Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(295,637)]
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([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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 | 393.1 | ||
Root | \(-1.34203 + 2.32446i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.393 |
Dual form | 637.2.f.g.295.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | 0.633316 | − | 0.773893i | \(-0.281693\pi\) |
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(3\) | −0.707107 | − | 1.22474i | −0.408248 | − | 0.707107i | 0.586445 | − | 0.809989i | \(-0.300527\pi\) |
−0.994694 | + | 0.102882i | \(0.967194\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.68406 | −1.20035 | −0.600174 | − | 0.799870i | \(-0.704902\pi\) | ||||
−0.600174 | + | 0.799870i | \(0.704902\pi\) | |||||||
\(6\) | −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 | −0.858084 | − | 0.513510i | \(-0.828345\pi\) |
−0.0156708 | − | 0.999877i | \(-0.504988\pi\) | |||||||
\(12\) | −1.41421 | −0.408248 | ||||||||
\(13\) | 2.75624 | + | 2.32446i | 0.764444 | + | 0.644690i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.89792 | + | 3.28729i | 0.490040 | + | 0.848774i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −2.75624 | + | 4.77395i | −0.668487 | + | 1.15785i | 0.309840 | + | 0.950789i | \(0.399724\pi\) |
−0.978327 | + | 0.207065i | \(0.933609\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.41421 | − | 2.44949i | 0.324443 | − | 0.561951i | −0.656957 | − | 0.753928i | \(-0.728157\pi\) |
0.981399 | + | 0.191977i | \(0.0614899\pi\) | |||||||
\(20\) | −1.34203 | + | 2.32446i | −0.300087 | + | 0.519766i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.89792 | + | 5.01934i | −0.617838 | + | 1.07013i | ||||
\(23\) | −0.897916 | − | 1.55524i | −0.187228 | − | 0.324289i | 0.757097 | − | 0.653303i | \(-0.226617\pi\) |
−0.944325 | + | 0.329014i | \(0.893284\pi\) | |||||||
\(24\) | 2.12132 | + | 3.67423i | 0.433013 | + | 0.750000i | ||||
\(25\) | 2.20417 | 0.440834 | ||||||||
\(26\) | 0.634922 | − | 3.54921i | 0.124519 | − | 0.696057i | ||||
\(27\) | −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 | ||||
\(31\) | −1.41421 | −0.254000 | −0.127000 | − | 0.991903i | \(-0.540535\pi\) | ||||
−0.127000 | + | 0.991903i | \(0.540535\pi\) | |||||||
\(32\) | −2.50000 | + | 4.33013i | −0.441942 | + | 0.765466i | ||||
\(33\) | −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 | ||||
\(37\) | 3.39792 | + | 5.88536i | 0.558614 | + | 0.967548i | 0.997613 | + | 0.0690599i | \(0.0220000\pi\) |
−0.438999 | + | 0.898488i | \(0.644667\pi\) | |||||||
\(38\) | −2.82843 | −0.458831 | ||||||||
\(39\) | 0.897916 | − | 5.01934i | 0.143782 | − | 0.803737i | ||||
\(40\) | 8.05217 | 1.27316 | ||||||||
\(41\) | −4.87756 | − | 8.44819i | −0.761747 | − | 1.31939i | −0.941949 | − | 0.335755i | \(-0.891008\pi\) |
0.180202 | − | 0.983630i | \(-0.442325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.897916 | − | 1.55524i | 0.136931 | − | 0.237171i | −0.789403 | − | 0.613876i | \(-0.789610\pi\) |
0.926333 | + | 0.376705i | \(0.122943\pi\) | |||||||
\(44\) | −5.79583 | −0.873754 | ||||||||
\(45\) | −1.34203 | + | 2.32446i | −0.200058 | + | 0.346510i | ||||
\(46\) | −0.897916 | + | 1.55524i | −0.132390 | + | 0.229307i | ||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0.707107 | − | 1.22474i | 0.102062 | − | 0.176777i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.10208 | − | 1.90887i | −0.155858 | − | 0.269954i | ||||
\(51\) | 7.79583 | 1.09163 | ||||||||
\(52\) | 3.39116 | − | 1.22474i | 0.470270 | − | 0.169842i | ||||
\(53\) | 6.59166 | 0.905435 | 0.452717 | − | 0.891654i | \(-0.350455\pi\) | ||||
0.452717 | + | 0.891654i | \(0.350455\pi\) | |||||||
\(54\) | 2.82843 | + | 4.89898i | 0.384900 | + | 0.666667i | ||||
\(55\) | 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 | ||||
\(59\) | −0.562738 | + | 0.974691i | −0.0732622 | + | 0.126894i | −0.900329 | − | 0.435209i | \(-0.856674\pi\) |
0.827067 | + | 0.562103i | \(0.190008\pi\) | |||||||
\(60\) | 3.79583 | 0.490040 | ||||||||
\(61\) | −0.779291 | + | 1.34977i | −0.0997780 | + | 0.172821i | −0.911593 | − | 0.411095i | \(-0.865147\pi\) |
0.811815 | + | 0.583915i | \(0.198480\pi\) | |||||||
\(62\) | 0.707107 | + | 1.22474i | 0.0898027 | + | 0.155543i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −7.39792 | − | 6.23899i | −0.917599 | − | 0.773852i | ||||
\(66\) | 8.19654 | 1.00892 | ||||||||
\(67\) | −2.89792 | − | 5.01934i | −0.354037 | − | 0.613210i | 0.632916 | − | 0.774221i | \(-0.281858\pi\) |
−0.986953 | + | 0.161011i | \(0.948525\pi\) | |||||||
\(68\) | 2.75624 | + | 4.77395i | 0.334244 | + | 0.578927i | ||||
\(69\) | −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 | ||||
\(73\) | −5.80122 | −0.678982 | −0.339491 | − | 0.940609i | \(-0.610255\pi\) | ||||
−0.339491 | + | 0.940609i | \(0.610255\pi\) | |||||||
\(74\) | 3.39792 | − | 5.88536i | 0.395000 | − | 0.684160i | ||||
\(75\) | −1.55858 | − | 2.69954i | −0.179970 | − | 0.311716i | ||||
\(76\) | −1.41421 | − | 2.44949i | −0.162221 | − | 0.280976i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.79583 | + | 1.73205i | −0.543021 | + | 0.196116i | ||||
\(79\) | −11.7958 | −1.32713 | −0.663567 | − | 0.748117i | \(-0.730958\pi\) | ||||
−0.663567 | + | 0.748117i | \(0.730958\pi\) | |||||||
\(80\) | −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 | \(-0.682827\pi\) | ||||
−0.543305 | + | 0.839535i | \(0.682827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.39792 | − | 12.8136i | 0.802417 | − | 1.38983i | ||||
\(86\) | −1.79583 | −0.193649 | ||||||||
\(87\) | 6.21959 | − | 10.7726i | 0.666810 | − | 1.15495i | ||||
\(88\) | 8.69375 | + | 15.0580i | 0.926757 | + | 1.60519i | ||||
\(89\) | −6.07522 | − | 10.5226i | −0.643972 | − | 1.11539i | −0.984538 | − | 0.175172i | \(-0.943952\pi\) |
0.340565 | − | 0.940221i | \(-0.389382\pi\) | |||||||
\(90\) | 2.68406 | 0.282925 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.79583 | −0.187228 | ||||||||
\(93\) | 1.00000 | + | 1.73205i | 0.103695 | + | 0.179605i | ||||
\(94\) | −1.41421 | − | 2.44949i | −0.145865 | − | 0.252646i | ||||
\(95\) | −3.79583 | + | 6.57457i | −0.389444 | + | 0.674537i | ||||
\(96\) | 7.07107 | 0.721688 | ||||||||
\(97\) | 2.12132 | − | 3.67423i | 0.215387 | − | 0.373062i | −0.738005 | − | 0.674795i | \(-0.764232\pi\) |
0.953392 | + | 0.301733i | \(0.0975652\pi\) | |||||||
\(98\) | 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 | \(-0.119415\pi\) |
−0.782550 | + | 0.622588i | \(0.786081\pi\) | |||||||
\(102\) | −3.89792 | − | 6.75139i | −0.385951 | − | 0.668487i | ||||
\(103\) | −8.19654 | −0.807629 | −0.403815 | − | 0.914841i | \(-0.632316\pi\) | ||||
−0.403815 | + | 0.914841i | \(0.632316\pi\) | |||||||
\(104\) | −8.26873 | − | 6.97339i | −0.810815 | − | 0.683797i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.29583 | − | 5.70855i | −0.320119 | − | 0.554463i | ||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | −2.82843 | + | 4.89898i | −0.272166 | + | 0.471405i | ||||
\(109\) | −17.5917 | −1.68498 | −0.842488 | − | 0.538715i | \(-0.818910\pi\) | ||||
−0.842488 | + | 0.538715i | \(0.818910\pi\) | |||||||
\(110\) | 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 | \(-0.118321\pi\) | |||||||
\(114\) | 2.00000 | + | 3.46410i | 0.187317 | + | 0.324443i | ||||
\(115\) | 2.41006 | + | 4.17434i | 0.224739 | + | 0.389260i | ||||
