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 | 47.5 | ||
Character | \(\chi\) | \(=\) | 690.47 |
Dual form | 690.2.i.f.323.5 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||
\(3\) | −0.0456124 | − | 1.73145i | −0.0263343 | − | 0.999653i | ||||
\(4\) | − | 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 | 0.799818 | − | 0.600243i | \(-0.204929\pi\) |
−0.600243 | + | 0.799818i | \(0.704929\pi\) | |||||||
\(8\) | 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 | \(-0.244396\pi\) | |||||||
\(12\) | −1.73145 | + | 0.0456124i | −0.499827 | + | 0.0131672i | ||||
\(13\) | 4.73992 | − | 4.73992i | 1.31462 | − | 1.31462i | 0.396645 | − | 0.917972i | \(-0.370174\pi\) |
0.917972 | − | 0.396645i | \(-0.129826\pi\) | |||||||
\(14\) | −0.746742 | −0.199575 | ||||||||
\(15\) | −2.87632 | − | 2.59360i | −0.742663 | − | 0.669666i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.32957 | + | 3.32957i | −0.807541 | + | 0.807541i | −0.984261 | − | 0.176721i | \(-0.943451\pi\) |
0.176721 | + | 0.984261i | \(0.443451\pi\) | |||||||
\(18\) | 2.00669 | − | 2.23007i | 0.472981 | − | 0.525632i | ||||
\(19\) | 5.21085i | 1.19545i | 0.801700 | + | 0.597726i | \(0.203929\pi\) | ||||
−0.801700 | + | 0.597726i | \(0.796071\pi\) | |||||||
\(20\) | −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 | ||||||||
\(27\) | 0.410132 | + | 5.17994i | 0.0789300 | + | 0.996880i | ||||
\(28\) | 0.528026 | − | 0.528026i | 0.0997876 | − | 0.0997876i | ||||
\(29\) | 2.50593 | 0.465339 | 0.232669 | − | 0.972556i | \(-0.425254\pi\) | ||||
0.232669 | + | 0.972556i | \(0.425254\pi\) | |||||||
\(30\) | 3.86782 | − | 0.199910i | 0.706164 | − | 0.0364985i | ||||
\(31\) | 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 | ||||
\(33\) | −7.97700 | + | 0.210142i | −1.38862 | + | 0.0365810i | ||||
\(34\) | − | 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 | −0.983516 | − | 0.180820i | \(-0.942125\pi\) |
−0.180820 | − | 0.983516i | \(-0.557875\pi\) | |||||||
\(38\) | −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 | \(-0.107168\pi\) | |||||||
\(42\) | 0.0340607 | + | 1.29295i | 0.00525568 | + | 0.199506i | ||||
\(43\) | −7.82352 | + | 7.82352i | −1.19308 | + | 1.19308i | −0.216877 | + | 0.976199i | \(0.569587\pi\) |
−0.976199 | + | 0.216877i | \(0.930413\pi\) | |||||||
\(44\) | −4.60712 | −0.694549 | ||||||||
\(45\) | −4.35950 | + | 5.09851i | −0.649876 | + | 0.760040i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −2.42130 | + | 2.42130i | −0.353184 | + | 0.353184i | −0.861293 | − | 0.508109i | \(-0.830345\pi\) |
0.508109 | + | 0.861293i | \(0.330345\pi\) | |||||||
\(48\) | 0.0456124 | + | 1.73145i | 0.00658358 | + | 0.249913i | ||||
\(49\) | − | 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 | \(-0.301582\pi\) |
−0.811929 | + | 0.583756i | \(0.801582\pi\) | |||||||
\(54\) | −3.95278 | − | 3.37276i | −0.537905 | − | 0.458975i | ||||
\(55\) | −7.46646 | − | 7.09787i | −1.00678 | − | 0.957077i | ||||
\(56\) | 0.746742i | 0.0997876i | ||||||||
\(57\) | 9.02233 | − | 0.237680i | 1.19504 | − | 0.0314814i | ||||
\(58\) | −1.77196 | + | 1.77196i | −0.232669 | + | 0.232669i | ||||
\(59\) | 12.7399 | 1.65860 | 0.829299 | − | 0.558806i | \(-0.188740\pi\) | ||||
0.829299 | + | 0.558806i | \(0.188740\pi\) | |||||||
\(60\) | −2.59360 | + | 2.87632i | −0.334833 | + | 0.371331i | ||||
\(61\) | −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 | ||||
\(63\) | −1.66528 | − | 1.49848i | −0.209806 | − | 0.188791i | ||||
\(64\) | 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 | 0.309498 | − | 0.950900i | \(-0.399839\pi\) |
−0.950900 | + | 0.309498i | \(0.899839\pi\) | |||||||
\(68\) | 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 | \(-0.224352\pi\) | |||||||
\(72\) | −2.23007 | − | 2.00669i | −0.262816 | − | 0.236491i | ||||
\(73\) | −5.55728 | + | 5.55728i | −0.650430 | + | 0.650430i | −0.953097 | − | 0.302667i | \(-0.902123\pi\) |
0.302667 | + | 0.953097i | \(0.402123\pi\) | |||||||
\(74\) | 10.0160 | 1.16434 | ||||||||
\(75\) | −8.63463 | + | 0.665678i | −0.997041 | + | 0.0768659i | ||||
\(76\) | 5.21085 | 0.597726 | ||||||||
\(77\) | 2.43268 | − | 2.43268i | 0.277230 | − | 0.277230i | ||||
\(78\) | 11.6064 | − | 0.305752i | 1.31416 | − | 0.0346196i | ||||
\(79\) | − | 6.67082i | − | 0.750526i | −0.926918 | − | 0.375263i | \(-0.877552\pi\) | ||
0.926918 | − | 0.375263i | \(-0.122448\pi\) | |||||||
\(80\) | −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 | 0.997886 | + | 0.0649958i | \(0.0207034\pi\) |
0.0649958 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(84\) | −0.938335 | − | 0.890166i | −0.102381 | − | 0.0971251i | ||||
\(85\) | 0.266380 | + | 10.5257i | 0.0288929 | + | 1.14167i | ||||
\(86\) | − | 11.0641i | − | 1.19308i | ||||||
\(87\) | −0.114301 | − | 4.33889i | −0.0122544 | − | 0.465178i | ||||
\(88\) | 3.25773 | − | 3.25773i | 0.347275 | − | 0.347275i | ||||
\(89\) | 9.07840 | 0.962309 | 0.481154 | − | 0.876636i | \(-0.340218\pi\) | ||||
0.481154 | + | 0.876636i | \(0.340218\pi\) | |||||||
\(90\) | −0.522555 | − | 6.68782i | −0.0550822 | − | 0.704958i | ||||
\(91\) | 5.00560 | 0.524730 | ||||||||
\(92\) | −0.707107 | + | 0.707107i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | −0.178788 | − | 6.78680i | −0.0185394 | − | 0.703759i | ||||
\(94\) | − | 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 | 0.934425 | − | 0.356159i | \(-0.115914\pi\) |
−0.356159 | + | 0.934425i | \(0.615914\pi\) | |||||||
\(98\) | 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 | \(0.869869\pi\) | |||||||
\(102\) | −8.15293 | + | 0.214777i | −0.807260 | + | 0.0212660i | ||||
\(103\) | 8.37328 | − | 8.37328i | 0.825044 | − | 0.825044i | −0.161783 | − | 0.986826i | \(-0.551724\pi\) |
0.986826 | + | 0.161783i | \(0.0517244\pi\) | |||||||
\(104\) | 6.70326 | 0.657308 | ||||||||
\(105\) | −0.149281 | − | 2.88826i | −0.0145684 | − | 0.281866i | ||||
\(106\) | 2.34919 | 0.228173 | ||||||||
\(107\) | −10.8290 | + | 10.8290i | −1.04688 | + | 1.04688i | −0.0480314 | + | 0.998846i | \(0.515295\pi\) |
−0.998846 | + | 0.0480314i | \(0.984705\pi\) | |||||||
\(108\) | 5.17994 | − | 0.410132i | 0.498440 | − | 0.0394650i | ||||
\(109\) | − | 5.81042i | − | 0.556538i | −0.960503 | − | 0.278269i | \(-0.910239\pi\) | ||
0.960503 | − | 0.278269i | \(-0.0897606\pi\) | |||||||
\(110\) | 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 | \(-0.236778\pi\) |
