Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(451,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, 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("975.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.i (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: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1714608.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 451.2 | ||
Root | \(0.500000 - 1.75780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.451 |
Dual form | 975.2.i.l.601.2 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.169938 | + | 0.294342i | −0.120165 | + | 0.208131i | −0.919832 | − | 0.392311i | \(-0.871676\pi\) |
0.799668 | + | 0.600443i | \(0.205009\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.942242 | + | 1.63201i | 0.471121 | + | 0.816005i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.169938 | − | 0.294342i | −0.0693771 | − | 0.120165i | ||||
\(7\) | 0.330062 | + | 0.571683i | 0.124752 | + | 0.216076i | 0.921636 | − | 0.388056i | \(-0.126853\pi\) |
−0.796884 | + | 0.604132i | \(0.793520\pi\) | |||||||
\(8\) | −1.32025 | −0.466778 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.339877 | + | 0.588684i | −0.102477 | + | 0.177495i | −0.912704 | − | 0.408620i | \(-0.866010\pi\) |
0.810228 | + | 0.586115i | \(0.199343\pi\) | |||||||
\(12\) | −1.88448 | −0.544004 | ||||||||
\(13\) | −1.93243 | − | 3.04397i | −0.535959 | − | 0.844244i | ||||
\(14\) | −0.224361 | −0.0599629 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.66012 | + | 2.87542i | −0.415031 | + | 0.718854i | ||||
\(17\) | 3.71455 | + | 6.43378i | 0.900910 | + | 1.56042i | 0.826316 | + | 0.563207i | \(0.190433\pi\) |
0.0745938 | + | 0.997214i | \(0.476234\pi\) | |||||||
\(18\) | 0.339877 | 0.0801098 | ||||||||
\(19\) | −0.0577581 | − | 0.100040i | −0.0132506 | − | 0.0229508i | 0.859324 | − | 0.511431i | \(-0.170885\pi\) |
−0.872575 | + | 0.488481i | \(0.837551\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.660123 | −0.144051 | ||||||||
\(22\) | −0.115516 | − | 0.200080i | −0.0246282 | − | 0.0426572i | ||||
\(23\) | −3.88448 | + | 6.72812i | −0.809971 | + | 1.40291i | 0.102913 | + | 0.994690i | \(0.467184\pi\) |
−0.912883 | + | 0.408220i | \(0.866150\pi\) | |||||||
\(24\) | 0.660123 | − | 1.14337i | 0.134747 | − | 0.233389i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.22436 | − | 0.0515075i | 0.240117 | − | 0.0101015i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.621996 | + | 1.07733i | −0.117546 | + | 0.203596i | ||||
\(29\) | −2.77230 | + | 4.80177i | −0.514804 | + | 0.891666i | 0.485049 | + | 0.874487i | \(0.338802\pi\) |
−0.999852 | + | 0.0171792i | \(0.994531\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.97370 | −1.79133 | −0.895664 | − | 0.444730i | \(-0.853299\pi\) | ||||
−0.895664 | + | 0.444730i | \(0.853299\pi\) | |||||||
\(32\) | −1.88448 | − | 3.26402i | −0.333133 | − | 0.577003i | ||||
\(33\) | −0.339877 | − | 0.588684i | −0.0591650 | − | 0.102477i | ||||
\(34\) | −2.52498 | −0.433030 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.942242 | − | 1.63201i | 0.157040 | − | 0.272002i | ||||
\(37\) | 4.88448 | − | 8.46017i | 0.803004 | − | 1.39084i | −0.114626 | − | 0.993409i | \(-0.536567\pi\) |
0.917630 | − | 0.397435i | \(-0.130100\pi\) | |||||||
\(38\) | 0.0392613 | 0.00636903 | ||||||||
\(39\) | 3.60236 | − | 0.151548i | 0.576840 | − | 0.0242670i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.11218 | + | 3.65840i | −0.329867 | + | 0.571347i | −0.982485 | − | 0.186340i | \(-0.940337\pi\) |
0.652618 | + | 0.757687i | \(0.273671\pi\) | |||||||
\(42\) | 0.112180 | − | 0.194302i | 0.0173098 | − | 0.0299814i | ||||
\(43\) | −0.272303 | − | 0.471643i | −0.0415259 | − | 0.0719249i | 0.844515 | − | 0.535531i | \(-0.179889\pi\) |
−0.886041 | + | 0.463606i | \(0.846555\pi\) | |||||||
\(44\) | −1.28098 | −0.193116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.32025 | − | 2.28673i | −0.194660 | − | 0.337160i | ||||
\(47\) | 5.01963 | 0.732188 | 0.366094 | − | 0.930578i | \(-0.380695\pi\) | ||||
0.366094 | + | 0.930578i | \(0.380695\pi\) | |||||||
\(48\) | −1.66012 | − | 2.87542i | −0.239618 | − | 0.415031i | ||||
\(49\) | 3.28212 | − | 5.68480i | 0.468874 | − | 0.812114i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.42909 | −1.04028 | ||||||||
\(52\) | 3.14697 | − | 6.02189i | 0.436406 | − | 0.835086i | ||||
\(53\) | −0.679754 | −0.0933714 | −0.0466857 | − | 0.998910i | \(-0.514866\pi\) | ||||
−0.0466857 | + | 0.998910i | \(0.514866\pi\) | |||||||
\(54\) | −0.169938 | + | 0.294342i | −0.0231257 | + | 0.0400549i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.435763 | − | 0.754763i | −0.0582312 | − | 0.100859i | ||||
\(57\) | 0.115516 | 0.0153005 | ||||||||
\(58\) | −0.942242 | − | 1.63201i | −0.123722 | − | 0.214294i | ||||
\(59\) | −1.11218 | − | 1.92635i | −0.144794 | − | 0.250790i | 0.784502 | − | 0.620126i | \(-0.212918\pi\) |
−0.929296 | + | 0.369336i | \(0.879585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.10236 | + | 3.64140i | 0.269180 | + | 0.466234i | 0.968650 | − | 0.248428i | \(-0.0799139\pi\) |
−0.699470 | + | 0.714662i | \(0.746581\pi\) | |||||||
\(62\) | 1.69491 | − | 2.93568i | 0.215254 | − | 0.372832i | ||||
\(63\) | 0.330062 | − | 0.571683i | 0.0415838 | − | 0.0720253i | ||||
\(64\) | −5.35951 | −0.669938 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.231033 | 0.0284381 | ||||||||
\(67\) | −3.81691 | + | 6.61108i | −0.466310 | + | 0.807672i | −0.999260 | − | 0.0384746i | \(-0.987750\pi\) |
0.532950 | + | 0.846147i | \(0.321083\pi\) | |||||||
\(68\) | −7.00000 | + | 12.1244i | −0.848875 | + | 1.47029i | ||||
\(69\) | −3.88448 | − | 6.72812i | −0.467637 | − | 0.809971i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.65679 | − | 6.33374i | −0.433981 | − | 0.751677i | 0.563231 | − | 0.826299i | \(-0.309558\pi\) |
−0.997212 | + | 0.0746227i | \(0.976225\pi\) | |||||||
\(72\) | 0.660123 | + | 1.14337i | 0.0777963 | + | 0.134747i | ||||
\(73\) | −8.01963 | −0.938627 | −0.469313 | − | 0.883032i | \(-0.655499\pi\) | ||||
−0.469313 | + | 0.883032i | \(0.655499\pi\) | |||||||
\(74\) | 1.66012 | + | 2.87542i | 0.192985 | + | 0.334261i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.108844 | − | 0.188524i | 0.0124853 | − | 0.0216252i | ||||
\(77\) | −0.448721 | −0.0511365 | ||||||||
\(78\) | −0.567573 | + | 1.08608i | −0.0642650 | + | 0.122974i | ||||
\(79\) | 9.97370 | 1.12213 | 0.561064 | − | 0.827772i | \(-0.310392\pi\) | ||||
0.561064 | + | 0.827772i | \(0.310392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.717881 | − | 1.24341i | −0.0792767 | − | 0.137311i | ||||
\(83\) | −1.76897 | −0.194169 | −0.0970847 | − | 0.995276i | \(-0.530952\pi\) | ||||
−0.0970847 | + | 0.995276i | \(0.530952\pi\) | |||||||
\(84\) | −0.621996 | − | 1.07733i | −0.0678653 | − | 0.117546i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.185099 | 0.0199598 | ||||||||
\(87\) | −2.77230 | − | 4.80177i | −0.297222 | − | 0.514804i | ||||
\(88\) | 0.448721 | − | 0.777208i | 0.0478338 | − | 0.0828506i | ||||
\(89\) | −6.77230 | + | 11.7300i | −0.717863 | + | 1.24337i | 0.243982 | + | 0.969780i | \(0.421546\pi\) |
−0.961845 | + | 0.273595i | \(0.911787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.10236 | − | 2.10943i | 0.115559 | − | 0.221129i | ||||
\(92\) | −14.6405 | −1.52638 | ||||||||
\(93\) | 4.98685 | − | 8.63748i | 0.517112 | − | 0.895664i | ||||
\(94\) | −0.853028 | + | 1.47749i | −0.0879831 | + | 0.152391i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.76897 | 0.384669 | ||||||||
\(97\) | 4.95206 | + | 8.57721i | 0.502805 | + | 0.870884i | 0.999995 | + | 0.00324223i | \(0.00103204\pi\) |
−0.497190 | + | 0.867642i | \(0.665635\pi\) | |||||||
\(98\) | 1.11552 | + | 1.93213i | 0.112684 | + | 0.195175i | ||||
\(99\) | 0.679754 | 0.0683178 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.67975 | − | 8.10557i | 0.465653 | − | 0.806534i | −0.533578 | − | 0.845751i | \(-0.679153\pi\) |
0.999231 | + | 0.0392165i | \(0.0124862\pi\) | |||||||
\(102\) | 1.26249 | − | 2.18669i | 0.125005 | − | 0.216515i | ||||
\(103\) | −4.50535 | −0.443925 | −0.221962 | − | 0.975055i | \(-0.571246\pi\) | ||||
−0.221962 | + | 0.975055i | \(0.571246\pi\) | |||||||
\(104\) | 2.55128 | + | 4.01878i | 0.250173 | + | 0.394074i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.115516 | − | 0.200080i | 0.0112199 | − | 0.0194335i | ||||
\(107\) | 0.285455 | − | 0.494422i | 0.0275960 | − | 0.0477976i | −0.851898 | − | 0.523708i | \(-0.824548\pi\) |
0.879494 | + | 0.475911i | \(0.157881\pi\) | |||||||
\(108\) | 0.942242 | + | 1.63201i | 0.0906673 | + | 0.157040i | ||||
\(109\) | 15.4095 | 1.47596 | 0.737979 | − | 0.674823i | \(-0.235780\pi\) | ||||
0.737979 | + | 0.674823i | \(0.235780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.88448 | + | 8.46017i | 0.463615 | + | 0.803004i | ||||
\(112\) | −2.19177 | −0.207103 | ||||||||
\(113\) | −2.66012 | − | 4.60747i | −0.250243 | − | 0.433434i | 0.713349 | − | 0.700809i | \(-0.247177\pi\) |
