Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), degree \(4\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 493.4 | ||
Root | \(-1.44378 + 0.833568i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.493 |
Dual form | 1050.2.bc.f.607.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 0.258819i | 0.683013 | + | 0.183013i | ||||
\(3\) | −0.258819 | − | 0.965926i | −0.149429 | − | 0.557678i | ||||
\(4\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 2.63306 | − | 0.258819i | 0.995204 | − | 0.0978244i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17884 | − | 2.04182i | 0.355435 | − | 0.615631i | −0.631758 | − | 0.775166i | \(-0.717666\pi\) |
0.987192 | + | 0.159535i | \(0.0509996\pi\) | |||||||
\(12\) | 0.258819 | − | 0.965926i | 0.0747146 | − | 0.278839i | ||||
\(13\) | −0.0968928 | + | 0.0968928i | −0.0268732 | + | 0.0268732i | −0.720416 | − | 0.693542i | \(-0.756049\pi\) |
0.693542 | + | 0.720416i | \(0.256049\pi\) | |||||||
\(14\) | 2.61033 | + | 0.431486i | 0.697640 | + | 0.115320i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 3.11092 | − | 0.833568i | 0.754508 | − | 0.202170i | 0.138991 | − | 0.990294i | \(-0.455614\pi\) |
0.615517 | + | 0.788124i | \(0.288947\pi\) | |||||||
\(18\) | −0.965926 | + | 0.258819i | −0.227671 | + | 0.0610042i | ||||
\(19\) | −0.434539 | − | 0.752644i | −0.0996901 | − | 0.172668i | 0.811866 | − | 0.583843i | \(-0.198452\pi\) |
−0.911556 | + | 0.411175i | \(0.865118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.931486 | − | 2.47635i | −0.203267 | − | 0.540385i | ||||
\(22\) | 1.66714 | − | 1.66714i | 0.355435 | − | 0.355435i | ||||
\(23\) | −0.833568 | + | 3.11092i | −0.173811 | + | 0.648671i | 0.822940 | + | 0.568128i | \(0.192332\pi\) |
−0.996751 | + | 0.0805432i | \(0.974335\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.118669 | + | 0.0685135i | −0.0232729 | + | 0.0134366i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 2.40971 | + | 1.09239i | 0.455392 | + | 0.206442i | ||||
\(29\) | − | 4.08363i | − | 0.758311i | −0.925333 | − | 0.379156i | \(-0.876214\pi\) | ||
0.925333 | − | 0.379156i | \(-0.123786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.747356 | − | 0.431486i | −0.134229 | − | 0.0774973i | 0.431382 | − | 0.902170i | \(-0.358026\pi\) |
−0.565611 | + | 0.824672i | \(0.691360\pi\) | |||||||
\(32\) | 0.258819 | + | 0.965926i | 0.0457532 | + | 0.170753i | ||||
\(33\) | −2.27735 | − | 0.610214i | −0.396436 | − | 0.106225i | ||||
\(34\) | 3.22066 | 0.552338 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 9.51079 | + | 2.54841i | 1.56356 | + | 0.418956i | 0.933790 | − | 0.357822i | \(-0.116481\pi\) |
0.629774 | + | 0.776778i | \(0.283147\pi\) | |||||||
\(38\) | −0.224934 | − | 0.839465i | −0.0364891 | − | 0.136179i | ||||
\(39\) | 0.118669 | + | 0.0685135i | 0.0190022 | + | 0.0109709i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.86297i | − | 1.07182i | −0.844276 | − | 0.535908i | \(-0.819969\pi\) | ||
0.844276 | − | 0.535908i | \(-0.180031\pi\) | |||||||
\(42\) | −0.258819 | − | 2.63306i | −0.0399366 | − | 0.406290i | ||||
\(43\) | 2.57551 | + | 2.57551i | 0.392761 | + | 0.392761i | 0.875670 | − | 0.482909i | \(-0.160420\pi\) |
−0.482909 | + | 0.875670i | \(0.660420\pi\) | |||||||
\(44\) | 2.04182 | − | 1.17884i | 0.307815 | − | 0.177717i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.61033 | + | 2.78917i | −0.237430 | + | 0.411241i | ||||
\(47\) | 0.223354 | − | 0.833568i | 0.0325795 | − | 0.121588i | −0.947721 | − | 0.319100i | \(-0.896619\pi\) |
0.980301 | + | 0.197512i | \(0.0632861\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 6.86603 | − | 1.36297i | 0.980861 | − | 0.194710i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61033 | − | 2.78917i | −0.225491 | − | 0.390562i | ||||
\(52\) | −0.132358 | + | 0.0354652i | −0.0183548 | + | 0.00491814i | ||||
\(53\) | −8.07290 | + | 2.16313i | −1.10890 | + | 0.297129i | −0.766383 | − | 0.642384i | \(-0.777946\pi\) |
−0.342516 | + | 0.939512i | \(0.611279\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.04487 | + | 1.67884i | 0.273257 | + | 0.224345i | ||||
\(57\) | −0.614531 | + | 0.614531i | −0.0813966 | + | 0.0813966i | ||||
\(58\) | 1.05692 | − | 3.94449i | 0.138781 | − | 0.517936i | ||||
\(59\) | 5.35769 | − | 9.27978i | 0.697511 | − | 1.20812i | −0.271815 | − | 0.962349i | \(-0.587624\pi\) |
0.969327 | − | 0.245776i | \(-0.0790426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.44351 | + | 4.29751i | −0.953044 | + | 0.550240i | −0.894025 | − | 0.448017i | \(-0.852130\pi\) |
−0.0590186 | + | 0.998257i | \(0.518797\pi\) | |||||||
\(62\) | −0.610214 | − | 0.610214i | −0.0774973 | − | 0.0774973i | ||||
\(63\) | −2.15089 | + | 1.54067i | −0.270986 | + | 0.194107i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.04182 | − | 1.17884i | −0.251330 | − | 0.145106i | ||||
\(67\) | 3.28148 | + | 12.2466i | 0.400896 | + | 1.49617i | 0.811501 | + | 0.584352i | \(0.198651\pi\) |
−0.410604 | + | 0.911814i | \(0.634682\pi\) | |||||||
\(68\) | 3.11092 | + | 0.833568i | 0.377254 | + | 0.101085i | ||||
\(69\) | 3.22066 | 0.387722 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.13703 | 0.609653 | 0.304826 | − | 0.952408i | \(-0.401402\pi\) | ||||
0.304826 | + | 0.952408i | \(0.401402\pi\) | |||||||
\(72\) | −0.965926 | − | 0.258819i | −0.113835 | − | 0.0305021i | ||||
\(73\) | −4.20718 | − | 15.7014i | −0.492413 | − | 1.83771i | −0.544064 | − | 0.839044i | \(-0.683115\pi\) |
0.0516512 | − | 0.998665i | \(-0.483552\pi\) | |||||||
\(74\) | 8.52714 | + | 4.92315i | 0.991260 | + | 0.572304i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.869078i | − | 0.0996901i | ||||||
\(77\) | 2.57551 | − | 5.68133i | 0.293506 | − | 0.647448i | ||||
\(78\) | 0.0968928 | + | 0.0968928i | 0.0109709 | + | 0.0109709i | ||||
\(79\) | −4.02036 | + | 2.32116i | −0.452326 | + | 0.261151i | −0.708812 | − | 0.705397i | \(-0.750769\pi\) |
0.256486 | + | 0.966548i | \(0.417435\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.77627 | − | 6.62912i | 0.196156 | − | 0.732064i | ||||
\(83\) | −7.13020 | + | 7.13020i | −0.782642 | + | 0.782642i | −0.980276 | − | 0.197634i | \(-0.936674\pi\) |
0.197634 | + | 0.980276i | \(0.436674\pi\) | |||||||
\(84\) | 0.431486 | − | 2.61033i | 0.0470790 | − | 0.284810i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.82116 | + | 3.15434i | 0.196380 | + | 0.340141i | ||||
\(87\) | −3.94449 | + | 1.05692i | −0.422893 | + | 0.113314i | ||||
\(88\) | 2.27735 | − | 0.610214i | 0.242766 | − | 0.0650490i | ||||
\(89\) | −4.98532 | − | 8.63484i | −0.528443 | − | 0.915291i | −0.999450 | − | 0.0331611i | \(-0.989443\pi\) |
0.471007 | − | 0.882130i | \(-0.343891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.230047 | + | 0.280202i | −0.0241155 | + | 0.0293732i | ||||
\(92\) | −2.27735 | + | 2.27735i | −0.237430 | + | 0.237430i | ||||
\(93\) | −0.223354 | + | 0.833568i | −0.0231607 | + | 0.0864370i | ||||
\(94\) | 0.431486 | − | 0.747356i | 0.0445044 | − | 0.0770839i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.866025 | − | 0.500000i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | 11.4245 | + | 11.4245i | 1.15998 | + | 1.15998i | 0.984479 | + | 0.175504i | \(0.0561555\pi\) |
0.175504 | + | 0.984479i | \(0.443845\pi\) | |||||||
\(98\) | 6.98483 | + | 0.460527i | 0.705575 | + | 0.0465203i | ||||
\(99\) | 2.35769i | 0.236956i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.547103 | − | 0.315870i | −0.0544388 | − | 0.0314302i | 0.472534 | − | 0.881313i | \(-0.343340\pi\) |
−0.526972 | + | 0.849882i | \(0.676673\pi\) | |||||||
\(102\) | −0.833568 | − | 3.11092i | −0.0825355 | − | 0.308027i | ||||
\(103\) | 1.57614 | + | 0.422325i | 0.155302 | + | 0.0416130i | 0.335632 | − | 0.941993i | \(-0.391050\pi\) |
−0.180331 | + | 0.983606i | \(0.557717\pi\) | |||||||
\(104\) | −0.137027 | −0.0134366 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.35769 | −0.811770 | ||||||||
\(107\) | −14.5929 | − | 3.91015i | −1.41075 | − | 0.378009i | −0.528556 | − | 0.848898i | \(-0.677266\pi\) |
−0.882192 | + | 0.470889i | \(0.843933\pi\) | |||||||
\(108\) | 0.258819 | + | 0.965926i | 0.0249049 | + | 0.0929463i | ||||
\(109\) | −7.45905 | − | 4.30648i | −0.714447 | − | 0.412486i | 0.0982585 | − | 0.995161i | \(-0.468673\pi\) |
−0.812705 | + | 0.582675i | \(0.802006\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.84629i | − | 0.934569i | ||||||
\(112\) | 1.54067 | + | 2.15089i | 0.145580 | + | 0.203240i | ||||
\(113\) | 12.4298 | + | 12.4298i | 1.16929 | + | 1.16929i | 0.982375 | + | 0.186919i | \(0.0598501\pi\) |
0.186919 | + | 0.982375i | \(0.440150\pi\) | |||||||
\(114\) | −0.752644 | + | 0.434539i | −0.0704915 | + | 0.0406983i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.04182 | − | 3.53653i | 0.189578 | − | 0.328358i | ||||
\(117\) | 0.0354652 | − | 0.132358i | 0.00327876 | − | 0.0122365i | ||||
\(118\) | 7.57691 | − | 7.57691i | 0.697511 | − | 0.697511i | ||||
\(119\) | 7.97549 | − | 3.00000i | 0.731112 | − | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.72066 | + | 4.71232i | 0.247333 | + | 0.428393i | ||||
\(122\) | −8.30216 | + | 2.22456i | −0.751642 | + | 0.201402i | ||||
\(123\) | −6.62912 | + | 1.77627i | −0.597728 | + | 0.160161i | ||||
