Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.16 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.f.47.16 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.73145 | − | 0.0456124i | 0.999653 | − | 0.0263343i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.54063 | − | 1.62063i | −0.688991 | − | 0.724770i | ||||
\(6\) | 1.25657 | + | 1.19207i | 0.512994 | + | 0.486659i | ||||
\(7\) | 0.528026 | − | 0.528026i | 0.199575 | − | 0.199575i | −0.600243 | − | 0.799818i | \(-0.704929\pi\) |
0.799818 | + | 0.600243i | \(0.204929\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.99584 | − | 0.157951i | 0.998613 | − | 0.0526504i | ||||
\(10\) | 0.0565714 | − | 2.23535i | 0.0178895 | − | 0.706880i | ||||
\(11\) | − | 4.60712i | − | 1.38910i | −0.719445 | − | 0.694549i | \(-0.755604\pi\) | ||
0.719445 | − | 0.694549i | \(-0.244396\pi\) | |||||||
\(12\) | 0.0456124 | + | 1.73145i | 0.0131672 | + | 0.499827i | ||||
\(13\) | 4.73992 | + | 4.73992i | 1.31462 | + | 1.31462i | 0.917972 | + | 0.396645i | \(0.129826\pi\) |
0.396645 | + | 0.917972i | \(0.370174\pi\) | |||||||
\(14\) | 0.746742 | 0.199575 | ||||||||
\(15\) | −2.74145 | − | 2.73578i | −0.707838 | − | 0.706374i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.32957 | + | 3.32957i | 0.807541 | + | 0.807541i | 0.984261 | − | 0.176721i | \(-0.0565489\pi\) |
−0.176721 | + | 0.984261i | \(0.556549\pi\) | |||||||
\(18\) | 2.23007 | + | 2.00669i | 0.525632 | + | 0.472981i | ||||
\(19\) | − | 5.21085i | − | 1.19545i | −0.801700 | − | 0.597726i | \(-0.796071\pi\) | ||
0.801700 | − | 0.597726i | \(-0.203929\pi\) | |||||||
\(20\) | 1.62063 | − | 1.54063i | 0.362385 | − | 0.344495i | ||||
\(21\) | 0.890166 | − | 0.938335i | 0.194250 | − | 0.204762i | ||||
\(22\) | 3.25773 | − | 3.25773i | 0.694549 | − | 0.694549i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | −1.19207 | + | 1.25657i | −0.243330 | + | 0.256497i | ||||
\(25\) | −0.252914 | + | 4.99360i | −0.0505828 | + | 0.998720i | ||||
\(26\) | 6.70326i | 1.31462i | ||||||||
\(27\) | 5.17994 | − | 0.410132i | 0.996880 | − | 0.0789300i | ||||
\(28\) | 0.528026 | + | 0.528026i | 0.0997876 | + | 0.0997876i | ||||
\(29\) | −2.50593 | −0.465339 | −0.232669 | − | 0.972556i | \(-0.574746\pi\) | ||||
−0.232669 | + | 0.972556i | \(0.574746\pi\) | |||||||
\(30\) | −0.00400919 | − | 3.87298i | −0.000731975 | − | 0.707106i | ||||
\(31\) | 3.91972 | 0.704003 | 0.352001 | − | 0.935999i | \(-0.385501\pi\) | ||||
0.352001 | + | 0.935999i | \(0.385501\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −0.210142 | − | 7.97700i | −0.0365810 | − | 1.38862i | ||||
\(34\) | 4.70873i | 0.807541i | ||||||||
\(35\) | −1.66923 | − | 0.0422442i | −0.282151 | − | 0.00714058i | ||||
\(36\) | 0.157951 | + | 2.99584i | 0.0263252 | + | 0.499307i | ||||
\(37\) | −7.08238 | + | 7.08238i | −1.16434 | + | 1.16434i | −0.180820 | + | 0.983516i | \(0.557875\pi\) |
−0.983516 | + | 0.180820i | \(0.942125\pi\) | |||||||
\(38\) | 3.68463 | − | 3.68463i | 0.597726 | − | 0.597726i | ||||
\(39\) | 8.42313 | + | 7.99073i | 1.34878 | + | 1.27954i | ||||
\(40\) | 2.23535 | + | 0.0565714i | 0.353440 | + | 0.00894473i | ||||
\(41\) | − | 4.23059i | − | 0.660707i | −0.943857 | − | 0.330353i | \(-0.892832\pi\) | ||
0.943857 | − | 0.330353i | \(-0.107168\pi\) | |||||||
\(42\) | 1.29295 | − | 0.0340607i | 0.199506 | − | 0.00525568i | ||||
\(43\) | −7.82352 | − | 7.82352i | −1.19308 | − | 1.19308i | −0.976199 | − | 0.216877i | \(-0.930413\pi\) |
−0.216877 | − | 0.976199i | \(-0.569587\pi\) | |||||||
\(44\) | 4.60712 | 0.694549 | ||||||||
\(45\) | −4.87146 | − | 4.61182i | −0.726195 | − | 0.687489i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.42130 | + | 2.42130i | 0.353184 | + | 0.353184i | 0.861293 | − | 0.508109i | \(-0.169655\pi\) |
−0.508109 | + | 0.861293i | \(0.669655\pi\) | |||||||
\(48\) | −1.73145 | + | 0.0456124i | −0.249913 | + | 0.00658358i | ||||
\(49\) | 6.44238i | 0.920340i | ||||||||
\(50\) | −3.70985 | + | 3.35217i | −0.524651 | + | 0.474069i | ||||
\(51\) | 5.91686 | + | 5.61312i | 0.828527 | + | 0.785994i | ||||
\(52\) | −4.73992 | + | 4.73992i | −0.657308 | + | 0.657308i | ||||
\(53\) | 1.66113 | − | 1.66113i | 0.228173 | − | 0.228173i | −0.583756 | − | 0.811929i | \(-0.698418\pi\) |
0.811929 | + | 0.583756i | \(0.198418\pi\) | |||||||
\(54\) | 3.95278 | + | 3.37276i | 0.537905 | + | 0.458975i | ||||
\(55\) | −7.46646 | + | 7.09787i | −1.00678 | + | 0.957077i | ||||
\(56\) | 0.746742i | 0.0997876i | ||||||||
\(57\) | −0.237680 | − | 9.02233i | −0.0314814 | − | 1.19504i | ||||
\(58\) | −1.77196 | − | 1.77196i | −0.232669 | − | 0.232669i | ||||
\(59\) | −12.7399 | −1.65860 | −0.829299 | − | 0.558806i | \(-0.811260\pi\) | ||||
−0.829299 | + | 0.558806i | \(0.811260\pi\) | |||||||
\(60\) | 2.73578 | − | 2.74145i | 0.353187 | − | 0.353919i | ||||
\(61\) | −1.51016 | −0.193356 | −0.0966778 | − | 0.995316i | \(-0.530822\pi\) | ||||
−0.0966778 | + | 0.995316i | \(0.530822\pi\) | |||||||
\(62\) | 2.77166 | + | 2.77166i | 0.352001 | + | 0.352001i | ||||
\(63\) | 1.49848 | − | 1.66528i | 0.188791 | − | 0.209806i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0.379213 | − | 14.9841i | 0.0470356 | − | 1.85855i | ||||
\(66\) | 5.49200 | − | 5.78918i | 0.676018 | − | 0.712599i | ||||
\(67\) | −5.25010 | + | 5.25010i | −0.641402 | + | 0.641402i | −0.950900 | − | 0.309498i | \(-0.899839\pi\) |
0.309498 | + | 0.950900i | \(0.399839\pi\) | |||||||
\(68\) | −3.32957 | + | 3.32957i | −0.403770 | + | 0.403770i | ||||
\(69\) | 1.19207 | − | 1.25657i | 0.143508 | − | 0.151274i | ||||
\(70\) | −1.15045 | − | 1.21020i | −0.137505 | − | 0.144646i | ||||
\(71\) | − | 10.9186i | − | 1.29580i | −0.761727 | − | 0.647898i | \(-0.775648\pi\) | ||
0.761727 | − | 0.647898i | \(-0.224352\pi\) | |||||||
\(72\) | −2.00669 | + | 2.23007i | −0.236491 | + | 0.262816i | ||||
\(73\) | −5.55728 | − | 5.55728i | −0.650430 | − | 0.650430i | 0.302667 | − | 0.953097i | \(-0.402123\pi\) |
−0.953097 | + | 0.302667i | \(0.902123\pi\) | |||||||
\(74\) | −10.0160 | −1.16434 | ||||||||
\(75\) | −0.210138 | + | 8.65770i | −0.0242647 | + | 0.999706i | ||||
\(76\) | 5.21085 | 0.597726 | ||||||||
\(77\) | −2.43268 | − | 2.43268i | −0.277230 | − | 0.277230i | ||||
\(78\) | 0.305752 | + | 11.6064i | 0.0346196 | + | 1.31416i | ||||
\(79\) | 6.67082i | 0.750526i | 0.926918 | + | 0.375263i | \(0.122448\pi\) | ||||
−0.926918 | + | 0.375263i | \(0.877552\pi\) | |||||||
\(80\) | 1.54063 | + | 1.62063i | 0.172248 | + | 0.181192i | ||||
\(81\) | 8.95010 | − | 0.946393i | 0.994456 | − | 0.105155i | ||||
\(82\) | 2.99148 | − | 2.99148i | 0.330353 | − | 0.330353i | ||||
\(83\) | −9.68331 | + | 9.68331i | −1.06288 | + | 1.06288i | −0.0649958 | + | 0.997886i | \(0.520703\pi\) |
−0.997886 | + | 0.0649958i | \(0.979297\pi\) | |||||||
\(84\) | 0.938335 | + | 0.890166i | 0.102381 | + | 0.0971251i | ||||
\(85\) | 0.266380 | − | 10.5257i | 0.0288929 | − | 1.14167i | ||||
\(86\) | − | 11.0641i | − | 1.19308i | ||||||
\(87\) | −4.33889 | + | 0.114301i | −0.465178 | + | 0.0122544i | ||||
\(88\) | 3.25773 | + | 3.25773i | 0.347275 | + | 0.347275i | ||||
\(89\) | −9.07840 | −0.962309 | −0.481154 | − | 0.876636i | \(-0.659782\pi\) | ||||
−0.481154 | + | 0.876636i | \(0.659782\pi\) | |||||||
\(90\) | −0.183598 | − | 6.70569i | −0.0193529 | − | 0.706842i | ||||
\(91\) | 5.00560 | 0.524730 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 6.78680 | − | 0.178788i | 0.703759 | − | 0.0185394i | ||||
\(94\) | 3.42424i | 0.353184i | ||||||||
\(95\) | −8.44489 | + | 8.02800i | −0.866428 | + | 0.823656i | ||||
\(96\) | −1.25657 | − | 1.19207i | −0.128248 | − | 0.121665i | ||||
\(97\) | 5.69526 | − | 5.69526i | 0.578266 | − | 0.578266i | −0.356159 | − | 0.934425i | \(-0.615914\pi\) |
0.934425 | + | 0.356159i | \(0.115914\pi\) | |||||||
\(98\) | −4.55545 | + | 4.55545i | −0.460170 | + | 0.460170i | ||||
\(99\) | −0.727700 | − | 13.8022i | −0.0731366 | − | 1.38717i | ||||
\(100\) | −4.99360 | − | 0.252914i | −0.499360 | − | 0.0252914i | ||||
\(101\) | 7.99014i | 0.795049i | 0.917592 | + | 0.397524i | \(0.130131\pi\) | ||||
−0.917592 | + | 0.397524i | \(0.869869\pi\) | |||||||
\(102\) | 0.214777 | + | 8.15293i | 0.0212660 | + | 0.807260i | ||||
\(103\) | 8.37328 | + | 8.37328i | 0.825044 | + | 0.825044i | 0.986826 | − | 0.161783i | \(-0.0517244\pi\) |
−0.161783 | + | 0.986826i | \(0.551724\pi\) | |||||||
\(104\) | −6.70326 | −0.657308 | ||||||||
\(105\) | −2.89212 | + | 0.00299383i | −0.282242 | + | 0.000292168i | ||||
\(106\) | 2.34919 | 0.228173 | ||||||||
\(107\) | 10.8290 | + | 10.8290i | 1.04688 | + | 1.04688i | 0.998846 | + | 0.0480314i | \(0.0152948\pi\) |
0.0480314 | + | 0.998846i | \(0.484705\pi\) | |||||||
\(108\) | 0.410132 | + | 5.17994i | 0.0394650 | + | 0.498440i | ||||
\(109\) | 5.81042i | 0.556538i | 0.960503 | + | 0.278269i | \(0.0897606\pi\) | ||||
−0.960503 | + | 0.278269i | \(0.910239\pi\) | |||||||
\(110\) | −10.2985 | − | 0.260631i | −0.981927 | − | 0.0248502i | ||||
\(111\) | −11.9397 | + | 12.5858i | −1.13327 | + | 1.19459i | ||||
\(112\) | −0.528026 | + | 0.528026i | −0.0498938 | + | 0.0498938i | ||||
\(113\) | −0.624299 | + | 0.624299i | −0.0587291 | + | 0.0587291i | −0.735861 | − | 0.677132i | \(-0.763222\pi\) |
0.677132 | + | 0.735861i | \(0.263222\pi\) | |||||||
\(114\) | 6.21169 | − | 6.54782i | 0.581778 | − | 0.613259i | ||||
\(115\) | −2.23535 | − | 0.0565714i | −0.208448 | − | 0.00527531i | ||||
\(116\) | − | 2.50593i | − | 0.232669i | ||||||
\(117\) | 14.9487 | + | 13.4514i | 1.38201 | + | 1.24358i | ||||
\(118\) | −9.00849 | − | 9.00849i | −0.829299 | − | 0.829299i | ||||
\(119\) | 3.51621 | 0.322330 | ||||||||
\(120\) | 3.87298 | − | 0.00400919i | 0.353553 | − | 0.000365988i | ||||
