Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(37,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 493.10 | ||
Root | \(-0.498616 - 0.498616i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.493 |
Dual form | 570.2.m.a.37.10 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.89390 | + | 1.18875i | 0.846979 | + | 0.531627i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.705149 | − | 0.705149i | 0.266521 | − | 0.266521i | −0.561175 | − | 0.827697i | \(-0.689651\pi\) |
0.827697 | + | 0.561175i | \(0.189651\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0.498616 | + | 2.17977i | 0.157676 | + | 0.689303i | ||||
\(11\) | 1.32903 | 0.400718 | 0.200359 | − | 0.979723i | \(-0.435789\pi\) | ||||
0.200359 | + | 0.979723i | \(0.435789\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −0.741383 | + | 0.741383i | −0.205623 | + | 0.205623i | −0.802404 | − | 0.596781i | \(-0.796446\pi\) |
0.596781 | + | 0.802404i | \(0.296446\pi\) | |||||||
\(14\) | 0.997232 | 0.266521 | ||||||||
\(15\) | 2.17977 | − | 0.498616i | 0.562813 | − | 0.128742i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.17373 | − | 2.17373i | 0.527208 | − | 0.527208i | −0.392531 | − | 0.919739i | \(-0.628400\pi\) |
0.919739 | + | 0.392531i | \(0.128400\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 0.939768 | + | 4.25639i | 0.215597 | + | 0.976482i | ||||
\(20\) | −1.18875 | + | 1.89390i | −0.265813 | + | 0.423489i | ||||
\(21\) | − | 0.997232i | − | 0.217614i | ||||||
\(22\) | 0.939768 | + | 0.939768i | 0.200359 | + | 0.200359i | ||||
\(23\) | −1.08266 | − | 1.08266i | −0.225749 | − | 0.225749i | 0.585165 | − | 0.810914i | \(-0.301030\pi\) |
−0.810914 | + | 0.585165i | \(0.801030\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 2.17373 | + | 4.50276i | 0.434746 | + | 0.900553i | ||||
\(26\) | −1.04847 | −0.205623 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0.705149 | + | 0.705149i | 0.133261 | + | 0.133261i | ||||
\(29\) | −5.95089 | −1.10505 | −0.552526 | − | 0.833496i | \(-0.686336\pi\) | ||||
−0.552526 | + | 0.833496i | \(0.686336\pi\) | |||||||
\(30\) | 1.89390 | + | 1.18875i | 0.345778 | + | 0.217036i | ||||
\(31\) | − | 5.95089i | − | 1.06881i | −0.845228 | − | 0.534406i | \(-0.820536\pi\) | ||
0.845228 | − | 0.534406i | \(-0.179464\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0.939768 | − | 0.939768i | 0.163593 | − | 0.163593i | ||||
\(34\) | 3.07412 | 0.527208 | ||||||||
\(35\) | 2.17373 | − | 0.497236i | 0.367428 | − | 0.0840481i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.33551 | − | 1.33551i | −0.219556 | − | 0.219556i | 0.588755 | − | 0.808311i | \(-0.299618\pi\) |
−0.808311 | + | 0.588755i | \(0.799618\pi\) | |||||||
\(38\) | −2.34520 | + | 3.67424i | −0.380442 | + | 0.596040i | ||||
\(39\) | 1.04847i | 0.167890i | ||||||||
\(40\) | −2.17977 | + | 0.498616i | −0.344651 | + | 0.0788381i | ||||
\(41\) | 0.531910i | 0.0830704i | 0.999137 | + | 0.0415352i | \(0.0132249\pi\) | ||||
−0.999137 | + | 0.0415352i | \(0.986775\pi\) | |||||||
\(42\) | 0.705149 | − | 0.705149i | 0.108807 | − | 0.108807i | ||||
\(43\) | 1.53142 | + | 1.53142i | 0.233539 | + | 0.233539i | 0.814168 | − | 0.580629i | \(-0.197193\pi\) |
−0.580629 | + | 0.814168i | \(0.697193\pi\) | |||||||
\(44\) | 1.32903i | 0.200359i | ||||||||
\(45\) | 1.18875 | − | 1.89390i | 0.177209 | − | 0.282326i | ||||
\(46\) | − | 1.53111i | − | 0.225749i | ||||||
\(47\) | 4.13113 | − | 4.13113i | 0.602587 | − | 0.602587i | −0.338411 | − | 0.940998i | \(-0.609889\pi\) |
0.940998 | + | 0.338411i | \(0.109889\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 6.00553i | 0.857933i | ||||||||
\(50\) | −1.64687 | + | 4.72100i | −0.232903 | + | 0.667650i | ||||
\(51\) | − | 3.07412i | − | 0.430463i | ||||||
\(52\) | −0.741383 | − | 0.741383i | −0.102811 | − | 0.102811i | ||||
\(53\) | −5.48557 | + | 5.48557i | −0.753501 | + | 0.753501i | −0.975131 | − | 0.221630i | \(-0.928862\pi\) |
0.221630 | + | 0.975131i | \(0.428862\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 2.51706 | + | 1.57989i | 0.339400 | + | 0.213032i | ||||
\(56\) | 0.997232i | 0.133261i | ||||||||
\(57\) | 3.67424 | + | 2.34520i | 0.486665 | + | 0.310630i | ||||
\(58\) | −4.20791 | − | 4.20791i | −0.552526 | − | 0.552526i | ||||
\(59\) | −3.53944 | −0.460796 | −0.230398 | − | 0.973096i | \(-0.574003\pi\) | ||||
−0.230398 | + | 0.973096i | \(0.574003\pi\) | |||||||
\(60\) | 0.498616 | + | 2.17977i | 0.0643710 | + | 0.281407i | ||||
\(61\) | 3.41030 | 0.436644 | 0.218322 | − | 0.975877i | \(-0.429942\pi\) | ||||
0.218322 | + | 0.975877i | \(0.429942\pi\) | |||||||
\(62\) | 4.20791 | − | 4.20791i | 0.534406 | − | 0.534406i | ||||
\(63\) | −0.705149 | − | 0.705149i | −0.0888405 | − | 0.0888405i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −2.28543 | + | 0.522786i | −0.283473 | + | 0.0648436i | ||||
\(66\) | 1.32903 | 0.163593 | ||||||||
\(67\) | −1.99446 | − | 1.99446i | −0.243662 | − | 0.243662i | 0.574701 | − | 0.818363i | \(-0.305118\pi\) |
−0.818363 | + | 0.574701i | \(0.805118\pi\) | |||||||
\(68\) | 2.17373 | + | 2.17373i | 0.263604 | + | 0.263604i | ||||
\(69\) | −1.53111 | −0.184323 | ||||||||
\(70\) | 1.88866 | + | 1.18546i | 0.225738 | + | 0.141690i | ||||
\(71\) | − | 8.71907i | − | 1.03476i | −0.855755 | − | 0.517381i | \(-0.826907\pi\) | ||
0.855755 | − | 0.517381i | \(-0.173093\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −5.83628 | − | 5.83628i | −0.683085 | − | 0.683085i | 0.277609 | − | 0.960694i | \(-0.410458\pi\) |
−0.960694 | + | 0.277609i | \(0.910458\pi\) | |||||||
\(74\) | − | 1.88869i | − | 0.219556i | ||||||
\(75\) | 4.72100 | + | 1.64687i | 0.545134 | + | 0.190165i | ||||
\(76\) | −4.25639 | + | 0.939768i | −0.488241 | + | 0.107799i | ||||
\(77\) | 0.937166 | − | 0.937166i | 0.106800 | − | 0.106800i | ||||
\(78\) | −0.741383 | + | 0.741383i | −0.0839451 | + | 0.0839451i | ||||
\(79\) | 9.31319 | 1.04782 | 0.523908 | − | 0.851775i | \(-0.324474\pi\) | ||||
0.523908 | + | 0.851775i | \(0.324474\pi\) | |||||||
\(80\) | −1.89390 | − | 1.18875i | −0.211745 | − | 0.132907i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −0.376117 | + | 0.376117i | −0.0415352 | + | 0.0415352i | ||||
\(83\) | −9.50276 | − | 9.50276i | −1.04306 | − | 1.04306i | −0.999030 | − | 0.0440339i | \(-0.985979\pi\) |
−0.0440339 | − | 0.999030i | \(-0.514021\pi\) | |||||||
\(84\) | 0.997232 | 0.108807 | ||||||||
\(85\) | 6.70087 | − | 1.53281i | 0.726811 | − | 0.166256i | ||||
\(86\) | 2.16575i | 0.233539i | ||||||||
\(87\) | −4.20791 | + | 4.20791i | −0.451136 | + | 0.451136i | ||||
\(88\) | −0.939768 | + | 0.939768i | −0.100180 | + | 0.100180i | ||||
\(89\) | −16.7874 | −1.77946 | −0.889729 | − | 0.456490i | \(-0.849106\pi\) | ||||
−0.889729 | + | 0.456490i | \(0.849106\pi\) | |||||||
\(90\) | 2.17977 | − | 0.498616i | 0.229768 | − | 0.0525587i | ||||
\(91\) | 1.04557i | 0.109606i | ||||||||
\(92\) | 1.08266 | − | 1.08266i | 0.112875 | − | 0.112875i | ||||
\(93\) | −4.20791 | − | 4.20791i | −0.436340 | − | 0.436340i | ||||
\(94\) | 5.84230 | 0.602587 | ||||||||
\(95\) | −3.27997 | + | 9.17833i | −0.336517 | + | 0.941677i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.11691 | + | 1.11691i | 0.113405 | + | 0.113405i | 0.761532 | − | 0.648127i | \(-0.224447\pi\) |
−0.648127 | + | 0.761532i | \(0.724447\pi\) | |||||||
\(98\) | −4.24655 | + | 4.24655i | −0.428966 | + | 0.428966i | ||||
\(99\) | − | 1.32903i | − | 0.133573i | ||||||
\(100\) | −4.50276 | + | 2.17373i | −0.450276 | + | 0.217373i | ||||
\(101\) | −15.7109 | −1.56329 | −0.781645 | − | 0.623723i | \(-0.785619\pi\) | ||||
−0.781645 | + | 0.623723i | \(0.785619\pi\) | |||||||
\(102\) | 2.17373 | − | 2.17373i | 0.215232 | − | 0.215232i | ||||
\(103\) | 10.7950 | − | 10.7950i | 1.06367 | − | 1.06367i | 0.0658345 | − | 0.997831i | \(-0.479029\pi\) |
0.997831 | − | 0.0658345i | \(-0.0209710\pi\) | |||||||
\(104\) | − | 1.04847i | − | 0.102811i | ||||||
\(105\) | 1.18546 | − | 1.88866i | 0.115689 | − | 0.184314i | ||||
\(106\) | −7.75776 | −0.753501 | ||||||||
\(107\) | −2.65129 | − | 2.65129i | −0.256309 | − | 0.256309i | 0.567242 | − | 0.823551i | \(-0.308010\pi\) |
−0.823551 | + | 0.567242i | \(0.808010\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | −5.83596 | −0.558984 | −0.279492 | − | 0.960148i | \(-0.590166\pi\) | ||||
−0.279492 | + | 0.960148i | \(0.590166\pi\) | |||||||
\(110\) | 0.662676 | + | 2.89698i | 0.0631837 | + | 0.276216i | ||||
\(111\) | −1.88869 | −0.179267 | ||||||||
\(112\) | −0.705149 | + | 0.705149i | −0.0666303 | + | 0.0666303i | ||||
\(113\) | −0.463357 | + | 0.463357i | −0.0435890 | + | 0.0435890i | −0.728565 | − | 0.684976i | \(-0.759813\pi\) |
0.684976 | + | 0.728565i | \(0.259813\pi\) | |||||||
\(114\) | 0.939768 | + | 4.25639i | 0.0880173 | + | 0.398647i | ||||
\(115\) | −0.763434 | − | 3.33745i | −0.0711906 | − | 0.311219i | ||||
\(116\) | − | 5.95089i | − | 0.552526i | ||||||
\(117\) | 0.741383 | + | 0.741383i | 0.0685409 | + | 0.0685409i | ||||
\(118\) | −2.50276 | − | 2.50276i | −0.230398 | − | 0.230398i | ||||
\(119\) | − | 3.06561i | − | 0.281024i | ||||||
\(120\) | −1.18875 | + | 1.89390i | −0.108518 | + | 0.172889i | ||||
\(121\) | −9.23367 | −0.839425 | ||||||||
\(122\) | 2.41145 | + | 2.41145i | 0.218322 | + | 0.218322i | ||||
\(123\) | 0.376117 | + | 0.376117i | 0.0339133 | + | 0.0339133i | ||||