−0.963593 | + | 0.267374i | \(0.913844\pi\) | |||||||
\(114\) | −0.0196307 | + | 0.0340013i | −0.00183858 | + | 0.00318451i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.4487 | −0.970139 | ||||||||
\(117\) | −1.66994 | + | 3.19551i | −0.154386 | + | 0.295425i | ||||
\(118\) | 0.756009 | 0.0695962 | ||||||||
\(119\) | −2.45206 | + | 4.24709i | −0.224780 | + | 0.389330i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.26897 | + | 9.12612i | 0.478997 | + | 0.829647i | ||||
\(122\) | −1.42909 | −0.129384 | ||||||||
\(123\) | −2.11218 | − | 3.65840i | −0.190449 | − | 0.329867i | ||||
\(124\) | −9.39764 | − | 16.2772i | −0.843933 | − | 1.46173i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.112180 | + | 0.194302i | 0.00999381 | + | 0.0173098i | ||||
\(127\) | −6.00982 | + | 10.4093i | −0.533285 | + | 0.923676i | 0.465959 | + | 0.884806i | \(0.345709\pi\) |
−0.999244 | + | 0.0388704i | \(0.987624\pi\) | |||||||
\(128\) | 4.67975 | − | 8.10557i | 0.413636 | − | 0.716438i | ||||
\(129\) | 0.544607 | 0.0479500 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9041 | 0.952697 | 0.476348 | − | 0.879257i | \(-0.341960\pi\) | ||||
0.476348 | + | 0.879257i | \(0.341960\pi\) | |||||||
\(132\) | 0.640492 | − | 1.10937i | 0.0557477 | − | 0.0965579i | ||||
\(133\) | 0.0381275 | − | 0.0660387i | 0.00330607 | − | 0.00572629i | ||||
\(134\) | −1.29728 | − | 2.24695i | −0.112068 | − | 0.194107i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.90411 | − | 8.49418i | −0.420524 | − | 0.728370i | ||||
\(137\) | 1.69491 | + | 2.93568i | 0.144806 | + | 0.250812i | 0.929301 | − | 0.369324i | \(-0.120411\pi\) |
−0.784494 | + | 0.620136i | \(0.787077\pi\) | |||||||
\(138\) | 2.64049 | 0.224774 | ||||||||
\(139\) | −7.40411 | − | 12.8243i | −0.628009 | − | 1.08774i | −0.987951 | − | 0.154768i | \(-0.950537\pi\) |
0.359942 | − | 0.932975i | \(-0.382796\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.50982 | + | 4.34713i | −0.211365 | + | 0.366094i | ||||
\(142\) | 2.48571 | 0.208597 | ||||||||
\(143\) | 2.44872 | − | 0.103015i | 0.204772 | − | 0.00861455i | ||||
\(144\) | 3.32025 | 0.276687 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.36284 | − | 2.36051i | 0.112790 | − | 0.195358i | ||||
\(147\) | 3.28212 | + | 5.68480i | 0.270705 | + | 0.468874i | ||||
\(148\) | 18.4095 | 1.51325 | ||||||||
\(149\) | 8.54461 | + | 14.7997i | 0.700001 | + | 1.21244i | 0.968465 | + | 0.249148i | \(0.0801507\pi\) |
−0.268464 | + | 0.963290i | \(0.586516\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0130 | 1.05898 | 0.529490 | − | 0.848316i | \(-0.322383\pi\) | ||||
0.529490 | + | 0.848316i | \(0.322383\pi\) | |||||||
\(152\) | 0.0762550 | + | 0.132077i | 0.00618510 | + | 0.0107129i | ||||
\(153\) | 3.71455 | − | 6.43378i | 0.300303 | − | 0.520140i | ||||
\(154\) | 0.0762550 | − | 0.132077i | 0.00614480 | − | 0.0106431i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.64163 | + | 5.73630i | 0.291563 | + | 0.459272i | ||||
\(157\) | 0.775639 | 0.0619028 | 0.0309514 | − | 0.999521i | \(-0.490146\pi\) | ||||
0.0309514 | + | 0.999521i | \(0.490146\pi\) | |||||||
\(158\) | −1.69491 | + | 2.93568i | −0.134840 | + | 0.233550i | ||||
\(159\) | 0.339877 | − | 0.588684i | 0.0269540 | − | 0.0466857i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.12847 | −0.404180 | ||||||||
\(162\) | −0.169938 | − | 0.294342i | −0.0133516 | − | 0.0231257i | ||||
\(163\) | 6.09903 | + | 10.5638i | 0.477713 | + | 0.827423i | 0.999674 | − | 0.0255466i | \(-0.00813262\pi\) |
−0.521961 | + | 0.852969i | \(0.674799\pi\) | |||||||
\(164\) | −7.96074 | −0.621629 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.300616 | − | 0.520681i | 0.0233323 | − | 0.0404127i | ||||
\(167\) | −0.795270 | + | 1.37745i | −0.0615398 | + | 0.106590i | −0.895154 | − | 0.445757i | \(-0.852934\pi\) |
0.833614 | + | 0.552347i | \(0.186268\pi\) | |||||||
\(168\) | 0.871525 | 0.0672396 | ||||||||
\(169\) | −5.53146 | + | 11.7645i | −0.425497 | + | 0.904960i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0577581 | + | 0.100040i | −0.00441688 | + | 0.00765025i | ||||
\(172\) | 0.513151 | − | 0.888804i | 0.0391274 | − | 0.0677707i | ||||
\(173\) | 6.37467 | + | 11.0412i | 0.484657 | + | 0.839451i | 0.999845 | − | 0.0176268i | \(-0.00561108\pi\) |
−0.515188 | + | 0.857077i | \(0.672278\pi\) | |||||||
\(174\) | 1.88448 | 0.142862 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.12847 | − | 1.95458i | −0.0850620 | − | 0.147332i | ||||
\(177\) | 2.22436 | 0.167193 | ||||||||
\(178\) | −2.30175 | − | 3.98675i | −0.172523 | − | 0.298819i | ||||
\(179\) | −8.88115 | + | 15.3826i | −0.663808 | + | 1.14975i | 0.315799 | + | 0.948826i | \(0.397728\pi\) |
−0.979607 | + | 0.200923i | \(0.935606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.02630 | 0.522261 | 0.261130 | − | 0.965304i | \(-0.415905\pi\) | ||||
0.261130 | + | 0.965304i | \(0.415905\pi\) | |||||||
\(182\) | 0.433560 | + | 0.682946i | 0.0321376 | + | 0.0506233i | ||||
\(183\) | −4.20473 | −0.310823 | ||||||||
\(184\) | 5.12847 | − | 8.88278i | 0.378076 | − | 0.654847i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.69491 | + | 2.93568i | 0.124277 | + | 0.215254i | ||||
\(187\) | −5.04995 | −0.369289 | ||||||||
\(188\) | 4.72971 | + | 8.19209i | 0.344949 | + | 0.597470i | ||||
\(189\) | 0.330062 | + | 0.571683i | 0.0240084 | + | 0.0415838i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.97703 | + | 12.0846i | 0.504840 | + | 0.874409i | 0.999984 | + | 0.00559828i | \(0.00178200\pi\) |
−0.495144 | + | 0.868811i | \(0.664885\pi\) | |||||||
\(192\) | 2.67975 | − | 4.64147i | 0.193395 | − | 0.334969i | ||||
\(193\) | 11.8747 | − | 20.5675i | 0.854757 | − | 1.48048i | −0.0221126 | − | 0.999755i | \(-0.507039\pi\) |
0.876870 | − | 0.480728i | \(-0.159627\pi\) | |||||||
\(194\) | −3.36618 | −0.241678 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.3702 | 0.883586 | ||||||||
\(197\) | 7.90411 | − | 13.6903i | 0.563145 | − | 0.975395i | −0.434075 | − | 0.900877i | \(-0.642925\pi\) |
0.997220 | − | 0.0745186i | \(-0.0237420\pi\) | |||||||
\(198\) | −0.115516 | + | 0.200080i | −0.00820939 | + | 0.0142191i | ||||
\(199\) | −4.38448 | − | 7.59415i | −0.310808 | − | 0.538335i | 0.667730 | − | 0.744404i | \(-0.267266\pi\) |
−0.978537 | + | 0.206069i | \(0.933933\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.81691 | − | 6.61108i | −0.269224 | − | 0.466310i | ||||
\(202\) | 1.59054 | + | 2.75490i | 0.111910 | + | 0.193834i | ||||
\(203\) | −3.66012 | −0.256890 | ||||||||
\(204\) | −7.00000 | − | 12.1244i | −0.490098 | − | 0.848875i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.765631 | − | 1.32611i | 0.0533441 | − | 0.0923946i | ||||
\(207\) | 7.76897 | 0.539981 | ||||||||
\(208\) | 11.9607 | − | 0.503175i | 0.829328 | − | 0.0348889i | ||||
\(209\) | 0.0785226 | 0.00543152 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.40411 | + | 7.62815i | −0.303192 | + | 0.525143i | −0.976857 | − | 0.213893i | \(-0.931386\pi\) |
0.673665 | + | 0.739037i | \(0.264719\pi\) | |||||||
\(212\) | −0.640492 | − | 1.10937i | −0.0439892 | − | 0.0761915i | ||||
\(213\) | 7.31357 | 0.501118 | ||||||||
\(214\) | 0.0970195 | + | 0.168043i | 0.00663211 | + | 0.0114872i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.32025 | −0.0898314 | ||||||||
\(217\) | −3.29193 | − | 5.70180i | −0.223471 | − | 0.387063i | ||||
\(218\) | −2.61866 | + | 4.53565i | −0.177358 | + | 0.307193i | ||||
\(219\) | 4.00982 | − | 6.94520i | 0.270958 | − | 0.469313i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.4061 | − | 23.7398i | 0.834526 | − | 1.59691i | ||||
\(222\) | −3.32025 | −0.222840 | ||||||||
\(223\) | 5.01963 | − | 8.69426i | 0.336139 | − | 0.582210i | −0.647564 | − | 0.762011i | \(-0.724212\pi\) |
0.983703 | + | 0.179801i | \(0.0575454\pi\) | |||||||
\(224\) | 1.24399 | − | 2.15466i | 0.0831177 | − | 0.143964i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.80823 | 0.120282 | ||||||||
\(227\) | 0.605701 | + | 1.04910i | 0.0402018 | + | 0.0696315i | 0.885426 | − | 0.464780i | \(-0.153867\pi\) |
−0.845224 | + | 0.534412i | \(0.820533\pi\) | |||||||
\(228\) | 0.108844 | + | 0.188524i | 0.00720839 | + | 0.0124853i | ||||
\(229\) | 19.2440 | 1.27168 | 0.635839 | − | 0.771821i | \(-0.280654\pi\) | ||||
0.635839 | + | 0.771821i | \(0.280654\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.224361 | − | 0.388604i | 0.0147618 | − | 0.0255683i | ||||
\(232\) | 3.66012 | − | 6.33952i | 0.240299 | − | 0.416210i | ||||
\(233\) | 23.9081 | 1.56627 | 0.783137 | − | 0.621849i | \(-0.213618\pi\) | ||||
0.783137 | + | 0.621849i | \(0.213618\pi\) | |||||||
\(234\) | −0.656787 | − | 1.03457i | −0.0429355 | − | 0.0676322i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.09589 | − | 3.63018i | 0.136431 | − | 0.236305i | ||||
\(237\) | −4.98685 | + | 8.63748i | −0.323931 | + | 0.561064i | ||||
\(238\) | −0.833398 | − | 1.44349i | −0.0540211 | − | 0.0935674i | ||||
\(239\) | 18.6798 | 1.20829 | 0.604146 | − | 0.796873i | \(-0.293514\pi\) | ||||
