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 | 943.4 | ||
Root | \(1.44378 - 0.833568i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.943 |
Dual form | 1050.2.bc.e.157.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | 0.965926 | + | 0.258819i | 0.557678 | + | 0.149429i | ||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −0.258819 | + | 2.63306i | −0.0978244 | + | 0.995204i | ||||
\(8\) | −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 | 0.987192 | − | 0.159535i | \(-0.0509996\pi\) |
−0.631758 | + | 0.775166i | \(0.717666\pi\) | |||||||
\(12\) | −0.965926 | + | 0.258819i | −0.278839 | + | 0.0747146i | ||||
\(13\) | −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 | ||||
\(17\) | −0.833568 | + | 3.11092i | −0.202170 | + | 0.754508i | 0.788124 | + | 0.615517i | \(0.211053\pi\) |
−0.990294 | + | 0.138991i | \(0.955614\pi\) | |||||||
\(18\) | −0.258819 | + | 0.965926i | −0.0610042 | + | 0.227671i | ||||
\(19\) | 0.434539 | − | 0.752644i | 0.0996901 | − | 0.172668i | −0.811866 | − | 0.583843i | \(-0.801548\pi\) |
0.911556 | + | 0.411175i | \(0.134882\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.931486 | + | 2.47635i | −0.203267 | + | 0.540385i | ||||
\(22\) | −1.66714 | + | 1.66714i | −0.355435 | + | 0.355435i | ||||
\(23\) | −3.11092 | + | 0.833568i | −0.648671 | + | 0.173811i | −0.568128 | − | 0.822940i | \(-0.692332\pi\) |
−0.0805432 | + | 0.996751i | \(0.525665\pi\) | |||||||
\(24\) | −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 | ||||
\(28\) | −1.09239 | − | 2.40971i | −0.206442 | − | 0.455392i | ||||
\(29\) | − | 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 | −0.565611 | − | 0.824672i | \(-0.691360\pi\) |
0.431382 | + | 0.902170i | \(0.358026\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | 0.610214 | + | 2.27735i | 0.106225 | + | 0.396436i | ||||
\(34\) | −3.22066 | −0.552338 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.54841 | + | 9.51079i | 0.418956 | + | 1.56356i | 0.776778 | + | 0.629774i | \(0.216853\pi\) |
−0.357822 | + | 0.933790i | \(0.616481\pi\) | |||||||
\(38\) | 0.839465 | + | 0.224934i | 0.136179 | + | 0.0364891i | ||||
\(39\) | −0.118669 | + | 0.0685135i | −0.0190022 | + | 0.0109709i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.86297i | 1.07182i | 0.844276 | + | 0.535908i | \(0.180031\pi\) | ||||
−0.844276 | + | 0.535908i | \(0.819969\pi\) | |||||||
\(42\) | −2.63306 | − | 0.258819i | −0.406290 | − | 0.0399366i | ||||
\(43\) | −2.57551 | − | 2.57551i | −0.392761 | − | 0.392761i | 0.482909 | − | 0.875670i | \(-0.339580\pi\) |
−0.875670 | + | 0.482909i | \(0.839580\pi\) | |||||||
\(44\) | −2.04182 | − | 1.17884i | −0.307815 | − | 0.177717i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.61033 | − | 2.78917i | −0.237430 | − | 0.411241i | ||||
\(47\) | −0.833568 | + | 0.223354i | −0.121588 | + | 0.0325795i | −0.319100 | − | 0.947721i | \(-0.603381\pi\) |
0.197512 | + | 0.980301i | \(0.436714\pi\) | |||||||
\(48\) | 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 | ||||
\(52\) | 0.0354652 | − | 0.132358i | 0.00491814 | − | 0.0183548i | ||||
\(53\) | −2.16313 | + | 8.07290i | −0.297129 | + | 1.10890i | 0.642384 | + | 0.766383i | \(0.277946\pi\) |
−0.939512 | + | 0.342516i | \(0.888721\pi\) | |||||||
\(54\) | −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 | ||||
\(58\) | 3.94449 | − | 1.05692i | 0.517936 | − | 0.138781i | ||||
\(59\) | −5.35769 | − | 9.27978i | −0.697511 | − | 1.20812i | −0.969327 | − | 0.245776i | \(-0.920957\pi\) |
0.271815 | − | 0.962349i | \(-0.412376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.44351 | − | 4.29751i | −0.953044 | − | 0.550240i | −0.0590186 | − | 0.998257i | \(-0.518797\pi\) |
−0.894025 | + | 0.448017i | \(0.852130\pi\) | |||||||
\(62\) | −0.610214 | − | 0.610214i | −0.0774973 | − | 0.0774973i | ||||
\(63\) | −1.54067 | + | 2.15089i | −0.194107 | + | 0.270986i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.04182 | + | 1.17884i | −0.251330 | + | 0.145106i | ||||
\(67\) | 12.2466 | + | 3.28148i | 1.49617 | + | 0.400896i | 0.911814 | − | 0.410604i | \(-0.134682\pi\) |
0.584352 | + | 0.811501i | \(0.301349\pi\) | |||||||
\(68\) | −0.833568 | − | 3.11092i | −0.101085 | − | 0.377254i | ||||
\(69\) | −3.22066 | −0.387722 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.13703 | 0.609653 | 0.304826 | − | 0.952408i | \(-0.401402\pi\) | ||||
0.304826 | + | 0.952408i | \(0.401402\pi\) | |||||||
\(72\) | −0.258819 | − | 0.965926i | −0.0305021 | − | 0.113835i | ||||
\(73\) | 15.7014 | + | 4.20718i | 1.83771 | + | 0.492413i | 0.998665 | − | 0.0516512i | \(-0.0164484\pi\) |
0.839044 | + | 0.544064i | \(0.183115\pi\) | |||||||
\(74\) | −8.52714 | + | 4.92315i | −0.991260 | + | 0.572304i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.869078i | 0.0996901i | ||||||||
\(77\) | −5.68133 | + | 2.57551i | −0.647448 | + | 0.293506i | ||||
\(78\) | −0.0968928 | − | 0.0968928i | −0.0109709 | − | 0.0109709i | ||||
\(79\) | 4.02036 | + | 2.32116i | 0.452326 | + | 0.261151i | 0.708812 | − | 0.705397i | \(-0.249231\pi\) |
−0.256486 | + | 0.966548i | \(0.582565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.62912 | + | 1.77627i | −0.732064 | + | 0.196156i | ||||
\(83\) | −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 | ||||
\(87\) | 1.05692 | − | 3.94449i | 0.113314 | − | 0.422893i | ||||
\(88\) | 0.610214 | − | 2.27735i | 0.0650490 | − | 0.242766i | ||||
\(89\) | 4.98532 | − | 8.63484i | 0.528443 | − | 0.915291i | −0.471007 | − | 0.882130i | \(-0.656109\pi\) |
0.999450 | − | 0.0331611i | \(-0.0105574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.230047 | − | 0.280202i | −0.0241155 | − | 0.0293732i | ||||
\(92\) | 2.27735 | − | 2.27735i | 0.237430 | − | 0.237430i | ||||
\(93\) | −0.833568 | + | 0.223354i | −0.0864370 | + | 0.0231607i | ||||
\(94\) | −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 | \(0.443845\pi\) | |||||||
\(98\) | −0.460527 | − | 6.98483i | −0.0465203 | − | 0.705575i | ||||
\(99\) | 2.35769i | 0.236956i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.547103 | + | 0.315870i | −0.0544388 | + | 0.0314302i | −0.526972 | − | 0.849882i | \(-0.676673\pi\) |
0.472534 | + | 0.881313i | \(0.343340\pi\) | |||||||
\(102\) | −3.11092 | − | 0.833568i | −0.308027 | − | 0.0825355i | ||||
\(103\) | −0.422325 | − | 1.57614i | −0.0416130 | − | 0.155302i | 0.941993 | − | 0.335632i | \(-0.108950\pi\) |
−0.983606 | + | 0.180331i | \(0.942283\pi\) | |||||||
\(104\) | 0.137027 | 0.0134366 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.35769 | −0.811770 | ||||||||
\(107\) | −3.91015 | − | 14.5929i | −0.378009 | − | 1.41075i | −0.848898 | − | 0.528556i | \(-0.822734\pi\) |
0.470889 | − | 0.882192i | \(-0.343933\pi\) | |||||||
\(108\) | −0.965926 | − | 0.258819i | −0.0929463 | − | 0.0249049i | ||||
\(109\) | 7.45905 | − | 4.30648i | 0.714447 | − | 0.412486i | −0.0982585 | − | 0.995161i | \(-0.531327\pi\) |
0.812705 | + | 0.582675i | \(0.197994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.84629i | 0.934569i | ||||||||
\(112\) | 2.15089 | + | 1.54067i | 0.203240 | + | 0.145580i | ||||
\(113\) | −12.4298 | − | 12.4298i | −1.16929 | − | 1.16929i | −0.982375 | − | 0.186919i | \(-0.940150\pi\) |
−0.186919 | − | 0.982375i | \(-0.559850\pi\) | |||||||
