Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5577,2,Mod(1,5577)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, 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("5577.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5577 = 3 \cdot 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5577.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(44.5325692073\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.42819\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5577.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.42819 | 1.00989 | 0.504943 | − | 0.863153i | \(-0.331514\pi\) | ||||
0.504943 | + | 0.863153i | \(0.331514\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.0397381 | 0.0198691 | ||||||||
\(5\) | 0.0606573 | 0.0271268 | 0.0135634 | − | 0.999908i | \(-0.495683\pi\) | ||||
0.0135634 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(6\) | 1.42819 | 0.583058 | ||||||||
\(7\) | −1.70646 | −0.644980 | −0.322490 | − | 0.946573i | \(-0.604520\pi\) | ||||
−0.322490 | + | 0.946573i | \(0.604520\pi\) | |||||||
\(8\) | −2.79963 | −0.989820 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.0866304 | 0.0273949 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.0397381 | 0.0114714 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.43715 | −0.651356 | ||||||||
\(15\) | 0.0606573 | 0.0156616 | ||||||||
\(16\) | −4.07790 | −1.01947 | ||||||||
\(17\) | 3.75599 | 0.910962 | 0.455481 | − | 0.890246i | \(-0.349467\pi\) | ||||
0.455481 | + | 0.890246i | \(0.349467\pi\) | |||||||
\(18\) | 1.42819 | 0.336629 | ||||||||
\(19\) | 2.02597 | 0.464790 | 0.232395 | − | 0.972621i | \(-0.425344\pi\) | ||||
0.232395 | + | 0.972621i | \(0.425344\pi\) | |||||||
\(20\) | 0.00241041 | 0.000538983 0 | ||||||||
\(21\) | −1.70646 | −0.372379 | ||||||||
\(22\) | 1.42819 | 0.304492 | ||||||||
\(23\) | 0.704722 | 0.146945 | 0.0734723 | − | 0.997297i | \(-0.476592\pi\) | ||||
0.0734723 | + | 0.997297i | \(0.476592\pi\) | |||||||
\(24\) | −2.79963 | −0.571473 | ||||||||
\(25\) | −4.99632 | −0.999264 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.0678114 | −0.0128151 | ||||||||
\(29\) | −0.0346842 | −0.00644069 | −0.00322035 | − | 0.999995i | \(-0.501025\pi\) | ||||
−0.00322035 | + | 0.999995i | \(0.501025\pi\) | |||||||
\(30\) | 0.0866304 | 0.0158165 | ||||||||
\(31\) | 1.85987 | 0.334042 | 0.167021 | − | 0.985953i | \(-0.446585\pi\) | ||||
0.167021 | + | 0.985953i | \(0.446585\pi\) | |||||||
\(32\) | −0.224760 | −0.0397323 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 5.36429 | 0.919967 | ||||||||
\(35\) | −0.103509 | −0.0174962 | ||||||||
\(36\) | 0.0397381 | 0.00662302 | ||||||||
\(37\) | 8.82674 | 1.45111 | 0.725553 | − | 0.688166i | \(-0.241584\pi\) | ||||
0.725553 | + | 0.688166i | \(0.241584\pi\) | |||||||
\(38\) | 2.89348 | 0.469385 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.169818 | −0.0268506 | ||||||||
\(41\) | 3.32960 | 0.519996 | 0.259998 | − | 0.965609i | \(-0.416278\pi\) | ||||
0.259998 | + | 0.965609i | \(0.416278\pi\) | |||||||
\(42\) | −2.43715 | −0.376061 | ||||||||
\(43\) | 5.29022 | 0.806751 | 0.403376 | − | 0.915035i | \(-0.367837\pi\) | ||||
0.403376 | + | 0.915035i | \(0.367837\pi\) | |||||||
\(44\) | 0.0397381 | 0.00599075 | ||||||||
\(45\) | 0.0606573 | 0.00904225 | ||||||||
\(46\) | 1.00648 | 0.148397 | ||||||||
\(47\) | 6.04622 | 0.881931 | 0.440966 | − | 0.897524i | \(-0.354636\pi\) | ||||
0.440966 | + | 0.897524i | \(0.354636\pi\) | |||||||
\(48\) | −4.07790 | −0.588594 | ||||||||
\(49\) | −4.08800 | −0.584001 | ||||||||
\(50\) | −7.13572 | −1.00914 | ||||||||
\(51\) | 3.75599 | 0.525944 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.6694 | −1.46555 | −0.732775 | − | 0.680471i | \(-0.761775\pi\) | ||||
−0.732775 | + | 0.680471i | \(0.761775\pi\) | |||||||
\(54\) | 1.42819 | 0.194353 | ||||||||
\(55\) | 0.0606573 | 0.00817903 | ||||||||
\(56\) | 4.77746 | 0.638414 | ||||||||
\(57\) | 2.02597 | 0.268347 | ||||||||
\(58\) | −0.0495358 | −0.00650436 | ||||||||
\(59\) | 3.34547 | 0.435543 | 0.217771 | − | 0.976000i | \(-0.430121\pi\) | ||||
0.217771 | + | 0.976000i | \(0.430121\pi\) | |||||||
\(60\) | 0.00241041 | 0.000311182 0 | ||||||||
\(61\) | 3.26757 | 0.418369 | 0.209185 | − | 0.977876i | \(-0.432919\pi\) | ||||
0.209185 | + | 0.977876i | \(0.432919\pi\) | |||||||
\(62\) | 2.65625 | 0.337344 | ||||||||
\(63\) | −1.70646 | −0.214993 | ||||||||
\(64\) | 7.83479 | 0.979349 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.42819 | 0.175799 | ||||||||
\(67\) | −10.9701 | −1.34021 | −0.670103 | − | 0.742268i | \(-0.733750\pi\) | ||||
−0.670103 | + | 0.742268i | \(0.733750\pi\) | |||||||
\(68\) | 0.149256 | 0.0181000 | ||||||||
\(69\) | 0.704722 | 0.0848385 | ||||||||
\(70\) | −0.147831 | −0.0176692 | ||||||||
\(71\) | 1.96928 | 0.233711 | 0.116855 | − | 0.993149i | \(-0.462719\pi\) | ||||
0.116855 | + | 0.993149i | \(0.462719\pi\) | |||||||
\(72\) | −2.79963 | −0.329940 | ||||||||
\(73\) | 15.3057 | 1.79140 | 0.895700 | − | 0.444659i | \(-0.146675\pi\) | ||||
0.895700 | + | 0.444659i | \(0.146675\pi\) | |||||||
\(74\) | 12.6063 | 1.46545 | ||||||||
\(75\) | −4.99632 | −0.576925 | ||||||||
\(76\) | 0.0805084 | 0.00923494 | ||||||||
\(77\) | −1.70646 | −0.194469 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5938 | 1.19190 | 0.595951 | − | 0.803021i | \(-0.296775\pi\) | ||||
0.595951 | + | 0.803021i | \(0.296775\pi\) | |||||||
\(80\) | −0.247354 | −0.0276550 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.75532 | 0.525137 | ||||||||
\(83\) | 4.19820 | 0.460812 | 0.230406 | − | 0.973095i | \(-0.425994\pi\) | ||||
0.230406 | + | 0.973095i | \(0.425994\pi\) | |||||||
\(84\) | −0.0678114 | −0.00739883 | ||||||||
\(85\) | 0.227828 | 0.0247114 | ||||||||
\(86\) | 7.55546 | 0.814726 | ||||||||
\(87\) | −0.0346842 | −0.00371854 | ||||||||
\(88\) | −2.79963 | −0.298442 | ||||||||
\(89\) | 14.3643 | 1.52261 | 0.761305 | − | 0.648393i | \(-0.224559\pi\) | ||||
0.761305 | + | 0.648393i | \(0.224559\pi\) | |||||||
\(90\) | 0.0866304 | 0.00913164 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.0280043 | 0.00291965 | ||||||||
\(93\) | 1.85987 | 0.192859 | ||||||||
\(94\) | 8.63517 | 0.890650 | ||||||||
\(95\) | 0.122890 | 0.0126082 | ||||||||
\(96\) | −0.224760 | −0.0229394 | ||||||||
\(97\) | 5.86228 | 0.595224 | 0.297612 | − | 0.954687i | \(-0.403810\pi\) | ||||
0.297612 | + | 0.954687i | \(0.403810\pi\) | |||||||
\(98\) | −5.83846 | −0.589774 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −0.198544 | −0.0198544 | ||||||||
\(101\) | −12.3706 | −1.23092 | −0.615460 | − | 0.788168i | \(-0.711030\pi\) | ||||
−0.615460 | + | 0.788168i | \(0.711030\pi\) | |||||||
\(102\) | 5.36429 | 0.531143 | ||||||||
\(103\) | 10.0788 | 0.993094 | 0.496547 | − | 0.868010i | \(-0.334601\pi\) | ||||
0.496547 | + | 0.868010i | \(0.334601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.103509 | −0.0101014 | ||||||||
\(106\) | −15.2379 | −1.48004 | ||||||||
\(107\) | 6.17793 | 0.597243 | 0.298622 | − | 0.954372i | \(-0.403473\pi\) | ||||
0.298622 | + | 0.954372i | \(0.403473\pi\) | |||||||
\(108\) | 0.0397381 | 0.00382380 | ||||||||
\(109\) | 4.64928 | 0.445320 | 0.222660 | − | 0.974896i | \(-0.428526\pi\) | ||||