−0.677132 | + | 0.735861i | \(0.736778\pi\) | |||||||
\(114\) | −6.21169 | + | 6.54782i | −0.581778 | + | 0.613259i | ||||
\(115\) | −2.23535 | + | 0.0565714i | −0.208448 | + | 0.00527531i | ||||
\(116\) | − | 2.50593i | − | 0.232669i | ||||||
\(117\) | −13.4514 | + | 14.9487i | −1.24358 | + | 1.38201i | ||||
\(118\) | −9.00849 | + | 9.00849i | −0.829299 | + | 0.829299i | ||||
\(119\) | −3.51621 | −0.322330 | ||||||||
\(120\) | −0.199910 | − | 3.86782i | −0.0182492 | − | 0.353082i | ||||
\(121\) | −10.2255 | −0.929595 | ||||||||
\(122\) | 1.06784 | − | 1.06784i | 0.0966778 | − | 0.0966778i | ||||
\(123\) | −7.32505 | + | 0.192967i | −0.660478 | + | 0.0173993i | ||||
\(124\) | − | 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 | 0.999789 | − | 0.0205641i | \(-0.00654623\pi\) |
−0.0205641 | + | 0.999789i | \(0.506546\pi\) | |||||||
\(128\) | −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 | \(0.858371\pi\) | |||||||
\(132\) | 0.210142 | + | 7.97700i | 0.0182905 | + | 0.694309i | ||||
\(133\) | −2.75147 | + | 2.75147i | −0.238582 | + | 0.238582i | ||||
\(134\) | 7.42476 | 0.641402 | ||||||||
\(135\) | 9.02666 | + | 7.31570i | 0.776891 | + | 0.629635i | ||||
\(136\) | −4.70873 | −0.403770 | ||||||||
\(137\) | 7.59469 | − | 7.59469i | 0.648858 | − | 0.648858i | −0.303859 | − | 0.952717i | \(-0.598275\pi\) |
0.952717 | + | 0.303859i | \(0.0982751\pi\) | |||||||
\(138\) | −0.0456124 | − | 1.73145i | −0.00388279 | − | 0.147391i | ||||
\(139\) | 14.6607i | 1.24350i | 0.783214 | + | 0.621752i | \(0.213579\pi\) | ||||
−0.783214 | + | 0.621752i | \(0.786421\pi\) | |||||||
\(140\) | −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 | ||||||
\(147\) | −11.1547 | + | 0.293852i | −0.920020 | + | 0.0242365i | ||||
\(148\) | −7.08238 | + | 7.08238i | −0.582168 | + | 0.582168i | ||||
\(149\) | 5.81897 | 0.476708 | 0.238354 | − | 0.971178i | \(-0.423392\pi\) | ||||
0.238354 | + | 0.971178i | \(0.423392\pi\) | |||||||
\(150\) | 5.63490 | − | 6.57631i | 0.460088 | − | 0.536954i | ||||
\(151\) | 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 | ||||
\(153\) | 9.44896 | − | 10.5008i | 0.763903 | − | 0.848938i | ||||
\(154\) | 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 | 0.407572 | − | 0.913173i | \(-0.366375\pi\) |
−0.913173 | + | 0.407572i | \(0.866375\pi\) | |||||||
\(158\) | 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 | ||||||
\(162\) | −5.65948 | + | 6.99788i | −0.444651 | + | 0.549805i | ||||
\(163\) | −3.13303 | + | 3.13303i | −0.245398 | + | 0.245398i | −0.819079 | − | 0.573681i | \(-0.805515\pi\) |
0.573681 | + | 0.819079i | \(0.305515\pi\) | |||||||
\(164\) | −4.23059 | −0.330353 | ||||||||
\(165\) | −11.9490 | + | 13.2516i | −0.930232 | + | 1.03163i | ||||
\(166\) | −13.6943 | −1.06288 | ||||||||
\(167\) | −5.90660 | + | 5.90660i | −0.457067 | + | 0.457067i | −0.897691 | − | 0.440625i | \(-0.854757\pi\) |
0.440625 | + | 0.897691i | \(0.354757\pi\) | |||||||
\(168\) | 1.29295 | − | 0.0340607i | 0.0997529 | − | 0.00262784i | ||||
\(169\) | − | 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 | \(-0.0670941\pi\) |
−0.209225 | + | 0.977868i | \(0.567094\pi\) | |||||||
\(174\) | 3.14888 | + | 2.98723i | 0.238716 | + | 0.226462i | ||||
\(175\) | 2.50321 | − | 2.77030i | 0.189225 | − | 0.209415i | ||||
\(176\) | 4.60712i | 0.347275i | ||||||||
\(177\) | −0.581099 | − | 22.0585i | −0.0436781 | − | 1.65802i | ||||
\(178\) | −6.41940 | + | 6.41940i | −0.481154 | + | 0.481154i | ||||
\(179\) | 10.7084 | 0.800386 | 0.400193 | − | 0.916431i | \(-0.368943\pi\) | ||||
0.400193 | + | 0.916431i | \(0.368943\pi\) | |||||||
\(180\) | 5.09851 | + | 4.35950i | 0.380020 | + | 0.324938i | ||||
\(181\) | 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 | ||||
\(183\) | 0.0688818 | + | 2.61476i | 0.00509189 | + | 0.193288i | ||||
\(184\) | − | 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 | \(0.798798\pi\) | |||||||
\(192\) | 1.73145 | − | 0.0456124i | 0.124957 | − | 0.00329179i | ||||
\(193\) | −4.44978 | + | 4.44978i | −0.320302 | + | 0.320302i | −0.848883 | − | 0.528581i | \(-0.822724\pi\) |
0.528581 | + | 0.848883i | \(0.322724\pi\) | |||||||
\(194\) | −8.05432 | −0.578266 | ||||||||
\(195\) | −25.9270 | + | 1.34005i | −1.85667 | + | 0.0959630i | ||||
\(196\) | −6.44238 | −0.460170 | ||||||||
\(197\) | 19.0107 | − | 19.0107i | 1.35446 | − | 1.35446i | 0.473858 | − | 0.880601i | \(-0.342861\pi\) |
0.880601 | − | 0.473858i | \(-0.157139\pi\) | |||||||
\(198\) | −10.2742 | − | 9.24506i | −0.730154 | − | 0.657018i | ||||
\(199\) | 19.6455i | 1.39263i | 0.717737 | + | 0.696315i | \(0.245178\pi\) | ||||
−0.717737 | + | 0.696315i | \(0.754822\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | 2.23007 | + | 2.00669i | 0.155000 | + | 0.139475i | ||||
\(208\) | −4.73992 | + | 4.73992i | −0.328654 | + | 0.328654i | ||||
\(209\) | 24.0070 | 1.66060 | ||||||||
\(210\) | 2.14787 | + | 1.93675i | 0.148217 | + | 0.133649i | ||||
\(211\) | −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 | ||||
\(213\) | −18.9050 | + | 0.498023i | −1.29535 | + | 0.0341239i | ||||
\(214\) | − | 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 | ||||||||
\(222\) | −0.456854 | − | 17.3422i | −0.0306620 | − | 1.16393i | ||||
\(223\) | 8.23185 | − | 8.23185i | 0.551245 | − | 0.551245i | −0.375555 | − | 0.926800i | \(-0.622548\pi\) |
0.926800 | + | 0.375555i | \(0.122548\pi\) | |||||||
\(224\) | 0.746742 | 0.0498938 | ||||||||
\(225\) | 1.54644 | + | 14.9201i | 0.103096 | + | 0.994671i | ||||
\(226\) | −0.882892 | −0.0587291 | ||||||||
\(227\) | 4.42457 | − | 4.42457i | 0.293669 | − | 0.293669i | −0.544859 | − | 0.838528i | \(-0.683417\pi\) |
0.838528 | + | 0.544859i | \(0.183417\pi\) | |||||||
\(228\) | −0.237680 | − | 9.02233i | −0.0157407 | − | 0.597519i | ||||
\(229\) | 0.539521i | 0.0356526i | 0.999841 | + | 0.0178263i | \(0.00567458\pi\) | ||||
−0.999841 | + | 0.0178263i | \(0.994325\pi\) | |||||||
\(230\) | 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 | \(-0.324659\pi\) |
−0.852080 | + | 0.523411i | \(0.824659\pi\) | |||||||
\(234\) | −1.05879 | − | 20.0819i | −0.0692151 | − | 1.31279i | ||||
\(235\) | 0.193714 | + | 7.65439i | 0.0126365 | + | 0.499317i | ||||
\(236\) | − | 12.7399i | − | 0.829299i | ||||||
\(237\) | −11.5502 | + | 0.304272i | −0.750265 | + | 0.0197646i | ||||
\(238\) | 2.48633 | − | 2.48633i | 0.161165 | − | 0.161165i | ||||