\(116\) | 8.79583 | 0.816672 | ||||||||
\(117\) | 3.39116 | − | 1.22474i | 0.313513 | − | 0.113228i | ||||
\(118\) | 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 | ||||
\(122\) | 1.55858 | 0.141107 | ||||||||
\(123\) | −6.89792 | + | 11.9475i | −0.621964 | + | 1.07727i | ||||
\(124\) | −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 | \(0.942687\pi\) | |||||||
\(128\) | 1.50000 | + | 2.59808i | 0.132583 | + | 0.229640i | ||||
\(129\) | −2.53969 | −0.223607 | ||||||||
\(130\) | −1.70417 | + | 9.52628i | −0.149465 | + | 0.835510i | ||||
\(131\) | −8.19654 | −0.716135 | −0.358068 | − | 0.933696i | \(-0.616564\pi\) | ||||
−0.358068 | + | 0.933696i | \(0.616564\pi\) | |||||||
\(132\) | 4.09827 | + | 7.09841i | 0.356709 | + | 0.617838i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.89792 | + | 5.01934i | −0.250342 | + | 0.433605i | ||||
\(135\) | 15.1833 | 1.30677 | ||||||||
\(136\) | 8.26873 | − | 14.3219i | 0.709038 | − | 1.22809i | ||||
\(137\) | 4.60208 | − | 7.97104i | 0.393183 | − | 0.681012i | −0.599685 | − | 0.800236i | \(-0.704707\pi\) |
0.992867 | + | 0.119224i | \(0.0380407\pi\) | |||||||
\(138\) | 2.53969 | 0.216193 | ||||||||
\(139\) | 7.63381 | − | 13.2221i | 0.647491 | − | 1.12149i | −0.336229 | − | 0.941780i | \(-0.609152\pi\) |
0.983720 | − | 0.179707i | \(-0.0575150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | − | 3.46410i | −0.168430 | − | 0.291730i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 3.67990 | − | 20.5706i | 0.307729 | − | 1.72020i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −11.8043 | − | 20.4456i | −0.980291 | − | 1.69791i | ||||
\(146\) | 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 | −0.944611 | − | 0.328193i | \(-0.893560\pi\) |
0.756529 | + | 0.653960i | \(0.226894\pi\) | |||||||
\(150\) | −1.55858 | + | 2.69954i | −0.127258 | + | 0.220417i | ||||
\(151\) | −17.5917 | −1.43159 | −0.715795 | − | 0.698311i | \(-0.753935\pi\) | ||||
−0.715795 | + | 0.698311i | \(0.753935\pi\) | |||||||
\(152\) | −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 | ||||||||
\(156\) | −3.89792 | − | 3.28729i | −0.312083 | − | 0.263194i | ||||
\(157\) | −6.92670 | −0.552811 | −0.276405 | − | 0.961041i | \(-0.589143\pi\) | ||||
−0.276405 | + | 0.961041i | \(0.589143\pi\) | |||||||
\(158\) | 5.89792 | + | 10.2155i | 0.469213 | + | 0.812701i | ||||
\(159\) | −4.66101 | − | 8.07311i | −0.369642 | − | 0.640239i | ||||
\(160\) | 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 | −0.475305 | − | 0.879821i | \(-0.657662\pi\) |
0.999600 | − | 0.0282841i | \(-0.00900432\pi\) | |||||||
\(164\) | −9.75513 | −0.761747 | ||||||||
\(165\) | 11.0000 | − | 19.0526i | 0.856349 | − | 1.48324i | ||||
\(166\) | 4.94975 | + | 8.57321i | 0.384175 | + | 0.665410i | ||||
\(167\) | −7.63381 | − | 13.2221i | −0.590722 | − | 1.02316i | −0.994135 | − | 0.108142i | \(-0.965510\pi\) |
0.403414 | − | 0.915018i | \(-0.367824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.19375 | + | 12.8136i | 0.168750 | + | 0.985659i | ||||
\(170\) | −14.7958 | −1.13479 | ||||||||
\(171\) | −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 | \(-0.948638\pi\) |
0.632640 | + | 0.774446i | \(0.281971\pi\) | |||||||
\(174\) | −12.4392 | −0.943012 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.89792 | − | 5.01934i | 0.218439 | − | 0.378347i | ||||
\(177\) | 1.59166 | 0.119637 | ||||||||
\(178\) | −6.07522 | + | 10.5226i | −0.455357 | + | 0.788702i | ||||
\(179\) | 0.204168 | + | 0.353630i | 0.0152603 | + | 0.0264316i | 0.873555 | − | 0.486726i | \(-0.161809\pi\) |
−0.858294 | + | 0.513158i | \(0.828476\pi\) | |||||||
\(180\) | 1.34203 | + | 2.32446i | 0.100029 | + | 0.173255i | ||||
\(181\) | −16.5375 | −1.22922 | −0.614610 | − | 0.788831i | \(-0.710686\pi\) | ||||
−0.614610 | + | 0.788831i | \(0.710686\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.20417 | 0.162937 | ||||||||
\(184\) | 2.69375 | + | 4.66571i | 0.198586 | + | 0.343960i | ||||
\(185\) | −9.12020 | − | 15.7967i | −0.670531 | − | 1.16139i | ||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 31.9494 | 2.33637 | ||||||||
\(188\) | 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 | 0.155553 | − | 0.987827i | \(-0.450284\pi\) |
0.777707 | − | 0.628627i | \(-0.216383\pi\) | |||||||
\(192\) | −4.94975 | − | 8.57321i | −0.357217 | − | 0.618718i | ||||
\(193\) | −1.70417 | − | 2.95171i | −0.122669 | − | 0.212468i | 0.798151 | − | 0.602458i | \(-0.205812\pi\) |
−0.920819 | + | 0.389990i | \(0.872479\pi\) | |||||||
\(194\) | −4.24264 | −0.304604 | ||||||||
\(195\) | −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 | \(0.741344\pi\) | |||||||
\(198\) | 2.89792 | + | 5.01934i | 0.205946 | + | 0.356709i | ||||
\(199\) | 11.0250 | − | 19.0958i | 0.781539 | − | 1.35367i | −0.149505 | − | 0.988761i | \(-0.547768\pi\) |
0.931045 | − | 0.364905i | \(-0.118899\pi\) | |||||||
\(200\) | −6.61251 | −0.467575 | ||||||||
\(201\) | −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 | ||||
\(205\) | 13.0917 | + | 22.6754i | 0.914361 | + | 1.58372i | ||||
\(206\) | 4.09827 | + | 7.09841i | 0.285540 | + | 0.494570i | ||||
\(207\) | −1.79583 | −0.124819 | ||||||||
\(208\) | −0.634922 | + | 3.54921i | −0.0440239 | + | 0.246093i | ||||
\(209\) | −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 | ||||
\(213\) | 8.48528 | 0.581402 | ||||||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | −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 | ||||
\(219\) | 4.10208 | + | 7.10502i | 0.277193 | + | 0.480113i | ||||
\(220\) | 15.5563 | 1.04881 | ||||||||
\(221\) | −18.6937 | + | 6.75139i | −1.25748 | + | 0.454148i | ||||
\(222\) | −9.61076 | −0.645032 | ||||||||
\(223\) | 2.82843 | + | 4.89898i | 0.189405 | + | 0.328060i | 0.945052 | − | 0.326920i | \(-0.106011\pi\) |
−0.755647 | + | 0.654979i | \(0.772677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.10208 | − | 1.90887i | 0.0734723 | − | 0.127258i | ||||
\(226\) | −16.5917 | −1.10366 | ||||||||
\(227\) | −10.4622 | + | 18.1211i | −0.694403 | + | 1.20274i | 0.275979 | + | 0.961164i | \(0.410998\pi\) |
−0.970382 | + | 0.241577i | \(0.922335\pi\) | |||||||
\(228\) | −2.00000 | + | 3.46410i | −0.132453 | + | 0.229416i | ||||
\(229\) | 12.7279 | 0.841085 | 0.420542 | − | 0.907273i | \(-0.361840\pi\) | ||||
0.420542 | + | 0.907273i | \(0.361840\pi\) | |||||||
\(230\) | 2.41006 | − | 4.17434i | 0.158915 | − | 0.275248i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.1937 | − | 22.8522i | −0.866212 | − | 1.50032i | ||||
\(233\) | −21.1833 | −1.38777 | −0.693883 | − | 0.720088i | \(-0.744101\pi\) | ||||
−0.693883 | + | 0.720088i | \(0.744101\pi\) | |||||||
\(234\) | −2.75624 | − | 2.32446i | −0.180181 | − | 0.151955i | ||||
\(235\) | −7.59166 | −0.495225 | ||||||||
\(236\) | 0.562738 | + | 0.974691i | 0.0366311 | + | 0.0634470i | ||||
\(237\) | 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 | ||||
\(241\) | −2.19350 | + | 3.79926i | −0.141296 | + | 0.244732i | −0.927985 | − | 0.372618i | \(-0.878460\pi\) |
0.786689 | + | 0.617350i | \(0.211794\pi\) | |||||||
\(242\) | 22.5917 | 1.45225 | ||||||||
\(243\) | −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 | ||||||||
\(247\) | 9.59166 | − | 3.46410i | 0.610303 | − | 0.220416i | ||||
\(248\) | 4.24264 | 0.269408 | ||||||||
\(249\) | 7.00000 | + | 12.1244i | 0.443607 | + | 0.768350i | ||||
