Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(46,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.j (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.4406832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.3 | ||
Root | \(1.43310 + 2.48220i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.226 |
Dual form | 315.2.j.f.46.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.933099 | − | 1.61618i | 0.659801 | − | 1.14281i | −0.320866 | − | 0.947124i | \(-0.603974\pi\) |
0.980667 | − | 0.195684i | \(-0.0626926\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.741348 | − | 1.28405i | −0.370674 | − | 0.642026i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.69175 | − | 2.03420i | 0.639422 | − | 0.768856i | ||||
\(8\) | 0.965392 | 0.341318 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.933099 | + | 1.61618i | 0.295072 | + | 0.511079i | ||||
\(11\) | −2.67445 | − | 4.63228i | −0.806376 | − | 1.39668i | −0.915358 | − | 0.402641i | \(-0.868092\pi\) |
0.108982 | − | 0.994044i | \(-0.465241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.34889 | 1.20617 | 0.603083 | − | 0.797678i | \(-0.293939\pi\) | ||||
0.603083 | + | 0.797678i | \(0.293939\pi\) | |||||||
\(14\) | −1.70906 | − | 4.63228i | −0.456764 | − | 1.23803i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.38350 | − | 4.12835i | 0.595876 | − | 1.03209i | ||||
\(17\) | −0.933099 | − | 1.61618i | −0.226310 | − | 0.391980i | 0.730402 | − | 0.683018i | \(-0.239333\pi\) |
−0.956712 | + | 0.291038i | \(0.905999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.62485 | + | 4.54637i | −0.602182 | + | 1.04301i | 0.390308 | + | 0.920684i | \(0.372368\pi\) |
−0.992490 | + | 0.122325i | \(0.960965\pi\) | |||||||
\(20\) | 1.48270 | 0.331541 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.98210 | −2.12819 | ||||||||
\(23\) | −3.45040 | + | 5.97627i | −0.719459 | + | 1.24614i | 0.241756 | + | 0.970337i | \(0.422277\pi\) |
−0.961214 | + | 0.275802i | \(0.911057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 4.05795 | − | 7.02857i | 0.795829 | − | 1.37842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.86620 | − | 0.664245i | −0.730643 | − | 0.125531i | ||||
\(29\) | 4.38350 | 0.813996 | 0.406998 | − | 0.913429i | \(-0.366576\pi\) | ||||
0.406998 | + | 0.913429i | \(0.366576\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.71509 | + | 8.16678i | 0.846856 | + | 1.46680i | 0.884000 | + | 0.467487i | \(0.154841\pi\) |
−0.0371443 | + | 0.999310i | \(0.511826\pi\) | |||||||
\(32\) | −3.48270 | − | 6.03221i | −0.615659 | − | 1.06635i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.48270 | −0.597277 | ||||||||
\(35\) | 0.915795 | + | 2.48220i | 0.154798 | + | 0.419568i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.08420 | + | 1.87790i | −0.178242 | + | 0.308725i | −0.941279 | − | 0.337631i | \(-0.890374\pi\) |
0.763036 | + | 0.646356i | \(0.223708\pi\) | |||||||
\(38\) | 4.89849 | + | 8.48444i | 0.794640 | + | 1.37636i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.482696 | + | 0.836054i | −0.0763209 | + | 0.132192i | ||||
\(41\) | −0.314286 | −0.0490832 | −0.0245416 | − | 0.999699i | \(-0.507813\pi\) | ||||
−0.0245416 | + | 0.999699i | \(0.507813\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.56399 | −1.15350 | −0.576749 | − | 0.816922i | \(-0.695679\pi\) | ||||
−0.576749 | + | 0.816922i | \(0.695679\pi\) | |||||||
\(44\) | −3.96539 | + | 6.86826i | −0.597805 | + | 1.03543i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.43914 | + | 11.1529i | 0.949399 | + | 1.64441i | ||||
\(47\) | −4.21509 | + | 7.30075i | −0.614834 | + | 1.06492i | 0.375579 | + | 0.926790i | \(0.377444\pi\) |
−0.990414 | + | 0.138134i | \(0.955889\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.27596 | − | 6.88273i | −0.182279 | − | 0.983247i | ||||
\(50\) | −1.86620 | −0.263920 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.22404 | − | 5.58421i | −0.447094 | − | 0.774390i | ||||
\(53\) | 1.86620 | + | 3.23235i | 0.256342 | + | 0.443997i | 0.965259 | − | 0.261294i | \(-0.0841493\pi\) |
−0.708917 | + | 0.705292i | \(0.750816\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.34889 | 0.721245 | ||||||||
\(56\) | 1.63320 | − | 1.96380i | 0.218246 | − | 0.262424i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.09024 | − | 7.08451i | 0.537075 | − | 0.930241i | ||||
\(59\) | −0.639839 | − | 1.10823i | −0.0832999 | − | 0.144280i | 0.821366 | − | 0.570402i | \(-0.193213\pi\) |
−0.904666 | + | 0.426122i | \(0.859879\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.39245 | − | 2.41180i | 0.178285 | − | 0.308799i | −0.763008 | − | 0.646389i | \(-0.776278\pi\) |
0.941293 | + | 0.337590i | \(0.109612\pi\) | |||||||
\(62\) | 17.5986 | 2.23502 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.46479 | −0.433099 | ||||||||
\(65\) | −2.17445 | + | 3.76625i | −0.269707 | + | 0.467146i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.04065 | − | 1.80245i | −0.127135 | − | 0.220204i | 0.795430 | − | 0.606045i | \(-0.207245\pi\) |
−0.922565 | + | 0.385841i | \(0.873911\pi\) | |||||||
\(68\) | −1.38350 | + | 2.39630i | −0.167774 | + | 0.290594i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.86620 | + | 0.836054i | 0.581622 | + | 0.0999276i | ||||
\(71\) | −6.81369 | −0.808636 | −0.404318 | − | 0.914618i | \(-0.632491\pi\) | ||||
−0.404318 | + | 0.914618i | \(0.632491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.81660 | + | 4.87850i | 0.329658 | + | 0.570985i | 0.982444 | − | 0.186558i | \(-0.0597331\pi\) |
−0.652786 | + | 0.757543i | \(0.726400\pi\) | |||||||
\(74\) | 2.02334 | + | 3.50453i | 0.235209 | + | 0.407393i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.78371 | 0.892853 | ||||||||
\(77\) | −13.9475 | − | 2.39630i | −1.58946 | − | 0.273083i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.97374 | − | 10.3468i | 0.672099 | − | 1.16411i | −0.305209 | − | 0.952285i | \(-0.598726\pi\) |
0.977308 | − | 0.211824i | \(-0.0679403\pi\) | |||||||
\(80\) | 2.38350 | + | 4.12835i | 0.266484 | + | 0.461563i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.293260 | + | 0.507941i | −0.0323852 | + | 0.0560927i | ||||
\(83\) | 3.16841 | 0.347778 | 0.173889 | − | 0.984765i | \(-0.444367\pi\) | ||||
0.173889 | + | 0.984765i | \(0.444367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.86620 | 0.202418 | ||||||||
\(86\) | −7.05795 | + | 12.2247i | −0.761078 | + | 1.31823i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.58189 | − | 4.47196i | −0.275230 | − | 0.476713i | ||||
\(89\) | 1.45935 | − | 2.52768i | 0.154691 | − | 0.267933i | −0.778255 | − | 0.627948i | \(-0.783895\pi\) |
0.932947 | + | 0.360015i | \(0.117228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.35725 | − | 8.84653i | 0.771249 | − | 0.927368i | ||||
\(92\) | 10.2318 | 1.06674 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.86620 | + | 13.6247i | 0.811336 | + | 1.40528i | ||||
\(95\) | −2.62485 | − | 4.54637i | −0.269304 | − | 0.466448i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.91288 | −1.00650 | −0.503250 | − | 0.864141i | \(-0.667863\pi\) | ||||
−0.503250 | + | 0.864141i | \(0.667863\pi\) | |||||||
\(98\) | −12.3143 | − | 4.36010i | −1.24393 | − | 0.440436i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.741348 | + | 1.28405i | −0.0741348 | + | 0.128405i | ||||
\(101\) | 8.75574 | + | 15.1654i | 0.871228 | + | 1.50901i | 0.860727 | + | 0.509067i | \(0.170010\pi\) |
0.0105017 | + | 0.999945i | \(0.496657\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.26469 | + | 10.8508i | −0.617278 | + | 1.06916i | 0.372702 | + | 0.927951i | \(0.378431\pi\) |
−0.989980 | + | 0.141206i | \(0.954902\pi\) | |||||||
\(104\) | 4.19839 | 0.411686 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.96539 | 0.676539 | ||||||||
\(107\) | −4.58420 | + | 7.94008i | −0.443172 | + | 0.767596i | −0.997923 | − | 0.0644203i | \(-0.979480\pi\) |
0.554751 | + | 0.832016i | \(0.312814\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.49105 | − | 7.77872i | −0.430164 | − | 0.745067i | 0.566723 | − | 0.823909i | \(-0.308211\pi\) |
−0.996887 | + | 0.0788419i | \(0.974878\pi\) | |||||||
\(110\) | 4.99105 | − | 8.64475i | 0.475878 | − | 0.824245i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.36560 | − | 11.8327i | −0.412510 | − | 1.11808i | ||||
\(113\) | 8.76700 | 0.824730 | 0.412365 | − | 0.911019i | \(-0.364703\pi\) | ||||