\(239\) | 3.23606 | 0.209324 | 0.104662 | − | 0.994508i | \(-0.466624\pi\) | ||||
0.104662 | + | 0.994508i | \(0.466624\pi\) | |||||||
\(240\) | 2.87632 | + | 2.59360i | 0.185666 | + | 0.167416i | ||||
\(241\) | 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 | ||||
\(243\) | −2.04687 | − | 15.4535i | −0.131307 | − | 0.991342i | ||||
\(244\) | 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 | \(-0.0544428\pi\) | |||||||
\(252\) | −1.49848 | + | 1.66528i | −0.0943953 | + | 0.104903i | ||||
\(253\) | −3.25773 | + | 3.25773i | −0.204811 | + | 0.204811i | ||||
\(254\) | −15.6063 | −0.979224 | ||||||||
\(255\) | 18.2125 | − | 0.941324i | 1.14051 | − | 0.0589480i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.454641 | + | 0.454641i | −0.0283597 | + | 0.0283597i | −0.721144 | − | 0.692785i | \(-0.756384\pi\) |
0.692785 | + | 0.721144i | \(0.256384\pi\) | |||||||
\(258\) | −19.1570 | + | 0.504662i | −1.19266 | + | 0.0314189i | ||||
\(259\) | − | 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 | \(-0.104828\pi\) |
−0.323407 | + | 0.946260i | \(0.604828\pi\) | |||||||
\(264\) | −5.78918 | − | 5.49200i | −0.356300 | − | 0.338009i | ||||
\(265\) | −5.25126 | + | 0.132897i | −0.322582 | + | 0.00816379i | ||||
\(266\) | − | 3.89116i | − | 0.238582i | ||||||
\(267\) | −0.414088 | − | 15.7188i | −0.0253418 | − | 0.961975i | ||||
\(268\) | −5.25010 | + | 5.25010i | −0.320701 | + | 0.320701i | ||||
\(269\) | 23.4948 | 1.43250 | 0.716252 | − | 0.697842i | \(-0.245856\pi\) | ||||
0.716252 | + | 0.697842i | \(0.245856\pi\) | |||||||
\(270\) | −11.5558 | + | 1.20983i | −0.703263 | + | 0.0736277i | ||||
\(271\) | −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 | ||||
\(273\) | −0.228318 | − | 8.66695i | −0.0138184 | − | 0.524548i | ||||
\(274\) | 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 | 0.999881 | − | 0.0153991i | \(-0.00490187\pi\) |
−0.0153991 | + | 0.999881i | \(0.504902\pi\) | |||||||
\(278\) | −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 | \(0.996730\pi\) | |||||||
\(282\) | −5.92890 | + | 0.156188i | −0.353061 | + | 0.00930086i | ||||
\(283\) | −1.89935 | + | 1.89935i | −0.112905 | + | 0.112905i | −0.761302 | − | 0.648397i | \(-0.775440\pi\) |
0.648397 | + | 0.761302i | \(0.275440\pi\) | |||||||
\(284\) | −10.9186 | −0.647898 | ||||||||
\(285\) | 13.5149 | − | 14.9881i | 0.800553 | − | 0.887818i | ||||
\(286\) | 30.8827 | 1.82613 | ||||||||
\(287\) | 2.23386 | − | 2.23386i | 0.131861 | − | 0.131861i | ||||
\(288\) | −2.00669 | + | 2.23007i | −0.118245 | + | 0.131408i | ||||
\(289\) | − | 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 | \(-0.247574\pi\) |
−0.701697 | + | 0.712475i | \(0.747574\pi\) | |||||||
\(294\) | 7.67975 | − | 8.09532i | 0.447892 | − | 0.472128i | ||||
\(295\) | 19.6275 | − | 20.6468i | 1.14276 | − | 1.20210i | ||||
\(296\) | − | 10.0160i | − | 0.582168i | ||||||
\(297\) | 23.8646 | − | 1.88953i | 1.38477 | − | 0.109642i | ||||
\(298\) | −4.11463 | + | 4.11463i | −0.238354 | + | 0.238354i | ||||
\(299\) | −6.70326 | −0.387659 | ||||||||
\(300\) | 0.665678 | + | 8.63463i | 0.0384330 | + | 0.498521i | ||||
\(301\) | −8.26205 | −0.476217 | ||||||||
\(302\) | −1.96613 | + | 1.96613i | −0.113138 | + | 0.113138i | ||||
\(303\) | 13.8345 | − | 0.364450i | 0.794773 | − | 0.0209371i | ||||
\(304\) | − | 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 | 0.546054 | − | 0.837750i | \(-0.316130\pi\) |
−0.837750 | + | 0.546054i | \(0.816130\pi\) | |||||||
\(308\) | −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 | \(-0.123489\pi\) | |||||||
\(312\) | −0.305752 | − | 11.6064i | −0.0173098 | − | 0.657081i | ||||
\(313\) | 5.87924 | − | 5.87924i | 0.332314 | − | 0.332314i | −0.521151 | − | 0.853465i | \(-0.674497\pi\) |
0.853465 | + | 0.521151i | \(0.174497\pi\) | |||||||
\(314\) | 8.95927 | 0.505601 | ||||||||
\(315\) | −4.99407 | + | 0.390214i | −0.281384 | + | 0.0219861i | ||||
\(316\) | −6.67082 | −0.375263 | ||||||||
\(317\) | −15.0768 | + | 15.0768i | −0.846797 | + | 0.846797i | −0.989732 | − | 0.142935i | \(-0.954346\pi\) |
0.142935 | + | 0.989732i | \(0.454346\pi\) | |||||||
\(318\) | −0.107152 | − | 4.06750i | −0.00600879 | − | 0.228094i | ||||
\(319\) | − | 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 | ||||||
\(327\) | −10.0605 | + | 0.265027i | −0.556345 | + | 0.0146561i | ||||
\(328\) | 2.99148 | − | 2.99148i | 0.165177 | − | 0.165177i | ||||
\(329\) | −2.55702 | −0.140973 | ||||||||
\(330\) | −0.921011 | − | 17.8195i | −0.0507000 | − | 0.980932i | ||||
\(331\) | 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 | ||||
\(333\) | 22.3363 | + | 20.0990i | 1.22402 | + | 1.10142i | ||||
\(334\) | − | 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 | 0.948247 | − | 0.317535i | \(-0.102855\pi\) |
−0.317535 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(338\) | 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 | ||||||
\(342\) | 11.6206 | + | 10.4566i | 0.628367 | + | 0.565426i | ||||
\(343\) | 7.09793 | − | 7.09793i | 0.383252 | − | 0.383252i | ||||
\(344\) | −11.0641 | −0.596538 | ||||||||
\(345\) | 0.199910 | + | 3.86782i | 0.0107628 | + | 0.208236i | ||||
\(346\) | −14.2976 | −0.768643 | ||||||||
\(347\) | −9.53609 | + | 9.53609i | −0.511924 | + | 0.511924i | −0.915116 | − | 0.403191i | \(-0.867901\pi\) |
0.403191 | + | 0.915116i | \(0.367901\pi\) | |||||||
\(348\) | −4.33889 | + | 0.114301i | −0.232589 | + | 0.00612720i | ||||
\(349\) | − | 22.7071i | − | 1.21549i | −0.794134 | − | 0.607743i | \(-0.792075\pi\) | ||
0.794134 | − | 0.607743i | \(-0.207925\pi\) | |||||||
\(350\) | 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 | −0.996902 | − | 0.0786597i | \(-0.974936\pi\) |
−0.0786597 | − | 0.996902i | \(-0.525064\pi\) | |||||||
\(354\) | 16.0086 | + | 15.1868i | 0.850850 | + | 0.807172i | ||||
\(355\) | −17.6950 | − | 16.8215i | −0.939155 | − | 0.892792i | ||||
\(356\) | − | 9.07840i | − | 0.481154i | ||||||
\(357\) | 0.160383 | + | 6.08813i | 0.00848835 | + | 0.322218i | ||||
\(358\) | −7.57201 | + | 7.57201i | −0.400193 | + | 0.400193i | ||||
\(359\) | −9.55317 | −0.504197 | −0.252098 | − | 0.967702i | \(-0.581121\pi\) | ||||
−0.252098 | + | 0.967702i | \(0.581121\pi\) | |||||||
\(360\) | −6.68782 | + | 0.522555i | −0.352479 | + | 0.0275411i | ||||
\(361\) | −8.15300 | −0.429105 | ||||||||
\(362\) | −13.6675 | + | 13.6675i | −0.718349 | + | 0.718349i | ||||
