Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.177 |
Dual form | 1078.2.e.p.67.2 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 0.707107 | + | 1.22474i | 0.408248 | + | 0.707107i | 0.994694 | − | 0.102882i | \(-0.0328064\pi\) |
−0.586445 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.12132 | − | 3.67423i | 0.948683 | − | 1.64317i | 0.200480 | − | 0.979698i | \(-0.435750\pi\) |
0.748203 | − | 0.663470i | \(-0.230917\pi\) | |||||||
\(6\) | −1.41421 | −0.577350 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.12132 | + | 3.67423i | 0.670820 | + | 1.16190i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0.707107 | − | 1.22474i | 0.204124 | − | 0.353553i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00000 | 1.54919 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.82843 | − | 4.89898i | −0.685994 | − | 1.18818i | −0.973123 | − | 0.230285i | \(-0.926034\pi\) |
0.287129 | − | 0.957892i | \(-0.407299\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | −4.24264 | −0.948683 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0.707107 | + | 1.22474i | 0.144338 | + | 0.250000i | ||||
\(25\) | −6.50000 | − | 11.2583i | −1.30000 | − | 2.25167i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −3.00000 | + | 5.19615i | −0.547723 | + | 0.948683i | ||||
\(31\) | −0.707107 | − | 1.22474i | −0.127000 | − | 0.219971i | 0.795513 | − | 0.605937i | \(-0.207202\pi\) |
−0.922513 | + | 0.385966i | \(0.873868\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.707107 | + | 1.22474i | −0.123091 | + | 0.213201i | ||||
\(34\) | 5.65685 | 0.970143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 5.00000 | − | 8.66025i | 0.821995 | − | 1.42374i | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) |
0.904194 | − | 0.427121i | \(-0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.12132 | − | 3.67423i | 0.335410 | − | 0.580948i | ||||
\(41\) | 11.3137 | 1.76690 | 0.883452 | − | 0.468521i | \(-0.155213\pi\) | ||||
0.883452 | + | 0.468521i | \(0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | −2.12132 | − | 3.67423i | −0.316228 | − | 0.547723i | ||||
\(46\) | −3.00000 | − | 5.19615i | −0.442326 | − | 0.766131i | ||||
\(47\) | 2.12132 | − | 3.67423i | 0.309426 | − | 0.535942i | −0.668811 | − | 0.743433i | \(-0.733196\pi\) |
0.978237 | + | 0.207491i | \(0.0665296\pi\) | |||||||
\(48\) | −1.41421 | −0.204124 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.0000 | 1.83848 | ||||||||
\(51\) | 4.00000 | − | 6.92820i | 0.560112 | − | 0.970143i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | − | 6.92820i | −0.549442 | − | 0.951662i | −0.998313 | − | 0.0580651i | \(-0.981507\pi\) |
0.448871 | − | 0.893597i | \(-0.351826\pi\) | |||||||
\(54\) | −2.82843 | + | 4.89898i | −0.384900 | + | 0.666667i | ||||
\(55\) | 4.24264 | 0.572078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.00000 | + | 1.73205i | −0.131306 | + | 0.227429i | ||||
\(59\) | 0.707107 | + | 1.22474i | 0.0920575 | + | 0.159448i | 0.908377 | − | 0.418153i | \(-0.137322\pi\) |
−0.816319 | + | 0.577601i | \(0.803989\pi\) | |||||||
\(60\) | −3.00000 | − | 5.19615i | −0.387298 | − | 0.670820i | ||||
\(61\) | −1.41421 | + | 2.44949i | −0.181071 | + | 0.313625i | −0.942246 | − | 0.334922i | \(-0.891290\pi\) |
0.761174 | + | 0.648547i | \(0.224623\pi\) | |||||||
\(62\) | 1.41421 | 0.179605 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.707107 | − | 1.22474i | −0.0870388 | − | 0.150756i | ||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | −2.82843 | + | 4.89898i | −0.342997 | + | 0.594089i | ||||
\(69\) | −8.48528 | −1.02151 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 4.24264 | + | 7.34847i | 0.496564 | + | 0.860073i | 0.999992 | − | 0.00396356i | \(-0.00126164\pi\) |
−0.503429 | + | 0.864037i | \(0.667928\pi\) | |||||||
\(74\) | 5.00000 | + | 8.66025i | 0.581238 | + | 1.00673i | ||||
\(75\) | 9.19239 | − | 15.9217i | 1.06145 | − | 1.83848i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | + | 13.8564i | −0.900070 | + | 1.55897i | −0.0726692 | + | 0.997356i | \(0.523152\pi\) |
−0.827401 | + | 0.561611i | \(0.810182\pi\) | |||||||
\(80\) | 2.12132 | + | 3.67423i | 0.237171 | + | 0.410792i | ||||
\(81\) | 2.50000 | + | 4.33013i | 0.277778 | + | 0.481125i | ||||
\(82\) | −5.65685 | + | 9.79796i | −0.624695 | + | 1.08200i | ||||
\(83\) | 16.9706 | 1.86276 | 0.931381 | − | 0.364047i | \(-0.118605\pi\) | ||||
0.931381 | + | 0.364047i | \(0.118605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.0000 | −2.60317 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 1.41421 | + | 2.44949i | 0.151620 | + | 0.262613i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | −3.53553 | + | 6.12372i | −0.374766 | + | 0.649113i | −0.990292 | − | 0.139003i | \(-0.955610\pi\) |
0.615526 | + | 0.788116i | \(0.288944\pi\) | |||||||
\(90\) | 4.24264 | 0.447214 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 1.00000 | − | 1.73205i | 0.103695 | − | 0.179605i | ||||
\(94\) | 2.12132 | + | 3.67423i | 0.218797 | + | 0.378968i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.707107 | − | 1.22474i | 0.0721688 | − | 0.125000i | ||||
\(97\) | 9.89949 | 1.00514 | 0.502571 | − | 0.864536i | \(-0.332388\pi\) | ||||
0.502571 | + | 0.864536i | \(0.332388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −6.50000 | + | 11.2583i | −0.650000 | + | 1.12583i | ||||
\(101\) | 2.82843 | + | 4.89898i | 0.281439 | + | 0.487467i | 0.971739 | − | 0.236056i | \(-0.0758550\pi\) |
−0.690300 | + | 0.723523i | \(0.742522\pi\) | |||||||
\(102\) | 4.00000 | + | 6.92820i | 0.396059 | + | 0.685994i | ||||
\(103\) | 9.19239 | − | 15.9217i | 0.905753 | − | 1.56881i | 0.0858496 | − | 0.996308i | \(-0.472640\pi\) |
0.819903 | − | 0.572502i | \(-0.194027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | −8.00000 | + | 13.8564i | −0.773389 | + | 1.33955i | 0.162306 | + | 0.986740i | \(0.448107\pi\) |
−0.935695 | + | 0.352809i | \(0.885227\pi\) | |||||||
\(108\) | −2.82843 | − | 4.89898i | −0.272166 | − | 0.471405i | ||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | −2.12132 | + | 3.67423i | −0.202260 | + | 0.350325i | ||||
\(111\) | 14.1421 | 1.34231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7279 | + | 22.0454i | 1.18688 | + | 2.05574i | ||||
\(116\) | −1.00000 | − | 1.73205i | −0.0928477 | − | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.41421 | −0.130189 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.00000 | 0.547723 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −1.41421 | − | 2.44949i | −0.128037 | − | 0.221766i | ||||
\(123\) | 8.00000 | + | 13.8564i | 0.721336 | + | 1.24939i | ||||
\(124\) | −0.707107 | + | 1.22474i | −0.0635001 | + | 0.109985i | ||||
\(125\) | −33.9411 | −3.03579 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −5.65685 | − | 9.79796i | −0.498058 | − | 0.862662i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.89949 | + | 17.1464i | −0.864923 | + | 1.49809i | 0.00220084 | + | 0.999998i | \(0.499299\pi\) |
−0.867124 | + | 0.498093i | \(0.834034\pi\) | |||||||
\(132\) | 1.41421 | 0.123091 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 12.0000 | − | 20.7846i | 1.03280 | − | 1.78885i | ||||
\(136\) | −2.82843 | − | 4.89898i | −0.242536 | − | 0.420084i | ||||
\(137\) | 9.00000 | + | 15.5885i | 0.768922 | + | 1.33181i | 0.938148 | + | 0.346235i | \(0.112540\pi\) |
−0.169226 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(138\) | 4.24264 | − | 7.34847i | 0.361158 | − | 0.625543i | ||||