\(124\) | 5.95089 | 0.534406 | ||||||||
\(125\) | −1.23584 | + | 11.1118i | −0.110537 | + | 0.993872i | ||||
\(126\) | − | 0.997232i | − | 0.0888405i | ||||||
\(127\) | 7.75499 | + | 7.75499i | 0.688144 | + | 0.688144i | 0.961821 | − | 0.273678i | \(-0.0882402\pi\) |
−0.273678 | + | 0.961821i | \(0.588240\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 2.16575 | 0.190684 | ||||||||
\(130\) | −1.98571 | − | 1.24638i | −0.174158 | − | 0.109314i | ||||
\(131\) | −13.2521 | −1.15784 | −0.578921 | − | 0.815384i | \(-0.696526\pi\) | ||||
−0.578921 | + | 0.815384i | \(0.696526\pi\) | |||||||
\(132\) | 0.939768 | + | 0.939768i | 0.0817963 | + | 0.0817963i | ||||
\(133\) | 3.66407 | + | 2.33871i | 0.317715 | + | 0.202792i | ||||
\(134\) | − | 2.82060i | − | 0.243662i | ||||||
\(135\) | −0.498616 | − | 2.17977i | −0.0429140 | − | 0.187604i | ||||
\(136\) | 3.07412i | 0.263604i | ||||||||
\(137\) | 4.42031 | − | 4.42031i | 0.377653 | − | 0.377653i | −0.492602 | − | 0.870255i | \(-0.663954\pi\) |
0.870255 | + | 0.492602i | \(0.163954\pi\) | |||||||
\(138\) | −1.08266 | − | 1.08266i | −0.0921617 | − | 0.0921617i | ||||
\(139\) | 2.68665i | 0.227879i | 0.993488 | + | 0.113939i | \(0.0363469\pi\) | ||||
−0.993488 | + | 0.113939i | \(0.963653\pi\) | |||||||
\(140\) | 0.497236 | + | 2.17373i | 0.0420241 | + | 0.183714i | ||||
\(141\) | − | 5.84230i | − | 0.492010i | ||||||
\(142\) | 6.16531 | − | 6.16531i | 0.517381 | − | 0.517381i | ||||
\(143\) | −0.985322 | + | 0.985322i | −0.0823968 | + | 0.0823968i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −11.2704 | − | 7.07414i | −0.935956 | − | 0.587475i | ||||
\(146\) | − | 8.25374i | − | 0.683085i | ||||||
\(147\) | 4.24655 | + | 4.24655i | 0.350250 | + | 0.350250i | ||||
\(148\) | 1.33551 | − | 1.33551i | 0.109778 | − | 0.109778i | ||||
\(149\) | − | 14.1380i | − | 1.15823i | −0.815244 | − | 0.579117i | \(-0.803397\pi\) | ||
0.815244 | − | 0.579117i | \(-0.196603\pi\) | |||||||
\(150\) | 2.17373 | + | 4.50276i | 0.177485 | + | 0.367649i | ||||
\(151\) | 9.45030i | 0.769054i | 0.923114 | + | 0.384527i | \(0.125635\pi\) | ||||
−0.923114 | + | 0.384527i | \(0.874365\pi\) | |||||||
\(152\) | −3.67424 | − | 2.34520i | −0.298020 | − | 0.190221i | ||||
\(153\) | −2.17373 | − | 2.17373i | −0.175736 | − | 0.175736i | ||||
\(154\) | 1.32535 | 0.106800 | ||||||||
\(155\) | 7.07414 | − | 11.2704i | 0.568208 | − | 0.905260i | ||||
\(156\) | −1.04847 | −0.0839451 | ||||||||
\(157\) | 13.7650 | − | 13.7650i | 1.09857 | − | 1.09857i | 0.103990 | − | 0.994578i | \(-0.466839\pi\) |
0.994578 | − | 0.103990i | \(-0.0331610\pi\) | |||||||
\(158\) | 6.58542 | + | 6.58542i | 0.523908 | + | 0.523908i | ||||
\(159\) | 7.75776i | 0.615231i | ||||||||
\(160\) | −0.498616 | − | 2.17977i | −0.0394190 | − | 0.172326i | ||||
\(161\) | −1.52687 | −0.120334 | ||||||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 0.792086 | + | 0.792086i | 0.0620410 | + | 0.0620410i | 0.737447 | − | 0.675406i | \(-0.236031\pi\) |
−0.675406 | + | 0.737447i | \(0.736031\pi\) | |||||||
\(164\) | −0.531910 | −0.0415352 | ||||||||
\(165\) | 2.89698 | − | 0.662676i | 0.225530 | − | 0.0515893i | ||||
\(166\) | − | 13.4389i | − | 1.04306i | ||||||
\(167\) | 11.1325 | + | 11.1325i | 0.861457 | + | 0.861457i | 0.991507 | − | 0.130051i | \(-0.0415140\pi\) |
−0.130051 | + | 0.991507i | \(0.541514\pi\) | |||||||
\(168\) | 0.705149 | + | 0.705149i | 0.0544035 | + | 0.0544035i | ||||
\(169\) | 11.9007i | 0.915439i | ||||||||
\(170\) | 5.82209 | + | 3.65437i | 0.446534 | + | 0.280278i | ||||
\(171\) | 4.25639 | − | 0.939768i | 0.325494 | − | 0.0718658i | ||||
\(172\) | −1.53142 | + | 1.53142i | −0.116769 | + | 0.116769i | ||||
\(173\) | 5.42532 | − | 5.42532i | 0.412479 | − | 0.412479i | −0.470122 | − | 0.882601i | \(-0.655790\pi\) |
0.882601 | + | 0.470122i | \(0.155790\pi\) | |||||||
\(174\) | −5.95089 | −0.451136 | ||||||||
\(175\) | 4.70793 | + | 1.64232i | 0.355886 | + | 0.124147i | ||||
\(176\) | −1.32903 | −0.100180 | ||||||||
\(177\) | −2.50276 | + | 2.50276i | −0.188119 | + | 0.188119i | ||||
\(178\) | −11.8705 | − | 11.8705i | −0.889729 | − | 0.889729i | ||||
\(179\) | −0.963050 | −0.0719817 | −0.0359909 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359909 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(180\) | 1.89390 | + | 1.18875i | 0.141163 | + | 0.0886044i | ||||
\(181\) | 20.4214i | 1.51791i | 0.651141 | + | 0.758956i | \(0.274290\pi\) | ||||
−0.651141 | + | 0.758956i | \(0.725710\pi\) | |||||||
\(182\) | −0.739331 | + | 0.739331i | −0.0548028 | + | 0.0548028i | ||||
\(183\) | 2.41145 | − | 2.41145i | 0.178259 | − | 0.178259i | ||||
\(184\) | 1.53111 | 0.112875 | ||||||||
\(185\) | −0.941732 | − | 4.11691i | −0.0692375 | − | 0.302681i | ||||
\(186\) | − | 5.95089i | − | 0.436340i | ||||||
\(187\) | 2.88896 | − | 2.88896i | 0.211262 | − | 0.211262i | ||||
\(188\) | 4.13113 | + | 4.13113i | 0.301294 | + | 0.301294i | ||||
\(189\) | −0.997232 | −0.0725379 | ||||||||
\(190\) | −8.80935 | + | 4.17078i | −0.639097 | + | 0.302580i | ||||
\(191\) | −7.34773 | −0.531663 | −0.265832 | − | 0.964019i | \(-0.585647\pi\) | ||||
−0.265832 | + | 0.964019i | \(0.585647\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 9.32428 | − | 9.32428i | 0.671176 | − | 0.671176i | −0.286811 | − | 0.957987i | \(-0.592595\pi\) |
0.957987 | + | 0.286811i | \(0.0925952\pi\) | |||||||
\(194\) | 1.57955i | 0.113405i | ||||||||
\(195\) | −1.24638 | + | 1.98571i | −0.0892549 | + | 0.142199i | ||||
\(196\) | −6.00553 | −0.428966 | ||||||||
\(197\) | 5.43012 | − | 5.43012i | 0.386880 | − | 0.386880i | −0.486693 | − | 0.873573i | \(-0.661797\pi\) |
0.873573 | + | 0.486693i | \(0.161797\pi\) | |||||||
\(198\) | 0.939768 | − | 0.939768i | 0.0667864 | − | 0.0667864i | ||||
\(199\) | − | 23.4987i | − | 1.66578i | −0.553440 | − | 0.832889i | \(-0.686685\pi\) | ||
0.553440 | − | 0.832889i | \(-0.313315\pi\) | |||||||
\(200\) | −4.72100 | − | 1.64687i | −0.333825 | − | 0.116452i | ||||
\(201\) | −2.82060 | −0.198950 | ||||||||
\(202\) | −11.1093 | − | 11.1093i | −0.781645 | − | 0.781645i | ||||
\(203\) | −4.19627 | + | 4.19627i | −0.294520 | + | 0.294520i | ||||
\(204\) | 3.07412 | 0.215232 | ||||||||
\(205\) | −0.632310 | + | 1.00739i | −0.0441624 | + | 0.0703589i | ||||
\(206\) | 15.2665 | 1.06367 | ||||||||
\(207\) | −1.08266 | + | 1.08266i | −0.0752498 | + | 0.0752498i | ||||
\(208\) | 0.741383 | − | 0.741383i | 0.0514057 | − | 0.0514057i | ||||
\(209\) | 1.24898 | + | 5.65688i | 0.0863938 | + | 0.391294i | ||||
\(210\) | 2.17373 | − | 0.497236i | 0.150002 | − | 0.0343125i | ||||
\(211\) | 8.16488i | 0.562094i | 0.959694 | + | 0.281047i | \(0.0906816\pi\) | ||||
−0.959694 | + | 0.281047i | \(0.909318\pi\) | |||||||
\(212\) | −5.48557 | − | 5.48557i | −0.376750 | − | 0.376750i | ||||
\(213\) | −6.16531 | − | 6.16531i | −0.422440 | − | 0.422440i | ||||
\(214\) | − | 3.74948i | − | 0.256309i | ||||||
\(215\) | 1.07988 | + | 4.72083i | 0.0736470 | + | 0.321958i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.19627 | − | 4.19627i | −0.284861 | − | 0.284861i | ||||
\(218\) | −4.12665 | − | 4.12665i | −0.279492 | − | 0.279492i | ||||
\(219\) | −8.25374 | −0.557736 | ||||||||
\(220\) | −1.57989 | + | 2.51706i | −0.106516 | + | 0.169700i | ||||
\(221\) | 3.22314i | 0.216812i | ||||||||
\(222\) | −1.33551 | − | 1.33551i | −0.0896334 | − | 0.0896334i | ||||
\(223\) | 0.212542 | − | 0.212542i | 0.0142329 | − | 0.0142329i | −0.699955 | − | 0.714187i | \(-0.746796\pi\) |
0.714187 | + | 0.699955i | \(0.246796\pi\) | |||||||
\(224\) | −0.997232 | −0.0666303 | ||||||||
\(225\) | 4.50276 | − | 2.17373i | 0.300184 | − | 0.144915i | ||||
\(226\) | −0.655286 | −0.0435890 | ||||||||
\(227\) | 16.9240 | + | 16.9240i | 1.12328 | + | 1.12328i | 0.991244 | + | 0.132040i | \(0.0421528\pi\) |
0.132040 | + | 0.991244i | \(0.457847\pi\) | |||||||
\(228\) | −2.34520 | + | 3.67424i | −0.155315 | + | 0.243332i | ||||
\(229\) | 7.59523i | 0.501907i | 0.967999 | + | 0.250953i | \(0.0807441\pi\) | ||||
−0.967999 | + | 0.250953i | \(0.919256\pi\) | |||||||
\(230\) | 1.82011 | − | 2.89977i | 0.120014 | − | 0.191205i | ||||
\(231\) | − | 1.32535i | − | 0.0872018i | ||||||
\(232\) | 4.20791 | − | 4.20791i | 0.276263 | − | 0.276263i | ||||
\(233\) | 0.816115 | + | 0.816115i | 0.0534655 | + | 0.0534655i | 0.733334 | − | 0.679869i | \(-0.237963\pi\) |
−0.679869 | + | 0.733334i | \(0.737963\pi\) | |||||||
\(234\) | 1.04847i | 0.0685409i | ||||||||
\(235\) | 12.7348 | − | 2.91306i | 0.830730 | − | 0.190027i | ||||
\(236\) | − | 3.53944i | − | 0.230398i | ||||||
\(237\) | 6.58542 | − | 6.58542i | 0.427769 | − | 0.427769i | ||||
\(238\) | 2.16771 | − | 2.16771i | 0.140512 | − | 0.140512i | ||||
\(239\) | 4.21103i | 0.272389i | 0.990682 | + | 0.136195i | \(0.0434872\pi\) | ||||
−0.990682 | + | 0.136195i | \(0.956513\pi\) | |||||||
\(240\) | −2.17977 | + | 0.498616i | −0.140703 | + | 0.0321855i | ||||
\(241\) | 24.8896i | 1.60328i | 0.597809 | + | 0.801638i | \(0.296038\pi\) | ||||
−0.597809 | + | 0.801638i | \(0.703962\pi\) | |||||||
\(242\) | −6.52919 | − | 6.52919i | −0.419712 | − | 0.419712i | ||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 3.41030i | 0.218322i | ||||||||
\(245\) | −7.13909 | + | 11.3739i | −0.456100 | + | 0.726651i | ||||
\(246\) | 0.531910i | 0.0339133i | ||||||||
\(247\) | −3.85234 | − | 2.45889i | −0.245119 | − | 0.156455i | ||||
