Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1485512441856.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 24x^{6} + 455x^{4} + 2904x^{2} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.3 | ||
Root | \(-1.34203 + 2.32446i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.471 |
Dual form | 637.2.h.k.165.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | 0.707107 | − | 1.22474i | 0.408248 | − | 0.707107i | −0.586445 | − | 0.809989i | \(-0.699473\pi\) |
0.994694 | + | 0.102882i | \(0.0328064\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.34203 | + | 2.32446i | −0.600174 | + | 1.03953i | 0.392621 | + | 0.919700i | \(0.371569\pi\) |
−0.992794 | + | 0.119831i | \(0.961765\pi\) | |||||||
\(6\) | 0.707107 | − | 1.22474i | 0.288675 | − | 0.500000i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −1.34203 | + | 2.32446i | −0.424387 | + | 0.735060i | ||||
\(11\) | −2.89792 | + | 5.01934i | −0.873754 | + | 1.51339i | −0.0156708 | + | 0.999877i | \(0.504988\pi\) |
−0.858084 | + | 0.513510i | \(0.828345\pi\) | |||||||
\(12\) | −0.707107 | + | 1.22474i | −0.204124 | + | 0.353553i | ||||
\(13\) | −2.75624 | − | 2.32446i | −0.764444 | − | 0.644690i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.89792 | + | 3.28729i | 0.490040 | + | 0.848774i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.51249 | −1.33697 | −0.668487 | − | 0.743724i | \(-0.733058\pi\) | ||||
−0.668487 | + | 0.743724i | \(0.733058\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −1.41421 | − | 2.44949i | −0.324443 | − | 0.561951i | 0.656957 | − | 0.753928i | \(-0.271843\pi\) |
−0.981399 | + | 0.191977i | \(0.938510\pi\) | |||||||
\(20\) | 1.34203 | − | 2.32446i | 0.300087 | − | 0.519766i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.89792 | + | 5.01934i | −0.617838 | + | 1.07013i | ||||
\(23\) | 1.79583 | 0.374457 | 0.187228 | − | 0.982316i | \(-0.440050\pi\) | ||||
0.187228 | + | 0.982316i | \(0.440050\pi\) | |||||||
\(24\) | −2.12132 | + | 3.67423i | −0.433013 | + | 0.750000i | ||||
\(25\) | −1.10208 | − | 1.90887i | −0.220417 | − | 0.381773i | ||||
\(26\) | −2.75624 | − | 2.32446i | −0.540544 | − | 0.455865i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.39792 | + | 7.61741i | 0.816672 | + | 1.41452i | 0.908121 | + | 0.418708i | \(0.137517\pi\) |
−0.0914483 | + | 0.995810i | \(0.529150\pi\) | |||||||
\(30\) | 1.89792 | + | 3.28729i | 0.346510 | + | 0.600174i | ||||
\(31\) | −0.707107 | − | 1.22474i | −0.127000 | − | 0.219971i | 0.795513 | − | 0.605937i | \(-0.207202\pi\) |
−0.922513 | + | 0.385966i | \(0.873868\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 4.09827 | + | 7.09841i | 0.713418 | + | 1.23568i | ||||
\(34\) | −5.51249 | −0.945383 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −6.79583 | −1.11723 | −0.558614 | − | 0.829428i | \(-0.688667\pi\) | ||||
−0.558614 | + | 0.829428i | \(0.688667\pi\) | |||||||
\(38\) | −1.41421 | − | 2.44949i | −0.229416 | − | 0.397360i | ||||
\(39\) | −4.79583 | + | 1.73205i | −0.767948 | + | 0.277350i | ||||
\(40\) | 4.02609 | − | 6.97339i | 0.636580 | − | 1.10259i | ||||
\(41\) | 4.87756 | + | 8.44819i | 0.761747 | + | 1.31939i | 0.941949 | + | 0.335755i | \(0.108992\pi\) |
−0.180202 | + | 0.983630i | \(0.557675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.897916 | − | 1.55524i | 0.136931 | − | 0.237171i | −0.789403 | − | 0.613876i | \(-0.789610\pi\) |
0.926333 | + | 0.376705i | \(0.122943\pi\) | |||||||
\(44\) | 2.89792 | − | 5.01934i | 0.436877 | − | 0.756694i | ||||
\(45\) | −2.68406 | −0.400116 | ||||||||
\(46\) | 1.79583 | 0.264781 | ||||||||
\(47\) | 1.41421 | − | 2.44949i | 0.206284 | − | 0.357295i | −0.744257 | − | 0.667893i | \(-0.767196\pi\) |
0.950541 | + | 0.310599i | \(0.100530\pi\) | |||||||
\(48\) | −0.707107 | + | 1.22474i | −0.102062 | + | 0.176777i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.10208 | − | 1.90887i | −0.155858 | − | 0.269954i | ||||
\(51\) | −3.89792 | + | 6.75139i | −0.545817 | + | 0.945383i | ||||
\(52\) | 2.75624 | + | 2.32446i | 0.382222 | + | 0.322345i | ||||
\(53\) | −3.29583 | − | 5.70855i | −0.452717 | − | 0.784129i | 0.545836 | − | 0.837892i | \(-0.316212\pi\) |
−0.998554 | + | 0.0537624i | \(0.982879\pi\) | |||||||
\(54\) | 5.65685 | 0.769800 | ||||||||
\(55\) | −7.77817 | − | 13.4722i | −1.04881 | − | 1.81659i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 4.39792 | + | 7.61741i | 0.577475 | + | 1.00022i | ||||
\(59\) | −1.12548 | −0.146524 | −0.0732622 | − | 0.997313i | \(-0.523341\pi\) | ||||
−0.0732622 | + | 0.997313i | \(0.523341\pi\) | |||||||
\(60\) | −1.89792 | − | 3.28729i | −0.245020 | − | 0.424387i | ||||
\(61\) | 0.779291 | + | 1.34977i | 0.0997780 | + | 0.172821i | 0.911593 | − | 0.411095i | \(-0.134853\pi\) |
−0.811815 | + | 0.583915i | \(0.801520\pi\) | |||||||
\(62\) | −0.707107 | − | 1.22474i | −0.0898027 | − | 0.155543i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 9.10208 | − | 3.28729i | 1.12897 | − | 0.407738i | ||||
\(66\) | 4.09827 | + | 7.09841i | 0.504462 | + | 0.873754i | ||||
\(67\) | −2.89792 | + | 5.01934i | −0.354037 | + | 0.613210i | −0.986953 | − | 0.161011i | \(-0.948525\pi\) |
0.632916 | + | 0.774221i | \(0.281858\pi\) | |||||||
\(68\) | 5.51249 | 0.668487 | ||||||||
\(69\) | 1.26984 | − | 2.19944i | 0.152871 | − | 0.264781i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | + | 5.19615i | −0.356034 | + | 0.616670i | −0.987294 | − | 0.158901i | \(-0.949205\pi\) |
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(72\) | −1.50000 | − | 2.59808i | −0.176777 | − | 0.306186i | ||||
\(73\) | −2.90061 | − | 5.02401i | −0.339491 | − | 0.588015i | 0.644846 | − | 0.764312i | \(-0.276921\pi\) |
−0.984337 | + | 0.176297i | \(0.943588\pi\) | |||||||
\(74\) | −6.79583 | −0.789999 | ||||||||
\(75\) | −3.11716 | −0.359939 | ||||||||
\(76\) | 1.41421 | + | 2.44949i | 0.162221 | + | 0.280976i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.79583 | + | 1.73205i | −0.543021 | + | 0.196116i | ||||
\(79\) | 5.89792 | − | 10.2155i | 0.663567 | − | 1.14933i | −0.316104 | − | 0.948724i | \(-0.602375\pi\) |
0.979672 | − | 0.200608i | \(-0.0642917\pi\) | |||||||
\(80\) | 1.34203 | − | 2.32446i | 0.150043 | − | 0.259883i | ||||
\(81\) | 2.50000 | − | 4.33013i | 0.277778 | − | 0.481125i | ||||
\(82\) | 4.87756 | + | 8.44819i | 0.538637 | + | 0.932946i | ||||
\(83\) | 9.89949 | 1.08661 | 0.543305 | − | 0.839535i | \(-0.317173\pi\) | ||||
0.543305 | + | 0.839535i | \(0.317173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.39792 | − | 12.8136i | 0.802417 | − | 1.38983i | ||||
\(86\) | 0.897916 | − | 1.55524i | 0.0968247 | − | 0.167705i | ||||
\(87\) | 12.4392 | 1.33362 | ||||||||
\(88\) | 8.69375 | − | 15.0580i | 0.926757 | − | 1.60519i | ||||
\(89\) | −12.1504 | −1.28794 | −0.643972 | − | 0.765049i | \(-0.722715\pi\) | ||||
−0.643972 | + | 0.765049i | \(0.722715\pi\) | |||||||
\(90\) | −2.68406 | −0.282925 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.79583 | −0.187228 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 1.41421 | − | 2.44949i | 0.145865 | − | 0.252646i | ||||
\(95\) | 7.59166 | 0.778888 | ||||||||
\(96\) | 3.53553 | − | 6.12372i | 0.360844 | − | 0.625000i | ||||
\(97\) | −2.12132 | + | 3.67423i | −0.215387 | + | 0.373062i | −0.953392 | − | 0.301733i | \(-0.902435\pi\) |
0.738005 | + | 0.674795i | \(0.235768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.79583 | −0.582503 | ||||||||
\(100\) | 1.10208 | + | 1.90887i | 0.110208 | + | 0.190887i | ||||
\(101\) | −1.48640 | + | 2.57452i | −0.147902 | + | 0.256174i | −0.930452 | − | 0.366414i | \(-0.880585\pi\) |
0.782550 | + | 0.622588i | \(0.213919\pi\) | |||||||
\(102\) | −3.89792 | + | 6.75139i | −0.385951 | + | 0.668487i | ||||
\(103\) | −4.09827 | + | 7.09841i | −0.403815 | + | 0.699428i | −0.994183 | − | 0.107707i | \(-0.965649\pi\) |
0.590368 | + | 0.807134i | \(0.298983\pi\) | |||||||
\(104\) | 8.26873 | + | 6.97339i | 0.810815 | + | 0.683797i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.29583 | − | 5.70855i | −0.320119 | − | 0.554463i | ||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | −5.65685 | −0.544331 | ||||||||
\(109\) | 8.79583 | + | 15.2348i | 0.842488 | + | 1.45923i | 0.887785 | + | 0.460258i | \(0.152243\pi\) |
−0.0452972 | + | 0.998974i | \(0.514423\pi\) | |||||||
\(110\) | −7.77817 | − | 13.4722i | −0.741620 | − | 1.28452i | ||||
\(111\) | −4.80538 | + | 8.32316i | −0.456106 | + | 0.789999i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.29583 | − | 14.3688i | 0.780406 | − | 1.35170i | −0.151299 | − | 0.988488i | \(-0.548346\pi\) |
0.931705 | − | 0.363215i | \(-0.118321\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | −2.41006 | + | 4.17434i | −0.224739 | + | 0.389260i | ||||
\(116\) | −4.39792 | − | 7.61741i | −0.408336 | − | 0.707259i | ||||
\(117\) | 0.634922 | − | 3.54921i | 0.0586986 | − | 0.328124i | ||||
\(118\) | −1.12548 | −0.103608 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.69375 | − | 9.86186i | −0.519766 | − | 0.900260i | ||||
\(121\) | −11.2958 | − | 19.5650i | −1.02689 | − | 1.77863i | ||||