0.222660 | + | 0.974896i | \(0.428526\pi\) | |||||||
\(110\) | 0.0866304 | 0.00825988 | ||||||||
\(111\) | 8.82674 | 0.837797 | ||||||||
\(112\) | 6.95876 | 0.657541 | ||||||||
\(113\) | 8.99146 | 0.845846 | 0.422923 | − | 0.906166i | \(-0.361004\pi\) | ||||
0.422923 | + | 0.906166i | \(0.361004\pi\) | |||||||
\(114\) | 2.89348 | 0.270999 | ||||||||
\(115\) | 0.0427465 | 0.00398613 | ||||||||
\(116\) | −0.00137828 | −0.000127971 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.77798 | 0.439848 | ||||||||
\(119\) | −6.40944 | −0.587552 | ||||||||
\(120\) | −0.169818 | −0.0155022 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.66672 | 0.422505 | ||||||||
\(123\) | 3.32960 | 0.300220 | ||||||||
\(124\) | 0.0739076 | 0.00663710 | ||||||||
\(125\) | −0.606350 | −0.0542336 | ||||||||
\(126\) | −2.43715 | −0.217119 | ||||||||
\(127\) | 1.74493 | 0.154837 | 0.0774187 | − | 0.996999i | \(-0.475332\pi\) | ||||
0.0774187 | + | 0.996999i | \(0.475332\pi\) | |||||||
\(128\) | 11.6391 | 1.02876 | ||||||||
\(129\) | 5.29022 | 0.465778 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8961 | −1.21411 | −0.607054 | − | 0.794661i | \(-0.707649\pi\) | ||||
−0.607054 | + | 0.794661i | \(0.707649\pi\) | |||||||
\(132\) | 0.0397381 | 0.00345876 | ||||||||
\(133\) | −3.45724 | −0.299780 | ||||||||
\(134\) | −15.6674 | −1.35345 | ||||||||
\(135\) | 0.0606573 | 0.00522055 | ||||||||
\(136\) | −10.5154 | −0.901689 | ||||||||
\(137\) | 3.08818 | 0.263841 | 0.131921 | − | 0.991260i | \(-0.457886\pi\) | ||||
0.131921 | + | 0.991260i | \(0.457886\pi\) | |||||||
\(138\) | 1.00648 | 0.0856772 | ||||||||
\(139\) | 1.92887 | 0.163605 | 0.0818023 | − | 0.996649i | \(-0.473932\pi\) | ||||
0.0818023 | + | 0.996649i | \(0.473932\pi\) | |||||||
\(140\) | −0.00411325 | −0.000347633 0 | ||||||||
\(141\) | 6.04622 | 0.509183 | ||||||||
\(142\) | 2.81252 | 0.236021 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.07790 | −0.339825 | ||||||||
\(145\) | −0.00210385 | −0.000174715 0 | ||||||||
\(146\) | 21.8595 | 1.80911 | ||||||||
\(147\) | −4.08800 | −0.337173 | ||||||||
\(148\) | 0.350758 | 0.0288321 | ||||||||
\(149\) | 9.05192 | 0.741563 | 0.370781 | − | 0.928720i | \(-0.379090\pi\) | ||||
0.370781 | + | 0.928720i | \(0.379090\pi\) | |||||||
\(150\) | −7.13572 | −0.582629 | ||||||||
\(151\) | 2.44462 | 0.198940 | 0.0994702 | − | 0.995041i | \(-0.468285\pi\) | ||||
0.0994702 | + | 0.995041i | \(0.468285\pi\) | |||||||
\(152\) | −5.67198 | −0.460059 | ||||||||
\(153\) | 3.75599 | 0.303654 | ||||||||
\(154\) | −2.43715 | −0.196391 | ||||||||
\(155\) | 0.112814 | 0.00906147 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.42793 | −0.672622 | −0.336311 | − | 0.941751i | \(-0.609179\pi\) | ||||
−0.336311 | + | 0.941751i | \(0.609179\pi\) | |||||||
\(158\) | 15.1301 | 1.20368 | ||||||||
\(159\) | −10.6694 | −0.846135 | ||||||||
\(160\) | −0.0136333 | −0.00107781 | ||||||||
\(161\) | −1.20258 | −0.0947763 | ||||||||
\(162\) | 1.42819 | 0.112210 | ||||||||
\(163\) | −17.3969 | −1.36263 | −0.681316 | − | 0.731990i | \(-0.738592\pi\) | ||||
−0.681316 | + | 0.731990i | \(0.738592\pi\) | |||||||
\(164\) | 0.132312 | 0.0103318 | ||||||||
\(165\) | 0.0606573 | 0.00472216 | ||||||||
\(166\) | 5.99585 | 0.465368 | ||||||||
\(167\) | 1.05104 | 0.0813320 | 0.0406660 | − | 0.999173i | \(-0.487052\pi\) | ||||
0.0406660 | + | 0.999173i | \(0.487052\pi\) | |||||||
\(168\) | 4.77746 | 0.368589 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.325383 | 0.0249557 | ||||||||
\(171\) | 2.02597 | 0.154930 | ||||||||
\(172\) | 0.210223 | 0.0160294 | ||||||||
\(173\) | 18.6654 | 1.41910 | 0.709552 | − | 0.704653i | \(-0.248897\pi\) | ||||
0.709552 | + | 0.704653i | \(0.248897\pi\) | |||||||
\(174\) | −0.0495358 | −0.00375530 | ||||||||
\(175\) | 8.52601 | 0.644505 | ||||||||
\(176\) | −4.07790 | −0.307383 | ||||||||
\(177\) | 3.34547 | 0.251461 | ||||||||
\(178\) | 20.5150 | 1.53766 | ||||||||
\(179\) | −24.2443 | −1.81210 | −0.906051 | − | 0.423168i | \(-0.860918\pi\) | ||||
−0.906051 | + | 0.423168i | \(0.860918\pi\) | |||||||
\(180\) | 0.00241041 | 0.000179661 0 | ||||||||
\(181\) | 20.9251 | 1.55535 | 0.777675 | − | 0.628666i | \(-0.216399\pi\) | ||||
0.777675 | + | 0.628666i | \(0.216399\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.26757 | 0.241545 | ||||||||
\(184\) | −1.97296 | −0.145449 | ||||||||
\(185\) | 0.535406 | 0.0393638 | ||||||||
\(186\) | 2.65625 | 0.194766 | ||||||||
\(187\) | 3.75599 | 0.274665 | ||||||||
\(188\) | 0.240265 | 0.0175231 | ||||||||
\(189\) | −1.70646 | −0.124126 | ||||||||
\(190\) | 0.175511 | 0.0127329 | ||||||||
\(191\) | 2.77108 | 0.200508 | 0.100254 | − | 0.994962i | \(-0.468034\pi\) | ||||
0.100254 | + | 0.994962i | \(0.468034\pi\) | |||||||
\(192\) | 7.83479 | 0.565428 | ||||||||
\(193\) | −8.50742 | −0.612378 | −0.306189 | − | 0.951971i | \(-0.599054\pi\) | ||||
−0.306189 | + | 0.951971i | \(0.599054\pi\) | |||||||
\(194\) | 8.37247 | 0.601108 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.162450 | −0.0116035 | ||||||||
\(197\) | −14.4278 | −1.02794 | −0.513968 | − | 0.857810i | \(-0.671825\pi\) | ||||
−0.513968 | + | 0.857810i | \(0.671825\pi\) | |||||||
\(198\) | 1.42819 | 0.101497 | ||||||||
\(199\) | 15.9351 | 1.12961 | 0.564806 | − | 0.825224i | \(-0.308951\pi\) | ||||
0.564806 | + | 0.825224i | \(0.308951\pi\) | |||||||
\(200\) | 13.9879 | 0.989092 | ||||||||
\(201\) | −10.9701 | −0.773768 | ||||||||
\(202\) | −17.6676 | −1.24309 | ||||||||
\(203\) | 0.0591871 | 0.00415412 | ||||||||
\(204\) | 0.149256 | 0.0104500 | ||||||||
\(205\) | 0.201965 | 0.0141058 | ||||||||
\(206\) | 14.3945 | 1.00291 | ||||||||
\(207\) | 0.704722 | 0.0489815 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.02597 | 0.140139 | ||||||||
\(210\) | −0.147831 | −0.0102013 | ||||||||
\(211\) | −16.6404 | −1.14557 | −0.572786 | − | 0.819705i | \(-0.694138\pi\) | ||||
−0.572786 | + | 0.819705i | \(0.694138\pi\) | |||||||
\(212\) | −0.423980 | −0.0291191 | ||||||||
\(213\) | 1.96928 | 0.134933 | ||||||||
\(214\) | 8.82329 | 0.603147 | ||||||||
\(215\) | 0.320890 | 0.0218845 | ||||||||
\(216\) | −2.79963 | −0.190491 | ||||||||
\(217\) | −3.17378 | −0.215450 | ||||||||
\(218\) | 6.64007 | 0.449722 | ||||||||
\(219\) | 15.3057 | 1.03427 | ||||||||
\(220\) | 0.00241041 | 0.000162510 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 12.6063 | 0.846079 | ||||||||
\(223\) | 29.6492 | 1.98546 | 0.992729 | − | 0.120372i | \(-0.0384088\pi\) | ||||
0.992729 | + | 0.120372i | \(0.0384088\pi\) | |||||||
\(224\) | 0.383543 | 0.0256265 | ||||||||
\(225\) | −4.99632 | −0.333088 | ||||||||
\(226\) | 12.8416 | 0.854208 | ||||||||
\(227\) | −2.17847 | −0.144590 | −0.0722951 | − | 0.997383i | \(-0.523032\pi\) | ||||
−0.0722951 | + | 0.997383i | \(0.523032\pi\) | |||||||
\(228\) | 0.0805084 | 0.00533180 | ||||||||
\(229\) | −2.89071 | −0.191024 | −0.0955118 | − | 0.995428i | \(-0.530449\pi\) | ||||
−0.0955118 | + | 0.995428i | \(0.530449\pi\) | |||||||
\(230\) | 0.0610503 | 0.00402554 | ||||||||
\(231\) | −1.70646 | −0.112277 | ||||||||
\(232\) | 0.0971031 | 0.00637513 | ||||||||
\(233\) | 8.88961 | 0.582377 | 0.291189 | − | 0.956666i | \(-0.405949\pi\) | ||||