\(124\) | −0.431486 | − | 0.747356i | −0.0387486 | − | 0.0671146i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.47635 | + | 0.931486i | −0.220611 | + | 0.0829834i | ||||
\(127\) | −9.62150 | + | 9.62150i | −0.853770 | + | 0.853770i | −0.990595 | − | 0.136825i | \(-0.956310\pi\) |
0.136825 | + | 0.990595i | \(0.456310\pi\) | |||||||
\(128\) | −0.258819 | + | 0.965926i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | 1.82116 | − | 3.15434i | 0.160344 | − | 0.277724i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.0418 | + | 6.37500i | −0.964728 | + | 0.556986i | −0.897625 | − | 0.440760i | \(-0.854709\pi\) |
−0.0671030 | + | 0.997746i | \(0.521376\pi\) | |||||||
\(132\) | −1.66714 | − | 1.66714i | −0.145106 | − | 0.145106i | ||||
\(133\) | −1.33897 | − | 1.86929i | −0.116103 | − | 0.162088i | ||||
\(134\) | 12.6787i | 1.09527i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.78917 | + | 1.61033i | 0.239170 | + | 0.138085i | ||||
\(137\) | 3.57258 | + | 13.3330i | 0.305226 | + | 1.13912i | 0.932751 | + | 0.360522i | \(0.117402\pi\) |
−0.627525 | + | 0.778597i | \(0.715932\pi\) | |||||||
\(138\) | 3.11092 | + | 0.833568i | 0.264819 | + | 0.0709580i | ||||
\(139\) | −13.9299 | −1.18152 | −0.590760 | − | 0.806847i | \(-0.701172\pi\) | ||||
−0.590760 | + | 0.806847i | \(0.701172\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.862973 | −0.0726754 | ||||||||
\(142\) | 4.96199 | + | 1.32956i | 0.416401 | + | 0.111574i | ||||
\(143\) | 0.0836158 | + | 0.312059i | 0.00699231 | + | 0.0260957i | ||||
\(144\) | −0.866025 | − | 0.500000i | −0.0721688 | − | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 16.2553i | − | 1.34530i | ||||||
\(147\) | −3.09359 | − | 6.27931i | −0.255155 | − | 0.517909i | ||||
\(148\) | 6.96238 | + | 6.96238i | 0.572304 | + | 0.572304i | ||||
\(149\) | −16.7851 | + | 9.69087i | −1.37509 | + | 0.793907i | −0.991563 | − | 0.129625i | \(-0.958623\pi\) |
−0.383523 | + | 0.923531i | \(0.625289\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.57380 | − | 2.72590i | 0.128074 | − | 0.221831i | −0.794856 | − | 0.606798i | \(-0.792454\pi\) |
0.922930 | + | 0.384967i | \(0.125787\pi\) | |||||||
\(152\) | 0.224934 | − | 0.839465i | 0.0182445 | − | 0.0680896i | ||||
\(153\) | −2.27735 | + | 2.27735i | −0.184113 | + | 0.184113i | ||||
\(154\) | 3.95818 | − | 4.82116i | 0.318960 | − | 0.388500i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0685135 | + | 0.118669i | 0.00548547 | + | 0.00950112i | ||||
\(157\) | −5.96135 | + | 1.59734i | −0.475768 | + | 0.127482i | −0.488731 | − | 0.872434i | \(-0.662540\pi\) |
0.0129635 | + | 0.999916i | \(0.495873\pi\) | |||||||
\(158\) | −4.48413 | + | 1.20152i | −0.356738 | + | 0.0955877i | ||||
\(159\) | 4.17884 | + | 7.23797i | 0.331404 | + | 0.574008i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.38967 | + | 8.40698i | −0.109521 | + | 0.662563i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −0.717766 | + | 2.67874i | −0.0562198 | + | 0.209815i | −0.988322 | − | 0.152380i | \(-0.951306\pi\) |
0.932102 | + | 0.362196i | \(0.117973\pi\) | |||||||
\(164\) | 3.43149 | − | 5.94351i | 0.267954 | − | 0.464110i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.73268 | + | 5.04182i | −0.677788 | + | 0.391321i | ||||
\(167\) | −12.1316 | − | 12.1316i | −0.938772 | − | 0.938772i | 0.0594585 | − | 0.998231i | \(-0.481063\pi\) |
−0.998231 | + | 0.0594585i | \(0.981063\pi\) | |||||||
\(168\) | 1.09239 | − | 2.40971i | 0.0842795 | − | 0.185913i | ||||
\(169\) | 12.9812i | 0.998556i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.752644 | + | 0.434539i | 0.0575561 | + | 0.0332300i | ||||
\(172\) | 0.942700 | + | 3.51821i | 0.0718802 | + | 0.268261i | ||||
\(173\) | 1.24086 | + | 0.332486i | 0.0943405 | + | 0.0252785i | 0.305681 | − | 0.952134i | \(-0.401116\pi\) |
−0.211340 | + | 0.977413i | \(0.567783\pi\) | |||||||
\(174\) | −4.08363 | −0.309579 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.35769 | 0.177717 | ||||||||
\(177\) | −10.3503 | − | 2.77334i | −0.777973 | − | 0.208457i | ||||
\(178\) | −2.58059 | − | 9.63091i | −0.193424 | − | 0.721867i | ||||
\(179\) | −16.7851 | − | 9.69087i | −1.25458 | − | 0.724329i | −0.282560 | − | 0.959249i | \(-0.591184\pi\) |
−0.972015 | + | 0.234920i | \(0.924517\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.1913i | 1.87246i | 0.351394 | + | 0.936228i | \(0.385708\pi\) | ||||
−0.351394 | + | 0.936228i | \(0.614292\pi\) | |||||||
\(182\) | −0.294730 | + | 0.211114i | −0.0218468 | + | 0.0156488i | ||||
\(183\) | 6.07760 | + | 6.07760i | 0.449269 | + | 0.449269i | ||||
\(184\) | −2.78917 | + | 1.61033i | −0.205621 | + | 0.118715i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.431486 | + | 0.747356i | −0.0316381 | + | 0.0547988i | ||||
\(187\) | 1.96529 | − | 7.33457i | 0.143716 | − | 0.536357i | ||||
\(188\) | 0.610214 | − | 0.610214i | 0.0445044 | − | 0.0445044i | ||||
\(189\) | 2.04487 | + | 1.67884i | 0.148742 | + | 0.122118i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.43149 | − | 5.94351i | −0.248294 | − | 0.430057i | 0.714759 | − | 0.699371i | \(-0.246536\pi\) |
−0.963052 | + | 0.269314i | \(0.913203\pi\) | |||||||
\(192\) | 0.965926 | − | 0.258819i | 0.0697097 | − | 0.0186787i | ||||
\(193\) | −2.68464 | + | 0.719346i | −0.193244 | + | 0.0517797i | −0.354143 | − | 0.935191i | \(-0.615227\pi\) |
0.160899 | + | 0.986971i | \(0.448561\pi\) | |||||||
\(194\) | 8.07834 | + | 13.9921i | 0.579991 | + | 1.00457i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.62764 | + | 2.25264i | 0.473403 | + | 0.160903i | ||||
\(197\) | 17.3662 | − | 17.3662i | 1.23729 | − | 1.23729i | 0.276190 | − | 0.961103i | \(-0.410928\pi\) |
0.961103 | − | 0.276190i | \(-0.0890720\pi\) | |||||||
\(198\) | −0.610214 | + | 2.27735i | −0.0433660 | + | 0.161844i | ||||
\(199\) | −5.26553 | + | 9.12016i | −0.373263 | + | 0.646511i | −0.990065 | − | 0.140607i | \(-0.955095\pi\) |
0.616802 | + | 0.787118i | \(0.288428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.9800 | − | 6.33933i | 0.774472 | − | 0.447142i | ||||
\(202\) | −0.446708 | − | 0.446708i | −0.0314302 | − | 0.0314302i | ||||
\(203\) | −1.05692 | − | 10.7525i | −0.0741814 | − | 0.754674i | ||||
\(204\) | − | 3.22066i | − | 0.225491i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.41313 | + | 0.815870i | 0.0984573 | + | 0.0568444i | ||||
\(207\) | −0.833568 | − | 3.11092i | −0.0579370 | − | 0.216224i | ||||
\(208\) | −0.132358 | − | 0.0354652i | −0.00917738 | − | 0.00245907i | ||||
\(209\) | −2.04901 | −0.141733 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6726 | 0.941257 | 0.470629 | − | 0.882331i | \(-0.344027\pi\) | ||||
0.470629 | + | 0.882331i | \(0.344027\pi\) | |||||||
\(212\) | −8.07290 | − | 2.16313i | −0.554449 | − | 0.148564i | ||||
\(213\) | −1.32956 | − | 4.96199i | −0.0911000 | − | 0.339990i | ||||
\(214\) | −13.0836 | − | 7.55384i | −0.894379 | − | 0.516370i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −2.07951 | − | 0.942700i | −0.141167 | − | 0.0639947i | ||||
\(218\) | −6.09028 | − | 6.09028i | −0.412486 | − | 0.412486i | ||||
\(219\) | −14.0775 | + | 8.12764i | −0.951268 | + | 0.549215i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.220659 | + | 0.382192i | −0.0148431 | + | 0.0257090i | ||||
\(222\) | 2.54841 | − | 9.51079i | 0.171038 | − | 0.638322i | ||||
\(223\) | −6.42310 | + | 6.42310i | −0.430122 | + | 0.430122i | −0.888670 | − | 0.458547i | \(-0.848370\pi\) |
0.458547 | + | 0.888670i | \(0.348370\pi\) | |||||||
\(224\) | 0.931486 | + | 2.47635i | 0.0622376 | + | 0.165458i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.78917 | + | 15.2233i | 0.584647 | + | 1.01264i | ||||
\(227\) | −15.0192 | + | 4.02438i | −0.996858 | + | 0.267107i | −0.720128 | − | 0.693841i | \(-0.755917\pi\) |
−0.276729 | + | 0.960948i | \(0.589250\pi\) | |||||||
\(228\) | −0.839465 | + | 0.224934i | −0.0555949 | + | 0.0148966i | ||||
\(229\) | −5.40393 | − | 9.35988i | −0.357102 | − | 0.618518i | 0.630374 | − | 0.776292i | \(-0.282902\pi\) |
−0.987475 | + | 0.157774i | \(0.949568\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.15434 | − | 1.01731i | −0.404926 | − | 0.0669341i | ||||
\(232\) | 2.88756 | − | 2.88756i | 0.189578 | − | 0.189578i | ||||
\(233\) | 3.25066 | − | 12.1316i | 0.212958 | − | 0.794768i | −0.773918 | − | 0.633286i | \(-0.781706\pi\) |
0.986876 | − | 0.161483i | \(-0.0516275\pi\) | |||||||
\(234\) | 0.0685135 | − | 0.118669i | 0.00447887 | − | 0.00775763i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.27978 | − | 5.35769i | 0.604062 | − | 0.348756i | ||||
\(237\) | 3.28261 | + | 3.28261i | 0.213229 | + | 0.213229i | ||||
\(238\) | 8.48019 | − | 0.833568i | 0.549689 | − | 0.0540322i | ||||
\(239\) | 15.9706i | 1.03306i | 0.856270 | + | 0.516528i | \(0.172776\pi\) | ||||
−0.856270 | + | 0.516528i | \(0.827224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6526 | + | 13.6558i | 1.52360 | + | 0.879649i | 0.999610 | + | 0.0279230i | \(0.00888932\pi\) |
0.523987 | + | 0.851726i | \(0.324444\pi\) | |||||||
\(242\) | 1.40832 | + | 5.25591i | 0.0905300 | + | 0.337863i | ||||
\(243\) | −0.965926 | − | 0.258819i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | −8.59502 | −0.550240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.86297 | −0.437567 | ||||||||