0.412365 | + | 0.911019i | \(0.364703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.45040 | − | 5.97627i | −0.321752 | − | 0.557290i | ||||
\(116\) | −3.24970 | − | 5.62865i | −0.301727 | − | 0.522607i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.38813 | −0.219845 | ||||||||
\(119\) | −4.86620 | − | 0.836054i | −0.446084 | − | 0.0766409i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.80533 | + | 15.2513i | −0.800485 | + | 1.38648i | ||||
\(122\) | −2.59859 | − | 4.50090i | −0.235266 | − | 0.407492i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.99105 | − | 12.1089i | 0.627815 | − | 1.08741i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.11590 | 0.0990200 | 0.0495100 | − | 0.998774i | \(-0.484234\pi\) | ||||
0.0495100 | + | 0.998774i | \(0.484234\pi\) | |||||||
\(128\) | 3.73240 | − | 6.46470i | 0.329900 | − | 0.571404i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.05795 | + | 7.02857i | 0.355906 | + | 0.616447i | ||||
\(131\) | 10.7791 | − | 18.6699i | 0.941773 | − | 1.63120i | 0.179685 | − | 0.983724i | \(-0.442492\pi\) |
0.762088 | − | 0.647474i | \(-0.224174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.80765 | + | 13.0308i | 0.416876 | + | 1.12991i | ||||
\(134\) | −3.88410 | −0.335535 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.900806 | − | 1.56024i | −0.0772435 | − | 0.133790i | ||||
\(137\) | 6.11358 | + | 10.5890i | 0.522319 | + | 0.904683i | 0.999663 | + | 0.0259661i | \(0.00826619\pi\) |
−0.477344 | + | 0.878716i | \(0.658400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.2843 | −1.04194 | −0.520971 | − | 0.853575i | \(-0.674430\pi\) | ||||
−0.520971 | + | 0.853575i | \(0.674430\pi\) | |||||||
\(140\) | 2.50835 | − | 3.01610i | 0.211994 | − | 0.254907i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.35785 | + | 11.0121i | −0.533539 | + | 0.924116i | ||||
\(143\) | −11.6309 | − | 20.1453i | −0.972624 | − | 1.68463i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.19175 | + | 3.79622i | −0.182015 | + | 0.315259i | ||||
\(146\) | 10.5127 | 0.870035 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.21509 | 0.264279 | ||||||||
\(149\) | 1.69779 | − | 2.94066i | 0.139088 | − | 0.240908i | −0.788064 | − | 0.615594i | \(-0.788916\pi\) |
0.927152 | + | 0.374686i | \(0.122249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.642154 | − | 1.11224i | −0.0522578 | − | 0.0905131i | 0.838713 | − | 0.544573i | \(-0.183308\pi\) |
−0.890971 | + | 0.454060i | \(0.849975\pi\) | |||||||
\(152\) | −2.53401 | + | 4.38903i | −0.205535 | + | 0.355998i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.8872 | + | 20.3056i | −1.36081 | + | 1.63627i | ||||
\(155\) | −9.43018 | −0.757451 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.90081 | − | 13.6846i | −0.630553 | − | 1.09215i | −0.987439 | − | 0.158002i | \(-0.949495\pi\) |
0.356886 | − | 0.934148i | \(-0.383839\pi\) | |||||||
\(158\) | −11.1482 | − | 19.3092i | −0.886903 | − | 1.53616i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.96539 | 0.550663 | ||||||||
\(161\) | 6.31972 | + | 17.1292i | 0.498064 | + | 1.34997i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.65111 | − | 4.59185i | 0.207651 | − | 0.359661i | −0.743323 | − | 0.668932i | \(-0.766752\pi\) |
0.950974 | + | 0.309271i | \(0.100085\pi\) | |||||||
\(164\) | 0.232995 | + | 0.403560i | 0.0181939 | + | 0.0315127i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.95644 | − | 5.12071i | 0.229464 | − | 0.397444i | ||||
\(167\) | −16.6332 | −1.28712 | −0.643558 | − | 0.765397i | \(-0.722542\pi\) | ||||
−0.643558 | + | 0.765397i | \(0.722542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.91288 | 0.454837 | ||||||||
\(170\) | 1.74135 | − | 3.01610i | 0.133555 | − | 0.231325i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.60755 | + | 9.71255i | 0.427571 | + | 0.740575i | ||||
\(173\) | 9.24970 | − | 16.0210i | 0.703242 | − | 1.21805i | −0.264081 | − | 0.964501i | \(-0.585069\pi\) |
0.967322 | − | 0.253550i | \(-0.0815982\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.60755 | − | 0.447998i | −0.197112 | − | 0.0338655i | ||||
\(176\) | −25.4982 | −1.92200 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.72345 | − | 4.71715i | −0.204131 | − | 0.353565i | ||||
\(179\) | −7.21509 | − | 12.4969i | −0.539281 | − | 0.934063i | −0.998943 | − | 0.0459685i | \(-0.985363\pi\) |
0.459662 | − | 0.888094i | \(-0.347971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9129 | −0.959807 | −0.479903 | − | 0.877321i | \(-0.659328\pi\) | ||||
−0.479903 | + | 0.877321i | \(0.659328\pi\) | |||||||
\(182\) | −7.43250 | − | 20.1453i | −0.550934 | − | 1.49327i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.33099 | + | 5.76945i | −0.245564 | + | 0.425329i | ||||
\(185\) | −1.08420 | − | 1.87790i | −0.0797123 | − | 0.138066i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.99105 | + | 8.64475i | −0.364982 | + | 0.632167i | ||||
\(188\) | 12.4994 | 0.911613 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.79698 | −0.710748 | ||||||||
\(191\) | −6.24970 | + | 10.8248i | −0.452212 | + | 0.783255i | −0.998523 | − | 0.0543276i | \(-0.982698\pi\) |
0.546311 | + | 0.837583i | \(0.316032\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.51439 | − | 16.4794i | −0.684861 | − | 1.18621i | −0.973481 | − | 0.228770i | \(-0.926530\pi\) |
0.288620 | − | 0.957444i | \(-0.406804\pi\) | |||||||
\(194\) | −9.24970 | + | 16.0210i | −0.664090 | + | 1.15024i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.89185 | + | 6.74089i | −0.563704 | + | 0.481492i | ||||
\(197\) | 26.6574 | 1.89926 | 0.949629 | − | 0.313377i | \(-0.101460\pi\) | ||||
0.949629 | + | 0.313377i | \(0.101460\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.78803 | − | 6.56106i | −0.268526 | − | 0.465101i | 0.699955 | − | 0.714187i | \(-0.253203\pi\) |
−0.968481 | + | 0.249086i | \(0.919870\pi\) | |||||||
\(200\) | −0.482696 | − | 0.836054i | −0.0341318 | − | 0.0591179i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32.6799 | 2.29935 | ||||||||
\(203\) | 7.41580 | − | 8.91693i | 0.520487 | − | 0.625846i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.157143 | − | 0.272180i | 0.0109753 | − | 0.0190099i | ||||
\(206\) | 11.6912 | + | 20.2497i | 0.814561 | + | 1.41086i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.3656 | − | 17.9537i | 0.718725 | − | 1.24487i | ||||
\(209\) | 28.0801 | 1.94234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4123 | 0.992182 | 0.496091 | − | 0.868270i | \(-0.334768\pi\) | ||||
0.496091 | + | 0.868270i | \(0.334768\pi\) | |||||||
\(212\) | 2.76700 | − | 4.79259i | 0.190039 | − | 0.329157i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.55504 | + | 14.8178i | 0.584810 | + | 1.01292i | ||||
\(215\) | 3.78199 | − | 6.55060i | 0.257930 | − | 0.446748i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.5896 | + | 4.22471i | 1.66925 | + | 0.286792i | ||||
\(218\) | −16.7624 | −1.13529 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.96539 | − | 6.86826i | −0.267347 | − | 0.463058i | ||||
\(221\) | −4.05795 | − | 7.02857i | −0.272967 | − | 0.472793i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.39558 | −0.0934547 | −0.0467274 | − | 0.998908i | \(-0.514879\pi\) | ||||
−0.0467274 | + | 0.998908i | \(0.514879\pi\) | |||||||
\(224\) | −18.1626 | − | 3.12048i | −1.21354 | − | 0.208496i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.18048 | − | 14.1690i | 0.544158 | − | 0.942509i | ||||
\(227\) | −4.18280 | − | 7.24482i | −0.277622 | − | 0.480856i | 0.693171 | − | 0.720773i | \(-0.256213\pi\) |
−0.970793 | + | 0.239917i | \(0.922880\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.19779 | − | 14.1990i | 0.541725 | − | 0.938295i | −0.457080 | − | 0.889426i | \(-0.651105\pi\) |
0.998805 | − | 0.0488698i | \(-0.0155620\pi\) | |||||||
\(230\) | −12.8783 | −0.849168 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.23180 | 0.277831 | ||||||||
\(233\) | −3.31429 | + | 5.74051i | −0.217126 | + | 0.376073i | −0.953928 | − | 0.300035i | \(-0.903002\pi\) |
0.736802 | + | 0.676109i | \(0.236335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.21509 | − | 7.30075i | −0.274962 | − | 0.476249i | ||||
\(236\) | −0.948687 | + | 1.64317i | −0.0617542 | + | 0.106961i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.89185 | + | 7.08451i | −0.381912 | + | 0.459220i | ||||
