Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1734,2,Mod(829,1734)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([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("1734.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1734 = 2 \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1734.f (of order \(4\), degree \(2\), not 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: | \(13.8460597105\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 102) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 829.3 | ||
Root | \(-0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1734.829 |
Dual form | 1734.2.f.m.1483.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times\).
\(n\) | \(1157\) | \(1159\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.306563 | − | 0.306563i | −0.137099 | − | 0.137099i | 0.635227 | − | 0.772326i | \(-0.280907\pi\) |
−0.772326 | + | 0.635227i | \(0.780907\pi\) | |||||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −2.41421 | + | 2.41421i | −0.912487 | + | 0.912487i | −0.996467 | − | 0.0839804i | \(-0.973237\pi\) |
0.0839804 | + | 0.996467i | \(0.473237\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −0.306563 | + | 0.306563i | −0.0969437 | + | 0.0969437i | ||||
\(11\) | −1.19891 | + | 1.19891i | −0.361486 | + | 0.361486i | −0.864360 | − | 0.502874i | \(-0.832276\pi\) |
0.502874 | + | 0.864360i | \(0.332276\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | 0.331821 | 0.0920307 | 0.0460153 | − | 0.998941i | \(-0.485348\pi\) | ||||
0.0460153 | + | 0.998941i | \(0.485348\pi\) | |||||||
\(14\) | 2.41421 | + | 2.41421i | 0.645226 | + | 0.645226i | ||||
\(15\) | − | 0.433546i | − | 0.111941i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | − | 2.14386i | − | 0.491835i | −0.969291 | − | 0.245918i | \(-0.920911\pi\) | ||
0.969291 | − | 0.245918i | \(-0.0790893\pi\) | |||||||
\(20\) | 0.306563 | + | 0.306563i | 0.0685496 | + | 0.0685496i | ||||
\(21\) | −3.41421 | −0.745042 | ||||||||
\(22\) | 1.19891 | + | 1.19891i | 0.255609 | + | 0.255609i | ||||
\(23\) | 1.33182 | − | 1.33182i | 0.277704 | − | 0.277704i | −0.554488 | − | 0.832192i | \(-0.687086\pi\) |
0.832192 | + | 0.554488i | \(0.187086\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | − | 4.81204i | − | 0.962408i | ||||||
\(26\) | − | 0.331821i | − | 0.0650755i | ||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.41421 | − | 2.41421i | 0.456243 | − | 0.456243i | ||||
\(29\) | −6.03780 | − | 6.03780i | −1.12119 | − | 1.12119i | −0.991563 | − | 0.129629i | \(-0.958621\pi\) |
−0.129629 | − | 0.991563i | \(-0.541379\pi\) | |||||||
\(30\) | −0.433546 | −0.0791542 | ||||||||
\(31\) | 1.82843 | + | 1.82843i | 0.328395 | + | 0.328395i | 0.851976 | − | 0.523581i | \(-0.175404\pi\) |
−0.523581 | + | 0.851976i | \(0.675404\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −1.69552 | −0.295152 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.48022 | 0.250202 | ||||||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −7.50548 | − | 7.50548i | −1.23389 | − | 1.23389i | −0.962456 | − | 0.271436i | \(-0.912501\pi\) |
−0.271436 | − | 0.962456i | \(-0.587499\pi\) | |||||||
\(38\) | −2.14386 | −0.347780 | ||||||||
\(39\) | 0.234633 | + | 0.234633i | 0.0375714 | + | 0.0375714i | ||||
\(40\) | 0.306563 | − | 0.306563i | 0.0484719 | − | 0.0484719i | ||||
\(41\) | −8.56854 | + | 8.56854i | −1.33818 | + | 1.33818i | −0.440358 | + | 0.897822i | \(0.645149\pi\) |
−0.897822 | + | 0.440358i | \(0.854851\pi\) | |||||||
\(42\) | 3.41421i | 0.526825i | ||||||||
\(43\) | − | 10.0933i | − | 1.53922i | −0.638514 | − | 0.769610i | \(-0.720451\pi\) | ||
0.638514 | − | 0.769610i | \(-0.279549\pi\) | |||||||
\(44\) | 1.19891 | − | 1.19891i | 0.180743 | − | 0.180743i | ||||
\(45\) | 0.306563 | − | 0.306563i | 0.0456997 | − | 0.0456997i | ||||
\(46\) | −1.33182 | − | 1.33182i | −0.196366 | − | 0.196366i | ||||
\(47\) | −2.38009 | −0.347171 | −0.173586 | − | 0.984819i | \(-0.555535\pi\) | ||||
−0.173586 | + | 0.984819i | \(0.555535\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 4.65685i | − | 0.665265i | ||||||
\(50\) | −4.81204 | −0.680525 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.331821 | −0.0460153 | ||||||||
\(53\) | 3.13066i | 0.430029i | 0.976611 | + | 0.215014i | \(0.0689798\pi\) | ||||
−0.976611 | + | 0.215014i | \(0.931020\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 0.735084 | 0.0991187 | ||||||||
\(56\) | −2.41421 | − | 2.41421i | −0.322613 | − | 0.322613i | ||||
\(57\) | 1.51594 | − | 1.51594i | 0.200791 | − | 0.200791i | ||||
\(58\) | −6.03780 | + | 6.03780i | −0.792802 | + | 0.792802i | ||||
\(59\) | − | 7.67459i | − | 0.999147i | −0.866272 | − | 0.499573i | \(-0.833490\pi\) | ||
0.866272 | − | 0.499573i | \(-0.166510\pi\) | |||||||
\(60\) | 0.433546i | 0.0559705i | ||||||||
\(61\) | −5.68506 | + | 5.68506i | −0.727897 | + | 0.727897i | −0.970200 | − | 0.242304i | \(-0.922097\pi\) |
0.242304 | + | 0.970200i | \(0.422097\pi\) | |||||||
\(62\) | 1.82843 | − | 1.82843i | 0.232210 | − | 0.232210i | ||||
\(63\) | −2.41421 | − | 2.41421i | −0.304162 | − | 0.304162i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.101724 | − | 0.101724i | −0.0126173 | − | 0.0126173i | ||||
\(66\) | 1.69552i | 0.208704i | ||||||||
\(67\) | −15.7711 | −1.92675 | −0.963375 | − | 0.268159i | \(-0.913585\pi\) | ||||
−0.963375 | + | 0.268159i | \(0.913585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.88348 | 0.226744 | ||||||||
\(70\) | − | 1.48022i | − | 0.176920i | ||||||
\(71\) | 0.160248 | + | 0.160248i | 0.0190180 | + | 0.0190180i | 0.716552 | − | 0.697534i | \(-0.245719\pi\) |
−0.697534 | + | 0.716552i | \(0.745719\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 8.58333 | + | 8.58333i | 1.00460 | + | 1.00460i | 0.999989 | + | 0.00461362i | \(0.00146857\pi\) |
0.00461362 | + | 0.999989i | \(0.498531\pi\) | |||||||
\(74\) | −7.50548 | + | 7.50548i | −0.872494 | + | 0.872494i | ||||
\(75\) | 3.40262 | − | 3.40262i | 0.392901 | − | 0.392901i | ||||
\(76\) | 2.14386i | 0.245918i | ||||||||
\(77\) | − | 5.78886i | − | 0.659702i | ||||||
\(78\) | 0.234633 | − | 0.234633i | 0.0265670 | − | 0.0265670i | ||||
\(79\) | 8.86672 | − | 8.86672i | 0.997584 | − | 0.997584i | −0.00241345 | − | 0.999997i | \(-0.500768\pi\) |
0.999997 | + | 0.00241345i | \(0.000768227\pi\) | |||||||
\(80\) | −0.306563 | − | 0.306563i | −0.0342748 | − | 0.0342748i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 8.56854 | + | 8.56854i | 0.946236 | + | 0.946236i | ||||
\(83\) | 1.04373i | 0.114564i | 0.998358 | + | 0.0572820i | \(0.0182434\pi\) | ||||
−0.998358 | + | 0.0572820i | \(0.981757\pi\) | |||||||
\(84\) | 3.41421 | 0.372521 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.0933 | −1.08839 | ||||||||
\(87\) | − | 8.53874i | − | 0.915449i | ||||||
\(88\) | −1.19891 | − | 1.19891i | −0.127804 | − | 0.127804i | ||||
\(89\) | −13.8281 | −1.46577 | −0.732885 | − | 0.680352i | \(-0.761827\pi\) | ||||
−0.732885 | + | 0.680352i | \(0.761827\pi\) | |||||||
\(90\) | −0.306563 | − | 0.306563i | −0.0323146 | − | 0.0323146i | ||||
\(91\) | −0.801088 | + | 0.801088i | −0.0839768 | + | 0.0839768i | ||||
\(92\) | −1.33182 | + | 1.33182i | −0.138852 | + | 0.138852i | ||||
\(93\) | 2.58579i | 0.268134i | ||||||||
\(94\) | 2.38009i | 0.245487i | ||||||||
\(95\) | −0.657228 | + | 0.657228i | −0.0674302 | + | 0.0674302i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 2.65546 | + | 2.65546i | 0.269621 | + | 0.269621i | 0.828948 | − | 0.559326i | \(-0.188940\pi\) |
−0.559326 | + | 0.828948i | \(0.688940\pi\) | |||||||
\(98\) | −4.65685 | −0.470413 | ||||||||
\(99\) | −1.19891 | − | 1.19891i | −0.120495 | − | 0.120495i | ||||
\(100\) | 4.81204i | 0.481204i | ||||||||
\(101\) | 0.636303 | 0.0633145 | 0.0316573 | − | 0.999499i | \(-0.489921\pi\) | ||||
0.0316573 | + | 0.999499i | \(0.489921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.59955 | 0.847339 | 0.423669 | − | 0.905817i | \(-0.360742\pi\) | ||||
0.423669 | + | 0.905817i | \(0.360742\pi\) | |||||||
\(104\) | 0.331821i | 0.0325378i | ||||||||
\(105\) | 1.04667 | + | 1.04667i | 0.102145 | + | 0.102145i | ||||
\(106\) | 3.13066 | 0.304076 | ||||||||
\(107\) | −1.53073 | − | 1.53073i | −0.147982 | − | 0.147982i | 0.629234 | − | 0.777216i | \(-0.283369\pi\) |
−0.777216 | + | 0.629234i | \(0.783369\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 5.59588 | − | 5.59588i | 0.535988 | − | 0.535988i | −0.386360 | − | 0.922348i | \(-0.626268\pi\) |
0.922348 | + | 0.386360i | \(0.126268\pi\) | |||||||
\(110\) | − | 0.735084i | − | 0.0700875i | ||||||
\(111\) | − | 10.6143i | − | 1.00747i | ||||||
\(112\) | −2.41421 | + | 2.41421i | −0.228122 | + | 0.228122i | ||||
\(113\) | −6.49709 | + | 6.49709i | −0.611195 | + | 0.611195i | −0.943257 | − | 0.332062i | \(-0.892256\pi\) |
0.332062 | + | 0.943257i | \(0.392256\pi\) | |||||||
\(114\) | −1.51594 | − | 1.51594i | −0.141981 | − | 0.141981i | ||||