0.604146 | + | 0.796873i | \(0.293514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.05776 | − | 5.29619i | −0.196968 | − | 0.341158i | 0.750576 | − | 0.660784i | \(-0.229776\pi\) |
−0.947544 | + | 0.319626i | \(0.896443\pi\) | |||||||
\(242\) | −3.58160 | −0.230234 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −3.96187 | + | 6.86216i | −0.253633 | + | 0.439305i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.43576 | 0.0915409 | ||||||||
\(247\) | −0.192905 | + | 0.369134i | −0.0122743 | + | 0.0234874i | ||||
\(248\) | 13.1677 | 0.836152 | ||||||||
\(249\) | 0.884484 | − | 1.53197i | 0.0560519 | − | 0.0970847i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.67975 | − | 2.90942i | −0.106025 | − | 0.183641i | 0.808131 | − | 0.589002i | \(-0.200479\pi\) |
−0.914157 | + | 0.405361i | \(0.867146\pi\) | |||||||
\(252\) | 1.24399 | 0.0783641 | ||||||||
\(253\) | −2.64049 | − | 4.57347i | −0.166006 | − | 0.287531i | ||||
\(254\) | −2.04260 | − | 3.53788i | −0.128164 | − | 0.221986i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.76897 | − | 6.52804i | −0.235560 | − | 0.408003i | ||||
\(257\) | −5.05442 | + | 8.75452i | −0.315286 | + | 0.546092i | −0.979498 | − | 0.201452i | \(-0.935434\pi\) |
0.664212 | + | 0.747544i | \(0.268767\pi\) | |||||||
\(258\) | −0.0925496 | + | 0.160301i | −0.00576189 | + | 0.00997988i | ||||
\(259\) | 6.44872 | 0.400704 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.54461 | 0.343203 | ||||||||
\(262\) | −1.85303 | + | 3.20954i | −0.114480 | + | 0.198286i | ||||
\(263\) | −11.2592 | + | 19.5014i | −0.694269 | + | 1.20251i | 0.276157 | + | 0.961112i | \(0.410939\pi\) |
−0.970426 | + | 0.241397i | \(0.922394\pi\) | |||||||
\(264\) | 0.448721 | + | 0.777208i | 0.0276169 | + | 0.0478338i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0129587 | + | 0.0224450i | 0.000794546 | + | 0.00137619i | ||||
\(267\) | −6.77230 | − | 11.7300i | −0.414458 | − | 0.717863i | ||||
\(268\) | −14.3858 | −0.878753 | ||||||||
\(269\) | −4.24733 | − | 7.35659i | −0.258964 | − | 0.448539i | 0.707001 | − | 0.707213i | \(-0.250048\pi\) |
−0.965965 | + | 0.258674i | \(0.916714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.68510 | + | 8.11483i | −0.284600 | + | 0.492941i | −0.972512 | − | 0.232853i | \(-0.925194\pi\) |
0.687912 | + | 0.725794i | \(0.258527\pi\) | |||||||
\(272\) | −24.6664 | −1.49562 | ||||||||
\(273\) | 1.27564 | + | 2.00939i | 0.0772052 | + | 0.121614i | ||||
\(274\) | −1.15212 | −0.0696024 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.32025 | − | 12.6790i | 0.440627 | − | 0.763188i | ||||
\(277\) | 0.359508 | + | 0.622685i | 0.0216007 | + | 0.0374135i | 0.876624 | − | 0.481177i | \(-0.159790\pi\) |
−0.855023 | + | 0.518590i | \(0.826457\pi\) | |||||||
\(278\) | 5.03297 | 0.301858 | ||||||||
\(279\) | 4.98685 | + | 8.63748i | 0.298555 | + | 0.517112i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.54461 | 0.0921435 | 0.0460718 | − | 0.998938i | \(-0.485330\pi\) | ||||
0.0460718 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(282\) | −0.853028 | − | 1.47749i | −0.0507971 | − | 0.0879831i | ||||
\(283\) | −9.05977 | + | 15.6920i | −0.538547 | + | 0.932791i | 0.460435 | + | 0.887693i | \(0.347693\pi\) |
−0.998983 | + | 0.0450980i | \(0.985640\pi\) | |||||||
\(284\) | 6.89116 | − | 11.9358i | 0.408915 | − | 0.708261i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.385810 | + | 0.738268i | −0.0228134 | + | 0.0436547i | ||||
\(287\) | −2.78860 | −0.164606 | ||||||||
\(288\) | −1.88448 | + | 3.26402i | −0.111044 | + | 0.192334i | ||||
\(289\) | −19.0957 | + | 33.0747i | −1.12328 | + | 1.94557i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.90411 | −0.580589 | ||||||||
\(292\) | −7.55643 | − | 13.0881i | −0.442207 | − | 0.765924i | ||||
\(293\) | −15.2525 | − | 26.4181i | −0.891059 | − | 1.54336i | −0.838607 | − | 0.544737i | \(-0.816630\pi\) |
−0.0524523 | − | 0.998623i | \(-0.516704\pi\) | |||||||
\(294\) | −2.23103 | −0.130116 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.44872 | + | 11.1695i | −0.374824 | + | 0.649215i | ||||
\(297\) | −0.339877 | + | 0.588684i | −0.0197217 | + | 0.0341589i | ||||
\(298\) | −5.80823 | −0.336462 | ||||||||
\(299\) | 27.9867 | − | 1.17737i | 1.61851 | − | 0.0680890i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.179754 | − | 0.311343i | 0.0103608 | − | 0.0179455i | ||||
\(302\) | −2.21140 | + | 3.83026i | −0.127252 | + | 0.220407i | ||||
\(303\) | 4.67975 | + | 8.10557i | 0.268845 | + | 0.465653i | ||||
\(304\) | 0.383543 | 0.0219977 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.26249 | + | 2.18669i | 0.0721716 | + | 0.125005i | ||||
\(307\) | 4.77564 | 0.272560 | 0.136280 | − | 0.990670i | \(-0.456485\pi\) | ||||
0.136280 | + | 0.990670i | \(0.456485\pi\) | |||||||
\(308\) | −0.422804 | − | 0.732318i | −0.0240915 | − | 0.0417277i | ||||
\(309\) | 2.25267 | − | 3.90174i | 0.128150 | − | 0.221962i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.5812 | 1.73410 | 0.867051 | − | 0.498220i | \(-0.166013\pi\) | ||||
0.867051 | + | 0.498220i | \(0.166013\pi\) | |||||||
\(312\) | −4.75601 | + | 0.200080i | −0.269256 | + | 0.0113273i | ||||
\(313\) | 26.7230 | 1.51048 | 0.755238 | − | 0.655451i | \(-0.227521\pi\) | ||||
0.755238 | + | 0.655451i | \(0.227521\pi\) | |||||||
\(314\) | −0.131811 | + | 0.228303i | −0.00743852 | + | 0.0128839i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.39764 | + | 16.2772i | 0.528658 | + | 0.915663i | ||||
\(317\) | 20.6271 | 1.15854 | 0.579268 | − | 0.815137i | \(-0.303338\pi\) | ||||
0.579268 | + | 0.815137i | \(0.303338\pi\) | |||||||
\(318\) | 0.115516 | + | 0.200080i | 0.00647783 | + | 0.0112199i | ||||
\(319\) | −1.88448 | − | 3.26402i | −0.105511 | − | 0.182750i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.285455 | + | 0.494422i | 0.0159325 | + | 0.0275960i | ||||
\(322\) | 0.871525 | − | 1.50953i | 0.0485682 | − | 0.0841226i | ||||
\(323\) | 0.429091 | − | 0.743207i | 0.0238752 | − | 0.0413531i | ||||
\(324\) | −1.88448 | −0.104694 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.14584 | −0.229617 | ||||||||
\(327\) | −7.70473 | + | 13.3450i | −0.426073 | + | 0.737979i | ||||
\(328\) | 2.78860 | − | 4.82999i | 0.153975 | − | 0.266692i | ||||
\(329\) | 1.65679 | + | 2.86964i | 0.0913416 | + | 0.158208i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.68510 | − | 4.65073i | −0.147586 | − | 0.255627i | 0.782749 | − | 0.622338i | \(-0.213817\pi\) |
−0.930335 | + | 0.366711i | \(0.880484\pi\) | |||||||
\(332\) | −1.66680 | − | 2.88697i | −0.0914773 | − | 0.158443i | ||||
\(333\) | −9.76897 | −0.535336 | ||||||||
\(334\) | −0.270294 | − | 0.468163i | −0.0147898 | − | 0.0256167i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.09589 | − | 1.89813i | 0.0597855 | − | 0.103551i | ||||
\(337\) | −28.7623 | −1.56678 | −0.783391 | − | 0.621529i | \(-0.786512\pi\) | ||||
−0.783391 | + | 0.621529i | \(0.786512\pi\) | |||||||
\(338\) | −2.52277 | − | 3.62738i | −0.137221 | − | 0.197303i | ||||
\(339\) | 5.32025 | 0.288956 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.38983 | − | 5.87136i | 0.183570 | − | 0.317952i | ||||
\(342\) | −0.0196307 | − | 0.0340013i | −0.00106150 | − | 0.00183858i | ||||
\(343\) | 8.95407 | 0.483474 | ||||||||
\(344\) | 0.359508 | + | 0.622685i | 0.0193833 | + | 0.0335729i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.33320 | −0.232955 | ||||||||
\(347\) | 11.1981 | + | 19.3956i | 0.601143 | + | 1.04121i | 0.992648 | + | 0.121035i | \(0.0386212\pi\) |
−0.391505 | + | 0.920176i | \(0.628045\pi\) | |||||||
\(348\) | 5.22436 | − | 9.04886i | 0.280055 | − | 0.485070i | ||||
\(349\) | 5.98685 | − | 10.3695i | 0.320469 | − | 0.555068i | −0.660116 | − | 0.751164i | \(-0.729493\pi\) |
0.980585 | + | 0.196096i | \(0.0628263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.93243 | − | 3.04397i | −0.103145 | − | 0.162475i | ||||
\(352\) | 2.56197 | 0.136553 | ||||||||
\(353\) | −8.51830 | + | 14.7541i | −0.453384 | + | 0.785283i | −0.998594 | − | 0.0530161i | \(-0.983117\pi\) |
0.545210 | + | 0.838299i | \(0.316450\pi\) | |||||||
\(354\) | −0.378004 | + | 0.654723i | −0.0200907 | + | 0.0347981i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −25.5246 | −1.35280 | ||||||||
\(357\) | −2.45206 | − | 4.24709i | −0.129777 | − | 0.224780i | ||||
\(358\) | −3.01850 | − | 5.22819i | −0.159533 | − | 0.276318i | ||||
\(359\) | −35.0825 | −1.85159 | −0.925793 | − | 0.378031i | \(-0.876601\pi\) | ||||
−0.925793 | + | 0.378031i | \(0.876601\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49333 | − | 16.4429i | 0.499649 | − | 0.865417i | ||||
\(362\) | −1.19404 | + | 2.06814i | −0.0627573 | + | 0.108699i | ||||
\(363\) | −10.5379 | −0.553098 | ||||||||
\(364\) | 4.48131 | − | 0.188524i | 0.234884 | − | 0.00988133i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.714545 | − | 1.23763i | 0.0373499 | − | 0.0646919i | ||||
\(367\) | 10.0413 | − | 17.3920i | 0.524150 | − | 0.907855i | −0.475455 | − | 0.879740i | \(-0.657716\pi\) |
