Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.173513.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.52979\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.65369 | −1.16933 | −0.584666 | − | 0.811274i | \(-0.698775\pi\) | ||||
−0.584666 | + | 0.811274i | \(0.698775\pi\) | |||||||
\(3\) | −1.14142 | −0.659000 | −0.329500 | − | 0.944156i | \(-0.606880\pi\) | ||||
−0.329500 | + | 0.944156i | \(0.606880\pi\) | |||||||
\(4\) | 0.734678 | 0.367339 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.88755 | 0.770591 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.09245 | 0.739791 | ||||||||
\(9\) | −1.69716 | −0.565718 | ||||||||
\(10\) | 1.65369 | 0.522941 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.838578 | −0.242076 | ||||||||
\(13\) | 5.60081 | 1.55339 | 0.776693 | − | 0.629879i | \(-0.216896\pi\) | ||||
0.776693 | + | 0.629879i | \(0.216896\pi\) | |||||||
\(14\) | −1.65369 | −0.441966 | ||||||||
\(15\) | 1.14142 | 0.294714 | ||||||||
\(16\) | −4.92960 | −1.23240 | ||||||||
\(17\) | −4.57876 | −1.11051 | −0.555257 | − | 0.831679i | \(-0.687380\pi\) | ||||
−0.555257 | + | 0.831679i | \(0.687380\pi\) | |||||||
\(18\) | 2.80656 | 0.661513 | ||||||||
\(19\) | 1.88149 | 0.431642 | 0.215821 | − | 0.976433i | \(-0.430757\pi\) | ||||
0.215821 | + | 0.976433i | \(0.430757\pi\) | |||||||
\(20\) | −0.734678 | −0.164279 | ||||||||
\(21\) | −1.14142 | −0.249079 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.08099 | 0.433917 | 0.216958 | − | 0.976181i | \(-0.430386\pi\) | ||||
0.216958 | + | 0.976181i | \(0.430386\pi\) | |||||||
\(24\) | −2.38836 | −0.487523 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.26199 | −1.81642 | ||||||||
\(27\) | 5.36144 | 1.03181 | ||||||||
\(28\) | 0.734678 | 0.138841 | ||||||||
\(29\) | −5.51585 | −1.02427 | −0.512134 | − | 0.858905i | \(-0.671145\pi\) | ||||
−0.512134 | + | 0.858905i | \(0.671145\pi\) | |||||||
\(30\) | −1.88755 | −0.344619 | ||||||||
\(31\) | −5.46081 | −0.980790 | −0.490395 | − | 0.871500i | \(-0.663148\pi\) | ||||
−0.490395 | + | 0.871500i | \(0.663148\pi\) | |||||||
\(32\) | 3.96713 | 0.701296 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.57184 | 1.29856 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.24686 | −0.207810 | ||||||||
\(37\) | −9.34694 | −1.53663 | −0.768314 | − | 0.640073i | \(-0.778904\pi\) | ||||
−0.768314 | + | 0.640073i | \(0.778904\pi\) | |||||||
\(38\) | −3.11139 | −0.504734 | ||||||||
\(39\) | −6.39289 | −1.02368 | ||||||||
\(40\) | −2.09245 | −0.330845 | ||||||||
\(41\) | 11.0136 | 1.72004 | 0.860020 | − | 0.510261i | \(-0.170451\pi\) | ||||
0.860020 | + | 0.510261i | \(0.170451\pi\) | |||||||
\(42\) | 1.88755 | 0.291256 | ||||||||
\(43\) | −8.43344 | −1.28609 | −0.643044 | − | 0.765829i | \(-0.722329\pi\) | ||||
−0.643044 | + | 0.765829i | \(0.722329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.69716 | 0.252997 | ||||||||
\(46\) | −3.44131 | −0.507393 | ||||||||
\(47\) | 1.60936 | 0.234749 | 0.117375 | − | 0.993088i | \(-0.462552\pi\) | ||||
0.117375 | + | 0.993088i | \(0.462552\pi\) | |||||||
\(48\) | 5.62676 | 0.812153 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.65369 | −0.233867 | ||||||||
\(51\) | 5.22630 | 0.731829 | ||||||||
\(52\) | 4.11479 | 0.570619 | ||||||||
\(53\) | 6.21331 | 0.853463 | 0.426732 | − | 0.904378i | \(-0.359665\pi\) | ||||
0.426732 | + | 0.904378i | \(0.359665\pi\) | |||||||
\(54\) | −8.86613 | −1.20653 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.09245 | 0.279615 | ||||||||
\(57\) | −2.14757 | −0.284453 | ||||||||
\(58\) | 9.12149 | 1.19771 | ||||||||
\(59\) | 13.5862 | 1.76877 | 0.884386 | − | 0.466756i | \(-0.154577\pi\) | ||||
0.884386 | + | 0.466756i | \(0.154577\pi\) | |||||||
\(60\) | 0.838578 | 0.108260 | ||||||||
\(61\) | −11.1145 | −1.42307 | −0.711533 | − | 0.702653i | \(-0.751999\pi\) | ||||
−0.711533 | + | 0.702653i | \(0.751999\pi\) | |||||||
\(62\) | 9.03046 | 1.14687 | ||||||||
\(63\) | −1.69716 | −0.213821 | ||||||||
\(64\) | 3.29883 | 0.412353 | ||||||||
\(65\) | −5.60081 | −0.694695 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.60924 | −0.685277 | −0.342639 | − | 0.939467i | \(-0.611321\pi\) | ||||
−0.342639 | + | 0.939467i | \(0.611321\pi\) | |||||||
\(68\) | −3.36392 | −0.407935 | ||||||||
\(69\) | −2.37529 | −0.285951 | ||||||||
\(70\) | 1.65369 | 0.197653 | ||||||||
\(71\) | 0.696594 | 0.0826705 | 0.0413353 | − | 0.999145i | \(-0.486839\pi\) | ||||
0.0413353 | + | 0.999145i | \(0.486839\pi\) | |||||||
\(72\) | −3.55121 | −0.418514 | ||||||||
\(73\) | 13.8873 | 1.62539 | 0.812694 | − | 0.582690i | \(-0.198000\pi\) | ||||
0.812694 | + | 0.582690i | \(0.198000\pi\) | |||||||
\(74\) | 15.4569 | 1.79683 | ||||||||
\(75\) | −1.14142 | −0.131800 | ||||||||
\(76\) | 1.38229 | 0.158559 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.5718 | 1.19702 | ||||||||
\(79\) | −8.47388 | −0.953386 | −0.476693 | − | 0.879070i | \(-0.658165\pi\) | ||||
−0.476693 | + | 0.879070i | \(0.658165\pi\) | |||||||
\(80\) | 4.92960 | 0.551146 | ||||||||
\(81\) | −1.02820 | −0.114244 | ||||||||
\(82\) | −18.2131 | −2.01130 | ||||||||
\(83\) | −9.50230 | −1.04301 | −0.521506 | − | 0.853247i | \(-0.674630\pi\) | ||||
−0.521506 | + | 0.853247i | \(0.674630\pi\) | |||||||
\(84\) | −0.838578 | −0.0914963 | ||||||||
\(85\) | 4.57876 | 0.496637 | ||||||||
\(86\) | 13.9463 | 1.50386 | ||||||||
\(87\) | 6.29592 | 0.674993 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.49863 | 0.158854 | 0.0794272 | − | 0.996841i | \(-0.474691\pi\) | ||||
0.0794272 | + | 0.996841i | \(0.474691\pi\) | |||||||
\(90\) | −2.80656 | −0.295838 | ||||||||
\(91\) | 5.60081 | 0.587125 | ||||||||
\(92\) | 1.52886 | 0.159395 | ||||||||
\(93\) | 6.23309 | 0.646341 | ||||||||
\(94\) | −2.66137 | −0.274500 | ||||||||
\(95\) | −1.88149 | −0.193036 | ||||||||
\(96\) | −4.52817 | −0.462154 | ||||||||
\(97\) | 5.93697 | 0.602808 | 0.301404 | − | 0.953497i | \(-0.402545\pi\) | ||||
0.301404 | + | 0.953497i | \(0.402545\pi\) | |||||||
\(98\) | −1.65369 | −0.167048 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.734678 | 0.0734678 | ||||||||
\(101\) | −3.15826 | −0.314259 | −0.157129 | − | 0.987578i | \(-0.550224\pi\) | ||||
−0.157129 | + | 0.987578i | \(0.550224\pi\) | |||||||
\(102\) | −8.64266 | −0.855751 | ||||||||
\(103\) | 1.24686 | 0.122857 | 0.0614285 | − | 0.998111i | \(-0.480434\pi\) | ||||
0.0614285 | + | 0.998111i | \(0.480434\pi\) | |||||||
\(104\) | 11.7194 | 1.14918 | ||||||||
\(105\) | 1.14142 | 0.111391 | ||||||||
\(106\) | −10.2749 | −0.997983 | ||||||||
\(107\) | 10.2684 | 0.992687 | 0.496343 | − | 0.868126i | \(-0.334676\pi\) | ||||
0.496343 | + | 0.868126i | \(0.334676\pi\) | |||||||
\(108\) | 3.93893 | 0.379024 | ||||||||
\(109\) | −5.67907 | −0.543956 | −0.271978 | − | 0.962303i | \(-0.587678\pi\) | ||||
−0.271978 | + | 0.962303i | \(0.587678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.6688 | 1.01264 | ||||||||
\(112\) | −4.92960 | −0.465804 | ||||||||
