Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(307,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.p (of order \(2\), degree \(1\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 307.11 | ||
Root | \(-1.40199 - 0.185533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.307 |
Dual form | 504.2.p.g.307.9 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.185533 | + | 1.40199i | 0.131192 | + | 0.991357i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.93115 | + | 0.520231i | −0.965577 | + | 0.260116i | ||||
\(5\) | −3.84444 | −1.71929 | −0.859644 | − | 0.510894i | \(-0.829314\pi\) | ||||
−0.859644 | + | 0.510894i | \(0.829314\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62140 | − | 2.09071i | 0.612831 | − | 0.790214i | ||||
\(8\) | −1.08765 | − | 2.61094i | −0.384543 | − | 0.923107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.713272 | − | 5.38987i | −0.225556 | − | 1.70443i | ||||
\(11\) | 4.54637 | 1.37078 | 0.685391 | − | 0.728175i | \(-0.259631\pi\) | ||||
0.685391 | + | 0.728175i | \(0.259631\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.81625 | −0.503738 | −0.251869 | − | 0.967761i | \(-0.581045\pi\) | ||||
−0.251869 | + | 0.967761i | \(0.581045\pi\) | |||||||
\(14\) | 3.23198 | + | 1.88529i | 0.863782 | + | 0.503865i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.45872 | − | 2.00929i | 0.864680 | − | 0.502324i | ||||
\(17\) | − | 3.49124i | − | 0.846751i | −0.905954 | − | 0.423375i | \(-0.860845\pi\) | ||
0.905954 | − | 0.423375i | \(-0.139155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.68700i | − | 0.387025i | −0.981098 | − | 0.193513i | \(-0.938012\pi\) | ||
0.981098 | − | 0.193513i | \(-0.0619881\pi\) | |||||||
\(20\) | 7.42422 | − | 2.00000i | 1.66011 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.843502 | + | 6.37397i | 0.179835 | + | 1.35893i | ||||
\(23\) | − | 5.00632i | − | 1.04389i | −0.852979 | − | 0.521945i | \(-0.825207\pi\) | ||
0.852979 | − | 0.521945i | \(-0.174793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.77975 | 1.95595 | ||||||||
\(26\) | −0.336975 | − | 2.54637i | −0.0660863 | − | 0.499384i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.04352 | + | 4.88099i | −0.386189 | + | 0.922420i | ||||
\(29\) | 1.81625i | 0.337270i | 0.985679 | + | 0.168635i | \(0.0539359\pi\) | ||||
−0.985679 | + | 0.168635i | \(0.946064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.34329 | 0.959683 | 0.479842 | − | 0.877355i | \(-0.340694\pi\) | ||||
0.479842 | + | 0.877355i | \(0.340694\pi\) | |||||||
\(32\) | 3.45872 | + | 4.47630i | 0.611421 | + | 0.791306i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.89469 | − | 0.647741i | 0.839433 | − | 0.111087i | ||||
\(35\) | −6.23338 | + | 8.03761i | −1.05363 | + | 1.35860i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.42654i | − | 0.234522i | −0.993101 | − | 0.117261i | \(-0.962589\pi\) | ||
0.993101 | − | 0.117261i | \(-0.0374114\pi\) | |||||||
\(38\) | 2.36516 | − | 0.312995i | 0.383680 | − | 0.0507745i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.18142 | + | 10.0376i | 0.661140 | + | 1.58709i | ||||
\(41\) | − | 8.97551i | − | 1.40174i | −0.713290 | − | 0.700869i | \(-0.752796\pi\) | ||
0.713290 | − | 0.700869i | \(-0.247204\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.03761 | −1.22572 | −0.612862 | − | 0.790190i | \(-0.709982\pi\) | ||||
−0.612862 | + | 0.790190i | \(0.709982\pi\) | |||||||
\(44\) | −8.77975 | + | 2.36516i | −1.32360 | + | 0.356562i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.01881 | − | 0.928837i | 1.03487 | − | 0.136950i | ||||
\(47\) | −4.83580 | −0.705374 | −0.352687 | − | 0.935741i | \(-0.614732\pi\) | ||||
−0.352687 | + | 0.935741i | \(0.614732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74213 | − | 6.77975i | −0.248876 | − | 0.968535i | ||||
\(50\) | 1.81447 | + | 13.7111i | 0.256604 | + | 1.93904i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50747 | − | 0.944872i | 0.486398 | − | 0.131030i | ||||
\(53\) | − | 5.87263i | − | 0.806668i | −0.915053 | − | 0.403334i | \(-0.867851\pi\) | ||
0.915053 | − | 0.403334i | \(-0.132149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.4783 | −2.35677 | ||||||||
\(56\) | −7.22224 | − | 1.95941i | −0.965112 | − | 0.261837i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.54637 | + | 0.336975i | −0.334355 | + | 0.0442470i | ||||
\(59\) | − | 8.46675i | − | 1.10228i | −0.834414 | − | 0.551139i | \(-0.814194\pi\) | ||
0.834414 | − | 0.551139i | \(-0.185806\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.01955 | 0.386613 | 0.193307 | − | 0.981138i | \(-0.438079\pi\) | ||||
0.193307 | + | 0.981138i | \(0.438079\pi\) | |||||||
\(62\) | 0.991357 | + | 7.49124i | 0.125903 | + | 0.951389i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.63402 | + | 5.67959i | −0.704253 | + | 0.709949i | ||||
\(65\) | 6.98249 | 0.866071 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.42914 | −0.541105 | −0.270553 | − | 0.962705i | \(-0.587206\pi\) | ||||
−0.270553 | + | 0.962705i | \(0.587206\pi\) | |||||||
\(68\) | 1.81625 | + | 6.74213i | 0.220253 | + | 0.817604i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.4252 | − | 7.24789i | −1.48509 | − | 0.866289i | ||||
\(71\) | − | 1.47928i | − | 0.175558i | −0.996140 | − | 0.0877791i | \(-0.972023\pi\) | ||
0.996140 | − | 0.0877791i | \(-0.0279769\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.98249i | 0.817238i | 0.912705 | + | 0.408619i | \(0.133990\pi\) | ||||
−0.912705 | + | 0.408619i | \(0.866010\pi\) | |||||||
\(74\) | 2.00000 | − | 0.264671i | 0.232495 | − | 0.0307674i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.877633 | + | 3.25787i | 0.100671 | + | 0.373703i | ||||
\(77\) | 7.37148 | − | 9.50514i | 0.840058 | − | 1.08321i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.97813i | − | 0.335065i | −0.985867 | − | 0.167533i | \(-0.946420\pi\) | ||
0.985867 | − | 0.167533i | \(-0.0535800\pi\) | |||||||
\(80\) | −13.2968 | + | 7.72462i | −1.48663 | + | 0.863639i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.5836 | − | 1.66525i | 1.38962 | − | 0.183897i | ||||
\(83\) | 10.5770i | 1.16098i | 0.814268 | + | 0.580489i | \(0.197138\pi\) | ||||
−0.814268 | + | 0.580489i | \(0.802862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.4219i | 1.45581i | ||||||||
\(86\) | −1.49124 | − | 11.2687i | −0.160805 | − | 1.21513i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.94487 | − | 11.8703i | −0.527125 | − | 1.26538i | ||||
\(89\) | 15.9580i | 1.69154i | 0.533544 | + | 0.845772i | \(0.320860\pi\) | ||||
−0.533544 | + | 0.845772i | \(0.679140\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.94487 | + | 3.79726i | −0.308707 | + | 0.398061i | ||||
\(92\) | 2.60444 | + | 9.66797i | 0.271532 | + | 1.00796i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.897201 | − | 6.77975i | −0.0925392 | − | 0.699278i | ||||
\(95\) | 6.48559i | 0.665408i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.6085i | − | 1.17866i | −0.807892 | − | 0.589331i | \(-0.799391\pi\) | ||
0.807892 | − | 0.589331i | \(-0.200609\pi\) | |||||||
\(98\) | 9.18192 | − | 3.70032i | 0.927514 | − | 0.373789i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.8862 | + | 5.08773i | −1.88862 | + | 0.508773i | ||||
\(101\) | 11.5333 | 1.14761 | 0.573805 | − | 0.818992i | \(-0.305467\pi\) | ||||
0.573805 | + | 0.818992i | \(0.305467\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.14230 | 0.112555 | 0.0562773 | − | 0.998415i | \(-0.482077\pi\) | ||||
0.0562773 | + | 0.998415i | \(0.482077\pi\) | |||||||
\(104\) | 1.97545 | + | 4.74213i | 0.193709 | + | 0.465004i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.23338 | − | 1.08957i | 0.799696 | − | 0.105828i | ||||
\(107\) | −0.0796192 | −0.00769707 | −0.00384854 | − | 0.999993i | \(-0.501225\pi\) | ||||
−0.00384854 | + | 0.999993i | \(0.501225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 20.1081i | − | 1.92601i | −0.269489 | − | 0.963004i | \(-0.586855\pi\) | ||
0.269489 | − | 0.963004i | \(-0.413145\pi\) | |||||||
\(110\) | −3.24280 | − | 24.5044i | −0.309189 | − | 2.33640i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.40711 | − | 10.4890i | 0.132959 | − | 0.991121i | ||||