0.291189 | + | 0.956666i | \(0.405949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.366747 | 0.0239239 | ||||||||
\(236\) | 0.132943 | 0.00865382 | ||||||||
\(237\) | 10.5938 | 0.688144 | ||||||||
\(238\) | −9.15392 | −0.593361 | ||||||||
\(239\) | 28.4940 | 1.84313 | 0.921563 | − | 0.388229i | \(-0.126913\pi\) | ||||
0.921563 | + | 0.388229i | \(0.126913\pi\) | |||||||
\(240\) | −0.247354 | −0.0159666 | ||||||||
\(241\) | −15.6266 | −1.00660 | −0.503299 | − | 0.864112i | \(-0.667881\pi\) | ||||
−0.503299 | + | 0.864112i | \(0.667881\pi\) | |||||||
\(242\) | 1.42819 | 0.0918078 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.129847 | 0.00831260 | ||||||||
\(245\) | −0.247967 | −0.0158420 | ||||||||
\(246\) | 4.75532 | 0.303188 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.20695 | −0.330641 | ||||||||
\(249\) | 4.19820 | 0.266050 | ||||||||
\(250\) | −0.865985 | −0.0547697 | ||||||||
\(251\) | 20.7286 | 1.30838 | 0.654189 | − | 0.756331i | \(-0.273010\pi\) | ||||
0.654189 | + | 0.756331i | \(0.273010\pi\) | |||||||
\(252\) | −0.0678114 | −0.00427172 | ||||||||
\(253\) | 0.704722 | 0.0443055 | ||||||||
\(254\) | 2.49210 | 0.156368 | ||||||||
\(255\) | 0.227828 | 0.0142672 | ||||||||
\(256\) | 0.953341 | 0.0595838 | ||||||||
\(257\) | −1.38511 | −0.0864008 | −0.0432004 | − | 0.999066i | \(-0.513755\pi\) | ||||
−0.0432004 | + | 0.999066i | \(0.513755\pi\) | |||||||
\(258\) | 7.55546 | 0.470383 | ||||||||
\(259\) | −15.0624 | −0.935935 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0346842 | −0.00214690 | ||||||||
\(262\) | −19.8463 | −1.22611 | ||||||||
\(263\) | −17.4668 | −1.07705 | −0.538524 | − | 0.842610i | \(-0.681018\pi\) | ||||
−0.538524 | + | 0.842610i | \(0.681018\pi\) | |||||||
\(264\) | −2.79963 | −0.172306 | ||||||||
\(265\) | −0.647174 | −0.0397556 | ||||||||
\(266\) | −4.93760 | −0.302744 | ||||||||
\(267\) | 14.3643 | 0.879080 | ||||||||
\(268\) | −0.435929 | −0.0266286 | ||||||||
\(269\) | 0.559556 | 0.0341167 | 0.0170584 | − | 0.999854i | \(-0.494570\pi\) | ||||
0.0170584 | + | 0.999854i | \(0.494570\pi\) | |||||||
\(270\) | 0.0866304 | 0.00527216 | ||||||||
\(271\) | −13.2324 | −0.803810 | −0.401905 | − | 0.915681i | \(-0.631652\pi\) | ||||
−0.401905 | + | 0.915681i | \(0.631652\pi\) | |||||||
\(272\) | −15.3166 | −0.928702 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.41053 | 0.266450 | ||||||||
\(275\) | −4.99632 | −0.301289 | ||||||||
\(276\) | 0.0280043 | 0.00168566 | ||||||||
\(277\) | −18.4921 | −1.11108 | −0.555541 | − | 0.831489i | \(-0.687489\pi\) | ||||
−0.555541 | + | 0.831489i | \(0.687489\pi\) | |||||||
\(278\) | 2.75480 | 0.165222 | ||||||||
\(279\) | 1.85987 | 0.111347 | ||||||||
\(280\) | 0.289787 | 0.0173181 | ||||||||
\(281\) | 25.8276 | 1.54075 | 0.770373 | − | 0.637593i | \(-0.220070\pi\) | ||||
0.770373 | + | 0.637593i | \(0.220070\pi\) | |||||||
\(282\) | 8.63517 | 0.514217 | ||||||||
\(283\) | 6.19965 | 0.368531 | 0.184265 | − | 0.982877i | \(-0.441009\pi\) | ||||
0.184265 | + | 0.982877i | \(0.441009\pi\) | |||||||
\(284\) | 0.0782556 | 0.00464362 | ||||||||
\(285\) | 0.122890 | 0.00727938 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.68182 | −0.335387 | ||||||||
\(288\) | −0.224760 | −0.0132441 | ||||||||
\(289\) | −2.89252 | −0.170148 | ||||||||
\(290\) | −0.00300470 | −0.000176442 0 | ||||||||
\(291\) | 5.86228 | 0.343653 | ||||||||
\(292\) | 0.608221 | 0.0355934 | ||||||||
\(293\) | −8.49366 | −0.496205 | −0.248102 | − | 0.968734i | \(-0.579807\pi\) | ||||
−0.248102 | + | 0.968734i | \(0.579807\pi\) | |||||||
\(294\) | −5.83846 | −0.340506 | ||||||||
\(295\) | 0.202927 | 0.0118149 | ||||||||
\(296\) | −24.7116 | −1.43633 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 12.9279 | 0.748893 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.198544 | −0.0114630 | ||||||||
\(301\) | −9.02753 | −0.520338 | ||||||||
\(302\) | 3.49139 | 0.200907 | ||||||||
\(303\) | −12.3706 | −0.710672 | ||||||||
\(304\) | −8.26171 | −0.473842 | ||||||||
\(305\) | 0.198202 | 0.0113490 | ||||||||
\(306\) | 5.36429 | 0.306656 | ||||||||
\(307\) | −10.6196 | −0.606095 | −0.303047 | − | 0.952976i | \(-0.598004\pi\) | ||||
−0.303047 | + | 0.952976i | \(0.598004\pi\) | |||||||
\(308\) | −0.0678114 | −0.00386391 | ||||||||
\(309\) | 10.0788 | 0.573363 | ||||||||
\(310\) | 0.161121 | 0.00915105 | ||||||||
\(311\) | −27.5052 | −1.55968 | −0.779838 | − | 0.625981i | \(-0.784699\pi\) | ||||
−0.779838 | + | 0.625981i | \(0.784699\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.791246 | 0.0447239 | 0.0223619 | − | 0.999750i | \(-0.492881\pi\) | ||||
0.0223619 | + | 0.999750i | \(0.492881\pi\) | |||||||
\(314\) | −12.0367 | −0.679271 | ||||||||
\(315\) | −0.103509 | −0.00583207 | ||||||||
\(316\) | 0.420980 | 0.0236820 | ||||||||
\(317\) | −10.4687 | −0.587983 | −0.293991 | − | 0.955808i | \(-0.594984\pi\) | ||||
−0.293991 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(318\) | −15.2379 | −0.854500 | ||||||||
\(319\) | −0.0346842 | −0.00194194 | ||||||||
\(320\) | 0.475237 | 0.0265666 | ||||||||
\(321\) | 6.17793 | 0.344819 | ||||||||
\(322\) | −1.71751 | −0.0957133 | ||||||||
\(323\) | 7.60954 | 0.423406 | ||||||||
\(324\) | 0.0397381 | 0.00220767 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −24.8462 | −1.37610 | ||||||||
\(327\) | 4.64928 | 0.257106 | ||||||||
\(328\) | −9.32167 | −0.514703 | ||||||||
\(329\) | −10.3176 | −0.568828 | ||||||||
\(330\) | 0.0866304 | 0.00476884 | ||||||||
\(331\) | 21.1531 | 1.16268 | 0.581339 | − | 0.813661i | \(-0.302529\pi\) | ||||
0.581339 | + | 0.813661i | \(0.302529\pi\) | |||||||
\(332\) | 0.166829 | 0.00915591 | ||||||||
\(333\) | 8.82674 | 0.483702 | ||||||||
\(334\) | 1.50109 | 0.0821361 | ||||||||
\(335\) | −0.665414 | −0.0363554 | ||||||||
\(336\) | 6.95876 | 0.379631 | ||||||||
\(337\) | −4.33688 | −0.236245 | −0.118123 | − | 0.992999i | \(-0.537688\pi\) | ||||
−0.118123 | + | 0.992999i | \(0.537688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.99146 | 0.488349 | ||||||||
\(340\) | 0.00905347 | 0.000490993 0 | ||||||||
\(341\) | 1.85987 | 0.100717 | ||||||||
\(342\) | 2.89348 | 0.156462 | ||||||||
\(343\) | 18.9212 | 1.02165 | ||||||||
\(344\) | −14.8107 | −0.798539 | ||||||||
\(345\) | 0.0427465 | 0.00230139 | ||||||||
\(346\) | 26.6578 | 1.43313 | ||||||||
\(347\) | −10.5906 | −0.568532 | −0.284266 | − | 0.958745i | \(-0.591750\pi\) | ||||
−0.284266 | + | 0.958745i | \(0.591750\pi\) | |||||||
\(348\) | −0.00137828 | −7.38838e−5 0 | ||||||||
\(349\) | 24.3761 | 1.30482 | 0.652412 | − | 0.757864i | \(-0.273757\pi\) | ||||
0.652412 | + | 0.757864i | \(0.273757\pi\) | |||||||
\(350\) | 12.1768 | 0.650877 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.224760 | −0.0119797 | ||||||||
\(353\) | −21.4564 | −1.14201 | −0.571004 | − | 0.820947i | \(-0.693446\pi\) | ||||
−0.571004 | + | 0.820947i | \(0.693446\pi\) | |||||||
\(354\) | 4.77798 | 0.253947 | ||||||||
\(355\) | 0.119451 | 0.00633982 | ||||||||
\(356\) | 0.570810 | 0.0302528 | ||||||||
\(357\) | −6.40944 | −0.339224 | ||||||||
\(358\) | −34.6255 | −1.83002 | ||||||||
\(359\) | −33.2863 | −1.75679 | −0.878393 | − | 0.477939i | \(-0.841384\pi\) | ||||
−0.878393 | + | 0.477939i | \(0.841384\pi\) | |||||||