\(113\) | 17.9797 | 1.69139 | 0.845694 | − | 0.533669i | \(-0.179187\pi\) | ||||
0.845694 | + | 0.533669i | \(0.179187\pi\) | |||||||
\(114\) | 3.55141 | 0.332620 | ||||||||
\(115\) | −2.08099 | −0.194053 | ||||||||
\(116\) | −4.05238 | −0.376254 | ||||||||
\(117\) | −9.50545 | −0.878779 | ||||||||
\(118\) | −22.4673 | −2.06828 | ||||||||
\(119\) | −4.57876 | −0.419734 | ||||||||
\(120\) | 2.38836 | 0.218027 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 18.3799 | 1.66404 | ||||||||
\(123\) | −12.5712 | −1.13351 | ||||||||
\(124\) | −4.01194 | −0.360282 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.80656 | 0.250028 | ||||||||
\(127\) | −12.0909 | −1.07289 | −0.536447 | − | 0.843934i | \(-0.680234\pi\) | ||||
−0.536447 | + | 0.843934i | \(0.680234\pi\) | |||||||
\(128\) | −13.3895 | −1.18347 | ||||||||
\(129\) | 9.62612 | 0.847533 | ||||||||
\(130\) | 9.26199 | 0.812330 | ||||||||
\(131\) | −1.04441 | −0.0912502 | −0.0456251 | − | 0.998959i | \(-0.514528\pi\) | ||||
−0.0456251 | + | 0.998959i | \(0.514528\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.88149 | 0.163146 | ||||||||
\(134\) | 9.27592 | 0.801317 | ||||||||
\(135\) | −5.36144 | −0.461439 | ||||||||
\(136\) | −9.58081 | −0.821548 | ||||||||
\(137\) | −1.43820 | −0.122874 | −0.0614368 | − | 0.998111i | \(-0.519568\pi\) | ||||
−0.0614368 | + | 0.998111i | \(0.519568\pi\) | |||||||
\(138\) | 3.92798 | 0.334372 | ||||||||
\(139\) | 21.6489 | 1.83623 | 0.918117 | − | 0.396310i | \(-0.129709\pi\) | ||||
0.918117 | + | 0.396310i | \(0.129709\pi\) | |||||||
\(140\) | −0.734678 | −0.0620916 | ||||||||
\(141\) | −1.83696 | −0.154700 | ||||||||
\(142\) | −1.15195 | −0.0966694 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.36630 | 0.697192 | ||||||||
\(145\) | 5.51585 | 0.458067 | ||||||||
\(146\) | −22.9653 | −1.90062 | ||||||||
\(147\) | −1.14142 | −0.0941429 | ||||||||
\(148\) | −6.86699 | −0.564463 | ||||||||
\(149\) | 12.6540 | 1.03666 | 0.518329 | − | 0.855181i | \(-0.326554\pi\) | ||||
0.518329 | + | 0.855181i | \(0.326554\pi\) | |||||||
\(150\) | 1.88755 | 0.154118 | ||||||||
\(151\) | −2.48546 | −0.202264 | −0.101132 | − | 0.994873i | \(-0.532246\pi\) | ||||
−0.101132 | + | 0.994873i | \(0.532246\pi\) | |||||||
\(152\) | 3.93691 | 0.319325 | ||||||||
\(153\) | 7.77087 | 0.628238 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.46081 | 0.438623 | ||||||||
\(156\) | −4.69672 | −0.376038 | ||||||||
\(157\) | −14.2773 | −1.13945 | −0.569727 | − | 0.821834i | \(-0.692951\pi\) | ||||
−0.569727 | + | 0.821834i | \(0.692951\pi\) | |||||||
\(158\) | 14.0131 | 1.11483 | ||||||||
\(159\) | −7.09201 | −0.562433 | ||||||||
\(160\) | −3.96713 | −0.313629 | ||||||||
\(161\) | 2.08099 | 0.164005 | ||||||||
\(162\) | 1.70032 | 0.133589 | ||||||||
\(163\) | −9.75758 | −0.764272 | −0.382136 | − | 0.924106i | \(-0.624811\pi\) | ||||
−0.382136 | + | 0.924106i | \(0.624811\pi\) | |||||||
\(164\) | 8.09147 | 0.631837 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.7138 | 1.21963 | ||||||||
\(167\) | −11.3890 | −0.881308 | −0.440654 | − | 0.897677i | \(-0.645253\pi\) | ||||
−0.440654 | + | 0.897677i | \(0.645253\pi\) | |||||||
\(168\) | −2.38836 | −0.184266 | ||||||||
\(169\) | 18.3691 | 1.41301 | ||||||||
\(170\) | −7.57184 | −0.580733 | ||||||||
\(171\) | −3.19317 | −0.244188 | ||||||||
\(172\) | −6.19586 | −0.472430 | ||||||||
\(173\) | −10.3544 | −0.787227 | −0.393613 | − | 0.919276i | \(-0.628775\pi\) | ||||
−0.393613 | + | 0.919276i | \(0.628775\pi\) | |||||||
\(174\) | −10.4115 | −0.789292 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.5076 | −1.16562 | ||||||||
\(178\) | −2.47826 | −0.185754 | ||||||||
\(179\) | 18.8195 | 1.40664 | 0.703318 | − | 0.710875i | \(-0.251701\pi\) | ||||
0.703318 | + | 0.710875i | \(0.251701\pi\) | |||||||
\(180\) | 1.24686 | 0.0929356 | ||||||||
\(181\) | −7.75369 | −0.576327 | −0.288164 | − | 0.957581i | \(-0.593045\pi\) | ||||
−0.288164 | + | 0.957581i | \(0.593045\pi\) | |||||||
\(182\) | −9.26199 | −0.686544 | ||||||||
\(183\) | 12.6863 | 0.937801 | ||||||||
\(184\) | 4.35436 | 0.321008 | ||||||||
\(185\) | 9.34694 | 0.687201 | ||||||||
\(186\) | −10.3076 | −0.755788 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.18236 | 0.0862325 | ||||||||
\(189\) | 5.36144 | 0.389987 | ||||||||
\(190\) | 3.11139 | 0.225724 | ||||||||
\(191\) | 15.9410 | 1.15345 | 0.576723 | − | 0.816939i | \(-0.304331\pi\) | ||||
0.576723 | + | 0.816939i | \(0.304331\pi\) | |||||||
\(192\) | −3.76535 | −0.271741 | ||||||||
\(193\) | −8.52230 | −0.613448 | −0.306724 | − | 0.951798i | \(-0.599233\pi\) | ||||
−0.306724 | + | 0.951798i | \(0.599233\pi\) | |||||||
\(194\) | −9.81789 | −0.704883 | ||||||||
\(195\) | 6.39289 | 0.457804 | ||||||||
\(196\) | 0.734678 | 0.0524770 | ||||||||
\(197\) | 19.0556 | 1.35765 | 0.678826 | − | 0.734299i | \(-0.262489\pi\) | ||||
0.678826 | + | 0.734299i | \(0.262489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7118 | −0.901118 | −0.450559 | − | 0.892747i | \(-0.648775\pi\) | ||||
−0.450559 | + | 0.892747i | \(0.648775\pi\) | |||||||
\(200\) | 2.09245 | 0.147958 | ||||||||
\(201\) | 6.40251 | 0.451598 | ||||||||
\(202\) | 5.22277 | 0.367473 | ||||||||
\(203\) | −5.51585 | −0.387137 | ||||||||
\(204\) | 3.83965 | 0.268829 | ||||||||
\(205\) | −11.0136 | −0.769225 | ||||||||
\(206\) | −2.06192 | −0.143661 | ||||||||
\(207\) | −3.53177 | −0.245475 | ||||||||
\(208\) | −27.6098 | −1.91439 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.88755 | −0.130254 | ||||||||
\(211\) | 28.4506 | 1.95862 | 0.979311 | − | 0.202363i | \(-0.0648620\pi\) | ||||
0.979311 | + | 0.202363i | \(0.0648620\pi\) | |||||||
\(212\) | 4.56478 | 0.313510 | ||||||||
\(213\) | −0.795108 | −0.0544799 | ||||||||
\(214\) | −16.9808 | −1.16078 | ||||||||
\(215\) | 8.43344 | 0.575156 | ||||||||
\(216\) | 11.2185 | 0.763323 | ||||||||
\(217\) | −5.46081 | −0.370704 | ||||||||
\(218\) | 9.39140 | 0.636066 | ||||||||
\(219\) | −15.8513 | −1.07113 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.6448 | −1.72506 | ||||||||
\(222\) | −17.6429 | −1.18411 | ||||||||
\(223\) | −23.9632 | −1.60470 | −0.802348 | − | 0.596856i | \(-0.796416\pi\) | ||||
−0.802348 | + | 0.596856i | \(0.796416\pi\) | |||||||
\(224\) | 3.96713 | 0.265065 | ||||||||
\(225\) | −1.69716 | −0.113144 | ||||||||
\(226\) | −29.7328 | −1.97779 | ||||||||
\(227\) | −20.6007 | −1.36732 | −0.683658 | − | 0.729803i | \(-0.739612\pi\) | ||||
−0.683658 | + | 0.729803i | \(0.739612\pi\) | |||||||
\(228\) | −1.57777 | −0.104490 | ||||||||
\(229\) | 0.903360 | 0.0596957 | 0.0298479 | − | 0.999554i | \(-0.490498\pi\) | ||||
0.0298479 | + | 0.999554i | \(0.490498\pi\) | |||||||
\(230\) | 3.44131 | 0.226913 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.5416 | −0.757745 | ||||||||
\(233\) | −23.2459 | −1.52289 | −0.761444 | − | 0.648231i | \(-0.775509\pi\) | ||||
−0.761444 | + | 0.648231i | \(0.775509\pi\) | |||||||
\(234\) | 15.7190 | 1.02759 | ||||||||
\(235\) | −1.60936 | −0.104983 | ||||||||
\(236\) | 9.98148 | 0.649739 | ||||||||