\(113\) | −4.98249 | −0.468713 | −0.234356 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234356 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.2465i | 1.79475i | ||||||||
\(116\) | −0.944872 | − | 3.50747i | −0.0877292 | − | 0.325660i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.8703 | − | 1.57086i | 1.09275 | − | 0.144610i | ||||
\(119\) | −7.29918 | − | 5.66070i | −0.669114 | − | 0.518915i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.66949 | 0.879045 | ||||||||
\(122\) | 0.560226 | + | 4.23338i | 0.0507205 | + | 0.383272i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.3187 | + | 2.77975i | −0.926649 | + | 0.249629i | ||||
\(125\) | −18.3755 | −1.64355 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.38471i | 0.477816i | 0.971042 | + | 0.238908i | \(0.0767894\pi\) | ||||
−0.971042 | + | 0.238908i | \(0.923211\pi\) | |||||||
\(128\) | −9.00803 | − | 6.84510i | −0.796205 | − | 0.605027i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.29548 | + | 9.78938i | 0.113621 | + | 0.858586i | ||||
\(131\) | − | 13.0927i | − | 1.14392i | −0.820282 | − | 0.571959i | \(-0.806184\pi\) | ||
0.820282 | − | 0.571959i | \(-0.193816\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.52704 | − | 2.73531i | −0.305833 | − | 0.237181i | ||||
\(134\) | −0.821752 | − | 6.20961i | −0.0709885 | − | 0.536428i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.11543 | + | 3.79726i | −0.781642 | + | 0.325612i | ||||
\(137\) | 19.5595 | 1.67108 | 0.835540 | − | 0.549429i | \(-0.185155\pi\) | ||||
0.835540 | + | 0.549429i | \(0.185155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.5910i | 1.23759i | 0.785553 | + | 0.618795i | \(0.212379\pi\) | ||||
−0.785553 | + | 0.618795i | \(0.787621\pi\) | |||||||
\(140\) | 7.85620 | − | 18.7647i | 0.663970 | − | 1.58590i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.07394 | − | 0.274455i | 0.174041 | − | 0.0230318i | ||||
\(143\) | −8.25737 | −0.690516 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.98249i | − | 0.579864i | ||||||
\(146\) | −9.78938 | + | 1.29548i | −0.810175 | + | 0.107215i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.742132 | + | 2.75488i | 0.0610029 | + | 0.226449i | ||||
\(149\) | 18.3973i | 1.50717i | 0.657352 | + | 0.753584i | \(0.271676\pi\) | ||||
−0.657352 | + | 0.753584i | \(0.728324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.88759i | 0.804641i | 0.915499 | + | 0.402320i | \(0.131796\pi\) | ||||
−0.915499 | + | 0.402320i | \(0.868204\pi\) | |||||||
\(152\) | −4.40467 | + | 1.83488i | −0.357266 | + | 0.148828i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.6938 | + | 8.57123i | 1.18406 | + | 0.690689i | ||||
\(155\) | −20.5420 | −1.64997 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.3582 | −0.986294 | −0.493147 | − | 0.869946i | \(-0.664154\pi\) | ||||
−0.493147 | + | 0.869946i | \(0.664154\pi\) | |||||||
\(158\) | 4.17531 | − | 0.552541i | 0.332169 | − | 0.0439578i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.2968 | − | 17.2089i | −1.05121 | − | 1.36048i | ||||
\(161\) | −10.4668 | − | 8.11723i | −0.824896 | − | 0.639728i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.57086 | −0.279692 | −0.139846 | − | 0.990173i | \(-0.544661\pi\) | ||||
−0.139846 | + | 0.990173i | \(0.544661\pi\) | |||||||
\(164\) | 4.66934 | + | 17.3331i | 0.364614 | + | 1.35349i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.8289 | + | 1.96239i | −1.15094 | + | 0.152311i | ||||
\(167\) | 19.5788 | 1.51505 | 0.757525 | − | 0.652806i | \(-0.226408\pi\) | ||||
0.757525 | + | 0.652806i | \(0.226408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.70122 | −0.746248 | ||||||||
\(170\) | −18.8174 | + | 2.49020i | −1.44323 | + | 0.190990i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.5219 | − | 4.18142i | 1.18353 | − | 0.318830i | ||||
\(173\) | −5.49424 | −0.417719 | −0.208860 | − | 0.977946i | \(-0.566975\pi\) | ||||
−0.208860 | + | 0.977946i | \(0.566975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.8569 | − | 20.4466i | 1.19867 | − | 1.54562i | ||||
\(176\) | 15.7246 | − | 9.13500i | 1.18529 | − | 0.688576i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.3730 | + | 2.96074i | −1.67692 | + | 0.221917i | ||||
\(179\) | −10.0306 | −0.749725 | −0.374862 | − | 0.927080i | \(-0.622310\pi\) | ||||
−0.374862 | + | 0.927080i | \(0.622310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.2481 | 1.80235 | 0.901174 | − | 0.433458i | \(-0.142707\pi\) | ||||
0.901174 | + | 0.433458i | \(0.142707\pi\) | |||||||
\(182\) | −5.87009 | − | 3.42417i | −0.435120 | − | 0.253816i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.0712 | + | 5.44513i | −0.963621 | + | 0.401420i | ||||
\(185\) | 5.48426i | 0.403211i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 15.8725i | − | 1.16071i | ||||||
\(188\) | 9.33868 | − | 2.51574i | 0.681093 | − | 0.183479i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.09274 | + | 1.20329i | −0.659657 | + | 0.0872960i | ||||
\(191\) | 8.49422i | 0.614620i | 0.951609 | + | 0.307310i | \(0.0994288\pi\) | ||||
−0.951609 | + | 0.307310i | \(0.900571\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2955 | −0.813067 | −0.406533 | − | 0.913636i | \(-0.633262\pi\) | ||||
−0.406533 | + | 0.913636i | \(0.633262\pi\) | |||||||
\(194\) | 16.2750 | − | 2.15376i | 1.16848 | − | 0.154631i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.89136 | + | 12.1864i | 0.492240 | + | 0.870459i | ||||
\(197\) | 2.38473i | 0.169905i | 0.996385 | + | 0.0849526i | \(0.0270739\pi\) | ||||
−0.996385 | + | 0.0849526i | \(0.972926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.46338 | 0.174624 | 0.0873120 | − | 0.996181i | \(-0.472172\pi\) | ||||
0.0873120 | + | 0.996181i | \(0.472172\pi\) | |||||||
\(200\) | −10.6370 | − | 25.5343i | −0.752147 | − | 1.80555i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.13981 | + | 16.1696i | 0.150557 | + | 1.13769i | ||||
\(203\) | 3.79726 | + | 2.94487i | 0.266515 | + | 0.206690i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.5058i | 2.40999i | ||||||||
\(206\) | 0.211935 | + | 1.60150i | 0.0147662 | + | 0.111582i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.28191 | + | 3.64939i | −0.435572 | + | 0.253040i | ||||
\(209\) | − | 7.66975i | − | 0.530528i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0376150 | −0.00258952 | −0.00129476 | − | 0.999999i | \(-0.500412\pi\) | ||||
−0.00129476 | + | 0.999999i | \(0.500412\pi\) | |||||||
\(212\) | 3.05513 | + | 11.3410i | 0.209827 | + | 0.778901i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.0147720 | − | 0.111625i | −0.00100979 | − | 0.00763055i | ||||
\(215\) | 30.9002 | 2.10737 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.66361 | − | 11.1713i | 0.588124 | − | 0.758355i | ||||
\(218\) | 28.1914 | − | 3.73072i | 1.90936 | − | 0.252676i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 33.7532 | − | 9.09274i | 2.27564 | − | 0.613033i | ||||
\(221\) | 6.34099i | 0.426541i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9144 | 0.864812 | 0.432406 | − | 0.901679i | \(-0.357665\pi\) | ||||
0.432406 | + | 0.901679i | \(0.357665\pi\) | |||||||
\(224\) | 14.9666 | + | 0.0266914i | 0.999998 | + | 0.00178340i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.924416 | − | 6.98540i | −0.0614913 | − | 0.464662i | ||||
\(227\) | − | 1.48426i | − | 0.0985141i | −0.998786 | − | 0.0492571i | \(-0.984315\pi\) | ||
0.998786 | − | 0.0492571i | \(-0.0156854\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.66934 | 0.308559 | 0.154279 | − | 0.988027i | \(-0.450694\pi\) | ||||
0.154279 | + | 0.988027i | \(0.450694\pi\) | |||||||
\(230\) | −26.9834 | + | 3.57086i | −1.77923 | + | 0.235456i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.74213 | − | 1.97545i | 0.311336 | − | 0.129695i | ||||
\(233\) | 8.35650 | 0.547452 | 0.273726 | − | 0.961808i | \(-0.411744\pi\) | ||||
0.273726 | + | 0.961808i | \(0.411744\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.5910 | 1.21274 | ||||||||
\(236\) | 4.40467 | + | 16.3506i | 0.286720 | + | 1.06433i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.58201 | − | 11.2836i | 0.426648 | − | 0.731409i | ||||
\(239\) | 19.8547i | 1.28430i | 0.766580 | + | 0.642148i | \(0.221957\pi\) | ||||
