Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, 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("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.746052.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 7x^{3} + 8x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.265608\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26561 | −0.894920 | −0.447460 | − | 0.894304i | \(-0.647671\pi\) | ||||
−0.447460 | + | 0.894304i | \(0.647671\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.398235 | −0.199118 | ||||||||
\(5\) | −2.90260 | −1.29808 | −0.649041 | − | 0.760753i | \(-0.724830\pi\) | ||||
−0.649041 | + | 0.760753i | \(0.724830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.03523 | 1.07311 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.67356 | 1.16168 | ||||||||
\(11\) | −2.03656 | −0.614047 | −0.307024 | − | 0.951702i | \(-0.599333\pi\) | ||||
−0.307024 | + | 0.951702i | \(0.599333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.04494 | −0.761235 | ||||||||
\(17\) | 3.99866 | 0.969818 | 0.484909 | − | 0.874565i | \(-0.338853\pi\) | ||||
0.484909 | + | 0.874565i | \(0.338853\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.96210 | −1.59722 | −0.798608 | − | 0.601852i | \(-0.794430\pi\) | ||||
−0.798608 | + | 0.601852i | \(0.794430\pi\) | |||||||
\(20\) | 1.15592 | 0.258471 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.57749 | 0.549523 | ||||||||
\(23\) | 0.627280 | 0.130797 | 0.0653985 | − | 0.997859i | \(-0.479168\pi\) | ||||
0.0653985 | + | 0.997859i | \(0.479168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.42509 | 0.685017 | ||||||||
\(26\) | 1.26561 | 0.248206 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.09606 | −0.203534 | −0.101767 | − | 0.994808i | \(-0.532450\pi\) | ||||
−0.101767 | + | 0.994808i | \(0.532450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4325 | 1.87373 | 0.936864 | − | 0.349693i | \(-0.113714\pi\) | ||||
0.936864 | + | 0.349693i | \(0.113714\pi\) | |||||||
\(32\) | −2.21675 | −0.391870 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.06074 | −0.867910 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.08537 | −0.507232 | −0.253616 | − | 0.967305i | \(-0.581620\pi\) | ||||
−0.253616 | + | 0.967305i | \(0.581620\pi\) | |||||||
\(38\) | 8.81129 | 1.42938 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.81005 | −1.39299 | ||||||||
\(41\) | −0.521150 | −0.0813900 | −0.0406950 | − | 0.999172i | \(-0.512957\pi\) | ||||
−0.0406950 | + | 0.999172i | \(0.512957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.329024 | 0.0501757 | 0.0250879 | − | 0.999685i | \(-0.492013\pi\) | ||||
0.0250879 | + | 0.999685i | \(0.492013\pi\) | |||||||
\(44\) | 0.811031 | 0.122268 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.793891 | −0.117053 | ||||||||
\(47\) | 10.5457 | 1.53825 | 0.769123 | − | 0.639101i | \(-0.220693\pi\) | ||||
0.769123 | + | 0.639101i | \(0.220693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.33482 | −0.613036 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.398235 | 0.0552253 | ||||||||
\(53\) | −7.11900 | −0.977870 | −0.488935 | − | 0.872320i | \(-0.662614\pi\) | ||||
−0.488935 | + | 0.872320i | \(0.662614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.91133 | 0.797084 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.38719 | 0.182147 | ||||||||
\(59\) | 2.03656 | 0.265138 | 0.132569 | − | 0.991174i | \(-0.457677\pi\) | ||||
0.132569 | + | 0.991174i | \(0.457677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.40081 | −0.307393 | −0.153696 | − | 0.988118i | \(-0.549118\pi\) | ||||
−0.153696 | + | 0.988118i | \(0.549118\pi\) | |||||||
\(62\) | −13.2034 | −1.67684 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.89542 | 1.11193 | ||||||||
\(65\) | 2.90260 | 0.360023 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.6942 | 1.79518 | 0.897589 | − | 0.440832i | \(-0.145317\pi\) | ||||
0.897589 | + | 0.440832i | \(0.145317\pi\) | |||||||
\(68\) | −1.59241 | −0.193108 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.60141 | −0.427409 | −0.213704 | − | 0.976898i | \(-0.568553\pi\) | ||||
−0.213704 | + | 0.976898i | \(0.568553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.97573 | −0.348283 | −0.174141 | − | 0.984721i | \(-0.555715\pi\) | ||||
−0.174141 | + | 0.984721i | \(0.555715\pi\) | |||||||
\(74\) | 3.90487 | 0.453932 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.77255 | 0.318034 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.76150 | −0.985746 | −0.492873 | − | 0.870101i | \(-0.664053\pi\) | ||||
−0.492873 | + | 0.870101i | \(0.664053\pi\) | |||||||
\(80\) | 8.83824 | 0.988145 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.659572 | 0.0728376 | ||||||||
\(83\) | 12.8039 | 1.40541 | 0.702703 | − | 0.711483i | \(-0.251976\pi\) | ||||
0.702703 | + | 0.711483i | \(0.251976\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6065 | −1.25890 | ||||||||
\(86\) | −0.416416 | −0.0449033 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.18143 | −0.658943 | ||||||||
\(89\) | −2.68098 | −0.284184 | −0.142092 | − | 0.989853i | \(-0.545383\pi\) | ||||
−0.142092 | + | 0.989853i | \(0.545383\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.249805 | −0.0260440 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.3467 | −1.37661 | ||||||||
\(95\) | 20.2082 | 2.07332 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.32902 | 0.236477 | 0.118238 | − | 0.992985i | \(-0.462275\pi\) | ||||
0.118238 | + | 0.992985i | \(0.462275\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.36399 | −0.136399 | ||||||||
\(101\) | 1.45324 | 0.144603 | 0.0723014 | − | 0.997383i | \(-0.476966\pi\) | ||||
0.0723014 | + | 0.997383i | \(0.476966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6353 | 1.14646 | 0.573230 | − | 0.819394i | \(-0.305690\pi\) | ||||
0.573230 | + | 0.819394i | \(0.305690\pi\) | |||||||
\(104\) | −3.03523 | −0.297628 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00987 | 0.875115 | ||||||||
\(107\) | −19.6259 | −1.89731 | −0.948656 | − | 0.316310i | \(-0.897556\pi\) | ||||
−0.948656 | + | 0.316310i | \(0.897556\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.10676 | −0.106008 | −0.0530040 | − | 0.998594i | \(-0.516880\pi\) | ||||
−0.0530040 | + | 0.998594i | \(0.516880\pi\) | |||||||