\(115\) | −0.816574 | −0.0761459 | ||||||||
\(116\) | 6.03780 | + | 6.03780i | 0.560596 | + | 0.560596i | ||||
\(117\) | 0.331821i | 0.0306769i | ||||||||
\(118\) | −7.67459 | −0.706504 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.433546 | 0.0395771 | ||||||||
\(121\) | 8.12522i | 0.738656i | ||||||||
\(122\) | 5.68506 | + | 5.68506i | 0.514701 | + | 0.514701i | ||||
\(123\) | −12.1177 | −1.09262 | ||||||||
\(124\) | −1.82843 | − | 1.82843i | −0.164198 | − | 0.164198i | ||||
\(125\) | −3.00801 | + | 3.00801i | −0.269044 | + | 0.269044i | ||||
\(126\) | −2.41421 | + | 2.41421i | −0.215075 | + | 0.215075i | ||||
\(127\) | − | 12.0843i | − | 1.07231i | −0.844121 | − | 0.536153i | \(-0.819877\pi\) | ||
0.844121 | − | 0.536153i | \(-0.180123\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 7.13707 | − | 7.13707i | 0.628384 | − | 0.628384i | ||||
\(130\) | −0.101724 | + | 0.101724i | −0.00892180 | + | 0.00892180i | ||||
\(131\) | −0.634051 | − | 0.634051i | −0.0553973 | − | 0.0553973i | 0.678865 | − | 0.734263i | \(-0.262472\pi\) |
−0.734263 | + | 0.678865i | \(0.762472\pi\) | |||||||
\(132\) | 1.69552 | 0.147576 | ||||||||
\(133\) | 5.17574 | + | 5.17574i | 0.448793 | + | 0.448793i | ||||
\(134\) | 15.7711i | 1.36242i | ||||||||
\(135\) | 0.433546 | 0.0373137 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6109 | 1.07742 | 0.538710 | − | 0.842491i | \(-0.318912\pi\) | ||||
0.538710 | + | 0.842491i | \(0.318912\pi\) | |||||||
\(138\) | − | 1.88348i | − | 0.160332i | ||||||
\(139\) | 12.0524 | + | 12.0524i | 1.02227 | + | 1.02227i | 0.999746 | + | 0.0225272i | \(0.00717125\pi\) |
0.0225272 | + | 0.999746i | \(0.492829\pi\) | |||||||
\(140\) | −1.48022 | −0.125101 | ||||||||
\(141\) | −1.68297 | − | 1.68297i | −0.141732 | − | 0.141732i | ||||
\(142\) | 0.160248 | − | 0.160248i | 0.0134478 | − | 0.0134478i | ||||
\(143\) | −0.397825 | + | 0.397825i | −0.0332678 | + | 0.0332678i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 3.70193i | 0.307429i | ||||||||
\(146\) | 8.58333 | − | 8.58333i | 0.710362 | − | 0.710362i | ||||
\(147\) | 3.29289 | − | 3.29289i | 0.271593 | − | 0.271593i | ||||
\(148\) | 7.50548 | + | 7.50548i | 0.616946 | + | 0.616946i | ||||
\(149\) | −17.5004 | −1.43369 | −0.716844 | − | 0.697234i | \(-0.754414\pi\) | ||||
−0.716844 | + | 0.697234i | \(0.754414\pi\) | |||||||
\(150\) | −3.40262 | − | 3.40262i | −0.277823 | − | 0.277823i | ||||
\(151\) | − | 9.64009i | − | 0.784500i | −0.919859 | − | 0.392250i | \(-0.871697\pi\) | ||
0.919859 | − | 0.392250i | \(-0.128303\pi\) | |||||||
\(152\) | 2.14386 | 0.173890 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.78886 | −0.466480 | ||||||||
\(155\) | − | 1.12106i | − | 0.0900454i | ||||||
\(156\) | −0.234633 | − | 0.234633i | −0.0187857 | − | 0.0187857i | ||||
\(157\) | 4.78976 | 0.382265 | 0.191132 | − | 0.981564i | \(-0.438784\pi\) | ||||
0.191132 | + | 0.981564i | \(0.438784\pi\) | |||||||
\(158\) | −8.86672 | − | 8.86672i | −0.705398 | − | 0.705398i | ||||
\(159\) | −2.21371 | + | 2.21371i | −0.175558 | + | 0.175558i | ||||
\(160\) | −0.306563 | + | 0.306563i | −0.0242359 | + | 0.0242359i | ||||
\(161\) | 6.43060i | 0.506802i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −12.5899 | + | 12.5899i | −0.986121 | + | 0.986121i | −0.999905 | − | 0.0137841i | \(-0.995612\pi\) |
0.0137841 | + | 0.999905i | \(0.495612\pi\) | |||||||
\(164\) | 8.56854 | − | 8.56854i | 0.669090 | − | 0.669090i | ||||
\(165\) | 0.519783 | + | 0.519783i | 0.0404651 | + | 0.0404651i | ||||
\(166\) | 1.04373 | 0.0810090 | ||||||||
\(167\) | −12.4416 | − | 12.4416i | −0.962756 | − | 0.962756i | 0.0365746 | − | 0.999331i | \(-0.488355\pi\) |
−0.999331 | + | 0.0365746i | \(0.988355\pi\) | |||||||
\(168\) | − | 3.41421i | − | 0.263412i | ||||||
\(169\) | −12.8899 | −0.991530 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.14386 | 0.163945 | ||||||||
\(172\) | 10.0933i | 0.769610i | ||||||||
\(173\) | −13.6799 | − | 13.6799i | −1.04006 | − | 1.04006i | −0.999163 | − | 0.0408971i | \(-0.986978\pi\) |
−0.0408971 | − | 0.999163i | \(-0.513022\pi\) | |||||||
\(174\) | −8.53874 | −0.647320 | ||||||||
\(175\) | 11.6173 | + | 11.6173i | 0.878184 | + | 0.878184i | ||||
\(176\) | −1.19891 | + | 1.19891i | −0.0903714 | + | 0.0903714i | ||||
\(177\) | 5.42676 | − | 5.42676i | 0.407900 | − | 0.407900i | ||||
\(178\) | 13.8281i | 1.03646i | ||||||||
\(179\) | − | 9.11933i | − | 0.681611i | −0.940134 | − | 0.340805i | \(-0.889300\pi\) | ||
0.940134 | − | 0.340805i | \(-0.110700\pi\) | |||||||
\(180\) | −0.306563 | + | 0.306563i | −0.0228499 | + | 0.0228499i | ||||
\(181\) | −0.549204 | + | 0.549204i | −0.0408220 | + | 0.0408220i | −0.727223 | − | 0.686401i | \(-0.759189\pi\) |
0.686401 | + | 0.727223i | \(0.259189\pi\) | |||||||
\(182\) | 0.801088 | + | 0.801088i | 0.0593806 | + | 0.0593806i | ||||
\(183\) | −8.03988 | −0.594325 | ||||||||
\(184\) | 1.33182 | + | 1.33182i | 0.0981832 | + | 0.0981832i | ||||
\(185\) | 4.60180i | 0.338331i | ||||||||
\(186\) | 2.58579 | 0.189599 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.38009 | 0.173586 | ||||||||
\(189\) | − | 3.41421i | − | 0.248347i | ||||||
\(190\) | 0.657228 | + | 0.657228i | 0.0476803 | + | 0.0476803i | ||||
\(191\) | 13.4248 | 0.971384 | 0.485692 | − | 0.874130i | \(-0.338568\pi\) | ||||
0.485692 | + | 0.874130i | \(0.338568\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 3.59850 | − | 3.59850i | 0.259026 | − | 0.259026i | −0.565632 | − | 0.824658i | \(-0.691368\pi\) |
0.824658 | + | 0.565632i | \(0.191368\pi\) | |||||||
\(194\) | 2.65546 | − | 2.65546i | 0.190651 | − | 0.190651i | ||||
\(195\) | − | 0.143860i | − | 0.0103020i | ||||||
\(196\) | 4.65685i | 0.332632i | ||||||||
\(197\) | 2.93767 | − | 2.93767i | 0.209300 | − | 0.209300i | −0.594670 | − | 0.803970i | \(-0.702717\pi\) |
0.803970 | + | 0.594670i | \(0.202717\pi\) | |||||||
\(198\) | −1.19891 | + | 1.19891i | −0.0852030 | + | 0.0852030i | ||||
\(199\) | 7.57221 | + | 7.57221i | 0.536780 | + | 0.536780i | 0.922582 | − | 0.385802i | \(-0.126075\pi\) |
−0.385802 | + | 0.922582i | \(0.626075\pi\) | |||||||
\(200\) | 4.81204 | 0.340262 | ||||||||
\(201\) | −11.1519 | − | 11.1519i | −0.786592 | − | 0.786592i | ||||
\(202\) | − | 0.636303i | − | 0.0447701i | ||||||
\(203\) | 29.1531 | 2.04615 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.25359 | 0.366927 | ||||||||
\(206\) | − | 8.59955i | − | 0.599159i | ||||||
\(207\) | 1.33182 | + | 1.33182i | 0.0925680 | + | 0.0925680i | ||||
\(208\) | 0.331821 | 0.0230077 | ||||||||
\(209\) | 2.57030 | + | 2.57030i | 0.177791 | + | 0.177791i | ||||
\(210\) | 1.04667 | − | 1.04667i | 0.0722272 | − | 0.0722272i | ||||
\(211\) | 3.33861 | − | 3.33861i | 0.229839 | − | 0.229839i | −0.582786 | − | 0.812626i | \(-0.698037\pi\) |
0.812626 | + | 0.582786i | \(0.198037\pi\) | |||||||
\(212\) | − | 3.13066i | − | 0.215014i | ||||||
\(213\) | 0.226626i | 0.0155281i | ||||||||
\(214\) | −1.53073 | + | 1.53073i | −0.104639 | + | 0.104639i | ||||
\(215\) | −3.09425 | + | 3.09425i | −0.211026 | + | 0.211026i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | −8.82843 | −0.599313 | ||||||||
\(218\) | −5.59588 | − | 5.59588i | −0.379000 | − | 0.379000i | ||||
\(219\) | 12.1387i | 0.820255i | ||||||||
\(220\) | −0.735084 | −0.0495594 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.6143 | −0.712388 | ||||||||
\(223\) | 15.6359i | 1.04706i | 0.852007 | + | 0.523530i | \(0.175385\pi\) | ||||
−0.852007 | + | 0.523530i | \(0.824615\pi\) | |||||||
\(224\) | 2.41421 | + | 2.41421i | 0.161306 | + | 0.161306i | ||||
\(225\) | 4.81204 | 0.320803 | ||||||||
\(226\) | 6.49709 | + | 6.49709i | 0.432180 | + | 0.432180i | ||||
\(227\) | −7.82164 | + | 7.82164i | −0.519140 | + | 0.519140i | −0.917311 | − | 0.398171i | \(-0.869645\pi\) |
0.398171 | + | 0.917311i | \(0.369645\pi\) | |||||||
\(228\) | −1.51594 | + | 1.51594i | −0.100395 | + | 0.100395i | ||||
\(229\) | − | 15.3852i | − | 1.01668i | −0.861157 | − | 0.508340i | \(-0.830259\pi\) | ||
0.861157 | − | 0.508340i | \(-0.169741\pi\) | |||||||
\(230\) | 0.816574i | 0.0538433i | ||||||||
\(231\) | 4.09334 | − | 4.09334i | 0.269322 | − | 0.269322i | ||||
\(232\) | 6.03780 | − | 6.03780i | 0.396401 | − | 0.396401i | ||||
\(233\) | −7.33806 | − | 7.33806i | −0.480733 | − | 0.480733i | 0.424633 | − | 0.905366i | \(-0.360403\pi\) |
−0.905366 | + | 0.424633i | \(0.860403\pi\) | |||||||
\(234\) | 0.331821 | 0.0216918 | ||||||||
\(235\) | 0.729646 | + | 0.729646i | 0.0475969 | + | 0.0475969i | ||||
\(236\) | 7.67459i | 0.499573i | ||||||||
\(237\) | 12.5394 | 0.814524 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.7803 | −1.60291 | −0.801454 | − | 0.598057i | \(-0.795940\pi\) | ||||
−0.801454 | + | 0.598057i | \(0.795940\pi\) | |||||||
\(240\) | − | 0.433546i | − | 0.0279852i | ||||||
\(241\) | −3.04422 | − | 3.04422i | −0.196095 | − | 0.196095i | 0.602229 | − | 0.798324i | \(-0.294280\pi\) |
−0.798324 | + | 0.602229i | \(0.794280\pi\) | |||||||