−0.766580 | + | 0.642148i | \(0.778043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.57701i | − | 0.423662i | −0.977306 | − | 0.211831i | \(-0.932057\pi\) | ||
0.977306 | − | 0.211831i | \(-0.0679427\pi\) | |||||||
\(242\) | 1.79401 | + | 13.5565i | 0.115323 | + | 0.871447i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.83121 | + | 1.57086i | −0.373305 | + | 0.100564i | ||||
\(245\) | 6.69753 | + | 26.0644i | 0.427889 | + | 1.66519i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.06403i | 0.194960i | ||||||||
\(248\) | −5.81164 | − | 13.9510i | −0.369040 | − | 0.885890i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.40926 | − | 25.7622i | −0.215620 | − | 1.62935i | ||||
\(251\) | 4.85827i | 0.306652i | 0.988176 | + | 0.153326i | \(0.0489984\pi\) | ||||
−0.988176 | + | 0.153326i | \(0.951002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 22.7606i | − | 1.43094i | ||||||
\(254\) | −7.54931 | + | 0.999042i | −0.473686 | + | 0.0626855i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92547 | − | 13.8992i | 0.495342 | − | 0.868698i | ||||
\(257\) | 9.20998i | 0.574503i | 0.957855 | + | 0.287251i | \(0.0927415\pi\) | ||||
−0.957855 | + | 0.287251i | \(0.907259\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.98249 | − | 2.31300i | −0.185323 | − | 0.143723i | ||||
\(260\) | −13.4843 | + | 3.63251i | −0.836259 | + | 0.225279i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.3559 | − | 2.42914i | 1.13403 | − | 0.150073i | ||||
\(263\) | − | 3.90849i | − | 0.241008i | −0.992713 | − | 0.120504i | \(-0.961549\pi\) | ||
0.992713 | − | 0.120504i | \(-0.0384511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.5770i | 1.38689i | ||||||||
\(266\) | 3.18049 | − | 5.45236i | 0.195009 | − | 0.334306i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.55335 | − | 2.30418i | 0.522479 | − | 0.140750i | ||||
\(269\) | 9.24872 | 0.563905 | 0.281952 | − | 0.959428i | \(-0.409018\pi\) | ||||
0.281952 | + | 0.959428i | \(0.409018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.5201 | −1.00352 | −0.501762 | − | 0.865006i | \(-0.667315\pi\) | ||||
−0.501762 | + | 0.865006i | \(0.667315\pi\) | |||||||
\(272\) | −7.01494 | − | 12.0752i | −0.425343 | − | 0.732168i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.62893 | + | 27.4222i | 0.219232 | + | 1.65664i | ||||
\(275\) | 44.4624 | 2.68118 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.26465i | 0.196154i | 0.995179 | + | 0.0980769i | \(0.0312691\pi\) | ||||
−0.995179 | + | 0.0980769i | \(0.968731\pi\) | |||||||
\(278\) | −20.4564 | + | 2.70711i | −1.22689 | + | 0.162361i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 27.7655 | + | 7.53284i | 1.65931 | + | 0.450174i | ||||
\(281\) | −19.1680 | −1.14347 | −0.571733 | − | 0.820440i | \(-0.693729\pi\) | ||||
−0.571733 | + | 0.820440i | \(0.693729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.2780i | − | 1.20540i | −0.797968 | − | 0.602700i | \(-0.794092\pi\) | ||
0.797968 | − | 0.602700i | \(-0.205908\pi\) | |||||||
\(284\) | 0.769567 | + | 2.85672i | 0.0456654 | + | 0.169515i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.53201 | − | 11.5767i | −0.0905899 | − | 0.684548i | ||||
\(287\) | −18.7652 | − | 14.5529i | −1.10767 | − | 0.859029i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.81122 | 0.283013 | ||||||||
\(290\) | 9.78938 | − | 1.29548i | 0.574852 | − | 0.0760734i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.63251 | − | 13.4843i | −0.212576 | − | 0.789107i | ||||
\(293\) | 5.07037 | 0.296214 | 0.148107 | − | 0.988971i | \(-0.452682\pi\) | ||||
0.148107 | + | 0.988971i | \(0.452682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.5500i | 1.89513i | ||||||||
\(296\) | −3.72462 | + | 1.55158i | −0.216489 | + | 0.0901839i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −25.7929 | + | 3.41331i | −1.49414 | + | 0.197728i | ||||
\(299\) | 9.09274i | 0.525847i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.0322 | + | 16.8043i | −0.751162 | + | 0.968585i | ||||
\(302\) | −13.8623 | + | 1.83448i | −0.797686 | + | 0.105562i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.38969 | − | 5.83488i | −0.194412 | − | 0.334653i | ||||
\(305\) | −11.6085 | −0.664700 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.2465i | − | 0.870164i | −0.900391 | − | 0.435082i | \(-0.856719\pi\) | ||
0.900391 | − | 0.435082i | \(-0.143281\pi\) | |||||||
\(308\) | −9.29060 | + | 22.1908i | −0.529381 | + | 1.26444i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.81122 | − | 28.7997i | −0.216463 | − | 1.63571i | ||||
\(311\) | −8.91481 | −0.505513 | −0.252756 | − | 0.967530i | \(-0.581337\pi\) | ||||
−0.252756 | + | 0.967530i | \(0.581337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9335i | 1.40932i | 0.709543 | + | 0.704662i | \(0.248902\pi\) | ||||
−0.709543 | + | 0.704662i | \(0.751098\pi\) | |||||||
\(314\) | −2.29286 | − | 17.3261i | −0.129394 | − | 0.977769i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.54931 | + | 5.75122i | 0.0871558 | + | 0.323532i | ||||
\(317\) | − | 16.1127i | − | 0.904980i | −0.891769 | − | 0.452490i | \(-0.850536\pi\) | ||
0.891769 | − | 0.452490i | \(-0.149464\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.25737i | 0.462324i | ||||||||
\(320\) | 21.6597 | − | 21.8349i | 1.21081 | − | 1.22061i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.43836 | − | 16.1803i | 0.525979 | − | 0.901693i | ||||
\(323\) | −5.88974 | −0.327714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.7625 | −0.985287 | ||||||||
\(326\) | −0.662513 | − | 5.00632i | −0.0366932 | − | 0.277274i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −23.4345 | + | 9.76223i | −1.29395 | + | 0.539029i | ||||
\(329\) | −7.84076 | + | 10.1103i | −0.432275 | + | 0.557396i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3802 | 1.23012 | 0.615062 | − | 0.788479i | \(-0.289131\pi\) | ||||
0.615062 | + | 0.788479i | \(0.289131\pi\) | |||||||
\(332\) | −5.50249 | − | 20.4258i | −0.301988 | − | 1.12101i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.63251 | + | 27.4492i | 0.198762 | + | 1.50196i | ||||
\(335\) | 17.0276 | 0.930315 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.22051 | 0.120959 | 0.0604795 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604795 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(338\) | −1.79990 | − | 13.6010i | −0.0979015 | − | 0.739798i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.98249 | − | 25.9197i | −0.378679 | − | 1.40570i | ||||
\(341\) | 24.2926 | 1.31552 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9992 | − | 7.35038i | −0.917869 | − | 0.396883i | ||||
\(344\) | 8.74213 | + | 20.9857i | 0.471344 | + | 1.13148i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.01936 | − | 7.70287i | −0.0548013 | − | 0.414109i | ||||
\(347\) | 17.4186 | 0.935080 | 0.467540 | − | 0.883972i | \(-0.345140\pi\) | ||||
0.467540 | + | 0.883972i | \(0.345140\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.0839 | 1.55683 | 0.778413 | − | 0.627753i | \(-0.216025\pi\) | ||||
0.778413 | + | 0.627753i | \(0.216025\pi\) | |||||||
\(350\) | 31.6079 | + | 18.4377i | 1.68951 | + | 0.985534i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.7246 | + | 20.3509i | 0.838125 | + | 1.08471i | ||||
\(353\) | − | 7.02449i | − | 0.373876i | −0.982372 | − | 0.186938i | \(-0.940144\pi\) | ||
0.982372 | − | 0.186938i | \(-0.0598563\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.68700i | 0.301835i | ||||||||
\(356\) | −8.30185 | − | 30.8174i | −0.439997 | − | 1.63332i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.86102 | − | 14.0629i | −0.0983577 | − | 0.743245i | ||||
\(359\) | 11.1509i | 0.588521i | 0.955725 | + | 0.294260i | \(0.0950733\pi\) | ||||
−0.955725 | + | 0.294260i | \(0.904927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1540 | 0.850211 | ||||||||
\(362\) | 4.49883 | + | 33.9956i | 0.236453 | + | 1.78677i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.71155 | − | 8.86511i | 0.194538 | − | 0.464658i | ||||
\(365\) | − | 26.8438i | − | 1.40507i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.42880 | 0.335581 | 0.167790 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167790 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(368\) | −10.0592 | − | 17.3154i | −0.524370 | − | 0.902630i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.68889 | + | 1.01751i | −0.399726 | + | 0.0528980i | ||||