\(247\) | 0.115029 | + | 0.0308220i | 0.00731915 | + | 0.00196116i | ||||
\(248\) | −0.223354 | − | 0.833568i | −0.0141830 | − | 0.0529316i | ||||
\(249\) | 8.73268 | + | 5.04182i | 0.553411 | + | 0.319512i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.45189i | 0.217881i | 0.994048 | + | 0.108941i | \(0.0347459\pi\) | ||||
−0.994048 | + | 0.108941i | \(0.965254\pi\) | |||||||
\(252\) | −2.63306 | + | 0.258819i | −0.165867 | + | 0.0163041i | ||||
\(253\) | 5.36927 | + | 5.36927i | 0.337563 | + | 0.337563i | ||||
\(254\) | −11.7839 | + | 6.80343i | −0.739387 | + | 0.426885i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.99415 | − | 7.44226i | 0.124392 | − | 0.464236i | −0.875426 | − | 0.483353i | \(-0.839419\pi\) |
0.999817 | + | 0.0191171i | \(0.00608554\pi\) | |||||||
\(258\) | 2.57551 | − | 2.57551i | 0.160344 | − | 0.160344i | ||||
\(259\) | 25.7021 | + | 4.24854i | 1.59705 | + | 0.263992i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.04182 | + | 3.53653i | 0.126385 | + | 0.218906i | ||||
\(262\) | −12.3155 | + | 3.29994i | −0.760857 | + | 0.203871i | ||||
\(263\) | −20.4976 | + | 5.49231i | −1.26394 | + | 0.338670i | −0.827704 | − | 0.561164i | \(-0.810354\pi\) |
−0.436231 | + | 0.899835i | \(0.643687\pi\) | |||||||
\(264\) | −1.17884 | − | 2.04182i | −0.0725528 | − | 0.125665i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.809534 | − | 2.15215i | −0.0496357 | − | 0.131956i | ||||
\(267\) | −7.05031 | + | 7.05031i | −0.431472 | + | 0.431472i | ||||
\(268\) | −3.28148 | + | 12.2466i | −0.200448 | + | 0.748083i | ||||
\(269\) | −0.595654 | + | 1.03170i | −0.0363177 | + | 0.0629041i | −0.883613 | − | 0.468218i | \(-0.844896\pi\) |
0.847295 | + | 0.531122i | \(0.178229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.05603 | + | 4.07380i | −0.428623 | + | 0.247466i | −0.698760 | − | 0.715356i | \(-0.746264\pi\) |
0.270137 | + | 0.962822i | \(0.412931\pi\) | |||||||
\(272\) | 2.27735 | + | 2.27735i | 0.138085 | + | 0.138085i | ||||
\(273\) | 0.330195 | + | 0.149687i | 0.0199843 | + | 0.00905944i | ||||
\(274\) | 13.8034i | 0.833893i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.78917 | + | 1.61033i | 0.167888 | + | 0.0969304i | ||||
\(277\) | 4.34472 | + | 16.2147i | 0.261049 | + | 0.974248i | 0.964625 | + | 0.263627i | \(0.0849189\pi\) |
−0.703576 | + | 0.710620i | \(0.748414\pi\) | |||||||
\(278\) | −13.4553 | − | 3.60533i | −0.806994 | − | 0.216233i | ||||
\(279\) | 0.862973 | 0.0516648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5053 | 0.626693 | 0.313346 | − | 0.949639i | \(-0.398550\pi\) | ||||
0.313346 | + | 0.949639i | \(0.398550\pi\) | |||||||
\(282\) | −0.833568 | − | 0.223354i | −0.0496382 | − | 0.0133005i | ||||
\(283\) | −6.47184 | − | 24.1532i | −0.384711 | − | 1.43576i | −0.838622 | − | 0.544714i | \(-0.816638\pi\) |
0.453911 | − | 0.891047i | \(-0.350028\pi\) | |||||||
\(284\) | 4.44880 | + | 2.56851i | 0.263987 | + | 0.152413i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.323067i | 0.0191033i | ||||||||
\(287\) | −1.77627 | − | 18.0706i | −0.104850 | − | 1.06668i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | −5.73946 | + | 3.31368i | −0.337615 | + | 0.194922i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.07834 | − | 13.9921i | 0.473561 | − | 0.820232i | ||||
\(292\) | 4.20718 | − | 15.7014i | 0.246206 | − | 0.918855i | ||||
\(293\) | 8.66269 | − | 8.66269i | 0.506080 | − | 0.506080i | −0.407241 | − | 0.913321i | \(-0.633509\pi\) |
0.913321 | + | 0.407241i | \(0.133509\pi\) | |||||||
\(294\) | −1.36297 | − | 6.86603i | −0.0794902 | − | 0.400435i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.92315 | + | 8.52714i | 0.286152 | + | 0.495630i | ||||
\(297\) | 2.27735 | − | 0.610214i | 0.132145 | − | 0.0354082i | ||||
\(298\) | −18.7213 | + | 5.01636i | −1.08450 | + | 0.290590i | ||||
\(299\) | −0.220659 | − | 0.382192i | −0.0127610 | − | 0.0221027i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.44805 | + | 6.11487i | 0.429299 | + | 0.352455i | ||||
\(302\) | 2.22569 | − | 2.22569i | 0.128074 | − | 0.128074i | ||||
\(303\) | −0.163506 | + | 0.610214i | −0.00939319 | + | 0.0350559i | ||||
\(304\) | 0.434539 | − | 0.752644i | 0.0249225 | − | 0.0431671i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.78917 | + | 1.61033i | −0.159446 | + | 0.0920564i | ||||
\(307\) | −6.28097 | − | 6.28097i | −0.358474 | − | 0.358474i | 0.504776 | − | 0.863250i | \(-0.331575\pi\) |
−0.863250 | + | 0.504776i | \(0.831575\pi\) | |||||||
\(308\) | 5.07112 | − | 3.63243i | 0.288954 | − | 0.206977i | ||||
\(309\) | − | 1.63174i | − | 0.0928264i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.1714 | − | 7.02714i | −0.690175 | − | 0.398473i | 0.113503 | − | 0.993538i | \(-0.463793\pi\) |
−0.803678 | + | 0.595065i | \(0.797126\pi\) | |||||||
\(312\) | 0.0354652 | + | 0.132358i | 0.00200782 | + | 0.00749330i | ||||
\(313\) | 19.0255 | + | 5.09785i | 1.07538 | + | 0.288148i | 0.752703 | − | 0.658361i | \(-0.228750\pi\) |
0.322679 | + | 0.946508i | \(0.395416\pi\) | |||||||
\(314\) | −6.17165 | −0.348286 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.64231 | −0.261151 | ||||||||
\(317\) | −2.29778 | − | 0.615688i | −0.129056 | − | 0.0345805i | 0.193713 | − | 0.981058i | \(-0.437947\pi\) |
−0.322769 | + | 0.946478i | \(0.604614\pi\) | |||||||
\(318\) | 2.16313 | + | 8.07290i | 0.121302 | + | 0.452706i | ||||
\(319\) | −8.33802 | − | 4.81396i | −0.466840 | − | 0.269530i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.1077i | 0.843228i | ||||||||
\(322\) | −3.51821 | + | 7.76085i | −0.196062 | + | 0.432495i | ||||
\(323\) | −1.97919 | − | 1.97919i | −0.110125 | − | 0.110125i | ||||
\(324\) | 0.866025 | − | 0.500000i | 0.0481125 | − | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.38662 | + | 2.40169i | −0.0767977 | + | 0.133017i | ||||
\(327\) | −2.22920 | + | 8.31948i | −0.123275 | + | 0.460069i | ||||
\(328\) | 4.85285 | − | 4.85285i | 0.267954 | − | 0.267954i | ||||
\(329\) | 0.372361 | − | 2.25264i | 0.0205289 | − | 0.124192i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8430 | − | 23.9768i | −0.760881 | − | 1.31788i | −0.942397 | − | 0.334496i | \(-0.891434\pi\) |
0.181516 | − | 0.983388i | \(-0.441899\pi\) | |||||||
\(332\) | −9.74004 | + | 2.60984i | −0.534554 | + | 0.143233i | ||||
\(333\) | −9.51079 | + | 2.54841i | −0.521188 | + | 0.139652i | ||||
\(334\) | −8.57834 | − | 14.8581i | −0.469386 | − | 0.813001i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.67884 | − | 2.04487i | 0.0915884 | − | 0.111557i | ||||
\(337\) | 3.18572 | − | 3.18572i | 0.173537 | − | 0.173537i | −0.614994 | − | 0.788532i | \(-0.710842\pi\) |
0.788532 | + | 0.614994i | \(0.210842\pi\) | |||||||
\(338\) | −3.35979 | + | 12.5389i | −0.182748 | + | 0.682026i | ||||
\(339\) | 8.78917 | − | 15.2233i | 0.477362 | − | 0.826816i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.76203 | + | 1.01731i | −0.0954194 | + | 0.0550904i | ||||
\(342\) | 0.614531 | + | 0.614531i | 0.0332300 | + | 0.0332300i | ||||
\(343\) | 17.7259 | − | 5.36585i | 0.957109 | − | 0.289729i | ||||
\(344\) | 3.64231i | 0.196380i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.11252 | + | 0.642314i | 0.0598095 | + | 0.0345310i | ||||
\(347\) | −1.49816 | − | 5.59119i | −0.0804252 | − | 0.300151i | 0.913983 | − | 0.405752i | \(-0.132990\pi\) |
−0.994409 | + | 0.105601i | \(0.966324\pi\) | |||||||
\(348\) | −3.94449 | − | 1.05692i | −0.211447 | − | 0.0566569i | ||||
\(349\) | 19.6326 | 1.05091 | 0.525455 | − | 0.850821i | \(-0.323895\pi\) | ||||
0.525455 | + | 0.850821i | \(0.323895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.137027 | −0.00731396 | ||||||||
\(352\) | 2.27735 | + | 0.610214i | 0.121383 | + | 0.0325245i | ||||
\(353\) | −6.73787 | − | 25.1461i | −0.358621 | − | 1.33839i | −0.875866 | − | 0.482554i | \(-0.839709\pi\) |
0.517246 | − | 0.855837i | \(-0.326957\pi\) | |||||||
\(354\) | −9.27978 | − | 5.35769i | −0.493215 | − | 0.284758i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 9.97065i | − | 0.528443i | ||||||
\(357\) | −4.96199 | − | 6.92728i | −0.262616 | − | 0.366630i | ||||
\(358\) | −13.7050 | − | 13.7050i | −0.724329 | − | 0.724329i | ||||
\(359\) | −6.41108 | + | 3.70144i | −0.338364 | + | 0.195355i | −0.659548 | − | 0.751662i | \(-0.729252\pi\) |
0.321184 | + | 0.947017i | \(0.395919\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.12235 | − | 15.8004i | 0.480124 | − | 0.831599i | ||||
\(362\) | −6.51999 | + | 24.3329i | −0.342683 | + | 1.27891i | ||||
\(363\) | 3.84759 | − | 3.84759i | 0.201946 | − | 0.201946i | ||||
\(364\) | −0.339328 | + | 0.127639i | −0.0177856 | + | 0.00669010i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.29751 | + | 7.44351i | 0.224635 | + | 0.389078i | ||||
\(367\) | −11.6580 | + | 3.12375i | −0.608542 | + | 0.163058i | −0.549914 | − | 0.835222i | \(-0.685339\pi\) |
−0.0586284 | + | 0.998280i | \(0.518673\pi\) | |||||||
\(368\) | −3.11092 | + | 0.833568i | −0.162168 | + | 0.0434527i | ||||
\(369\) | 3.43149 | + | 5.94351i | 0.178636 | + | 0.309407i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.6966 | + | 7.78507i | −1.07451 | + | 0.404181i | ||||
\(372\) | −0.610214 | + | 0.610214i | −0.0316381 | + | 0.0316381i | ||||
\(373\) | −0.0308220 | + | 0.115029i | −0.00159590 | + | 0.00595600i | −0.966719 | − | 0.255840i | \(-0.917648\pi\) |
