Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(45.7782354788\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4507648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.35100\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17619 | 0.831689 | 0.415845 | − | 0.909436i | \(-0.363486\pi\) | ||||
0.415845 | + | 0.909436i | \(0.363486\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.616586 | −0.308293 | ||||||||
\(5\) | 3.14862 | 1.40811 | 0.704054 | − | 0.710147i | \(-0.251371\pi\) | ||||
0.704054 | + | 0.710147i | \(0.251371\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.07759 | −1.08809 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.70337 | 1.17111 | ||||||||
\(11\) | 0.773390 | 0.233186 | 0.116593 | − | 0.993180i | \(-0.462803\pi\) | ||||
0.116593 | + | 0.993180i | \(0.462803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.38665 | −0.596663 | ||||||||
\(17\) | −5.75340 | −1.39540 | −0.697702 | − | 0.716388i | \(-0.745794\pi\) | ||||
−0.697702 | + | 0.716388i | \(0.745794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.22298 | 0.280571 | 0.140285 | − | 0.990111i | \(-0.455198\pi\) | ||||
0.140285 | + | 0.990111i | \(0.455198\pi\) | |||||||
\(20\) | −1.94140 | −0.434109 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.909650 | 0.193938 | ||||||||
\(23\) | 2.99182 | 0.623838 | 0.311919 | − | 0.950109i | \(-0.399028\pi\) | ||||
0.311919 | + | 0.950109i | \(0.399028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.91383 | 0.982767 | ||||||||
\(26\) | −1.17619 | −0.230669 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.46882 | 0.458449 | 0.229224 | − | 0.973374i | \(-0.426381\pi\) | ||||
0.229224 | + | 0.973374i | \(0.426381\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.13487 | 1.10185 | 0.550927 | − | 0.834553i | \(-0.314274\pi\) | ||||
0.550927 | + | 0.834553i | \(0.314274\pi\) | |||||||
\(32\) | 3.34804 | 0.591855 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.76707 | −1.16054 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.99933 | 0.821884 | 0.410942 | − | 0.911661i | \(-0.365200\pi\) | ||||
0.410942 | + | 0.911661i | \(0.365200\pi\) | |||||||
\(38\) | 1.43845 | 0.233348 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.69018 | −1.53215 | ||||||||
\(41\) | −2.55981 | −0.399774 | −0.199887 | − | 0.979819i | \(-0.564058\pi\) | ||||
−0.199887 | + | 0.979819i | \(0.564058\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.73150 | −0.416550 | −0.208275 | − | 0.978070i | \(-0.566785\pi\) | ||||
−0.208275 | + | 0.978070i | \(0.566785\pi\) | |||||||
\(44\) | −0.476861 | −0.0718895 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.51894 | 0.518839 | ||||||||
\(47\) | 5.37169 | 0.783542 | 0.391771 | − | 0.920063i | \(-0.371863\pi\) | ||||
0.391771 | + | 0.920063i | \(0.371863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.77958 | 0.817357 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.616586 | 0.0855050 | ||||||||
\(53\) | 9.79015 | 1.34478 | 0.672390 | − | 0.740197i | \(-0.265268\pi\) | ||||
0.672390 | + | 0.740197i | \(0.265268\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.43511 | 0.328351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.90379 | 0.381287 | ||||||||
\(59\) | 2.50456 | 0.326066 | 0.163033 | − | 0.986621i | \(-0.447872\pi\) | ||||
0.163033 | + | 0.986621i | \(0.447872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9167 | 1.39774 | 0.698870 | − | 0.715248i | \(-0.253686\pi\) | ||||
0.698870 | + | 0.715248i | \(0.253686\pi\) | |||||||
\(62\) | 7.21575 | 0.916401 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.71122 | 1.08890 | ||||||||
\(65\) | −3.14862 | −0.390539 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.32518 | 0.528404 | 0.264202 | − | 0.964467i | \(-0.414891\pi\) | ||||
0.264202 | + | 0.964467i | \(0.414891\pi\) | |||||||
\(68\) | 3.54746 | 0.430193 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6649 | −1.26570 | −0.632848 | − | 0.774276i | \(-0.718114\pi\) | ||||
−0.632848 | + | 0.774276i | \(0.718114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.17450 | 0.605630 | 0.302815 | − | 0.953049i | \(-0.402074\pi\) | ||||
0.302815 | + | 0.953049i | \(0.402074\pi\) | |||||||
\(74\) | 5.88014 | 0.683552 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.754072 | −0.0864979 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.542038 | −0.0609841 | −0.0304920 | − | 0.999535i | \(-0.509707\pi\) | ||||
−0.0304920 | + | 0.999535i | \(0.509707\pi\) | |||||||
\(80\) | −7.51467 | −0.840165 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.01081 | −0.332488 | ||||||||
\(83\) | 15.2259 | 1.67125 | 0.835627 | − | 0.549297i | \(-0.185104\pi\) | ||||
0.835627 | + | 0.549297i | \(0.185104\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.1153 | −1.96488 | ||||||||
\(86\) | −3.21275 | −0.346440 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.38018 | −0.253728 | ||||||||
\(89\) | 9.23208 | 0.978599 | 0.489299 | − | 0.872116i | \(-0.337253\pi\) | ||||
0.489299 | + | 0.872116i | \(0.337253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.84471 | −0.192325 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.31811 | 0.651663 | ||||||||
\(95\) | 3.85070 | 0.395074 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.26291 | 0.128229 | 0.0641145 | − | 0.997943i | \(-0.479578\pi\) | ||||
0.0641145 | + | 0.997943i | \(0.479578\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.02980 | −0.302980 | ||||||||
\(101\) | 0.605447 | 0.0602443 | 0.0301221 | − | 0.999546i | \(-0.490410\pi\) | ||||
0.0301221 | + | 0.999546i | \(0.490410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.64804 | −0.753584 | −0.376792 | − | 0.926298i | \(-0.622973\pi\) | ||||
−0.376792 | + | 0.926298i | \(0.622973\pi\) | |||||||
\(104\) | 3.07759 | 0.301783 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.5150 | 1.11844 | ||||||||
\(107\) | −4.82965 | −0.466900 | −0.233450 | − | 0.972369i | \(-0.575001\pi\) | ||||
−0.233450 | + | 0.972369i | \(0.575001\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.23092 | 0.692596 | 0.346298 | − | 0.938125i | \(-0.387439\pi\) | ||||
0.346298 | + | 0.938125i | \(0.387439\pi\) | |||||||