\(121\) | −10.2255 | −0.929595 | ||||||||
\(122\) | −1.06784 | − | 1.06784i | −0.0966778 | − | 0.0966778i | ||||
\(123\) | −0.192967 | − | 7.32505i | −0.0173993 | − | 0.660478i | ||||
\(124\) | 3.91972i | 0.352001i | ||||||||
\(125\) | 8.48245 | − | 7.28341i | 0.758693 | − | 0.651448i | ||||
\(126\) | 2.23712 | − | 0.117949i | 0.199298 | − | 0.0105077i | ||||
\(127\) | 11.0353 | − | 11.0353i | 0.979224 | − | 0.979224i | −0.0205641 | − | 0.999789i | \(-0.506546\pi\) |
0.999789 | + | 0.0205641i | \(0.00654623\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −13.9029 | − | 13.1892i | −1.22408 | − | 1.16124i | ||||
\(130\) | 10.8635 | − | 10.3272i | 0.952795 | − | 0.905759i | ||||
\(131\) | 9.85239i | 0.860807i | 0.902637 | + | 0.430404i | \(0.141629\pi\) | ||||
−0.902637 | + | 0.430404i | \(0.858371\pi\) | |||||||
\(132\) | 7.97700 | − | 0.210142i | 0.694309 | − | 0.0182905i | ||||
\(133\) | −2.75147 | − | 2.75147i | −0.238582 | − | 0.238582i | ||||
\(134\) | −7.42476 | −0.641402 | ||||||||
\(135\) | −8.64505 | − | 7.76293i | −0.744048 | − | 0.668127i | ||||
\(136\) | −4.70873 | −0.403770 | ||||||||
\(137\) | −7.59469 | − | 7.59469i | −0.648858 | − | 0.648858i | 0.303859 | − | 0.952717i | \(-0.401725\pi\) |
−0.952717 | + | 0.303859i | \(0.901725\pi\) | |||||||
\(138\) | 1.73145 | − | 0.0456124i | 0.147391 | − | 0.00388279i | ||||
\(139\) | − | 14.6607i | − | 1.24350i | −0.783214 | − | 0.621752i | \(-0.786421\pi\) | ||
0.783214 | − | 0.621752i | \(-0.213579\pi\) | |||||||
\(140\) | 0.0422442 | − | 1.66923i | 0.00357029 | − | 0.141076i | ||||
\(141\) | 4.30281 | + | 4.08193i | 0.362362 | + | 0.343760i | ||||
\(142\) | 7.72060 | − | 7.72060i | 0.647898 | − | 0.647898i | ||||
\(143\) | 21.8374 | − | 21.8374i | 1.82613 | − | 1.82613i | ||||
\(144\) | −2.99584 | + | 0.157951i | −0.249653 | + | 0.0131626i | ||||
\(145\) | 3.86071 | + | 4.06119i | 0.320614 | + | 0.337264i | ||||
\(146\) | − | 7.85918i | − | 0.650430i | ||||||
\(147\) | 0.293852 | + | 11.1547i | 0.0242365 | + | 0.920020i | ||||
\(148\) | −7.08238 | − | 7.08238i | −0.582168 | − | 0.582168i | ||||
\(149\) | −5.81897 | −0.476708 | −0.238354 | − | 0.971178i | \(-0.576608\pi\) | ||||
−0.238354 | + | 0.971178i | \(0.576608\pi\) | |||||||
\(150\) | −6.27051 | + | 5.97333i | −0.511985 | + | 0.487720i | ||||
\(151\) | 2.78052 | 0.226276 | 0.113138 | − | 0.993579i | \(-0.463910\pi\) | ||||
0.113138 | + | 0.993579i | \(0.463910\pi\) | |||||||
\(152\) | 3.68463 | + | 3.68463i | 0.298863 | + | 0.298863i | ||||
\(153\) | 10.5008 | + | 9.44896i | 0.848938 | + | 0.763903i | ||||
\(154\) | − | 3.44033i | − | 0.277230i | ||||||
\(155\) | −6.03884 | − | 6.35244i | −0.485052 | − | 0.510240i | ||||
\(156\) | −7.99073 | + | 8.42313i | −0.639771 | + | 0.674390i | ||||
\(157\) | −6.33516 | + | 6.33516i | −0.505601 | + | 0.505601i | −0.913173 | − | 0.407572i | \(-0.866375\pi\) |
0.407572 | + | 0.913173i | \(0.366375\pi\) | |||||||
\(158\) | −4.71698 | + | 4.71698i | −0.375263 | + | 0.375263i | ||||
\(159\) | 2.80039 | − | 2.95192i | 0.222085 | − | 0.234103i | ||||
\(160\) | −0.0565714 | + | 2.23535i | −0.00447236 | + | 0.176720i | ||||
\(161\) | − | 0.746742i | − | 0.0588515i | ||||||
\(162\) | 6.99788 | + | 5.65948i | 0.549805 | + | 0.444651i | ||||
\(163\) | −3.13303 | − | 3.13303i | −0.245398 | − | 0.245398i | 0.573681 | − | 0.819079i | \(-0.305515\pi\) |
−0.819079 | + | 0.573681i | \(0.805515\pi\) | |||||||
\(164\) | 4.23059 | 0.330353 | ||||||||
\(165\) | −12.6040 | + | 12.6302i | −0.981224 | + | 0.983257i | ||||
\(166\) | −13.6943 | −1.06288 | ||||||||
\(167\) | 5.90660 | + | 5.90660i | 0.457067 | + | 0.457067i | 0.897691 | − | 0.440625i | \(-0.145243\pi\) |
−0.440625 | + | 0.897691i | \(0.645243\pi\) | |||||||
\(168\) | 0.0340607 | + | 1.29295i | 0.00262784 | + | 0.0997529i | ||||
\(169\) | 31.9337i | 2.45644i | ||||||||
\(170\) | 7.63113 | − | 7.25441i | 0.585281 | − | 0.556388i | ||||
\(171\) | −0.823061 | − | 15.6109i | −0.0629410 | − | 1.19379i | ||||
\(172\) | 7.82352 | − | 7.82352i | 0.596538 | − | 0.596538i | ||||
\(173\) | −10.1099 | + | 10.1099i | −0.768643 | + | 0.768643i | −0.977868 | − | 0.209225i | \(-0.932906\pi\) |
0.209225 | + | 0.977868i | \(0.432906\pi\) | |||||||
\(174\) | −3.14888 | − | 2.98723i | −0.238716 | − | 0.226462i | ||||
\(175\) | 2.50321 | + | 2.77030i | 0.189225 | + | 0.209415i | ||||
\(176\) | 4.60712i | 0.347275i | ||||||||
\(177\) | −22.0585 | + | 0.581099i | −1.65802 | + | 0.0436781i | ||||
\(178\) | −6.41940 | − | 6.41940i | −0.481154 | − | 0.481154i | ||||
\(179\) | −10.7084 | −0.800386 | −0.400193 | − | 0.916431i | \(-0.631057\pi\) | ||||
−0.400193 | + | 0.916431i | \(0.631057\pi\) | |||||||
\(180\) | 4.61182 | − | 4.87146i | 0.343744 | − | 0.363097i | ||||
\(181\) | 19.3288 | 1.43670 | 0.718349 | − | 0.695683i | \(-0.244898\pi\) | ||||
0.718349 | + | 0.695683i | \(0.244898\pi\) | |||||||
\(182\) | 3.53949 | + | 3.53949i | 0.262365 | + | 0.262365i | ||||
\(183\) | −2.61476 | + | 0.0688818i | −0.193288 | + | 0.00509189i | ||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | 22.3893 | + | 0.566619i | 1.64609 | + | 0.0416587i | ||||
\(186\) | 4.92542 | + | 4.67257i | 0.361149 | + | 0.342610i | ||||
\(187\) | 15.3397 | − | 15.3397i | 1.12175 | − | 1.12175i | ||||
\(188\) | −2.42130 | + | 2.42130i | −0.176592 | + | 0.176592i | ||||
\(189\) | 2.51858 | − | 2.95170i | 0.183200 | − | 0.214705i | ||||
\(190\) | −11.6481 | − | 0.294785i | −0.845042 | − | 0.0213860i | ||||
\(191\) | 16.3310i | 1.18167i | 0.806792 | + | 0.590835i | \(0.201202\pi\) | ||||
−0.806792 | + | 0.590835i | \(0.798798\pi\) | |||||||
\(192\) | −0.0456124 | − | 1.73145i | −0.00329179 | − | 0.124957i | ||||
\(193\) | −4.44978 | − | 4.44978i | −0.320302 | − | 0.320302i | 0.528581 | − | 0.848883i | \(-0.322724\pi\) |
−0.848883 | + | 0.528581i | \(0.822724\pi\) | |||||||
\(194\) | 8.05432 | 0.578266 | ||||||||
\(195\) | −0.0268747 | − | 25.9616i | −0.00192453 | − | 1.85915i | ||||
\(196\) | −6.44238 | −0.460170 | ||||||||
\(197\) | −19.0107 | − | 19.0107i | −1.35446 | − | 1.35446i | −0.880601 | − | 0.473858i | \(-0.842861\pi\) |
−0.473858 | − | 0.880601i | \(-0.657139\pi\) | |||||||
\(198\) | 9.24506 | − | 10.2742i | 0.657018 | − | 0.730154i | ||||
\(199\) | − | 19.6455i | − | 1.39263i | −0.717737 | − | 0.696315i | \(-0.754822\pi\) | ||
0.717737 | − | 0.696315i | \(-0.245178\pi\) | |||||||
\(200\) | −3.35217 | − | 3.70985i | −0.237034 | − | 0.262326i | ||||
\(201\) | −8.85081 | + | 9.32975i | −0.624288 | + | 0.658070i | ||||
\(202\) | −5.64988 | + | 5.64988i | −0.397524 | + | 0.397524i | ||||
\(203\) | −1.32319 | + | 1.32319i | −0.0928701 | + | 0.0928701i | ||||
\(204\) | −5.61312 | + | 5.91686i | −0.392997 | + | 0.414263i | ||||
\(205\) | −6.85624 | + | 6.51777i | −0.478860 | + | 0.455221i | ||||
\(206\) | 11.8416i | 0.825044i | ||||||||
\(207\) | 2.00669 | − | 2.23007i | 0.139475 | − | 0.155000i | ||||
\(208\) | −4.73992 | − | 4.73992i | −0.328654 | − | 0.328654i | ||||
\(209\) | −24.0070 | −1.66060 | ||||||||
\(210\) | −2.04715 | − | 2.04292i | −0.141267 | − | 0.140975i | ||||
\(211\) | −4.38087 | −0.301592 | −0.150796 | − | 0.988565i | \(-0.548184\pi\) | ||||
−0.150796 | + | 0.988565i | \(0.548184\pi\) | |||||||
\(212\) | 1.66113 | + | 1.66113i | 0.114087 | + | 0.114087i | ||||
\(213\) | −0.498023 | − | 18.9050i | −0.0341239 | − | 1.29535i | ||||
\(214\) | 15.3145i | 1.04688i | ||||||||
\(215\) | −0.625914 | + | 24.7322i | −0.0426870 | + | 1.68672i | ||||
\(216\) | −3.37276 | + | 3.95278i | −0.229488 | + | 0.268953i | ||||
\(217\) | 2.06972 | − | 2.06972i | 0.140501 | − | 0.140501i | ||||
\(218\) | −4.10859 | + | 4.10859i | −0.278269 | + | 0.278269i | ||||
\(219\) | −9.87563 | − | 9.36867i | −0.667333 | − | 0.633076i | ||||
\(220\) | −7.09787 | − | 7.46646i | −0.478538 | − | 0.503388i | ||||
\(221\) | 31.5638i | 2.12321i | ||||||||
\(222\) | −17.3422 | + | 0.456854i | −1.16393 | + | 0.0306620i | ||||
\(223\) | 8.23185 | + | 8.23185i | 0.551245 | + | 0.551245i | 0.926800 | − | 0.375555i | \(-0.122548\pi\) |
−0.375555 | + | 0.926800i | \(0.622548\pi\) | |||||||
\(224\) | −0.746742 | −0.0498938 | ||||||||
\(225\) | 0.0310551 | + | 15.0000i | 0.00207034 | + | 0.999998i | ||||
\(226\) | −0.882892 | −0.0587291 | ||||||||
\(227\) | −4.42457 | − | 4.42457i | −0.293669 | − | 0.293669i | 0.544859 | − | 0.838528i | \(-0.316583\pi\) |
−0.838528 | + | 0.544859i | \(0.816583\pi\) | |||||||
\(228\) | 9.02233 | − | 0.237680i | 0.597519 | − | 0.0157407i | ||||
\(229\) | − | 0.539521i | − | 0.0356526i | −0.999841 | − | 0.0178263i | \(-0.994325\pi\) | ||
0.999841 | − | 0.0178263i | \(-0.00567458\pi\) | |||||||
\(230\) | −1.54063 | − | 1.62063i | −0.101586 | − | 0.106861i | ||||
\(231\) | −4.32302 | − | 4.10110i | −0.284434 | − | 0.269833i | ||||
\(232\) | 1.77196 | − | 1.77196i | 0.116335 | − | 0.116335i | ||||
\(233\) | 5.01691 | − | 5.01691i | 0.328669 | − | 0.328669i | −0.523411 | − | 0.852080i | \(-0.675341\pi\) |
0.852080 | + | 0.523411i | \(0.175341\pi\) | |||||||
\(234\) | 1.05879 | + | 20.0819i | 0.0692151 | + | 1.31279i | ||||
\(235\) | 0.193714 | − | 7.65439i | 0.0126365 | − | 0.499317i | ||||
\(236\) | − | 12.7399i | − | 0.829299i | ||||||
\(237\) | 0.304272 | + | 11.5502i | 0.0197646 | + | 0.750265i | ||||
\(238\) | 2.48633 | + | 2.48633i | 0.161165 | + | 0.161165i | ||||
\(239\) | −3.23606 | −0.209324 | −0.104662 | − | 0.994508i | \(-0.533376\pi\) | ||||
−0.104662 | + | 0.994508i | \(0.533376\pi\) | |||||||
\(240\) | 2.74145 | + | 2.73578i | 0.176960 | + | 0.176594i | ||||
\(241\) | 2.49371 | 0.160634 | 0.0803171 | − | 0.996769i | \(-0.474407\pi\) | ||||
0.0803171 | + | 0.996769i | \(0.474407\pi\) | |||||||
\(242\) | −7.23056 | − | 7.23056i | −0.464798 | − | 0.464798i | ||||
\(243\) | 15.4535 | − | 2.04687i | 0.991342 | − | 0.131307i | ||||
