Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(126,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("325.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.e (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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 8x^{8} - 2x^{7} + 52x^{6} - 5x^{5} + 97x^{4} + 60x^{3} + 141x^{2} + 36x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 126.1 | ||
Root | \(-1.30241 + 2.25583i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.126 |
Dual form | 325.2.e.c.276.1 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30241 | + | 2.25583i | −0.920941 | + | 1.59512i | −0.122978 | + | 0.992409i | \(0.539244\pi\) |
−0.797963 | + | 0.602707i | \(0.794089\pi\) | |||||||
\(3\) | −0.0676602 | + | 0.117191i | −0.0390636 | + | 0.0676602i | −0.884896 | − | 0.465788i | \(-0.845771\pi\) |
0.845833 | + | 0.533448i | \(0.179104\pi\) | |||||||
\(4\) | −2.39253 | − | 4.14398i | −1.19626 | − | 2.07199i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.176242 | − | 0.305261i | −0.0719506 | − | 0.124622i | ||||
\(7\) | 1.62616 | + | 2.81660i | 0.614632 | + | 1.06457i | 0.990449 | + | 0.137880i | \(0.0440290\pi\) |
−0.375816 | + | 0.926694i | \(0.622638\pi\) | |||||||
\(8\) | 7.25455 | 2.56487 | ||||||||
\(9\) | 1.49084 | + | 2.58222i | 0.496948 | + | 0.860739i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.176242 | + | 0.305261i | −0.0531390 | + | 0.0920395i | −0.891371 | − | 0.453274i | \(-0.850256\pi\) |
0.838232 | + | 0.545313i | \(0.183589\pi\) | |||||||
\(12\) | 0.647516 | 0.186922 | ||||||||
\(13\) | −0.400724 | + | 3.58321i | −0.111141 | + | 0.993805i | ||||
\(14\) | −8.47171 | −2.26416 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.66332 | + | 8.07710i | −1.16583 | + | 2.01928i | ||||
\(17\) | −3.37118 | − | 5.83905i | −0.817630 | − | 1.41618i | −0.907424 | − | 0.420217i | \(-0.861954\pi\) |
0.0897934 | − | 0.995960i | \(-0.471379\pi\) | |||||||
\(18\) | −7.76674 | −1.83064 | ||||||||
\(19\) | −1.39253 | − | 2.41193i | −0.319468 | − | 0.553334i | 0.660909 | − | 0.750466i | \(-0.270171\pi\) |
−0.980377 | + | 0.197132i | \(0.936837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.440107 | −0.0960391 | ||||||||
\(22\) | −0.459078 | − | 0.795147i | −0.0978758 | − | 0.169526i | ||||
\(23\) | −3.55031 | + | 6.14931i | −0.740290 | + | 1.28222i | 0.212073 | + | 0.977254i | \(0.431979\pi\) |
−0.952363 | + | 0.304967i | \(0.901355\pi\) | |||||||
\(24\) | −0.490844 | + | 0.850167i | −0.100193 | + | 0.173540i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.56123 | − | 5.57077i | −1.48288 | − | 1.09252i | ||||
\(27\) | −0.809445 | −0.155778 | ||||||||
\(28\) | 7.78129 | − | 13.4776i | 1.47052 | − | 2.54702i | ||||
\(29\) | −4.06500 | + | 7.04079i | −0.754852 | + | 1.30744i | 0.190596 | + | 0.981669i | \(0.438958\pi\) |
−0.945448 | + | 0.325773i | \(0.894375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.11923 | 1.27865 | 0.639325 | − | 0.768936i | \(-0.279214\pi\) | ||||
0.639325 | + | 0.768936i | \(0.279214\pi\) | |||||||
\(32\) | −4.89253 | − | 8.47411i | −0.864885 | − | 1.49802i | ||||
\(33\) | −0.0238492 | − | 0.0413080i | −0.00415161 | − | 0.00719080i | ||||
\(34\) | 17.5626 | 3.01196 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.13377 | − | 12.3561i | 1.18896 | − | 2.05934i | ||||
\(37\) | −2.04092 | + | 3.53498i | −0.335525 | + | 0.581147i | −0.983586 | − | 0.180442i | \(-0.942247\pi\) |
0.648060 | + | 0.761589i | \(0.275581\pi\) | |||||||
\(38\) | 7.25455 | 1.17684 | ||||||||
\(39\) | −0.392807 | − | 0.289402i | −0.0628995 | − | 0.0463414i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.202022 | − | 0.349912i | 0.0315505 | − | 0.0546470i | −0.849819 | − | 0.527075i | \(-0.823289\pi\) |
0.881369 | + | 0.472428i | \(0.156622\pi\) | |||||||
\(42\) | 0.573198 | − | 0.992808i | 0.0884463 | − | 0.153194i | ||||
\(43\) | −0.877834 | − | 1.52045i | −0.133868 | − | 0.231867i | 0.791296 | − | 0.611433i | \(-0.209407\pi\) |
−0.925165 | + | 0.379566i | \(0.876073\pi\) | |||||||
\(44\) | 1.68666 | 0.254273 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.24789 | − | 16.0178i | −1.36353 | − | 2.36170i | ||||
\(47\) | −3.75653 | −0.547946 | −0.273973 | − | 0.961737i | \(-0.588338\pi\) | ||||
−0.273973 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(48\) | −0.631042 | − | 1.09300i | −0.0910831 | − | 0.157761i | ||||
\(49\) | −1.78882 | + | 3.09833i | −0.255546 | + | 0.442619i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.912378 | 0.127758 | ||||||||
\(52\) | 15.8075 | − | 6.91234i | 2.19211 | − | 0.958570i | ||||
\(53\) | −3.44334 | −0.472980 | −0.236490 | − | 0.971634i | \(-0.575997\pi\) | ||||
−0.236490 | + | 0.971634i | \(0.575997\pi\) | |||||||
\(54\) | 1.05423 | − | 1.82597i | 0.143462 | − | 0.248483i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.7971 | + | 20.4332i | 1.57645 | + | 2.73050i | ||||
\(57\) | 0.376875 | 0.0499183 | ||||||||
\(58\) | −10.5886 | − | 18.3399i | −1.39035 | − | 2.40815i | ||||
\(59\) | 1.12712 | + | 1.95224i | 0.146739 | + | 0.254159i | 0.930020 | − | 0.367508i | \(-0.119789\pi\) |
−0.783281 | + | 0.621667i | \(0.786456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.05961 | + | 5.29941i | 0.391743 | + | 0.678519i | 0.992680 | − | 0.120778i | \(-0.0385388\pi\) |
−0.600936 | + | 0.799297i | \(0.705205\pi\) | |||||||
\(62\) | −9.27213 | + | 16.0598i | −1.17756 | + | 2.03960i | ||||
\(63\) | −4.84872 | + | 8.39822i | −0.610881 | + | 1.05808i | ||||
\(64\) | 6.83497 | 0.854371 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.124245 | 0.0152935 | ||||||||
\(67\) | 5.85663 | − | 10.1440i | 0.715502 | − | 1.23929i | −0.247264 | − | 0.968948i | \(-0.579532\pi\) |
0.962766 | − | 0.270337i | \(-0.0871351\pi\) | |||||||
\(68\) | −16.1313 | + | 27.9402i | −1.95620 | + | 3.38824i | ||||
\(69\) | −0.480429 | − | 0.832128i | −0.0578369 | − | 0.100176i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.857592 | + | 1.48539i | 0.101777 | + | 0.176284i | 0.912417 | − | 0.409262i | \(-0.134214\pi\) |
−0.810640 | + | 0.585545i | \(0.800880\pi\) | |||||||
\(72\) | 10.8154 | + | 18.7328i | 1.27461 | + | 2.20768i | ||||
\(73\) | 10.5626 | 1.23626 | 0.618128 | − | 0.786078i | \(-0.287891\pi\) | ||||
0.618128 | + | 0.786078i | \(0.287891\pi\) | |||||||
\(74\) | −5.31622 | − | 9.20797i | −0.617998 | − | 1.07040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.66332 | + | 11.5412i | −0.764335 | + | 1.32387i | ||||
\(77\) | −1.14640 | −0.130644 | ||||||||
\(78\) | 1.16444 | − | 0.509188i | 0.131847 | − | 0.0576542i | ||||
\(79\) | 8.62003 | 0.969829 | 0.484914 | − | 0.874562i | \(-0.338851\pi\) | ||||
0.484914 | + | 0.874562i | \(0.338851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.41777 | + | 7.65179i | −0.490863 | + | 0.850199i | ||||
\(82\) | 0.526228 | + | 0.911454i | 0.0581122 | + | 0.100653i | ||||
\(83\) | 7.81830 | 0.858170 | 0.429085 | − | 0.903264i | \(-0.358836\pi\) | ||||
0.429085 | + | 0.903264i | \(0.358836\pi\) | |||||||
\(84\) | 1.05297 | + | 1.82379i | 0.114888 | + | 0.198992i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.57319 | 0.493139 | ||||||||
\(87\) | −0.550078 | − | 0.952762i | −0.0589745 | − | 0.102147i | ||||
\(88\) | −1.27856 | + | 2.21453i | −0.136295 | + | 0.236069i | ||||
\(89\) | 3.59455 | − | 6.22594i | 0.381021 | − | 0.659948i | −0.610187 | − | 0.792257i | \(-0.708906\pi\) |
0.991209 | + | 0.132309i | \(0.0422391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.7441 | + | 4.69822i | −1.12629 | + | 0.492507i | ||||
\(92\) | 33.9768 | 3.54233 | ||||||||
\(93\) | −0.481688 | + | 0.834309i | −0.0499488 | + | 0.0865138i | ||||
\(94\) | 4.89253 | − | 8.47411i | 0.504626 | − | 0.874037i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.32412 | 0.135142 | ||||||||
\(97\) | 3.43618 | + | 5.95163i | 0.348891 | + | 0.604297i | 0.986053 | − | 0.166433i | \(-0.0532250\pi\) |
−0.637162 | + | 0.770730i | \(0.719892\pi\) | |||||||
\(98\) | −4.65955 | − | 8.07058i | −0.470686 | − | 0.815251i | ||||
\(99\) | −1.05100 | −0.105629 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.76164 | − | 4.78329i | 0.274793 | − | 0.475955i | −0.695290 | − | 0.718729i | \(-0.744724\pi\) |
0.970083 | + | 0.242774i | \(0.0780574\pi\) | |||||||
\(102\) | −1.18829 | + | 2.05817i | −0.117658 | + | 0.203790i | ||||
\(103\) | 10.2573 | 1.01068 | 0.505342 | − | 0.862919i | \(-0.331366\pi\) | ||||
0.505342 | + | 0.862919i | \(0.331366\pi\) | |||||||
\(104\) | −2.90707 | + | 25.9946i | −0.285062 | + | 2.54898i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.48464 | − | 7.76762i | 0.435586 | − | 0.754458i | ||||
\(107\) | 0.507606 | − | 0.879199i | 0.0490721 | − | 0.0849954i | −0.840446 | − | 0.541895i | \(-0.817707\pi\) |
0.889518 | + | 0.456900i | \(0.151040\pi\) | |||||||
\(108\) | 1.93662 | + | 3.35432i | 0.186351 | + | 0.322770i | ||||
\(109\) | −13.6200 | −1.30456 | −0.652281 | − | 0.757977i | \(-0.726188\pi\) | ||||