\(110\) | 2.86415 | 0.273086 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.19375 | 0.864875 | 0.432438 | − | 0.901664i | \(-0.357654\pi\) | ||||
0.432438 | + | 0.901664i | \(0.357654\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.42012 | 0.878430 | ||||||||
\(116\) | −1.52224 | −0.141336 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.94583 | 0.271186 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4019 | −0.945624 | ||||||||
\(122\) | 12.8401 | 1.16249 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.78267 | −0.339694 | ||||||||
\(125\) | −0.271305 | −0.0242663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2118 | −0.994888 | −0.497444 | − | 0.867496i | \(-0.665728\pi\) | ||||
−0.497444 | + | 0.867496i | \(0.665728\pi\) | |||||||
\(128\) | 3.54994 | 0.313773 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.70337 | −0.324807 | ||||||||
\(131\) | 15.7380 | 1.37503 | 0.687517 | − | 0.726169i | \(-0.258701\pi\) | ||||
0.687517 | + | 0.726169i | \(0.258701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.08721 | 0.439468 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.7066 | 1.51833 | ||||||||
\(137\) | 18.6210 | 1.59090 | 0.795449 | − | 0.606020i | \(-0.207235\pi\) | ||||
0.795449 | + | 0.606020i | \(0.207235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9137 | 1.01050 | 0.505252 | − | 0.862972i | \(-0.331399\pi\) | ||||
0.505252 | + | 0.862972i | \(0.331399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.5440 | −1.05267 | ||||||||
\(143\) | −0.773390 | −0.0646741 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.77339 | 0.645545 | ||||||||
\(146\) | 6.08618 | 0.503696 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.08251 | −0.253381 | ||||||||
\(149\) | −11.3753 | −0.931904 | −0.465952 | − | 0.884810i | \(-0.654288\pi\) | ||||
−0.465952 | + | 0.884810i | \(0.654288\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.69250 | −0.300492 | −0.150246 | − | 0.988649i | \(-0.548007\pi\) | ||||
−0.150246 | + | 0.988649i | \(0.548007\pi\) | |||||||
\(152\) | −3.76383 | −0.305287 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.3164 | 1.55153 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.12065 | −0.0894374 | −0.0447187 | − | 0.999000i | \(-0.514239\pi\) | ||||
−0.0447187 | + | 0.999000i | \(0.514239\pi\) | |||||||
\(158\) | −0.637538 | −0.0507198 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.5417 | 0.833396 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.3435 | −1.59342 | −0.796712 | − | 0.604359i | \(-0.793429\pi\) | ||||
−0.796712 | + | 0.604359i | \(0.793429\pi\) | |||||||
\(164\) | 1.57834 | 0.123248 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.9084 | 1.38996 | ||||||||
\(167\) | 13.0063 | 1.00646 | 0.503228 | − | 0.864154i | \(-0.332146\pi\) | ||||
0.503228 | + | 0.864154i | \(0.332146\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −21.3070 | −1.63417 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.68420 | 0.128419 | ||||||||
\(173\) | −25.9110 | −1.96998 | −0.984989 | − | 0.172616i | \(-0.944778\pi\) | ||||
−0.984989 | + | 0.172616i | \(0.944778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.84581 | −0.139133 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.8587 | 0.813890 | ||||||||
\(179\) | −9.64163 | −0.720649 | −0.360325 | − | 0.932827i | \(-0.617334\pi\) | ||||
−0.360325 | + | 0.932827i | \(0.617334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.92683 | 0.217550 | 0.108775 | − | 0.994066i | \(-0.465307\pi\) | ||||
0.108775 | + | 0.994066i | \(0.465307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.20760 | −0.678793 | ||||||||
\(185\) | 15.7410 | 1.15730 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.44962 | −0.325388 | ||||||||
\(188\) | −3.31211 | −0.241560 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.52914 | 0.328579 | ||||||||
\(191\) | 16.1364 | 1.16759 | 0.583796 | − | 0.811901i | \(-0.301567\pi\) | ||||
0.583796 | + | 0.811901i | \(0.301567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0863817 | −0.00621789 | −0.00310894 | − | 0.999995i | \(-0.500990\pi\) | ||||
−0.00310894 | + | 0.999995i | \(0.500990\pi\) | |||||||
\(194\) | 1.48542 | 0.106647 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.0589 | −1.07290 | −0.536451 | − | 0.843932i | \(-0.680235\pi\) | ||||
−0.536451 | + | 0.843932i | \(0.680235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.4466 | −1.09498 | −0.547492 | − | 0.836811i | \(-0.684417\pi\) | ||||
−0.547492 | + | 0.836811i | \(0.684417\pi\) | |||||||
\(200\) | −15.1228 | −1.06934 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.712119 | 0.0501045 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.05987 | −0.562925 | ||||||||
\(206\) | −8.99552 | −0.626748 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.38665 | 0.165484 | ||||||||
\(209\) | 0.945840 | 0.0654251 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0561 | −1.72493 | −0.862466 | − | 0.506115i | \(-0.831081\pi\) | ||||
−0.862466 | + | 0.506115i | \(0.831081\pi\) | |||||||
\(212\) | −6.03647 | −0.414586 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.68057 | −0.388316 | ||||||||
\(215\) | −8.60047 | −0.586547 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.50491 | 0.576025 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.50146 | −0.101228 | ||||||||
\(221\) | 5.75340 | 0.387015 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.6640 | 1.38376 | 0.691881 | − | 0.722012i | \(-0.256782\pi\) | ||||
0.691881 | + | 0.722012i | \(0.256782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8136 | 0.719307 | ||||||||
\(227\) | 0.982378 | 0.0652027 | 0.0326013 | − | 0.999468i | \(-0.489621\pi\) | ||||
0.0326013 | + | 0.999468i | \(0.489621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.2742 | 0.943269 | 0.471634 | − | 0.881794i | \(-0.343664\pi\) | ||||
0.471634 | + | 0.881794i | \(0.343664\pi\) | |||||||
\(230\) | 11.0798 | 0.730581 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.59802 | −0.498835 | ||||||||
\(233\) | −1.39534 | −0.0914119 | −0.0457060 | − | 0.998955i | \(-0.514554\pi\) | ||||
−0.0457060 | + | 0.998955i | \(0.514554\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9134 | 1.10331 | ||||||||