\(242\) | 8.12522 | 0.522309 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 5.68506 | − | 5.68506i | 0.363948 | − | 0.363948i | ||||
\(245\) | −1.42762 | + | 1.42762i | −0.0912072 | + | 0.0912072i | ||||
\(246\) | 12.1177i | 0.772599i | ||||||||
\(247\) | − | 0.711378i | − | 0.0452639i | ||||||
\(248\) | −1.82843 | + | 1.82843i | −0.116105 | + | 0.116105i | ||||
\(249\) | −0.738027 | + | 0.738027i | −0.0467706 | + | 0.0467706i | ||||
\(250\) | 3.00801 | + | 3.00801i | 0.190243 | + | 0.190243i | ||||
\(251\) | 19.0639 | 1.20330 | 0.601652 | − | 0.798759i | \(-0.294510\pi\) | ||||
0.601652 | + | 0.798759i | \(0.294510\pi\) | |||||||
\(252\) | 2.41421 | + | 2.41421i | 0.152081 | + | 0.152081i | ||||
\(253\) | 3.19347i | 0.200772i | ||||||||
\(254\) | −12.0843 | −0.758235 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.7594i | 1.66921i | 0.550851 | + | 0.834603i | \(0.314303\pi\) | ||||
−0.550851 | + | 0.834603i | \(0.685697\pi\) | |||||||
\(258\) | −7.13707 | − | 7.13707i | −0.444335 | − | 0.444335i | ||||
\(259\) | 36.2396 | 2.25182 | ||||||||
\(260\) | 0.101724 | + | 0.101724i | 0.00630866 | + | 0.00630866i | ||||
\(261\) | 6.03780 | − | 6.03780i | 0.373731 | − | 0.373731i | ||||
\(262\) | −0.634051 | + | 0.634051i | −0.0391718 | + | 0.0391718i | ||||
\(263\) | 27.5122i | 1.69648i | 0.529614 | + | 0.848239i | \(0.322337\pi\) | ||||
−0.529614 | + | 0.848239i | \(0.677663\pi\) | |||||||
\(264\) | − | 1.69552i | − | 0.104352i | ||||||
\(265\) | 0.959743 | − | 0.959743i | 0.0589566 | − | 0.0589566i | ||||
\(266\) | 5.17574 | − | 5.17574i | 0.317345 | − | 0.317345i | ||||
\(267\) | −9.77791 | − | 9.77791i | −0.598398 | − | 0.598398i | ||||
\(268\) | 15.7711 | 0.963375 | ||||||||
\(269\) | −7.08153 | − | 7.08153i | −0.431769 | − | 0.431769i | 0.457461 | − | 0.889230i | \(-0.348759\pi\) |
−0.889230 | + | 0.457461i | \(0.848759\pi\) | |||||||
\(270\) | − | 0.433546i | − | 0.0263847i | ||||||
\(271\) | 9.20949 | 0.559437 | 0.279718 | − | 0.960082i | \(-0.409759\pi\) | ||||
0.279718 | + | 0.960082i | \(0.409759\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.13291 | −0.0685668 | ||||||||
\(274\) | − | 12.6109i | − | 0.761851i | ||||||
\(275\) | 5.76921 | + | 5.76921i | 0.347897 | + | 0.347897i | ||||
\(276\) | −1.88348 | −0.113372 | ||||||||
\(277\) | 5.91515 | + | 5.91515i | 0.355407 | + | 0.355407i | 0.862117 | − | 0.506710i | \(-0.169138\pi\) |
−0.506710 | + | 0.862117i | \(0.669138\pi\) | |||||||
\(278\) | 12.0524 | − | 12.0524i | 0.722857 | − | 0.722857i | ||||
\(279\) | −1.82843 | + | 1.82843i | −0.109465 | + | 0.109465i | ||||
\(280\) | 1.48022i | 0.0884599i | ||||||||
\(281\) | 10.9996i | 0.656183i | 0.944646 | + | 0.328091i | \(0.106405\pi\) | ||||
−0.944646 | + | 0.328091i | \(0.893595\pi\) | |||||||
\(282\) | −1.68297 | + | 1.68297i | −0.100220 | + | 0.100220i | ||||
\(283\) | −14.9469 | + | 14.9469i | −0.888498 | + | 0.888498i | −0.994379 | − | 0.105880i | \(-0.966234\pi\) |
0.105880 | + | 0.994379i | \(0.466234\pi\) | |||||||
\(284\) | −0.160248 | − | 0.160248i | −0.00950900 | − | 0.00950900i | ||||
\(285\) | −0.929461 | −0.0550565 | ||||||||
\(286\) | 0.397825 | + | 0.397825i | 0.0235239 | + | 0.0235239i | ||||
\(287\) | − | 41.3725i | − | 2.44214i | ||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 3.70193 | 0.217385 | ||||||||
\(291\) | 3.75539i | 0.220145i | ||||||||
\(292\) | −8.58333 | − | 8.58333i | −0.502301 | − | 0.502301i | ||||
\(293\) | −25.1277 | −1.46797 | −0.733987 | − | 0.679164i | \(-0.762343\pi\) | ||||
−0.733987 | + | 0.679164i | \(0.762343\pi\) | |||||||
\(294\) | −3.29289 | − | 3.29289i | −0.192045 | − | 0.192045i | ||||
\(295\) | −2.35275 | + | 2.35275i | −0.136982 | + | 0.136982i | ||||
\(296\) | 7.50548 | − | 7.50548i | 0.436247 | − | 0.436247i | ||||
\(297\) | − | 1.69552i | − | 0.0983839i | ||||||
\(298\) | 17.5004i | 1.01377i | ||||||||
\(299\) | 0.441927 | − | 0.441927i | 0.0255573 | − | 0.0255573i | ||||
\(300\) | −3.40262 | + | 3.40262i | −0.196451 | + | 0.196451i | ||||
\(301\) | 24.3675 | + | 24.3675i | 1.40452 | + | 1.40452i | ||||
\(302\) | −9.64009 | −0.554725 | ||||||||
\(303\) | 0.449934 | + | 0.449934i | 0.0258481 | + | 0.0258481i | ||||
\(304\) | − | 2.14386i | − | 0.122959i | ||||||
\(305\) | 3.48566 | 0.199588 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.3433 | 0.875688 | 0.437844 | − | 0.899051i | \(-0.355742\pi\) | ||||
0.437844 | + | 0.899051i | \(0.355742\pi\) | |||||||
\(308\) | 5.78886i | 0.329851i | ||||||||
\(309\) | 6.08080 | + | 6.08080i | 0.345925 | + | 0.345925i | ||||
\(310\) | −1.12106 | −0.0636717 | ||||||||
\(311\) | −15.3318 | − | 15.3318i | −0.869388 | − | 0.869388i | 0.123017 | − | 0.992405i | \(-0.460743\pi\) |
−0.992405 | + | 0.123017i | \(0.960743\pi\) | |||||||
\(312\) | −0.234633 | + | 0.234633i | −0.0132835 | + | 0.0132835i | ||||
\(313\) | 5.93154 | − | 5.93154i | 0.335271 | − | 0.335271i | −0.519313 | − | 0.854584i | \(-0.673812\pi\) |
0.854584 | + | 0.519313i | \(0.173812\pi\) | |||||||
\(314\) | − | 4.78976i | − | 0.270302i | ||||||
\(315\) | 1.48022i | 0.0834008i | ||||||||
\(316\) | −8.86672 | + | 8.86672i | −0.498792 | + | 0.498792i | ||||
\(317\) | −16.9566 | + | 16.9566i | −0.952379 | + | 0.952379i | −0.998917 | − | 0.0465374i | \(-0.985181\pi\) |
0.0465374 | + | 0.998917i | \(0.485181\pi\) | |||||||
\(318\) | 2.21371 | + | 2.21371i | 0.124139 | + | 0.124139i | ||||
\(319\) | 14.4776 | 0.810589 | ||||||||
\(320\) | 0.306563 | + | 0.306563i | 0.0171374 | + | 0.0171374i | ||||
\(321\) | − | 2.16478i | − | 0.120826i | ||||||
\(322\) | 6.43060 | 0.358363 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | − | 1.59674i | − | 0.0885710i | ||||||
\(326\) | 12.5899 | + | 12.5899i | 0.697293 | + | 0.697293i | ||||
\(327\) | 7.91376 | 0.437632 | ||||||||
\(328\) | −8.56854 | − | 8.56854i | −0.473118 | − | 0.473118i | ||||
\(329\) | 5.74603 | − | 5.74603i | 0.316789 | − | 0.316789i | ||||
\(330\) | 0.519783 | − | 0.519783i | 0.0286131 | − | 0.0286131i | ||||
\(331\) | − | 4.07733i | − | 0.224110i | −0.993702 | − | 0.112055i | \(-0.964257\pi\) | ||
0.993702 | − | 0.112055i | \(-0.0357433\pi\) | |||||||
\(332\) | − | 1.04373i | − | 0.0572820i | ||||||
\(333\) | 7.50548 | − | 7.50548i | 0.411298 | − | 0.411298i | ||||
\(334\) | −12.4416 | + | 12.4416i | −0.680771 | + | 0.680771i | ||||
\(335\) | 4.83484 | + | 4.83484i | 0.264156 | + | 0.264156i | ||||
\(336\) | −3.41421 | −0.186261 | ||||||||
\(337\) | 7.08288 | + | 7.08288i | 0.385829 | + | 0.385829i | 0.873197 | − | 0.487368i | \(-0.162043\pi\) |
−0.487368 | + | 0.873197i | \(0.662043\pi\) | |||||||
\(338\) | 12.8899i | 0.701118i | ||||||||
\(339\) | −9.18828 | −0.499039 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.38425 | −0.237420 | ||||||||
\(342\) | − | 2.14386i | − | 0.115927i | ||||||
\(343\) | −5.65685 | − | 5.65685i | −0.305441 | − | 0.305441i | ||||
\(344\) | 10.0933 | 0.544197 | ||||||||
\(345\) | −0.577405 | − | 0.577405i | −0.0310864 | − | 0.0310864i | ||||
\(346\) | −13.6799 | + | 13.6799i | −0.735434 | + | 0.735434i | ||||
\(347\) | 6.11236 | − | 6.11236i | 0.328129 | − | 0.328129i | −0.523746 | − | 0.851875i | \(-0.675466\pi\) |
0.851875 | + | 0.523746i | \(0.175466\pi\) | |||||||
\(348\) | 8.53874i | 0.457725i | ||||||||
\(349\) | 20.8126i | 1.11407i | 0.830488 | + | 0.557036i | \(0.188062\pi\) | ||||
−0.830488 | + | 0.557036i | \(0.811938\pi\) | |||||||
\(350\) | 11.6173 | − | 11.6173i | 0.620970 | − | 0.620970i | ||||
\(351\) | −0.234633 | + | 0.234633i | −0.0125238 | + | 0.0125238i | ||||
\(352\) | 1.19891 | + | 1.19891i | 0.0639022 | + | 0.0639022i | ||||
\(353\) | 20.1049 | 1.07007 | 0.535037 | − | 0.844829i | \(-0.320298\pi\) | ||||
0.535037 | + | 0.844829i | \(0.320298\pi\) | |||||||
\(354\) | −5.42676 | − | 5.42676i | −0.288429 | − | 0.288429i | ||||
\(355\) | − | 0.0982525i | − | 0.00521470i | ||||||
\(356\) | 13.8281 | 0.732885 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.11933 | −0.481972 | ||||||||
\(359\) | − | 25.3001i | − | 1.33529i | −0.744480 | − | 0.667645i | \(-0.767302\pi\) | ||
0.744480 | − | 0.667645i | \(-0.232698\pi\) | |||||||
\(360\) | 0.306563 | + | 0.306563i | 0.0161573 | + | 0.0161573i | ||||
\(361\) | 14.4039 | 0.758098 | ||||||||
\(362\) | 0.549204 | + | 0.549204i | 0.0288655 | + | 0.0288655i | ||||
\(363\) | −5.74540 | + | 5.74540i | −0.301555 | + | 0.301555i | ||||
\(364\) | 0.801088 | − | 0.801088i | 0.0419884 | − | 0.0419884i | ||||
\(365\) | − | 5.26266i | − | 0.275460i | ||||||
\(366\) | 8.03988i | 0.420251i | ||||||||
\(367\) | −7.29732 | + | 7.29732i | −0.380917 | + | 0.380917i | −0.871432 | − | 0.490515i | \(-0.836809\pi\) |
0.490515 | + | 0.871432i | \(0.336809\pi\) | |||||||
\(368\) | 1.33182 | − | 1.33182i | 0.0694260 | − | 0.0694260i | ||||
\(369\) | −8.56854 | − | 8.56854i | −0.446060 | − | 0.446060i | ||||
\(370\) | 4.60180 | 0.239236 | ||||||||
\(371\) | −7.55807 | − | 7.55807i | −0.392396 | − | 0.392396i | ||||