0.999605 | − | 0.0281143i | \(-0.00895024\pi\) | |||||||
\(368\) | −12.8974 | − | 22.3390i | −0.672326 | − | 1.16450i | ||||
\(369\) | 4.22436 | 0.219911 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.224361 | − | 0.388604i | −0.0116482 | − | 0.0201753i | ||||
\(372\) | 18.7953 | 0.974489 | ||||||||
\(373\) | −11.7395 | − | 20.3334i | −0.607849 | − | 1.05283i | −0.991594 | − | 0.129387i | \(-0.958699\pi\) |
0.383745 | − | 0.923439i | \(-0.374634\pi\) | |||||||
\(374\) | 0.858181 | − | 1.48641i | 0.0443755 | − | 0.0768606i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.62715 | −0.341769 | ||||||||
\(377\) | 19.9737 | − | 0.840272i | 1.02870 | − | 0.0432762i | ||||
\(378\) | −0.224361 | −0.0115399 | ||||||||
\(379\) | −10.5707 | + | 18.3090i | −0.542981 | + | 0.940471i | 0.455750 | + | 0.890108i | \(0.349371\pi\) |
−0.998731 | + | 0.0503631i | \(0.983962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00982 | − | 10.4093i | −0.307892 | − | 0.533285i | ||||
\(382\) | −4.74266 | −0.242656 | ||||||||
\(383\) | 0.869323 | + | 1.50571i | 0.0444203 | + | 0.0769383i | 0.887381 | − | 0.461037i | \(-0.152523\pi\) |
−0.842960 | + | 0.537976i | \(0.819189\pi\) | |||||||
\(384\) | 4.67975 | + | 8.10557i | 0.238813 | + | 0.413636i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.03593 | + | 6.99043i | 0.205423 | + | 0.355803i | ||||
\(387\) | −0.272303 | + | 0.471643i | −0.0138420 | + | 0.0239750i | ||||
\(388\) | −9.33207 | + | 16.1636i | −0.473764 | + | 0.820584i | ||||
\(389\) | −26.6664 | −1.35204 | −0.676020 | − | 0.736883i | \(-0.736297\pi\) | ||||
−0.676020 | + | 0.736883i | \(0.736297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.7164 | −2.91884 | ||||||||
\(392\) | −4.33320 | + | 7.50533i | −0.218860 | + | 0.379076i | ||||
\(393\) | −5.45206 | + | 9.44324i | −0.275020 | + | 0.476348i | ||||
\(394\) | 2.68643 | + | 4.65303i | 0.135340 | + | 0.234416i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.640492 | + | 1.10937i | 0.0321860 | + | 0.0557477i | ||||
\(397\) | 7.27230 | + | 12.5960i | 0.364986 | + | 0.632175i | 0.988774 | − | 0.149419i | \(-0.0477403\pi\) |
−0.623788 | + | 0.781594i | \(0.714407\pi\) | |||||||
\(398\) | 2.98037 | 0.149392 | ||||||||
\(399\) | 0.0381275 | + | 0.0660387i | 0.00190876 | + | 0.00330607i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.18510 | − | 7.24880i | 0.208994 | − | 0.361988i | −0.742404 | − | 0.669952i | \(-0.766314\pi\) |
0.951398 | + | 0.307964i | \(0.0996478\pi\) | |||||||
\(402\) | 2.59456 | 0.129405 | ||||||||
\(403\) | 19.2734 | + | 30.3596i | 0.960078 | + | 1.51232i | ||||
\(404\) | 17.6378 | 0.877515 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.621996 | − | 1.07733i | 0.0308691 | − | 0.0534669i | ||||
\(407\) | 3.32025 | + | 5.75084i | 0.164578 | + | 0.285058i | ||||
\(408\) | 9.80823 | 0.485580 | ||||||||
\(409\) | −8.62734 | − | 14.9430i | −0.426595 | − | 0.738883i | 0.569973 | − | 0.821663i | \(-0.306954\pi\) |
−0.996568 | + | 0.0827798i | \(0.973620\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.38983 | −0.167208 | ||||||||
\(412\) | −4.24513 | − | 7.35277i | −0.209142 | − | 0.362245i | ||||
\(413\) | 0.734176 | − | 1.27163i | 0.0361264 | − | 0.0625728i | ||||
\(414\) | −1.32025 | + | 2.28673i | −0.0648866 | + | 0.112387i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.29394 | + | 12.0438i | −0.308586 | + | 0.590495i | ||||
\(417\) | 14.8082 | 0.725162 | ||||||||
\(418\) | −0.0133440 | + | 0.0231125i | −0.000652677 | + | 0.00113047i | ||||
\(419\) | −6.43243 | + | 11.1413i | −0.314245 | + | 0.544288i | −0.979277 | − | 0.202527i | \(-0.935085\pi\) |
0.665032 | + | 0.746815i | \(0.268418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.5616 | 1.19706 | 0.598529 | − | 0.801101i | \(-0.295752\pi\) | ||||
0.598529 | + | 0.801101i | \(0.295752\pi\) | |||||||
\(422\) | −1.49686 | − | 2.59263i | −0.0728658 | − | 0.126207i | ||||
\(423\) | −2.50982 | − | 4.34713i | −0.122031 | − | 0.211365i | ||||
\(424\) | 0.897442 | 0.0435837 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.24286 | + | 2.15269i | −0.0602166 | + | 0.104298i | ||||
\(427\) | −1.38782 | + | 2.40377i | −0.0671613 | + | 0.116327i | ||||
\(428\) | 1.07587 | 0.0520041 | ||||||||
\(429\) | −1.13515 | + | 2.17216i | −0.0548054 | + | 0.104873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3898 | + | 21.4598i | −0.596797 | + | 1.03368i | 0.396493 | + | 0.918038i | \(0.370227\pi\) |
−0.993291 | + | 0.115645i | \(0.963106\pi\) | |||||||
\(432\) | −1.66012 | + | 2.87542i | −0.0798727 | + | 0.138344i | ||||
\(433\) | −7.02945 | − | 12.1754i | −0.337814 | − | 0.585110i | 0.646208 | − | 0.763162i | \(-0.276354\pi\) |
−0.984021 | + | 0.178051i | \(0.943021\pi\) | |||||||
\(434\) | 2.23770 | 0.107413 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.5194 | + | 25.1484i | 0.695355 | + | 1.20439i | ||||
\(437\) | 0.897442 | 0.0429305 | ||||||||
\(438\) | 1.36284 | + | 2.36051i | 0.0651192 | + | 0.112790i | ||||
\(439\) | −10.4226 | + | 18.0525i | −0.497444 | + | 0.861598i | −0.999996 | − | 0.00294880i | \(-0.999061\pi\) |
0.502552 | + | 0.864547i | \(0.332395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.56424 | −0.312583 | ||||||||
\(442\) | 4.87933 | + | 7.68594i | 0.232086 | + | 0.365583i | ||||
\(443\) | 11.4291 | 0.543012 | 0.271506 | − | 0.962437i | \(-0.412478\pi\) | ||||
0.271506 | + | 0.962437i | \(0.412478\pi\) | |||||||
\(444\) | −9.20473 | + | 15.9431i | −0.436837 | + | 0.756624i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.70606 | + | 2.95498i | 0.0807841 | + | 0.139922i | ||||
\(447\) | −17.0892 | −0.808292 | ||||||||
\(448\) | −1.76897 | − | 3.06394i | −0.0835759 | − | 0.144758i | ||||
\(449\) | −12.9541 | − | 22.4371i | −0.611340 | − | 1.05887i | −0.991015 | − | 0.133752i | \(-0.957297\pi\) |
0.379675 | − | 0.925120i | \(-0.376036\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.43576 | − | 2.48681i | −0.0676074 | − | 0.117099i | ||||
\(452\) | 5.01296 | − | 8.68270i | 0.235790 | − | 0.408400i | ||||
\(453\) | −6.50648 | + | 11.2696i | −0.305701 | + | 0.529490i | ||||
\(454\) | −0.411728 | −0.0193233 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.152510 | −0.00714193 | ||||||||
\(457\) | 2.95206 | − | 5.11311i | 0.138091 | − | 0.239181i | −0.788683 | − | 0.614800i | \(-0.789237\pi\) |
0.926774 | + | 0.375619i | \(0.122570\pi\) | |||||||
\(458\) | −3.27029 | + | 5.66432i | −0.152811 | + | 0.264676i | ||||
\(459\) | 3.71455 | + | 6.43378i | 0.173380 | + | 0.300303i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.74600 | + | 13.4165i | 0.360767 | + | 0.624867i | 0.988087 | − | 0.153894i | \(-0.0491815\pi\) |
−0.627320 | + | 0.778762i | \(0.715848\pi\) | |||||||
\(462\) | 0.0762550 | + | 0.132077i | 0.00354770 | + | 0.00614480i | ||||
\(463\) | −17.4420 | −0.810601 | −0.405300 | − | 0.914184i | \(-0.632833\pi\) | ||||
−0.405300 | + | 0.914184i | \(0.632833\pi\) | |||||||
\(464\) | −9.20473 | − | 15.9431i | −0.427319 | − | 0.740138i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.06291 | + | 7.03717i | −0.188211 | + | 0.325991i | ||||
\(467\) | 20.4790 | 0.947657 | 0.473829 | − | 0.880617i | \(-0.342872\pi\) | ||||
0.473829 | + | 0.880617i | \(0.342872\pi\) | |||||||
\(468\) | −6.78860 | + | 0.285589i | −0.313803 | + | 0.0132014i | ||||
\(469\) | −5.03926 | −0.232691 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.387820 | + | 0.671723i | −0.0178698 | + | 0.0309514i | ||||
\(472\) | 1.46835 | + | 2.54326i | 0.0675864 | + | 0.117063i | ||||
\(473\) | 0.370199 | 0.0170217 | ||||||||
\(474\) | −1.69491 | − | 2.93568i | −0.0778500 | − | 0.134840i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.24172 | −0.423594 | ||||||||
\(477\) | 0.339877 | + | 0.588684i | 0.0155619 | + | 0.0269540i | ||||
\(478\) | −3.17441 | + | 5.49824i | −0.145194 | + | 0.251483i | ||||
\(479\) | 20.4953 | − | 35.4990i | 0.936456 | − | 1.62199i | 0.164439 | − | 0.986387i | \(-0.447419\pi\) |
0.772017 | − | 0.635602i | \(-0.219248\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.1914 | + | 1.48046i | −1.60459 | + | 0.0675033i | ||||
\(482\) | 2.07852 | 0.0946741 | ||||||||
\(483\) | 2.56424 | − | 4.44139i | 0.116677 | − | 0.202090i | ||||
\(484\) | −9.92928 | + | 17.1980i | −0.451331 | + | 0.781728i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.339877 | 0.0154171 | ||||||||
\(487\) | 12.0315 | + | 20.8391i | 0.545197 | + | 0.944309i | 0.998594 | + | 0.0530008i | \(0.0168786\pi\) |
−0.453397 | + | 0.891309i | \(0.649788\pi\) | |||||||
\(488\) | −2.77564 | − | 4.80755i | −0.125647 | − | 0.217627i | ||||
\(489\) | −12.1981 | −0.551615 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.3865 | + | 31.8463i | −0.829771 | + | 1.43721i | 0.0684471 | + | 0.997655i | \(0.478196\pi\) |
−0.898218 | + | 0.439550i | \(0.855138\pi\) | |||||||
\(492\) | 3.98037 | − | 6.89420i | 0.179449 | − | 0.310815i | ||||
\(493\) | −41.1914 | −1.85517 | ||||||||