\(363\) | 0.466412 | + | 17.7050i | 0.0244803 | + | 0.929273i | ||||
\(364\) | − | 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 | 0.157823 | − | 0.987467i | \(-0.449553\pi\) |
−0.987467 | + | 0.157823i | \(0.949553\pi\) | |||||||
\(368\) | 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 | ||||||
\(372\) | −6.78680 | + | 0.178788i | −0.351879 | + | 0.00926972i | ||||
\(373\) | 21.9117 | − | 21.9117i | 1.13455 | − | 1.13455i | 0.145135 | − | 0.989412i | \(-0.453638\pi\) |
0.989412 | − | 0.145135i | \(-0.0463617\pi\) | |||||||
\(374\) | −21.6937 | −1.12175 | ||||||||
\(375\) | −12.2240 | + | 15.0191i | −0.631242 | + | 0.775586i | ||||
\(376\) | −3.42424 | −0.176592 | ||||||||
\(377\) | 11.8779 | − | 11.8779i | 0.611742 | − | 0.611742i | ||||
\(378\) | −0.306263 | − | 3.86808i | −0.0157525 | − | 0.198952i | ||||
\(379\) | 3.01254i | 0.154744i | 0.997002 | + | 0.0773719i | \(0.0246529\pi\) | ||||
−0.997002 | + | 0.0773719i | \(0.975347\pi\) | |||||||
\(380\) | 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 | \(-0.471448\pi\) |
−0.995980 | + | 0.0895800i | \(0.971448\pi\) | |||||||
\(384\) | −1.19207 | + | 1.25657i | −0.0608324 | + | 0.0641242i | ||||
\(385\) | −0.194624 | − | 7.69035i | −0.00991897 | − | 0.391936i | ||||
\(386\) | − | 6.29293i | − | 0.320302i | ||||||
\(387\) | 22.2023 | − | 24.6738i | 1.12861 | − | 1.25424i | ||||
\(388\) | 5.69526 | − | 5.69526i | 0.289133 | − | 0.289133i | ||||
\(389\) | −20.0679 | −1.01748 | −0.508742 | − | 0.860919i | \(-0.669889\pi\) | ||||
−0.508742 | + | 0.860919i | \(0.669889\pi\) | |||||||
\(390\) | 17.3856 | − | 19.2807i | 0.880354 | − | 0.976317i | ||||
\(391\) | 4.70873 | 0.238131 | ||||||||
\(392\) | 4.55545 | − | 4.55545i | 0.230085 | − | 0.230085i | ||||
\(393\) | 17.0589 | − | 0.449391i | 0.860509 | − | 0.0226688i | ||||
\(394\) | 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 | 0.921190 | + | 0.389114i | \(0.127219\pi\) |
0.389114 | + | 0.921190i | \(0.372781\pi\) | |||||||
\(398\) | −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 | \(0.814978\pi\) | |||||||
\(402\) | −0.338661 | − | 12.8556i | −0.0168909 | − | 0.641179i | ||||
\(403\) | 18.5792 | − | 18.5792i | 0.925494 | − | 0.925494i | ||||
\(404\) | 7.99014 | 0.397524 | ||||||||
\(405\) | 12.2550 | − | 15.9629i | 0.608958 | − | 0.793202i | ||||
\(406\) | −1.87128 | −0.0928701 | ||||||||
\(407\) | −32.6294 | + | 32.6294i | −1.61738 | + | 1.61738i | ||||
\(408\) | 0.214777 | + | 8.15293i | 0.0106330 | + | 0.403630i | ||||
\(409\) | − | 38.2076i | − | 1.88924i | −0.328159 | − | 0.944622i | \(-0.606428\pi\) | ||
0.328159 | − | 0.944622i | \(-0.393572\pi\) | |||||||
\(410\) | 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 | ||||||
\(417\) | 25.3843 | − | 0.668710i | 1.24307 | − | 0.0327469i | ||||
\(418\) | −16.9755 | + | 16.9755i | −0.830300 | + | 0.830300i | ||||
\(419\) | 9.14872 | 0.446944 | 0.223472 | − | 0.974710i | \(-0.428261\pi\) | ||||
0.223472 | + | 0.974710i | \(0.428261\pi\) | |||||||
\(420\) | −2.88826 | + | 0.149281i | −0.140933 | + | 0.00728419i | ||||
\(421\) | −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 | ||||
\(423\) | 6.87139 | − | 7.63629i | 0.334099 | − | 0.371289i | ||||
\(424\) | − | 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 | \(0.913668\pi\) | |||||||
\(432\) | −0.410132 | − | 5.17994i | −0.0197325 | − | 0.249220i | ||||
\(433\) | −20.0373 | + | 20.0373i | −0.962929 | + | 0.962929i | −0.999337 | − | 0.0364075i | \(-0.988409\pi\) |
0.0364075 | + | 0.999337i | \(0.488409\pi\) | |||||||
\(434\) | −2.92702 | −0.140501 | ||||||||
\(435\) | −7.20785 | − | 6.49938i | −0.345590 | − | 0.311622i | ||||
\(436\) | −5.81042 | −0.278269 | ||||||||
\(437\) | 3.68463 | − | 3.68463i | 0.176260 | − | 0.176260i | ||||
\(438\) | −13.6078 | + | 0.358476i | −0.650204 | + | 0.0171286i | ||||
\(439\) | 13.8002i | 0.658647i | 0.944217 | + | 0.329324i | \(0.106821\pi\) | ||||
−0.944217 | + | 0.329324i | \(0.893179\pi\) | |||||||
\(440\) | −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 | \(-0.206200\pi\) |
−0.603430 | + | 0.797416i | \(0.706200\pi\) | |||||||
\(444\) | 12.5858 | + | 11.9397i | 0.597297 | + | 0.566635i | ||||
\(445\) | 13.9865 | − | 14.7128i | 0.663022 | − | 0.697452i | ||||
\(446\) | 11.6416i | 0.551245i | ||||||||
\(447\) | −0.265417 | − | 10.0753i | −0.0125538 | − | 0.476543i | ||||
\(448\) | −0.528026 | + | 0.528026i | −0.0249469 | + | 0.0249469i | ||||
\(449\) | −5.80447 | −0.273930 | −0.136965 | − | 0.990576i | \(-0.543735\pi\) | ||||
−0.136965 | + | 0.990576i | \(0.543735\pi\) | |||||||
\(450\) | −11.6436 | − | 9.45659i | −0.548884 | − | 0.445788i | ||||
\(451\) | −19.4908 | −0.917787 | ||||||||
\(452\) | 0.624299 | − | 0.624299i | 0.0293645 | − | 0.0293645i | ||||
\(453\) | −0.126826 | − | 4.81433i | −0.00595882 | − | 0.226197i | ||||
\(454\) | 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 | 0.632243 | − | 0.774770i | \(-0.282135\pi\) |
−0.774770 | + | 0.632243i | \(0.782135\pi\) | |||||||
\(458\) | −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 | \(-0.0812697\pi\) | |||||||
\(462\) | 5.95676 | − | 0.156922i | 0.277133 | − | 0.00730066i | ||||
\(463\) | −0.966000 | + | 0.966000i | −0.0448939 | + | 0.0448939i | −0.729197 | − | 0.684303i | \(-0.760106\pi\) |
0.684303 | + | 0.729197i | \(0.260106\pi\) | |||||||
\(464\) | −2.50593 | −0.116335 | ||||||||
\(465\) | −11.2744 | − | 10.1662i | −0.522837 | − | 0.471446i | ||||
\(466\) | 7.09498 | 0.328669 | ||||||||
\(467\) | −4.97855 | + | 4.97855i | −0.230380 | + | 0.230380i | −0.812851 | − | 0.582471i | \(-0.802086\pi\) |
0.582471 | + | 0.812851i | \(0.302086\pi\) | |||||||
\(468\) | 14.9487 | + | 13.4514i | 0.691004 | + | 0.621789i | ||||
\(469\) | − | 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 | ||||||||
\(477\) | 5.23884 | + | 4.71409i | 0.239870 | + | 0.215843i | ||||
\(478\) | −2.28824 | + | 2.28824i | −0.104662 | + | 0.104662i | ||||
\(479\) | 19.7275 | 0.901373 | 0.450686 | − | 0.892682i | \(-0.351179\pi\) | ||||
0.450686 | + | 0.892682i | \(0.351179\pi\) | |||||||
\(480\) | −3.86782 | + | 0.199910i | −0.176541 | + | 0.00912462i | ||||
\(481\) | −67.1398 | −3.06131 | ||||||||
\(482\) | −1.76332 | + | 1.76332i | −0.0803171 | + | 0.0803171i | ||||
\(483\) | −1.29295 | + | 0.0340607i | −0.0588311 | + | 0.00154981i | ||||