\(239\) | 27.3956 | 1.77207 | 0.886036 | − | 0.463616i | \(-0.153448\pi\) | ||||
0.886036 | + | 0.463616i | \(0.153448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.07817 | + | 1.86744i | 0.0694509 | + | 0.120292i | 0.898660 | − | 0.438646i | \(-0.144542\pi\) |
−0.829209 | + | 0.558939i | \(0.811209\pi\) | |||||||
\(242\) | 16.4325 | + | 28.4619i | 1.05632 | + | 1.82960i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.12917 | −0.264343 | ||||||||
\(245\) | 6.59859 | + | 2.33635i | 0.421569 | + | 0.149264i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.4152 | + | 19.7717i | −0.726332 | + | 1.25804i | ||||
\(248\) | 4.55191 | + | 7.88414i | 0.289047 | + | 0.500644i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.933099 | − | 1.61618i | 0.0590144 | − | 0.102216i | ||||
\(251\) | −17.8483 | −1.12657 | −0.563287 | − | 0.826261i | \(-0.690464\pi\) | ||||
−0.563287 | + | 0.826261i | \(0.690464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.9117 | 2.32062 | ||||||||
\(254\) | 1.04124 | − | 1.80349i | 0.0653335 | − | 0.113161i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.4302 | − | 18.0656i | −0.651887 | − | 1.12910i | ||||
\(257\) | −10.8114 | + | 18.7258i | −0.674395 | + | 1.16809i | 0.302251 | + | 0.953229i | \(0.402262\pi\) |
−0.976645 | + | 0.214858i | \(0.931071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.98582 | + | 5.38243i | 0.123393 | + | 0.334448i | ||||
\(260\) | 6.44809 | 0.399893 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.1159 | − | 34.8418i | −1.24276 | − | 2.15253i | ||||
\(263\) | 0.732397 | + | 1.26855i | 0.0451615 | + | 0.0782220i | 0.887723 | − | 0.460379i | \(-0.152286\pi\) |
−0.842561 | + | 0.538601i | \(0.818953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.73240 | −0.229279 | ||||||||
\(266\) | 25.5461 | + | 4.38903i | 1.56633 | + | 0.269109i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.54296 | + | 2.67249i | −0.0942513 | + | 0.163248i | ||||
\(269\) | −8.93541 | − | 15.4766i | −0.544802 | − | 0.943624i | −0.998619 | − | 0.0525298i | \(-0.983272\pi\) |
0.453818 | − | 0.891095i | \(-0.350062\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.22404 | − | 2.12011i | 0.0743554 | − | 0.128787i | −0.826450 | − | 0.563010i | \(-0.809643\pi\) |
0.900806 | + | 0.434222i | \(0.142977\pi\) | |||||||
\(272\) | −8.89618 | −0.539410 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.8183 | 1.37850 | ||||||||
\(275\) | −2.67445 | + | 4.63228i | −0.161275 | + | 0.279337i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.26469 | + | 12.5828i | 0.436493 | + | 0.756028i | 0.997416 | − | 0.0718399i | \(-0.0228871\pi\) |
−0.560923 | + | 0.827868i | \(0.689554\pi\) | |||||||
\(278\) | −11.4625 | + | 19.8536i | −0.687474 | + | 1.19074i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.884101 | + | 2.39630i | 0.0528352 | + | 0.143206i | ||||
\(281\) | 1.63903 | 0.0977764 | 0.0488882 | − | 0.998804i | \(-0.484432\pi\) | ||||
0.0488882 | + | 0.998804i | \(0.484432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.29930 | + | 10.9107i | 0.374454 | + | 0.648574i | 0.990245 | − | 0.139336i | \(-0.0444967\pi\) |
−0.615791 | + | 0.787910i | \(0.711163\pi\) | |||||||
\(284\) | 5.05131 | + | 8.74913i | 0.299740 | + | 0.519165i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −43.4111 | −2.56695 | ||||||||
\(287\) | −0.531694 | + | 0.639321i | −0.0313849 | + | 0.0377380i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.75865 | − | 11.7063i | 0.397568 | − | 0.688608i | ||||
\(290\) | 4.09024 | + | 7.08451i | 0.240187 | + | 0.416017i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.17616 | − | 7.23333i | 0.244391 | − | 0.423298i | ||||
\(293\) | −5.87083 | −0.342977 | −0.171489 | − | 0.985186i | \(-0.554858\pi\) | ||||
−0.171489 | + | 0.985186i | \(0.554858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.27968 | 0.0745057 | ||||||||
\(296\) | −1.04668 | + | 1.81291i | −0.0608372 | + | 0.105373i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.16841 | − | 5.48785i | −0.183541 | − | 0.317902i | ||||
\(299\) | −15.0054 | + | 25.9902i | −0.867787 | + | 1.50305i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.7964 | + | 15.3867i | −0.737571 | + | 0.886873i | ||||
\(302\) | −2.39677 | −0.137919 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.5127 | + | 21.6726i | 0.717651 | + | 1.24301i | ||||
\(305\) | 1.39245 | + | 2.41180i | 0.0797317 | + | 0.138099i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.72032 | 0.554768 | 0.277384 | − | 0.960759i | \(-0.410533\pi\) | ||||
0.277384 | + | 0.960759i | \(0.410533\pi\) | |||||||
\(308\) | 7.26297 | + | 19.6858i | 0.413846 | + | 1.12170i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.79930 | + | 15.2408i | −0.499767 | + | 0.865621i | ||||
\(311\) | 0.889540 | + | 1.54073i | 0.0504412 | + | 0.0873667i | 0.890144 | − | 0.455680i | \(-0.150604\pi\) |
−0.839702 | + | 0.543047i | \(0.817271\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.7641 | + | 27.3042i | −0.891039 | + | 1.54332i | −0.0524076 | + | 0.998626i | \(0.516689\pi\) |
−0.838632 | + | 0.544699i | \(0.816644\pi\) | |||||||
\(314\) | −29.4889 | −1.66416 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.7145 | −0.996518 | ||||||||
\(317\) | 5.31660 | − | 9.20862i | 0.298610 | − | 0.517208i | −0.677208 | − | 0.735792i | \(-0.736810\pi\) |
0.975818 | + | 0.218584i | \(0.0701437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7234 | − | 20.3056i | −0.656387 | − | 1.13690i | ||||
\(320\) | 1.73240 | − | 3.00060i | 0.0968439 | − | 0.167739i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 33.5807 | + | 5.76945i | 1.87138 | + | 0.321519i | ||||
\(323\) | 9.79698 | 0.545119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.17445 | − | 3.76625i | −0.120617 | − | 0.208914i | ||||
\(326\) | −4.94749 | − | 8.56930i | −0.274016 | − | 0.474610i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.303409 | −0.0167530 | ||||||||
\(329\) | 7.72032 | + | 20.9254i | 0.425635 | + | 1.15366i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.71509 | − | 2.97063i | 0.0942700 | − | 0.163280i | −0.815034 | − | 0.579414i | \(-0.803282\pi\) |
0.909304 | + | 0.416133i | \(0.136615\pi\) | |||||||
\(332\) | −2.34889 | − | 4.06840i | −0.128912 | − | 0.223283i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.5204 | + | 26.8822i | −0.849240 | + | 1.47093i | ||||
\(335\) | 2.08129 | 0.113713 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.67525 | 0.200204 | 0.100102 | − | 0.994977i | \(-0.468083\pi\) | ||||
0.100102 | + | 0.994977i | \(0.468083\pi\) | |||||||
\(338\) | 5.51730 | − | 9.55625i | 0.300102 | − | 0.519792i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.38350 | − | 2.39630i | −0.0750309 | − | 0.129957i | ||||
\(341\) | 25.2205 | − | 43.6832i | 1.36577 | − | 2.36558i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1595 | − | 9.04831i | −0.872529 | − | 0.488563i | ||||
\(344\) | −7.30221 | −0.393709 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.2618 | − | 29.8983i | −0.927999 | − | 1.60734i | ||||
\(347\) | −9.48270 | − | 16.4245i | −0.509058 | − | 0.881714i | −0.999945 | − | 0.0104908i | \(-0.996661\pi\) |
0.490887 | − | 0.871223i | \(-0.336673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.475252 | −0.0254397 | −0.0127198 | − | 0.999919i | \(-0.504049\pi\) | ||||
−0.0127198 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(350\) | −3.15714 | + | 3.79622i | −0.168756 | + | 0.202917i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.6286 | + | 32.2656i | −0.992906 | + | 1.71976i | ||||
\(353\) | 7.91520 | + | 13.7095i | 0.421283 | + | 0.729684i | 0.996065 | − | 0.0886224i | \(-0.0282464\pi\) |
−0.574782 | + | 0.818307i | \(0.694913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.40684 | − | 5.90083i | 0.180816 | − | 0.313183i | ||||
\(356\) | −4.32756 | −0.229360 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.9296 | −1.42327 | ||||||||
\(359\) | 15.0054 | − | 25.9902i | 0.791957 | − | 1.37171i | −0.132797 | − | 0.991143i | \(-0.542396\pi\) |
0.924754 | − | 0.380566i | \(-0.124271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.27968 | − | 7.41262i | −0.225246 | − | 0.390138i | ||||
\(362\) | −12.0490 | + | 20.8695i | −0.633281 | + | 1.09688i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.8137 | − | 2.88873i | −0.881277 | − | 0.151411i | ||||
