||
\(866\) | 35.0402 | 1.19071 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.0479 | 0.374990 | ||||||||
\(869\) | −23.5349 | −0.798367 | ||||||||
\(870\) | 1.81204 | 0.0614339 | ||||||||
\(871\) | −0.715093 | −0.0242300 | ||||||||
\(872\) | 2.89668 | 0.0980941 | ||||||||
\(873\) | −1.91082 | −0.0646714 | ||||||||
\(874\) | 18.8831 | 0.638731 | ||||||||
\(875\) | 1.08239 | 0.0365915 | ||||||||
\(876\) | −10.1985 | −0.344577 | ||||||||
\(877\) | −39.7081 | −1.34085 | −0.670423 | − | 0.741979i | \(-0.733888\pi\) | ||||
−0.670423 | + | 0.741979i | \(0.733888\pi\) | |||||||
\(878\) | −7.38340 | −0.249178 | ||||||||
\(879\) | 17.7251 | 0.597853 | ||||||||
\(880\) | 1.41421 | 0.0476731 | ||||||||
\(881\) | −20.6022 | −0.694107 | −0.347054 | − | 0.937845i | \(-0.612818\pi\) | ||||
−0.347054 | + | 0.937845i | \(0.612818\pi\) | |||||||
\(882\) | 5.82843 | 0.196253 | ||||||||
\(883\) | −37.5631 | −1.26410 | −0.632050 | − | 0.774928i | \(-0.717786\pi\) | ||||
−0.632050 | + | 0.774928i | \(0.717786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.86550 | −0.0627080 | ||||||||
\(886\) | −22.0539 | −0.740916 | ||||||||
\(887\) | 12.6912 | 0.426130 | 0.213065 | − | 0.977038i | \(-0.431655\pi\) | ||||
0.213065 | + | 0.977038i | \(0.431655\pi\) | |||||||
\(888\) | −7.39104 | −0.248027 | ||||||||
\(889\) | −18.0219 | −0.604435 | ||||||||
\(890\) | 4.60127 | 0.154235 | ||||||||
\(891\) | 1.41421 | 0.0473779 | ||||||||
\(892\) | 13.5854 | 0.454873 | ||||||||
\(893\) | −15.2482 | −0.510260 | ||||||||
\(894\) | −3.36075 | −0.112400 | ||||||||
\(895\) | −17.2388 | −0.576229 | ||||||||
\(896\) | −1.08239 | −0.0361602 | ||||||||
\(897\) | −1.01639 | −0.0339362 | ||||||||
\(898\) | 37.9191 | 1.26538 | ||||||||
\(899\) | 18.4953 | 0.616854 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 8.25813 | 0.274966 | ||||||||
\(903\) | 11.9446 | 0.397491 | ||||||||
\(904\) | 9.46767 | 0.314890 | ||||||||
\(905\) | 14.4557 | 0.480523 | ||||||||
\(906\) | −4.74150 | −0.157526 | ||||||||
\(907\) | 18.0101 | 0.598017 | 0.299008 | − | 0.954251i | \(-0.403344\pi\) | ||||
0.299008 | + | 0.954251i | \(0.403344\pi\) | |||||||
\(908\) | 6.87992 | 0.228318 | ||||||||
\(909\) | 6.27836 | 0.208240 | ||||||||
\(910\) | 0.164784 | 0.00546255 | ||||||||
\(911\) | 0.133468 | 0.00442200 | 0.00221100 | − | 0.999998i | \(-0.499296\pi\) | ||||
0.00221100 | + | 0.999998i | \(0.499296\pi\) | |||||||
\(912\) | −2.82843 | −0.0936586 | ||||||||
\(913\) | −2.55354 | −0.0845098 | ||||||||
\(914\) | 6.09785 | 0.201699 | ||||||||
\(915\) | −5.53073 | −0.182840 | ||||||||
\(916\) | −8.59539 | −0.284000 | ||||||||
\(917\) | −18.3333 | −0.605420 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.2426 | −0.469821 | −0.234911 | − | 0.972017i | \(-0.575480\pi\) | ||||
−0.234911 | + | 0.972017i | \(0.575480\pi\) | |||||||
\(920\) | 6.67619 | 0.220107 | ||||||||
\(921\) | −18.2348 | −0.600857 | ||||||||
\(922\) | −19.1647 | −0.631154 | ||||||||
\(923\) | 0.494353 | 0.0162718 | ||||||||
\(924\) | −1.53073 | −0.0503574 | ||||||||
\(925\) | −7.39104 | −0.243016 | ||||||||
\(926\) | −11.9896 | −0.394003 | ||||||||
\(927\) | 5.58541 | 0.183449 | ||||||||
\(928\) | −1.81204 | −0.0594831 | ||||||||
\(929\) | −49.4896 | −1.62370 | −0.811851 | − | 0.583865i | \(-0.801540\pi\) | ||||
−0.811851 | + | 0.583865i | \(0.801540\pi\) | |||||||
\(930\) | 10.2069 | 0.334698 | ||||||||
\(931\) | −16.4853 | −0.540283 | ||||||||
\(932\) | 19.6945 | 0.645114 | ||||||||
\(933\) | −31.7112 | −1.03818 | ||||||||
\(934\) | 31.3388 | 1.02544 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.152241 | 0.00497615 | ||||||||
\(937\) | 4.51757 | 0.147583 | 0.0737914 | − | 0.997274i | \(-0.476490\pi\) | ||||
0.0737914 | + | 0.997274i | \(0.476490\pi\) | |||||||
\(938\) | −5.08412 | −0.166002 | ||||||||