\(110\) | −7.48143 | −0.713326 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.09606 | 0.103109 | 0.0515545 | − | 0.998670i | \(-0.483582\pi\) | ||||
0.0515545 | + | 0.998670i | \(0.483582\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.82074 | −0.169785 | ||||||||
\(116\) | 0.436491 | 0.0405272 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.57749 | −0.237277 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.85241 | −0.622946 | ||||||||
\(122\) | 3.03849 | 0.275092 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.15458 | −0.373092 | ||||||||
\(125\) | 4.57134 | 0.408873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.18143 | 0.459778 | 0.229889 | − | 0.973217i | \(-0.426164\pi\) | ||||
0.229889 | + | 0.973217i | \(0.426164\pi\) | |||||||
\(128\) | −6.82461 | −0.603216 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.67356 | −0.322192 | ||||||||
\(131\) | 10.5667 | 0.923217 | 0.461609 | − | 0.887084i | \(-0.347272\pi\) | ||||
0.461609 | + | 0.887084i | \(0.347272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −18.5971 | −1.60654 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.1368 | 1.04073 | ||||||||
\(137\) | 5.87177 | 0.501659 | 0.250830 | − | 0.968031i | \(-0.419297\pi\) | ||||
0.250830 | + | 0.968031i | \(0.419297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.55797 | 0.382497 | ||||||||
\(143\) | 2.03656 | 0.170306 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.18143 | 0.264204 | ||||||||
\(146\) | 3.76611 | 0.311685 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.22870 | 0.100999 | ||||||||
\(149\) | 10.1054 | 0.827868 | 0.413934 | − | 0.910307i | \(-0.364154\pi\) | ||||
0.413934 | + | 0.910307i | \(0.364154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.187726 | −0.0152769 | −0.00763847 | − | 0.999971i | \(-0.502431\pi\) | ||||
−0.00763847 | + | 0.999971i | \(0.502431\pi\) | |||||||
\(152\) | −21.1316 | −1.71400 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.2813 | −2.43225 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0718 | 0.963434 | 0.481717 | − | 0.876327i | \(-0.340013\pi\) | ||||
0.481717 | + | 0.876327i | \(0.340013\pi\) | |||||||
\(158\) | 11.0886 | 0.882164 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.43435 | 0.508680 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.9136 | 1.16812 | 0.584060 | − | 0.811711i | \(-0.301463\pi\) | ||||
0.584060 | + | 0.811711i | \(0.301463\pi\) | |||||||
\(164\) | 0.207540 | 0.0162062 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.2047 | −1.25773 | ||||||||
\(167\) | 5.05664 | 0.391294 | 0.195647 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195647 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 14.6893 | 1.12662 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.131029 | −0.00999087 | ||||||||
\(173\) | −0.595615 | −0.0452837 | −0.0226419 | − | 0.999744i | \(-0.507208\pi\) | ||||
−0.0226419 | + | 0.999744i | \(0.507208\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.20121 | 0.467434 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.39308 | 0.254322 | ||||||||
\(179\) | −8.07664 | −0.603676 | −0.301838 | − | 0.953359i | \(-0.597600\pi\) | ||||
−0.301838 | + | 0.953359i | \(0.597600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.89324 | −0.140724 | −0.0703618 | − | 0.997522i | \(-0.522415\pi\) | ||||
−0.0703618 | + | 0.997522i | \(0.522415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.90394 | 0.140360 | ||||||||
\(185\) | 8.95559 | 0.658428 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.14353 | −0.595514 | ||||||||
\(188\) | −4.19966 | −0.306292 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.5757 | −1.85545 | ||||||||
\(191\) | −3.70174 | −0.267849 | −0.133924 | − | 0.990992i | \(-0.542758\pi\) | ||||
−0.133924 | + | 0.990992i | \(0.542758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.5875 | 0.978047 | 0.489024 | − | 0.872271i | \(-0.337353\pi\) | ||||
0.489024 | + | 0.872271i | \(0.337353\pi\) | |||||||
\(194\) | −2.94763 | −0.211628 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.70258 | 0.691280 | 0.345640 | − | 0.938367i | \(-0.387662\pi\) | ||||
0.345640 | + | 0.938367i | \(0.387662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.2720 | −1.86237 | −0.931185 | − | 0.364547i | \(-0.881224\pi\) | ||||
−0.931185 | + | 0.364547i | \(0.881224\pi\) | |||||||
\(200\) | 10.3959 | 0.735102 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.83923 | −0.129408 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.51269 | 0.105651 | ||||||||
\(206\) | −14.7257 | −1.02599 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.04494 | 0.211128 | ||||||||
\(209\) | 14.1788 | 0.980765 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0338 | 0.690758 | 0.345379 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345379 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(212\) | 2.83504 | 0.194711 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24.8388 | 1.69794 | ||||||||
\(215\) | −0.955026 | −0.0651322 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.40072 | 0.0948688 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.35410 | −0.158713 | ||||||||
\(221\) | −3.99866 | −0.268979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.4961 | −1.17163 | −0.585813 | − | 0.810446i | \(-0.699225\pi\) | ||||
−0.585813 | + | 0.810446i | \(0.699225\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.38719 | −0.0922743 | ||||||||
\(227\) | −9.51630 | −0.631619 | −0.315810 | − | 0.948823i | \(-0.602276\pi\) | ||||
−0.315810 | + | 0.948823i | \(0.602276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.1170 | −1.39545 | −0.697725 | − | 0.716366i | \(-0.745804\pi\) | ||||
−0.697725 | + | 0.716366i | \(0.745804\pi\) | |||||||
\(230\) | 2.30435 | 0.151944 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.32680 | −0.218415 | ||||||||
\(233\) | −14.1788 | −0.928881 | −0.464441 | − | 0.885604i | \(-0.653745\pi\) | ||||
−0.464441 | + | 0.885604i | \(0.653745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.6099 | −1.99677 | ||||||||
\(236\) | −0.811031 | −0.0527936 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.5275 | 1.06907 | 0.534536 | − | 0.845145i | \(-0.320486\pi\) | ||||