\(365\) | −5.63320 | −0.294855 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.12194 | + | 8.87145i | 0.267363 | + | 0.463086i | 0.968180 | − | 0.250255i | \(-0.0805144\pi\) |
−0.700817 | + | 0.713341i | \(0.747181\pi\) | |||||||
\(368\) | 16.4481 | + | 28.4889i | 0.857416 | + | 1.48509i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.04668 | −0.210377 | ||||||||
\(371\) | 9.73240 | + | 1.67211i | 0.505281 | + | 0.0868115i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.57002 | + | 14.8437i | −0.443739 | + | 0.768579i | −0.997963 | − | 0.0637888i | \(-0.979682\pi\) |
0.554224 | + | 0.832367i | \(0.313015\pi\) | |||||||
\(374\) | 9.31429 | + | 16.1328i | 0.481630 | + | 0.834208i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.06922 | + | 7.04809i | −0.209854 | + | 0.363477i | ||||
\(377\) | 19.0634 | 0.981814 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6978 | 1.11454 | 0.557270 | − | 0.830331i | \(-0.311849\pi\) | ||||
0.557270 | + | 0.830331i | \(0.311849\pi\) | |||||||
\(380\) | −3.89185 | + | 6.74089i | −0.199648 | + | 0.345800i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.6632 | + | 20.2012i | 0.596740 | + | 1.03358i | ||||
\(383\) | −12.9008 | + | 22.3449i | −0.659200 | + | 1.14177i | 0.321623 | + | 0.946868i | \(0.395772\pi\) |
−0.980823 | + | 0.194901i | \(0.937562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.04900 | − | 10.8807i | 0.461180 | − | 0.554533i | ||||
\(386\) | −35.5115 | −1.80749 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.34889 | + | 12.7287i | 0.373084 | + | 0.646200i | ||||
\(389\) | 1.94205 | + | 3.36373i | 0.0984659 | + | 0.170548i | 0.911050 | − | 0.412296i | \(-0.135273\pi\) |
−0.812584 | + | 0.582844i | \(0.801940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.8783 | 0.651282 | ||||||||
\(392\) | −1.23180 | − | 6.64453i | −0.0622152 | − | 0.335599i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.8740 | − | 43.0829i | 1.25313 | − | 2.17049i | ||||
\(395\) | 5.97374 | + | 10.3468i | 0.300572 | + | 0.520605i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.95040 | − | 17.2346i | 0.499396 | − | 0.864980i | −0.500603 | − | 0.865677i | \(-0.666888\pi\) |
1.00000 | 0.000696814i | \(0.000221803\pi\) | ||||||||
\(398\) | −14.1384 | −0.708696 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.76700 | −0.238350 | ||||||||
\(401\) | 2.20302 | − | 3.81574i | 0.110013 | − | 0.190549i | −0.805762 | − | 0.592240i | \(-0.798244\pi\) |
0.915775 | + | 0.401691i | \(0.131577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.5054 | + | 35.5165i | 1.02145 | + | 1.76920i | ||||
\(404\) | 12.9821 | − | 22.4857i | 0.645883 | − | 1.11870i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.49165 | − | 20.3056i | −0.371804 | − | 1.00775i | ||||
\(407\) | 11.5986 | 0.574921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0640 | + | 27.8236i | 0.794313 | + | 1.37579i | 0.923274 | + | 0.384141i | \(0.125502\pi\) |
−0.128961 | + | 0.991650i | \(0.541164\pi\) | |||||||
\(410\) | −0.293260 | − | 0.507941i | −0.0144831 | − | 0.0250854i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.5773 | 0.915236 | ||||||||
\(413\) | −3.33682 | − | 0.573294i | −0.164194 | − | 0.0282099i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.58420 | + | 2.74392i | −0.0777656 | + | 0.134694i | ||||
\(416\) | −15.1459 | − | 26.2334i | −0.742588 | − | 1.28620i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.2015 | − | 45.3823i | 1.28156 | − | 2.21972i | ||||
\(419\) | −10.8720 | −0.531133 | −0.265567 | − | 0.964093i | \(-0.585559\pi\) | ||||
−0.265567 | + | 0.964093i | \(0.585559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.7386 | −1.79053 | −0.895266 | − | 0.445532i | \(-0.853014\pi\) | ||||
−0.895266 | + | 0.445532i | \(0.853014\pi\) | |||||||
\(422\) | 13.4481 | − | 23.2928i | 0.654643 | − | 1.13387i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.80161 | + | 3.12048i | 0.0874940 | + | 0.151544i | ||||
\(425\) | −0.933099 | + | 1.61618i | −0.0452620 | + | 0.0783960i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.55040 | − | 6.91270i | −0.123423 | − | 0.334529i | ||||
\(428\) | 13.5940 | 0.657089 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.05795 | − | 12.2247i | −0.340365 | − | 0.589529i | ||||
\(431\) | −0.796982 | − | 1.38041i | −0.0383893 | − | 0.0664922i | 0.846192 | − | 0.532878i | \(-0.178889\pi\) |
−0.884582 | + | 0.466385i | \(0.845556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3489 | −0.593450 | −0.296725 | − | 0.954963i | \(-0.595894\pi\) | ||||
−0.296725 | + | 0.954963i | \(0.595894\pi\) | |||||||
\(434\) | 29.7724 | − | 35.7991i | 1.42912 | − | 1.71841i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.65886 | + | 11.5335i | −0.318902 | + | 0.552354i | ||||
\(437\) | −18.1136 | − | 31.3736i | −0.866490 | − | 1.50081i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.99105 | − | 17.3050i | 0.476847 | − | 0.825923i | −0.522801 | − | 0.852455i | \(-0.675113\pi\) |
0.999648 | + | 0.0265318i | \(0.00844634\pi\) | |||||||
\(440\) | 5.16378 | 0.246174 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.1459 | −0.720416 | ||||||||
\(443\) | −3.00000 | + | 5.19615i | −0.142534 | + | 0.246877i | −0.928450 | − | 0.371457i | \(-0.878858\pi\) |
0.785916 | + | 0.618333i | \(0.212192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.45935 | + | 2.52768i | 0.0691800 | + | 0.119823i | ||||
\(446\) | −1.30221 | + | 2.25550i | −0.0616615 | + | 0.106801i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.86157 | + | 7.04809i | −0.276933 | + | 0.332991i | ||||
\(449\) | −24.4994 | −1.15620 | −0.578099 | − | 0.815967i | \(-0.696205\pi\) | ||||
−0.578099 | + | 0.815967i | \(0.696205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.840542 | + | 1.45586i | 0.0395796 | + | 0.0685538i | ||||
\(452\) | −6.49940 | − | 11.2573i | −0.305706 | − | 0.529499i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.6119 | −0.732701 | ||||||||
\(455\) | 3.98270 | + | 10.7948i | 0.186712 | + | 0.506069i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2032 | − | 19.4046i | 0.524065 | − | 0.907707i | −0.475543 | − | 0.879693i | \(-0.657748\pi\) |
0.999608 | − | 0.0280143i | \(-0.00891839\pi\) | |||||||
\(458\) | −15.2987 | − | 26.4981i | −0.714861 | − | 1.23818i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.11590 | + | 8.86100i | −0.238530 | + | 0.413146i | ||||
\(461\) | −28.4169 | −1.32351 | −0.661754 | − | 0.749721i | \(-0.730188\pi\) | ||||
−0.661754 | + | 0.749721i | \(0.730188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0225 | 0.512261 | 0.256130 | − | 0.966642i | \(-0.417552\pi\) | ||||
0.256130 | + | 0.966642i | \(0.417552\pi\) | |||||||
\(464\) | 10.4481 | − | 18.0966i | 0.485040 | − | 0.840114i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.18512 | + | 10.7129i | 0.286520 | + | 0.496267i | ||||
\(467\) | 9.79698 | − | 16.9689i | 0.453350 | − | 0.785226i | −0.545241 | − | 0.838279i | \(-0.683562\pi\) |
0.998592 | + | 0.0530534i | \(0.0168953\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.42706 | − | 0.932415i | −0.250598 | − | 0.0430549i | ||||
\(470\) | −15.7324 | −0.725681 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.617695 | − | 1.06988i | −0.0284317 | − | 0.0492452i | ||||
\(473\) | 20.2295 | + | 35.0385i | 0.930153 | + | 1.61107i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.24970 | 0.240873 | ||||||||
\(476\) | 2.53401 | + | 6.86826i | 0.116146 | + | 0.314806i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.5628 | − | 44.2760i | 1.16921 | − | 2.02514i | ||||
\(479\) | −15.1626 | − | 26.2624i | −0.692796 | − | 1.19996i | −0.970918 | − | 0.239412i | \(-0.923045\pi\) |
0.278122 | − | 0.960546i | \(-0.410288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.71509 | + | 8.16678i | −0.214990 | + | 0.372373i | ||||
\(482\) | 4.02415 | 0.183295 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 26.1113 | 1.18688 | ||||||||
\(485\) | 4.95644 | − | 8.58481i | 0.225060 | − | 0.389816i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.10523 | − | 12.3066i | −0.321969 | − | 0.557666i | 0.658925 | − | 0.752208i | \(-0.271011\pi\) |
−0.980894 | + | 0.194542i | \(0.937678\pi\) | |||||||
\(488\) | 1.34426 | − | 2.32833i | 0.0608520 | − | 0.105399i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.93310 | − | 8.48444i | 0.448732 | − | 0.383288i | ||||
\(491\) | 19.8016 | 0.893634 | 0.446817 | − | 0.894625i | \(-0.352557\pi\) | ||||