\(250\) | −3.75209 | − | 6.49881i | −0.237303 | − | 0.411021i | ||||
\(251\) | 1.55858 | − | 2.69954i | 0.0983769 | − | 0.170394i | −0.812636 | − | 0.582771i | \(-0.801968\pi\) |
0.911013 | + | 0.412378i | \(0.135302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.20417 | + | 9.01388i | −0.327183 | + | 0.566698i | ||||
\(254\) | −3.79583 | + | 6.57457i | −0.238172 | + | 0.412525i | ||||
\(255\) | −20.9245 | −1.31034 | ||||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | −7.70599 | − | 13.3472i | −0.480686 | − | 0.832573i | 0.519068 | − | 0.854733i | \(-0.326279\pi\) |
−0.999754 | + | 0.0221596i | \(0.992946\pi\) | |||||||
\(258\) | 1.26984 | + | 2.19944i | 0.0790571 | + | 0.136931i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.10208 | + | 3.28729i | −0.564487 | + | 0.203869i | ||||
\(261\) | 8.79583 | 0.544448 | ||||||||
\(262\) | 4.09827 | + | 7.09841i | 0.253192 | + | 0.438542i | ||||
\(263\) | 12.6937 | + | 21.9862i | 0.782730 | + | 1.35573i | 0.930346 | + | 0.366683i | \(0.119507\pi\) |
−0.147616 | + | 0.989045i | \(0.547160\pi\) | |||||||
\(264\) | 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 | ||||
\(268\) | −5.79583 | −0.354037 | ||||||||
\(269\) | 0.562738 | − | 0.974691i | 0.0343107 | − | 0.0594279i | −0.848360 | − | 0.529420i | \(-0.822410\pi\) |
0.882671 | + | 0.469992i | \(0.155743\pi\) | |||||||
\(270\) | −7.59166 | − | 13.1491i | −0.462014 | − | 0.800232i | ||||
\(271\) | 11.5877 | + | 20.0705i | 0.703903 | + | 1.21920i | 0.967086 | + | 0.254450i | \(0.0818944\pi\) |
−0.263183 | + | 0.964746i | \(0.584772\pi\) | |||||||
\(272\) | −5.51249 | −0.334244 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.20417 | −0.556044 | ||||||||
\(275\) | −6.38749 | − | 11.0635i | −0.385180 | − | 0.667152i | ||||
\(276\) | 1.26984 | + | 2.19944i | 0.0764357 | + | 0.132390i | ||||
\(277\) | 3.09166 | − | 5.35492i | 0.185760 | − | 0.321746i | −0.758072 | − | 0.652170i | \(-0.773859\pi\) |
0.943832 | + | 0.330425i | \(0.107192\pi\) | |||||||
\(278\) | −15.2676 | −0.915690 | ||||||||
\(279\) | −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 | 0.857704 | + | 0.514145i | \(0.171891\pi\) |
0.0164104 | + | 0.999865i | \(0.494776\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | 10.7362 | 0.635960 | ||||||||
\(286\) | −19.6546 | + | 7.09841i | −1.16220 | + | 0.419738i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.50000 | + | 4.33013i | 0.147314 | + | 0.255155i | ||||
\(289\) | −6.69375 | − | 11.5939i | −0.393750 | − | 0.681995i | ||||
\(290\) | −11.8043 | + | 20.4456i | −0.693170 | + | 1.20061i | ||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | −2.90061 | + | 5.02401i | −0.169745 | + | 0.294008i | ||||
\(293\) | 4.87756 | − | 8.44819i | 0.284950 | − | 0.493548i | −0.687647 | − | 0.726045i | \(-0.741356\pi\) |
0.972597 | + | 0.232497i | \(0.0746896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51042 | − | 2.61613i | 0.0879401 | − | 0.152317i | ||||
\(296\) | −10.1937 | − | 17.6561i | −0.592500 | − | 1.02624i | ||||
\(297\) | 16.3931 | + | 28.3937i | 0.951223 | + | 1.64757i | ||||
\(298\) | 4.59166 | 0.265988 | ||||||||
\(299\) | 1.14021 | − | 6.37378i | 0.0659403 | − | 0.368605i | ||||
\(300\) | −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 | ||||
\(304\) | 2.82843 | 0.162221 | ||||||||
\(305\) | 2.09166 | − | 3.62287i | 0.119768 | − | 0.207445i | ||||
\(306\) | 2.75624 | − | 4.77395i | 0.157564 | − | 0.272909i | ||||
\(307\) | 34.2004 | 1.95192 | 0.975960 | − | 0.217951i | \(-0.0699374\pi\) | ||||
0.975960 | + | 0.217951i | \(0.0699374\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.79583 | + | 10.0387i | 0.329713 | + | 0.571080i | ||||
\(310\) | −1.89792 | − | 3.28729i | −0.107794 | − | 0.186705i | ||||
\(311\) | 11.8617 | 0.672616 | 0.336308 | − | 0.941752i | \(-0.390822\pi\) | ||||
0.336308 | + | 0.941752i | \(0.390822\pi\) | |||||||
\(312\) | −2.69375 | + | 15.0580i | −0.152503 | + | 0.852492i | ||||
\(313\) | 1.70295 | 0.0962565 | 0.0481283 | − | 0.998841i | \(-0.484674\pi\) | ||||
0.0481283 | + | 0.998841i | \(0.484674\pi\) | |||||||
\(314\) | 3.46335 | + | 5.99870i | 0.195448 | + | 0.338526i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.89792 | + | 10.2155i | −0.331784 | + | 0.574666i | ||||
\(317\) | −12.5917 | −0.707218 | −0.353609 | − | 0.935393i | \(-0.615046\pi\) | ||||
−0.353609 | + | 0.935393i | \(0.615046\pi\) | |||||||
\(318\) | −4.66101 | + | 8.07311i | −0.261376 | + | 0.452717i | ||||
\(319\) | 25.4896 | − | 44.1492i | 1.42714 | − | 2.47188i | ||||
\(320\) | −18.7884 | −1.05030 | ||||||||
\(321\) | 4.24264 | − | 7.34847i | 0.236801 | − | 0.410152i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.79583 | + | 13.5028i | 0.433772 | + | 0.751315i | ||||
\(324\) | 5.00000 | 0.277778 | ||||||||
\(325\) | 6.07522 | + | 5.12351i | 0.336993 | + | 0.284201i | ||||
\(326\) | −13.3875 | −0.741465 | ||||||||
\(327\) | 12.4392 | + | 21.5453i | 0.687888 | + | 1.19146i | ||||
\(328\) | 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 | −0.874319 | − | 0.485351i | \(-0.838692\pi\) |
0.857486 | + | 0.514507i | \(0.172025\pi\) | |||||||
\(332\) | −4.94975 | + | 8.57321i | −0.271653 | + | 0.470516i | ||||
\(333\) | 6.79583 | 0.372409 | ||||||||
\(334\) | −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 | \(0.804108\pi\) | |||||||
\(338\) | 10.0000 | − | 8.30662i | 0.543928 | − | 0.451821i | ||||
\(339\) | −23.4642 | −1.27440 | ||||||||
\(340\) | −7.39792 | − | 12.8136i | −0.401208 | − | 0.694913i | ||||
\(341\) | 4.09827 | + | 7.09841i | 0.221934 | + | 0.384401i | ||||
\(342\) | −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 | ||||
\(346\) | 9.32202 | 0.501155 | ||||||||
\(347\) | −7.48958 | + | 12.9723i | −0.402062 | + | 0.696391i | −0.993975 | − | 0.109611i | \(-0.965040\pi\) |
0.591913 | + | 0.806002i | \(0.298373\pi\) | |||||||
\(348\) | −6.21959 | − | 10.7726i | −0.333405 | − | 0.577475i | ||||
\(349\) | −6.50833 | − | 11.2728i | −0.348383 | − | 0.603417i | 0.637579 | − | 0.770385i | \(-0.279936\pi\) |
−0.985962 | + | 0.166968i | \(0.946602\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.5917 | − | 13.1491i | −0.832221 | − | 0.701849i | ||||
\(352\) | 28.9792 | 1.54459 | ||||||||
\(353\) | 7.56162 | + | 13.0971i | 0.402464 | + | 0.697089i | 0.994023 | − | 0.109173i | \(-0.0348204\pi\) |
−0.591558 | + | 0.806262i | \(0.701487\pi\) | |||||||
\(354\) | −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 | ||||
\(359\) | −4.00000 | −0.211112 | −0.105556 | − | 0.994413i | \(-0.533662\pi\) | ||||
−0.105556 | + | 0.994413i | \(0.533662\pi\) | |||||||
\(360\) | 4.02609 | − | 6.97339i | 0.212193 | − | 0.367530i | ||||
\(361\) | 5.50000 | + | 9.52628i | 0.289474 | + | 0.501383i | ||||
\(362\) | 8.26873 | + | 14.3219i | 0.434595 | + | 0.752740i | ||||
\(363\) | 31.9494 | 1.67691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5708 | 0.815014 | ||||||||
\(366\) | −1.10208 | − | 1.90887i | −0.0576069 | − | 0.0997780i | ||||
\(367\) | −10.6066 | − | 18.3712i | −0.553660 | − | 0.958967i | −0.998006 | − | 0.0631123i | \(-0.979897\pi\) |
0.444346 | − | 0.895855i | \(-0.353436\pi\) | |||||||
\(368\) | 0.897916 | − | 1.55524i | 0.0468071 | − | 0.0810723i | ||||
\(369\) | −9.75513 | −0.507832 | ||||||||
\(370\) | −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 | −0.655726 | − | 0.754999i | \(-0.727637\pi\) |
0.981711 | + | 0.190375i | \(0.0609705\pi\) | |||||||