\(237\) | 9.67228 | 0.628282 | ||||||||
\(238\) | 7.57184 | 0.490809 | ||||||||
\(239\) | −8.21214 | −0.531199 | −0.265600 | − | 0.964083i | \(-0.585570\pi\) | ||||
−0.265600 | + | 0.964083i | \(0.585570\pi\) | |||||||
\(240\) | −5.62676 | −0.363206 | ||||||||
\(241\) | 8.33040 | 0.536608 | 0.268304 | − | 0.963334i | \(-0.413537\pi\) | ||||
0.268304 | + | 0.963334i | \(0.413537\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9107 | −0.956522 | ||||||||
\(244\) | −8.16557 | −0.522747 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 20.7888 | 1.32545 | ||||||||
\(247\) | 10.5378 | 0.670507 | ||||||||
\(248\) | −11.4264 | −0.725580 | ||||||||
\(249\) | 10.8461 | 0.687346 | ||||||||
\(250\) | 1.65369 | 0.104588 | ||||||||
\(251\) | −9.77541 | −0.617018 | −0.308509 | − | 0.951221i | \(-0.599830\pi\) | ||||
−0.308509 | + | 0.951221i | \(0.599830\pi\) | |||||||
\(252\) | −1.24686 | −0.0785450 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.9946 | 1.25457 | ||||||||
\(255\) | −5.22630 | −0.327284 | ||||||||
\(256\) | 15.5443 | 0.971521 | ||||||||
\(257\) | 4.10056 | 0.255786 | 0.127893 | − | 0.991788i | \(-0.459179\pi\) | ||||
0.127893 | + | 0.991788i | \(0.459179\pi\) | |||||||
\(258\) | −15.9186 | −0.991047 | ||||||||
\(259\) | −9.34694 | −0.580791 | ||||||||
\(260\) | −4.11479 | −0.255189 | ||||||||
\(261\) | 9.36126 | 0.579448 | ||||||||
\(262\) | 1.72712 | 0.106702 | ||||||||
\(263\) | −25.6453 | −1.58136 | −0.790678 | − | 0.612232i | \(-0.790272\pi\) | ||||
−0.790678 | + | 0.612232i | \(0.790272\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.21331 | −0.381680 | ||||||||
\(266\) | −3.11139 | −0.190771 | ||||||||
\(267\) | −1.71057 | −0.104685 | ||||||||
\(268\) | −4.12098 | −0.251729 | ||||||||
\(269\) | 13.7027 | 0.835470 | 0.417735 | − | 0.908569i | \(-0.362824\pi\) | ||||
0.417735 | + | 0.908569i | \(0.362824\pi\) | |||||||
\(270\) | 8.86613 | 0.539576 | ||||||||
\(271\) | 8.60468 | 0.522697 | 0.261349 | − | 0.965244i | \(-0.415833\pi\) | ||||
0.261349 | + | 0.965244i | \(0.415833\pi\) | |||||||
\(272\) | 22.5715 | 1.36860 | ||||||||
\(273\) | −6.39289 | −0.386915 | ||||||||
\(274\) | 2.37833 | 0.143680 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.74507 | −0.105041 | ||||||||
\(277\) | −28.8920 | −1.73595 | −0.867975 | − | 0.496607i | \(-0.834579\pi\) | ||||
−0.867975 | + | 0.496607i | \(0.834579\pi\) | |||||||
\(278\) | −35.8005 | −2.14717 | ||||||||
\(279\) | 9.26784 | 0.554851 | ||||||||
\(280\) | −2.09245 | −0.125048 | ||||||||
\(281\) | −7.98397 | −0.476284 | −0.238142 | − | 0.971230i | \(-0.576538\pi\) | ||||
−0.238142 | + | 0.971230i | \(0.576538\pi\) | |||||||
\(282\) | 3.03775 | 0.180895 | ||||||||
\(283\) | 7.39498 | 0.439586 | 0.219793 | − | 0.975547i | \(-0.429462\pi\) | ||||
0.219793 | + | 0.975547i | \(0.429462\pi\) | |||||||
\(284\) | 0.511772 | 0.0303681 | ||||||||
\(285\) | 2.14757 | 0.127211 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.0136 | 0.650114 | ||||||||
\(288\) | −6.73283 | −0.396736 | ||||||||
\(289\) | 3.96507 | 0.233239 | ||||||||
\(290\) | −9.12149 | −0.535632 | ||||||||
\(291\) | −6.77659 | −0.397251 | ||||||||
\(292\) | 10.2027 | 0.597068 | ||||||||
\(293\) | −13.7881 | −0.805508 | −0.402754 | − | 0.915308i | \(-0.631947\pi\) | ||||
−0.402754 | + | 0.915308i | \(0.631947\pi\) | |||||||
\(294\) | 1.88755 | 0.110084 | ||||||||
\(295\) | −13.5862 | −0.791019 | ||||||||
\(296\) | −19.5580 | −1.13678 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.9258 | −1.21220 | ||||||||
\(299\) | 11.6552 | 0.674040 | ||||||||
\(300\) | −0.838578 | −0.0484153 | ||||||||
\(301\) | −8.43344 | −0.486096 | ||||||||
\(302\) | 4.11017 | 0.236514 | ||||||||
\(303\) | 3.60491 | 0.207097 | ||||||||
\(304\) | −9.27498 | −0.531957 | ||||||||
\(305\) | 11.1145 | 0.636414 | ||||||||
\(306\) | −12.8506 | −0.734619 | ||||||||
\(307\) | 5.89759 | 0.336593 | 0.168297 | − | 0.985736i | \(-0.446173\pi\) | ||||
0.168297 | + | 0.985736i | \(0.446173\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.42320 | −0.0809628 | ||||||||
\(310\) | −9.03046 | −0.512896 | ||||||||
\(311\) | −26.0053 | −1.47462 | −0.737311 | − | 0.675553i | \(-0.763905\pi\) | ||||
−0.737311 | + | 0.675553i | \(0.763905\pi\) | |||||||
\(312\) | −13.3768 | −0.757311 | ||||||||
\(313\) | −12.1886 | −0.688938 | −0.344469 | − | 0.938798i | \(-0.611941\pi\) | ||||
−0.344469 | + | 0.938798i | \(0.611941\pi\) | |||||||
\(314\) | 23.6102 | 1.33240 | ||||||||
\(315\) | 1.69716 | 0.0956239 | ||||||||
\(316\) | −6.22557 | −0.350216 | ||||||||
\(317\) | 13.5894 | 0.763258 | 0.381629 | − | 0.924316i | \(-0.375363\pi\) | ||||
0.381629 | + | 0.924316i | \(0.375363\pi\) | |||||||
\(318\) | 11.7280 | 0.657671 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.29883 | −0.184410 | ||||||||
\(321\) | −11.7206 | −0.654181 | ||||||||
\(322\) | −3.44131 | −0.191777 | ||||||||
\(323\) | −8.61488 | −0.479345 | ||||||||
\(324\) | −0.755394 | −0.0419663 | ||||||||
\(325\) | 5.60081 | 0.310677 | ||||||||
\(326\) | 16.1360 | 0.893689 | ||||||||
\(327\) | 6.48222 | 0.358468 | ||||||||
\(328\) | 23.0454 | 1.27247 | ||||||||
\(329\) | 1.60936 | 0.0887268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.3402 | 1.00807 | 0.504034 | − | 0.863684i | \(-0.331849\pi\) | ||||
0.504034 | + | 0.863684i | \(0.331849\pi\) | |||||||
\(332\) | −6.98113 | −0.383139 | ||||||||
\(333\) | 15.8632 | 0.869299 | ||||||||
\(334\) | 18.8338 | 1.03054 | ||||||||
\(335\) | 5.60924 | 0.306465 | ||||||||
\(336\) | 5.62676 | 0.306965 | ||||||||
\(337\) | −25.2973 | −1.37803 | −0.689015 | − | 0.724747i | \(-0.741957\pi\) | ||||
−0.689015 | + | 0.724747i | \(0.741957\pi\) | |||||||
\(338\) | −30.3767 | −1.65228 | ||||||||
\(339\) | −20.5224 | −1.11462 | ||||||||
\(340\) | 3.36392 | 0.182434 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.28051 | 0.285537 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −17.6465 | −0.951437 | ||||||||
\(345\) | 2.37529 | 0.127881 | ||||||||
\(346\) | 17.1228 | 0.920530 | ||||||||
\(347\) | −14.4944 | −0.778098 | −0.389049 | − | 0.921217i | \(-0.627196\pi\) | ||||
−0.389049 | + | 0.921217i | \(0.627196\pi\) | |||||||
\(348\) | 4.62547 | 0.247951 | ||||||||
\(349\) | −2.97717 | −0.159364 | −0.0796822 | − | 0.996820i | \(-0.525391\pi\) | ||||
−0.0796822 | + | 0.996820i | \(0.525391\pi\) | |||||||
\(350\) | −1.65369 | −0.0883932 | ||||||||
\(351\) | 30.0284 | 1.60280 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0782 | 0.749304 | 0.374652 | − | 0.927165i | \(-0.377762\pi\) | ||||
0.374652 | + | 0.927165i | \(0.377762\pi\) | |||||||
\(354\) | 25.6447 | 1.36300 | ||||||||
\(355\) | −0.696594 | −0.0369714 | ||||||||
\(356\) | 1.10101 | 0.0583534 | ||||||||
\(357\) | 5.22630 | 0.276605 | ||||||||
\(358\) | −31.1216 | −1.64483 | ||||||||
\(359\) | −15.3313 | −0.809154 | −0.404577 | − | 0.914504i | \(-0.632581\pi\) | ||||
−0.404577 | + | 0.914504i | \(0.632581\pi\) | |||||||
\(360\) | 3.55121 | 0.187165 | ||||||||
\(361\) | −15.4600 | −0.813685 | ||||||||