\(360\) | −0.169818 | −0.00895020 | ||||||||
\(361\) | −14.8954 | −0.783970 | ||||||||
\(362\) | 29.8851 | 1.57073 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.928404 | 0.0485949 | ||||||||
\(366\) | 4.66672 | 0.243933 | ||||||||
\(367\) | 15.3463 | 0.801073 | 0.400536 | − | 0.916281i | \(-0.368824\pi\) | ||||
0.400536 | + | 0.916281i | \(0.368824\pi\) | |||||||
\(368\) | −2.87378 | −0.149806 | ||||||||
\(369\) | 3.32960 | 0.173332 | ||||||||
\(370\) | 0.764663 | 0.0397529 | ||||||||
\(371\) | 18.2068 | 0.945250 | ||||||||
\(372\) | 0.0739076 | 0.00383193 | ||||||||
\(373\) | −22.1576 | −1.14728 | −0.573638 | − | 0.819109i | \(-0.694469\pi\) | ||||
−0.573638 | + | 0.819109i | \(0.694469\pi\) | |||||||
\(374\) | 5.36429 | 0.277381 | ||||||||
\(375\) | −0.606350 | −0.0313118 | ||||||||
\(376\) | −16.9272 | −0.872954 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.43715 | −0.125354 | ||||||||
\(379\) | −21.0884 | −1.08324 | −0.541619 | − | 0.840624i | \(-0.682188\pi\) | ||||
−0.541619 | + | 0.840624i | \(0.682188\pi\) | |||||||
\(380\) | 0.00488342 | 0.000250514 0 | ||||||||
\(381\) | 1.74493 | 0.0893955 | ||||||||
\(382\) | 3.95764 | 0.202490 | ||||||||
\(383\) | 6.90976 | 0.353072 | 0.176536 | − | 0.984294i | \(-0.443511\pi\) | ||||
0.176536 | + | 0.984294i | \(0.443511\pi\) | |||||||
\(384\) | 11.6391 | 0.593957 | ||||||||
\(385\) | −0.103509 | −0.00527531 | ||||||||
\(386\) | −12.1502 | −0.618431 | ||||||||
\(387\) | 5.29022 | 0.268917 | ||||||||
\(388\) | 0.232956 | 0.0118265 | ||||||||
\(389\) | −32.7232 | −1.65913 | −0.829565 | − | 0.558410i | \(-0.811412\pi\) | ||||
−0.829565 | + | 0.558410i | \(0.811412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.64693 | 0.133861 | ||||||||
\(392\) | 11.4449 | 0.578056 | ||||||||
\(393\) | −13.8961 | −0.700966 | ||||||||
\(394\) | −20.6056 | −1.03810 | ||||||||
\(395\) | 0.642594 | 0.0323324 | ||||||||
\(396\) | 0.0397381 | 0.00199692 | ||||||||
\(397\) | −10.1016 | −0.506987 | −0.253494 | − | 0.967337i | \(-0.581580\pi\) | ||||
−0.253494 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(398\) | 22.7585 | 1.14078 | ||||||||
\(399\) | −3.45724 | −0.173078 | ||||||||
\(400\) | 20.3745 | 1.01872 | ||||||||
\(401\) | 18.3377 | 0.915739 | 0.457870 | − | 0.889019i | \(-0.348613\pi\) | ||||
0.457870 | + | 0.889019i | \(0.348613\pi\) | |||||||
\(402\) | −15.6674 | −0.781417 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.491584 | −0.0244572 | ||||||||
\(405\) | 0.0606573 | 0.00301408 | ||||||||
\(406\) | 0.0845306 | 0.00419518 | ||||||||
\(407\) | 8.82674 | 0.437525 | ||||||||
\(408\) | −10.5154 | −0.520590 | ||||||||
\(409\) | −5.60283 | −0.277042 | −0.138521 | − | 0.990359i | \(-0.544235\pi\) | ||||
−0.138521 | + | 0.990359i | \(0.544235\pi\) | |||||||
\(410\) | 0.288445 | 0.0142453 | ||||||||
\(411\) | 3.08818 | 0.152329 | ||||||||
\(412\) | 0.400513 | 0.0197318 | ||||||||
\(413\) | −5.70890 | −0.280916 | ||||||||
\(414\) | 1.00648 | 0.0494657 | ||||||||
\(415\) | 0.254651 | 0.0125003 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.92887 | 0.0944572 | ||||||||
\(418\) | 2.89348 | 0.141525 | ||||||||
\(419\) | −24.6413 | −1.20380 | −0.601902 | − | 0.798570i | \(-0.705590\pi\) | ||||
−0.601902 | + | 0.798570i | \(0.705590\pi\) | |||||||
\(420\) | −0.00411325 | −0.000200706 0 | ||||||||
\(421\) | 25.4002 | 1.23793 | 0.618964 | − | 0.785419i | \(-0.287553\pi\) | ||||
0.618964 | + | 0.785419i | \(0.287553\pi\) | |||||||
\(422\) | −23.7657 | −1.15690 | ||||||||
\(423\) | 6.04622 | 0.293977 | ||||||||
\(424\) | 29.8703 | 1.45063 | ||||||||
\(425\) | −18.7661 | −0.910292 | ||||||||
\(426\) | 2.81252 | 0.136267 | ||||||||
\(427\) | −5.57596 | −0.269840 | ||||||||
\(428\) | 0.245499 | 0.0118667 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.458294 | 0.0221009 | ||||||||
\(431\) | 33.6254 | 1.61968 | 0.809838 | − | 0.586653i | \(-0.199555\pi\) | ||||
0.809838 | + | 0.586653i | \(0.199555\pi\) | |||||||
\(432\) | −4.07790 | −0.196198 | ||||||||
\(433\) | 9.72637 | 0.467420 | 0.233710 | − | 0.972306i | \(-0.424913\pi\) | ||||
0.233710 | + | 0.972306i | \(0.424913\pi\) | |||||||
\(434\) | −4.53278 | −0.217580 | ||||||||
\(435\) | −0.00210385 | −0.000100872 0 | ||||||||
\(436\) | 0.184754 | 0.00884809 | ||||||||
\(437\) | 1.42775 | 0.0682984 | ||||||||
\(438\) | 21.8595 | 1.04449 | ||||||||
\(439\) | 17.0758 | 0.814986 | 0.407493 | − | 0.913208i | \(-0.366403\pi\) | ||||
0.407493 | + | 0.913208i | \(0.366403\pi\) | |||||||
\(440\) | −0.169818 | −0.00809576 | ||||||||
\(441\) | −4.08800 | −0.194667 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.8637 | 1.03878 | 0.519389 | − | 0.854538i | \(-0.326160\pi\) | ||||
0.519389 | + | 0.854538i | \(0.326160\pi\) | |||||||
\(444\) | 0.350758 | 0.0166462 | ||||||||
\(445\) | 0.871298 | 0.0413035 | ||||||||
\(446\) | 42.3448 | 2.00509 | ||||||||
\(447\) | 9.05192 | 0.428141 | ||||||||
\(448\) | −13.3697 | −0.631661 | ||||||||
\(449\) | −8.95803 | −0.422755 | −0.211378 | − | 0.977404i | \(-0.567795\pi\) | ||||
−0.211378 | + | 0.977404i | \(0.567795\pi\) | |||||||
\(450\) | −7.13572 | −0.336381 | ||||||||
\(451\) | 3.32960 | 0.156785 | ||||||||
\(452\) | 0.357304 | 0.0168062 | ||||||||
\(453\) | 2.44462 | 0.114858 | ||||||||
\(454\) | −3.11128 | −0.146020 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.67198 | −0.265615 | ||||||||
\(457\) | −37.7837 | −1.76744 | −0.883722 | − | 0.468011i | \(-0.844971\pi\) | ||||
−0.883722 | + | 0.468011i | \(0.844971\pi\) | |||||||
\(458\) | −4.12850 | −0.192912 | ||||||||
\(459\) | 3.75599 | 0.175315 | ||||||||
\(460\) | 0.00169867 | 7.92007e−5 0 | ||||||||
\(461\) | −6.10348 | −0.284268 | −0.142134 | − | 0.989847i | \(-0.545396\pi\) | ||||
−0.142134 | + | 0.989847i | \(0.545396\pi\) | |||||||
\(462\) | −2.43715 | −0.113387 | ||||||||
\(463\) | −37.1501 | −1.72651 | −0.863255 | − | 0.504768i | \(-0.831578\pi\) | ||||
−0.863255 | + | 0.504768i | \(0.831578\pi\) | |||||||
\(464\) | 0.141439 | 0.00656612 | ||||||||
\(465\) | 0.112814 | 0.00523164 | ||||||||
\(466\) | 12.6961 | 0.588135 | ||||||||
\(467\) | −10.3642 | −0.479598 | −0.239799 | − | 0.970823i | \(-0.577081\pi\) | ||||
−0.239799 | + | 0.970823i | \(0.577081\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7199 | 0.864406 | ||||||||
\(470\) | 0.523786 | 0.0241604 | ||||||||
\(471\) | −8.42793 | −0.388338 | ||||||||
\(472\) | −9.36608 | −0.431109 | ||||||||
\(473\) | 5.29022 | 0.243245 | ||||||||
\(474\) | 15.1301 | 0.694947 | ||||||||
\(475\) | −10.1224 | −0.464448 | ||||||||
\(476\) | −0.254699 | −0.0116741 | ||||||||
\(477\) | −10.6694 | −0.488516 | ||||||||
\(478\) | 40.6950 | 1.86135 | ||||||||
\(479\) | 20.4038 | 0.932273 | 0.466136 | − | 0.884713i | \(-0.345646\pi\) | ||||
0.466136 | + | 0.884713i | \(0.345646\pi\) | |||||||
\(480\) | −0.0136333 | −0.000622273 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.3178 | −1.01655 | ||||||||
\(483\) | −1.20258 | −0.0547191 | ||||||||
\(484\) | 0.0397381 | 0.00180628 | ||||||||
\(485\) | 0.355590 | 0.0161465 | ||||||||
\(486\) | 1.42819 | 0.0647842 | ||||||||
\(487\) | 18.1762 | 0.823644 | 0.411822 | − | 0.911264i | \(-0.364893\pi\) | ||||
0.411822 | + | 0.911264i | \(0.364893\pi\) | |||||||