\(371\) | −12.2780 | − | 9.52188i | −0.637440 | − | 0.494351i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.75527i | − | 0.0908842i | −0.998967 | − | 0.0454421i | \(-0.985530\pi\) | ||
0.998967 | − | 0.0454421i | \(-0.0144697\pi\) | |||||||
\(374\) | 22.2531 | − | 2.94487i | 1.15068 | − | 0.152276i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.25967 | + | 12.6260i | 0.271247 | + | 0.651136i | ||||
\(377\) | − | 3.29878i | − | 0.169896i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0061 | −0.976280 | −0.488140 | − | 0.872765i | \(-0.662324\pi\) | ||||
−0.488140 | + | 0.872765i | \(0.662324\pi\) | |||||||
\(380\) | −3.37401 | − | 12.5247i | −0.173083 | − | 0.642503i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.9088 | + | 1.57596i | −0.609308 | + | 0.0806330i | ||||
\(383\) | −28.4936 | −1.45595 | −0.727977 | − | 0.685602i | \(-0.759539\pi\) | ||||
−0.727977 | + | 0.685602i | \(0.759539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.3392 | + | 36.5420i | −1.44430 | + | 1.86235i | ||||
\(386\) | −2.09569 | − | 15.8362i | −0.106668 | − | 0.806039i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.03909 | + | 22.4178i | 0.306589 | + | 1.13809i | ||||
\(389\) | − | 29.3858i | − | 1.48992i | −0.667110 | − | 0.744960i | \(-0.732469\pi\) | ||
0.667110 | − | 0.744960i | \(-0.267531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.4783 | −0.883914 | ||||||||
\(392\) | −15.8067 | + | 11.9226i | −0.798358 | + | 0.602183i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.34337 | + | 0.442447i | −0.168437 | + | 0.0222902i | ||||
\(395\) | 11.4492i | 0.576074i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5442 | −0.780143 | −0.390071 | − | 0.920785i | \(-0.627550\pi\) | ||||
−0.390071 | + | 0.920785i | \(0.627550\pi\) | |||||||
\(398\) | 0.457038 | + | 3.45363i | 0.0229092 | + | 0.173115i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 33.8254 | − | 19.6504i | 1.69127 | − | 0.982520i | ||||
\(401\) | 15.5595 | 0.777004 | 0.388502 | − | 0.921448i | \(-0.372993\pi\) | ||||
0.388502 | + | 0.921448i | \(0.372993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.70478 | −0.483429 | ||||||||
\(404\) | −22.2726 | + | 6.00000i | −1.10811 | + | 0.298511i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.42417 | + | 5.87009i | −0.169938 | + | 0.291328i | ||||
\(407\) | − | 6.48559i | − | 0.321479i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.3565i | − | 0.907670i | −0.891086 | − | 0.453835i | \(-0.850055\pi\) | ||
0.891086 | − | 0.453835i | \(-0.149945\pi\) | |||||||
\(410\) | −48.3769 | + | 6.40198i | −2.38916 | + | 0.316171i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.20597 | + | 0.594262i | −0.108680 | + | 0.0292772i | ||||
\(413\) | −17.7015 | − | 13.7280i | −0.871035 | − | 0.675510i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 40.6627i | − | 1.99605i | ||||||
\(416\) | −6.28191 | − | 8.13010i | −0.307996 | − | 0.398611i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.7529 | − | 1.42299i | 0.525942 | − | 0.0696008i | ||||
\(419\) | − | 21.1680i | − | 1.03412i | −0.855948 | − | 0.517062i | \(-0.827026\pi\) | ||
0.855948 | − | 0.517062i | \(-0.172974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.20597i | − | 0.107512i | −0.998554 | − | 0.0537561i | \(-0.982881\pi\) | ||
0.998554 | − | 0.0537561i | \(-0.0171193\pi\) | |||||||
\(422\) | −0.00697882 | − | 0.0527358i | −0.000339724 | − | 0.00256714i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.3331 | + | 6.38738i | −0.744641 | + | 0.310199i | ||||
\(425\) | − | 34.1435i | − | 1.65620i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.89589 | − | 6.31300i | 0.236929 | − | 0.305507i | ||||
\(428\) | 0.153757 | − | 0.0414204i | 0.00743212 | − | 0.00200213i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.73300 | + | 43.3217i | 0.276470 | + | 2.08916i | ||||
\(431\) | 17.4255i | 0.839358i | 0.907673 | + | 0.419679i | \(0.137857\pi\) | ||||
−0.907673 | + | 0.419679i | \(0.862143\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.18549i | 0.105028i | 0.998620 | + | 0.0525139i | \(0.0167234\pi\) | ||||
−0.998620 | + | 0.0525139i | \(0.983277\pi\) | |||||||
\(434\) | 17.2694 | + | 10.0737i | 0.828958 | + | 0.483551i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.4609 | + | 38.8319i | 0.500985 | + | 1.85971i | ||||
\(437\) | −8.44568 | −0.404012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.5128 | 1.31311 | 0.656556 | − | 0.754277i | \(-0.272013\pi\) | ||||
0.656556 | + | 0.754277i | \(0.272013\pi\) | |||||||
\(440\) | 19.0103 | + | 45.6347i | 0.906280 | + | 2.17555i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.89000 | + | 1.17646i | −0.422854 | + | 0.0559586i | ||||
\(443\) | −3.37840 | −0.160513 | −0.0802563 | − | 0.996774i | \(-0.525574\pi\) | ||||
−0.0802563 | + | 0.996774i | \(0.525574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 61.3496i | − | 2.90825i | ||||||
\(446\) | 2.39605 | + | 18.1059i | 0.113456 | + | 0.857338i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.73938 | + | 20.9880i | 0.129424 | + | 0.991589i | ||||
\(449\) | −1.76553 | −0.0833206 | −0.0416603 | − | 0.999132i | \(-0.513265\pi\) | ||||
−0.0416603 | + | 0.999132i | \(0.513265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 40.8060i | − | 1.92148i | ||||||
\(452\) | 9.62195 | − | 2.59205i | 0.452579 | − | 0.121920i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.08093 | − | 0.275380i | 0.0976627 | − | 0.0129242i | ||||
\(455\) | 11.3214 | − | 14.5984i | 0.530755 | − | 0.684381i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.4178 | −1.14222 | −0.571108 | − | 0.820875i | \(-0.693486\pi\) | ||||
−0.571108 | + | 0.820875i | \(0.693486\pi\) | |||||||
\(458\) | 0.866317 | + | 6.54637i | 0.0404803 | + | 0.305892i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.0126 | − | 37.1680i | −0.466841 | − | 1.73297i | ||||
\(461\) | −7.77884 | −0.362297 | −0.181148 | − | 0.983456i | \(-0.557981\pi\) | ||||
−0.181148 | + | 0.983456i | \(0.557981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.5615i | − | 0.769678i | −0.922984 | − | 0.384839i | \(-0.874257\pi\) | ||
0.922984 | − | 0.384839i | \(-0.125743\pi\) | |||||||
\(464\) | 3.64939 | + | 6.28191i | 0.169419 | + | 0.291630i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.55041 | + | 11.7157i | 0.0718212 | + | 0.542721i | ||||
\(467\) | 14.1103i | 0.652945i | 0.945207 | + | 0.326472i | \(0.105860\pi\) | ||||
−0.945207 | + | 0.326472i | \(0.894140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.18140 | + | 9.26004i | −0.331606 | + | 0.427589i | ||||
\(470\) | 3.44924 | + | 26.0644i | 0.159102 | + | 1.20226i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.1062 | + | 9.20888i | −1.01752 | + | 0.423873i | ||||
\(473\) | −36.5420 | −1.68020 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 16.4985i | − | 0.757002i | ||||||
\(476\) | 17.0407 | + | 7.13442i | 0.781060 | + | 0.327006i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.8362 | + | 3.68371i | −1.27320 | + | 0.168489i | ||||
\(479\) | −8.74757 | −0.399687 | −0.199843 | − | 0.979828i | \(-0.564043\pi\) | ||||
−0.199843 | + | 0.979828i | \(0.564043\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.59097i | 0.118138i | ||||||||
\(482\) | 9.22090 | − | 1.22025i | 0.420001 | − | 0.0555810i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.6733 | + | 5.03037i | −0.848786 | + | 0.228653i | ||||
\(485\) | 44.6281i | 2.02646i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.0252i | 1.40589i | 0.711246 | + | 0.702943i | \(0.248131\pi\) | ||||
−0.711246 | + | 0.702943i | \(0.751869\pi\) | |||||||
\(488\) | −3.28422 | − | 7.88386i | −0.148670 | − | 0.356885i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −35.2994 | + | 14.2257i | −1.59466 | + | 0.642650i | ||||
\(491\) | 22.0446 | 0.994859 | 0.497429 | − | 0.867505i | \(-0.334277\pi\) | ||||
0.497429 | + | 0.867505i | \(0.334277\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.34099 | 0.285584 | ||||||||
\(494\) | −4.29574 | + | 0.568479i | −0.193275 | + | 0.0255771i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.4809 | − | 10.7362i | 0.829819 | − | 0.482072i | ||||