\(494\) | −0.0758696 | − | 0.119510i | −0.00341354 | − | 0.00537701i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.5576 | − | 28.6785i | 0.743457 | − | 1.28770i | ||||
\(497\) | 2.41393 | − | 4.18105i | 0.108280 | − | 0.187546i | ||||
\(498\) | 0.300616 | + | 0.520681i | 0.0134709 | + | 0.0233323i | ||||
\(499\) | 34.8212 | 1.55881 | 0.779405 | − | 0.626520i | \(-0.215521\pi\) | ||||
0.779405 | + | 0.626520i | \(0.215521\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.795270 | − | 1.37745i | −0.0355300 | − | 0.0615398i | ||||
\(502\) | 1.14182 | 0.0509619 | ||||||||
\(503\) | −16.0130 | − | 27.7353i | −0.713983 | − | 1.23665i | −0.963351 | − | 0.268245i | \(-0.913556\pi\) |
0.249368 | − | 0.968409i | \(-0.419777\pi\) | |||||||
\(504\) | −0.435763 | + | 0.754763i | −0.0194104 | + | 0.0336198i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.79488 | 0.0797924 | ||||||||
\(507\) | −7.42261 | − | 10.6726i | −0.329650 | − | 0.473988i | ||||
\(508\) | −22.6508 | −1.00497 | ||||||||
\(509\) | 20.6731 | − | 35.8068i | 0.916318 | − | 1.58711i | 0.111359 | − | 0.993780i | \(-0.464480\pi\) |
0.804960 | − | 0.593329i | \(-0.202187\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.64697 | − | 4.58469i | −0.117095 | − | 0.202815i | ||||
\(512\) | 21.2810 | 0.940496 | ||||||||
\(513\) | −0.0577581 | − | 0.100040i | −0.00255008 | − | 0.00441688i | ||||
\(514\) | −1.71788 | − | 2.97546i | −0.0757725 | − | 0.131242i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.513151 | + | 0.888804i | 0.0225902 | + | 0.0391274i | ||||
\(517\) | −1.70606 | + | 2.95498i | −0.0750323 | + | 0.129960i | ||||
\(518\) | −1.09589 | + | 1.89813i | −0.0481505 | + | 0.0833990i | ||||
\(519\) | −12.7493 | −0.559634 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.40279 | 0.192890 | 0.0964448 | − | 0.995338i | \(-0.469253\pi\) | ||||
0.0964448 | + | 0.995338i | \(0.469253\pi\) | |||||||
\(522\) | −0.942242 | + | 1.63201i | −0.0412408 | + | 0.0714312i | ||||
\(523\) | −16.2244 | + | 28.1014i | −0.709442 | + | 1.22879i | 0.255623 | + | 0.966777i | \(0.417720\pi\) |
−0.965064 | + | 0.262013i | \(0.915614\pi\) | |||||||
\(524\) | 10.2743 | + | 17.7956i | 0.448835 | + | 0.777406i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.82673 | − | 6.62808i | −0.166853 | − | 0.288998i | ||||
\(527\) | −37.0478 | − | 64.1686i | −1.61383 | − | 2.79523i | ||||
\(528\) | 2.25695 | 0.0982211 | ||||||||
\(529\) | −18.6784 | − | 32.3520i | −0.812106 | − | 1.40661i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.11218 | + | 1.92635i | −0.0482645 | + | 0.0835966i | ||||
\(532\) | 0.143701 | 0.00623024 | ||||||||
\(533\) | 15.2177 | − | 0.640192i | 0.659151 | − | 0.0277298i | ||||
\(534\) | 4.60350 | 0.199213 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.03926 | − | 8.72826i | 0.217663 | − | 0.377003i | ||||
\(537\) | −8.88115 | − | 15.3826i | −0.383250 | − | 0.663808i | ||||
\(538\) | 2.88714 | 0.124473 | ||||||||
\(539\) | 2.23103 | + | 3.86426i | 0.0960974 | + | 0.166446i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.57720 | −0.368762 | −0.184381 | − | 0.982855i | \(-0.559028\pi\) | ||||
−0.184381 | + | 0.982855i | \(0.559028\pi\) | |||||||
\(542\) | −1.59236 | − | 2.75804i | −0.0683976 | − | 0.118468i | ||||
\(543\) | −3.51315 | + | 6.08496i | −0.150764 | + | 0.261130i | ||||
\(544\) | 14.0000 | − | 24.2487i | 0.600245 | − | 1.03965i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.808229 | + | 0.0340013i | −0.0345890 | + | 0.00145512i | ||||
\(547\) | 32.4920 | 1.38926 | 0.694629 | − | 0.719368i | \(-0.255569\pi\) | ||||
0.694629 | + | 0.719368i | \(0.255569\pi\) | |||||||
\(548\) | −3.19404 | + | 5.53224i | −0.136443 | + | 0.236325i | ||||
\(549\) | 2.10236 | − | 3.64140i | 0.0897268 | − | 0.155411i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.640492 | 0.0272859 | ||||||||
\(552\) | 5.12847 | + | 8.88278i | 0.218282 | + | 0.378076i | ||||
\(553\) | 3.29193 | + | 5.70180i | 0.139987 | + | 0.242465i | ||||
\(554\) | −0.244377 | −0.0103826 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.9529 | − | 24.1672i | 0.591736 | − | 1.02492i | ||||
\(557\) | −20.6075 | + | 35.6933i | −0.873169 | + | 1.51237i | −0.0144676 | + | 0.999895i | \(0.504605\pi\) |
−0.858701 | + | 0.512477i | \(0.828728\pi\) | |||||||
\(558\) | −3.38983 | −0.143503 | ||||||||
\(559\) | −0.909460 | + | 1.74030i | −0.0384661 | + | 0.0736068i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.52498 | − | 4.37339i | 0.106605 | − | 0.184645i | ||||
\(562\) | −0.262488 | + | 0.454643i | −0.0110724 | + | 0.0191779i | ||||
\(563\) | −6.08921 | − | 10.5468i | −0.256630 | − | 0.444496i | 0.708707 | − | 0.705503i | \(-0.249279\pi\) |
−0.965337 | + | 0.261007i | \(0.915945\pi\) | |||||||
\(564\) | −9.45941 | −0.398313 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.07921 | − | 5.33334i | −0.129429 | − | 0.224177i | ||||
\(567\) | −0.660123 | −0.0277226 | ||||||||
\(568\) | 4.82786 | + | 8.36210i | 0.202572 | + | 0.350866i | ||||
\(569\) | −3.47169 | + | 6.01314i | −0.145541 | + | 0.252084i | −0.929575 | − | 0.368634i | \(-0.879826\pi\) |
0.784034 | + | 0.620718i | \(0.213159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.51429 | 0.147068 | 0.0735341 | − | 0.997293i | \(-0.476572\pi\) | ||||
0.0735341 | + | 0.997293i | \(0.476572\pi\) | |||||||
\(572\) | 2.47541 | + | 3.89927i | 0.103502 | + | 0.163037i | ||||
\(573\) | −13.9541 | −0.582939 | ||||||||
\(574\) | 0.473890 | − | 0.820802i | 0.0197798 | − | 0.0342596i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.67975 | + | 4.64147i | 0.111656 | + | 0.193395i | ||||
\(577\) | −3.14182 | −0.130796 | −0.0653978 | − | 0.997859i | \(-0.520832\pi\) | ||||
−0.0653978 | + | 0.997859i | \(0.520832\pi\) | |||||||
\(578\) | −6.49018 | − | 11.2413i | −0.269956 | − | 0.467578i | ||||
\(579\) | 11.8747 | + | 20.5675i | 0.493494 | + | 0.854757i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.583868 | − | 1.01129i | −0.0242229 | − | 0.0419553i | ||||
\(582\) | 1.68309 | − | 2.91520i | 0.0697663 | − | 0.120839i | ||||
\(583\) | 0.231033 | − | 0.400160i | 0.00956839 | − | 0.0165729i | ||||
\(584\) | 10.5879 | 0.438130 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.3679 | 0.428295 | ||||||||
\(587\) | 18.9889 | − | 32.8897i | 0.783754 | − | 1.35750i | −0.145987 | − | 0.989287i | \(-0.546636\pi\) |
0.929741 | − | 0.368215i | \(-0.120031\pi\) | |||||||
\(588\) | −6.18510 | + | 10.7129i | −0.255069 | + | 0.441793i | ||||
\(589\) | 0.576062 | + | 0.997769i | 0.0237362 | + | 0.0411124i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.90411 | + | 13.6903i | 0.325132 | + | 0.563145i | ||||
\(592\) | 16.2177 | + | 28.0899i | 0.666543 | + | 1.15449i | ||||
\(593\) | −10.4487 | −0.429078 | −0.214539 | − | 0.976715i | \(-0.568825\pi\) | ||||
−0.214539 | + | 0.976715i | \(0.568825\pi\) | |||||||
\(594\) | −0.115516 | − | 0.200080i | −0.00473969 | − | 0.00820939i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.1022 | + | 27.8898i | −0.659571 | + | 1.14241i | ||||
\(597\) | 8.76897 | 0.358890 | ||||||||
\(598\) | −4.40946 | + | 8.43773i | −0.180316 | + | 0.345044i | ||||
\(599\) | −45.5705 | −1.86196 | −0.930981 | − | 0.365069i | \(-0.881045\pi\) | ||||
−0.930981 | + | 0.365069i | \(0.881045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.39096 | − | 12.8015i | 0.301484 | − | 0.522185i | −0.674989 | − | 0.737828i | \(-0.735851\pi\) |
0.976472 | + | 0.215643i | \(0.0691848\pi\) | |||||||
\(602\) | 0.0610942 | + | 0.105818i | 0.00249001 | + | 0.00431283i | ||||
\(603\) | 7.63382 | 0.310873 | ||||||||
\(604\) | 12.2614 | + | 21.2373i | 0.498907 | + | 0.864133i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.18108 | −0.129223 | ||||||||
\(607\) | −9.46722 | − | 16.3977i | −0.384263 | − | 0.665562i | 0.607404 | − | 0.794393i | \(-0.292211\pi\) |
−0.991667 | + | 0.128831i | \(0.958878\pi\) | |||||||
\(608\) | −0.217689 | + | 0.377048i | −0.00882844 | + | 0.0152913i | ||||
\(609\) | 1.83006 | − | 3.16976i | 0.0741578 | − | 0.128445i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.70007 | − | 15.2796i | −0.392423 | − | 0.618146i | ||||
\(612\) | 14.0000 | 0.565916 | ||||||||
\(613\) | −1.29193 | + | 2.23770i | −0.0521807 | + | 0.0903797i | −0.890936 | − | 0.454129i | \(-0.849951\pi\) |
0.838755 | + | 0.544509i | \(0.183284\pi\) | |||||||
\(614\) | −0.811565 | + | 1.40567i | −0.0327521 | + | 0.0567283i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.592422 | 0.0238694 | ||||||||
\(617\) | 7.01963 | + | 12.1584i | 0.282600 | + | 0.489477i | 0.972024 | − | 0.234880i | \(-0.0754699\pi\) |
−0.689425 | + | 0.724357i | \(0.742137\pi\) | |||||||
\(618\) | 0.765631 | + | 1.32611i | 0.0307982 | + | 0.0533441i | ||||
\(619\) | −17.8582 | −0.717781 | −0.358890 | − | 0.933380i | \(-0.616845\pi\) | ||||
−0.358890 | + | 0.933380i | \(0.616845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.88448 | + | 6.72812i | −0.155879 | + | 0.269990i | ||||
\(622\) | −5.19692 | + | 9.00134i | −0.208378 | + | 0.360921i | ||||
\(623\) | −8.94111 | −0.358218 | ||||||||