0.534536 | + | 0.845145i | \(0.320486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.6890 | 0.881786 | 0.440893 | − | 0.897560i | \(-0.354662\pi\) | ||||
0.440893 | + | 0.897560i | \(0.354662\pi\) | |||||||
\(242\) | 8.67247 | 0.557487 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.956089 | 0.0612073 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.96210 | 0.442988 | ||||||||
\(248\) | 31.6649 | 2.01073 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.78553 | −0.365909 | ||||||||
\(251\) | −14.6603 | −0.925349 | −0.462674 | − | 0.886528i | \(-0.653110\pi\) | ||||
−0.462674 | + | 0.886528i | \(0.653110\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.27750 | −0.0803155 | ||||||||
\(254\) | −6.55767 | −0.411464 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.15355 | −0.572097 | ||||||||
\(257\) | −1.75277 | −0.109335 | −0.0546675 | − | 0.998505i | \(-0.517410\pi\) | ||||
−0.0546675 | + | 0.998505i | \(0.517410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.15592 | −0.0716870 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.3733 | −0.826206 | ||||||||
\(263\) | −26.9416 | −1.66129 | −0.830645 | − | 0.556802i | \(-0.812028\pi\) | ||||
−0.830645 | + | 0.556802i | \(0.812028\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.6636 | 1.26936 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.85174 | −0.357452 | ||||||||
\(269\) | −22.0691 | −1.34558 | −0.672789 | − | 0.739835i | \(-0.734904\pi\) | ||||
−0.672789 | + | 0.739835i | \(0.734904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.96210 | 0.544409 | 0.272204 | − | 0.962239i | \(-0.412247\pi\) | ||||
0.272204 | + | 0.962239i | \(0.412247\pi\) | |||||||
\(272\) | −12.1757 | −0.738259 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.43137 | −0.448945 | ||||||||
\(275\) | −6.97541 | −0.420633 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.52925 | −0.452389 | −0.226194 | − | 0.974082i | \(-0.572628\pi\) | ||||
−0.226194 | + | 0.974082i | \(0.572628\pi\) | |||||||
\(278\) | −5.06243 | −0.303625 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.7762 | −1.77630 | −0.888151 | − | 0.459553i | \(-0.848010\pi\) | ||||
−0.888151 | + | 0.459553i | \(0.848010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.301451 | −0.0179194 | −0.00895970 | − | 0.999960i | \(-0.502852\pi\) | ||||
−0.00895970 | + | 0.999960i | \(0.502852\pi\) | |||||||
\(284\) | 1.43421 | 0.0851046 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.57749 | −0.152410 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.01069 | −0.0594526 | ||||||||
\(290\) | −4.02645 | −0.236441 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.18504 | 0.0693492 | ||||||||
\(293\) | −19.2471 | −1.12443 | −0.562214 | − | 0.826992i | \(-0.690050\pi\) | ||||
−0.562214 | + | 0.826992i | \(0.690050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.91133 | −0.344171 | ||||||||
\(296\) | −9.36480 | −0.544318 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.7895 | −0.740876 | ||||||||
\(299\) | −0.627280 | −0.0362765 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.237588 | 0.0136716 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 21.1992 | 1.21586 | ||||||||
\(305\) | 6.96860 | 0.399021 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.57779 | 0.204195 | 0.102098 | − | 0.994774i | \(-0.467445\pi\) | ||||
0.102098 | + | 0.994774i | \(0.467445\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 38.3243 | 2.17667 | ||||||||
\(311\) | −23.8306 | −1.35131 | −0.675655 | − | 0.737218i | \(-0.736139\pi\) | ||||
−0.675655 | + | 0.737218i | \(0.736139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0814 | 1.02202 | 0.511009 | − | 0.859575i | \(-0.329272\pi\) | ||||
0.511009 | + | 0.859575i | \(0.329272\pi\) | |||||||
\(314\) | −15.2782 | −0.862196 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.48914 | 0.196279 | ||||||||
\(317\) | 27.5482 | 1.54726 | 0.773630 | − | 0.633638i | \(-0.218439\pi\) | ||||
0.773630 | + | 0.633638i | \(0.218439\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.23220 | 0.124979 | ||||||||
\(320\) | −25.8198 | −1.44337 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.8391 | −1.54901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.42509 | −0.189990 | ||||||||
\(326\) | −18.8747 | −1.04537 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.58181 | −0.0873408 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1814 | −0.999339 | −0.499669 | − | 0.866216i | \(-0.666545\pi\) | ||||
−0.499669 | + | 0.866216i | \(0.666545\pi\) | |||||||
\(332\) | −5.09895 | −0.279841 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.39972 | −0.350177 | ||||||||
\(335\) | −42.6513 | −2.33029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1381 | −0.933572 | −0.466786 | − | 0.884370i | \(-0.654588\pi\) | ||||
−0.466786 | + | 0.884370i | \(0.654588\pi\) | |||||||
\(338\) | −1.26561 | −0.0688400 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.62212 | 0.250670 | ||||||||
\(341\) | −21.2464 | −1.15056 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.998663 | 0.0538443 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.753815 | 0.0405253 | ||||||||
\(347\) | −22.2688 | −1.19545 | −0.597725 | − | 0.801701i | \(-0.703929\pi\) | ||||
−0.597725 | + | 0.801701i | \(0.703929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.9368 | −1.06719 | −0.533595 | − | 0.845740i | \(-0.679159\pi\) | ||||
−0.533595 | + | 0.845740i | \(0.679159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.51456 | 0.240627 | ||||||||
\(353\) | 22.9152 | 1.21965 | 0.609825 | − | 0.792536i | \(-0.291240\pi\) | ||||
0.609825 | + | 0.792536i | \(0.291240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4535 | 0.554812 | ||||||||
\(356\) | 1.06766 | 0.0565860 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.2219 | 0.540242 | ||||||||
\(359\) | −27.2314 | −1.43722 | −0.718610 | − | 0.695413i | \(-0.755221\pi\) | ||||
−0.718610 | + | 0.695413i | \(0.755221\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.4708 | 1.55110 | ||||||||
\(362\) | 2.39611 | 0.125936 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.63735 | 0.452099 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8564 | 0.566702 | 0.283351 | − | 0.959016i | \(-0.408554\pi\) | ||||
0.283351 | + | 0.959016i | \(0.408554\pi\) | |||||||