\(939\) | 19.1144 | 0.623776 | ||||||||
\(940\) | −5.39104 | −0.175836 | ||||||||
\(941\) | −40.2291 | −1.31143 | −0.655715 | − | 0.755009i | \(-0.727633\pi\) | ||||
−0.655715 | + | 0.755009i | \(0.727633\pi\) | |||||||
\(942\) | −9.67112 | −0.315102 | ||||||||
\(943\) | 38.9848 | 1.26952 | ||||||||
\(944\) | 1.86550 | 0.0607168 | ||||||||
\(945\) | −1.08239 | −0.0352102 | ||||||||
\(946\) | 15.6063 | 0.507406 | ||||||||
\(947\) | 24.5264 | 0.797000 | 0.398500 | − | 0.917168i | \(-0.369531\pi\) | ||||
0.398500 | + | 0.917168i | \(0.369531\pi\) | |||||||
\(948\) | 16.6417 | 0.540497 | ||||||||
\(949\) | −1.55264 | −0.0504007 | ||||||||
\(950\) | −2.82843 | −0.0917663 | ||||||||
\(951\) | 21.9195 | 0.710788 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.00154 | 0.0972293 | 0.0486146 | − | 0.998818i | \(-0.484519\pi\) | ||||
0.0486146 | + | 0.998818i | \(0.484519\pi\) | |||||||
\(954\) | 6.35916 | 0.205885 | ||||||||
\(955\) | 9.44572 | 0.305656 | ||||||||
\(956\) | −8.32638 | −0.269294 | ||||||||
\(957\) | −2.56261 | −0.0828374 | ||||||||
\(958\) | 18.4111 | 0.594834 | ||||||||
\(959\) | 13.8875 | 0.448449 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 73.1812 | 2.36068 | ||||||||
\(962\) | −1.12522 | −0.0362785 | ||||||||
\(963\) | 3.45929 | 0.111474 | ||||||||
\(964\) | 8.33476 | 0.268445 | ||||||||
\(965\) | 10.0177 | 0.322482 | ||||||||
\(966\) | −7.22625 | −0.232501 | ||||||||
\(967\) | 20.1867 | 0.649160 | 0.324580 | − | 0.945858i | \(-0.394777\pi\) | ||||
0.324580 | + | 0.945858i | \(0.394777\pi\) | |||||||
\(968\) | 9.00000 | 0.289271 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.91082 | 0.0613527 | ||||||||
\(971\) | −38.9735 | −1.25072 | −0.625360 | − | 0.780336i | \(-0.715048\pi\) | ||||
−0.625360 | + | 0.780336i | \(0.715048\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −2.58069 | −0.0827332 | ||||||||
\(974\) | −15.1280 | −0.484732 | ||||||||
\(975\) | 0.152241 | 0.00487561 | ||||||||
\(976\) | 5.53073 | 0.177034 | ||||||||
\(977\) | −20.2941 | −0.649265 | −0.324633 | − | 0.945840i | \(-0.605241\pi\) | ||||
−0.324633 | + | 0.945840i | \(0.605241\pi\) | |||||||
\(978\) | −1.44381 | −0.0461678 | ||||||||
\(979\) | −6.50718 | −0.207970 | ||||||||
\(980\) | −5.82843 | −0.186182 | ||||||||
\(981\) | −2.89668 | −0.0924840 | ||||||||
\(982\) | −13.6457 | −0.435452 | ||||||||
\(983\) | −11.1960 | −0.357096 | −0.178548 | − | 0.983931i | \(-0.557140\pi\) | ||||
−0.178548 | + | 0.983931i | \(0.557140\pi\) | |||||||
\(984\) | −5.83938 | −0.186153 | ||||||||
\(985\) | −1.47605 | −0.0470310 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.83522 | 0.185737 | ||||||||
\(988\) | −0.430602 | −0.0136993 | ||||||||
\(989\) | 73.6740 | 2.34270 | ||||||||
\(990\) | −1.41421 | −0.0449467 | ||||||||
\(991\) | −44.9865 | −1.42904 | −0.714522 | − | 0.699613i | \(-0.753356\pi\) | ||||
−0.714522 | + | 0.699613i | \(0.753356\pi\) | |||||||
\(992\) | −10.2069 | −0.324070 | ||||||||
\(993\) | 18.7402 | 0.594703 | ||||||||
\(994\) | 3.51472 | 0.111480 | ||||||||
\(995\) | 20.6239 | 0.653823 | ||||||||
\(996\) | 1.80562 | 0.0572134 | ||||||||
\(997\) | 26.7639 | 0.847622 | 0.423811 | − | 0.905751i | \(-0.360692\pi\) | ||||
0.423811 | + | 0.905751i | \(0.360692\pi\) | |||||||
\(998\) | −31.3433 | −0.992155 | ||||||||
\(999\) | 7.39104 | 0.233842 |
(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 | 8670.2.a.bu.1.3 | 4 | ||
17.3 | odd | 16 | 510.2.u.b.451.1 | yes | 8 | ||
17.6 | odd | 16 | 510.2.u.b.121.1 | ✓ | 8 | ||
17.16 | even | 2 | 8670.2.a.bv.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
510.2.u.b.121.1 | ✓ | 8 | 17.6 | odd | 16 | ||
510.2.u.b.451.1 | yes | 8 | 17.3 | odd | 16 | ||
8670.2.a.bu.1.3 | 4 | 1.1 | even | 1 | trivial | ||
8670.2.a.bv.1.2 | 4 | 17.16 | even | 2 |