\(374\) | −15.9747 | − | 27.6690i | −0.826033 | − | 1.43073i | ||||
\(375\) | −5.30625 | − | 9.19070i | −0.274014 | − | 0.474606i | ||||
\(376\) | −8.48528 | −0.437595 | ||||||||
\(377\) | −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 | \(0.805605\pi\) | |||||||
\(380\) | 3.79583 | + | 6.57457i | 0.194722 | + | 0.337268i | ||||
\(381\) | −5.36812 | + | 9.29785i | −0.275017 | + | 0.476343i | ||||
\(382\) | −25.7958 | −1.31983 | ||||||||
\(383\) | 7.48944 | − | 12.9721i | 0.382692 | − | 0.662843i | −0.608754 | − | 0.793359i | \(-0.708330\pi\) |
0.991446 | + | 0.130517i | \(0.0416636\pi\) | |||||||
\(384\) | 2.12132 | − | 3.67423i | 0.108253 | − | 0.187500i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.70417 | + | 2.95171i | −0.0867399 | + | 0.150238i | ||||
\(387\) | −0.897916 | − | 1.55524i | −0.0456436 | − | 0.0790571i | ||||
\(388\) | −2.12132 | − | 3.67423i | −0.107694 | − | 0.186531i | ||||
\(389\) | 28.3875 | 1.43930 | 0.719652 | − | 0.694335i | \(-0.244302\pi\) | ||||
0.719652 | + | 0.694335i | \(0.244302\pi\) | |||||||
\(390\) | 12.8723 | − | 4.64893i | 0.651814 | − | 0.235407i | ||||
\(391\) | 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 | ||||
\(395\) | 31.6607 | 1.59302 | ||||||||
\(396\) | −2.89792 | + | 5.01934i | −0.145626 | + | 0.252231i | ||||
\(397\) | −3.53553 | + | 6.12372i | −0.177443 | + | 0.307341i | −0.941004 | − | 0.338395i | \(-0.890116\pi\) |
0.763561 | + | 0.645736i | \(0.223449\pi\) | |||||||
\(398\) | −22.0499 | −1.10526 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.10208 | + | 1.90887i | 0.0551042 | + | 0.0954433i | ||||
\(401\) | −12.1937 | − | 21.1202i | −0.608927 | − | 1.05469i | −0.991418 | − | 0.130733i | \(-0.958267\pi\) |
0.382491 | − | 0.923959i | \(-0.375066\pi\) | |||||||
\(402\) | 8.19654 | 0.408806 | ||||||||
\(403\) | −3.89792 | − | 3.28729i | −0.194169 | − | 0.163751i | ||||
\(404\) | 2.97280 | 0.147902 | ||||||||
\(405\) | −6.71015 | − | 11.6223i | −0.333430 | − | 0.577517i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.6937 | − | 34.1106i | 0.976183 | − | 1.69080i | ||||
\(408\) | −23.3875 | −1.15785 | ||||||||
\(409\) | 14.3440 | − | 24.8445i | 0.709263 | − | 1.22848i | −0.255868 | − | 0.966712i | \(-0.582361\pi\) |
0.965131 | − | 0.261767i | \(-0.0843053\pi\) | |||||||
\(410\) | 13.0917 | − | 22.6754i | 0.646551 | − | 1.11986i | ||||
\(411\) | −13.0167 | −0.642064 | ||||||||
\(412\) | −4.09827 | + | 7.09841i | −0.201907 | + | 0.349714i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.897916 | + | 1.55524i | 0.0441302 | + | 0.0764357i | ||||
\(415\) | 26.5708 | 1.30431 | ||||||||
\(416\) | −16.9558 | + | 6.12372i | −0.831328 | + | 0.300240i | ||||
\(417\) | −21.5917 | −1.05735 | ||||||||
\(418\) | 8.19654 | + | 14.1968i | 0.400906 | + | 0.694390i | ||||
\(419\) | −14.2718 | − | 24.7194i | −0.697221 | − | 1.20762i | −0.969426 | − | 0.245384i | \(-0.921086\pi\) |
0.272205 | − | 0.962239i | \(-0.412247\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | 1.41421 | − | 2.44949i | 0.0687614 | − | 0.119098i | ||||
\(424\) | −19.7750 | −0.960358 | ||||||||
\(425\) | −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 | ||||||||
\(429\) | −27.7958 | + | 10.0387i | −1.34200 | + | 0.484672i | ||||
\(430\) | 4.82012 | 0.232447 | ||||||||
\(431\) | 2.59166 | + | 4.48889i | 0.124836 | + | 0.216222i | 0.921669 | − | 0.387978i | \(-0.126826\pi\) |
−0.796833 | + | 0.604200i | \(0.793493\pi\) | |||||||
\(432\) | −2.82843 | − | 4.89898i | −0.136083 | − | 0.235702i | ||||
\(433\) | −6.71015 | + | 11.6223i | −0.322469 | + | 0.558533i | −0.980997 | − | 0.194024i | \(-0.937846\pi\) |
0.658528 | + | 0.752556i | \(0.271179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.6937 | + | 28.9144i | −0.800404 | + | 1.38634i | ||||
\(436\) | −8.79583 | + | 15.2348i | −0.421244 | + | 0.729616i | ||||
\(437\) | −5.07938 | −0.242980 | ||||||||
\(438\) | 4.10208 | − | 7.10502i | 0.196005 | − | 0.339491i | ||||
\(439\) | −17.1002 | − | 29.6184i | −0.816148 | − | 1.41361i | −0.908501 | − | 0.417883i | \(-0.862772\pi\) |
0.0923531 | − | 0.995726i | \(-0.470561\pi\) | |||||||
\(440\) | −23.3345 | − | 40.4166i | −1.11243 | − | 1.92678i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.1937 | + | 12.8136i | 0.722693 | + | 0.609479i | ||||
\(443\) | 10.0000 | 0.475114 | 0.237557 | − | 0.971374i | \(-0.423653\pi\) | ||||
0.237557 | + | 0.971374i | \(0.423653\pi\) | |||||||
\(444\) | −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 | \(0.199838\pi\) | |||||||
\(450\) | −2.20417 | −0.103905 | ||||||||
\(451\) | −28.2695 | + | 48.9643i | −1.33116 | + | 2.30564i | ||||
\(452\) | −8.29583 | − | 14.3688i | −0.390203 | − | 0.675852i | ||||
\(453\) | 12.4392 | + | 21.5453i | 0.584444 | + | 1.01229i | ||||
\(454\) | 20.9245 | 0.982034 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.0000 | 0.561951 | ||||||||
\(457\) | 7.29583 | + | 12.6368i | 0.341285 | + | 0.591122i | 0.984672 | − | 0.174419i | \(-0.0558047\pi\) |
−0.643387 | + | 0.765541i | \(0.722471\pi\) | |||||||
\(458\) | −6.36396 | − | 11.0227i | −0.297368 | − | 0.515057i | ||||
\(459\) | 15.5917 | − | 27.0056i | 0.727757 | − | 1.26051i | ||||
\(460\) | 4.82012 | 0.224739 | ||||||||
\(461\) | −15.4842 | + | 26.8194i | −0.721169 | + | 1.24910i | 0.239362 | + | 0.970930i | \(0.423062\pi\) |
−0.960531 | + | 0.278172i | \(0.910272\pi\) | |||||||
\(462\) | 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 | ||||
\(467\) | −4.82012 | −0.223048 | −0.111524 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111524 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(468\) | 0.634922 | − | 3.54921i | 0.0293493 | − | 0.164062i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.79583 | + | 6.57457i | 0.175089 | + | 0.303262i | ||||
\(471\) | 4.89792 | + | 8.48344i | 0.225684 | + | 0.390896i | ||||
\(472\) | 1.68821 | − | 2.92407i | 0.0777063 | − | 0.134591i | ||||
\(473\) | −10.4083 | −0.478576 | ||||||||
\(474\) | 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 | ||||
\(478\) | 9.89792 | + | 17.1437i | 0.452720 | + | 0.784134i | ||||
\(479\) | 3.67990 | + | 6.37378i | 0.168139 | + | 0.291225i | 0.937766 | − | 0.347269i | \(-0.112891\pi\) |
−0.769627 | + | 0.638494i | \(0.779558\pi\) | |||||||
\(480\) | −18.9792 | −0.866276 | ||||||||
\(481\) | −4.31483 | + | 24.1198i | −0.196739 | + | 1.09977i | ||||
\(482\) | 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 | ||||
\(486\) | 9.89949 | 0.449050 | ||||||||
\(487\) | −9.79583 | + | 16.9669i | −0.443891 | + | 0.768843i | −0.997974 | − | 0.0636190i | \(-0.979736\pi\) |
0.554083 | + | 0.832462i | \(0.313069\pi\) | |||||||
\(488\) | 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 | \(0.763891\pi\) | |||||||
\(492\) | 6.89792 | + | 11.9475i | 0.310982 | + | 0.538637i | ||||
\(493\) | −48.4869 | −2.18374 | ||||||||
\(494\) | −7.79583 | − | 6.57457i | −0.350751 | − | 0.295804i | ||||
\(495\) | 15.5563 | 0.699206 | ||||||||
\(496\) | −0.707107 | − | 1.22474i | −0.0317500 | − | 0.0549927i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.00000 | − | 12.1244i | 0.313678 | − | 0.543305i | ||||
\(499\) | 16.2042 | 0.725398 | 0.362699 | − | 0.931906i | \(-0.381855\pi\) | ||||
0.362699 | + | 0.931906i | \(0.381855\pi\) | |||||||
\(500\) | 3.75209 | − | 6.49881i | 0.167798 | − | 0.290635i | ||||
\(501\) | −10.7958 | + | 18.6989i | −0.482322 | + | 0.835407i | ||||