\(372\) | − | 2.58579i | − | 0.134067i | ||||||
\(373\) | 18.2719 | 0.946083 | 0.473041 | − | 0.881040i | \(-0.343156\pi\) | ||||
0.473041 | + | 0.881040i | \(0.343156\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.25397 | −0.219674 | ||||||||
\(376\) | − | 2.38009i | − | 0.122744i | ||||||
\(377\) | −2.00347 | − | 2.00347i | −0.103184 | − | 0.103184i | ||||
\(378\) | −3.41421 | −0.175608 | ||||||||
\(379\) | −14.8011 | − | 14.8011i | −0.760281 | − | 0.760281i | 0.216092 | − | 0.976373i | \(-0.430669\pi\) |
−0.976373 | + | 0.216092i | \(0.930669\pi\) | |||||||
\(380\) | 0.657228 | − | 0.657228i | 0.0337151 | − | 0.0337151i | ||||
\(381\) | 8.54487 | − | 8.54487i | 0.437767 | − | 0.437767i | ||||
\(382\) | − | 13.4248i | − | 0.686872i | ||||||
\(383\) | 22.9974i | 1.17511i | 0.809184 | + | 0.587555i | \(0.199910\pi\) | ||||
−0.809184 | + | 0.587555i | \(0.800090\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −1.77465 | + | 1.77465i | −0.0904446 | + | 0.0904446i | ||||
\(386\) | −3.59850 | − | 3.59850i | −0.183159 | − | 0.183159i | ||||
\(387\) | 10.0933 | 0.513073 | ||||||||
\(388\) | −2.65546 | − | 2.65546i | −0.134811 | − | 0.134811i | ||||
\(389\) | 9.07748i | 0.460247i | 0.973161 | + | 0.230123i | \(0.0739130\pi\) | ||||
−0.973161 | + | 0.230123i | \(0.926087\pi\) | |||||||
\(390\) | −0.143860 | −0.00728462 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 4.65685 | 0.235207 | ||||||||
\(393\) | − | 0.896683i | − | 0.0452317i | ||||||
\(394\) | −2.93767 | − | 2.93767i | −0.147998 | − | 0.147998i | ||||
\(395\) | −5.43641 | −0.273536 | ||||||||
\(396\) | 1.19891 | + | 1.19891i | 0.0602476 | + | 0.0602476i | ||||
\(397\) | −5.52149 | + | 5.52149i | −0.277116 | + | 0.277116i | −0.831957 | − | 0.554841i | \(-0.812779\pi\) |
0.554841 | + | 0.831957i | \(0.312779\pi\) | |||||||
\(398\) | 7.57221 | − | 7.57221i | 0.379561 | − | 0.379561i | ||||
\(399\) | 7.31959i | 0.366438i | ||||||||
\(400\) | − | 4.81204i | − | 0.240602i | ||||||
\(401\) | −12.2759 | + | 12.2759i | −0.613030 | + | 0.613030i | −0.943734 | − | 0.330705i | \(-0.892714\pi\) |
0.330705 | + | 0.943734i | \(0.392714\pi\) | |||||||
\(402\) | −11.1519 | + | 11.1519i | −0.556205 | + | 0.556205i | ||||
\(403\) | 0.606711 | + | 0.606711i | 0.0302224 | + | 0.0302224i | ||||
\(404\) | −0.636303 | −0.0316573 | ||||||||
\(405\) | 0.306563 | + | 0.306563i | 0.0152332 | + | 0.0152332i | ||||
\(406\) | − | 29.1531i | − | 1.44684i | ||||||
\(407\) | 17.9968 | 0.892069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.42153 | 0.218631 | 0.109315 | − | 0.994007i | \(-0.465134\pi\) | ||||
0.109315 | + | 0.994007i | \(0.465134\pi\) | |||||||
\(410\) | − | 5.25359i | − | 0.259456i | ||||||
\(411\) | 8.91723 | + | 8.91723i | 0.439855 | + | 0.439855i | ||||
\(412\) | −8.59955 | −0.423669 | ||||||||
\(413\) | 18.5281 | + | 18.5281i | 0.911709 | + | 0.911709i | ||||
\(414\) | 1.33182 | − | 1.33182i | 0.0654554 | − | 0.0654554i | ||||
\(415\) | 0.319968 | − | 0.319968i | 0.0157066 | − | 0.0157066i | ||||
\(416\) | − | 0.331821i | − | 0.0162689i | ||||||
\(417\) | 17.0447i | 0.834683i | ||||||||
\(418\) | 2.57030 | − | 2.57030i | 0.125717 | − | 0.125717i | ||||
\(419\) | −16.3811 | + | 16.3811i | −0.800267 | + | 0.800267i | −0.983137 | − | 0.182870i | \(-0.941461\pi\) |
0.182870 | + | 0.983137i | \(0.441461\pi\) | |||||||
\(420\) | −1.04667 | − | 1.04667i | −0.0510723 | − | 0.0510723i | ||||
\(421\) | 20.0524 | 0.977295 | 0.488648 | − | 0.872481i | \(-0.337490\pi\) | ||||
0.488648 | + | 0.872481i | \(0.337490\pi\) | |||||||
\(422\) | −3.33861 | − | 3.33861i | −0.162521 | − | 0.162521i | ||||
\(423\) | − | 2.38009i | − | 0.115724i | ||||||
\(424\) | −3.13066 | −0.152038 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.226626 | 0.0109800 | ||||||||
\(427\) | − | 27.4499i | − | 1.32839i | ||||||
\(428\) | 1.53073 | + | 1.53073i | 0.0739908 | + | 0.0739908i | ||||
\(429\) | −0.562609 | −0.0271630 | ||||||||
\(430\) | 3.09425 | + | 3.09425i | 0.149218 | + | 0.149218i | ||||
\(431\) | 28.3880 | − | 28.3880i | 1.36740 | − | 1.36740i | 0.503280 | − | 0.864123i | \(-0.332126\pi\) |
0.864123 | − | 0.503280i | \(-0.167874\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | − | 21.8499i | − | 1.05004i | −0.851090 | − | 0.525020i | \(-0.824058\pi\) | ||
0.851090 | − | 0.525020i | \(-0.175942\pi\) | |||||||
\(434\) | 8.82843i | 0.423778i | ||||||||
\(435\) | −2.61766 | + | 2.61766i | −0.125507 | + | 0.125507i | ||||
\(436\) | −5.59588 | + | 5.59588i | −0.267994 | + | 0.267994i | ||||
\(437\) | −2.85524 | − | 2.85524i | −0.136585 | − | 0.136585i | ||||
\(438\) | 12.1387 | 0.580008 | ||||||||
\(439\) | −0.593103 | − | 0.593103i | −0.0283073 | − | 0.0283073i | 0.692811 | − | 0.721119i | \(-0.256372\pi\) |
−0.721119 | + | 0.692811i | \(0.756372\pi\) | |||||||
\(440\) | 0.735084i | 0.0350438i | ||||||||
\(441\) | 4.65685 | 0.221755 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.21267 | −0.152639 | −0.0763194 | − | 0.997083i | \(-0.524317\pi\) | ||||
−0.0763194 | + | 0.997083i | \(0.524317\pi\) | |||||||
\(444\) | 10.6143i | 0.503735i | ||||||||
\(445\) | 4.23917 | + | 4.23917i | 0.200956 | + | 0.200956i | ||||
\(446\) | 15.6359 | 0.740383 | ||||||||
\(447\) | −12.3746 | − | 12.3746i | −0.585301 | − | 0.585301i | ||||
\(448\) | 2.41421 | − | 2.41421i | 0.114061 | − | 0.114061i | ||||
\(449\) | 20.3281 | − | 20.3281i | 0.959342 | − | 0.959342i | −0.0398632 | − | 0.999205i | \(-0.512692\pi\) |
0.999205 | + | 0.0398632i | \(0.0126922\pi\) | |||||||
\(450\) | − | 4.81204i | − | 0.226842i | ||||||
\(451\) | − | 20.5458i | − | 0.967466i | ||||||
\(452\) | 6.49709 | − | 6.49709i | 0.305598 | − | 0.305598i | ||||
\(453\) | 6.81657 | − | 6.81657i | 0.320271 | − | 0.320271i | ||||
\(454\) | 7.82164 | + | 7.82164i | 0.367088 | + | 0.367088i | ||||
\(455\) | 0.491168 | 0.0230263 | ||||||||
\(456\) | 1.51594 | + | 1.51594i | 0.0709903 | + | 0.0709903i | ||||
\(457\) | 7.45097i | 0.348542i | 0.984698 | + | 0.174271i | \(0.0557568\pi\) | ||||
−0.984698 | + | 0.174271i | \(0.944243\pi\) | |||||||
\(458\) | −15.3852 | −0.718901 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.816574 | 0.0380730 | ||||||||
\(461\) | − | 25.6378i | − | 1.19407i | −0.802214 | − | 0.597037i | \(-0.796345\pi\) | ||
0.802214 | − | 0.597037i | \(-0.203655\pi\) | |||||||
\(462\) | −4.09334 | − | 4.09334i | −0.190440 | − | 0.190440i | ||||
\(463\) | 10.7747 | 0.500744 | 0.250372 | − | 0.968150i | \(-0.419447\pi\) | ||||
0.250372 | + | 0.968150i | \(0.419447\pi\) | |||||||
\(464\) | −6.03780 | − | 6.03780i | −0.280298 | − | 0.280298i | ||||
\(465\) | 0.792706 | − | 0.792706i | 0.0367609 | − | 0.0367609i | ||||
\(466\) | −7.33806 | + | 7.33806i | −0.339929 | + | 0.339929i | ||||
\(467\) | 35.6492i | 1.64965i | 0.565391 | + | 0.824823i | \(0.308725\pi\) | ||||
−0.565391 | + | 0.824823i | \(0.691275\pi\) | |||||||
\(468\) | − | 0.331821i | − | 0.0153384i | ||||||
\(469\) | 38.0749 | − | 38.0749i | 1.75813 | − | 1.75813i | ||||
\(470\) | 0.729646 | − | 0.729646i | 0.0336561 | − | 0.0336561i | ||||
\(471\) | 3.38687 | + | 3.38687i | 0.156059 | + | 0.156059i | ||||
\(472\) | 7.67459 | 0.353252 | ||||||||
\(473\) | 12.1010 | + | 12.1010i | 0.556406 | + | 0.556406i | ||||
\(474\) | − | 12.5394i | − | 0.575955i | ||||||
\(475\) | −10.3163 | −0.473346 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.13066 | −0.143343 | ||||||||
\(478\) | 24.7803i | 1.13343i | ||||||||
\(479\) | −9.94911 | − | 9.94911i | −0.454586 | − | 0.454586i | 0.442287 | − | 0.896874i | \(-0.354167\pi\) |
−0.896874 | + | 0.442287i | \(0.854167\pi\) | |||||||
\(480\) | −0.433546 | −0.0197886 | ||||||||
\(481\) | −2.49048 | − | 2.49048i | −0.113556 | − | 0.113556i | ||||
\(482\) | −3.04422 | + | 3.04422i | −0.138660 | + | 0.138660i | ||||
\(483\) | −4.54712 | + | 4.54712i | −0.206901 | + | 0.206901i | ||||
\(484\) | − | 8.12522i | − | 0.369328i | ||||||
\(485\) | − | 1.62813i | − | 0.0739297i | ||||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 17.0643 | − | 17.0643i | 0.773256 | − | 0.773256i | −0.205418 | − | 0.978674i | \(-0.565855\pi\) |
0.978674 | + | 0.205418i | \(0.0658554\pi\) | |||||||
\(488\) | −5.68506 | − | 5.68506i | −0.257350 | − | 0.257350i | ||||
\(489\) | −17.8049 | −0.805164 | ||||||||
\(490\) | 1.42762 | + | 1.42762i | 0.0644933 | + | 0.0644933i | ||||
\(491\) | − | 26.5200i | − | 1.19683i | −0.801186 | − | 0.598416i | \(-0.795797\pi\) | ||
0.801186 | − | 0.598416i | \(-0.204203\pi\) | |||||||
\(492\) | 12.1177 | 0.546310 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −0.711378 | −0.0320064 | ||||||||
\(495\) | 0.735084i | 0.0330396i | ||||||||
\(496\) | 1.82843 | + | 1.82843i | 0.0820988 | + | 0.0820988i | ||||
\(497\) | −0.773748 | −0.0347073 | ||||||||
\(498\) | 0.738027 | + | 0.738027i | 0.0330718 | + | 0.0330718i | ||||
\(499\) | −3.21024 | + | 3.21024i | −0.143710 | + | 0.143710i | −0.775301 | − | 0.631591i | \(-0.782402\pi\) |