\(122\) | 0.779291 | + | 1.34977i | 0.0705537 | + | 0.122203i | ||||
\(123\) | 13.7958 | 1.24393 | ||||||||
\(124\) | 0.707107 | + | 1.22474i | 0.0635001 | + | 0.109985i | ||||
\(125\) | −7.50417 | −0.671194 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.79583 | − | 6.57457i | −0.336826 | − | 0.583399i | 0.647008 | − | 0.762483i | \(-0.276020\pi\) |
−0.983834 | + | 0.179084i | \(0.942687\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | −1.26984 | − | 2.19944i | −0.111804 | − | 0.193649i | ||||
\(130\) | 9.10208 | − | 3.28729i | 0.798306 | − | 0.288314i | ||||
\(131\) | −4.09827 | + | 7.09841i | −0.358068 | + | 0.620191i | −0.987638 | − | 0.156752i | \(-0.949898\pi\) |
0.629570 | + | 0.776944i | \(0.283231\pi\) | |||||||
\(132\) | −4.09827 | − | 7.09841i | −0.356709 | − | 0.617838i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.89792 | + | 5.01934i | −0.250342 | + | 0.433605i | ||||
\(135\) | −7.59166 | + | 13.1491i | −0.653386 | + | 1.13170i | ||||
\(136\) | 16.5375 | 1.41808 | ||||||||
\(137\) | −9.20417 | −0.786365 | −0.393183 | − | 0.919460i | \(-0.628626\pi\) | ||||
−0.393183 | + | 0.919460i | \(0.628626\pi\) | |||||||
\(138\) | 1.26984 | − | 2.19944i | 0.108096 | − | 0.187228i | ||||
\(139\) | −7.63381 | + | 13.2221i | −0.647491 | + | 1.12149i | 0.336229 | + | 0.941780i | \(0.390848\pi\) |
−0.983720 | + | 0.179707i | \(0.942485\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | − | 3.46410i | −0.168430 | − | 0.291730i | ||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | 19.6546 | − | 7.09841i | 1.64360 | − | 0.593599i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −23.6085 | −1.96058 | ||||||||
\(146\) | −2.90061 | − | 5.02401i | −0.240056 | − | 0.415790i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.79583 | 0.558614 | ||||||||
\(149\) | −2.29583 | − | 3.97650i | −0.188082 | − | 0.325767i | 0.756529 | − | 0.653960i | \(-0.226894\pi\) |
−0.944611 | + | 0.328193i | \(0.893560\pi\) | |||||||
\(150\) | −3.11716 | −0.254515 | ||||||||
\(151\) | 8.79583 | + | 15.2348i | 0.715795 | + | 1.23979i | 0.962652 | + | 0.270741i | \(0.0872687\pi\) |
−0.246858 | + | 0.969052i | \(0.579398\pi\) | |||||||
\(152\) | 4.24264 | + | 7.34847i | 0.344124 | + | 0.596040i | ||||
\(153\) | −2.75624 | − | 4.77395i | −0.222829 | − | 0.385951i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.79583 | 0.304889 | ||||||||
\(156\) | 4.79583 | − | 1.73205i | 0.383974 | − | 0.138675i | ||||
\(157\) | −3.46335 | − | 5.99870i | −0.276405 | − | 0.478748i | 0.694083 | − | 0.719895i | \(-0.255810\pi\) |
−0.970489 | + | 0.241146i | \(0.922477\pi\) | |||||||
\(158\) | 5.89792 | − | 10.2155i | 0.469213 | − | 0.812701i | ||||
\(159\) | −9.32202 | −0.739284 | ||||||||
\(160\) | −6.71015 | + | 11.6223i | −0.530484 | + | 0.918825i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.50000 | − | 4.33013i | 0.196419 | − | 0.340207i | ||||
\(163\) | 6.69375 | + | 11.5939i | 0.524295 | + | 0.908105i | 0.999600 | + | 0.0282841i | \(0.00900432\pi\) |
−0.475305 | + | 0.879821i | \(0.657662\pi\) | |||||||
\(164\) | −4.87756 | − | 8.44819i | −0.380874 | − | 0.659693i | ||||
\(165\) | −22.0000 | −1.71270 | ||||||||
\(166\) | 9.89949 | 0.768350 | ||||||||
\(167\) | 7.63381 | + | 13.2221i | 0.590722 | + | 1.02316i | 0.994135 | + | 0.108142i | \(0.0344902\pi\) |
−0.403414 | + | 0.915018i | \(0.632176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.19375 | + | 12.8136i | 0.168750 | + | 0.985659i | ||||
\(170\) | 7.39792 | − | 12.8136i | 0.567394 | − | 0.982756i | ||||
\(171\) | 1.41421 | − | 2.44949i | 0.108148 | − | 0.187317i | ||||
\(172\) | −0.897916 | + | 1.55524i | −0.0684654 | + | 0.118586i | ||||
\(173\) | 4.66101 | + | 8.07311i | 0.354370 | + | 0.613787i | 0.987010 | − | 0.160659i | \(-0.0513620\pi\) |
−0.632640 | + | 0.774446i | \(0.718029\pi\) | |||||||
\(174\) | 12.4392 | 0.943012 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.89792 | − | 5.01934i | 0.218439 | − | 0.378347i | ||||
\(177\) | −0.795832 | + | 1.37842i | −0.0598184 | + | 0.103608i | ||||
\(178\) | −12.1504 | −0.910714 | ||||||||
\(179\) | 0.204168 | − | 0.353630i | 0.0152603 | − | 0.0264316i | −0.858294 | − | 0.513158i | \(-0.828476\pi\) |
0.873555 | + | 0.486726i | \(0.161809\pi\) | |||||||
\(180\) | 2.68406 | 0.200058 | ||||||||
\(181\) | 16.5375 | 1.22922 | 0.614610 | − | 0.788831i | \(-0.289314\pi\) | ||||
0.614610 | + | 0.788831i | \(0.289314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.20417 | 0.162937 | ||||||||
\(184\) | −5.38749 | −0.397171 | ||||||||
\(185\) | 9.12020 | − | 15.7967i | 0.670531 | − | 1.16139i | ||||
\(186\) | −2.00000 | −0.146647 | ||||||||
\(187\) | 15.9747 | − | 27.6690i | 1.16819 | − | 2.02336i | ||||
\(188\) | −1.41421 | + | 2.44949i | −0.103142 | + | 0.178647i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.59166 | 0.550757 | ||||||||
\(191\) | 12.8979 | + | 22.3398i | 0.933260 | + | 1.61645i | 0.777707 | + | 0.628627i | \(0.216383\pi\) |
0.155553 | + | 0.987827i | \(0.450284\pi\) | |||||||
\(192\) | 4.94975 | − | 8.57321i | 0.357217 | − | 0.618718i | ||||
\(193\) | −1.70417 | + | 2.95171i | −0.122669 | + | 0.212468i | −0.920819 | − | 0.389990i | \(-0.872479\pi\) |
0.798151 | + | 0.602458i | \(0.205812\pi\) | |||||||
\(194\) | −2.12132 | + | 3.67423i | −0.152302 | + | 0.263795i | ||||
\(195\) | 2.41006 | − | 13.4722i | 0.172588 | − | 0.964764i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | + | 6.92820i | 0.284988 | + | 0.493614i | 0.972606 | − | 0.232458i | \(-0.0746770\pi\) |
−0.687618 | + | 0.726073i | \(0.741344\pi\) | |||||||
\(198\) | −5.79583 | −0.411892 | ||||||||
\(199\) | 22.0499 | 1.56308 | 0.781539 | − | 0.623856i | \(-0.214435\pi\) | ||||
0.781539 | + | 0.623856i | \(0.214435\pi\) | |||||||
\(200\) | 3.30625 | + | 5.72660i | 0.233787 | + | 0.404932i | ||||
\(201\) | 4.09827 | + | 7.09841i | 0.289070 | + | 0.500684i | ||||
\(202\) | −1.48640 | + | 2.57452i | −0.104583 | + | 0.181142i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.89792 | − | 6.75139i | 0.272909 | − | 0.472692i | ||||
\(205\) | −26.1833 | −1.82872 | ||||||||
\(206\) | −4.09827 | + | 7.09841i | −0.285540 | + | 0.494570i | ||||
\(207\) | 0.897916 | + | 1.55524i | 0.0624095 | + | 0.108096i | ||||
\(208\) | 2.75624 | + | 2.32446i | 0.191111 | + | 0.161172i | ||||
\(209\) | 16.3931 | 1.13393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.897916 | + | 1.55524i | 0.0618151 | + | 0.107067i | 0.895277 | − | 0.445510i | \(-0.146978\pi\) |
−0.833462 | + | 0.552577i | \(0.813644\pi\) | |||||||
\(212\) | 3.29583 | + | 5.70855i | 0.226359 | + | 0.392065i | ||||
\(213\) | 4.24264 | + | 7.34847i | 0.290701 | + | 0.503509i | ||||
\(214\) | −6.00000 | −0.410152 | ||||||||
\(215\) | 2.41006 | + | 4.17434i | 0.164365 | + | 0.284688i | ||||
\(216\) | −16.9706 | −1.15470 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.79583 | + | 15.2348i | 0.595729 | + | 1.03183i | ||||
\(219\) | −8.20417 | −0.554386 | ||||||||
\(220\) | 7.77817 | + | 13.4722i | 0.524404 | + | 0.908295i | ||||
\(221\) | 15.1937 | + | 12.8136i | 1.02204 | + | 0.861934i | ||||
\(222\) | −4.80538 | + | 8.32316i | −0.322516 | + | 0.558614i | ||||
\(223\) | −2.82843 | − | 4.89898i | −0.189405 | − | 0.328060i | 0.755647 | − | 0.654979i | \(-0.227323\pi\) |
−0.945052 | + | 0.326920i | \(0.893989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.10208 | − | 1.90887i | 0.0734723 | − | 0.127258i | ||||
\(226\) | 8.29583 | − | 14.3688i | 0.551831 | − | 0.955798i | ||||
\(227\) | −20.9245 | −1.38881 | −0.694403 | − | 0.719587i | \(-0.744331\pi\) | ||||
−0.694403 | + | 0.719587i | \(0.744331\pi\) | |||||||
\(228\) | 4.00000 | 0.264906 | ||||||||
\(229\) | 6.36396 | − | 11.0227i | 0.420542 | − | 0.728401i | −0.575450 | − | 0.817837i | \(-0.695173\pi\) |
0.995993 | + | 0.0894361i | \(0.0285065\pi\) | |||||||
\(230\) | −2.41006 | + | 4.17434i | −0.158915 | + | 0.275248i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.1937 | − | 22.8522i | −0.866212 | − | 1.50032i | ||||
\(233\) | 10.5917 | − | 18.3453i | 0.693883 | − | 1.20184i | −0.276673 | − | 0.960964i | \(-0.589232\pi\) |
0.970556 | − | 0.240876i | \(-0.0774348\pi\) | |||||||
\(234\) | 0.634922 | − | 3.54921i | 0.0415062 | − | 0.232019i | ||||
\(235\) | 3.79583 | + | 6.57457i | 0.247613 | + | 0.428878i | ||||
\(236\) | 1.12548 | 0.0732622 | ||||||||
\(237\) | −8.34091 | − | 14.4469i | −0.541800 | − | 0.938426i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.7958 | −1.28049 | −0.640243 | − | 0.768172i | \(-0.721166\pi\) | ||||
−0.640243 | + | 0.768172i | \(0.721166\pi\) | |||||||
\(240\) | −1.89792 | − | 3.28729i | −0.122510 | − | 0.212193i | ||||
\(241\) | −4.38701 | −0.282592 | −0.141296 | − | 0.989967i | \(-0.545127\pi\) | ||||
−0.141296 | + | 0.989967i | \(0.545127\pi\) | |||||||
\(242\) | −11.2958 | − | 19.5650i | −0.726124 | − | 1.25768i | ||||
\(243\) | 4.94975 | + | 8.57321i | 0.317526 | + | 0.549972i | ||||
\(244\) | −0.779291 | − | 1.34977i | −0.0498890 | − | 0.0864103i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.7958 | 0.879590 | ||||||||