−0.652281 | + | 0.757977i | \(0.726188\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.276178 | − | 0.478355i | −0.0262137 | − | 0.0454034i | ||||
\(112\) | −30.3333 | −2.86623 | ||||||||
\(113\) | −6.01773 | − | 10.4230i | −0.566101 | − | 0.980515i | −0.996946 | − | 0.0780895i | \(-0.975118\pi\) |
0.430846 | − | 0.902426i | \(-0.358215\pi\) | |||||||
\(114\) | −0.490844 | + | 0.850167i | −0.0459718 | + | 0.0796254i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 38.9025 | 3.61201 | ||||||||
\(117\) | −9.85006 | + | 4.30726i | −0.910638 | + | 0.398206i | ||||
\(118\) | −5.87189 | −0.540552 | ||||||||
\(119\) | 10.9642 | − | 18.9905i | 1.00508 | − | 1.74086i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.43788 | + | 9.41868i | 0.494352 | + | 0.856244i | ||||
\(122\) | −15.9394 | −1.44309 | ||||||||
\(123\) | 0.0273376 | + | 0.0473502i | 0.00246495 | + | 0.00426942i | ||||
\(124\) | −17.0329 | − | 29.5019i | −1.52960 | − | 2.64935i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.6300 | − | 21.8758i | −1.12517 | − | 1.94885i | ||||
\(127\) | 4.62639 | − | 8.01315i | 0.410526 | − | 0.711052i | −0.584421 | − | 0.811450i | \(-0.698678\pi\) |
0.994947 | + | 0.100398i | \(0.0320117\pi\) | |||||||
\(128\) | 0.883141 | − | 1.52965i | 0.0780594 | − | 0.135203i | ||||
\(129\) | 0.237578 | 0.0209175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50080 | −0.131125 | −0.0655627 | − | 0.997848i | \(-0.520884\pi\) | ||||
−0.0655627 | + | 0.997848i | \(0.520884\pi\) | |||||||
\(132\) | −0.114120 | + | 0.197661i | −0.00993283 | + | 0.0172042i | ||||
\(133\) | 4.52896 | − | 7.84438i | 0.392710 | − | 0.680194i | ||||
\(134\) | 15.2554 | + | 26.4232i | 1.31787 | + | 2.28262i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.4564 | − | 42.3597i | −2.09712 | − | 3.63231i | ||||
\(137\) | −0.585922 | − | 1.01485i | −0.0500587 | − | 0.0867042i | 0.839910 | − | 0.542725i | \(-0.182608\pi\) |
−0.889969 | + | 0.456021i | \(0.849274\pi\) | |||||||
\(138\) | 2.50286 | 0.213057 | ||||||||
\(139\) | 6.26702 | + | 10.8548i | 0.531562 | + | 0.920692i | 0.999321 | + | 0.0368364i | \(0.0117280\pi\) |
−0.467759 | + | 0.883856i | \(0.654939\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.254167 | − | 0.440231i | 0.0214048 | − | 0.0370741i | ||||
\(142\) | −4.46774 | −0.374924 | ||||||||
\(143\) | −1.02319 | − | 0.753839i | −0.0855634 | − | 0.0630392i | ||||
\(144\) | −27.8091 | −2.31743 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.7568 | + | 23.8274i | −1.13852 | + | 1.97197i | ||||
\(147\) | −0.242064 | − | 0.419268i | −0.0199651 | − | 0.0345806i | ||||
\(148\) | 19.5318 | 1.60551 | ||||||||
\(149\) | 9.78121 | + | 16.9415i | 0.801308 | + | 1.38791i | 0.918756 | + | 0.394826i | \(0.129195\pi\) |
−0.117448 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.94414 | 0.809243 | 0.404621 | − | 0.914484i | \(-0.367403\pi\) | ||||
0.404621 | + | 0.914484i | \(0.367403\pi\) | |||||||
\(152\) | −10.1022 | − | 17.4974i | −0.819393 | − | 1.41923i | ||||
\(153\) | 10.0518 | − | 17.4102i | 0.812640 | − | 1.40753i | ||||
\(154\) | 1.49307 | − | 2.58608i | 0.120315 | − | 0.208392i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.259475 | + | 2.32019i | −0.0207746 | + | 0.185764i | ||||
\(157\) | 6.60923 | 0.527474 | 0.263737 | − | 0.964595i | \(-0.415045\pi\) | ||||
0.263737 | + | 0.964595i | \(0.415045\pi\) | |||||||
\(158\) | −11.2268 | + | 19.4454i | −0.893155 | + | 1.54699i | ||||
\(159\) | 0.232977 | − | 0.403529i | 0.0184763 | − | 0.0320019i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.0935 | −1.82003 | ||||||||
\(162\) | −11.5075 | − | 19.9315i | −0.904111 | − | 1.56597i | ||||
\(163\) | −3.81571 | − | 6.60901i | −0.298870 | − | 0.517657i | 0.677008 | − | 0.735976i | \(-0.263276\pi\) |
−0.975878 | + | 0.218318i | \(0.929943\pi\) | |||||||
\(164\) | −1.93337 | −0.150971 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.1826 | + | 17.6368i | −0.790324 | + | 1.36888i | ||||
\(167\) | 9.81762 | − | 17.0046i | 0.759710 | − | 1.31586i | −0.183288 | − | 0.983059i | \(-0.558674\pi\) |
0.942998 | − | 0.332797i | \(-0.107993\pi\) | |||||||
\(168\) | −3.19277 | −0.246328 | ||||||||
\(169\) | −12.6788 | − | 2.87176i | −0.975295 | − | 0.220905i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.15208 | − | 7.19162i | 0.317518 | − | 0.549957i | ||||
\(172\) | −4.20048 | + | 7.27545i | −0.320284 | + | 0.554748i | ||||
\(173\) | 3.63865 | + | 6.30232i | 0.276641 | + | 0.479157i | 0.970548 | − | 0.240908i | \(-0.0774453\pi\) |
−0.693907 | + | 0.720065i | \(0.744112\pi\) | |||||||
\(174\) | 2.86570 | 0.217248 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.64375 | − | 2.84705i | −0.123902 | − | 0.214605i | ||||
\(177\) | −0.305046 | −0.0229286 | ||||||||
\(178\) | 9.36313 | + | 16.2174i | 0.701796 | + | 1.21555i | ||||
\(179\) | 7.42636 | − | 12.8628i | 0.555072 | − | 0.961413i | −0.442826 | − | 0.896608i | \(-0.646024\pi\) |
0.997898 | − | 0.0648057i | \(-0.0206428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2959 | −0.913948 | −0.456974 | − | 0.889480i | \(-0.651067\pi\) | ||||
−0.456974 | + | 0.889480i | \(0.651067\pi\) | |||||||
\(182\) | 3.39482 | − | 30.3560i | 0.251641 | − | 2.25013i | ||||
\(183\) | −0.828056 | −0.0612117 | ||||||||
\(184\) | −25.7559 | + | 44.6105i | −1.89875 | + | 3.28873i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.25471 | − | 2.17322i | −0.0919997 | − | 0.159348i | ||||
\(187\) | 2.37657 | 0.173792 | ||||||||
\(188\) | 8.98759 | + | 15.5670i | 0.655488 | + | 1.13534i | ||||
\(189\) | −1.31629 | − | 2.27988i | −0.0957460 | − | 0.165837i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.838301 | + | 1.45198i | 0.0606573 | + | 0.105062i | 0.894759 | − | 0.446549i | \(-0.147347\pi\) |
−0.834102 | + | 0.551610i | \(0.814014\pi\) | |||||||
\(192\) | −0.462456 | + | 0.800997i | −0.0333749 | + | 0.0578069i | ||||
\(193\) | −1.44232 | + | 2.49817i | −0.103820 | + | 0.179822i | −0.913256 | − | 0.407387i | \(-0.866440\pi\) |
0.809435 | + | 0.587209i | \(0.199773\pi\) | |||||||
\(194\) | −17.9012 | −1.28523 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.1192 | 1.22280 | ||||||||
\(197\) | −2.49152 | + | 4.31545i | −0.177514 | + | 0.307463i | −0.941028 | − | 0.338328i | \(-0.890139\pi\) |
0.763515 | + | 0.645791i | \(0.223472\pi\) | |||||||
\(198\) | 1.36883 | − | 2.37088i | 0.0972784 | − | 0.168491i | ||||
\(199\) | −11.4591 | − | 19.8477i | −0.812312 | − | 1.40697i | −0.911242 | − | 0.411871i | \(-0.864875\pi\) |
0.0989305 | − | 0.995094i | \(-0.468458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.792522 | + | 1.37269i | 0.0559002 | + | 0.0968220i | ||||
\(202\) | 7.19354 | + | 12.4596i | 0.506136 | + | 0.876653i | ||||
\(203\) | −26.4414 | −1.85583 | ||||||||
\(204\) | −2.18289 | − | 3.78087i | −0.152833 | − | 0.264714i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.3592 | + | 23.1388i | −0.930780 | + | 1.61216i | ||||
\(207\) | −21.1718 | −1.47154 | ||||||||
\(208\) | −27.0733 | − | 19.9464i | −1.87719 | − | 1.38303i | ||||
\(209\) | 0.981688 | 0.0679048 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.627865 | + | 1.08749i | −0.0432240 | + | 0.0748661i | −0.886828 | − | 0.462100i | \(-0.847096\pi\) |
0.843604 | + | 0.536966i | \(0.180430\pi\) | |||||||
\(212\) | 8.23830 | + | 14.2691i | 0.565808 | + | 0.980009i | ||||
\(213\) | −0.232099 | −0.0159032 | ||||||||
\(214\) | 1.32222 | + | 2.29015i | 0.0903850 | + | 0.156551i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.87215 | −0.399549 | ||||||||
\(217\) | 11.5770 | + | 20.0520i | 0.785900 | + | 1.36122i | ||||
\(218\) | 17.7388 | − | 30.7245i | 1.20142 | − | 2.08093i | ||||
\(219\) | −0.714666 | + | 1.23784i | −0.0482926 | + | 0.0836453i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.2735 | − | 9.73980i | 1.49828 | − | 0.655170i | ||||
\(222\) | 1.43879 | 0.0965650 | ||||||||
\(223\) | −2.12446 | + | 3.67968i | −0.142265 | + | 0.246410i | −0.928349 | − | 0.371710i | \(-0.878772\pi\) |
0.786084 | + | 0.618119i | \(0.212105\pi\) | |||||||
\(224\) | 15.9121 | − | 27.5606i | 1.06317 | − | 1.84147i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.3501 | 2.08538 | ||||||||
\(227\) | 7.50392 | + | 12.9972i | 0.498052 | + | 0.862652i | 0.999997 | − | 0.00224733i | \(-0.000715348\pi\) |
−0.501945 | + | 0.864900i | \(0.667382\pi\) | |||||||
\(228\) | −0.901683 | − | 1.56176i | −0.0597154 | − | 0.103430i | ||||
\(229\) | −1.86852 | −0.123475 | −0.0617375 | − | 0.998092i | \(-0.519664\pi\) | ||||
−0.0617375 | + | 0.998092i | \(0.519664\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0775654 | − | 0.134347i | 0.00510343 | − | 0.00883939i | ||||
\(232\) | −29.4897 | + | 51.0777i | −1.93610 | + | 3.35342i | ||||
\(233\) | 15.0743 | 0.987551 | 0.493775 | − | 0.869590i | \(-0.335617\pi\) | ||||
0.493775 | + | 0.869590i | \(0.335617\pi\) | |||||||
\(234\) | 3.11232 | − | 27.8299i | 0.203459 | − | 1.81930i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.39335 | − | 9.34155i | 0.351077 | − | 0.608083i | ||||