\(484\) | 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 | 0.817351 | − | 0.576140i | \(-0.195442\pi\) |
−0.576140 | + | 0.817351i | \(0.695442\pi\) | |||||||
\(488\) | −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 | \(-0.0457817\pi\) | |||||||
\(492\) | 0.192967 | + | 7.32505i | 0.00869964 | + | 0.330239i | ||||
\(493\) | −8.34367 | + | 8.34367i | −0.375780 | + | 0.375780i | ||||
\(494\) | −34.9297 | −1.57156 | ||||||||
\(495\) | 23.4894 | + | 20.0847i | 1.05577 | + | 0.902742i | ||||
\(496\) | −3.91972 | −0.176001 | ||||||||
\(497\) | 5.76529 | − | 5.76529i | 0.258609 | − | 0.258609i | ||||
\(498\) | 0.624629 | + | 23.7109i | 0.0279903 | + | 1.06251i | ||||
\(499\) | 26.5555i | 1.18879i | 0.804174 | + | 0.594394i | \(0.202608\pi\) | ||||
−0.804174 | + | 0.594394i | \(0.797392\pi\) | |||||||
\(500\) | −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 | \(-0.477313\pi\) |
−0.997461 | + | 0.0712128i | \(0.977313\pi\) | |||||||
\(504\) | −0.117949 | − | 2.23712i | −0.00525386 | − | 0.0996492i | ||||
\(505\) | 12.9491 | + | 12.3099i | 0.576227 | + | 0.547781i | ||||
\(506\) | − | 4.60712i | − | 0.204811i | ||||||
\(507\) | −55.2915 | + | 1.45657i | −2.45558 | + | 0.0646886i | ||||
\(508\) | 11.0353 | − | 11.0353i | 0.489612 | − | 0.489612i | ||||
\(509\) | −3.09578 | −0.137218 | −0.0686090 | − | 0.997644i | \(-0.521856\pi\) | ||||
−0.0686090 | + | 0.997644i | \(0.521856\pi\) | |||||||
\(510\) | −12.2126 | + | 13.5438i | −0.540782 | + | 0.599730i | ||||
\(511\) | −5.86877 | −0.259619 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −26.9919 | + | 2.13714i | −1.19172 | + | 0.0943570i | ||||
\(514\) | − | 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 | \(-0.0560389\pi\) | |||||||
\(522\) | 5.02862 | − | 5.58838i | 0.220097 | − | 0.244597i | ||||
\(523\) | −16.4846 | + | 16.4846i | −0.720823 | + | 0.720823i | −0.968773 | − | 0.247950i | \(-0.920243\pi\) |
0.247950 | + | 0.968773i | \(0.420243\pi\) | |||||||
\(524\) | 9.85239 | 0.430404 | ||||||||
\(525\) | −4.91081 | − | 4.20782i | −0.214325 | − | 0.183644i | ||||
\(526\) | −14.2850 | −0.622853 | ||||||||
\(527\) | −13.0510 | + | 13.0510i | −0.568511 | + | 0.568511i | ||||
\(528\) | 7.97700 | − | 0.210142i | 0.347154 | − | 0.00914525i | ||||
\(529\) | 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 | ||||||
\(537\) | −0.488437 | − | 18.5411i | −0.0210776 | − | 0.800108i | ||||
\(538\) | −16.6133 | + | 16.6133i | −0.716252 | + | 0.716252i | ||||
\(539\) | −29.6808 | −1.27844 | ||||||||
\(540\) | 7.31570 | − | 9.02666i | 0.314818 | − | 0.388445i | ||||
\(541\) | −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 | ||||
\(543\) | −0.881633 | − | 33.4668i | −0.0378345 | − | 1.43620i | ||||
\(544\) | 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 | 0.180284 | − | 0.983615i | \(-0.442298\pi\) |
−0.983615 | + | 0.180284i | \(0.942298\pi\) | |||||||
\(548\) | −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 | ||||||||
\(552\) | −1.73145 | + | 0.0456124i | −0.0736954 | + | 0.00194139i | ||||
\(553\) | 3.52237 | − | 3.52237i | 0.149786 | − | 0.149786i | ||||
\(554\) | −23.1720 | −0.984482 | ||||||||
\(555\) | 2.00230 | + | 38.7401i | 0.0849930 | + | 1.64443i | ||||
\(556\) | 14.6607 | 0.621752 | ||||||||
\(557\) | −17.0441 | + | 17.0441i | −0.722182 | + | 0.722182i | −0.969049 | − | 0.246867i | \(-0.920599\pi\) |
0.246867 | + | 0.969049i | \(0.420599\pi\) | |||||||
\(558\) | 7.86566 | − | 8.74124i | 0.332980 | − | 0.370046i | ||||
\(559\) | 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 | \(-0.281982\pi\) |
−0.774467 | + | 0.632614i | \(0.781982\pi\) | |||||||
\(564\) | 4.08193 | − | 4.30281i | 0.171880 | − | 0.181181i | ||||
\(565\) | 1.97357 | − | 0.0499465i | 0.0830289 | − | 0.00210126i | ||||
\(566\) | − | 2.68608i | − | 0.112905i | ||||||
\(567\) | 5.22561 | + | 4.22617i | 0.219455 | + | 0.177482i | ||||
\(568\) | 7.72060 | − | 7.72060i | 0.323949 | − | 0.323949i | ||||
\(569\) | −34.6119 | −1.45100 | −0.725502 | − | 0.688220i | \(-0.758393\pi\) | ||||
−0.725502 | + | 0.688220i | \(0.758393\pi\) | |||||||
\(570\) | 1.04170 | + | 20.1546i | 0.0436322 | + | 0.844185i | ||||
\(571\) | 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 | ||||
\(573\) | 28.2763 | − | 0.744897i | 1.18126 | − | 0.0311185i | ||||
\(574\) | 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 | 0.999121 | − | 0.0419120i | \(-0.0133449\pi\) |
−0.0419120 | + | 0.999121i | \(0.513345\pi\) | |||||||
\(578\) | 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 | ||||||||
\(582\) | 0.367377 | + | 13.9457i | 0.0152283 | + | 0.578066i | ||||
\(583\) | −7.65301 | + | 7.65301i | −0.316955 | + | 0.316955i | ||||
\(584\) | −7.85918 | −0.325215 | ||||||||
\(585\) | 3.50282 | + | 44.8302i | 0.144824 | + | 1.85350i | ||||
\(586\) | −0.260905 | −0.0107779 | ||||||||
\(587\) | 27.0582 | − | 27.0582i | 1.11681 | − | 1.11681i | 0.124605 | − | 0.992206i | \(-0.460234\pi\) |
0.992206 | − | 0.124605i | \(-0.0397665\pi\) | |||||||
\(588\) | 0.293852 | + | 11.1547i | 0.0121183 | + | 0.460010i | ||||
\(589\) | 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 | \(-0.212347\pi\) |
−0.618717 | + | 0.785614i | \(0.712347\pi\) | |||||||
\(594\) | −15.5387 | + | 18.2109i | −0.637562 | + | 0.747203i | ||||
\(595\) | −5.41717 | + | 5.69848i | −0.222082 | + | 0.233615i | ||||
\(596\) | − | 5.81897i | − | 0.238354i | ||||||
\(597\) | 34.0151 | − | 0.896076i | 1.39215 | − | 0.0366740i | ||||
\(598\) | 4.73992 | − | 4.73992i | 0.193830 | − | 0.193830i | ||||
\(599\) | −3.30686 | −0.135115 | −0.0675574 | − | 0.997715i | \(-0.521521\pi\) | ||||
−0.0675574 | + | 0.997715i | \(0.521521\pi\) | |||||||
\(600\) | −6.57631 | − | 5.63490i | −0.268477 | − | 0.230044i | ||||
\(601\) | 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 | ||||
\(603\) | 16.5577 | + | 14.8992i | 0.674282 | + | 0.606742i | ||||
\(604\) | − | 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 | 0.0918938 | − | 0.995769i | \(-0.470708\pi\) |
−0.995769 | + | 0.0918938i | \(0.970708\pi\) | |||||||
\(608\) | 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 | ||||||||
\(612\) | −10.5008 | − | 9.44896i | −0.424469 | − | 0.381952i | ||||
\(613\) | 5.89129 | − | 5.89129i | 0.237947 | − | 0.237947i | −0.578053 | − | 0.816000i | \(-0.696187\pi\) |
0.816000 | + | 0.578053i | \(0.196187\pi\) | |||||||
\(614\) | 7.22796 | 0.291697 | ||||||||
\(615\) | −10.9725 | + | 12.1685i | −0.442453 | + | 0.490682i | ||||
