Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.d.191.2 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.41421 | + | 1.00000i | 0.816497 | + | 0.577350i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 1.70711 | − | 0.292893i | 0.696923 | − | 0.119573i | ||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 1.00000 | − | 1.41421i | 0.288675 | − | 0.408248i | ||||
\(13\) | 1.00000 | − | 1.00000i | 0.277350 | − | 0.277350i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) |
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 1.41421 | − | 1.41421i | 0.377964 | − | 0.377964i | ||||
\(15\) | 0.292893 | + | 1.70711i | 0.0756247 | + | 0.440773i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.24264 | + | 4.24264i | 1.02899 | + | 1.02899i | 0.999567 | + | 0.0294245i | \(0.00936746\pi\) |
0.0294245 | + | 0.999567i | \(0.490633\pi\) | |||||||
\(18\) | 2.70711 | + | 1.29289i | 0.638071 | + | 0.304738i | ||||
\(19\) | −3.00000 | + | 3.00000i | −0.688247 | + | 0.688247i | −0.961844 | − | 0.273597i | \(-0.911786\pi\) |
0.273597 | + | 0.961844i | \(0.411786\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | 2.82843 | + | 2.00000i | 0.617213 | + | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | − | 2.82843i | −0.589768 | − | 0.589768i | 0.347801 | − | 0.937568i | \(-0.386929\pi\) |
−0.937568 | + | 0.347801i | \(0.886929\pi\) | |||||||
\(24\) | −0.292893 | − | 1.70711i | −0.0597866 | − | 0.348462i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | − | 1.41421i | − | 0.277350i | ||||||
\(27\) | −1.41421 | + | 5.00000i | −0.272166 | + | 0.962250i | ||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | 4.24264 | − | 4.24264i | 0.787839 | − | 0.787839i | −0.193301 | − | 0.981140i | \(-0.561919\pi\) |
0.981140 | + | 0.193301i | \(0.0619194\pi\) | |||||||
\(30\) | 1.41421 | + | 1.00000i | 0.258199 | + | 0.182574i | ||||
\(31\) | −7.00000 | − | 7.00000i | −1.25724 | − | 1.25724i | −0.952407 | − | 0.304830i | \(-0.901400\pi\) |
−0.304830 | − | 0.952407i | \(-0.598600\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 1.41421 | + | 1.41421i | 0.239046 | + | 0.239046i | ||||
\(36\) | 2.82843 | − | 1.00000i | 0.471405 | − | 0.166667i | ||||
\(37\) | −1.00000 | + | 6.00000i | −0.164399 | + | 0.986394i | ||||
\(38\) | 4.24264i | 0.688247i | ||||||||
\(39\) | 2.41421 | − | 0.414214i | 0.386584 | − | 0.0663273i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 3.41421 | − | 0.585786i | 0.526825 | − | 0.0903888i | ||||
\(43\) | 7.00000 | − | 7.00000i | 1.06749 | − | 1.06749i | 0.0699387 | − | 0.997551i | \(-0.477720\pi\) |
0.997551 | − | 0.0699387i | \(-0.0222804\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.29289 | + | 2.70711i | −0.192733 | + | 0.403552i | ||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | − | 2.82843i | − | 0.412568i | −0.978492 | − | 0.206284i | \(-0.933863\pi\) | ||
0.978492 | − | 0.206284i | \(-0.0661372\pi\) | |||||||
\(48\) | −1.41421 | − | 1.00000i | −0.204124 | − | 0.144338i | ||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0.707107 | + | 0.707107i | 0.100000 | + | 0.100000i | ||||
\(51\) | 1.75736 | + | 10.2426i | 0.246080 | + | 1.43426i | ||||