0.631591 | + | 0.775301i | \(0.282402\pi\) | |||||||
\(500\) | 3.00801 | − | 3.00801i | 0.134522 | − | 0.134522i | ||||
\(501\) | − | 17.5950i | − | 0.786087i | ||||||
\(502\) | − | 19.0639i | − | 0.850864i | ||||||
\(503\) | 2.82655 | − | 2.82655i | 0.126030 | − | 0.126030i | −0.641279 | − | 0.767308i | \(-0.721596\pi\) |
0.767308 | + | 0.641279i | \(0.221596\pi\) | |||||||
\(504\) | 2.41421 | − | 2.41421i | 0.107538 | − | 0.107538i | ||||
\(505\) | −0.195067 | − | 0.195067i | −0.00868037 | − | 0.00868037i | ||||
\(506\) | 3.19347 | 0.141967 | ||||||||
\(507\) | −9.11453 | − | 9.11453i | −0.404791 | − | 0.404791i | ||||
\(508\) | 12.0843i | 0.536153i | ||||||||
\(509\) | −22.9751 | −1.01835 | −0.509176 | − | 0.860662i | \(-0.670050\pi\) | ||||
−0.509176 | + | 0.860662i | \(0.670050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.4440 | −1.83337 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.51594 | + | 1.51594i | 0.0669303 | + | 0.0669303i | ||||
\(514\) | 26.7594 | 1.18031 | ||||||||
\(515\) | −2.63630 | − | 2.63630i | −0.116169 | − | 0.116169i | ||||
\(516\) | −7.13707 | + | 7.13707i | −0.314192 | + | 0.314192i | ||||
\(517\) | 2.85351 | − | 2.85351i | 0.125497 | − | 0.125497i | ||||
\(518\) | − | 36.2396i | − | 1.59228i | ||||||
\(519\) | − | 19.3462i | − | 0.849206i | ||||||
\(520\) | 0.101724 | − | 0.101724i | 0.00446090 | − | 0.00446090i | ||||
\(521\) | 11.9380 | − | 11.9380i | 0.523011 | − | 0.523011i | −0.395468 | − | 0.918480i | \(-0.629418\pi\) |
0.918480 | + | 0.395468i | \(0.129418\pi\) | |||||||
\(522\) | −6.03780 | − | 6.03780i | −0.264267 | − | 0.264267i | ||||
\(523\) | 15.5903 | 0.681717 | 0.340859 | − | 0.940115i | \(-0.389282\pi\) | ||||
0.340859 | + | 0.940115i | \(0.389282\pi\) | |||||||
\(524\) | 0.634051 | + | 0.634051i | 0.0276986 | + | 0.0276986i | ||||
\(525\) | 16.4293i | 0.717035i | ||||||||
\(526\) | 27.5122 | 1.19959 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.69552 | −0.0737880 | ||||||||
\(529\) | 19.4525i | 0.845761i | ||||||||
\(530\) | −0.959743 | − | 0.959743i | −0.0416886 | − | 0.0416886i | ||||
\(531\) | 7.67459 | 0.333049 | ||||||||
\(532\) | −5.17574 | − | 5.17574i | −0.224397 | − | 0.224397i | ||||
\(533\) | −2.84322 | + | 2.84322i | −0.123154 | + | 0.123154i | ||||
\(534\) | −9.77791 | + | 9.77791i | −0.423132 | + | 0.423132i | ||||
\(535\) | 0.938533i | 0.0405763i | ||||||||
\(536\) | − | 15.7711i | − | 0.681209i | ||||||
\(537\) | 6.44834 | − | 6.44834i | 0.278266 | − | 0.278266i | ||||
\(538\) | −7.08153 | + | 7.08153i | −0.305306 | + | 0.305306i | ||||
\(539\) | 5.58316 | + | 5.58316i | 0.240484 | + | 0.240484i | ||||
\(540\) | −0.433546 | −0.0186568 | ||||||||
\(541\) | −10.6989 | − | 10.6989i | −0.459984 | − | 0.459984i | 0.438666 | − | 0.898650i | \(-0.355451\pi\) |
−0.898650 | + | 0.438666i | \(0.855451\pi\) | |||||||
\(542\) | − | 9.20949i | − | 0.395581i | ||||||
\(543\) | −0.776691 | −0.0333310 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.43098 | −0.146967 | ||||||||
\(546\) | 1.13291i | 0.0484840i | ||||||||
\(547\) | −1.87163 | − | 1.87163i | −0.0800250 | − | 0.0800250i | 0.665961 | − | 0.745986i | \(-0.268022\pi\) |
−0.745986 | + | 0.665961i | \(0.768022\pi\) | |||||||
\(548\) | −12.6109 | −0.538710 | ||||||||
\(549\) | −5.68506 | − | 5.68506i | −0.242632 | − | 0.242632i | ||||
\(550\) | 5.76921 | − | 5.76921i | 0.246000 | − | 0.246000i | ||||
\(551\) | −12.9442 | + | 12.9442i | −0.551441 | + | 0.551441i | ||||
\(552\) | 1.88348i | 0.0801662i | ||||||||
\(553\) | 42.8123i | 1.82056i | ||||||||
\(554\) | 5.91515 | − | 5.91515i | 0.251311 | − | 0.251311i | ||||
\(555\) | −3.25397 | + | 3.25397i | −0.138123 | + | 0.138123i | ||||
\(556\) | −12.0524 | − | 12.0524i | −0.511137 | − | 0.511137i | ||||
\(557\) | 12.4900 | 0.529217 | 0.264609 | − | 0.964356i | \(-0.414757\pi\) | ||||
0.264609 | + | 0.964356i | \(0.414757\pi\) | |||||||
\(558\) | 1.82843 | + | 1.82843i | 0.0774035 | + | 0.0774035i | ||||
\(559\) | − | 3.34919i | − | 0.141656i | ||||||
\(560\) | 1.48022 | 0.0625506 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.9996 | 0.463991 | ||||||||
\(563\) | − | 1.98226i | − | 0.0835423i | −0.999127 | − | 0.0417712i | \(-0.986700\pi\) | ||
0.999127 | − | 0.0417712i | \(-0.0133000\pi\) | |||||||
\(564\) | 1.68297 | + | 1.68297i | 0.0708660 | + | 0.0708660i | ||||
\(565\) | 3.98354 | 0.167589 | ||||||||
\(566\) | 14.9469 | + | 14.9469i | 0.628263 | + | 0.628263i | ||||
\(567\) | 2.41421 | − | 2.41421i | 0.101387 | − | 0.101387i | ||||
\(568\) | −0.160248 | + | 0.160248i | −0.00672388 | + | 0.00672388i | ||||
\(569\) | 16.7666i | 0.702892i | 0.936208 | + | 0.351446i | \(0.114310\pi\) | ||||
−0.936208 | + | 0.351446i | \(0.885690\pi\) | |||||||
\(570\) | 0.929461i | 0.0389308i | ||||||||
\(571\) | −21.3001 | + | 21.3001i | −0.891383 | + | 0.891383i | −0.994653 | − | 0.103271i | \(-0.967069\pi\) |
0.103271 | + | 0.994653i | \(0.467069\pi\) | |||||||
\(572\) | 0.397825 | − | 0.397825i | 0.0166339 | − | 0.0166339i | ||||
\(573\) | 9.49276 | + | 9.49276i | 0.396566 | + | 0.396566i | ||||
\(574\) | −41.3725 | −1.72686 | ||||||||
\(575\) | −6.40878 | − | 6.40878i | −0.267264 | − | 0.267264i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | −19.8204 | −0.825132 | −0.412566 | − | 0.910928i | \(-0.635367\pi\) | ||||
−0.412566 | + | 0.910928i | \(0.635367\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.08905 | 0.211494 | ||||||||
\(580\) | − | 3.70193i | − | 0.153714i | ||||||
\(581\) | −2.51978 | − | 2.51978i | −0.104538 | − | 0.104538i | ||||
\(582\) | 3.75539 | 0.155666 | ||||||||
\(583\) | −3.75338 | − | 3.75338i | −0.155449 | − | 0.155449i | ||||
\(584\) | −8.58333 | + | 8.58333i | −0.355181 | + | 0.355181i | ||||
\(585\) | 0.101724 | − | 0.101724i | 0.00420578 | − | 0.00420578i | ||||
\(586\) | 25.1277i | 1.03801i | ||||||||
\(587\) | 12.8612i | 0.530839i | 0.964133 | + | 0.265419i | \(0.0855104\pi\) | ||||
−0.964133 | + | 0.265419i | \(0.914490\pi\) | |||||||
\(588\) | −3.29289 | + | 3.29289i | −0.135797 | + | 0.135797i | ||||
\(589\) | 3.91989 | − | 3.91989i | 0.161516 | − | 0.161516i | ||||
\(590\) | 2.35275 | + | 2.35275i | 0.0968610 | + | 0.0968610i | ||||
\(591\) | 4.15449 | 0.170893 | ||||||||
\(592\) | −7.50548 | − | 7.50548i | −0.308473 | − | 0.308473i | ||||
\(593\) | 35.8300i | 1.47136i | 0.677328 | + | 0.735681i | \(0.263138\pi\) | ||||
−0.677328 | + | 0.735681i | \(0.736862\pi\) | |||||||
\(594\) | −1.69552 | −0.0695680 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.5004 | 0.716844 | ||||||||
\(597\) | 10.7087i | 0.438279i | ||||||||
\(598\) | −0.441927 | − | 0.441927i | −0.0180717 | − | 0.0180717i | ||||
\(599\) | 21.1148 | 0.862728 | 0.431364 | − | 0.902178i | \(-0.358032\pi\) | ||||
0.431364 | + | 0.902178i | \(0.358032\pi\) | |||||||
\(600\) | 3.40262 | + | 3.40262i | 0.138912 | + | 0.138912i | ||||
\(601\) | 10.7725 | − | 10.7725i | 0.439420 | − | 0.439420i | −0.452397 | − | 0.891817i | \(-0.649431\pi\) |
0.891817 | + | 0.452397i | \(0.149431\pi\) | |||||||
\(602\) | 24.3675 | − | 24.3675i | 0.993145 | − | 0.993145i | ||||
\(603\) | − | 15.7711i | − | 0.642250i | ||||||
\(604\) | 9.64009i | 0.392250i | ||||||||
\(605\) | 2.49089 | − | 2.49089i | 0.101269 | − | 0.101269i | ||||
\(606\) | 0.449934 | − | 0.449934i | 0.0182773 | − | 0.0182773i | ||||
\(607\) | −27.1421 | − | 27.1421i | −1.10167 | − | 1.10167i | −0.994210 | − | 0.107455i | \(-0.965730\pi\) |
−0.107455 | − | 0.994210i | \(-0.534270\pi\) | |||||||
\(608\) | −2.14386 | −0.0869450 | ||||||||
\(609\) | 20.6143 | + | 20.6143i | 0.835335 | + | 0.835335i | ||||
\(610\) | − | 3.48566i | − | 0.141130i | ||||||
\(611\) | −0.789763 | −0.0319504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.39554 | −0.0563654 | −0.0281827 | − | 0.999603i | \(-0.508972\pi\) | ||||
−0.0281827 | + | 0.999603i | \(0.508972\pi\) | |||||||
\(614\) | − | 15.3433i | − | 0.619205i | ||||||
\(615\) | 3.71485 | + | 3.71485i | 0.149797 | + | 0.149797i | ||||
\(616\) | 5.78886 | 0.233240 | ||||||||
\(617\) | −5.95021 | − | 5.95021i | −0.239547 | − | 0.239547i | 0.577116 | − | 0.816662i | \(-0.304178\pi\) |
−0.816662 | + | 0.577116i | \(0.804178\pi\) | |||||||
\(618\) | 6.08080 | − | 6.08080i | 0.244606 | − | 0.244606i | ||||
\(619\) | 3.77828 | − | 3.77828i | 0.151862 | − | 0.151862i | −0.627087 | − | 0.778949i | \(-0.715753\pi\) |
0.778949 | + | 0.627087i | \(0.215753\pi\) | |||||||
\(620\) | 1.12106i | 0.0450227i | ||||||||
\(621\) | 1.88348i | 0.0755814i | ||||||||
\(622\) | −15.3318 | + | 15.3318i | −0.614750 | + | 0.614750i | ||||
\(623\) | 33.3839 | − | 33.3839i | 1.33750 | − | 1.33750i | ||||
\(624\) | 0.234633 | + | 0.234633i | 0.00939284 | + | 0.00939284i | ||||
\(625\) | −22.2159 | −0.888636 | ||||||||
\(626\) | −5.93154 | − | 5.93154i | −0.237072 | − | 0.237072i | ||||
\(627\) | 3.63495i | 0.145166i | ||||||||
\(628\) | −4.78976 | −0.191132 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.48022 | 0.0589733 | ||||||||