\(139\) | −11.3137 | −0.959616 | −0.479808 | − | 0.877373i | \(-0.659294\pi\) | ||||
−0.479808 | + | 0.877373i | \(0.659294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 1.00000 | − | 1.73205i | 0.0839181 | − | 0.145350i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 4.24264 | − | 7.34847i | 0.352332 | − | 0.610257i | ||||
\(146\) | −8.48528 | −0.702247 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | −0.821995 | ||||||||
\(149\) | 5.00000 | − | 8.66025i | 0.409616 | − | 0.709476i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.994847 | + | 0.101391i | \(0.0323294\pi\) | |||||||
\(150\) | 9.19239 | + | 15.9217i | 0.750555 | + | 1.30000i | ||||
\(151\) | −2.00000 | − | 3.46410i | −0.162758 | − | 0.281905i | 0.773099 | − | 0.634285i | \(-0.218706\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.65685 | −0.457330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.12132 | + | 3.67423i | 0.169300 | + | 0.293236i | 0.938174 | − | 0.346164i | \(-0.112516\pi\) |
−0.768874 | + | 0.639400i | \(0.779183\pi\) | |||||||
\(158\) | −8.00000 | − | 13.8564i | −0.636446 | − | 1.10236i | ||||
\(159\) | 5.65685 | − | 9.79796i | 0.448618 | − | 0.777029i | ||||
\(160\) | −4.24264 | −0.335410 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.00000 | −0.392837 | ||||||||
\(163\) | 5.00000 | − | 8.66025i | 0.391630 | − | 0.678323i | −0.601035 | − | 0.799223i | \(-0.705245\pi\) |
0.992665 | + | 0.120900i | \(0.0385779\pi\) | |||||||
\(164\) | −5.65685 | − | 9.79796i | −0.441726 | − | 0.765092i | ||||
\(165\) | 3.00000 | + | 5.19615i | 0.233550 | + | 0.404520i | ||||
\(166\) | −8.48528 | + | 14.6969i | −0.658586 | + | 1.14070i | ||||
\(167\) | −5.65685 | −0.437741 | −0.218870 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218870 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 12.0000 | − | 20.7846i | 0.920358 | − | 1.59411i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | + | 6.92820i | 0.304997 | + | 0.528271i | ||||
\(173\) | −5.65685 | + | 9.79796i | −0.430083 | + | 0.744925i | −0.996880 | − | 0.0789322i | \(-0.974849\pi\) |
0.566797 | + | 0.823857i | \(0.308182\pi\) | |||||||
\(174\) | −2.82843 | −0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −1.00000 | + | 1.73205i | −0.0751646 | + | 0.130189i | ||||
\(178\) | −3.53553 | − | 6.12372i | −0.264999 | − | 0.458993i | ||||
\(179\) | −6.00000 | − | 10.3923i | −0.448461 | − | 0.776757i | 0.549825 | − | 0.835280i | \(-0.314694\pi\) |
−0.998286 | + | 0.0585225i | \(0.981361\pi\) | |||||||
\(180\) | −2.12132 | + | 3.67423i | −0.158114 | + | 0.273861i | ||||
\(181\) | 7.07107 | 0.525588 | 0.262794 | − | 0.964852i | \(-0.415356\pi\) | ||||
0.262794 | + | 0.964852i | \(0.415356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −3.00000 | + | 5.19615i | −0.221163 | + | 0.383065i | ||||
\(185\) | −21.2132 | − | 36.7423i | −1.55963 | − | 2.70135i | ||||
\(186\) | 1.00000 | + | 1.73205i | 0.0733236 | + | 0.127000i | ||||
\(187\) | 2.82843 | − | 4.89898i | 0.206835 | − | 0.358249i | ||||
\(188\) | −4.24264 | −0.309426 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | + | 13.8564i | −0.578860 | + | 1.00261i | 0.416751 | + | 0.909021i | \(0.363169\pi\) |
−0.995610 | + | 0.0935936i | \(0.970165\pi\) | |||||||
\(192\) | 0.707107 | + | 1.22474i | 0.0510310 | + | 0.0883883i | ||||
\(193\) | 3.00000 | + | 5.19615i | 0.215945 | + | 0.374027i | 0.953564 | − | 0.301189i | \(-0.0973836\pi\) |
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(194\) | −4.94975 | + | 8.57321i | −0.355371 | + | 0.615521i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.0000 | 1.56744 | 0.783718 | − | 0.621117i | \(-0.213321\pi\) | ||||
0.783718 | + | 0.621117i | \(0.213321\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | −0.707107 | − | 1.22474i | −0.0501255 | − | 0.0868199i | 0.839874 | − | 0.542781i | \(-0.182629\pi\) |
−0.889999 | + | 0.455962i | \(0.849295\pi\) | |||||||
\(200\) | −6.50000 | − | 11.2583i | −0.459619 | − | 0.796084i | ||||
\(201\) | 1.41421 | − | 2.44949i | 0.0997509 | − | 0.172774i | ||||
\(202\) | −5.65685 | −0.398015 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.00000 | −0.560112 | ||||||||
\(205\) | 24.0000 | − | 41.5692i | 1.67623 | − | 2.90332i | ||||
\(206\) | 9.19239 | + | 15.9217i | 0.640464 | + | 1.10932i | ||||
\(207\) | 3.00000 | + | 5.19615i | 0.208514 | + | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −4.00000 | + | 6.92820i | −0.274721 | + | 0.475831i | ||||
\(213\) | −1.41421 | − | 2.44949i | −0.0969003 | − | 0.167836i | ||||
\(214\) | −8.00000 | − | 13.8564i | −0.546869 | − | 0.947204i | ||||
\(215\) | −16.9706 | + | 29.3939i | −1.15738 | + | 2.00465i | ||||
\(216\) | 5.65685 | 0.384900 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | −6.00000 | + | 10.3923i | −0.405442 | + | 0.702247i | ||||
\(220\) | −2.12132 | − | 3.67423i | −0.143019 | − | 0.247717i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.07107 | + | 12.2474i | −0.474579 | + | 0.821995i | ||||
\(223\) | 21.2132 | 1.42054 | 0.710271 | − | 0.703929i | \(-0.248573\pi\) | ||||
0.710271 | + | 0.703929i | \(0.248573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0000 | −0.866667 | ||||||||
\(226\) | 1.00000 | − | 1.73205i | 0.0665190 | − | 0.115214i | ||||
\(227\) | −7.07107 | − | 12.2474i | −0.469323 | − | 0.812892i | 0.530062 | − | 0.847959i | \(-0.322169\pi\) |
−0.999385 | + | 0.0350674i | \(0.988835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.94975 | − | 8.57321i | 0.327089 | − | 0.566534i | −0.654844 | − | 0.755764i | \(-0.727266\pi\) |
0.981933 | + | 0.189230i | \(0.0605991\pi\) | |||||||
\(230\) | −25.4558 | −1.67851 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | −7.00000 | + | 12.1244i | −0.458585 | + | 0.794293i | −0.998886 | − | 0.0471787i | \(-0.984977\pi\) |
0.540301 | + | 0.841472i | \(0.318310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | − | 15.5885i | −0.587095 | − | 1.01688i | ||||
\(236\) | 0.707107 | − | 1.22474i | 0.0460287 | − | 0.0797241i | ||||
\(237\) | −22.6274 | −1.46981 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | −3.00000 | + | 5.19615i | −0.193649 | + | 0.335410i | ||||
\(241\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | 4.94975 | − | 8.57321i | 0.317526 | − | 0.549972i | ||||
\(244\) | 2.82843 | 0.181071 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.0000 | −1.02012 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.707107 | − | 1.22474i | −0.0449013 | − | 0.0777714i | ||||
\(249\) | 12.0000 | + | 20.7846i | 0.760469 | + | 1.31717i | ||||
\(250\) | 16.9706 | − | 29.3939i | 1.07331 | − | 1.85903i | ||||
\(251\) | −18.3848 | −1.16044 | −0.580218 | − | 0.814461i | \(-0.697033\pi\) | ||||
−0.580218 | + | 0.814461i | \(0.697033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | −8.00000 | + | 13.8564i | −0.501965 | + | 0.869428i | ||||
\(255\) | −16.9706 | − | 29.3939i | −1.06274 | − | 1.84072i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.707107 | − | 1.22474i | 0.0441081 | − | 0.0763975i | −0.843129 | − | 0.537712i | \(-0.819289\pi\) |
0.887237 | + | 0.461315i | \(0.152622\pi\) | |||||||
\(258\) | 11.3137 | 0.704361 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | − | 1.73205i | 0.0618984 | − | 0.107211i | ||||
\(262\) | −9.89949 | − | 17.1464i | −0.611593 | − | 1.05931i | ||||
\(263\) | 4.00000 | + | 6.92820i | 0.246651 | + | 0.427211i | 0.962594 | − | 0.270947i | \(-0.0873367\pi\) |
−0.715944 | + | 0.698158i | \(0.754003\pi\) | |||||||
\(264\) | −0.707107 | + | 1.22474i | −0.0435194 | + | 0.0753778i | ||||