\(616\) | 3.44033 | 0.138615 | ||||||||
\(617\) | 21.2085 | − | 21.2085i | 0.853823 | − | 0.853823i | −0.136778 | − | 0.990602i | \(-0.543675\pi\) |
0.990602 | + | 0.136778i | \(0.0436748\pi\) | |||||||
\(618\) | 20.5031 | − | 0.540124i | 0.824758 | − | 0.0217270i | ||||
\(619\) | − | 6.49659i | − | 0.261120i | −0.991440 | − | 0.130560i | \(-0.958322\pi\) | ||
0.991440 | − | 0.130560i | \(-0.0416775\pi\) | |||||||
\(620\) | −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 | ||||||||
\(627\) | −1.09502 | − | 41.5670i | −0.0437308 | − | 1.66002i | ||||
\(628\) | −6.33516 | + | 6.33516i | −0.252800 | + | 0.252800i | ||||
\(629\) | 47.1626 | 1.88050 | ||||||||
\(630\) | 3.25542 | − | 3.80727i | 0.129699 | − | 0.151685i | ||||
\(631\) | −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 | ||||
\(633\) | 0.199822 | + | 7.58526i | 0.00794222 | + | 0.301487i | ||||
\(634\) | − | 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 | \(-0.136198\pi\) | |||||||
\(642\) | −26.5163 | + | 0.698531i | −1.04651 | + | 0.0275688i | ||||
\(643\) | −23.8932 | + | 23.8932i | −0.942254 | + | 0.942254i | −0.998421 | − | 0.0561671i | \(-0.982112\pi\) |
0.0561671 | + | 0.998421i | \(0.482112\pi\) | |||||||
\(644\) | −0.746742 | −0.0294257 | ||||||||
\(645\) | 42.7941 | − | 2.21184i | 1.68502 | − | 0.0870909i | ||||
\(646\) | 24.5365 | 0.965376 | ||||||||
\(647\) | −1.33655 | + | 1.33655i | −0.0525450 | + | 0.0525450i | −0.732891 | − | 0.680346i | \(-0.761830\pi\) |
0.680346 | + | 0.732891i | \(0.261830\pi\) | |||||||
\(648\) | 6.99788 | + | 5.65948i | 0.274903 | + | 0.222325i | ||||
\(649\) | − | 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 | 0.996177 | + | 0.0873627i | \(0.0278439\pi\) |
0.0873627 | + | 0.996177i | \(0.472156\pi\) | |||||||
\(654\) | 6.92642 | − | 7.30122i | 0.270844 | − | 0.285500i | ||||
\(655\) | 15.9671 | + | 15.1789i | 0.623887 | + | 0.593088i | ||||
\(656\) | 4.23059i | 0.165177i | ||||||||
\(657\) | 15.7709 | − | 17.5265i | 0.615282 | − | 0.683773i | ||||
\(658\) | 1.80809 | − | 1.80809i | 0.0704867 | − | 0.0704867i | ||||
\(659\) | −26.7954 | −1.04380 | −0.521901 | − | 0.853006i | \(-0.674777\pi\) | ||||
−0.521901 | + | 0.853006i | \(0.674777\pi\) | |||||||
\(660\) | 13.2516 | + | 11.9490i | 0.515816 | + | 0.465116i | ||||
\(661\) | 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 | ||||
\(663\) | 54.6512 | − | 1.43970i | 2.12248 | − | 0.0559134i | ||||
\(664\) | 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 | ||||||||
\(672\) | −0.0340607 | − | 1.29295i | −0.00131392 | − | 0.0498765i | ||||
\(673\) | −10.7591 | + | 10.7591i | −0.414733 | + | 0.414733i | −0.883384 | − | 0.468651i | \(-0.844740\pi\) |
0.468651 | + | 0.883384i | \(0.344740\pi\) | |||||||
\(674\) | −16.3742 | −0.630712 | ||||||||
\(675\) | 25.7628 | − | 3.35812i | 0.991612 | − | 0.129254i | ||||
\(676\) | −31.9337 | −1.22822 | ||||||||
\(677\) | 21.0042 | − | 21.0042i | 0.807257 | − | 0.807257i | −0.176961 | − | 0.984218i | \(-0.556627\pi\) |
0.984218 | + | 0.176961i | \(0.0566266\pi\) | |||||||
\(678\) | 0.0402708 | + | 1.52868i | 0.00154659 | + | 0.0587087i | ||||
\(679\) | 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 | \(-0.449269\pi\) |
−0.987326 | + | 0.158702i | \(0.949269\pi\) | |||||||
\(684\) | −15.6109 | + | 0.823061i | −0.596897 | + | 0.0314705i | ||||
\(685\) | −0.607606 | − | 24.0088i | −0.0232154 | − | 0.917330i | ||||
\(686\) | 10.0380i | 0.383252i | ||||||||
\(687\) | 0.934154 | − | 0.0246089i | 0.0356402 | − | 0.000938886i | ||||
\(688\) | 7.82352 | − | 7.82352i | 0.298269 | − | 0.298269i | ||||
\(689\) | −15.7472 | −0.599921 | ||||||||
\(690\) | −2.87632 | − | 2.59360i | −0.109500 | − | 0.0987368i | ||||
\(691\) | −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 | ||||
\(693\) | −6.90367 | + | 7.67216i | −0.262249 | + | 0.291441i | ||||
\(694\) | − | 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 | \(-0.0487573\pi\) | |||||||
\(702\) | −34.7225 | + | 2.74922i | −1.31052 | + | 0.103763i | ||||
\(703\) | 36.9053 | − | 36.9053i | 1.39191 | − | 1.39191i | ||||
\(704\) | 4.60712 | 0.173637 | ||||||||
\(705\) | 13.2444 | − | 0.684542i | 0.498811 | − | 0.0257813i | ||||
\(706\) | 28.5784 | 1.07556 | ||||||||
\(707\) | −4.21900 | + | 4.21900i | −0.158672 | + | 0.158672i | ||||
\(708\) | −22.0585 | + | 0.581099i | −0.829011 | + | 0.0218390i | ||||
\(709\) | 3.66459i | 0.137627i | 0.997630 | + | 0.0688133i | \(0.0219213\pi\) | ||||
−0.997630 | + | 0.0688133i | \(0.978079\pi\) | |||||||
\(710\) | 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 | ||||||
\(717\) | −0.147605 | − | 5.60308i | −0.00551240 | − | 0.209251i | ||||
\(718\) | 6.75511 | − | 6.75511i | 0.252098 | − | 0.252098i | ||||
\(719\) | −2.43829 | −0.0909327 | −0.0454664 | − | 0.998966i | \(-0.514477\pi\) | ||||
−0.0454664 | + | 0.998966i | \(0.514477\pi\) | |||||||
\(720\) | 4.35950 | − | 5.09851i | 0.162469 | − | 0.190010i | ||||
\(721\) | 8.84262 | 0.329316 | ||||||||
\(722\) | 5.76504 | − | 5.76504i | 0.214553 | − | 0.214553i | ||||
\(723\) | −0.113744 | − | 4.31774i | −0.00423020 | − | 0.160579i | ||||
\(724\) | − | 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 | 0.974403 | − | 0.224807i | \(-0.0721751\pi\) |
−0.224807 | + | 0.974403i | \(0.572175\pi\) | |||||||
\(728\) | 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 | ||||||
\(732\) | 2.61476 | − | 0.0688818i | 0.0966442 | − | 0.00254594i | ||||
\(733\) | −27.8025 | + | 27.8025i | −1.02691 | + | 1.02691i | −0.0272828 | + | 0.999628i | \(0.508685\pi\) |
−0.999628 | + | 0.0272828i | \(0.991315\pi\) | |||||||
\(734\) | 22.4771 | 0.829645 | ||||||||
\(735\) | −16.7090 | + | 18.5303i | −0.616320 | + | 0.683502i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −24.1878 | + | 24.1878i | −0.890970 | + | 0.890970i | ||||
\(738\) | −9.43449 | − | 8.48948i | −0.347288 | − | 0.312502i | ||||
\(739\) | 4.34293i | 0.159757i | 0.996805 | + | 0.0798786i | \(0.0254533\pi\) | ||||
−0.996805 | + | 0.0798786i | \(0.974547\pi\) | |||||||
\(740\) | 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 | \(-0.0445821\pi\) |
−0.139601 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(744\) | 4.67257 | − | 4.92542i | 0.171305 | − | 0.180575i | ||||
\(745\) | 8.96488 | − | 9.43042i | 0.328448 | − | 0.345504i | ||||
\(746\) | 30.9879i | 1.13455i | ||||||||