\(248\) | 4.20791 | + | 4.20791i | 0.267203 | + | 0.267203i | ||||
\(249\) | −13.4389 | −0.851658 | ||||||||
\(250\) | −8.73112 | + | 6.98338i | −0.552204 | + | 0.441668i | ||||
\(251\) | −0.952848 | −0.0601432 | −0.0300716 | − | 0.999548i | \(-0.509574\pi\) | ||||
−0.0300716 | + | 0.999548i | \(0.509574\pi\) | |||||||
\(252\) | 0.705149 | − | 0.705149i | 0.0444202 | − | 0.0444202i | ||||
\(253\) | −1.43888 | − | 1.43888i | −0.0904619 | − | 0.0904619i | ||||
\(254\) | 10.9672i | 0.688144i | ||||||||
\(255\) | 3.65437 | − | 5.82209i | 0.228846 | − | 0.364593i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.4298 | + | 12.4298i | 0.775349 | + | 0.775349i | 0.979036 | − | 0.203687i | \(-0.0652924\pi\) |
−0.203687 | + | 0.979036i | \(0.565292\pi\) | |||||||
\(258\) | 1.53142 | + | 1.53142i | 0.0953419 | + | 0.0953419i | ||||
\(259\) | −1.88346 | −0.117033 | ||||||||
\(260\) | −0.522786 | − | 2.28543i | −0.0324218 | − | 0.141736i | ||||
\(261\) | 5.95089i | 0.368351i | ||||||||
\(262\) | −9.37065 | − | 9.37065i | −0.578921 | − | 0.578921i | ||||
\(263\) | 3.37612 | + | 3.37612i | 0.208180 | + | 0.208180i | 0.803494 | − | 0.595313i | \(-0.202972\pi\) |
−0.595313 | + | 0.803494i | \(0.702972\pi\) | |||||||
\(264\) | 1.32903i | 0.0817963i | ||||||||
\(265\) | −16.9101 | + | 3.86814i | −1.03878 | + | 0.237618i | ||||
\(266\) | 0.937166 | + | 4.24460i | 0.0574613 | + | 0.260253i | ||||
\(267\) | −11.8705 | + | 11.8705i | −0.726460 | + | 0.726460i | ||||
\(268\) | 1.99446 | − | 1.99446i | 0.121831 | − | 0.121831i | ||||
\(269\) | 1.10025 | 0.0670834 | 0.0335417 | − | 0.999437i | \(-0.489321\pi\) | ||||
0.0335417 | + | 0.999437i | \(0.489321\pi\) | |||||||
\(270\) | 1.18875 | − | 1.89390i | 0.0723452 | − | 0.115259i | ||||
\(271\) | 18.3193 | 1.11282 | 0.556409 | − | 0.830909i | \(-0.312179\pi\) | ||||
0.556409 | + | 0.830909i | \(0.312179\pi\) | |||||||
\(272\) | −2.17373 | + | 2.17373i | −0.131802 | + | 0.131802i | ||||
\(273\) | 0.739331 | + | 0.739331i | 0.0447463 | + | 0.0447463i | ||||
\(274\) | 6.25126 | 0.377653 | ||||||||
\(275\) | 2.88896 | + | 5.98432i | 0.174211 | + | 0.360868i | ||||
\(276\) | − | 1.53111i | − | 0.0921617i | ||||||
\(277\) | −6.48039 | + | 6.48039i | −0.389369 | + | 0.389369i | −0.874462 | − | 0.485093i | \(-0.838786\pi\) |
0.485093 | + | 0.874462i | \(0.338786\pi\) | |||||||
\(278\) | −1.89975 | + | 1.89975i | −0.113939 | + | 0.113939i | ||||
\(279\) | −5.95089 | −0.356270 | ||||||||
\(280\) | −1.18546 | + | 1.88866i | −0.0708449 | + | 0.112869i | ||||
\(281\) | 12.6675i | 0.755678i | 0.925871 | + | 0.377839i | \(0.123333\pi\) | ||||
−0.925871 | + | 0.377839i | \(0.876667\pi\) | |||||||
\(282\) | 4.13113 | − | 4.13113i | 0.246005 | − | 0.246005i | ||||
\(283\) | 11.2107 | + | 11.2107i | 0.666406 | + | 0.666406i | 0.956882 | − | 0.290476i | \(-0.0938136\pi\) |
−0.290476 | + | 0.956882i | \(0.593814\pi\) | |||||||
\(284\) | 8.71907 | 0.517381 | ||||||||
\(285\) | 4.17078 | + | 8.80935i | 0.247055 | + | 0.521821i | ||||
\(286\) | −1.39346 | −0.0823968 | ||||||||
\(287\) | 0.375076 | + | 0.375076i | 0.0221400 | + | 0.0221400i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 7.54978i | 0.444104i | ||||||||
\(290\) | −2.96721 | − | 12.9715i | −0.174240 | − | 0.761716i | ||||
\(291\) | 1.57955 | 0.0925948 | ||||||||
\(292\) | 5.83628 | − | 5.83628i | 0.341542 | − | 0.341542i | ||||
\(293\) | 0.128802 | − | 0.128802i | 0.00752471 | − | 0.00752471i | −0.703334 | − | 0.710859i | \(-0.748306\pi\) |
0.710859 | + | 0.703334i | \(0.248306\pi\) | |||||||
\(294\) | 6.00553i | 0.350250i | ||||||||
\(295\) | −6.70336 | − | 4.20752i | −0.390285 | − | 0.244972i | ||||
\(296\) | 1.88869 | 0.109778 | ||||||||
\(297\) | −0.939768 | − | 0.939768i | −0.0545308 | − | 0.0545308i | ||||
\(298\) | 9.99711 | − | 9.99711i | 0.579117 | − | 0.579117i | ||||
\(299\) | 1.60532 | 0.0928383 | ||||||||
\(300\) | −1.64687 | + | 4.72100i | −0.0950823 | + | 0.272567i | ||||
\(301\) | 2.15976 | 0.124486 | ||||||||
\(302\) | −6.68237 | + | 6.68237i | −0.384527 | + | 0.384527i | ||||
\(303\) | −11.1093 | + | 11.1093i | −0.638211 | + | 0.638211i | ||||
\(304\) | −0.939768 | − | 4.25639i | −0.0538994 | − | 0.244121i | ||||
\(305\) | 6.45877 | + | 4.05400i | 0.369828 | + | 0.232132i | ||||
\(306\) | − | 3.07412i | − | 0.175736i | ||||||
\(307\) | 15.7940 | + | 15.7940i | 0.901413 | + | 0.901413i | 0.995558 | − | 0.0941458i | \(-0.0300120\pi\) |
−0.0941458 | + | 0.995558i | \(0.530012\pi\) | |||||||
\(308\) | 0.937166 | + | 0.937166i | 0.0534000 | + | 0.0534000i | ||||
\(309\) | − | 15.2665i | − | 0.868479i | ||||||
\(310\) | 12.9715 | − | 2.96721i | 0.736734 | − | 0.168526i | ||||
\(311\) | 14.6924 | 0.833132 | 0.416566 | − | 0.909105i | \(-0.363233\pi\) | ||||
0.416566 | + | 0.909105i | \(0.363233\pi\) | |||||||
\(312\) | −0.741383 | − | 0.741383i | −0.0419726 | − | 0.0419726i | ||||
\(313\) | −1.77069 | − | 1.77069i | −0.100086 | − | 0.100086i | 0.655291 | − | 0.755377i | \(-0.272546\pi\) |
−0.755377 | + | 0.655291i | \(0.772546\pi\) | |||||||
\(314\) | 19.4667 | 1.09857 | ||||||||
\(315\) | −0.497236 | − | 2.17373i | −0.0280160 | − | 0.122476i | ||||
\(316\) | 9.31319i | 0.523908i | ||||||||
\(317\) | −4.63384 | − | 4.63384i | −0.260262 | − | 0.260262i | 0.564898 | − | 0.825161i | \(-0.308915\pi\) |
−0.825161 | + | 0.564898i | \(0.808915\pi\) | |||||||
\(318\) | −5.48557 | + | 5.48557i | −0.307615 | + | 0.307615i | ||||
\(319\) | −7.90892 | −0.442815 | ||||||||
\(320\) | 1.18875 | − | 1.89390i | 0.0664533 | − | 0.105872i | ||||
\(321\) | −3.74948 | −0.209276 | ||||||||
\(322\) | −1.07966 | − | 1.07966i | −0.0601670 | − | 0.0601670i | ||||
\(323\) | 11.2951 | + | 7.20944i | 0.628473 | + | 0.401144i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −4.94984 | − | 1.72670i | −0.274568 | − | 0.0957804i | ||||
\(326\) | 1.12018i | 0.0620410i | ||||||||
\(327\) | −4.12665 | + | 4.12665i | −0.228204 | + | 0.228204i | ||||
\(328\) | −0.376117 | − | 0.376117i | −0.0207676 | − | 0.0207676i | ||||
\(329\) | − | 5.82613i | − | 0.321205i | ||||||
\(330\) | 2.51706 | + | 1.57989i | 0.138559 | + | 0.0869701i | ||||
\(331\) | 10.5075i | 0.577544i | 0.957398 | + | 0.288772i | \(0.0932470\pi\) | ||||
−0.957398 | + | 0.288772i | \(0.906753\pi\) | |||||||
\(332\) | 9.50276 | − | 9.50276i | 0.521532 | − | 0.521532i | ||||
\(333\) | −1.33551 | + | 1.33551i | −0.0731853 | + | 0.0731853i | ||||
\(334\) | 15.7437i | 0.861457i | ||||||||
\(335\) | −1.40639 | − | 6.14824i | −0.0768395 | − | 0.335914i | ||||
\(336\) | 0.997232i | 0.0544035i | ||||||||
\(337\) | −18.8126 | − | 18.8126i | −1.02479 | − | 1.02479i | −0.999685 | − | 0.0251053i | \(-0.992008\pi\) |
−0.0251053 | − | 0.999685i | \(-0.507992\pi\) | |||||||
\(338\) | −8.41507 | + | 8.41507i | −0.457719 | + | 0.457719i | ||||
\(339\) | 0.655286i | 0.0355903i | ||||||||
\(340\) | 1.53281 | + | 6.70087i | 0.0831281 | + | 0.363406i | ||||
\(341\) | − | 7.90892i | − | 0.428292i | ||||||
\(342\) | 3.67424 | + | 2.34520i | 0.198680 | + | 0.126814i | ||||
\(343\) | 9.17084 | + | 9.17084i | 0.495179 | + | 0.495179i | ||||
\(344\) | −2.16575 | −0.116769 | ||||||||
\(345\) | −2.89977 | − | 1.82011i | −0.156118 | − | 0.0979913i | ||||
\(346\) | 7.67256 | 0.412479 | ||||||||
\(347\) | 16.9775 | − | 16.9775i | 0.911399 | − | 0.911399i | −0.0849832 | − | 0.996382i | \(-0.527084\pi\) |
0.996382 | + | 0.0849832i | \(0.0270836\pi\) | |||||||
\(348\) | −4.20791 | − | 4.20791i | −0.225568 | − | 0.225568i | ||||
\(349\) | 16.3106i | 0.873086i | 0.899683 | + | 0.436543i | \(0.143797\pi\) | ||||
−0.899683 | + | 0.436543i | \(0.856203\pi\) | |||||||
\(350\) | 2.16771 | + | 4.49030i | 0.115869 | + | 0.240017i | ||||
\(351\) | 1.04847 | 0.0559634 | ||||||||
\(352\) | −0.939768 | − | 0.939768i | −0.0500898 | − | 0.0500898i | ||||
\(353\) | 7.93890 | + | 7.93890i | 0.422545 | + | 0.422545i | 0.886079 | − | 0.463534i | \(-0.153419\pi\) |
−0.463534 | + | 0.886079i | \(0.653419\pi\) | |||||||
\(354\) | −3.53944 | −0.188119 | ||||||||
\(355\) | 10.3648 | − | 16.5131i | 0.550107 | − | 0.876422i | ||||
\(356\) | − | 16.7874i | − | 0.889729i | ||||||
\(357\) | −2.16771 | − | 2.16771i | −0.114728 | − | 0.114728i | ||||
\(358\) | −0.680979 | − | 0.680979i | −0.0359909 | − | 0.0359909i | ||||
\(359\) | 26.2304i | 1.38439i | 0.721712 | + | 0.692193i | \(0.243355\pi\) | ||||
−0.721712 | + | 0.692193i | \(0.756645\pi\) | |||||||
\(360\) | 0.498616 | + | 2.17977i | 0.0262794 | + | 0.114884i | ||||
\(361\) | −17.2337 | + | 8.00003i | −0.907035 | + | 0.421054i | ||||
\(362\) | −14.4401 | + | 14.4401i | −0.758956 | + | 0.758956i | ||||
\(363\) | −6.52919 | + | 6.52919i | −0.342694 | + | 0.342694i | ||||
\(364\) | −1.04557 | −0.0548028 | ||||||||
\(365\) | −4.11545 | − | 17.9912i | −0.215412 | − | 0.941704i | ||||
\(366\) | 3.41030 | 0.178259 | ||||||||
\(367\) | −1.62269 | + | 1.62269i | −0.0847040 | + | 0.0847040i | −0.748189 | − | 0.663485i | \(-0.769077\pi\) |
0.663485 | + | 0.748189i | \(0.269077\pi\) | |||||||
\(368\) | 1.08266 | + | 1.08266i | 0.0564373 | + | 0.0564373i | ||||
\(369\) | 0.531910 | 0.0276901 | ||||||||
\(370\) | 2.24519 | − | 3.57700i | 0.116722 | − | 0.185959i | ||||
\(371\) | 7.73629i | 0.401648i | ||||||||
\(372\) | 4.20791 | − | 4.20791i | 0.218170 | − | 0.218170i | ||||
\(373\) | 9.00900 | − | 9.00900i | 0.466468 | − | 0.466468i | −0.434300 | − | 0.900768i | \(-0.643004\pi\) |