\(368\) | −1.91003 | −0.0995671 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.3343 | −0.589241 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.37144 | −0.122789 | −0.0613943 | − | 0.998114i | \(-0.519555\pi\) | ||||
−0.0613943 | + | 0.998114i | \(0.519555\pi\) | |||||||
\(374\) | 10.3065 | 0.532938 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.0085 | 1.65071 | ||||||||
\(377\) | 1.09606 | 0.0564501 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.2197 | −1.50092 | −0.750458 | − | 0.660918i | \(-0.770167\pi\) | ||||
−0.750458 | + | 0.660918i | \(0.770167\pi\) | |||||||
\(380\) | −8.04761 | −0.412834 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.68496 | 0.239703 | ||||||||
\(383\) | −3.06595 | −0.156663 | −0.0783313 | − | 0.996927i | \(-0.524959\pi\) | ||||
−0.0783313 | + | 0.996927i | \(0.524959\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.1964 | −0.875274 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.927499 | −0.0470866 | ||||||||
\(389\) | −27.7410 | −1.40652 | −0.703261 | − | 0.710932i | \(-0.748274\pi\) | ||||
−0.703261 | + | 0.710932i | \(0.748274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.50828 | 0.126849 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.2797 | −0.618641 | ||||||||
\(395\) | 25.4311 | 1.27958 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.2312 | −0.864808 | −0.432404 | − | 0.901680i | \(-0.642335\pi\) | ||||
−0.432404 | + | 0.901680i | \(0.642335\pi\) | |||||||
\(398\) | 33.2500 | 1.66667 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.4292 | −0.521459 | ||||||||
\(401\) | −16.6440 | −0.831163 | −0.415582 | − | 0.909556i | \(-0.636422\pi\) | ||||
−0.415582 | + | 0.909556i | \(0.636422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.4325 | −0.519679 | ||||||||
\(404\) | −0.578731 | −0.0287930 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.28355 | 0.311464 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6338 | 0.674147 | 0.337073 | − | 0.941478i | \(-0.390563\pi\) | ||||
0.337073 | + | 0.941478i | \(0.390563\pi\) | |||||||
\(410\) | −1.91447 | −0.0945491 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.63359 | −0.228280 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.1645 | −1.82433 | ||||||||
\(416\) | 2.21675 | 0.108685 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.9448 | −0.877707 | ||||||||
\(419\) | −10.8502 | −0.530066 | −0.265033 | − | 0.964239i | \(-0.585383\pi\) | ||||
−0.265033 | + | 0.964239i | \(0.585383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | −12.6989 | −0.618173 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21.6078 | −1.04937 | ||||||||
\(425\) | 13.6958 | 0.664342 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.81574 | 0.377788 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.20869 | 0.0582881 | ||||||||
\(431\) | −1.20953 | −0.0582609 | −0.0291304 | − | 0.999576i | \(-0.509274\pi\) | ||||
−0.0291304 | + | 0.999576i | \(0.509274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.56422 | 0.267399 | 0.133700 | − | 0.991022i | \(-0.457314\pi\) | ||||
0.133700 | + | 0.991022i | \(0.457314\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.440749 | 0.0211081 | ||||||||
\(437\) | −4.36719 | −0.208911 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7192 | 0.941146 | 0.470573 | − | 0.882361i | \(-0.344047\pi\) | ||||
0.470573 | + | 0.882361i | \(0.344047\pi\) | |||||||
\(440\) | 17.9422 | 0.855362 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.06074 | 0.240715 | ||||||||
\(443\) | −22.2310 | −1.05623 | −0.528113 | − | 0.849174i | \(-0.677100\pi\) | ||||
−0.528113 | + | 0.849174i | \(0.677100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.78182 | 0.368894 | ||||||||
\(446\) | 22.1432 | 1.04851 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.4579 | −0.871082 | −0.435541 | − | 0.900169i | \(-0.643443\pi\) | ||||
−0.435541 | + | 0.900169i | \(0.643443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06136 | 0.0499773 | ||||||||
\(452\) | −0.436491 | −0.0205308 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0439 | 0.565249 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.9819 | −1.40250 | −0.701248 | − | 0.712917i | \(-0.747373\pi\) | ||||
−0.701248 | + | 0.712917i | \(0.747373\pi\) | |||||||
\(458\) | 26.7258 | 1.24882 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.725084 | 0.0338072 | ||||||||
\(461\) | 29.1498 | 1.35764 | 0.678821 | − | 0.734304i | \(-0.262491\pi\) | ||||
0.678821 | + | 0.734304i | \(0.262491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.55900 | 0.0724530 | 0.0362265 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362265 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(464\) | 3.33744 | 0.154937 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.9448 | 0.831275 | ||||||||
\(467\) | 12.4231 | 0.574874 | 0.287437 | − | 0.957800i | \(-0.407197\pi\) | ||||
0.287437 | + | 0.957800i | \(0.407197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 38.7402 | 1.78695 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.18143 | 0.284523 | ||||||||
\(473\) | −0.670079 | −0.0308103 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.8458 | −1.09412 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.9173 | −0.956735 | ||||||||
\(479\) | 36.0558 | 1.64743 | 0.823716 | − | 0.567003i | \(-0.191897\pi\) | ||||
0.823716 | + | 0.567003i | \(0.191897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.08537 | 0.140681 | ||||||||
\(482\) | −17.3249 | −0.789128 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.72887 | 0.124040 | ||||||||
\(485\) | −6.76023 | −0.306966 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.30004 | 0.330796 | 0.165398 | − | 0.986227i | \(-0.447109\pi\) | ||||
0.165398 | + | 0.986227i | \(0.447109\pi\) | |||||||
\(488\) | −7.28702 | −0.329868 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.49178 | −0.202711 | −0.101356 | − | 0.994850i | \(-0.532318\pi\) | ||||
−0.101356 | + | 0.994850i | \(0.532318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.38279 | −0.197391 | ||||||||
\(494\) | −8.81129 | −0.396439 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.7663 | −1.42635 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3674 | 0.508873 | 0.254437 | − | 0.967089i | \(-0.418110\pi\) | ||||