\(237\) | −0.583233 | + | 1.01019i | −0.0378850 | + | 0.0656188i | ||||
\(238\) | 28.5596 | + | 49.4667i | 1.85125 | + | 3.20645i | ||||
\(239\) | 22.2262 | 1.43769 | 0.718847 | − | 0.695169i | \(-0.244670\pi\) | ||||
0.718847 | + | 0.695169i | \(0.244670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.66206 | + | 4.61082i | 0.171478 | + | 0.297009i | 0.938937 | − | 0.344089i | \(-0.111812\pi\) |
−0.767459 | + | 0.641098i | \(0.778479\pi\) | |||||||
\(242\) | −28.3293 | −1.82108 | ||||||||
\(243\) | −1.81198 | − | 3.13844i | −0.116239 | − | 0.201331i | ||||
\(244\) | 14.6404 | − | 25.3579i | 0.937257 | − | 1.62338i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.142419 | −0.00908030 | ||||||||
\(247\) | 9.20047 | − | 4.02321i | 0.585412 | − | 0.255990i | ||||
\(248\) | 51.6468 | 3.27957 | ||||||||
\(249\) | −0.528988 | + | 0.916234i | −0.0335232 | + | 0.0580640i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.4151 | − | 18.0394i | −0.657393 | − | 1.13864i | −0.981288 | − | 0.192544i | \(-0.938326\pi\) |
0.323896 | − | 0.946093i | \(-0.395007\pi\) | |||||||
\(252\) | 46.4027 | 2.92310 | ||||||||
\(253\) | −1.25143 | − | 2.16754i | −0.0786766 | − | 0.136272i | ||||
\(254\) | 12.0509 | + | 20.8728i | 0.756140 | + | 1.30967i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.13539 | + | 15.8230i | 0.570962 | + | 0.988935i | ||||
\(257\) | −7.96972 | + | 13.8040i | −0.497138 | + | 0.861068i | −0.999995 | − | 0.00330197i | \(-0.998949\pi\) |
0.502857 | + | 0.864370i | \(0.332282\pi\) | |||||||
\(258\) | −0.309423 | + | 0.535936i | −0.0192638 | + | 0.0333659i | ||||
\(259\) | −13.2755 | −0.824899 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.2411 | −1.50049 | ||||||||
\(262\) | 1.95465 | − | 3.38555i | 0.120759 | − | 0.209160i | ||||
\(263\) | 8.85021 | − | 15.3290i | 0.545727 | − | 0.945227i | −0.452834 | − | 0.891595i | \(-0.649587\pi\) |
0.998561 | − | 0.0536320i | \(-0.0170798\pi\) | |||||||
\(264\) | −0.173015 | − | 0.299671i | −0.0106483 | − | 0.0184435i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.7971 | + | 20.4332i | 0.723326 | + | 1.25284i | ||||
\(267\) | 0.486416 | + | 0.842497i | 0.0297682 | + | 0.0515600i | ||||
\(268\) | −56.0486 | −3.42371 | ||||||||
\(269\) | 0.755787 | + | 1.30906i | 0.0460811 | + | 0.0798148i | 0.888146 | − | 0.459561i | \(-0.151993\pi\) |
−0.842065 | + | 0.539376i | \(0.818660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6501 | − | 23.6427i | 0.829185 | − | 1.43619i | −0.0694927 | − | 0.997582i | \(-0.522138\pi\) |
0.898678 | − | 0.438609i | \(-0.144529\pi\) | |||||||
\(272\) | 62.8835 | 3.81287 | ||||||||
\(273\) | 0.176361 | − | 1.57700i | 0.0106739 | − | 0.0954441i | ||||
\(274\) | 3.05244 | 0.184404 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.29888 | + | 3.98178i | −0.138376 | + | 0.239675i | ||||
\(277\) | −1.31171 | − | 2.27195i | −0.0788132 | − | 0.136508i | 0.823925 | − | 0.566699i | \(-0.191780\pi\) |
−0.902738 | + | 0.430190i | \(0.858446\pi\) | |||||||
\(278\) | −32.6489 | −1.95815 | ||||||||
\(279\) | 10.6137 | + | 18.3834i | 0.635423 | + | 1.10059i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.98774 | 0.536164 | 0.268082 | − | 0.963396i | \(-0.413610\pi\) | ||||
0.268082 | + | 0.963396i | \(0.413610\pi\) | |||||||
\(282\) | 0.662059 | + | 1.14672i | 0.0394250 | + | 0.0682862i | ||||
\(283\) | −11.7196 | + | 20.2989i | −0.696658 | + | 1.20665i | 0.272961 | + | 0.962025i | \(0.411997\pi\) |
−0.969619 | + | 0.244621i | \(0.921336\pi\) | |||||||
\(284\) | 4.10362 | − | 7.10769i | 0.243505 | − | 0.421764i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.03314 | − | 1.32634i | 0.179354 | − | 0.0784282i | ||||
\(287\) | 1.31408 | 0.0775678 | ||||||||
\(288\) | 14.5880 | − | 25.2671i | 0.859606 | − | 1.48888i | ||||
\(289\) | −14.2297 | + | 24.6465i | −0.837039 | + | 1.44979i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.929970 | −0.0545158 | ||||||||
\(292\) | −25.2712 | − | 43.7711i | −1.47889 | − | 2.56151i | ||||
\(293\) | 0.588332 | + | 1.01902i | 0.0343707 | + | 0.0595318i | 0.882699 | − | 0.469939i | \(-0.155724\pi\) |
−0.848328 | + | 0.529470i | \(0.822391\pi\) | |||||||
\(294\) | 1.26106 | 0.0735468 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.8060 | + | 25.6447i | −0.860579 | + | 1.49057i | ||||
\(297\) | 0.142658 | − | 0.247091i | 0.00827788 | − | 0.0143377i | ||||
\(298\) | −50.9564 | −2.95183 | ||||||||
\(299\) | −20.6116 | − | 15.1857i | −1.19200 | − | 0.878211i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.85500 | − | 4.94501i | 0.164560 | − | 0.285026i | ||||
\(302\) | −12.9513 | + | 22.4323i | −0.745265 | + | 1.29084i | ||||
\(303\) | 0.373706 | + | 0.647277i | 0.0214688 | + | 0.0371851i | ||||
\(304\) | 25.9752 | 1.48978 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 26.1831 | + | 45.3504i | 1.49679 | + | 2.59251i | ||||
\(307\) | 16.6150 | 0.948269 | 0.474134 | − | 0.880453i | \(-0.342761\pi\) | ||||
0.474134 | + | 0.880453i | \(0.342761\pi\) | |||||||
\(308\) | 2.74278 | + | 4.75064i | 0.156285 | + | 0.270693i | ||||
\(309\) | −0.694013 | + | 1.20207i | −0.0394810 | + | 0.0683831i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7129 | −0.834294 | −0.417147 | − | 0.908839i | \(-0.636970\pi\) | ||||
−0.417147 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(312\) | −2.84964 | − | 2.09948i | −0.161329 | − | 0.118860i | ||||
\(313\) | 1.86190 | 0.105241 | 0.0526204 | − | 0.998615i | \(-0.483243\pi\) | ||||
0.0526204 | + | 0.998615i | \(0.483243\pi\) | |||||||
\(314\) | −8.60791 | + | 14.9093i | −0.485773 | + | 0.841383i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.6236 | − | 35.7212i | −1.16017 | − | 2.00947i | ||||
\(317\) | −13.9811 | −0.785258 | −0.392629 | − | 0.919697i | \(-0.628434\pi\) | ||||
−0.392629 | + | 0.919697i | \(0.628434\pi\) | |||||||
\(318\) | 0.606863 | + | 1.05112i | 0.0340312 | + | 0.0589437i | ||||
\(319\) | −1.43285 | − | 2.48177i | −0.0802242 | − | 0.138952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0686894 | + | 0.118974i | 0.00383387 | + | 0.00664046i | ||||
\(322\) | 30.0772 | − | 52.0952i | 1.67614 | − | 2.90315i | ||||
\(323\) | −9.38891 | + | 16.2621i | −0.522413 | + | 0.904846i | ||||
\(324\) | 42.2785 | 2.34881 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.8784 | 1.10096 | ||||||||
\(327\) | 0.921534 | − | 1.59614i | 0.0509609 | − | 0.0882669i | ||||
\(328\) | 1.46557 | − | 2.53845i | 0.0809228 | − | 0.140162i | ||||
\(329\) | −6.10873 | − | 10.5806i | −0.336785 | − | 0.583329i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.15262 | − | 12.3887i | −0.393144 | − | 0.680945i | 0.599719 | − | 0.800211i | \(-0.295279\pi\) |
−0.992862 | + | 0.119266i | \(0.961946\pi\) | |||||||
\(332\) | −18.7055 | − | 32.3989i | −1.02660 | − | 1.77812i | ||||
\(333\) | −12.1708 | −0.666955 | ||||||||
\(334\) | 25.5731 | + | 44.2939i | 1.39930 | + | 2.42365i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.05236 | − | 3.55479i | 0.111965 | − | 0.193929i | ||||
\(337\) | −9.24507 | −0.503611 | −0.251805 | − | 0.967778i | \(-0.581024\pi\) | ||||
−0.251805 | + | 0.967778i | \(0.581024\pi\) | |||||||
\(338\) | 22.9912 | − | 24.8612i | 1.25056 | − | 1.35227i | ||||
\(339\) | 1.62864 | 0.0884558 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.25471 | + | 2.17322i | −0.0679463 | + | 0.117686i | ||||
\(342\) | 10.8154 | + | 18.7328i | 0.584830 | + | 1.01296i | ||||
\(343\) | 11.1306 | 0.600997 | ||||||||
\(344\) | −6.36829 | − | 11.0302i | −0.343355 | − | 0.594708i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.9560 | −1.01908 | ||||||||
\(347\) | 2.27065 | + | 3.93288i | 0.121895 | + | 0.211128i | 0.920515 | − | 0.390707i | \(-0.127770\pi\) |
−0.798620 | + | 0.601836i | \(0.794436\pi\) | |||||||
\(348\) | −2.63215 | + | 4.55902i | −0.141098 | + | 0.244389i | ||||
\(349\) | −10.6508 | + | 18.4476i | −0.570122 | + | 0.987480i | 0.426431 | + | 0.904520i | \(0.359771\pi\) |
−0.996553 | + | 0.0829598i | \(0.973563\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.324364 | − | 2.90041i | 0.0173133 | − | 0.154813i | ||||
\(352\) | 3.44908 | 0.183837 | ||||||||
\(353\) | −12.0176 | + | 20.8150i | −0.639631 | + | 1.10787i | 0.345883 | + | 0.938278i | \(0.387579\pi\) |
−0.985514 | + | 0.169595i | \(0.945754\pi\) | |||||||
\(354\) | 0.397294 | − | 0.688133i | 0.0211159 | − | 0.0365738i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −34.4002 | −1.82321 | ||||||||
\(357\) | 1.48368 | + | 2.56980i | 0.0785245 | + | 0.136008i | ||||
\(358\) | 19.3443 | + | 33.5053i | 1.02238 | + | 1.77081i | ||||
\(359\) | 3.56759 | 0.188290 | 0.0941451 | − | 0.995558i | \(-0.469988\pi\) | ||||
0.0941451 | + | 0.995558i | \(0.469988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.62174 | − | 9.73713i | 0.295881 | − | 0.512481i | ||||
\(362\) | 16.0143 | − | 27.7375i | 0.841692 | − | 1.45785i | ||||
\(363\) | −1.47171 | −0.0772448 | ||||||||