0.900768 | + | 0.434300i | \(0.143004\pi\) | |||||||
\(374\) | 4.08561 | 0.211262 | ||||||||
\(375\) | 6.98338 | + | 8.73112i | 0.360620 | + | 0.450873i | ||||
\(376\) | 5.84230i | 0.301294i | ||||||||
\(377\) | 4.41189 | − | 4.41189i | 0.227224 | − | 0.227224i | ||||
\(378\) | −0.705149 | − | 0.705149i | −0.0362690 | − | 0.0362690i | ||||
\(379\) | 4.49635 | 0.230962 | 0.115481 | − | 0.993310i | \(-0.463159\pi\) | ||||
0.115481 | + | 0.993310i | \(0.463159\pi\) | |||||||
\(380\) | −9.17833 | − | 3.27997i | −0.470839 | − | 0.168259i | ||||
\(381\) | 10.9672 | 0.561867 | ||||||||
\(382\) | −5.19563 | − | 5.19563i | −0.265832 | − | 0.265832i | ||||
\(383\) | 22.5064 | − | 22.5064i | 1.15003 | − | 1.15003i | 0.163478 | − | 0.986547i | \(-0.447729\pi\) |
0.986547 | − | 0.163478i | \(-0.0522713\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 2.88896 | − | 0.660842i | 0.147235 | − | 0.0336796i | ||||
\(386\) | 13.1865 | 0.671176 | ||||||||
\(387\) | 1.53142 | − | 1.53142i | 0.0778463 | − | 0.0778463i | ||||
\(388\) | −1.11691 | + | 1.11691i | −0.0567025 | + | 0.0567025i | ||||
\(389\) | − | 26.1672i | − | 1.32673i | −0.748297 | − | 0.663364i | \(-0.769128\pi\) | ||
0.748297 | − | 0.663364i | \(-0.230872\pi\) | |||||||
\(390\) | −2.28543 | + | 0.522786i | −0.115727 | + | 0.0264723i | ||||
\(391\) | −4.70681 | −0.238033 | ||||||||
\(392\) | −4.24655 | − | 4.24655i | −0.214483 | − | 0.214483i | ||||
\(393\) | −9.37065 | + | 9.37065i | −0.472687 | + | 0.472687i | ||||
\(394\) | 7.67935 | 0.386880 | ||||||||
\(395\) | 17.6383 | + | 11.0711i | 0.887478 | + | 0.557047i | ||||
\(396\) | 1.32903 | 0.0667864 | ||||||||
\(397\) | −15.5911 | + | 15.5911i | −0.782497 | + | 0.782497i | −0.980252 | − | 0.197754i | \(-0.936635\pi\) |
0.197754 | + | 0.980252i | \(0.436635\pi\) | |||||||
\(398\) | 16.6161 | − | 16.6161i | 0.832889 | − | 0.832889i | ||||
\(399\) | 4.24460 | − | 0.937166i | 0.212496 | − | 0.0469170i | ||||
\(400\) | −2.17373 | − | 4.50276i | −0.108687 | − | 0.225138i | ||||
\(401\) | − | 13.8440i | − | 0.691337i | −0.938357 | − | 0.345668i | \(-0.887652\pi\) | ||
0.938357 | − | 0.345668i | \(-0.112348\pi\) | |||||||
\(402\) | −1.99446 | − | 1.99446i | −0.0994748 | − | 0.0994748i | ||||
\(403\) | 4.41189 | + | 4.41189i | 0.219772 | + | 0.219772i | ||||
\(404\) | − | 15.7109i | − | 0.781645i | ||||||
\(405\) | −1.89390 | − | 1.18875i | −0.0941088 | − | 0.0590696i | ||||
\(406\) | −5.93441 | −0.294520 | ||||||||
\(407\) | −1.77493 | − | 1.77493i | −0.0879801 | − | 0.0879801i | ||||
\(408\) | 2.17373 | + | 2.17373i | 0.107616 | + | 0.107616i | ||||
\(409\) | −9.17657 | −0.453752 | −0.226876 | − | 0.973924i | \(-0.572851\pi\) | ||||
−0.226876 | + | 0.973924i | \(0.572851\pi\) | |||||||
\(410\) | −1.15944 | + | 0.265219i | −0.0572606 | + | 0.0130982i | ||||
\(411\) | − | 6.25126i | − | 0.308352i | ||||||
\(412\) | 10.7950 | + | 10.7950i | 0.531833 | + | 0.531833i | ||||
\(413\) | −2.49584 | + | 2.49584i | −0.122812 | + | 0.122812i | ||||
\(414\) | −1.53111 | −0.0752498 | ||||||||
\(415\) | −6.70087 | − | 29.2937i | −0.328933 | − | 1.43797i | ||||
\(416\) | 1.04847 | 0.0514057 | ||||||||
\(417\) | 1.89975 | + | 1.89975i | 0.0930311 | + | 0.0930311i | ||||
\(418\) | −3.11685 | + | 4.88318i | −0.152450 | + | 0.238844i | ||||
\(419\) | 21.8535i | 1.06762i | 0.845606 | + | 0.533808i | \(0.179239\pi\) | ||||
−0.845606 | + | 0.533808i | \(0.820761\pi\) | |||||||
\(420\) | 1.88866 | + | 1.18546i | 0.0921571 | + | 0.0578446i | ||||
\(421\) | 29.4223i | 1.43396i | 0.697095 | + | 0.716978i | \(0.254475\pi\) | ||||
−0.697095 | + | 0.716978i | \(0.745525\pi\) | |||||||
\(422\) | −5.77344 | + | 5.77344i | −0.281047 | + | 0.281047i | ||||
\(423\) | −4.13113 | − | 4.13113i | −0.200862 | − | 0.200862i | ||||
\(424\) | − | 7.75776i | − | 0.376750i | ||||||
\(425\) | 14.5129 | + | 5.06269i | 0.703980 | + | 0.245577i | ||||
\(426\) | − | 8.71907i | − | 0.422440i | ||||||
\(427\) | 2.40477 | − | 2.40477i | 0.116375 | − | 0.116375i | ||||
\(428\) | 2.65129 | − | 2.65129i | 0.128155 | − | 0.128155i | ||||
\(429\) | 1.39346i | 0.0672767i | ||||||||
\(430\) | −2.57454 | + | 4.10172i | −0.124155 | + | 0.197803i | ||||
\(431\) | − | 36.4149i | − | 1.75404i | −0.480452 | − | 0.877021i | \(-0.659527\pi\) | ||
0.480452 | − | 0.877021i | \(-0.340473\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 16.4903 | − | 16.4903i | 0.792475 | − | 0.792475i | −0.189421 | − | 0.981896i | \(-0.560661\pi\) |
0.981896 | + | 0.189421i | \(0.0606610\pi\) | |||||||
\(434\) | − | 5.93441i | − | 0.284861i | ||||||
\(435\) | −12.9715 | + | 2.96721i | −0.621938 | + | 0.142267i | ||||
\(436\) | − | 5.83596i | − | 0.279492i | ||||||
\(437\) | 3.59076 | − | 5.62565i | 0.171769 | − | 0.269111i | ||||
\(438\) | −5.83628 | − | 5.83628i | −0.278868 | − | 0.278868i | ||||
\(439\) | 13.3446 | 0.636903 | 0.318452 | − | 0.947939i | \(-0.396837\pi\) | ||||
0.318452 | + | 0.947939i | \(0.396837\pi\) | |||||||
\(440\) | −2.89698 | + | 0.662676i | −0.138108 | + | 0.0315919i | ||||
\(441\) | 6.00553 | 0.285978 | ||||||||
\(442\) | −2.27910 | + | 2.27910i | −0.108406 | + | 0.108406i | ||||
\(443\) | −17.4215 | − | 17.4215i | −0.827720 | − | 0.827720i | 0.159481 | − | 0.987201i | \(-0.449018\pi\) |
−0.987201 | + | 0.159481i | \(0.949018\pi\) | |||||||
\(444\) | − | 1.88869i | − | 0.0896334i | ||||||
\(445\) | −31.7936 | − | 19.9560i | −1.50716 | − | 0.946007i | ||||
\(446\) | 0.300580 | 0.0142329 | ||||||||
\(447\) | −9.99711 | − | 9.99711i | −0.472847 | − | 0.472847i | ||||
\(448\) | −0.705149 | − | 0.705149i | −0.0333152 | − | 0.0333152i | ||||
\(449\) | 39.0761 | 1.84412 | 0.922058 | − | 0.387051i | \(-0.126506\pi\) | ||||
0.922058 | + | 0.387051i | \(0.126506\pi\) | |||||||
\(450\) | 4.72100 | + | 1.64687i | 0.222550 | + | 0.0776344i | ||||
\(451\) | 0.706926i | 0.0332878i | ||||||||
\(452\) | −0.463357 | − | 0.463357i | −0.0217945 | − | 0.0217945i | ||||
\(453\) | 6.68237 | + | 6.68237i | 0.313965 | + | 0.313965i | ||||
\(454\) | 23.9341i | 1.12328i | ||||||||
\(455\) | −1.24293 | + | 1.98021i | −0.0582693 | + | 0.0928337i | ||||
\(456\) | −4.25639 | + | 0.939768i | −0.199324 | + | 0.0440087i | ||||
\(457\) | −25.9258 | + | 25.9258i | −1.21276 | + | 1.21276i | −0.242643 | + | 0.970116i | \(0.578014\pi\) |
−0.970116 | + | 0.242643i | \(0.921986\pi\) | |||||||
\(458\) | −5.37064 | + | 5.37064i | −0.250953 | + | 0.250953i | ||||
\(459\) | −3.07412 | −0.143488 | ||||||||
\(460\) | 3.33745 | − | 0.763434i | 0.155610 | − | 0.0355953i | ||||
\(461\) | −16.3202 | −0.760108 | −0.380054 | − | 0.924964i | \(-0.624095\pi\) | ||||
−0.380054 | + | 0.924964i | \(0.624095\pi\) | |||||||
\(462\) | 0.937166 | − | 0.937166i | 0.0436009 | − | 0.0436009i | ||||
\(463\) | −4.26074 | − | 4.26074i | −0.198013 | − | 0.198013i | 0.601135 | − | 0.799148i | \(-0.294716\pi\) |
−0.799148 | + | 0.601135i | \(0.794716\pi\) | |||||||
\(464\) | 5.95089 | 0.276263 | ||||||||
\(465\) | −2.96721 | − | 12.9715i | −0.137601 | − | 0.601541i | ||||
\(466\) | 1.15416i | 0.0534655i | ||||||||
\(467\) | −24.0643 | + | 24.0643i | −1.11356 | + | 1.11356i | −0.120897 | + | 0.992665i | \(0.538577\pi\) |
−0.992665 | + | 0.120897i | \(0.961423\pi\) | |||||||
\(468\) | −0.741383 | + | 0.741383i | −0.0342704 | + | 0.0342704i | ||||
\(469\) | −2.81279 | −0.129883 | ||||||||
\(470\) | 11.0647 | + | 6.94505i | 0.510379 | + | 0.320351i | ||||
\(471\) | − | 19.4667i | − | 0.896977i | ||||||
\(472\) | 2.50276 | − | 2.50276i | 0.115199 | − | 0.115199i | ||||
\(473\) | 2.03530 | + | 2.03530i | 0.0935833 | + | 0.0935833i | ||||
\(474\) | 9.31319 | 0.427769 | ||||||||
\(475\) | −17.1227 | + | 13.4838i | −0.785644 | + | 0.618679i | ||||
\(476\) | 3.06561 | 0.140512 | ||||||||
\(477\) | 5.48557 | + | 5.48557i | 0.251167 | + | 0.251167i | ||||
\(478\) | −2.97765 | + | 2.97765i | −0.136195 | + | 0.136195i | ||||
\(479\) | − | 19.7176i | − | 0.900920i | −0.892797 | − | 0.450460i | \(-0.851260\pi\) | ||
0.892797 | − | 0.450460i | \(-0.148740\pi\) | |||||||
\(480\) | −1.89390 | − | 1.18875i | −0.0864444 | − | 0.0542589i | ||||
\(481\) | 1.98024 | 0.0902914 | ||||||||
\(482\) | −17.5996 | + | 17.5996i | −0.801638 | + | 0.801638i | ||||
\(483\) | −1.07966 | + | 1.07966i | −0.0491262 | + | 0.0491262i | ||||
\(484\) | − | 9.23367i | − | 0.419712i | ||||||
\(485\) | 0.787588 | + | 3.44305i | 0.0357625 | + | 0.156341i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −23.8855 | − | 23.8855i | −1.08236 | − | 1.08236i | −0.996289 | − | 0.0860674i | \(-0.972570\pi\) |
−0.0860674 | − | 0.996289i | \(-0.527430\pi\) | |||||||
\(488\) | −2.41145 | + | 2.41145i | −0.109161 | + | 0.109161i | ||||
\(489\) | 1.12018 | 0.0506563 | ||||||||
\(490\) | −13.0907 | + | 2.99445i | −0.591375 | + | 0.135276i | ||||
\(491\) | 21.2521 | 0.959094 | 0.479547 | − | 0.877516i | \(-0.340801\pi\) | ||||
0.479547 | + | 0.877516i | \(0.340801\pi\) | |||||||
\(492\) | −0.376117 | + | 0.376117i | −0.0169567 | + | 0.0169567i | ||||
\(493\) | −12.9356 | + | 12.9356i | −0.582592 | + | 0.582592i | ||||
\(494\) | −0.985322 | − | 4.46271i | −0.0443317 | − | 0.200787i | ||||
\(495\) | 1.57989 | − | 2.51706i | 0.0710108 | − | 0.113133i | ||||
\(496\) | 5.95089i | 0.267203i | ||||||||
\(497\) | −6.14824 | − | 6.14824i | −0.275786 | − | 0.275786i | ||||
\(498\) | −9.50276 | − | 9.50276i | −0.425829 | − | 0.425829i | ||||