\(244\) | − | 1.51016i | − | 0.0966778i | ||||||
\(245\) | 10.4407 | − | 9.92532i | 0.667034 | − | 0.634106i | ||||
\(246\) | 5.04315 | − | 5.31604i | 0.321539 | − | 0.338939i | ||||
\(247\) | 24.6990 | − | 24.6990i | 1.57156 | − | 1.57156i | ||||
\(248\) | −2.77166 | + | 2.77166i | −0.176001 | + | 0.176001i | ||||
\(249\) | −16.3245 | + | 17.2078i | −1.03452 | + | 1.09050i | ||||
\(250\) | 11.1481 | + | 0.847847i | 0.705071 | + | 0.0536226i | ||||
\(251\) | − | 5.39309i | − | 0.340409i | −0.985409 | − | 0.170205i | \(-0.945557\pi\) | ||
0.985409 | − | 0.170205i | \(-0.0544428\pi\) | |||||||
\(252\) | 1.66528 | + | 1.49848i | 0.104903 | + | 0.0943953i | ||||
\(253\) | −3.25773 | − | 3.25773i | −0.204811 | − | 0.204811i | ||||
\(254\) | 15.6063 | 0.979224 | ||||||||
\(255\) | −0.0188782 | − | 18.2368i | −0.00118220 | − | 1.14203i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.454641 | + | 0.454641i | 0.0283597 | + | 0.0283597i | 0.721144 | − | 0.692785i | \(-0.243616\pi\) |
−0.692785 | + | 0.721144i | \(0.743616\pi\) | |||||||
\(258\) | −0.504662 | − | 19.1570i | −0.0314189 | − | 1.19266i | ||||
\(259\) | 7.47937i | 0.464745i | ||||||||
\(260\) | 14.9841 | + | 0.379213i | 0.929277 | + | 0.0235178i | ||||
\(261\) | −7.50735 | + | 0.395814i | −0.464693 | + | 0.0245003i | ||||
\(262\) | −6.96669 | + | 6.96669i | −0.430404 | + | 0.430404i | ||||
\(263\) | −10.1010 | + | 10.1010i | −0.622853 | + | 0.622853i | −0.946260 | − | 0.323407i | \(-0.895172\pi\) |
0.323407 | + | 0.946260i | \(0.395172\pi\) | |||||||
\(264\) | 5.78918 | + | 5.49200i | 0.356300 | + | 0.338009i | ||||
\(265\) | −5.25126 | − | 0.132897i | −0.322582 | − | 0.00816379i | ||||
\(266\) | − | 3.89116i | − | 0.238582i | ||||||
\(267\) | −15.7188 | + | 0.414088i | −0.961975 | + | 0.0253418i | ||||
\(268\) | −5.25010 | − | 5.25010i | −0.320701 | − | 0.320701i | ||||
\(269\) | −23.4948 | −1.43250 | −0.716252 | − | 0.697842i | \(-0.754144\pi\) | ||||
−0.716252 | + | 0.697842i | \(0.754144\pi\) | |||||||
\(270\) | −0.623753 | − | 11.6022i | −0.0379604 | − | 0.706087i | ||||
\(271\) | −6.16572 | −0.374541 | −0.187270 | − | 0.982308i | \(-0.559964\pi\) | ||||
−0.187270 | + | 0.982308i | \(0.559964\pi\) | |||||||
\(272\) | −3.32957 | − | 3.32957i | −0.201885 | − | 0.201885i | ||||
\(273\) | 8.66695 | − | 0.228318i | 0.524548 | − | 0.0138184i | ||||
\(274\) | − | 10.7405i | − | 0.648858i | ||||||
\(275\) | 23.0061 | + | 1.16521i | 1.38732 | + | 0.0702645i | ||||
\(276\) | 1.25657 | + | 1.19207i | 0.0756368 | + | 0.0717540i | ||||
\(277\) | 16.3851 | − | 16.3851i | 0.984482 | − | 0.984482i | −0.0153991 | − | 0.999881i | \(-0.504902\pi\) |
0.999881 | + | 0.0153991i | \(0.00490187\pi\) | |||||||
\(278\) | 10.3667 | − | 10.3667i | 0.621752 | − | 0.621752i | ||||
\(279\) | 11.7429 | − | 0.619125i | 0.703026 | − | 0.0370660i | ||||
\(280\) | 1.21020 | − | 1.15045i | 0.0723230 | − | 0.0687527i | ||||
\(281\) | 0.344451i | 0.0205482i | 0.999947 | + | 0.0102741i | \(0.00327041\pi\) | ||||
−0.999947 | + | 0.0102741i | \(0.996730\pi\) | |||||||
\(282\) | 0.156188 | + | 5.92890i | 0.00930086 | + | 0.353061i | ||||
\(283\) | −1.89935 | − | 1.89935i | −0.112905 | − | 0.112905i | 0.648397 | − | 0.761302i | \(-0.275440\pi\) |
−0.761302 | + | 0.648397i | \(0.775440\pi\) | |||||||
\(284\) | 10.9186 | 0.647898 | ||||||||
\(285\) | −14.2557 | + | 14.2853i | −0.844437 | + | 0.846187i | ||||
\(286\) | 30.8827 | 1.82613 | ||||||||
\(287\) | −2.23386 | − | 2.23386i | −0.131861 | − | 0.131861i | ||||
\(288\) | −2.23007 | − | 2.00669i | −0.131408 | − | 0.118245i | ||||
\(289\) | 5.17214i | 0.304243i | ||||||||
\(290\) | −0.141764 | + | 5.60163i | −0.00832466 | + | 0.328939i | ||||
\(291\) | 9.60129 | − | 10.1208i | 0.562838 | − | 0.593294i | ||||
\(292\) | 5.55728 | − | 5.55728i | 0.325215 | − | 0.325215i | ||||
\(293\) | −0.184488 | + | 0.184488i | −0.0107779 | + | 0.0107779i | −0.712475 | − | 0.701697i | \(-0.752426\pi\) |
0.701697 | + | 0.712475i | \(0.252426\pi\) | |||||||
\(294\) | −7.67975 | + | 8.09532i | −0.447892 | + | 0.472128i | ||||
\(295\) | 19.6275 | + | 20.6468i | 1.14276 | + | 1.20210i | ||||
\(296\) | − | 10.0160i | − | 0.582168i | ||||||
\(297\) | −1.88953 | − | 23.8646i | −0.109642 | − | 1.38477i | ||||
\(298\) | −4.11463 | − | 4.11463i | −0.238354 | − | 0.238354i | ||||
\(299\) | 6.70326 | 0.387659 | ||||||||
\(300\) | −8.65770 | − | 0.210138i | −0.499853 | − | 0.0121323i | ||||
\(301\) | −8.26205 | −0.476217 | ||||||||
\(302\) | 1.96613 | + | 1.96613i | 0.113138 | + | 0.113138i | ||||
\(303\) | 0.364450 | + | 13.8345i | 0.0209371 | + | 0.794773i | ||||
\(304\) | 5.21085i | 0.298863i | ||||||||
\(305\) | 2.32659 | + | 2.44741i | 0.133220 | + | 0.140138i | ||||
\(306\) | 0.743750 | + | 14.1066i | 0.0425173 | + | 0.806420i | ||||
\(307\) | −5.11094 | + | 5.11094i | −0.291697 | + | 0.291697i | −0.837750 | − | 0.546054i | \(-0.816130\pi\) |
0.546054 | + | 0.837750i | \(0.316130\pi\) | |||||||
\(308\) | 2.43268 | − | 2.43268i | 0.138615 | − | 0.138615i | ||||
\(309\) | 14.8798 | + | 14.1160i | 0.846484 | + | 0.803031i | ||||
\(310\) | 0.221744 | − | 8.76196i | 0.0125942 | − | 0.497646i | ||||
\(311\) | − | 13.3425i | − | 0.756584i | −0.925686 | − | 0.378292i | \(-0.876511\pi\) | ||
0.925686 | − | 0.378292i | \(-0.123489\pi\) | |||||||
\(312\) | −11.6064 | + | 0.305752i | −0.657081 | + | 0.0173098i | ||||
\(313\) | 5.87924 | + | 5.87924i | 0.332314 | + | 0.332314i | 0.853465 | − | 0.521151i | \(-0.174497\pi\) |
−0.521151 | + | 0.853465i | \(0.674497\pi\) | |||||||
\(314\) | −8.95927 | −0.505601 | ||||||||
\(315\) | −5.00742 | + | 0.137100i | −0.282136 | + | 0.00772471i | ||||
\(316\) | −6.67082 | −0.375263 | ||||||||
\(317\) | 15.0768 | + | 15.0768i | 0.846797 | + | 0.846797i | 0.989732 | − | 0.142935i | \(-0.0456540\pi\) |
−0.142935 | + | 0.989732i | \(0.545654\pi\) | |||||||
\(318\) | 4.06750 | − | 0.107152i | 0.228094 | − | 0.00600879i | ||||
\(319\) | 11.5451i | 0.646402i | ||||||||
\(320\) | −1.62063 | + | 1.54063i | −0.0905962 | + | 0.0861239i | ||||
\(321\) | 19.2438 | + | 18.2559i | 1.07408 | + | 1.01895i | ||||
\(322\) | 0.528026 | − | 0.528026i | 0.0294257 | − | 0.0294257i | ||||
\(323\) | 17.3499 | − | 17.3499i | 0.965376 | − | 0.965376i | ||||
\(324\) | 0.946393 | + | 8.95010i | 0.0525774 | + | 0.497228i | ||||
\(325\) | −24.8680 | + | 22.4705i | −1.37943 | + | 1.24644i | ||||
\(326\) | − | 4.43077i | − | 0.245398i | ||||||
\(327\) | 0.265027 | + | 10.0605i | 0.0146561 | + | 0.556345i | ||||
\(328\) | 2.99148 | + | 2.99148i | 0.165177 | + | 0.165177i | ||||
\(329\) | 2.55702 | 0.140973 | ||||||||
\(330\) | −17.8433 | + | 0.0184708i | −0.982241 | + | 0.00101679i | ||||
\(331\) | 18.7391 | 1.02999 | 0.514996 | − | 0.857192i | \(-0.327793\pi\) | ||||
0.514996 | + | 0.857192i | \(0.327793\pi\) | |||||||
\(332\) | −9.68331 | − | 9.68331i | −0.531441 | − | 0.531441i | ||||
\(333\) | −20.0990 | + | 22.3363i | −1.10142 | + | 1.22402i | ||||
\(334\) | 8.35320i | 0.457067i | ||||||||
\(335\) | 16.5970 | + | 0.420029i | 0.906788 | + | 0.0229487i | ||||
\(336\) | −0.890166 | + | 0.938335i | −0.0485626 | + | 0.0511904i | ||||
\(337\) | 11.5783 | − | 11.5783i | 0.630712 | − | 0.630712i | −0.317535 | − | 0.948247i | \(-0.602855\pi\) |
0.948247 | + | 0.317535i | \(0.102855\pi\) | |||||||
\(338\) | −22.5805 | + | 22.5805i | −1.22822 | + | 1.22822i | ||||
\(339\) | −1.05247 | + | 1.10942i | −0.0571621 | + | 0.0602553i | ||||
\(340\) | 10.5257 | + | 0.266380i | 0.570835 | + | 0.0144465i | ||||
\(341\) | − | 18.0586i | − | 0.977929i | ||||||
\(342\) | 10.4566 | − | 11.6206i | 0.565426 | − | 0.628367i | ||||
\(343\) | 7.09793 | + | 7.09793i | 0.383252 | + | 0.383252i | ||||
\(344\) | 11.0641 | 0.596538 | ||||||||
\(345\) | −3.87298 | + | 0.00400919i | −0.208514 | + | 0.000215848i | ||||
\(346\) | −14.2976 | −0.768643 | ||||||||
\(347\) | 9.53609 | + | 9.53609i | 0.511924 | + | 0.511924i | 0.915116 | − | 0.403191i | \(-0.132099\pi\) |
−0.403191 | + | 0.915116i | \(0.632099\pi\) | |||||||
\(348\) | −0.114301 | − | 4.33889i | −0.00612720 | − | 0.232589i | ||||
\(349\) | 22.7071i | 1.21549i | 0.794134 | + | 0.607743i | \(0.207925\pi\) | ||||
−0.794134 | + | 0.607743i | \(0.792075\pi\) | |||||||
\(350\) | −0.188862 | + | 3.72893i | −0.0100951 | + | 0.199320i | ||||
\(351\) | 26.4965 | + | 22.6085i | 1.41428 | + | 1.20675i | ||||
\(352\) | −3.25773 | + | 3.25773i | −0.173637 | + | 0.173637i | ||||
\(353\) | 20.2080 | − | 20.2080i | 1.07556 | − | 1.07556i | 0.0786597 | − | 0.996902i | \(-0.474936\pi\) |
0.996902 | − | 0.0786597i | \(-0.0250641\pi\) | |||||||
\(354\) | −16.0086 | − | 15.1868i | −0.850850 | − | 0.807172i | ||||
\(355\) | −17.6950 | + | 16.8215i | −0.939155 | + | 0.892792i | ||||
\(356\) | − | 9.07840i | − | 0.481154i | ||||||
\(357\) | 6.08813 | − | 0.160383i | 0.322218 | − | 0.00848835i | ||||
\(358\) | −7.57201 | − | 7.57201i | −0.400193 | − | 0.400193i | ||||
\(359\) | 9.55317 | 0.504197 | 0.252098 | − | 0.967702i | \(-0.418879\pi\) | ||||
0.252098 | + | 0.967702i | \(0.418879\pi\) | |||||||
\(360\) | 6.70569 | − | 0.183598i | 0.353421 | − | 0.00967645i | ||||
\(361\) | −8.15300 | −0.429105 | ||||||||
\(362\) | 13.6675 | + | 13.6675i | 0.718349 | + | 0.718349i | ||||
\(363\) | −17.7050 | + | 0.466412i | −0.929273 | + | 0.0244803i | ||||
\(364\) | 5.00560i | 0.262365i | ||||||||
\(365\) | −0.444605 | + | 17.5680i | −0.0232717 | + | 0.919552i | ||||
\(366\) | −1.89762 | − | 1.80021i | −0.0991902 | − | 0.0940983i | ||||
\(367\) | −15.8937 | + | 15.8937i | −0.829645 | + | 0.829645i | −0.987467 | − | 0.157823i | \(-0.949553\pi\) |
0.157823 | + | 0.987467i | \(0.449553\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | −0.668227 | − | 12.6742i | −0.0347865 | − | 0.659790i | ||||