\(624\) | −5.54461 | + | 10.6099i | −0.221962 | + | 0.424736i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.54127 | + | 7.86571i | −0.181506 | + | 0.314377i | ||||
\(627\) | −0.0392613 | + | 0.0680026i | −0.00156795 | + | 0.00271576i | ||||
\(628\) | 0.730840 | + | 1.26585i | 0.0291637 | + | 0.0505130i | ||||
\(629\) | 72.5745 | 2.89374 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4815 | + | 21.6186i | 0.496881 | + | 0.860623i | 0.999994 | − | 0.00359801i | \(-0.00114528\pi\) |
−0.503113 | + | 0.864221i | \(0.667812\pi\) | |||||||
\(632\) | −13.1677 | −0.523784 | ||||||||
\(633\) | −4.40411 | − | 7.62815i | −0.175048 | − | 0.303192i | ||||
\(634\) | −3.50535 | + | 6.07144i | −0.139215 | + | 0.241128i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.28098 | 0.0507944 | ||||||||
\(637\) | −23.6468 | + | 0.994794i | −0.936920 | + | 0.0394152i | ||||
\(638\) | 1.28098 | 0.0507147 | ||||||||
\(639\) | −3.65679 | + | 6.33374i | −0.144660 | + | 0.250559i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.6535 | − | 20.1844i | −0.460284 | − | 0.797235i | 0.538691 | − | 0.842503i | \(-0.318919\pi\) |
−0.998975 | + | 0.0452686i | \(0.985586\pi\) | |||||||
\(642\) | −0.194039 | −0.00765811 | ||||||||
\(643\) | 22.7395 | + | 39.3860i | 0.896759 | + | 1.55323i | 0.831612 | + | 0.555357i | \(0.187418\pi\) |
0.0651470 | + | 0.997876i | \(0.479248\pi\) | |||||||
\(644\) | −4.83226 | − | 8.36973i | −0.190418 | − | 0.329813i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.145838 | + | 0.252599i | 0.00573792 | + | 0.00993836i | ||||
\(647\) | 3.20473 | − | 5.55076i | 0.125991 | − | 0.218223i | −0.796129 | − | 0.605127i | \(-0.793122\pi\) |
0.922120 | + | 0.386904i | \(0.126456\pi\) | |||||||
\(648\) | 0.660123 | − | 1.14337i | 0.0259321 | − | 0.0449157i | ||||
\(649\) | 1.51202 | 0.0593519 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.58387 | 0.258042 | ||||||||
\(652\) | −11.4935 | + | 19.9074i | −0.450121 | + | 0.779632i | ||||
\(653\) | 0.740848 | − | 1.28319i | 0.0289916 | − | 0.0502150i | −0.851166 | − | 0.524897i | \(-0.824104\pi\) |
0.880157 | + | 0.474682i | \(0.157437\pi\) | |||||||
\(654\) | −2.61866 | − | 4.53565i | −0.102398 | − | 0.177358i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.01296 | − | 12.1468i | −0.273810 | − | 0.474253i | ||||
\(657\) | 4.00982 | + | 6.94520i | 0.156438 | + | 0.270958i | ||||
\(658\) | −1.12621 | −0.0439041 | ||||||||
\(659\) | 3.54461 | + | 6.13944i | 0.138078 | + | 0.239159i | 0.926769 | − | 0.375631i | \(-0.122574\pi\) |
−0.788691 | + | 0.614790i | \(0.789241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.589214 | + | 1.02055i | −0.0229178 | + | 0.0396947i | −0.877257 | − | 0.480021i | \(-0.840629\pi\) |
0.854339 | + | 0.519716i | \(0.173962\pi\) | |||||||
\(662\) | 1.82521 | 0.0709387 | ||||||||
\(663\) | 14.3562 | + | 22.6139i | 0.557548 | + | 0.878251i | ||||
\(664\) | 2.33547 | 0.0906339 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.66012 | − | 2.87542i | 0.0643285 | − | 0.111420i | ||||
\(667\) | −21.5379 | − | 37.3048i | −0.833952 | − | 1.44445i | ||||
\(668\) | −2.99735 | −0.115971 | ||||||||
\(669\) | 5.01963 | + | 8.69426i | 0.194070 | + | 0.336139i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.85818 | −0.110339 | ||||||||
\(672\) | 1.24399 | + | 2.15466i | 0.0479880 | + | 0.0831177i | ||||
\(673\) | 6.77878 | − | 11.7412i | 0.261303 | − | 0.452590i | −0.705286 | − | 0.708923i | \(-0.749181\pi\) |
0.966588 | + | 0.256334i | \(0.0825145\pi\) | |||||||
\(674\) | 4.88782 | − | 8.46595i | 0.188272 | − | 0.326096i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.4117 | + | 2.05759i | −0.938913 | + | 0.0791381i | ||||
\(677\) | −9.53793 | −0.366573 | −0.183286 | − | 0.983060i | \(-0.558674\pi\) | ||||
−0.183286 | + | 0.983060i | \(0.558674\pi\) | |||||||
\(678\) | −0.904114 | + | 1.56597i | −0.0347223 | + | 0.0601408i | ||||
\(679\) | −3.26897 | + | 5.66202i | −0.125451 | + | 0.217288i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.21140 | −0.0464210 | ||||||||
\(682\) | 1.15212 | + | 1.99554i | 0.0441171 | + | 0.0764131i | ||||
\(683\) | −22.2592 | − | 38.5540i | −0.851723 | − | 1.47523i | −0.879652 | − | 0.475617i | \(-0.842225\pi\) |
0.0279296 | − | 0.999610i | \(-0.491109\pi\) | |||||||
\(684\) | −0.217689 | −0.00832353 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.52164 | + | 2.63556i | −0.0580965 | + | 0.100626i | ||||
\(687\) | −9.62200 | + | 16.6658i | −0.367102 | + | 0.635839i | ||||
\(688\) | 1.80823 | 0.0689381 | ||||||||
\(689\) | 1.31357 | + | 2.06915i | 0.0500432 | + | 0.0788282i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.64030 | − | 4.57313i | 0.100442 | − | 0.173970i | −0.811425 | − | 0.584457i | \(-0.801308\pi\) |
0.911867 | + | 0.410486i | \(0.134641\pi\) | |||||||
\(692\) | −12.0130 | + | 20.8071i | −0.456664 | + | 0.790966i | ||||
\(693\) | 0.224361 | + | 0.388604i | 0.00852275 | + | 0.0147618i | ||||
\(694\) | −7.61192 | −0.288945 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.66012 | + | 6.33952i | 0.138737 | + | 0.240299i | ||||
\(697\) | −31.3832 | −1.18872 | ||||||||
\(698\) | 2.03479 | + | 3.52436i | 0.0770180 | + | 0.133399i | ||||
\(699\) | −11.9541 | + | 20.7051i | −0.452144 | + | 0.783137i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.1392 | 0.760646 | 0.380323 | − | 0.924854i | \(-0.375813\pi\) | ||||
0.380323 | + | 0.924854i | \(0.375813\pi\) | |||||||
\(702\) | 1.22436 | − | 0.0515075i | 0.0462105 | − | 0.00194403i | ||||
\(703\) | −1.12847 | −0.0425612 | ||||||||
\(704\) | 1.82157 | − | 3.15506i | 0.0686531 | − | 0.118911i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.89517 | − | 5.01459i | −0.108961 | − | 0.188727i | ||||
\(707\) | 6.17843 | 0.232364 | ||||||||
\(708\) | 2.09589 | + | 3.63018i | 0.0787682 | + | 0.136431i | ||||
\(709\) | −0.770294 | − | 1.33419i | −0.0289290 | − | 0.0501065i | 0.851198 | − | 0.524844i | \(-0.175876\pi\) |
−0.880127 | + | 0.474737i | \(0.842543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.98685 | − | 8.63748i | −0.187021 | − | 0.323931i | ||||
\(712\) | 8.94111 | − | 15.4865i | 0.335082 | − | 0.580379i | ||||
\(713\) | 38.7427 | − | 67.1043i | 1.45092 | − | 2.51307i | ||||
\(714\) | 1.66680 | 0.0623782 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.4728 | −1.25094 | ||||||||
\(717\) | −9.33988 | + | 16.1771i | −0.348804 | + | 0.604146i | ||||
\(718\) | 5.96187 | − | 10.3263i | 0.222495 | − | 0.385373i | ||||
\(719\) | −18.5020 | − | 32.0464i | −0.690009 | − | 1.19513i | −0.971835 | − | 0.235664i | \(-0.924273\pi\) |
0.281826 | − | 0.959466i | \(-0.409060\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.48704 | − | 2.57563i | −0.0553803 | − | 0.0959215i | ||||
\(722\) | 3.22656 | + | 5.58857i | 0.120080 | + | 0.207985i | ||||
\(723\) | 6.11552 | 0.227438 | ||||||||
\(724\) | 6.62048 | + | 11.4670i | 0.246048 | + | 0.426168i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.79080 | − | 3.10176i | 0.0664628 | − | 0.115117i | ||||
\(727\) | 44.9015 | 1.66530 | 0.832652 | − | 0.553797i | \(-0.186822\pi\) | ||||
0.832652 | + | 0.553797i | \(0.186822\pi\) | |||||||
\(728\) | −1.45539 | + | 2.78497i | −0.0539405 | + | 0.103218i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.02297 | − | 3.50388i | 0.0748221 | − | 0.129596i | ||||
\(732\) | −3.96187 | − | 6.86216i | −0.146435 | − | 0.253633i | ||||
\(733\) | 4.94072 | 0.182490 | 0.0912449 | − | 0.995828i | \(-0.470915\pi\) | ||||
0.0912449 | + | 0.995828i | \(0.470915\pi\) | |||||||
\(734\) | 3.41280 | + | 5.91114i | 0.125969 | + | 0.218184i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.2810 | 1.07931 | ||||||||
\(737\) | −2.59456 | − | 4.49391i | −0.0955718 | − | 0.165535i | ||||
\(738\) | −0.717881 | + | 1.24341i | −0.0264256 | + | 0.0457704i | ||||
\(739\) | −3.01963 | + | 5.23015i | −0.111079 | + | 0.192394i | −0.916206 | − | 0.400709i | \(-0.868764\pi\) |
0.805127 | + | 0.593103i | \(0.202097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.223227 | − | 0.351628i | −0.00820044 | − | 0.0129174i | ||||
\(742\) | 0.152510 | 0.00559882 | ||||||||
\(743\) | −6.52945 | + | 11.3093i | −0.239542 | + | 0.414899i | −0.960583 | − | 0.277993i | \(-0.910331\pi\) |
0.721041 | + | 0.692893i | \(0.243664\pi\) | |||||||
\(744\) | −6.58387 | + | 11.4036i | −0.241376 | + | 0.418076i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.97998 | 0.292168 | ||||||||
\(747\) | 0.884484 | + | 1.53197i | 0.0323616 | + | 0.0560519i | ||||
\(748\) | −4.75828 | − | 8.24158i | −0.173980 | − | 0.301342i | ||||
\(749\) | 0.376871 | 0.0137706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0118 | + | 41.5897i | −0.876204 | + | 1.51763i | −0.0207292 | + | 0.999785i | \(0.506599\pi\) |
−0.855475 | + | 0.517845i | \(0.826735\pi\) | |||||||
\(752\) | −8.33320 | + | 14.4335i | −0.303881 | + | 0.526337i | ||||
\(753\) | 3.35951 | 0.122427 | ||||||||
\(754\) | −3.14697 | + | 6.02189i | −0.114606 | + | 0.219304i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.621996 | + | 1.07733i | −0.0226218 | + | 0.0391820i | ||||