\(499\) | − | 39.2906i | − | 1.75889i | −0.476002 | − | 0.879444i | \(-0.657915\pi\) | ||
0.476002 | − | 0.879444i | \(-0.342085\pi\) | |||||||
\(500\) | −11.1118 | − | 1.23584i | −0.496936 | − | 0.0552684i | ||||
\(501\) | 15.7437 | 0.703377 | ||||||||
\(502\) | −0.673765 | − | 0.673765i | −0.0300716 | − | 0.0300716i | ||||
\(503\) | 7.92010 | + | 7.92010i | 0.353140 | + | 0.353140i | 0.861276 | − | 0.508137i | \(-0.169666\pi\) |
−0.508137 | + | 0.861276i | \(0.669666\pi\) | |||||||
\(504\) | 0.997232 | 0.0444202 | ||||||||
\(505\) | −29.7549 | − | 18.6764i | −1.32407 | − | 0.831087i | ||||
\(506\) | − | 2.03489i | − | 0.0904619i | ||||||
\(507\) | 8.41507 | + | 8.41507i | 0.373726 | + | 0.373726i | ||||
\(508\) | −7.75499 | + | 7.75499i | −0.344072 | + | 0.344072i | ||||
\(509\) | 19.7948 | 0.877389 | 0.438695 | − | 0.898636i | \(-0.355441\pi\) | ||||
0.438695 | + | 0.898636i | \(0.355441\pi\) | |||||||
\(510\) | 6.70087 | − | 1.53281i | 0.296719 | − | 0.0678738i | ||||
\(511\) | −8.23090 | −0.364113 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 2.34520 | − | 3.67424i | 0.103543 | − | 0.162222i | ||||
\(514\) | 17.5784i | 0.775349i | ||||||||
\(515\) | 33.2773 | − | 7.61210i | 1.46637 | − | 0.335429i | ||||
\(516\) | 2.16575i | 0.0953419i | ||||||||
\(517\) | 5.49040 | − | 5.49040i | 0.241468 | − | 0.241468i | ||||
\(518\) | −1.33181 | − | 1.33181i | −0.0585164 | − | 0.0585164i | ||||
\(519\) | − | 7.67256i | − | 0.336788i | ||||||
\(520\) | 1.24638 | − | 1.98571i | 0.0546572 | − | 0.0870790i | ||||
\(521\) | 32.9001i | 1.44138i | 0.693257 | + | 0.720691i | \(0.256175\pi\) | ||||
−0.693257 | + | 0.720691i | \(0.743825\pi\) | |||||||
\(522\) | −4.20791 | + | 4.20791i | −0.184175 | + | 0.184175i | ||||
\(523\) | −5.26214 | + | 5.26214i | −0.230098 | + | 0.230098i | −0.812733 | − | 0.582636i | \(-0.802021\pi\) |
0.582636 | + | 0.812733i | \(0.302021\pi\) | |||||||
\(524\) | − | 13.2521i | − | 0.578921i | ||||||
\(525\) | 4.49030 | − | 2.16771i | 0.195973 | − | 0.0946068i | ||||
\(526\) | 4.77455i | 0.208180i | ||||||||
\(527\) | −12.9356 | − | 12.9356i | −0.563485 | − | 0.563485i | ||||
\(528\) | −0.939768 | + | 0.939768i | −0.0408981 | + | 0.0408981i | ||||
\(529\) | − | 20.6557i | − | 0.898075i | ||||||
\(530\) | −14.6924 | − | 9.22206i | −0.638199 | − | 0.400581i | ||||
\(531\) | 3.53944i | 0.153599i | ||||||||
\(532\) | −2.33871 | + | 3.66407i | −0.101396 | + | 0.158857i | ||||
\(533\) | −0.394349 | − | 0.394349i | −0.0170812 | − | 0.0170812i | ||||
\(534\) | −16.7874 | −0.726460 | ||||||||
\(535\) | −1.86955 | − | 8.17300i | −0.0808278 | − | 0.353350i | ||||
\(536\) | 2.82060 | 0.121831 | ||||||||
\(537\) | −0.680979 | + | 0.680979i | −0.0293864 | + | 0.0293864i | ||||
\(538\) | 0.777994 | + | 0.777994i | 0.0335417 | + | 0.0335417i | ||||
\(539\) | 7.98154i | 0.343789i | ||||||||
\(540\) | 2.17977 | − | 0.498616i | 0.0938022 | − | 0.0214570i | ||||
\(541\) | −3.97998 | −0.171113 | −0.0855563 | − | 0.996333i | \(-0.527267\pi\) | ||||
−0.0855563 | + | 0.996333i | \(0.527267\pi\) | |||||||
\(542\) | 12.9537 | + | 12.9537i | 0.556409 | + | 0.556409i | ||||
\(543\) | 14.4401 | + | 14.4401i | 0.619685 | + | 0.619685i | ||||
\(544\) | −3.07412 | −0.131802 | ||||||||
\(545\) | −11.0527 | − | 6.93752i | −0.473447 | − | 0.297171i | ||||
\(546\) | 1.04557i | 0.0447463i | ||||||||
\(547\) | 17.5769 | + | 17.5769i | 0.751533 | + | 0.751533i | 0.974765 | − | 0.223232i | \(-0.0716608\pi\) |
−0.223232 | + | 0.974765i | \(0.571661\pi\) | |||||||
\(548\) | 4.42031 | + | 4.42031i | 0.188826 | + | 0.188826i | ||||
\(549\) | − | 3.41030i | − | 0.145548i | ||||||
\(550\) | −2.18875 | + | 6.27436i | −0.0933286 | + | 0.267539i | ||||
\(551\) | −5.59245 | − | 25.3293i | −0.238246 | − | 1.07906i | ||||
\(552\) | 1.08266 | − | 1.08266i | 0.0460809 | − | 0.0460809i | ||||
\(553\) | 6.56719 | − | 6.56719i | 0.279265 | − | 0.279265i | ||||
\(554\) | −9.16466 | −0.389369 | ||||||||
\(555\) | −3.57700 | − | 2.24519i | −0.151835 | − | 0.0953029i | ||||
\(556\) | −2.68665 | −0.113939 | ||||||||
\(557\) | 10.5795 | − | 10.5795i | 0.448267 | − | 0.448267i | −0.446511 | − | 0.894778i | \(-0.647334\pi\) |
0.894778 | + | 0.446511i | \(0.147334\pi\) | |||||||
\(558\) | −4.20791 | − | 4.20791i | −0.178135 | − | 0.178135i | ||||
\(559\) | −2.27073 | −0.0960418 | ||||||||
\(560\) | −2.17373 | + | 0.497236i | −0.0918570 | + | 0.0210120i | ||||
\(561\) | − | 4.08561i | − | 0.172494i | ||||||
\(562\) | −8.95726 | + | 8.95726i | −0.377839 | + | 0.377839i | ||||
\(563\) | −1.06530 | + | 1.06530i | −0.0448971 | + | 0.0448971i | −0.729199 | − | 0.684302i | \(-0.760107\pi\) |
0.684302 | + | 0.729199i | \(0.260107\pi\) | |||||||
\(564\) | 5.84230 | 0.246005 | ||||||||
\(565\) | −1.42837 | + | 0.326736i | −0.0600920 | + | 0.0137459i | ||||
\(566\) | 15.8543i | 0.666406i | ||||||||
\(567\) | −0.705149 | + | 0.705149i | −0.0296135 | + | 0.0296135i | ||||
\(568\) | 6.16531 | + | 6.16531i | 0.258691 | + | 0.258691i | ||||
\(569\) | −17.2827 | −0.724528 | −0.362264 | − | 0.932076i | \(-0.617996\pi\) | ||||
−0.362264 | + | 0.932076i | \(0.617996\pi\) | |||||||
\(570\) | −3.27997 | + | 9.17833i | −0.137383 | + | 0.384438i | ||||
\(571\) | 10.3420 | 0.432798 | 0.216399 | − | 0.976305i | \(-0.430569\pi\) | ||||
0.216399 | + | 0.976305i | \(0.430569\pi\) | |||||||
\(572\) | −0.985322 | − | 0.985322i | −0.0411984 | − | 0.0411984i | ||||
\(573\) | −5.19563 | + | 5.19563i | −0.217051 | + | 0.217051i | ||||
\(574\) | 0.530438i | 0.0221400i | ||||||||
\(575\) | 2.52154 | − | 7.22835i | 0.105155 | − | 0.301443i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −25.5328 | + | 25.5328i | −1.06294 | + | 1.06294i | −0.0650631 | + | 0.997881i | \(0.520725\pi\) |
−0.997881 | + | 0.0650631i | \(0.979275\pi\) | |||||||
\(578\) | −5.33850 | + | 5.33850i | −0.222052 | + | 0.222052i | ||||
\(579\) | − | 13.1865i | − | 0.548013i | ||||||
\(580\) | 7.07414 | − | 11.2704i | 0.293738 | − | 0.467978i | ||||
\(581\) | −13.4017 | −0.555998 | ||||||||
\(582\) | 1.11691 | + | 1.11691i | 0.0462974 | + | 0.0462974i | ||||
\(583\) | −7.29049 | + | 7.29049i | −0.301941 | + | 0.301941i | ||||
\(584\) | 8.25374 | 0.341542 | ||||||||
\(585\) | 0.522786 | + | 2.28543i | 0.0216145 | + | 0.0944908i | ||||
\(586\) | 0.182154 | 0.00752471 | ||||||||
\(587\) | −25.3120 | + | 25.3120i | −1.04474 | + | 1.04474i | −0.0457889 | + | 0.998951i | \(0.514580\pi\) |
−0.998951 | + | 0.0457889i | \(0.985420\pi\) | |||||||
\(588\) | −4.24655 | + | 4.24655i | −0.175125 | + | 0.175125i | ||||
\(589\) | 25.3293 | − | 5.59245i | 1.04368 | − | 0.230433i | ||||
\(590\) | −1.76482 | − | 7.71516i | −0.0726566 | − | 0.317628i | ||||
\(591\) | − | 7.67935i | − | 0.315886i | ||||||
\(592\) | 1.33551 | + | 1.33551i | 0.0548890 | + | 0.0548890i | ||||
\(593\) | −9.66808 | − | 9.66808i | −0.397020 | − | 0.397020i | 0.480160 | − | 0.877181i | \(-0.340578\pi\) |
−0.877181 | + | 0.480160i | \(0.840578\pi\) | |||||||
\(594\) | − | 1.32903i | − | 0.0545308i | ||||||
\(595\) | 3.64426 | − | 5.80597i | 0.149400 | − | 0.238022i | ||||
\(596\) | 14.1380 | 0.579117 | ||||||||
\(597\) | −16.6161 | − | 16.6161i | −0.680051 | − | 0.680051i | ||||
\(598\) | 1.13514 | + | 1.13514i | 0.0464192 | + | 0.0464192i | ||||
\(599\) | −28.5298 | −1.16569 | −0.582847 | − | 0.812582i | \(-0.698061\pi\) | ||||
−0.582847 | + | 0.812582i | \(0.698061\pi\) | |||||||
\(600\) | −4.50276 | + | 2.17373i | −0.183825 | + | 0.0887423i | ||||
\(601\) | 24.3760i | 0.994317i | 0.867660 | + | 0.497159i | \(0.165623\pi\) | ||||
−0.867660 | + | 0.497159i | \(0.834377\pi\) | |||||||
\(602\) | 1.52718 | + | 1.52718i | 0.0622431 | + | 0.0622431i | ||||
\(603\) | −1.99446 | + | 1.99446i | −0.0812208 | + | 0.0812208i | ||||
\(604\) | −9.45030 | −0.384527 | ||||||||
\(605\) | −17.4877 | − | 10.9766i | −0.710975 | − | 0.446261i | ||||
\(606\) | −15.7109 | −0.638211 | ||||||||
\(607\) | −27.0140 | − | 27.0140i | −1.09647 | − | 1.09647i | −0.994821 | − | 0.101646i | \(-0.967589\pi\) |
−0.101646 | − | 0.994821i | \(-0.532411\pi\) | |||||||
\(608\) | 2.34520 | − | 3.67424i | 0.0951106 | − | 0.149010i | ||||
\(609\) | 5.93441i | 0.240475i | ||||||||
\(610\) | 1.70043 | + | 7.43365i | 0.0688484 | + | 0.300980i | ||||
\(611\) | 6.12550i | 0.247811i | ||||||||
\(612\) | 2.17373 | − | 2.17373i | 0.0878679 | − | 0.0878679i | ||||
\(613\) | 17.2695 | + | 17.2695i | 0.697508 | + | 0.697508i | 0.963872 | − | 0.266364i | \(-0.0858224\pi\) |
−0.266364 | + | 0.963872i | \(0.585822\pi\) | |||||||
\(614\) | 22.3361i | 0.901413i | ||||||||
\(615\) | 0.265219 | + | 1.15944i | 0.0106947 | + | 0.0467531i | ||||
\(616\) | 1.32535i | 0.0534000i | ||||||||
\(617\) | 34.2253 | − | 34.2253i | 1.37786 | − | 1.37786i | 0.529625 | − | 0.848232i | \(-0.322333\pi\) |
0.848232 | − | 0.529625i | \(-0.177667\pi\) | |||||||
\(618\) | 10.7950 | − | 10.7950i | 0.434239 | − | 0.434239i | ||||
\(619\) | − | 34.9000i | − | 1.40275i | −0.712792 | − | 0.701375i | \(-0.752570\pi\) | ||
0.712792 | − | 0.701375i | \(-0.247430\pi\) | |||||||
\(620\) | 11.2704 | + | 7.07414i | 0.452630 | + | 0.284104i | ||||
\(621\) | 1.53111i | 0.0614412i | ||||||||
\(622\) | 10.3891 | + | 10.3891i | 0.416566 | + | 0.416566i | ||||
\(623\) | −11.8376 | + | 11.8376i | −0.474263 | + | 0.474263i | ||||
\(624\) | − | 1.04847i | − | 0.0419726i | ||||||
\(625\) | −15.5498 | + | 19.5756i | −0.621991 | + | 0.783024i | ||||