0.965123 | + | 0.261796i | \(0.0843147\pi\) | |||||||
\(374\) | 3.79665 | − | 6.57599i | 0.196320 | − | 0.340036i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.747356 | − | 0.431486i | 0.0385420 | − | 0.0222522i | ||||
\(377\) | 0.395674 | + | 0.395674i | 0.0203783 | + | 0.0203783i | ||||
\(378\) | 1.54067 | + | 2.15089i | 0.0792438 | + | 0.110630i | ||||
\(379\) | 8.83801i | 0.453978i | 0.973897 | + | 0.226989i | \(0.0728881\pi\) | ||||
−0.973897 | + | 0.226989i | \(0.927112\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7839 | + | 6.80343i | 0.603707 | + | 0.348550i | ||||
\(382\) | −1.77627 | − | 6.62912i | −0.0908818 | − | 0.339175i | ||||
\(383\) | 37.3678 | + | 10.0127i | 1.90941 | + | 0.511624i | 0.994042 | + | 0.108999i | \(0.0347644\pi\) |
0.915365 | + | 0.402625i | \(0.131902\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.77934 | −0.141465 | ||||||||
\(387\) | −3.51821 | − | 0.942700i | −0.178840 | − | 0.0479201i | ||||
\(388\) | 4.18166 | + | 15.6062i | 0.212292 | + | 0.792283i | ||||
\(389\) | −26.3005 | − | 15.1846i | −1.33349 | − | 0.769888i | −0.347654 | − | 0.937623i | \(-0.613021\pi\) |
−0.985832 | + | 0.167735i | \(0.946355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3726i | 0.524567i | ||||||||
\(392\) | 5.81878 | + | 3.89125i | 0.293893 | + | 0.196538i | ||||
\(393\) | 9.01560 | + | 9.01560i | 0.454777 | + | 0.454777i | ||||
\(394\) | 21.2692 | − | 12.2798i | 1.07153 | − | 0.618647i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.17884 | + | 2.04182i | −0.0592391 | + | 0.102605i | ||||
\(397\) | 6.97566 | − | 26.0335i | 0.350098 | − | 1.30658i | −0.536444 | − | 0.843936i | \(-0.680233\pi\) |
0.886542 | − | 0.462648i | \(-0.153101\pi\) | |||||||
\(398\) | −7.44658 | + | 7.44658i | −0.373263 | + | 0.373263i | ||||
\(399\) | −1.45905 | + | 1.77715i | −0.0730436 | + | 0.0889688i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.86297 | − | 11.8870i | −0.342721 | − | 0.593609i | 0.642216 | − | 0.766523i | \(-0.278015\pi\) |
−0.984937 | + | 0.172914i | \(0.944682\pi\) | |||||||
\(402\) | 12.2466 | − | 3.28148i | 0.610807 | − | 0.163665i | ||||
\(403\) | 0.114221 | − | 0.0306055i | 0.00568977 | − | 0.00152457i | ||||
\(404\) | −0.315870 | − | 0.547103i | −0.0157151 | − | 0.0272194i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.76203 | − | 10.6596i | 0.0874482 | − | 0.529028i | ||||
\(407\) | 16.4151 | − | 16.4151i | 0.813667 | − | 0.813667i | ||||
\(408\) | 0.833568 | − | 3.11092i | 0.0412678 | − | 0.154013i | ||||
\(409\) | 2.11119 | − | 3.65669i | 0.104392 | − | 0.180812i | −0.809098 | − | 0.587674i | \(-0.800044\pi\) |
0.913489 | + | 0.406862i | \(0.133377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9541 | − | 6.90169i | 0.589651 | − | 0.340435i | ||||
\(412\) | 1.15381 | + | 1.15381i | 0.0568444 | + | 0.0568444i | ||||
\(413\) | 11.7053 | − | 25.8209i | 0.575982 | − | 1.27056i | ||||
\(414\) | − | 3.22066i | − | 0.158287i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.118669 | − | 0.0685135i | −0.00581822 | − | 0.00335915i | ||||
\(417\) | 3.60533 | + | 13.4553i | 0.176554 | + | 0.658908i | ||||
\(418\) | −1.97919 | − | 0.530323i | −0.0968056 | − | 0.0259390i | ||||
\(419\) | 28.1807 | 1.37672 | 0.688359 | − | 0.725370i | \(-0.258331\pi\) | ||||
0.688359 | + | 0.725370i | \(0.258331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.31486 | −0.161557 | −0.0807783 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807783 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(422\) | 13.2067 | + | 3.53872i | 0.642891 | + | 0.172262i | ||||
\(423\) | 0.223354 | + | 0.833568i | 0.0108598 | + | 0.0405295i | ||||
\(424\) | −7.23797 | − | 4.17884i | −0.351507 | − | 0.202943i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 5.13703i | − | 0.248890i | ||||||
\(427\) | −18.4869 | + | 13.2421i | −0.894646 | + | 0.640832i | ||||
\(428\) | −10.6827 | − | 10.6827i | −0.516370 | − | 0.516370i | ||||
\(429\) | 0.279784 | − | 0.161533i | 0.0135081 | − | 0.00779891i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.08773 | + | 3.61606i | −0.100563 | + | 0.174179i | −0.911917 | − | 0.410376i | \(-0.865398\pi\) |
0.811354 | + | 0.584555i | \(0.198731\pi\) | |||||||
\(432\) | −0.258819 | + | 0.965926i | −0.0124524 | + | 0.0464731i | ||||
\(433\) | −4.81820 | + | 4.81820i | −0.231548 | + | 0.231548i | −0.813339 | − | 0.581791i | \(-0.802352\pi\) |
0.581791 | + | 0.813339i | \(0.302352\pi\) | |||||||
\(434\) | −1.76467 | − | 1.44880i | −0.0847067 | − | 0.0695444i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.30648 | − | 7.45905i | −0.206243 | − | 0.357223i | ||||
\(437\) | 2.70363 | − | 0.724435i | 0.129332 | − | 0.0346544i | ||||
\(438\) | −15.7014 | + | 4.20718i | −0.750242 | + | 0.201027i | ||||
\(439\) | 1.24102 | + | 2.14951i | 0.0592307 | + | 0.102591i | 0.894120 | − | 0.447827i | \(-0.147802\pi\) |
−0.834890 | + | 0.550417i | \(0.814469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.26467 | + | 4.61338i | −0.250698 | + | 0.219685i | ||||
\(442\) | −0.312059 | + | 0.312059i | −0.0148431 | + | 0.0148431i | ||||
\(443\) | −3.83026 | + | 14.2947i | −0.181981 | + | 0.679164i | 0.813275 | + | 0.581879i | \(0.197682\pi\) |
−0.995257 | + | 0.0972845i | \(0.968984\pi\) | |||||||
\(444\) | 4.92315 | − | 8.52714i | 0.233642 | − | 0.404680i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.86666 | + | 4.54182i | −0.372497 | + | 0.215061i | ||||
\(447\) | 13.7050 | + | 13.7050i | 0.648222 | + | 0.648222i | ||||
\(448\) | 0.258819 | + | 2.63306i | 0.0122281 | + | 0.124400i | ||||
\(449\) | − | 0.554300i | − | 0.0261590i | −0.999914 | − | 0.0130795i | \(-0.995837\pi\) | ||
0.999914 | − | 0.0130795i | \(-0.00416346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0129 | − | 8.09037i | −0.659843 | − | 0.380961i | ||||
\(452\) | 4.54961 | + | 16.9794i | 0.213996 | + | 0.798643i | ||||
\(453\) | −3.04035 | − | 0.814659i | −0.142848 | − | 0.0382760i | ||||
\(454\) | −15.5490 | −0.729750 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.869078 | −0.0406983 | ||||||||
\(457\) | 30.9884 | + | 8.30331i | 1.44958 | + | 0.388413i | 0.895876 | − | 0.444304i | \(-0.146549\pi\) |
0.553699 | + | 0.832717i | \(0.313216\pi\) | |||||||
\(458\) | −2.79728 | − | 10.4396i | −0.130708 | − | 0.487810i | ||||
\(459\) | 2.78917 | + | 1.61033i | 0.130187 | + | 0.0751637i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.441317i | − | 0.0205542i | −0.999947 | − | 0.0102771i | \(-0.996729\pi\) | ||
0.999947 | − | 0.0102771i | \(-0.00327136\pi\) | |||||||
\(462\) | −5.68133 | − | 2.57551i | −0.264320 | − | 0.119823i | ||||
\(463\) | 26.0183 | + | 26.0183i | 1.20917 | + | 1.20917i | 0.971295 | + | 0.237877i | \(0.0764516\pi\) |
0.237877 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(464\) | 3.53653 | − | 2.04182i | 0.164179 | − | 0.0947889i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.27978 | − | 10.8769i | 0.290905 | − | 0.503863i | ||||
\(467\) | −5.06565 | + | 18.9052i | −0.234410 | + | 0.874831i | 0.744004 | + | 0.668175i | \(0.232924\pi\) |
−0.978414 | + | 0.206655i | \(0.933742\pi\) | |||||||
\(468\) | 0.0968928 | − | 0.0968928i | 0.00447887 | − | 0.00447887i | ||||
\(469\) | 11.8100 | + | 31.3968i | 0.545335 | + | 1.44977i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.08582 | + | 5.34480i | 0.142187 | + | 0.246275i | ||||
\(472\) | 10.3503 | − | 2.77334i | 0.476409 | − | 0.127653i | ||||
\(473\) | 8.29482 | − | 2.22259i | 0.381396 | − | 0.102195i | ||||
\(474\) | 2.32116 | + | 4.02036i | 0.106614 | + | 0.184661i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.40698 | + | 1.38967i | 0.385333 | + | 0.0636954i | ||||
\(477\) | 5.90978 | − | 5.90978i | 0.270590 | − | 0.270590i | ||||
\(478\) | −4.13351 | + | 15.4265i | −0.189062 | + | 0.705590i | ||||
\(479\) | 15.3363 | − | 26.5632i | 0.700732 | − | 1.21370i | −0.267477 | − | 0.963564i | \(-0.586190\pi\) |
0.968210 | − | 0.250140i | \(-0.0804766\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.16845 | + | 0.674604i | −0.0532767 | + | 0.0307593i | ||||
\(482\) | 19.3123 | + | 19.3123i | 0.879649 | + | 0.879649i | ||||
\(483\) | 8.48019 | − | 0.833568i | 0.385862 | − | 0.0379286i | ||||
\(484\) | 5.44132i | 0.247333i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.866025 | − | 0.500000i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | −6.37653 | − | 23.7975i | −0.288948 | − | 1.07837i | −0.945906 | − | 0.324441i | \(-0.894824\pi\) |
0.656958 | − | 0.753927i | \(-0.271843\pi\) | |||||||
\(488\) | −8.30216 | − | 2.22456i | −0.375821 | − | 0.100701i | ||||
\(489\) | 2.77324 | 0.125410 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.08275 | 0.139122 | 0.0695612 | − | 0.997578i | \(-0.477840\pi\) | ||||
0.0695612 | + | 0.997578i | \(0.477840\pi\) | |||||||
\(492\) | −6.62912 | − | 1.77627i | −0.298864 | − | 0.0800804i | ||||
\(493\) | −3.40398 | − | 12.7038i | −0.153308 | − | 0.572152i | ||||
\(494\) | 0.103133 | + | 0.0595436i | 0.00464015 | + | 0.00267899i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.862973i | − | 0.0387486i | ||||||
\(497\) | 13.5261 | − | 1.32956i | 0.606729 | − | 0.0596389i | ||||
\(498\) | 7.13020 | + | 7.13020i | 0.319512 | + | 0.319512i | ||||