\(52\) | −1.00000 | − | 1.00000i | −0.138675 | − | 0.138675i | ||||
\(53\) | 5.65685i | 0.777029i | 0.921443 | + | 0.388514i | \(0.127012\pi\) | ||||
−0.921443 | + | 0.388514i | \(0.872988\pi\) | |||||||
\(54\) | 2.53553 | + | 4.53553i | 0.345042 | + | 0.617208i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.41421 | − | 1.41421i | −0.188982 | − | 0.188982i | ||||
\(57\) | −7.24264 | + | 1.24264i | −0.959311 | + | 0.164592i | ||||
\(58\) | − | 6.00000i | − | 0.787839i | ||||||
\(59\) | 5.65685 | + | 5.65685i | 0.736460 | + | 0.736460i | 0.971891 | − | 0.235431i | \(-0.0756503\pi\) |
−0.235431 | + | 0.971891i | \(0.575650\pi\) | |||||||
\(60\) | 1.70711 | − | 0.292893i | 0.220387 | − | 0.0378124i | ||||
\(61\) | −9.00000 | − | 9.00000i | −1.15233 | − | 1.15233i | −0.986084 | − | 0.166248i | \(-0.946835\pi\) |
−0.166248 | − | 0.986084i | \(-0.553165\pi\) | |||||||
\(62\) | −9.89949 | −1.25724 | ||||||||
\(63\) | 2.00000 | + | 5.65685i | 0.251976 | + | 0.712697i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 1.41421 | 0.175412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 4.24264 | − | 4.24264i | 0.514496 | − | 0.514496i | ||||
\(69\) | −1.17157 | − | 6.82843i | −0.141041 | − | 0.822046i | ||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | 2.82843i | 0.335673i | 0.985815 | + | 0.167836i | \(0.0536780\pi\) | ||||
−0.985815 | + | 0.167836i | \(0.946322\pi\) | |||||||
\(72\) | 1.29289 | − | 2.70711i | 0.152369 | − | 0.319036i | ||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 3.53553 | + | 4.94975i | 0.410997 | + | 0.575396i | ||||
\(75\) | −1.00000 | + | 1.41421i | −0.115470 | + | 0.163299i | ||||
\(76\) | 3.00000 | + | 3.00000i | 0.344124 | + | 0.344124i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.41421 | − | 2.00000i | 0.160128 | − | 0.226455i | ||||
\(79\) | 3.00000 | − | 3.00000i | 0.337526 | − | 0.337526i | −0.517909 | − | 0.855436i | \(-0.673290\pi\) |
0.855436 | + | 0.517909i | \(0.173290\pi\) | |||||||
\(80\) | −0.707107 | − | 0.707107i | −0.0790569 | − | 0.0790569i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 4.00000 | − | 4.00000i | 0.441726 | − | 0.441726i | ||||
\(83\) | 2.82843i | 0.310460i | 0.987878 | + | 0.155230i | \(0.0496119\pi\) | ||||
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | 2.00000 | − | 2.82843i | 0.218218 | − | 0.308607i | ||||
\(85\) | 6.00000i | 0.650791i | ||||||||
\(86\) | − | 9.89949i | − | 1.06749i | ||||||
\(87\) | 10.2426 | − | 1.75736i | 1.09813 | − | 0.188409i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41421 | + | 1.41421i | −0.149906 | + | 0.149906i | −0.778076 | − | 0.628170i | \(-0.783804\pi\) |
0.628170 | + | 0.778076i | \(0.283804\pi\) | |||||||
\(90\) | 1.00000 | + | 2.82843i | 0.105409 | + | 0.298142i | ||||
\(91\) | 2.00000 | − | 2.00000i | 0.209657 | − | 0.209657i | ||||
\(92\) | −2.82843 | + | 2.82843i | −0.294884 | + | 0.294884i | ||||
\(93\) | −2.89949 | − | 16.8995i | −0.300664 | − | 1.75240i | ||||
\(94\) | −2.00000 | − | 2.00000i | −0.206284 | − | 0.206284i | ||||
\(95\) | −4.24264 | −0.435286 | ||||||||
\(96\) | −1.70711 | + | 0.292893i | −0.174231 | + | 0.0298933i | ||||