\(247\) | −1.79583 | + | 10.0387i | −0.114266 | + | 0.638746i | ||||
\(248\) | 2.12132 | + | 3.67423i | 0.134704 | + | 0.233314i | ||||
\(249\) | 7.00000 | − | 12.1244i | 0.443607 | − | 0.768350i | ||||
\(250\) | −7.50417 | −0.474606 | ||||||||
\(251\) | −1.55858 | + | 2.69954i | −0.0983769 | + | 0.170394i | −0.911013 | − | 0.412378i | \(-0.864698\pi\) |
0.812636 | + | 0.582771i | \(0.198032\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.20417 | + | 9.01388i | −0.327183 | + | 0.566698i | ||||
\(254\) | −3.79583 | − | 6.57457i | −0.238172 | − | 0.412525i | ||||
\(255\) | −10.4622 | − | 18.1211i | −0.655170 | − | 1.13479i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −15.4120 | −0.961373 | −0.480686 | − | 0.876893i | \(-0.659612\pi\) | ||||
−0.480686 | + | 0.876893i | \(0.659612\pi\) | |||||||
\(258\) | −1.26984 | − | 2.19944i | −0.0790571 | − | 0.136931i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.10208 | + | 3.28729i | −0.564487 | + | 0.203869i | ||||
\(261\) | −4.39792 | + | 7.61741i | −0.272224 | + | 0.471506i | ||||
\(262\) | −4.09827 | + | 7.09841i | −0.253192 | + | 0.438542i | ||||
\(263\) | 12.6937 | − | 21.9862i | 0.782730 | − | 1.35573i | −0.147616 | − | 0.989045i | \(-0.547160\pi\) |
0.930346 | − | 0.366683i | \(-0.119507\pi\) | |||||||
\(264\) | −12.2948 | − | 21.2952i | −0.756694 | − | 1.31063i | ||||
\(265\) | 17.6924 | 1.08684 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.59166 | + | 14.8812i | −0.525801 | + | 0.910714i | ||||
\(268\) | 2.89792 | − | 5.01934i | 0.177018 | − | 0.306605i | ||||
\(269\) | 1.12548 | 0.0686215 | 0.0343107 | − | 0.999411i | \(-0.489076\pi\) | ||||
0.0343107 | + | 0.999411i | \(0.489076\pi\) | |||||||
\(270\) | −7.59166 | + | 13.1491i | −0.462014 | + | 0.800232i | ||||
\(271\) | 23.1754 | 1.40781 | 0.703903 | − | 0.710296i | \(-0.251439\pi\) | ||||
0.703903 | + | 0.710296i | \(0.251439\pi\) | |||||||
\(272\) | 5.51249 | 0.334244 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.20417 | −0.556044 | ||||||||
\(275\) | 12.7750 | 0.770361 | ||||||||
\(276\) | −1.26984 | + | 2.19944i | −0.0764357 | + | 0.132390i | ||||
\(277\) | −6.18333 | −0.371520 | −0.185760 | − | 0.982595i | \(-0.559475\pi\) | ||||
−0.185760 | + | 0.982595i | \(0.559475\pi\) | |||||||
\(278\) | −7.63381 | + | 13.2221i | −0.457845 | + | 0.793011i | ||||
\(279\) | 0.707107 | − | 1.22474i | 0.0423334 | − | 0.0733236i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2042 | 0.907005 | 0.453502 | − | 0.891255i | \(-0.350174\pi\) | ||||
0.453502 | + | 0.891255i | \(0.350174\pi\) | |||||||
\(282\) | −2.00000 | − | 3.46410i | −0.119098 | − | 0.206284i | ||||
\(283\) | −14.7049 | + | 25.4696i | −0.874114 | + | 1.51401i | −0.0164104 | + | 0.999865i | \(0.505224\pi\) |
−0.857704 | + | 0.514145i | \(0.828109\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 5.36812 | − | 9.29785i | 0.317980 | − | 0.550757i | ||||
\(286\) | 19.6546 | − | 7.09841i | 1.16220 | − | 0.419738i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.50000 | + | 4.33013i | 0.147314 | + | 0.255155i | ||||
\(289\) | 13.3875 | 0.787500 | ||||||||
\(290\) | −23.6085 | −1.38634 | ||||||||
\(291\) | 3.00000 | + | 5.19615i | 0.175863 | + | 0.304604i | ||||
\(292\) | 2.90061 | + | 5.02401i | 0.169745 | + | 0.294008i | ||||
\(293\) | −4.87756 | + | 8.44819i | −0.284950 | + | 0.493548i | −0.972597 | − | 0.232497i | \(-0.925310\pi\) |
0.687647 | + | 0.726045i | \(0.258644\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51042 | − | 2.61613i | 0.0879401 | − | 0.152317i | ||||
\(296\) | 20.3875 | 1.18500 | ||||||||
\(297\) | −16.3931 | + | 28.3937i | −0.951223 | + | 1.64757i | ||||
\(298\) | −2.29583 | − | 3.97650i | −0.132994 | − | 0.230352i | ||||
\(299\) | −4.94975 | − | 4.17434i | −0.286251 | − | 0.241409i | ||||
\(300\) | 3.11716 | 0.179970 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.79583 | + | 15.2348i | 0.506143 | + | 0.876666i | ||||
\(303\) | 2.10208 | + | 3.64092i | 0.120762 | + | 0.209165i | ||||
\(304\) | 1.41421 | + | 2.44949i | 0.0811107 | + | 0.140488i | ||||
\(305\) | −4.18333 | −0.239537 | ||||||||
\(306\) | −2.75624 | − | 4.77395i | −0.157564 | − | 0.272909i | ||||
\(307\) | −34.2004 | −1.95192 | −0.975960 | − | 0.217951i | \(-0.930063\pi\) | ||||
−0.975960 | + | 0.217951i | \(0.930063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.79583 | + | 10.0387i | 0.329713 | + | 0.571080i | ||||
\(310\) | 3.79583 | 0.215589 | ||||||||
\(311\) | 5.93085 | + | 10.2725i | 0.336308 | + | 0.582502i | 0.983735 | − | 0.179625i | \(-0.0574884\pi\) |
−0.647427 | + | 0.762127i | \(0.724155\pi\) | |||||||
\(312\) | 14.3875 | − | 5.19615i | 0.814531 | − | 0.294174i | ||||
\(313\) | 0.851476 | − | 1.47480i | 0.0481283 | − | 0.0833606i | −0.840958 | − | 0.541101i | \(-0.818008\pi\) |
0.889086 | + | 0.457740i | \(0.151341\pi\) | |||||||
\(314\) | −3.46335 | − | 5.99870i | −0.195448 | − | 0.338526i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.89792 | + | 10.2155i | −0.331784 | + | 0.574666i | ||||
\(317\) | 6.29583 | − | 10.9047i | 0.353609 | − | 0.612469i | −0.633270 | − | 0.773931i | \(-0.718288\pi\) |
0.986879 | + | 0.161462i | \(0.0516210\pi\) | |||||||
\(318\) | −9.32202 | −0.522753 | ||||||||
\(319\) | −50.9792 | −2.85428 | ||||||||
\(320\) | −9.39420 | + | 16.2712i | −0.525152 | + | 0.909590i | ||||
\(321\) | −4.24264 | + | 7.34847i | −0.236801 | + | 0.410152i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.79583 | + | 13.5028i | 0.433772 | + | 0.751315i | ||||
\(324\) | −2.50000 | + | 4.33013i | −0.138889 | + | 0.240563i | ||||
\(325\) | −1.39948 | + | 7.82305i | −0.0776289 | + | 0.433945i | ||||
\(326\) | 6.69375 | + | 11.5939i | 0.370732 | + | 0.642127i | ||||
\(327\) | 24.8784 | 1.37578 | ||||||||
\(328\) | −14.6327 | − | 25.3446i | −0.807955 | − | 1.39942i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −22.0000 | −1.21106 | ||||||||
\(331\) | −0.306253 | − | 0.530445i | −0.0168332 | − | 0.0291559i | 0.857486 | − | 0.514507i | \(-0.172025\pi\) |
−0.874319 | + | 0.485351i | \(0.838692\pi\) | |||||||
\(332\) | −9.89949 | −0.543305 | ||||||||
\(333\) | −3.39792 | − | 5.88536i | −0.186205 | − | 0.322516i | ||||
\(334\) | 7.63381 | + | 13.2221i | 0.417703 | + | 0.723483i | ||||
\(335\) | −7.77817 | − | 13.4722i | −0.424967 | − | 0.736065i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.9792 | −1.63307 | −0.816534 | − | 0.577297i | \(-0.804108\pi\) | ||||
−0.816534 | + | 0.577297i | \(0.804108\pi\) | |||||||
\(338\) | 2.19375 | + | 12.8136i | 0.119324 | + | 0.696966i | ||||
\(339\) | −11.7321 | − | 20.3206i | −0.637199 | − | 1.10366i | ||||
\(340\) | −7.39792 | + | 12.8136i | −0.401208 | + | 0.694913i | ||||
\(341\) | 8.19654 | 0.443868 | ||||||||
\(342\) | 1.41421 | − | 2.44949i | 0.0764719 | − | 0.132453i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.69375 | + | 4.66571i | −0.145237 | + | 0.251558i | ||||
\(345\) | 3.40834 | + | 5.90341i | 0.183499 | + | 0.317829i | ||||
\(346\) | 4.66101 | + | 8.07311i | 0.250577 | + | 0.434013i | ||||
\(347\) | 14.9792 | 0.804123 | 0.402062 | − | 0.915613i | \(-0.368294\pi\) | ||||
0.402062 | + | 0.915613i | \(0.368294\pi\) | |||||||
\(348\) | −12.4392 | −0.666810 | ||||||||
\(349\) | 6.50833 | + | 11.2728i | 0.348383 | + | 0.603417i | 0.985962 | − | 0.166968i | \(-0.0533976\pi\) |
−0.637579 | + | 0.770385i | \(0.720064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.5917 | − | 13.1491i | −0.832221 | − | 0.701849i | ||||
\(352\) | −14.4896 | + | 25.0967i | −0.772297 | + | 1.33766i | ||||
\(353\) | −7.56162 | + | 13.0971i | −0.402464 | + | 0.697089i | −0.994023 | − | 0.109173i | \(-0.965180\pi\) |
0.591558 | + | 0.806262i | \(0.298513\pi\) | |||||||
\(354\) | −0.795832 | + | 1.37842i | −0.0422980 | + | 0.0732622i | ||||
\(355\) | −8.05217 | − | 13.9468i | −0.427365 | − | 0.740218i | ||||
\(356\) | 12.1504 | 0.643972 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.204168 | − | 0.353630i | 0.0107906 | − | 0.0186899i | ||||
\(359\) | 2.00000 | − | 3.46410i | 0.105556 | − | 0.182828i | −0.808409 | − | 0.588621i | \(-0.799671\pi\) |
0.913965 | + | 0.405793i | \(0.133004\pi\) | |||||||
\(360\) | 8.05217 | 0.424387 | ||||||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | 16.5375 | 0.869189 | ||||||||
\(363\) | −31.9494 | −1.67691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5708 | 0.815014 | ||||||||
\(366\) | 2.20417 | 0.115214 | ||||||||
\(367\) | 10.6066 | − | 18.3712i | 0.553660 | − | 0.958967i | −0.444346 | − | 0.895855i | \(-0.646564\pi\) |
0.998006 | − | 0.0631123i | \(-0.0201026\pi\) | |||||||
\(368\) | −1.79583 | −0.0936142 | ||||||||
\(369\) | −4.87756 | + | 8.44819i | −0.253916 | + | 0.439795i | ||||
\(370\) | 9.12020 | − | 15.7967i | 0.474137 | − | 0.821229i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 6.29583 | + | 10.9047i | 0.325986 | + | 0.564624i | 0.981711 | − | 0.190375i | \(-0.0609705\pi\) |
−0.655726 | + | 0.754999i | \(0.727637\pi\) | |||||||
\(374\) | 15.9747 | − | 27.6690i | 0.826033 | − | 1.43073i | ||||