\(265\) | −33.9411 | −2.08499 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | −1.00000 | + | 1.73205i | −0.0610847 | + | 0.105802i | ||||
\(269\) | 9.19239 | + | 15.9217i | 0.560470 | + | 0.970762i | 0.997455 | + | 0.0712937i | \(0.0227127\pi\) |
−0.436986 | + | 0.899469i | \(0.643954\pi\) | |||||||
\(270\) | 12.0000 | + | 20.7846i | 0.730297 | + | 1.26491i | ||||
\(271\) | −4.24264 | + | 7.34847i | −0.257722 | + | 0.446388i | −0.965631 | − | 0.259916i | \(-0.916305\pi\) |
0.707909 | + | 0.706303i | \(0.249639\pi\) | |||||||
\(272\) | 5.65685 | 0.342997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 6.50000 | − | 11.2583i | 0.391965 | − | 0.678903i | ||||
\(276\) | 4.24264 | + | 7.34847i | 0.255377 | + | 0.442326i | ||||
\(277\) | 1.00000 | + | 1.73205i | 0.0600842 | + | 0.104069i | 0.894503 | − | 0.447062i | \(-0.147530\pi\) |
−0.834419 | + | 0.551131i | \(0.814196\pi\) | |||||||
\(278\) | 5.65685 | − | 9.79796i | 0.339276 | − | 0.587643i | ||||
\(279\) | −1.41421 | −0.0846668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | −3.00000 | + | 5.19615i | −0.178647 | + | 0.309426i | ||||
\(283\) | −9.89949 | − | 17.1464i | −0.588464 | − | 1.01925i | −0.994434 | − | 0.105363i | \(-0.966400\pi\) |
0.405970 | − | 0.913886i | \(-0.366934\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −7.50000 | + | 12.9904i | −0.441176 | + | 0.764140i | ||||
\(290\) | 4.24264 | + | 7.34847i | 0.249136 | + | 0.431517i | ||||
\(291\) | 7.00000 | + | 12.1244i | 0.410347 | + | 0.710742i | ||||
\(292\) | 4.24264 | − | 7.34847i | 0.248282 | − | 0.430037i | ||||
\(293\) | 8.48528 | 0.495715 | 0.247858 | − | 0.968796i | \(-0.420273\pi\) | ||||
0.247858 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 5.00000 | − | 8.66025i | 0.290619 | − | 0.503367i | ||||
\(297\) | 2.82843 | + | 4.89898i | 0.164122 | + | 0.284268i | ||||
\(298\) | 5.00000 | + | 8.66025i | 0.289642 | + | 0.501675i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −18.3848 | −1.06145 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.00000 | 0.230174 | ||||||||
\(303\) | −4.00000 | + | 6.92820i | −0.229794 | + | 0.398015i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | + | 10.3923i | 0.343559 | + | 0.595062i | ||||
\(306\) | 2.82843 | − | 4.89898i | 0.161690 | − | 0.280056i | ||||
\(307\) | 25.4558 | 1.45284 | 0.726421 | − | 0.687250i | \(-0.241182\pi\) | ||||
0.726421 | + | 0.687250i | \(0.241182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.0000 | 1.47909 | ||||||||
\(310\) | 3.00000 | − | 5.19615i | 0.170389 | − | 0.295122i | ||||
\(311\) | 9.19239 | + | 15.9217i | 0.521253 | + | 0.902836i | 0.999694 | + | 0.0247167i | \(0.00786836\pi\) |
−0.478442 | + | 0.878119i | \(0.658798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.36396 | + | 11.0227i | −0.359712 | + | 0.623040i | −0.987913 | − | 0.155012i | \(-0.950459\pi\) |
0.628200 | + | 0.778052i | \(0.283792\pi\) | |||||||
\(314\) | −4.24264 | −0.239426 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | −15.0000 | + | 25.9808i | −0.842484 | + | 1.45922i | 0.0453045 | + | 0.998973i | \(0.485574\pi\) |
−0.887788 | + | 0.460252i | \(0.847759\pi\) | |||||||
\(318\) | 5.65685 | + | 9.79796i | 0.317221 | + | 0.549442i | ||||
\(319\) | 1.00000 | + | 1.73205i | 0.0559893 | + | 0.0969762i | ||||
\(320\) | 2.12132 | − | 3.67423i | 0.118585 | − | 0.205396i | ||||
\(321\) | −22.6274 | −1.26294 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.50000 | − | 4.33013i | 0.138889 | − | 0.240563i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.00000 | + | 8.66025i | 0.276924 | + | 0.479647i | ||||
\(327\) | −1.41421 | + | 2.44949i | −0.0782062 | + | 0.135457i | ||||
\(328\) | 11.3137 | 0.624695 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.00000 | −0.330289 | ||||||||
\(331\) | −10.0000 | + | 17.3205i | −0.549650 | + | 0.952021i | 0.448649 | + | 0.893708i | \(0.351905\pi\) |
−0.998298 | + | 0.0583130i | \(0.981428\pi\) | |||||||
\(332\) | −8.48528 | − | 14.6969i | −0.465690 | − | 0.806599i | ||||
\(333\) | −5.00000 | − | 8.66025i | −0.273998 | − | 0.474579i | ||||
\(334\) | 2.82843 | − | 4.89898i | 0.154765 | − | 0.268060i | ||||
\(335\) | −8.48528 | −0.463600 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 6.50000 | − | 11.2583i | 0.353553 | − | 0.612372i | ||||
\(339\) | −1.41421 | − | 2.44949i | −0.0768095 | − | 0.133038i | ||||
\(340\) | 12.0000 | + | 20.7846i | 0.650791 | + | 1.12720i | ||||
\(341\) | 0.707107 | − | 1.22474i | 0.0382920 | − | 0.0663237i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −18.0000 | + | 31.1769i | −0.969087 | + | 1.67851i | ||||
\(346\) | −5.65685 | − | 9.79796i | −0.304114 | − | 0.526742i | ||||
\(347\) | −10.0000 | − | 17.3205i | −0.536828 | − | 0.929814i | −0.999072 | − | 0.0430610i | \(-0.986289\pi\) |
0.462244 | − | 0.886753i | \(-0.347044\pi\) | |||||||
\(348\) | 1.41421 | − | 2.44949i | 0.0758098 | − | 0.131306i | ||||
\(349\) | −14.1421 | −0.757011 | −0.378506 | − | 0.925599i | \(-0.623562\pi\) | ||||
−0.378506 | + | 0.925599i | \(0.623562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 0.707107 | + | 1.22474i | 0.0376355 | + | 0.0651866i | 0.884230 | − | 0.467052i | \(-0.154684\pi\) |
−0.846594 | + | 0.532239i | \(0.821351\pi\) | |||||||
\(354\) | −1.00000 | − | 1.73205i | −0.0531494 | − | 0.0920575i | ||||
\(355\) | −4.24264 | + | 7.34847i | −0.225176 | + | 0.390016i | ||||
\(356\) | 7.07107 | 0.374766 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | 6.00000 | − | 10.3923i | 0.316668 | − | 0.548485i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(360\) | −2.12132 | − | 3.67423i | −0.111803 | − | 0.193649i | ||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | −3.53553 | + | 6.12372i | −0.185824 | + | 0.321856i | ||||
\(363\) | −1.41421 | −0.0742270 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0000 | 1.88433 | ||||||||
\(366\) | 2.00000 | − | 3.46410i | 0.104542 | − | 0.181071i | ||||
\(367\) | −10.6066 | − | 18.3712i | −0.553660 | − | 0.958967i | −0.998006 | − | 0.0631123i | \(-0.979897\pi\) |
0.444346 | − | 0.895855i | \(-0.353436\pi\) | |||||||
\(368\) | −3.00000 | − | 5.19615i | −0.156386 | − | 0.270868i | ||||
\(369\) | 5.65685 | − | 9.79796i | 0.294484 | − | 0.510061i | ||||
\(370\) | 42.4264 | 2.20564 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 2.82843 | + | 4.89898i | 0.146254 | + | 0.253320i | ||||
\(375\) | −24.0000 | − | 41.5692i | −1.23935 | − | 2.14663i | ||||
\(376\) | 2.12132 | − | 3.67423i | 0.109399 | − | 0.189484i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.00000 | −0.308199 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3137 | + | 19.5959i | 0.579619 | + | 1.00393i | ||||
\(382\) | −8.00000 | − | 13.8564i | −0.409316 | − | 0.708955i | ||||
\(383\) | 7.77817 | − | 13.4722i | 0.397446 | − | 0.688397i | −0.595964 | − | 0.803011i | \(-0.703230\pi\) |
0.993410 | + | 0.114614i | \(0.0365632\pi\) | |||||||
\(384\) | −1.41421 | −0.0721688 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | −4.94975 | − | 8.57321i | −0.251285 | − | 0.435239i | ||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.9411 | 1.71648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.0000 | −1.41241 | ||||||||
\(394\) | −11.0000 | + | 19.0526i | −0.554172 | + | 0.959854i | ||||
\(395\) | 33.9411 | + | 58.7878i | 1.70776 | + | 2.95793i | ||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 6.36396 | − | 11.0227i | 0.319398 | − | 0.553214i | −0.660965 | − | 0.750417i | \(-0.729853\pi\) |