\(499\) | 28.7283 | − | 16.5863i | 1.28605 | − | 0.742503i | 0.308105 | − | 0.951352i | \(-0.400305\pi\) |
0.977948 | + | 0.208849i | \(0.0669717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.57834 | + | 14.8581i | −0.383252 | + | 0.663812i | ||||
\(502\) | −0.893415 | + | 3.33427i | −0.0398751 | + | 0.148816i | ||||
\(503\) | −23.7377 | + | 23.7377i | −1.05841 | + | 1.05841i | −0.0602259 | + | 0.998185i | \(0.519182\pi\) |
−0.998185 | + | 0.0602259i | \(0.980818\pi\) | |||||||
\(504\) | −2.61033 | − | 0.431486i | −0.116273 | − | 0.0192199i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.79665 | + | 6.57599i | 0.168782 | + | 0.292339i | ||||
\(507\) | 12.5389 | − | 3.35979i | 0.556872 | − | 0.149213i | ||||
\(508\) | −13.1432 | + | 3.52171i | −0.583136 | + | 0.156251i | ||||
\(509\) | 13.6202 | + | 23.5908i | 0.603703 | + | 1.04564i | 0.992255 | + | 0.124217i | \(0.0396420\pi\) |
−0.388552 | + | 0.921427i | \(0.627025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.1416 | − | 40.2538i | −0.669824 | − | 1.78072i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0.224934 | − | 0.839465i | 0.00993107 | − | 0.0370633i | ||||
\(514\) | 3.85240 | − | 6.67255i | 0.169922 | − | 0.294314i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.15434 | − | 1.82116i | 0.138862 | − | 0.0801720i | ||||
\(517\) | −1.43869 | − | 1.43869i | −0.0632736 | − | 0.0632736i | ||||
\(518\) | 23.7267 | + | 10.7560i | 1.04249 | + | 0.472590i | ||||
\(519\) | − | 1.28463i | − | 0.0563889i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8599 | − | 6.26995i | −0.475780 | − | 0.274692i | 0.242876 | − | 0.970057i | \(-0.421909\pi\) |
−0.718656 | + | 0.695366i | \(0.755242\pi\) | |||||||
\(522\) | 1.05692 | + | 3.94449i | 0.0462602 | + | 0.172645i | ||||
\(523\) | −1.61327 | − | 0.432274i | −0.0705433 | − | 0.0189020i | 0.223375 | − | 0.974733i | \(-0.428293\pi\) |
−0.293918 | + | 0.955831i | \(0.594959\pi\) | |||||||
\(524\) | −12.7500 | −0.556986 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2207 | −0.925265 | ||||||||
\(527\) | −2.68464 | − | 0.719346i | −0.116945 | − | 0.0313352i | ||||
\(528\) | −0.610214 | − | 2.27735i | −0.0265562 | − | 0.0991089i | ||||
\(529\) | 10.9356 | + | 6.31368i | 0.475461 | + | 0.274508i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.7154i | 0.465008i | ||||||||
\(532\) | −0.224934 | − | 2.28834i | −0.00975212 | − | 0.0992119i | ||||
\(533\) | 0.664973 | + | 0.664973i | 0.0288032 | + | 0.0288032i | ||||
\(534\) | −8.63484 | + | 4.98532i | −0.373666 | + | 0.215736i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.33933 | + | 10.9800i | −0.273817 | + | 0.474265i | ||||
\(537\) | −5.01636 | + | 18.7213i | −0.216472 | + | 0.807884i | ||||
\(538\) | −0.842382 | + | 0.842382i | −0.0363177 | + | 0.0363177i | ||||
\(539\) | 5.31103 | − | 15.6259i | 0.228762 | − | 0.673055i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.9661 | − | 24.1900i | −0.600450 | − | 1.04001i | −0.992753 | − | 0.120174i | \(-0.961655\pi\) |
0.392303 | − | 0.919836i | \(-0.371678\pi\) | |||||||
\(542\) | −7.86998 | + | 2.10875i | −0.338045 | + | 0.0905788i | ||||
\(543\) | 24.3329 | − | 6.51999i | 1.04423 | − | 0.279800i | ||||
\(544\) | 1.61033 | + | 2.78917i | 0.0690423 | + | 0.119585i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.280202 | + | 0.230047i | 0.0119916 | + | 0.00984510i | ||||
\(547\) | −3.01203 | + | 3.01203i | −0.128785 | + | 0.128785i | −0.768561 | − | 0.639776i | \(-0.779027\pi\) |
0.639776 | + | 0.768561i | \(0.279027\pi\) | |||||||
\(548\) | −3.57258 | + | 13.3330i | −0.152613 | + | 0.569560i | ||||
\(549\) | 4.29751 | − | 7.44351i | 0.183413 | − | 0.317681i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.07352 | + | 1.77450i | −0.130936 | + | 0.0755961i | ||||
\(552\) | 2.27735 | + | 2.27735i | 0.0969304 | + | 0.0969304i | ||||
\(553\) | −9.98510 | + | 7.15230i | −0.424610 | + | 0.304147i | ||||
\(554\) | 16.7867i | 0.713199i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0637 | − | 6.96496i | −0.511614 | − | 0.295380i | ||||
\(557\) | 5.58276 | + | 20.8352i | 0.236549 | + | 0.882814i | 0.977444 | + | 0.211193i | \(0.0677349\pi\) |
−0.740895 | + | 0.671621i | \(0.765598\pi\) | |||||||
\(558\) | 0.833568 | + | 0.223354i | 0.0352877 | + | 0.00945532i | ||||
\(559\) | −0.499096 | −0.0211095 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.59330 | −0.320589 | ||||||||
\(562\) | 10.1473 | + | 2.71897i | 0.428039 | + | 0.114693i | ||||
\(563\) | 8.06743 | + | 30.1081i | 0.340002 | + | 1.26890i | 0.898344 | + | 0.439293i | \(0.144771\pi\) |
−0.558342 | + | 0.829611i | \(0.688562\pi\) | |||||||
\(564\) | −0.747356 | − | 0.431486i | −0.0314694 | − | 0.0181689i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 25.0053i | − | 1.05105i | ||||||
\(567\) | 1.09239 | − | 2.40971i | 0.0458759 | − | 0.101198i | ||||
\(568\) | 3.63243 | + | 3.63243i | 0.152413 | + | 0.152413i | ||||
\(569\) | −2.12720 | + | 1.22814i | −0.0891767 | + | 0.0514862i | −0.543925 | − | 0.839134i | \(-0.683062\pi\) |
0.454749 | + | 0.890620i | \(0.349729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.62235 | − | 8.00615i | 0.193439 | − | 0.335047i | −0.752948 | − | 0.658080i | \(-0.771369\pi\) |
0.946388 | + | 0.323033i | \(0.104702\pi\) | |||||||
\(572\) | −0.0836158 | + | 0.312059i | −0.00349615 | + | 0.0130478i | ||||
\(573\) | −4.85285 | + | 4.85285i | −0.202731 | + | 0.202731i | ||||
\(574\) | 2.96128 | − | 17.9146i | 0.123601 | − | 0.747742i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −45.0669 | + | 12.0756i | −1.87616 | + | 0.502715i | −0.876381 | + | 0.481618i | \(0.840049\pi\) |
−0.999777 | + | 0.0210977i | \(0.993284\pi\) | |||||||
\(578\) | −6.40154 | + | 1.71529i | −0.266269 | + | 0.0713465i | ||||
\(579\) | 1.38967 | + | 2.40698i | 0.0577527 | + | 0.100031i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.9288 | + | 20.6197i | −0.702326 | + | 0.855449i | ||||
\(582\) | 11.4245 | − | 11.4245i | 0.473561 | − | 0.473561i | ||||
\(583\) | −5.09998 | + | 19.0334i | −0.211219 | + | 0.788282i | ||||
\(584\) | 8.12764 | − | 14.0775i | 0.336324 | − | 0.582530i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.6096 | − | 6.12545i | 0.438278 | − | 0.253040i | ||||
\(587\) | −0.512695 | − | 0.512695i | −0.0211612 | − | 0.0211612i | 0.696447 | − | 0.717608i | \(-0.254763\pi\) |
−0.717608 | + | 0.696447i | \(0.754763\pi\) | |||||||
\(588\) | 0.460527 | − | 6.98483i | 0.0189918 | − | 0.288050i | ||||
\(589\) | 0.749991i | 0.0309028i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.2692 | − | 12.2798i | −0.874898 | − | 0.505123i | ||||
\(592\) | 2.54841 | + | 9.51079i | 0.104739 | + | 0.390891i | ||||
\(593\) | 22.5910 | + | 6.05324i | 0.927701 | + | 0.248577i | 0.690874 | − | 0.722975i | \(-0.257226\pi\) |
0.236827 | + | 0.971552i | \(0.423893\pi\) | |||||||
\(594\) | 2.35769 | 0.0967370 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.3817 | −0.793907 | ||||||||
\(597\) | 10.1722 | + | 2.72564i | 0.416321 | + | 0.111553i | ||||
\(598\) | −0.114221 | − | 0.426280i | −0.00467086 | − | 0.0174319i | ||||
\(599\) | 9.39922 | + | 5.42664i | 0.384042 | + | 0.221727i | 0.679575 | − | 0.733606i | \(-0.262164\pi\) |
−0.295534 | + | 0.955332i | \(0.595497\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.5701i | 0.961443i | 0.876873 | + | 0.480721i | \(0.159625\pi\) | ||||
−0.876873 | + | 0.480721i | \(0.840375\pi\) | |||||||
\(602\) | 5.61162 | + | 7.83421i | 0.228713 | + | 0.319299i | ||||
\(603\) | −8.96516 | − | 8.96516i | −0.365090 | − | 0.365090i | ||||
\(604\) | 2.72590 | − | 1.57380i | 0.110915 | − | 0.0640370i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.315870 | + | 0.547103i | −0.0128313 | + | 0.0222245i | ||||
\(607\) | 7.58314 | − | 28.3006i | 0.307790 | − | 1.14869i | −0.622727 | − | 0.782439i | \(-0.713975\pi\) |
0.930517 | − | 0.366249i | \(-0.119358\pi\) | |||||||
\(608\) | 0.614531 | − | 0.614531i | 0.0249225 | − | 0.0249225i | ||||
\(609\) | −10.1125 | + | 3.80385i | −0.409780 | + | 0.154140i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0591253 | + | 0.102408i | 0.00239195 | + | 0.00414299i | ||||
\(612\) | −3.11092 | + | 0.833568i | −0.125751 | + | 0.0336950i | ||||
\(613\) | −3.03612 | + | 0.813525i | −0.122628 | + | 0.0328580i | −0.319611 | − | 0.947549i | \(-0.603552\pi\) |
0.196983 | + | 0.980407i | \(0.436886\pi\) | |||||||
\(614\) | −4.44132 | − | 7.69259i | −0.179237 | − | 0.310448i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.83847 | − | 2.19615i | 0.235239 | − | 0.0884855i | ||||
\(617\) | 26.2183 | − | 26.2183i | 1.05551 | − | 1.05551i | 0.0571445 | − | 0.998366i | \(-0.481800\pi\) |
0.998366 | − | 0.0571445i | \(-0.0181996\pi\) | |||||||
\(618\) | 0.422325 | − | 1.57614i | 0.0169884 | − | 0.0634016i | ||||
\(619\) | 11.7918 | − | 20.4240i | 0.473953 | − | 0.820910i | −0.525603 | − | 0.850730i | \(-0.676160\pi\) |
0.999555 | + | 0.0298201i | \(0.00949342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.78917 | + | 1.61033i | −0.111926 | + | 0.0646203i | ||||
\(622\) | −9.93788 | − | 9.93788i | −0.398473 | − | 0.398473i | ||||
\(623\) | −15.3615 | − | 21.4458i | −0.615447 | − | 0.859206i | ||||
\(624\) | 0.137027i | 0.00548547i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.0578 | + | 9.84830i | 0.681765 | + | 0.393617i | ||||