\(97\) | 7.00000 | − | 7.00000i | 0.710742 | − | 0.710742i | −0.255948 | − | 0.966691i | \(-0.582388\pi\) |
0.966691 | + | 0.255948i | \(0.0823876\pi\) | |||||||
\(98\) | −2.12132 | + | 2.12132i | −0.214286 | + | 0.214286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.82843 | −0.281439 | −0.140720 | − | 0.990050i | \(-0.544942\pi\) | ||||
−0.140720 | + | 0.990050i | \(0.544942\pi\) | |||||||
\(102\) | 8.48528 | + | 6.00000i | 0.840168 | + | 0.594089i | ||||
\(103\) | −5.00000 | − | 5.00000i | −0.492665 | − | 0.492665i | 0.416480 | − | 0.909145i | \(-0.363264\pi\) |
−0.909145 | + | 0.416480i | \(0.863264\pi\) | |||||||
\(104\) | −1.41421 | −0.138675 | ||||||||
\(105\) | 0.585786 | + | 3.41421i | 0.0571669 | + | 0.333193i | ||||
\(106\) | 4.00000 | + | 4.00000i | 0.388514 | + | 0.388514i | ||||
\(107\) | − | 11.3137i | − | 1.09374i | −0.837218 | − | 0.546869i | \(-0.815820\pi\) | ||
0.837218 | − | 0.546869i | \(-0.184180\pi\) | |||||||
\(108\) | 5.00000 | + | 1.41421i | 0.481125 | + | 0.136083i | ||||
\(109\) | −3.00000 | + | 3.00000i | −0.287348 | + | 0.287348i | −0.836031 | − | 0.548683i | \(-0.815129\pi\) |
0.548683 | + | 0.836031i | \(0.315129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.41421 | + | 7.48528i | −0.703726 | + | 0.710471i | ||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | −1.41421 | + | 1.41421i | −0.133038 | + | 0.133038i | −0.770490 | − | 0.637452i | \(-0.779988\pi\) |
0.637452 | + | 0.770490i | \(0.279988\pi\) | |||||||
\(114\) | −4.24264 | + | 6.00000i | −0.397360 | + | 0.561951i | ||||
\(115\) | − | 4.00000i | − | 0.373002i | ||||||
\(116\) | −4.24264 | − | 4.24264i | −0.393919 | − | 0.393919i | ||||
\(117\) | 3.82843 | + | 1.82843i | 0.353938 | + | 0.169038i | ||||
\(118\) | 8.00000 | 0.736460 | ||||||||
\(119\) | 8.48528 | + | 8.48528i | 0.777844 | + | 0.777844i | ||||
\(120\) | 1.00000 | − | 1.41421i | 0.0912871 | − | 0.129099i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | −12.7279 | −1.15233 | ||||||||
\(123\) | 8.00000 | + | 5.65685i | 0.721336 | + | 0.510061i | ||||
\(124\) | −7.00000 | + | 7.00000i | −0.628619 | + | 0.628619i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 5.41421 | + | 2.58579i | 0.482336 | + | 0.230360i | ||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 16.8995 | − | 2.89949i | 1.48792 | − | 0.255286i | ||||
\(130\) | 1.00000 | − | 1.00000i | 0.0877058 | − | 0.0877058i | ||||
\(131\) | −11.3137 | + | 11.3137i | −0.988483 | + | 0.988483i | −0.999934 | − | 0.0114511i | \(-0.996355\pi\) |
0.0114511 | + | 0.999934i | \(0.496355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | 2.82843 | + | 2.82843i | 0.244339 | + | 0.244339i | ||||
\(135\) | −4.53553 | + | 2.53553i | −0.390357 | + | 0.218224i | ||||
\(136\) | − | 6.00000i | − | 0.514496i | ||||||
\(137\) | 2.82843i | 0.241649i | 0.992674 | + | 0.120824i | \(0.0385538\pi\) | ||||
−0.992674 | + | 0.120824i | \(0.961446\pi\) | |||||||
\(138\) | −5.65685 | − | 4.00000i | −0.481543 | − | 0.340503i | ||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 1.41421 | − | 1.41421i | 0.119523 | − | 0.119523i | ||||
\(141\) | 2.82843 | − | 4.00000i | 0.238197 | − | 0.336861i | ||||