\(497\) | −3.09274 | − | 2.39850i | −0.138728 | − | 0.107587i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.6409 | 1.81934 | 0.909668 | − | 0.415337i | \(-0.136336\pi\) | ||||
0.909668 | + | 0.415337i | \(0.136336\pi\) | |||||||
\(500\) | 35.4859 | − | 9.55949i | 1.58698 | − | 0.427514i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.81125 | + | 0.901371i | −0.304001 | + | 0.0402301i | ||||
\(503\) | −33.1848 | −1.47964 | −0.739818 | − | 0.672807i | \(-0.765088\pi\) | ||||
−0.739818 | + | 0.672807i | \(0.765088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.3392 | −1.97307 | ||||||||
\(506\) | 31.9101 | − | 4.22284i | 1.41858 | − | 0.187728i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.80130 | − | 10.3987i | −0.124287 | − | 0.461368i | ||||
\(509\) | −35.5240 | −1.57457 | −0.787287 | − | 0.616586i | \(-0.788515\pi\) | ||||
−0.787287 | + | 0.616586i | \(0.788515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5984 | + | 11.3214i | 0.645793 | + | 0.500829i | ||||
\(512\) | 20.9569 | + | 8.53268i | 0.926175 | + | 0.377095i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.9123 | + | 1.70876i | −0.569537 | + | 0.0753700i | ||||
\(515\) | −4.39152 | −0.193514 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.9853 | −0.966914 | ||||||||
\(518\) | 2.68945 | − | 4.61056i | 0.118168 | − | 0.202576i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.59452 | − | 18.2309i | −0.333042 | − | 0.799476i | ||||
\(521\) | 26.4737i | 1.15984i | 0.814675 | + | 0.579918i | \(0.196915\pi\) | ||||
−0.814675 | + | 0.579918i | \(0.803085\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.7100i | 1.82385i | 0.410358 | + | 0.911924i | \(0.365404\pi\) | ||||
−0.410358 | + | 0.911924i | \(0.634596\pi\) | |||||||
\(524\) | 6.81125 | + | 25.2841i | 0.297551 | + | 1.10454i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.47967 | − | 0.725155i | 0.238925 | − | 0.0316183i | ||||
\(527\) | − | 18.6547i | − | 0.812613i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.06320 | −0.0897043 | ||||||||
\(530\) | −31.6528 | + | 4.18878i | −1.37491 | + | 0.181949i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.23425 | + | 3.44743i | 0.357000 | + | 0.149465i | ||||
\(533\) | 16.3018i | 0.706110i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.306091 | 0.0132335 | ||||||||
\(536\) | 4.81736 | + | 11.5642i | 0.208078 | + | 0.499498i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.71594 | + | 12.9666i | 0.0739796 | + | 0.559031i | ||||
\(539\) | −7.92038 | − | 30.8232i | −0.341155 | − | 1.32765i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.3187i | 0.443637i | 0.975088 | + | 0.221818i | \(0.0711992\pi\) | ||||
−0.975088 | + | 0.221818i | \(0.928801\pi\) | |||||||
\(542\) | −3.06502 | − | 23.1610i | −0.131654 | − | 0.994850i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.6279 | − | 12.0752i | 0.670039 | − | 0.517721i | ||||
\(545\) | 77.3045i | 3.31136i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.6461 | 0.840006 | 0.420003 | − | 0.907523i | \(-0.362029\pi\) | ||||
0.420003 | + | 0.907523i | \(0.362029\pi\) | |||||||
\(548\) | −37.7724 | + | 10.1755i | −1.61356 | + | 0.434674i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.24924 | + | 62.3358i | 0.351749 | + | 2.65801i | ||||
\(551\) | 3.06403 | 0.130532 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.22640 | − | 4.82873i | −0.264773 | − | 0.205339i | ||||
\(554\) | −4.57701 | + | 0.605701i | −0.194458 | + | 0.0257337i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.59068 | − | 28.1774i | −0.321916 | − | 1.19499i | ||||
\(557\) | − | 30.0989i | − | 1.27533i | −0.770314 | − | 0.637665i | \(-0.779900\pi\) | ||
0.770314 | − | 0.637665i | \(-0.220100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5984 | 0.617445 | ||||||||
\(560\) | −5.40956 | + | 40.3245i | −0.228596 | + | 1.70402i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.55629 | − | 26.8733i | −0.150013 | − | 1.13358i | ||||
\(563\) | 6.35650i | 0.267894i | 0.990988 | + | 0.133947i | \(0.0427653\pi\) | ||||
−0.990988 | + | 0.133947i | \(0.957235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.1549 | 0.805852 | ||||||||
\(566\) | 28.4295 | − | 3.76223i | 1.19498 | − | 0.158139i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.86231 | + | 1.60894i | −0.162059 | + | 0.0675097i | ||||
\(569\) | 37.7589 | 1.58294 | 0.791469 | − | 0.611210i | \(-0.209317\pi\) | ||||
0.791469 | + | 0.611210i | \(0.209317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.0324 | −1.21497 | −0.607484 | − | 0.794332i | \(-0.707821\pi\) | ||||
−0.607484 | + | 0.794332i | \(0.707821\pi\) | |||||||
\(572\) | 15.9463 | − | 4.29574i | 0.666746 | − | 0.179614i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.9214 | − | 29.0086i | 0.706287 | − | 1.21080i | ||||
\(575\) | − | 48.9605i | − | 2.04179i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.4060i | 1.59886i | 0.600758 | + | 0.799431i | \(0.294866\pi\) | ||||
−0.600758 | + | 0.799431i | \(0.705134\pi\) | |||||||
\(578\) | 0.892640 | + | 6.74528i | 0.0371289 | + | 0.280567i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.63251 | + | 13.4843i | 0.150832 | + | 0.559904i | ||||
\(581\) | 22.1134 | + | 17.1495i | 0.917420 | + | 0.711483i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 26.6992i | − | 1.10577i | ||||||
\(584\) | 18.2309 | − | 7.59452i | 0.754398 | − | 0.314263i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.940721 | + | 7.10861i | 0.0388608 | + | 0.293654i | ||||
\(587\) | − | 0.157054i | − | 0.00648231i | −0.999995 | − | 0.00324116i | \(-0.998968\pi\) | ||
0.999995 | − | 0.00324116i | \(-0.00103169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.01416i | − | 0.371422i | ||||||
\(590\) | −45.6347 | + | 6.03909i | −1.87875 | + | 0.248626i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.86635 | − | 4.93401i | −0.117806 | − | 0.202787i | ||||
\(593\) | − | 37.5927i | − | 1.54375i | −0.635776 | − | 0.771874i | \(-0.719320\pi\) | ||
0.635776 | − | 0.771874i | \(-0.280680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.0613 | + | 21.7622i | 1.15040 | + | 0.892165i | ||||
\(596\) | −9.57086 | − | 35.5281i | −0.392038 | − | 1.45529i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.7479 | + | 1.68700i | −0.521302 | + | 0.0689868i | ||||
\(599\) | 18.7569i | 0.766387i | 0.923668 | + | 0.383194i | \(0.125176\pi\) | ||||
−0.923668 | + | 0.383194i | \(0.874824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.44051i | 0.0995503i | 0.998760 | + | 0.0497751i | \(0.0158505\pi\) | ||||
−0.998760 | + | 0.0497751i | \(0.984150\pi\) | |||||||
\(602\) | −25.9774 | − | 15.1532i | −1.05876 | − | 0.617600i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.14383 | − | 19.0945i | −0.209300 | − | 0.776943i | ||||
\(605\) | −37.1738 | −1.51133 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.4839 | −1.64319 | −0.821596 | − | 0.570070i | \(-0.806916\pi\) | ||||
−0.821596 | + | 0.570070i | \(0.806916\pi\) | |||||||
\(608\) | 7.55154 | − | 5.83488i | 0.306255 | − | 0.236635i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.15376 | − | 16.2750i | −0.0872031 | − | 0.658955i | ||||
\(611\) | 8.78304 | 0.355324 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.57378i | 0.346292i | 0.984896 | + | 0.173146i | \(0.0553932\pi\) | ||||
−0.984896 | + | 0.173146i | \(0.944607\pi\) | |||||||
\(614\) | 21.3754 | − | 2.82873i | 0.862643 | − | 0.114158i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −32.8350 | − | 8.90821i | −1.32296 | − | 0.358922i | ||||
\(617\) | −31.3390 | −1.26166 | −0.630830 | − | 0.775921i | \(-0.717285\pi\) | ||||
−0.630830 | + | 0.775921i | \(0.717285\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.5595i | 1.67042i | 0.549933 | + | 0.835209i | \(0.314653\pi\) | ||||
−0.549933 | + | 0.835209i | \(0.685347\pi\) | |||||||
\(620\) | 39.6698 | − | 10.6866i | 1.59318 | − | 0.429183i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.65399 | − | 12.4985i | −0.0663191 | − | 0.501143i | ||||
\(623\) | 33.3635 | + | 25.8743i | 1.33668 | + | 1.03663i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7447 | 0.869789 | ||||||||