\(488\) | −9.14799 | −0.414110 | ||||||||
\(489\) | −17.3969 | −0.786716 | ||||||||
\(490\) | −0.354145 | −0.0159987 | ||||||||
\(491\) | −19.2029 | −0.866613 | −0.433307 | − | 0.901247i | \(-0.642653\pi\) | ||||
−0.433307 | + | 0.901247i | \(0.642653\pi\) | |||||||
\(492\) | 0.132312 | 0.00596509 | ||||||||
\(493\) | −0.130274 | −0.00586723 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0606573 | 0.00272634 | ||||||||
\(496\) | −7.58434 | −0.340547 | ||||||||
\(497\) | −3.36050 | −0.150739 | ||||||||
\(498\) | 5.99585 | 0.268680 | ||||||||
\(499\) | −6.46441 | −0.289387 | −0.144693 | − | 0.989477i | \(-0.546220\pi\) | ||||
−0.144693 | + | 0.989477i | \(0.546220\pi\) | |||||||
\(500\) | −0.0240952 | −0.00107757 | ||||||||
\(501\) | 1.05104 | 0.0469571 | ||||||||
\(502\) | 29.6045 | 1.32131 | ||||||||
\(503\) | −23.6756 | −1.05564 | −0.527821 | − | 0.849355i | \(-0.676991\pi\) | ||||
−0.527821 | + | 0.849355i | \(0.676991\pi\) | |||||||
\(504\) | 4.77746 | 0.212805 | ||||||||
\(505\) | −0.750367 | −0.0333909 | ||||||||
\(506\) | 1.00648 | 0.0447435 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.0693402 | 0.00307648 | ||||||||
\(509\) | 29.5632 | 1.31037 | 0.655183 | − | 0.755470i | \(-0.272591\pi\) | ||||
0.655183 | + | 0.755470i | \(0.272591\pi\) | |||||||
\(510\) | 0.325383 | 0.0144082 | ||||||||
\(511\) | −26.1186 | −1.15542 | ||||||||
\(512\) | −21.9167 | −0.968590 | ||||||||
\(513\) | 2.02597 | 0.0894489 | ||||||||
\(514\) | −1.97821 | −0.0872550 | ||||||||
\(515\) | 0.611353 | 0.0269394 | ||||||||
\(516\) | 0.210223 | 0.00925457 | ||||||||
\(517\) | 6.04622 | 0.265912 | ||||||||
\(518\) | −21.5121 | −0.945187 | ||||||||
\(519\) | 18.6654 | 0.819320 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.0790 | 1.53684 | 0.768420 | − | 0.639946i | \(-0.221043\pi\) | ||||
0.768420 | + | 0.639946i | \(0.221043\pi\) | |||||||
\(522\) | −0.0495358 | −0.00216812 | ||||||||
\(523\) | 12.7792 | 0.558797 | 0.279399 | − | 0.960175i | \(-0.409865\pi\) | ||||
0.279399 | + | 0.960175i | \(0.409865\pi\) | |||||||
\(524\) | −0.552205 | −0.0241232 | ||||||||
\(525\) | 8.52601 | 0.372105 | ||||||||
\(526\) | −24.9459 | −1.08769 | ||||||||
\(527\) | 6.98564 | 0.304299 | ||||||||
\(528\) | −4.07790 | −0.177468 | ||||||||
\(529\) | −22.5034 | −0.978407 | ||||||||
\(530\) | −0.924290 | −0.0401486 | ||||||||
\(531\) | 3.34547 | 0.145181 | ||||||||
\(532\) | −0.137384 | −0.00595635 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 20.5150 | 0.887770 | ||||||||
\(535\) | 0.374737 | 0.0162013 | ||||||||
\(536\) | 30.7121 | 1.32656 | ||||||||
\(537\) | −24.2443 | −1.04622 | ||||||||
\(538\) | 0.799155 | 0.0344540 | ||||||||
\(539\) | −4.08800 | −0.176083 | ||||||||
\(540\) | 0.00241041 | 0.000103727 0 | ||||||||
\(541\) | 16.4144 | 0.705711 | 0.352856 | − | 0.935678i | \(-0.385211\pi\) | ||||
0.352856 | + | 0.935678i | \(0.385211\pi\) | |||||||
\(542\) | −18.8984 | −0.811756 | ||||||||
\(543\) | 20.9251 | 0.897982 | ||||||||
\(544\) | −0.844196 | −0.0361946 | ||||||||
\(545\) | 0.282013 | 0.0120801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.0865 | −1.28640 | −0.643202 | − | 0.765696i | \(-0.722395\pi\) | ||||
−0.643202 | + | 0.765696i | \(0.722395\pi\) | |||||||
\(548\) | 0.122719 | 0.00524228 | ||||||||
\(549\) | 3.26757 | 0.139456 | ||||||||
\(550\) | −7.13572 | −0.304268 | ||||||||
\(551\) | −0.0702692 | −0.00299357 | ||||||||
\(552\) | −1.97296 | −0.0839749 | ||||||||
\(553\) | −18.0779 | −0.768753 | ||||||||
\(554\) | −26.4103 | −1.12207 | ||||||||
\(555\) | 0.535406 | 0.0227267 | ||||||||
\(556\) | 0.0766497 | 0.00325067 | ||||||||
\(557\) | −9.18200 | −0.389054 | −0.194527 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194527 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(558\) | 2.65625 | 0.112448 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.422099 | 0.0178369 | ||||||||
\(561\) | 3.75599 | 0.158578 | ||||||||
\(562\) | 36.8868 | 1.55598 | ||||||||
\(563\) | −15.8217 | −0.666804 | −0.333402 | − | 0.942785i | \(-0.608197\pi\) | ||||
−0.333402 | + | 0.942785i | \(0.608197\pi\) | |||||||
\(564\) | 0.240265 | 0.0101170 | ||||||||
\(565\) | 0.545398 | 0.0229451 | ||||||||
\(566\) | 8.85430 | 0.372174 | ||||||||
\(567\) | −1.70646 | −0.0716645 | ||||||||
\(568\) | −5.51327 | −0.231332 | ||||||||
\(569\) | −35.8645 | −1.50352 | −0.751760 | − | 0.659437i | \(-0.770795\pi\) | ||||
−0.751760 | + | 0.659437i | \(0.770795\pi\) | |||||||
\(570\) | 0.175511 | 0.00735134 | ||||||||
\(571\) | 0.130007 | 0.00544063 | 0.00272032 | − | 0.999996i | \(-0.499134\pi\) | ||||
0.00272032 | + | 0.999996i | \(0.499134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.77108 | 0.115763 | ||||||||
\(574\) | −8.11474 | −0.338703 | ||||||||
\(575\) | −3.52101 | −0.146836 | ||||||||
\(576\) | 7.83479 | 0.326450 | ||||||||
\(577\) | −24.3812 | −1.01500 | −0.507502 | − | 0.861650i | \(-0.669431\pi\) | ||||
−0.507502 | + | 0.861650i | \(0.669431\pi\) | |||||||
\(578\) | −4.13108 | −0.171830 | ||||||||
\(579\) | −8.50742 | −0.353556 | ||||||||
\(580\) | −8.36030e−5 0 | −3.47143e−6 0 | ||||||||
\(581\) | −7.16405 | −0.297215 | ||||||||
\(582\) | 8.37247 | 0.347050 | ||||||||
\(583\) | −10.6694 | −0.441880 | ||||||||
\(584\) | −42.8504 | −1.77316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.1306 | −0.501110 | ||||||||
\(587\) | 6.61208 | 0.272910 | 0.136455 | − | 0.990646i | \(-0.456429\pi\) | ||||
0.136455 | + | 0.990646i | \(0.456429\pi\) | |||||||
\(588\) | −0.162450 | −0.00669931 | ||||||||
\(589\) | 3.76804 | 0.155259 | ||||||||
\(590\) | 0.289819 | 0.0119317 | ||||||||
\(591\) | −14.4278 | −0.593479 | ||||||||
\(592\) | −35.9945 | −1.47937 | ||||||||
\(593\) | −26.4128 | −1.08464 | −0.542322 | − | 0.840170i | \(-0.682455\pi\) | ||||
−0.542322 | + | 0.840170i | \(0.682455\pi\) | |||||||
\(594\) | 1.42819 | 0.0585995 | ||||||||
\(595\) | −0.388779 | −0.0159384 | ||||||||
\(596\) | 0.359706 | 0.0147342 | ||||||||
\(597\) | 15.9351 | 0.652182 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.4702 | 0.877248 | 0.438624 | − | 0.898671i | \(-0.355466\pi\) | ||||
0.438624 | + | 0.898671i | \(0.355466\pi\) | |||||||
\(600\) | 13.9879 | 0.571052 | ||||||||
\(601\) | −9.57861 | −0.390720 | −0.195360 | − | 0.980732i | \(-0.562587\pi\) | ||||
−0.195360 | + | 0.980732i | \(0.562587\pi\) | |||||||
\(602\) | −12.8931 | −0.525482 | ||||||||
\(603\) | −10.9701 | −0.446735 | ||||||||
\(604\) | 0.0971446 | 0.00395276 | ||||||||
\(605\) | 0.0606573 | 0.00246607 | ||||||||
\(606\) | −17.6676 | −0.717698 | ||||||||
\(607\) | −28.5549 | −1.15901 | −0.579504 | − | 0.814969i | \(-0.696754\pi\) | ||||
−0.579504 | + | 0.814969i | \(0.696754\pi\) | |||||||
\(608\) | −0.455357 | −0.0184672 | ||||||||
\(609\) | 0.0591871 | 0.00239838 | ||||||||
\(610\) | 0.283070 | 0.0114612 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.149256 | 0.00603332 | ||||||||
\(613\) | −25.5390 | −1.03151 | −0.515755 | − | 0.856736i | \(-0.672488\pi\) | ||||
−0.515755 | + | 0.856736i | \(0.672488\pi\) | |||||||
\(614\) | −15.1669 | −0.612086 | ||||||||
\(615\) | 0.201965 | 0.00814400 | ||||||||
\(616\) | 4.77746 | 0.192489 | ||||||||
\(617\) | 33.4193 | 1.34541 | 0.672706 | − | 0.739910i | \(-0.265132\pi\) | ||||