\(757\) | −2.28212 | + | 3.95275i | −0.0829450 | + | 0.143665i | −0.904514 | − | 0.426445i | \(-0.859766\pi\) |
0.821569 | + | 0.570110i | \(0.193099\pi\) | |||||||
\(758\) | −3.59274 | − | 6.22281i | −0.130494 | − | 0.226023i | ||||
\(759\) | 5.28098 | 0.191688 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5446 | − | 18.2638i | −0.382242 | − | 0.662062i | 0.609141 | − | 0.793062i | \(-0.291514\pi\) |
−0.991382 | + | 0.131000i | \(0.958181\pi\) | |||||||
\(762\) | 4.08519 | 0.147991 | ||||||||
\(763\) | 5.08607 | + | 8.80933i | 0.184128 | + | 0.318919i | ||||
\(764\) | −13.1481 | + | 22.7732i | −0.475682 | + | 0.823905i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.590926 | −0.0213510 | ||||||||
\(767\) | −3.71455 | + | 7.10797i | −0.134124 | + | 0.256654i | ||||
\(768\) | 7.53793 | 0.272002 | ||||||||
\(769\) | −21.1666 | + | 36.6616i | −0.763287 | + | 1.32205i | 0.177860 | + | 0.984056i | \(0.443083\pi\) |
−0.941147 | + | 0.337996i | \(0.890251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.05442 | − | 8.75452i | −0.182031 | − | 0.315286i | ||||
\(772\) | 44.7552 | 1.61078 | ||||||||
\(773\) | 25.1218 | + | 43.5122i | 0.903568 | + | 1.56503i | 0.822827 | + | 0.568291i | \(0.192395\pi\) |
0.0807410 | + | 0.996735i | \(0.474271\pi\) | |||||||
\(774\) | −0.0925496 | − | 0.160301i | −0.00332663 | − | 0.00576189i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.53793 | − | 11.3240i | −0.234698 | − | 0.406509i | ||||
\(777\) | −3.22436 | + | 5.58476i | −0.115673 | + | 0.200352i | ||||
\(778\) | 4.53165 | − | 7.84904i | 0.162467 | − | 0.281402i | ||||
\(779\) | 0.487982 | 0.0174838 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.97143 | 0.177892 | ||||||||
\(782\) | 9.80823 | − | 16.9884i | 0.350742 | − | 0.607502i | ||||
\(783\) | −2.77230 | + | 4.80177i | −0.0990740 | + | 0.171601i | ||||
\(784\) | 10.8974 | + | 18.8749i | 0.389194 | + | 0.674104i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.85303 | − | 3.20954i | −0.0660953 | − | 0.114480i | ||||
\(787\) | −5.29080 | − | 9.16393i | −0.188597 | − | 0.326659i | 0.756186 | − | 0.654357i | \(-0.227061\pi\) |
−0.944783 | + | 0.327698i | \(0.893727\pi\) | |||||||
\(788\) | 29.7903 | 1.06124 | ||||||||
\(789\) | −11.2592 | − | 19.5014i | −0.400836 | − | 0.694269i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.75601 | − | 3.04150i | 0.0624365 | − | 0.108143i | ||||
\(792\) | −0.897442 | −0.0318892 | ||||||||
\(793\) | 7.02164 | − | 13.4363i | 0.249346 | − | 0.477136i | ||||
\(794\) | −4.94338 | −0.175434 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.26249 | − | 14.3110i | 0.292856 | − | 0.507242i | ||||
\(797\) | −10.0741 | − | 17.4488i | −0.356841 | − | 0.618067i | 0.630590 | − | 0.776116i | \(-0.282813\pi\) |
−0.987431 | + | 0.158049i | \(0.949480\pi\) | |||||||
\(798\) | −0.0259173 | −0.000917463 | ||||||||
\(799\) | 18.6456 | + | 32.2952i | 0.659636 | + | 1.14252i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.5446 | 0.478575 | ||||||||
\(802\) | 1.42242 | + | 2.46370i | 0.0502273 | + | 0.0869963i | ||||
\(803\) | 2.72569 | − | 4.72103i | 0.0961874 | − | 0.166601i | ||||
\(804\) | 7.19291 | − | 12.4585i | 0.253674 | − | 0.439377i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.2114 | + | 0.513720i | −0.430128 | + | 0.0180950i | ||||
\(807\) | 8.49465 | 0.299026 | ||||||||
\(808\) | −6.17843 | + | 10.7013i | −0.217356 | + | 0.376472i | ||||
\(809\) | −6.45539 | + | 11.1811i | −0.226960 | + | 0.393105i | −0.956906 | − | 0.290399i | \(-0.906212\pi\) |
0.729946 | + | 0.683505i | \(0.239545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.8974 | −0.558235 | −0.279117 | − | 0.960257i | \(-0.590042\pi\) | ||||
−0.279117 | + | 0.960257i | \(0.590042\pi\) | |||||||
\(812\) | −3.44872 | − | 5.97336i | −0.121026 | − | 0.209624i | ||||
\(813\) | −4.68510 | − | 8.11483i | −0.164314 | − | 0.284600i | ||||
\(814\) | −2.25695 | −0.0791061 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.3332 | − | 21.3617i | 0.431749 | − | 0.747810i | ||||
\(817\) | −0.0314555 | + | 0.0544825i | −0.00110049 | + | 0.00190610i | ||||
\(818\) | 5.86447 | 0.205046 | ||||||||
\(819\) | −2.37800 | + | 0.100040i | −0.0830942 | + | 0.00349568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.6142 | − | 32.2407i | 0.649640 | − | 1.12521i | −0.333569 | − | 0.942726i | \(-0.608253\pi\) |
0.983209 | − | 0.182483i | \(-0.0584136\pi\) | |||||||
\(822\) | 0.576062 | − | 0.997769i | 0.0200925 | − | 0.0348012i | ||||
\(823\) | −2.44872 | − | 4.24131i | −0.0853571 | − | 0.147843i | 0.820186 | − | 0.572097i | \(-0.193870\pi\) |
−0.905543 | + | 0.424254i | \(0.860536\pi\) | |||||||
\(824\) | 5.94817 | 0.207214 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.249529 | + | 0.432198i | 0.00868224 | + | 0.0150381i | ||||
\(827\) | −37.6334 | −1.30864 | −0.654321 | − | 0.756217i | \(-0.727046\pi\) | ||||
−0.654321 | + | 0.756217i | \(0.727046\pi\) | |||||||
\(828\) | 7.32025 | + | 12.6790i | 0.254396 | + | 0.440627i | ||||
\(829\) | 24.4552 | − | 42.3576i | 0.849364 | − | 1.47114i | −0.0324123 | − | 0.999475i | \(-0.510319\pi\) |
0.881777 | − | 0.471667i | \(-0.156348\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.719015 | −0.0249424 | ||||||||
\(832\) | 10.3569 | + | 16.3142i | 0.359059 | + | 0.565592i | ||||
\(833\) | 48.7663 | 1.68965 | ||||||||
\(834\) | −2.51649 | + | 4.35868i | −0.0871388 | + | 0.150929i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.0739873 | + | 0.128150i | 0.00255890 | + | 0.00443215i | ||||
\(837\) | −9.97370 | −0.344741 | ||||||||
\(838\) | −2.18623 | − | 3.78667i | −0.0755222 | − | 0.130808i | ||||
\(839\) | −24.1392 | − | 41.8103i | −0.833377 | − | 1.44345i | −0.895345 | − | 0.445372i | \(-0.853071\pi\) |
0.0619688 | − | 0.998078i | \(-0.480262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.871332 | − | 1.50919i | −0.0300459 | − | 0.0520411i | ||||
\(842\) | −4.17396 | + | 7.22951i | −0.143844 | + | 0.249145i | ||||
\(843\) | −0.772303 | + | 1.33767i | −0.0265995 | + | 0.0460718i | ||||
\(844\) | −16.5990 | −0.571360 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.70606 | 0.0586554 | ||||||||
\(847\) | −3.47817 | + | 6.02436i | −0.119511 | + | 0.207000i | ||||
\(848\) | 1.12847 | − | 1.95458i | 0.0387520 | − | 0.0671204i | ||||
\(849\) | −9.05977 | − | 15.6920i | −0.310930 | − | 0.538547i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.9474 | + | 65.7268i | 1.30082 | + | 2.25309i | ||||
\(852\) | 6.89116 | + | 11.9358i | 0.236087 | + | 0.408915i | ||||
\(853\) | 14.4291 | 0.494043 | 0.247021 | − | 0.969010i | \(-0.420548\pi\) | ||||
0.247021 | + | 0.969010i | \(0.420548\pi\) | |||||||
\(854\) | −0.471688 | − | 0.816987i | −0.0161408 | − | 0.0279567i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.376871 | + | 0.652759i | −0.0128812 | + | 0.0223108i | ||||
\(857\) | −3.64678 | −0.124572 | −0.0622858 | − | 0.998058i | \(-0.519839\pi\) | ||||
−0.0622858 | + | 0.998058i | \(0.519839\pi\) | |||||||
\(858\) | −0.446454 | − | 0.703255i | −0.0152417 | − | 0.0240087i | ||||
\(859\) | 21.7427 | 0.741850 | 0.370925 | − | 0.928663i | \(-0.379041\pi\) | ||||
0.370925 | + | 0.928663i | \(0.379041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.39430 | − | 2.41500i | 0.0475176 | − | 0.0823029i | ||||
\(862\) | −4.21102 | − | 7.29369i | −0.143428 | − | 0.248424i | ||||
\(863\) | 17.0892 | 0.581724 | 0.290862 | − | 0.956765i | \(-0.406058\pi\) | ||||
0.290862 | + | 0.956765i | \(0.406058\pi\) | |||||||
\(864\) | −1.88448 | − | 3.26402i | −0.0641114 | − | 0.111044i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.77829 | 0.162373 | ||||||||
\(867\) | −19.0957 | − | 33.0747i | −0.648524 | − | 1.12328i | ||||
\(868\) | 6.20360 | − | 10.7449i | 0.210564 | − | 0.364707i | ||||
\(869\) | −3.38983 | + | 5.87136i | −0.114992 | + | 0.199172i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.4998 | − | 1.15689i | 0.931795 | − | 0.0391996i | ||||
\(872\) | −20.3443 | −0.688944 | ||||||||
\(873\) | 4.95206 | − | 8.57721i | 0.167602 | − | 0.290295i | ||||
\(874\) | −0.152510 | + | 0.264155i | −0.00515873 | + | 0.00893518i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.1129 | 0.510616 | ||||||||
\(877\) | −2.42909 | − | 4.20731i | −0.0820246 | − | 0.142071i | 0.822095 | − | 0.569351i | \(-0.192805\pi\) |
−0.904119 | + | 0.427280i | \(0.859472\pi\) | |||||||
\(878\) | −3.54240 | − | 6.13562i | −0.119550 | − | 0.207067i | ||||
\(879\) | 30.5050 | 1.02891 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.6601 | − | 20.1959i | 0.392840 | − | 0.680418i | −0.599983 | − | 0.800013i | \(-0.704826\pi\) |
0.992823 | + | 0.119595i | \(0.0381595\pi\) | |||||||
\(882\) | 1.11552 | − | 1.93213i | 0.0375614 | − | 0.0650582i | ||||
\(883\) | 12.8934 | 0.433898 | 0.216949 | − | 0.976183i | \(-0.430389\pi\) | ||||
0.216949 | + | 0.976183i | \(0.430389\pi\) | |||||||
\(884\) | 50.4331 | − | 2.12167i | 1.69625 | − | 0.0713593i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.94224 | + | 3.36406i | −0.0652509 | + | 0.113018i | ||||