\(626\) | −34.9565 | + | 4.62599i | −1.39714 | + | 0.184892i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.8657 | − | 6.42914i | 0.952343 | − | 0.256551i | ||||
\(629\) | −4.98041 | −0.198582 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 48.0528i | − | 1.91295i | −0.291814 | − | 0.956475i | \(-0.594259\pi\) | ||
0.291814 | − | 0.956475i | \(-0.405741\pi\) | |||||||
\(632\) | −7.77571 | + | 3.23917i | −0.309301 | + | 0.128847i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.5899 | − | 2.98944i | 0.897158 | − | 0.118726i | ||||
\(635\) | − | 20.7012i | − | 0.821503i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.16416 | + | 12.3137i | 0.125368 | + | 0.487888i | ||||
\(638\) | −11.5767 | + | 1.53201i | −0.458328 | + | 0.0606530i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 34.6309 | + | 26.3156i | 1.36891 | + | 1.04021i | ||||
\(641\) | 26.9335 | 1.06381 | 0.531905 | − | 0.846804i | \(-0.321476\pi\) | ||||
0.531905 | + | 0.846804i | \(0.321476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20.2780i | − | 0.799685i | −0.916584 | − | 0.399843i | \(-0.869065\pi\) | ||
0.916584 | − | 0.399843i | \(-0.130935\pi\) | |||||||
\(644\) | 24.4358 | + | 10.2305i | 0.962904 | + | 0.403138i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.09274 | − | 8.25737i | −0.0429934 | − | 0.324882i | ||||
\(647\) | 16.3928 | 0.644466 | 0.322233 | − | 0.946660i | \(-0.395567\pi\) | ||||
0.322233 | + | 0.946660i | \(0.395567\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 38.4930i | − | 1.51098i | ||||||
\(650\) | −3.29553 | − | 24.9029i | −0.129261 | − | 0.976771i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.89589 | − | 1.85767i | 0.270064 | − | 0.0727522i | ||||
\(653\) | − | 27.4567i | − | 1.07447i | −0.843434 | − | 0.537233i | \(-0.819470\pi\) | ||
0.843434 | − | 0.537233i | \(-0.180530\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 50.3343i | 1.96672i | ||||||||
\(656\) | −18.0344 | − | 31.0438i | −0.704127 | − | 1.21206i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.6292 | − | 9.11689i | −0.609290 | − | 0.355413i | ||||
\(659\) | −34.1059 | −1.32858 | −0.664288 | − | 0.747477i | \(-0.731265\pi\) | ||||
−0.664288 | + | 0.747477i | \(0.731265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.0551 | 1.63575 | 0.817877 | − | 0.575393i | \(-0.195151\pi\) | ||||
0.817877 | + | 0.575393i | \(0.195151\pi\) | |||||||
\(662\) | 4.15226 | + | 31.3768i | 0.161382 | + | 1.21949i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.6159 | − | 11.5041i | 1.07171 | − | 0.446446i | ||||
\(665\) | 13.5595 | + | 10.5157i | 0.525815 | + | 0.407783i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.09274 | 0.352072 | ||||||||
\(668\) | −37.8096 | + | 10.1855i | −1.46290 | + | 0.394088i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.15918 | + | 23.8725i | 0.122050 | + | 0.922275i | ||||
\(671\) | 13.7280 | 0.529963 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.0405 | 1.65909 | 0.829544 | − | 0.558441i | \(-0.188600\pi\) | ||||
0.829544 | + | 0.558441i | \(0.188600\pi\) | |||||||
\(674\) | 0.411978 | + | 3.11313i | 0.0158688 | + | 0.119913i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.7346 | − | 5.04688i | 0.720560 | − | 0.194111i | ||||
\(677\) | 5.91811 | 0.227451 | 0.113726 | − | 0.993512i | \(-0.463722\pi\) | ||||
0.113726 | + | 0.993512i | \(0.463722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.2700 | − | 18.8220i | −0.931395 | − | 0.722321i | ||||
\(680\) | 35.0438 | − | 14.5984i | 1.34387 | − | 0.559821i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.50708 | + | 34.0580i | 0.172585 | + | 1.30415i | ||||
\(683\) | 1.50261 | 0.0574958 | 0.0287479 | − | 0.999587i | \(-0.490848\pi\) | ||||
0.0287479 | + | 0.999587i | \(0.490848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −75.1954 | −2.87307 | ||||||||
\(686\) | 7.15126 | − | 25.1964i | 0.273036 | − | 0.962004i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.7998 | + | 16.1499i | −1.05986 | + | 0.615711i | ||||
\(689\) | 10.6662i | 0.406350i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.62599i | − | 0.328148i | −0.986448 | − | 0.164074i | \(-0.947536\pi\) | ||
0.986448 | − | 0.164074i | \(-0.0524636\pi\) | |||||||
\(692\) | 10.6102 | − | 2.85827i | 0.403340 | − | 0.108655i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.23173 | + | 24.4207i | 0.122675 | + | 0.926998i | ||||
\(695\) | − | 56.0941i | − | 2.12777i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.3357 | −1.18692 | ||||||||
\(698\) | 5.39603 | + | 40.7754i | 0.204243 | + | 1.54337i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −19.9851 | + | 47.7348i | −0.755366 | + | 1.80421i | ||||
\(701\) | − | 10.4065i | − | 0.393050i | −0.980499 | − | 0.196525i | \(-0.937034\pi\) | ||
0.980499 | − | 0.196525i | \(-0.0629656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.40659 | −0.0907661 | ||||||||
\(704\) | −25.6144 | + | 25.8215i | −0.965378 | + | 0.973186i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.84827 | − | 1.30328i | 0.370645 | − | 0.0490494i | ||||
\(707\) | 18.7001 | − | 24.1128i | 0.703291 | − | 0.906857i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.8737i | 1.30971i | 0.755755 | + | 0.654855i | \(0.227270\pi\) | ||||
−0.755755 | + | 0.654855i | \(0.772730\pi\) | |||||||
\(710\) | −7.97313 | + | 1.05513i | −0.299226 | + | 0.0395982i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 41.6654 | − | 17.3568i | 1.56148 | − | 0.650472i | ||||
\(713\) | − | 26.7502i | − | 1.00180i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.7450 | 1.18719 | ||||||||
\(716\) | 19.3707 | − | 5.21825i | 0.723918 | − | 0.195015i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.6334 | + | 2.06886i | −0.583434 | + | 0.0772091i | ||||
\(719\) | −8.74757 | −0.326229 | −0.163115 | − | 0.986607i | \(-0.552154\pi\) | ||||
−0.163115 | + | 0.986607i | \(0.552154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.85213 | − | 2.38823i | 0.0689769 | − | 0.0889422i | ||||
\(722\) | 2.99710 | + | 22.6478i | 0.111541 | + | 0.842863i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −46.8268 | + | 12.6146i | −1.74031 | + | 0.468819i | ||||
\(725\) | 17.7625i | 0.659683i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.7851 | −0.882140 | −0.441070 | − | 0.897473i | \(-0.645401\pi\) | ||||
−0.441070 | + | 0.897473i | \(0.645401\pi\) | |||||||
\(728\) | 13.1174 | + | 3.55879i | 0.486164 | + | 0.131897i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 37.6347 | − | 4.98041i | 1.39292 | − | 0.184333i | ||||
\(731\) | 28.0613i | 1.03788i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.79132 | 0.176971 | 0.0884857 | − | 0.996077i | \(-0.471797\pi\) | ||||
0.0884857 | + | 0.996077i | \(0.471797\pi\) | |||||||
\(734\) | 1.19276 | + | 9.01312i | 0.0440254 | + | 0.332680i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.4098 | − | 17.3154i | 0.826035 | − | 0.638256i | ||||
\(737\) | −20.1365 | −0.741738 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.7563 | 0.506035 | 0.253018 | − | 0.967462i | \(-0.418577\pi\) | ||||
0.253018 | + | 0.967462i | \(0.418577\pi\) | |||||||
\(740\) | −2.85309 | − | 10.5910i | −0.104882 | − | 0.389332i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.0716 | − | 18.9802i | 0.406452 | − | 0.696786i | ||||
\(743\) | 11.5310i | 0.423033i | 0.977374 | + | 0.211517i | \(0.0678402\pi\) | ||||
−0.977374 | + | 0.211517i | \(0.932160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 70.7275i | − | 2.59125i | ||||||
\(746\) | 2.46087 | − | 0.325660i | 0.0900987 | − | 0.0119233i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.25737 | + | 30.6522i | 0.301919 | + | 1.12076i | ||||
\(749\) | −0.129094 | + | 0.166461i | −0.00471701 | + | 0.00608234i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.8541i | 1.49079i | 0.666625 | + | 0.745393i | \(0.267738\pi\) | ||||
−0.666625 | + | 0.745393i | \(0.732262\pi\) | |||||||
\(752\) | −16.7257 | + | 9.71655i | −0.609923 | + | 0.354326i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.62486 | − | 0.612033i | 0.168427 | − | 0.0222889i | ||||
\(755\) | − | 38.0123i | − | 1.38341i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 27.8196i | − | 1.01112i | −0.862791 | − | 0.505561i | \(-0.831286\pi\) | ||