\(236\) | −1.54428 | −0.100524 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.54875 | −0.164865 | −0.0824326 | − | 0.996597i | \(-0.526269\pi\) | ||||
−0.0824326 | + | 0.996597i | \(0.526269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.6746 | −1.91151 | −0.955755 | − | 0.294164i | \(-0.904959\pi\) | ||||
−0.955755 | + | 0.294164i | \(0.904959\pi\) | |||||||
\(242\) | −12.2345 | −0.786466 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.73108 | −0.430913 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.22298 | −0.0778163 | ||||||||
\(248\) | −18.8806 | −1.19892 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.319106 | −0.0201820 | ||||||||
\(251\) | 18.0858 | 1.14157 | 0.570784 | − | 0.821100i | \(-0.306639\pi\) | ||||
0.570784 | + | 0.821100i | \(0.306639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.31384 | 0.145470 | ||||||||
\(254\) | −13.1872 | −0.827437 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.2470 | −0.827940 | ||||||||
\(257\) | 14.7403 | 0.919473 | 0.459737 | − | 0.888055i | \(-0.347944\pi\) | ||||
0.459737 | + | 0.888055i | \(0.347944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.94140 | 0.120400 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.5108 | 1.14360 | ||||||||
\(263\) | 8.15922 | 0.503119 | 0.251560 | − | 0.967842i | \(-0.419057\pi\) | ||||
0.251560 | + | 0.967842i | \(0.419057\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.8255 | 1.89360 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.66684 | −0.162903 | ||||||||
\(269\) | 0.442582 | 0.0269847 | 0.0134924 | − | 0.999909i | \(-0.495705\pi\) | ||||
0.0134924 | + | 0.999909i | \(0.495705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0831 | 1.28071 | 0.640354 | − | 0.768080i | \(-0.278788\pi\) | ||||
0.640354 | + | 0.768080i | \(0.278788\pi\) | |||||||
\(272\) | 13.7314 | 0.832586 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.9018 | 1.32313 | ||||||||
\(275\) | 3.80031 | 0.229167 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.59421 | 0.215955 | 0.107977 | − | 0.994153i | \(-0.465563\pi\) | ||||
0.107977 | + | 0.994153i | \(0.465563\pi\) | |||||||
\(278\) | 14.0127 | 0.840426 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.01252 | 0.537642 | 0.268821 | − | 0.963190i | \(-0.413366\pi\) | ||||
0.268821 | + | 0.963190i | \(0.413366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.7411 | −1.64904 | −0.824520 | − | 0.565833i | \(-0.808555\pi\) | ||||
−0.824520 | + | 0.565833i | \(0.808555\pi\) | |||||||
\(284\) | 6.57585 | 0.390205 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.909650 | −0.0537887 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1016 | 0.947153 | ||||||||
\(290\) | 9.14296 | 0.536893 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.19052 | −0.186711 | ||||||||
\(293\) | 12.7409 | 0.744333 | 0.372167 | − | 0.928166i | \(-0.378615\pi\) | ||||
0.372167 | + | 0.928166i | \(0.378615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.88593 | 0.459137 | ||||||||
\(296\) | −15.3859 | −0.894287 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.3795 | −0.775055 | ||||||||
\(299\) | −2.99182 | −0.173021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.34307 | −0.249916 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.91883 | −0.167406 | ||||||||
\(305\) | 34.3726 | 1.96817 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.1384 | −0.578626 | −0.289313 | − | 0.957235i | \(-0.593427\pi\) | ||||
−0.289313 | + | 0.957235i | \(0.593427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.7197 | 1.29039 | ||||||||
\(311\) | 20.6013 | 1.16819 | 0.584096 | − | 0.811685i | \(-0.301449\pi\) | ||||
0.584096 | + | 0.811685i | \(0.301449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.5456 | −0.935213 | −0.467606 | − | 0.883937i | \(-0.654883\pi\) | ||||
−0.467606 | + | 0.883937i | \(0.654883\pi\) | |||||||
\(314\) | −1.31809 | −0.0743841 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.334213 | 0.0188010 | ||||||||
\(317\) | 21.2340 | 1.19262 | 0.596310 | − | 0.802754i | \(-0.296633\pi\) | ||||
0.596310 | + | 0.802754i | \(0.296633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.90936 | 0.106904 | ||||||||
\(320\) | 27.4284 | 1.53329 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.03629 | −0.391510 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.91383 | −0.272570 | ||||||||
\(326\) | −23.9277 | −1.32523 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.87804 | 0.434992 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2415 | 0.892712 | 0.446356 | − | 0.894855i | \(-0.352721\pi\) | ||||
0.446356 | + | 0.894855i | \(0.352721\pi\) | |||||||
\(332\) | −9.38804 | −0.515236 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.2978 | 0.837058 | ||||||||
\(335\) | 13.6184 | 0.744050 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.42141 | 0.349797 | 0.174898 | − | 0.984586i | \(-0.444040\pi\) | ||||
0.174898 | + | 0.984586i | \(0.444040\pi\) | |||||||
\(338\) | 1.17619 | 0.0639761 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.1696 | 0.605758 | ||||||||
\(341\) | 4.74464 | 0.256937 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.40645 | 0.453245 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.4762 | −1.63841 | ||||||||
\(347\) | −14.4809 | −0.777376 | −0.388688 | − | 0.921369i | \(-0.627072\pi\) | ||||
−0.388688 | + | 0.921369i | \(0.627072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.74500 | −0.0934079 | −0.0467040 | − | 0.998909i | \(-0.514872\pi\) | ||||
−0.0467040 | + | 0.998909i | \(0.514872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.58934 | 0.138012 | ||||||||
\(353\) | 15.9580 | 0.849358 | 0.424679 | − | 0.905344i | \(-0.360387\pi\) | ||||
0.424679 | + | 0.905344i | \(0.360387\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.5799 | −1.78224 | ||||||||
\(356\) | −5.69237 | −0.301695 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.3404 | −0.599356 | ||||||||
\(359\) | −8.81400 | −0.465185 | −0.232593 | − | 0.972574i | \(-0.574721\pi\) | ||||
−0.232593 | + | 0.972574i | \(0.574721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5043 | −0.921280 | ||||||||
\(362\) | 3.44250 | 0.180934 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.2926 | 0.852792 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7080 | 1.02875 | 0.514374 | − | 0.857566i | \(-0.328024\pi\) | ||||