\(627\) | 0.530323 | + | 1.97919i | 0.0211791 | + | 0.0790414i | ||||
\(628\) | −5.96135 | − | 1.59734i | −0.237884 | − | 0.0637408i | ||||
\(629\) | 31.7116 | 1.26442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.97684 | −0.357362 | −0.178681 | − | 0.983907i | \(-0.557183\pi\) | ||||
−0.178681 | + | 0.983907i | \(0.557183\pi\) | |||||||
\(632\) | −4.48413 | − | 1.20152i | −0.178369 | − | 0.0477939i | ||||
\(633\) | −3.53872 | − | 13.2067i | −0.140651 | − | 0.524918i | ||||
\(634\) | −2.06013 | − | 1.18942i | −0.0818182 | − | 0.0472378i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.35769i | 0.331404i | ||||||||
\(637\) | −0.533206 | + | 0.797331i | −0.0211264 | + | 0.0315914i | ||||
\(638\) | −6.80797 | − | 6.80797i | −0.269530 | − | 0.269530i | ||||
\(639\) | −4.44880 | + | 2.56851i | −0.175992 | + | 0.101609i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.96802 | − | 12.0690i | 0.275220 | − | 0.476695i | −0.694971 | − | 0.719038i | \(-0.744583\pi\) |
0.970191 | + | 0.242343i | \(0.0779160\pi\) | |||||||
\(642\) | −3.91015 | + | 14.5929i | −0.154321 | + | 0.575936i | ||||
\(643\) | −25.1156 | + | 25.1156i | −0.990461 | + | 0.990461i | −0.999955 | − | 0.00949415i | \(-0.996978\pi\) |
0.00949415 | + | 0.999955i | \(0.496978\pi\) | |||||||
\(644\) | −5.40698 | + | 6.58582i | −0.213065 | + | 0.259518i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.39950 | − | 2.42401i | −0.0550627 | − | 0.0953713i | ||||
\(647\) | 41.2236 | − | 11.0458i | 1.62067 | − | 0.434256i | 0.669470 | − | 0.742839i | \(-0.266521\pi\) |
0.951197 | + | 0.308583i | \(0.0998547\pi\) | |||||||
\(648\) | 0.965926 | − | 0.258819i | 0.0379452 | − | 0.0101674i | ||||
\(649\) | −12.6317 | − | 21.8788i | −0.495839 | − | 0.858819i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.372361 | + | 2.25264i | −0.0145940 | + | 0.0882881i | ||||
\(652\) | −1.96097 | + | 1.96097i | −0.0767977 | + | 0.0767977i | ||||
\(653\) | 7.90392 | − | 29.4978i | 0.309304 | − | 1.15434i | −0.619872 | − | 0.784703i | \(-0.712815\pi\) |
0.929176 | − | 0.369637i | \(-0.120518\pi\) | |||||||
\(654\) | −4.30648 | + | 7.45905i | −0.168397 | + | 0.291672i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.94351 | − | 3.43149i | 0.232055 | − | 0.133977i | ||||
\(657\) | 11.4942 | + | 11.4942i | 0.448432 | + | 0.448432i | ||||
\(658\) | 0.942700 | − | 2.07951i | 0.0367503 | − | 0.0810678i | ||||
\(659\) | − | 29.4442i | − | 1.14698i | −0.819211 | − | 0.573492i | \(-0.805588\pi\) | ||
0.819211 | − | 0.573492i | \(-0.194412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.4306 | + | 6.59945i | 0.444598 | + | 0.256689i | 0.705546 | − | 0.708664i | \(-0.250702\pi\) |
−0.260948 | + | 0.965353i | \(0.584035\pi\) | |||||||
\(662\) | −7.16567 | − | 26.7426i | −0.278502 | − | 1.03938i | ||||
\(663\) | 0.426280 | + | 0.114221i | 0.0165553 | + | 0.00443599i | ||||
\(664\) | −10.0836 | −0.391321 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.84629 | −0.381536 | ||||||||
\(667\) | 12.7038 | + | 3.40398i | 0.491895 | + | 0.131803i | ||||
\(668\) | −4.44048 | − | 16.5721i | −0.171807 | − | 0.641193i | ||||
\(669\) | 7.86666 | + | 4.54182i | 0.304142 | + | 0.175597i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.2644i | 0.782297i | ||||||||
\(672\) | 2.15089 | − | 1.54067i | 0.0829723 | − | 0.0594328i | ||||
\(673\) | 8.91749 | + | 8.91749i | 0.343744 | + | 0.343744i | 0.857773 | − | 0.514029i | \(-0.171848\pi\) |
−0.514029 | + | 0.857773i | \(0.671848\pi\) | |||||||
\(674\) | 3.90169 | − | 2.25264i | 0.150288 | − | 0.0867686i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.49061 | + | 11.2421i | −0.249639 | + | 0.432387i | ||||
\(677\) | −10.8769 | + | 40.5930i | −0.418031 | + | 1.56011i | 0.360654 | + | 0.932700i | \(0.382554\pi\) |
−0.778685 | + | 0.627415i | \(0.784113\pi\) | |||||||
\(678\) | 12.4298 | − | 12.4298i | 0.477362 | − | 0.477362i | ||||
\(679\) | 33.0383 | + | 27.1245i | 1.26789 | + | 1.04094i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.77450 | + | 13.4658i | 0.297919 | + | 0.516011i | ||||
\(682\) | −1.96529 | + | 0.526598i | −0.0752549 | + | 0.0201645i | ||||
\(683\) | 4.14885 | − | 1.11168i | 0.158751 | − | 0.0425373i | −0.178568 | − | 0.983928i | \(-0.557146\pi\) |
0.337319 | + | 0.941390i | \(0.390480\pi\) | |||||||
\(684\) | 0.434539 | + | 0.752644i | 0.0166150 | + | 0.0287780i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.5107 | − | 0.595211i | 0.706742 | − | 0.0227253i | ||||
\(687\) | −7.64231 | + | 7.64231i | −0.291572 | + | 0.291572i | ||||
\(688\) | −0.942700 | + | 3.51821i | −0.0359401 | + | 0.134130i | ||||
\(689\) | 0.572615 | − | 0.991798i | 0.0218149 | − | 0.0377845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.4983 | − | 18.7629i | 1.23629 | − | 0.713773i | 0.267958 | − | 0.963431i | \(-0.413651\pi\) |
0.968334 | + | 0.249657i | \(0.0803180\pi\) | |||||||
\(692\) | 0.908369 | + | 0.908369i | 0.0345310 | + | 0.0345310i | ||||
\(693\) | 0.610214 | + | 6.20793i | 0.0231801 | + | 0.235820i | ||||
\(694\) | − | 5.78843i | − | 0.219726i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.53653 | − | 2.04182i | −0.134052 | − | 0.0773948i | ||||
\(697\) | −5.72075 | − | 21.3501i | −0.216689 | − | 0.808694i | ||||
\(698\) | 18.9637 | + | 5.08130i | 0.717785 | + | 0.192330i | ||||
\(699\) | −12.5596 | −0.475046 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.7644 | 0.482104 | 0.241052 | − | 0.970512i | \(-0.422508\pi\) | ||||
0.241052 | + | 0.970512i | \(0.422508\pi\) | |||||||
\(702\) | −0.132358 | − | 0.0354652i | −0.00499553 | − | 0.00133855i | ||||
\(703\) | −2.21477 | − | 8.26562i | −0.0835315 | − | 0.311744i | ||||
\(704\) | 2.04182 | + | 1.17884i | 0.0769538 | + | 0.0444293i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 26.0331i | − | 0.979770i | ||||||
\(707\) | −1.52231 | − | 0.690104i | −0.0572523 | − | 0.0259541i | ||||
\(708\) | −7.57691 | − | 7.57691i | −0.284758 | − | 0.284758i | ||||
\(709\) | 43.1134 | − | 24.8916i | 1.61916 | − | 0.934822i | 0.632022 | − | 0.774951i | \(-0.282225\pi\) |
0.987138 | − | 0.159872i | \(-0.0511080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.32116 | − | 4.02036i | 0.0870502 | − | 0.150775i | ||||
\(712\) | 2.58059 | − | 9.63091i | 0.0967118 | − | 0.360934i | ||||
\(713\) | 1.96529 | − | 1.96529i | 0.0736007 | − | 0.0736007i | ||||
\(714\) | −3.00000 | − | 7.97549i | −0.112272 | − | 0.298475i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.69087 | − | 16.7851i | −0.362165 | − | 0.627288i | ||||
\(717\) | 15.4265 | − | 4.13351i | 0.576112 | − | 0.154369i | ||||
\(718\) | −7.15063 | + | 1.91601i | −0.266859 | + | 0.0715047i | ||||
\(719\) | 23.1988 | + | 40.1815i | 0.865169 | + | 1.49852i | 0.866880 | + | 0.498518i | \(0.166122\pi\) |
−0.00171077 | + | 0.999999i | \(0.500545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.25938 | + | 0.704074i | 0.158628 | + | 0.0262211i | ||||
\(722\) | 12.9010 | − | 12.9010i | 0.480124 | − | 0.480124i | ||||
\(723\) | 7.06878 | − | 26.3810i | 0.262891 | − | 0.981121i | ||||
\(724\) | −12.5957 | + | 21.8163i | −0.468114 | + | 0.810797i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.71232 | − | 2.72066i | 0.174891 | − | 0.100973i | ||||
\(727\) | −16.5504 | − | 16.5504i | −0.613820 | − | 0.613820i | 0.330119 | − | 0.943939i | \(-0.392911\pi\) |
−0.943939 | + | 0.330119i | \(0.892911\pi\) | |||||||
\(728\) | −0.360801 | + | 0.0354652i | −0.0133722 | + | 0.00131443i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1590 | + | 5.86533i | 0.375746 | + | 0.216937i | ||||
\(732\) | 2.22456 | + | 8.30216i | 0.0822219 | + | 0.306856i | ||||
\(733\) | −37.4254 | − | 10.0281i | −1.38234 | − | 0.370396i | −0.510368 | − | 0.859956i | \(-0.670491\pi\) |
−0.871970 | + | 0.489560i | \(0.837158\pi\) | |||||||
\(734\) | −12.0692 | −0.445484 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.22066 | −0.118715 | ||||||||
\(737\) | 28.8737 | + | 7.73669i | 1.06358 | + | 0.284985i | ||||
\(738\) | 1.77627 | + | 6.62912i | 0.0653853 | + | 0.244021i | ||||
\(739\) | −34.4840 | − | 19.9093i | −1.26851 | − | 0.732377i | −0.293807 | − | 0.955865i | \(-0.594922\pi\) |
−0.974707 | + | 0.223488i | \(0.928256\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.119087i | − | 0.00437478i | ||||||
\(742\) | −22.0063 | + | 2.16313i | −0.807877 | + | 0.0794109i | ||||
\(743\) | 28.0880 | + | 28.0880i | 1.03045 | + | 1.03045i | 0.999522 | + | 0.0309276i | \(0.00984614\pi\) |
0.0309276 | + | 0.999522i | \(0.490154\pi\) | |||||||
\(744\) | −0.747356 | + | 0.431486i | −0.0273994 | + | 0.0158191i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.0595436 | + | 0.103133i | −0.00218005 | + | 0.00377595i | ||||
\(747\) | 2.60984 | − | 9.74004i | 0.0954889 | − | 0.356369i | ||||
\(748\) | 5.36927 | − | 5.36927i | 0.196320 | − | 0.196320i | ||||
\(749\) | −39.4360 | − | 6.51876i | −1.44096 | − | 0.238190i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.5445 | − | 28.6558i | −0.603716 | − | 1.04567i | −0.992253 | − | 0.124233i | \(-0.960353\pi\) |
0.388538 | − | 0.921433i | \(-0.372980\pi\) | |||||||
\(752\) | 0.833568 | − | 0.223354i | 0.0303971 | − | 0.00814488i | ||||
\(753\) | 3.33427 | − | 0.893415i | 0.121508 | − | 0.0325579i | ||||