\(375\) | −5.30625 | + | 9.19070i | −0.274014 | + | 0.474606i | ||||
\(376\) | −4.24264 | + | 7.34847i | −0.218797 | + | 0.378968i | ||||
\(377\) | 5.58467 | − | 31.2182i | 0.287625 | − | 1.60782i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.69375 | + | 2.93366i | 0.0870020 | + | 0.150692i | 0.906243 | − | 0.422758i | \(-0.138938\pi\) |
−0.819241 | + | 0.573450i | \(0.805605\pi\) | |||||||
\(380\) | −7.59166 | −0.389444 | ||||||||
\(381\) | −10.7362 | −0.550034 | ||||||||
\(382\) | 12.8979 | + | 22.3398i | 0.659915 | + | 1.14301i | ||||
\(383\) | −7.48944 | − | 12.9721i | −0.382692 | − | 0.662843i | 0.608754 | − | 0.793359i | \(-0.291670\pi\) |
−0.991446 | + | 0.130517i | \(0.958336\pi\) | |||||||
\(384\) | −2.12132 | + | 3.67423i | −0.108253 | + | 0.187500i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.70417 | + | 2.95171i | −0.0867399 | + | 0.150238i | ||||
\(387\) | 1.79583 | 0.0912872 | ||||||||
\(388\) | 2.12132 | − | 3.67423i | 0.107694 | − | 0.186531i | ||||
\(389\) | −14.1937 | − | 24.5843i | −0.719652 | − | 1.24647i | −0.961138 | − | 0.276069i | \(-0.910968\pi\) |
0.241486 | − | 0.970404i | \(-0.422365\pi\) | |||||||
\(390\) | 2.41006 | − | 13.4722i | 0.122038 | − | 0.682191i | ||||
\(391\) | −9.89949 | −0.500639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.79583 | + | 10.0387i | 0.292361 | + | 0.506384i | ||||
\(394\) | 4.00000 | + | 6.92820i | 0.201517 | + | 0.349038i | ||||
\(395\) | 15.8303 | + | 27.4190i | 0.796511 | + | 1.37960i | ||||
\(396\) | 5.79583 | 0.291251 | ||||||||
\(397\) | 3.53553 | + | 6.12372i | 0.177443 | + | 0.307341i | 0.941004 | − | 0.338395i | \(-0.109884\pi\) |
−0.763561 | + | 0.645736i | \(0.776551\pi\) | |||||||
\(398\) | 22.0499 | 1.10526 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.10208 | + | 1.90887i | 0.0551042 | + | 0.0954433i | ||||
\(401\) | 24.3875 | 1.21785 | 0.608927 | − | 0.793227i | \(-0.291600\pi\) | ||||
0.608927 | + | 0.793227i | \(0.291600\pi\) | |||||||
\(402\) | 4.09827 | + | 7.09841i | 0.204403 | + | 0.354037i | ||||
\(403\) | −0.897916 | + | 5.01934i | −0.0447284 | + | 0.250031i | ||||
\(404\) | 1.48640 | − | 2.57452i | 0.0739511 | − | 0.128087i | ||||
\(405\) | 6.71015 | + | 11.6223i | 0.333430 | + | 0.577517i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.6937 | − | 34.1106i | 0.976183 | − | 1.69080i | ||||
\(408\) | 11.6937 | − | 20.2542i | 0.578927 | − | 1.00273i | ||||
\(409\) | 28.6879 | 1.41853 | 0.709263 | − | 0.704944i | \(-0.249028\pi\) | ||||
0.709263 | + | 0.704944i | \(0.249028\pi\) | |||||||
\(410\) | −26.1833 | −1.29310 | ||||||||
\(411\) | −6.50833 | + | 11.2728i | −0.321032 | + | 0.556044i | ||||
\(412\) | 4.09827 | − | 7.09841i | 0.201907 | − | 0.349714i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.897916 | + | 1.55524i | 0.0441302 | + | 0.0764357i | ||||
\(415\) | −13.2854 | + | 23.0110i | −0.652155 | + | 1.12957i | ||||
\(416\) | −13.7812 | − | 11.6223i | −0.675680 | − | 0.569831i | ||||
\(417\) | 10.7958 | + | 18.6989i | 0.528674 | + | 0.915690i | ||||
\(418\) | 16.3931 | 0.801812 | ||||||||
\(419\) | 14.2718 | + | 24.7194i | 0.697221 | + | 1.20762i | 0.969426 | + | 0.245384i | \(0.0789139\pi\) |
−0.272205 | + | 0.962239i | \(0.587753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.59166 | −0.321258 | −0.160629 | − | 0.987015i | \(-0.551352\pi\) | ||||
−0.160629 | + | 0.987015i | \(0.551352\pi\) | |||||||
\(422\) | 0.897916 | + | 1.55524i | 0.0437099 | + | 0.0757077i | ||||
\(423\) | 2.82843 | 0.137523 | ||||||||
\(424\) | 9.88749 | + | 17.1256i | 0.480179 | + | 0.831695i | ||||
\(425\) | 6.07522 | + | 10.5226i | 0.294692 | + | 0.510421i | ||||
\(426\) | 4.24264 | + | 7.34847i | 0.205557 | + | 0.356034i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 5.20417 | − | 29.0912i | 0.251260 | − | 1.40454i | ||||
\(430\) | 2.41006 | + | 4.17434i | 0.116223 | + | 0.201305i | ||||
\(431\) | 2.59166 | − | 4.48889i | 0.124836 | − | 0.216222i | −0.796833 | − | 0.604200i | \(-0.793493\pi\) |
0.921669 | + | 0.387978i | \(0.126826\pi\) | |||||||
\(432\) | −5.65685 | −0.272166 | ||||||||
\(433\) | 6.71015 | − | 11.6223i | 0.322469 | − | 0.558533i | −0.658528 | − | 0.752556i | \(-0.728821\pi\) |
0.980997 | + | 0.194024i | \(0.0621539\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.6937 | + | 28.9144i | −0.800404 | + | 1.38634i | ||||
\(436\) | −8.79583 | − | 15.2348i | −0.421244 | − | 0.729616i | ||||
\(437\) | −2.53969 | − | 4.39887i | −0.121490 | − | 0.210427i | ||||
\(438\) | −8.20417 | −0.392010 | ||||||||
\(439\) | −34.2004 | −1.63230 | −0.816148 | − | 0.577843i | \(-0.803894\pi\) | ||||
−0.816148 | + | 0.577843i | \(0.803894\pi\) | |||||||
\(440\) | 23.3345 | + | 40.4166i | 1.11243 | + | 1.92678i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.1937 | + | 12.8136i | 0.722693 | + | 0.609479i | ||||
\(443\) | −5.00000 | + | 8.66025i | −0.237557 | + | 0.411461i | −0.960013 | − | 0.279956i | \(-0.909680\pi\) |
0.722456 | + | 0.691417i | \(0.243013\pi\) | |||||||
\(444\) | 4.80538 | − | 8.32316i | 0.228053 | − | 0.395000i | ||||
\(445\) | 16.3063 | − | 28.2433i | 0.772991 | − | 1.33886i | ||||
\(446\) | −2.82843 | − | 4.89898i | −0.133930 | − | 0.231973i | ||||
\(447\) | −6.49359 | −0.307136 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.20417 | + | 3.81773i | −0.104021 | + | 0.180170i | −0.913338 | − | 0.407203i | \(-0.866504\pi\) |
0.809317 | + | 0.587372i | \(0.199838\pi\) | |||||||
\(450\) | 1.10208 | − | 1.90887i | 0.0519527 | − | 0.0899848i | ||||
\(451\) | −56.5391 | −2.66232 | ||||||||
\(452\) | −8.29583 | + | 14.3688i | −0.390203 | + | 0.675852i | ||||
\(453\) | 24.8784 | 1.16889 | ||||||||
\(454\) | −20.9245 | −0.982034 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.0000 | 0.561951 | ||||||||
\(457\) | −14.5917 | −0.682569 | −0.341285 | − | 0.939960i | \(-0.610862\pi\) | ||||
−0.341285 | + | 0.939960i | \(0.610862\pi\) | |||||||
\(458\) | 6.36396 | − | 11.0227i | 0.297368 | − | 0.515057i | ||||
\(459\) | −31.1833 | −1.45551 | ||||||||
\(460\) | 2.41006 | − | 4.17434i | 0.112370 | − | 0.194630i | ||||
\(461\) | 15.4842 | − | 26.8194i | 0.721169 | − | 1.24910i | −0.239362 | − | 0.970930i | \(-0.576938\pi\) |
0.960531 | − | 0.278172i | \(-0.0897284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3875 | 0.529222 | 0.264611 | − | 0.964355i | \(-0.414756\pi\) | ||||
0.264611 | + | 0.964355i | \(0.414756\pi\) | |||||||
\(464\) | −4.39792 | − | 7.61741i | −0.204168 | − | 0.353630i | ||||
\(465\) | 2.68406 | − | 4.64893i | 0.124470 | − | 0.215589i | ||||
\(466\) | 10.5917 | − | 18.3453i | 0.490649 | − | 0.849830i | ||||
\(467\) | −2.41006 | + | 4.17434i | −0.111524 | + | 0.193166i | −0.916385 | − | 0.400298i | \(-0.868907\pi\) |
0.804861 | + | 0.593464i | \(0.202240\pi\) | |||||||
\(468\) | −0.634922 | + | 3.54921i | −0.0293493 | + | 0.164062i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.79583 | + | 6.57457i | 0.175089 | + | 0.303262i | ||||
\(471\) | −9.79583 | −0.451368 | ||||||||
\(472\) | 3.37643 | 0.155413 | ||||||||
\(473\) | 5.20417 | + | 9.01388i | 0.239288 | + | 0.414459i | ||||
\(474\) | −8.34091 | − | 14.4469i | −0.383111 | − | 0.663567i | ||||
\(475\) | −3.11716 | + | 5.39909i | −0.143025 | + | 0.247727i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.29583 | − | 5.70855i | 0.150906 | − | 0.261376i | ||||
\(478\) | −19.7958 | −0.905440 | ||||||||
\(479\) | −3.67990 | + | 6.37378i | −0.168139 | + | 0.291225i | −0.937766 | − | 0.347269i | \(-0.887109\pi\) |
0.769627 | + | 0.638494i | \(0.220442\pi\) | |||||||
\(480\) | 9.48958 | + | 16.4364i | 0.433138 | + | 0.750217i | ||||
\(481\) | 18.7310 | + | 15.7967i | 0.854058 | + | 0.720266i | ||||
\(482\) | −4.38701 | −0.199823 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.2958 | + | 19.5650i | 0.513447 | + | 0.889316i | ||||
\(485\) | −5.69375 | − | 9.86186i | −0.258540 | − | 0.447804i | ||||
\(486\) | 4.94975 | + | 8.57321i | 0.224525 | + | 0.388889i | ||||
\(487\) | 19.5917 | 0.887783 | 0.443891 | − | 0.896081i | \(-0.353598\pi\) | ||||
0.443891 | + | 0.896081i | \(0.353598\pi\) | |||||||
\(488\) | −2.33787 | − | 4.04932i | −0.105831 | − | 0.183304i | ||||
\(489\) | 18.9328 | 0.856170 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.79583 | + | 8.30662i | 0.216433 | + | 0.374873i | 0.953715 | − | 0.300712i | \(-0.0972244\pi\) |
−0.737282 | + | 0.675585i | \(0.763891\pi\) | |||||||
\(492\) | −13.7958 | −0.621964 | ||||||||
\(493\) | −24.2434 | − | 41.9909i | −1.09187 | − | 1.89117i | ||||
\(494\) | −1.79583 | + | 10.0387i | −0.0807983 | + | 0.451661i | ||||
\(495\) | 7.77817 | − | 13.4722i | 0.349603 | − | 0.605530i | ||||
\(496\) | 0.707107 | + | 1.22474i | 0.0317500 | + | 0.0549927i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.00000 | − | 12.1244i | 0.313678 | − | 0.543305i | ||||
\(499\) | −8.10208 | + | 14.0332i | −0.362699 | + | 0.628213i | −0.988404 | − | 0.151847i | \(-0.951478\pi\) |
0.625705 | + | 0.780060i | \(0.284811\pi\) | |||||||
\(500\) | 7.50417 | 0.335597 | ||||||||
\(501\) | 21.5917 | 0.964644 | ||||||||