0.446817 | + | 0.894625i | \(0.352557\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.09024 | − | 7.08451i | −0.184215 | − | 0.319070i | ||||
\(494\) | 21.3030 | + | 36.8979i | 0.958468 | + | 1.66012i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 44.9537 | 2.01848 | ||||||||
\(497\) | −11.5271 | + | 13.8604i | −0.517059 | + | 0.621725i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.58129 | + | 9.66708i | −0.249853 | + | 0.432758i | −0.963485 | − | 0.267763i | \(-0.913716\pi\) |
0.713632 | + | 0.700521i | \(0.247049\pi\) | |||||||
\(500\) | −0.741348 | − | 1.28405i | −0.0331541 | − | 0.0574246i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.6542 | + | 28.8460i | −0.743315 | + | 1.28746i | ||||
\(503\) | −26.9296 | −1.20073 | −0.600365 | − | 0.799726i | \(-0.704978\pi\) | ||||
−0.600365 | + | 0.799726i | \(0.704978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.5115 | −0.779250 | ||||||||
\(506\) | 34.4423 | − | 59.6557i | 1.53115 | − | 2.65202i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.827269 | − | 1.43287i | −0.0367041 | − | 0.0635734i | ||||
\(509\) | 5.09919 | − | 8.83206i | 0.226018 | − | 0.391474i | −0.730607 | − | 0.682799i | \(-0.760763\pi\) |
0.956624 | + | 0.291324i | \(0.0940959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6888 | + | 2.52367i | 0.649796 | + | 0.111640i | ||||
\(512\) | −24.0000 | −1.06066 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.1762 | + | 34.9461i | 0.889932 | + | 1.54141i | ||||
\(515\) | −6.26469 | − | 10.8508i | −0.276055 | − | 0.478142i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.0922 | 1.98315 | ||||||||
\(518\) | 10.5519 | + | 1.81291i | 0.463624 | + | 0.0796546i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.09919 | + | 3.63591i | −0.0920557 | + | 0.159445i | ||||
\(521\) | −10.3835 | − | 17.9848i | −0.454909 | − | 0.787926i | 0.543774 | − | 0.839232i | \(-0.316995\pi\) |
−0.998683 | + | 0.0513057i | \(0.983662\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.790945 | + | 1.36996i | −0.0345856 | + | 0.0599040i | −0.882800 | − | 0.469749i | \(-0.844344\pi\) |
0.848214 | + | 0.529653i | \(0.177678\pi\) | |||||||
\(524\) | −31.9642 | −1.39636 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.73359 | 0.119190 | ||||||||
\(527\) | 8.79930 | − | 15.2408i | 0.383303 | − | 0.663901i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.3106 | − | 21.3225i | −0.535242 | − | 0.927066i | ||||
\(530\) | −3.48270 | + | 6.03221i | −0.151279 | + | 0.262022i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.1681 | − | 15.8336i | 0.570910 | − | 0.686475i | ||||
\(533\) | −1.36680 | −0.0592026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.58420 | − | 7.94008i | −0.198192 | − | 0.343279i | ||||
\(536\) | −1.00463 | − | 1.74007i | −0.0433934 | − | 0.0751596i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −33.3505 | −1.43784 | ||||||||
\(539\) | −28.4702 | + | 24.3181i | −1.22630 | + | 1.04745i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.81429 | − | 6.60654i | 0.163989 | − | 0.284037i | −0.772307 | − | 0.635250i | \(-0.780897\pi\) |
0.936296 | + | 0.351212i | \(0.114231\pi\) | |||||||
\(542\) | −2.28431 | − | 3.95654i | −0.0981195 | − | 0.169948i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.49940 | + | 11.2573i | −0.278660 | + | 0.482652i | ||||
\(545\) | 8.98210 | 0.384751 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.7553 | −1.82809 | −0.914043 | − | 0.405617i | \(-0.867057\pi\) | ||||
−0.914043 | + | 0.405617i | \(0.867057\pi\) | |||||||
\(548\) | 9.06459 | − | 15.7003i | 0.387220 | − | 0.670685i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.99105 | + | 8.64475i | 0.212819 | + | 0.368613i | ||||
\(551\) | −11.5060 | + | 19.9290i | −0.490174 | + | 0.849006i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9415 | − | 29.6561i | −0.465278 | − | 1.26110i | ||||
\(554\) | 27.1147 | 1.15199 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.10695 | + | 15.7737i | 0.386221 | + | 0.668954i | ||||
\(557\) | 14.0346 | + | 24.3087i | 0.594665 | + | 1.02999i | 0.993594 | + | 0.113009i | \(0.0360488\pi\) |
−0.398929 | + | 0.916982i | \(0.630618\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.8950 | −1.39131 | ||||||||
\(560\) | 12.4302 | + | 2.13561i | 0.525271 | + | 0.0902460i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.52938 | − | 2.64896i | 0.0645129 | − | 0.111740i | ||||
\(563\) | 1.27968 | + | 2.21647i | 0.0539320 | + | 0.0934130i | 0.891731 | − | 0.452566i | \(-0.149491\pi\) |
−0.837799 | + | 0.545979i | \(0.816158\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.38350 | + | 7.59245i | −0.184415 | + | 0.319417i | ||||
\(566\) | 23.5115 | 0.988261 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.57788 | −0.276002 | ||||||||
\(569\) | −22.7678 | + | 39.4350i | −0.954476 | + | 1.65320i | −0.218914 | + | 0.975744i | \(0.570252\pi\) |
−0.735562 | + | 0.677457i | \(0.763082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.6941 | − | 21.9868i | −0.531230 | − | 0.920118i | −0.999336 | − | 0.0364450i | \(-0.988397\pi\) |
0.468106 | − | 0.883673i | \(-0.344937\pi\) | |||||||
\(572\) | −17.2451 | + | 29.8693i | −0.721053 | + | 1.24890i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.537132 | + | 1.45586i | 0.0224195 | + | 0.0607665i | ||||
\(575\) | 6.90081 | 0.287784 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.41952 | + | 4.19073i | 0.100726 | + | 0.174462i | 0.911984 | − | 0.410226i | \(-0.134550\pi\) |
−0.811258 | + | 0.584688i | \(0.801217\pi\) | |||||||
\(578\) | −12.6130 | − | 21.8463i | −0.524631 | − | 0.908688i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.49940 | 0.269873 | ||||||||
\(581\) | 5.36016 | − | 6.44519i | 0.222377 | − | 0.267391i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.98210 | − | 17.2895i | 0.413416 | − | 0.716058i | ||||
\(584\) | 2.71912 | + | 4.70966i | 0.112518 | + | 0.194887i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.47807 | + | 9.48829i | −0.226297 | + | 0.391958i | ||||
\(587\) | −1.52938 | −0.0631242 | −0.0315621 | − | 0.999502i | \(-0.510048\pi\) | ||||
−0.0315621 | + | 0.999502i | \(0.510048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.5056 | −2.03984 | ||||||||
\(590\) | 1.19407 | − | 2.06818i | 0.0491589 | − | 0.0851458i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.16841 | + | 8.95195i | 0.212420 | + | 0.367923i | ||||
\(593\) | 14.3166 | − | 24.7971i | 0.587912 | − | 1.01829i | −0.406593 | − | 0.913609i | \(-0.633283\pi\) |
0.994505 | − | 0.104685i | \(-0.0333833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.15714 | − | 3.79622i | 0.129430 | − | 0.155630i | ||||
\(596\) | −5.03461 | −0.206226 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.0031 | + | 48.5028i | 1.14513 | + | 1.98343i | ||||
\(599\) | −6.66781 | − | 11.5490i | −0.272439 | − | 0.471879i | 0.697047 | − | 0.717026i | \(-0.254497\pi\) |
−0.969486 | + | 0.245147i | \(0.921164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.37887 | −0.0562453 | −0.0281227 | − | 0.999604i | \(-0.508953\pi\) | ||||
−0.0281227 | + | 0.999604i | \(0.508953\pi\) | |||||||
\(602\) | 12.9273 | + | 35.0385i | 0.526876 | + | 1.42806i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.952120 | + | 1.64912i | −0.0387412 | + | 0.0671017i | ||||
\(605\) | −8.80533 | − | 15.2513i | −0.357988 | − | 0.620053i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.6738 | + | 41.0043i | −0.960892 | + | 1.66431i | −0.240623 | + | 0.970619i | \(0.577352\pi\) |
−0.720269 | + | 0.693695i | \(0.755982\pi\) | |||||||
\(608\) | 36.5662 | 1.48296 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.19719 | 0.210428 | ||||||||
\(611\) | −18.3310 | + | 31.7502i | −0.741593 | + | 1.28448i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1023 | + | 24.4259i | 0.569587 | + | 0.986554i | 0.996607 | + | 0.0823115i | \(0.0262303\pi\) |
−0.427019 | + | 0.904242i | \(0.640436\pi\) | |||||||
\(614\) | 9.07002 | − | 15.7097i | 0.366036 | − | 0.633994i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.4648 | − | 2.31337i | −0.542512 | − | 0.0932081i | ||||
\(617\) | 8.13843 | 0.327641 | 0.163820 | − | 0.986490i | \(-0.447618\pi\) | ||||
0.163820 | + | 0.986490i | \(0.447618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.435414 | + | 0.754160i | 0.0175008 | + | 0.0303122i | 0.874643 | − | 0.484767i | \(-0.161096\pi\) |