\(626\) | − | 2.50414i | − | 0.100086i | ||||||
\(627\) | 4.88318 | + | 3.11685i | 0.195015 | + | 0.124475i | ||||
\(628\) | 13.7650 | + | 13.7650i | 0.549284 | + | 0.549284i | ||||
\(629\) | −5.80607 | −0.231503 | ||||||||
\(630\) | 1.18546 | − | 1.88866i | 0.0472299 | − | 0.0752460i | ||||
\(631\) | 33.8489 | 1.34750 | 0.673752 | − | 0.738957i | \(-0.264682\pi\) | ||||
0.673752 | + | 0.738957i | \(0.264682\pi\) | |||||||
\(632\) | −6.58542 | + | 6.58542i | −0.261954 | + | 0.261954i | ||||
\(633\) | 5.77344 | + | 5.77344i | 0.229474 | + | 0.229474i | ||||
\(634\) | − | 6.55324i | − | 0.260262i | ||||||
\(635\) | 5.46842 | + | 23.9060i | 0.217008 | + | 0.948679i | ||||
\(636\) | −7.75776 | −0.307615 | ||||||||
\(637\) | −4.45240 | − | 4.45240i | −0.176410 | − | 0.176410i | ||||
\(638\) | −5.59245 | − | 5.59245i | −0.221407 | − | 0.221407i | ||||
\(639\) | −8.71907 | −0.344921 | ||||||||
\(640\) | 2.17977 | − | 0.498616i | 0.0861628 | − | 0.0197095i | ||||
\(641\) | − | 38.3389i | − | 1.51429i | −0.653245 | − | 0.757147i | \(-0.726593\pi\) | ||
0.653245 | − | 0.757147i | \(-0.273407\pi\) | |||||||
\(642\) | −2.65129 | − | 2.65129i | −0.104638 | − | 0.104638i | ||||
\(643\) | −21.8777 | − | 21.8777i | −0.862773 | − | 0.862773i | 0.128886 | − | 0.991659i | \(-0.458860\pi\) |
−0.991659 | + | 0.128886i | \(0.958860\pi\) | |||||||
\(644\) | − | 1.52687i | − | 0.0601670i | ||||||
\(645\) | 4.10172 | + | 2.57454i | 0.161505 | + | 0.101373i | ||||
\(646\) | 2.88896 | + | 13.0847i | 0.113665 | + | 0.514809i | ||||
\(647\) | −11.5954 | + | 11.5954i | −0.455863 | + | 0.455863i | −0.897295 | − | 0.441432i | \(-0.854471\pi\) |
0.441432 | + | 0.897295i | \(0.354471\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | −4.70403 | −0.184649 | ||||||||
\(650\) | −2.27910 | − | 4.72103i | −0.0893937 | − | 0.185174i | ||||
\(651\) | −5.93441 | −0.232588 | ||||||||
\(652\) | −0.792086 | + | 0.792086i | −0.0310205 | + | 0.0310205i | ||||
\(653\) | −11.6996 | − | 11.6996i | −0.457842 | − | 0.457842i | 0.440105 | − | 0.897946i | \(-0.354941\pi\) |
−0.897946 | + | 0.440105i | \(0.854941\pi\) | |||||||
\(654\) | −5.83596 | −0.228204 | ||||||||
\(655\) | −25.0982 | − | 15.7535i | −0.980668 | − | 0.615539i | ||||
\(656\) | − | 0.531910i | − | 0.0207676i | ||||||
\(657\) | −5.83628 | + | 5.83628i | −0.227695 | + | 0.227695i | ||||
\(658\) | 4.11969 | − | 4.11969i | 0.160602 | − | 0.160602i | ||||
\(659\) | −44.6662 | −1.73995 | −0.869974 | − | 0.493097i | \(-0.835865\pi\) | ||||
−0.869974 | + | 0.493097i | \(0.835865\pi\) | |||||||
\(660\) | 0.662676 | + | 2.89698i | 0.0257946 | + | 0.112765i | ||||
\(661\) | − | 46.5099i | − | 1.80902i | −0.426447 | − | 0.904512i | \(-0.640235\pi\) | ||
0.426447 | − | 0.904512i | \(-0.359765\pi\) | |||||||
\(662\) | −7.42992 | + | 7.42992i | −0.288772 | + | 0.288772i | ||||
\(663\) | 2.27910 | + | 2.27910i | 0.0885130 | + | 0.0885130i | ||||
\(664\) | 13.4389 | 0.521532 | ||||||||
\(665\) | 4.15923 | + | 8.78496i | 0.161288 | + | 0.340666i | ||||
\(666\) | −1.88869 | −0.0731853 | ||||||||
\(667\) | 6.44276 | + | 6.44276i | 0.249465 | + | 0.249465i | ||||
\(668\) | −11.1325 | + | 11.1325i | −0.430728 | + | 0.430728i | ||||
\(669\) | − | 0.300580i | − | 0.0116211i | ||||||
\(670\) | 3.35299 | − | 5.34194i | 0.129537 | − | 0.206377i | ||||
\(671\) | 4.53240 | 0.174971 | ||||||||
\(672\) | −0.705149 | + | 0.705149i | −0.0272017 | + | 0.0272017i | ||||
\(673\) | 17.8598 | − | 17.8598i | 0.688446 | − | 0.688446i | −0.273443 | − | 0.961888i | \(-0.588162\pi\) |
0.961888 | + | 0.273443i | \(0.0881624\pi\) | |||||||
\(674\) | − | 26.6051i | − | 1.02479i | ||||||
\(675\) | 1.64687 | − | 4.72100i | 0.0633882 | − | 0.181711i | ||||
\(676\) | −11.9007 | −0.457719 | ||||||||
\(677\) | 20.6616 | + | 20.6616i | 0.794092 | + | 0.794092i | 0.982157 | − | 0.188065i | \(-0.0602215\pi\) |
−0.188065 | + | 0.982157i | \(0.560222\pi\) | |||||||
\(678\) | −0.463357 | + | 0.463357i | −0.0177951 | + | 0.0177951i | ||||
\(679\) | 1.57518 | 0.0604497 | ||||||||
\(680\) | −3.65437 | + | 5.82209i | −0.140139 | + | 0.223267i | ||||
\(681\) | 23.9341 | 0.917158 | ||||||||
\(682\) | 5.59245 | − | 5.59245i | 0.214146 | − | 0.214146i | ||||
\(683\) | −23.8243 | + | 23.8243i | −0.911610 | + | 0.911610i | −0.996399 | − | 0.0847893i | \(-0.972978\pi\) |
0.0847893 | + | 0.996399i | \(0.472978\pi\) | |||||||
\(684\) | 0.939768 | + | 4.25639i | 0.0359329 | + | 0.162747i | ||||
\(685\) | 13.6263 | − | 3.11698i | 0.520634 | − | 0.119094i | ||||
\(686\) | 12.9695i | 0.495179i | ||||||||
\(687\) | 5.37064 | + | 5.37064i | 0.204903 | + | 0.204903i | ||||
\(688\) | −1.53142 | − | 1.53142i | −0.0583847 | − | 0.0583847i | ||||
\(689\) | − | 8.13381i | − | 0.309874i | ||||||
\(690\) | −0.763434 | − | 3.33745i | −0.0290634 | − | 0.127055i | ||||
\(691\) | −4.34746 | −0.165385 | −0.0826927 | − | 0.996575i | \(-0.526352\pi\) | ||||
−0.0826927 | + | 0.996575i | \(0.526352\pi\) | |||||||
\(692\) | 5.42532 | + | 5.42532i | 0.206240 | + | 0.206240i | ||||
\(693\) | −0.937166 | − | 0.937166i | −0.0356000 | − | 0.0356000i | ||||
\(694\) | 24.0098 | 0.911399 | ||||||||
\(695\) | −3.19376 | + | 5.08825i | −0.121146 | + | 0.193008i | ||||
\(696\) | − | 5.95089i | − | 0.225568i | ||||||
\(697\) | 1.15623 | + | 1.15623i | 0.0437953 | + | 0.0437953i | ||||
\(698\) | −11.5333 | + | 11.5333i | −0.436543 | + | 0.436543i | ||||
\(699\) | 1.15416 | 0.0436544 | ||||||||
\(700\) | −1.64232 | + | 4.70793i | −0.0620737 | + | 0.177943i | ||||
\(701\) | −1.61462 | −0.0609832 | −0.0304916 | − | 0.999535i | \(-0.509707\pi\) | ||||
−0.0304916 | + | 0.999535i | \(0.509707\pi\) | |||||||
\(702\) | 0.741383 | + | 0.741383i | 0.0279817 | + | 0.0279817i | ||||
\(703\) | 4.42937 | − | 6.93950i | 0.167057 | − | 0.261728i | ||||
\(704\) | − | 1.32903i | − | 0.0500898i | ||||||
\(705\) | 6.94505 | − | 11.0647i | 0.261566 | − | 0.416722i | ||||
\(706\) | 11.2273i | 0.422545i | ||||||||
\(707\) | −11.0785 | + | 11.0785i | −0.416650 | + | 0.416650i | ||||
\(708\) | −2.50276 | − | 2.50276i | −0.0940596 | − | 0.0940596i | ||||
\(709\) | 45.1909i | 1.69718i | 0.529052 | + | 0.848589i | \(0.322548\pi\) | ||||
−0.529052 | + | 0.848589i | \(0.677452\pi\) | |||||||
\(710\) | 19.0055 | − | 4.34746i | 0.713265 | − | 0.163157i | ||||
\(711\) | − | 9.31319i | − | 0.349272i | ||||||
\(712\) | 11.8705 | − | 11.8705i | 0.444864 | − | 0.444864i | ||||
\(713\) | −6.44276 | + | 6.44276i | −0.241283 | + | 0.241283i | ||||
\(714\) | − | 3.06561i | − | 0.114728i | ||||||
\(715\) | −3.03741 | + | 0.694799i | −0.113593 | + | 0.0259840i | ||||
\(716\) | − | 0.963050i | − | 0.0359909i | ||||||
\(717\) | 2.97765 | + | 2.97765i | 0.111202 | + | 0.111202i | ||||
\(718\) | −18.5477 | + | 18.5477i | −0.692193 | + | 0.692193i | ||||
\(719\) | 8.72035i | 0.325214i | 0.986691 | + | 0.162607i | \(0.0519903\pi\) | ||||
−0.986691 | + | 0.162607i | \(0.948010\pi\) | |||||||
\(720\) | −1.18875 | + | 1.89390i | −0.0443022 | + | 0.0705816i | ||||
\(721\) | − | 15.2242i | − | 0.566979i | ||||||
\(722\) | −17.8429 | − | 6.52917i | −0.664045 | − | 0.242991i | ||||
\(723\) | 17.5996 | + | 17.5996i | 0.654535 | + | 0.654535i | ||||
\(724\) | −20.4214 | −0.758956 | ||||||||
\(725\) | −12.9356 | − | 26.7955i | −0.480418 | − | 0.995158i | ||||
\(726\) | −9.23367 | −0.342694 | ||||||||
\(727\) | 16.9674 | − | 16.9674i | 0.629286 | − | 0.629286i | −0.318602 | − | 0.947889i | \(-0.603213\pi\) |
0.947889 | + | 0.318602i | \(0.103213\pi\) | |||||||
\(728\) | −0.739331 | − | 0.739331i | −0.0274014 | − | 0.0274014i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 9.81166 | − | 15.6318i | 0.363146 | − | 0.578558i | ||||
\(731\) | 6.65778 | 0.246247 | ||||||||
\(732\) | 2.41145 | + | 2.41145i | 0.0891296 | + | 0.0891296i | ||||
\(733\) | 25.1664 | + | 25.1664i | 0.929541 | + | 0.929541i | 0.997676 | − | 0.0681355i | \(-0.0217050\pi\) |
−0.0681355 | + | 0.997676i | \(0.521705\pi\) | |||||||
\(734\) | −2.29484 | −0.0847040 | ||||||||
\(735\) | 2.99445 | + | 13.0907i | 0.110452 | + | 0.482856i | ||||
\(736\) | 1.53111i | 0.0564373i | ||||||||
\(737\) | −2.65071 | − | 2.65071i | −0.0976400 | − | 0.0976400i | ||||
\(738\) | 0.376117 | + | 0.376117i | 0.0138451 | + | 0.0138451i | ||||
\(739\) | − | 14.7543i | − | 0.542747i | −0.962474 | − | 0.271373i | \(-0.912522\pi\) | ||
0.962474 | − | 0.271373i | \(-0.0874778\pi\) | |||||||
\(740\) | 4.11691 | − | 0.941732i | 0.151341 | − | 0.0346188i | ||||
\(741\) | −4.46271 | + | 0.985322i | −0.163942 | + | 0.0361967i | ||||
\(742\) | −5.47038 | + | 5.47038i | −0.200824 | + | 0.200824i | ||||
\(743\) | −8.61240 | + | 8.61240i | −0.315958 | + | 0.315958i | −0.847213 | − | 0.531254i | \(-0.821721\pi\) |
0.531254 | + | 0.847213i | \(0.321721\pi\) | |||||||
\(744\) | 5.95089 | 0.218170 | ||||||||
\(745\) | 16.8066 | − | 26.7761i | 0.615748 | − | 0.981000i | ||||
\(746\) | 12.7407 | 0.466468 | ||||||||
\(747\) | −9.50276 | + | 9.50276i | −0.347688 | + | 0.347688i | ||||
\(748\) | 2.88896 | + | 2.88896i | 0.105631 | + | 0.105631i | ||||
\(749\) | −3.73910 | −0.136624 | ||||||||
\(750\) | −1.23584 | + | 11.1118i | −0.0451264 | + | 0.405747i | ||||
\(751\) | − | 44.6100i | − | 1.62784i | −0.580974 | − | 0.813922i | \(-0.697328\pi\) | ||
0.580974 | − | 0.813922i | \(-0.302672\pi\) | |||||||
\(752\) | −4.13113 | + | 4.13113i | −0.150647 | + | 0.150647i | ||||