\(887\) | 15.4639 | − | 26.7842i | 0.519226 | − | 0.899326i | −0.480524 | − | 0.876982i | \(-0.659553\pi\) |
0.999750 | − | 0.0223448i | \(-0.00711317\pi\) | |||||||
\(888\) | −6.44872 | − | 11.1695i | −0.216405 | − | 0.374824i | ||||
\(889\) | −7.93444 | −0.266112 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.339877 | − | 0.588684i | −0.0113863 | − | 0.0197217i | ||||
\(892\) | 18.9188 | 0.633449 | ||||||||
\(893\) | −0.289925 | − | 0.502164i | −0.00970196 | − | 0.0168043i | ||||
\(894\) | 2.90411 | − | 5.03007i | 0.0971281 | − | 0.168231i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.17843 | 0.206407 | ||||||||
\(897\) | −12.9737 | + | 24.8258i | −0.433179 | + | 0.828911i | ||||
\(898\) | 8.80558 | 0.293846 | ||||||||
\(899\) | 27.6501 | − | 47.8914i | 0.922183 | − | 1.59727i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.52498 | − | 4.37339i | −0.0841192 | − | 0.145699i | ||||
\(902\) | 0.975965 | 0.0324961 | ||||||||
\(903\) | 0.179754 | + | 0.311343i | 0.00598183 | + | 0.0103608i | ||||
\(904\) | 3.51202 | + | 6.08299i | 0.116808 | + | 0.202317i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.21140 | − | 3.83026i | −0.0734689 | − | 0.127252i | ||||
\(907\) | −8.48018 | + | 14.6881i | −0.281580 | + | 0.487710i | −0.971774 | − | 0.235914i | \(-0.924192\pi\) |
0.690194 | + | 0.723624i | \(0.257525\pi\) | |||||||
\(908\) | −1.14143 | + | 1.97702i | −0.0378798 | + | 0.0656097i | ||||
\(909\) | −9.35951 | −0.310435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.7297 | 1.25004 | 0.625020 | − | 0.780608i | \(-0.285091\pi\) | ||||
0.625020 | + | 0.780608i | \(0.285091\pi\) | |||||||
\(912\) | −0.191771 | + | 0.332158i | −0.00635018 | + | 0.0109988i | ||||
\(913\) | 0.601231 | − | 1.04136i | 0.0198978 | − | 0.0344641i | ||||
\(914\) | 1.00334 | + | 1.73783i | 0.0331874 | + | 0.0574823i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.1325 | + | 31.4064i | 0.599114 | + | 1.03770i | ||||
\(917\) | 3.59903 | + | 6.23370i | 0.118850 | + | 0.205855i | ||||
\(918\) | −2.52498 | −0.0833366 | ||||||||
\(919\) | −20.0814 | − | 34.7820i | −0.662425 | − | 1.14735i | −0.979977 | − | 0.199112i | \(-0.936194\pi\) |
0.317552 | − | 0.948241i | \(-0.397139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.38782 | + | 4.13583i | −0.0786813 | + | 0.136280i | ||||
\(922\) | −5.26537 | −0.173406 | ||||||||
\(923\) | −12.2132 | + | 23.3706i | −0.402003 | + | 0.769253i | ||||
\(924\) | 0.845608 | 0.0278185 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.96407 | − | 5.13393i | 0.0974055 | − | 0.168711i | ||||
\(927\) | 2.25267 | + | 3.90174i | 0.0739875 | + | 0.128150i | ||||
\(928\) | 20.8974 | 0.685992 | ||||||||
\(929\) | −11.8845 | − | 20.5845i | −0.389917 | − | 0.675357i | 0.602521 | − | 0.798103i | \(-0.294163\pi\) |
−0.992438 | + | 0.122747i | \(0.960830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.758276 | −0.0248515 | ||||||||
\(932\) | 22.5272 | + | 39.0183i | 0.737904 | + | 1.27809i | ||||
\(933\) | −15.2906 | + | 26.4841i | −0.500592 | + | 0.867051i | ||||
\(934\) | −3.48018 | + | 6.02784i | −0.113875 | + | 0.197237i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.20473 | − | 4.21886i | 0.0720639 | − | 0.137898i | ||||
\(937\) | 7.43803 | 0.242990 | 0.121495 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121495 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(938\) | 0.856364 | − | 1.48327i | 0.0279613 | − | 0.0484304i | ||||
\(939\) | −13.3615 | + | 23.1428i | −0.436037 | + | 0.755238i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.3528 | −0.630884 | −0.315442 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(942\) | −0.131811 | − | 0.228303i | −0.00429463 | − | 0.00743852i | ||||
\(943\) | −16.4095 | − | 28.4220i | −0.534366 | − | 0.925548i | ||||
\(944\) | 7.38542 | 0.240375 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0629110 | + | 0.108965i | −0.00204541 | + | 0.00354276i | ||||
\(947\) | 6.95854 | − | 12.0525i | 0.226122 | − | 0.391655i | −0.730533 | − | 0.682877i | \(-0.760729\pi\) |
0.956655 | + | 0.291222i | \(0.0940618\pi\) | |||||||
\(948\) | −18.7953 | −0.610442 | ||||||||
\(949\) | 15.4973 | + | 24.4115i | 0.503065 | + | 0.792430i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.3136 | + | 17.8636i | −0.334441 | + | 0.579268i | ||||
\(952\) | 3.23732 | − | 5.60720i | 0.104922 | − | 0.181730i | ||||
\(953\) | −5.31357 | − | 9.20338i | −0.172124 | − | 0.298127i | 0.767039 | − | 0.641601i | \(-0.221729\pi\) |
−0.939162 | + | 0.343474i | \(0.888396\pi\) | |||||||
\(954\) | −0.231033 | −0.00747996 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17.6008 | + | 30.4856i | 0.569252 | + | 0.985973i | ||||
\(957\) | 3.76897 | 0.121833 | ||||||||
\(958\) | 6.96589 | + | 12.0653i | 0.225058 | + | 0.389811i | ||||
\(959\) | −1.11885 | + | 1.93791i | −0.0361296 | + | 0.0625783i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 68.4746 | 2.20886 | ||||||||
\(962\) | 5.54461 | − | 10.6099i | 0.178765 | − | 0.342077i | ||||
\(963\) | −0.570909 | −0.0183973 | ||||||||
\(964\) | 5.76230 | − | 9.98059i | 0.185591 | − | 0.321453i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.871525 | + | 1.50953i | 0.0280409 | + | 0.0485682i | ||||
\(967\) | −51.6771 | −1.66182 | −0.830912 | − | 0.556404i | \(-0.812181\pi\) | ||||
−0.830912 | + | 0.556404i | \(0.812181\pi\) | |||||||
\(968\) | −6.95633 | − | 12.0487i | −0.223585 | − | 0.387261i | ||||
\(969\) | 0.429091 | + | 0.743207i | 0.0137844 | + | 0.0238752i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.4487 | + | 37.1503i | 0.688322 | + | 1.19221i | 0.972380 | + | 0.233402i | \(0.0749858\pi\) |
−0.284058 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(972\) | 0.942242 | − | 1.63201i | 0.0302224 | − | 0.0523468i | ||||
\(973\) | 4.88763 | − | 8.46562i | 0.156690 | − | 0.271395i | ||||
\(974\) | −8.17843 | −0.262054 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.9607 | −0.446872 | ||||||||
\(977\) | 9.08254 | − | 15.7314i | 0.290576 | − | 0.503293i | −0.683370 | − | 0.730072i | \(-0.739486\pi\) |
0.973946 | + | 0.226780i | \(0.0728197\pi\) | |||||||
\(978\) | 2.07292 | − | 3.59040i | 0.0662846 | − | 0.114808i | ||||
\(979\) | −4.60350 | − | 7.97349i | −0.147128 | − | 0.254834i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.70473 | − | 13.3450i | −0.245993 | − | 0.426073i | ||||
\(982\) | −6.24914 | − | 10.8238i | −0.199418 | − | 0.345402i | ||||
\(983\) | 10.8582 | 0.346322 | 0.173161 | − | 0.984894i | \(-0.444602\pi\) | ||||
0.173161 | + | 0.984894i | \(0.444602\pi\) | |||||||
\(984\) | 2.78860 | + | 4.82999i | 0.0888973 | + | 0.153975i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.00000 | − | 12.1244i | 0.222925 | − | 0.386118i | ||||
\(987\) | −3.31357 | −0.105472 | ||||||||
\(988\) | −0.784194 | + | 0.0329902i | −0.0249485 | + | 0.00104956i | ||||
\(989\) | 4.23103 | 0.134539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.1862 | − | 19.3751i | 0.355342 | − | 0.615471i | −0.631834 | − | 0.775104i | \(-0.717698\pi\) |
0.987177 | + | 0.159633i | \(0.0510309\pi\) | |||||||
\(992\) | 18.7953 | + | 32.5544i | 0.596750 | + | 1.03360i | ||||
\(993\) | 5.37020 | 0.170418 | ||||||||
\(994\) | 0.820439 | + | 1.42104i | 0.0260227 | + | 0.0450727i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.33359 | 0.105629 | ||||||||
\(997\) | −12.1187 | − | 20.9901i | −0.383802 | − | 0.664764i | 0.607800 | − | 0.794090i | \(-0.292052\pi\) |
−0.991602 | + | 0.129326i | \(0.958719\pi\) | |||||||
\(998\) | −5.91746 | + | 10.2493i | −0.187314 | + | 0.324437i | ||||
\(999\) | 4.88448 | − | 8.46017i | 0.154538 | − | 0.267668i |
(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 | 975.2.i.l.451.2 | 6 | ||
5.2 | odd | 4 | 975.2.bb.k.724.3 | 12 | |||
5.3 | odd | 4 | 975.2.bb.k.724.4 | 12 | |||
5.4 | even | 2 | 195.2.i.d.61.2 | yes | 6 | ||
13.3 | even | 3 | inner | 975.2.i.l.601.2 | 6 | ||
15.14 | odd | 2 | 585.2.j.f.451.2 | 6 | |||
65.3 | odd | 12 | 975.2.bb.k.874.3 | 12 | |||
65.4 | even | 6 | 2535.2.a.ba.1.2 | 3 | |||
65.9 | even | 6 | 2535.2.a.bb.1.2 | 3 | |||
65.29 | even | 6 | 195.2.i.d.16.2 | ✓ | 6 | ||
65.42 | odd | 12 | 975.2.bb.k.874.4 | 12 | |||
195.29 | odd | 6 | 585.2.j.f.406.2 | 6 | |||
195.74 | odd | 6 | 7605.2.a.bv.1.2 | 3 | |||
195.134 | odd | 6 | 7605.2.a.bw.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.2 | ✓ | 6 | 65.29 | even | 6 | ||
195.2.i.d.61.2 | yes | 6 | 5.4 | even | 2 | ||
585.2.j.f.406.2 | 6 | 195.29 | odd | 6 | |||
585.2.j.f.451.2 | 6 | 15.14 | odd | 2 | |||
975.2.i.l.451.2 | 6 | 1.1 | even | 1 | trivial | ||
975.2.i.l.601.2 | 6 | 13.3 | even | 3 | inner | ||
975.2.bb.k.724.3 | 12 | 5.2 | odd | 4 | |||
975.2.bb.k.724.4 | 12 | 5.3 | odd | 4 | |||
975.2.bb.k.874.3 | 12 | 65.3 | odd | 12 | |||
975.2.bb.k.874.4 | 12 | 65.42 | odd | 12 | |||
2535.2.a.ba.1.2 | 3 | 65.4 | even | 6 | |||
2535.2.a.bb.1.2 | 3 | 65.9 | even | 6 | |||
7605.2.a.bv.1.2 | 3 | 195.74 | odd | 6 | |||
7605.2.a.bw.1.2 | 3 | 195.134 | odd | 6 |