\(362\) | 12.8222 | 0.673918 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.11479 | 0.215674 | ||||||||
\(365\) | −13.8873 | −0.726896 | ||||||||
\(366\) | −20.9792 | −1.09660 | ||||||||
\(367\) | 13.7180 | 0.716072 | 0.358036 | − | 0.933708i | \(-0.383447\pi\) | ||||
0.358036 | + | 0.933708i | \(0.383447\pi\) | |||||||
\(368\) | −10.2585 | −0.534759 | ||||||||
\(369\) | −18.6918 | −0.973058 | ||||||||
\(370\) | −15.4569 | −0.803567 | ||||||||
\(371\) | 6.21331 | 0.322579 | ||||||||
\(372\) | 4.57931 | 0.237426 | ||||||||
\(373\) | −12.6631 | −0.655670 | −0.327835 | − | 0.944735i | \(-0.606319\pi\) | ||||
−0.327835 | + | 0.944735i | \(0.606319\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.14142 | 0.0589428 | ||||||||
\(376\) | 3.36750 | 0.173665 | ||||||||
\(377\) | −30.8933 | −1.59108 | ||||||||
\(378\) | −8.86613 | −0.456025 | ||||||||
\(379\) | 12.0373 | 0.618314 | 0.309157 | − | 0.951011i | \(-0.399953\pi\) | ||||
0.309157 | + | 0.951011i | \(0.399953\pi\) | |||||||
\(380\) | −1.38229 | −0.0709098 | ||||||||
\(381\) | 13.8008 | 0.707038 | ||||||||
\(382\) | −26.3613 | −1.34876 | ||||||||
\(383\) | −9.96182 | −0.509025 | −0.254513 | − | 0.967069i | \(-0.581915\pi\) | ||||
−0.254513 | + | 0.967069i | \(0.581915\pi\) | |||||||
\(384\) | 15.2830 | 0.779910 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0932 | 0.717325 | ||||||||
\(387\) | 14.3129 | 0.727564 | ||||||||
\(388\) | 4.36176 | 0.221435 | ||||||||
\(389\) | 22.1252 | 1.12179 | 0.560895 | − | 0.827887i | \(-0.310457\pi\) | ||||
0.560895 | + | 0.827887i | \(0.310457\pi\) | |||||||
\(390\) | −10.5718 | −0.535326 | ||||||||
\(391\) | −9.52837 | −0.481870 | ||||||||
\(392\) | 2.09245 | 0.105684 | ||||||||
\(393\) | 1.19211 | 0.0601339 | ||||||||
\(394\) | −31.5119 | −1.58755 | ||||||||
\(395\) | 8.47388 | 0.426367 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.4968 | −1.32984 | −0.664918 | − | 0.746916i | \(-0.731533\pi\) | ||||
−0.664918 | + | 0.746916i | \(0.731533\pi\) | |||||||
\(398\) | 21.0214 | 1.05371 | ||||||||
\(399\) | −2.14757 | −0.107513 | ||||||||
\(400\) | −4.92960 | −0.246480 | ||||||||
\(401\) | −2.98212 | −0.148920 | −0.0744600 | − | 0.997224i | \(-0.523723\pi\) | ||||
−0.0744600 | + | 0.997224i | \(0.523723\pi\) | |||||||
\(402\) | −10.5877 | −0.528068 | ||||||||
\(403\) | −30.5850 | −1.52355 | ||||||||
\(404\) | −2.32031 | −0.115439 | ||||||||
\(405\) | 1.02820 | 0.0510915 | ||||||||
\(406\) | 9.12149 | 0.452692 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 10.9358 | 0.541400 | ||||||||
\(409\) | −1.71895 | −0.0849966 | −0.0424983 | − | 0.999097i | \(-0.513532\pi\) | ||||
−0.0424983 | + | 0.999097i | \(0.513532\pi\) | |||||||
\(410\) | 18.2131 | 0.899480 | ||||||||
\(411\) | 1.64159 | 0.0809738 | ||||||||
\(412\) | 0.916042 | 0.0451302 | ||||||||
\(413\) | 13.5862 | 0.668533 | ||||||||
\(414\) | 5.84043 | 0.287042 | ||||||||
\(415\) | 9.50230 | 0.466449 | ||||||||
\(416\) | 22.2191 | 1.08938 | ||||||||
\(417\) | −24.7105 | −1.21008 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.6056 | −1.20206 | −0.601031 | − | 0.799226i | \(-0.705243\pi\) | ||||
−0.601031 | + | 0.799226i | \(0.705243\pi\) | |||||||
\(420\) | 0.838578 | 0.0409184 | ||||||||
\(421\) | −29.8732 | −1.45593 | −0.727965 | − | 0.685615i | \(-0.759533\pi\) | ||||
−0.727965 | + | 0.685615i | \(0.759533\pi\) | |||||||
\(422\) | −47.0484 | −2.29028 | ||||||||
\(423\) | −2.73133 | −0.132802 | ||||||||
\(424\) | 13.0010 | 0.631385 | ||||||||
\(425\) | −4.57876 | −0.222103 | ||||||||
\(426\) | 1.31486 | 0.0637052 | ||||||||
\(427\) | −11.1145 | −0.537868 | ||||||||
\(428\) | 7.54399 | 0.364652 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.9463 | −0.672549 | ||||||||
\(431\) | 15.5900 | 0.750943 | 0.375472 | − | 0.926834i | \(-0.377481\pi\) | ||||
0.375472 | + | 0.926834i | \(0.377481\pi\) | |||||||
\(432\) | −26.4298 | −1.27160 | ||||||||
\(433\) | 10.6888 | 0.513671 | 0.256835 | − | 0.966455i | \(-0.417320\pi\) | ||||
0.256835 | + | 0.966455i | \(0.417320\pi\) | |||||||
\(434\) | 9.03046 | 0.433476 | ||||||||
\(435\) | −6.29592 | −0.301866 | ||||||||
\(436\) | −4.17229 | −0.199816 | ||||||||
\(437\) | 3.91536 | 0.187297 | ||||||||
\(438\) | 26.2131 | 1.25251 | ||||||||
\(439\) | −18.1537 | −0.866427 | −0.433214 | − | 0.901291i | \(-0.642620\pi\) | ||||
−0.433214 | + | 0.901291i | \(0.642620\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.69716 | −0.0808169 | ||||||||
\(442\) | 42.4084 | 2.01716 | ||||||||
\(443\) | −9.93668 | −0.472106 | −0.236053 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236053 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(444\) | 7.83814 | 0.371982 | ||||||||
\(445\) | −1.49863 | −0.0710418 | ||||||||
\(446\) | 39.6277 | 1.87642 | ||||||||
\(447\) | −14.4436 | −0.683158 | ||||||||
\(448\) | 3.29883 | 0.155855 | ||||||||
\(449\) | −18.0920 | −0.853813 | −0.426906 | − | 0.904296i | \(-0.640397\pi\) | ||||
−0.426906 | + | 0.904296i | \(0.640397\pi\) | |||||||
\(450\) | 2.80656 | 0.132303 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.2093 | 0.621312 | ||||||||
\(453\) | 2.83696 | 0.133292 | ||||||||
\(454\) | 34.0671 | 1.59885 | ||||||||
\(455\) | −5.60081 | −0.262570 | ||||||||
\(456\) | −4.49367 | −0.210436 | ||||||||
\(457\) | 15.9901 | 0.747987 | 0.373993 | − | 0.927431i | \(-0.377988\pi\) | ||||
0.373993 | + | 0.927431i | \(0.377988\pi\) | |||||||
\(458\) | −1.49387 | −0.0698041 | ||||||||
\(459\) | −24.5487 | −1.14584 | ||||||||
\(460\) | −1.52886 | −0.0712834 | ||||||||
\(461\) | −27.9612 | −1.30228 | −0.651140 | − | 0.758957i | \(-0.725709\pi\) | ||||
−0.651140 | + | 0.758957i | \(0.725709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.8389 | −1.43320 | −0.716602 | − | 0.697482i | \(-0.754304\pi\) | ||||
−0.716602 | + | 0.697482i | \(0.754304\pi\) | |||||||
\(464\) | 27.1910 | 1.26231 | ||||||||
\(465\) | −6.23309 | −0.289053 | ||||||||
\(466\) | 38.4414 | 1.78076 | ||||||||
\(467\) | −8.41735 | −0.389509 | −0.194754 | − | 0.980852i | \(-0.562391\pi\) | ||||
−0.194754 | + | 0.980852i | \(0.562391\pi\) | |||||||
\(468\) | −6.98344 | −0.322810 | ||||||||
\(469\) | −5.60924 | −0.259011 | ||||||||
\(470\) | 2.66137 | 0.122760 | ||||||||
\(471\) | 16.2964 | 0.750900 | ||||||||
\(472\) | 28.4284 | 1.30852 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.9949 | −0.734671 | ||||||||
\(475\) | 1.88149 | 0.0863285 | ||||||||
\(476\) | −3.36392 | −0.154185 | ||||||||
\(477\) | −10.5449 | −0.482820 | ||||||||
\(478\) | 13.5803 | 0.621149 | ||||||||
\(479\) | −29.6865 | −1.35641 | −0.678205 | − | 0.734873i | \(-0.737242\pi\) | ||||
−0.678205 | + | 0.734873i | \(0.737242\pi\) | |||||||
\(480\) | 4.52817 | 0.206682 | ||||||||
\(481\) | −52.3505 | −2.38698 | ||||||||
\(482\) | −13.7759 | −0.627474 | ||||||||
\(483\) | −2.37529 | −0.108079 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.93697 | −0.269584 | ||||||||
\(486\) | 24.6576 | 1.11849 | ||||||||
\(487\) | 37.8313 | 1.71430 | 0.857150 | − | 0.515067i | \(-0.172233\pi\) | ||||