\(370\) | 15.4310 | + | 16.2323i | 0.802217 | + | 0.843876i | ||||
\(371\) | − | 1.75424i | − | 0.0910754i | ||||||
\(372\) | 0.178788 | + | 6.78680i | 0.00926972 | + | 0.351879i | ||||
\(373\) | 21.9117 | + | 21.9117i | 1.13455 | + | 1.13455i | 0.989412 | + | 0.145135i | \(0.0463617\pi\) |
0.145135 | + | 0.989412i | \(0.453638\pi\) | |||||||
\(374\) | 21.6937 | 1.12175 | ||||||||
\(375\) | 14.3547 | − | 12.9978i | 0.741275 | − | 0.671202i | ||||
\(376\) | −3.42424 | −0.176592 | ||||||||
\(377\) | −11.8779 | − | 11.8779i | −0.611742 | − | 0.611742i | ||||
\(378\) | 3.86808 | − | 0.306263i | 0.198952 | − | 0.0157525i | ||||
\(379\) | − | 3.01254i | − | 0.154744i | −0.997002 | − | 0.0773719i | \(-0.975347\pi\) | ||
0.997002 | − | 0.0773719i | \(-0.0246529\pi\) | |||||||
\(380\) | −8.02800 | − | 8.44489i | −0.411828 | − | 0.433214i | ||||
\(381\) | 18.6037 | − | 19.6104i | 0.953098 | − | 1.00467i | ||||
\(382\) | −11.5478 | + | 11.5478i | −0.590835 | + | 0.590835i | ||||
\(383\) | 17.7386 | − | 17.7386i | 0.906400 | − | 0.906400i | −0.0895800 | − | 0.995980i | \(-0.528552\pi\) |
0.995980 | + | 0.0895800i | \(0.0285525\pi\) | |||||||
\(384\) | 1.19207 | − | 1.25657i | 0.0608324 | − | 0.0641242i | ||||
\(385\) | −0.194624 | + | 7.69035i | −0.00991897 | + | 0.391936i | ||||
\(386\) | − | 6.29293i | − | 0.320302i | ||||||
\(387\) | −24.6738 | − | 22.2023i | −1.25424 | − | 1.12861i | ||||
\(388\) | 5.69526 | + | 5.69526i | 0.289133 | + | 0.289133i | ||||
\(389\) | 20.0679 | 1.01748 | 0.508742 | − | 0.860919i | \(-0.330111\pi\) | ||||
0.508742 | + | 0.860919i | \(0.330111\pi\) | |||||||
\(390\) | 18.3386 | − | 18.3766i | 0.928612 | − | 0.930536i | ||||
\(391\) | 4.70873 | 0.238131 | ||||||||
\(392\) | −4.55545 | − | 4.55545i | −0.230085 | − | 0.230085i | ||||
\(393\) | 0.449391 | + | 17.0589i | 0.0226688 | + | 0.860509i | ||||
\(394\) | − | 26.8853i | − | 1.35446i | ||||||
\(395\) | 10.8110 | − | 10.2773i | 0.543958 | − | 0.517105i | ||||
\(396\) | 13.8022 | − | 0.727700i | 0.693586 | − | 0.0365683i | ||||
\(397\) | 26.1076 | − | 26.1076i | 1.31030 | − | 1.31030i | 0.389114 | − | 0.921190i | \(-0.372781\pi\) |
0.921190 | − | 0.389114i | \(-0.127219\pi\) | |||||||
\(398\) | 13.8914 | − | 13.8914i | 0.696315 | − | 0.696315i | ||||
\(399\) | −4.88953 | − | 4.63853i | −0.244783 | − | 0.232217i | ||||
\(400\) | 0.252914 | − | 4.99360i | 0.0126457 | − | 0.249680i | ||||
\(401\) | 21.9907i | 1.09816i | 0.835769 | + | 0.549082i | \(0.185022\pi\) | ||||
−0.835769 | + | 0.549082i | \(0.814978\pi\) | |||||||
\(402\) | −12.8556 | + | 0.338661i | −0.641179 | + | 0.0168909i | ||||
\(403\) | 18.5792 | + | 18.5792i | 0.925494 | + | 0.925494i | ||||
\(404\) | −7.99014 | −0.397524 | ||||||||
\(405\) | −15.3226 | − | 13.0468i | −0.761384 | − | 0.648301i | ||||
\(406\) | −1.87128 | −0.0928701 | ||||||||
\(407\) | 32.6294 | + | 32.6294i | 1.61738 | + | 1.61738i | ||||
\(408\) | −8.15293 | + | 0.214777i | −0.403630 | + | 0.0106330i | ||||
\(409\) | 38.2076i | 1.88924i | 0.328159 | + | 0.944622i | \(0.393572\pi\) | ||||
−0.328159 | + | 0.944622i | \(0.606428\pi\) | |||||||
\(410\) | −9.45685 | − | 0.239330i | −0.467041 | − | 0.0118197i | ||||
\(411\) | −13.4962 | − | 12.8034i | −0.665721 | − | 0.631546i | ||||
\(412\) | −8.37328 | + | 8.37328i | −0.412522 | + | 0.412522i | ||||
\(413\) | −6.72701 | + | 6.72701i | −0.331015 | + | 0.331015i | ||||
\(414\) | 2.99584 | − | 0.157951i | 0.147237 | − | 0.00776288i | ||||
\(415\) | 30.6115 | + | 0.774704i | 1.50266 | + | 0.0380287i | ||||
\(416\) | − | 6.70326i | − | 0.328654i | ||||||
\(417\) | −0.668710 | − | 25.3843i | −0.0327469 | − | 1.24307i | ||||
\(418\) | −16.9755 | − | 16.9755i | −0.830300 | − | 0.830300i | ||||
\(419\) | −9.14872 | −0.446944 | −0.223472 | − | 0.974710i | \(-0.571739\pi\) | ||||
−0.223472 | + | 0.974710i | \(0.571739\pi\) | |||||||
\(420\) | −0.00299383 | − | 2.89212i | −0.000146084 | − | 0.141121i | ||||
\(421\) | −28.4290 | −1.38554 | −0.692772 | − | 0.721157i | \(-0.743611\pi\) | ||||
−0.692772 | + | 0.721157i | \(0.743611\pi\) | |||||||
\(422\) | −3.09774 | − | 3.09774i | −0.150796 | − | 0.150796i | ||||
\(423\) | 7.63629 | + | 6.87139i | 0.371289 | + | 0.334099i | ||||
\(424\) | 2.34919i | 0.114087i | ||||||||
\(425\) | −17.4687 | + | 15.7845i | −0.847354 | + | 0.765659i | ||||
\(426\) | 13.0157 | − | 13.7200i | 0.630612 | − | 0.664736i | ||||
\(427\) | −0.797401 | + | 0.797401i | −0.0385890 | + | 0.0385890i | ||||
\(428\) | −10.8290 | + | 10.8290i | −0.523439 | + | 0.523439i | ||||
\(429\) | 36.8143 | − | 38.8064i | 1.77741 | − | 1.87359i | ||||
\(430\) | −17.9309 | + | 17.0457i | −0.864706 | + | 0.822019i | ||||
\(431\) | 11.1238i | 0.535814i | 0.963445 | + | 0.267907i | \(0.0863321\pi\) | ||||
−0.963445 | + | 0.267907i | \(0.913668\pi\) | |||||||
\(432\) | −5.17994 | + | 0.410132i | −0.249220 | + | 0.0197325i | ||||
\(433\) | −20.0373 | − | 20.0373i | −0.962929 | − | 0.962929i | 0.0364075 | − | 0.999337i | \(-0.488409\pi\) |
−0.999337 | + | 0.0364075i | \(0.988409\pi\) | |||||||
\(434\) | 2.92702 | 0.140501 | ||||||||
\(435\) | 6.86986 | + | 6.85565i | 0.329385 | + | 0.328703i | ||||
\(436\) | −5.81042 | −0.278269 | ||||||||
\(437\) | −3.68463 | − | 3.68463i | −0.176260 | − | 0.176260i | ||||
\(438\) | −0.358476 | − | 13.6078i | −0.0171286 | − | 0.650204i | ||||
\(439\) | − | 13.8002i | − | 0.658647i | −0.944217 | − | 0.329324i | \(-0.893179\pi\) | ||
0.944217 | − | 0.329324i | \(-0.106821\pi\) | |||||||
\(440\) | 0.260631 | − | 10.2985i | 0.0124251 | − | 0.490963i | ||||
\(441\) | 1.01758 | + | 19.3003i | 0.0484563 | + | 0.919063i | ||||
\(442\) | −22.3190 | + | 22.3190i | −1.06161 | + | 1.06161i | ||||
\(443\) | −4.08292 | + | 4.08292i | −0.193986 | + | 0.193986i | −0.797416 | − | 0.603430i | \(-0.793800\pi\) |
0.603430 | + | 0.797416i | \(0.293800\pi\) | |||||||
\(444\) | −12.5858 | − | 11.9397i | −0.597297 | − | 0.566635i | ||||
\(445\) | 13.9865 | + | 14.7128i | 0.663022 | + | 0.697452i | ||||
\(446\) | 11.6416i | 0.551245i | ||||||||
\(447\) | −10.0753 | + | 0.265417i | −0.476543 | + | 0.0125538i | ||||
\(448\) | −0.528026 | − | 0.528026i | −0.0249469 | − | 0.0249469i | ||||
\(449\) | 5.80447 | 0.273930 | 0.136965 | − | 0.990576i | \(-0.456265\pi\) | ||||
0.136965 | + | 0.990576i | \(0.456265\pi\) | |||||||
\(450\) | −10.5846 | + | 10.6285i | −0.498964 | + | 0.501034i | ||||
\(451\) | −19.4908 | −0.917787 | ||||||||
\(452\) | −0.624299 | − | 0.624299i | −0.0293645 | − | 0.0293645i | ||||
\(453\) | 4.81433 | − | 0.126826i | 0.226197 | − | 0.00595882i | ||||
\(454\) | − | 6.25729i | − | 0.293669i | ||||||
\(455\) | −7.71178 | − | 8.11225i | −0.361534 | − | 0.380308i | ||||
\(456\) | 6.54782 | + | 6.21169i | 0.306630 | + | 0.290889i | ||||
\(457\) | −3.04689 | + | 3.04689i | −0.142528 | + | 0.142528i | −0.774770 | − | 0.632243i | \(-0.782135\pi\) |
0.632243 | + | 0.774770i | \(0.282135\pi\) | |||||||
\(458\) | 0.381499 | − | 0.381499i | 0.0178263 | − | 0.0178263i | ||||
\(459\) | 18.6126 | + | 15.8814i | 0.868760 | + | 0.741282i | ||||
\(460\) | 0.0565714 | − | 2.23535i | 0.00263766 | − | 0.104224i | ||||
\(461\) | − | 10.8450i | − | 0.505103i | −0.967583 | − | 0.252551i | \(-0.918730\pi\) | ||
0.967583 | − | 0.252551i | \(-0.0812697\pi\) | |||||||
\(462\) | −0.156922 | − | 5.95676i | −0.00730066 | − | 0.277133i | ||||
\(463\) | −0.966000 | − | 0.966000i | −0.0448939 | − | 0.0448939i | 0.684303 | − | 0.729197i | \(-0.260106\pi\) |
−0.729197 | + | 0.684303i | \(0.760106\pi\) | |||||||
\(464\) | 2.50593 | 0.116335 | ||||||||
\(465\) | −10.7457 | − | 10.7235i | −0.498320 | − | 0.497290i | ||||
\(466\) | 7.09498 | 0.328669 | ||||||||
\(467\) | 4.97855 | + | 4.97855i | 0.230380 | + | 0.230380i | 0.812851 | − | 0.582471i | \(-0.197914\pi\) |
−0.582471 | + | 0.812851i | \(0.697914\pi\) | |||||||
\(468\) | −13.4514 | + | 14.9487i | −0.621789 | + | 0.691004i | ||||
\(469\) | 5.54438i | 0.256016i | ||||||||
\(470\) | 5.54945 | − | 5.27549i | 0.255977 | − | 0.243340i | ||||
\(471\) | −10.6800 | + | 11.2580i | −0.492111 | + | 0.518740i | ||||
\(472\) | 9.00849 | − | 9.00849i | 0.414649 | − | 0.414649i | ||||
\(473\) | −36.0439 | + | 36.0439i | −1.65730 | + | 1.65730i | ||||
\(474\) | −7.95206 | + | 8.38237i | −0.365250 | + | 0.385015i | ||||
\(475\) | 26.0209 | + | 1.31790i | 1.19392 | + | 0.0604693i | ||||
\(476\) | 3.51621i | 0.161165i | ||||||||
\(477\) | 4.71409 | − | 5.23884i | 0.215843 | − | 0.239870i | ||||
\(478\) | −2.28824 | − | 2.28824i | −0.104662 | − | 0.104662i | ||||
\(479\) | −19.7275 | −0.901373 | −0.450686 | − | 0.892682i | \(-0.648821\pi\) | ||||
−0.450686 | + | 0.892682i | \(0.648821\pi\) | |||||||
\(480\) | 0.00400919 | + | 3.87298i | 0.000182994 | + | 0.176777i | ||||
\(481\) | −67.1398 | −3.06131 | ||||||||
\(482\) | 1.76332 | + | 1.76332i | 0.0803171 | + | 0.0803171i | ||||
\(483\) | −0.0340607 | − | 1.29295i | −0.00154981 | − | 0.0588311i | ||||
\(484\) | − | 10.2255i | − | 0.464798i | ||||||
\(485\) | −18.0042 | − | 0.455644i | −0.817530 | − | 0.0206897i | ||||
\(486\) | 12.3746 | + | 9.47991i | 0.561324 | + | 0.430018i | ||||
\(487\) | 5.32308 | − | 5.32308i | 0.241212 | − | 0.241212i | −0.576140 | − | 0.817351i | \(-0.695442\pi\) |
0.817351 | + | 0.576140i | \(0.195442\pi\) | |||||||
\(488\) | 1.06784 | − | 1.06784i | 0.0483389 | − | 0.0483389i | ||||
\(489\) | −5.56758 | − | 5.28177i | −0.251775 | − | 0.238850i | ||||
\(490\) | 14.4010 | + | 0.364454i | 0.650570 | + | 0.0164644i | ||||
\(491\) | − | 6.35205i | − | 0.286664i | −0.989675 | − | 0.143332i | \(-0.954218\pi\) | ||
0.989675 | − | 0.143332i | \(-0.0457817\pi\) | |||||||
\(492\) | 7.32505 | − | 0.192967i | 0.330239 | − | 0.00869964i | ||||
\(493\) | −8.34367 | − | 8.34367i | −0.375780 | − | 0.375780i | ||||