0.672706 | + | 0.739910i | \(0.265132\pi\) | |||||||
\(618\) | 14.3945 | 0.579031 | ||||||||
\(619\) | 34.5887 | 1.39024 | 0.695119 | − | 0.718895i | \(-0.255352\pi\) | ||||
0.695119 | + | 0.718895i | \(0.255352\pi\) | |||||||
\(620\) | 0.00448303 | 0.000180043 0 | ||||||||
\(621\) | 0.704722 | 0.0282795 | ||||||||
\(622\) | −39.2827 | −1.57509 | ||||||||
\(623\) | −24.5120 | −0.982054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9448 | 0.997793 | ||||||||
\(626\) | 1.13005 | 0.0451660 | ||||||||
\(627\) | 2.02597 | 0.0809096 | ||||||||
\(628\) | −0.334910 | −0.0133644 | ||||||||
\(629\) | 33.1532 | 1.32190 | ||||||||
\(630\) | −0.147831 | −0.00588973 | ||||||||
\(631\) | −12.7021 | −0.505662 | −0.252831 | − | 0.967510i | \(-0.581362\pi\) | ||||
−0.252831 | + | 0.967510i | \(0.581362\pi\) | |||||||
\(632\) | −29.6589 | −1.17977 | ||||||||
\(633\) | −16.6404 | −0.661397 | ||||||||
\(634\) | −14.9514 | −0.593796 | ||||||||
\(635\) | 0.105843 | 0.00420024 | ||||||||
\(636\) | −0.423980 | −0.0168119 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.0495358 | −0.00196114 | ||||||||
\(639\) | 1.96928 | 0.0779036 | ||||||||
\(640\) | 0.705998 | 0.0279070 | ||||||||
\(641\) | −25.9825 | −1.02625 | −0.513124 | − | 0.858314i | \(-0.671512\pi\) | ||||
−0.513124 | + | 0.858314i | \(0.671512\pi\) | |||||||
\(642\) | 8.82329 | 0.348227 | ||||||||
\(643\) | 32.8848 | 1.29685 | 0.648425 | − | 0.761278i | \(-0.275428\pi\) | ||||
0.648425 | + | 0.761278i | \(0.275428\pi\) | |||||||
\(644\) | −0.0477881 | −0.00188312 | ||||||||
\(645\) | 0.320890 | 0.0126350 | ||||||||
\(646\) | 10.8679 | 0.427592 | ||||||||
\(647\) | 2.75086 | 0.108148 | 0.0540738 | − | 0.998537i | \(-0.482779\pi\) | ||||
0.0540738 | + | 0.998537i | \(0.482779\pi\) | |||||||
\(648\) | −2.79963 | −0.109980 | ||||||||
\(649\) | 3.34547 | 0.131321 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.17378 | −0.124390 | ||||||||
\(652\) | −0.691321 | −0.0270742 | ||||||||
\(653\) | 27.4851 | 1.07557 | 0.537787 | − | 0.843081i | \(-0.319260\pi\) | ||||
0.537787 | + | 0.843081i | \(0.319260\pi\) | |||||||
\(654\) | 6.64007 | 0.259647 | ||||||||
\(655\) | −0.842900 | −0.0329348 | ||||||||
\(656\) | −13.5778 | −0.530123 | ||||||||
\(657\) | 15.3057 | 0.597133 | ||||||||
\(658\) | −14.7355 | −0.574451 | ||||||||
\(659\) | 17.2631 | 0.672474 | 0.336237 | − | 0.941777i | \(-0.390846\pi\) | ||||
0.336237 | + | 0.941777i | \(0.390846\pi\) | |||||||
\(660\) | 0.00241041 | 9.38249e−5 0 | ||||||||
\(661\) | −2.44386 | −0.0950551 | −0.0475276 | − | 0.998870i | \(-0.515134\pi\) | ||||
−0.0475276 | + | 0.998870i | \(0.515134\pi\) | |||||||
\(662\) | 30.2107 | 1.17417 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.7534 | −0.456122 | ||||||||
\(665\) | −0.209706 | −0.00813207 | ||||||||
\(666\) | 12.6063 | 0.488484 | ||||||||
\(667\) | −0.0244427 | −0.000946425 0 | ||||||||
\(668\) | 0.0417664 | 0.00161599 | ||||||||
\(669\) | 29.6492 | 1.14630 | ||||||||
\(670\) | −0.950340 | −0.0367148 | ||||||||
\(671\) | 3.26757 | 0.126143 | ||||||||
\(672\) | 0.383543 | 0.0147955 | ||||||||
\(673\) | 26.7842 | 1.03246 | 0.516228 | − | 0.856451i | \(-0.327336\pi\) | ||||
0.516228 | + | 0.856451i | \(0.327336\pi\) | |||||||
\(674\) | −6.19391 | −0.238581 | ||||||||
\(675\) | −4.99632 | −0.192308 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.7769 | −0.990687 | −0.495343 | − | 0.868697i | \(-0.664958\pi\) | ||||
−0.495343 | + | 0.868697i | \(0.664958\pi\) | |||||||
\(678\) | 12.8416 | 0.493177 | ||||||||
\(679\) | −10.0037 | −0.383908 | ||||||||
\(680\) | −0.637836 | −0.0244599 | ||||||||
\(681\) | −2.17847 | −0.0834792 | ||||||||
\(682\) | 2.65625 | 0.101713 | ||||||||
\(683\) | 12.8667 | 0.492329 | 0.246165 | − | 0.969228i | \(-0.420830\pi\) | ||||
0.246165 | + | 0.969228i | \(0.420830\pi\) | |||||||
\(684\) | 0.0805084 | 0.00307831 | ||||||||
\(685\) | 0.187321 | 0.00715716 | ||||||||
\(686\) | 27.0231 | 1.03175 | ||||||||
\(687\) | −2.89071 | −0.110288 | ||||||||
\(688\) | −21.5730 | −0.822462 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.0610503 | 0.00232414 | ||||||||
\(691\) | −33.9707 | −1.29230 | −0.646152 | − | 0.763208i | \(-0.723623\pi\) | ||||
−0.646152 | + | 0.763208i | \(0.723623\pi\) | |||||||
\(692\) | 0.741728 | 0.0281963 | ||||||||
\(693\) | −1.70646 | −0.0648229 | ||||||||
\(694\) | −15.1254 | −0.574152 | ||||||||
\(695\) | 0.117000 | 0.00443806 | ||||||||
\(696\) | 0.0971031 | 0.00368068 | ||||||||
\(697\) | 12.5060 | 0.473697 | ||||||||
\(698\) | 34.8138 | 1.31772 | ||||||||
\(699\) | 8.88961 | 0.336236 | ||||||||
\(700\) | 0.338807 | 0.0128057 | ||||||||
\(701\) | −18.4719 | −0.697675 | −0.348837 | − | 0.937183i | \(-0.613423\pi\) | ||||
−0.348837 | + | 0.937183i | \(0.613423\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.8827 | 0.674460 | ||||||||
\(704\) | 7.83479 | 0.295285 | ||||||||
\(705\) | 0.366747 | 0.0138125 | ||||||||
\(706\) | −30.6439 | −1.15330 | ||||||||
\(707\) | 21.1099 | 0.793919 | ||||||||
\(708\) | 0.132943 | 0.00499629 | ||||||||
\(709\) | 33.8830 | 1.27250 | 0.636251 | − | 0.771482i | \(-0.280484\pi\) | ||||
0.636251 | + | 0.771482i | \(0.280484\pi\) | |||||||
\(710\) | 0.170600 | 0.00640249 | ||||||||
\(711\) | 10.5938 | 0.397300 | ||||||||
\(712\) | −40.2147 | −1.50711 | ||||||||
\(713\) | 1.31069 | 0.0490856 | ||||||||
\(714\) | −9.15392 | −0.342577 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.963422 | −0.0360048 | ||||||||
\(717\) | 28.4940 | 1.06413 | ||||||||
\(718\) | −47.5393 | −1.77415 | ||||||||
\(719\) | 31.1501 | 1.16170 | 0.580851 | − | 0.814010i | \(-0.302720\pi\) | ||||
0.580851 | + | 0.814010i | \(0.302720\pi\) | |||||||
\(720\) | −0.247354 | −0.00921834 | ||||||||
\(721\) | −17.1990 | −0.640526 | ||||||||
\(722\) | −21.2736 | −0.791720 | ||||||||
\(723\) | −15.6266 | −0.581160 | ||||||||
\(724\) | 0.831524 | 0.0309034 | ||||||||
\(725\) | 0.173293 | 0.00643595 | ||||||||
\(726\) | 1.42819 | 0.0530053 | ||||||||
\(727\) | 1.50815 | 0.0559341 | 0.0279671 | − | 0.999609i | \(-0.491097\pi\) | ||||
0.0279671 | + | 0.999609i | \(0.491097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.32594 | 0.0490753 | ||||||||
\(731\) | 19.8700 | 0.734920 | ||||||||
\(732\) | 0.129847 | 0.00479928 | ||||||||
\(733\) | −4.42002 | −0.163257 | −0.0816285 | − | 0.996663i | \(-0.526012\pi\) | ||||
−0.0816285 | + | 0.996663i | \(0.526012\pi\) | |||||||
\(734\) | 21.9176 | 0.808992 | ||||||||
\(735\) | −0.247967 | −0.00914641 | ||||||||
\(736\) | −0.158393 | −0.00583844 | ||||||||
\(737\) | −10.9701 | −0.404087 | ||||||||
\(738\) | 4.75532 | 0.175046 | ||||||||
\(739\) | −13.7640 | −0.506317 | −0.253159 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253159 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(740\) | 0.0212760 | 0.000782122 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.0028 | 0.954594 | ||||||||
\(743\) | 52.1763 | 1.91416 | 0.957081 | − | 0.289819i | \(-0.0935952\pi\) | ||||
0.957081 | + | 0.289819i | \(0.0935952\pi\) | |||||||
\(744\) | −5.20695 | −0.190896 | ||||||||
\(745\) | 0.549065 | 0.0201162 | ||||||||
\(746\) | −31.6453 | −1.15862 | ||||||||
\(747\) | 4.19820 | 0.153604 | ||||||||