\(502\) | −1.55858 | + | 2.69954i | −0.0695629 | + | 0.120487i | ||||
\(503\) | −14.2718 | + | 24.7194i | −0.636347 | + | 1.10218i | 0.349881 | + | 0.936794i | \(0.386222\pi\) |
−0.986228 | + | 0.165391i | \(0.947111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.98958 | − | 6.91015i | −0.177534 | − | 0.307498i | ||||
\(506\) | −5.20417 | + | 9.01388i | −0.231354 | + | 0.400716i | ||||
\(507\) | 17.2446 | + | 6.37378i | 0.765858 | + | 0.283069i | ||||
\(508\) | 3.79583 | + | 6.57457i | 0.168413 | + | 0.291700i | ||||
\(509\) | −26.4370 | −1.17180 | −0.585899 | − | 0.810384i | \(-0.699258\pi\) | ||||
−0.585899 | + | 0.810384i | \(0.699258\pi\) | |||||||
\(510\) | −10.4622 | − | 18.1211i | −0.463275 | − | 0.802417i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | −8.00000 | − | 13.8564i | −0.353209 | − | 0.611775i | ||||
\(514\) | −15.4120 | −0.679793 | ||||||||
\(515\) | −11.0000 | − | 19.0526i | −0.484718 | − | 0.839556i | ||||
\(516\) | 1.26984 | + | 2.19944i | 0.0559018 | + | 0.0968247i | ||||
\(517\) | 8.19654 | + | 14.1968i | 0.360484 | + | 0.624376i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1833 | 0.578684 | ||||||||
\(520\) | −27.3063 | + | 9.86186i | −1.19746 | + | 0.432471i | ||||
\(521\) | 12.5114 | + | 21.6703i | 0.548133 | + | 0.949394i | 0.998403 | + | 0.0565015i | \(0.0179946\pi\) |
−0.450269 | + | 0.892893i | \(0.648672\pi\) | |||||||
\(522\) | −4.39792 | + | 7.61741i | −0.192492 | + | 0.333405i | ||||
\(523\) | −28.5730 | −1.24941 | −0.624705 | − | 0.780861i | \(-0.714781\pi\) | ||||
−0.624705 | + | 0.780861i | \(0.714781\pi\) | |||||||
\(524\) | 4.09827 | − | 7.09841i | 0.179034 | − | 0.310096i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.6937 | − | 21.9862i | 0.553474 | − | 0.958645i | ||||
\(527\) | 3.89792 | + | 6.75139i | 0.169796 | + | 0.294095i | ||||
\(528\) | −4.09827 | − | 7.09841i | −0.178354 | − | 0.308919i | ||||
\(529\) | −19.7750 | −0.859782 | ||||||||
\(530\) | 17.6924 | 0.768509 | ||||||||
\(531\) | −0.562738 | − | 0.974691i | −0.0244207 | − | 0.0422980i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.19375 | − | 34.6230i | 0.268281 | − | 1.49969i | ||||
\(534\) | −8.59166 | + | 14.8812i | −0.371798 | + | 0.643972i | ||||
\(535\) | 8.05217 | − | 13.9468i | 0.348126 | − | 0.602972i | ||||
\(536\) | 8.69375 | − | 15.0580i | 0.375513 | − | 0.650407i | ||||
\(537\) | −0.288738 | − | 0.500109i | −0.0124600 | − | 0.0215813i | ||||
\(538\) | 1.12548 | 0.0485227 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.59166 | − | 13.1491i | 0.326693 | − | 0.565849i | ||||
\(541\) | 6.29583 | − | 10.9047i | 0.270679 | − | 0.468830i | −0.698357 | − | 0.715750i | \(-0.746085\pi\) |
0.969036 | + | 0.246920i | \(0.0794185\pi\) | |||||||
\(542\) | 23.1754 | 0.995469 | ||||||||
\(543\) | 11.6937 | − | 20.2542i | 0.501827 | − | 0.869189i | ||||
\(544\) | −27.5624 | −1.18173 | ||||||||
\(545\) | −47.2170 | −2.02256 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9792 | −1.58111 | −0.790557 | − | 0.612388i | \(-0.790209\pi\) | ||||
−0.790557 | + | 0.612388i | \(0.790209\pi\) | |||||||
\(548\) | 9.20417 | 0.393183 | ||||||||
\(549\) | −0.779291 | + | 1.34977i | −0.0332593 | + | 0.0576069i | ||||
\(550\) | 12.7750 | 0.544727 | ||||||||
\(551\) | 12.4392 | − | 21.5453i | 0.529927 | − | 0.917861i | ||||
\(552\) | −3.80953 | + | 6.59831i | −0.162145 | + | 0.280843i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.18333 | −0.262704 | ||||||||
\(555\) | −12.8979 | − | 22.3398i | −0.547486 | − | 0.948274i | ||||
\(556\) | 7.63381 | − | 13.2221i | 0.323745 | − | 0.560744i | ||||
\(557\) | −10.2958 | + | 17.8329i | −0.436248 | + | 0.755604i | −0.997397 | − | 0.0721110i | \(-0.977026\pi\) |
0.561148 | + | 0.827715i | \(0.310360\pi\) | |||||||
\(558\) | 0.707107 | − | 1.22474i | 0.0299342 | − | 0.0518476i | ||||
\(559\) | −6.08996 | + | 2.19944i | −0.257578 | + | 0.0930262i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5917 | − | 39.1299i | −0.953821 | − | 1.65207i | ||||
\(562\) | 15.2042 | 0.641349 | ||||||||
\(563\) | 1.12548 | 0.0474331 | 0.0237166 | − | 0.999719i | \(-0.492450\pi\) | ||||
0.0237166 | + | 0.999719i | \(0.492450\pi\) | |||||||
\(564\) | 2.00000 | + | 3.46410i | 0.0842152 | + | 0.145865i | ||||
\(565\) | 22.2665 | + | 38.5667i | 0.936758 | + | 1.62251i | ||||
\(566\) | −14.7049 | + | 25.4696i | −0.618092 | + | 1.07057i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.00000 | − | 15.5885i | 0.377632 | − | 0.654077i | ||||
\(569\) | 6.40834 | 0.268651 | 0.134326 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134326 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(570\) | 5.36812 | − | 9.29785i | 0.224846 | − | 0.389444i | ||||
\(571\) | −7.59166 | − | 13.1491i | −0.317701 | − | 0.550275i | 0.662307 | − | 0.749233i | \(-0.269578\pi\) |
−0.980008 | + | 0.198958i | \(0.936244\pi\) | |||||||
\(572\) | −19.6546 | + | 7.09841i | −0.821801 | + | 0.296800i | ||||
\(573\) | 36.4808 | 1.52401 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.97916 | − | 3.42800i | −0.0825366 | − | 0.142958i | ||||
\(576\) | 3.50000 | + | 6.06218i | 0.145833 | + | 0.252591i | ||||
\(577\) | −4.58883 | − | 7.94808i | −0.191035 | − | 0.330883i | 0.754558 | − | 0.656233i | \(-0.227851\pi\) |
−0.945594 | + | 0.325350i | \(0.894518\pi\) | |||||||
\(578\) | 13.3875 | 0.556846 | ||||||||
\(579\) | 2.41006 | + | 4.17434i | 0.100159 | + | 0.173480i | ||||
\(580\) | 23.6085 | 0.980291 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.00000 | + | 5.19615i | 0.124354 | + | 0.215387i | ||||
\(583\) | 38.2042 | 1.58225 | ||||||||
\(584\) | 8.70183 | + | 15.0720i | 0.360084 | + | 0.623685i | ||||
\(585\) | 7.39792 | + | 6.23899i | 0.305866 | + | 0.257951i | ||||
\(586\) | −4.87756 | + | 8.44819i | −0.201490 | + | 0.348991i | ||||
\(587\) | 1.55858 | + | 2.69954i | 0.0643296 | + | 0.111422i | 0.896396 | − | 0.443253i | \(-0.146176\pi\) |
−0.832067 | + | 0.554675i | \(0.812842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | 1.51042 | − | 2.61613i | 0.0621831 | − | 0.107704i | ||||
\(591\) | 11.3137 | 0.465384 | ||||||||
\(592\) | 6.79583 | 0.279307 | ||||||||
\(593\) | −0.779291 | + | 1.34977i | −0.0320017 | + | 0.0554285i | −0.881583 | − | 0.472030i | \(-0.843522\pi\) |
0.849581 | + | 0.527458i | \(0.176855\pi\) | |||||||
\(594\) | −16.3931 | + | 28.3937i | −0.672617 | + | 1.16501i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.29583 | + | 3.97650i | 0.0940409 | + | 0.162884i | ||||
\(597\) | 15.5917 | − | 27.0056i | 0.638124 | − | 1.10526i | ||||
\(598\) | −4.94975 | − | 4.17434i | −0.202410 | − | 0.170702i | ||||
\(599\) | 7.20417 | + | 12.4780i | 0.294354 | + | 0.509837i | 0.974834 | − | 0.222930i | \(-0.0715621\pi\) |
−0.680480 | + | 0.732767i | \(0.738229\pi\) | |||||||
\(600\) | 9.35149 | 0.381773 | ||||||||
\(601\) | −15.4842 | − | 26.8194i | −0.631612 | − | 1.09398i | −0.987222 | − | 0.159350i | \(-0.949060\pi\) |
0.355610 | − | 0.934634i | \(-0.384273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.79583 | −0.236025 | ||||||||
\(604\) | −8.79583 | − | 15.2348i | −0.357897 | − | 0.619896i | ||||
\(605\) | 60.6373 | 2.46526 | ||||||||
\(606\) | 2.10208 | + | 3.64092i | 0.0853913 | + | 0.147902i | ||||
\(607\) | −17.9517 | − | 31.0932i | −0.728636 | − | 1.26203i | −0.957460 | − | 0.288566i | \(-0.906821\pi\) |
0.228824 | − | 0.973468i | \(-0.426512\pi\) | |||||||
\(608\) | −7.07107 | − | 12.2474i | −0.286770 | − | 0.496700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.18333 | −0.169378 | ||||||||
\(611\) | −9.59166 | + | 3.46410i | −0.388037 | + | 0.140143i | ||||
\(612\) | 2.75624 | + | 4.77395i | 0.111415 | + | 0.192976i | ||||
\(613\) | 2.98958 | − | 5.17810i | 0.120748 | − | 0.209142i | −0.799315 | − | 0.600912i | \(-0.794804\pi\) |
0.920063 | + | 0.391771i | \(0.128137\pi\) | |||||||
\(614\) | −34.2004 | −1.38022 | ||||||||
\(615\) | −18.5144 | + | 32.0679i | −0.746573 | + | 1.29310i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1937 | − | 21.1202i | 0.490902 | − | 0.850267i | −0.509043 | − | 0.860741i | \(-0.670001\pi\) |
0.999945 | + | 0.0104740i | \(0.00333405\pi\) | |||||||
\(618\) | 5.79583 | + | 10.0387i | 0.233143 | + | 0.403815i | ||||
\(619\) | 16.9558 | + | 29.3684i | 0.681512 | + | 1.18041i | 0.974519 | + | 0.224303i | \(0.0720107\pi\) |
−0.293007 | + | 0.956110i | \(0.594656\pi\) | |||||||
\(620\) | −3.79583 | −0.152444 | ||||||||
\(621\) | 10.1588 | 0.407657 | ||||||||
\(622\) | 5.93085 | + | 10.2725i | 0.237806 | + | 0.411891i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.79583 | − | 1.73205i | 0.191987 | − | 0.0693375i | ||||
\(625\) | 15.5812 | − | 26.9875i | 0.623250 | − | 1.07950i | ||||
\(626\) | 0.851476 | − | 1.47480i | 0.0340318 | − | 0.0589448i | ||||
\(627\) | 11.5917 | − | 20.0773i | 0.462926 | − | 0.801812i | ||||
\(628\) | 3.46335 | + | 5.99870i | 0.138203 | + | 0.239374i | ||||
\(629\) | 37.4619 | 1.49370 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2042 | − | 17.6741i | 0.406222 | − | 0.703596i | −0.588241 | − | 0.808685i | \(-0.700179\pi\) |