0.514374 | + | 0.857566i | \(0.328024\pi\) | |||||||
\(368\) | −7.14043 | −0.372221 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.5144 | 0.962515 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.365792 | −0.0189400 | −0.00947000 | − | 0.999955i | \(-0.503014\pi\) | ||||
−0.00947000 | + | 0.999955i | \(0.503014\pi\) | |||||||
\(374\) | −5.23358 | −0.270622 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.5319 | −0.852566 | ||||||||
\(377\) | −2.46882 | −0.127151 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.39215 | 0.379709 | 0.189855 | − | 0.981812i | \(-0.439198\pi\) | ||||
0.189855 | + | 0.981812i | \(0.439198\pi\) | |||||||
\(380\) | −2.37429 | −0.121798 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.9795 | 0.971073 | ||||||||
\(383\) | −3.35364 | −0.171363 | −0.0856814 | − | 0.996323i | \(-0.527307\pi\) | ||||
−0.0856814 | + | 0.996323i | \(0.527307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.101601 | −0.00517135 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.778692 | −0.0395321 | ||||||||
\(389\) | 2.59344 | 0.131492 | 0.0657462 | − | 0.997836i | \(-0.479057\pi\) | ||||
0.0657462 | + | 0.997836i | \(0.479057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.2131 | −0.870506 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.7121 | −0.892321 | ||||||||
\(395\) | −1.70668 | −0.0858721 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4914 | 1.68088 | 0.840441 | − | 0.541902i | \(-0.182296\pi\) | ||||
0.840441 | + | 0.541902i | \(0.182296\pi\) | |||||||
\(398\) | −18.1681 | −0.910686 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.7276 | −0.586380 | ||||||||
\(401\) | −39.5156 | −1.97331 | −0.986657 | − | 0.162811i | \(-0.947944\pi\) | ||||
−0.986657 | + | 0.162811i | \(0.947944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.13487 | −0.305599 | ||||||||
\(404\) | −0.373310 | −0.0185729 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.86643 | 0.191652 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.9799 | 0.542922 | 0.271461 | − | 0.962449i | \(-0.412493\pi\) | ||||
0.271461 | + | 0.962449i | \(0.412493\pi\) | |||||||
\(410\) | −9.47990 | −0.468179 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.71567 | 0.232324 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.9405 | 2.35331 | ||||||||
\(416\) | −3.34804 | −0.164151 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.11248 | 0.0544134 | ||||||||
\(419\) | 31.5621 | 1.54191 | 0.770954 | − | 0.636891i | \(-0.219780\pi\) | ||||
0.770954 | + | 0.636891i | \(0.219780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7055 | −0.862914 | −0.431457 | − | 0.902134i | \(-0.642000\pi\) | ||||
−0.431457 | + | 0.902134i | \(0.642000\pi\) | |||||||
\(422\) | −29.4706 | −1.43461 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.1301 | −1.46325 | ||||||||
\(425\) | −28.2712 | −1.37136 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.97789 | 0.143942 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.1158 | −0.487825 | ||||||||
\(431\) | 21.4816 | 1.03473 | 0.517367 | − | 0.855764i | \(-0.326912\pi\) | ||||
0.517367 | + | 0.855764i | \(0.326912\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.7200 | −1.66854 | −0.834269 | − | 0.551358i | \(-0.814110\pi\) | ||||
−0.834269 | + | 0.551358i | \(0.814110\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.45848 | −0.213522 | ||||||||
\(437\) | 3.65894 | 0.175031 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.728505 | −0.0347697 | −0.0173848 | − | 0.999849i | \(-0.505534\pi\) | ||||
−0.0173848 | + | 0.999849i | \(0.505534\pi\) | |||||||
\(440\) | −7.49428 | −0.357276 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.76707 | 0.321877 | ||||||||
\(443\) | −0.837291 | −0.0397809 | −0.0198904 | − | 0.999802i | \(-0.506332\pi\) | ||||
−0.0198904 | + | 0.999802i | \(0.506332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.0684 | 1.37797 | ||||||||
\(446\) | 24.3047 | 1.15086 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.4312 | −1.24737 | −0.623683 | − | 0.781677i | \(-0.714365\pi\) | ||||
−0.623683 | + | 0.781677i | \(0.714365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.97973 | −0.0932217 | ||||||||
\(452\) | −5.66873 | −0.266635 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.15546 | 0.0542284 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.40475 | −0.112489 | −0.0562447 | − | 0.998417i | \(-0.517913\pi\) | ||||
−0.0562447 | + | 0.998417i | \(0.517913\pi\) | |||||||
\(458\) | 16.7892 | 0.784507 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.80831 | −0.270814 | ||||||||
\(461\) | −22.2702 | −1.03722 | −0.518612 | − | 0.855010i | \(-0.673551\pi\) | ||||
−0.518612 | + | 0.855010i | \(0.673551\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.3085 | 1.50151 | 0.750753 | − | 0.660583i | \(-0.229691\pi\) | ||||
0.750753 | + | 0.660583i | \(0.229691\pi\) | |||||||
\(464\) | −5.89221 | −0.273539 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.64118 | −0.0760263 | ||||||||
\(467\) | −12.8744 | −0.595756 | −0.297878 | − | 0.954604i | \(-0.596279\pi\) | ||||
−0.297878 | + | 0.954604i | \(0.596279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.8934 | 0.917612 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.70802 | −0.354791 | ||||||||
\(473\) | −2.11251 | −0.0971335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00952 | 0.275736 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.99781 | −0.137117 | ||||||||
\(479\) | 10.5419 | 0.481670 | 0.240835 | − | 0.970566i | \(-0.422579\pi\) | ||||
0.240835 | + | 0.970566i | \(0.422579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.99933 | −0.227950 | ||||||||
\(482\) | −34.9029 | −1.58978 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.41364 | 0.291529 | ||||||||
\(485\) | 3.97643 | 0.180560 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.2416 | 1.73289 | 0.866446 | − | 0.499271i | \(-0.166399\pi\) | ||||
0.866446 | + | 0.499271i | \(0.166399\pi\) | |||||||
\(488\) | −33.5972 | −1.52087 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.4291 | 0.696306 | 0.348153 | − | 0.937438i | \(-0.386809\pi\) | ||||