\(502\) | −3.11716 | −0.139126 | ||||||||
\(503\) | 14.2718 | − | 24.7194i | 0.636347 | − | 1.10218i | −0.349881 | − | 0.936794i | \(-0.613778\pi\) |
0.986228 | − | 0.165391i | \(-0.0528885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.98958 | − | 6.91015i | −0.177534 | − | 0.307498i | ||||
\(506\) | 10.4083 | 0.462707 | ||||||||
\(507\) | 14.1421 | − | 11.7473i | 0.628074 | − | 0.521718i | ||||
\(508\) | −7.59166 | −0.336826 | ||||||||
\(509\) | −13.2185 | − | 22.8951i | −0.585899 | − | 1.01481i | −0.994763 | − | 0.102211i | \(-0.967408\pi\) |
0.408864 | − | 0.912595i | \(-0.365925\pi\) | |||||||
\(510\) | 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 | ||||
\(514\) | −7.70599 | + | 13.3472i | −0.339897 | + | 0.588718i | ||||
\(515\) | 22.0000 | 0.969436 | ||||||||
\(516\) | −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 | ||||||||
\(520\) | 22.1937 | + | 18.7170i | 0.973260 | + | 0.820794i | ||||
\(521\) | 25.0227 | 1.09627 | 0.548133 | − | 0.836391i | \(-0.315339\pi\) | ||||
0.548133 | + | 0.836391i | \(0.315339\pi\) | |||||||
\(522\) | −4.39792 | − | 7.61741i | −0.192492 | − | 0.333405i | ||||
\(523\) | −14.2865 | − | 24.7450i | −0.624705 | − | 1.08202i | −0.988598 | − | 0.150580i | \(-0.951886\pi\) |
0.363893 | − | 0.931441i | \(-0.381448\pi\) | |||||||
\(524\) | −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 | ||||
\(528\) | −8.19654 | −0.356709 | ||||||||
\(529\) | 9.88749 | − | 17.1256i | 0.429891 | − | 0.744593i | ||||
\(530\) | 8.84620 | + | 15.3221i | 0.384255 | + | 0.665548i | ||||
\(531\) | 0.562738 | + | 0.974691i | 0.0244207 | + | 0.0422980i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.19375 | − | 34.6230i | 0.268281 | − | 1.49969i | ||||
\(534\) | 17.1833 | 0.743595 | ||||||||
\(535\) | −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 | ||||
\(541\) | −12.5917 | −0.541358 | −0.270679 | − | 0.962670i | \(-0.587248\pi\) | ||||
−0.270679 | + | 0.962670i | \(0.587248\pi\) | |||||||
\(542\) | 11.5877 | − | 20.0705i | 0.497735 | − | 0.862102i | ||||
\(543\) | 11.6937 | + | 20.2542i | 0.501827 | + | 0.869189i | ||||
\(544\) | −13.7812 | − | 23.8698i | −0.590865 | − | 1.02341i | ||||
\(545\) | 47.2170 | 2.02256 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9792 | −1.58111 | −0.790557 | − | 0.612388i | \(-0.790209\pi\) | ||||
−0.790557 | + | 0.612388i | \(0.790209\pi\) | |||||||
\(548\) | −4.60208 | − | 7.97104i | −0.196591 | − | 0.340506i | ||||
\(549\) | 0.779291 | + | 1.34977i | 0.0332593 | + | 0.0576069i | ||||
\(550\) | −6.38749 | + | 11.0635i | −0.272364 | + | 0.471748i | ||||
\(551\) | 24.8784 | 1.05985 | ||||||||
\(552\) | 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 | 0.561148 | − | 0.827715i | \(-0.310360\pi\) |
−0.997397 | + | 0.0721110i | \(0.977026\pi\) | |||||||
\(558\) | 1.41421 | 0.0598684 | ||||||||
\(559\) | 6.08996 | − | 2.19944i | 0.257578 | − | 0.0930262i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5917 | − | 39.1299i | −0.953821 | − | 1.65207i | ||||
\(562\) | −7.60208 | − | 13.1672i | −0.320675 | − | 0.555425i | ||||
\(563\) | 0.562738 | − | 0.974691i | 0.0237166 | − | 0.0410783i | −0.853924 | − | 0.520399i | \(-0.825783\pi\) |
0.877640 | + | 0.479320i | \(0.159117\pi\) | |||||||
\(564\) | −4.00000 | −0.168430 | ||||||||
\(565\) | −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 | ||||
\(569\) | −3.20417 | − | 5.54978i | −0.134326 | − | 0.232659i | 0.791014 | − | 0.611798i | \(-0.209554\pi\) |
−0.925340 | + | 0.379139i | \(0.876220\pi\) | |||||||
\(570\) | −5.36812 | − | 9.29785i | −0.224846 | − | 0.389444i | ||||
\(571\) | 15.1833 | 0.635402 | 0.317701 | − | 0.948191i | \(-0.397089\pi\) | ||||
0.317701 | + | 0.948191i | \(0.397089\pi\) | |||||||
\(572\) | −15.9747 | − | 13.4722i | −0.667937 | − | 0.563301i | ||||
\(573\) | −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 | ||||
\(577\) | −9.17765 | −0.382071 | −0.191035 | − | 0.981583i | \(-0.561184\pi\) | ||||
−0.191035 | + | 0.981583i | \(0.561184\pi\) | |||||||
\(578\) | −6.69375 | + | 11.5939i | −0.278423 | + | 0.482243i | ||||
\(579\) | −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 | ||||
\(583\) | −19.1021 | − | 33.0858i | −0.791127 | − | 1.37027i | ||||
\(584\) | 17.4037 | 0.720169 | ||||||||
\(585\) | −9.10208 | + | 3.28729i | −0.376325 | + | 0.135913i | ||||
\(586\) | −9.75513 | −0.402981 | ||||||||
\(587\) | −1.55858 | − | 2.69954i | −0.0643296 | − | 0.111422i | 0.832067 | − | 0.554675i | \(-0.187158\pi\) |
−0.896396 | + | 0.443253i | \(0.853824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | −3.02084 | −0.124366 | ||||||||
\(591\) | 5.65685 | − | 9.79796i | 0.232692 | − | 0.403034i | ||||
\(592\) | −3.39792 | + | 5.88536i | −0.139653 | + | 0.241887i | ||||
\(593\) | −1.55858 | −0.0640033 | −0.0320017 | − | 0.999488i | \(-0.510188\pi\) | ||||
−0.0320017 | + | 0.999488i | \(0.510188\pi\) | |||||||
\(594\) | 16.3931 | − | 28.3937i | 0.672617 | − | 1.16501i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.29583 | + | 3.97650i | 0.0940409 | + | 0.162884i | ||||
\(597\) | −31.1833 | −1.27625 | ||||||||
\(598\) | −6.08996 | + | 2.19944i | −0.249037 | + | 0.0899416i | ||||
\(599\) | −14.4083 | −0.588709 | −0.294354 | − | 0.955696i | \(-0.595105\pi\) | ||||
−0.294354 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(600\) | 4.67575 | + | 8.09863i | 0.190887 | + | 0.330625i | ||||
\(601\) | 15.4842 | + | 26.8194i | 0.631612 | + | 1.09398i | 0.987222 | + | 0.159350i | \(0.0509398\pi\) |
−0.355610 | + | 0.934634i | \(0.615727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.79583 | −0.236025 | ||||||||
\(604\) | −8.79583 | + | 15.2348i | −0.357897 | + | 0.619896i | ||||
\(605\) | 30.3187 | − | 52.5135i | 1.23263 | − | 2.13498i | ||||
\(606\) | −4.20417 | −0.170783 | ||||||||
\(607\) | 17.9517 | − | 31.0932i | 0.728636 | − | 1.26203i | −0.228824 | − | 0.973468i | \(-0.573488\pi\) |
0.957460 | − | 0.288566i | \(-0.0931786\pi\) | |||||||
\(608\) | 7.07107 | + | 12.2474i | 0.286770 | + | 0.496700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.18333 | −0.169378 | ||||||||
\(611\) | 7.79583 | + | 6.57457i | 0.315386 | + | 0.265979i | ||||
\(612\) | 5.51249 | 0.222829 | ||||||||
\(613\) | 2.98958 | + | 5.17810i | 0.120748 | + | 0.209142i | 0.920063 | − | 0.391771i | \(-0.128137\pi\) |
−0.799315 | + | 0.600912i | \(0.794804\pi\) | |||||||
\(614\) | −17.1002 | − | 29.6184i | −0.690108 | − | 1.19530i | ||||
\(615\) | 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 | ||||
\(619\) | 33.9116 | 1.36302 | 0.681512 | − | 0.731807i | \(-0.261323\pi\) | ||||
0.681512 | + | 0.731807i | \(0.261323\pi\) | |||||||
\(620\) | 1.89792 | − | 3.28729i | 0.0762221 | − | 0.132021i | ||||
\(621\) | 5.07938 | + | 8.79774i | 0.203828 | + | 0.353041i | ||||
\(622\) | −5.93085 | − | 10.2725i | −0.237806 | − | 0.411891i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.79583 | − | 1.73205i | 0.191987 | − | 0.0693375i | ||||
\(625\) | −31.1625 | −1.24650 | ||||||||
\(626\) | −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 | \(0.0335128\pi\) | |||||||
\(632\) | 35.3875 | 1.40764 | ||||||||
\(633\) | 1.26984 | − | 2.19944i | 0.0504718 | − | 0.0874197i | ||||
\(634\) | 6.29583 | + | 10.9047i | 0.250039 | + | 0.433081i | ||||
\(635\) | 10.1882 | + | 17.6465i | 0.404308 | + | 0.700281i | ||||