0.254437 | + | 0.967089i | \(0.418110\pi\) | |||||||
\(500\) | −1.82047 | −0.0814139 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.5542 | 0.828113 | ||||||||
\(503\) | 17.1080 | 0.762806 | 0.381403 | − | 0.924409i | \(-0.375441\pi\) | ||||
0.381403 | + | 0.924409i | \(0.375441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.21818 | −0.187706 | ||||||||
\(506\) | 1.61681 | 0.0718759 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.06343 | −0.0915498 | ||||||||
\(509\) | 3.28284 | 0.145509 | 0.0727547 | − | 0.997350i | \(-0.476821\pi\) | ||||
0.0727547 | + | 0.997350i | \(0.476821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25.2340 | 1.11520 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.21833 | 0.0978462 | ||||||||
\(515\) | −33.7726 | −1.48820 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.4770 | −0.944555 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.81005 | 0.386346 | ||||||||
\(521\) | −4.77061 | −0.209004 | −0.104502 | − | 0.994525i | \(-0.533325\pi\) | ||||
−0.104502 | + | 0.994525i | \(0.533325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5124 | −1.11558 | −0.557789 | − | 0.829983i | \(-0.688350\pi\) | ||||
−0.557789 | + | 0.829983i | \(0.688350\pi\) | |||||||
\(524\) | −4.20803 | −0.183829 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.0975 | 1.48672 | ||||||||
\(527\) | 41.7160 | 1.81718 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6065 | −0.982892 | ||||||||
\(530\) | −26.1520 | −1.13597 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.521150 | 0.0225735 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 56.9663 | 2.46287 | ||||||||
\(536\) | 44.6001 | 1.92643 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.9309 | 1.20418 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.5157 | −0.710064 | −0.355032 | − | 0.934854i | \(-0.615530\pi\) | ||||
−0.355032 | + | 0.934854i | \(0.615530\pi\) | |||||||
\(542\) | −11.3425 | −0.487202 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.86405 | −0.380043 | ||||||||
\(545\) | 3.21247 | 0.137607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3317 | 0.997591 | 0.498796 | − | 0.866720i | \(-0.333776\pi\) | ||||
0.498796 | + | 0.866720i | \(0.333776\pi\) | |||||||
\(548\) | −2.33835 | −0.0998892 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.82814 | 0.376433 | ||||||||
\(551\) | 7.63090 | 0.325087 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.52909 | 0.404852 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.59294 | −0.0675557 | ||||||||
\(557\) | 20.0471 | 0.849422 | 0.424711 | − | 0.905329i | \(-0.360376\pi\) | ||||
0.424711 | + | 0.905329i | \(0.360376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.329024 | −0.0139162 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 37.6851 | 1.58965 | ||||||||
\(563\) | −40.5284 | −1.70807 | −0.854034 | − | 0.520218i | \(-0.825851\pi\) | ||||
−0.854034 | + | 0.520218i | \(0.825851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.18143 | −0.133844 | ||||||||
\(566\) | 0.381519 | 0.0160364 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.9311 | −0.458659 | ||||||||
\(569\) | 21.4504 | 0.899246 | 0.449623 | − | 0.893219i | \(-0.351558\pi\) | ||||
0.449623 | + | 0.893219i | \(0.351558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.9559 | −0.458489 | −0.229244 | − | 0.973369i | \(-0.573625\pi\) | ||||
−0.229244 | + | 0.973369i | \(0.573625\pi\) | |||||||
\(572\) | −0.811031 | −0.0339109 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.14849 | 0.0895982 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.7415 | −1.44631 | −0.723154 | − | 0.690687i | \(-0.757308\pi\) | ||||
−0.723154 | + | 0.690687i | \(0.757308\pi\) | |||||||
\(578\) | 1.27914 | 0.0532053 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.26696 | −0.0526076 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.4983 | 0.600458 | ||||||||
\(584\) | −9.03201 | −0.373747 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.3593 | 1.00627 | ||||||||
\(587\) | −22.8463 | −0.942967 | −0.471483 | − | 0.881875i | \(-0.656281\pi\) | ||||
−0.471483 | + | 0.881875i | \(0.656281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −72.6320 | −2.99275 | ||||||||
\(590\) | 7.48143 | 0.308006 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.39476 | 0.386122 | ||||||||
\(593\) | 17.5935 | 0.722480 | 0.361240 | − | 0.932473i | \(-0.382354\pi\) | ||||
0.361240 | + | 0.932473i | \(0.382354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.02433 | −0.164843 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.793891 | 0.0324646 | ||||||||
\(599\) | −31.0073 | −1.26692 | −0.633461 | − | 0.773774i | \(-0.718366\pi\) | ||||
−0.633461 | + | 0.773774i | \(0.718366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43754 | 0.0586385 | 0.0293193 | − | 0.999570i | \(-0.490666\pi\) | ||||
0.0293193 | + | 0.999570i | \(0.490666\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0747591 | 0.00304191 | ||||||||
\(605\) | 19.8898 | 0.808635 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.0171 | 1.34012 | 0.670061 | − | 0.742306i | \(-0.266268\pi\) | ||||
0.670061 | + | 0.742306i | \(0.266268\pi\) | |||||||
\(608\) | 15.4333 | 0.625901 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.81953 | −0.357092 | ||||||||
\(611\) | −10.5457 | −0.426633 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.1657 | −1.74345 | −0.871723 | − | 0.489999i | \(-0.836997\pi\) | ||||
−0.871723 | + | 0.489999i | \(0.836997\pi\) | |||||||
\(614\) | −4.52808 | −0.182738 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.45772 | −0.0989441 | −0.0494721 | − | 0.998776i | \(-0.515754\pi\) | ||||
−0.0494721 | + | 0.998776i | \(0.515754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.7789 | −1.51846 | −0.759231 | − | 0.650822i | \(-0.774425\pi\) | ||||
−0.759231 | + | 0.650822i | \(0.774425\pi\) | |||||||
\(620\) | 12.0591 | 0.484305 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.1602 | 1.20932 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3942 | −1.21577 | ||||||||
\(626\) | −22.8839 | −0.914625 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.80741 | −0.191837 | ||||||||
\(629\) | −12.3374 | −0.491922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.4828 | −1.13388 | −0.566942 | − | 0.823758i | \(-0.691874\pi\) | ||||