0.348153 | + | 0.937438i | \(0.386809\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2041 | −0.639721 | ||||||||
\(494\) | −1.43845 | −0.0647190 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.6418 | −0.657436 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.8212 | −1.73788 | −0.868938 | − | 0.494921i | \(-0.835197\pi\) | ||||
−0.868938 | + | 0.494921i | \(0.835197\pi\) | |||||||
\(500\) | 0.167283 | 0.00748112 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.2723 | 0.949430 | ||||||||
\(503\) | −27.0935 | −1.20804 | −0.604020 | − | 0.796969i | \(-0.706435\pi\) | ||||
−0.604020 | + | 0.796969i | \(0.706435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.90633 | 0.0848304 | ||||||||
\(506\) | 2.72151 | 0.120986 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.91304 | 0.306717 | ||||||||
\(509\) | −15.7693 | −0.698961 | −0.349480 | − | 0.936944i | \(-0.613642\pi\) | ||||
−0.349480 | + | 0.936944i | \(0.613642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6809 | −1.00236 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.3373 | 0.764716 | ||||||||
\(515\) | −24.0808 | −1.06113 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.15441 | 0.182711 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.69018 | 0.424943 | ||||||||
\(521\) | 7.30737 | 0.320142 | 0.160071 | − | 0.987106i | \(-0.448828\pi\) | ||||
0.160071 | + | 0.987106i | \(0.448828\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0826 | −0.615788 | −0.307894 | − | 0.951421i | \(-0.599624\pi\) | ||||
−0.307894 | + | 0.951421i | \(0.599624\pi\) | |||||||
\(524\) | −9.70381 | −0.423913 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.59677 | 0.418439 | ||||||||
\(527\) | −35.2963 | −1.53753 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0490 | −0.610827 | ||||||||
\(530\) | 36.2565 | 1.57488 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.55981 | 0.110877 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.2067 | −0.657445 | ||||||||
\(536\) | −13.3111 | −0.574953 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.520559 | 0.0224429 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.1750 | −1.68426 | −0.842132 | − | 0.539271i | \(-0.818700\pi\) | ||||
−0.842132 | + | 0.539271i | \(0.818700\pi\) | |||||||
\(542\) | 24.7977 | 1.06515 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.2626 | −0.825877 | ||||||||
\(545\) | 22.7674 | 0.975250 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.7917 | 1.65862 | 0.829308 | − | 0.558792i | \(-0.188735\pi\) | ||||
0.829308 | + | 0.558792i | \(0.188735\pi\) | |||||||
\(548\) | −11.4814 | −0.490463 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.46987 | 0.190596 | ||||||||
\(551\) | 3.01932 | 0.128627 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.22746 | 0.179607 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.34580 | −0.311531 | ||||||||
\(557\) | 27.4693 | 1.16391 | 0.581956 | − | 0.813220i | \(-0.302287\pi\) | ||||
0.581956 | + | 0.813220i | \(0.302287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.73150 | 0.115530 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.6004 | 0.447151 | ||||||||
\(563\) | 14.1210 | 0.595129 | 0.297565 | − | 0.954702i | \(-0.403826\pi\) | ||||
0.297565 | + | 0.954702i | \(0.403826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.9477 | 1.21784 | ||||||||
\(566\) | −32.6288 | −1.37149 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 32.8223 | 1.37720 | ||||||||
\(569\) | 8.28649 | 0.347388 | 0.173694 | − | 0.984800i | \(-0.444430\pi\) | ||||
0.173694 | + | 0.984800i | \(0.444430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.5274 | −0.984591 | −0.492295 | − | 0.870428i | \(-0.663842\pi\) | ||||
−0.492295 | + | 0.870428i | \(0.663842\pi\) | |||||||
\(572\) | 0.476861 | 0.0199386 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.7013 | 0.613087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.7732 | 0.739906 | 0.369953 | − | 0.929050i | \(-0.379374\pi\) | ||||
0.369953 | + | 0.929050i | \(0.379374\pi\) | |||||||
\(578\) | 18.9385 | 0.787737 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.79296 | −0.199017 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.57160 | 0.313584 | ||||||||
\(584\) | −15.9250 | −0.658982 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.9857 | 0.619054 | ||||||||
\(587\) | −6.64096 | −0.274102 | −0.137051 | − | 0.990564i | \(-0.543762\pi\) | ||||
−0.137051 | + | 0.990564i | \(0.543762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.50282 | 0.309148 | ||||||||
\(590\) | 9.27532 | 0.381859 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.9317 | −0.490388 | ||||||||
\(593\) | 34.0504 | 1.39828 | 0.699141 | − | 0.714984i | \(-0.253566\pi\) | ||||
0.699141 | + | 0.714984i | \(0.253566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.01387 | 0.287299 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.51894 | −0.143900 | ||||||||
\(599\) | −9.38441 | −0.383437 | −0.191718 | − | 0.981450i | \(-0.561406\pi\) | ||||
−0.191718 | + | 0.981450i | \(0.561406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.80294 | −0.359079 | −0.179540 | − | 0.983751i | \(-0.557461\pi\) | ||||
−0.179540 | + | 0.983751i | \(0.557461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.27675 | 0.0926394 | ||||||||
\(605\) | −32.7516 | −1.33154 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.7720 | −0.721342 | −0.360671 | − | 0.932693i | \(-0.617452\pi\) | ||||
−0.360671 | + | 0.932693i | \(0.617452\pi\) | |||||||
\(608\) | 4.09458 | 0.166057 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 40.4286 | 1.63691 | ||||||||
\(611\) | −5.37169 | −0.217315 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6081 | 0.428457 | 0.214228 | − | 0.976784i | \(-0.431276\pi\) | ||||
0.214228 | + | 0.976784i | \(0.431276\pi\) | |||||||
\(614\) | −11.9246 | −0.481237 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −49.3483 | −1.98669 | −0.993344 | − | 0.115188i | \(-0.963253\pi\) | ||||
−0.993344 | + | 0.115188i | \(0.963253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.42203 | −0.298317 | −0.149158 | − | 0.988813i | \(-0.547656\pi\) | ||||
−0.149158 | + | 0.988813i | \(0.547656\pi\) | |||||||