\(636\) | −9.32202 | −0.369642 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −50.9792 | −2.01828 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | −4.02609 | − | 6.97339i | −0.159145 | − | 0.275647i | ||||
\(641\) | −2.39792 | + | 4.15331i | −0.0947120 | + | 0.164046i | −0.909488 | − | 0.415729i | \(-0.863526\pi\) |
0.814776 | + | 0.579775i | \(0.196860\pi\) | |||||||
\(642\) | −8.48528 | −0.334887 | ||||||||
\(643\) | −2.82843 | + | 4.89898i | −0.111542 | + | 0.193197i | −0.916392 | − | 0.400281i | \(-0.868912\pi\) |
0.804850 | + | 0.593478i | \(0.202246\pi\) | |||||||
\(644\) | 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 | \(-0.154386\pi\) |
−0.846095 | + | 0.533032i | \(0.821053\pi\) | |||||||
\(648\) | −7.50000 | − | 12.9904i | −0.294628 | − | 0.510310i | ||||
\(649\) | 6.52307 | 0.256053 | ||||||||
\(650\) | 1.39948 | − | 7.82305i | 0.0548920 | − | 0.306845i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.69375 | − | 11.5939i | −0.262147 | − | 0.454053i | ||||
\(653\) | −12.5917 | − | 21.8094i | −0.492750 | − | 0.853468i | 0.507215 | − | 0.861819i | \(-0.330675\pi\) |
−0.999965 | + | 0.00835161i | \(0.997342\pi\) | |||||||
\(654\) | 12.4392 | − | 21.5453i | 0.486411 | − | 0.842488i | ||||
\(655\) | 22.0000 | 0.859611 | ||||||||
\(656\) | 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 | \(-0.0948311\pi\) | |||||||
\(660\) | −11.0000 | − | 19.0526i | −0.428174 | − | 0.741620i | ||||
\(661\) | −13.9256 | − | 24.1198i | −0.541642 | − | 0.938152i | −0.998810 | − | 0.0487715i | \(-0.984469\pi\) |
0.457168 | − | 0.889381i | \(-0.348864\pi\) | |||||||
\(662\) | 0.612505 | 0.0238057 | ||||||||
\(663\) | 21.4872 | + | 18.1211i | 0.834494 | + | 0.703766i | ||||
\(664\) | 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 | ||||
\(668\) | −15.2676 | −0.590722 | ||||||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 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 | \(0.986260\pi\) | |||||||
\(674\) | 14.9896 | + | 25.9627i | 0.577377 | + | 1.00005i | ||||
\(675\) | −12.4687 | −0.479919 | ||||||||
\(676\) | 12.1937 | + | 4.50694i | 0.468990 | + | 0.173344i | ||||
\(677\) | 34.7779 | 1.33662 | 0.668311 | − | 0.743882i | \(-0.267018\pi\) | ||||
0.668311 | + | 0.743882i | \(0.267018\pi\) | |||||||
\(678\) | 11.7321 | + | 20.3206i | 0.450568 | + | 0.780406i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −22.1937 | + | 38.4407i | −0.851091 | + | 1.47413i | ||||
\(681\) | 29.5917 | 1.13395 | ||||||||
\(682\) | 4.09827 | − | 7.09841i | 0.156931 | − | 0.271812i | ||||
\(683\) | −25.3875 | + | 43.9724i | −0.971425 | + | 1.68256i | −0.280166 | + | 0.959952i | \(0.590390\pi\) |
−0.691259 | + | 0.722607i | \(0.742944\pi\) | |||||||
\(684\) | −2.82843 | −0.108148 | ||||||||
\(685\) | −12.3523 | + | 21.3947i | −0.471956 | + | 0.817451i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.00000 | − | 15.5885i | −0.343371 | − | 0.594737i | ||||
\(688\) | 1.79583 | 0.0684654 | ||||||||
\(689\) | 18.1682 | + | 15.3221i | 0.692154 | + | 0.583725i | ||||
\(690\) | −6.81667 | −0.259506 | ||||||||
\(691\) | −5.51249 | − | 9.54790i | −0.209705 | − | 0.363219i | 0.741917 | − | 0.670492i | \(-0.233917\pi\) |
−0.951622 | + | 0.307273i | \(0.900584\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | −18.6588 | + | 32.3179i | −0.707259 | + | 1.22501i | ||||
\(697\) | 53.7750 | 2.03687 | ||||||||
\(698\) | −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 | \(0.562977\pi\) | |||||||
\(702\) | −3.59166 | + | 20.0773i | −0.135559 | + | 0.757771i | ||||
\(703\) | 19.2215 | 0.724953 | ||||||||
\(704\) | −20.2854 | − | 35.1354i | −0.764535 | − | 1.32421i | ||||
\(705\) | 5.36812 | + | 9.29785i | 0.202175 | + | 0.350177i | ||||
\(706\) | 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 | −0.633818 | − | 0.773482i | \(-0.718513\pi\) |
0.986764 | + | 0.162162i | \(0.0518466\pi\) | |||||||
\(710\) | −16.1043 | −0.604385 | ||||||||
\(711\) | −5.89792 | + | 10.2155i | −0.221189 | + | 0.383111i | ||||
\(712\) | 18.2257 | + | 31.5678i | 0.683036 | + | 1.18305i | ||||
\(713\) | 1.26984 | + | 2.19944i | 0.0475561 | + | 0.0823695i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.87707 | + | 55.2127i | −0.369382 | + | 2.06484i | ||||
\(716\) | 0.408337 | 0.0152603 | ||||||||
\(717\) | 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 | 0.455714 | + | 0.890126i | \(0.349384\pi\) |
−0.998729 | + | 0.0504035i | \(0.983949\pi\) | |||||||
\(720\) | −2.68406 | −0.100029 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.50000 | − | 9.52628i | 0.204689 | − | 0.354531i | ||||
\(723\) | 6.20417 | 0.230736 | ||||||||
\(724\) | −8.26873 | + | 14.3219i | −0.307305 | + | 0.532268i | ||||
\(725\) | 9.69375 | + | 16.7901i | 0.360017 | + | 0.623567i | ||||
\(726\) | −15.9747 | − | 27.6690i | −0.592877 | − | 1.02689i | ||||
\(727\) | −35.3259 | −1.31016 | −0.655082 | − | 0.755558i | \(-0.727366\pi\) | ||||
−0.655082 | + | 0.755558i | \(0.727366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −7.78541 | − | 13.4847i | −0.288151 | − | 0.499092i | ||||
\(731\) | 4.94975 | + | 8.57321i | 0.183073 | + | 0.317092i | ||||
\(732\) | 1.10208 | − | 1.90887i | 0.0407342 | − | 0.0705537i | ||||
\(733\) | 0.692369 | 0.0255732 | 0.0127866 | − | 0.999918i | \(-0.495930\pi\) | ||||
0.0127866 | + | 0.999918i | \(0.495930\pi\) | |||||||
\(734\) | −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 | 0.691938 | − | 0.721957i | \(-0.256757\pi\) |
−0.971202 | + | 0.238258i | \(0.923424\pi\) | |||||||
\(740\) | −18.2404 | −0.670531 | ||||||||
\(741\) | −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 | \(0.887210\pi\) | |||||||
\(744\) | −3.00000 | − | 5.19615i | −0.109985 | − | 0.190500i | ||||
\(745\) | 6.16215 | − | 10.6731i | 0.225764 | − | 0.391034i | ||||
\(746\) | −12.5917 | −0.461014 | ||||||||
\(747\) | −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 | ||||
\(751\) | −0.897916 | − | 1.55524i | −0.0327654 | − | 0.0567514i | 0.849178 | − | 0.528107i | \(-0.177098\pi\) |
−0.881943 | + | 0.471356i | \(0.843765\pi\) | |||||||
\(752\) | 1.41421 | + | 2.44949i | 0.0515711 | + | 0.0893237i | ||||
\(753\) | −4.40834 | −0.160649 | ||||||||
\(754\) | 29.8281 | − | 10.7726i | 1.08628 | − | 0.392317i | ||||
\(755\) | 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 | ||||
\(759\) | 14.7196 | 0.534288 | ||||||||
\(760\) | 11.3875 | − | 19.7237i | 0.413068 | − | 0.715454i | ||||
\(761\) | −4.66101 | + | 8.07311i | −0.168961 | + | 0.292650i | −0.938055 | − | 0.346486i | \(-0.887375\pi\) |
0.769094 | + | 0.639136i | \(0.220708\pi\) | |||||||
\(762\) | 10.7362 | 0.388933 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.8979 | − | 22.3398i | −0.466630 | − | 0.808227i | ||||
\(765\) | −7.39792 | − | 12.8136i | −0.267472 | − | 0.463275i | ||||
\(766\) | −14.9789 | −0.541209 | ||||||||
\(767\) | −3.81667 | + | 1.37842i | −0.137812 | + | 0.0497719i | ||||
\(768\) | −24.0416 | −0.867528 | ||||||||
\(769\) | −2.12132 | − | 3.67423i | −0.0764968 | − | 0.132496i | 0.825239 | − | 0.564783i | \(-0.191040\pi\) |
−0.901736 | + | 0.432287i | \(0.857707\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.8979 | + | 18.8757i | −0.392479 | + | 0.679793i | ||||
\(772\) | −3.40834 | −0.122669 | ||||||||
\(773\) | −3.82427 | + | 6.62383i | −0.137549 | + | 0.238243i | −0.926568 | − | 0.376126i | \(-0.877256\pi\) |
0.789019 | + | 0.614369i | \(0.210589\pi\) | |||||||
\(774\) | −0.897916 | + | 1.55524i | −0.0322749 | + | 0.0559018i | ||||