\(753\) | −0.673765 | + | 0.673765i | −0.0245534 | + | 0.0245534i | ||||
\(754\) | 6.23935 | 0.227224 | ||||||||
\(755\) | −11.2341 | + | 17.8979i | −0.408850 | + | 0.651373i | ||||
\(756\) | − | 0.997232i | − | 0.0362690i | ||||||
\(757\) | 2.38067 | − | 2.38067i | 0.0865268 | − | 0.0865268i | −0.662519 | − | 0.749045i | \(-0.730512\pi\) |
0.749045 | + | 0.662519i | \(0.230512\pi\) | |||||||
\(758\) | 3.17940 | + | 3.17940i | 0.115481 | + | 0.115481i | ||||
\(759\) | −2.03489 | −0.0738618 | ||||||||
\(760\) | −4.17078 | − | 8.80935i | −0.151290 | − | 0.319549i | ||||
\(761\) | 4.25052 | 0.154081 | 0.0770406 | − | 0.997028i | \(-0.475453\pi\) | ||||
0.0770406 | + | 0.997028i | \(0.475453\pi\) | |||||||
\(762\) | 7.75499 | + | 7.75499i | 0.280934 | + | 0.280934i | ||||
\(763\) | −4.11522 | + | 4.11522i | −0.148981 | + | 0.148981i | ||||
\(764\) | − | 7.34773i | − | 0.265832i | ||||||
\(765\) | −1.53281 | − | 6.70087i | −0.0554187 | − | 0.242270i | ||||
\(766\) | 31.8289 | 1.15003 | ||||||||
\(767\) | 2.62408 | − | 2.62408i | 0.0947502 | − | 0.0947502i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 3.40202i | − | 0.122680i | −0.998117 | − | 0.0613400i | \(-0.980463\pi\) | ||
0.998117 | − | 0.0613400i | \(-0.0195374\pi\) | |||||||
\(770\) | 2.51009 | + | 1.57552i | 0.0904573 | + | 0.0567777i | ||||
\(771\) | 17.5784 | 0.633070 | ||||||||
\(772\) | 9.32428 | + | 9.32428i | 0.335588 | + | 0.335588i | ||||
\(773\) | 21.7310 | − | 21.7310i | 0.781611 | − | 0.781611i | −0.198491 | − | 0.980103i | \(-0.563604\pi\) |
0.980103 | + | 0.198491i | \(0.0636042\pi\) | |||||||
\(774\) | 2.16575 | 0.0778463 | ||||||||
\(775\) | 26.7955 | − | 12.9356i | 0.962521 | − | 0.464662i | ||||
\(776\) | −1.57955 | −0.0567025 | ||||||||
\(777\) | −1.33181 | + | 1.33181i | −0.0477784 | + | 0.0477784i | ||||
\(778\) | 18.5030 | − | 18.5030i | 0.663364 | − | 0.663364i | ||||
\(779\) | −2.26402 | + | 0.499872i | −0.0811168 | + | 0.0179098i | ||||
\(780\) | −1.98571 | − | 1.24638i | −0.0710997 | − | 0.0446274i | ||||
\(781\) | − | 11.5879i | − | 0.414648i | ||||||
\(782\) | −3.32821 | − | 3.32821i | −0.119017 | − | 0.119017i | ||||
\(783\) | 4.20791 | + | 4.20791i | 0.150379 | + | 0.150379i | ||||
\(784\) | − | 6.00553i | − | 0.214483i | ||||||
\(785\) | 42.4328 | − | 9.70640i | 1.51449 | − | 0.346436i | ||||
\(786\) | −13.2521 | −0.472687 | ||||||||
\(787\) | −8.02221 | − | 8.02221i | −0.285961 | − | 0.285961i | 0.549520 | − | 0.835481i | \(-0.314811\pi\) |
−0.835481 | + | 0.549520i | \(0.814811\pi\) | |||||||
\(788\) | 5.43012 | + | 5.43012i | 0.193440 | + | 0.193440i | ||||
\(789\) | 4.77455 | 0.169979 | ||||||||
\(790\) | 4.64370 | + | 20.3006i | 0.165216 | + | 0.722262i | ||||
\(791\) | 0.653472i | 0.0232348i | ||||||||
\(792\) | 0.939768 | + | 0.939768i | 0.0333932 | + | 0.0333932i | ||||
\(793\) | −2.52834 | + | 2.52834i | −0.0897839 | + | 0.0897839i | ||||
\(794\) | −22.0492 | −0.782497 | ||||||||
\(795\) | −9.22206 | + | 14.6924i | −0.327073 | + | 0.521087i | ||||
\(796\) | 23.4987 | 0.832889 | ||||||||
\(797\) | −29.0862 | − | 29.0862i | −1.03029 | − | 1.03029i | −0.999527 | − | 0.0307591i | \(-0.990208\pi\) |
−0.0307591 | − | 0.999527i | \(-0.509792\pi\) | |||||||
\(798\) | 3.66407 | + | 2.33871i | 0.129707 | + | 0.0827895i | ||||
\(799\) | − | 17.9599i | − | 0.635377i | ||||||
\(800\) | 1.64687 | − | 4.72100i | 0.0582258 | − | 0.166912i | ||||
\(801\) | 16.7874i | 0.593152i | ||||||||
\(802\) | 9.78919 | − | 9.78919i | 0.345668 | − | 0.345668i | ||||
\(803\) | −7.75660 | − | 7.75660i | −0.273725 | − | 0.273725i | ||||
\(804\) | − | 2.82060i | − | 0.0994748i | ||||||
\(805\) | −2.89174 | − | 1.81507i | −0.101920 | − | 0.0639728i | ||||
\(806\) | 6.23935i | 0.219772i | ||||||||
\(807\) | 0.777994 | − | 0.777994i | 0.0273867 | − | 0.0273867i | ||||
\(808\) | 11.1093 | − | 11.1093i | 0.390823 | − | 0.390823i | ||||
\(809\) | 26.9228i | 0.946556i | 0.880913 | + | 0.473278i | \(0.156929\pi\) | ||||
−0.880913 | + | 0.473278i | \(0.843071\pi\) | |||||||
\(810\) | −0.498616 | − | 2.17977i | −0.0175196 | − | 0.0765892i | ||||
\(811\) | 38.9518i | 1.36778i | 0.729584 | + | 0.683891i | \(0.239714\pi\) | ||||
−0.729584 | + | 0.683891i | \(0.760286\pi\) | |||||||
\(812\) | −4.19627 | − | 4.19627i | −0.147260 | − | 0.147260i | ||||
\(813\) | 12.9537 | − | 12.9537i | 0.454306 | − | 0.454306i | ||||
\(814\) | − | 2.51013i | − | 0.0879801i | ||||||
\(815\) | 0.558539 | + | 2.44173i | 0.0195648 | + | 0.0855300i | ||||
\(816\) | 3.07412i | 0.107616i | ||||||||
\(817\) | −5.07913 | + | 7.95748i | −0.177696 | + | 0.278397i | ||||
\(818\) | −6.48881 | − | 6.48881i | −0.226876 | − | 0.226876i | ||||
\(819\) | 1.04557 | 0.0365352 | ||||||||
\(820\) | −1.00739 | − | 0.632310i | −0.0351794 | − | 0.0220812i | ||||
\(821\) | 27.0500 | 0.944053 | 0.472026 | − | 0.881584i | \(-0.343523\pi\) | ||||
0.472026 | + | 0.881584i | \(0.343523\pi\) | |||||||
\(822\) | 4.42031 | − | 4.42031i | 0.154176 | − | 0.154176i | ||||
\(823\) | −7.85319 | − | 7.85319i | −0.273745 | − | 0.273745i | 0.556861 | − | 0.830606i | \(-0.312006\pi\) |
−0.830606 | + | 0.556861i | \(0.812006\pi\) | |||||||
\(824\) | 15.2665i | 0.531833i | ||||||||
\(825\) | 6.27436 | + | 2.18875i | 0.218445 | + | 0.0762025i | ||||
\(826\) | −3.52965 | −0.122812 | ||||||||
\(827\) | 13.3020 | + | 13.3020i | 0.462557 | + | 0.462557i | 0.899493 | − | 0.436936i | \(-0.143936\pi\) |
−0.436936 | + | 0.899493i | \(0.643936\pi\) | |||||||
\(828\) | −1.08266 | − | 1.08266i | −0.0376249 | − | 0.0376249i | ||||
\(829\) | 53.6495 | 1.86332 | 0.931662 | − | 0.363326i | \(-0.118359\pi\) | ||||
0.931662 | + | 0.363326i | \(0.118359\pi\) | |||||||
\(830\) | 15.9756 | − | 25.4520i | 0.554520 | − | 0.883453i | ||||
\(831\) | 9.16466i | 0.317918i | ||||||||
\(832\) | 0.741383 | + | 0.741383i | 0.0257028 | + | 0.0257028i | ||||
\(833\) | 13.0544 | + | 13.0544i | 0.452309 | + | 0.452309i | ||||
\(834\) | 2.68665i | 0.0930311i | ||||||||
\(835\) | 7.85006 | + | 34.3176i | 0.271662 | + | 1.18761i | ||||
\(836\) | −5.65688 | + | 1.24898i | −0.195647 | + | 0.0431969i | ||||
\(837\) | −4.20791 | + | 4.20791i | −0.145447 | + | 0.145447i | ||||
\(838\) | −15.4528 | + | 15.4528i | −0.533808 | + | 0.533808i | ||||
\(839\) | −32.8129 | −1.13283 | −0.566413 | − | 0.824122i | \(-0.691669\pi\) | ||||
−0.566413 | + | 0.824122i | \(0.691669\pi\) | |||||||
\(840\) | 0.497236 | + | 2.17373i | 0.0171563 | + | 0.0750009i | ||||
\(841\) | 6.41308 | 0.221141 | ||||||||
\(842\) | −20.8047 | + | 20.8047i | −0.716978 | + | 0.716978i | ||||
\(843\) | 8.95726 | + | 8.95726i | 0.308504 | + | 0.308504i | ||||
\(844\) | −8.16488 | −0.281047 | ||||||||
\(845\) | −14.1470 | + | 22.5388i | −0.486671 | + | 0.775357i | ||||
\(846\) | − | 5.84230i | − | 0.200862i | ||||||
\(847\) | −6.51112 | + | 6.51112i | −0.223725 | + | 0.223725i | ||||
\(848\) | 5.48557 | − | 5.48557i | 0.188375 | − | 0.188375i | ||||
\(849\) | 15.8543 | 0.544119 | ||||||||
\(850\) | 6.68232 | + | 13.8420i | 0.229202 | + | 0.474778i | ||||
\(851\) | 2.89179i | 0.0991292i | ||||||||
\(852\) | 6.16531 | − | 6.16531i | 0.211220 | − | 0.211220i | ||||
\(853\) | 23.9591 | + | 23.9591i | 0.820342 | + | 0.820342i | 0.986157 | − | 0.165815i | \(-0.0530253\pi\) |
−0.165815 | + | 0.986157i | \(0.553025\pi\) | |||||||
\(854\) | 3.40086 | 0.116375 | ||||||||
\(855\) | 9.17833 | + | 3.27997i | 0.313892 | + | 0.112172i | ||||
\(856\) | 3.74948 | 0.128155 | ||||||||
\(857\) | 24.8412 | + | 24.8412i | 0.848560 | + | 0.848560i | 0.989953 | − | 0.141394i | \(-0.0451584\pi\) |
−0.141394 | + | 0.989953i | \(0.545158\pi\) | |||||||
\(858\) | −0.985322 | + | 0.985322i | −0.0336383 | + | 0.0336383i | ||||
\(859\) | 20.5100i | 0.699792i | 0.936789 | + | 0.349896i | \(0.113783\pi\) | ||||
−0.936789 | + | 0.349896i | \(0.886217\pi\) | |||||||
\(860\) | −4.72083 | + | 1.07988i | −0.160979 | + | 0.0368235i | ||||
\(861\) | 0.530438 | 0.0180773 | ||||||||
\(862\) | 25.7492 | − | 25.7492i | 0.877021 | − | 0.877021i | ||||
\(863\) | −36.4695 | + | 36.4695i | −1.24144 | + | 1.24144i | −0.282033 | + | 0.959405i | \(0.591009\pi\) |
−0.959405 | + | 0.282033i | \(0.908991\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 16.7244 | − | 3.82566i | 0.568646 | − | 0.130076i | ||||
\(866\) | 23.3209 | 0.792475 | ||||||||
\(867\) | 5.33850 | + | 5.33850i | 0.181305 | + | 0.181305i | ||||
\(868\) | 4.19627 | − | 4.19627i | 0.142431 | − | 0.142431i | ||||
\(869\) | 12.3775 | 0.419879 | ||||||||
\(870\) | −11.2704 | − | 7.07414i | −0.382102 | − | 0.239836i | ||||
\(871\) | 2.95732 | 0.100205 | ||||||||
\(872\) | 4.12665 | − | 4.12665i | 0.139746 | − | 0.139746i | ||||
\(873\) | 1.11691 | − | 1.11691i | 0.0378017 | − | 0.0378017i | ||||
\(874\) | 6.51698 | − | 1.43888i | 0.220440 | − | 0.0486710i | ||||
\(875\) | 6.96405 | + | 8.70695i | 0.235428 | + | 0.294349i | ||||
\(876\) | − | 8.25374i | − | 0.278868i | ||||||
\(877\) | 4.63012 | + | 4.63012i | 0.156348 | + | 0.156348i | 0.780946 | − | 0.624598i | \(-0.214737\pi\) |
−0.624598 | + | 0.780946i | \(0.714737\pi\) | |||||||
\(878\) | 9.43606 | + | 9.43606i | 0.318452 | + | 0.318452i | ||||
\(879\) | − | 0.182154i | − | 0.00614390i | ||||||
\(880\) | −2.51706 | − | 1.57989i | −0.0848500 | − | 0.0532581i | ||||
\(881\) | 24.1826 | 0.814731 | 0.407365 | − | 0.913265i | \(-0.366448\pi\) | ||||
0.407365 | + | 0.913265i | \(0.366448\pi\) | |||||||