\(114\) | 0.752644 | + | 0.434539i | 0.0704915 | + | 0.0406983i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.04182 | + | 3.53653i | 0.189578 | + | 0.328358i | ||||
\(117\) | −0.132358 | + | 0.0354652i | −0.0122365 | + | 0.00327876i | ||||
\(118\) | 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 | ||||
\(122\) | 2.22456 | − | 8.30216i | 0.201402 | − | 0.751642i | ||||
\(123\) | −1.77627 | + | 6.62912i | −0.160161 | + | 0.597728i | ||||
\(124\) | 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 | −0.136825 | − | 0.990595i | \(-0.543690\pi\) |
0.990595 | + | 0.136825i | \(0.0436898\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | −1.82116 | − | 3.15434i | −0.160344 | − | 0.277724i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.0418 | − | 6.37500i | −0.964728 | − | 0.556986i | −0.0671030 | − | 0.997746i | \(-0.521376\pi\) |
−0.897625 | + | 0.440760i | \(0.854709\pi\) | |||||||
\(132\) | −1.66714 | − | 1.66714i | −0.145106 | − | 0.145106i | ||||
\(133\) | 1.86929 | + | 1.33897i | 0.162088 | + | 0.116103i | ||||
\(134\) | 12.6787i | 1.09527i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.78917 | − | 1.61033i | 0.239170 | − | 0.138085i | ||||
\(137\) | 13.3330 | + | 3.57258i | 1.13912 | + | 0.305226i | 0.778597 | − | 0.627525i | \(-0.215932\pi\) |
0.360522 | + | 0.932751i | \(0.382598\pi\) | |||||||
\(138\) | −0.833568 | − | 3.11092i | −0.0709580 | − | 0.264819i | ||||
\(139\) | 13.9299 | 1.18152 | 0.590760 | − | 0.806847i | \(-0.298828\pi\) | ||||
0.590760 | + | 0.806847i | \(0.298828\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.862973 | −0.0726754 | ||||||||
\(142\) | 1.32956 | + | 4.96199i | 0.111574 | + | 0.416401i | ||||
\(143\) | −0.312059 | − | 0.0836158i | −0.0260957 | − | 0.00699231i | ||||
\(144\) | 0.866025 | − | 0.500000i | 0.0721688 | − | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.2553i | 1.34530i | ||||||||
\(147\) | −6.27931 | − | 3.09359i | −0.517909 | − | 0.255155i | ||||
\(148\) | −6.96238 | − | 6.96238i | −0.572304 | − | 0.572304i | ||||
\(149\) | 16.7851 | + | 9.69087i | 1.37509 | + | 0.793907i | 0.991563 | − | 0.129625i | \(-0.0413772\pi\) |
0.383523 | + | 0.923531i | \(0.374711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.57380 | + | 2.72590i | 0.128074 | + | 0.221831i | 0.922930 | − | 0.384967i | \(-0.125787\pi\) |
−0.794856 | + | 0.606798i | \(0.792454\pi\) | |||||||
\(152\) | −0.839465 | + | 0.224934i | −0.0680896 | + | 0.0182445i | ||||
\(153\) | −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 | ||||
\(157\) | 1.59734 | − | 5.96135i | 0.127482 | − | 0.475768i | −0.872434 | − | 0.488731i | \(-0.837460\pi\) |
0.999916 | + | 0.0129635i | \(0.00412653\pi\) | |||||||
\(158\) | −1.20152 | + | 4.48413i | −0.0955877 | + | 0.356738i | ||||
\(159\) | −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 | ||||
\(163\) | −2.67874 | + | 0.717766i | −0.209815 | + | 0.0562198i | −0.362196 | − | 0.932102i | \(-0.617973\pi\) |
0.152380 | + | 0.988322i | \(0.451306\pi\) | |||||||
\(164\) | −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 | \(0.981063\pi\) | |||||||
\(168\) | 2.40971 | − | 1.09239i | 0.185913 | − | 0.0842795i | ||||
\(169\) | 12.9812i | 0.998556i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.752644 | − | 0.434539i | 0.0575561 | − | 0.0332300i | ||||
\(172\) | 3.51821 | + | 0.942700i | 0.268261 | + | 0.0718802i | ||||
\(173\) | −0.332486 | − | 1.24086i | −0.0252785 | − | 0.0943405i | 0.952134 | − | 0.305681i | \(-0.0988839\pi\) |
−0.977413 | + | 0.211340i | \(0.932217\pi\) | |||||||
\(174\) | 4.08363 | 0.309579 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.35769 | 0.177717 | ||||||||
\(177\) | −2.77334 | − | 10.3503i | −0.208457 | − | 0.777973i | ||||
\(178\) | 9.63091 | + | 2.58059i | 0.721867 | + | 0.193424i | ||||
\(179\) | 16.7851 | − | 9.69087i | 1.25458 | − | 0.724329i | 0.282560 | − | 0.959249i | \(-0.408816\pi\) |
0.972015 | + | 0.234920i | \(0.0754829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 25.1913i | − | 1.87246i | −0.351394 | − | 0.936228i | \(-0.614292\pi\) | ||
0.351394 | − | 0.936228i | \(-0.385708\pi\) | |||||||
\(182\) | 0.211114 | − | 0.294730i | 0.0156488 | − | 0.0218468i | ||||
\(183\) | −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 | ||||
\(187\) | −7.33457 | + | 1.96529i | −0.536357 | + | 0.143716i | ||||
\(188\) | 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 | −0.963052 | − | 0.269314i | \(-0.913203\pi\) |
0.714759 | + | 0.699371i | \(0.246536\pi\) | |||||||
\(192\) | −0.258819 | + | 0.965926i | −0.0186787 | + | 0.0697097i | ||||
\(193\) | −0.719346 | + | 2.68464i | −0.0517797 | + | 0.193244i | −0.986971 | − | 0.160899i | \(-0.948561\pi\) |
0.935191 | + | 0.354143i | \(0.115227\pi\) | |||||||
\(194\) | −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 | \(0.589072\pi\) |
−0.961103 | + | 0.276190i | \(0.910928\pi\) | |||||||
\(198\) | −2.27735 | + | 0.610214i | −0.161844 | + | 0.0433660i | ||||
\(199\) | 5.26553 | + | 9.12016i | 0.373263 | + | 0.646511i | 0.990065 | − | 0.140607i | \(-0.0449055\pi\) |
−0.616802 | + | 0.787118i | \(0.711572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.9800 | + | 6.33933i | 0.774472 | + | 0.447142i | ||||
\(202\) | −0.446708 | − | 0.446708i | −0.0314302 | − | 0.0314302i | ||||
\(203\) | 10.7525 | + | 1.05692i | 0.754674 | + | 0.0741814i | ||||
\(204\) | − | 3.22066i | − | 0.225491i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.41313 | − | 0.815870i | 0.0984573 | − | 0.0568444i | ||||
\(207\) | −3.11092 | − | 0.833568i | −0.216224 | − | 0.0579370i | ||||
\(208\) | 0.0354652 | + | 0.132358i | 0.00245907 | + | 0.00917738i | ||||
\(209\) | 2.04901 | 0.141733 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6726 | 0.941257 | 0.470629 | − | 0.882331i | \(-0.344027\pi\) | ||||
0.470629 | + | 0.882331i | \(0.344027\pi\) | |||||||
\(212\) | −2.16313 | − | 8.07290i | −0.148564 | − | 0.554449i | ||||
\(213\) | 4.96199 | + | 1.32956i | 0.339990 | + | 0.0911000i | ||||
\(214\) | 13.0836 | − | 7.55384i | 0.894379 | − | 0.516370i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −0.942700 | − | 2.07951i | −0.0639947 | − | 0.141167i | ||||
\(218\) | 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 | ||||
\(222\) | −9.51079 | + | 2.54841i | −0.638322 | + | 0.171038i | ||||
\(223\) | −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 | ||||
\(227\) | 4.02438 | − | 15.0192i | 0.267107 | − | 0.996858i | −0.693841 | − | 0.720128i | \(-0.744083\pi\) |
0.960948 | − | 0.276729i | \(-0.0892505\pi\) | |||||||
\(228\) | −0.224934 | + | 0.839465i | −0.0148966 | + | 0.0555949i | ||||
\(229\) | 5.40393 | − | 9.35988i | 0.357102 | − | 0.618518i | −0.630374 | − | 0.776292i | \(-0.717098\pi\) |
0.987475 | + | 0.157774i | \(0.0504317\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.15434 | + | 1.01731i | −0.404926 | + | 0.0669341i | ||||
\(232\) | −2.88756 | + | 2.88756i | −0.189578 | + | 0.189578i | ||||
\(233\) | 12.1316 | − | 3.25066i | 0.794768 | − | 0.212958i | 0.161483 | − | 0.986876i | \(-0.448372\pi\) |
0.633286 | + | 0.773918i | \(0.281706\pi\) | |||||||
\(234\) | −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 | ||||
\(238\) | 0.833568 | − | 8.48019i | 0.0540322 | − | 0.549689i | ||||
\(239\) | 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 | 0.523987 | − | 0.851726i | \(-0.324444\pi\) |