\(364\) | 45.1749 | + | 33.2828i | 2.36781 | + | 1.74449i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.07847 | − | 1.86796i | 0.0563723 | − | 0.0976397i | ||||
\(367\) | −13.2523 | + | 22.9537i | −0.691765 | + | 1.19817i | 0.279494 | + | 0.960148i | \(0.409833\pi\) |
−0.971259 | + | 0.238025i | \(0.923500\pi\) | |||||||
\(368\) | −33.1124 | − | 57.3524i | −1.72610 | − | 2.98970i | ||||
\(369\) | 1.20473 | 0.0627158 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.59945 | − | 9.69852i | −0.290709 | − | 0.503522i | ||||
\(372\) | 4.60981 | 0.239008 | ||||||||
\(373\) | −12.4356 | − | 21.5391i | −0.643891 | − | 1.11525i | −0.984556 | − | 0.175067i | \(-0.943986\pi\) |
0.340666 | − | 0.940185i | \(-0.389348\pi\) | |||||||
\(374\) | −3.09527 | + | 5.36116i | −0.160052 | + | 0.277219i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.2519 | −1.40541 | ||||||||
\(377\) | −23.5997 | − | 17.3872i | −1.21545 | − | 0.895485i | ||||
\(378\) | 6.85738 | 0.352706 | ||||||||
\(379\) | 16.1404 | − | 27.9560i | 0.829078 | − | 1.43600i | −0.0696852 | − | 0.997569i | \(-0.522199\pi\) |
0.898763 | − | 0.438435i | \(-0.144467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.626046 | + | 1.08434i | 0.0320733 | + | 0.0555526i | ||||
\(382\) | −4.36724 | −0.223447 | ||||||||
\(383\) | 0.416177 | + | 0.720840i | 0.0212657 | + | 0.0368332i | 0.876462 | − | 0.481470i | \(-0.159897\pi\) |
−0.855197 | + | 0.518304i | \(0.826564\pi\) | |||||||
\(384\) | 0.119507 | + | 0.206992i | 0.00609857 | + | 0.0105630i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.75697 | − | 6.50726i | −0.191225 | − | 0.331211i | ||||
\(387\) | 2.61743 | − | 4.53352i | 0.133051 | − | 0.230452i | ||||
\(388\) | 16.4423 | − | 28.4789i | 0.834731 | − | 1.44580i | ||||
\(389\) | −36.0627 | −1.82845 | −0.914225 | − | 0.405207i | \(-0.867200\pi\) | ||||
−0.914225 | + | 0.405207i | \(0.867200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 47.8749 | 2.42114 | ||||||||
\(392\) | −12.9771 | + | 22.4770i | −0.655442 | + | 1.13526i | ||||
\(393\) | 0.101544 | − | 0.175880i | 0.00512223 | − | 0.00887197i | ||||
\(394\) | −6.48995 | − | 11.2409i | −0.326959 | − | 0.566310i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.51454 | + | 4.35532i | 0.126361 | + | 0.218863i | ||||
\(397\) | 3.80059 | + | 6.58281i | 0.190746 | + | 0.330382i | 0.945498 | − | 0.325629i | \(-0.105576\pi\) |
−0.754752 | + | 0.656011i | \(0.772243\pi\) | |||||||
\(398\) | 59.6975 | 2.99236 | ||||||||
\(399\) | 0.612860 | + | 1.06151i | 0.0306814 | + | 0.0531417i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.66466 | − | 16.7397i | 0.482630 | − | 0.835940i | −0.517171 | − | 0.855882i | \(-0.673015\pi\) |
0.999801 | + | 0.0199424i | \(0.00634828\pi\) | |||||||
\(402\) | −4.12874 | −0.205923 | ||||||||
\(403\) | −2.85284 | + | 25.5097i | −0.142110 | + | 1.27073i | ||||
\(404\) | −26.4291 | −1.31490 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.4375 | − | 59.6475i | 1.70911 | − | 2.96026i | ||||
\(407\) | −0.719393 | − | 1.24603i | −0.0356590 | − | 0.0617632i | ||||
\(408\) | 6.61889 | 0.327684 | ||||||||
\(409\) | 7.79244 | + | 13.4969i | 0.385311 | + | 0.667379i | 0.991812 | − | 0.127704i | \(-0.0407607\pi\) |
−0.606501 | + | 0.795083i | \(0.707427\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.158574 | 0.00782190 | ||||||||
\(412\) | −24.5409 | − | 42.5061i | −1.20904 | − | 2.09413i | ||||
\(413\) | −3.66578 | + | 6.34931i | −0.180381 | + | 0.312429i | ||||
\(414\) | 27.5743 | − | 47.7601i | 1.35520 | − | 2.34728i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 32.3251 | − | 14.1352i | 1.58487 | − | 0.693035i | ||||
\(417\) | −1.69611 | −0.0830590 | ||||||||
\(418\) | −1.27856 | + | 2.21453i | −0.0625363 | + | 0.108316i | ||||
\(419\) | 12.6596 | − | 21.9271i | 0.618463 | − | 1.07121i | −0.371303 | − | 0.928512i | \(-0.621089\pi\) |
0.989766 | − | 0.142698i | \(-0.0455778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.65115 | −0.421631 | −0.210816 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210816 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(422\) | −1.63547 | − | 2.83272i | −0.0796135 | − | 0.137895i | ||||
\(423\) | −5.60040 | − | 9.70017i | −0.272301 | − | 0.471639i | ||||
\(424\) | −24.9799 | −1.21313 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.302288 | − | 0.523578i | 0.0146459 | − | 0.0253674i | ||||
\(427\) | −9.95087 | + | 17.2354i | −0.481556 | + | 0.834080i | ||||
\(428\) | −4.85784 | −0.234813 | ||||||||
\(429\) | 0.157572 | − | 0.0689036i | 0.00760766 | − | 0.00332670i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.70929 | + | 11.6208i | −0.323175 | + | 0.559756i | −0.981141 | − | 0.193292i | \(-0.938084\pi\) |
0.657966 | + | 0.753047i | \(0.271417\pi\) | |||||||
\(432\) | 3.77470 | − | 6.53797i | 0.181610 | − | 0.314558i | ||||
\(433\) | −18.0854 | − | 31.3248i | −0.869129 | − | 1.50538i | −0.862888 | − | 0.505395i | \(-0.831347\pi\) |
−0.00624076 | − | 0.999981i | \(-0.501987\pi\) | |||||||
\(434\) | −60.3120 | −2.89507 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 32.5863 | + | 56.4411i | 1.56060 | + | 2.70304i | ||||
\(437\) | 19.7756 | 0.945995 | ||||||||
\(438\) | −1.86157 | − | 3.22434i | −0.0889493 | − | 0.154065i | ||||
\(439\) | −16.5319 | + | 28.6342i | −0.789027 | + | 1.36663i | 0.137537 | + | 0.990497i | \(0.456081\pi\) |
−0.926564 | + | 0.376138i | \(0.877252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.6674 | −0.507973 | ||||||||
\(442\) | −7.03774 | + | 62.9304i | −0.334751 | + | 2.99330i | ||||
\(443\) | −17.7778 | −0.844650 | −0.422325 | − | 0.906444i | \(-0.638786\pi\) | ||||
−0.422325 | + | 0.906444i | \(0.638786\pi\) | |||||||
\(444\) | −1.32153 | + | 2.28895i | −0.0627170 | + | 0.108629i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.53383 | − | 9.58488i | −0.262035 | − | 0.453857i | ||||
\(447\) | −2.64719 | −0.125208 | ||||||||
\(448\) | 11.1148 | + | 19.2514i | 0.525124 | + | 0.909542i | ||||
\(449\) | 15.9153 | + | 27.5662i | 0.751091 | + | 1.30093i | 0.947294 | + | 0.320365i | \(0.103805\pi\) |
−0.196203 | + | 0.980563i | \(0.562861\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0712095 | + | 0.123338i | 0.00335312 | + | 0.00580778i | ||||
\(452\) | −28.7952 | + | 49.8747i | −1.35441 | + | 2.34591i | ||||
\(453\) | −0.672823 | + | 1.16536i | −0.0316120 | + | 0.0547535i | ||||
\(454\) | −39.0926 | −1.83471 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.73406 | 0.128034 | ||||||||
\(457\) | 10.9985 | − | 19.0500i | 0.514490 | − | 0.891122i | −0.485369 | − | 0.874309i | \(-0.661315\pi\) |
0.999859 | − | 0.0168127i | \(-0.00535189\pi\) | |||||||
\(458\) | 2.43357 | − | 4.21506i | 0.113713 | − | 0.196957i | ||||
\(459\) | 2.72878 | + | 4.72639i | 0.127369 | + | 0.220609i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.86668 | + | 11.8934i | 0.319813 | + | 0.553933i | 0.980449 | − | 0.196774i | \(-0.0630465\pi\) |
−0.660636 | + | 0.750707i | \(0.729713\pi\) | |||||||
\(462\) | 0.202043 | + | 0.349949i | 0.00939991 | + | 0.0162811i | ||||
\(463\) | 7.26980 | 0.337856 | 0.168928 | − | 0.985628i | \(-0.445969\pi\) | ||||
0.168928 | + | 0.985628i | \(0.445969\pi\) | |||||||
\(464\) | −37.9128 | − | 65.6669i | −1.76006 | − | 3.04851i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.6329 | + | 34.0051i | −0.909476 | + | 1.57526i | ||||
\(467\) | 30.9639 | 1.43284 | 0.716418 | − | 0.697671i | \(-0.245780\pi\) | ||||
0.716418 | + | 0.697671i | \(0.245780\pi\) | |||||||
\(468\) | 41.4157 | + | 30.5132i | 1.91444 | + | 1.41047i | ||||
\(469\) | 38.0954 | 1.75908 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.447182 | + | 0.774542i | −0.0206051 | + | 0.0356890i | ||||
\(472\) | 8.17677 | + | 14.1626i | 0.376366 | + | 0.651886i | ||||
\(473\) | 0.618846 | 0.0284545 | ||||||||
\(474\) | −1.51921 | − | 2.63135i | −0.0697797 | − | 0.120862i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −104.928 | −4.80938 | ||||||||
\(477\) | −5.13349 | − | 8.89147i | −0.235046 | − | 0.407112i | ||||
\(478\) | −28.9476 | + | 50.1386i | −1.32403 | + | 2.29329i | ||||
\(479\) | 4.12407 | − | 7.14310i | 0.188434 | − | 0.326377i | −0.756294 | − | 0.654231i | \(-0.772992\pi\) |
0.944728 | + | 0.327855i | \(0.106326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.8487 | − | 8.72961i | −0.540256 | − | 0.398036i | ||||
\(482\) | −13.8683 | −0.631685 | ||||||||
\(483\) | 1.56251 | − | 2.70635i | 0.0710968 | − | 0.123143i | ||||
\(484\) | 26.0205 | − | 45.0689i | 1.18275 | − | 2.04859i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.43974 | 0.428195 | ||||||||
\(487\) | 14.8995 | + | 25.8068i | 0.675163 | + | 1.16942i | 0.976421 | + | 0.215874i | \(0.0692600\pi\) |
−0.301258 | + | 0.953543i | \(0.597407\pi\) | |||||||
\(488\) | 22.1961 | + | 38.4448i | 1.00477 | + | 1.74031i | ||||
\(489\) | 1.03269 | 0.0466997 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.1828 | + | 33.2256i | −0.865709 | + | 1.49945i | 0.000633368 | 1.00000i | \(0.499798\pi\) | |
−0.866342 | + | 0.499451i | \(0.833535\pi\) | |||||||