\(775\) | −3.11716 | −0.111972 | ||||||||
\(776\) | −6.36396 | + | 11.0227i | −0.228453 | + | 0.395692i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.1937 | − | 24.5843i | −0.508870 | − | 0.881390i | ||||
\(779\) | −27.5917 | −0.988574 | ||||||||
\(780\) | 10.4622 | + | 8.82327i | 0.374608 | + | 0.315924i | ||||
\(781\) | 34.7750 | 1.24435 | ||||||||
\(782\) | −4.94975 | − | 8.57321i | −0.177003 | − | 0.306578i | ||||
\(783\) | −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 | ||||
\(787\) | −12.7132 | + | 22.0199i | −0.453176 | + | 0.784924i | −0.998581 | − | 0.0532485i | \(-0.983042\pi\) |
0.545405 | + | 0.838173i | \(0.316376\pi\) | |||||||
\(788\) | 8.00000 | 0.284988 | ||||||||
\(789\) | 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 | ||||||||
\(793\) | −5.28541 | + | 1.90887i | −0.187690 | + | 0.0677858i | ||||
\(794\) | 7.07107 | 0.250943 | ||||||||
\(795\) | 12.5104 | + | 21.6687i | 0.443699 | + | 0.768509i | ||||
\(796\) | −11.0250 | − | 19.0958i | −0.390770 | − | 0.676833i | ||||
\(797\) | 13.1463 | − | 22.7700i | 0.465666 | − | 0.806556i | −0.533566 | − | 0.845759i | \(-0.679148\pi\) |
0.999231 | + | 0.0392022i | \(0.0124817\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.79583 | + | 13.5028i | −0.275797 | + | 0.477694i | ||||
\(800\) | −5.51042 | + | 9.54433i | −0.194823 | + | 0.337443i | ||||
\(801\) | −12.1504 | −0.429315 | ||||||||
\(802\) | −12.1937 | + | 21.1202i | −0.430576 | + | 0.745780i | ||||
\(803\) | 16.8115 | + | 29.1183i | 0.593263 | + | 1.02756i | ||||
\(804\) | 4.09827 | + | 7.09841i | 0.144535 | + | 0.250342i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.897916 | + | 5.01934i | −0.0316277 | + | 0.176799i | ||||
\(807\) | −1.59166 | −0.0560292 | ||||||||
\(808\) | −4.45919 | − | 7.72355i | −0.156874 | − | 0.271714i | ||||
\(809\) | −19.6833 | − | 34.0925i | −0.692029 | − | 1.19863i | −0.971172 | − | 0.238380i | \(-0.923384\pi\) |
0.279143 | − | 0.960250i | \(-0.409950\pi\) | |||||||
\(810\) | −6.71015 | + | 11.6223i | −0.235770 | + | 0.408366i | ||||
\(811\) | −38.4725 | −1.35095 | −0.675476 | − | 0.737382i | \(-0.736062\pi\) | ||||
−0.675476 | + | 0.737382i | \(0.736062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.3875 | − | 28.3840i | 0.574735 | − | 0.995469i | ||||
\(814\) | −39.3875 | −1.38053 | ||||||||
\(815\) | −17.9664 | + | 31.1187i | −0.629336 | + | 1.09004i | ||||
\(816\) | 3.89792 | + | 6.75139i | 0.136454 | + | 0.236346i | ||||
\(817\) | −2.53969 | − | 4.39887i | −0.0888525 | − | 0.153897i | ||||
\(818\) | −28.6879 | −1.00305 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.1833 | 0.914361 | ||||||||
\(821\) | 20.1833 | + | 34.9585i | 0.704403 | + | 1.22006i | 0.966907 | + | 0.255131i | \(0.0821185\pi\) |
−0.262504 | + | 0.964931i | \(0.584548\pi\) | |||||||
\(822\) | 6.50833 | + | 11.2728i | 0.227004 | + | 0.393183i | ||||
\(823\) | −18.3875 | + | 31.8481i | −0.640948 | + | 1.11015i | 0.344274 | + | 0.938869i | \(0.388125\pi\) |
−0.985222 | + | 0.171285i | \(0.945208\pi\) | |||||||
\(824\) | 24.5896 | 0.856620 | ||||||||
\(825\) | −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 | \(-0.280768\pi\) |
−0.986396 | + | 0.164389i | \(0.947435\pi\) | |||||||
\(830\) | −13.2854 | − | 23.0110i | −0.461143 | − | 0.798724i | ||||
\(831\) | −8.74454 | −0.303345 | ||||||||
\(832\) | 19.2937 | + | 16.2712i | 0.668889 | + | 0.564104i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.7958 | + | 18.6989i | 0.373829 | + | 0.647491i | ||||
\(835\) | 20.4896 | + | 35.4890i | 0.709071 | + | 1.22815i | ||||
\(836\) | −8.19654 | + | 14.1968i | −0.283483 | + | 0.491008i | ||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | −14.2718 | + | 24.7194i | −0.493010 | + | 0.853918i | ||||
\(839\) | −2.82843 | + | 4.89898i | −0.0976481 | + | 0.169132i | −0.910711 | − | 0.413045i | \(-0.864465\pi\) |
0.813063 | + | 0.582176i | \(0.197799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1833 | + | 41.8867i | −0.833908 | + | 1.44437i | ||||
\(842\) | 3.29583 | + | 5.70855i | 0.113582 | + | 0.196730i | ||||
\(843\) | −10.7510 | − | 18.6212i | −0.370283 | − | 0.641349i | ||||
\(844\) | 1.79583 | 0.0618151 | ||||||||
\(845\) | −5.88815 | − | 34.3924i | −0.202558 | − | 1.18313i | ||||
\(846\) | −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 | ||||
\(850\) | 12.1504 | 0.416757 | ||||||||
\(851\) | 6.10208 | − | 10.5691i | 0.209177 | − | 0.362305i | ||||
\(852\) | 4.24264 | − | 7.34847i | 0.145350 | − | 0.251754i | ||||
\(853\) | −13.1610 | −0.450625 | −0.225313 | − | 0.974287i | \(-0.572340\pi\) | ||||
−0.225313 | + | 0.974287i | \(0.572340\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.79583 | + | 6.57457i | 0.129815 | + | 0.224846i | ||||
\(856\) | −9.00000 | − | 15.5885i | −0.307614 | − | 0.532803i | ||||
\(857\) | −37.7507 | −1.28954 | −0.644769 | − | 0.764377i | \(-0.723046\pi\) | ||||
−0.644769 | + | 0.764377i | \(0.723046\pi\) | |||||||
\(858\) | 22.5917 | + | 19.0526i | 0.771267 | + | 0.650444i | ||||
\(859\) | 23.7529 | 0.810438 | 0.405219 | − | 0.914220i | \(-0.367195\pi\) | ||||
0.405219 | + | 0.914220i | \(0.367195\pi\) | |||||||
\(860\) | 2.41006 | + | 4.17434i | 0.0821823 | + | 0.142344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.59166 | − | 4.48889i | 0.0882724 | − | 0.152892i | ||||
\(863\) | 17.7958 | 0.605777 | 0.302889 | − | 0.953026i | \(-0.402049\pi\) | ||||
0.302889 | + | 0.953026i | \(0.402049\pi\) | |||||||
\(864\) | 14.1421 | − | 24.4949i | 0.481125 | − | 0.833333i | ||||
\(865\) | 12.5104 | − | 21.6687i | 0.425367 | − | 0.736757i | ||||
\(866\) | 13.4203 | 0.456040 | ||||||||
\(867\) | −9.46639 | + | 16.3963i | −0.321495 | + | 0.556846i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.1833 | + | 59.2073i | 1.15959 | + | 2.00847i | ||||
\(870\) | 33.3875 | 1.13194 | ||||||||
\(871\) | 3.67990 | − | 20.5706i | 0.124689 | − | 0.697008i | ||||
\(872\) | 52.7750 | 1.78719 | ||||||||
\(873\) | −2.12132 | − | 3.67423i | −0.0717958 | − | 0.124354i | ||||
\(874\) | 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 | −0.822696 | − | 0.568482i | \(-0.807531\pi\) |
0.903668 | + | 0.428235i | \(0.140864\pi\) | |||||||
\(878\) | −17.1002 | + | 29.6184i | −0.577104 | + | 0.999573i | ||||
\(879\) | −13.7958 | −0.465322 | ||||||||
\(880\) | −7.77817 | + | 13.4722i | −0.262202 | + | 0.454148i | ||||
\(881\) | 11.6599 | + | 20.1955i | 0.392832 | + | 0.680405i | 0.992822 | − | 0.119603i | \(-0.0381621\pi\) |
−0.599990 | + | 0.800007i | \(0.704829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.6125 | −0.559055 | −0.279528 | − | 0.960138i | \(-0.590178\pi\) | ||||
−0.279528 | + | 0.960138i | \(0.590178\pi\) | |||||||
\(884\) | −3.50000 | + | 19.5650i | −0.117718 | + | 0.658041i | ||||
\(885\) | −4.27212 | −0.143606 | ||||||||
\(886\) | −5.00000 | − | 8.66025i | −0.167978 | − | 0.290947i | ||||
\(887\) | 14.2865 | + | 24.7450i | 0.479694 | + | 0.830854i | 0.999729 | − | 0.0232909i | \(-0.00741439\pi\) |
−0.520035 | + | 0.854145i | \(0.674081\pi\) | |||||||
\(888\) | −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 | ||||
\(892\) | 5.65685 | 0.189405 | ||||||||
\(893\) | 4.00000 | − | 6.92820i | 0.133855 | − | 0.231843i | ||||
\(894\) | −3.24680 | − | 5.62362i | −0.108589 | − | 0.188082i | ||||
\(895\) | −0.548000 | − | 0.949164i | −0.0183176 | − | 0.0317271i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.61251 | + | 3.11047i | −0.287563 | + | 0.103856i | ||||