0.999610 | − | 0.0279230i | \(-0.00888932\pi\) | |||||||
\(242\) | 5.25591 | + | 1.40832i | 0.337863 | + | 0.0905300i | ||||
\(243\) | 0.258819 | + | 0.965926i | 0.0166032 | + | 0.0619642i | ||||
\(244\) | 8.59502 | 0.550240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.86297 | −0.437567 | ||||||||
\(247\) | 0.0308220 | + | 0.115029i | 0.00196116 | + | 0.00731915i | ||||
\(248\) | 0.833568 | + | 0.223354i | 0.0529316 | + | 0.0141830i | ||||
\(249\) | −8.73268 | + | 5.04182i | −0.553411 | + | 0.319512i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.45189i | − | 0.217881i | −0.994048 | − | 0.108941i | \(-0.965254\pi\) | ||
0.994048 | − | 0.108941i | \(-0.0347459\pi\) | |||||||
\(252\) | 0.258819 | − | 2.63306i | 0.0163041 | − | 0.165867i | ||||
\(253\) | −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 | ||||
\(257\) | −7.44226 | + | 1.99415i | −0.464236 | + | 0.124392i | −0.483353 | − | 0.875426i | \(-0.660581\pi\) |
0.0191171 | + | 0.999817i | \(0.493914\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | 3.29994 | − | 12.3155i | 0.203871 | − | 0.760857i | ||||
\(263\) | −5.49231 | + | 20.4976i | −0.338670 | + | 1.26394i | 0.561164 | + | 0.827704i | \(0.310354\pi\) |
−0.899835 | + | 0.436231i | \(0.856313\pi\) | |||||||
\(264\) | 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 | ||||
\(268\) | −12.2466 | + | 3.28148i | −0.748083 | + | 0.200448i | ||||
\(269\) | 0.595654 | + | 1.03170i | 0.0363177 | + | 0.0629041i | 0.883613 | − | 0.468218i | \(-0.155104\pi\) |
−0.847295 | + | 0.531122i | \(0.821771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.05603 | − | 4.07380i | −0.428623 | − | 0.247466i | 0.270137 | − | 0.962822i | \(-0.412931\pi\) |
−0.698760 | + | 0.715356i | \(0.746264\pi\) | |||||||
\(272\) | 2.27735 | + | 2.27735i | 0.138085 | + | 0.138085i | ||||
\(273\) | −0.149687 | − | 0.330195i | −0.00905944 | − | 0.0199843i | ||||
\(274\) | 13.8034i | 0.833893i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.78917 | − | 1.61033i | 0.167888 | − | 0.0969304i | ||||
\(277\) | 16.2147 | + | 4.34472i | 0.974248 | + | 0.261049i | 0.710620 | − | 0.703576i | \(-0.248414\pi\) |
0.263627 | + | 0.964625i | \(0.415081\pi\) | |||||||
\(278\) | 3.60533 | + | 13.4553i | 0.216233 | + | 0.806994i | ||||
\(279\) | −0.862973 | −0.0516648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5053 | 0.626693 | 0.313346 | − | 0.949639i | \(-0.398550\pi\) | ||||
0.313346 | + | 0.949639i | \(0.398550\pi\) | |||||||
\(282\) | −0.223354 | − | 0.833568i | −0.0133005 | − | 0.0496382i | ||||
\(283\) | 24.1532 | + | 6.47184i | 1.43576 | + | 0.384711i | 0.891047 | − | 0.453911i | \(-0.149972\pi\) |
0.544714 | + | 0.838622i | \(0.316638\pi\) | |||||||
\(284\) | −4.44880 | + | 2.56851i | −0.263987 | + | 0.152413i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.323067i | − | 0.0191033i | ||||||
\(287\) | −18.0706 | − | 1.77627i | −1.06668 | − | 0.104850i | ||||
\(288\) | 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 | ||||
\(292\) | −15.7014 | + | 4.20718i | −0.918855 | + | 0.246206i | ||||
\(293\) | 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 | ||||
\(297\) | −0.610214 | + | 2.27735i | −0.0354082 | + | 0.132145i | ||||
\(298\) | −5.01636 | + | 18.7213i | −0.290590 | + | 1.08450i | ||||
\(299\) | 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 | ||||
\(303\) | −0.610214 | + | 0.163506i | −0.0350559 | + | 0.00939319i | ||||
\(304\) | −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 | \(0.831575\pi\) | |||||||
\(308\) | 3.63243 | − | 5.07112i | 0.206977 | − | 0.288954i | ||||
\(309\) | − | 1.63174i | − | 0.0928264i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.1714 | + | 7.02714i | −0.690175 | + | 0.398473i | −0.803678 | − | 0.595065i | \(-0.797126\pi\) |
0.113503 | + | 0.993538i | \(0.463793\pi\) | |||||||
\(312\) | 0.132358 | + | 0.0354652i | 0.00749330 | + | 0.00200782i | ||||
\(313\) | −5.09785 | − | 19.0255i | −0.288148 | − | 1.07538i | −0.946508 | − | 0.322679i | \(-0.895416\pi\) |
0.658361 | − | 0.752703i | \(-0.271250\pi\) | |||||||
\(314\) | 6.17165 | 0.348286 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.64231 | −0.261151 | ||||||||
\(317\) | −0.615688 | − | 2.29778i | −0.0345805 | − | 0.129056i | 0.946478 | − | 0.322769i | \(-0.104614\pi\) |
−0.981058 | + | 0.193713i | \(0.937947\pi\) | |||||||
\(318\) | −8.07290 | − | 2.16313i | −0.452706 | − | 0.121302i | ||||
\(319\) | 8.33802 | − | 4.81396i | 0.466840 | − | 0.269530i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 15.1077i | − | 0.843228i | ||||||
\(322\) | 7.76085 | − | 3.51821i | 0.432495 | − | 0.196062i | ||||
\(323\) | 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 | ||||
\(327\) | 8.31948 | − | 2.22920i | 0.460069 | − | 0.123275i | ||||
\(328\) | 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 | 0.181516 | + | 0.983388i | \(0.441899\pi\) |
−0.942397 | + | 0.334496i | \(0.891434\pi\) | |||||||
\(332\) | 2.60984 | − | 9.74004i | 0.143233 | − | 0.534554i | ||||
\(333\) | −2.54841 | + | 9.51079i | −0.139652 | + | 0.521188i | ||||
\(334\) | 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 | −0.788532 | − | 0.614994i | \(-0.789158\pi\) |
0.614994 | + | 0.788532i | \(0.289158\pi\) | |||||||
\(338\) | −12.5389 | + | 3.35979i | −0.682026 | + | 0.182748i | ||||
\(339\) | −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 | ||||
\(343\) | 5.36585 | − | 17.7259i | 0.289729 | − | 0.957109i | ||||
\(344\) | 3.64231i | 0.196380i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.11252 | − | 0.642314i | 0.0598095 | − | 0.0345310i | ||||
\(347\) | −5.59119 | − | 1.49816i | −0.300151 | − | 0.0804252i | 0.105601 | − | 0.994409i | \(-0.466324\pi\) |
−0.405752 | + | 0.913983i | \(0.632990\pi\) | |||||||
\(348\) | 1.05692 | + | 3.94449i | 0.0566569 | + | 0.211447i | ||||
\(349\) | −19.6326 | −1.05091 | −0.525455 | − | 0.850821i | \(-0.676105\pi\) | ||||
−0.525455 | + | 0.850821i | \(0.676105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.137027 | −0.00731396 | ||||||||
\(352\) | 0.610214 | + | 2.27735i | 0.0325245 | + | 0.121383i | ||||
\(353\) | 25.1461 | + | 6.73787i | 1.33839 | + | 0.358621i | 0.855837 | − | 0.517246i | \(-0.173043\pi\) |
0.482554 | + | 0.875866i | \(0.339709\pi\) | |||||||
\(354\) | 9.27978 | − | 5.35769i | 0.493215 | − | 0.284758i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.97065i | 0.528443i | ||||||||
\(357\) | −6.92728 | − | 4.96199i | −0.366630 | − | 0.262616i | ||||
\(358\) | 13.7050 | + | 13.7050i | 0.724329 | + | 0.724329i | ||||
\(359\) | 6.41108 | + | 3.70144i | 0.338364 | + | 0.195355i | 0.659548 | − | 0.751662i | \(-0.270748\pi\) |
−0.321184 | + | 0.947017i | \(0.604081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.12235 | + | 15.8004i | 0.480124 | + | 0.831599i | ||||
\(362\) | 24.3329 | − | 6.51999i | 1.27891 | − | 0.342683i | ||||
\(363\) | 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 | ||||
\(367\) | 3.12375 | − | 11.6580i | 0.163058 | − | 0.608542i | −0.835222 | − | 0.549914i | \(-0.814661\pi\) |
0.998280 | − | 0.0586284i | \(-0.0186727\pi\) | |||||||
\(368\) | −0.833568 | + | 3.11092i | −0.0434527 | + | 0.162168i | ||||
\(369\) | −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 | ||||
\(373\) | −0.115029 | + | 0.0308220i | −0.00595600 | + | 0.00159590i | −0.261796 | − | 0.965123i | \(-0.584315\pi\) |