\(631\) | 1.46282i | 0.0582340i | 0.999576 | + | 0.0291170i | \(0.00926953\pi\) | ||||
−0.999576 | + | 0.0291170i | \(0.990730\pi\) | |||||||
\(632\) | 8.86672 | + | 8.86672i | 0.352699 | + | 0.352699i | ||||
\(633\) | 4.72151 | 0.187663 | ||||||||
\(634\) | 16.9566 | + | 16.9566i | 0.673434 | + | 0.673434i | ||||
\(635\) | −3.70459 | + | 3.70459i | −0.147012 | + | 0.147012i | ||||
\(636\) | 2.21371 | − | 2.21371i | 0.0877792 | − | 0.0877792i | ||||
\(637\) | − | 1.54524i | − | 0.0612248i | ||||||
\(638\) | − | 14.4776i | − | 0.573173i | ||||||
\(639\) | −0.160248 | + | 0.160248i | −0.00633933 | + | 0.00633933i | ||||
\(640\) | 0.306563 | − | 0.306563i | 0.0121180 | − | 0.0121180i | ||||
\(641\) | −0.338967 | − | 0.338967i | −0.0133884 | − | 0.0133884i | 0.700381 | − | 0.713769i | \(-0.253013\pi\) |
−0.713769 | + | 0.700381i | \(0.753013\pi\) | |||||||
\(642\) | −2.16478 | −0.0854372 | ||||||||
\(643\) | 22.7016 | + | 22.7016i | 0.895262 | + | 0.895262i | 0.995012 | − | 0.0997504i | \(-0.0318044\pi\) |
−0.0997504 | + | 0.995012i | \(0.531804\pi\) | |||||||
\(644\) | − | 6.43060i | − | 0.253401i | ||||||
\(645\) | −4.37592 | −0.172302 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.4802 | 0.923103 | 0.461551 | − | 0.887114i | \(-0.347293\pi\) | ||||
0.461551 | + | 0.887114i | \(0.347293\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 9.20116 | + | 9.20116i | 0.361177 | + | 0.361177i | ||||
\(650\) | −1.59674 | −0.0626292 | ||||||||
\(651\) | −6.24264 | − | 6.24264i | −0.244668 | − | 0.244668i | ||||
\(652\) | 12.5899 | − | 12.5899i | 0.493060 | − | 0.493060i | ||||
\(653\) | −32.0806 | + | 32.0806i | −1.25541 | + | 1.25541i | −0.302152 | + | 0.953260i | \(0.597705\pi\) |
−0.953260 | + | 0.302152i | \(0.902295\pi\) | |||||||
\(654\) | − | 7.91376i | − | 0.309453i | ||||||
\(655\) | 0.388753i | 0.0151898i | ||||||||
\(656\) | −8.56854 | + | 8.56854i | −0.334545 | + | 0.334545i | ||||
\(657\) | −8.58333 | + | 8.58333i | −0.334868 | + | 0.334868i | ||||
\(658\) | −5.74603 | − | 5.74603i | −0.224004 | − | 0.224004i | ||||
\(659\) | −12.8417 | −0.500240 | −0.250120 | − | 0.968215i | \(-0.580470\pi\) | ||||
−0.250120 | + | 0.968215i | \(0.580470\pi\) | |||||||
\(660\) | −0.519783 | − | 0.519783i | −0.0202325 | − | 0.0202325i | ||||
\(661\) | 27.1878i | 1.05748i | 0.848783 | + | 0.528741i | \(0.177336\pi\) | ||||
−0.848783 | + | 0.528741i | \(0.822664\pi\) | |||||||
\(662\) | −4.07733 | −0.158470 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.04373 | −0.0405045 | ||||||||
\(665\) | − | 3.17338i | − | 0.123058i | ||||||
\(666\) | −7.50548 | − | 7.50548i | −0.290831 | − | 0.290831i | ||||
\(667\) | −16.0825 | −0.622719 | ||||||||
\(668\) | 12.4416 | + | 12.4416i | 0.481378 | + | 0.481378i | ||||
\(669\) | −11.0563 | + | 11.0563i | −0.427460 | + | 0.427460i | ||||
\(670\) | 4.83484 | − | 4.83484i | 0.186786 | − | 0.186786i | ||||
\(671\) | − | 13.6318i | − | 0.526249i | ||||||
\(672\) | 3.41421i | 0.131706i | ||||||||
\(673\) | 11.7925 | − | 11.7925i | 0.454569 | − | 0.454569i | −0.442299 | − | 0.896868i | \(-0.645837\pi\) |
0.896868 | + | 0.442299i | \(0.145837\pi\) | |||||||
\(674\) | 7.08288 | − | 7.08288i | 0.272822 | − | 0.272822i | ||||
\(675\) | 3.40262 | + | 3.40262i | 0.130967 | + | 0.130967i | ||||
\(676\) | 12.8899 | 0.495765 | ||||||||
\(677\) | −1.84048 | − | 1.84048i | −0.0707355 | − | 0.0707355i | 0.670854 | − | 0.741589i | \(-0.265928\pi\) |
−0.741589 | + | 0.670854i | \(0.765928\pi\) | |||||||
\(678\) | 9.18828i | 0.352874i | ||||||||
\(679\) | −12.8217 | −0.492052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0615 | −0.423876 | ||||||||
\(682\) | 4.38425i | 0.167882i | ||||||||
\(683\) | 8.65689 | + | 8.65689i | 0.331247 | + | 0.331247i | 0.853060 | − | 0.521813i | \(-0.174744\pi\) |
−0.521813 | + | 0.853060i | \(0.674744\pi\) | |||||||
\(684\) | −2.14386 | −0.0819725 | ||||||||
\(685\) | −3.86603 | − | 3.86603i | −0.147713 | − | 0.147713i | ||||
\(686\) | −5.65685 | + | 5.65685i | −0.215980 | + | 0.215980i | ||||
\(687\) | 10.8789 | − | 10.8789i | 0.415058 | − | 0.415058i | ||||
\(688\) | − | 10.0933i | − | 0.384805i | ||||||
\(689\) | 1.03882i | 0.0395758i | ||||||||
\(690\) | −0.577405 | + | 0.577405i | −0.0219814 | + | 0.0219814i | ||||
\(691\) | 11.0829 | − | 11.0829i | 0.421614 | − | 0.421614i | −0.464145 | − | 0.885759i | \(-0.653638\pi\) |
0.885759 | + | 0.464145i | \(0.153638\pi\) | |||||||
\(692\) | 13.6799 | + | 13.6799i | 0.520030 | + | 0.520030i | ||||
\(693\) | 5.78886 | 0.219901 | ||||||||
\(694\) | −6.11236 | − | 6.11236i | −0.232022 | − | 0.232022i | ||||
\(695\) | − | 7.38966i | − | 0.280306i | ||||||
\(696\) | 8.53874 | 0.323660 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 20.8126 | 0.787768 | ||||||||
\(699\) | − | 10.3776i | − | 0.392517i | ||||||
\(700\) | −11.6173 | − | 11.6173i | −0.439092 | − | 0.439092i | ||||
\(701\) | −30.8222 | −1.16414 | −0.582070 | − | 0.813139i | \(-0.697757\pi\) | ||||
−0.582070 | + | 0.813139i | \(0.697757\pi\) | |||||||
\(702\) | 0.234633 | + | 0.234633i | 0.00885566 | + | 0.00885566i | ||||
\(703\) | −16.0907 | + | 16.0907i | −0.606872 | + | 0.606872i | ||||
\(704\) | 1.19891 | − | 1.19891i | 0.0451857 | − | 0.0451857i | ||||
\(705\) | 1.03188i | 0.0388627i | ||||||||
\(706\) | − | 20.1049i | − | 0.756656i | ||||||
\(707\) | −1.53617 | + | 1.53617i | −0.0577737 | + | 0.0577737i | ||||
\(708\) | −5.42676 | + | 5.42676i | −0.203950 | + | 0.203950i | ||||
\(709\) | 0.279223 | + | 0.279223i | 0.0104865 | + | 0.0104865i | 0.712331 | − | 0.701844i | \(-0.247640\pi\) |
−0.701844 | + | 0.712331i | \(0.747640\pi\) | |||||||
\(710\) | −0.0982525 | −0.00368735 | ||||||||
\(711\) | 8.86672 | + | 8.86672i | 0.332528 | + | 0.332528i | ||||
\(712\) | − | 13.8281i | − | 0.518228i | ||||||
\(713\) | 4.87028 | 0.182393 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.243917 | 0.00912197 | ||||||||
\(716\) | 9.11933i | 0.340805i | ||||||||
\(717\) | −17.5224 | − | 17.5224i | −0.654384 | − | 0.654384i | ||||
\(718\) | −25.3001 | −0.944193 | ||||||||
\(719\) | 7.84617 | + | 7.84617i | 0.292613 | + | 0.292613i | 0.838112 | − | 0.545499i | \(-0.183660\pi\) |
−0.545499 | + | 0.838112i | \(0.683660\pi\) | |||||||
\(720\) | 0.306563 | − | 0.306563i | 0.0114249 | − | 0.0114249i | ||||
\(721\) | −20.7611 | + | 20.7611i | −0.773186 | + | 0.773186i | ||||
\(722\) | − | 14.4039i | − | 0.536056i | ||||||
\(723\) | − | 4.30517i | − | 0.160111i | ||||||
\(724\) | 0.549204 | − | 0.549204i | 0.0204110 | − | 0.0204110i | ||||
\(725\) | −29.0541 | + | 29.0541i | −1.07904 | + | 1.07904i | ||||
\(726\) | 5.74540 | + | 5.74540i | 0.213232 | + | 0.213232i | ||||
\(727\) | −27.2866 | −1.01200 | −0.506001 | − | 0.862533i | \(-0.668877\pi\) | ||||
−0.506001 | + | 0.862533i | \(0.668877\pi\) | |||||||
\(728\) | −0.801088 | − | 0.801088i | −0.0296903 | − | 0.0296903i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −5.26266 | −0.194780 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 8.03988 | 0.297163 | ||||||||
\(733\) | 29.2870i | 1.08174i | 0.841106 | + | 0.540870i | \(0.181905\pi\) | ||||
−0.841106 | + | 0.540870i | \(0.818095\pi\) | |||||||
\(734\) | 7.29732 | + | 7.29732i | 0.269349 | + | 0.269349i | ||||
\(735\) | −2.01896 | −0.0744704 | ||||||||
\(736\) | −1.33182 | − | 1.33182i | −0.0490916 | − | 0.0490916i | ||||
\(737\) | 18.9082 | − | 18.9082i | 0.696492 | − | 0.696492i | ||||
\(738\) | −8.56854 | + | 8.56854i | −0.315412 | + | 0.315412i | ||||
\(739\) | 37.0534i | 1.36303i | 0.731803 | + | 0.681516i | \(0.238679\pi\) | ||||
−0.731803 | + | 0.681516i | \(0.761321\pi\) | |||||||
\(740\) | − | 4.60180i | − | 0.169166i | ||||||
\(741\) | 0.503021 | − | 0.503021i | 0.0184789 | − | 0.0184789i | ||||
\(742\) | −7.55807 | + | 7.55807i | −0.277466 | + | 0.277466i | ||||
\(743\) | 10.2440 | + | 10.2440i | 0.375816 | + | 0.375816i | 0.869590 | − | 0.493774i | \(-0.164383\pi\) |
−0.493774 | + | 0.869590i | \(0.664383\pi\) | |||||||
\(744\) | −2.58579 | −0.0947995 | ||||||||
\(745\) | 5.36497 | + | 5.36497i | 0.196557 | + | 0.196557i | ||||
\(746\) | − | 18.2719i | − | 0.668981i | ||||||
\(747\) | −1.04373 | −0.0381880 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.39104 | 0.270063 | ||||||||
\(750\) | 4.25397i | 0.155333i | ||||||||
\(751\) | 31.0867 | + | 31.0867i | 1.13437 | + | 1.13437i | 0.989442 | + | 0.144928i | \(0.0462950\pi\) |
0.144928 | + | 0.989442i | \(0.453705\pi\) | |||||||
\(752\) | −2.38009 | −0.0867928 | ||||||||
\(753\) | 13.4802 | + | 13.4802i | 0.491246 | + | 0.491246i | ||||
\(754\) | −2.00347 | + | 2.00347i | −0.0729621 | + | 0.0729621i | ||||
\(755\) | −2.95530 | + | 2.95530i | −0.107554 | + | 0.107554i | ||||
\(756\) | 3.41421i | 0.124174i | ||||||||
\(757\) | − | 37.8588i | − | 1.37600i | −0.725710 | − | 0.688001i | \(-0.758489\pi\) | ||
0.725710 | − | 0.688001i | \(-0.241511\pi\) | |||||||
\(758\) | −14.8011 | + | 14.8011i | −0.537600 | + | 0.537600i | ||||