0.980363 | + | 0.197203i | \(0.0631860\pi\) | |||||||
\(398\) | 1.41421 | 0.0708881 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.0000 | 0.650000 | ||||||||
\(401\) | −6.00000 | + | 10.3923i | −0.299626 | + | 0.518967i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) |
0.676425 | + | 0.736512i | \(0.263528\pi\) | |||||||
\(402\) | 1.41421 | + | 2.44949i | 0.0705346 | + | 0.122169i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.82843 | − | 4.89898i | 0.140720 | − | 0.243733i | ||||
\(405\) | 21.2132 | 1.05409 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000 | 0.495682 | ||||||||
\(408\) | 4.00000 | − | 6.92820i | 0.198030 | − | 0.342997i | ||||
\(409\) | −1.41421 | − | 2.44949i | −0.0699284 | − | 0.121119i | 0.828941 | − | 0.559336i | \(-0.188944\pi\) |
−0.898870 | + | 0.438216i | \(0.855610\pi\) | |||||||
\(410\) | 24.0000 | + | 41.5692i | 1.18528 | + | 2.05296i | ||||
\(411\) | −12.7279 | + | 22.0454i | −0.627822 | + | 1.08742i | ||||
\(412\) | −18.3848 | −0.905753 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | 36.0000 | − | 62.3538i | 1.76717 | − | 3.06083i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.00000 | − | 13.8564i | −0.391762 | − | 0.678551i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0416 | −1.17451 | −0.587255 | − | 0.809402i | \(-0.699792\pi\) | ||||
−0.587255 | + | 0.809402i | \(0.699792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | −4.00000 | + | 6.92820i | −0.194717 | + | 0.337260i | ||||
\(423\) | −2.12132 | − | 3.67423i | −0.103142 | − | 0.178647i | ||||
\(424\) | −4.00000 | − | 6.92820i | −0.194257 | − | 0.336463i | ||||
\(425\) | −36.7696 | + | 63.6867i | −1.78359 | + | 3.08926i | ||||
\(426\) | 2.82843 | 0.137038 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.0000 | 0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.9706 | − | 29.3939i | −0.818393 | − | 1.41750i | ||||
\(431\) | −16.0000 | − | 27.7128i | −0.770693 | − | 1.33488i | −0.937184 | − | 0.348836i | \(-0.886577\pi\) |
0.166491 | − | 0.986043i | \(-0.446756\pi\) | |||||||
\(432\) | −2.82843 | + | 4.89898i | −0.136083 | + | 0.235702i | ||||
\(433\) | 12.7279 | 0.611665 | 0.305832 | − | 0.952085i | \(-0.401065\pi\) | ||||
0.305832 | + | 0.952085i | \(0.401065\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0000 | 0.575356 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.00000 | − | 10.3923i | −0.286691 | − | 0.496564i | ||||
\(439\) | −12.7279 | + | 22.0454i | −0.607471 | + | 1.05217i | 0.384185 | + | 0.923256i | \(0.374482\pi\) |
−0.991656 | + | 0.128914i | \(0.958851\pi\) | |||||||
\(440\) | 4.24264 | 0.202260 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0000 | + | 31.1769i | −0.855206 | + | 1.48126i | 0.0212481 | + | 0.999774i | \(0.493236\pi\) |
−0.876454 | + | 0.481486i | \(0.840097\pi\) | |||||||
\(444\) | −7.07107 | − | 12.2474i | −0.335578 | − | 0.581238i | ||||
\(445\) | 15.0000 | + | 25.9808i | 0.711068 | + | 1.23161i | ||||
\(446\) | −10.6066 | + | 18.3712i | −0.502237 | + | 0.869900i | ||||
\(447\) | 14.1421 | 0.668900 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.0000 | −0.943858 | −0.471929 | − | 0.881636i | \(-0.656442\pi\) | ||||
−0.471929 | + | 0.881636i | \(0.656442\pi\) | |||||||
\(450\) | 6.50000 | − | 11.2583i | 0.306413 | − | 0.530723i | ||||
\(451\) | 5.65685 | + | 9.79796i | 0.266371 | + | 0.461368i | ||||
\(452\) | 1.00000 | + | 1.73205i | 0.0470360 | + | 0.0814688i | ||||
\(453\) | 2.82843 | − | 4.89898i | 0.132891 | − | 0.230174i | ||||
\(454\) | 14.1421 | 0.663723 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00000 | + | 12.1244i | −0.327446 | + | 0.567153i | −0.982004 | − | 0.188858i | \(-0.939521\pi\) |
0.654558 | + | 0.756012i | \(0.272855\pi\) | |||||||
\(458\) | 4.94975 | + | 8.57321i | 0.231287 | + | 0.400600i | ||||
\(459\) | −16.0000 | − | 27.7128i | −0.746816 | − | 1.29352i | ||||
\(460\) | 12.7279 | − | 22.0454i | 0.593442 | − | 1.02787i | ||||
\(461\) | −2.82843 | −0.131733 | −0.0658665 | − | 0.997828i | \(-0.520981\pi\) | ||||
−0.0658665 | + | 0.997828i | \(0.520981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | −1.00000 | + | 1.73205i | −0.0464238 | + | 0.0804084i | ||||
\(465\) | −4.24264 | − | 7.34847i | −0.196748 | − | 0.340777i | ||||
\(466\) | −7.00000 | − | 12.1244i | −0.324269 | − | 0.561650i | ||||
\(467\) | −2.12132 | + | 3.67423i | −0.0981630 | + | 0.170023i | −0.910924 | − | 0.412574i | \(-0.864630\pi\) |
0.812761 | + | 0.582597i | \(0.197963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.0000 | 0.830278 | ||||||||
\(471\) | −3.00000 | + | 5.19615i | −0.138233 | + | 0.239426i | ||||
\(472\) | 0.707107 | + | 1.22474i | 0.0325472 | + | 0.0563735i | ||||
\(473\) | −4.00000 | − | 6.92820i | −0.183920 | − | 0.318559i | ||||
\(474\) | 11.3137 | − | 19.5959i | 0.519656 | − | 0.900070i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.00000 | −0.366295 | ||||||||
\(478\) | 6.00000 | − | 10.3923i | 0.274434 | − | 0.475333i | ||||
\(479\) | 1.41421 | + | 2.44949i | 0.0646171 | + | 0.111920i | 0.896524 | − | 0.442995i | \(-0.146084\pi\) |
−0.831907 | + | 0.554915i | \(0.812751\pi\) | |||||||
\(480\) | −3.00000 | − | 5.19615i | −0.136931 | − | 0.237171i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 21.0000 | − | 36.3731i | 0.953561 | − | 1.65162i | ||||
\(486\) | 4.94975 | + | 8.57321i | 0.224525 | + | 0.388889i | ||||
\(487\) | −1.00000 | − | 1.73205i | −0.0453143 | − | 0.0784867i | 0.842479 | − | 0.538730i | \(-0.181096\pi\) |
−0.887793 | + | 0.460243i | \(0.847762\pi\) | |||||||
\(488\) | −1.41421 | + | 2.44949i | −0.0640184 | + | 0.110883i | ||||
\(489\) | 14.1421 | 0.639529 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 8.00000 | − | 13.8564i | 0.360668 | − | 0.624695i | ||||
\(493\) | −5.65685 | − | 9.79796i | −0.254772 | − | 0.441278i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.12132 | − | 3.67423i | 0.0953463 | − | 0.165145i | ||||
\(496\) | 1.41421 | 0.0635001 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −24.0000 | −1.07547 | ||||||||
\(499\) | −3.00000 | + | 5.19615i | −0.134298 | + | 0.232612i | −0.925329 | − | 0.379165i | \(-0.876211\pi\) |
0.791031 | + | 0.611776i | \(0.209545\pi\) | |||||||
\(500\) | 16.9706 | + | 29.3939i | 0.758947 | + | 1.31453i | ||||
\(501\) | −4.00000 | − | 6.92820i | −0.178707 | − | 0.309529i | ||||
\(502\) | 9.19239 | − | 15.9217i | 0.410276 | − | 0.710620i | ||||
\(503\) | −31.1127 | −1.38725 | −0.693623 | − | 0.720338i | \(-0.743987\pi\) | ||||
−0.693623 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | 1.06799 | ||||||||
\(506\) | 3.00000 | − | 5.19615i | 0.133366 | − | 0.230997i | ||||
\(507\) | −9.19239 | − | 15.9217i | −0.408248 | − | 0.707107i | ||||
\(508\) | −8.00000 | − | 13.8564i | −0.354943 | − | 0.614779i | ||||
\(509\) | 6.36396 | − | 11.0227i | 0.282078 | − | 0.488573i | −0.689819 | − | 0.723982i | \(-0.742310\pi\) |
0.971896 | + | 0.235409i | \(0.0756431\pi\) | |||||||
\(510\) | 33.9411 | 1.50294 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.707107 | + | 1.22474i | 0.0311891 | + | 0.0540212i | ||||
\(515\) | −39.0000 | − | 67.5500i | −1.71855 | − | 2.97661i | ||||
\(516\) | −5.65685 | + | 9.79796i | −0.249029 | + | 0.431331i | ||||
\(517\) | 4.24264 | 0.186591 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.707107 | + | 1.22474i | 0.0309789 | + | 0.0536570i | 0.881099 | − | 0.472931i | \(-0.156804\pi\) |
−0.850120 | + | 0.526589i | \(0.823471\pi\) | |||||||
\(522\) | 1.00000 | + | 1.73205i | 0.0437688 | + | 0.0758098i | ||||