\(620\) | −11.9102 | −0.478325 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.2309 | 0.971573 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.4234 | −1.01694 | ||||||||
\(626\) | −19.4607 | −0.777806 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.690975 | 0.0275729 | ||||||||
\(629\) | −28.7631 | −1.14686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5184 | 1.41396 | 0.706982 | − | 0.707231i | \(-0.250056\pi\) | ||||
0.706982 | + | 0.707231i | \(0.250056\pi\) | |||||||
\(632\) | 1.66817 | 0.0663564 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.9752 | 0.991890 | ||||||||
\(635\) | −35.3018 | −1.40091 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.24576 | 0.0889106 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.1774 | 0.441827 | ||||||||
\(641\) | −37.1554 | −1.46755 | −0.733775 | − | 0.679393i | \(-0.762243\pi\) | ||||
−0.733775 | + | 0.679393i | \(0.762243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.7694 | −1.56835 | −0.784176 | − | 0.620538i | \(-0.786914\pi\) | ||||
−0.784176 | + | 0.620538i | \(0.786914\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.27599 | −0.325614 | ||||||||
\(647\) | 22.9754 | 0.903256 | 0.451628 | − | 0.892206i | \(-0.350843\pi\) | ||||
0.451628 | + | 0.892206i | \(0.350843\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.93700 | 0.0760340 | ||||||||
\(650\) | −5.77958 | −0.226694 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.5435 | 0.491241 | ||||||||
\(653\) | −18.1757 | −0.711268 | −0.355634 | − | 0.934625i | \(-0.615735\pi\) | ||||
−0.355634 | + | 0.934625i | \(0.615735\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49.5530 | 1.93619 | ||||||||
\(656\) | 6.10936 | 0.238531 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1044 | −0.549431 | −0.274716 | − | 0.961526i | \(-0.588584\pi\) | ||||
−0.274716 | + | 0.961526i | \(0.588584\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8557 | 0.500027 | 0.250013 | − | 0.968242i | \(-0.419565\pi\) | ||||
0.250013 | + | 0.968242i | \(0.419565\pi\) | |||||||
\(662\) | 19.1030 | 0.742459 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −46.8590 | −1.81848 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.38627 | 0.285997 | ||||||||
\(668\) | −8.01948 | −0.310283 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.0177 | 0.618819 | ||||||||
\(671\) | 8.44287 | 0.325933 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.6138 | −1.75828 | −0.879141 | − | 0.476561i | \(-0.841883\pi\) | ||||
−0.879141 | + | 0.476561i | \(0.841883\pi\) | |||||||
\(674\) | 7.55278 | 0.290922 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.616586 | −0.0237148 | ||||||||
\(677\) | 10.2469 | 0.393821 | 0.196910 | − | 0.980421i | \(-0.436909\pi\) | ||||
0.196910 | + | 0.980421i | \(0.436909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 55.7515 | 2.13797 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.58058 | 0.213692 | ||||||||
\(683\) | −2.90040 | −0.110981 | −0.0554904 | − | 0.998459i | \(-0.517672\pi\) | ||||
−0.0554904 | + | 0.998459i | \(0.517672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 58.6305 | 2.24016 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.51914 | 0.248540 | ||||||||
\(689\) | −9.79015 | −0.372975 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.91470 | −0.263048 | −0.131524 | − | 0.991313i | \(-0.541987\pi\) | ||||
−0.131524 | + | 0.991313i | \(0.541987\pi\) | |||||||
\(692\) | 15.9764 | 0.607330 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.0323 | −0.646536 | ||||||||
\(695\) | 37.5117 | 1.42290 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7276 | 0.557847 | ||||||||
\(698\) | −2.05245 | −0.0776864 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0973 | 0.985682 | 0.492841 | − | 0.870119i | \(-0.335958\pi\) | ||||
0.492841 | + | 0.870119i | \(0.335958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.11408 | 0.230597 | ||||||||
\(704\) | 6.73717 | 0.253916 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.7696 | 0.706402 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.38472 | −0.127116 | −0.0635580 | − | 0.997978i | \(-0.520245\pi\) | ||||
−0.0635580 | + | 0.997978i | \(0.520245\pi\) | |||||||
\(710\) | −39.4962 | −1.48227 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −28.4126 | −1.06481 | ||||||||
\(713\) | 18.3544 | 0.687378 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.43511 | −0.0910681 | ||||||||
\(716\) | 5.94489 | 0.222171 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.3669 | −0.386890 | ||||||||
\(719\) | −2.41574 | −0.0900918 | −0.0450459 | − | 0.998985i | \(-0.514343\pi\) | ||||
−0.0450459 | + | 0.998985i | \(0.514343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −20.5883 | −0.766219 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.80464 | −0.0670691 | ||||||||
\(725\) | 12.1314 | 0.450548 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0150 | −0.631050 | −0.315525 | − | 0.948917i | \(-0.602181\pi\) | ||||
−0.315525 | + | 0.948917i | \(0.602181\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.1631 | 0.709258 | ||||||||
\(731\) | 15.7154 | 0.581256 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.18453 | −0.154559 | −0.0772795 | − | 0.997009i | \(-0.524623\pi\) | ||||
−0.0772795 | + | 0.997009i | \(0.524623\pi\) | |||||||
\(734\) | 23.1803 | 0.855599 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.0167 | 0.369221 | ||||||||
\(737\) | 3.34505 | 0.123216 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.0794 | −1.03292 | −0.516458 | − | 0.856312i | \(-0.672750\pi\) | ||||
−0.516458 | + | 0.856312i | \(0.672750\pi\) | |||||||
\(740\) | −9.70567 | −0.356788 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.5210 | 0.972961 | 0.486481 | − | 0.873691i | \(-0.338280\pi\) | ||||
0.486481 | + | 0.873691i | \(0.338280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.8167 | −1.31222 | ||||||||
\(746\) | −0.430240 | −0.0157522 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.74357 | 0.100315 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.7162 | −0.865418 | −0.432709 | − | 0.901534i | \(-0.642442\pi\) | ||||
−0.432709 | + | 0.901534i | \(0.642442\pi\) | |||||||