0.255840 | + | 0.966719i | \(0.417648\pi\) | |||||||
\(374\) | −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 | ||||
\(378\) | −2.15089 | − | 1.54067i | −0.110630 | − | 0.0792438i | ||||
\(379\) | 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 | ||||
\(382\) | −6.62912 | − | 1.77627i | −0.339175 | − | 0.0908818i | ||||
\(383\) | −10.0127 | − | 37.3678i | −0.511624 | − | 1.90941i | −0.402625 | − | 0.915365i | \(-0.631902\pi\) |
−0.108999 | − | 0.994042i | \(-0.534764\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.77934 | −0.141465 | ||||||||
\(387\) | −0.942700 | − | 3.51821i | −0.0479201 | − | 0.178840i | ||||
\(388\) | −15.6062 | − | 4.18166i | −0.792283 | − | 0.212292i | ||||
\(389\) | 26.3005 | − | 15.1846i | 1.33349 | − | 0.769888i | 0.347654 | − | 0.937623i | \(-0.386979\pi\) |
0.985832 | + | 0.167735i | \(0.0536452\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.3726i | − | 0.524567i | ||||||
\(392\) | 3.89125 | + | 5.81878i | 0.196538 | + | 0.293893i | ||||
\(393\) | −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 | ||||
\(397\) | −26.0335 | + | 6.97566i | −1.30658 | + | 0.350098i | −0.843936 | − | 0.536444i | \(-0.819767\pi\) |
−0.462648 | + | 0.886542i | \(0.653101\pi\) | |||||||
\(398\) | −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 | −0.984937 | − | 0.172914i | \(-0.944682\pi\) |
0.642216 | + | 0.766523i | \(0.278015\pi\) | |||||||
\(402\) | −3.28148 | + | 12.2466i | −0.163665 | + | 0.610807i | ||||
\(403\) | 0.0306055 | − | 0.114221i | 0.00152457 | − | 0.00568977i | ||||
\(404\) | 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 | ||||
\(408\) | 3.11092 | − | 0.833568i | 0.154013 | − | 0.0412678i | ||||
\(409\) | −2.11119 | − | 3.65669i | −0.104392 | − | 0.180812i | 0.809098 | − | 0.587674i | \(-0.199956\pi\) |
−0.913489 | + | 0.406862i | \(0.866623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9541 | + | 6.90169i | 0.589651 | + | 0.340435i | ||||
\(412\) | 1.15381 | + | 1.15381i | 0.0568444 | + | 0.0568444i | ||||
\(413\) | 25.8209 | − | 11.7053i | 1.27056 | − | 0.575982i | ||||
\(414\) | − | 3.22066i | − | 0.158287i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.118669 | + | 0.0685135i | −0.00581822 | + | 0.00335915i | ||||
\(417\) | 13.4553 | + | 3.60533i | 0.658908 | + | 0.176554i | ||||
\(418\) | 0.530323 | + | 1.97919i | 0.0259390 | + | 0.0968056i | ||||
\(419\) | −28.1807 | −1.37672 | −0.688359 | − | 0.725370i | \(-0.741669\pi\) | ||||
−0.688359 | + | 0.725370i | \(0.741669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.31486 | −0.161557 | −0.0807783 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807783 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(422\) | 3.53872 | + | 13.2067i | 0.172262 | + | 0.642891i | ||||
\(423\) | −0.833568 | − | 0.223354i | −0.0405295 | − | 0.0108598i | ||||
\(424\) | 7.23797 | − | 4.17884i | 0.351507 | − | 0.202943i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.13703i | 0.248890i | ||||||||
\(427\) | 13.2421 | − | 18.4869i | 0.640832 | − | 0.894646i | ||||
\(428\) | 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 | 0.811354 | − | 0.584555i | \(-0.198731\pi\) |
−0.911917 | + | 0.410376i | \(0.865398\pi\) | |||||||
\(432\) | 0.965926 | − | 0.258819i | 0.0464731 | − | 0.0124524i | ||||
\(433\) | −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 | ||||
\(437\) | −0.724435 | + | 2.70363i | −0.0346544 | + | 0.129332i | ||||
\(438\) | −4.20718 | + | 15.7014i | −0.201027 | + | 0.750242i | ||||
\(439\) | −1.24102 | + | 2.14951i | −0.0592307 | + | 0.102591i | −0.894120 | − | 0.447827i | \(-0.852198\pi\) |
0.834890 | + | 0.550417i | \(0.185531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.26467 | − | 4.61338i | −0.250698 | − | 0.219685i | ||||
\(442\) | 0.312059 | − | 0.312059i | 0.0148431 | − | 0.0148431i | ||||
\(443\) | −14.2947 | + | 3.83026i | −0.679164 | + | 0.181981i | −0.581879 | − | 0.813275i | \(-0.697682\pi\) |
−0.0972845 | + | 0.995257i | \(0.531016\pi\) | |||||||
\(444\) | −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 | ||||
\(448\) | −2.63306 | − | 0.258819i | −0.124400 | − | 0.0122281i | ||||
\(449\) | − | 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 | ||||
\(452\) | 16.9794 | + | 4.54961i | 0.798643 | + | 0.213996i | ||||
\(453\) | 0.814659 | + | 3.04035i | 0.0382760 | + | 0.142848i | ||||
\(454\) | 15.5490 | 0.729750 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.869078 | −0.0406983 | ||||||||
\(457\) | 8.30331 | + | 30.9884i | 0.388413 | + | 1.44958i | 0.832717 | + | 0.553699i | \(0.186784\pi\) |
−0.444304 | + | 0.895876i | \(0.646549\pi\) | |||||||
\(458\) | 10.4396 | + | 2.79728i | 0.487810 | + | 0.130708i | ||||
\(459\) | −2.78917 | + | 1.61033i | −0.130187 | + | 0.0751637i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.441317i | 0.0205542i | 0.999947 | + | 0.0102771i | \(0.00327136\pi\) | ||||
−0.999947 | + | 0.0102771i | \(0.996729\pi\) | |||||||
\(462\) | −2.57551 | − | 5.68133i | −0.119823 | − | 0.264320i | ||||
\(463\) | −26.0183 | − | 26.0183i | −1.20917 | − | 1.20917i | −0.971295 | − | 0.237877i | \(-0.923548\pi\) |
−0.237877 | − | 0.971295i | \(-0.576452\pi\) | |||||||
\(464\) | −3.53653 | − | 2.04182i | −0.164179 | − | 0.0947889i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.27978 | + | 10.8769i | 0.290905 | + | 0.503863i | ||||
\(467\) | 18.9052 | − | 5.06565i | 0.874831 | − | 0.234410i | 0.206655 | − | 0.978414i | \(-0.433742\pi\) |
0.668175 | + | 0.744004i | \(0.267076\pi\) | |||||||
\(468\) | 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 | ||||
\(472\) | −2.77334 | + | 10.3503i | −0.127653 | + | 0.476409i | ||||
\(473\) | 2.22259 | − | 8.29482i | 0.102195 | − | 0.381396i | ||||
\(474\) | −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 | ||||
\(478\) | −15.4265 | + | 4.13351i | −0.705590 | + | 0.189062i | ||||
\(479\) | −15.3363 | − | 26.5632i | −0.700732 | − | 1.21370i | −0.968210 | − | 0.250140i | \(-0.919523\pi\) |
0.267477 | − | 0.963564i | \(-0.413810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.16845 | − | 0.674604i | −0.0532767 | − | 0.0307593i | ||||
\(482\) | 19.3123 | + | 19.3123i | 0.879649 | + | 0.879649i | ||||
\(483\) | 0.833568 | − | 8.48019i | 0.0379286 | − | 0.385862i | ||||
\(484\) | 5.44132i | 0.247333i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −23.7975 | − | 6.37653i | −1.07837 | − | 0.288948i | −0.324441 | − | 0.945906i | \(-0.605176\pi\) |
−0.753927 | + | 0.656958i | \(0.771843\pi\) | |||||||
\(488\) | 2.22456 | + | 8.30216i | 0.100701 | + | 0.375821i | ||||
\(489\) | −2.77324 | −0.125410 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.08275 | 0.139122 | 0.0695612 | − | 0.997578i | \(-0.477840\pi\) | ||||
0.0695612 | + | 0.997578i | \(0.477840\pi\) | |||||||
\(492\) | −1.77627 | − | 6.62912i | −0.0800804 | − | 0.298864i | ||||
\(493\) | 12.7038 | + | 3.40398i | 0.572152 | + | 0.153308i | ||||
\(494\) | −0.103133 | + | 0.0595436i | −0.00464015 | + | 0.00267899i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.862973i | 0.0387486i | ||||||||
\(497\) | −1.32956 | + | 13.5261i | −0.0596389 | + | 0.606729i | ||||
\(498\) | −7.13020 | − | 7.13020i | −0.319512 | − | 0.319512i | ||||
\(499\) | −28.7283 | − | 16.5863i | −1.28605 | − | 0.742503i | −0.308105 | − | 0.951352i | \(-0.599695\pi\) |