\(492\) | 0.130812 | − | 0.226573i | 0.00589746 | − | 0.0102147i | ||||
\(493\) | 54.8153 | 2.46876 | ||||||||
\(494\) | −2.90707 | + | 25.9946i | −0.130795 | + | 1.16955i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33.1992 | + | 57.5027i | −1.49069 | + | 2.58195i | ||||
\(497\) | −2.78917 | + | 4.83099i | −0.125111 | + | 0.216699i | ||||
\(498\) | −1.37791 | − | 2.38662i | −0.0617458 | − | 0.106947i | ||||
\(499\) | −29.9843 | −1.34228 | −0.671141 | − | 0.741329i | \(-0.734196\pi\) | ||||
−0.671141 | + | 0.741329i | \(0.734196\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32852 | + | 2.30107i | 0.0593541 | + | 0.102804i | ||||
\(502\) | 54.2586 | 2.42168 | ||||||||
\(503\) | 14.0174 | + | 24.2788i | 0.625003 | + | 1.08254i | 0.988540 | + | 0.150958i | \(0.0482357\pi\) |
−0.363537 | + | 0.931580i | \(0.618431\pi\) | |||||||
\(504\) | −35.1752 | + | 60.9253i | −1.56683 | + | 2.71383i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.51948 | 0.289826 | ||||||||
\(507\) | 1.19440 | − | 1.29154i | 0.0530450 | − | 0.0573594i | ||||
\(508\) | −44.2751 | −1.96439 | ||||||||
\(509\) | 19.2106 | − | 33.2737i | 0.851495 | − | 1.47483i | −0.0283637 | − | 0.999598i | \(-0.509030\pi\) |
0.879859 | − | 0.475235i | \(-0.157637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.1765 | + | 29.7505i | 0.759843 | + | 1.31609i | ||||
\(512\) | −44.0594 | −1.94717 | ||||||||
\(513\) | 1.12717 | + | 1.95232i | 0.0497659 | + | 0.0861971i | ||||
\(514\) | −20.7596 | − | 35.9568i | −0.915669 | − | 1.58598i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.568411 | − | 0.984517i | −0.0250229 | − | 0.0433409i | ||||
\(517\) | 0.662059 | − | 1.14672i | 0.0291173 | − | 0.0504327i | ||||
\(518\) | 17.2901 | − | 29.9473i | 0.759683 | − | 1.31581i | ||||
\(519\) | −0.984767 | −0.0432265 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.893030 | −0.0391243 | −0.0195622 | − | 0.999809i | \(-0.506227\pi\) | ||||
−0.0195622 | + | 0.999809i | \(0.506227\pi\) | |||||||
\(522\) | 31.5718 | − | 54.6840i | 1.38186 | − | 2.39345i | ||||
\(523\) | 5.11256 | − | 8.85522i | 0.223557 | − | 0.387212i | −0.732329 | − | 0.680951i | \(-0.761567\pi\) |
0.955885 | + | 0.293740i | \(0.0948999\pi\) | |||||||
\(524\) | 3.59070 | + | 6.21928i | 0.156860 | + | 0.271690i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.0531 | + | 39.9292i | 1.00516 | + | 1.74100i | ||||
\(527\) | −24.0002 | − | 41.5695i | −1.04546 | − | 1.81080i | ||||
\(528\) | 0.444865 | 0.0193603 | ||||||||
\(529\) | −13.7094 | − | 23.7453i | −0.596060 | − | 1.03241i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.36073 | + | 5.82096i | −0.145843 | + | 0.252608i | ||||
\(532\) | −43.3426 | −1.87914 | ||||||||
\(533\) | 1.17285 | + | 0.864104i | 0.0508019 | + | 0.0374285i | ||||
\(534\) | −2.53405 | −0.109659 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 42.4872 | − | 73.5900i | 1.83517 | − | 3.17861i | ||||
\(537\) | 1.00494 | + | 1.74060i | 0.0433663 | + | 0.0751126i | ||||
\(538\) | −3.93737 | −0.169752 | ||||||||
\(539\) | −0.630532 | − | 1.09211i | −0.0271589 | − | 0.0470407i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4261 | −0.663219 | −0.331609 | − | 0.943417i | \(-0.607592\pi\) | ||||
−0.331609 | + | 0.943417i | \(0.607592\pi\) | |||||||
\(542\) | 35.5560 | + | 61.5848i | 1.52726 | + | 2.64529i | ||||
\(543\) | 0.831944 | − | 1.44097i | 0.0357021 | − | 0.0618379i | ||||
\(544\) | −32.9871 | + | 57.1354i | −1.41431 | + | 2.44966i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.32775 | + | 2.45173i | 0.142414 | + | 0.104924i | ||||
\(547\) | 10.7393 | 0.459177 | 0.229589 | − | 0.973288i | \(-0.426262\pi\) | ||||
0.229589 | + | 0.973288i | \(0.426262\pi\) | |||||||
\(548\) | −2.80367 | + | 4.85610i | −0.119767 | + | 0.207442i | ||||
\(549\) | −9.12281 | + | 15.8012i | −0.389352 | + | 0.674378i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.6425 | 0.964603 | ||||||||
\(552\) | −3.48530 | − | 6.03671i | −0.148344 | − | 0.256939i | ||||
\(553\) | 14.0176 | + | 24.2792i | 0.596088 | + | 1.03245i | ||||
\(554\) | 6.83353 | 0.290329 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29.9880 | − | 51.9408i | 1.27178 | − | 2.20278i | ||||
\(557\) | −9.25021 | + | 16.0218i | −0.391944 | + | 0.678867i | −0.992706 | − | 0.120561i | \(-0.961531\pi\) |
0.600762 | + | 0.799428i | \(0.294864\pi\) | |||||||
\(558\) | −55.2932 | −2.34075 | ||||||||
\(559\) | 5.79988 | − | 2.53618i | 0.245309 | − | 0.107269i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.160800 | + | 0.278513i | −0.00678896 | + | 0.0117588i | ||||
\(562\) | −11.7057 | + | 20.2749i | −0.493775 | + | 0.855244i | ||||
\(563\) | −19.9411 | − | 34.5389i | −0.840415 | − | 1.45564i | −0.889544 | − | 0.456849i | \(-0.848978\pi\) |
0.0491288 | − | 0.998792i | \(-0.484356\pi\) | |||||||
\(564\) | −2.43241 | −0.102423 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −30.5274 | − | 52.8749i | −1.28316 | − | 2.22250i | ||||
\(567\) | −28.7361 | −1.20680 | ||||||||
\(568\) | 6.22144 | + | 10.7759i | 0.261046 | + | 0.452145i | ||||
\(569\) | −0.385811 | + | 0.668245i | −0.0161741 | + | 0.0280143i | −0.873999 | − | 0.485927i | \(-0.838482\pi\) |
0.857825 | + | 0.513942i | \(0.171815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.1208 | −1.26052 | −0.630259 | − | 0.776385i | \(-0.717051\pi\) | ||||
−0.630259 | + | 0.776385i | \(0.717051\pi\) | |||||||
\(572\) | −0.675884 | + | 6.04365i | −0.0282601 | + | 0.252698i | ||||
\(573\) | −0.226878 | −0.00947798 | ||||||||
\(574\) | −1.71147 | + | 2.96435i | −0.0714353 | + | 0.123730i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.1899 | + | 17.6494i | 0.424578 | + | 0.735391i | ||||
\(577\) | 15.2295 | 0.634014 | 0.317007 | − | 0.948423i | \(-0.397322\pi\) | ||||
0.317007 | + | 0.948423i | \(0.397322\pi\) | |||||||
\(578\) | −37.0656 | − | 64.1995i | −1.54173 | − | 2.67035i | ||||
\(579\) | −0.195175 | − | 0.338053i | −0.00811119 | − | 0.0140490i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7138 | + | 22.0210i | 0.527459 | + | 0.913586i | ||||
\(582\) | 1.21120 | − | 2.09786i | 0.0502058 | − | 0.0869590i | ||||
\(583\) | 0.606863 | − | 1.05112i | 0.0251337 | − | 0.0435328i | ||||
\(584\) | 76.6267 | 3.17083 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.06499 | −0.126614 | ||||||||
\(587\) | 19.9117 | − | 34.4881i | 0.821845 | − | 1.42348i | −0.0824611 | − | 0.996594i | \(-0.526278\pi\) |
0.904307 | − | 0.426884i | \(-0.140389\pi\) | |||||||
\(588\) | −1.15829 | + | 2.00622i | −0.0477671 | + | 0.0827350i | ||||
\(589\) | −9.91372 | − | 17.1711i | −0.408488 | − | 0.707521i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.337154 | − | 0.583968i | −0.0138687 | − | 0.0240212i | ||||
\(592\) | −19.0349 | − | 32.9695i | −0.782331 | − | 1.35504i | ||||
\(593\) | −7.45086 | −0.305970 | −0.152985 | − | 0.988229i | \(-0.548889\pi\) | ||||
−0.152985 | + | 0.988229i | \(0.548889\pi\) | |||||||
\(594\) | 0.371598 | + | 0.643627i | 0.0152469 | + | 0.0264083i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 46.8036 | − | 81.0662i | 1.91715 | − | 3.32060i | ||||
\(597\) | 3.10129 | 0.126927 | ||||||||
\(598\) | 61.1011 | − | 26.7184i | 2.49861 | − | 1.09260i | ||||
\(599\) | 9.61411 | 0.392822 | 0.196411 | − | 0.980522i | \(-0.437071\pi\) | ||||
0.196411 | + | 0.980522i | \(0.437071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.75437 | − | 4.77070i | 0.112353 | − | 0.194601i | −0.804366 | − | 0.594135i | \(-0.797495\pi\) |
0.916719 | + | 0.399534i | \(0.130828\pi\) | |||||||
\(602\) | 7.43675 | + | 12.8808i | 0.303099 | + | 0.524984i | ||||
\(603\) | 34.9253 | 1.42227 | ||||||||
\(604\) | −23.7916 | − | 41.2083i | −0.968068 | − | 1.67674i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.94687 | −0.0790861 | ||||||||
\(607\) | −15.1939 | − | 26.3166i | −0.616702 | − | 1.06816i | −0.990083 | − | 0.140481i | \(-0.955135\pi\) |
0.373381 | − | 0.927678i | \(-0.378198\pi\) | |||||||
\(608\) | −13.6260 | + | 23.6008i | −0.552605 | + | 0.957141i | ||||
\(609\) | 1.78903 | − | 3.09870i | 0.0724953 | − | 0.125566i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.50533 | − | 13.4604i | 0.0608991 | − | 0.544551i | ||||
\(612\) | −96.1968 | −3.88852 | ||||||||
\(613\) | 16.2506 | − | 28.1469i | 0.656357 | − | 1.13684i | −0.325195 | − | 0.945647i | \(-0.605430\pi\) |
0.981552 | − | 0.191196i | \(-0.0612367\pi\) | |||||||
\(614\) | −21.6395 | + | 37.4807i | −0.873299 | + | 1.51260i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.31658 | −0.335085 | ||||||||
\(617\) | −3.79833 | − | 6.57890i | −0.152915 | − | 0.264856i | 0.779383 | − | 0.626548i | \(-0.215533\pi\) |
−0.932298 | + | 0.361691i | \(0.882199\pi\) | |||||||
\(618\) | −1.80777 | − | 3.13116i | −0.0727193 | − | 0.125954i | ||||
\(619\) | 35.4509 | 1.42489 | 0.712445 | − | 0.701728i | \(-0.247588\pi\) | ||||
0.712445 | + | 0.701728i | \(0.247588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.87378 | − | 4.97753i | 0.115321 | − | 0.199741i | ||||