\(494\) | 34.9297 | 1.57156 | ||||||||
\(495\) | −21.2472 | + | 22.4434i | −0.954990 | + | 1.00876i | ||||
\(496\) | −3.91972 | −0.176001 | ||||||||
\(497\) | −5.76529 | − | 5.76529i | −0.258609 | − | 0.258609i | ||||
\(498\) | −23.7109 | + | 0.624629i | −1.06251 | + | 0.0279903i | ||||
\(499\) | − | 26.5555i | − | 1.18879i | −0.804174 | − | 0.594394i | \(-0.797392\pi\) | ||
0.804174 | − | 0.594394i | \(-0.202608\pi\) | |||||||
\(500\) | 7.28341 | + | 8.48245i | 0.325724 | + | 0.379347i | ||||
\(501\) | 10.4964 | + | 9.95758i | 0.468945 | + | 0.444872i | ||||
\(502\) | 3.81349 | − | 3.81349i | 0.170205 | − | 0.170205i | ||||
\(503\) | 20.7736 | − | 20.7736i | 0.926248 | − | 0.926248i | −0.0712128 | − | 0.997461i | \(-0.522687\pi\) |
0.997461 | + | 0.0712128i | \(0.0226869\pi\) | |||||||
\(504\) | 0.117949 | + | 2.23712i | 0.00525386 | + | 0.0996492i | ||||
\(505\) | 12.9491 | − | 12.3099i | 0.576227 | − | 0.547781i | ||||
\(506\) | − | 4.60712i | − | 0.204811i | ||||||
\(507\) | 1.45657 | + | 55.2915i | 0.0646886 | + | 2.45558i | ||||
\(508\) | 11.0353 | + | 11.0353i | 0.489612 | + | 0.489612i | ||||
\(509\) | 3.09578 | 0.137218 | 0.0686090 | − | 0.997644i | \(-0.478144\pi\) | ||||
0.0686090 | + | 0.997644i | \(0.478144\pi\) | |||||||
\(510\) | 12.8820 | − | 12.9087i | 0.570426 | − | 0.571608i | ||||
\(511\) | −5.86877 | −0.259619 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −2.13714 | − | 26.9919i | −0.0943570 | − | 1.19172i | ||||
\(514\) | 0.642960i | 0.0283597i | ||||||||
\(515\) | 0.669896 | − | 26.4702i | 0.0295192 | − | 1.16641i | ||||
\(516\) | 13.1892 | − | 13.9029i | 0.580622 | − | 0.612041i | ||||
\(517\) | 11.1552 | − | 11.1552i | 0.490607 | − | 0.490607i | ||||
\(518\) | −5.28871 | + | 5.28871i | −0.232373 | + | 0.232373i | ||||
\(519\) | −17.0437 | + | 17.9660i | −0.748134 | + | 0.788618i | ||||
\(520\) | 10.3272 | + | 10.8635i | 0.452880 | + | 0.476397i | ||||
\(521\) | − | 7.99544i | − | 0.350287i | −0.984543 | − | 0.175143i | \(-0.943961\pi\) | ||
0.984543 | − | 0.175143i | \(-0.0560389\pi\) | |||||||
\(522\) | −5.58838 | − | 5.02862i | −0.244597 | − | 0.220097i | ||||
\(523\) | −16.4846 | − | 16.4846i | −0.720823 | − | 0.720823i | 0.247950 | − | 0.968773i | \(-0.420243\pi\) |
−0.968773 | + | 0.247950i | \(0.920243\pi\) | |||||||
\(524\) | −9.85239 | −0.430404 | ||||||||
\(525\) | 4.46054 | + | 4.68245i | 0.194674 | + | 0.204359i | ||||
\(526\) | −14.2850 | −0.622853 | ||||||||
\(527\) | 13.0510 | + | 13.0510i | 0.568511 | + | 0.568511i | ||||
\(528\) | 0.210142 | + | 7.97700i | 0.00914525 | + | 0.347154i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −3.61923 | − | 3.80717i | −0.157209 | − | 0.165373i | ||||
\(531\) | −38.1668 | + | 2.01229i | −1.65630 | + | 0.0873258i | ||||
\(532\) | 2.75147 | − | 2.75147i | 0.119291 | − | 0.119291i | ||||
\(533\) | 20.0526 | − | 20.0526i | 0.868576 | − | 0.868576i | ||||
\(534\) | −11.4077 | − | 10.8221i | −0.493658 | − | 0.468317i | ||||
\(535\) | 0.866363 | − | 34.2333i | 0.0374561 | − | 1.48003i | ||||
\(536\) | − | 7.42476i | − | 0.320701i | ||||||
\(537\) | −18.5411 | + | 0.488437i | −0.800108 | + | 0.0210776i | ||||
\(538\) | −16.6133 | − | 16.6133i | −0.716252 | − | 0.716252i | ||||
\(539\) | 29.6808 | 1.27844 | ||||||||
\(540\) | 7.76293 | − | 8.64505i | 0.334063 | − | 0.372024i | ||||
\(541\) | −19.2338 | −0.826927 | −0.413463 | − | 0.910521i | \(-0.635681\pi\) | ||||
−0.413463 | + | 0.910521i | \(0.635681\pi\) | |||||||
\(542\) | −4.35982 | − | 4.35982i | −0.187270 | − | 0.187270i | ||||
\(543\) | 33.4668 | − | 0.881633i | 1.43620 | − | 0.0378345i | ||||
\(544\) | − | 4.70873i | − | 0.201885i | ||||||
\(545\) | 9.41658 | − | 8.95172i | 0.403362 | − | 0.383450i | ||||
\(546\) | 6.28990 | + | 5.96701i | 0.269183 | + | 0.255365i | ||||
\(547\) | −18.7883 | + | 18.7883i | −0.803330 | + | 0.803330i | −0.983615 | − | 0.180284i | \(-0.942298\pi\) |
0.180284 | + | 0.983615i | \(0.442298\pi\) | |||||||
\(548\) | 7.59469 | − | 7.59469i | 0.324429 | − | 0.324429i | ||||
\(549\) | −4.52418 | + | 0.238531i | −0.193087 | + | 0.0101802i | ||||
\(550\) | 15.4439 | + | 17.0917i | 0.658528 | + | 0.728793i | ||||
\(551\) | 13.0580i | 0.556290i | ||||||||
\(552\) | 0.0456124 | + | 1.73145i | 0.00194139 | + | 0.0736954i | ||||
\(553\) | 3.52237 | + | 3.52237i | 0.149786 | + | 0.149786i | ||||
\(554\) | 23.1720 | 0.984482 | ||||||||
\(555\) | 38.7918 | − | 0.0401561i | 1.64662 | − | 0.00170453i | ||||
\(556\) | 14.6607 | 0.621752 | ||||||||
\(557\) | 17.0441 | + | 17.0441i | 0.722182 | + | 0.722182i | 0.969049 | − | 0.246867i | \(-0.0794012\pi\) |
−0.246867 | + | 0.969049i | \(0.579401\pi\) | |||||||
\(558\) | 8.74124 | + | 7.86566i | 0.370046 | + | 0.332980i | ||||
\(559\) | − | 74.1657i | − | 3.13688i | ||||||
\(560\) | 1.66923 | + | 0.0422442i | 0.0705379 | + | 0.00178515i | ||||
\(561\) | 25.8603 | − | 27.2597i | 1.09182 | − | 1.15091i | ||||
\(562\) | −0.243563 | + | 0.243563i | −0.0102741 | + | 0.0102741i | ||||
\(563\) | 3.36582 | − | 3.36582i | 0.141852 | − | 0.141852i | −0.632614 | − | 0.774467i | \(-0.718018\pi\) |
0.774467 | + | 0.632614i | \(0.218018\pi\) | |||||||
\(564\) | −4.08193 | + | 4.30281i | −0.171880 | + | 0.181181i | ||||
\(565\) | 1.97357 | + | 0.0499465i | 0.0830289 | + | 0.00210126i | ||||
\(566\) | − | 2.68608i | − | 0.112905i | ||||||
\(567\) | 4.22617 | − | 5.22561i | 0.177482 | − | 0.219455i | ||||
\(568\) | 7.72060 | + | 7.72060i | 0.323949 | + | 0.323949i | ||||
\(569\) | 34.6119 | 1.45100 | 0.725502 | − | 0.688220i | \(-0.241607\pi\) | ||||
0.725502 | + | 0.688220i | \(0.241607\pi\) | |||||||
\(570\) | −20.1815 | + | 0.0208913i | −0.845312 | + | 0.000875042i | ||||
\(571\) | 10.0717 | 0.421486 | 0.210743 | − | 0.977541i | \(-0.432412\pi\) | ||||
0.210743 | + | 0.977541i | \(0.432412\pi\) | |||||||
\(572\) | 21.8374 | + | 21.8374i | 0.913066 | + | 0.913066i | ||||
\(573\) | 0.744897 | + | 28.2763i | 0.0311185 | + | 1.18126i | ||||
\(574\) | − | 3.15916i | − | 0.131861i | ||||||
\(575\) | 3.35217 | + | 3.70985i | 0.139795 | + | 0.154711i | ||||
\(576\) | −0.157951 | − | 2.99584i | −0.00658130 | − | 0.124827i | ||||
\(577\) | 22.9930 | − | 22.9930i | 0.957209 | − | 0.957209i | −0.0419120 | − | 0.999121i | \(-0.513345\pi\) |
0.999121 | + | 0.0419120i | \(0.0133449\pi\) | |||||||
\(578\) | −3.65725 | + | 3.65725i | −0.152122 | + | 0.152122i | ||||
\(579\) | −7.90753 | − | 7.50160i | −0.328626 | − | 0.311756i | ||||
\(580\) | −4.06119 | + | 3.86071i | −0.168632 | + | 0.160307i | ||||
\(581\) | 10.2261i | 0.424249i | ||||||||
\(582\) | 13.9457 | − | 0.367377i | 0.578066 | − | 0.0152283i | ||||
\(583\) | −7.65301 | − | 7.65301i | −0.316955 | − | 0.316955i | ||||
\(584\) | 7.85918 | 0.325215 | ||||||||
\(585\) | −1.23070 | − | 44.9500i | −0.0508833 | − | 1.85845i | ||||
\(586\) | −0.260905 | −0.0107779 | ||||||||
\(587\) | −27.0582 | − | 27.0582i | −1.11681 | − | 1.11681i | −0.992206 | − | 0.124605i | \(-0.960234\pi\) |
−0.124605 | − | 0.992206i | \(-0.539766\pi\) | |||||||
\(588\) | −11.1547 | + | 0.293852i | −0.460010 | + | 0.0121183i | ||||
\(589\) | − | 20.4251i | − | 0.841601i | ||||||
\(590\) | −0.720716 | + | 28.4782i | −0.0296714 | + | 1.17243i | ||||
\(591\) | −33.7833 | − | 32.0490i | −1.38966 | − | 1.31832i | ||||
\(592\) | 7.08238 | − | 7.08238i | 0.291084 | − | 0.291084i | ||||
\(593\) | −4.06419 | + | 4.06419i | −0.166896 | + | 0.166896i | −0.785614 | − | 0.618717i | \(-0.787653\pi\) |
0.618717 | + | 0.785614i | \(0.287653\pi\) | |||||||
\(594\) | 15.5387 | − | 18.2109i | 0.637562 | − | 0.747203i | ||||
\(595\) | −5.41717 | − | 5.69848i | −0.222082 | − | 0.233615i | ||||
\(596\) | − | 5.81897i | − | 0.238354i | ||||||
\(597\) | −0.896076 | − | 34.0151i | −0.0366740 | − | 1.39215i | ||||
\(598\) | 4.73992 | + | 4.73992i | 0.193830 | + | 0.193830i | ||||
\(599\) | 3.30686 | 0.135115 | 0.0675574 | − | 0.997715i | \(-0.478479\pi\) | ||||
0.0675574 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(600\) | −5.97333 | − | 6.27051i | −0.243860 | − | 0.255993i | ||||
\(601\) | 9.16480 | 0.373840 | 0.186920 | − | 0.982375i | \(-0.440149\pi\) | ||||
0.186920 | + | 0.982375i | \(0.440149\pi\) | |||||||
\(602\) | −5.84215 | − | 5.84215i | −0.238108 | − | 0.238108i | ||||
\(603\) | −14.8992 | + | 16.5577i | −0.606742 | + | 0.674282i | ||||
\(604\) | 2.78052i | 0.113138i | ||||||||
\(605\) | 15.7538 | + | 16.5719i | 0.640483 | + | 0.673743i | ||||
\(606\) | −9.52479 | + | 10.0402i | −0.386918 | + | 0.407855i | ||||
\(607\) | −22.2691 | + | 22.2691i | −0.903875 | + | 0.903875i | −0.995769 | − | 0.0918938i | \(-0.970708\pi\) |
0.0918938 | + | 0.995769i | \(0.470708\pi\) | |||||||
\(608\) | −3.68463 | + | 3.68463i | −0.149431 | + | 0.149431i | ||||
\(609\) | −2.23069 | + | 2.35140i | −0.0903922 | + | 0.0952835i | ||||
\(610\) | −0.0854316 | + | 3.37573i | −0.00345903 | + | 0.136679i | ||||
\(611\) | 22.9536i | 0.928602i | ||||||||
\(612\) | −9.44896 | + | 10.5008i | −0.381952 | + | 0.424469i | ||||
\(613\) | 5.89129 | + | 5.89129i | 0.237947 | + | 0.237947i | 0.816000 | − | 0.578053i | \(-0.196187\pi\) |
−0.578053 | + | 0.816000i | \(0.696187\pi\) | |||||||
\(614\) | −7.22796 | −0.291697 | ||||||||
\(615\) | −11.5739 | + | 11.5979i | −0.466706 | + | 0.467674i | ||||
\(616\) | 3.44033 | 0.138615 | ||||||||
\(617\) | −21.2085 | − | 21.2085i | −0.853823 | − | 0.853823i | 0.136778 | − | 0.990602i | \(-0.456325\pi\) |
−0.990602 | + | 0.136778i | \(0.956325\pi\) | |||||||
\(618\) | 0.540124 | + | 20.5031i | 0.0217270 | + | 0.824758i | ||||
\(619\) | 6.49659i | 0.261120i | 0.991440 | + | 0.130560i | \(0.0416775\pi\) | ||||
−0.991440 | + | 0.130560i | \(0.958322\pi\) | |||||||
\(620\) | 6.35244 | − | 6.03884i | 0.255120 | − | 0.242526i | ||||