−0.977948 | + | 0.208849i | \(0.933028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.57834 | − | 14.8581i | −0.383252 | − | 0.663812i | ||||
\(502\) | 3.33427 | − | 0.893415i | 0.148816 | − | 0.0398751i | ||||
\(503\) | −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 | ||||
\(507\) | −3.35979 | + | 12.5389i | −0.149213 | + | 0.556872i | ||||
\(508\) | −3.52171 | + | 13.1432i | −0.156251 | + | 0.583136i | ||||
\(509\) | −13.6202 | + | 23.5908i | −0.603703 | + | 1.04564i | 0.388552 | + | 0.921427i | \(0.372975\pi\) |
−0.992255 | + | 0.124217i | \(0.960358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.1416 | + | 40.2538i | −0.669824 | + | 1.78072i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.839465 | − | 0.224934i | 0.0370633 | − | 0.00993107i | ||||
\(514\) | −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 | ||||
\(518\) | −10.7560 | − | 23.7267i | −0.472590 | − | 1.04249i | ||||
\(519\) | − | 1.28463i | − | 0.0563889i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8599 | + | 6.26995i | −0.475780 | + | 0.274692i | −0.718656 | − | 0.695366i | \(-0.755242\pi\) |
0.242876 | + | 0.970057i | \(0.421909\pi\) | |||||||
\(522\) | 3.94449 | + | 1.05692i | 0.172645 | + | 0.0462602i | ||||
\(523\) | 0.432274 | + | 1.61327i | 0.0189020 | + | 0.0705433i | 0.974733 | − | 0.223375i | \(-0.0717074\pi\) |
−0.955831 | + | 0.293918i | \(0.905041\pi\) | |||||||
\(524\) | 12.7500 | 0.556986 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2207 | −0.925265 | ||||||||
\(527\) | −0.719346 | − | 2.68464i | −0.0313352 | − | 0.116945i | ||||
\(528\) | 2.27735 | + | 0.610214i | 0.0991089 | + | 0.0265562i | ||||
\(529\) | −10.9356 | + | 6.31368i | −0.475461 | + | 0.274508i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 10.7154i | − | 0.465008i | ||||||
\(532\) | −2.28834 | − | 0.224934i | −0.0992119 | − | 0.00975212i | ||||
\(533\) | −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 | ||||
\(537\) | 18.7213 | − | 5.01636i | 0.807884 | − | 0.216472i | ||||
\(538\) | −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 | 0.392303 | + | 0.919836i | \(0.371678\pi\) |
−0.992753 | + | 0.120174i | \(0.961655\pi\) | |||||||
\(542\) | 2.10875 | − | 7.86998i | 0.0905788 | − | 0.338045i | ||||
\(543\) | 6.51999 | − | 24.3329i | 0.279800 | − | 1.04423i | ||||
\(544\) | −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 | −0.639776 | − | 0.768561i | \(-0.720973\pi\) |
0.768561 | + | 0.639776i | \(0.220973\pi\) | |||||||
\(548\) | −13.3330 | + | 3.57258i | −0.569560 | + | 0.152613i | ||||
\(549\) | −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 | ||||
\(553\) | −7.15230 | + | 9.98510i | −0.304147 | + | 0.424610i | ||||
\(554\) | 16.7867i | 0.713199i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0637 | + | 6.96496i | −0.511614 | + | 0.295380i | ||||
\(557\) | 20.8352 | + | 5.58276i | 0.882814 | + | 0.236549i | 0.671621 | − | 0.740895i | \(-0.265598\pi\) |
0.211193 | + | 0.977444i | \(0.432265\pi\) | |||||||
\(558\) | −0.223354 | − | 0.833568i | −0.00945532 | − | 0.0352877i | ||||
\(559\) | 0.499096 | 0.0211095 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.59330 | −0.320589 | ||||||||
\(562\) | 2.71897 | + | 10.1473i | 0.114693 | + | 0.428039i | ||||
\(563\) | −30.1081 | − | 8.06743i | −1.26890 | − | 0.340002i | −0.439293 | − | 0.898344i | \(-0.644771\pi\) |
−0.829611 | + | 0.558342i | \(0.811438\pi\) | |||||||
\(564\) | 0.747356 | − | 0.431486i | 0.0314694 | − | 0.0181689i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.0053i | 1.05105i | ||||||||
\(567\) | −2.40971 | + | 1.09239i | −0.101198 | + | 0.0458759i | ||||
\(568\) | −3.63243 | − | 3.63243i | −0.152413 | − | 0.152413i | ||||
\(569\) | 2.12720 | + | 1.22814i | 0.0891767 | + | 0.0514862i | 0.543925 | − | 0.839134i | \(-0.316938\pi\) |
−0.454749 | + | 0.890620i | \(0.650271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.62235 | + | 8.00615i | 0.193439 | + | 0.335047i | 0.946388 | − | 0.323033i | \(-0.104702\pi\) |
−0.752948 | + | 0.658080i | \(0.771369\pi\) | |||||||
\(572\) | 0.312059 | − | 0.0836158i | 0.0130478 | − | 0.00349615i | ||||
\(573\) | −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 | ||||
\(577\) | 12.0756 | − | 45.0669i | 0.502715 | − | 1.87616i | 0.0210977 | − | 0.999777i | \(-0.493284\pi\) |
0.481618 | − | 0.876381i | \(-0.340049\pi\) | |||||||
\(578\) | −1.71529 | + | 6.40154i | −0.0713465 | + | 0.266269i | ||||
\(579\) | −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 | ||||
\(583\) | −19.0334 | + | 5.09998i | −0.788282 | + | 0.211219i | ||||
\(584\) | −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 | \(0.754763\pi\) | |||||||
\(588\) | 6.98483 | − | 0.460527i | 0.288050 | − | 0.0189918i | ||||
\(589\) | 0.749991i | 0.0309028i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.2692 | + | 12.2798i | −0.874898 | + | 0.505123i | ||||
\(592\) | 9.51079 | + | 2.54841i | 0.390891 | + | 0.104739i | ||||
\(593\) | −6.05324 | − | 22.5910i | −0.248577 | − | 0.927701i | −0.971552 | − | 0.236827i | \(-0.923893\pi\) |
0.722975 | − | 0.690874i | \(-0.242774\pi\) | |||||||
\(594\) | −2.35769 | −0.0967370 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.3817 | −0.793907 | ||||||||
\(597\) | 2.72564 | + | 10.1722i | 0.111553 | + | 0.416321i | ||||
\(598\) | 0.426280 | + | 0.114221i | 0.0174319 | + | 0.00467086i | ||||
\(599\) | −9.39922 | + | 5.42664i | −0.384042 | + | 0.221727i | −0.679575 | − | 0.733606i | \(-0.737836\pi\) |
0.295534 | + | 0.955332i | \(0.404503\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.5701i | − | 0.961443i | −0.876873 | − | 0.480721i | \(-0.840375\pi\) | ||
0.876873 | − | 0.480721i | \(-0.159625\pi\) | |||||||
\(602\) | 7.83421 | + | 5.61162i | 0.319299 | + | 0.228713i | ||||
\(603\) | 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 | ||||
\(607\) | −28.3006 | + | 7.58314i | −1.14869 | + | 0.307790i | −0.782439 | − | 0.622727i | \(-0.786025\pi\) |
−0.366249 | + | 0.930517i | \(0.619358\pi\) | |||||||
\(608\) | 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 | ||||
\(612\) | 0.833568 | − | 3.11092i | 0.0336950 | − | 0.125751i | ||||
\(613\) | −0.813525 | + | 3.03612i | −0.0328580 | + | 0.122628i | −0.980407 | − | 0.196983i | \(-0.936886\pi\) |
0.947549 | + | 0.319611i | \(0.103552\pi\) | |||||||
\(614\) | 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 | \(0.518200\pi\) |
−0.998366 | + | 0.0571445i | \(0.981800\pi\) | |||||||
\(618\) | 1.57614 | − | 0.422325i | 0.0634016 | − | 0.0169884i | ||||
\(619\) | −11.7918 | − | 20.4240i | −0.473953 | − | 0.820910i | 0.525603 | − | 0.850730i | \(-0.323840\pi\) |
−0.999555 | + | 0.0298201i | \(0.990507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.78917 | − | 1.61033i | −0.111926 | − | 0.0646203i | ||||
\(622\) | −9.93788 | − | 9.93788i | −0.398473 | − | 0.398473i | ||||
\(623\) | 21.4458 | + | 15.3615i | 0.859206 | + | 0.615447i | ||||
\(624\) | 0.137027i | 0.00548547i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.0578 | − | 9.84830i | 0.681765 | − | 0.393617i | ||||
\(627\) | 1.97919 | + | 0.530323i | 0.0790414 | + | 0.0211791i | ||||
\(628\) | 1.59734 | + | 5.96135i | 0.0637408 | + | 0.237884i | ||||
\(629\) | −31.7116 | −1.26442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.97684 | −0.357362 | −0.178681 | − | 0.983907i | \(-0.557183\pi\) | ||||