\(622\) | 19.1622 | − | 33.1899i | 0.768335 | − | 1.33080i | ||||
\(623\) | 23.3813 | 0.936752 | ||||||||
\(624\) | 4.16932 | − | 1.82317i | 0.166906 | − | 0.0729852i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.42495 | + | 4.20014i | −0.0969206 | + | 0.167871i | ||||
\(627\) | −0.0664212 | + | 0.115045i | −0.00265261 | + | 0.00459445i | ||||
\(628\) | −15.8128 | − | 27.3885i | −0.630998 | − | 1.09292i | ||||
\(629\) | 27.5212 | 1.09734 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.20395 | + | 5.54940i | 0.127547 | + | 0.220918i | 0.922726 | − | 0.385457i | \(-0.125956\pi\) |
−0.795179 | + | 0.606375i | \(0.792623\pi\) | |||||||
\(632\) | 62.5344 | 2.48748 | ||||||||
\(633\) | −0.0849629 | − | 0.147160i | −0.00337697 | − | 0.00584909i | ||||
\(634\) | 18.2091 | − | 31.5391i | 0.723176 | − | 1.25258i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.22962 | −0.0884102 | ||||||||
\(637\) | −10.3852 | − | 7.65131i | −0.411475 | − | 0.303156i | ||||
\(638\) | 7.46461 | 0.295527 | ||||||||
\(639\) | −2.55707 | + | 4.42898i | −0.101156 | + | 0.175208i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.63046 | − | 4.55610i | −0.103897 | − | 0.179955i | 0.809390 | − | 0.587272i | \(-0.199798\pi\) |
−0.913287 | + | 0.407317i | \(0.866465\pi\) | |||||||
\(642\) | −0.357846 | −0.0141231 | ||||||||
\(643\) | −3.77459 | − | 6.53778i | −0.148855 | − | 0.257825i | 0.781949 | − | 0.623342i | \(-0.214226\pi\) |
−0.930805 | + | 0.365517i | \(0.880892\pi\) | |||||||
\(644\) | 55.2519 | + | 95.6991i | 2.17723 | + | 3.77107i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.4564 | − | 42.3597i | −0.962223 | − | 1.66662i | ||||
\(647\) | −5.77316 | + | 9.99940i | −0.226966 | + | 0.393117i | −0.956908 | − | 0.290393i | \(-0.906214\pi\) |
0.729941 | + | 0.683510i | \(0.239547\pi\) | |||||||
\(648\) | −32.0489 | + | 55.5103i | −1.25900 | + | 2.18065i | ||||
\(649\) | −0.794587 | −0.0311903 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.13322 | −0.122801 | ||||||||
\(652\) | −18.2584 | + | 31.6245i | −0.715054 | + | 1.23851i | ||||
\(653\) | 10.9418 | − | 18.9517i | 0.428185 | − | 0.741639i | −0.568527 | − | 0.822665i | \(-0.692486\pi\) |
0.996712 | + | 0.0810263i | \(0.0258198\pi\) | |||||||
\(654\) | 2.40042 | + | 4.15766i | 0.0938640 | + | 0.162577i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.88418 | + | 3.26350i | 0.0735649 | + | 0.127418i | ||||
\(657\) | 15.7471 | + | 27.2749i | 0.614355 | + | 1.06409i | ||||
\(658\) | 31.8242 | 1.24064 | ||||||||
\(659\) | 16.8561 | + | 29.1957i | 0.656622 | + | 1.13730i | 0.981485 | + | 0.191542i | \(0.0613487\pi\) |
−0.324862 | + | 0.945761i | \(0.605318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.3781 | + | 38.7599i | −0.870405 | + | 1.50759i | −0.00882737 | + | 0.999961i | \(0.502810\pi\) |
−0.861578 | + | 0.507625i | \(0.830523\pi\) | |||||||
\(662\) | 37.2625 | 1.44825 | ||||||||
\(663\) | −0.365612 | + | 3.26925i | −0.0141992 | + | 0.126967i | ||||
\(664\) | 56.7182 | 2.20109 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.8513 | − | 27.4553i | 0.614226 | − | 1.06387i | ||||
\(667\) | −28.8640 | − | 49.9939i | −1.11762 | − | 1.93577i | ||||
\(668\) | −93.9557 | −3.63525 | ||||||||
\(669\) | −0.287483 | − | 0.497936i | −0.0111148 | − | 0.0192513i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.15693 | −0.0832675 | ||||||||
\(672\) | 2.15323 | + | 3.72951i | 0.0830628 | + | 0.143869i | ||||
\(673\) | −6.04859 | + | 10.4765i | −0.233156 | + | 0.403838i | −0.958735 | − | 0.284301i | \(-0.908239\pi\) |
0.725579 | + | 0.688139i | \(0.241572\pi\) | |||||||
\(674\) | 12.0408 | − | 20.8553i | 0.463796 | − | 0.803318i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.4340 | + | 59.4116i | 0.708999 | + | 2.28506i | ||||
\(677\) | 23.3796 | 0.898549 | 0.449275 | − | 0.893394i | \(-0.351682\pi\) | ||||
0.449275 | + | 0.893394i | \(0.351682\pi\) | |||||||
\(678\) | −2.12116 | + | 3.67395i | −0.0814626 | + | 0.141097i | ||||
\(679\) | −11.1756 | + | 19.3567i | −0.428879 | + | 0.742841i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.03087 | −0.0778230 | ||||||||
\(682\) | −3.26828 | − | 5.66083i | −0.125149 | − | 0.216764i | ||||
\(683\) | −3.81319 | − | 6.60464i | −0.145908 | − | 0.252719i | 0.783804 | − | 0.621009i | \(-0.213277\pi\) |
−0.929711 | + | 0.368289i | \(0.879944\pi\) | |||||||
\(684\) | −39.7359 | −1.51934 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14.4966 | + | 25.1088i | −0.553483 | + | 0.958660i | ||||
\(687\) | 0.126424 | − | 0.218973i | 0.00482338 | − | 0.00835434i | ||||
\(688\) | 16.3745 | 0.624271 | ||||||||
\(689\) | 1.37983 | − | 12.3382i | 0.0525674 | − | 0.470050i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8125 | + | 18.7278i | −0.411328 | + | 0.712440i | −0.995035 | − | 0.0995235i | \(-0.968268\pi\) |
0.583707 | + | 0.811964i | \(0.301601\pi\) | |||||||
\(692\) | 17.4111 | − | 30.1570i | 0.661872 | − | 1.14640i | ||||
\(693\) | −1.70910 | − | 2.96024i | −0.0649232 | − | 0.112450i | ||||
\(694\) | −11.8292 | −0.449032 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.99056 | − | 6.91186i | −0.151262 | − | 0.261993i | ||||
\(697\) | −2.72420 | −0.103186 | ||||||||
\(698\) | −27.7432 | − | 48.0527i | −1.05010 | − | 1.81882i | ||||
\(699\) | −1.01993 | + | 1.76657i | −0.0385773 | + | 0.0668179i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.9225 | 0.601386 | 0.300693 | − | 0.953721i | \(-0.402782\pi\) | ||||
0.300693 | + | 0.953721i | \(0.402782\pi\) | |||||||
\(702\) | 6.12040 | + | 4.50923i | 0.231000 | + | 0.170190i | ||||
\(703\) | 11.3682 | 0.428758 | ||||||||
\(704\) | −1.20461 | + | 2.08645i | −0.0454005 | + | 0.0786359i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.3035 | − | 54.2193i | −1.17812 | − | 2.04057i | ||||
\(707\) | 17.9635 | 0.675587 | ||||||||
\(708\) | 0.729830 | + | 1.26410i | 0.0274287 | + | 0.0475079i | ||||
\(709\) | −8.24352 | − | 14.2782i | −0.309592 | − | 0.536229i | 0.668681 | − | 0.743549i | \(-0.266859\pi\) |
−0.978273 | + | 0.207320i | \(0.933526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.8511 | + | 22.2588i | 0.481954 | + | 0.834770i | ||||
\(712\) | 26.0768 | − | 45.1664i | 0.977270 | − | 1.69268i | ||||
\(713\) | −25.2754 | + | 43.7784i | −0.946573 | + | 1.63951i | ||||
\(714\) | −7.72940 | −0.289266 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −71.0711 | −2.65605 | ||||||||
\(717\) | −1.50383 | + | 2.60471i | −0.0561615 | + | 0.0972746i | ||||
\(718\) | −4.64645 | + | 8.04789i | −0.173404 | + | 0.300345i | ||||
\(719\) | −3.59455 | − | 6.22594i | −0.134054 | − | 0.232188i | 0.791182 | − | 0.611581i | \(-0.209466\pi\) |
−0.925236 | + | 0.379393i | \(0.876133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.6801 | + | 28.8908i | 0.621199 | + | 1.07595i | ||||
\(722\) | 14.6436 | + | 25.3634i | 0.544977 | + | 0.943929i | ||||
\(723\) | −0.720462 | −0.0267943 | ||||||||
\(724\) | 29.4183 | + | 50.9540i | 1.09332 | + | 1.89369i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.91677 | − | 3.31994i | 0.0711379 | − | 0.123214i | ||||
\(727\) | −23.2523 | −0.862380 | −0.431190 | − | 0.902261i | \(-0.641906\pi\) | ||||
−0.431190 | + | 0.902261i | \(0.641906\pi\) | |||||||
\(728\) | −77.9437 | + | 34.0834i | −2.88879 | + | 1.26322i | ||||
\(729\) | −26.0162 | −0.963563 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.91866 | + | 10.2514i | −0.218910 | + | 0.379163i | ||||
\(732\) | 1.98115 | + | 3.43145i | 0.0732253 | + | 0.126830i | ||||
\(733\) | −14.5437 | −0.537184 | −0.268592 | − | 0.963254i | \(-0.586558\pi\) | ||||
−0.268592 | + | 0.963254i | \(0.586558\pi\) | |||||||
\(734\) | −34.5198 | − | 59.7901i | −1.27415 | − | 2.20689i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 69.4799 | 2.56106 | ||||||||
\(737\) | 2.06437 | + | 3.57560i | 0.0760421 | + | 0.131709i | ||||
\(738\) | −1.56905 | + | 2.71767i | −0.0577575 | + | 0.100039i | ||||
\(739\) | −14.2972 | + | 24.7635i | −0.525931 | + | 0.910940i | 0.473612 | + | 0.880733i | \(0.342950\pi\) |
−0.999544 | + | 0.0302064i | \(0.990384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.151023 | + | 1.35042i | −0.00554796 | + | 0.0496090i | ||||
\(742\) | 29.1710 | 1.07090 | ||||||||
\(743\) | 1.10527 | − | 1.91439i | 0.0405486 | − | 0.0702322i | −0.845039 | − | 0.534705i | \(-0.820423\pi\) |
0.885587 | + | 0.464473i | \(0.153756\pi\) | |||||||
\(744\) | −3.49443 | + | 6.05253i | −0.128112 | + | 0.221897i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 64.7848 | 2.37194 | ||||||||
\(747\) | 11.6559 | + | 20.1886i | 0.426466 | + | 0.738661i | ||||
\(748\) | −5.68602 | − | 9.84847i | −0.207901 | − | 0.360096i | ||||
\(749\) | 3.30180 | 0.120645 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.1966 | − | 17.6610i | 0.372078 | − | 0.644458i | −0.617807 | − | 0.786330i | \(-0.711979\pi\) |
0.989885 | + | 0.141872i | \(0.0453121\pi\) | |||||||
\(752\) | 17.5179 | − | 30.3419i | 0.638811 | − | 1.10645i | ||||