0.994463 | + | 0.105089i | \(0.0335128\pi\) | |||||||
\(632\) | −17.6937 | + | 30.6465i | −0.703819 | + | 1.21905i | ||||
\(633\) | 2.53969 | 0.100944 | ||||||||
\(634\) | 6.29583 | − | 10.9047i | 0.250039 | − | 0.433081i | ||||
\(635\) | 20.3765 | 0.808615 | ||||||||
\(636\) | 9.32202 | 0.369642 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −50.9792 | −2.01828 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 4.02609 | − | 6.97339i | 0.159145 | − | 0.275647i | ||||
\(641\) | 4.79583 | 0.189424 | 0.0947120 | − | 0.995505i | \(-0.469807\pi\) | ||||
0.0947120 | + | 0.995505i | \(0.469807\pi\) | |||||||
\(642\) | −4.24264 | + | 7.34847i | −0.167444 | + | 0.290021i | ||||
\(643\) | 2.82843 | − | 4.89898i | 0.111542 | − | 0.193197i | −0.804850 | − | 0.593478i | \(-0.797754\pi\) |
0.916392 | + | 0.400281i | \(0.131088\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.81667 | 0.268406 | ||||||||
\(646\) | 7.79583 | + | 13.5028i | 0.306723 | + | 0.531260i | ||||
\(647\) | −0.981107 | + | 1.69933i | −0.0385713 | + | 0.0668074i | −0.884667 | − | 0.466224i | \(-0.845614\pi\) |
0.846095 | + | 0.533032i | \(0.178947\pi\) | |||||||
\(648\) | −7.50000 | + | 12.9904i | −0.294628 | + | 0.510310i | ||||
\(649\) | 3.26153 | − | 5.64914i | 0.128026 | − | 0.221748i | ||||
\(650\) | −1.39948 | + | 7.82305i | −0.0548920 | + | 0.306845i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.69375 | − | 11.5939i | −0.262147 | − | 0.454053i | ||||
\(653\) | 25.1833 | 0.985500 | 0.492750 | − | 0.870171i | \(-0.335992\pi\) | ||||
0.492750 | + | 0.870171i | \(0.335992\pi\) | |||||||
\(654\) | 24.8784 | 0.972821 | ||||||||
\(655\) | −11.0000 | − | 19.0526i | −0.429806 | − | 0.744445i | ||||
\(656\) | −4.87756 | − | 8.44819i | −0.190437 | − | 0.329846i | ||||
\(657\) | 2.90061 | − | 5.02401i | 0.113164 | − | 0.196005i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.7958 | − | 32.5553i | 0.732182 | − | 1.26818i | −0.223767 | − | 0.974643i | \(-0.571836\pi\) |
0.955949 | − | 0.293533i | \(-0.0948311\pi\) | |||||||
\(660\) | 22.0000 | 0.856349 | ||||||||
\(661\) | 13.9256 | − | 24.1198i | 0.541642 | − | 0.938152i | −0.457168 | − | 0.889381i | \(-0.651136\pi\) |
0.998810 | − | 0.0487715i | \(-0.0155306\pi\) | |||||||
\(662\) | −0.306253 | − | 0.530445i | −0.0119028 | − | 0.0206163i | ||||
\(663\) | 26.4370 | − | 9.54790i | 1.02673 | − | 0.370810i | ||||
\(664\) | −29.6985 | −1.15252 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.39792 | − | 5.88536i | −0.131667 | − | 0.228053i | ||||
\(667\) | 7.89792 | + | 13.6796i | 0.305809 | + | 0.529676i | ||||
\(668\) | −7.63381 | − | 13.2221i | −0.295361 | − | 0.511580i | ||||
\(669\) | −8.00000 | −0.309298 | ||||||||
\(670\) | −7.77817 | − | 13.4722i | −0.300497 | − | 0.520476i | ||||
\(671\) | −9.03328 | −0.348726 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.9896 | − | 20.7666i | −0.462164 | − | 0.800492i | 0.536904 | − | 0.843643i | \(-0.319594\pi\) |
−0.999069 | + | 0.0431511i | \(0.986260\pi\) | |||||||
\(674\) | −29.9792 | −1.15475 | ||||||||
\(675\) | −6.23433 | − | 10.7982i | −0.239959 | − | 0.415622i | ||||
\(676\) | −2.19375 | − | 12.8136i | −0.0843749 | − | 0.492829i | ||||
\(677\) | 17.3889 | − | 30.1185i | 0.668311 | − | 1.15755i | −0.310065 | − | 0.950715i | \(-0.600351\pi\) |
0.978376 | − | 0.206833i | \(-0.0663158\pi\) | |||||||
\(678\) | −11.7321 | − | 20.3206i | −0.450568 | − | 0.780406i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −22.1937 | + | 38.4407i | −0.851091 | + | 1.47413i | ||||
\(681\) | −14.7958 | + | 25.6271i | −0.566977 | + | 0.982034i | ||||
\(682\) | 8.19654 | 0.313862 | ||||||||
\(683\) | 50.7750 | 1.94285 | 0.971425 | − | 0.237345i | \(-0.0762771\pi\) | ||||
0.971425 | + | 0.237345i | \(0.0762771\pi\) | |||||||
\(684\) | −1.41421 | + | 2.44949i | −0.0540738 | + | 0.0936586i | ||||
\(685\) | 12.3523 | − | 21.3947i | 0.471956 | − | 0.817451i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.00000 | − | 15.5885i | −0.343371 | − | 0.594737i | ||||
\(688\) | −0.897916 | + | 1.55524i | −0.0342327 | + | 0.0592928i | ||||
\(689\) | −4.18519 | + | 23.3952i | −0.159443 | + | 0.891285i | ||||
\(690\) | 3.40834 | + | 5.90341i | 0.129753 | + | 0.224739i | ||||
\(691\) | −11.0250 | −0.419410 | −0.209705 | − | 0.977765i | \(-0.567250\pi\) | ||||
−0.209705 | + | 0.977765i | \(0.567250\pi\) | |||||||
\(692\) | −4.66101 | − | 8.07311i | −0.177185 | − | 0.306893i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.9792 | 0.568601 | ||||||||
\(695\) | −20.4896 | − | 35.4890i | −0.777214 | − | 1.34617i | ||||
\(696\) | −37.3176 | −1.41452 | ||||||||
\(697\) | −26.8875 | − | 46.5705i | −1.01844 | − | 1.76398i | ||||
\(698\) | 6.50833 | + | 11.2728i | 0.246344 | + | 0.426680i | ||||
\(699\) | −14.9789 | − | 25.9442i | −0.566553 | − | 0.981299i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.4083 | −0.393117 | −0.196559 | − | 0.980492i | \(-0.562977\pi\) | ||||
−0.196559 | + | 0.980492i | \(0.562977\pi\) | |||||||
\(702\) | −15.5917 | − | 13.1491i | −0.588469 | − | 0.496283i | ||||
\(703\) | 9.61076 | + | 16.6463i | 0.362477 | + | 0.627828i | ||||
\(704\) | −20.2854 | + | 35.1354i | −0.764535 | + | 1.32421i | ||||
\(705\) | 10.7362 | 0.404350 | ||||||||
\(706\) | −7.56162 | + | 13.0971i | −0.284585 | + | 0.492916i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.795832 | − | 1.37842i | 0.0299092 | − | 0.0518042i | ||||
\(709\) | 9.39792 | + | 16.2777i | 0.352946 | + | 0.611321i | 0.986764 | − | 0.162162i | \(-0.0518466\pi\) |
−0.633818 | + | 0.773482i | \(0.718513\pi\) | |||||||
\(710\) | −8.05217 | − | 13.9468i | −0.302193 | − | 0.523413i | ||||
\(711\) | 11.7958 | 0.442378 | ||||||||
\(712\) | 36.4513 | 1.36607 | ||||||||
\(713\) | −1.26984 | − | 2.19944i | −0.0475561 | − | 0.0823695i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.87707 | + | 55.2127i | −0.369382 | + | 2.06484i | ||||
\(716\) | −0.204168 | + | 0.353630i | −0.00763013 | + | 0.0132158i | ||||
\(717\) | −13.9978 | + | 24.2448i | −0.522756 | + | 0.905440i | ||||
\(718\) | 2.00000 | − | 3.46410i | 0.0746393 | − | 0.129279i | ||||
\(719\) | 14.5605 | + | 25.2195i | 0.543015 | + | 0.940530i | 0.998729 | + | 0.0504035i | \(0.0160507\pi\) |
−0.455714 | + | 0.890126i | \(0.650616\pi\) | |||||||
\(720\) | 2.68406 | 0.100029 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.50000 | − | 9.52628i | 0.204689 | − | 0.354531i | ||||
\(723\) | −3.10208 | + | 5.37297i | −0.115368 | + | 0.199823i | ||||
\(724\) | −16.5375 | −0.614610 | ||||||||
\(725\) | 9.69375 | − | 16.7901i | 0.360017 | − | 0.623567i | ||||
\(726\) | −31.9494 | −1.18575 | ||||||||
\(727\) | 35.3259 | 1.31016 | 0.655082 | − | 0.755558i | \(-0.272634\pi\) | ||||
0.655082 | + | 0.755558i | \(0.272634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 15.5708 | 0.576302 | ||||||||
\(731\) | −4.94975 | + | 8.57321i | −0.183073 | + | 0.317092i | ||||
\(732\) | −2.20417 | −0.0814684 | ||||||||
\(733\) | 0.346184 | − | 0.599609i | 0.0127866 | − | 0.0221471i | −0.859561 | − | 0.511033i | \(-0.829263\pi\) |
0.872348 | + | 0.488886i | \(0.162596\pi\) | |||||||
\(734\) | 10.6066 | − | 18.3712i | 0.391497 | − | 0.678092i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.97916 | 0.330976 | ||||||||
\(737\) | −16.7958 | − | 29.0912i | −0.618682 | − | 1.07159i | ||||
\(738\) | −4.87756 | + | 8.44819i | −0.179546 | + | 0.310982i | ||||
\(739\) | −7.59166 | + | 13.1491i | −0.279264 | + | 0.483699i | −0.971202 | − | 0.238258i | \(-0.923424\pi\) |
0.691938 | + | 0.721957i | \(0.256757\pi\) | |||||||
\(740\) | −9.12020 | + | 15.7967i | −0.335265 | + | 0.580697i | ||||
\(741\) | 11.0250 | + | 9.29785i | 0.405012 | + | 0.341565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.59166 | − | 7.95299i | −0.168452 | − | 0.291767i | 0.769424 | − | 0.638738i | \(-0.220543\pi\) |
−0.937876 | + | 0.346971i | \(0.887210\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 12.3243 | 0.451527 | ||||||||
\(746\) | 6.29583 | + | 10.9047i | 0.230507 | + | 0.399249i | ||||
\(747\) | 4.94975 | + | 8.57321i | 0.181102 | + | 0.313678i | ||||
\(748\) | −15.9747 | + | 27.6690i | −0.584094 | + | 1.01168i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.30625 | + | 9.19070i | −0.193757 | + | 0.335597i | ||||
\(751\) | 1.79583 | 0.0655308 | 0.0327654 | − | 0.999463i | \(-0.489569\pi\) | ||||
0.0327654 | + | 0.999463i | \(0.489569\pi\) | |||||||
\(752\) | −1.41421 | + | 2.44949i | −0.0515711 | + | 0.0893237i | ||||
\(753\) | 2.20417 | + | 3.81773i | 0.0803244 | + | 0.139126i | ||||
\(754\) | 5.58467 | − | 31.2182i | 0.203382 | − | 1.13690i | ||||
\(755\) | −47.2170 | −1.71840 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.5917 | + | 21.8094i | 0.457652 | + | 0.792676i | 0.998836 | − | 0.0482277i | \(-0.0153573\pi\) |
−0.541185 | + | 0.840904i | \(0.682024\pi\) | |||||||
\(758\) | 1.69375 | + | 2.93366i | 0.0615197 | + | 0.106555i | ||||
\(759\) | 7.35981 | + | 12.7476i | 0.267144 | + | 0.462707i | ||||
\(760\) | −22.7750 | −0.826136 | ||||||||