\(621\) | 3.37276 | − | 3.95278i | 0.135344 | − | 0.158620i | ||||
\(622\) | 9.43458 | − | 9.43458i | 0.378292 | − | 0.378292i | ||||
\(623\) | −4.79363 | + | 4.79363i | −0.192053 | + | 0.192053i | ||||
\(624\) | −8.42313 | − | 7.99073i | −0.337195 | − | 0.319885i | ||||
\(625\) | −24.8721 | − | 2.52590i | −0.994883 | − | 0.101036i | ||||
\(626\) | 8.31450i | 0.332314i | ||||||||
\(627\) | −41.5670 | + | 1.09502i | −1.66002 | + | 0.0437308i | ||||
\(628\) | −6.33516 | − | 6.33516i | −0.252800 | − | 0.252800i | ||||
\(629\) | −47.1626 | −1.88050 | ||||||||
\(630\) | −3.63772 | − | 3.44384i | −0.144930 | − | 0.137206i | ||||
\(631\) | −18.5689 | −0.739217 | −0.369609 | − | 0.929188i | \(-0.620508\pi\) | ||||
−0.369609 | + | 0.929188i | \(0.620508\pi\) | |||||||
\(632\) | −4.71698 | − | 4.71698i | −0.187631 | − | 0.187631i | ||||
\(633\) | −7.58526 | + | 0.199822i | −0.301487 | + | 0.00794222i | ||||
\(634\) | 21.3218i | 0.846797i | ||||||||
\(635\) | −34.8855 | − | 0.882869i | −1.38439 | − | 0.0350356i | ||||
\(636\) | 2.95192 | + | 2.80039i | 0.117051 | + | 0.111043i | ||||
\(637\) | −30.5363 | + | 30.5363i | −1.20989 | + | 1.20989i | ||||
\(638\) | −8.16362 | + | 8.16362i | −0.323201 | + | 0.323201i | ||||
\(639\) | −1.72460 | − | 32.7103i | −0.0682242 | − | 1.29400i | ||||
\(640\) | −2.23535 | − | 0.0565714i | −0.0883601 | − | 0.00223618i | ||||
\(641\) | − | 21.0110i | − | 0.829884i | −0.909848 | − | 0.414942i | \(-0.863802\pi\) | ||
0.909848 | − | 0.414942i | \(-0.136198\pi\) | |||||||
\(642\) | 0.698531 | + | 26.5163i | 0.0275688 | + | 1.04651i | ||||
\(643\) | −23.8932 | − | 23.8932i | −0.942254 | − | 0.942254i | 0.0561671 | − | 0.998421i | \(-0.482112\pi\) |
−0.998421 | + | 0.0561671i | \(0.982112\pi\) | |||||||
\(644\) | 0.746742 | 0.0294257 | ||||||||
\(645\) | 0.0443583 | + | 42.8512i | 0.00174661 | + | 1.68726i | ||||
\(646\) | 24.5365 | 0.965376 | ||||||||
\(647\) | 1.33655 | + | 1.33655i | 0.0525450 | + | 0.0525450i | 0.732891 | − | 0.680346i | \(-0.238170\pi\) |
−0.680346 | + | 0.732891i | \(0.738170\pi\) | |||||||
\(648\) | −5.65948 | + | 6.99788i | −0.222325 | + | 0.274903i | ||||
\(649\) | 58.6944i | 2.30396i | ||||||||
\(650\) | −33.4734 | − | 1.69535i | −1.31293 | − | 0.0664970i | ||||
\(651\) | 3.48920 | − | 3.67801i | 0.136753 | − | 0.144153i | ||||
\(652\) | 3.13303 | − | 3.13303i | 0.122699 | − | 0.122699i | ||||
\(653\) | −27.6886 | + | 27.6886i | −1.08354 | + | 1.08354i | −0.0873627 | + | 0.996177i | \(0.527844\pi\) |
−0.996177 | + | 0.0873627i | \(0.972156\pi\) | |||||||
\(654\) | −6.92642 | + | 7.30122i | −0.270844 | + | 0.285500i | ||||
\(655\) | 15.9671 | − | 15.1789i | 0.623887 | − | 0.593088i | ||||
\(656\) | 4.23059i | 0.165177i | ||||||||
\(657\) | −17.5265 | − | 15.7709i | −0.683773 | − | 0.615282i | ||||
\(658\) | 1.80809 | + | 1.80809i | 0.0704867 | + | 0.0704867i | ||||
\(659\) | 26.7954 | 1.04380 | 0.521901 | − | 0.853006i | \(-0.325223\pi\) | ||||
0.521901 | + | 0.853006i | \(0.325223\pi\) | |||||||
\(660\) | −12.6302 | − | 12.6040i | −0.491629 | − | 0.490612i | ||||
\(661\) | 19.6886 | 0.765797 | 0.382899 | − | 0.923790i | \(-0.374926\pi\) | ||||
0.382899 | + | 0.923790i | \(0.374926\pi\) | |||||||
\(662\) | 13.2505 | + | 13.2505i | 0.514996 | + | 0.514996i | ||||
\(663\) | 1.43970 | + | 54.6512i | 0.0559134 | + | 2.12248i | ||||
\(664\) | − | 13.6943i | − | 0.531441i | ||||||
\(665\) | −0.220129 | + | 8.69812i | −0.00853622 | + | 0.337299i | ||||
\(666\) | −30.0063 | + | 1.58204i | −1.16272 | + | 0.0613028i | ||||
\(667\) | −1.77196 | + | 1.77196i | −0.0686105 | + | 0.0686105i | ||||
\(668\) | −5.90660 | + | 5.90660i | −0.228533 | + | 0.228533i | ||||
\(669\) | 14.6285 | + | 13.8776i | 0.565571 | + | 0.536537i | ||||
\(670\) | 11.4388 | + | 12.0328i | 0.441920 | + | 0.464869i | ||||
\(671\) | 6.95746i | 0.268590i | ||||||||
\(672\) | −1.29295 | + | 0.0340607i | −0.0498765 | + | 0.00131392i | ||||
\(673\) | −10.7591 | − | 10.7591i | −0.414733 | − | 0.414733i | 0.468651 | − | 0.883384i | \(-0.344740\pi\) |
−0.883384 | + | 0.468651i | \(0.844740\pi\) | |||||||
\(674\) | 16.3742 | 0.630712 | ||||||||
\(675\) | 0.737955 | + | 25.9703i | 0.0284039 | + | 0.999597i | ||||
\(676\) | −31.9337 | −1.22822 | ||||||||
\(677\) | −21.0042 | − | 21.0042i | −0.807257 | − | 0.807257i | 0.176961 | − | 0.984218i | \(-0.443373\pi\) |
−0.984218 | + | 0.176961i | \(0.943373\pi\) | |||||||
\(678\) | −1.52868 | + | 0.0402708i | −0.0587087 | + | 0.00154659i | ||||
\(679\) | − | 6.01450i | − | 0.230815i | ||||||
\(680\) | 7.25441 | + | 7.63113i | 0.278194 | + | 0.292641i | ||||
\(681\) | −7.86275 | − | 7.45912i | −0.301301 | − | 0.285834i | ||||
\(682\) | 12.7694 | − | 12.7694i | 0.488965 | − | 0.488965i | ||||
\(683\) | 21.6555 | − | 21.6555i | 0.828624 | − | 0.828624i | −0.158702 | − | 0.987326i | \(-0.550731\pi\) |
0.987326 | + | 0.158702i | \(0.0507310\pi\) | |||||||
\(684\) | 15.6109 | − | 0.823061i | 0.596897 | − | 0.0314705i | ||||
\(685\) | −0.607606 | + | 24.0088i | −0.0232154 | + | 0.917330i | ||||
\(686\) | 10.0380i | 0.383252i | ||||||||
\(687\) | −0.0246089 | − | 0.934154i | −0.000938886 | − | 0.0356402i | ||||
\(688\) | 7.82352 | + | 7.82352i | 0.298269 | + | 0.298269i | ||||
\(689\) | 15.7472 | 0.599921 | ||||||||
\(690\) | −2.74145 | − | 2.73578i | −0.104365 | − | 0.104149i | ||||
\(691\) | −10.1870 | −0.387532 | −0.193766 | − | 0.981048i | \(-0.562070\pi\) | ||||
−0.193766 | + | 0.981048i | \(0.562070\pi\) | |||||||
\(692\) | −10.1099 | − | 10.1099i | −0.384321 | − | 0.384321i | ||||
\(693\) | −7.67216 | − | 6.90367i | −0.291441 | − | 0.262249i | ||||
\(694\) | 13.4861i | 0.511924i | ||||||||
\(695\) | −23.7596 | + | 22.5867i | −0.901255 | + | 0.856763i | ||||
\(696\) | 2.98723 | − | 3.14888i | 0.113231 | − | 0.119358i | ||||
\(697\) | 14.0861 | − | 14.0861i | 0.533548 | − | 0.533548i | ||||
\(698\) | −16.0564 | + | 16.0564i | −0.607743 | + | 0.607743i | ||||
\(699\) | 8.45769 | − | 8.91536i | 0.319899 | − | 0.337210i | ||||
\(700\) | −2.77030 | + | 2.50321i | −0.104707 | + | 0.0946123i | ||||
\(701\) | − | 8.07940i | − | 0.305155i | −0.988292 | − | 0.152577i | \(-0.951243\pi\) | ||
0.988292 | − | 0.152577i | \(-0.0487573\pi\) | |||||||
\(702\) | 2.74922 | + | 34.7225i | 0.103763 | + | 1.31052i | ||||
\(703\) | 36.9053 | + | 36.9053i | 1.39191 | + | 1.39191i | ||||
\(704\) | −4.60712 | −0.173637 | ||||||||
\(705\) | −0.0137285 | − | 13.2620i | −0.000517044 | − | 0.499477i | ||||
\(706\) | 28.5784 | 1.07556 | ||||||||
\(707\) | 4.21900 | + | 4.21900i | 0.158672 | + | 0.158672i | ||||
\(708\) | −0.581099 | − | 22.0585i | −0.0218390 | − | 0.829011i | ||||
\(709\) | − | 3.66459i | − | 0.137627i | −0.997630 | − | 0.0688133i | \(-0.978079\pi\) | ||
0.997630 | − | 0.0688133i | \(-0.0219213\pi\) | |||||||
\(710\) | −24.4069 | − | 0.617680i | −0.915973 | − | 0.0231811i | ||||
\(711\) | 1.05366 | + | 19.9847i | 0.0395155 | + | 0.749485i | ||||
\(712\) | 6.41940 | − | 6.41940i | 0.240577 | − | 0.240577i | ||||
\(713\) | 2.77166 | − | 2.77166i | 0.103800 | − | 0.103800i | ||||
\(714\) | 4.41837 | + | 4.19155i | 0.165353 | + | 0.156865i | ||||
\(715\) | −69.0337 | − | 1.74708i | −2.58172 | − | 0.0653370i | ||||
\(716\) | − | 10.7084i | − | 0.400193i | ||||||
\(717\) | −5.60308 | + | 0.147605i | −0.209251 | + | 0.00551240i | ||||
\(718\) | 6.75511 | + | 6.75511i | 0.252098 | + | 0.252098i | ||||
\(719\) | 2.43829 | 0.0909327 | 0.0454664 | − | 0.998966i | \(-0.485523\pi\) | ||||
0.0454664 | + | 0.998966i | \(0.485523\pi\) | |||||||
\(720\) | 4.87146 | + | 4.61182i | 0.181549 | + | 0.171872i | ||||
\(721\) | 8.84262 | 0.329316 | ||||||||
\(722\) | −5.76504 | − | 5.76504i | −0.214553 | − | 0.214553i | ||||
\(723\) | 4.31774 | − | 0.113744i | 0.160579 | − | 0.00423020i | ||||
\(724\) | 19.3288i | 0.718349i | ||||||||
\(725\) | 0.633784 | − | 12.5136i | 0.0235382 | − | 0.464743i | ||||
\(726\) | −12.8491 | − | 12.1895i | −0.476877 | − | 0.452396i | ||||
\(727\) | 20.2113 | − | 20.2113i | 0.749597 | − | 0.749597i | −0.224807 | − | 0.974403i | \(-0.572175\pi\) |
0.974403 | + | 0.224807i | \(0.0721751\pi\) | |||||||
\(728\) | −3.53949 | + | 3.53949i | −0.131182 | + | 0.131182i | ||||
\(729\) | 26.6636 | − | 4.24892i | 0.987540 | − | 0.157367i | ||||
\(730\) | −12.7369 | + | 12.1081i | −0.471412 | + | 0.448140i | ||||
\(731\) | − | 52.0980i | − | 1.92691i | ||||||
\(732\) | −0.0688818 | − | 2.61476i | −0.00254594 | − | 0.0966442i | ||||
\(733\) | −27.8025 | − | 27.8025i | −1.02691 | − | 1.02691i | −0.999628 | − | 0.0272828i | \(-0.991315\pi\) |
−0.0272828 | − | 0.999628i | \(-0.508685\pi\) | |||||||
\(734\) | −22.4771 | −0.829645 | ||||||||
\(735\) | 17.6249 | − | 17.6614i | 0.650104 | − | 0.651452i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 24.1878 | + | 24.1878i | 0.890970 | + | 0.890970i | ||||
\(738\) | 8.48948 | − | 9.43449i | 0.312502 | − | 0.347288i | ||||
\(739\) | − | 4.34293i | − | 0.159757i | −0.996805 | − | 0.0798786i | \(-0.974547\pi\) | ||
0.996805 | − | 0.0798786i | \(-0.0254533\pi\) | |||||||
\(740\) | −0.566619 | + | 22.3893i | −0.0208293 | + | 0.823047i | ||||
\(741\) | 41.6385 | − | 43.8917i | 1.52963 | − | 1.61240i | ||||
\(742\) | 1.24043 | − | 1.24043i | 0.0455377 | − | 0.0455377i | ||||
\(743\) | −23.1858 | + | 23.1858i | −0.850606 | + | 0.850606i | −0.990208 | − | 0.139601i | \(-0.955418\pi\) |
0.139601 | + | 0.990208i | \(0.455418\pi\) | |||||||
\(744\) | −4.67257 | + | 4.92542i | −0.171305 | + | 0.180575i | ||||
\(745\) | 8.96488 | + | 9.43042i | 0.328448 | + | 0.345504i | ||||
\(746\) | 30.9879i | 1.13455i | ||||||||
\(747\) | −27.4801 | + | 30.5391i | −1.00545 | + | 1.11737i | ||||
\(748\) | 15.3397 | + | 15.3397i | 0.560877 | + | 0.560877i | ||||
\(749\) | 11.4360 | 0.417861 | ||||||||
\(750\) | 19.3411 | + | 0.959511i | 0.706238 | + | 0.0350364i | ||||