\(523\) | 4.24264 | − | 7.34847i | 0.185518 | − | 0.321326i | −0.758233 | − | 0.651984i | \(-0.773937\pi\) |
0.943751 | + | 0.330657i | \(0.107270\pi\) | |||||||
\(524\) | 19.7990 | 0.864923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | −0.348817 | ||||||||
\(527\) | −4.00000 | + | 6.92820i | −0.174243 | + | 0.301797i | ||||
\(528\) | −0.707107 | − | 1.22474i | −0.0307729 | − | 0.0533002i | ||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 16.9706 | − | 29.3939i | 0.737154 | − | 1.27679i | ||||
\(531\) | 1.41421 | 0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.00000 | − | 8.66025i | 0.216371 | − | 0.374766i | ||||
\(535\) | 33.9411 | + | 58.7878i | 1.46740 | + | 2.54162i | ||||
\(536\) | −1.00000 | − | 1.73205i | −0.0431934 | − | 0.0748132i | ||||
\(537\) | 8.48528 | − | 14.6969i | 0.366167 | − | 0.634220i | ||||
\(538\) | −18.3848 | −0.792624 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −24.0000 | −1.03280 | ||||||||
\(541\) | 15.0000 | − | 25.9808i | 0.644900 | − | 1.11700i | −0.339424 | − | 0.940633i | \(-0.610232\pi\) |
0.984325 | − | 0.176367i | \(-0.0564345\pi\) | |||||||
\(542\) | −4.24264 | − | 7.34847i | −0.182237 | − | 0.315644i | ||||
\(543\) | 5.00000 | + | 8.66025i | 0.214571 | + | 0.371647i | ||||
\(544\) | −2.82843 | + | 4.89898i | −0.121268 | + | 0.210042i | ||||
\(545\) | 8.48528 | 0.363470 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.0000 | 1.88130 | 0.940652 | − | 0.339372i | \(-0.110215\pi\) | ||||
0.940652 | + | 0.339372i | \(0.110215\pi\) | |||||||
\(548\) | 9.00000 | − | 15.5885i | 0.384461 | − | 0.665906i | ||||
\(549\) | 1.41421 | + | 2.44949i | 0.0603572 | + | 0.104542i | ||||
\(550\) | 6.50000 | + | 11.2583i | 0.277161 | + | 0.480057i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −8.48528 | −0.361158 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 30.0000 | − | 51.9615i | 1.27343 | − | 2.20564i | ||||
\(556\) | 5.65685 | + | 9.79796i | 0.239904 | + | 0.415526i | ||||
\(557\) | 15.0000 | + | 25.9808i | 0.635570 | + | 1.10084i | 0.986394 | + | 0.164399i | \(0.0525683\pi\) |
−0.350824 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(558\) | 0.707107 | − | 1.22474i | 0.0299342 | − | 0.0518476i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 7.00000 | − | 12.1244i | 0.295277 | − | 0.511435i | ||||
\(563\) | 11.3137 | + | 19.5959i | 0.476816 | + | 0.825869i | 0.999647 | − | 0.0265668i | \(-0.00845748\pi\) |
−0.522831 | + | 0.852436i | \(0.675124\pi\) | |||||||
\(564\) | −3.00000 | − | 5.19615i | −0.126323 | − | 0.218797i | ||||
\(565\) | −4.24264 | + | 7.34847i | −0.178489 | + | 0.309152i | ||||
\(566\) | 19.7990 | 0.832214 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.00000 | −0.0839181 | ||||||||
\(569\) | −15.0000 | + | 25.9808i | −0.628833 | + | 1.08917i | 0.358954 | + | 0.933355i | \(0.383134\pi\) |
−0.987786 | + | 0.155815i | \(0.950200\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | − | 6.92820i | −0.167395 | − | 0.289936i | 0.770108 | − | 0.637913i | \(-0.220202\pi\) |
−0.937503 | + | 0.347977i | \(0.886869\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.6274 | −0.945274 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 78.0000 | 3.25282 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −3.53553 | − | 6.12372i | −0.147186 | − | 0.254934i | 0.783000 | − | 0.622021i | \(-0.213688\pi\) |
−0.930186 | + | 0.367087i | \(0.880355\pi\) | |||||||
\(578\) | −7.50000 | − | 12.9904i | −0.311959 | − | 0.540329i | ||||
\(579\) | −4.24264 | + | 7.34847i | −0.176318 | + | 0.305392i | ||||
\(580\) | −8.48528 | −0.352332 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −14.0000 | −0.580319 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 4.24264 | + | 7.34847i | 0.175562 | + | 0.304082i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.24264 | + | 7.34847i | −0.175262 | + | 0.303562i | ||||
\(587\) | 26.8701 | 1.10905 | 0.554523 | − | 0.832168i | \(-0.312901\pi\) | ||||
0.554523 | + | 0.832168i | \(0.312901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.00000 | + | 5.19615i | −0.123508 | + | 0.213922i | ||||
\(591\) | 15.5563 | + | 26.9444i | 0.639903 | + | 1.10834i | ||||
\(592\) | 5.00000 | + | 8.66025i | 0.205499 | + | 0.355934i | ||||
\(593\) | 21.2132 | − | 36.7423i | 0.871122 | − | 1.50883i | 0.0102845 | − | 0.999947i | \(-0.496726\pi\) |
0.860837 | − | 0.508880i | \(-0.169940\pi\) | |||||||
\(594\) | −5.65685 | −0.232104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | 1.00000 | − | 1.73205i | 0.0409273 | − | 0.0708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.00000 | + | 5.19615i | 0.122577 | + | 0.212309i | 0.920783 | − | 0.390075i | \(-0.127551\pi\) |
−0.798206 | + | 0.602384i | \(0.794218\pi\) | |||||||
\(600\) | 9.19239 | − | 15.9217i | 0.375278 | − | 0.650000i | ||||
\(601\) | −5.65685 | −0.230748 | −0.115374 | − | 0.993322i | \(-0.536807\pi\) | ||||
−0.115374 | + | 0.993322i | \(0.536807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | −2.00000 | + | 3.46410i | −0.0813788 | + | 0.140952i | ||||
\(605\) | 2.12132 | + | 3.67423i | 0.0862439 | + | 0.149379i | ||||
\(606\) | −4.00000 | − | 6.92820i | −0.162489 | − | 0.281439i | ||||
\(607\) | 8.48528 | − | 14.6969i | 0.344407 | − | 0.596530i | −0.640839 | − | 0.767675i | \(-0.721413\pi\) |
0.985246 | + | 0.171145i | \(0.0547467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | −0.485866 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.82843 | + | 4.89898i | 0.114332 | + | 0.198030i | ||||
\(613\) | 5.00000 | + | 8.66025i | 0.201948 | + | 0.349784i | 0.949156 | − | 0.314806i | \(-0.101939\pi\) |
−0.747208 | + | 0.664590i | \(0.768606\pi\) | |||||||
\(614\) | −12.7279 | + | 22.0454i | −0.513657 | + | 0.889680i | ||||
\(615\) | 67.8823 | 2.73728 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000 | 1.36879 | 0.684394 | − | 0.729112i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729112i | \(0.260067\pi\) | |||||||
\(618\) | −13.0000 | + | 22.5167i | −0.522937 | + | 0.905753i | ||||
\(619\) | 4.94975 | + | 8.57321i | 0.198947 | + | 0.344587i | 0.948187 | − | 0.317712i | \(-0.102914\pi\) |
−0.749240 | + | 0.662298i | \(0.769581\pi\) | |||||||
\(620\) | 3.00000 | + | 5.19615i | 0.120483 | + | 0.208683i | ||||
\(621\) | −16.9706 | + | 29.3939i | −0.681005 | + | 1.17954i | ||||
\(622\) | −18.3848 | −0.737162 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −39.5000 | + | 68.4160i | −1.58000 | + | 2.73664i | ||||
\(626\) | −6.36396 | − | 11.0227i | −0.254355 | − | 0.440556i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.12132 | − | 3.67423i | 0.0846499 | − | 0.146618i | ||||
\(629\) | −56.5685 | −2.25554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | −8.00000 | + | 13.8564i | −0.318223 | + | 0.551178i | ||||
\(633\) | 5.65685 | + | 9.79796i | 0.224840 | + | 0.389434i | ||||
\(634\) | −15.0000 | − | 25.9808i | −0.595726 | − | 1.03183i | ||||
\(635\) | 33.9411 | − | 58.7878i | 1.34691 | − | 2.33292i | ||||
\(636\) | −11.3137 | −0.448618 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | −1.00000 | + | 1.73205i | −0.0395594 | + | 0.0685189i | ||||
\(640\) | 2.12132 | + | 3.67423i | 0.0838525 | + | 0.145237i | ||||
\(641\) | 17.0000 | + | 29.4449i | 0.671460 | + | 1.16300i | 0.977490 | + | 0.210981i | \(0.0676657\pi\) |
−0.306031 | + | 0.952022i | \(0.599001\pi\) | |||||||
\(642\) | 11.3137 | − | 19.5959i | 0.446516 | − | 0.773389i | ||||
\(643\) | 38.1838 | 1.50582 | 0.752910 | − | 0.658123i | \(-0.228649\pi\) | ||||