\(752\) | −12.8204 | −0.467510 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.90379 | −0.105750 | ||||||||
\(755\) | −11.6263 | −0.423125 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.3661 | −1.90328 | −0.951639 | − | 0.307219i | \(-0.900602\pi\) | ||||
−0.951639 | + | 0.307219i | \(0.900602\pi\) | |||||||
\(758\) | 8.69454 | 0.315800 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.8509 | −0.429877 | ||||||||
\(761\) | 23.8695 | 0.865268 | 0.432634 | − | 0.901570i | \(-0.357584\pi\) | ||||
0.432634 | + | 0.901570i | \(0.357584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.94949 | −0.359960 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.94450 | −0.142521 | ||||||||
\(767\) | −2.50456 | −0.0904345 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.7599 | −1.50590 | −0.752950 | − | 0.658077i | \(-0.771370\pi\) | ||||
−0.752950 | + | 0.658077i | \(0.771370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.0532617 | 0.00191693 | ||||||||
\(773\) | 2.97178 | 0.106888 | 0.0534438 | − | 0.998571i | \(-0.482980\pi\) | ||||
0.0534438 | + | 0.998571i | \(0.482980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.1457 | 1.08287 | ||||||||
\(776\) | −3.88672 | −0.139525 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.05037 | 0.109361 | ||||||||
\(779\) | −3.13059 | −0.112165 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.24815 | −0.295142 | ||||||||
\(782\) | −20.2459 | −0.723990 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.52850 | −0.125937 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.6142 | 1.73291 | 0.866454 | − | 0.499256i | \(-0.166393\pi\) | ||||
0.866454 | + | 0.499256i | \(0.166393\pi\) | |||||||
\(788\) | 9.28509 | 0.330768 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.00737 | −0.0714189 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9167 | −0.387664 | ||||||||
\(794\) | 39.3921 | 1.39797 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.52418 | 0.337576 | ||||||||
\(797\) | 25.6470 | 0.908463 | 0.454232 | − | 0.890884i | \(-0.349914\pi\) | ||||
0.454232 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.9055 | −1.09336 | ||||||||
\(800\) | 16.4517 | 0.581655 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −46.4777 | −1.64118 | ||||||||
\(803\) | 4.00191 | 0.141224 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.21575 | −0.254164 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.86332 | −0.0655514 | ||||||||
\(809\) | 11.9205 | 0.419101 | 0.209550 | − | 0.977798i | \(-0.432800\pi\) | ||||
0.209550 | + | 0.977798i | \(0.432800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.5564 | 0.370685 | 0.185343 | − | 0.982674i | \(-0.440661\pi\) | ||||
0.185343 | + | 0.982674i | \(0.440661\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.54764 | 0.159395 | ||||||||
\(815\) | −64.0540 | −2.24371 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.34057 | −0.116872 | ||||||||
\(818\) | 12.9144 | 0.451543 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.96960 | 0.173546 | ||||||||
\(821\) | 46.2139 | 1.61288 | 0.806438 | − | 0.591319i | \(-0.201393\pi\) | ||||
0.806438 | + | 0.591319i | \(0.201393\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.2171 | 1.43674 | 0.718368 | − | 0.695663i | \(-0.244889\pi\) | ||||
0.718368 | + | 0.695663i | \(0.244889\pi\) | |||||||
\(824\) | 23.5375 | 0.819969 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.94430 | −0.206704 | −0.103352 | − | 0.994645i | \(-0.532957\pi\) | ||||
−0.103352 | + | 0.994645i | \(0.532957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.8106 | −1.20902 | −0.604511 | − | 0.796596i | \(-0.706632\pi\) | ||||
−0.604511 | + | 0.796596i | \(0.706632\pi\) | |||||||
\(830\) | 56.3869 | 1.95722 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.71122 | −0.302007 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.9519 | 1.41720 | ||||||||
\(836\) | −0.583191 | −0.0201701 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.1229 | 1.28239 | ||||||||
\(839\) | 10.7896 | 0.372500 | 0.186250 | − | 0.982502i | \(-0.440367\pi\) | ||||
0.186250 | + | 0.982502i | \(0.440367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.9049 | −0.789825 | ||||||||
\(842\) | −20.8250 | −0.717676 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.4492 | 0.531784 | ||||||||
\(845\) | 3.14862 | 0.108316 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −23.3657 | −0.802381 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −33.2523 | −1.14054 | ||||||||
\(851\) | 14.9571 | 0.512722 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.1053 | −1.33894 | −0.669470 | − | 0.742839i | \(-0.733479\pi\) | ||||
−0.669470 | + | 0.742839i | \(0.733479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.8637 | 0.508030 | ||||||||
\(857\) | −33.3654 | −1.13974 | −0.569870 | − | 0.821735i | \(-0.693006\pi\) | ||||
−0.569870 | + | 0.821735i | \(0.693006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.4914 | 1.00623 | 0.503116 | − | 0.864219i | \(-0.332187\pi\) | ||||
0.503116 | + | 0.864219i | \(0.332187\pi\) | |||||||
\(860\) | 5.30293 | 0.180828 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.2664 | 0.860578 | ||||||||
\(863\) | 24.6224 | 0.838157 | 0.419079 | − | 0.907950i | \(-0.362353\pi\) | ||||
0.419079 | + | 0.907950i | \(0.362353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −81.5841 | −2.77394 | ||||||||
\(866\) | −40.8372 | −1.38771 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.419207 | −0.0142206 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.32518 | −0.146553 | ||||||||
\(872\) | −22.2538 | −0.753609 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.30359 | 0.145571 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.62556 | −0.156194 | −0.0780971 | − | 0.996946i | \(-0.524884\pi\) | ||||
−0.0780971 | + | 0.996946i | \(0.524884\pi\) | |||||||
\(878\) | −0.856858 | −0.0289176 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.81177 | −0.195915 | ||||||||
\(881\) | −42.1720 | −1.42081 | −0.710405 | − | 0.703793i | \(-0.751488\pi\) | ||||
−0.710405 | + | 0.703793i | \(0.751488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.7992 | 0.699950 | 0.349975 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349975 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(884\) | −3.54746 | −0.119314 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.984810 | −0.0330853 | ||||||||