\(753\) | 2.81874 | 0.102721 | ||||||||
\(754\) | 69.9590 | − | 30.5919i | 2.54776 | − | 1.11409i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.29852 | + | 10.9094i | −0.229075 | + | 0.396769i | ||||
\(757\) | 17.4224 | − | 30.1764i | 0.633227 | − | 1.09678i | −0.353661 | − | 0.935374i | \(-0.615063\pi\) |
0.986888 | − | 0.161408i | \(-0.0516034\pi\) | |||||||
\(758\) | 42.0428 | + | 72.8202i | 1.52706 | + | 2.64495i | ||||
\(759\) | 0.338688 | 0.0122936 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.0535 | + | 39.9298i | 0.835689 | + | 1.44746i | 0.893469 | + | 0.449126i | \(0.148264\pi\) |
−0.0577800 | + | 0.998329i | \(0.518402\pi\) | |||||||
\(762\) | −3.26146 | −0.118150 | ||||||||
\(763\) | −22.1484 | − | 38.3622i | −0.801826 | − | 1.38880i | ||||
\(764\) | 4.01132 | − | 6.94780i | 0.145124 | − | 0.251363i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.16813 | −0.0783377 | ||||||||
\(767\) | −7.44694 | + | 3.25642i | −0.268894 | + | 0.117582i | ||||
\(768\) | −2.47241 | −0.0892154 | ||||||||
\(769\) | 1.02903 | − | 1.78233i | 0.0371077 | − | 0.0642725i | −0.846875 | − | 0.531792i | \(-0.821519\pi\) |
0.883983 | + | 0.467519i | \(0.154852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.07847 | − | 1.86796i | −0.0388400 | − | 0.0672729i | ||||
\(772\) | 13.8031 | 0.496785 | ||||||||
\(773\) | 17.7036 | + | 30.6635i | 0.636754 | + | 1.10289i | 0.986141 | + | 0.165912i | \(0.0530566\pi\) |
−0.349387 | + | 0.936979i | \(0.613610\pi\) | |||||||
\(774\) | 6.81791 | + | 11.8090i | 0.245065 | + | 0.424464i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.9279 | + | 43.1764i | 0.894860 | + | 1.54994i | ||||
\(777\) | 0.898223 | − | 1.55577i | 0.0322236 | − | 0.0558129i | ||||
\(778\) | 46.9683 | − | 81.3514i | 1.68389 | − | 2.91659i | ||||
\(779\) | −1.12528 | −0.0403174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.604576 | −0.0216334 | ||||||||
\(782\) | −62.3525 | + | 107.998i | −2.22972 | + | 3.86199i | ||||
\(783\) | 3.29039 | − | 5.69913i | 0.117589 | − | 0.203670i | ||||
\(784\) | −16.6837 | − | 28.8970i | −0.595846 | − | 1.03204i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.264504 | + | 0.458134i | 0.00943455 | + | 0.0163411i | ||||
\(787\) | 9.46456 | + | 16.3931i | 0.337375 | + | 0.584351i | 0.983938 | − | 0.178510i | \(-0.0571277\pi\) |
−0.646563 | + | 0.762860i | \(0.723794\pi\) | |||||||
\(788\) | 23.8441 | 0.849413 | ||||||||
\(789\) | 1.19761 | + | 2.07433i | 0.0426362 | + | 0.0738480i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.5716 | − | 33.8991i | 0.695888 | − | 1.20531i | ||||
\(792\) | −7.62452 | −0.270926 | ||||||||
\(793\) | −20.2150 | + | 8.83965i | −0.717854 | + | 0.313905i | ||||
\(794\) | −19.7996 | −0.702663 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −54.8323 | + | 94.9723i | −1.94348 | + | 3.36620i | ||||
\(797\) | −8.07586 | − | 13.9878i | −0.286062 | − | 0.495473i | 0.686805 | − | 0.726842i | \(-0.259013\pi\) |
−0.972866 | + | 0.231369i | \(0.925680\pi\) | |||||||
\(798\) | −3.19277 | −0.113023 | ||||||||
\(799\) | 12.6639 | + | 21.9345i | 0.448017 | + | 0.775988i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.4356 | 0.757391 | ||||||||
\(802\) | 25.1746 | + | 43.6037i | 0.888947 | + | 1.53970i | ||||
\(803\) | −1.86157 | + | 3.22434i | −0.0656934 | + | 0.113784i | ||||
\(804\) | 3.79226 | − | 6.56839i | 0.133743 | − | 0.231649i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −53.8301 | − | 39.6596i | −1.89609 | − | 1.39695i | ||||
\(807\) | −0.204547 | −0.00720038 | ||||||||
\(808\) | 20.0344 | − | 34.7006i | 0.704808 | − | 1.22076i | ||||
\(809\) | 11.4370 | − | 19.8095i | 0.402104 | − | 0.696465i | −0.591876 | − | 0.806029i | \(-0.701612\pi\) |
0.993980 | + | 0.109565i | \(0.0349457\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.7279 | −1.88664 | −0.943321 | − | 0.331882i | \(-0.892316\pi\) | ||||
−0.943321 | + | 0.331882i | \(0.892316\pi\) | |||||||
\(812\) | 63.2619 | + | 109.573i | 2.22006 | + | 3.84525i | ||||
\(813\) | 1.84714 | + | 3.19934i | 0.0647820 | + | 0.112206i | ||||
\(814\) | 3.74777 | 0.131359 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.25471 | + | 7.36937i | −0.148945 | + | 0.257980i | ||||
\(817\) | −2.44481 | + | 4.23454i | −0.0855332 | + | 0.148148i | ||||
\(818\) | −40.5957 | −1.41940 | ||||||||
\(819\) | −28.1496 | − | 20.7394i | −0.983628 | − | 0.724692i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.4717 | − | 25.0657i | 0.505066 | − | 0.874800i | −0.494917 | − | 0.868940i | \(-0.664801\pi\) |
0.999983 | − | 0.00585988i | \(-0.00186527\pi\) | |||||||
\(822\) | −0.206528 | + | 0.357718i | −0.00720351 | + | 0.0124768i | ||||
\(823\) | 20.8724 | + | 36.1520i | 0.727565 | + | 1.26018i | 0.957910 | + | 0.287070i | \(0.0926811\pi\) |
−0.230345 | + | 0.973109i | \(0.573986\pi\) | |||||||
\(824\) | 74.4123 | 2.59227 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.54867 | − | 16.5388i | −0.332241 | − | 0.575458i | ||||
\(827\) | 11.5286 | 0.400888 | 0.200444 | − | 0.979705i | \(-0.435761\pi\) | ||||
0.200444 | + | 0.979705i | \(0.435761\pi\) | |||||||
\(828\) | 50.6542 | + | 87.7356i | 1.76035 | + | 3.04902i | ||||
\(829\) | 14.4032 | − | 24.9471i | 0.500244 | − | 0.866448i | −0.499756 | − | 0.866166i | \(-0.666577\pi\) |
1.00000 | 0.000281967i | \(-8.97530e-5\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.355003 | 0.0123149 | ||||||||
\(832\) | −2.73894 | + | 24.4912i | −0.0949555 | + | 0.849078i | ||||
\(833\) | 24.1217 | 0.835769 | ||||||||
\(834\) | 2.20903 | − | 3.82615i | 0.0764924 | − | 0.132489i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.34872 | − | 4.06810i | −0.0812320 | − | 0.140698i | ||||
\(837\) | −5.76262 | −0.199185 | ||||||||
\(838\) | 32.9760 | + | 57.1161i | 1.13914 | + | 1.97304i | ||||
\(839\) | −9.38900 | − | 16.2622i | −0.324144 | − | 0.561434i | 0.657195 | − | 0.753721i | \(-0.271743\pi\) |
−0.981339 | + | 0.192287i | \(0.938410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.5485 | − | 32.1269i | −0.639602 | − | 1.10782i | ||||
\(842\) | 11.2673 | − | 19.5156i | 0.388298 | − | 0.672551i | ||||
\(843\) | −0.608113 | + | 1.05328i | −0.0209445 | + | 0.0362770i | ||||
\(844\) | 6.00873 | 0.206829 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.1760 | 1.00309 | ||||||||
\(847\) | −17.6858 | + | 30.6326i | −0.607690 | + | 1.05255i | ||||
\(848\) | 16.0574 | − | 27.8123i | 0.551414 | − | 0.955077i | ||||
\(849\) | −1.58590 | − | 2.74686i | −0.0544280 | − | 0.0942720i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.4918 | − | 25.1005i | −0.496773 | − | 0.860435i | ||||
\(852\) | 0.555304 | + | 0.961815i | 0.0190244 | + | 0.0329512i | ||||
\(853\) | −26.7981 | −0.917550 | −0.458775 | − | 0.888553i | \(-0.651712\pi\) | ||||
−0.458775 | + | 0.888553i | \(0.651712\pi\) | |||||||
\(854\) | −25.9202 | − | 44.8950i | −0.886970 | − | 1.53628i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.68245 | − | 6.37819i | 0.125864 | − | 0.218002i | ||||
\(857\) | −5.34675 | −0.182641 | −0.0913207 | − | 0.995822i | \(-0.529109\pi\) | ||||
−0.0913207 | + | 0.995822i | \(0.529109\pi\) | |||||||
\(858\) | −0.0497881 | + | 0.445197i | −0.00169974 | + | 0.0151988i | ||||
\(859\) | −28.4574 | −0.970954 | −0.485477 | − | 0.874249i | \(-0.661354\pi\) | ||||
−0.485477 | + | 0.874249i | \(0.661354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0889110 | + | 0.153998i | −0.00303008 | + | 0.00524825i | ||||
\(862\) | −17.4764 | − | 30.2701i | −0.595250 | − | 1.03100i | ||||
\(863\) | 12.2695 | 0.417659 | 0.208830 | − | 0.977952i | \(-0.433035\pi\) | ||||
0.208830 | + | 0.977952i | \(0.433035\pi\) | |||||||
\(864\) | 3.96023 | + | 6.85932i | 0.134730 | + | 0.233359i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 94.2182 | 3.20166 | ||||||||
\(867\) | −1.92556 | − | 3.33517i | −0.0653956 | − | 0.113268i | ||||
\(868\) | 55.3967 | − | 95.9500i | 1.88029 | − | 3.25675i | ||||
\(869\) | −1.51921 | + | 2.63135i | −0.0515358 | + | 0.0892625i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.0012 | + | 25.0505i | 1.15209 | + | 0.848804i | ||||
\(872\) | −98.8071 | −3.34603 | ||||||||
\(873\) | −10.2456 | + | 17.7459i | −0.346761 | + | 0.600608i | ||||
\(874\) | −25.7559 | + | 44.6105i | −0.871206 | + | 1.50897i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.83943 | 0.231083 | ||||||||
\(877\) | −23.5508 | − | 40.7912i | −0.795255 | − | 1.37742i | −0.922677 | − | 0.385573i | \(-0.874004\pi\) |
0.127422 | − | 0.991849i | \(-0.459330\pi\) | |||||||
\(878\) | −43.0626 | − | 74.5867i | −1.45329 | − | 2.51718i | ||||
\(879\) | −0.159227 | −0.00537058 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.11197 | − | 12.3183i | 0.239608 | − | 0.415014i | −0.720994 | − | 0.692942i | \(-0.756314\pi\) |
0.960602 | + | 0.277928i | \(0.0896476\pi\) | |||||||
\(882\) | 13.8933 | − | 24.0639i | 0.467813 | − | 0.810275i | ||||
\(883\) | −8.05745 | −0.271155 | −0.135577 | − | 0.990767i | \(-0.543289\pi\) | ||||
−0.135577 | + | 0.990767i | \(0.543289\pi\) | |||||||