−0.178681 | + | 0.983907i | \(0.557183\pi\) | |||||||
\(632\) | −1.20152 | − | 4.48413i | −0.0477939 | − | 0.178369i | ||||
\(633\) | 13.2067 | + | 3.53872i | 0.524918 | + | 0.140651i | ||||
\(634\) | 2.06013 | − | 1.18942i | 0.0818182 | − | 0.0472378i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 8.35769i | − | 0.331404i | ||||||
\(637\) | 0.797331 | − | 0.533206i | 0.0315914 | − | 0.0211264i | ||||
\(638\) | 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 | 0.970191 | − | 0.242343i | \(-0.0779160\pi\) |
−0.694971 | + | 0.719038i | \(0.744583\pi\) | |||||||
\(642\) | 14.5929 | − | 3.91015i | 0.575936 | − | 0.154321i | ||||
\(643\) | −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 | ||||
\(647\) | −11.0458 | + | 41.2236i | −0.434256 | + | 1.62067i | 0.308583 | + | 0.951197i | \(0.400145\pi\) |
−0.742839 | + | 0.669470i | \(0.766521\pi\) | |||||||
\(648\) | 0.258819 | − | 0.965926i | 0.0101674 | − | 0.0379452i | ||||
\(649\) | 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 | ||||
\(653\) | 29.4978 | − | 7.90392i | 1.15434 | − | 0.309304i | 0.369637 | − | 0.929176i | \(-0.379482\pi\) |
0.784703 | + | 0.619872i | \(0.212815\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | 2.07951 | − | 0.942700i | 0.0810678 | − | 0.0367503i | ||||
\(659\) | − | 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 | −0.260948 | − | 0.965353i | \(-0.584035\pi\) |
0.705546 | + | 0.708664i | \(0.250702\pi\) | |||||||
\(662\) | −26.7426 | − | 7.16567i | −1.03938 | − | 0.278502i | ||||
\(663\) | −0.114221 | − | 0.426280i | −0.00443599 | − | 0.0165553i | ||||
\(664\) | 10.0836 | 0.391321 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.84629 | −0.381536 | ||||||||
\(667\) | 3.40398 | + | 12.7038i | 0.131803 | + | 0.491895i | ||||
\(668\) | 16.5721 | + | 4.44048i | 0.641193 | + | 0.171807i | ||||
\(669\) | −7.86666 | + | 4.54182i | −0.304142 | + | 0.175597i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 20.2644i | − | 0.782297i | ||||||
\(672\) | −1.54067 | + | 2.15089i | −0.0594328 | + | 0.0829723i | ||||
\(673\) | −8.91749 | − | 8.91749i | −0.343744 | − | 0.343744i | 0.514029 | − | 0.857773i | \(-0.328152\pi\) |
−0.857773 | + | 0.514029i | \(0.828152\pi\) | |||||||
\(674\) | −3.90169 | − | 2.25264i | −0.150288 | − | 0.0867686i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.49061 | − | 11.2421i | −0.249639 | − | 0.432387i | ||||
\(677\) | 40.5930 | − | 10.8769i | 1.56011 | − | 0.418031i | 0.627415 | − | 0.778685i | \(-0.284113\pi\) |
0.932700 | + | 0.360654i | \(0.117446\pi\) | |||||||
\(678\) | 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 | ||||
\(682\) | 0.526598 | − | 1.96529i | 0.0201645 | − | 0.0752549i | ||||
\(683\) | 1.11168 | − | 4.14885i | 0.0425373 | − | 0.158751i | −0.941390 | − | 0.337319i | \(-0.890480\pi\) |
0.983928 | + | 0.178568i | \(0.0571465\pi\) | |||||||
\(684\) | −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 | ||||
\(688\) | −3.51821 | + | 0.942700i | −0.134130 | + | 0.0359401i | ||||
\(689\) | −0.572615 | − | 0.991798i | −0.0218149 | − | 0.0377845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.4983 | + | 18.7629i | 1.23629 | + | 0.713773i | 0.968334 | − | 0.249657i | \(-0.0803180\pi\) |
0.267958 | + | 0.963431i | \(0.413651\pi\) | |||||||
\(692\) | 0.908369 | + | 0.908369i | 0.0345310 | + | 0.0345310i | ||||
\(693\) | −6.20793 | − | 0.610214i | −0.235820 | − | 0.0231801i | ||||
\(694\) | − | 5.78843i | − | 0.219726i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.53653 | + | 2.04182i | −0.134052 | + | 0.0773948i | ||||
\(697\) | −21.3501 | − | 5.72075i | −0.808694 | − | 0.216689i | ||||
\(698\) | −5.08130 | − | 18.9637i | −0.192330 | − | 0.717785i | ||||
\(699\) | 12.5596 | 0.475046 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.7644 | 0.482104 | 0.241052 | − | 0.970512i | \(-0.422508\pi\) | ||||
0.241052 | + | 0.970512i | \(0.422508\pi\) | |||||||
\(702\) | −0.0354652 | − | 0.132358i | −0.00133855 | − | 0.00499553i | ||||
\(703\) | 8.26562 | + | 2.21477i | 0.311744 | + | 0.0835315i | ||||
\(704\) | −2.04182 | + | 1.17884i | −0.0769538 | + | 0.0444293i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.0331i | 0.979770i | ||||||||
\(707\) | −0.690104 | − | 1.52231i | −0.0259541 | − | 0.0572523i | ||||
\(708\) | 7.57691 | + | 7.57691i | 0.284758 | + | 0.284758i | ||||
\(709\) | −43.1134 | − | 24.8916i | −1.61916 | − | 0.934822i | −0.987138 | − | 0.159872i | \(-0.948892\pi\) |
−0.632022 | − | 0.774951i | \(-0.717775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.32116 | + | 4.02036i | 0.0870502 | + | 0.150775i | ||||
\(712\) | −9.63091 | + | 2.58059i | −0.360934 | + | 0.0967118i | ||||
\(713\) | 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 | ||||
\(717\) | −4.13351 | + | 15.4265i | −0.154369 | + | 0.576112i | ||||
\(718\) | −1.91601 | + | 7.15063i | −0.0715047 | + | 0.266859i | ||||
\(719\) | −23.1988 | + | 40.1815i | −0.865169 | + | 1.49852i | 0.00171077 | + | 0.999999i | \(0.499455\pi\) |
−0.866880 | + | 0.498518i | \(0.833878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.25938 | − | 0.704074i | 0.158628 | − | 0.0262211i | ||||
\(722\) | −12.9010 | + | 12.9010i | −0.480124 | + | 0.480124i | ||||
\(723\) | 26.3810 | − | 7.06878i | 0.981121 | − | 0.262891i | ||||
\(724\) | 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 | \(0.892911\pi\) | |||||||
\(728\) | −0.0354652 | + | 0.360801i | −0.00131443 | + | 0.0133722i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1590 | − | 5.86533i | 0.375746 | − | 0.216937i | ||||
\(732\) | 8.30216 | + | 2.22456i | 0.306856 | + | 0.0822219i | ||||
\(733\) | 10.0281 | + | 37.4254i | 0.370396 | + | 1.38234i | 0.859956 | + | 0.510368i | \(0.170491\pi\) |
−0.489560 | + | 0.871970i | \(0.662842\pi\) | |||||||
\(734\) | 12.0692 | 0.445484 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.22066 | −0.118715 | ||||||||
\(737\) | 7.73669 | + | 28.8737i | 0.284985 | + | 1.06358i | ||||
\(738\) | −6.62912 | − | 1.77627i | −0.244021 | − | 0.0653853i | ||||
\(739\) | 34.4840 | − | 19.9093i | 1.26851 | − | 0.732377i | 0.293807 | − | 0.955865i | \(-0.405078\pi\) |
0.974707 | + | 0.223488i | \(0.0717444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.119087i | 0.00437478i | ||||||||
\(742\) | 2.16313 | − | 22.0063i | 0.0794109 | − | 0.807877i | ||||
\(743\) | −28.0880 | − | 28.0880i | −1.03045 | − | 1.03045i | −0.999522 | − | 0.0309276i | \(-0.990154\pi\) |
−0.0309276 | − | 0.999522i | \(-0.509846\pi\) | |||||||
\(744\) | 0.747356 | + | 0.431486i | 0.0273994 | + | 0.0158191i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.0595436 | − | 0.103133i | −0.00218005 | − | 0.00377595i | ||||
\(747\) | −9.74004 | + | 2.60984i | −0.356369 | + | 0.0954889i | ||||
\(748\) | 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 | 0.388538 | + | 0.921433i | \(0.372980\pi\) |
−0.992253 | + | 0.124233i | \(0.960353\pi\) | |||||||
\(752\) | −0.223354 | + | 0.833568i | −0.00814488 | + | 0.0303971i | ||||
\(753\) | 0.893415 | − | 3.33427i | 0.0325579 | − | 0.121508i | ||||
\(754\) | −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 | −0.844281 | − | 0.535900i | \(-0.819972\pi\) |
0.535900 | + | 0.844281i | \(0.319972\pi\) | |||||||
\(758\) | −8.53686 | + | 2.28744i | −0.310073 | + | 0.0830837i | ||||