0.752910 | + | 0.658123i | \(0.228649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −48.0000 | −1.89000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.77817 | − | 13.4722i | −0.305792 | − | 0.529647i | 0.671646 | − | 0.740873i | \(-0.265588\pi\) |
−0.977437 | + | 0.211226i | \(0.932254\pi\) | |||||||
\(648\) | 2.50000 | + | 4.33013i | 0.0982093 | + | 0.170103i | ||||
\(649\) | −0.707107 | + | 1.22474i | −0.0277564 | + | 0.0480754i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0000 | −0.391630 | ||||||||
\(653\) | −6.00000 | + | 10.3923i | −0.234798 | + | 0.406682i | −0.959214 | − | 0.282681i | \(-0.908776\pi\) |
0.724416 | + | 0.689363i | \(0.242110\pi\) | |||||||
\(654\) | −1.41421 | − | 2.44949i | −0.0553001 | − | 0.0957826i | ||||
\(655\) | 42.0000 | + | 72.7461i | 1.64108 | + | 2.84243i | ||||
\(656\) | −5.65685 | + | 9.79796i | −0.220863 | + | 0.382546i | ||||
\(657\) | 8.48528 | 0.331042 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 3.00000 | − | 5.19615i | 0.116775 | − | 0.202260i | ||||
\(661\) | 6.36396 | + | 11.0227i | 0.247529 | + | 0.428733i | 0.962840 | − | 0.270073i | \(-0.0870480\pi\) |
−0.715310 | + | 0.698807i | \(0.753715\pi\) | |||||||
\(662\) | −10.0000 | − | 17.3205i | −0.388661 | − | 0.673181i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.9706 | 0.658586 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0000 | 0.387492 | ||||||||
\(667\) | −6.00000 | + | 10.3923i | −0.232321 | + | 0.402392i | ||||
\(668\) | 2.82843 | + | 4.89898i | 0.109435 | + | 0.189547i | ||||
\(669\) | 15.0000 | + | 25.9808i | 0.579934 | + | 1.00447i | ||||
\(670\) | 4.24264 | − | 7.34847i | 0.163908 | − | 0.283896i | ||||
\(671\) | −2.82843 | −0.109190 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0000 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(674\) | −1.00000 | + | 1.73205i | −0.0385186 | + | 0.0667161i | ||||
\(675\) | −36.7696 | − | 63.6867i | −1.41526 | − | 2.45130i | ||||
\(676\) | 6.50000 | + | 11.2583i | 0.250000 | + | 0.433013i | ||||
\(677\) | −19.7990 | + | 34.2929i | −0.760937 | + | 1.31798i | 0.181431 | + | 0.983404i | \(0.441927\pi\) |
−0.942368 | + | 0.334578i | \(0.891406\pi\) | |||||||
\(678\) | 2.82843 | 0.108625 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −24.0000 | −0.920358 | ||||||||
\(681\) | 10.0000 | − | 17.3205i | 0.383201 | − | 0.663723i | ||||
\(682\) | 0.707107 | + | 1.22474i | 0.0270765 | + | 0.0468979i | ||||
\(683\) | 14.0000 | + | 24.2487i | 0.535695 | + | 0.927851i | 0.999129 | + | 0.0417198i | \(0.0132837\pi\) |
−0.463434 | + | 0.886131i | \(0.653383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 76.3675 | 2.91785 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0000 | 0.534133 | ||||||||
\(688\) | 4.00000 | − | 6.92820i | 0.152499 | − | 0.264135i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −18.0000 | − | 31.1769i | −0.685248 | − | 1.18688i | ||||
\(691\) | 7.77817 | − | 13.4722i | 0.295896 | − | 0.512506i | −0.679297 | − | 0.733863i | \(-0.737715\pi\) |
0.975193 | + | 0.221357i | \(0.0710486\pi\) | |||||||
\(692\) | 11.3137 | 0.430083 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.0000 | 0.759190 | ||||||||
\(695\) | −24.0000 | + | 41.5692i | −0.910372 | + | 1.57681i | ||||
\(696\) | 1.41421 | + | 2.44949i | 0.0536056 | + | 0.0928477i | ||||
\(697\) | −32.0000 | − | 55.4256i | −1.21209 | − | 2.09940i | ||||
\(698\) | 7.07107 | − | 12.2474i | 0.267644 | − | 0.463573i | ||||
\(699\) | −19.7990 | −0.748867 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.0000 | 1.88847 | 0.944237 | − | 0.329267i | \(-0.106802\pi\) | ||||
0.944237 | + | 0.329267i | \(0.106802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 12.7279 | − | 22.0454i | 0.479361 | − | 0.830278i | ||||
\(706\) | −1.41421 | −0.0532246 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.00000 | 0.0751646 | ||||||||
\(709\) | 10.0000 | − | 17.3205i | 0.375558 | − | 0.650485i | −0.614852 | − | 0.788642i | \(-0.710784\pi\) |
0.990410 | + | 0.138157i | \(0.0441178\pi\) | |||||||
\(710\) | −4.24264 | − | 7.34847i | −0.159223 | − | 0.275783i | ||||
\(711\) | 8.00000 | + | 13.8564i | 0.300023 | + | 0.519656i | ||||
\(712\) | −3.53553 | + | 6.12372i | −0.132500 | + | 0.229496i | ||||
\(713\) | 8.48528 | 0.317776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | + | 10.3923i | −0.224231 | + | 0.388379i | ||||
\(717\) | −8.48528 | − | 14.6969i | −0.316889 | − | 0.548867i | ||||
\(718\) | 6.00000 | + | 10.3923i | 0.223918 | + | 0.387837i | ||||
\(719\) | 9.19239 | − | 15.9217i | 0.342818 | − | 0.593779i | −0.642137 | − | 0.766590i | \(-0.721952\pi\) |
0.984955 | + | 0.172812i | \(0.0552852\pi\) | |||||||
\(720\) | 4.24264 | 0.158114 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −19.0000 | −0.707107 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.53553 | − | 6.12372i | −0.131397 | − | 0.227586i | ||||
\(725\) | −13.0000 | − | 22.5167i | −0.482808 | − | 0.836248i | ||||
\(726\) | 0.707107 | − | 1.22474i | 0.0262432 | − | 0.0454545i | ||||
\(727\) | −12.7279 | −0.472052 | −0.236026 | − | 0.971747i | \(-0.575845\pi\) | ||||
−0.236026 | + | 0.971747i | \(0.575845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −18.0000 | + | 31.1769i | −0.666210 | + | 1.15391i | ||||
\(731\) | 22.6274 | + | 39.1918i | 0.836905 | + | 1.44956i | ||||
\(732\) | 2.00000 | + | 3.46410i | 0.0739221 | + | 0.128037i | ||||
\(733\) | 7.07107 | − | 12.2474i | 0.261176 | − | 0.452370i | −0.705379 | − | 0.708831i | \(-0.749223\pi\) |
0.966555 | + | 0.256461i | \(0.0825564\pi\) | |||||||
\(734\) | 21.2132 | 0.782994 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 1.00000 | − | 1.73205i | 0.0368355 | − | 0.0638009i | ||||
\(738\) | 5.65685 | + | 9.79796i | 0.208232 | + | 0.360668i | ||||
\(739\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(740\) | −21.2132 | + | 36.7423i | −0.779813 | + | 1.35068i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.0000 | −1.61420 | −0.807102 | − | 0.590412i | \(-0.798965\pi\) | ||||
−0.807102 | + | 0.590412i | \(0.798965\pi\) | |||||||
\(744\) | 1.00000 | − | 1.73205i | 0.0366618 | − | 0.0635001i | ||||
\(745\) | −21.2132 | − | 36.7423i | −0.777192 | − | 1.34614i | ||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 8.48528 | − | 14.6969i | 0.310460 | − | 0.537733i | ||||
\(748\) | −5.65685 | −0.206835 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 48.0000 | 1.75271 | ||||||||
\(751\) | 7.00000 | − | 12.1244i | 0.255434 | − | 0.442424i | −0.709580 | − | 0.704625i | \(-0.751115\pi\) |
0.965013 | + | 0.262201i | \(0.0844484\pi\) | |||||||
\(752\) | 2.12132 | + | 3.67423i | 0.0773566 | + | 0.133986i | ||||
\(753\) | −13.0000 | − | 22.5167i | −0.473746 | − | 0.820553i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.9706 | −0.617622 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.00000 | −0.290765 | −0.145382 | − | 0.989376i | \(-0.546441\pi\) | ||||
−0.145382 | + | 0.989376i | \(0.546441\pi\) | |||||||
\(758\) | 3.00000 | − | 5.19615i | 0.108965 | − | 0.188733i | ||||
\(759\) | −4.24264 | − | 7.34847i | −0.153998 | − | 0.266733i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.2132 | + | 36.7423i | −0.768978 | + | 1.33191i | 0.169140 | + | 0.985592i | \(0.445901\pi\) |
−0.938118 | + | 0.346317i | \(0.887432\pi\) | |||||||
\(762\) | −22.6274 | −0.819705 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | −12.0000 | + | 20.7846i | −0.433861 | + | 0.751469i | ||||