0.857150 | + | 0.515067i | \(0.172233\pi\) | |||||||
\(488\) | −23.2565 | −1.05277 | ||||||||
\(489\) | 11.1375 | 0.503656 | ||||||||
\(490\) | 1.65369 | 0.0747059 | ||||||||
\(491\) | −18.6985 | −0.843850 | −0.421925 | − | 0.906631i | \(-0.638645\pi\) | ||||
−0.421925 | + | 0.906631i | \(0.638645\pi\) | |||||||
\(492\) | −9.23578 | −0.416381 | ||||||||
\(493\) | 25.2558 | 1.13746 | ||||||||
\(494\) | −17.4263 | −0.784046 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.9196 | 1.20873 | ||||||||
\(497\) | 0.696594 | 0.0312465 | ||||||||
\(498\) | −17.9361 | −0.803736 | ||||||||
\(499\) | 22.8758 | 1.02406 | 0.512030 | − | 0.858967i | \(-0.328894\pi\) | ||||
0.512030 | + | 0.858967i | \(0.328894\pi\) | |||||||
\(500\) | −0.734678 | −0.0328558 | ||||||||
\(501\) | 12.9997 | 0.580782 | ||||||||
\(502\) | 16.1655 | 0.721499 | ||||||||
\(503\) | 11.6087 | 0.517607 | 0.258804 | − | 0.965930i | \(-0.416672\pi\) | ||||
0.258804 | + | 0.965930i | \(0.416672\pi\) | |||||||
\(504\) | −3.55121 | −0.158183 | ||||||||
\(505\) | 3.15826 | 0.140541 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.9669 | −0.931173 | ||||||||
\(508\) | −8.88292 | −0.394116 | ||||||||
\(509\) | −13.8562 | −0.614163 | −0.307082 | − | 0.951683i | \(-0.599353\pi\) | ||||
−0.307082 | + | 0.951683i | \(0.599353\pi\) | |||||||
\(510\) | 8.64266 | 0.382704 | ||||||||
\(511\) | 13.8873 | 0.614339 | ||||||||
\(512\) | 1.07349 | 0.0474422 | ||||||||
\(513\) | 10.0875 | 0.445373 | ||||||||
\(514\) | −6.78105 | −0.299099 | ||||||||
\(515\) | −1.24686 | −0.0549433 | ||||||||
\(516\) | 7.07210 | 0.311332 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 15.4569 | 0.679138 | ||||||||
\(519\) | 11.8187 | 0.518783 | ||||||||
\(520\) | −11.7194 | −0.513930 | ||||||||
\(521\) | −25.2028 | −1.10415 | −0.552077 | − | 0.833793i | \(-0.686165\pi\) | ||||
−0.552077 | + | 0.833793i | \(0.686165\pi\) | |||||||
\(522\) | −15.4806 | −0.677567 | ||||||||
\(523\) | 28.9229 | 1.26471 | 0.632355 | − | 0.774679i | \(-0.282089\pi\) | ||||
0.632355 | + | 0.774679i | \(0.282089\pi\) | |||||||
\(524\) | −0.767303 | −0.0335198 | ||||||||
\(525\) | −1.14142 | −0.0498157 | ||||||||
\(526\) | 42.4093 | 1.84913 | ||||||||
\(527\) | 25.0038 | 1.08918 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6695 | −0.811716 | ||||||||
\(530\) | 10.2749 | 0.446311 | ||||||||
\(531\) | −23.0579 | −1.00063 | ||||||||
\(532\) | 1.38229 | 0.0599297 | ||||||||
\(533\) | 61.6852 | 2.67188 | ||||||||
\(534\) | 2.82874 | 0.122412 | ||||||||
\(535\) | −10.2684 | −0.443943 | ||||||||
\(536\) | −11.7370 | −0.506962 | ||||||||
\(537\) | −21.4810 | −0.926974 | ||||||||
\(538\) | −22.6600 | −0.976943 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.93893 | −0.169505 | ||||||||
\(541\) | −13.9092 | −0.598003 | −0.299001 | − | 0.954253i | \(-0.596653\pi\) | ||||
−0.299001 | + | 0.954253i | \(0.596653\pi\) | |||||||
\(542\) | −14.2294 | −0.611207 | ||||||||
\(543\) | 8.85023 | 0.379800 | ||||||||
\(544\) | −18.1645 | −0.778798 | ||||||||
\(545\) | 5.67907 | 0.243265 | ||||||||
\(546\) | 10.5718 | 0.452433 | ||||||||
\(547\) | −12.4603 | −0.532766 | −0.266383 | − | 0.963867i | \(-0.585829\pi\) | ||||
−0.266383 | + | 0.963867i | \(0.585829\pi\) | |||||||
\(548\) | −1.05661 | −0.0451363 | ||||||||
\(549\) | 18.8630 | 0.805054 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3780 | −0.442118 | ||||||||
\(552\) | −4.97017 | −0.211544 | ||||||||
\(553\) | −8.47388 | −0.360346 | ||||||||
\(554\) | 47.7783 | 2.02990 | ||||||||
\(555\) | −10.6688 | −0.452866 | ||||||||
\(556\) | 15.9050 | 0.674520 | ||||||||
\(557\) | −37.5067 | −1.58921 | −0.794605 | − | 0.607127i | \(-0.792322\pi\) | ||||
−0.794605 | + | 0.607127i | \(0.792322\pi\) | |||||||
\(558\) | −15.3261 | −0.648806 | ||||||||
\(559\) | −47.2341 | −1.99779 | ||||||||
\(560\) | 4.92960 | 0.208314 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.2030 | 0.556934 | ||||||||
\(563\) | 24.5527 | 1.03477 | 0.517387 | − | 0.855752i | \(-0.326905\pi\) | ||||
0.517387 | + | 0.855752i | \(0.326905\pi\) | |||||||
\(564\) | −1.34957 | −0.0568272 | ||||||||
\(565\) | −17.9797 | −0.756411 | ||||||||
\(566\) | −12.2290 | −0.514022 | ||||||||
\(567\) | −1.02820 | −0.0431802 | ||||||||
\(568\) | 1.45759 | 0.0611590 | ||||||||
\(569\) | 39.6609 | 1.66267 | 0.831336 | − | 0.555771i | \(-0.187577\pi\) | ||||
0.831336 | + | 0.555771i | \(0.187577\pi\) | |||||||
\(570\) | −3.55141 | −0.148752 | ||||||||
\(571\) | −31.3014 | −1.30992 | −0.654961 | − | 0.755663i | \(-0.727315\pi\) | ||||
−0.654961 | + | 0.755663i | \(0.727315\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.1954 | −0.760122 | ||||||||
\(574\) | −18.2131 | −0.760199 | ||||||||
\(575\) | 2.08099 | 0.0867834 | ||||||||
\(576\) | −5.59862 | −0.233276 | ||||||||
\(577\) | −33.8941 | −1.41103 | −0.705516 | − | 0.708694i | \(-0.749285\pi\) | ||||
−0.705516 | + | 0.708694i | \(0.749285\pi\) | |||||||
\(578\) | −6.55698 | −0.272734 | ||||||||
\(579\) | 9.72754 | 0.404263 | ||||||||
\(580\) | 4.05238 | 0.168266 | ||||||||
\(581\) | −9.50230 | −0.394222 | ||||||||
\(582\) | 11.2064 | 0.464518 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 29.0585 | 1.20245 | ||||||||
\(585\) | 9.50545 | 0.393002 | ||||||||
\(586\) | 22.8011 | 0.941907 | ||||||||
\(587\) | −32.3331 | −1.33453 | −0.667264 | − | 0.744821i | \(-0.732535\pi\) | ||||
−0.667264 | + | 0.744821i | \(0.732535\pi\) | |||||||
\(588\) | −0.838578 | −0.0345824 | ||||||||
\(589\) | −10.2744 | −0.423351 | ||||||||
\(590\) | 22.4673 | 0.924964 | ||||||||
\(591\) | −21.7504 | −0.894693 | ||||||||
\(592\) | 46.0767 | 1.89374 | ||||||||
\(593\) | −25.6741 | −1.05431 | −0.527153 | − | 0.849770i | \(-0.676741\pi\) | ||||
−0.527153 | + | 0.849770i | \(0.676741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.57876 | 0.187711 | ||||||||
\(596\) | 9.29663 | 0.380805 | ||||||||
\(597\) | 14.5096 | 0.593837 | ||||||||
\(598\) | −19.2741 | −0.788177 | ||||||||
\(599\) | −21.7518 | −0.888756 | −0.444378 | − | 0.895839i | \(-0.646575\pi\) | ||||
−0.444378 | + | 0.895839i | \(0.646575\pi\) | |||||||
\(600\) | −2.38836 | −0.0975046 | ||||||||
\(601\) | 15.6850 | 0.639806 | 0.319903 | − | 0.947450i | \(-0.396350\pi\) | ||||
0.319903 | + | 0.947450i | \(0.396350\pi\) | |||||||
\(602\) | 13.9463 | 0.568407 | ||||||||
\(603\) | 9.51975 | 0.387674 | ||||||||
\(604\) | −1.82601 | −0.0742994 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.96139 | −0.242165 | ||||||||
\(607\) | −22.9458 | −0.931343 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(608\) | 7.46409 | 0.302709 | ||||||||
\(609\) | 6.29592 | 0.255123 | ||||||||
\(610\) | −18.3799 | −0.744180 | ||||||||
\(611\) | 9.01372 | 0.364656 | ||||||||
\(612\) | 5.70909 | 0.230776 | ||||||||
\(613\) | −40.0317 | −1.61687 | −0.808433 | − | 0.588588i | \(-0.799684\pi\) | ||||
−0.808433 | + | 0.588588i | \(0.799684\pi\) | |||||||
\(614\) | −9.75276 | −0.393589 | ||||||||