\(748\) | 0.149256 | 0.00545734 | ||||||||
\(749\) | −10.5424 | −0.385210 | ||||||||
\(750\) | −0.865985 | −0.0316213 | ||||||||
\(751\) | 13.4236 | 0.489836 | 0.244918 | − | 0.969544i | \(-0.421239\pi\) | ||||
0.244918 | + | 0.969544i | \(0.421239\pi\) | |||||||
\(752\) | −24.6559 | −0.899106 | ||||||||
\(753\) | 20.7286 | 0.755393 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.148284 | 0.00539661 | ||||||||
\(756\) | −0.0678114 | −0.00246628 | ||||||||
\(757\) | 12.9431 | 0.470426 | 0.235213 | − | 0.971944i | \(-0.424421\pi\) | ||||
0.235213 | + | 0.971944i | \(0.424421\pi\) | |||||||
\(758\) | −30.1183 | −1.09395 | ||||||||
\(759\) | 0.704722 | 0.0255798 | ||||||||
\(760\) | −0.344047 | −0.0124799 | ||||||||
\(761\) | 24.5952 | 0.891576 | 0.445788 | − | 0.895139i | \(-0.352923\pi\) | ||||
0.445788 | + | 0.895139i | \(0.352923\pi\) | |||||||
\(762\) | 2.49210 | 0.0902792 | ||||||||
\(763\) | −7.93379 | −0.287223 | ||||||||
\(764\) | 0.110117 | 0.00398391 | ||||||||
\(765\) | 0.227828 | 0.00823715 | ||||||||
\(766\) | 9.86847 | 0.356562 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.953341 | 0.0344007 | ||||||||
\(769\) | −48.0101 | −1.73129 | −0.865644 | − | 0.500660i | \(-0.833091\pi\) | ||||
−0.865644 | + | 0.500660i | \(0.833091\pi\) | |||||||
\(770\) | −0.147831 | −0.00532746 | ||||||||
\(771\) | −1.38511 | −0.0498835 | ||||||||
\(772\) | −0.338069 | −0.0121674 | ||||||||
\(773\) | −20.9744 | −0.754398 | −0.377199 | − | 0.926132i | \(-0.623113\pi\) | ||||
−0.377199 | + | 0.926132i | \(0.623113\pi\) | |||||||
\(774\) | 7.55546 | 0.271575 | ||||||||
\(775\) | −9.29249 | −0.333796 | ||||||||
\(776\) | −16.4122 | −0.589165 | ||||||||
\(777\) | −15.0624 | −0.540362 | ||||||||
\(778\) | −46.7350 | −1.67553 | ||||||||
\(779\) | 6.74568 | 0.241689 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.96928 | 0.0704665 | ||||||||
\(782\) | 3.78033 | 0.135184 | ||||||||
\(783\) | −0.0346842 | −0.00123951 | ||||||||
\(784\) | 16.6705 | 0.595374 | ||||||||
\(785\) | −0.511215 | −0.0182460 | ||||||||
\(786\) | −19.8463 | −0.707895 | ||||||||
\(787\) | 42.1206 | 1.50144 | 0.750719 | − | 0.660622i | \(-0.229707\pi\) | ||||
0.750719 | + | 0.660622i | \(0.229707\pi\) | |||||||
\(788\) | −0.573332 | −0.0204241 | ||||||||
\(789\) | −17.4668 | −0.621834 | ||||||||
\(790\) | 0.917749 | 0.0326520 | ||||||||
\(791\) | −15.3435 | −0.545554 | ||||||||
\(792\) | −2.79963 | −0.0994807 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −14.4271 | −0.511999 | ||||||||
\(795\) | −0.647174 | −0.0229529 | ||||||||
\(796\) | 0.633232 | 0.0224443 | ||||||||
\(797\) | 24.5853 | 0.870855 | 0.435428 | − | 0.900224i | \(-0.356597\pi\) | ||||
0.435428 | + | 0.900224i | \(0.356597\pi\) | |||||||
\(798\) | −4.93760 | −0.174789 | ||||||||
\(799\) | 22.7095 | 0.803406 | ||||||||
\(800\) | 1.12297 | 0.0397030 | ||||||||
\(801\) | 14.3643 | 0.507537 | ||||||||
\(802\) | 26.1897 | 0.924792 | ||||||||
\(803\) | 15.3057 | 0.540127 | ||||||||
\(804\) | −0.435929 | −0.0153740 | ||||||||
\(805\) | −0.0729450 | −0.00257097 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.559556 | 0.0196973 | ||||||||
\(808\) | 34.6332 | 1.21839 | ||||||||
\(809\) | −23.9067 | −0.840516 | −0.420258 | − | 0.907405i | \(-0.638060\pi\) | ||||
−0.420258 | + | 0.907405i | \(0.638060\pi\) | |||||||
\(810\) | 0.0866304 | 0.00304388 | ||||||||
\(811\) | −13.7011 | −0.481110 | −0.240555 | − | 0.970636i | \(-0.577329\pi\) | ||||
−0.240555 | + | 0.970636i | \(0.577329\pi\) | |||||||
\(812\) | 0.00235198 | 8.25384e−5 0 | ||||||||
\(813\) | −13.2324 | −0.464080 | ||||||||
\(814\) | 12.6063 | 0.441850 | ||||||||
\(815\) | −1.05525 | −0.0369638 | ||||||||
\(816\) | −15.3166 | −0.536187 | ||||||||
\(817\) | 10.7178 | 0.374970 | ||||||||
\(818\) | −8.00193 | −0.279781 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.00802569 | 0.000280269 0 | ||||||||
\(821\) | −35.5107 | −1.23933 | −0.619666 | − | 0.784866i | \(-0.712732\pi\) | ||||
−0.619666 | + | 0.784866i | \(0.712732\pi\) | |||||||
\(822\) | 4.41053 | 0.153835 | ||||||||
\(823\) | −33.6096 | −1.17156 | −0.585778 | − | 0.810471i | \(-0.699211\pi\) | ||||
−0.585778 | + | 0.810471i | \(0.699211\pi\) | |||||||
\(824\) | −28.2170 | −0.982984 | ||||||||
\(825\) | −4.99632 | −0.173950 | ||||||||
\(826\) | −8.15341 | −0.283693 | ||||||||
\(827\) | 33.8892 | 1.17844 | 0.589221 | − | 0.807972i | \(-0.299435\pi\) | ||||
0.589221 | + | 0.807972i | \(0.299435\pi\) | |||||||
\(828\) | 0.0280043 | 0.000973217 0 | ||||||||
\(829\) | 1.03923 | 0.0360941 | 0.0180470 | − | 0.999837i | \(-0.494255\pi\) | ||||
0.0180470 | + | 0.999837i | \(0.494255\pi\) | |||||||
\(830\) | 0.363692 | 0.0126239 | ||||||||
\(831\) | −18.4921 | −0.641484 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.3545 | −0.532002 | ||||||||
\(834\) | 2.75480 | 0.0953909 | ||||||||
\(835\) | 0.0637533 | 0.00220627 | ||||||||
\(836\) | 0.0805084 | 0.00278444 | ||||||||
\(837\) | 1.85987 | 0.0642864 | ||||||||
\(838\) | −35.1925 | −1.21570 | ||||||||
\(839\) | 53.9422 | 1.86229 | 0.931146 | − | 0.364646i | \(-0.118810\pi\) | ||||
0.931146 | + | 0.364646i | \(0.118810\pi\) | |||||||
\(840\) | 0.289787 | 0.00999862 | ||||||||
\(841\) | −28.9988 | −0.999959 | ||||||||
\(842\) | 36.2764 | 1.25017 | ||||||||
\(843\) | 25.8276 | 0.889550 | ||||||||
\(844\) | −0.661258 | −0.0227615 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.63517 | 0.296883 | ||||||||
\(847\) | −1.70646 | −0.0586346 | ||||||||
\(848\) | 43.5085 | 1.49409 | ||||||||
\(849\) | 6.19965 | 0.212771 | ||||||||
\(850\) | −26.8017 | −0.919291 | ||||||||
\(851\) | 6.22039 | 0.213232 | ||||||||
\(852\) | 0.0782556 | 0.00268099 | ||||||||
\(853\) | 20.4632 | 0.700647 | 0.350324 | − | 0.936629i | \(-0.386072\pi\) | ||||
0.350324 | + | 0.936629i | \(0.386072\pi\) | |||||||
\(854\) | −7.96355 | −0.272507 | ||||||||
\(855\) | 0.122890 | 0.00420275 | ||||||||
\(856\) | −17.2959 | −0.591163 | ||||||||
\(857\) | 24.3582 | 0.832059 | 0.416029 | − | 0.909351i | \(-0.363421\pi\) | ||||
0.416029 | + | 0.909351i | \(0.363421\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.8900 | 0.508042 | 0.254021 | − | 0.967199i | \(-0.418247\pi\) | ||||
0.254021 | + | 0.967199i | \(0.418247\pi\) | |||||||
\(860\) | 0.0127516 | 0.000434825 0 | ||||||||
\(861\) | −5.68182 | −0.193636 | ||||||||
\(862\) | 48.0235 | 1.63569 | ||||||||
\(863\) | −7.78442 | −0.264985 | −0.132492 | − | 0.991184i | \(-0.542298\pi\) | ||||
−0.132492 | + | 0.991184i | \(0.542298\pi\) | |||||||
\(864\) | −0.224760 | −0.00764648 | ||||||||
\(865\) | 1.13219 | 0.0384957 | ||||||||
\(866\) | 13.8911 | 0.472040 | ||||||||
\(867\) | −2.89252 | −0.0982351 | ||||||||
\(868\) | −0.126120 | −0.00428080 | ||||||||
\(869\) | 10.5938 | 0.359372 | ||||||||
\(870\) | −0.00300470 | −0.000101869 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −13.0163 | −0.440787 | ||||||||
\(873\) | 5.86228 | 0.198408 | ||||||||
\(874\) | 2.03910 | 0.0689736 | ||||||||
\(875\) | 1.03471 | 0.0349796 | ||||||||
\(876\) | 0.608221 | 0.0205499 | ||||||||
\(877\) | 26.9967 | 0.911614 | 0.455807 | − | 0.890079i | \(-0.349351\pi\) | ||||
0.455807 | + | 0.890079i | \(0.349351\pi\) | |||||||
\(878\) | 24.3876 | 0.823042 | ||||||||