\(142\) | 2.00000 | + | 2.00000i | 0.167836 | + | 0.167836i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | − | 2.82843i | −0.0833333 | − | 0.235702i | ||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | −4.24264 | − | 4.24264i | −0.351123 | − | 0.351123i | ||||
\(147\) | −4.24264 | − | 3.00000i | −0.349927 | − | 0.247436i | ||||
\(148\) | 6.00000 | + | 1.00000i | 0.493197 | + | 0.0821995i | ||||
\(149\) | − | 19.7990i | − | 1.62200i | −0.585049 | − | 0.810998i | \(-0.698925\pi\) | ||
0.585049 | − | 0.810998i | \(-0.301075\pi\) | |||||||
\(150\) | 0.292893 | + | 1.70711i | 0.0239146 | + | 0.139385i | ||||
\(151\) | − | 18.0000i | − | 1.46482i | −0.680864 | − | 0.732410i | \(-0.738396\pi\) | ||
0.680864 | − | 0.732410i | \(-0.261604\pi\) | |||||||
\(152\) | 4.24264 | 0.344124 | ||||||||
\(153\) | −7.75736 | + | 16.2426i | −0.627145 | + | 1.31314i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 9.89949i | − | 0.795147i | ||||||
\(156\) | −0.414214 | − | 2.41421i | −0.0331636 | − | 0.193292i | ||||
\(157\) | −4.00000 | −0.319235 | −0.159617 | − | 0.987179i | \(-0.551026\pi\) | ||||
−0.159617 | + | 0.987179i | \(0.551026\pi\) | |||||||
\(158\) | − | 4.24264i | − | 0.337526i | ||||||
\(159\) | −5.65685 | + | 8.00000i | −0.448618 | + | 0.634441i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −5.65685 | − | 5.65685i | −0.445823 | − | 0.445823i | ||||
\(162\) | −0.949747 | + | 8.94975i | −0.0746192 | + | 0.703159i | ||||
\(163\) | −15.0000 | − | 15.0000i | −1.17489 | − | 1.17489i | −0.981029 | − | 0.193862i | \(-0.937899\pi\) |
−0.193862 | − | 0.981029i | \(-0.562101\pi\) | |||||||
\(164\) | − | 5.65685i | − | 0.441726i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | + | 2.00000i | 0.155230 | + | 0.155230i | ||||
\(167\) | 11.3137 | + | 11.3137i | 0.875481 | + | 0.875481i | 0.993063 | − | 0.117582i | \(-0.0375143\pi\) |
−0.117582 | + | 0.993063i | \(0.537514\pi\) | |||||||
\(168\) | −0.585786 | − | 3.41421i | −0.0451944 | − | 0.263412i | ||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 4.24264 | + | 4.24264i | 0.325396 | + | 0.325396i | ||||
\(171\) | −11.4853 | − | 5.48528i | −0.878301 | − | 0.419470i | ||||
\(172\) | −7.00000 | − | 7.00000i | −0.533745 | − | 0.533745i | ||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 6.00000 | − | 8.48528i | 0.454859 | − | 0.643268i | ||||
\(175\) | 2.00000i | 0.151186i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.34315 | + | 13.6569i | 0.176122 | + | 1.02651i | ||||
\(178\) | 2.00000i | 0.149906i | ||||||||
\(179\) | 11.3137 | − | 11.3137i | 0.845626 | − | 0.845626i | −0.143958 | − | 0.989584i | \(-0.545983\pi\) |
0.989584 | + | 0.143958i | \(0.0459829\pi\) | |||||||
\(180\) | 2.70711 | + | 1.29289i | 0.201776 | + | 0.0963666i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | − | 2.82843i | − | 0.209657i | ||||||
\(183\) | −3.72792 | − | 21.7279i | −0.275576 | − | 1.60617i | ||||
\(184\) | 4.00000i | 0.294884i | ||||||||
\(185\) | −4.94975 | + | 3.53553i | −0.363913 | + | 0.259938i | ||||
\(186\) | −14.0000 | − | 9.89949i | −1.02653 | − | 0.725866i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.82843 | −0.206284 | ||||||||
\(189\) | −2.82843 | + | 10.0000i | −0.205738 | + | 0.727393i | ||||