−0.857142 | + | 0.515080i | \(0.827762\pi\) | |||||||
\(620\) | 6.99105 | + | 12.1089i | 0.280767 | + | 0.486303i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.32011 | 0.133124 | ||||||||
\(623\) | −2.67294 | − | 7.24482i | −0.107089 | − | 0.290258i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 29.4189 | + | 50.9551i | 1.17582 | + | 2.03657i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.7145 | + | 20.2901i | −0.467459 | + | 0.809663i | ||||
\(629\) | 4.04668 | 0.161352 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.30221 | −0.211078 | −0.105539 | − | 0.994415i | \(-0.533657\pi\) | ||||
−0.105539 | + | 0.994415i | \(0.533657\pi\) | |||||||
\(632\) | 5.76700 | − | 9.98875i | 0.229399 | − | 0.397331i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.92183 | − | 17.1851i | −0.394046 | − | 0.682508i | ||||
\(635\) | −0.557949 | + | 0.966397i | −0.0221415 | + | 0.0383503i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.54900 | − | 29.9323i | −0.219859 | − | 1.18596i | ||||
\(638\) | −43.7565 | −1.73234 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.73240 | + | 6.46470i | 0.147536 | + | 0.255540i | ||||
\(641\) | 19.5574 | + | 33.8743i | 0.772469 | + | 1.33796i | 0.936206 | + | 0.351451i | \(0.114312\pi\) |
−0.163737 | + | 0.986504i | \(0.552355\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.4885 | −0.531935 | −0.265968 | − | 0.963982i | \(-0.585691\pi\) | ||||
−0.265968 | + | 0.963982i | \(0.585691\pi\) | |||||||
\(644\) | 17.3097 | − | 20.8135i | 0.682096 | − | 0.820169i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.14156 | − | 15.8336i | 0.359670 | − | 0.622966i | ||||
\(647\) | 6.70010 | + | 11.6049i | 0.263408 | + | 0.456236i | 0.967145 | − | 0.254224i | \(-0.0818200\pi\) |
−0.703737 | + | 0.710460i | \(0.748487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.42243 | + | 5.92782i | −0.134342 | + | 0.232687i | ||||
\(650\) | −8.11590 | −0.318332 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.86157 | −0.307883 | ||||||||
\(653\) | −2.08361 | + | 3.60891i | −0.0815378 | + | 0.141228i | −0.903911 | − | 0.427721i | \(-0.859316\pi\) |
0.822373 | + | 0.568949i | \(0.192650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.7791 | + | 18.6699i | 0.421173 | + | 0.729494i | ||||
\(656\) | −0.749102 | + | 1.29748i | −0.0292475 | + | 0.0506582i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 41.0230 | + | 7.04809i | 1.59924 | + | 0.274763i | ||||
\(659\) | −0.325163 | −0.0126666 | −0.00633328 | − | 0.999980i | \(-0.502016\pi\) | ||||
−0.00633328 | + | 0.999980i | \(0.502016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9558 | + | 27.6363i | 0.620610 | + | 1.07493i | 0.989372 | + | 0.145405i | \(0.0464484\pi\) |
−0.368762 | + | 0.929524i | \(0.620218\pi\) | |||||||
\(662\) | −3.20070 | − | 5.54378i | −0.124399 | − | 0.215465i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.05876 | 0.118703 | ||||||||
\(665\) | −13.6888 | − | 2.35186i | −0.530830 | − | 0.0912011i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.1249 | + | 26.1970i | −0.585637 | + | 1.01435i | ||||
\(668\) | 12.3310 | + | 21.3579i | 0.477100 | + | 0.826362i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.94205 | − | 3.36373i | 0.0750280 | − | 0.129952i | ||||
\(671\) | −14.8962 | −0.575060 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.70867 | −0.220053 | −0.110026 | − | 0.993929i | \(-0.535094\pi\) | ||||
−0.110026 | + | 0.993929i | \(0.535094\pi\) | |||||||
\(674\) | 3.42938 | − | 5.93986i | 0.132095 | − | 0.228795i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.38350 | − | 7.59245i | −0.168596 | − | 0.292017i | ||||
\(677\) | 0.346579 | − | 0.600292i | 0.0133201 | − | 0.0230711i | −0.859289 | − | 0.511491i | \(-0.829093\pi\) |
0.872609 | + | 0.488420i | \(0.162427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.7701 | + | 20.1648i | −0.643578 | + | 0.773854i | ||||
\(680\) | 1.80161 | 0.0690887 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −47.0665 | − | 81.5216i | −1.80227 | − | 3.12162i | ||||
\(683\) | −4.64879 | − | 8.05194i | −0.177881 | − | 0.308099i | 0.763274 | − | 0.646075i | \(-0.223591\pi\) |
−0.941155 | + | 0.337977i | \(0.890258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.2272 | −0.467176 | ||||||||
\(686\) | −29.7020 | + | 17.6735i | −1.13403 | + | 0.674779i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.0288 | + | 31.2268i | −0.687341 | + | 1.19051i | ||||
\(689\) | 8.11590 | + | 14.0571i | 0.309191 | + | 0.535535i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.87143 | − | 10.1696i | 0.223360 | − | 0.386870i | −0.732466 | − | 0.680803i | \(-0.761631\pi\) |
0.955826 | + | 0.293933i | \(0.0949642\pi\) | |||||||
\(692\) | −27.4290 | −1.04269 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.3932 | −1.34351 | ||||||||
\(695\) | 6.14215 | − | 10.6385i | 0.232985 | − | 0.403542i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.293260 | + | 0.507941i | 0.0111080 | + | 0.0192397i | ||||
\(698\) | −0.443457 | + | 0.768090i | −0.0167851 | + | 0.0290727i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.35785 | + | 3.68035i | 0.0513217 | + | 0.139104i | ||||
\(701\) | −23.5565 | −0.889718 | −0.444859 | − | 0.895601i | \(-0.646746\pi\) | ||||
−0.444859 | + | 0.895601i | \(0.646746\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.69175 | − | 9.85840i | −0.214668 | − | 0.371817i | ||||
\(704\) | 9.26641 | + | 16.0499i | 0.349241 | + | 0.604903i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.5427 | 1.11185 | ||||||||
\(707\) | 45.6620 | + | 7.84511i | 1.71730 | + | 0.295046i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1536 | − | 43.5674i | 0.944664 | − | 1.63621i | 0.188243 | − | 0.982123i | \(-0.439721\pi\) |
0.756422 | − | 0.654084i | \(-0.226946\pi\) | |||||||
\(710\) | −6.35785 | − | 11.0121i | −0.238606 | − | 0.413277i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.40885 | − | 2.44020i | 0.0527989 | − | 0.0914503i | ||||
\(713\) | −65.0759 | −2.43711 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.2618 | 0.869941 | ||||||||
\(716\) | −10.6978 | + | 18.5291i | −0.399795 | + | 0.692465i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.0031 | − | 48.5028i | −1.04507 | − | 1.81011i | ||||
\(719\) | −23.7445 | + | 41.1266i | −0.885519 | + | 1.53376i | −0.0404021 | + | 0.999184i | \(0.512864\pi\) |
−0.845117 | + | 0.534581i | \(0.820469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.4743 | + | 31.1004i | 0.427327 | + | 1.15824i | ||||
\(722\) | −15.9735 | −0.594470 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.57294 | + | 16.5808i | 0.355775 | + | 0.616221i | ||||
\(725\) | −2.19175 | − | 3.79622i | −0.0813996 | − | 0.140988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.04044 | 0.0385877 | 0.0192938 | − | 0.999814i | \(-0.493858\pi\) | ||||
0.0192938 | + | 0.999814i | \(0.493858\pi\) | |||||||
\(728\) | 7.10263 | − | 8.54037i | 0.263241 | − | 0.316527i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.25634 | + | 9.10424i | −0.194546 | + | 0.336963i | ||||
\(731\) | 7.05795 | + | 12.2247i | 0.261048 | + | 0.452148i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.7205 | − | 23.7647i | 0.506779 | − | 0.877768i | −0.493190 | − | 0.869922i | \(-0.664169\pi\) |
0.999969 | − | 0.00784592i | \(-0.00249746\pi\) | |||||||
\(734\) | 19.1171 | 0.705625 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 48.0668 | 1.77177 | ||||||||
\(737\) | −5.56630 | + | 9.64112i | −0.205037 | + | 0.355135i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.7407 | + | 30.7279i | 0.652604 | + | 1.13034i | 0.982489 | + | 0.186322i | \(0.0596568\pi\) |
−0.329885 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(740\) | −1.60755 | + | 2.78435i | −0.0590946 | + | 0.102355i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.7837 | − | 14.1690i | 0.432594 | − | 0.520161i | ||||
\(743\) | 30.5640 | 1.12128 | 0.560642 | − | 0.828058i | \(-0.310554\pi\) | ||||
0.560642 | + | 0.828058i | \(0.310554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.69779 | + | 2.94066i | 0.0622022 | + | 0.107737i | ||||
\(746\) | 15.9934 | + | 27.7013i | 0.585559 | + | 1.01422i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.8004 | 0.541157 | ||||||||
\(749\) | 8.39638 | + | 22.7578i | 0.306797 | + | 0.831553i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.3829 | − | 45.6965i | 0.962726 | − | 1.66749i | 0.247121 | − | 0.968985i | \(-0.420515\pi\) |