\(615\) | 12.5712 | 0.506920 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.7371 | 0.593293 | 0.296647 | − | 0.954987i | \(-0.404132\pi\) | ||||
0.296647 | + | 0.954987i | \(0.404132\pi\) | |||||||
\(618\) | 2.35352 | 0.0946725 | ||||||||
\(619\) | 25.4079 | 1.02123 | 0.510616 | − | 0.859809i | \(-0.329417\pi\) | ||||
0.510616 | + | 0.859809i | \(0.329417\pi\) | |||||||
\(620\) | 4.01194 | 0.161123 | ||||||||
\(621\) | 11.1571 | 0.447719 | ||||||||
\(622\) | 43.0045 | 1.72432 | ||||||||
\(623\) | 1.49863 | 0.0600413 | ||||||||
\(624\) | 31.5144 | 1.26159 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 20.1560 | 0.805597 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.4892 | −0.418566 | ||||||||
\(629\) | 42.7974 | 1.70645 | ||||||||
\(630\) | −2.80656 | −0.111816 | ||||||||
\(631\) | −26.1912 | −1.04265 | −0.521327 | − | 0.853357i | \(-0.674563\pi\) | ||||
−0.521327 | + | 0.853357i | \(0.674563\pi\) | |||||||
\(632\) | −17.7311 | −0.705307 | ||||||||
\(633\) | −32.4742 | −1.29073 | ||||||||
\(634\) | −22.4726 | −0.892503 | ||||||||
\(635\) | 12.0909 | 0.479813 | ||||||||
\(636\) | −5.21034 | −0.206603 | ||||||||
\(637\) | 5.60081 | 0.221912 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.18223 | −0.0467683 | ||||||||
\(640\) | 13.3895 | 0.529266 | ||||||||
\(641\) | 8.22192 | 0.324746 | 0.162373 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162373 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(642\) | 19.3822 | 0.764955 | ||||||||
\(643\) | 31.8519 | 1.25612 | 0.628059 | − | 0.778166i | \(-0.283850\pi\) | ||||
0.628059 | + | 0.778166i | \(0.283850\pi\) | |||||||
\(644\) | 1.52886 | 0.0602455 | ||||||||
\(645\) | −9.62612 | −0.379028 | ||||||||
\(646\) | 14.2463 | 0.560513 | ||||||||
\(647\) | −22.5883 | −0.888036 | −0.444018 | − | 0.896018i | \(-0.646447\pi\) | ||||
−0.444018 | + | 0.896018i | \(0.646447\pi\) | |||||||
\(648\) | −2.15145 | −0.0845168 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −9.26199 | −0.363285 | ||||||||
\(651\) | 6.23309 | 0.244294 | ||||||||
\(652\) | −7.16867 | −0.280747 | ||||||||
\(653\) | −0.763209 | −0.0298667 | −0.0149333 | − | 0.999888i | \(-0.504754\pi\) | ||||
−0.0149333 | + | 0.999888i | \(0.504754\pi\) | |||||||
\(654\) | −10.7196 | −0.419168 | ||||||||
\(655\) | 1.04441 | 0.0408083 | ||||||||
\(656\) | −54.2928 | −2.11978 | ||||||||
\(657\) | −23.5690 | −0.919512 | ||||||||
\(658\) | −2.66137 | −0.103751 | ||||||||
\(659\) | 42.2863 | 1.64724 | 0.823619 | − | 0.567143i | \(-0.191951\pi\) | ||||
0.823619 | + | 0.567143i | \(0.191951\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.2730 | −0.671843 | −0.335921 | − | 0.941890i | \(-0.609048\pi\) | ||||
−0.335921 | + | 0.941890i | \(0.609048\pi\) | |||||||
\(662\) | −30.3289 | −1.17877 | ||||||||
\(663\) | 29.2715 | 1.13681 | ||||||||
\(664\) | −19.8830 | −0.771612 | ||||||||
\(665\) | −1.88149 | −0.0729609 | ||||||||
\(666\) | −26.2328 | −1.01650 | ||||||||
\(667\) | −11.4784 | −0.444447 | ||||||||
\(668\) | −8.36725 | −0.323739 | ||||||||
\(669\) | 27.3522 | 1.05750 | ||||||||
\(670\) | −9.27592 | −0.358360 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.52817 | −0.174678 | ||||||||
\(673\) | 39.3343 | 1.51623 | 0.758113 | − | 0.652124i | \(-0.226122\pi\) | ||||
0.758113 | + | 0.652124i | \(0.226122\pi\) | |||||||
\(674\) | 41.8338 | 1.61138 | ||||||||
\(675\) | 5.36144 | 0.206362 | ||||||||
\(676\) | 13.4954 | 0.519053 | ||||||||
\(677\) | −4.86816 | −0.187098 | −0.0935492 | − | 0.995615i | \(-0.529821\pi\) | ||||
−0.0935492 | + | 0.995615i | \(0.529821\pi\) | |||||||
\(678\) | 33.9376 | 1.30337 | ||||||||
\(679\) | 5.93697 | 0.227840 | ||||||||
\(680\) | 9.58081 | 0.367407 | ||||||||
\(681\) | 23.5141 | 0.901062 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.9705 | 1.10853 | 0.554263 | − | 0.832341i | \(-0.313000\pi\) | ||||
0.554263 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(684\) | −2.34595 | −0.0896998 | ||||||||
\(685\) | 1.43820 | 0.0549507 | ||||||||
\(686\) | −1.65369 | −0.0631380 | ||||||||
\(687\) | −1.03112 | −0.0393395 | ||||||||
\(688\) | 41.5735 | 1.58498 | ||||||||
\(689\) | 34.7996 | 1.32576 | ||||||||
\(690\) | −3.92798 | −0.149536 | ||||||||
\(691\) | −15.4179 | −0.586526 | −0.293263 | − | 0.956032i | \(-0.594741\pi\) | ||||
−0.293263 | + | 0.956032i | \(0.594741\pi\) | |||||||
\(692\) | −7.60711 | −0.289179 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.9691 | 0.909855 | ||||||||
\(695\) | −21.6489 | −0.821189 | ||||||||
\(696\) | 13.1739 | 0.499354 | ||||||||
\(697\) | −50.4288 | −1.91013 | ||||||||
\(698\) | 4.92331 | 0.186350 | ||||||||
\(699\) | 26.5334 | 1.00358 | ||||||||
\(700\) | 0.734678 | 0.0277682 | ||||||||
\(701\) | −6.78227 | −0.256163 | −0.128081 | − | 0.991764i | \(-0.540882\pi\) | ||||
−0.128081 | + | 0.991764i | \(0.540882\pi\) | |||||||
\(702\) | −49.6576 | −1.87420 | ||||||||
\(703\) | −17.5861 | −0.663274 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.83696 | 0.0691838 | ||||||||
\(706\) | −23.2808 | −0.876186 | ||||||||
\(707\) | −3.15826 | −0.118779 | ||||||||
\(708\) | −11.3931 | −0.428178 | ||||||||
\(709\) | −21.1656 | −0.794891 | −0.397446 | − | 0.917626i | \(-0.630103\pi\) | ||||
−0.397446 | + | 0.917626i | \(0.630103\pi\) | |||||||
\(710\) | 1.15195 | 0.0432319 | ||||||||
\(711\) | 14.3815 | 0.539348 | ||||||||
\(712\) | 3.13580 | 0.117519 | ||||||||
\(713\) | −11.3639 | −0.425581 | ||||||||
\(714\) | −8.64266 | −0.323443 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.8263 | 0.516712 | ||||||||
\(717\) | 9.37352 | 0.350061 | ||||||||
\(718\) | 25.3531 | 0.946170 | ||||||||
\(719\) | 32.6186 | 1.21647 | 0.608234 | − | 0.793758i | \(-0.291878\pi\) | ||||
0.608234 | + | 0.793758i | \(0.291878\pi\) | |||||||
\(720\) | −8.36630 | −0.311794 | ||||||||
\(721\) | 1.24686 | 0.0464356 | ||||||||
\(722\) | 25.5660 | 0.951468 | ||||||||
\(723\) | −9.50851 | −0.353625 | ||||||||
\(724\) | −5.69646 | −0.211707 | ||||||||
\(725\) | −5.51585 | −0.204854 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4245 | 0.831678 | 0.415839 | − | 0.909438i | \(-0.363488\pi\) | ||||
0.415839 | + | 0.909438i | \(0.363488\pi\) | |||||||
\(728\) | 11.7194 | 0.434350 | ||||||||
\(729\) | 20.1040 | 0.744593 | ||||||||
\(730\) | 22.9653 | 0.849983 | ||||||||
\(731\) | 38.6147 | 1.42822 | ||||||||
\(732\) | 9.32037 | 0.344491 | ||||||||
\(733\) | −28.7607 | −1.06230 | −0.531150 | − | 0.847278i | \(-0.678240\pi\) | ||||
−0.531150 | + | 0.847278i | \(0.678240\pi\) | |||||||
\(734\) | −22.6852 | −0.837326 | ||||||||
\(735\) | 1.14142 | 0.0421020 | ||||||||
\(736\) | 8.25556 | 0.304304 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 30.9104 | 1.13783 | ||||||||
\(739\) | 2.12241 | 0.0780742 | 0.0390371 | − | 0.999238i | \(-0.487571\pi\) | ||||
0.0390371 | + | 0.999238i | \(0.487571\pi\) | |||||||
\(740\) | 6.86699 | 0.252436 | ||||||||
\(741\) | −12.0281 | −0.441865 | ||||||||
\(742\) | −10.2749 | −0.377202 | ||||||||
\(743\) | 38.6935 | 1.41953 | 0.709763 | − | 0.704440i | \(-0.248802\pi\) | ||||
0.709763 | + | 0.704440i | \(0.248802\pi\) | |||||||