−0.566942 | + | 0.823758i | \(0.691874\pi\) | |||||||
\(632\) | −26.5932 | −1.05782 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −34.8652 | −1.38467 | ||||||||
\(635\) | −15.0396 | −0.596829 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.82509 | −0.111847 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.8091 | 0.783024 | ||||||||
\(641\) | 27.1922 | 1.07403 | 0.537014 | − | 0.843573i | \(-0.319552\pi\) | ||||
0.537014 | + | 0.843573i | \(0.319552\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.1664 | 1.46570 | 0.732849 | − | 0.680391i | \(-0.238190\pi\) | ||||
0.732849 | + | 0.680391i | \(0.238190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35.2334 | 1.38624 | ||||||||
\(647\) | 18.8319 | 0.740357 | 0.370178 | − | 0.928961i | \(-0.379297\pi\) | ||||
0.370178 | + | 0.928961i | \(0.379297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.14759 | −0.162807 | ||||||||
\(650\) | 4.33482 | 0.170026 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.93910 | −0.232593 | ||||||||
\(653\) | 26.0185 | 1.01818 | 0.509090 | − | 0.860713i | \(-0.329982\pi\) | ||||
0.509090 | + | 0.860713i | \(0.329982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.6709 | −1.19841 | ||||||||
\(656\) | 1.58687 | 0.0619569 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3339 | 1.29851 | 0.649253 | − | 0.760573i | \(-0.275082\pi\) | ||||
0.649253 | + | 0.760573i | \(0.275082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.29841 | −0.244980 | −0.122490 | − | 0.992470i | \(-0.539088\pi\) | ||||
−0.122490 | + | 0.992470i | \(0.539088\pi\) | |||||||
\(662\) | 23.0105 | 0.894329 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 38.8626 | 1.50816 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.687538 | −0.0266216 | ||||||||
\(668\) | −2.01373 | −0.0779136 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 53.9799 | 2.08542 | ||||||||
\(671\) | 4.88941 | 0.188754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.3188 | 0.706137 | 0.353068 | − | 0.935598i | \(-0.385138\pi\) | ||||
0.353068 | + | 0.935598i | \(0.385138\pi\) | |||||||
\(674\) | 21.6901 | 0.835473 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.398235 | −0.0153167 | ||||||||
\(677\) | 24.3392 | 0.935430 | 0.467715 | − | 0.883879i | \(-0.345077\pi\) | ||||
0.467715 | + | 0.883879i | \(0.345077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −35.2284 | −1.35095 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26.8896 | 1.02966 | ||||||||
\(683\) | −11.7682 | −0.450297 | −0.225149 | − | 0.974324i | \(-0.572287\pi\) | ||||
−0.225149 | + | 0.974324i | \(0.572287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.0434 | −0.651195 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00186 | −0.0381955 | ||||||||
\(689\) | 7.11900 | 0.271212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.17785 | −0.0448074 | −0.0224037 | − | 0.999749i | \(-0.507132\pi\) | ||||
−0.0224037 | + | 0.999749i | \(0.507132\pi\) | |||||||
\(692\) | 0.237195 | 0.00901679 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.1835 | 1.06983 | ||||||||
\(695\) | −11.6104 | −0.440408 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.08390 | −0.0789335 | ||||||||
\(698\) | 25.2321 | 0.955050 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.2867 | 1.18168 | 0.590841 | − | 0.806788i | \(-0.298796\pi\) | ||||
0.590841 | + | 0.806788i | \(0.298796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.4806 | 0.810158 | ||||||||
\(704\) | −18.1161 | −0.682776 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.0016 | −1.09149 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.3748 | 0.577411 | 0.288706 | − | 0.957418i | \(-0.406775\pi\) | ||||
0.288706 | + | 0.957418i | \(0.406775\pi\) | |||||||
\(710\) | −13.2300 | −0.496512 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.13739 | −0.304962 | ||||||||
\(713\) | 6.54409 | 0.245078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.91133 | −0.221071 | ||||||||
\(716\) | 3.21640 | 0.120203 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.4643 | 1.28620 | ||||||||
\(719\) | −11.1417 | −0.415517 | −0.207759 | − | 0.978180i | \(-0.566617\pi\) | ||||
−0.207759 | + | 0.978180i | \(0.566617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −37.2985 | −1.38811 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.753956 | 0.0280206 | ||||||||
\(725\) | −3.75411 | −0.139424 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.24735 | 0.231702 | 0.115851 | − | 0.993267i | \(-0.463041\pi\) | ||||
0.115851 | + | 0.993267i | \(0.463041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.9315 | −0.404593 | ||||||||
\(731\) | 1.31566 | 0.0486613 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.9669 | −1.14379 | −0.571894 | − | 0.820327i | \(-0.693791\pi\) | ||||
−0.571894 | + | 0.820327i | \(0.693791\pi\) | |||||||
\(734\) | −13.7400 | −0.507153 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.39053 | −0.0512554 | ||||||||
\(737\) | −29.9256 | −1.10232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.33744 | 0.0859843 | 0.0429921 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429921 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(740\) | −3.56643 | −0.131105 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.3612 | −0.893726 | −0.446863 | − | 0.894603i | \(-0.647459\pi\) | ||||
−0.446863 | + | 0.894603i | \(0.647459\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.3320 | −1.07464 | ||||||||
\(746\) | 3.00132 | 0.109886 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.24304 | 0.118577 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0253 | −0.438810 | −0.219405 | − | 0.975634i | \(-0.570412\pi\) | ||||
−0.219405 | + | 0.975634i | \(0.570412\pi\) | |||||||
\(752\) | −32.1110 | −1.17097 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.38719 | −0.0505184 | ||||||||
\(755\) | 0.544894 | 0.0198307 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.9905 | 0.944641 | 0.472321 | − | 0.881427i | \(-0.343416\pi\) | ||||
0.472321 | + | 0.881427i | \(0.343416\pi\) | |||||||
\(758\) | 36.9807 | 1.34320 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 61.3364 | 2.22491 | ||||||||