\(759\) | −2.25813 | + | 2.25813i | −0.0819648 | + | 0.0819648i | ||||
\(760\) | −0.657228 | − | 0.657228i | −0.0238402 | − | 0.0238402i | ||||
\(761\) | 9.82880 | 0.356294 | 0.178147 | − | 0.984004i | \(-0.442990\pi\) | ||||
0.178147 | + | 0.984004i | \(0.442990\pi\) | |||||||
\(762\) | −8.54487 | − | 8.54487i | −0.309548 | − | 0.309548i | ||||
\(763\) | 27.0193i | 0.978163i | ||||||||
\(764\) | −13.4248 | −0.485692 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.9974 | 0.830929 | ||||||||
\(767\) | − | 2.54659i | − | 0.0919522i | ||||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −41.1522 | −1.48398 | −0.741992 | − | 0.670408i | \(-0.766119\pi\) | ||||
−0.741992 | + | 0.670408i | \(0.766119\pi\) | |||||||
\(770\) | 1.77465 | + | 1.77465i | 0.0639540 | + | 0.0639540i | ||||
\(771\) | −18.9218 | + | 18.9218i | −0.681451 | + | 0.681451i | ||||
\(772\) | −3.59850 | + | 3.59850i | −0.129513 | + | 0.129513i | ||||
\(773\) | 21.7456i | 0.782136i | 0.920362 | + | 0.391068i | \(0.127894\pi\) | ||||
−0.920362 | + | 0.391068i | \(0.872106\pi\) | |||||||
\(774\) | − | 10.0933i | − | 0.362798i | ||||||
\(775\) | 8.79846 | − | 8.79846i | 0.316050 | − | 0.316050i | ||||
\(776\) | −2.65546 | + | 2.65546i | −0.0953256 | + | 0.0953256i | ||||
\(777\) | 25.6253 | + | 25.6253i | 0.919302 | + | 0.919302i | ||||
\(778\) | 9.07748 | 0.325444 | ||||||||
\(779\) | 18.3697 | + | 18.3697i | 0.658164 | + | 0.658164i | ||||
\(780\) | 0.143860i | 0.00515100i | ||||||||
\(781\) | −0.384248 | −0.0137495 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.53874 | 0.305150 | ||||||||
\(784\) | − | 4.65685i | − | 0.166316i | ||||||
\(785\) | −1.46836 | − | 1.46836i | −0.0524082 | − | 0.0524082i | ||||
\(786\) | −0.896683 | −0.0319836 | ||||||||
\(787\) | −33.6597 | − | 33.6597i | −1.19984 | − | 1.19984i | −0.974214 | − | 0.225626i | \(-0.927557\pi\) |
−0.225626 | − | 0.974214i | \(-0.572443\pi\) | |||||||
\(788\) | −2.93767 | + | 2.93767i | −0.104650 | + | 0.104650i | ||||
\(789\) | −19.4541 | + | 19.4541i | −0.692584 | + | 0.692584i | ||||
\(790\) | 5.43641i | 0.193419i | ||||||||
\(791\) | − | 31.3707i | − | 1.11542i | ||||||
\(792\) | 1.19891 | − | 1.19891i | 0.0426015 | − | 0.0426015i | ||||
\(793\) | −1.88642 | + | 1.88642i | −0.0669888 | + | 0.0669888i | ||||
\(794\) | 5.52149 | + | 5.52149i | 0.195950 | + | 0.195950i | ||||
\(795\) | 1.35728 | 0.0481378 | ||||||||
\(796\) | −7.57221 | − | 7.57221i | −0.268390 | − | 0.268390i | ||||
\(797\) | 37.8984i | 1.34243i | 0.741263 | + | 0.671215i | \(0.234227\pi\) | ||||
−0.741263 | + | 0.671215i | \(0.765773\pi\) | |||||||
\(798\) | 7.31959 | 0.259111 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.81204 | −0.170131 | ||||||||
\(801\) | − | 13.8281i | − | 0.488590i | ||||||
\(802\) | 12.2759 | + | 12.2759i | 0.433477 | + | 0.433477i | ||||
\(803\) | −20.5813 | −0.726299 | ||||||||
\(804\) | 11.1519 | + | 11.1519i | 0.393296 | + | 0.393296i | ||||
\(805\) | 1.97138 | − | 1.97138i | 0.0694822 | − | 0.0694822i | ||||
\(806\) | 0.606711 | − | 0.606711i | 0.0213705 | − | 0.0213705i | ||||
\(807\) | − | 10.0148i | − | 0.352538i | ||||||
\(808\) | 0.636303i | 0.0223851i | ||||||||
\(809\) | −27.2753 | + | 27.2753i | −0.958948 | + | 0.958948i | −0.999190 | − | 0.0402418i | \(-0.987187\pi\) |
0.0402418 | + | 0.999190i | \(0.487187\pi\) | |||||||
\(810\) | 0.306563 | − | 0.306563i | 0.0107715 | − | 0.0107715i | ||||
\(811\) | −13.7457 | − | 13.7457i | −0.482677 | − | 0.482677i | 0.423309 | − | 0.905985i | \(-0.360869\pi\) |
−0.905985 | + | 0.423309i | \(0.860869\pi\) | |||||||
\(812\) | −29.1531 | −1.02307 | ||||||||
\(813\) | 6.51209 | + | 6.51209i | 0.228389 | + | 0.228389i | ||||
\(814\) | − | 17.9968i | − | 0.630788i | ||||||
\(815\) | 7.71922 | 0.270393 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.6387 | −0.757043 | ||||||||
\(818\) | − | 4.42153i | − | 0.154595i | ||||||
\(819\) | −0.801088 | − | 0.801088i | −0.0279923 | − | 0.0279923i | ||||
\(820\) | −5.25359 | −0.183463 | ||||||||
\(821\) | −0.163922 | − | 0.163922i | −0.00572093 | − | 0.00572093i | 0.704241 | − | 0.709961i | \(-0.251288\pi\) |
−0.709961 | + | 0.704241i | \(0.751288\pi\) | |||||||
\(822\) | 8.91723 | − | 8.91723i | 0.311024 | − | 0.311024i | ||||
\(823\) | 15.9050 | − | 15.9050i | 0.554414 | − | 0.554414i | −0.373298 | − | 0.927712i | \(-0.621773\pi\) |
0.927712 | + | 0.373298i | \(0.121773\pi\) | |||||||
\(824\) | 8.59955i | 0.299579i | ||||||||
\(825\) | 8.15890i | 0.284056i | ||||||||
\(826\) | 18.5281 | − | 18.5281i | 0.644675 | − | 0.644675i | ||||
\(827\) | 36.9902 | − | 36.9902i | 1.28628 | − | 1.28628i | 0.349244 | − | 0.937032i | \(-0.386439\pi\) |
0.937032 | − | 0.349244i | \(-0.113561\pi\) | |||||||
\(828\) | −1.33182 | − | 1.33182i | −0.0462840 | − | 0.0462840i | ||||
\(829\) | −23.3260 | −0.810144 | −0.405072 | − | 0.914285i | \(-0.632754\pi\) | ||||
−0.405072 | + | 0.914285i | \(0.632754\pi\) | |||||||
\(830\) | −0.319968 | − | 0.319968i | −0.0111063 | − | 0.0111063i | ||||
\(831\) | 8.36529i | 0.290189i | ||||||||
\(832\) | −0.331821 | −0.0115038 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 17.0447 | 0.590210 | ||||||||
\(835\) | 7.62824i | 0.263986i | ||||||||
\(836\) | −2.57030 | − | 2.57030i | −0.0888957 | − | 0.0888957i | ||||
\(837\) | −2.58579 | −0.0893779 | ||||||||
\(838\) | 16.3811 | + | 16.3811i | 0.565874 | + | 0.565874i | ||||
\(839\) | −9.49019 | + | 9.49019i | −0.327638 | + | 0.327638i | −0.851688 | − | 0.524050i | \(-0.824421\pi\) |
0.524050 | + | 0.851688i | \(0.324421\pi\) | |||||||
\(840\) | −1.04667 | + | 1.04667i | −0.0361136 | + | 0.0361136i | ||||
\(841\) | 43.9101i | 1.51414i | ||||||||
\(842\) | − | 20.0524i | − | 0.691052i | ||||||
\(843\) | −7.77791 | + | 7.77791i | −0.267885 | + | 0.267885i | ||||
\(844\) | −3.33861 | + | 3.33861i | −0.114920 | + | 0.114920i | ||||
\(845\) | 3.95156 | + | 3.95156i | 0.135938 | + | 0.135938i | ||||
\(846\) | −2.38009 | −0.0818290 | ||||||||
\(847\) | −19.6160 | − | 19.6160i | −0.674014 | − | 0.674014i | ||||
\(848\) | 3.13066i | 0.107507i | ||||||||
\(849\) | −21.1380 | −0.725456 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.9919 | −0.685314 | ||||||||
\(852\) | − | 0.226626i | − | 0.00776406i | ||||||
\(853\) | −35.3094 | − | 35.3094i | −1.20897 | − | 1.20897i | −0.971361 | − | 0.237609i | \(-0.923636\pi\) |
−0.237609 | − | 0.971361i | \(-0.576364\pi\) | |||||||
\(854\) | −27.4499 | −0.939315 | ||||||||
\(855\) | −0.657228 | − | 0.657228i | −0.0224767 | − | 0.0224767i | ||||
\(856\) | 1.53073 | − | 1.53073i | 0.0523194 | − | 0.0523194i | ||||
\(857\) | −12.1453 | + | 12.1453i | −0.414875 | + | 0.414875i | −0.883433 | − | 0.468558i | \(-0.844774\pi\) |
0.468558 | + | 0.883433i | \(0.344774\pi\) | |||||||
\(858\) | 0.562609i | 0.0192072i | ||||||||
\(859\) | 8.76362i | 0.299011i | 0.988761 | + | 0.149505i | \(0.0477681\pi\) | ||||
−0.988761 | + | 0.149505i | \(0.952232\pi\) | |||||||
\(860\) | 3.09425 | − | 3.09425i | 0.105513 | − | 0.105513i | ||||
\(861\) | 29.2548 | − | 29.2548i | 0.997001 | − | 0.997001i | ||||
\(862\) | −28.3880 | − | 28.3880i | −0.966900 | − | 0.966900i | ||||
\(863\) | −35.9177 | −1.22265 | −0.611326 | − | 0.791379i | \(-0.709364\pi\) | ||||
−0.611326 | + | 0.791379i | \(0.709364\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 8.38748i | 0.285183i | ||||||||
\(866\) | −21.8499 | −0.742490 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.82843 | 0.299656 | ||||||||
\(869\) | 21.2608i | 0.721224i | ||||||||
\(870\) | 2.61766 | + | 2.61766i | 0.0887470 | + | 0.0887470i | ||||
\(871\) | −5.23320 | −0.177320 | ||||||||
\(872\) | 5.59588 | + | 5.59588i | 0.189500 | + | 0.189500i | ||||
\(873\) | −2.65546 | + | 2.65546i | −0.0898738 | + | 0.0898738i | ||||
\(874\) | −2.85524 | + | 2.85524i | −0.0965799 | + | 0.0965799i | ||||
\(875\) | − | 14.5239i | − | 0.490999i | ||||||
\(876\) | − | 12.1387i | − | 0.410127i | ||||||
\(877\) | −2.98766 | + | 2.98766i | −0.100886 | + | 0.100886i | −0.755748 | − | 0.654862i | \(-0.772727\pi\) |
0.654862 | + | 0.755748i | \(0.272727\pi\) | |||||||
\(878\) | −0.593103 | + | 0.593103i | −0.0200163 | + | 0.0200163i | ||||
\(879\) | −17.7679 | − | 17.7679i | −0.599298 | − | 0.599298i | ||||
\(880\) | 0.735084 | 0.0247797 | ||||||||
\(881\) | 21.2102 | + | 21.2102i | 0.714590 | + | 0.714590i | 0.967492 | − | 0.252902i | \(-0.0813849\pi\) |
−0.252902 | + | 0.967492i | \(0.581385\pi\) | |||||||
\(882\) | − | 4.65685i | − | 0.156804i | ||||||
\(883\) | 13.9714 | 0.470175 | 0.235087 | − | 0.971974i | \(-0.424462\pi\) | ||||
0.235087 | + | 0.971974i | \(0.424462\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.32729 | −0.111845 | ||||||||
\(886\) | 3.21267i | 0.107932i | ||||||||
\(887\) | −15.5758 | − | 15.5758i | −0.522986 | − | 0.522986i | 0.395486 | − | 0.918472i | \(-0.370576\pi\) |
−0.918472 | + | 0.395486i | \(0.870576\pi\) | |||||||
\(888\) | 10.6143 | 0.356194 | ||||||||