\(884\) | −93.6514 | − | 68.9980i | −3.14984 | − | 2.32066i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.1540 | − | 40.1039i | 0.777873 | − | 1.34732i | ||||
\(887\) | −14.3419 | + | 24.8408i | −0.481552 | + | 0.834073i | −0.999776 | − | 0.0211719i | \(-0.993260\pi\) |
0.518223 | + | 0.855245i | \(0.326594\pi\) | |||||||
\(888\) | −2.00355 | − | 3.47025i | −0.0672347 | − | 0.116454i | ||||
\(889\) | 30.0931 | 1.00929 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.55719 | − | 2.69714i | −0.0521680 | − | 0.0903575i | ||||
\(892\) | 20.3314 | 0.680744 | ||||||||
\(893\) | 5.23107 | + | 9.06047i | 0.175051 | + | 0.303197i | ||||
\(894\) | 3.44772 | − | 5.97163i | 0.115309 | − | 0.199721i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.74453 | 0.191911 | ||||||||
\(897\) | 3.17421 | − | 1.38803i | 0.105984 | − | 0.0463449i | ||||
\(898\) | −82.9130 | −2.76684 | ||||||||
\(899\) | −28.9397 | + | 50.1250i | −0.965192 | + | 1.67176i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6081 | + | 20.1059i | 0.386723 | + | 0.669823i | ||||
\(902\) | −0.370975 | −0.0123521 | ||||||||
\(903\) | 0.386340 | + | 0.669161i | 0.0128566 | + | 0.0222683i | ||||
\(904\) | −43.6559 | − | 75.6143i | −1.45197 | − | 2.51489i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.75258 | − | 3.03555i | −0.0582255 | − | 0.100850i | ||||
\(907\) | −14.4414 | + | 25.0133i | −0.479520 | + | 0.830553i | −0.999724 | − | 0.0234890i | \(-0.992523\pi\) |
0.520204 | + | 0.854042i | \(0.325856\pi\) | |||||||
\(908\) | 35.9067 | − | 62.1921i | 1.19160 | − | 2.06392i | ||||
\(909\) | 16.4687 | 0.546231 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.3270 | −0.805991 | −0.402995 | − | 0.915202i | \(-0.632031\pi\) | ||||
−0.402995 | + | 0.915202i | \(0.632031\pi\) | |||||||
\(912\) | −1.75749 | + | 3.04406i | −0.0581962 | + | 0.100799i | ||||
\(913\) | −1.37791 | + | 2.38662i | −0.0456023 | + | 0.0789855i | ||||
\(914\) | 28.6491 | + | 49.6217i | 0.947629 | + | 1.64134i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.47048 | + | 7.74309i | 0.147709 | + | 0.255839i | ||||
\(917\) | −2.44054 | − | 4.22715i | −0.0805939 | − | 0.139593i | ||||
\(918\) | −14.2159 | −0.469196 | ||||||||
\(919\) | 5.86947 | + | 10.1662i | 0.193616 | + | 0.335353i | 0.946446 | − | 0.322862i | \(-0.104645\pi\) |
−0.752830 | + | 0.658215i | \(0.771312\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.12417 | + | 1.94713i | −0.0370428 | + | 0.0641600i | ||||
\(922\) | −35.7728 | −1.17812 | ||||||||
\(923\) | −5.66614 | + | 2.47770i | −0.186503 | + | 0.0815546i | ||||
\(924\) | −0.742309 | −0.0244202 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.46823 | + | 16.3995i | −0.311145 | + | 0.538920i | ||||
\(927\) | 15.2921 | + | 26.4866i | 0.502258 | + | 0.869936i | ||||
\(928\) | 79.5525 | 2.61144 | ||||||||
\(929\) | 21.6632 | + | 37.5218i | 0.710746 | + | 1.23105i | 0.964577 | + | 0.263800i | \(0.0849760\pi\) |
−0.253831 | + | 0.967249i | \(0.581691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.96394 | 0.326555 | ||||||||
\(932\) | −36.0657 | − | 62.4676i | −1.18137 | − | 2.04619i | ||||
\(933\) | 0.995480 | − | 1.72422i | 0.0325905 | − | 0.0564485i | ||||
\(934\) | −40.3275 | + | 69.8493i | −1.31956 | + | 2.28554i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −71.4577 | + | 31.2472i | −2.33567 | + | 1.02135i | ||||
\(937\) | −29.8349 | −0.974663 | −0.487331 | − | 0.873217i | \(-0.662030\pi\) | ||||
−0.487331 | + | 0.873217i | \(0.662030\pi\) | |||||||
\(938\) | −49.6157 | + | 85.9369i | −1.62001 | + | 2.80594i | ||||
\(939\) | −0.125977 | + | 0.218198i | −0.00411109 | + | 0.00712062i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.53619 | −0.245673 | −0.122836 | − | 0.992427i | \(-0.539199\pi\) | ||||
−0.122836 | + | 0.992427i | \(0.539199\pi\) | |||||||
\(942\) | −1.16483 | − | 2.01754i | −0.0379521 | − | 0.0657349i | ||||
\(943\) | 1.43448 | + | 2.48459i | 0.0467130 | + | 0.0809093i | ||||
\(944\) | −21.0245 | −0.684291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.805989 | + | 1.39601i | −0.0262050 | + | 0.0453883i | ||||
\(947\) | 0.953323 | − | 1.65120i | 0.0309788 | − | 0.0536569i | −0.850120 | − | 0.526588i | \(-0.823471\pi\) |
0.881099 | + | 0.472932i | \(0.156804\pi\) | |||||||
\(948\) | 5.58160 | 0.181282 | ||||||||
\(949\) | −4.23267 | + | 37.8480i | −0.137398 | + | 1.22860i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.945966 | − | 1.63846i | 0.0306751 | − | 0.0531307i | ||||
\(952\) | 79.5401 | − | 137.768i | 2.57791 | − | 4.46507i | ||||
\(953\) | −8.40543 | − | 14.5586i | −0.272279 | − | 0.471600i | 0.697166 | − | 0.716909i | \(-0.254444\pi\) |
−0.969445 | + | 0.245309i | \(0.921111\pi\) | |||||||
\(954\) | 26.7436 | 0.865855 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −53.1768 | − | 92.1049i | −1.71986 | − | 2.97888i | ||||
\(957\) | 0.387788 | 0.0125354 | ||||||||
\(958\) | 10.7424 | + | 18.6065i | 0.347073 | + | 0.601147i | ||||
\(959\) | 1.90561 | − | 3.30062i | 0.0615354 | − | 0.106582i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.6834 | 0.634948 | ||||||||
\(962\) | 35.1244 | − | 15.3593i | 1.13246 | − | 0.495204i | ||||
\(963\) | 3.02704 | 0.0975452 | ||||||||
\(964\) | 12.7381 | − | 22.0630i | 0.410266 | − | 0.710602i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.07006 | + | 7.04955i | 0.130952 | + | 0.226815i | ||||
\(967\) | 36.1265 | 1.16175 | 0.580874 | − | 0.813993i | \(-0.302711\pi\) | ||||
0.580874 | + | 0.813993i | \(0.302711\pi\) | |||||||
\(968\) | 39.4493 | + | 68.3283i | 1.26795 | + | 2.19615i | ||||
\(969\) | −1.27051 | − | 2.20059i | −0.0408147 | − | 0.0706931i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.42596 | − | 16.3262i | −0.302494 | − | 0.523934i | 0.674207 | − | 0.738543i | \(-0.264486\pi\) |
−0.976700 | + | 0.214609i | \(0.931152\pi\) | |||||||
\(972\) | −8.67043 | + | 15.0176i | −0.278104 | + | 0.481690i | ||||
\(973\) | −20.3824 | + | 35.3034i | −0.653430 | + | 1.13177i | ||||
\(974\) | −77.6211 | −2.48714 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.0718 | −1.82682 | ||||||||
\(977\) | 16.1888 | − | 28.0399i | 0.517926 | − | 0.897074i | −0.481857 | − | 0.876250i | \(-0.660038\pi\) |
0.999783 | − | 0.0208245i | \(-0.00662913\pi\) | |||||||
\(978\) | −1.34498 | + | 2.32957i | −0.0430077 | + | 0.0744915i | ||||
\(979\) | 1.26702 | + | 2.19455i | 0.0404942 | + | 0.0701380i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.3053 | − | 35.1699i | −0.648299 | − | 1.12289i | ||||
\(982\) | −49.9677 | − | 86.5465i | −1.59453 | − | 2.76181i | ||||
\(983\) | −19.3591 | −0.617459 | −0.308729 | − | 0.951150i | \(-0.599904\pi\) | ||||
−0.308729 | + | 0.951150i | \(0.599904\pi\) | |||||||
\(984\) | 0.198322 | + | 0.343504i | 0.00632228 | + | 0.0109505i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −71.3919 | + | 123.654i | −2.27358 | + | 3.93796i | ||||
\(987\) | 1.65327 | 0.0526242 | ||||||||
\(988\) | −38.6845 | − | 28.5009i | −1.23072 | − | 0.906735i | ||||
\(989\) | 12.4663 | 0.396406 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4005 | + | 33.6027i | −0.616278 | + | 1.06742i | 0.373881 | + | 0.927477i | \(0.378027\pi\) |
−0.990159 | + | 0.139948i | \(0.955307\pi\) | |||||||
\(992\) | −34.8310 | − | 60.3291i | −1.10589 | − | 1.91545i | ||||
\(993\) | 1.93579 | 0.0614305 | ||||||||
\(994\) | −7.26527 | − | 12.5838i | −0.230440 | − | 0.399135i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.06247 | 0.160411 | ||||||||
\(997\) | 26.3337 | + | 45.6114i | 0.833998 | + | 1.44453i | 0.894844 | + | 0.446379i | \(0.147287\pi\) |
−0.0608463 | + | 0.998147i | \(0.519380\pi\) | |||||||
\(998\) | 39.0518 | − | 67.6397i | 1.23616 | − | 2.14110i | ||||
\(999\) | 1.65201 | − | 2.86137i | 0.0522674 | − | 0.0905298i |
(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 | 325.2.e.c.126.1 | ✓ | 10 | |
5.2 | odd | 4 | 325.2.o.c.74.1 | 20 | |||
5.3 | odd | 4 | 325.2.o.c.74.10 | 20 | |||
5.4 | even | 2 | 325.2.e.d.126.5 | yes | 10 | ||
13.3 | even | 3 | inner | 325.2.e.c.276.1 | yes | 10 | |
13.4 | even | 6 | 4225.2.a.bo.1.1 | 5 | |||
13.9 | even | 3 | 4225.2.a.bp.1.5 | 5 | |||
65.3 | odd | 12 | 325.2.o.c.224.1 | 20 | |||
65.4 | even | 6 | 4225.2.a.bm.1.5 | 5 | |||
65.9 | even | 6 | 4225.2.a.bn.1.1 | 5 | |||
65.29 | even | 6 | 325.2.e.d.276.5 | yes | 10 | ||
65.42 | odd | 12 | 325.2.o.c.224.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.e.c.126.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
325.2.e.c.276.1 | yes | 10 | 13.3 | even | 3 | inner | |
325.2.e.d.126.5 | yes | 10 | 5.4 | even | 2 | ||
325.2.e.d.276.5 | yes | 10 | 65.29 | even | 6 | ||
325.2.o.c.74.1 | 20 | 5.2 | odd | 4 | |||
325.2.o.c.74.10 | 20 | 5.3 | odd | 4 | |||
325.2.o.c.224.1 | 20 | 65.3 | odd | 12 | |||
325.2.o.c.224.10 | 20 | 65.42 | odd | 12 | |||
4225.2.a.bm.1.5 | 5 | 65.4 | even | 6 | |||
4225.2.a.bn.1.1 | 5 | 65.9 | even | 6 | |||
4225.2.a.bo.1.1 | 5 | 13.4 | even | 6 | |||
4225.2.a.bp.1.5 | 5 | 13.9 | even | 3 |