\(754\) | 0.279784 | + | 0.484600i | 0.0101891 | + | 0.0176481i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.931486 | + | 2.47635i | 0.0338778 | + | 0.0900642i | ||||
\(757\) | 8.48469 | − | 8.48469i | 0.308381 | − | 0.308381i | −0.535900 | − | 0.844281i | \(-0.680028\pi\) |
0.844281 | + | 0.535900i | \(0.180028\pi\) | |||||||
\(758\) | −2.28744 | + | 8.53686i | −0.0830837 | + | 0.310073i | ||||
\(759\) | 3.79665 | − | 6.57599i | 0.137810 | − | 0.238693i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.4199 | − | 14.6762i | 0.921471 | − | 0.532011i | 0.0373669 | − | 0.999302i | \(-0.488103\pi\) |
0.884104 | + | 0.467290i | \(0.154770\pi\) | |||||||
\(762\) | 9.62150 | + | 9.62150i | 0.348550 | + | 0.348550i | ||||
\(763\) | −20.7547 | − | 9.40869i | −0.751371 | − | 0.340617i | ||||
\(764\) | − | 6.86297i | − | 0.248294i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.5031 | + | 19.3430i | 1.21052 | + | 0.698891i | ||||
\(767\) | 0.380023 | + | 1.41827i | 0.0137218 | + | 0.0512106i | ||||
\(768\) | 0.965926 | + | 0.258819i | 0.0348548 | + | 0.00933933i | ||||
\(769\) | −21.4307 | −0.772812 | −0.386406 | − | 0.922329i | \(-0.626284\pi\) | ||||
−0.386406 | + | 0.922329i | \(0.626284\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.70480 | −0.277482 | ||||||||
\(772\) | −2.68464 | − | 0.719346i | −0.0966222 | − | 0.0258898i | ||||
\(773\) | −2.96745 | − | 11.0747i | −0.106732 | − | 0.398329i | 0.891804 | − | 0.452422i | \(-0.149440\pi\) |
−0.998536 | + | 0.0540931i | \(0.982773\pi\) | |||||||
\(774\) | −3.15434 | − | 1.82116i | −0.113380 | − | 0.0654601i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.1567i | 0.579991i | ||||||||
\(777\) | −2.54841 | − | 25.9259i | −0.0914236 | − | 0.930086i | ||||
\(778\) | −21.4742 | − | 21.4742i | −0.769888 | − | 0.769888i | ||||
\(779\) | −5.16537 | + | 2.98223i | −0.185069 | + | 0.106849i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.05575 | − | 10.4889i | 0.216692 | − | 0.375321i | ||||
\(782\) | −2.68464 | + | 10.0192i | −0.0960024 | + | 0.358286i | ||||
\(783\) | 2.88756 | − | 2.88756i | 0.103193 | − | 0.103193i | ||||
\(784\) | 4.61338 | + | 5.26467i | 0.164764 | + | 0.188024i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.37500 | + | 11.0418i | 0.227389 | + | 0.393849i | ||||
\(787\) | −14.6555 | + | 3.92694i | −0.522414 | + | 0.139980i | −0.510383 | − | 0.859947i | \(-0.670496\pi\) |
−0.0120308 | + | 0.999928i | \(0.503830\pi\) | |||||||
\(788\) | 23.7227 | − | 6.35648i | 0.845087 | − | 0.226440i | ||||
\(789\) | 10.6103 | + | 18.3776i | 0.377738 | + | 0.654261i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.9454 | + | 29.5113i | 1.27807 | + | 1.04930i | ||||
\(792\) | −1.66714 | + | 1.66714i | −0.0592391 | + | 0.0592391i | ||||
\(793\) | 0.304824 | − | 1.13762i | 0.0108246 | − | 0.0403981i | ||||
\(794\) | 13.4759 | − | 23.3410i | 0.478243 | − | 0.828341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.12016 | + | 5.26553i | −0.323256 | + | 0.186632i | ||||
\(797\) | −22.6110 | − | 22.6110i | −0.800924 | − | 0.800924i | 0.182316 | − | 0.983240i | \(-0.441641\pi\) |
−0.983240 | + | 0.182316i | \(0.941641\pi\) | |||||||
\(798\) | −1.86929 | + | 1.33897i | −0.0661721 | + | 0.0473989i | ||||
\(799\) | − | 2.77934i | − | 0.0983260i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.63484 | + | 4.98532i | 0.305097 | + | 0.176148i | ||||
\(802\) | −3.55254 | − | 13.2582i | −0.125444 | − | 0.468165i | ||||
\(803\) | −37.0190 | − | 9.91920i | −1.30637 | − | 0.350041i | ||||
\(804\) | 12.6787 | 0.447142 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.118251 | 0.00416520 | ||||||||
\(807\) | 1.15072 | + | 0.308333i | 0.0405071 | + | 0.0108538i | ||||
\(808\) | −0.163506 | − | 0.610214i | −0.00575213 | − | 0.0214673i | ||||
\(809\) | −21.9812 | − | 12.6909i | −0.772819 | − | 0.446187i | 0.0610605 | − | 0.998134i | \(-0.480552\pi\) |
−0.833879 | + | 0.551947i | \(0.813885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.1094i | − | 0.776366i | −0.921582 | − | 0.388183i | \(-0.873103\pi\) | ||
0.921582 | − | 0.388183i | \(-0.126897\pi\) | |||||||
\(812\) | 4.46091 | − | 9.84036i | 0.156547 | − | 0.345329i | ||||
\(813\) | 5.76122 | + | 5.76122i | 0.202055 | + | 0.202055i | ||||
\(814\) | 20.1043 | − | 11.6072i | 0.704656 | − | 0.406833i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.61033 | − | 2.78917i | 0.0563728 | − | 0.0976406i | ||||
\(817\) | 0.819280 | − | 3.05759i | 0.0286630 | − | 0.106972i | ||||
\(818\) | 2.98567 | − | 2.98567i | 0.104392 | − | 0.104392i | ||||
\(819\) | 0.0591253 | − | 0.357686i | 0.00206601 | − | 0.0124986i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.2971 | + | 23.0312i | 0.464072 | + | 0.803796i | 0.999159 | − | 0.0410009i | \(-0.0130546\pi\) |
−0.535087 | + | 0.844797i | \(0.679721\pi\) | |||||||
\(822\) | 13.3330 | − | 3.57258i | 0.465043 | − | 0.124608i | ||||
\(823\) | 12.4049 | − | 3.32388i | 0.432407 | − | 0.115863i | −0.0360489 | − | 0.999350i | \(-0.511477\pi\) |
0.468456 | + | 0.883487i | \(0.344811\pi\) | |||||||
\(824\) | 0.815870 | + | 1.41313i | 0.0284222 | + | 0.0492287i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.9894 | − | 21.9115i | 0.625932 | − | 0.762399i | ||||
\(827\) | −32.9668 | + | 32.9668i | −1.14637 | + | 1.14637i | −0.159105 | + | 0.987262i | \(0.550861\pi\) |
−0.987262 | + | 0.159105i | \(0.949139\pi\) | |||||||
\(828\) | 0.833568 | − | 3.11092i | 0.0289685 | − | 0.108112i | ||||
\(829\) | −20.0547 | + | 34.7358i | −0.696528 | + | 1.20642i | 0.273134 | + | 0.961976i | \(0.411940\pi\) |
−0.969663 | + | 0.244447i | \(0.921394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5377 | − | 8.39335i | 0.504308 | − | 0.291162i | ||||
\(832\) | −0.0968928 | − | 0.0968928i | −0.00335915 | − | 0.00335915i | ||||
\(833\) | 20.2235 | − | 9.96339i | 0.700703 | − | 0.345211i | ||||
\(834\) | 13.9299i | 0.482354i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.77450 | − | 1.02451i | −0.0613723 | − | 0.0354333i | ||||
\(837\) | −0.223354 | − | 0.833568i | −0.00772024 | − | 0.0288123i | ||||
\(838\) | 27.2205 | + | 7.29371i | 0.940317 | + | 0.251957i | ||||
\(839\) | −16.4841 | −0.569096 | −0.284548 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284548 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3240 | 0.424964 | ||||||||
\(842\) | −3.20191 | − | 0.857950i | −0.110345 | − | 0.0295669i | ||||
\(843\) | −2.71897 | − | 10.1473i | −0.0936462 | − | 0.349493i | ||||
\(844\) | 11.8408 | + | 6.83628i | 0.407576 | + | 0.235314i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.862973i | 0.0296696i | ||||||||
\(847\) | 8.38330 | + | 11.7037i | 0.288054 | + | 0.402143i | ||||
\(848\) | −5.90978 | − | 5.90978i | −0.202943 | − | 0.202943i | ||||
\(849\) | −21.6552 | + | 12.5026i | −0.743204 | + | 0.429089i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8558 | + | 27.4630i | −0.543529 | + | 0.941420i | ||||
\(852\) | 1.32956 | − | 4.96199i | 0.0455500 | − | 0.169995i | ||||
\(853\) | −5.36308 | + | 5.36308i | −0.183628 | + | 0.183628i | −0.792935 | − | 0.609307i | \(-0.791448\pi\) |
0.609307 | + | 0.792935i | \(0.291448\pi\) | |||||||
\(854\) | −21.2843 | + | 8.00615i | −0.728335 | + | 0.273965i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.55384 | − | 13.0836i | −0.258185 | − | 0.447189i | ||||
\(857\) | −8.27727 | + | 2.21789i | −0.282746 | + | 0.0757616i | −0.397405 | − | 0.917643i | \(-0.630089\pi\) |
0.114659 | + | 0.993405i | \(0.463422\pi\) | |||||||
\(858\) | 0.312059 | − | 0.0836158i | 0.0106535 | − | 0.00285460i | ||||
\(859\) | −17.0418 | − | 29.5173i | −0.581459 | − | 1.00712i | −0.995307 | − | 0.0967707i | \(-0.969149\pi\) |
0.413847 | − | 0.910346i | \(-0.364185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.9952 | + | 6.39277i | −0.579193 | + | 0.217865i | ||||
\(862\) | −2.95250 | + | 2.95250i | −0.100563 | + | 0.100563i | ||||
\(863\) | −4.53093 | + | 16.9097i | −0.154235 | + | 0.575612i | 0.844935 | + | 0.534869i | \(0.179639\pi\) |
−0.999170 | + | 0.0407427i | \(0.987028\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.90106 | + | 3.40698i | −0.200526 | + | 0.115774i | ||||
\(867\) | 4.68625 | + | 4.68625i | 0.159153 | + | 0.159153i | ||||
\(868\) | −1.32956 | − | 1.85616i | −0.0451282 | − | 0.0630021i | ||||
\(869\) | 10.9451i | 0.371288i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.50456 | − | 0.868660i | −0.0509802 | − | 0.0294334i | ||||
\(872\) | −2.22920 | − | 8.31948i | −0.0754902 | − | 0.281733i | ||||
\(873\) | −15.6062 | − | 4.18166i | −0.528189 | − | 0.141528i | ||||
\(874\) | 2.79900 | 0.0946777 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.2553 | −0.549215 | ||||||||
\(877\) | 5.62211 | + | 1.50644i | 0.189845 | + | 0.0508689i | 0.352489 | − | 0.935816i | \(-0.385335\pi\) |
−0.162644 | + | 0.986685i | \(0.552002\pi\) | |||||||
\(878\) | 0.642400 | + | 2.39747i | 0.0216799 | + | 0.0809106i | ||||
\(879\) | −10.6096 | − | 6.12545i | −0.357852 | − | 0.206606i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.13703i | 0.173071i | 0.996249 | + | 0.0865354i | \(0.0275796\pi\) | ||||
−0.996249 | + | 0.0865354i | \(0.972420\pi\) | |||||||
\(882\) | −6.27931 | + | 3.09359i | −0.211435 | + | 0.104167i | ||||
\(883\) | −33.6563 | − | 33.6563i | −1.13262 | − | 1.13262i | −0.989739 | − | 0.142885i | \(-0.954362\pi\) |