\(889\) | 29.1740 | + | 29.1740i | 0.978465 | + | 0.978465i | ||||
\(890\) | 4.23917 | − | 4.23917i | 0.142097 | − | 0.142097i | ||||
\(891\) | 1.19891 | − | 1.19891i | 0.0401651 | − | 0.0401651i | ||||
\(892\) | − | 15.6359i | − | 0.523530i | ||||||
\(893\) | 5.10257i | 0.170751i | ||||||||
\(894\) | −12.3746 | + | 12.3746i | −0.413870 | + | 0.413870i | ||||
\(895\) | −2.79565 | + | 2.79565i | −0.0934483 | + | 0.0934483i | ||||
\(896\) | −2.41421 | − | 2.41421i | −0.0806532 | − | 0.0806532i | ||||
\(897\) | 0.624979 | 0.0208674 | ||||||||
\(898\) | −20.3281 | − | 20.3281i | −0.678357 | − | 0.678357i | ||||
\(899\) | − | 22.0794i | − | 0.736388i | ||||||
\(900\) | −4.81204 | −0.160401 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −20.5458 | −0.684102 | ||||||||
\(903\) | 34.4608i | 1.14678i | ||||||||
\(904\) | −6.49709 | − | 6.49709i | −0.216090 | − | 0.216090i | ||||
\(905\) | 0.336731 | 0.0111933 | ||||||||
\(906\) | −6.81657 | − | 6.81657i | −0.226466 | − | 0.226466i | ||||
\(907\) | −19.0287 | + | 19.0287i | −0.631837 | + | 0.631837i | −0.948529 | − | 0.316691i | \(-0.897428\pi\) |
0.316691 | + | 0.948529i | \(0.397428\pi\) | |||||||
\(908\) | 7.82164 | − | 7.82164i | 0.259570 | − | 0.259570i | ||||
\(909\) | 0.636303i | 0.0211048i | ||||||||
\(910\) | − | 0.491168i | − | 0.0162820i | ||||||
\(911\) | −25.0916 | + | 25.0916i | −0.831322 | + | 0.831322i | −0.987698 | − | 0.156375i | \(-0.950019\pi\) |
0.156375 | + | 0.987698i | \(0.450019\pi\) | |||||||
\(912\) | 1.51594 | − | 1.51594i | 0.0501977 | − | 0.0501977i | ||||
\(913\) | −1.25134 | − | 1.25134i | −0.0414133 | − | 0.0414133i | ||||
\(914\) | 7.45097 | 0.246456 | ||||||||
\(915\) | 2.46473 | + | 2.46473i | 0.0814815 | + | 0.0814815i | ||||
\(916\) | 15.3852i | 0.508340i | ||||||||
\(917\) | 3.06147 | 0.101099 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.6107 | −1.27365 | −0.636824 | − | 0.771009i | \(-0.719752\pi\) | ||||
−0.636824 | + | 0.771009i | \(0.719752\pi\) | |||||||
\(920\) | − | 0.816574i | − | 0.0269217i | ||||||
\(921\) | 10.8494 | + | 10.8494i | 0.357498 | + | 0.357498i | ||||
\(922\) | −25.6378 | −0.844337 | ||||||||
\(923\) | 0.0531739 | + | 0.0531739i | 0.00175024 | + | 0.00175024i | ||||
\(924\) | −4.09334 | + | 4.09334i | −0.134661 | + | 0.134661i | ||||
\(925\) | −36.1166 | + | 36.1166i | −1.18751 | + | 1.18751i | ||||
\(926\) | − | 10.7747i | − | 0.354079i | ||||||
\(927\) | 8.59955i | 0.282446i | ||||||||
\(928\) | −6.03780 | + | 6.03780i | −0.198201 | + | 0.198201i | ||||
\(929\) | −16.1891 | + | 16.1891i | −0.531148 | + | 0.531148i | −0.920914 | − | 0.389766i | \(-0.872556\pi\) |
0.389766 | + | 0.920914i | \(0.372556\pi\) | |||||||
\(930\) | −0.792706 | − | 0.792706i | −0.0259939 | − | 0.0259939i | ||||
\(931\) | −9.98364 | −0.327201 | ||||||||
\(932\) | 7.33806 | + | 7.33806i | 0.240366 | + | 0.240366i | ||||
\(933\) | − | 21.6825i | − | 0.709852i | ||||||
\(934\) | 35.6492 | 1.16648 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.331821 | −0.0108459 | ||||||||
\(937\) | − | 39.6793i | − | 1.29627i | −0.761527 | − | 0.648133i | \(-0.775550\pi\) | ||
0.761527 | − | 0.648133i | \(-0.224450\pi\) | |||||||
\(938\) | −38.0749 | − | 38.0749i | −1.24319 | − | 1.24319i | ||||
\(939\) | 8.38847 | 0.273747 | ||||||||
\(940\) | −0.729646 | − | 0.729646i | −0.0237984 | − | 0.0237984i | ||||
\(941\) | −37.2398 | + | 37.2398i | −1.21398 | + | 1.21398i | −0.244279 | + | 0.969705i | \(0.578551\pi\) |
−0.969705 | + | 0.244279i | \(0.921449\pi\) | |||||||
\(942\) | 3.38687 | − | 3.38687i | 0.110350 | − | 0.110350i | ||||
\(943\) | 22.8235i | 0.743236i | ||||||||
\(944\) | − | 7.67459i | − | 0.249787i | ||||||
\(945\) | −1.04667 | + | 1.04667i | −0.0340482 | + | 0.0340482i | ||||
\(946\) | 12.1010 | − | 12.1010i | 0.393439 | − | 0.393439i | ||||
\(947\) | −1.07974 | − | 1.07974i | −0.0350867 | − | 0.0350867i | 0.689346 | − | 0.724432i | \(-0.257898\pi\) |
−0.724432 | + | 0.689346i | \(0.757898\pi\) | |||||||
\(948\) | −12.5394 | −0.407262 | ||||||||
\(949\) | 2.84813 | + | 2.84813i | 0.0924543 | + | 0.0924543i | ||||
\(950\) | 10.3163i | 0.334706i | ||||||||
\(951\) | −23.9803 | −0.777614 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.95360 | 0.322429 | 0.161214 | − | 0.986919i | \(-0.448459\pi\) | ||||
0.161214 | + | 0.986919i | \(0.448459\pi\) | |||||||
\(954\) | 3.13066i | 0.101359i | ||||||||
\(955\) | −4.11554 | − | 4.11554i | −0.133176 | − | 0.133176i | ||||
\(956\) | 24.7803 | 0.801454 | ||||||||
\(957\) | 10.2372 | + | 10.2372i | 0.330922 | + | 0.330922i | ||||
\(958\) | −9.94911 | + | 9.94911i | −0.321441 | + | 0.321441i | ||||
\(959\) | −30.4453 | + | 30.4453i | −0.983131 | + | 0.983131i | ||||
\(960\) | 0.433546i | 0.0139926i | ||||||||
\(961\) | − | 24.3137i | − | 0.784313i | ||||||
\(962\) | −2.49048 | + | 2.49048i | −0.0802962 | + | 0.0802962i | ||||
\(963\) | 1.53073 | − | 1.53073i | 0.0493272 | − | 0.0493272i | ||||
\(964\) | 3.04422 | + | 3.04422i | 0.0980476 | + | 0.0980476i | ||||
\(965\) | −2.20633 | −0.0710244 | ||||||||
\(966\) | 4.54712 | + | 4.54712i | 0.146301 | + | 0.146301i | ||||
\(967\) | − | 5.88843i | − | 0.189359i | −0.995508 | − | 0.0946796i | \(-0.969817\pi\) | ||
0.995508 | − | 0.0946796i | \(-0.0301827\pi\) | |||||||
\(968\) | −8.12522 | −0.261154 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.62813 | −0.0522762 | ||||||||
\(971\) | − | 18.9670i | − | 0.608681i | −0.952563 | − | 0.304341i | \(-0.901564\pi\) | ||
0.952563 | − | 0.304341i | \(-0.0984361\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −58.1943 | −1.86562 | ||||||||
\(974\) | −17.0643 | − | 17.0643i | −0.546775 | − | 0.546775i | ||||
\(975\) | 1.12906 | − | 1.12906i | 0.0361590 | − | 0.0361590i | ||||
\(976\) | −5.68506 | + | 5.68506i | −0.181974 | + | 0.181974i | ||||
\(977\) | 32.3172i | 1.03392i | 0.856010 | + | 0.516959i | \(0.172936\pi\) | ||||
−0.856010 | + | 0.516959i | \(0.827064\pi\) | |||||||
\(978\) | 17.8049i | 0.569337i | ||||||||
\(979\) | 16.5786 | − | 16.5786i | 0.529855 | − | 0.529855i | ||||
\(980\) | 1.42762 | − | 1.42762i | 0.0456036 | − | 0.0456036i | ||||
\(981\) | 5.59588 | + | 5.59588i | 0.178663 | + | 0.178663i | ||||
\(982\) | −26.5200 | −0.846288 | ||||||||
\(983\) | 22.9359 | + | 22.9359i | 0.731542 | + | 0.731542i | 0.970925 | − | 0.239383i | \(-0.0769453\pi\) |
−0.239383 | + | 0.970925i | \(0.576945\pi\) | |||||||
\(984\) | − | 12.1177i | − | 0.386299i | ||||||
\(985\) | −1.80116 | −0.0573898 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.12612 | 0.258657 | ||||||||
\(988\) | 0.711378i | 0.0226320i | ||||||||
\(989\) | −13.4425 | − | 13.4425i | −0.427448 | − | 0.427448i | ||||
\(990\) | 0.735084 | 0.0233625 | ||||||||
\(991\) | −33.1640 | − | 33.1640i | −1.05349 | − | 1.05349i | −0.998486 | − | 0.0550042i | \(-0.982483\pi\) |
−0.0550042 | − | 0.998486i | \(-0.517517\pi\) | |||||||
\(992\) | 1.82843 | − | 1.82843i | 0.0580526 | − | 0.0580526i | ||||
\(993\) | 2.88311 | − | 2.88311i | 0.0914926 | − | 0.0914926i | ||||
\(994\) | 0.773748i | 0.0245418i | ||||||||
\(995\) | − | 4.64272i | − | 0.147184i | ||||||
\(996\) | 0.738027 | − | 0.738027i | 0.0233853 | − | 0.0233853i | ||||
\(997\) | 33.5572 | − | 33.5572i | 1.06277 | − | 1.06277i | 0.0648741 | − | 0.997893i | \(-0.479335\pi\) |
0.997893 | − | 0.0648741i | \(-0.0206646\pi\) | |||||||
\(998\) | 3.21024 | + | 3.21024i | 0.101618 | + | 0.101618i | ||||
\(999\) | 10.6143 | 0.335823 |
(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 | 1734.2.f.m.829.3 | 8 | ||
17.2 | even | 8 | 1734.2.a.w.1.2 | 4 | |||
17.3 | odd | 16 | 102.2.h.a.49.2 | yes | 8 | ||
17.4 | even | 4 | inner | 1734.2.f.m.1483.3 | 8 | ||
17.7 | odd | 16 | 102.2.h.a.25.2 | ✓ | 8 | ||
17.8 | even | 8 | 1734.2.b.k.577.3 | 8 | |||
17.9 | even | 8 | 1734.2.b.k.577.6 | 8 | |||
17.13 | even | 4 | 1734.2.f.j.1483.2 | 8 | |||
17.15 | even | 8 | 1734.2.a.v.1.3 | 4 | |||
17.16 | even | 2 | 1734.2.f.j.829.2 | 8 | |||
51.2 | odd | 8 | 5202.2.a.bt.1.3 | 4 | |||
51.20 | even | 16 | 306.2.l.d.253.2 | 8 | |||
51.32 | odd | 8 | 5202.2.a.br.1.2 | 4 | |||
51.41 | even | 16 | 306.2.l.d.127.2 | 8 | |||
68.3 | even | 16 | 816.2.bq.b.49.1 | 8 | |||
68.7 | even | 16 | 816.2.bq.b.433.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.2.h.a.25.2 | ✓ | 8 | 17.7 | odd | 16 | ||
102.2.h.a.49.2 | yes | 8 | 17.3 | odd | 16 | ||
306.2.l.d.127.2 | 8 | 51.41 | even | 16 | |||
306.2.l.d.253.2 | 8 | 51.20 | even | 16 | |||
816.2.bq.b.49.1 | 8 | 68.3 | even | 16 | |||
816.2.bq.b.433.1 | 8 | 68.7 | even | 16 | |||
1734.2.a.v.1.3 | 4 | 17.15 | even | 8 | |||
1734.2.a.w.1.2 | 4 | 17.2 | even | 8 | |||
1734.2.b.k.577.3 | 8 | 17.8 | even | 8 | |||
1734.2.b.k.577.6 | 8 | 17.9 | even | 8 | |||
1734.2.f.j.829.2 | 8 | 17.16 | even | 2 | |||
1734.2.f.j.1483.2 | 8 | 17.13 | even | 4 | |||
1734.2.f.m.829.3 | 8 | 1.1 | even | 1 | trivial | ||
1734.2.f.m.1483.3 | 8 | 17.4 | even | 4 | inner | ||
5202.2.a.br.1.2 | 4 | 51.32 | odd | 8 | |||
5202.2.a.bt.1.3 | 4 | 51.2 | odd | 8 |