0.715605 | − | 0.698505i | \(-0.246151\pi\) | |||||||
\(752\) | 20.0934 | + | 34.8027i | 0.732730 | + | 1.26912i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.7880 | − | 30.8098i | 0.647802 | − | 1.12203i | ||||
\(755\) | 1.28431 | 0.0467408 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.3368 | −0.593772 | −0.296886 | − | 0.954913i | \(-0.595948\pi\) | ||||
−0.296886 | + | 0.954913i | \(0.595948\pi\) | |||||||
\(758\) | 20.2462 | − | 35.0674i | 0.735375 | − | 1.27371i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.53401 | − | 4.38903i | −0.0919182 | − | 0.159207i | ||||
\(761\) | −23.1213 | + | 40.0473i | −0.838148 | + | 1.45171i | 0.0532937 | + | 0.998579i | \(0.483028\pi\) |
−0.891442 | + | 0.453136i | \(0.850305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.4212 | − | 4.02397i | −0.847906 | − | 0.145677i | ||||
\(764\) | 18.5328 | 0.670494 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0755 | + | 41.6999i | 0.869882 | + | 1.50668i | ||||
\(767\) | −2.78259 | − | 4.81959i | −0.100474 | − | 0.174025i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.3073 | 1.85019 | 0.925094 | − | 0.379739i | \(-0.123986\pi\) | ||||
0.925094 | + | 0.379739i | \(0.123986\pi\) | |||||||
\(770\) | −9.14156 | − | 24.7776i | −0.329439 | − | 0.892922i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.1069 | + | 24.4339i | −0.507720 | + | 0.879397i | ||||
\(773\) | −10.9152 | − | 18.9057i | −0.392592 | − | 0.679990i | 0.600198 | − | 0.799851i | \(-0.295088\pi\) |
−0.992791 | + | 0.119861i | \(0.961755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.71509 | − | 8.16678i | 0.169371 | − | 0.293359i | ||||
\(776\) | −9.56982 | −0.343536 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.24850 | 0.259871 | ||||||||
\(779\) | 0.824954 | − | 1.42886i | 0.0295570 | − | 0.0511943i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.2228 | + | 31.5629i | 0.652065 | + | 1.12941i | ||||
\(782\) | 12.0167 | − | 20.8135i | 0.429717 | − | 0.744291i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −31.4555 | − | 11.1374i | −1.12341 | − | 0.397765i | ||||
\(785\) | 15.8016 | 0.563984 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.2093 | − | 45.3958i | −0.934259 | − | 1.61818i | −0.775949 | − | 0.630795i | \(-0.782729\pi\) |
−0.158310 | − | 0.987389i | \(-0.550605\pi\) | |||||||
\(788\) | −19.7624 | − | 34.2294i | −0.704005 | − | 1.21937i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.2964 | 0.793270 | ||||||||
\(791\) | 14.8316 | − | 17.8339i | 0.527351 | − | 0.634099i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.05563 | − | 10.4887i | 0.215042 | − | 0.372463i | ||||
\(794\) | −18.5694 | − | 32.1632i | −0.659004 | − | 1.14143i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.61650 | + | 9.72806i | −0.199071 | + | 0.344802i | ||||
\(797\) | 6.06459 | 0.214819 | 0.107409 | − | 0.994215i | \(-0.465744\pi\) | ||||
0.107409 | + | 0.994215i | \(0.465744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.7324 | 0.556572 | ||||||||
\(800\) | −3.48270 | + | 6.03221i | −0.123132 | + | 0.213271i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.11127 | − | 7.12093i | −0.145174 | − | 0.251449i | ||||
\(803\) | 15.0657 | − | 26.0946i | 0.531657 | − | 0.920857i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.9942 | − | 3.09155i | −0.634211 | − | 0.108963i | ||||
\(806\) | 76.5344 | 2.69581 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.45272 | + | 14.6405i | 0.297366 | + | 0.515052i | ||||
\(809\) | −14.1101 | − | 24.4394i | −0.496084 | − | 0.859242i | 0.503906 | − | 0.863758i | \(-0.331896\pi\) |
−0.999990 | + | 0.00451631i | \(0.998562\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.47224 | 0.157041 | 0.0785207 | − | 0.996912i | \(-0.474980\pi\) | ||||
0.0785207 | + | 0.996912i | \(0.474980\pi\) | |||||||
\(812\) | −16.9475 | − | 2.91172i | −0.594740 | − | 0.102181i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.8226 | − | 18.7454i | 0.379333 | − | 0.657025i | ||||
\(815\) | 2.65111 | + | 4.59185i | 0.0928642 | + | 0.160845i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.8543 | − | 34.3887i | 0.694615 | − | 1.20311i | ||||
\(818\) | 59.9572 | 2.09635 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.465991 | −0.0162731 | ||||||||
\(821\) | −7.14507 | + | 12.3756i | −0.249365 | + | 0.431912i | −0.963350 | − | 0.268249i | \(-0.913555\pi\) |
0.713985 | + | 0.700161i | \(0.246888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.19407 | + | 15.9246i | 0.320485 | + | 0.555096i | 0.980588 | − | 0.196079i | \(-0.0628208\pi\) |
−0.660103 | + | 0.751175i | \(0.729487\pi\) | |||||||
\(824\) | −6.04788 | + | 10.4752i | −0.210688 | + | 0.364922i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.04013 | + | 4.85794i | −0.140574 | + | 0.169030i | ||||
\(827\) | −16.5236 | −0.574580 | −0.287290 | − | 0.957844i | \(-0.592754\pi\) | ||||
−0.287290 | + | 0.957844i | \(0.592754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.27013 | − | 10.8602i | −0.217771 | − | 0.377190i | 0.736356 | − | 0.676595i | \(-0.236545\pi\) |
−0.954126 | + | 0.299405i | \(0.903212\pi\) | |||||||
\(830\) | 2.95644 | + | 5.12071i | 0.102620 | + | 0.177742i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.0680 | −0.522390 | ||||||||
\(833\) | −9.93310 | + | 8.48444i | −0.344161 | + | 0.293968i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.31660 | − | 14.4048i | 0.287808 | − | 0.498498i | ||||
\(836\) | −20.8171 | − | 36.0563i | −0.719975 | − | 1.24703i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.1447 | + | 17.5711i | −0.350442 | + | 0.606984i | ||||
\(839\) | 38.6036 | 1.33275 | 0.666373 | − | 0.745619i | \(-0.267846\pi\) | ||||
0.666373 | + | 0.745619i | \(0.267846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.78491 | −0.337411 | ||||||||
\(842\) | −34.2808 | + | 59.3761i | −1.18139 | + | 2.04623i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.6845 | − | 18.5061i | −0.367776 | − | 0.637007i | ||||
\(845\) | −2.95644 | + | 5.12071i | −0.101705 | + | 0.176158i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.1278 | + | 43.7132i | 0.554157 | + | 1.50200i | ||||
\(848\) | 17.7924 | 0.610992 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.74135 | + | 3.01610i | 0.0597277 | + | 0.103451i | ||||
\(851\) | −7.48189 | − | 12.9590i | −0.256476 | − | 0.444229i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4590 | −0.392347 | −0.196174 | − | 0.980569i | \(-0.562852\pi\) | ||||
−0.196174 | + | 0.980569i | \(0.562852\pi\) | |||||||
\(854\) | −13.5519 | − | 2.32833i | −0.463737 | − | 0.0796739i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.42555 | + | 7.66528i | −0.151262 | + | 0.261994i | ||||
\(857\) | 4.43250 | + | 7.67732i | 0.151411 | + | 0.262252i | 0.931747 | − | 0.363109i | \(-0.118285\pi\) |
−0.780335 | + | 0.625361i | \(0.784952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3699 | − | 17.9612i | 0.353817 | − | 0.612829i | −0.633098 | − | 0.774072i | \(-0.718217\pi\) |
0.986915 | + | 0.161243i | \(0.0515502\pi\) | |||||||
\(860\) | −11.2151 | −0.382431 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.97465 | −0.101317 | ||||||||
\(863\) | −6.33099 | + | 10.9656i | −0.215509 | + | 0.373273i | −0.953430 | − | 0.301614i | \(-0.902475\pi\) |
0.737921 | + | 0.674888i | \(0.235808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.24970 | + | 16.0210i | 0.314499 | + | 0.544729i | ||||
\(866\) | −11.5227 | + | 19.9580i | −0.391559 | + | 0.678200i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.8047 | − | 34.7064i | −0.434621 | − | 1.17801i | ||||
\(869\) | −63.9059 | −2.16786 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.52566 | − | 7.83867i | −0.153346 | − | 0.265603i | ||||
\(872\) | −4.33562 | − | 7.50952i | −0.146823 | − | 0.254304i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −67.6071 | −2.28684 | ||||||||
\(875\) | 1.69175 | − | 2.03420i | 0.0571916 | − | 0.0687686i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.8483 | + | 32.6462i | −0.636462 | + | 1.10238i | 0.349742 | + | 0.936846i | \(0.386269\pi\) |
−0.986203 | + | 0.165538i | \(0.947064\pi\) | |||||||
\(878\) | −18.6453 | − | 32.2946i | −0.629248 | − | 1.08989i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.7491 | − | 22.0821i | 0.429772 | − | 0.744387i | ||||