\(882\) | 4.24655 | + | 4.24655i | 0.142989 | + | 0.142989i | ||||
\(883\) | 4.73940 | + | 4.73940i | 0.159494 | + | 0.159494i | 0.782342 | − | 0.622849i | \(-0.214025\pi\) |
−0.622849 | + | 0.782342i | \(0.714025\pi\) | |||||||
\(884\) | −3.22314 | −0.108406 | ||||||||
\(885\) | −7.71516 | + | 1.76482i | −0.259342 | + | 0.0593239i | ||||
\(886\) | − | 24.6377i | − | 0.827720i | ||||||
\(887\) | −17.0631 | − | 17.0631i | −0.572921 | − | 0.572921i | 0.360022 | − | 0.932944i | \(-0.382769\pi\) |
−0.932944 | + | 0.360022i | \(0.882769\pi\) | |||||||
\(888\) | 1.33551 | − | 1.33551i | 0.0448167 | − | 0.0448167i | ||||
\(889\) | 10.9368 | 0.366810 | ||||||||
\(890\) | −8.37045 | − | 36.5925i | −0.280578 | − | 1.22658i | ||||
\(891\) | −1.32903 | −0.0445243 | ||||||||
\(892\) | 0.212542 | + | 0.212542i | 0.00711644 | + | 0.00711644i | ||||
\(893\) | 21.4660 | + | 13.7014i | 0.718332 | + | 0.458499i | ||||
\(894\) | − | 14.1380i | − | 0.472847i | ||||||
\(895\) | −1.82392 | − | 1.14483i | −0.0609670 | − | 0.0382674i | ||||
\(896\) | − | 0.997232i | − | 0.0333152i | ||||||
\(897\) | 1.13514 | − | 1.13514i | 0.0379011 | − | 0.0379011i | ||||
\(898\) | 27.6310 | + | 27.6310i | 0.922058 | + | 0.922058i | ||||
\(899\) | 35.4131i | 1.18109i | ||||||||
\(900\) | 2.17373 | + | 4.50276i | 0.0724577 | + | 0.150092i | ||||
\(901\) | 23.8483i | 0.794502i | ||||||||
\(902\) | −0.499872 | + | 0.499872i | −0.0166439 | + | 0.0166439i | ||||
\(903\) | 1.52718 | − | 1.52718i | 0.0508213 | − | 0.0508213i | ||||
\(904\) | − | 0.655286i | − | 0.0217945i | ||||||
\(905\) | −24.2760 | + | 38.6762i | −0.806963 | + | 1.28564i | ||||
\(906\) | 9.45030i | 0.313965i | ||||||||
\(907\) | 40.9598 | + | 40.9598i | 1.36005 | + | 1.36005i | 0.873845 | + | 0.486204i | \(0.161619\pi\) |
0.486204 | + | 0.873845i | \(0.338381\pi\) | |||||||
\(908\) | −16.9240 | + | 16.9240i | −0.561642 | + | 0.561642i | ||||
\(909\) | 15.7109i | 0.521097i | ||||||||
\(910\) | −2.27910 | + | 0.521339i | −0.0755515 | + | 0.0172822i | ||||
\(911\) | − | 30.8795i | − | 1.02308i | −0.859259 | − | 0.511541i | \(-0.829075\pi\) | ||
0.859259 | − | 0.511541i | \(-0.170925\pi\) | |||||||
\(912\) | −3.67424 | − | 2.34520i | −0.121666 | − | 0.0776575i | ||||
\(913\) | −12.6295 | − | 12.6295i | −0.417975 | − | 0.417975i | ||||
\(914\) | −36.6647 | −1.21276 | ||||||||
\(915\) | 7.43365 | − | 1.70043i | 0.245749 | − | 0.0562144i | ||||
\(916\) | −7.59523 | −0.250953 | ||||||||
\(917\) | −9.34471 | + | 9.34471i | −0.308590 | + | 0.308590i | ||||
\(918\) | −2.17373 | − | 2.17373i | −0.0717439 | − | 0.0717439i | ||||
\(919\) | − | 7.02277i | − | 0.231660i | −0.993269 | − | 0.115830i | \(-0.963047\pi\) | ||
0.993269 | − | 0.115830i | \(-0.0369528\pi\) | |||||||
\(920\) | 2.89977 | + | 1.82011i | 0.0956024 | + | 0.0600071i | ||||
\(921\) | 22.3361 | 0.736000 | ||||||||
\(922\) | −11.5401 | − | 11.5401i | −0.380054 | − | 0.380054i | ||||
\(923\) | 6.46417 | + | 6.46417i | 0.212771 | + | 0.212771i | ||||
\(924\) | 1.32535 | 0.0436009 | ||||||||
\(925\) | 3.11044 | − | 8.91651i | 0.102271 | − | 0.293173i | ||||
\(926\) | − | 6.02559i | − | 0.198013i | ||||||
\(927\) | −10.7950 | − | 10.7950i | −0.354555 | − | 0.354555i | ||||
\(928\) | 4.20791 | + | 4.20791i | 0.138132 | + | 0.138132i | ||||
\(929\) | − | 6.87722i | − | 0.225634i | −0.993616 | − | 0.112817i | \(-0.964013\pi\) | ||
0.993616 | − | 0.112817i | \(-0.0359874\pi\) | |||||||
\(930\) | 7.07414 | − | 11.2704i | 0.231970 | − | 0.369571i | ||||
\(931\) | −25.5619 | + | 5.64380i | −0.837756 | + | 0.184968i | ||||
\(932\) | −0.816115 | + | 0.816115i | −0.0267327 | + | 0.0267327i | ||||
\(933\) | 10.3891 | − | 10.3891i | 0.340125 | − | 0.340125i | ||||
\(934\) | −34.0320 | −1.11356 | ||||||||
\(935\) | 8.90567 | − | 2.03715i | 0.291247 | − | 0.0666219i | ||||
\(936\) | −1.04847 | −0.0342704 | ||||||||
\(937\) | −29.1041 | + | 29.1041i | −0.950788 | + | 0.950788i | −0.998845 | − | 0.0480562i | \(-0.984697\pi\) |
0.0480562 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(938\) | −1.98894 | − | 1.98894i | −0.0649413 | − | 0.0649413i | ||||
\(939\) | −2.50414 | −0.0817195 | ||||||||
\(940\) | 2.91306 | + | 12.7348i | 0.0950136 | + | 0.415365i | ||||
\(941\) | 56.1970i | 1.83197i | 0.401213 | + | 0.915985i | \(0.368589\pi\) | ||||
−0.401213 | + | 0.915985i | \(0.631411\pi\) | |||||||
\(942\) | 13.7650 | − | 13.7650i | 0.448489 | − | 0.448489i | ||||
\(943\) | 0.575875 | − | 0.575875i | 0.0187531 | − | 0.0187531i | ||||
\(944\) | 3.53944 | 0.115199 | ||||||||
\(945\) | −1.88866 | − | 1.18546i | −0.0614381 | − | 0.0385631i | ||||
\(946\) | 2.87835i | 0.0935833i | ||||||||
\(947\) | −4.56166 | + | 4.56166i | −0.148234 | + | 0.148234i | −0.777329 | − | 0.629095i | \(-0.783426\pi\) |
0.629095 | + | 0.777329i | \(0.283426\pi\) | |||||||
\(948\) | 6.58542 | + | 6.58542i | 0.213884 | + | 0.213884i | ||||
\(949\) | 8.65384 | 0.280915 | ||||||||
\(950\) | −21.6421 | − | 2.57310i | −0.702161 | − | 0.0834823i | ||||
\(951\) | −6.55324 | −0.212503 | ||||||||
\(952\) | 2.16771 | + | 2.16771i | 0.0702560 | + | 0.0702560i | ||||
\(953\) | −2.55998 | + | 2.55998i | −0.0829258 | + | 0.0829258i | −0.747353 | − | 0.664427i | \(-0.768676\pi\) |
0.664427 | + | 0.747353i | \(0.268676\pi\) | |||||||
\(954\) | 7.75776i | 0.251167i | ||||||||
\(955\) | −13.9159 | − | 8.73464i | −0.450308 | − | 0.282646i | ||||
\(956\) | −4.21103 | −0.136195 | ||||||||
\(957\) | −5.59245 | + | 5.59245i | −0.180778 | + | 0.180778i | ||||
\(958\) | 13.9424 | − | 13.9424i | 0.450460 | − | 0.450460i | ||||
\(959\) | − | 6.23396i | − | 0.201305i | ||||||
\(960\) | −0.498616 | − | 2.17977i | −0.0160928 | − | 0.0703517i | ||||
\(961\) | −4.41308 | −0.142357 | ||||||||
\(962\) | 1.40024 | + | 1.40024i | 0.0451457 | + | 0.0451457i | ||||
\(963\) | −2.65129 | + | 2.65129i | −0.0854365 | + | 0.0854365i | ||||
\(964\) | −24.8896 | −0.801638 | ||||||||
\(965\) | 28.7435 | − | 6.57501i | 0.925287 | − | 0.211657i | ||||
\(966\) | −1.52687 | −0.0491262 | ||||||||
\(967\) | 28.9011 | − | 28.9011i | 0.929398 | − | 0.929398i | −0.0682690 | − | 0.997667i | \(-0.521748\pi\) |
0.997667 | + | 0.0682690i | \(0.0217476\pi\) | |||||||
\(968\) | 6.52919 | − | 6.52919i | 0.209856 | − | 0.209856i | ||||
\(969\) | 13.0847 | − | 2.88896i | 0.420340 | − | 0.0928068i | ||||
\(970\) | −1.87769 | + | 2.99151i | −0.0602891 | + | 0.0960516i | ||||
\(971\) | 7.01480i | 0.225116i | 0.993645 | + | 0.112558i | \(0.0359044\pi\) | ||||
−0.993645 | + | 0.112558i | \(0.964096\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 1.89449 | + | 1.89449i | 0.0607345 | + | 0.0607345i | ||||
\(974\) | − | 33.7792i | − | 1.08236i | ||||||
\(975\) | −4.72103 | + | 2.27910i | −0.151194 | + | 0.0729897i | ||||
\(976\) | −3.41030 | −0.109161 | ||||||||
\(977\) | 22.3335 | + | 22.3335i | 0.714512 | + | 0.714512i | 0.967476 | − | 0.252964i | \(-0.0814053\pi\) |
−0.252964 | + | 0.967476i | \(0.581405\pi\) | |||||||
\(978\) | 0.792086 | + | 0.792086i | 0.0253281 | + | 0.0253281i | ||||
\(979\) | −22.3109 | −0.713061 | ||||||||
\(980\) | −11.3739 | − | 7.13909i | −0.363325 | − | 0.228050i | ||||
\(981\) | 5.83596i | 0.186328i | ||||||||
\(982\) | 15.0275 | + | 15.0275i | 0.479547 | + | 0.479547i | ||||
\(983\) | −4.61128 | + | 4.61128i | −0.147077 | + | 0.147077i | −0.776811 | − | 0.629734i | \(-0.783164\pi\) |
0.629734 | + | 0.776811i | \(0.283164\pi\) | |||||||
\(984\) | −0.531910 | −0.0169567 | ||||||||
\(985\) | 16.7392 | − | 3.82905i | 0.533355 | − | 0.122004i | ||||
\(986\) | −18.2938 | −0.582592 | ||||||||
\(987\) | −4.11969 | − | 4.11969i | −0.131131 | − | 0.131131i | ||||
\(988\) | 2.45889 | − | 3.85234i | 0.0782276 | − | 0.122559i | ||||
\(989\) | − | 3.31599i | − | 0.105442i | ||||||
\(990\) | 2.89698 | − | 0.662676i | 0.0920721 | − | 0.0210612i | ||||
\(991\) | − | 30.5890i | − | 0.971691i | −0.874045 | − | 0.485845i | \(-0.838512\pi\) | ||
0.874045 | − | 0.485845i | \(-0.161488\pi\) | |||||||
\(992\) | −4.20791 | + | 4.20791i | −0.133601 | + | 0.133601i | ||||
\(993\) | 7.42992 | + | 7.42992i | 0.235781 | + | 0.235781i | ||||
\(994\) | − | 8.69493i | − | 0.275786i | ||||||
\(995\) | 27.9341 | − | 44.5042i | 0.885572 | − | 1.41088i | ||||
\(996\) | − | 13.4389i | − | 0.425829i | ||||||
\(997\) | 10.7588 | − | 10.7588i | 0.340735 | − | 0.340735i | −0.515909 | − | 0.856644i | \(-0.672546\pi\) |
0.856644 | + | 0.515909i | \(0.172546\pi\) | |||||||
\(998\) | 27.7826 | − | 27.7826i | 0.879444 | − | 0.879444i | ||||
\(999\) | 1.88869i | 0.0597556i |
(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 | 570.2.m.a.493.10 | yes | 20 | |
3.2 | odd | 2 | 1710.2.p.d.1063.1 | 20 | |||
5.2 | odd | 4 | inner | 570.2.m.a.37.5 | ✓ | 20 | |
15.2 | even | 4 | 1710.2.p.d.37.6 | 20 | |||
19.18 | odd | 2 | inner | 570.2.m.a.493.5 | yes | 20 | |
57.56 | even | 2 | 1710.2.p.d.1063.6 | 20 | |||
95.37 | even | 4 | inner | 570.2.m.a.37.10 | yes | 20 | |
285.227 | odd | 4 | 1710.2.p.d.37.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.a.37.5 | ✓ | 20 | 5.2 | odd | 4 | inner | |
570.2.m.a.37.10 | yes | 20 | 95.37 | even | 4 | inner | |
570.2.m.a.493.5 | yes | 20 | 19.18 | odd | 2 | inner | |
570.2.m.a.493.10 | yes | 20 | 1.1 | even | 1 | trivial | |
1710.2.p.d.37.1 | 20 | 285.227 | odd | 4 | |||
1710.2.p.d.37.6 | 20 | 15.2 | even | 4 | |||
1710.2.p.d.1063.1 | 20 | 3.2 | odd | 2 | |||
1710.2.p.d.1063.6 | 20 | 57.56 | even | 2 |