\(887\) | 34.4889 | 1.15802 | 0.579012 | − | 0.815319i | \(-0.303438\pi\) | ||||
0.579012 | + | 0.815319i | \(0.303438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 34.1898 | 1.14605 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.7411 | −0.426604 | ||||||||
\(893\) | 6.56947 | 0.219839 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.3579 | −1.01475 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.0880 | −1.03742 | ||||||||
\(899\) | 15.1459 | 0.505144 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −56.3267 | −1.87651 | ||||||||
\(902\) | −2.32853 | −0.0775315 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.2946 | −0.941065 | ||||||||
\(905\) | 9.21550 | 0.306334 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3619 | 0.443675 | 0.221838 | − | 0.975084i | \(-0.428795\pi\) | ||||
0.221838 | + | 0.975084i | \(0.428795\pi\) | |||||||
\(908\) | −0.605720 | −0.0201015 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.29058 | −0.175285 | −0.0876424 | − | 0.996152i | \(-0.527933\pi\) | ||||
−0.0876424 | + | 0.996152i | \(0.527933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7755 | 0.389713 | ||||||||
\(914\) | −2.82843 | −0.0935562 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.80129 | −0.290803 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.8306 | −0.621164 | −0.310582 | − | 0.950547i | \(-0.600524\pi\) | ||||
−0.310582 | + | 0.950547i | \(0.600524\pi\) | |||||||
\(920\) | −28.9913 | −0.955814 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.1939 | −0.862649 | ||||||||
\(923\) | 10.6649 | 0.351041 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.5659 | 0.807721 | ||||||||
\(926\) | 38.0009 | 1.24879 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.26571 | 0.271335 | ||||||||
\(929\) | −44.9537 | −1.47488 | −0.737442 | − | 0.675411i | \(-0.763966\pi\) | ||||
−0.737442 | + | 0.675411i | \(0.763966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.860348 | 0.0281816 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.1427 | −0.495484 | ||||||||
\(935\) | −14.0102 | −0.458182 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.9272 | −1.23903 | −0.619514 | − | 0.784986i | \(-0.712670\pi\) | ||||
−0.619514 | + | 0.784986i | \(0.712670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.4286 | −0.340143 | ||||||||
\(941\) | 35.7869 | 1.16662 | 0.583310 | − | 0.812250i | \(-0.301757\pi\) | ||||
0.583310 | + | 0.812250i | \(0.301757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.65848 | −0.249394 | ||||||||
\(944\) | −5.97752 | −0.194552 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.48471 | −0.0807849 | ||||||||
\(947\) | 14.7443 | 0.479125 | 0.239563 | − | 0.970881i | \(-0.422996\pi\) | ||||
0.239563 | + | 0.970881i | \(0.422996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.17450 | −0.167971 | ||||||||
\(950\) | 7.06831 | 0.229326 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.649669 | −0.0210448 | −0.0105224 | − | 0.999945i | \(-0.503349\pi\) | ||||
−0.0105224 | + | 0.999945i | \(0.503349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.8076 | 1.64409 | ||||||||
\(956\) | 1.57153 | 0.0508268 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.3992 | 0.400600 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.63659 | 0.214083 | ||||||||
\(962\) | −5.88014 | −0.189583 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.2969 | 0.589305 | ||||||||
\(965\) | −0.271983 | −0.00875545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0802 | −0.420632 | −0.210316 | − | 0.977633i | \(-0.567449\pi\) | ||||
−0.210316 | + | 0.977633i | \(0.567449\pi\) | |||||||
\(968\) | 32.0127 | 1.02893 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.67702 | 0.150170 | ||||||||
\(971\) | −29.1203 | −0.934515 | −0.467258 | − | 0.884121i | \(-0.654758\pi\) | ||||
−0.467258 | + | 0.884121i | \(0.654758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 44.9792 | 1.44123 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.0544 | −0.833980 | ||||||||
\(977\) | 18.5000 | 0.591868 | 0.295934 | − | 0.955208i | \(-0.404369\pi\) | ||||
0.295934 | + | 0.955208i | \(0.404369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.14000 | 0.228195 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.1475 | 0.579111 | ||||||||
\(983\) | −11.0462 | −0.352318 | −0.176159 | − | 0.984362i | \(-0.556367\pi\) | ||||
−0.176159 | + | 0.984362i | \(0.556367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.4148 | −1.51076 | ||||||||
\(986\) | −16.7067 | −0.532049 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.754072 | 0.0239902 | ||||||||
\(989\) | −8.17216 | −0.259860 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.4757 | −1.28575 | −0.642877 | − | 0.765969i | \(-0.722259\pi\) | ||||
−0.642877 | + | 0.765969i | \(0.722259\pi\) | |||||||
\(992\) | 20.5398 | 0.652138 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.6357 | −1.54185 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.0623 | 0.382018 | 0.191009 | − | 0.981588i | \(-0.438824\pi\) | ||||
0.191009 | + | 0.981588i | \(0.438824\pi\) | |||||||
\(998\) | −45.6610 | −1.44537 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5733.2.a.bu.1.5 | 6 | ||
3.2 | odd | 2 | 637.2.a.m.1.2 | ✓ | 6 | ||
7.6 | odd | 2 | 5733.2.a.br.1.5 | 6 | |||
21.2 | odd | 6 | 637.2.e.o.508.5 | 12 | |||
21.5 | even | 6 | 637.2.e.n.508.5 | 12 | |||
21.11 | odd | 6 | 637.2.e.o.79.5 | 12 | |||
21.17 | even | 6 | 637.2.e.n.79.5 | 12 | |||
21.20 | even | 2 | 637.2.a.n.1.2 | yes | 6 | ||
39.38 | odd | 2 | 8281.2.a.cc.1.5 | 6 | |||
273.272 | even | 2 | 8281.2.a.cd.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.a.m.1.2 | ✓ | 6 | 3.2 | odd | 2 | ||
637.2.a.n.1.2 | yes | 6 | 21.20 | even | 2 | ||
637.2.e.n.79.5 | 12 | 21.17 | even | 6 | |||
637.2.e.n.508.5 | 12 | 21.5 | even | 6 | |||
637.2.e.o.79.5 | 12 | 21.11 | odd | 6 | |||
637.2.e.o.508.5 | 12 | 21.2 | odd | 6 | |||
5733.2.a.br.1.5 | 6 | 7.6 | odd | 2 | |||
5733.2.a.bu.1.5 | 6 | 1.1 | even | 1 | trivial | ||
8281.2.a.cc.1.5 | 6 | 39.38 | odd | 2 | |||
8281.2.a.cd.1.5 | 6 | 273.272 | even | 2 |