0.862791 | − | 0.505561i | \(-0.168714\pi\) | |||||||
\(758\) | −3.52627 | − | 26.6464i | −0.128080 | − | 0.967842i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.9335 | − | 7.05407i | 0.614243 | − | 0.255878i | ||||
\(761\) | − | 26.4737i | − | 0.959672i | −0.877358 | − | 0.479836i | \(-0.840696\pi\) | ||
0.877358 | − | 0.479836i | \(-0.159304\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.0402 | − | 32.6033i | −1.52196 | − | 1.18032i | ||||
\(764\) | −4.41896 | − | 16.4036i | −0.159872 | − | 0.593463i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.28650 | − | 39.9477i | −0.191009 | − | 1.44337i | ||||
\(767\) | 15.3778i | 0.555259i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.5945i | − | 1.13933i | −0.821878 | − | 0.569664i | \(-0.807073\pi\) | ||
0.821878 | − | 0.569664i | \(-0.192927\pi\) | |||||||
\(770\) | −56.4894 | − | 32.9516i | −2.03574 | − | 1.18749i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.8133 | − | 5.87626i | 0.785079 | − | 0.211491i | ||||
\(773\) | 33.5413 | 1.20640 | 0.603199 | − | 0.797591i | \(-0.293893\pi\) | ||||
0.603199 | + | 0.797591i | \(0.293893\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 52.2560 | 1.87709 | ||||||||
\(776\) | −30.3090 | + | 12.6260i | −1.08803 | + | 0.453247i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.1986 | − | 5.45204i | 1.47704 | − | 0.195465i | ||||
\(779\) | −15.1417 | −0.542509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.72535i | − | 0.240652i | ||||||
\(782\) | −3.24280 | − | 24.5044i | −0.115962 | − | 0.876274i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.6481 | − | 19.9488i | −0.701716 | − | 0.712457i | ||||
\(785\) | 47.5105 | 1.69572 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03147i | 0.0367679i | 0.999831 | + | 0.0183840i | \(0.00585213\pi\) | ||||
−0.999831 | + | 0.0183840i | \(0.994148\pi\) | |||||||
\(788\) | −1.24061 | − | 4.60529i | −0.0441950 | − | 0.164057i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.0517 | + | 2.12421i | −0.571095 | + | 0.0755761i | ||||
\(791\) | −8.07860 | + | 10.4169i | −0.287242 | + | 0.370384i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.48426 | −0.194752 | ||||||||
\(794\) | −2.88397 | − | 21.7929i | −0.102348 | − | 0.773400i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.75716 | + | 1.28152i | −0.168613 | + | 0.0454224i | ||||
\(797\) | 22.2199 | 0.787070 | 0.393535 | − | 0.919310i | \(-0.371252\pi\) | ||||
0.393535 | + | 0.919310i | \(0.371252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8830i | 0.597276i | ||||||||
\(800\) | 33.8254 | + | 43.7771i | 1.19591 | + | 1.54775i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.88680 | + | 21.8143i | 0.101937 | + | 0.770288i | ||||
\(803\) | 31.7450i | 1.12026i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.2388 | + | 31.2062i | 1.41823 | + | 1.09988i | ||||
\(806\) | −1.80056 | − | 13.6060i | −0.0634219 | − | 0.479251i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.5443 | − | 30.1128i | −0.441305 | − | 1.05937i | ||||
\(809\) | 52.4790 | 1.84506 | 0.922532 | − | 0.385920i | \(-0.126116\pi\) | ||||
0.922532 | + | 0.385920i | \(0.126116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.40548i | − | 0.154697i | −0.997004 | − | 0.0773487i | \(-0.975355\pi\) | ||
0.997004 | − | 0.0773487i | \(-0.0246455\pi\) | |||||||
\(812\) | −8.86511 | − | 3.71155i | −0.311104 | − | 0.130250i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.09274 | − | 1.20329i | 0.318700 | − | 0.0421754i | ||||
\(815\) | 13.7280 | 0.480870 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5595i | 0.474387i | ||||||||
\(818\) | 25.7356 | − | 3.40574i | 0.899825 | − | 0.119079i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.9510 | − | 66.6361i | −0.626877 | − | 2.32703i | ||||
\(821\) | 21.2067i | 0.740119i | 0.929008 | + | 0.370060i | \(0.120663\pi\) | ||||
−0.929008 | + | 0.370060i | \(0.879337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.3609i | 1.02346i | 0.859148 | + | 0.511728i | \(0.170994\pi\) | ||||
−0.859148 | + | 0.511728i | \(0.829006\pi\) | |||||||
\(824\) | −1.24243 | − | 2.98249i | −0.0432821 | − | 0.103900i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.9623 | − | 27.3644i | 0.555399 | − | 0.952128i | ||||
\(827\) | 28.2161 | 0.981171 | 0.490585 | − | 0.871393i | \(-0.336783\pi\) | ||||
0.490585 | + | 0.871393i | \(0.336783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.77173 | 0.339386 | 0.169693 | − | 0.985497i | \(-0.445722\pi\) | ||||
0.169693 | + | 0.985497i | \(0.445722\pi\) | |||||||
\(830\) | 57.0087 | − | 7.54428i | 1.97880 | − | 0.261866i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.2328 | − | 10.3156i | 0.354759 | − | 0.357629i | ||||
\(833\) | −23.6698 | + | 6.08221i | −0.820108 | + | 0.210736i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −75.2694 | −2.60481 | ||||||||
\(836\) | 3.99004 | + | 14.8115i | 0.137999 | + | 0.512266i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.6773 | − | 3.92736i | 1.02519 | − | 0.135668i | ||||
\(839\) | −35.0785 | −1.21104 | −0.605522 | − | 0.795828i | \(-0.707036\pi\) | ||||
−0.605522 | + | 0.795828i | \(0.707036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.7012 | 0.886249 | ||||||||
\(842\) | 3.09274 | − | 0.409280i | 0.106583 | − | 0.0141047i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0726403 | − | 0.0195685i | 0.00250038 | − | 0.000673575i | ||||
\(845\) | 37.2958 | 1.28301 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.6781 | − | 20.2161i | 0.538706 | − | 0.694633i | ||||
\(848\) | −11.7998 | − | 20.3118i | −0.405209 | − | 0.697510i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 47.8688 | − | 6.33475i | 1.64189 | − | 0.217280i | ||||
\(851\) | −7.14173 | −0.244815 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.3536 | −0.628416 | −0.314208 | − | 0.949354i | \(-0.601739\pi\) | ||||
−0.314208 | + | 0.949354i | \(0.601739\pi\) | |||||||
\(854\) | 9.75911 | + | 5.69272i | 0.333950 | + | 0.194801i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0865980 | + | 0.207881i | 0.00295986 | + | 0.00710522i | ||||
\(857\) | − | 7.62775i | − | 0.260559i | −0.991477 | − | 0.130279i | \(-0.958413\pi\) | ||
0.991477 | − | 0.130279i | \(-0.0415874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.9075i | 0.474518i | 0.971446 | + | 0.237259i | \(0.0762491\pi\) | ||||
−0.971446 | + | 0.237259i | \(0.923751\pi\) | |||||||
\(860\) | −59.6730 | + | 16.0752i | −2.03483 | + | 0.548161i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.4304 | + | 3.23301i | −0.832104 | + | 0.110117i | ||||
\(863\) | 13.3074i | 0.452989i | 0.974012 | + | 0.226494i | \(0.0727265\pi\) | ||||
−0.974012 | + | 0.226494i | \(0.927274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.1223 | 0.718179 | ||||||||
\(866\) | −3.06403 | + | 0.405480i | −0.104120 | + | 0.0137788i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.9191 | + | 26.0805i | −0.370619 | + | 0.885231i | ||||
\(869\) | − | 13.5397i | − | 0.459302i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.04444 | 0.272575 | ||||||||
\(872\) | −52.5011 | + | 21.8706i | −1.77791 | + | 0.740633i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.56695 | − | 11.8408i | −0.0530030 | − | 0.400520i | ||||
\(875\) | −29.7940 | + | 38.4178i | −1.00722 | + | 1.29876i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 25.0885i | − | 0.847179i | −0.905854 | − | 0.423589i | \(-0.860770\pi\) | ||
0.905854 | − | 0.423589i | \(-0.139230\pi\) | |||||||
\(878\) | 5.10453 | + | 38.5726i | 0.172269 | + | 1.30176i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −60.4524 | + | 35.1190i | −2.03785 | + | 1.18386i | ||||
\(881\) | 5.29180i | 0.178285i | 0.996019 | + | 0.0891426i | \(0.0284127\pi\) | ||||
−0.996019 | + | 0.0891426i | \(0.971587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5219 | −0.724269 | −0.362134 | − | 0.932126i | \(-0.617952\pi\) | ||||
−0.362134 | + | 0.932126i | \(0.617952\pi\) | |||||||
\(884\) | −3.29878 | − | 12.2454i | −0.110950 | − | 0.411858i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.626805 | − | 4.73648i | −0.0210579 | − | 0.159125i | ||||
\(887\) | −14.7656 | −0.495780 | −0.247890 | − | 0.968788i | \(-0.579737\pi\) | ||||