\(761\) | 13.3270 | 0.483103 | 0.241552 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241552 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.47416 | 0.0533334 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.88029 | 0.140200 | ||||||||
\(767\) | −2.03656 | −0.0735361 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.24486 | −0.333378 | −0.166689 | − | 0.986010i | \(-0.553308\pi\) | ||||
−0.166689 | + | 0.986010i | \(0.553308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.41101 | −0.194746 | ||||||||
\(773\) | −10.1419 | −0.364780 | −0.182390 | − | 0.983226i | \(-0.558383\pi\) | ||||
−0.182390 | + | 0.983226i | \(0.558383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.7322 | 1.28354 | ||||||||
\(776\) | 7.06912 | 0.253766 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.1092 | 1.25873 | ||||||||
\(779\) | 3.62830 | 0.129997 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.33450 | 0.262449 | ||||||||
\(782\) | −3.17450 | −0.113520 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −35.0396 | −1.25062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.2823 | −1.61414 | −0.807070 | − | 0.590456i | \(-0.798948\pi\) | ||||
−0.807070 | + | 0.590456i | \(0.798948\pi\) | |||||||
\(788\) | −3.86391 | −0.137646 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.1859 | −1.14512 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.40081 | 0.0852554 | ||||||||
\(794\) | 21.8079 | 0.773935 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.4624 | 0.370831 | ||||||||
\(797\) | 27.0784 | 0.959165 | 0.479583 | − | 0.877497i | \(-0.340788\pi\) | ||||
0.479583 | + | 0.877497i | \(0.340788\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.1686 | 1.49182 | ||||||||
\(800\) | −7.59257 | −0.268438 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.0648 | 0.743825 | ||||||||
\(803\) | 6.06026 | 0.213862 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.2034 | 0.465071 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.41091 | 0.155175 | ||||||||
\(809\) | 25.7798 | 0.906370 | 0.453185 | − | 0.891417i | \(-0.350288\pi\) | ||||
0.453185 | + | 0.891417i | \(0.350288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.7829 | 0.905362 | 0.452681 | − | 0.891673i | \(-0.350468\pi\) | ||||
0.452681 | + | 0.891673i | \(0.350468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.95252 | −0.278736 | ||||||||
\(815\) | −43.2881 | −1.51632 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.29070 | −0.0801414 | ||||||||
\(818\) | −17.2550 | −0.603308 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.602407 | −0.0210370 | ||||||||
\(821\) | 1.71073 | 0.0597050 | 0.0298525 | − | 0.999554i | \(-0.490496\pi\) | ||||
0.0298525 | + | 0.999554i | \(0.490496\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.3773 | −1.40747 | −0.703733 | − | 0.710465i | \(-0.748485\pi\) | ||||
−0.703733 | + | 0.710465i | \(0.748485\pi\) | |||||||
\(824\) | 35.3158 | 1.23028 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.5698 | −0.680509 | −0.340254 | − | 0.940333i | \(-0.610513\pi\) | ||||
−0.340254 | + | 0.940333i | \(0.610513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.5742 | −1.44393 | −0.721966 | − | 0.691928i | \(-0.756761\pi\) | ||||
−0.721966 | + | 0.691928i | \(0.756761\pi\) | |||||||
\(830\) | 47.0357 | 1.63263 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.89542 | −0.308393 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6774 | −0.507932 | ||||||||
\(836\) | −5.64648 | −0.195288 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.7321 | 0.474367 | ||||||||
\(839\) | 45.8480 | 1.58285 | 0.791425 | − | 0.611266i | \(-0.209340\pi\) | ||||
0.791425 | + | 0.611266i | \(0.209340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7986 | −0.958574 | ||||||||
\(842\) | 12.6561 | 0.436157 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.99583 | −0.137542 | ||||||||
\(845\) | −2.90260 | −0.0998525 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 21.6769 | 0.744388 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.3335 | −0.594534 | ||||||||
\(851\) | −1.93539 | −0.0663443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.0236 | −1.37038 | −0.685191 | − | 0.728364i | \(-0.740281\pi\) | ||||
−0.685191 | + | 0.728364i | \(0.740281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −59.5692 | −2.03603 | ||||||||
\(857\) | 32.8702 | 1.12282 | 0.561412 | − | 0.827536i | \(-0.310258\pi\) | ||||
0.561412 | + | 0.827536i | \(0.310258\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.0503 | 1.16178 | 0.580891 | − | 0.813981i | \(-0.302704\pi\) | ||||
0.580891 | + | 0.813981i | \(0.302704\pi\) | |||||||
\(860\) | 0.380325 | 0.0129690 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.53079 | 0.0521388 | ||||||||
\(863\) | 14.0642 | 0.478749 | 0.239375 | − | 0.970927i | \(-0.423058\pi\) | ||||
0.239375 | + | 0.970927i | \(0.423058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.72883 | 0.0587820 | ||||||||
\(866\) | −7.04212 | −0.239301 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8434 | 0.605295 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6942 | −0.497893 | ||||||||
\(872\) | −3.35926 | −0.113759 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.52715 | 0.186959 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.0669 | 1.72441 | 0.862204 | − | 0.506562i | \(-0.169084\pi\) | ||||
0.862204 | + | 0.506562i | \(0.169084\pi\) | |||||||
\(878\) | −24.9568 | −0.842251 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −17.9996 | −0.606768 | ||||||||
\(881\) | −18.4203 | −0.620597 | −0.310298 | − | 0.950639i | \(-0.600429\pi\) | ||||
−0.310298 | + | 0.950639i | \(0.600429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.126678 | 0.00426305 | 0.00213153 | − | 0.999998i | \(-0.499322\pi\) | ||||
0.00213153 | + | 0.999998i | \(0.499322\pi\) | |||||||
\(884\) | 1.59241 | 0.0535585 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.1357 | 0.945239 | ||||||||
\(887\) | 3.87470 | 0.130100 | 0.0650498 | − | 0.997882i | \(-0.479279\pi\) | ||||
0.0650498 | + | 0.997882i | \(0.479279\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.84874 | −0.330131 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.96757 | 0.233291 | ||||||||
\(893\) | −73.4201 | −2.45691 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.4433 | 0.783622 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.3605 | 0.779549 | ||||||||