\(761\) | 4.66101 | + | 8.07311i | 0.168961 | + | 0.292650i | 0.938055 | − | 0.346486i | \(-0.112625\pi\) |
−0.769094 | + | 0.639136i | \(0.779292\pi\) | |||||||
\(762\) | −10.7362 | −0.388933 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.8979 | − | 22.3398i | −0.466630 | − | 0.808227i | ||||
\(765\) | 14.7958 | 0.534944 | ||||||||
\(766\) | −7.48944 | − | 12.9721i | −0.270604 | − | 0.468700i | ||||
\(767\) | 3.10208 | + | 2.61613i | 0.112010 | + | 0.0944628i | ||||
\(768\) | −12.0208 | + | 20.8207i | −0.433764 | + | 0.751301i | ||||
\(769\) | 2.12132 | + | 3.67423i | 0.0764968 | + | 0.132496i | 0.901736 | − | 0.432287i | \(-0.142293\pi\) |
−0.825239 | + | 0.564783i | \(0.808960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.8979 | + | 18.8757i | −0.392479 | + | 0.679793i | ||||
\(772\) | 1.70417 | − | 2.95171i | 0.0613344 | − | 0.106234i | ||||
\(773\) | −7.64854 | −0.275099 | −0.137549 | − | 0.990495i | \(-0.543923\pi\) | ||||
−0.137549 | + | 0.990495i | \(0.543923\pi\) | |||||||
\(774\) | 1.79583 | 0.0645498 | ||||||||
\(775\) | −1.55858 | + | 2.69954i | −0.0559859 | + | 0.0969705i | ||||
\(776\) | 6.36396 | − | 11.0227i | 0.228453 | − | 0.395692i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.1937 | − | 24.5843i | −0.508870 | − | 0.881390i | ||||
\(779\) | 13.7958 | − | 23.8951i | 0.494287 | − | 0.856130i | ||||
\(780\) | −2.41006 | + | 13.4722i | −0.0862939 | + | 0.482382i | ||||
\(781\) | −17.3875 | − | 30.1160i | −0.622173 | − | 1.07764i | ||||
\(782\) | −9.89949 | −0.354005 | ||||||||
\(783\) | 24.8784 | + | 43.0906i | 0.889080 | + | 1.53993i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.5917 | 0.663565 | ||||||||
\(786\) | 5.79583 | + | 10.0387i | 0.206730 | + | 0.358068i | ||||
\(787\) | −25.4264 | −0.906352 | −0.453176 | − | 0.891421i | \(-0.649709\pi\) | ||||
−0.453176 | + | 0.891421i | \(0.649709\pi\) | |||||||
\(788\) | −4.00000 | − | 6.92820i | −0.142494 | − | 0.246807i | ||||
\(789\) | −17.9517 | − | 31.0932i | −0.639096 | − | 1.10695i | ||||
\(790\) | 15.8303 | + | 27.4190i | 0.563219 | + | 0.975523i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 17.3875 | 0.617838 | ||||||||
\(793\) | 0.989579 | − | 5.53173i | 0.0351410 | − | 0.196438i | ||||
\(794\) | 3.53553 | + | 6.12372i | 0.125471 | + | 0.217323i | ||||
\(795\) | 12.5104 | − | 21.6687i | 0.443699 | − | 0.768509i | ||||
\(796\) | −22.0499 | −0.781539 | ||||||||
\(797\) | −13.1463 | + | 22.7700i | −0.465666 | + | 0.806556i | −0.999231 | − | 0.0392022i | \(-0.987518\pi\) |
0.533566 | + | 0.845759i | \(0.320852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.79583 | + | 13.5028i | −0.275797 | + | 0.477694i | ||||
\(800\) | −5.51042 | − | 9.54433i | −0.194823 | − | 0.337443i | ||||
\(801\) | −6.07522 | − | 10.5226i | −0.214657 | − | 0.371798i | ||||
\(802\) | 24.3875 | 0.861152 | ||||||||
\(803\) | 33.6229 | 1.18653 | ||||||||
\(804\) | −4.09827 | − | 7.09841i | −0.144535 | − | 0.250342i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.897916 | + | 5.01934i | −0.0316277 | + | 0.176799i | ||||
\(807\) | 0.795832 | − | 1.37842i | 0.0280146 | − | 0.0485227i | ||||
\(808\) | 4.45919 | − | 7.72355i | 0.156874 | − | 0.271714i | ||||
\(809\) | −19.6833 | + | 34.0925i | −0.692029 | + | 1.19863i | 0.279143 | + | 0.960250i | \(0.409950\pi\) |
−0.971172 | + | 0.238380i | \(0.923384\pi\) | |||||||
\(810\) | 6.71015 | + | 11.6223i | 0.235770 | + | 0.408366i | ||||
\(811\) | 38.4725 | 1.35095 | 0.675476 | − | 0.737382i | \(-0.263938\pi\) | ||||
0.675476 | + | 0.737382i | \(0.263938\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.3875 | − | 28.3840i | 0.574735 | − | 0.995469i | ||||
\(814\) | 19.6937 | − | 34.1106i | 0.690265 | − | 1.19557i | ||||
\(815\) | −35.9328 | −1.25867 | ||||||||
\(816\) | 3.89792 | − | 6.75139i | 0.136454 | − | 0.236346i | ||||
\(817\) | −5.07938 | −0.177705 | ||||||||
\(818\) | 28.6879 | 1.00305 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.1833 | 0.914361 | ||||||||
\(821\) | −40.3667 | −1.40881 | −0.704403 | − | 0.709800i | \(-0.748785\pi\) | ||||
−0.704403 | + | 0.709800i | \(0.748785\pi\) | |||||||
\(822\) | −6.50833 | + | 11.2728i | −0.227004 | + | 0.393183i | ||||
\(823\) | 36.7750 | 1.28190 | 0.640948 | − | 0.767584i | \(-0.278542\pi\) | ||||
0.640948 | + | 0.767584i | \(0.278542\pi\) | |||||||
\(824\) | 12.2948 | − | 21.2952i | 0.428310 | − | 0.741855i | ||||
\(825\) | 9.03328 | − | 15.6461i | 0.314498 | − | 0.544727i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.9792 | 0.938157 | 0.469079 | − | 0.883156i | \(-0.344586\pi\) | ||||
0.469079 | + | 0.883156i | \(0.344586\pi\) | |||||||
\(828\) | −0.897916 | − | 1.55524i | −0.0312047 | − | 0.0540482i | ||||
\(829\) | 10.1013 | − | 17.4960i | 0.350833 | − | 0.607661i | −0.635563 | − | 0.772049i | \(-0.719232\pi\) |
0.986396 | + | 0.164389i | \(0.0525651\pi\) | |||||||
\(830\) | −13.2854 | + | 23.0110i | −0.461143 | + | 0.798724i | ||||
\(831\) | −4.37227 | + | 7.57300i | −0.151672 | + | 0.262704i | ||||
\(832\) | −19.2937 | − | 16.2712i | −0.668889 | − | 0.564104i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.7958 | + | 18.6989i | 0.373829 | + | 0.647491i | ||||
\(835\) | −40.9792 | −1.41814 | ||||||||
\(836\) | −16.3931 | −0.566967 | ||||||||
\(837\) | −4.00000 | − | 6.92820i | −0.138260 | − | 0.239474i | ||||
\(838\) | 14.2718 | + | 24.7194i | 0.493010 | + | 0.853918i | ||||
\(839\) | 2.82843 | − | 4.89898i | 0.0976481 | − | 0.169132i | −0.813063 | − | 0.582176i | \(-0.802201\pi\) |
0.910711 | + | 0.413045i | \(0.135535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1833 | + | 41.8867i | −0.833908 | + | 1.44437i | ||||
\(842\) | −6.59166 | −0.227164 | ||||||||
\(843\) | 10.7510 | − | 18.6212i | 0.370283 | − | 0.641349i | ||||
\(844\) | −0.897916 | − | 1.55524i | −0.0309075 | − | 0.0535334i | ||||
\(845\) | −32.7287 | − | 12.0969i | −1.12590 | − | 0.416146i | ||||
\(846\) | 2.82843 | 0.0972433 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.29583 | + | 5.70855i | 0.113179 | + | 0.196032i | ||||
\(849\) | 20.7958 | + | 36.0194i | 0.713711 | + | 1.23618i | ||||
\(850\) | 6.07522 | + | 10.5226i | 0.208378 | + | 0.360922i | ||||
\(851\) | −12.2042 | −0.418354 | ||||||||
\(852\) | −4.24264 | − | 7.34847i | −0.145350 | − | 0.251754i | ||||
\(853\) | 13.1610 | 0.450625 | 0.225313 | − | 0.974287i | \(-0.427660\pi\) | ||||
0.225313 | + | 0.974287i | \(0.427660\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.79583 | + | 6.57457i | 0.129815 | + | 0.224846i | ||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | −18.8753 | − | 32.6930i | −0.644769 | − | 1.11677i | −0.984355 | − | 0.176198i | \(-0.943620\pi\) |
0.339586 | − | 0.940575i | \(-0.389713\pi\) | |||||||
\(858\) | 5.20417 | − | 29.0912i | 0.177667 | − | 0.993158i | ||||
\(859\) | 11.8764 | − | 20.5706i | 0.405219 | − | 0.701860i | −0.589128 | − | 0.808040i | \(-0.700529\pi\) |
0.994347 | + | 0.106180i | \(0.0338619\pi\) | |||||||
\(860\) | −2.41006 | − | 4.17434i | −0.0821823 | − | 0.142344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.59166 | − | 4.48889i | 0.0882724 | − | 0.152892i | ||||
\(863\) | −8.89792 | + | 15.4116i | −0.302889 | + | 0.524618i | −0.976789 | − | 0.214204i | \(-0.931284\pi\) |
0.673900 | + | 0.738822i | \(0.264618\pi\) | |||||||
\(864\) | 28.2843 | 0.962250 | ||||||||
\(865\) | −25.0208 | −0.850734 | ||||||||
\(866\) | 6.71015 | − | 11.6223i | 0.228020 | − | 0.394942i | ||||
\(867\) | 9.46639 | − | 16.3963i | 0.321495 | − | 0.556846i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.1833 | + | 59.2073i | 1.15959 | + | 2.00847i | ||||
\(870\) | −16.6937 | + | 28.9144i | −0.565971 | + | 0.980291i | ||||
\(871\) | 19.6546 | − | 7.09841i | 0.665971 | − | 0.240521i | ||||
\(872\) | −26.3875 | − | 45.7045i | −0.893593 | − | 1.54775i | ||||
\(873\) | −4.24264 | −0.143592 | ||||||||
\(874\) | −2.53969 | − | 4.39887i | −0.0859063 | − | 0.148794i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.20417 | 0.277193 | ||||||||
\(877\) | 2.39792 | + | 4.15331i | 0.0809719 | + | 0.140247i | 0.903668 | − | 0.428235i | \(-0.140864\pi\) |
−0.822696 | + | 0.568482i | \(0.807531\pi\) | |||||||
\(878\) | −34.2004 | −1.15421 | ||||||||
\(879\) | 6.89792 | + | 11.9475i | 0.232661 | + | 0.402981i | ||||
\(880\) | 7.77817 | + | 13.4722i | 0.262202 | + | 0.454148i | ||||
\(881\) | −11.6599 | − | 20.1955i | −0.392832 | − | 0.680405i | 0.599990 | − | 0.800007i | \(-0.295171\pi\) |
−0.992822 | + | 0.119603i | \(0.961838\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.6125 | −0.559055 | −0.279528 | − | 0.960138i | \(-0.590178\pi\) | ||||
−0.279528 | + | 0.960138i | \(0.590178\pi\) | |||||||
\(884\) | −15.1937 | − | 12.8136i | −0.511021 | − | 0.430967i | ||||
\(885\) | −2.13606 | − | 3.69976i | −0.0718028 | − | 0.124366i | ||||
\(886\) | −5.00000 | + | 8.66025i | −0.167978 | + | 0.290947i | ||||
\(887\) | 28.5730 | 0.959388 | 0.479694 | − | 0.877436i | \(-0.340748\pi\) | ||||
0.479694 | + | 0.877436i | \(0.340748\pi\) | |||||||
\(888\) | 14.4161 | − | 24.9695i | 0.483774 | − | 0.837921i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.3063 | − | 28.2433i | 0.546587 | − | 0.946716i | ||||