\(751\) | 4.73251 | 0.172692 | 0.0863459 | − | 0.996265i | \(-0.472481\pi\) | ||||
0.0863459 | + | 0.996265i | \(0.472481\pi\) | |||||||
\(752\) | −2.42130 | − | 2.42130i | −0.0882959 | − | 0.0882959i | ||||
\(753\) | −0.245992 | − | 9.33787i | −0.00896445 | − | 0.340291i | ||||
\(754\) | − | 16.7979i | − | 0.611742i | ||||||
\(755\) | −4.28376 | − | 4.50621i | −0.155902 | − | 0.163998i | ||||
\(756\) | 2.95170 | + | 2.51858i | 0.107352 | + | 0.0916000i | ||||
\(757\) | 5.16180 | − | 5.16180i | 0.187609 | − | 0.187609i | −0.607053 | − | 0.794662i | \(-0.707648\pi\) |
0.794662 | + | 0.607053i | \(0.207648\pi\) | |||||||
\(758\) | 2.13019 | − | 2.13019i | 0.0773719 | − | 0.0773719i | ||||
\(759\) | −5.78918 | − | 5.49200i | −0.210134 | − | 0.199347i | ||||
\(760\) | 0.294785 | − | 11.6481i | 0.0106930 | − | 0.422521i | ||||
\(761\) | − | 17.2128i | − | 0.623963i | −0.950088 | − | 0.311982i | \(-0.899007\pi\) | ||
0.950088 | − | 0.311982i | \(-0.100993\pi\) | |||||||
\(762\) | 27.0215 | − | 0.711839i | 0.978885 | − | 0.0257872i | ||||
\(763\) | 3.06806 | + | 3.06806i | 0.111071 | + | 0.111071i | ||||
\(764\) | −16.3310 | −0.590835 | ||||||||
\(765\) | −0.864512 | − | 31.5753i | −0.0312565 | − | 1.14161i | ||||
\(766\) | 25.0862 | 0.906400 | ||||||||
\(767\) | −60.3862 | − | 60.3862i | −2.18042 | − | 2.18042i | ||||
\(768\) | 1.73145 | − | 0.0456124i | 0.0624783 | − | 0.00164590i | ||||
\(769\) | − | 41.6311i | − | 1.50126i | −0.660725 | − | 0.750628i | \(-0.729751\pi\) | ||
0.660725 | − | 0.750628i | \(-0.270249\pi\) | |||||||
\(770\) | −5.57552 | + | 5.30028i | −0.200928 | + | 0.191009i | ||||
\(771\) | 0.807926 | + | 0.766451i | 0.0290967 | + | 0.0276031i | ||||
\(772\) | 4.44978 | − | 4.44978i | 0.160151 | − | 0.160151i | ||||
\(773\) | −19.8333 | + | 19.8333i | −0.713355 | + | 0.713355i | −0.967235 | − | 0.253881i | \(-0.918293\pi\) |
0.253881 | + | 0.967235i | \(0.418293\pi\) | |||||||
\(774\) | −1.74759 | − | 33.1464i | −0.0628159 | − | 1.19142i | ||||
\(775\) | −0.991353 | + | 19.5735i | −0.0356104 | + | 0.703102i | ||||
\(776\) | 8.05432i | 0.289133i | ||||||||
\(777\) | 0.341152 | + | 12.9501i | 0.0122388 | + | 0.464584i | ||||
\(778\) | 14.1902 | + | 14.1902i | 0.508742 | + | 0.508742i | ||||
\(779\) | −22.0450 | −0.789843 | ||||||||
\(780\) | 25.9616 | − | 0.0268747i | 0.929574 | − | 0.000962267i | ||||
\(781\) | −50.3032 | −1.79999 | ||||||||
\(782\) | 3.32957 | + | 3.32957i | 0.119065 | + | 0.119065i | ||||
\(783\) | −12.9806 | + | 1.02776i | −0.463887 | + | 0.0367292i | ||||
\(784\) | − | 6.44238i | − | 0.230085i | ||||||
\(785\) | 20.0271 | + | 0.506838i | 0.714798 | + | 0.0180898i | ||||
\(786\) | −11.7447 | + | 12.3802i | −0.418920 | + | 0.441589i | ||||
\(787\) | 9.89797 | − | 9.89797i | 0.352824 | − | 0.352824i | −0.508335 | − | 0.861159i | \(-0.669739\pi\) |
0.861159 | + | 0.508335i | \(0.169739\pi\) | |||||||
\(788\) | 19.0107 | − | 19.0107i | 0.677230 | − | 0.677230i | ||||
\(789\) | −17.0286 | + | 17.9501i | −0.606235 | + | 0.639040i | ||||
\(790\) | 14.9116 | + | 0.377378i | 0.530532 | + | 0.0134265i | ||||
\(791\) | 0.659292i | 0.0234417i | ||||||||
\(792\) | 10.2742 | + | 9.24506i | 0.365077 | + | 0.328509i | ||||
\(793\) | −7.15801 | − | 7.15801i | −0.254188 | − | 0.254188i | ||||
\(794\) | 36.9217 | 1.31030 | ||||||||
\(795\) | −9.09836 | + | 0.00941835i | −0.322685 | + | 0.000334034i | ||||
\(796\) | 19.6455 | 0.696315 | ||||||||
\(797\) | 20.9341 | + | 20.9341i | 0.741522 | + | 0.741522i | 0.972871 | − | 0.231349i | \(-0.0743138\pi\) |
−0.231349 | + | 0.972871i | \(0.574314\pi\) | |||||||
\(798\) | −0.177485 | − | 6.73735i | −0.00628291 | − | 0.238500i | ||||
\(799\) | 16.1238i | 0.570420i | ||||||||
\(800\) | 3.70985 | − | 3.35217i | 0.131163 | − | 0.118517i | ||||
\(801\) | −27.1974 | + | 1.43394i | −0.960974 | + | 0.0506659i | ||||
\(802\) | −15.5498 | + | 15.5498i | −0.549082 | + | 0.549082i | ||||
\(803\) | −25.6030 | + | 25.6030i | −0.903512 | + | 0.903512i | ||||
\(804\) | −9.32975 | − | 8.85081i | −0.329035 | − | 0.312144i | ||||
\(805\) | −1.21020 | + | 1.15045i | −0.0426538 | + | 0.0405481i | ||||
\(806\) | 26.2749i | 0.925494i | ||||||||
\(807\) | −40.6801 | + | 1.07166i | −1.43201 | + | 0.0377241i | ||||
\(808\) | −5.64988 | − | 5.64988i | −0.198762 | − | 0.198762i | ||||
\(809\) | 1.00481 | 0.0353272 | 0.0176636 | − | 0.999844i | \(-0.494377\pi\) | ||||
0.0176636 | + | 0.999844i | \(0.494377\pi\) | |||||||
\(810\) | −1.60920 | − | 20.0602i | −0.0565416 | − | 0.704843i | ||||
\(811\) | 47.6896 | 1.67461 | 0.837305 | − | 0.546736i | \(-0.184130\pi\) | ||||
0.837305 | + | 0.546736i | \(0.184130\pi\) | |||||||
\(812\) | −1.32319 | − | 1.32319i | −0.0464350 | − | 0.0464350i | ||||
\(813\) | −10.6756 | + | 0.281233i | −0.374411 | + | 0.00986328i | ||||
\(814\) | 46.1449i | 1.61738i | ||||||||
\(815\) | −0.250655 | + | 9.90433i | −0.00878006 | + | 0.346933i | ||||
\(816\) | −5.91686 | − | 5.61312i | −0.207132 | − | 0.196499i | ||||
\(817\) | −40.7672 | + | 40.7672i | −1.42627 | + | 1.42627i | ||||
\(818\) | −27.0169 | + | 27.0169i | −0.944622 | + | 0.944622i | ||||
\(819\) | 14.9960 | − | 0.790641i | 0.524002 | − | 0.0276272i | ||||
\(820\) | −6.51777 | − | 6.85624i | −0.227611 | − | 0.239430i | ||||
\(821\) | 22.9888i | 0.802315i | 0.916009 | + | 0.401157i | \(0.131392\pi\) | ||||
−0.916009 | + | 0.401157i | \(0.868608\pi\) | |||||||
\(822\) | −0.489901 | − | 18.5967i | −0.0170873 | − | 0.648633i | ||||
\(823\) | 23.9384 | + | 23.9384i | 0.834442 | + | 0.834442i | 0.988121 | − | 0.153679i | \(-0.0491122\pi\) |
−0.153679 | + | 0.988121i | \(0.549112\pi\) | |||||||
\(824\) | −11.8416 | −0.412522 | ||||||||
\(825\) | 39.8871 | + | 0.968131i | 1.38869 | + | 0.0337060i | ||||
\(826\) | −9.51343 | −0.331015 | ||||||||
\(827\) | 12.6490 | + | 12.6490i | 0.439849 | + | 0.439849i | 0.891961 | − | 0.452112i | \(-0.149329\pi\) |
−0.452112 | + | 0.891961i | \(0.649329\pi\) | |||||||
\(828\) | 2.23007 | + | 2.00669i | 0.0775002 | + | 0.0697373i | ||||
\(829\) | − | 36.2001i | − | 1.25728i | −0.777696 | − | 0.628641i | \(-0.783612\pi\) | ||
0.777696 | − | 0.628641i | \(-0.216388\pi\) | |||||||
\(830\) | 21.0978 | + | 22.1934i | 0.732316 | + | 0.770344i | ||||
\(831\) | 27.6225 | − | 29.1173i | 0.958215 | − | 1.01007i | ||||
\(832\) | 4.73992 | − | 4.73992i | 0.164327 | − | 0.164327i | ||||
\(833\) | −21.4504 | + | 21.4504i | −0.743211 | + | 0.743211i | ||||
\(834\) | 17.4765 | − | 18.4222i | 0.605163 | − | 0.637910i | ||||
\(835\) | 0.472552 | − | 18.6723i | 0.0163534 | − | 0.646183i | ||||
\(836\) | − | 24.0070i | − | 0.830300i | ||||||
\(837\) | 20.3039 | − | 1.60760i | 0.701806 | − | 0.0555669i | ||||
\(838\) | −6.46912 | − | 6.46912i | −0.223472 | − | 0.223472i | ||||
\(839\) | −40.1271 | −1.38534 | −0.692671 | − | 0.721254i | \(-0.743566\pi\) | ||||
−0.692671 | + | 0.721254i | \(0.743566\pi\) | |||||||
\(840\) | 2.04292 | − | 2.04715i | 0.0704874 | − | 0.0706335i | ||||
\(841\) | −22.7203 | −0.783460 | ||||||||
\(842\) | −20.1023 | − | 20.1023i | −0.692772 | − | 0.692772i | ||||
\(843\) | 0.0157112 | + | 0.596399i | 0.000541123 | + | 0.0205411i | ||||
\(844\) | − | 4.38087i | − | 0.150796i | ||||||
\(845\) | 51.7528 | − | 49.1980i | 1.78035 | − | 1.69246i | ||||
\(846\) | 0.540863 | + | 10.2585i | 0.0185953 | + | 0.352694i | ||||
\(847\) | −5.39936 | + | 5.39936i | −0.185524 | + | 0.185524i | ||||
\(848\) | −1.66113 | + | 1.66113i | −0.0570433 | + | 0.0570433i | ||||
\(849\) | −3.37526 | − | 3.20199i | −0.115839 | − | 0.109892i | ||||
\(850\) | −23.5135 | − | 1.19090i | −0.806507 | − | 0.0408477i | ||||
\(851\) | 10.0160i | 0.343344i | ||||||||
\(852\) | 18.9050 | − | 0.498023i | 0.647674 | − | 0.0170620i | ||||
\(853\) | −32.6791 | − | 32.6791i | −1.11891 | − | 1.11891i | −0.991901 | − | 0.127011i | \(-0.959461\pi\) |
−0.127011 | − | 0.991901i | \(-0.540539\pi\) | |||||||
\(854\) | −1.12770 | −0.0385890 | ||||||||
\(855\) | −24.0315 | + | 25.3845i | −0.821860 | + | 0.868131i | ||||
\(856\) | −15.3145 | −0.523439 | ||||||||
\(857\) | 38.3689 | + | 38.3689i | 1.31066 | + | 1.31066i | 0.920931 | + | 0.389725i | \(0.127430\pi\) |
0.389725 | + | 0.920931i | \(0.372570\pi\) | |||||||
\(858\) | 53.4719 | − | 1.40863i | 1.82550 | − | 0.0480900i | ||||
\(859\) | − | 27.0975i | − | 0.924554i | −0.886736 | − | 0.462277i | \(-0.847033\pi\) | ||
0.886736 | − | 0.462277i | \(-0.152967\pi\) | |||||||
\(860\) | −24.7322 | − | 0.625914i | −0.843362 | − | 0.0213435i | ||||
\(861\) | −3.96971 | − | 3.76593i | −0.135287 | − | 0.128342i | ||||
\(862\) | −7.86571 | + | 7.86571i | −0.267907 | + | 0.267907i | ||||
\(863\) | 18.8147 | − | 18.8147i | 0.640459 | − | 0.640459i | −0.310209 | − | 0.950668i | \(-0.600399\pi\) |
0.950668 | + | 0.310209i | \(0.100399\pi\) | |||||||
\(864\) | −3.95278 | − | 3.37276i | −0.134476 | − | 0.114744i | ||||
\(865\) | 31.9601 | + | 0.808834i | 1.08668 | + | 0.0275012i | ||||
\(866\) | − | 28.3370i | − | 0.962929i | ||||||
\(867\) | 0.235914 | + | 8.95530i | 0.00801205 | + | 0.304138i | ||||
\(868\) | 2.06972 | + | 2.06972i | 0.0702507 | + | 0.0702507i | ||||
\(869\) | 30.7333 | 1.04255 | ||||||||
\(870\) | 0.0100467 | + | 9.70541i | 0.000340617 | + | 0.329044i | ||||
\(871\) | −49.7701 | −1.68639 | ||||||||
\(872\) | −4.10859 | − | 4.10859i | −0.139134 | − | 0.139134i | ||||
\(873\) | 16.1625 | − | 17.9617i | 0.547018 | − | 0.607910i | ||||
\(874\) | − | 5.21085i | − | 0.176260i | ||||||
\(875\) | 0.633123 | − | 8.32479i | 0.0214035 | − | 0.281429i | ||||
\(876\) | 9.36867 | − | 9.87563i | 0.316538 | − | 0.333667i | ||||
\(877\) | 5.03549 | − | 5.03549i | 0.170037 | − | 0.170037i | −0.616959 | − | 0.786995i | \(-0.711636\pi\) |
0.786995 | + | 0.616959i | \(0.211636\pi\) | |||||||