−0.142885 | − | 0.989739i | \(-0.545638\pi\) | |||||||
\(884\) | −0.382192 | + | 0.220659i | −0.0128545 | + | 0.00742156i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.39950 | + | 12.8163i | −0.248591 | + | 0.430572i | ||||
\(887\) | −1.77118 | + | 6.61013i | −0.0594704 | + | 0.221946i | −0.989265 | − | 0.146132i | \(-0.953318\pi\) |
0.929795 | + | 0.368078i | \(0.119984\pi\) | |||||||
\(888\) | 6.96238 | − | 6.96238i | 0.233642 | − | 0.233642i | ||||
\(889\) | −22.8438 | + | 27.8242i | −0.766156 | + | 0.933195i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.17884 | − | 2.04182i | −0.0394927 | − | 0.0684034i | ||||
\(892\) | −8.77411 | + | 2.35102i | −0.293779 | + | 0.0787179i | ||||
\(893\) | −0.724435 | + | 0.194112i | −0.0242423 | + | 0.00649571i | ||||
\(894\) | 9.69087 | + | 16.7851i | 0.324111 | + | 0.561377i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.431486 | + | 2.61033i | −0.0144150 | + | 0.0872050i | ||||
\(897\) | −0.312059 | + | 0.312059i | −0.0104193 | + | 0.0104193i | ||||
\(898\) | 0.143463 | − | 0.535412i | 0.00478743 | − | 0.0178669i | ||||
\(899\) | −1.76203 | + | 3.05193i | −0.0587670 | + | 0.101788i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.3110 | + | 13.4586i | −0.776603 | + | 0.448372i | ||||
\(902\) | −11.4415 | − | 11.4415i | −0.380961 | − | 0.380961i | ||||
\(903\) | 3.97882 | − | 8.77691i | 0.132407 | − | 0.292077i | ||||
\(904\) | 17.5783i | 0.584647i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.72590 | − | 1.57380i | −0.0905620 | − | 0.0522860i | ||||
\(907\) | −10.9195 | − | 40.7520i | −0.362575 | − | 1.35315i | −0.870679 | − | 0.491852i | \(-0.836320\pi\) |
0.508104 | − | 0.861296i | \(-0.330347\pi\) | |||||||
\(908\) | −15.0192 | − | 4.02438i | −0.498429 | − | 0.133554i | ||||
\(909\) | 0.631740 | 0.0209535 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.7456 | 0.852990 | 0.426495 | − | 0.904490i | \(-0.359748\pi\) | ||||
0.426495 | + | 0.904490i | \(0.359748\pi\) | |||||||
\(912\) | −0.839465 | − | 0.224934i | −0.0277975 | − | 0.00744831i | ||||
\(913\) | 6.15317 | + | 22.9640i | 0.203640 | + | 0.759996i | ||||
\(914\) | 27.7834 | + | 16.0408i | 0.918994 | + | 0.530581i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 10.8079i | − | 0.357102i | ||||||
\(917\) | −27.4238 | + | 19.6436i | −0.905614 | + | 0.648688i | ||||
\(918\) | 2.27735 | + | 2.27735i | 0.0751637 | + | 0.0751637i | ||||
\(919\) | −24.6604 | + | 14.2377i | −0.813471 | + | 0.469658i | −0.848160 | − | 0.529740i | \(-0.822289\pi\) |
0.0346885 | + | 0.999398i | \(0.488956\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.44132 | + | 7.69259i | −0.146346 | + | 0.253479i | ||||
\(922\) | 0.114221 | − | 0.426280i | 0.00376168 | − | 0.0140388i | ||||
\(923\) | −0.497741 | + | 0.497741i | −0.0163833 | + | 0.0163833i | ||||
\(924\) | −4.82116 | − | 3.95818i | −0.158604 | − | 0.130215i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.3977 | + | 31.8658i | 0.604586 | + | 1.04717i | ||||
\(927\) | −1.57614 | + | 0.422325i | −0.0517672 | + | 0.0138710i | ||||
\(928\) | 3.94449 | − | 1.05692i | 0.129484 | − | 0.0346952i | ||||
\(929\) | −10.5249 | − | 18.2297i | −0.345312 | − | 0.598099i | 0.640098 | − | 0.768293i | \(-0.278894\pi\) |
−0.985410 | + | 0.170195i | \(0.945560\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00939 | − | 4.57540i | −0.131402 | − | 0.149953i | ||||
\(932\) | 8.88096 | − | 8.88096i | 0.290905 | − | 0.290905i | ||||
\(933\) | −3.63752 | + | 13.5754i | −0.119087 | + | 0.444438i | ||||
\(934\) | −9.78608 | + | 16.9500i | −0.320210 | + | 0.554620i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.118669 | − | 0.0685135i | 0.00387882 | − | 0.00223944i | ||||
\(937\) | −32.9912 | − | 32.9912i | −1.07778 | − | 1.07778i | −0.996709 | − | 0.0810686i | \(-0.974167\pi\) |
−0.0810686 | − | 0.996709i | \(-0.525833\pi\) | |||||||
\(938\) | 3.28148 | + | 33.3837i | 0.107144 | + | 1.09002i | ||||
\(939\) | − | 19.6966i | − | 0.642774i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.25912 | + | 0.726951i | 0.0410460 | + | 0.0236979i | 0.520383 | − | 0.853933i | \(-0.325789\pi\) |
−0.479337 | + | 0.877631i | \(0.659123\pi\) | |||||||
\(942\) | 1.59734 | + | 5.96135i | 0.0520441 | + | 0.194231i | ||||
\(943\) | 21.3501 | + | 5.72075i | 0.695256 | + | 0.186293i | ||||
\(944\) | 10.7154 | 0.348756 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.58743 | 0.279202 | ||||||||
\(947\) | −29.0716 | − | 7.78970i | −0.944699 | − | 0.253131i | −0.246588 | − | 0.969120i | \(-0.579309\pi\) |
−0.698111 | + | 0.715989i | \(0.745976\pi\) | |||||||
\(948\) | 1.20152 | + | 4.48413i | 0.0390235 | + | 0.145638i | ||||
\(949\) | 1.92900 | + | 1.11371i | 0.0626179 | + | 0.0361524i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.37883i | 0.0771390i | ||||||||
\(952\) | 7.76085 | + | 3.51821i | 0.251530 | + | 0.114026i | ||||
\(953\) | −6.23201 | − | 6.23201i | −0.201875 | − | 0.201875i | 0.598928 | − | 0.800803i | \(-0.295594\pi\) |
−0.800803 | + | 0.598928i | \(0.795594\pi\) | |||||||
\(954\) | 7.23797 | − | 4.17884i | 0.234338 | − | 0.135295i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.98532 | + | 13.8310i | −0.258264 | + | 0.447326i | ||||
\(957\) | −2.49189 | + | 9.29986i | −0.0805513 | + | 0.300622i | ||||
\(958\) | 21.6888 | − | 21.6888i | 0.700732 | − | 0.700732i | ||||
\(959\) | 12.8577 | + | 34.1821i | 0.415196 | + | 1.10380i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1276 | − | 26.2018i | −0.487988 | − | 0.845221i | ||||
\(962\) | −1.30324 | + | 0.349201i | −0.0420180 | + | 0.0112587i | ||||
\(963\) | 14.5929 | − | 3.91015i | 0.470249 | − | 0.126003i | ||||
\(964\) | 13.6558 | + | 23.6526i | 0.439825 | + | 0.761799i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.40698 | + | 1.38967i | 0.270490 | + | 0.0447119i | ||||
\(967\) | −31.4386 | + | 31.4386i | −1.01100 | + | 1.01100i | −0.0110583 | + | 0.999939i | \(0.503520\pi\) |
−0.999939 | + | 0.0110583i | \(0.996480\pi\) | |||||||
\(968\) | −1.40832 | + | 5.25591i | −0.0452650 | + | 0.168931i | ||||
\(969\) | −1.39950 | + | 2.42401i | −0.0449585 | + | 0.0778704i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.2192 | + | 6.47740i | −0.360041 | + | 0.207870i | −0.669099 | − | 0.743174i | \(-0.733320\pi\) |
0.309058 | + | 0.951043i | \(0.399986\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −36.6783 | + | 3.60533i | −1.17585 | + | 0.115582i | ||||
\(974\) | − | 24.6370i | − | 0.789421i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.44351 | − | 4.29751i | −0.238261 | − | 0.137560i | ||||
\(977\) | 9.29470 | + | 34.6883i | 0.297364 | + | 1.10978i | 0.939322 | + | 0.343037i | \(0.111456\pi\) |
−0.641958 | + | 0.766740i | \(0.721878\pi\) | |||||||
\(978\) | 2.67874 | + | 0.717766i | 0.0856567 | + | 0.0229516i | ||||
\(979\) | −23.5077 | −0.751308 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.61296 | 0.274991 | ||||||||
\(982\) | 2.97770 | + | 0.797873i | 0.0950224 | + | 0.0254612i | ||||
\(983\) | 10.7718 | + | 40.2010i | 0.343568 | + | 1.28221i | 0.894276 | + | 0.447515i | \(0.147691\pi\) |
−0.550708 | + | 0.834698i | \(0.685642\pi\) | |||||||
\(984\) | −5.94351 | − | 3.43149i | −0.189472 | − | 0.109392i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 13.1520i | − | 0.418844i | ||||||
\(987\) | −2.27226 | + | 0.223354i | −0.0723269 | + | 0.00710943i | ||||
\(988\) | 0.0842074 | + | 0.0842074i | 0.00267899 | + | 0.00267899i | ||||
\(989\) | −10.1590 | + | 5.86533i | −0.323039 | + | 0.186506i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1291 | + | 22.7402i | −0.417059 | + | 0.722368i | −0.995642 | − | 0.0932558i | \(-0.970273\pi\) |
0.578583 | + | 0.815624i | \(0.303606\pi\) | |||||||
\(992\) | 0.223354 | − | 0.833568i | 0.00709149 | − | 0.0264658i | ||||
\(993\) | −19.5770 | + | 19.5770i | −0.621256 | + | 0.621256i | ||||
\(994\) | 13.4093 | + | 2.21656i | 0.425318 | + | 0.0703049i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.04182 | + | 8.73268i | 0.159756 | + | 0.276706i | ||||
\(997\) | −17.7010 | + | 4.74297i | −0.560597 | + | 0.150211i | −0.527980 | − | 0.849257i | \(-0.677051\pi\) |
−0.0326163 | + | 0.999468i | \(0.510384\pi\) | |||||||
\(998\) | 32.0422 | − | 8.58568i | 1.01428 | − | 0.271775i | ||||
\(999\) | 4.92315 | + | 8.52714i | 0.155761 | + | 0.269787i |
(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 | 1050.2.bc.f.493.4 | yes | 16 | |
5.2 | odd | 4 | 1050.2.bc.e.157.2 | ✓ | 16 | ||
5.3 | odd | 4 | 1050.2.bc.e.157.3 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.2.bc.f.493.1 | yes | 16 | |
7.5 | odd | 6 | 1050.2.bc.e.943.1 | yes | 16 | ||
35.12 | even | 12 | inner | 1050.2.bc.f.607.4 | yes | 16 | |
35.19 | odd | 6 | 1050.2.bc.e.943.4 | yes | 16 | ||
35.33 | even | 12 | inner | 1050.2.bc.f.607.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.e.157.2 | ✓ | 16 | 5.2 | odd | 4 | ||
1050.2.bc.e.157.3 | yes | 16 | 5.3 | odd | 4 | ||
1050.2.bc.e.943.1 | yes | 16 | 7.5 | odd | 6 | ||
1050.2.bc.e.943.4 | yes | 16 | 35.19 | odd | 6 | ||
1050.2.bc.f.493.1 | yes | 16 | 5.4 | even | 2 | inner | |
1050.2.bc.f.493.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1050.2.bc.f.607.1 | yes | 16 | 35.33 | even | 12 | inner | |
1050.2.bc.f.607.4 | yes | 16 | 35.12 | even | 12 | inner |