\(190\) | −3.00000 | + | 3.00000i | −0.217643 | + | 0.217643i | ||||
\(191\) | −5.65685 | − | 5.65685i | −0.409316 | − | 0.409316i | 0.472184 | − | 0.881500i | \(-0.343466\pi\) |
−0.881500 | + | 0.472184i | \(0.843466\pi\) | |||||||
\(192\) | −1.00000 | + | 1.41421i | −0.0721688 | + | 0.102062i | ||||
\(193\) | −1.00000 | + | 1.00000i | −0.0719816 | + | 0.0719816i | −0.742181 | − | 0.670199i | \(-0.766209\pi\) |
0.670199 | + | 0.742181i | \(0.266209\pi\) | |||||||
\(194\) | − | 9.89949i | − | 0.710742i | ||||||
\(195\) | 2.00000 | + | 1.41421i | 0.143223 | + | 0.101274i | ||||
\(196\) | 3.00000i | 0.214286i | ||||||||
\(197\) | 2.82843i | 0.201517i | 0.994911 | + | 0.100759i | \(0.0321270\pi\) | ||||
−0.994911 | + | 0.100759i | \(0.967873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.00000 | + | 1.00000i | 0.0708881 | + | 0.0708881i | 0.741662 | − | 0.670774i | \(-0.234038\pi\) |
−0.670774 | + | 0.741662i | \(0.734038\pi\) | |||||||
\(200\) | 0.707107 | − | 0.707107i | 0.0500000 | − | 0.0500000i | ||||
\(201\) | −4.00000 | + | 5.65685i | −0.282138 | + | 0.399004i | ||||
\(202\) | −2.00000 | + | 2.00000i | −0.140720 | + | 0.140720i | ||||
\(203\) | 8.48528 | − | 8.48528i | 0.595550 | − | 0.595550i | ||||
\(204\) | 10.2426 | − | 1.75736i | 0.717128 | − | 0.123040i | ||||
\(205\) | 4.00000 | + | 4.00000i | 0.279372 | + | 0.279372i | ||||
\(206\) | −7.07107 | −0.492665 | ||||||||
\(207\) | 5.17157 | − | 10.8284i | 0.359449 | − | 0.752628i | ||||
\(208\) | −1.00000 | + | 1.00000i | −0.0693375 | + | 0.0693375i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.82843 | + | 2.00000i | 0.195180 | + | 0.138013i | ||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 5.65685 | 0.388514 | ||||||||
\(213\) | −2.82843 | + | 4.00000i | −0.193801 | + | 0.274075i | ||||
\(214\) | −8.00000 | − | 8.00000i | −0.546869 | − | 0.546869i | ||||
\(215\) | 9.89949 | 0.675140 | ||||||||
\(216\) | 4.53553 | − | 2.53553i | 0.308604 | − | 0.172521i | ||||
\(217\) | −14.0000 | − | 14.0000i | −0.950382 | − | 0.950382i | ||||
\(218\) | 4.24264i | 0.287348i | ||||||||
\(219\) | 6.00000 | − | 8.48528i | 0.405442 | − | 0.573382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.48528 | 0.570782 | ||||||||
\(222\) | 0.0502525 | + | 10.5355i | 0.00337273 | + | 0.707099i | ||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | −1.41421 | + | 1.41421i | −0.0944911 | + | 0.0944911i | ||||
\(225\) | −2.82843 | + | 1.00000i | −0.188562 | + | 0.0666667i | ||||
\(226\) | 2.00000i | 0.133038i | ||||||||
\(227\) | −16.9706 | − | 16.9706i | −1.12638 | − | 1.12638i | −0.990762 | − | 0.135614i | \(-0.956699\pi\) |
−0.135614 | − | 0.990762i | \(-0.543301\pi\) | |||||||
\(228\) | 1.24264 | + | 7.24264i | 0.0822959 | + | 0.479656i | ||||
\(229\) | −26.0000 | −1.71813 | −0.859064 | − | 0.511868i | \(-0.828954\pi\) | ||||
−0.859064 | + | 0.511868i | \(0.828954\pi\) | |||||||
\(230\) | −2.82843 | − | 2.82843i | −0.186501 | − | 0.186501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | 28.2843 | 1.85296 | 0.926482 | − | 0.376339i | \(-0.122817\pi\) | ||||
0.926482 | + | 0.376339i | \(0.122817\pi\) | |||||||
\(234\) | 4.00000 | − | 1.41421i | 0.261488 | − | 0.0924500i | ||||