\(878\) | 9.75821 | − | 9.75821i | 0.329324 | − | 0.329324i | ||||
\(879\) | −0.311016 | + | 0.327846i | −0.0104903 | + | 0.0110580i | ||||
\(880\) | 7.46646 | − | 7.09787i | 0.251694 | − | 0.239269i | ||||
\(881\) | − | 32.0410i | − | 1.07949i | −0.841829 | − | 0.539744i | \(-0.818521\pi\) | ||
0.841829 | − | 0.539744i | \(-0.181479\pi\) | |||||||
\(882\) | −12.9279 | + | 14.3669i | −0.435303 | + | 0.483760i | ||||
\(883\) | 20.5528 | + | 20.5528i | 0.691656 | + | 0.691656i | 0.962596 | − | 0.270940i | \(-0.0873346\pi\) |
−0.270940 | + | 0.962596i | \(0.587335\pi\) | |||||||
\(884\) | −31.5638 | −1.06161 | ||||||||
\(885\) | 34.9258 | + | 34.8536i | 1.17402 | + | 1.17159i | ||||
\(886\) | −5.77413 | −0.193986 | ||||||||
\(887\) | 3.65344 | + | 3.65344i | 0.122671 | + | 0.122671i | 0.765777 | − | 0.643106i | \(-0.222355\pi\) |
−0.643106 | + | 0.765777i | \(0.722355\pi\) | |||||||
\(888\) | −0.456854 | − | 17.3422i | −0.0153310 | − | 0.581966i | ||||
\(889\) | − | 11.6539i | − | 0.390858i | ||||||
\(890\) | −0.513578 | + | 20.2934i | −0.0172152 | + | 0.680237i | ||||
\(891\) | −4.36014 | − | 41.2342i | −0.146070 | − | 1.38140i | ||||
\(892\) | −8.23185 | + | 8.23185i | −0.275623 | + | 0.275623i | ||||
\(893\) | 12.6171 | − | 12.6171i | 0.422214 | − | 0.422214i | ||||
\(894\) | −7.31196 | − | 6.93660i | −0.244548 | − | 0.231995i | ||||
\(895\) | 16.4977 | + | 17.3545i | 0.551459 | + | 0.580096i | ||||
\(896\) | − | 0.746742i | − | 0.0249469i | ||||||
\(897\) | 11.6064 | − | 0.305752i | 0.387525 | − | 0.0102088i | ||||
\(898\) | 4.10438 | + | 4.10438i | 0.136965 | + | 0.136965i | ||||
\(899\) | −9.82253 | −0.327600 | ||||||||
\(900\) | −15.0000 | + | 0.0310551i | −0.499999 | + | 0.00103517i | ||||
\(901\) | 11.0617 | 0.368518 | ||||||||
\(902\) | −13.7821 | − | 13.7821i | −0.458894 | − | 0.458894i | ||||
\(903\) | −14.3053 | + | 0.376852i | −0.476051 | + | 0.0125408i | ||||
\(904\) | − | 0.882892i | − | 0.0293645i | ||||||
\(905\) | −29.7785 | − | 31.3249i | −0.989872 | − | 1.04128i | ||||
\(906\) | 3.49393 | + | 3.31457i | 0.116078 | + | 0.110119i | ||||
\(907\) | 15.6822 | − | 15.6822i | 0.520720 | − | 0.520720i | −0.397069 | − | 0.917789i | \(-0.629972\pi\) |
0.917789 | + | 0.397069i | \(0.129972\pi\) | |||||||
\(908\) | 4.42457 | − | 4.42457i | 0.146835 | − | 0.146835i | ||||
\(909\) | 1.26205 | + | 23.9372i | 0.0418596 | + | 0.793946i | ||||
\(910\) | 0.283174 | − | 11.1893i | 0.00938713 | − | 0.370921i | ||||
\(911\) | − | 17.1132i | − | 0.566984i | −0.958975 | − | 0.283492i | \(-0.908507\pi\) | ||
0.958975 | − | 0.283492i | \(-0.0914930\pi\) | |||||||
\(912\) | 0.237680 | + | 9.02233i | 0.00787036 | + | 0.298759i | ||||
\(913\) | 44.6122 | + | 44.6122i | 1.47645 | + | 1.47645i | ||||
\(914\) | −4.30896 | −0.142528 | ||||||||
\(915\) | 4.14001 | + | 4.13145i | 0.136864 | + | 0.136581i | ||||
\(916\) | 0.539521 | 0.0178263 | ||||||||
\(917\) | 5.20232 | + | 5.20232i | 0.171796 | + | 0.171796i | ||||
\(918\) | 1.93120 | + | 24.3909i | 0.0637391 | + | 0.805021i | ||||
\(919\) | 38.6421i | 1.27469i | 0.770580 | + | 0.637343i | \(0.219967\pi\) | ||||
−0.770580 | + | 0.637343i | \(0.780033\pi\) | |||||||
\(920\) | 1.62063 | − | 1.54063i | 0.0534307 | − | 0.0507931i | ||||
\(921\) | −8.61622 | + | 9.08246i | −0.283914 | + | 0.299277i | ||||
\(922\) | 7.66859 | − | 7.66859i | 0.252551 | − | 0.252551i | ||||
\(923\) | 51.7532 | − | 51.7532i | 1.70348 | − | 1.70348i | ||||
\(924\) | 4.10110 | − | 4.32302i | 0.134916 | − | 0.142217i | ||||
\(925\) | −33.5753 | − | 37.1578i | −1.10395 | − | 1.22174i | ||||
\(926\) | − | 1.36613i | − | 0.0448939i | ||||||
\(927\) | 26.4076 | + | 23.7624i | 0.867338 | + | 0.780460i | ||||
\(928\) | 1.77196 | + | 1.77196i | 0.0581674 | + | 0.0581674i | ||||
\(929\) | 4.79606 | 0.157354 | 0.0786768 | − | 0.996900i | \(-0.474930\pi\) | ||||
0.0786768 | + | 0.996900i | \(0.474930\pi\) | |||||||
\(930\) | −0.0157149 | − | 15.1810i | −0.000515313 | − | 0.497805i | ||||
\(931\) | 33.5703 | 1.10022 | ||||||||
\(932\) | 5.01691 | + | 5.01691i | 0.164334 | + | 0.164334i | ||||
\(933\) | −0.608584 | − | 23.1019i | −0.0199241 | − | 0.756322i | ||||
\(934\) | 7.04073i | 0.230380i | ||||||||
\(935\) | −48.4930 | − | 1.22724i | −1.58589 | − | 0.0401351i | ||||
\(936\) | −20.0819 | + | 1.05879i | −0.656397 | + | 0.0346076i | ||||
\(937\) | 9.71119 | − | 9.71119i | 0.317251 | − | 0.317251i | −0.530460 | − | 0.847710i | \(-0.677981\pi\) |
0.847710 | + | 0.530460i | \(0.177981\pi\) | |||||||
\(938\) | −3.92047 | + | 3.92047i | −0.128008 | + | 0.128008i | ||||
\(939\) | 10.4478 | + | 9.91144i | 0.340950 | + | 0.323448i | ||||
\(940\) | 7.65439 | + | 0.193714i | 0.249659 | + | 0.00631826i | ||||
\(941\) | − | 6.87914i | − | 0.224254i | −0.993694 | − | 0.112127i | \(-0.964234\pi\) | ||
0.993694 | − | 0.112127i | \(-0.0357663\pi\) | |||||||
\(942\) | −15.5125 | + | 0.408654i | −0.505425 | + | 0.0133147i | ||||
\(943\) | −2.99148 | − | 2.99148i | −0.0974159 | − | 0.0974159i | ||||
\(944\) | 12.7399 | 0.414649 | ||||||||
\(945\) | −8.66384 | + | 0.465782i | −0.281835 | + | 0.0151519i | ||||
\(946\) | −50.9738 | −1.65730 | ||||||||
\(947\) | 7.17276 | + | 7.17276i | 0.233083 | + | 0.233083i | 0.813978 | − | 0.580895i | \(-0.197297\pi\) |
−0.580895 | + | 0.813978i | \(0.697297\pi\) | |||||||
\(948\) | −11.5502 | + | 0.304272i | −0.375133 | + | 0.00988230i | ||||
\(949\) | − | 52.6821i | − | 1.71013i | ||||||
\(950\) | 17.4677 | + | 19.3315i | 0.566726 | + | 0.627195i | ||||
\(951\) | 26.7924 | + | 25.4170i | 0.868803 | + | 0.824204i | ||||
\(952\) | −2.48633 | + | 2.48633i | −0.0805825 | + | 0.0805825i | ||||
\(953\) | 1.36152 | − | 1.36152i | 0.0441038 | − | 0.0441038i | −0.684711 | − | 0.728815i | \(-0.740072\pi\) |
0.728815 | + | 0.684711i | \(0.240072\pi\) | |||||||
\(954\) | 7.03779 | − | 0.371057i | 0.227857 | − | 0.0120134i | ||||
\(955\) | 26.4666 | − | 25.1601i | 0.856439 | − | 0.814160i | ||||
\(956\) | − | 3.23606i | − | 0.104662i | ||||||
\(957\) | 0.526600 | + | 19.9898i | 0.0170226 | + | 0.646178i | ||||
\(958\) | −13.9494 | − | 13.9494i | −0.450686 | − | 0.450686i | ||||
\(959\) | −8.02039 | −0.258992 | ||||||||
\(960\) | −2.73578 | + | 2.74145i | −0.0882968 | + | 0.0884798i | ||||
\(961\) | −15.6358 | −0.504380 | ||||||||
\(962\) | −47.4750 | − | 47.4750i | −1.53066 | − | 1.53066i | ||||
\(963\) | 34.1523 | + | 30.7314i | 1.10054 | + | 0.990307i | ||||
\(964\) | 2.49371i | 0.0803171i | ||||||||
\(965\) | −0.356000 | + | 14.0669i | −0.0114601 | + | 0.452830i | ||||
\(966\) | 0.890166 | − | 0.938335i | 0.0286406 | − | 0.0301904i | ||||
\(967\) | −3.08307 | + | 3.08307i | −0.0991448 | + | 0.0991448i | −0.754939 | − | 0.655795i | \(-0.772334\pi\) |
0.655795 | + | 0.754939i | \(0.272334\pi\) | |||||||
\(968\) | 7.23056 | − | 7.23056i | 0.232399 | − | 0.232399i | ||||
\(969\) | 29.2492 | − | 30.8319i | 0.939619 | − | 0.990464i | ||||
\(970\) | −12.4087 | − | 13.0531i | −0.398420 | − | 0.419110i | ||||
\(971\) | − | 34.8356i | − | 1.11793i | −0.829192 | − | 0.558965i | \(-0.811199\pi\) | ||
0.829192 | − | 0.558965i | \(-0.188801\pi\) | |||||||
\(972\) | 2.04687 | + | 15.4535i | 0.0656533 | + | 0.495671i | ||||
\(973\) | −7.74123 | − | 7.74123i | −0.248173 | − | 0.248173i | ||||
\(974\) | 7.52797 | 0.241212 | ||||||||
\(975\) | −42.0329 | + | 40.0408i | −1.34613 | + | 1.28233i | ||||
\(976\) | 1.51016 | 0.0483389 | ||||||||
\(977\) | 34.9877 | + | 34.9877i | 1.11936 | + | 1.11936i | 0.991836 | + | 0.127521i | \(0.0407020\pi\) |
0.127521 | + | 0.991836i | \(0.459298\pi\) | |||||||
\(978\) | −0.202098 | − | 7.67165i | −0.00646238 | − | 0.245312i | ||||
\(979\) | 41.8253i | 1.33674i | ||||||||
\(980\) | 9.92532 | + | 10.4407i | 0.317053 | + | 0.333517i | ||||
\(981\) | 0.917764 | + | 17.4071i | 0.0293019 | + | 0.555766i | ||||
\(982\) | 4.49158 | − | 4.49158i | 0.143332 | − | 0.143332i | ||||
\(983\) | −2.48551 | + | 2.48551i | −0.0792755 | + | 0.0792755i | −0.745633 | − | 0.666357i | \(-0.767853\pi\) |
0.666357 | + | 0.745633i | \(0.267853\pi\) | |||||||
\(984\) | 5.31604 | + | 5.04315i | 0.169469 | + | 0.160770i | ||||
\(985\) | −1.52094 | + | 60.0980i | −0.0484611 | + | 1.91488i | ||||
\(986\) | − | 11.7997i | − | 0.375780i | ||||||
\(987\) | 4.42736 | − | 0.116632i | 0.140924 | − | 0.00371244i | ||||
\(988\) | 24.6990 | + | 24.6990i | 0.785781 | + | 0.785781i | ||||
\(989\) | −11.0641 | −0.351819 | ||||||||
\(990\) | −30.8939 | + | 0.845857i | −0.981873 | + | 0.0268831i | ||||
\(991\) | 35.3250 | 1.12214 | 0.561068 | − | 0.827770i | \(-0.310391\pi\) | ||||
0.561068 | + | 0.827770i | \(0.310391\pi\) | |||||||
\(992\) | −2.77166 | − | 2.77166i | −0.0880003 | − | 0.0880003i | ||||
\(993\) | 32.4458 | − | 0.854734i | 1.02964 | − | 0.0271242i | ||||
\(994\) | − | 8.15336i | − | 0.258609i | ||||||
\(995\) | −31.8381 | + | 30.2664i | −1.00934 | + | 0.959509i | ||||
\(996\) | −17.2078 | − | 16.3245i | −0.545252 | − | 0.517261i | ||||
\(997\) | −26.5260 | + | 26.5260i | −0.840088 | + | 0.840088i | −0.988870 | − | 0.148782i | \(-0.952465\pi\) |
0.148782 | + | 0.988870i | \(0.452465\pi\) | |||||||
\(998\) | 18.7776 | − | 18.7776i | 0.594394 | − | 0.594394i | ||||
\(999\) | −33.7816 | + | 39.5910i | −1.06880 | + | 1.25260i |
(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 | 690.2.i.f.323.16 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.323.5 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.f.47.5 | ✓ | 32 | |
15.2 | even | 4 | inner | 690.2.i.f.47.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.5 | ✓ | 32 | 5.2 | odd | 4 | inner | |
690.2.i.f.47.16 | yes | 32 | 15.2 | even | 4 | inner | |
690.2.i.f.323.5 | yes | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.323.16 | yes | 32 | 1.1 | even | 1 | trivial |