\(766\) | 7.77817 | + | 13.4722i | 0.281037 | + | 0.486770i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.707107 | − | 1.22474i | 0.0255155 | − | 0.0441942i | ||||
\(769\) | −19.7990 | −0.713970 | −0.356985 | − | 0.934110i | \(-0.616195\pi\) | ||||
−0.356985 | + | 0.934110i | \(0.616195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000 | 0.0720282 | ||||||||
\(772\) | 3.00000 | − | 5.19615i | 0.107972 | − | 0.187014i | ||||
\(773\) | 0.707107 | + | 1.22474i | 0.0254329 | + | 0.0440510i | 0.878462 | − | 0.477813i | \(-0.158570\pi\) |
−0.853029 | + | 0.521864i | \(0.825237\pi\) | |||||||
\(774\) | −4.00000 | − | 6.92820i | −0.143777 | − | 0.249029i | ||||
\(775\) | −9.19239 | + | 15.9217i | −0.330200 | + | 0.571924i | ||||
\(776\) | 9.89949 | 0.355371 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.00000 | − | 1.73205i | −0.0357828 | − | 0.0619777i | ||||
\(782\) | −16.9706 | + | 29.3939i | −0.606866 | + | 1.05112i | ||||
\(783\) | 11.3137 | 0.404319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.0000 | 0.642448 | ||||||||
\(786\) | 14.0000 | − | 24.2487i | 0.499363 | − | 0.864923i | ||||
\(787\) | −2.82843 | − | 4.89898i | −0.100823 | − | 0.174630i | 0.811201 | − | 0.584767i | \(-0.198814\pi\) |
−0.912024 | + | 0.410137i | \(0.865481\pi\) | |||||||
\(788\) | −11.0000 | − | 19.0526i | −0.391859 | − | 0.678719i | ||||
\(789\) | −5.65685 | + | 9.79796i | −0.201389 | + | 0.348817i | ||||
\(790\) | −67.8823 | −2.41514 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6.36396 | + | 11.0227i | 0.225849 | + | 0.391181i | ||||
\(795\) | −24.0000 | − | 41.5692i | −0.851192 | − | 1.47431i | ||||
\(796\) | −0.707107 | + | 1.22474i | −0.0250627 | + | 0.0434099i | ||||
\(797\) | −7.07107 | −0.250470 | −0.125235 | − | 0.992127i | \(-0.539968\pi\) | ||||
−0.125235 | + | 0.992127i | \(0.539968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −6.50000 | + | 11.2583i | −0.229810 | + | 0.398042i | ||||
\(801\) | 3.53553 | + | 6.12372i | 0.124922 | + | 0.216371i | ||||
\(802\) | −6.00000 | − | 10.3923i | −0.211867 | − | 0.366965i | ||||
\(803\) | −4.24264 | + | 7.34847i | −0.149720 | + | 0.259322i | ||||
\(804\) | −2.82843 | −0.0997509 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.0000 | + | 22.5167i | −0.457622 | + | 0.792624i | ||||
\(808\) | 2.82843 | + | 4.89898i | 0.0995037 | + | 0.172345i | ||||
\(809\) | −27.0000 | − | 46.7654i | −0.949269 | − | 1.64418i | −0.746968 | − | 0.664860i | \(-0.768491\pi\) |
−0.202301 | − | 0.979323i | \(-0.564842\pi\) | |||||||
\(810\) | −10.6066 | + | 18.3712i | −0.372678 | + | 0.645497i | ||||
\(811\) | −36.7696 | −1.29115 | −0.645577 | − | 0.763695i | \(-0.723383\pi\) | ||||
−0.645577 | + | 0.763695i | \(0.723383\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | −0.420858 | ||||||||
\(814\) | −5.00000 | + | 8.66025i | −0.175250 | + | 0.303542i | ||||
\(815\) | −21.2132 | − | 36.7423i | −0.743066 | − | 1.28703i | ||||
\(816\) | 4.00000 | + | 6.92820i | 0.140028 | + | 0.242536i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.82843 | 0.0988936 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.0000 | −1.67623 | ||||||||
\(821\) | 19.0000 | − | 32.9090i | 0.663105 | − | 1.14853i | −0.316691 | − | 0.948529i | \(-0.602572\pi\) |
0.979795 | − | 0.200002i | \(-0.0640949\pi\) | |||||||
\(822\) | −12.7279 | − | 22.0454i | −0.443937 | − | 0.768922i | ||||
\(823\) | −20.0000 | − | 34.6410i | −0.697156 | − | 1.20751i | −0.969448 | − | 0.245295i | \(-0.921115\pi\) |
0.272292 | − | 0.962215i | \(-0.412218\pi\) | |||||||
\(824\) | 9.19239 | − | 15.9217i | 0.320232 | − | 0.554658i | ||||
\(825\) | 18.3848 | 0.640076 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.0000 | −1.11275 | −0.556375 | − | 0.830932i | \(-0.687808\pi\) | ||||
−0.556375 | + | 0.830932i | \(0.687808\pi\) | |||||||
\(828\) | 3.00000 | − | 5.19615i | 0.104257 | − | 0.180579i | ||||
\(829\) | −2.12132 | − | 3.67423i | −0.0736765 | − | 0.127611i | 0.826833 | − | 0.562447i | \(-0.190140\pi\) |
−0.900510 | + | 0.434835i | \(0.856807\pi\) | |||||||
\(830\) | 36.0000 | + | 62.3538i | 1.24958 | + | 2.16433i | ||||
\(831\) | −1.41421 | + | 2.44949i | −0.0490585 | + | 0.0849719i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.0000 | 0.554035 | ||||||||
\(835\) | −12.0000 | + | 20.7846i | −0.415277 | + | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | − | 6.92820i | −0.138260 | − | 0.239474i | ||||
\(838\) | 12.0208 | − | 20.8207i | 0.415252 | − | 0.719238i | ||||
\(839\) | −1.41421 | −0.0488241 | −0.0244120 | − | 0.999702i | \(-0.507771\pi\) | ||||
−0.0244120 | + | 0.999702i | \(0.507771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 10.0000 | − | 17.3205i | 0.344623 | − | 0.596904i | ||||
\(843\) | −9.89949 | − | 17.1464i | −0.340957 | − | 0.590554i | ||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | −27.5772 | + | 47.7650i | −0.948683 | + | 1.64317i | ||||
\(846\) | 4.24264 | 0.145865 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.00000 | 0.274721 | ||||||||
\(849\) | 14.0000 | − | 24.2487i | 0.480479 | − | 0.832214i | ||||
\(850\) | −36.7696 | − | 63.6867i | −1.26119 | − | 2.18444i | ||||
\(851\) | 30.0000 | + | 51.9615i | 1.02839 | + | 1.78122i | ||||
\(852\) | −1.41421 | + | 2.44949i | −0.0484502 | + | 0.0839181i | ||||
\(853\) | −28.2843 | −0.968435 | −0.484218 | − | 0.874948i | \(-0.660896\pi\) | ||||
−0.484218 | + | 0.874948i | \(0.660896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.00000 | + | 13.8564i | −0.273434 | + | 0.473602i | ||||
\(857\) | −12.7279 | − | 22.0454i | −0.434778 | − | 0.753057i | 0.562500 | − | 0.826797i | \(-0.309840\pi\) |
−0.997277 | + | 0.0737406i | \(0.976506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.36396 | − | 11.0227i | 0.217136 | − | 0.376090i | −0.736796 | − | 0.676116i | \(-0.763662\pi\) |
0.953931 | + | 0.300026i | \(0.0969953\pi\) | |||||||
\(860\) | 33.9411 | 1.15738 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.0000 | 1.08992 | ||||||||
\(863\) | 12.0000 | − | 20.7846i | 0.408485 | − | 0.707516i | −0.586235 | − | 0.810141i | \(-0.699391\pi\) |
0.994720 | + | 0.102624i | \(0.0327240\pi\) | |||||||
\(864\) | −2.82843 | − | 4.89898i | −0.0962250 | − | 0.166667i | ||||
\(865\) | 24.0000 | + | 41.5692i | 0.816024 | + | 1.41340i | ||||
\(866\) | −6.36396 | + | 11.0227i | −0.216256 | + | 0.374567i | ||||
\(867\) | −21.2132 | −0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | −6.00000 | + | 10.3923i | −0.203419 | + | 0.352332i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.00000 | + | 1.73205i | 0.0338643 | + | 0.0586546i | ||||
\(873\) | 4.94975 | − | 8.57321i | 0.167524 | − | 0.290159i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | −17.0000 | + | 29.4449i | −0.574049 | + | 0.994282i | 0.422095 | + | 0.906552i | \(0.361295\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | −12.7279 | − | 22.0454i | −0.429547 | − | 0.743996i | ||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | −2.12132 | + | 3.67423i | −0.0715097 | + | 0.123858i | ||||
\(881\) | 29.6985 | 1.00057 | 0.500284 | − | 0.865862i | \(-0.333229\pi\) | ||||
0.500284 | + | 0.865862i | \(0.333229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0000 | −1.21150 | −0.605748 | − | 0.795656i | \(-0.707126\pi\) | ||||
−0.605748 | + | 0.795656i | \(0.707126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.24264 | + | 7.34847i | 0.142615 | + | 0.247016i | ||||
\(886\) | −18.0000 | − | 31.1769i | −0.604722 | − | 1.04741i | ||||
\(887\) | 18.3848 | − | 31.8434i | 0.617300 | − | 1.06920i | −0.372676 | − | 0.927962i | \(-0.621560\pi\) |