\(744\) | 13.0424 | 0.478158 | ||||||||
\(745\) | −12.6540 | −0.463607 | ||||||||
\(746\) | 20.9408 | 0.766696 | ||||||||
\(747\) | 16.1269 | 0.590052 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2684 | 0.375200 | ||||||||
\(750\) | −1.88755 | −0.0689237 | ||||||||
\(751\) | 2.01833 | 0.0736498 | 0.0368249 | − | 0.999322i | \(-0.488276\pi\) | ||||
0.0368249 | + | 0.999322i | \(0.488276\pi\) | |||||||
\(752\) | −7.93350 | −0.289305 | ||||||||
\(753\) | 11.1579 | 0.406615 | ||||||||
\(754\) | 51.0878 | 1.86051 | ||||||||
\(755\) | 2.48546 | 0.0904551 | ||||||||
\(756\) | 3.93893 | 0.143257 | ||||||||
\(757\) | 39.9006 | 1.45021 | 0.725107 | − | 0.688637i | \(-0.241790\pi\) | ||||
0.725107 | + | 0.688637i | \(0.241790\pi\) | |||||||
\(758\) | −19.9059 | −0.723015 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.93691 | −0.142807 | ||||||||
\(761\) | −28.9628 | −1.04990 | −0.524950 | − | 0.851133i | \(-0.675916\pi\) | ||||
−0.524950 | + | 0.851133i | \(0.675916\pi\) | |||||||
\(762\) | −22.8222 | −0.826762 | ||||||||
\(763\) | −5.67907 | −0.205596 | ||||||||
\(764\) | 11.7115 | 0.423706 | ||||||||
\(765\) | −7.77087 | −0.280956 | ||||||||
\(766\) | 16.4737 | 0.595220 | ||||||||
\(767\) | 76.0937 | 2.74759 | ||||||||
\(768\) | −17.7427 | −0.640233 | ||||||||
\(769\) | −5.26499 | −0.189860 | −0.0949302 | − | 0.995484i | \(-0.530263\pi\) | ||||
−0.0949302 | + | 0.995484i | \(0.530263\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.68047 | −0.168563 | ||||||||
\(772\) | −6.26114 | −0.225344 | ||||||||
\(773\) | −0.286828 | −0.0103165 | −0.00515825 | − | 0.999987i | \(-0.501642\pi\) | ||||
−0.00515825 | + | 0.999987i | \(0.501642\pi\) | |||||||
\(774\) | −23.6690 | −0.850764 | ||||||||
\(775\) | −5.46081 | −0.196158 | ||||||||
\(776\) | 12.4228 | 0.445952 | ||||||||
\(777\) | 10.6688 | 0.382741 | ||||||||
\(778\) | −36.5881 | −1.31175 | ||||||||
\(779\) | 20.7220 | 0.742442 | ||||||||
\(780\) | 4.69672 | 0.168169 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 15.7569 | 0.563467 | ||||||||
\(783\) | −29.5729 | −1.05685 | ||||||||
\(784\) | −4.92960 | −0.176057 | ||||||||
\(785\) | 14.2773 | 0.509579 | ||||||||
\(786\) | −1.97137 | −0.0703166 | ||||||||
\(787\) | −27.4622 | −0.978923 | −0.489462 | − | 0.872025i | \(-0.662807\pi\) | ||||
−0.489462 | + | 0.872025i | \(0.662807\pi\) | |||||||
\(788\) | 13.9997 | 0.498718 | ||||||||
\(789\) | 29.2721 | 1.04211 | ||||||||
\(790\) | −14.0131 | −0.498565 | ||||||||
\(791\) | 17.9797 | 0.639284 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.2502 | −2.21057 | ||||||||
\(794\) | 43.8174 | 1.55502 | ||||||||
\(795\) | 7.09201 | 0.251528 | ||||||||
\(796\) | −9.33911 | −0.331016 | ||||||||
\(797\) | 22.6304 | 0.801609 | 0.400805 | − | 0.916164i | \(-0.368731\pi\) | ||||
0.400805 | + | 0.916164i | \(0.368731\pi\) | |||||||
\(798\) | 3.55141 | 0.125718 | ||||||||
\(799\) | −7.36887 | −0.260692 | ||||||||
\(800\) | 3.96713 | 0.140259 | ||||||||
\(801\) | −2.54341 | −0.0898668 | ||||||||
\(802\) | 4.93149 | 0.174137 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.70378 | 0.165890 | ||||||||
\(805\) | −2.08099 | −0.0733453 | ||||||||
\(806\) | 50.5779 | 1.78153 | ||||||||
\(807\) | −15.6406 | −0.550575 | ||||||||
\(808\) | −6.60849 | −0.232486 | ||||||||
\(809\) | 37.2584 | 1.30994 | 0.654968 | − | 0.755656i | \(-0.272682\pi\) | ||||
0.654968 | + | 0.755656i | \(0.272682\pi\) | |||||||
\(810\) | −1.70032 | −0.0597430 | ||||||||
\(811\) | 0.190250 | 0.00668059 | 0.00334030 | − | 0.999994i | \(-0.498937\pi\) | ||||
0.00334030 | + | 0.999994i | \(0.498937\pi\) | |||||||
\(812\) | −4.05238 | −0.142211 | ||||||||
\(813\) | −9.82158 | −0.344458 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.75758 | 0.341793 | ||||||||
\(816\) | −25.7636 | −0.901906 | ||||||||
\(817\) | −15.8674 | −0.555130 | ||||||||
\(818\) | 2.84260 | 0.0993893 | ||||||||
\(819\) | −9.50545 | −0.332147 | ||||||||
\(820\) | −8.09147 | −0.282566 | ||||||||
\(821\) | 30.0724 | 1.04953 | 0.524767 | − | 0.851246i | \(-0.324152\pi\) | ||||
0.524767 | + | 0.851246i | \(0.324152\pi\) | |||||||
\(822\) | −2.71468 | −0.0946853 | ||||||||
\(823\) | 20.6546 | 0.719975 | 0.359987 | − | 0.932957i | \(-0.382781\pi\) | ||||
0.359987 | + | 0.932957i | \(0.382781\pi\) | |||||||
\(824\) | 2.60899 | 0.0908885 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.4673 | −0.781738 | ||||||||
\(827\) | −25.3871 | −0.882795 | −0.441397 | − | 0.897312i | \(-0.645517\pi\) | ||||
−0.441397 | + | 0.897312i | \(0.645517\pi\) | |||||||
\(828\) | −2.59471 | −0.0901724 | ||||||||
\(829\) | 6.53298 | 0.226900 | 0.113450 | − | 0.993544i | \(-0.463810\pi\) | ||||
0.113450 | + | 0.993544i | \(0.463810\pi\) | |||||||
\(830\) | −15.7138 | −0.545435 | ||||||||
\(831\) | 32.9779 | 1.14399 | ||||||||
\(832\) | 18.4761 | 0.640544 | ||||||||
\(833\) | −4.57876 | −0.158645 | ||||||||
\(834\) | 40.8634 | 1.41498 | ||||||||
\(835\) | 11.3890 | 0.394133 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.2778 | −1.01199 | ||||||||
\(838\) | 40.6899 | 1.40561 | ||||||||
\(839\) | −13.3320 | −0.460271 | −0.230136 | − | 0.973159i | \(-0.573917\pi\) | ||||
−0.230136 | + | 0.973159i | \(0.573917\pi\) | |||||||
\(840\) | 2.38836 | 0.0824064 | ||||||||
\(841\) | 1.42465 | 0.0491257 | ||||||||
\(842\) | 49.4008 | 1.70247 | ||||||||
\(843\) | 9.11308 | 0.313871 | ||||||||
\(844\) | 20.9020 | 0.719478 | ||||||||
\(845\) | −18.3691 | −0.631916 | ||||||||
\(846\) | 4.51677 | 0.155290 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −30.6291 | −1.05181 | ||||||||
\(849\) | −8.44080 | −0.289687 | ||||||||
\(850\) | 7.57184 | 0.259712 | ||||||||
\(851\) | −19.4509 | −0.666769 | ||||||||
\(852\) | −0.584148 | −0.0200126 | ||||||||
\(853\) | −45.3221 | −1.55180 | −0.775899 | − | 0.630857i | \(-0.782704\pi\) | ||||
−0.775899 | + | 0.630857i | \(0.782704\pi\) | |||||||
\(854\) | 18.3799 | 0.628947 | ||||||||
\(855\) | 3.19317 | 0.109204 | ||||||||
\(856\) | 21.4861 | 0.734381 | ||||||||
\(857\) | −26.0895 | −0.891199 | −0.445599 | − | 0.895232i | \(-0.647009\pi\) | ||||
−0.445599 | + | 0.895232i | \(0.647009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0079 | 1.36505 | 0.682527 | − | 0.730861i | \(-0.260881\pi\) | ||||
0.682527 | + | 0.730861i | \(0.260881\pi\) | |||||||
\(860\) | 6.19586 | 0.211277 | ||||||||
\(861\) | −12.5712 | −0.428425 | ||||||||
\(862\) | −25.7809 | −0.878103 | ||||||||
\(863\) | 58.6608 | 1.99684 | 0.998418 | − | 0.0562309i | \(-0.0179083\pi\) | ||||
0.998418 | + | 0.0562309i | \(0.0179083\pi\) | |||||||
\(864\) | 21.2695 | 0.723603 | ||||||||
\(865\) | 10.3544 | 0.352059 | ||||||||
\(866\) | −17.6759 | −0.600652 | ||||||||
\(867\) | −4.52582 | −0.153705 | ||||||||
\(868\) | −4.01194 | −0.136174 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 10.4115 | 0.352982 | ||||||||
\(871\) | −31.4163 | −1.06450 | ||||||||
\(872\) | −11.8832 | −0.402414 | ||||||||
\(873\) | −10.0760 | −0.341020 | ||||||||