\(759\) | −3.79665 | − | 6.57599i | −0.137810 | − | 0.238693i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.4199 | + | 14.6762i | 0.921471 | + | 0.532011i | 0.884104 | − | 0.467290i | \(-0.154770\pi\) |
0.0373669 | + | 0.999302i | \(0.488103\pi\) | |||||||
\(762\) | 9.62150 | + | 9.62150i | 0.348550 | + | 0.348550i | ||||
\(763\) | 9.40869 | + | 20.7547i | 0.340617 | + | 0.751371i | ||||
\(764\) | − | 6.86297i | − | 0.248294i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.5031 | − | 19.3430i | 1.21052 | − | 0.698891i | ||||
\(767\) | 1.41827 | + | 0.380023i | 0.0512106 | + | 0.0137218i | ||||
\(768\) | −0.258819 | − | 0.965926i | −0.00933933 | − | 0.0348548i | ||||
\(769\) | 21.4307 | 0.772812 | 0.386406 | − | 0.922329i | \(-0.373716\pi\) | ||||
0.386406 | + | 0.922329i | \(0.373716\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.70480 | −0.277482 | ||||||||
\(772\) | −0.719346 | − | 2.68464i | −0.0258898 | − | 0.0966222i | ||||
\(773\) | 11.0747 | + | 2.96745i | 0.398329 | + | 0.106732i | 0.452422 | − | 0.891804i | \(-0.350560\pi\) |
−0.0540931 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(774\) | 3.15434 | − | 1.82116i | 0.113380 | − | 0.0654601i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 16.1567i | − | 0.579991i | ||||||
\(777\) | −25.9259 | − | 2.54841i | −0.930086 | − | 0.0914236i | ||||
\(778\) | 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 | ||||
\(782\) | 10.0192 | − | 2.68464i | 0.358286 | − | 0.0960024i | ||||
\(783\) | 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 | ||||
\(787\) | 3.92694 | − | 14.6555i | 0.139980 | − | 0.522414i | −0.859947 | − | 0.510383i | \(-0.829504\pi\) |
0.999928 | − | 0.0120308i | \(-0.00382961\pi\) | |||||||
\(788\) | 6.35648 | − | 23.7227i | 0.226440 | − | 0.845087i | ||||
\(789\) | −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 | ||||
\(793\) | 1.13762 | − | 0.304824i | 0.0403981 | − | 0.0108246i | ||||
\(794\) | −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 | \(0.941641\pi\) | |||||||
\(798\) | −1.33897 | + | 1.86929i | −0.0473989 | + | 0.0661721i | ||||
\(799\) | − | 2.77934i | − | 0.0983260i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.63484 | − | 4.98532i | 0.305097 | − | 0.176148i | ||||
\(802\) | −13.2582 | − | 3.55254i | −0.468165 | − | 0.125444i | ||||
\(803\) | 9.91920 | + | 37.0190i | 0.350041 | + | 1.30637i | ||||
\(804\) | −12.6787 | −0.447142 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.118251 | 0.00416520 | ||||||||
\(807\) | 0.308333 | + | 1.15072i | 0.0108538 | + | 0.0405071i | ||||
\(808\) | 0.610214 | + | 0.163506i | 0.0214673 | + | 0.00575213i | ||||
\(809\) | 21.9812 | − | 12.6909i | 0.772819 | − | 0.446187i | −0.0610605 | − | 0.998134i | \(-0.519448\pi\) |
0.833879 | + | 0.551947i | \(0.186115\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1094i | 0.776366i | 0.921582 | + | 0.388183i | \(0.126897\pi\) | ||||
−0.921582 | + | 0.388183i | \(0.873103\pi\) | |||||||
\(812\) | −9.84036 | + | 4.46091i | −0.345329 | + | 0.156547i | ||||
\(813\) | −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 | ||||
\(817\) | −3.05759 | + | 0.819280i | −0.106972 | + | 0.0286630i | ||||
\(818\) | 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 | −0.535087 | − | 0.844797i | \(-0.679721\pi\) |
0.999159 | + | 0.0410009i | \(0.0130546\pi\) | |||||||
\(822\) | −3.57258 | + | 13.3330i | −0.124608 | + | 0.465043i | ||||
\(823\) | 3.32388 | − | 12.4049i | 0.115863 | − | 0.432407i | −0.883487 | − | 0.468456i | \(-0.844811\pi\) |
0.999350 | + | 0.0360489i | \(0.0114772\pi\) | |||||||
\(824\) | −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 | \(-0.449139\pi\) |
0.987262 | − | 0.159105i | \(-0.0508609\pi\) | |||||||
\(828\) | 3.11092 | − | 0.833568i | 0.108112 | − | 0.0289685i | ||||
\(829\) | 20.0547 | + | 34.7358i | 0.696528 | + | 1.20642i | 0.969663 | + | 0.244447i | \(0.0786064\pi\) |
−0.273134 | + | 0.961976i | \(0.588060\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5377 | + | 8.39335i | 0.504308 | + | 0.291162i | ||||
\(832\) | −0.0968928 | − | 0.0968928i | −0.00335915 | − | 0.00335915i | ||||
\(833\) | 9.96339 | − | 20.2235i | 0.345211 | − | 0.700703i | ||||
\(834\) | 13.9299i | 0.482354i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.77450 | + | 1.02451i | −0.0613723 | + | 0.0354333i | ||||
\(837\) | −0.833568 | − | 0.223354i | −0.0288123 | − | 0.00772024i | ||||
\(838\) | −7.29371 | − | 27.2205i | −0.251957 | − | 0.940317i | ||||
\(839\) | 16.4841 | 0.569096 | 0.284548 | − | 0.958662i | \(-0.408157\pi\) | ||||
0.284548 | + | 0.958662i | \(0.408157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3240 | 0.424964 | ||||||||
\(842\) | −0.857950 | − | 3.20191i | −0.0295669 | − | 0.110345i | ||||
\(843\) | 10.1473 | + | 2.71897i | 0.349493 | + | 0.0936462i | ||||
\(844\) | −11.8408 | + | 6.83628i | −0.407576 | + | 0.235314i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 0.862973i | − | 0.0296696i | ||||||
\(847\) | 11.7037 | + | 8.38330i | 0.402143 | + | 0.288054i | ||||
\(848\) | 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 | ||||
\(852\) | −4.96199 | + | 1.32956i | −0.169995 | + | 0.0455500i | ||||
\(853\) | −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 | ||||
\(857\) | 2.21789 | − | 8.27727i | 0.0757616 | − | 0.282746i | −0.917643 | − | 0.397405i | \(-0.869911\pi\) |
0.993405 | + | 0.114659i | \(0.0365775\pi\) | |||||||
\(858\) | 0.0836158 | − | 0.312059i | 0.00285460 | − | 0.0106535i | ||||
\(859\) | 17.0418 | − | 29.5173i | 0.581459 | − | 1.00712i | −0.413847 | − | 0.910346i | \(-0.635815\pi\) |
0.995307 | − | 0.0967707i | \(-0.0308514\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.9952 | − | 6.39277i | −0.579193 | − | 0.217865i | ||||
\(862\) | 2.95250 | − | 2.95250i | 0.100563 | − | 0.100563i | ||||
\(863\) | −16.9097 | + | 4.53093i | −0.575612 | + | 0.154235i | −0.534869 | − | 0.844935i | \(-0.679639\pi\) |
−0.0407427 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(864\) | 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 | ||||
\(868\) | 1.85616 | + | 1.32956i | 0.0630021 | + | 0.0451282i | ||||
\(869\) | 10.9451i | 0.371288i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.50456 | + | 0.868660i | −0.0509802 | + | 0.0294334i | ||||
\(872\) | −8.31948 | − | 2.22920i | −0.281733 | − | 0.0754902i | ||||
\(873\) | 4.18166 | + | 15.6062i | 0.141528 | + | 0.528189i | ||||
\(874\) | −2.79900 | −0.0946777 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.2553 | −0.549215 | ||||||||
\(877\) | 1.50644 | + | 5.62211i | 0.0508689 | + | 0.189845i | 0.986685 | − | 0.162644i | \(-0.0520021\pi\) |
−0.935816 | + | 0.352489i | \(0.885335\pi\) | |||||||
\(878\) | −2.39747 | − | 0.642400i | −0.0809106 | − | 0.0216799i | ||||
\(879\) | 10.6096 | − | 6.12545i | 0.357852 | − | 0.206606i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.13703i | − | 0.173071i | −0.996249 | − | 0.0865354i | \(-0.972420\pi\) | ||
0.996249 | − | 0.0865354i | \(-0.0275796\pi\) | |||||||
\(882\) | 3.09359 | − | 6.27931i | 0.104167 | − | 0.211435i | ||||
\(883\) | 33.6563 | + | 33.6563i | 1.13262 | + | 1.13262i | 0.989739 | + | 0.142885i | \(0.0456378\pi\) |
0.142885 | + | 0.989739i | \(0.454362\pi\) | |||||||
\(884\) | 0.382192 | + | 0.220659i | 0.0128545 | + | 0.00742156i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.39950 | − | 12.8163i | −0.248591 | − | 0.430572i | ||||