\(747\) | −30.5391 | − | 27.4801i | −1.11737 | − | 1.00545i | ||||
\(748\) | 15.3397 | − | 15.3397i | 0.560877 | − | 0.560877i | ||||
\(749\) | −11.4360 | −0.417861 | ||||||||
\(750\) | −1.97650 | − | 19.2638i | −0.0721715 | − | 0.703414i | ||||
\(751\) | 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 | ||||
\(753\) | −9.33787 | + | 0.245992i | −0.340291 | + | 0.00896445i | ||||
\(754\) | 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 | 0.794662 | − | 0.607053i | \(-0.207648\pi\) |
−0.607053 | + | 0.794662i | \(0.707648\pi\) | |||||||
\(758\) | −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 | \(-0.100993\pi\) | |||||||
\(762\) | 0.711839 | + | 27.0215i | 0.0257872 | + | 0.978885i | ||||
\(763\) | 3.06806 | − | 3.06806i | 0.111071 | − | 0.111071i | ||||
\(764\) | 16.3310 | 0.590835 | ||||||||
\(765\) | −2.46057 | − | 31.4911i | −0.0889622 | − | 1.13856i | ||||
\(766\) | 25.0862 | 0.906400 | ||||||||
\(767\) | 60.3862 | − | 60.3862i | 2.18042 | − | 2.18042i | ||||
\(768\) | −0.0456124 | − | 1.73145i | −0.00164590 | − | 0.0624783i | ||||
\(769\) | 41.6311i | 1.50126i | 0.660725 | + | 0.750628i | \(0.270249\pi\) | ||||
−0.660725 | + | 0.750628i | \(0.729751\pi\) | |||||||
\(770\) | 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 | \(-0.0817071\pi\) |
−0.253881 | + | 0.967235i | \(0.581707\pi\) | |||||||
\(774\) | 1.74759 | + | 33.1464i | 0.0628159 | + | 1.19142i | ||||
\(775\) | −0.991353 | − | 19.5735i | −0.0356104 | − | 0.703102i | ||||
\(776\) | 8.05432i | 0.289133i | ||||||||
\(777\) | −12.9501 | + | 0.341152i | −0.464584 | + | 0.0122388i | ||||
\(778\) | 14.1902 | − | 14.1902i | 0.508742 | − | 0.508742i | ||||
\(779\) | 22.0450 | 0.789843 | ||||||||
\(780\) | 1.34005 | + | 25.9270i | 0.0479815 | + | 0.928335i | ||||
\(781\) | −50.3032 | −1.79999 | ||||||||
\(782\) | −3.32957 | + | 3.32957i | −0.119065 | + | 0.119065i | ||||
\(783\) | 1.02776 | + | 12.9806i | 0.0367292 | + | 0.463887i | ||||
\(784\) | 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 | 0.861159 | − | 0.508335i | \(-0.169739\pi\) |
−0.508335 | + | 0.861159i | \(0.669739\pi\) | |||||||
\(788\) | −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 | ||||||||
\(792\) | −9.24506 | + | 10.2742i | −0.328509 | + | 0.365077i | ||||
\(793\) | −7.15801 | + | 7.15801i | −0.254188 | + | 0.254188i | ||||
\(794\) | −36.9217 | −1.31030 | ||||||||
\(795\) | 0.469627 | + | 9.08623i | 0.0166559 | + | 0.322255i | ||||
\(796\) | 19.6455 | 0.696315 | ||||||||
\(797\) | −20.9341 | + | 20.9341i | −0.741522 | + | 0.741522i | −0.972871 | − | 0.231349i | \(-0.925686\pi\) |
0.231349 | + | 0.972871i | \(0.425686\pi\) | |||||||
\(798\) | −6.73735 | + | 0.177485i | −0.238500 | + | 0.00628291i | ||||
\(799\) | − | 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 | ||||||||
\(807\) | −1.07166 | − | 40.6801i | −0.0377241 | − | 1.43201i | ||||
\(808\) | −5.64988 | + | 5.64988i | −0.198762 | + | 0.198762i | ||||
\(809\) | −1.00481 | −0.0353272 | −0.0176636 | − | 0.999844i | \(-0.505623\pi\) | ||||
−0.0176636 | + | 0.999844i | \(0.505623\pi\) | |||||||
\(810\) | 2.62184 | + | 19.9531i | 0.0921221 | + | 0.701080i | ||||
\(811\) | 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 | ||||
\(813\) | 0.281233 | + | 10.6756i | 0.00986328 | + | 0.374411i | ||||
\(814\) | − | 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 | \(0.868608\pi\) | |||||||
\(822\) | 18.5967 | − | 0.489901i | 0.648633 | − | 0.0170873i | ||||
\(823\) | 23.9384 | − | 23.9384i | 0.834442 | − | 0.834442i | −0.153679 | − | 0.988121i | \(-0.549112\pi\) |
0.988121 | + | 0.153679i | \(0.0491122\pi\) | |||||||
\(824\) | 11.8416 | 0.412522 | ||||||||
\(825\) | 3.06686 | + | 39.7808i | 0.106774 | + | 1.38499i | ||||
\(826\) | −9.51343 | −0.331015 | ||||||||
\(827\) | −12.6490 | + | 12.6490i | −0.439849 | + | 0.439849i | −0.891961 | − | 0.452112i | \(-0.850671\pi\) |
0.452112 | + | 0.891961i | \(0.350671\pi\) | |||||||
\(828\) | 2.00669 | − | 2.23007i | 0.0697373 | − | 0.0775002i | ||||
\(829\) | 36.2001i | 1.25728i | 0.777696 | + | 0.628641i | \(0.216388\pi\) | ||||
−0.777696 | + | 0.628641i | \(0.783612\pi\) | |||||||
\(830\) | −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 | ||||||
\(837\) | 1.60760 | + | 20.3039i | 0.0555669 | + | 0.701806i | ||||
\(838\) | −6.46912 | + | 6.46912i | −0.223472 | + | 0.223472i | ||||
\(839\) | 40.1271 | 1.38534 | 0.692671 | − | 0.721254i | \(-0.256434\pi\) | ||||
0.692671 | + | 0.721254i | \(0.256434\pi\) | |||||||
\(840\) | 1.93675 | − | 2.14787i | 0.0668243 | − | 0.0741085i | ||||
\(841\) | −22.7203 | −0.783460 | ||||||||
\(842\) | 20.1023 | − | 20.1023i | 0.692772 | − | 0.692772i | ||||
\(843\) | 0.596399 | − | 0.0157112i | 0.0205411 | − | 0.000541123i | ||||
\(844\) | 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 | ||||||||
\(852\) | 0.498023 | + | 18.9050i | 0.0170620 | + | 0.647674i | ||||
\(853\) | −32.6791 | + | 32.6791i | −1.11891 | + | 1.11891i | −0.127011 | + | 0.991901i | \(0.540539\pi\) |
−0.991901 | + | 0.127011i | \(0.959461\pi\) | |||||||
\(854\) | 1.12770 | 0.0385890 | ||||||||
\(855\) | −26.5676 | − | 22.7167i | −0.908592 | − | 0.776895i | ||||
\(856\) | −15.3145 | −0.523439 | ||||||||
\(857\) | −38.3689 | + | 38.3689i | −1.31066 | + | 1.31066i | −0.389725 | + | 0.920931i | \(0.627430\pi\) |
−0.920931 | + | 0.389725i | \(0.872570\pi\) | |||||||
\(858\) | −1.40863 | − | 53.4719i | −0.0480900 | − | 1.82550i | ||||
\(859\) | 27.0975i | 0.924554i | 0.886736 | + | 0.462277i | \(0.152967\pi\) | ||||
−0.886736 | + | 0.462277i | \(0.847033\pi\) | |||||||
\(860\) | 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 | \(-0.399601\pi\) |
−0.950668 | + | 0.310209i | \(0.899601\pi\) | |||||||
\(864\) | 3.95278 | + | 3.37276i | 0.134476 | + | 0.114744i | ||||
\(865\) | 31.9601 | − | 0.808834i | 1.08668 | − | 0.0275012i | ||||
\(866\) | − | 28.3370i | − | 0.962929i | ||||||
\(867\) | −8.95530 | + | 0.235914i | −0.304138 | + | 0.00801205i | ||||
\(868\) | 2.06972 | − | 2.06972i | 0.0702507 | − | 0.0702507i | ||||
\(869\) | −30.7333 | −1.04255 | ||||||||
\(870\) | 9.69247 | − | 0.500961i | 0.328606 | − | 0.0169842i | ||||
\(871\) | −49.7701 | −1.68639 | ||||||||
\(872\) | 4.10859 | − | 4.10859i | 0.139134 | − | 0.139134i | ||||
\(873\) | −17.9617 | − | 16.1625i | −0.607910 | − | 0.547018i | ||||
\(874\) | 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 | 0.786995 | − | 0.616959i | \(-0.211636\pi\) |