\(899\) | −11.4347 | −0.381367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.4665 | −0.948356 | ||||||||
\(902\) | −1.34326 | −0.0447257 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.32680 | 0.110648 | ||||||||
\(905\) | 5.49533 | 0.182671 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.7741 | −1.55311 | −0.776555 | − | 0.630050i | \(-0.783035\pi\) | ||||
−0.776555 | + | 0.630050i | \(0.783035\pi\) | |||||||
\(908\) | 3.78973 | 0.125766 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.93675 | −0.196693 | −0.0983467 | − | 0.995152i | \(-0.531355\pi\) | ||||
−0.0983467 | + | 0.995152i | \(0.531355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.0759 | −0.862986 | ||||||||
\(914\) | 37.9454 | 1.25512 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.40952 | 0.277858 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.58701 | −0.283259 | −0.141630 | − | 0.989920i | \(-0.545234\pi\) | ||||
−0.141630 | + | 0.989920i | \(0.545234\pi\) | |||||||
\(920\) | −5.52637 | −0.182199 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.8922 | −1.21498 | ||||||||
\(923\) | 3.60141 | 0.118542 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5677 | −0.347463 | ||||||||
\(926\) | −1.97309 | −0.0648396 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.42970 | 0.0797589 | ||||||||
\(929\) | −8.45945 | −0.277546 | −0.138773 | − | 0.990324i | \(-0.544316\pi\) | ||||
−0.138773 | + | 0.990324i | \(0.544316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.64648 | 0.184957 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.7228 | −0.514466 | ||||||||
\(935\) | 23.6374 | 0.773026 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.3596 | 1.08981 | 0.544905 | − | 0.838498i | \(-0.316566\pi\) | ||||
0.544905 | + | 0.838498i | \(0.316566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.1899 | 0.397592 | ||||||||
\(941\) | −13.4037 | −0.436949 | −0.218475 | − | 0.975843i | \(-0.570108\pi\) | ||||
−0.218475 | + | 0.975843i | \(0.570108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.326907 | −0.0106456 | ||||||||
\(944\) | −6.20121 | −0.201832 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.848057 | 0.0275727 | ||||||||
\(947\) | −43.0794 | −1.39989 | −0.699946 | − | 0.714196i | \(-0.746793\pi\) | ||||
−0.699946 | + | 0.714196i | \(0.746793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.97573 | 0.0965962 | ||||||||
\(950\) | 30.1794 | 0.979150 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.7332 | −0.542040 | −0.271020 | − | 0.962574i | \(-0.587361\pi\) | ||||
−0.271020 | + | 0.962574i | \(0.587361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.7447 | 0.347690 | ||||||||
\(956\) | −6.58182 | −0.212871 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45.6325 | −1.47432 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 77.8366 | 2.51086 | ||||||||
\(962\) | −3.90487 | −0.125898 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.45144 | −0.175579 | ||||||||
\(965\) | −39.4390 | −1.26959 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.7594 | 1.43937 | 0.719683 | − | 0.694303i | \(-0.244287\pi\) | ||||
0.719683 | + | 0.694303i | \(0.244287\pi\) | |||||||
\(968\) | −20.7986 | −0.668493 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.55580 | 0.274710 | ||||||||
\(971\) | −4.20259 | −0.134867 | −0.0674337 | − | 0.997724i | \(-0.521481\pi\) | ||||
−0.0674337 | + | 0.997724i | \(0.521481\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.23899 | −0.296036 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.31033 | 0.233998 | ||||||||
\(977\) | 25.6899 | 0.821892 | 0.410946 | − | 0.911660i | \(-0.365199\pi\) | ||||
0.410946 | + | 0.911660i | \(0.365199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.45999 | 0.174502 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.68483 | 0.181410 | ||||||||
\(983\) | −31.8244 | −1.01504 | −0.507520 | − | 0.861640i | \(-0.669438\pi\) | ||||
−0.507520 | + | 0.861640i | \(0.669438\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.1627 | −0.897339 | ||||||||
\(986\) | 5.54689 | 0.176649 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.77255 | −0.0882067 | ||||||||
\(989\) | 0.206390 | 0.00656283 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.47478 | 0.300976 | 0.150488 | − | 0.988612i | \(-0.451915\pi\) | ||||
0.150488 | + | 0.988612i | \(0.451915\pi\) | |||||||
\(992\) | −23.1262 | −0.734259 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 76.2570 | 2.41751 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.9511 | −0.695198 | −0.347599 | − | 0.937643i | \(-0.613003\pi\) | ||||
−0.347599 | + | 0.937643i | \(0.613003\pi\) | |||||||
\(998\) | −14.3866 | −0.455401 | ||||||||
\(999\) | 0 | 0 |
(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 | 5733.2.a.bm.1.3 | 5 | ||
3.2 | odd | 2 | 637.2.a.k.1.3 | 5 | |||
7.3 | odd | 6 | 819.2.j.h.352.3 | 10 | |||
7.5 | odd | 6 | 819.2.j.h.235.3 | 10 | |||
7.6 | odd | 2 | 5733.2.a.bl.1.3 | 5 | |||
21.2 | odd | 6 | 637.2.e.m.508.3 | 10 | |||
21.5 | even | 6 | 91.2.e.c.53.3 | ✓ | 10 | ||
21.11 | odd | 6 | 637.2.e.m.79.3 | 10 | |||
21.17 | even | 6 | 91.2.e.c.79.3 | yes | 10 | ||
21.20 | even | 2 | 637.2.a.l.1.3 | 5 | |||
39.38 | odd | 2 | 8281.2.a.bx.1.3 | 5 | |||
84.47 | odd | 6 | 1456.2.r.p.417.1 | 10 | |||
84.59 | odd | 6 | 1456.2.r.p.625.1 | 10 | |||
273.38 | even | 6 | 1183.2.e.f.170.3 | 10 | |||
273.194 | even | 6 | 1183.2.e.f.508.3 | 10 | |||
273.272 | even | 2 | 8281.2.a.bw.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.3 | ✓ | 10 | 21.5 | even | 6 | ||
91.2.e.c.79.3 | yes | 10 | 21.17 | even | 6 | ||
637.2.a.k.1.3 | 5 | 3.2 | odd | 2 | |||
637.2.a.l.1.3 | 5 | 21.20 | even | 2 | |||
637.2.e.m.79.3 | 10 | 21.11 | odd | 6 | |||
637.2.e.m.508.3 | 10 | 21.2 | odd | 6 | |||
819.2.j.h.235.3 | 10 | 7.5 | odd | 6 | |||
819.2.j.h.352.3 | 10 | 7.3 | odd | 6 | |||
1183.2.e.f.170.3 | 10 | 273.38 | even | 6 | |||
1183.2.e.f.508.3 | 10 | 273.194 | even | 6 | |||
1456.2.r.p.417.1 | 10 | 84.47 | odd | 6 | |||
1456.2.r.p.625.1 | 10 | 84.59 | odd | 6 | |||
5733.2.a.bl.1.3 | 5 | 7.6 | odd | 2 | |||
5733.2.a.bm.1.3 | 5 | 1.1 | even | 1 | trivial | ||
8281.2.a.bw.1.3 | 5 | 273.272 | even | 2 | |||
8281.2.a.bx.1.3 | 5 | 39.38 | odd | 2 |