0.989976 | − | 0.141234i | \(-0.0451070\pi\) | |||||||
\(888\) | 14.1421 | 0.474579 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −30.0000 | −1.00560 | ||||||||
\(891\) | −2.50000 | + | 4.33013i | −0.0837532 | + | 0.145065i | ||||
\(892\) | −10.6066 | − | 18.3712i | −0.355135 | − | 0.615112i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −7.07107 | + | 12.2474i | −0.236492 | + | 0.409616i | ||||
\(895\) | −50.9117 | −1.70179 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0000 | − | 17.3205i | 0.333704 | − | 0.577993i | ||||
\(899\) | −1.41421 | − | 2.44949i | −0.0471667 | − | 0.0816951i | ||||
\(900\) | 6.50000 | + | 11.2583i | 0.216667 | + | 0.375278i | ||||
\(901\) | −22.6274 | + | 39.1918i | −0.753829 | + | 1.30567i | ||||
\(902\) | −11.3137 | −0.376705 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.00000 | −0.0665190 | ||||||||
\(905\) | 15.0000 | − | 25.9808i | 0.498617 | − | 0.863630i | ||||
\(906\) | 2.82843 | + | 4.89898i | 0.0939682 | + | 0.162758i | ||||
\(907\) | 7.00000 | + | 12.1244i | 0.232431 | + | 0.402583i | 0.958523 | − | 0.285015i | \(-0.0919986\pi\) |
−0.726092 | + | 0.687598i | \(0.758665\pi\) | |||||||
\(908\) | −7.07107 | + | 12.2474i | −0.234662 | + | 0.406446i | ||||
\(909\) | 5.65685 | 0.187626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.48528 | + | 14.6969i | 0.280822 | + | 0.486398i | ||||
\(914\) | −7.00000 | − | 12.1244i | −0.231539 | − | 0.401038i | ||||
\(915\) | −8.48528 | + | 14.6969i | −0.280515 | + | 0.485866i | ||||
\(916\) | −9.89949 | −0.327089 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 32.0000 | 1.05616 | ||||||||
\(919\) | −4.00000 | + | 6.92820i | −0.131948 | + | 0.228540i | −0.924427 | − | 0.381358i | \(-0.875456\pi\) |
0.792480 | + | 0.609898i | \(0.208790\pi\) | |||||||
\(920\) | 12.7279 | + | 22.0454i | 0.419627 | + | 0.726816i | ||||
\(921\) | 18.0000 | + | 31.1769i | 0.593120 | + | 1.02731i | ||||
\(922\) | 1.41421 | − | 2.44949i | 0.0465746 | − | 0.0806696i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −130.000 | −4.27437 | ||||||||
\(926\) | −13.0000 | + | 22.5167i | −0.427207 | + | 0.739943i | ||||
\(927\) | −9.19239 | − | 15.9217i | −0.301918 | − | 0.522937i | ||||
\(928\) | −1.00000 | − | 1.73205i | −0.0328266 | − | 0.0568574i | ||||
\(929\) | −16.2635 | + | 28.1691i | −0.533587 | + | 0.924199i | 0.465644 | + | 0.884972i | \(0.345823\pi\) |
−0.999230 | + | 0.0392269i | \(0.987510\pi\) | |||||||
\(930\) | 8.48528 | 0.278243 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.0000 | 0.458585 | ||||||||
\(933\) | −13.0000 | + | 22.5167i | −0.425601 | + | 0.737162i | ||||
\(934\) | −2.12132 | − | 3.67423i | −0.0694117 | − | 0.120225i | ||||
\(935\) | −12.0000 | − | 20.7846i | −0.392442 | − | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.4558 | −0.831606 | −0.415803 | − | 0.909455i | \(-0.636499\pi\) | ||||
−0.415803 | + | 0.909455i | \(0.636499\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.0000 | −0.587408 | ||||||||
\(940\) | −9.00000 | + | 15.5885i | −0.293548 | + | 0.508439i | ||||
\(941\) | 15.5563 | + | 26.9444i | 0.507122 | + | 0.878362i | 0.999966 | + | 0.00824396i | \(0.00262416\pi\) |
−0.492844 | + | 0.870118i | \(0.664043\pi\) | |||||||
\(942\) | −3.00000 | − | 5.19615i | −0.0977453 | − | 0.169300i | ||||
\(943\) | −33.9411 | + | 58.7878i | −1.10528 | + | 1.91439i | ||||
\(944\) | −1.41421 | −0.0460287 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | −26.0000 | + | 45.0333i | −0.844886 | + | 1.46339i | 0.0408333 | + | 0.999166i | \(0.486999\pi\) |
−0.885720 | + | 0.464220i | \(0.846335\pi\) | |||||||
\(948\) | 11.3137 | + | 19.5959i | 0.367452 | + | 0.636446i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42.4264 | −1.37577 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0000 | 0.453504 | 0.226752 | − | 0.973952i | \(-0.427189\pi\) | ||||
0.226752 | + | 0.973952i | \(0.427189\pi\) | |||||||
\(954\) | 4.00000 | − | 6.92820i | 0.129505 | − | 0.224309i | ||||
\(955\) | 33.9411 | + | 58.7878i | 1.09831 | + | 1.90233i | ||||
\(956\) | 6.00000 | + | 10.3923i | 0.194054 | + | 0.336111i | ||||
\(957\) | −1.41421 | + | 2.44949i | −0.0457150 | + | 0.0791808i | ||||
\(958\) | −2.82843 | −0.0913823 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.00000 | 0.193649 | ||||||||
\(961\) | 14.5000 | − | 25.1147i | 0.467742 | − | 0.810153i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.00000 | + | 13.8564i | 0.257796 | + | 0.446516i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.4558 | 0.819453 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.0000 | + | 36.3731i | 0.674269 | + | 1.16787i | ||||
\(971\) | 26.1630 | − | 45.3156i | 0.839609 | − | 1.45425i | −0.0506128 | − | 0.998718i | \(-0.516117\pi\) |
0.890222 | − | 0.455527i | \(-0.150549\pi\) | |||||||
\(972\) | −9.89949 | −0.317526 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.41421 | − | 2.44949i | −0.0452679 | − | 0.0784063i | ||||
\(977\) | −26.0000 | − | 45.0333i | −0.831814 | − | 1.44074i | −0.896599 | − | 0.442844i | \(-0.853969\pi\) |
0.0647848 | − | 0.997899i | \(-0.479364\pi\) | |||||||
\(978\) | −7.07107 | + | 12.2474i | −0.226108 | + | 0.391630i | ||||
\(979\) | −7.07107 | −0.225992 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | 0.707107 | + | 1.22474i | 0.0225532 | + | 0.0390633i | 0.877082 | − | 0.480341i | \(-0.159487\pi\) |
−0.854529 | + | 0.519404i | \(0.826154\pi\) | |||||||
\(984\) | 8.00000 | + | 13.8564i | 0.255031 | + | 0.441726i | ||||
\(985\) | 46.6690 | − | 80.8332i | 1.48700 | − | 2.57556i | ||||
\(986\) | 11.3137 | 0.360302 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | − | 41.5692i | 0.763156 | − | 1.32182i | ||||
\(990\) | 2.12132 | + | 3.67423i | 0.0674200 | + | 0.116775i | ||||
\(991\) | 23.0000 | + | 39.8372i | 0.730619 | + | 1.26547i | 0.956619 | + | 0.291342i | \(0.0941018\pi\) |
−0.226000 | + | 0.974127i | \(0.572565\pi\) | |||||||
\(992\) | −0.707107 | + | 1.22474i | −0.0224507 | + | 0.0388857i | ||||
\(993\) | −28.2843 | −0.897574 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.00000 | −0.190213 | ||||||||
\(996\) | 12.0000 | − | 20.7846i | 0.380235 | − | 0.658586i | ||||
\(997\) | 8.48528 | + | 14.6969i | 0.268732 | + | 0.465457i | 0.968535 | − | 0.248879i | \(-0.0800622\pi\) |
−0.699803 | + | 0.714336i | \(0.746729\pi\) | |||||||
\(998\) | −3.00000 | − | 5.19615i | −0.0949633 | − | 0.164481i | ||||
\(999\) | 28.2843 | − | 48.9898i | 0.894875 | − | 1.54997i |
(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 | 1078.2.e.p.177.2 | 4 | ||
7.2 | even | 3 | 1078.2.a.u.1.1 | ✓ | 2 | ||
7.3 | odd | 6 | inner | 1078.2.e.p.67.1 | 4 | ||
7.4 | even | 3 | inner | 1078.2.e.p.67.2 | 4 | ||
7.5 | odd | 6 | 1078.2.a.u.1.2 | yes | 2 | ||
7.6 | odd | 2 | inner | 1078.2.e.p.177.1 | 4 | ||
21.2 | odd | 6 | 9702.2.a.cp.1.2 | 2 | |||
21.5 | even | 6 | 9702.2.a.cp.1.1 | 2 | |||
28.19 | even | 6 | 8624.2.a.bs.1.1 | 2 | |||
28.23 | odd | 6 | 8624.2.a.bs.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.a.u.1.1 | ✓ | 2 | 7.2 | even | 3 | ||
1078.2.a.u.1.2 | yes | 2 | 7.5 | odd | 6 | ||
1078.2.e.p.67.1 | 4 | 7.3 | odd | 6 | inner | ||
1078.2.e.p.67.2 | 4 | 7.4 | even | 3 | inner | ||
1078.2.e.p.177.1 | 4 | 7.6 | odd | 2 | inner | ||
1078.2.e.p.177.2 | 4 | 1.1 | even | 1 | trivial | ||
8624.2.a.bs.1.1 | 2 | 28.19 | even | 6 | |||
8624.2.a.bs.1.2 | 2 | 28.23 | odd | 6 | |||
9702.2.a.cp.1.1 | 2 | 21.5 | even | 6 | |||
9702.2.a.cp.1.2 | 2 | 21.2 | odd | 6 |