\(881\) | 49.4648 | 1.66651 | 0.833256 | − | 0.552888i | \(-0.186474\pi\) | ||||
0.833256 | + | 0.552888i | \(0.186474\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.4256 | 0.519111 | 0.259556 | − | 0.965728i | \(-0.416424\pi\) | ||||
0.259556 | + | 0.965728i | \(0.416424\pi\) | |||||||
\(884\) | −6.01671 | + | 10.4212i | −0.202364 | + | 0.350504i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.59859 | + | 9.69705i | 0.188088 | + | 0.325779i | ||||
\(887\) | 24.7756 | − | 42.9125i | 0.831882 | − | 1.44086i | −0.0646618 | − | 0.997907i | \(-0.520597\pi\) |
0.896544 | − | 0.442955i | \(-0.146070\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.88782 | − | 2.26996i | 0.0633156 | − | 0.0761321i | ||||
\(890\) | 5.44689 | 0.182580 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.03461 | + | 1.79199i | 0.0346412 | + | 0.0600004i | ||||
\(893\) | −22.1280 | − | 38.3268i | −0.740484 | − | 1.28256i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.4302 | 0.482348 | ||||||||
\(896\) | −6.83622 | − | 18.5291i | −0.228382 | − | 0.619014i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.8604 | + | 39.5953i | −0.762860 | + | 1.32131i | ||||
\(899\) | 20.6686 | + | 35.7991i | 0.689337 | + | 1.19397i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.48270 | − | 6.03221i | 0.116025 | − | 0.200962i | ||||
\(902\) | 3.13723 | 0.104458 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.46360 | 0.281495 | ||||||||
\(905\) | 6.45644 | − | 11.1829i | 0.214619 | − | 0.371732i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.36388 | − | 4.09437i | −0.0784914 | − | 0.135951i | 0.824108 | − | 0.566433i | \(-0.191677\pi\) |
−0.902599 | + | 0.430482i | \(0.858344\pi\) | |||||||
\(908\) | −6.20182 | + | 10.7419i | −0.205815 | + | 0.356481i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 21.1626 | + | 3.63591i | 0.701533 | + | 0.120529i | ||||
\(911\) | 37.2680 | 1.23474 | 0.617372 | − | 0.786671i | \(-0.288197\pi\) | ||||
0.617372 | + | 0.786671i | \(0.288197\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.47374 | − | 14.6770i | −0.280440 | − | 0.485736i | ||||
\(914\) | −20.9074 | − | 36.2128i | −0.691557 | − | 1.19781i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.3097 | −0.803214 | ||||||||
\(917\) | −19.7429 | − | 53.5117i | −0.651967 | − | 1.76711i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.9423 | + | 43.2013i | −0.822769 | + | 1.42508i | 0.0808431 | + | 0.996727i | \(0.474239\pi\) |
−0.903612 | + | 0.428351i | \(0.859095\pi\) | |||||||
\(920\) | −3.33099 | − | 5.76945i | −0.109820 | − | 0.190213i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.5158 | + | 45.9267i | −0.873251 | + | 1.51252i | ||||
\(923\) | −29.6320 | −0.975349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.16841 | 0.0712969 | ||||||||
\(926\) | 10.2851 | − | 17.8143i | 0.337990 | − | 0.585416i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.2664 | − | 26.4422i | −0.501144 | − | 0.868007i | ||||
\(929\) | 8.42475 | − | 14.5921i | 0.276407 | − | 0.478751i | −0.694082 | − | 0.719896i | \(-0.744190\pi\) |
0.970489 | + | 0.241145i | \(0.0775229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.6406 | + | 12.2652i | 1.13530 | + | 0.401974i | ||||
\(932\) | 9.82816 | 0.321932 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.2831 | − | 31.6673i | −0.598242 | − | 1.03618i | ||||
\(935\) | −4.99105 | − | 8.64475i | −0.163225 | − | 0.282714i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.87666 | −0.322656 | −0.161328 | − | 0.986901i | \(-0.551578\pi\) | ||||
−0.161328 | + | 0.986901i | \(0.551578\pi\) | |||||||
\(938\) | −6.57093 | + | 7.90105i | −0.214549 | + | 0.257978i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.24970 | + | 10.8248i | −0.203843 | + | 0.353066i | ||||
\(941\) | −28.1980 | − | 48.8404i | −0.919228 | − | 1.59215i | −0.800590 | − | 0.599213i | \(-0.795480\pi\) |
−0.118639 | − | 0.992937i | \(-0.537853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.08441 | − | 1.87826i | 0.0353134 | − | 0.0611646i | ||||
\(944\) | −6.10023 | −0.198546 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 75.5044 | 2.45486 | ||||||||
\(947\) | −20.6309 | + | 35.7337i | −0.670414 | + | 1.16119i | 0.307373 | + | 0.951589i | \(0.400550\pi\) |
−0.977787 | + | 0.209602i | \(0.932783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.2491 | + | 21.2161i | 0.397623 | + | 0.688703i | ||||
\(950\) | 4.89849 | − | 8.48444i | 0.158928 | − | 0.275271i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.69779 | − | 0.807120i | −0.152256 | − | 0.0261589i | ||||
\(953\) | −13.3022 | −0.430901 | −0.215450 | − | 0.976515i | \(-0.569122\pi\) | ||||
−0.215450 | + | 0.976515i | \(0.569122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.24970 | − | 10.8248i | −0.202236 | − | 0.350282i | ||||
\(956\) | −20.3097 | − | 35.1774i | −0.656861 | − | 1.13772i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −56.5928 | −1.82843 | ||||||||
\(959\) | 31.8829 | + | 5.47775i | 1.02955 | + | 0.176886i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9642 | + | 50.1675i | −0.934329 | + | 1.61831i | ||||
\(962\) | 8.79930 | + | 15.2408i | 0.283701 | + | 0.491384i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.59859 | − | 2.76885i | 0.0514873 | − | 0.0891786i | ||||
\(965\) | 19.0288 | 0.612558 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.6678 | −0.536001 | −0.268000 | − | 0.963419i | \(-0.586363\pi\) | ||||
−0.268000 | + | 0.963419i | \(0.586363\pi\) | |||||||
\(968\) | −8.50060 | + | 14.7235i | −0.273220 | + | 0.473230i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.24970 | − | 16.0210i | −0.296990 | − | 0.514402i | ||||
\(971\) | −17.0934 | + | 29.6066i | −0.548552 | + | 0.950120i | 0.449822 | + | 0.893118i | \(0.351487\pi\) |
−0.998374 | + | 0.0570020i | \(0.981846\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.7820 | + | 24.9888i | −0.666240 | + | 0.801103i | ||||
\(974\) | −26.5195 | −0.849741 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.63783 | − | 11.4971i | −0.212472 | − | 0.368012i | ||||
\(977\) | −7.16027 | − | 12.4019i | −0.229077 | − | 0.396773i | 0.728458 | − | 0.685091i | \(-0.240237\pi\) |
−0.957535 | + | 0.288317i | \(0.906904\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.6119 | −0.498957 | ||||||||
\(980\) | −1.89185 | − | 10.2050i | −0.0604331 | − | 0.325987i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.4769 | − | 32.0029i | 0.589621 | − | 1.02125i | ||||
\(983\) | 28.6597 | + | 49.6400i | 0.914101 | + | 1.58327i | 0.808212 | + | 0.588892i | \(0.200436\pi\) |
0.105890 | + | 0.994378i | \(0.466231\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.3287 | + | 23.0859i | −0.424687 | + | 0.735579i | ||||
\(986\) | −15.2664 | −0.486181 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.8505 | 1.07693 | ||||||||
\(989\) | 26.0988 | − | 45.2045i | 0.829894 | − | 1.43742i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.73612 | + | 3.00705i | 0.0551496 | + | 0.0955219i | 0.892282 | − | 0.451478i | \(-0.149103\pi\) |
−0.837133 | + | 0.547000i | \(0.815770\pi\) | |||||||
\(992\) | 32.8425 | − | 56.8848i | 1.04275 | − | 1.80609i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.6450 | + | 31.5629i | 0.369356 | + | 1.00111i | ||||
\(995\) | 7.57606 | 0.240177 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.29930 | + | 16.1069i | 0.294512 | + | 0.510109i | 0.974871 | − | 0.222769i | \(-0.0715097\pi\) |
−0.680359 | + | 0.732879i | \(0.738176\pi\) | |||||||
\(998\) | 10.4158 | + | 18.0407i | 0.329706 | + | 0.571068i | ||||
\(999\) | 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 | 315.2.j.f.226.3 | yes | 6 | |
3.2 | odd | 2 | 315.2.j.g.226.1 | yes | 6 | ||
7.2 | even | 3 | 2205.2.a.be.1.1 | 3 | |||
7.4 | even | 3 | inner | 315.2.j.f.46.3 | ✓ | 6 | |
7.5 | odd | 6 | 2205.2.a.bd.1.1 | 3 | |||
21.2 | odd | 6 | 2205.2.a.bb.1.3 | 3 | |||
21.5 | even | 6 | 2205.2.a.bc.1.3 | 3 | |||
21.11 | odd | 6 | 315.2.j.g.46.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.j.f.46.3 | ✓ | 6 | 7.4 | even | 3 | inner | |
315.2.j.f.226.3 | yes | 6 | 1.1 | even | 1 | trivial | |
315.2.j.g.46.1 | yes | 6 | 21.11 | odd | 6 | ||
315.2.j.g.226.1 | yes | 6 | 3.2 | odd | 2 | ||
2205.2.a.bb.1.3 | 3 | 21.2 | odd | 6 | |||
2205.2.a.bc.1.3 | 3 | 21.5 | even | 6 | |||
2205.2.a.bd.1.1 | 3 | 7.5 | odd | 6 | |||
2205.2.a.be.1.1 | 3 | 7.2 | even | 3 |