−0.247890 | + | 0.968788i | \(0.579737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.2579 | + | 8.73076i | 0.377577 | + | 0.292820i | ||||
\(890\) | 86.0116 | − | 11.3824i | 2.88311 | − | 0.381538i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.9397 | + | 6.71848i | −0.835043 | + | 0.224951i | ||||
\(893\) | 8.15802i | 0.272998i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.5622 | 1.28899 | ||||||||
\(896\) | −28.9167 | + | 7.73455i | −0.966040 | + | 0.258393i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.327565 | − | 2.47526i | −0.0109310 | − | 0.0826005i | ||||
\(899\) | 9.70478i | 0.323672i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.5028 | −0.683047 | ||||||||
\(902\) | 57.2096 | − | 7.57086i | 1.90487 | − | 0.252082i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.41922 | + | 13.0090i | 0.180240 | + | 0.432672i | ||||
\(905\) | −93.2205 | −3.09875 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.8609 | 1.55599 | 0.777995 | − | 0.628271i | \(-0.216237\pi\) | ||||
0.777995 | + | 0.628271i | \(0.216237\pi\) | |||||||
\(908\) | 0.772161 | + | 2.86635i | 0.0256251 | + | 0.0951230i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.5672 | + | 13.1640i | 0.748097 | + | 0.436383i | ||||
\(911\) | 54.6440i | 1.81044i | 0.424945 | + | 0.905219i | \(0.360293\pi\) | ||||
−0.424945 | + | 0.905219i | \(0.639707\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0870i | 1.59145i | ||||||||
\(914\) | −4.53030 | − | 34.2335i | −0.149849 | − | 1.13234i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.01722 | + | 2.42914i | −0.297937 | + | 0.0802610i | ||||
\(917\) | −27.3731 | − | 21.2286i | −0.903940 | − | 0.701029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28.6186i | − | 0.944041i | −0.881588 | − | 0.472020i | \(-0.843525\pi\) | ||
0.881588 | − | 0.472020i | \(-0.156475\pi\) | |||||||
\(920\) | 50.2515 | − | 20.9335i | 1.65674 | − | 0.690157i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.44323 | − | 10.9059i | −0.0475304 | − | 0.359166i | ||||
\(923\) | 2.68675i | 0.0884353i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 13.9512i | − | 0.458714i | ||||||
\(926\) | 23.2191 | − | 3.07271i | 0.763026 | − | 0.100975i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.13010 | + | 6.28191i | −0.266884 | + | 0.206214i | ||||
\(929\) | 29.6885i | 0.974048i | 0.873389 | + | 0.487024i | \(0.161918\pi\) | ||||
−0.873389 | + | 0.487024i | \(0.838082\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.4375 | + | 2.93899i | −0.374848 | + | 0.0963214i | ||||
\(932\) | −16.1377 | + | 4.34731i | −0.528608 | + | 0.142401i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.7824 | + | 2.61792i | −0.647301 | + | 0.0856609i | ||||
\(935\) | 61.0209i | 1.99560i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.4055i | 1.05864i | 0.848422 | + | 0.529320i | \(0.177553\pi\) | ||||
−0.848422 | + | 0.529320i | \(0.822447\pi\) | |||||||
\(938\) | −14.3149 | − | 8.35021i | −0.467397 | − | 0.272644i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35.9020 | + | 9.67160i | −1.17100 | + | 0.315453i | ||||
\(941\) | −10.5656 | −0.344429 | −0.172214 | − | 0.985060i | \(-0.555092\pi\) | ||||
−0.172214 | + | 0.985060i | \(0.555092\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.9342 | −1.46326 | ||||||||
\(944\) | −17.0122 | − | 29.2841i | −0.553700 | − | 0.953117i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.77975 | − | 51.2315i | −0.220429 | − | 1.66568i | ||||
\(947\) | 3.44186 | 0.111845 | 0.0559226 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559226 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.6820i | − | 0.411674i | ||||||
\(950\) | 23.1307 | − | 3.06101i | 0.750459 | − | 0.0993124i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.84078 | + | 25.2146i | −0.221711 | + | 0.817210i | ||||
\(953\) | 38.5559 | 1.24895 | 0.624475 | − | 0.781045i | \(-0.285313\pi\) | ||||
0.624475 | + | 0.781045i | \(0.285313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 32.6555i | − | 1.05671i | ||||||
\(956\) | −10.3291 | − | 38.3426i | −0.334066 | − | 1.24009i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.62296 | − | 12.2640i | −0.0524356 | − | 0.396232i | ||||
\(959\) | 31.7137 | − | 40.8932i | 1.02409 | − | 1.32051i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.44924 | −0.0790077 | ||||||||
\(962\) | −3.63251 | + | 0.480710i | −0.117117 | + | 0.0154987i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.42157 | + | 12.7012i | 0.110201 | + | 0.409079i | ||||
\(965\) | 43.4248 | 1.39790 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0322i | 0.322614i | 0.986904 | + | 0.161307i | \(0.0515709\pi\) | ||||
−0.986904 | + | 0.161307i | \(0.948429\pi\) | |||||||
\(968\) | −10.5170 | − | 25.2465i | −0.338031 | − | 0.811452i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −62.5682 | + | 8.28000i | −2.00894 | + | 0.265855i | ||||
\(971\) | 28.4807i | 0.913989i | 0.889469 | + | 0.456995i | \(0.151074\pi\) | ||||
−0.889469 | + | 0.456995i | \(0.848926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.5055 | + | 23.6578i | 0.977960 | + | 0.758433i | ||||
\(974\) | −43.4970 | + | 5.75620i | −1.39373 | + | 0.184441i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.4438 | − | 6.06716i | 0.334297 | − | 0.194205i | ||||
\(977\) | −8.98249 | −0.287375 | −0.143688 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143688 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.5510i | 2.31874i | ||||||||
\(980\) | −26.4935 | − | 46.8500i | −0.846303 | − | 1.49657i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.09000 | + | 30.9063i | 0.130517 | + | 0.986260i | ||||
\(983\) | 11.1768 | 0.356484 | 0.178242 | − | 0.983987i | \(-0.442959\pi\) | ||||
0.178242 | + | 0.983987i | \(0.442959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.16797i | − | 0.292116i | ||||||
\(986\) | 1.17646 | + | 8.89000i | 0.0374662 | + | 0.283115i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.59400 | − | 5.91712i | −0.0507120 | − | 0.188249i | ||||
\(989\) | 40.2388i | 1.27952i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5500i | 0.684559i | 0.939598 | + | 0.342279i | \(0.111199\pi\) | ||||
−0.939598 | + | 0.342279i | \(0.888801\pi\) | |||||||
\(992\) | 18.4809 | + | 23.9182i | 0.586770 | + | 0.759403i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.78887 | − | 4.78100i | 0.0884576 | − | 0.151644i | ||||
\(995\) | −9.47031 | −0.300229 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.2116 | 1.21017 | 0.605087 | − | 0.796159i | \(-0.293138\pi\) | ||||
0.605087 | + | 0.796159i | \(0.293138\pi\) | |||||||
\(998\) | 7.54023 | + | 56.9781i | 0.238682 | + | 1.80361i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.p.g.307.11 | 16 | ||
3.2 | odd | 2 | 168.2.p.a.139.5 | ✓ | 16 | ||
4.3 | odd | 2 | 2016.2.p.g.559.2 | 16 | |||
7.6 | odd | 2 | inner | 504.2.p.g.307.12 | 16 | ||
8.3 | odd | 2 | inner | 504.2.p.g.307.10 | 16 | ||
8.5 | even | 2 | 2016.2.p.g.559.15 | 16 | |||
12.11 | even | 2 | 672.2.p.a.559.16 | 16 | |||
21.20 | even | 2 | 168.2.p.a.139.6 | yes | 16 | ||
24.5 | odd | 2 | 672.2.p.a.559.9 | 16 | |||
24.11 | even | 2 | 168.2.p.a.139.7 | yes | 16 | ||
28.27 | even | 2 | 2016.2.p.g.559.16 | 16 | |||
56.13 | odd | 2 | 2016.2.p.g.559.1 | 16 | |||
56.27 | even | 2 | inner | 504.2.p.g.307.9 | 16 | ||
84.83 | odd | 2 | 672.2.p.a.559.1 | 16 | |||
168.83 | odd | 2 | 168.2.p.a.139.8 | yes | 16 | ||
168.125 | even | 2 | 672.2.p.a.559.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.p.a.139.5 | ✓ | 16 | 3.2 | odd | 2 | ||
168.2.p.a.139.6 | yes | 16 | 21.20 | even | 2 | ||
168.2.p.a.139.7 | yes | 16 | 24.11 | even | 2 | ||
168.2.p.a.139.8 | yes | 16 | 168.83 | odd | 2 | ||
504.2.p.g.307.9 | 16 | 56.27 | even | 2 | inner | ||
504.2.p.g.307.10 | 16 | 8.3 | odd | 2 | inner | ||
504.2.p.g.307.11 | 16 | 1.1 | even | 1 | trivial | ||
504.2.p.g.307.12 | 16 | 7.6 | odd | 2 | inner | ||
672.2.p.a.559.1 | 16 | 84.83 | odd | 2 | |||
672.2.p.a.559.8 | 16 | 168.125 | even | 2 | |||
672.2.p.a.559.9 | 16 | 24.5 | odd | 2 | |||
672.2.p.a.559.16 | 16 | 12.11 | even | 2 | |||
2016.2.p.g.559.1 | 16 | 56.13 | odd | 2 | |||
2016.2.p.g.559.2 | 16 | 4.3 | odd | 2 | |||
2016.2.p.g.559.15 | 16 | 8.5 | even | 2 | |||
2016.2.p.g.559.16 | 16 | 28.27 | even | 2 |