\(879\) | −8.49366 | −0.286484 | ||||||||
\(880\) | −0.247354 | −0.00833831 | ||||||||
\(881\) | 18.7865 | 0.632934 | 0.316467 | − | 0.948603i | \(-0.397503\pi\) | ||||
0.316467 | + | 0.948603i | \(0.397503\pi\) | |||||||
\(882\) | −5.83846 | −0.196591 | ||||||||
\(883\) | 34.5728 | 1.16347 | 0.581734 | − | 0.813379i | \(-0.302375\pi\) | ||||
0.581734 | + | 0.813379i | \(0.302375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.202927 | 0.00682131 | ||||||||
\(886\) | 31.2257 | 1.04905 | ||||||||
\(887\) | −32.8755 | −1.10385 | −0.551926 | − | 0.833893i | \(-0.686107\pi\) | ||||
−0.551926 | + | 0.833893i | \(0.686107\pi\) | |||||||
\(888\) | −24.7116 | −0.829268 | ||||||||
\(889\) | −2.97765 | −0.0998671 | ||||||||
\(890\) | 1.24438 | 0.0417118 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 1.17820 | 0.0394492 | ||||||||
\(893\) | 12.2495 | 0.409913 | ||||||||
\(894\) | 12.9279 | 0.432374 | ||||||||
\(895\) | −1.47059 | −0.0491565 | ||||||||
\(896\) | −19.8617 | −0.663532 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.7938 | −0.426935 | ||||||||
\(899\) | −0.0645080 | −0.00215146 | ||||||||
\(900\) | −0.198544 | −0.00661815 | ||||||||
\(901\) | −40.0740 | −1.33506 | ||||||||
\(902\) | 4.75532 | 0.158335 | ||||||||
\(903\) | −9.02753 | −0.300418 | ||||||||
\(904\) | −25.1728 | −0.837235 | ||||||||
\(905\) | 1.26926 | 0.0421916 | ||||||||
\(906\) | 3.49139 | 0.115994 | ||||||||
\(907\) | −5.02982 | −0.167013 | −0.0835063 | − | 0.996507i | \(-0.526612\pi\) | ||||
−0.0835063 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(908\) | −0.0865684 | −0.00287287 | ||||||||
\(909\) | −12.3706 | −0.410307 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.8563 | 0.757263 | 0.378632 | − | 0.925547i | \(-0.376395\pi\) | ||||
0.378632 | + | 0.925547i | \(0.376395\pi\) | |||||||
\(912\) | −8.26171 | −0.273573 | ||||||||
\(913\) | 4.19820 | 0.138940 | ||||||||
\(914\) | −53.9624 | −1.78492 | ||||||||
\(915\) | 0.198202 | 0.00655235 | ||||||||
\(916\) | −0.114871 | −0.00379546 | ||||||||
\(917\) | 23.7131 | 0.783075 | ||||||||
\(918\) | 5.36429 | 0.177048 | ||||||||
\(919\) | 2.37935 | 0.0784875 | 0.0392437 | − | 0.999230i | \(-0.487505\pi\) | ||||
0.0392437 | + | 0.999230i | \(0.487505\pi\) | |||||||
\(920\) | −0.119675 | −0.00394555 | ||||||||
\(921\) | −10.6196 | −0.349929 | ||||||||
\(922\) | −8.71696 | −0.287078 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.0678114 | −0.00223083 | ||||||||
\(925\) | −44.1012 | −1.45004 | ||||||||
\(926\) | −53.0575 | −1.74358 | ||||||||
\(927\) | 10.0788 | 0.331031 | ||||||||
\(928\) | 0.00779561 | 0.000255903 0 | ||||||||
\(929\) | 8.06120 | 0.264480 | 0.132240 | − | 0.991218i | \(-0.457783\pi\) | ||||
0.132240 | + | 0.991218i | \(0.457783\pi\) | |||||||
\(930\) | 0.161121 | 0.00528336 | ||||||||
\(931\) | −8.28219 | −0.271438 | ||||||||
\(932\) | 0.353256 | 0.0115713 | ||||||||
\(933\) | −27.5052 | −0.900479 | ||||||||
\(934\) | −14.8021 | −0.484339 | ||||||||
\(935\) | 0.227828 | 0.00745078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.3236 | −0.794618 | −0.397309 | − | 0.917685i | \(-0.630056\pi\) | ||||
−0.397309 | + | 0.917685i | \(0.630056\pi\) | |||||||
\(938\) | 26.7357 | 0.872951 | ||||||||
\(939\) | 0.791246 | 0.0258213 | ||||||||
\(940\) | 0.0145738 | 0.000475346 0 | ||||||||
\(941\) | 17.0623 | 0.556215 | 0.278107 | − | 0.960550i | \(-0.410293\pi\) | ||||
0.278107 | + | 0.960550i | \(0.410293\pi\) | |||||||
\(942\) | −12.0367 | −0.392177 | ||||||||
\(943\) | 2.34644 | 0.0764107 | ||||||||
\(944\) | −13.6425 | −0.444025 | ||||||||
\(945\) | −0.103509 | −0.00336715 | ||||||||
\(946\) | 7.55546 | 0.245649 | ||||||||
\(947\) | 57.1623 | 1.85753 | 0.928763 | − | 0.370673i | \(-0.120873\pi\) | ||||
0.928763 | + | 0.370673i | \(0.120873\pi\) | |||||||
\(948\) | 0.420980 | 0.0136728 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −14.4568 | −0.469039 | ||||||||
\(951\) | −10.4687 | −0.339472 | ||||||||
\(952\) | 17.9441 | 0.581571 | ||||||||
\(953\) | −2.88446 | −0.0934370 | −0.0467185 | − | 0.998908i | \(-0.514876\pi\) | ||||
−0.0467185 | + | 0.998908i | \(0.514876\pi\) | |||||||
\(954\) | −15.2379 | −0.493346 | ||||||||
\(955\) | 0.168086 | 0.00543914 | ||||||||
\(956\) | 1.13230 | 0.0366212 | ||||||||
\(957\) | −0.0346842 | −0.00112118 | ||||||||
\(958\) | 29.1406 | 0.941489 | ||||||||
\(959\) | −5.26985 | −0.170172 | ||||||||
\(960\) | 0.475237 | 0.0153382 | ||||||||
\(961\) | −27.5409 | −0.888416 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.17793 | 0.199081 | ||||||||
\(964\) | −0.620972 | −0.0200002 | ||||||||
\(965\) | −0.516037 | −0.0166118 | ||||||||
\(966\) | −1.71751 | −0.0552601 | ||||||||
\(967\) | −44.8041 | −1.44080 | −0.720402 | − | 0.693557i | \(-0.756043\pi\) | ||||
−0.720402 | + | 0.693557i | \(0.756043\pi\) | |||||||
\(968\) | −2.79963 | −0.0899837 | ||||||||
\(969\) | 7.60954 | 0.244454 | ||||||||
\(970\) | 0.507851 | 0.0163061 | ||||||||
\(971\) | 36.2237 | 1.16247 | 0.581237 | − | 0.813735i | \(-0.302569\pi\) | ||||
0.581237 | + | 0.813735i | \(0.302569\pi\) | |||||||
\(972\) | 0.0397381 | 0.00127460 | ||||||||
\(973\) | −3.29153 | −0.105522 | ||||||||
\(974\) | 25.9592 | 0.831786 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.3248 | −0.426516 | ||||||||
\(977\) | 8.12311 | 0.259881 | 0.129941 | − | 0.991522i | \(-0.458521\pi\) | ||||
0.129941 | + | 0.991522i | \(0.458521\pi\) | |||||||
\(978\) | −24.8462 | −0.794493 | ||||||||
\(979\) | 14.3643 | 0.459084 | ||||||||
\(980\) | −0.00985375 | −0.000314767 0 | ||||||||
\(981\) | 4.64928 | 0.148440 | ||||||||
\(982\) | −27.4254 | −0.875180 | ||||||||
\(983\) | 16.3355 | 0.521020 | 0.260510 | − | 0.965471i | \(-0.416109\pi\) | ||||
0.260510 | + | 0.965471i | \(0.416109\pi\) | |||||||
\(984\) | −9.32167 | −0.297164 | ||||||||
\(985\) | −0.875149 | −0.0278846 | ||||||||
\(986\) | −0.186056 | −0.00592523 | ||||||||
\(987\) | −10.3176 | −0.328413 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.72813 | 0.118548 | ||||||||
\(990\) | 0.0866304 | 0.00275329 | ||||||||
\(991\) | 19.8188 | 0.629565 | 0.314783 | − | 0.949164i | \(-0.398068\pi\) | ||||
0.314783 | + | 0.949164i | \(0.398068\pi\) | |||||||
\(992\) | −0.418023 | −0.0132722 | ||||||||
\(993\) | 21.1531 | 0.671273 | ||||||||
\(994\) | −4.79944 | −0.152229 | ||||||||
\(995\) | 0.966582 | 0.0306427 | ||||||||
\(996\) | 0.166829 | 0.00528617 | ||||||||
\(997\) | 37.6595 | 1.19269 | 0.596344 | − | 0.802729i | \(-0.296619\pi\) | ||||
0.596344 | + | 0.802729i | \(0.296619\pi\) | |||||||
\(998\) | −9.23243 | −0.292248 | ||||||||
\(999\) | 8.82674 | 0.279266 |
(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 | 5577.2.a.y.1.5 | 7 | ||
13.5 | odd | 4 | 429.2.b.b.298.4 | ✓ | 14 | ||
13.8 | odd | 4 | 429.2.b.b.298.11 | yes | 14 | ||
13.12 | even | 2 | 5577.2.a.x.1.3 | 7 | |||
39.5 | even | 4 | 1287.2.b.c.298.11 | 14 | |||
39.8 | even | 4 | 1287.2.b.c.298.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.4 | ✓ | 14 | 13.5 | odd | 4 | ||
429.2.b.b.298.11 | yes | 14 | 13.8 | odd | 4 | ||
1287.2.b.c.298.4 | 14 | 39.8 | even | 4 | |||
1287.2.b.c.298.11 | 14 | 39.5 | even | 4 | |||
5577.2.a.x.1.3 | 7 | 13.12 | even | 2 | |||
5577.2.a.y.1.5 | 7 | 1.1 | even | 1 | trivial |