\(887\) | 6.61013 | − | 1.77118i | 0.221946 | − | 0.0594704i | −0.146132 | − | 0.989265i | \(-0.546682\pi\) |
0.368078 | + | 0.929795i | \(0.380016\pi\) | |||||||
\(888\) | 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 | ||||
\(892\) | 2.35102 | − | 8.77411i | 0.0787179 | − | 0.293779i | ||||
\(893\) | −0.194112 | + | 0.724435i | −0.00649571 | + | 0.0242423i | ||||
\(894\) | −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 | ||||
\(898\) | 0.535412 | − | 0.143463i | 0.0178669 | − | 0.00478743i | ||||
\(899\) | 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 | ||||
\(903\) | 8.77691 | − | 3.97882i | 0.292077 | − | 0.132407i | ||||
\(904\) | 17.5783i | 0.584647i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.72590 | + | 1.57380i | −0.0905620 | + | 0.0522860i | ||||
\(907\) | −40.7520 | − | 10.9195i | −1.35315 | − | 0.362575i | −0.491852 | − | 0.870679i | \(-0.663680\pi\) |
−0.861296 | + | 0.508104i | \(0.830347\pi\) | |||||||
\(908\) | 4.02438 | + | 15.0192i | 0.133554 | + | 0.498429i | ||||
\(909\) | −0.631740 | −0.0209535 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.7456 | 0.852990 | 0.426495 | − | 0.904490i | \(-0.359748\pi\) | ||||
0.426495 | + | 0.904490i | \(0.359748\pi\) | |||||||
\(912\) | −0.224934 | − | 0.839465i | −0.00744831 | − | 0.0277975i | ||||
\(913\) | −22.9640 | − | 6.15317i | −0.759996 | − | 0.203640i | ||||
\(914\) | −27.7834 | + | 16.0408i | −0.918994 | + | 0.530581i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.8079i | 0.357102i | ||||||||
\(917\) | 19.6436 | − | 27.4238i | 0.648688 | − | 0.905614i | ||||
\(918\) | −2.27735 | − | 2.27735i | −0.0751637 | − | 0.0751637i | ||||
\(919\) | 24.6604 | + | 14.2377i | 0.813471 | + | 0.469658i | 0.848160 | − | 0.529740i | \(-0.177711\pi\) |
−0.0346885 | + | 0.999398i | \(0.511044\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.44132 | − | 7.69259i | −0.146346 | − | 0.253479i | ||||
\(922\) | −0.426280 | + | 0.114221i | −0.0140388 | + | 0.00376168i | ||||
\(923\) | −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 | ||||
\(927\) | 0.422325 | − | 1.57614i | 0.0138710 | − | 0.0517672i | ||||
\(928\) | 1.05692 | − | 3.94449i | 0.0346952 | − | 0.129484i | ||||
\(929\) | 10.5249 | − | 18.2297i | 0.345312 | − | 0.598099i | −0.640098 | − | 0.768293i | \(-0.721106\pi\) |
0.985410 | + | 0.170195i | \(0.0544396\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00939 | + | 4.57540i | −0.131402 | + | 0.149953i | ||||
\(932\) | −8.88096 | + | 8.88096i | −0.290905 | + | 0.290905i | ||||
\(933\) | −13.5754 | + | 3.63752i | −0.444438 | + | 0.119087i | ||||
\(934\) | 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 | \(-0.525833\pi\) | |||||||
\(938\) | −33.3837 | − | 3.28148i | −1.09002 | − | 0.107144i | ||||
\(939\) | − | 19.6966i | − | 0.642774i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.25912 | − | 0.726951i | 0.0410460 | − | 0.0236979i | −0.479337 | − | 0.877631i | \(-0.659123\pi\) |
0.520383 | + | 0.853933i | \(0.325789\pi\) | |||||||
\(942\) | 5.96135 | + | 1.59734i | 0.194231 | + | 0.0520441i | ||||
\(943\) | −5.72075 | − | 21.3501i | −0.186293 | − | 0.695256i | ||||
\(944\) | −10.7154 | −0.348756 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.58743 | 0.279202 | ||||||||
\(947\) | −7.78970 | − | 29.0716i | −0.253131 | − | 0.944699i | −0.969120 | − | 0.246588i | \(-0.920691\pi\) |
0.715989 | − | 0.698111i | \(-0.245976\pi\) | |||||||
\(948\) | −4.48413 | − | 1.20152i | −0.145638 | − | 0.0390235i | ||||
\(949\) | −1.92900 | + | 1.11371i | −0.0626179 | + | 0.0361524i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2.37883i | − | 0.0771390i | ||||||
\(952\) | 3.51821 | + | 7.76085i | 0.114026 | + | 0.251530i | ||||
\(953\) | 6.23201 | + | 6.23201i | 0.201875 | + | 0.201875i | 0.800803 | − | 0.598928i | \(-0.204406\pi\) |
−0.598928 | + | 0.800803i | \(0.704406\pi\) | |||||||
\(954\) | −7.23797 | − | 4.17884i | −0.234338 | − | 0.135295i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.98532 | − | 13.8310i | −0.258264 | − | 0.447326i | ||||
\(957\) | 9.29986 | − | 2.49189i | 0.300622 | − | 0.0805513i | ||||
\(958\) | 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 | ||||
\(962\) | 0.349201 | − | 1.30324i | 0.0112587 | − | 0.0420180i | ||||
\(963\) | 3.91015 | − | 14.5929i | 0.126003 | − | 0.470249i | ||||
\(964\) | −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 | \(-0.496480\pi\) |
0.999939 | − | 0.0110583i | \(-0.00352005\pi\) | |||||||
\(968\) | −5.25591 | + | 1.40832i | −0.168931 | + | 0.0452650i | ||||
\(969\) | 1.39950 | + | 2.42401i | 0.0449585 | + | 0.0778704i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.2192 | − | 6.47740i | −0.360041 | − | 0.207870i | 0.309058 | − | 0.951043i | \(-0.399986\pi\) |
−0.669099 | + | 0.743174i | \(0.733320\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −3.60533 | + | 36.6783i | −0.115582 | + | 1.17585i | ||||
\(974\) | − | 24.6370i | − | 0.789421i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.44351 | + | 4.29751i | −0.238261 | + | 0.137560i | ||||
\(977\) | 34.6883 | + | 9.29470i | 1.10978 | + | 0.297364i | 0.766740 | − | 0.641958i | \(-0.221878\pi\) |
0.343037 | + | 0.939322i | \(0.388544\pi\) | |||||||
\(978\) | −0.717766 | − | 2.67874i | −0.0229516 | − | 0.0856567i | ||||
\(979\) | 23.5077 | 0.751308 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.61296 | 0.274991 | ||||||||
\(982\) | 0.797873 | + | 2.97770i | 0.0254612 | + | 0.0950224i | ||||
\(983\) | −40.2010 | − | 10.7718i | −1.28221 | − | 0.343568i | −0.447515 | − | 0.894276i | \(-0.647691\pi\) |
−0.834698 | + | 0.550708i | \(0.814358\pi\) | |||||||
\(984\) | 5.94351 | − | 3.43149i | 0.189472 | − | 0.109392i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.1520i | 0.418844i | ||||||||
\(987\) | 0.223354 | − | 2.27226i | 0.00710943 | − | 0.0723269i | ||||
\(988\) | −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 | 0.578583 | − | 0.815624i | \(-0.303606\pi\) |
−0.995642 | + | 0.0932558i | \(0.970273\pi\) | |||||||
\(992\) | −0.833568 | + | 0.223354i | −0.0264658 | + | 0.00709149i | ||||
\(993\) | −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 | ||||
\(997\) | 4.74297 | − | 17.7010i | 0.150211 | − | 0.560597i | −0.849257 | − | 0.527980i | \(-0.822949\pi\) |
0.999468 | − | 0.0326163i | \(-0.0103839\pi\) | |||||||
\(998\) | 8.58568 | − | 32.0422i | 0.271775 | − | 1.01428i | ||||
\(999\) | −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.e.943.4 | yes | 16 | |
5.2 | odd | 4 | 1050.2.bc.f.607.1 | yes | 16 | ||
5.3 | odd | 4 | 1050.2.bc.f.607.4 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.2.bc.e.943.1 | yes | 16 | |
7.3 | odd | 6 | 1050.2.bc.f.493.1 | yes | 16 | ||
35.3 | even | 12 | inner | 1050.2.bc.e.157.2 | ✓ | 16 | |
35.17 | even | 12 | inner | 1050.2.bc.e.157.3 | yes | 16 | |
35.24 | odd | 6 | 1050.2.bc.f.493.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.e.157.2 | ✓ | 16 | 35.3 | even | 12 | inner | |
1050.2.bc.e.157.3 | yes | 16 | 35.17 | even | 12 | inner | |
1050.2.bc.e.943.1 | yes | 16 | 5.4 | even | 2 | inner | |
1050.2.bc.e.943.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1050.2.bc.f.493.1 | yes | 16 | 7.3 | odd | 6 | ||
1050.2.bc.f.493.4 | yes | 16 | 35.24 | odd | 6 | ||
1050.2.bc.f.607.1 | yes | 16 | 5.2 | odd | 4 | ||
1050.2.bc.f.607.4 | yes | 16 | 5.3 | odd | 4 |