\(891\) | 14.4896 | + | 25.0967i | 0.485419 | + | 0.840771i | ||||
\(892\) | 2.82843 | + | 4.89898i | 0.0947027 | + | 0.164030i | ||||
\(893\) | −8.00000 | −0.267710 | ||||||||
\(894\) | −6.49359 | −0.217178 | ||||||||
\(895\) | 0.548000 | + | 0.949164i | 0.0183176 | + | 0.0317271i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.61251 | + | 3.11047i | −0.287563 | + | 0.103856i | ||||
\(898\) | −2.20417 | + | 3.81773i | −0.0735541 | + | 0.127399i | ||||
\(899\) | 6.21959 | − | 10.7726i | 0.207435 | − | 0.359288i | ||||
\(900\) | −1.10208 | + | 1.90887i | −0.0367361 | + | 0.0636289i | ||||
\(901\) | 18.1682 | + | 31.4683i | 0.605271 | + | 1.04836i | ||||
\(902\) | −56.5391 | −1.88255 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.8875 | + | 43.1064i | −0.827746 | + | 1.43370i | ||||
\(905\) | −22.1937 | + | 38.4407i | −0.737745 | + | 1.27781i | ||||
\(906\) | 24.8784 | 0.826528 | ||||||||
\(907\) | −24.6937 | + | 42.7708i | −0.819942 | + | 1.42018i | 0.0857816 | + | 0.996314i | \(0.472661\pi\) |
−0.905724 | + | 0.423868i | \(0.860672\pi\) | |||||||
\(908\) | 20.9245 | 0.694403 | ||||||||
\(909\) | −2.97280 | −0.0986014 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.1833 | −1.43073 | −0.715364 | − | 0.698752i | \(-0.753739\pi\) | ||||
−0.715364 | + | 0.698752i | \(0.753739\pi\) | |||||||
\(912\) | 4.00000 | 0.132453 | ||||||||
\(913\) | −28.6879 | + | 49.6889i | −0.949431 | + | 1.64446i | ||||
\(914\) | −14.5917 | −0.482649 | ||||||||
\(915\) | −2.95806 | + | 5.12351i | −0.0977904 | + | 0.169378i | ||||
\(916\) | −6.36396 | + | 11.0227i | −0.210271 | + | 0.364200i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −31.1833 | −1.02920 | ||||||||
\(919\) | −5.00000 | − | 8.66025i | −0.164935 | − | 0.285675i | 0.771697 | − | 0.635990i | \(-0.219408\pi\) |
−0.936632 | + | 0.350315i | \(0.886075\pi\) | |||||||
\(920\) | 7.23017 | − | 12.5230i | 0.238372 | − | 0.412872i | ||||
\(921\) | −24.1833 | + | 41.8867i | −0.796868 | + | 1.38022i | ||||
\(922\) | 15.4842 | − | 26.8194i | 0.509944 | − | 0.883249i | ||||
\(923\) | 20.3470 | − | 7.34847i | 0.669729 | − | 0.241878i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48958 | + | 12.9723i | 0.246256 | + | 0.426528i | ||||
\(926\) | 11.3875 | 0.374216 | ||||||||
\(927\) | −8.19654 | −0.269210 | ||||||||
\(928\) | 21.9896 | + | 38.0871i | 0.721843 | + | 1.25027i | ||||
\(929\) | −14.0700 | − | 24.3699i | −0.461620 | − | 0.799550i | 0.537422 | − | 0.843314i | \(-0.319398\pi\) |
−0.999042 | + | 0.0437641i | \(0.986065\pi\) | |||||||
\(930\) | 2.68406 | − | 4.64893i | 0.0880137 | − | 0.152444i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.5917 | + | 18.3453i | −0.346941 | + | 0.600920i | ||||
\(933\) | 16.7750 | 0.549188 | ||||||||
\(934\) | −2.41006 | + | 4.17434i | −0.0788595 | + | 0.136589i | ||||
\(935\) | 42.8771 | + | 74.2653i | 1.40223 | + | 2.42873i | ||||
\(936\) | −1.90477 | + | 10.6476i | −0.0622593 | + | 0.348028i | ||||
\(937\) | −6.63796 | −0.216853 | −0.108426 | − | 0.994104i | \(-0.534581\pi\) | ||||
−0.108426 | + | 0.994104i | \(0.534581\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.20417 | − | 2.08568i | −0.0392966 | − | 0.0680636i | ||||
\(940\) | −3.79583 | − | 6.57457i | −0.123806 | − | 0.214439i | ||||
\(941\) | −11.7321 | − | 20.3206i | −0.382455 | − | 0.662431i | 0.608958 | − | 0.793203i | \(-0.291588\pi\) |
−0.991413 | + | 0.130772i | \(0.958255\pi\) | |||||||
\(942\) | −9.79583 | −0.319165 | ||||||||
\(943\) | 8.75928 | + | 15.1715i | 0.285241 | + | 0.494053i | ||||
\(944\) | 1.12548 | 0.0366311 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.20417 | + | 9.01388i | 0.169202 | + | 0.293067i | ||||
\(947\) | 28.2042 | 0.916512 | 0.458256 | − | 0.888820i | \(-0.348474\pi\) | ||||
0.458256 | + | 0.888820i | \(0.348474\pi\) | |||||||
\(948\) | 8.34091 | + | 14.4469i | 0.270900 | + | 0.469213i | ||||
\(949\) | −3.68333 | + | 20.5897i | −0.119566 | + | 0.668371i | ||||
\(950\) | −3.11716 | + | 5.39909i | −0.101134 | + | 0.175170i | ||||
\(951\) | −8.90365 | − | 15.4216i | −0.288721 | − | 0.500079i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.40834 | − | 4.17136i | 0.0780137 | − | 0.135124i | −0.824379 | − | 0.566038i | \(-0.808476\pi\) |
0.902393 | + | 0.430914i | \(0.141809\pi\) | |||||||
\(954\) | 3.29583 | − | 5.70855i | 0.106706 | − | 0.184821i | ||||
\(955\) | −69.2375 | −2.24047 | ||||||||
\(956\) | 19.7958 | 0.640243 | ||||||||
\(957\) | −36.0477 | + | 62.4365i | −1.16526 | + | 2.01828i | ||||
\(958\) | −3.67990 | + | 6.37378i | −0.118892 | + | 0.205927i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.2854 | + | 23.0110i | 0.428785 | + | 0.742677i | ||||
\(961\) | 14.5000 | − | 25.1147i | 0.467742 | − | 0.810153i | ||||
\(962\) | 18.7310 | + | 15.7967i | 0.603910 | + | 0.509305i | ||||
\(963\) | −3.00000 | − | 5.19615i | −0.0966736 | − | 0.167444i | ||||
\(964\) | 4.38701 | 0.141296 | ||||||||
\(965\) | −4.57409 | − | 7.92255i | −0.147245 | − | 0.255036i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3875 | 0.366197 | 0.183099 | − | 0.983095i | \(-0.441387\pi\) | ||||
0.183099 | + | 0.983095i | \(0.441387\pi\) | |||||||
\(968\) | 33.8875 | + | 58.6949i | 1.08919 | + | 1.88652i | ||||
\(969\) | 22.0499 | 0.708346 | ||||||||
\(970\) | −5.69375 | − | 9.86186i | −0.182815 | − | 0.316645i | ||||
\(971\) | −11.3137 | − | 19.5959i | −0.363074 | − | 0.628863i | 0.625391 | − | 0.780312i | \(-0.284940\pi\) |
−0.988465 | + | 0.151449i | \(0.951606\pi\) | |||||||
\(972\) | −4.94975 | − | 8.57321i | −0.158763 | − | 0.274986i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.5917 | 0.627757 | ||||||||
\(975\) | 8.59166 | + | 7.24573i | 0.275153 | + | 0.232049i | ||||
\(976\) | −0.779291 | − | 1.34977i | −0.0249445 | − | 0.0432051i | ||||
\(977\) | −0.193747 | + | 0.335580i | −0.00619852 | + | 0.0107362i | −0.869108 | − | 0.494622i | \(-0.835306\pi\) |
0.862910 | + | 0.505358i | \(0.168640\pi\) | |||||||
\(978\) | 18.9328 | 0.605403 | ||||||||
\(979\) | 35.2110 | − | 60.9872i | 1.12535 | − | 1.94916i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.79583 | + | 15.2348i | −0.280829 | + | 0.486411i | ||||
\(982\) | 4.79583 | + | 8.30662i | 0.153041 | + | 0.265075i | ||||
\(983\) | 20.7801 | + | 35.9922i | 0.662782 | + | 1.14797i | 0.979882 | + | 0.199580i | \(0.0639578\pi\) |
−0.317099 | + | 0.948392i | \(0.602709\pi\) | |||||||
\(984\) | −41.3875 | −1.31939 | ||||||||
\(985\) | −21.4725 | −0.684170 | ||||||||
\(986\) | −24.2434 | − | 41.9909i | −0.772069 | − | 1.33726i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.79583 | − | 10.0387i | 0.0571330 | − | 0.319373i | ||||
\(989\) | 1.61251 | − | 2.79294i | 0.0512747 | − | 0.0888104i | ||||
\(990\) | 7.77817 | − | 13.4722i | 0.247207 | − | 0.428174i | ||||
\(991\) | −9.10208 | + | 15.7653i | −0.289137 | + | 0.500800i | −0.973604 | − | 0.228244i | \(-0.926702\pi\) |
0.684467 | + | 0.729044i | \(0.260035\pi\) | |||||||
\(992\) | −3.53553 | − | 6.12372i | −0.112253 | − | 0.194428i | ||||
\(993\) | −0.866213 | −0.0274885 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.5917 | + | 51.2543i | −0.938119 | + | 1.62487i | ||||
\(996\) | −7.00000 | + | 12.1244i | −0.221803 | + | 0.384175i | ||||
\(997\) | 5.51249 | 0.174582 | 0.0872911 | − | 0.996183i | \(-0.472179\pi\) | ||||
0.0872911 | + | 0.996183i | \(0.472179\pi\) | |||||||
\(998\) | −8.10208 | + | 14.0332i | −0.256467 | + | 0.444214i | ||||
\(999\) | −38.4430 | −1.21628 |
(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 | 637.2.h.k.471.3 | 8 | ||
7.2 | even | 3 | 637.2.f.g.393.4 | yes | 8 | ||
7.3 | odd | 6 | 637.2.g.h.263.4 | 8 | |||
7.4 | even | 3 | 637.2.g.h.263.1 | 8 | |||
7.5 | odd | 6 | 637.2.f.g.393.1 | yes | 8 | ||
7.6 | odd | 2 | inner | 637.2.h.k.471.2 | 8 | ||
13.9 | even | 3 | 637.2.g.h.373.1 | 8 | |||
91.9 | even | 3 | 637.2.f.g.295.4 | yes | 8 | ||
91.16 | even | 3 | 8281.2.a.bv.1.2 | 4 | |||
91.23 | even | 6 | 8281.2.a.bn.1.1 | 4 | |||
91.48 | odd | 6 | 637.2.g.h.373.4 | 8 | |||
91.61 | odd | 6 | 637.2.f.g.295.1 | ✓ | 8 | ||
91.68 | odd | 6 | 8281.2.a.bv.1.3 | 4 | |||
91.74 | even | 3 | inner | 637.2.h.k.165.3 | 8 | ||
91.75 | odd | 6 | 8281.2.a.bn.1.4 | 4 | |||
91.87 | odd | 6 | inner | 637.2.h.k.165.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.g.295.1 | ✓ | 8 | 91.61 | odd | 6 | ||
637.2.f.g.295.4 | yes | 8 | 91.9 | even | 3 | ||
637.2.f.g.393.1 | yes | 8 | 7.5 | odd | 6 | ||
637.2.f.g.393.4 | yes | 8 | 7.2 | even | 3 | ||
637.2.g.h.263.1 | 8 | 7.4 | even | 3 | |||
637.2.g.h.263.4 | 8 | 7.3 | odd | 6 | |||
637.2.g.h.373.1 | 8 | 13.9 | even | 3 | |||
637.2.g.h.373.4 | 8 | 91.48 | odd | 6 | |||
637.2.h.k.165.2 | 8 | 91.87 | odd | 6 | inner | ||
637.2.h.k.165.3 | 8 | 91.74 | even | 3 | inner | ||
637.2.h.k.471.2 | 8 | 7.6 | odd | 2 | inner | ||
637.2.h.k.471.3 | 8 | 1.1 | even | 1 | trivial | ||
8281.2.a.bn.1.1 | 4 | 91.23 | even | 6 | |||
8281.2.a.bn.1.4 | 4 | 91.75 | odd | 6 | |||
8281.2.a.bv.1.2 | 4 | 91.16 | even | 3 | |||
8281.2.a.bv.1.3 | 4 | 91.68 | odd | 6 |