−0.616959 | + | 0.786995i | \(0.711636\pi\) | |||||||
\(878\) | −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 | \(-0.181479\pi\) | |||||||
\(882\) | −14.3669 | − | 12.9279i | −0.483760 | − | 0.435303i | ||||
\(883\) | 20.5528 | − | 20.5528i | 0.691656 | − | 0.691656i | −0.270940 | − | 0.962596i | \(-0.587335\pi\) |
0.962596 | + | 0.270940i | \(0.0873346\pi\) | |||||||
\(884\) | 31.5638 | 1.06161 | ||||||||
\(885\) | −36.6441 | − | 33.0423i | −1.23178 | − | 1.11071i | ||||
\(886\) | −5.77413 | −0.193986 | ||||||||
\(887\) | −3.65344 | + | 3.65344i | −0.122671 | + | 0.122671i | −0.765777 | − | 0.643106i | \(-0.777645\pi\) |
0.643106 | + | 0.765777i | \(0.277645\pi\) | |||||||
\(888\) | −17.3422 | + | 0.456854i | −0.581966 | + | 0.0153310i | ||||
\(889\) | 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 | ||||||
\(897\) | 0.305752 | + | 11.6064i | 0.0102088 | + | 0.387525i | ||||
\(898\) | 4.10438 | − | 4.10438i | 0.136965 | − | 0.136965i | ||||
\(899\) | 9.82253 | 0.327600 | ||||||||
\(900\) | 14.9201 | − | 1.54644i | 0.497336 | − | 0.0515478i | ||||
\(901\) | 11.0617 | 0.368518 | ||||||||
\(902\) | 13.7821 | − | 13.7821i | 0.458894 | − | 0.458894i | ||||
\(903\) | 0.376852 | + | 14.3053i | 0.0125408 | + | 0.476051i | ||||
\(904\) | 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 | 0.917789 | − | 0.397069i | \(-0.129972\pi\) |
−0.397069 | + | 0.917789i | \(0.629972\pi\) | |||||||
\(908\) | −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 | \(-0.0914930\pi\) | |||||||
\(912\) | −9.02233 | + | 0.237680i | −0.298759 | + | 0.00787036i | ||||
\(913\) | 44.6122 | − | 44.6122i | 1.47645 | − | 1.47645i | ||||
\(914\) | 4.30896 | 0.142528 | ||||||||
\(915\) | 4.34369 | + | 3.91674i | 0.143598 | + | 0.129484i | ||||
\(916\) | 0.539521 | 0.0178263 | ||||||||
\(917\) | −5.20232 | + | 5.20232i | −0.171796 | + | 0.171796i | ||||
\(918\) | 24.3909 | − | 1.93120i | 0.805021 | − | 0.0637391i | ||||
\(919\) | − | 38.6421i | − | 1.27469i | −0.770580 | − | 0.637343i | \(-0.780033\pi\) | ||
0.770580 | − | 0.637343i | \(-0.219967\pi\) | |||||||
\(920\) | −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 | ||||||
\(927\) | −23.7624 | + | 26.4076i | −0.780460 | + | 0.867338i | ||||
\(928\) | 1.77196 | − | 1.77196i | 0.0581674 | − | 0.0581674i | ||||
\(929\) | −4.79606 | −0.157354 | −0.0786768 | − | 0.996900i | \(-0.525070\pi\) | ||||
−0.0786768 | + | 0.996900i | \(0.525070\pi\) | |||||||
\(930\) | 15.1608 | − | 0.783593i | 0.497142 | − | 0.0256950i | ||||
\(931\) | 33.5703 | 1.10022 | ||||||||
\(932\) | −5.01691 | + | 5.01691i | −0.164334 | + | 0.164334i | ||||
\(933\) | −23.1019 | + | 0.608584i | −0.756322 | + | 0.0199241i | ||||
\(934\) | − | 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 | 0.847710 | − | 0.530460i | \(-0.177981\pi\) |
−0.530460 | + | 0.847710i | \(0.677981\pi\) | |||||||
\(938\) | 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 | \(-0.0357663\pi\) | |||||||
\(942\) | −0.408654 | − | 15.5125i | −0.0133147 | − | 0.505425i | ||||
\(943\) | −2.99148 | + | 2.99148i | −0.0974159 | + | 0.0974159i | ||||
\(944\) | −12.7399 | −0.414649 | ||||||||
\(945\) | 0.903428 | + | 8.62919i | 0.0293885 | + | 0.280708i | ||||
\(946\) | −50.9738 | −1.65730 | ||||||||
\(947\) | −7.17276 | + | 7.17276i | −0.233083 | + | 0.233083i | −0.813978 | − | 0.580895i | \(-0.802703\pi\) |
0.580895 | + | 0.813978i | \(0.302703\pi\) | |||||||
\(948\) | 0.304272 | + | 11.5502i | 0.00988230 | + | 0.375133i | ||||
\(949\) | 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 | \(-0.259928\pi\) |
−0.728815 | + | 0.684711i | \(0.759928\pi\) | |||||||
\(954\) | −7.03779 | + | 0.371057i | −0.227857 | + | 0.0120134i | ||||
\(955\) | 26.4666 | + | 25.1601i | 0.856439 | + | 0.814160i | ||||
\(956\) | − | 3.23606i | − | 0.104662i | ||||||
\(957\) | −19.9898 | + | 0.526600i | −0.646178 | + | 0.0170226i | ||||
\(958\) | −13.9494 | + | 13.9494i | −0.450686 | + | 0.450686i | ||||
\(959\) | 8.02039 | 0.258992 | ||||||||
\(960\) | 2.59360 | − | 2.87632i | 0.0837082 | − | 0.0928328i | ||||
\(961\) | −15.6358 | −0.504380 | ||||||||
\(962\) | 47.4750 | − | 47.4750i | 1.53066 | − | 1.53066i | ||||
\(963\) | 30.7314 | − | 34.1523i | 0.990307 | − | 1.10054i | ||||
\(964\) | − | 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 | 0.655795 | − | 0.754939i | \(-0.272334\pi\) |
−0.754939 | + | 0.655795i | \(0.772334\pi\) | |||||||
\(968\) | −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 | \(-0.188801\pi\) | |||||||
\(972\) | −15.4535 | + | 2.04687i | −0.495671 | + | 0.0656533i | ||||
\(973\) | −7.74123 | + | 7.74123i | −0.248173 | + | 0.248173i | ||||
\(974\) | −7.52797 | −0.241212 | ||||||||
\(975\) | −37.7722 | + | 44.0827i | −1.20968 | + | 1.41178i | ||||
\(976\) | 1.51016 | 0.0483389 | ||||||||
\(977\) | −34.9877 | + | 34.9877i | −1.11936 | + | 1.11936i | −0.127521 | + | 0.991836i | \(0.540702\pi\) |
−0.991836 | + | 0.127521i | \(0.959298\pi\) | |||||||
\(978\) | −7.67165 | + | 0.202098i | −0.245312 | + | 0.00646238i | ||||
\(979\) | − | 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 | \(-0.232147\pi\) |
−0.666357 | + | 0.745633i | \(0.732147\pi\) | |||||||
\(984\) | −5.31604 | − | 5.04315i | −0.169469 | − | 0.160770i | ||||
\(985\) | −1.52094 | − | 60.0980i | −0.0484611 | − | 1.91488i | ||||
\(986\) | − | 11.7997i | − | 0.375780i | ||||||
\(987\) | 0.116632 | + | 4.42736i | 0.00371244 | + | 0.140924i | ||||
\(988\) | 24.6990 | − | 24.6990i | 0.785781 | − | 0.785781i | ||||
\(989\) | 11.0641 | 0.351819 | ||||||||
\(990\) | −30.8116 | + | 2.40748i | −0.979256 | + | 0.0765146i | ||||
\(991\) | 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 | ||||
\(993\) | −0.854734 | − | 32.4458i | −0.0271242 | − | 1.02964i | ||||
\(994\) | 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 | 0.148782 | − | 0.988870i | \(-0.452465\pi\) |
−0.988870 | + | 0.148782i | \(0.952465\pi\) | |||||||
\(998\) | −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.47.5 | ✓ | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.47.16 | yes | 32 | |
5.3 | odd | 4 | inner | 690.2.i.f.323.16 | yes | 32 | |
15.8 | even | 4 | inner | 690.2.i.f.323.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.2.i.f.47.16 | yes | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.323.5 | yes | 32 | 15.8 | even | 4 | inner | |
690.2.i.f.323.16 | yes | 32 | 5.3 | odd | 4 | inner |