\(874\) | −6.47477 | −0.219012 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −11.6456 | −0.393468 | ||||||||
\(877\) | −33.3513 | −1.12619 | −0.563096 | − | 0.826392i | \(-0.690390\pi\) | ||||
−0.563096 | + | 0.826392i | \(0.690390\pi\) | |||||||
\(878\) | 30.0205 | 1.01314 | ||||||||
\(879\) | 15.7380 | 0.530830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4875 | 0.723933 | 0.361967 | − | 0.932191i | \(-0.382105\pi\) | ||||
0.361967 | + | 0.932191i | \(0.382105\pi\) | |||||||
\(882\) | 2.80656 | 0.0945019 | ||||||||
\(883\) | −43.7638 | −1.47277 | −0.736385 | − | 0.676563i | \(-0.763469\pi\) | ||||
−0.736385 | + | 0.676563i | \(0.763469\pi\) | |||||||
\(884\) | −18.8407 | −0.633680 | ||||||||
\(885\) | 15.5076 | 0.521282 | ||||||||
\(886\) | 16.4321 | 0.552049 | ||||||||
\(887\) | 4.54756 | 0.152692 | 0.0763460 | − | 0.997081i | \(-0.475675\pi\) | ||||
0.0763460 | + | 0.997081i | \(0.475675\pi\) | |||||||
\(888\) | 22.3239 | 0.749141 | ||||||||
\(889\) | −12.0909 | −0.405516 | ||||||||
\(890\) | 2.47826 | 0.0830715 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.6053 | −0.589467 | ||||||||
\(893\) | 3.02799 | 0.101328 | ||||||||
\(894\) | 23.8851 | 0.798839 | ||||||||
\(895\) | −18.8195 | −0.629067 | ||||||||
\(896\) | −13.3895 | −0.447311 | ||||||||
\(897\) | −13.3036 | −0.444193 | ||||||||
\(898\) | 29.9184 | 0.998391 | ||||||||
\(899\) | 30.1210 | 1.00459 | ||||||||
\(900\) | −1.24686 | −0.0415621 | ||||||||
\(901\) | −28.4493 | −0.947782 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.62612 | 0.320337 | ||||||||
\(904\) | 37.6215 | 1.25127 | ||||||||
\(905\) | 7.75369 | 0.257741 | ||||||||
\(906\) | −4.69144 | −0.155863 | ||||||||
\(907\) | −17.4034 | −0.577869 | −0.288935 | − | 0.957349i | \(-0.593301\pi\) | ||||
−0.288935 | + | 0.957349i | \(0.593301\pi\) | |||||||
\(908\) | −15.1349 | −0.502268 | ||||||||
\(909\) | 5.36006 | 0.177782 | ||||||||
\(910\) | 9.26199 | 0.307032 | ||||||||
\(911\) | 4.17760 | 0.138410 | 0.0692050 | − | 0.997602i | \(-0.477954\pi\) | ||||
0.0692050 | + | 0.997602i | \(0.477954\pi\) | |||||||
\(912\) | 10.5867 | 0.350560 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.4427 | −0.874645 | ||||||||
\(915\) | −12.6863 | −0.419397 | ||||||||
\(916\) | 0.663678 | 0.0219286 | ||||||||
\(917\) | −1.04441 | −0.0344894 | ||||||||
\(918\) | 40.5959 | 1.33987 | ||||||||
\(919\) | −18.4017 | −0.607018 | −0.303509 | − | 0.952829i | \(-0.598158\pi\) | ||||
−0.303509 | + | 0.952829i | \(0.598158\pi\) | |||||||
\(920\) | −4.35436 | −0.143559 | ||||||||
\(921\) | −6.73164 | −0.221815 | ||||||||
\(922\) | 46.2390 | 1.52280 | ||||||||
\(923\) | 3.90149 | 0.128419 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.34694 | −0.307326 | ||||||||
\(926\) | 50.9978 | 1.67589 | ||||||||
\(927\) | −2.11612 | −0.0695025 | ||||||||
\(928\) | −21.8821 | −0.718315 | ||||||||
\(929\) | −52.1959 | −1.71249 | −0.856245 | − | 0.516569i | \(-0.827209\pi\) | ||||
−0.856245 | + | 0.516569i | \(0.827209\pi\) | |||||||
\(930\) | 10.3076 | 0.337999 | ||||||||
\(931\) | 1.88149 | 0.0616632 | ||||||||
\(932\) | −17.0782 | −0.559416 | ||||||||
\(933\) | 29.6830 | 0.971777 | ||||||||
\(934\) | 13.9197 | 0.455465 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −19.8896 | −0.650113 | ||||||||
\(937\) | 12.3471 | 0.403363 | 0.201681 | − | 0.979451i | \(-0.435359\pi\) | ||||
0.201681 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(938\) | 9.27592 | 0.302869 | ||||||||
\(939\) | 13.9123 | 0.454010 | ||||||||
\(940\) | −1.18236 | −0.0385643 | ||||||||
\(941\) | −13.8509 | −0.451525 | −0.225763 | − | 0.974182i | \(-0.572487\pi\) | ||||
−0.225763 | + | 0.974182i | \(0.572487\pi\) | |||||||
\(942\) | −26.9492 | −0.878052 | ||||||||
\(943\) | 22.9193 | 0.746354 | ||||||||
\(944\) | −66.9746 | −2.17984 | ||||||||
\(945\) | −5.36144 | −0.174408 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.7800 | −0.707756 | −0.353878 | − | 0.935292i | \(-0.615137\pi\) | ||||
−0.353878 | + | 0.935292i | \(0.615137\pi\) | |||||||
\(948\) | 7.10601 | 0.230792 | ||||||||
\(949\) | 77.7803 | 2.52486 | ||||||||
\(950\) | −3.11139 | −0.100947 | ||||||||
\(951\) | −15.5113 | −0.502988 | ||||||||
\(952\) | −9.58081 | −0.310516 | ||||||||
\(953\) | −7.56150 | −0.244941 | −0.122471 | − | 0.992472i | \(-0.539082\pi\) | ||||
−0.122471 | + | 0.992472i | \(0.539082\pi\) | |||||||
\(954\) | 17.4380 | 0.564577 | ||||||||
\(955\) | −15.9410 | −0.515837 | ||||||||
\(956\) | −6.03328 | −0.195130 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 49.0921 | 1.58609 | ||||||||
\(959\) | −1.43820 | −0.0464419 | ||||||||
\(960\) | 3.76535 | 0.121526 | ||||||||
\(961\) | −1.17956 | −0.0380503 | ||||||||
\(962\) | 86.5713 | 2.79117 | ||||||||
\(963\) | −17.4271 | −0.561581 | ||||||||
\(964\) | 6.12016 | 0.197117 | ||||||||
\(965\) | 8.52230 | 0.274343 | ||||||||
\(966\) | 3.92798 | 0.126381 | ||||||||
\(967\) | 24.0488 | 0.773357 | 0.386679 | − | 0.922215i | \(-0.373622\pi\) | ||||
0.386679 | + | 0.922215i | \(0.373622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.83321 | 0.315888 | ||||||||
\(970\) | 9.81789 | 0.315233 | ||||||||
\(971\) | 16.0049 | 0.513622 | 0.256811 | − | 0.966462i | \(-0.417328\pi\) | ||||
0.256811 | + | 0.966462i | \(0.417328\pi\) | |||||||
\(972\) | −10.9546 | −0.351368 | ||||||||
\(973\) | 21.6489 | 0.694031 | ||||||||
\(974\) | −62.5611 | −2.00459 | ||||||||
\(975\) | −6.39289 | −0.204736 | ||||||||
\(976\) | 54.7901 | 1.75379 | ||||||||
\(977\) | 16.4515 | 0.526330 | 0.263165 | − | 0.964751i | \(-0.415234\pi\) | ||||
0.263165 | + | 0.964751i | \(0.415234\pi\) | |||||||
\(978\) | −18.4180 | −0.588941 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.734678 | −0.0234684 | ||||||||
\(981\) | 9.63827 | 0.307726 | ||||||||
\(982\) | 30.9214 | 0.986741 | ||||||||
\(983\) | 30.2550 | 0.964984 | 0.482492 | − | 0.875900i | \(-0.339732\pi\) | ||||
0.482492 | + | 0.875900i | \(0.339732\pi\) | |||||||
\(984\) | −26.3045 | −0.838558 | ||||||||
\(985\) | −19.0556 | −0.607160 | ||||||||
\(986\) | −41.7651 | −1.33007 | ||||||||
\(987\) | −1.83696 | −0.0584710 | ||||||||
\(988\) | 7.74192 | 0.246303 | ||||||||
\(989\) | −17.5499 | −0.558055 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0778 | −0.415428 | −0.207714 | − | 0.978190i | \(-0.566602\pi\) | ||||
−0.207714 | + | 0.978190i | \(0.566602\pi\) | |||||||
\(992\) | −21.6637 | −0.687824 | ||||||||
\(993\) | −20.9339 | −0.664317 | ||||||||
\(994\) | −1.15195 | −0.0365376 | ||||||||
\(995\) | 12.7118 | 0.402992 | ||||||||
\(996\) | 7.96841 | 0.252489 | ||||||||
\(997\) | −31.8380 | −1.00832 | −0.504160 | − | 0.863610i | \(-0.668198\pi\) | ||||
−0.504160 | + | 0.863610i | \(0.668198\pi\) | |||||||
\(998\) | −37.8294 | −1.19747 | ||||||||
\(999\) | −50.1131 | −1.58551 |
(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 | 4235.2.a.y.1.2 | ✓ | 5 | |
11.10 | odd | 2 | 4235.2.a.be.1.4 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.y.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4235.2.a.be.1.4 | yes | 5 | 11.10 | odd | 2 |