\(898\) | 4.40834 | 0.147108 | ||||||||
\(899\) | −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 | ||||
\(905\) | 44.3875 | 1.47549 | ||||||||
\(906\) | 12.4392 | − | 21.5453i | 0.413264 | − | 0.715795i | ||||
\(907\) | −24.6937 | − | 42.7708i | −0.819942 | − | 1.42018i | −0.905724 | − | 0.423868i | \(-0.860672\pi\) |
0.0857816 | − | 0.996314i | \(-0.472661\pi\) | |||||||
\(908\) | 10.4622 | + | 18.1211i | 0.347201 | + | 0.601370i | ||||
\(909\) | 2.97280 | 0.0986014 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.1833 | −1.43073 | −0.715364 | − | 0.698752i | \(-0.753739\pi\) | ||||
−0.715364 | + | 0.698752i | \(0.753739\pi\) | |||||||
\(912\) | −2.00000 | − | 3.46410i | −0.0662266 | − | 0.114708i | ||||
\(913\) | 28.6879 | + | 49.6889i | 0.949431 | + | 1.64446i | ||||
\(914\) | 7.29583 | − | 12.6368i | 0.241325 | − | 0.417987i | ||||
\(915\) | −5.91612 | −0.195581 | ||||||||
\(916\) | 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 | −0.936632 | − | 0.350315i | \(-0.886075\pi\) |
0.771697 | + | 0.635990i | \(0.219408\pi\) | |||||||
\(920\) | −7.23017 | − | 12.5230i | −0.238372 | − | 0.412872i | ||||
\(921\) | −24.1833 | − | 41.8867i | −0.796868 | − | 1.38022i | ||||
\(922\) | 30.9683 | 1.01989 | ||||||||
\(923\) | −20.3470 | + | 7.34847i | −0.669729 | + | 0.241878i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48958 | + | 12.9723i | 0.246256 | + | 0.426528i | ||||
\(926\) | −5.69375 | − | 9.86186i | −0.187108 | − | 0.324081i | ||||
\(927\) | −4.09827 | + | 7.09841i | −0.134605 | + | 0.233143i | ||||
\(928\) | −43.9792 | −1.44369 | ||||||||
\(929\) | 14.0700 | − | 24.3699i | 0.461620 | − | 0.799550i | −0.537422 | − | 0.843314i | \(-0.680602\pi\) |
0.999042 | + | 0.0437641i | \(0.0139350\pi\) | |||||||
\(930\) | −2.68406 | + | 4.64893i | −0.0880137 | + | 0.152444i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.5917 | + | 18.3453i | −0.346941 | + | 0.600920i | ||||
\(933\) | −8.38749 | − | 14.5276i | −0.274594 | − | 0.475611i | ||||
\(934\) | 2.41006 | + | 4.17434i | 0.0788595 | + | 0.136589i | ||||
\(935\) | −85.7541 | −2.80446 | ||||||||
\(936\) | −10.1735 | + | 3.67423i | −0.332531 | + | 0.120096i | ||||
\(937\) | 6.63796 | 0.216853 | 0.108426 | − | 0.994104i | \(-0.465419\pi\) | ||||
0.108426 | + | 0.994104i | \(0.465419\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.20417 | − | 2.08568i | −0.0392966 | − | 0.0680636i | ||||
\(940\) | −3.79583 | + | 6.57457i | −0.123806 | + | 0.214439i | ||||
\(941\) | −23.4642 | −0.764910 | −0.382455 | − | 0.923974i | \(-0.624921\pi\) | ||||
−0.382455 | + | 0.923974i | \(0.624921\pi\) | |||||||
\(942\) | 4.89792 | − | 8.48344i | 0.159583 | − | 0.276405i | ||||
\(943\) | −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 | ||||
\(947\) | −14.1021 | − | 24.4255i | −0.458256 | − | 0.793723i | 0.540613 | − | 0.841272i | \(-0.318192\pi\) |
−0.998869 | + | 0.0475486i | \(0.984859\pi\) | |||||||
\(948\) | 16.6818 | 0.541800 | ||||||||
\(949\) | −15.9896 | − | 13.4847i | −0.519044 | − | 0.437733i | ||||
\(950\) | −6.23433 | −0.202268 | ||||||||
\(951\) | 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 | \(0.141809\pi\) | |||||||
\(954\) | −6.59166 | −0.213413 | ||||||||
\(955\) | −34.6188 | + | 59.9614i | −1.12024 | + | 1.94031i | ||||
\(956\) | −9.89792 | + | 17.1437i | −0.320121 | + | 0.554467i | ||||
\(957\) | −72.0954 | −2.33051 | ||||||||
\(958\) | 3.67990 | − | 6.37378i | 0.118892 | − | 0.205927i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.2854 | + | 23.0110i | 0.428785 | + | 0.742677i | ||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | 23.0458 | − | 8.32316i | 0.743026 | − | 0.268349i | ||||
\(963\) | 6.00000 | 0.193347 | ||||||||
\(964\) | 2.19350 | + | 3.79926i | 0.0706480 | + | 0.122366i | ||||
\(965\) | 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 | ||||
\(969\) | 11.0250 | − | 19.0958i | 0.354173 | − | 0.613446i | ||||
\(970\) | 11.3875 | 0.365630 | ||||||||
\(971\) | 11.3137 | − | 19.5959i | 0.363074 | − | 0.628863i | −0.625391 | − | 0.780312i | \(-0.715060\pi\) |
0.988465 | + | 0.151449i | \(0.0483938\pi\) | |||||||
\(972\) | 4.94975 | + | 8.57321i | 0.158763 | + | 0.274986i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.5917 | 0.627757 | ||||||||
\(975\) | 1.97916 | − | 11.0635i | 0.0633838 | − | 0.354314i | ||||
\(976\) | −1.55858 | −0.0498890 | ||||||||
\(977\) | −0.193747 | − | 0.335580i | −0.00619852 | − | 0.0107362i | 0.862910 | − | 0.505358i | \(-0.168640\pi\) |
−0.869108 | + | 0.494622i | \(0.835306\pi\) | |||||||
\(978\) | 9.46639 | + | 16.3963i | 0.302702 | + | 0.524295i | ||||
\(979\) | −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 | ||||
\(983\) | 41.5602 | 1.32556 | 0.662782 | − | 0.748812i | \(-0.269376\pi\) | ||||
0.662782 | + | 0.748812i | \(0.269376\pi\) | |||||||
\(984\) | 20.6937 | − | 35.8426i | 0.659693 | − | 1.14262i | ||||
\(985\) | −10.7362 | − | 18.5957i | −0.342085 | − | 0.592508i | ||||
\(986\) | 24.2434 | + | 41.9909i | 0.772069 | + | 1.33726i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.79583 | − | 10.0387i | 0.0571330 | − | 0.319373i | ||||
\(989\) | −3.22501 | −0.102549 | ||||||||
\(990\) | −7.77817 | − | 13.4722i | −0.247207 | − | 0.428174i | ||||
\(991\) | −9.10208 | − | 15.7653i | −0.289137 | − | 0.500800i | 0.684467 | − | 0.729044i | \(-0.260035\pi\) |
−0.973604 | + | 0.228244i | \(0.926702\pi\) | |||||||
\(992\) | 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 | ||||
\(996\) | 14.0000 | 0.443607 | ||||||||
\(997\) | 2.75624 | − | 4.77395i | 0.0872911 | − | 0.151193i | −0.819074 | − | 0.573688i | \(-0.805512\pi\) |
0.906365 | + | 0.422495i | \(0.138846\pi\) | |||||||
\(998\) | −8.10208 | − | 14.0332i | −0.256467 | − | 0.444214i | ||||
\(999\) | −19.2215 | − | 33.2926i | −0.608142 | − | 1.05333i |
(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.f.g.393.1 | yes | 8 | |
7.2 | even | 3 | 637.2.g.h.263.4 | 8 | |||
7.3 | odd | 6 | 637.2.h.k.471.3 | 8 | |||
7.4 | even | 3 | 637.2.h.k.471.2 | 8 | |||
7.5 | odd | 6 | 637.2.g.h.263.1 | 8 | |||
7.6 | odd | 2 | inner | 637.2.f.g.393.4 | yes | 8 | |
13.3 | even | 3 | 8281.2.a.bv.1.3 | 4 | |||
13.9 | even | 3 | inner | 637.2.f.g.295.1 | ✓ | 8 | |
13.10 | even | 6 | 8281.2.a.bn.1.4 | 4 | |||
91.9 | even | 3 | 637.2.h.k.165.2 | 8 | |||
91.48 | odd | 6 | inner | 637.2.f.g.295.4 | yes | 8 | |
91.55 | odd | 6 | 8281.2.a.bv.1.2 | 4 | |||
91.61 | odd | 6 | 637.2.h.k.165.3 | 8 | |||
91.62 | odd | 6 | 8281.2.a.bn.1.1 | 4 | |||
91.74 | even | 3 | 637.2.g.h.373.4 | 8 | |||
91.87 | odd | 6 | 637.2.g.h.373.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.g.295.1 | ✓ | 8 | 13.9 | even | 3 | inner | |
637.2.f.g.295.4 | yes | 8 | 91.48 | odd | 6 | inner | |
637.2.f.g.393.1 | yes | 8 | 1.1 | even | 1 | trivial | |
637.2.f.g.393.4 | yes | 8 | 7.6 | odd | 2 | inner | |
637.2.g.h.263.1 | 8 | 7.5 | odd | 6 | |||
637.2.g.h.263.4 | 8 | 7.2 | even | 3 | |||
637.2.g.h.373.1 | 8 | 91.87 | odd | 6 | |||
637.2.g.h.373.4 | 8 | 91.74 | even | 3 | |||
637.2.h.k.165.2 | 8 | 91.9 | even | 3 | |||
637.2.h.k.165.3 | 8 | 91.61 | odd | 6 | |||
637.2.h.k.471.2 | 8 | 7.4 | even | 3 | |||
637.2.h.k.471.3 | 8 | 7.3 | odd | 6 | |||
8281.2.a.bn.1.1 | 4 | 91.62 | odd | 6 | |||
8281.2.a.bn.1.4 | 4 | 13.10 | even | 6 | |||
8281.2.a.bv.1.2 | 4 | 91.55 | odd | 6 | |||
8281.2.a.bv.1.3 | 4 | 13.3 | even | 3 |