\(235\) | 2.00000 | − | 2.00000i | 0.130466 | − | 0.130466i | ||||
\(236\) | 5.65685 | − | 5.65685i | 0.368230 | − | 0.368230i | ||||
\(237\) | 7.24264 | − | 1.24264i | 0.470460 | − | 0.0807182i | ||||
\(238\) | 12.0000 | 0.777844 | ||||||||
\(239\) | 14.1421 | + | 14.1421i | 0.914779 | + | 0.914779i | 0.996643 | − | 0.0818647i | \(-0.0260876\pi\) |
−0.0818647 | + | 0.996643i | \(0.526088\pi\) | |||||||
\(240\) | −0.292893 | − | 1.70711i | −0.0189062 | − | 0.110193i | ||||
\(241\) | −11.0000 | + | 11.0000i | −0.708572 | + | 0.708572i | −0.966235 | − | 0.257663i | \(-0.917048\pi\) |
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | −7.77817 | + | 7.77817i | −0.500000 | + | 0.500000i | ||||
\(243\) | −15.5563 | + | 1.00000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | −9.00000 | + | 9.00000i | −0.576166 | + | 0.576166i | ||||
\(245\) | −2.12132 | − | 2.12132i | −0.135526 | − | 0.135526i | ||||
\(246\) | 9.65685 | − | 1.65685i | 0.615699 | − | 0.105637i | ||||
\(247\) | 6.00000i | 0.381771i | ||||||||
\(248\) | 9.89949i | 0.628619i | ||||||||
\(249\) | −2.82843 | + | 4.00000i | −0.179244 | + | 0.253490i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −8.48528 | + | 8.48528i | −0.535586 | + | 0.535586i | −0.922229 | − | 0.386643i | \(-0.873635\pi\) |
0.386643 | + | 0.922229i | \(0.373635\pi\) | |||||||
\(252\) | 5.65685 | − | 2.00000i | 0.356348 | − | 0.125988i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −11.3137 | + | 11.3137i | −0.709885 | + | 0.709885i | ||||
\(255\) | −6.00000 | + | 8.48528i | −0.375735 | + | 0.531369i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.89949 | − | 9.89949i | −0.617514 | − | 0.617514i | 0.327379 | − | 0.944893i | \(-0.393834\pi\) |
−0.944893 | + | 0.327379i | \(0.893834\pi\) | |||||||
\(258\) | 9.89949 | − | 14.0000i | 0.616316 | − | 0.871602i | ||||
\(259\) | −2.00000 | + | 12.0000i | −0.124274 | + | 0.745644i | ||||
\(260\) | − | 1.41421i | − | 0.0877058i | ||||||
\(261\) | 16.2426 | + | 7.75736i | 1.00539 | + | 0.480168i | ||||
\(262\) | 16.0000i | 0.988483i | ||||||||
\(263\) | −31.1127 | −1.91849 | −0.959246 | − | 0.282574i | \(-0.908812\pi\) | ||||
−0.959246 | + | 0.282574i | \(0.908812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | + | 4.00000i | −0.245718 | + | 0.245718i | ||||
\(266\) | 8.48528i | 0.520266i | ||||||||
\(267\) | −3.41421 | + | 0.585786i | −0.208946 | + | 0.0358495i | ||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 19.7990i | 1.20717i | 0.797300 | + | 0.603583i | \(0.206261\pi\) | ||||
−0.797300 | + | 0.603583i | \(0.793739\pi\) | |||||||
\(270\) | −1.41421 | + | 5.00000i | −0.0860663 | + | 0.304290i | ||||
\(271\) | 10.0000 | 0.607457 | 0.303728 | − | 0.952759i | \(-0.401768\pi\) | ||||
0.303728 | + | 0.952759i | \(0.401768\pi\) | |||||||
\(272\) | −4.24264 | − | 4.24264i | −0.257248 | − | 0.257248i | ||||
\(273\) | 4.82843 | − | 0.828427i | 0.292230 | − | 0.0501387i | ||||
\(274\) | 2.00000 | + | 2.00000i | 0.120824 | + | 0.120824i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.82843 | + | 1.17157i | −0.411023 | + | 0.0705204i | ||||
\(277\) | 11.0000 | + | 11.0000i | 0.660926 | + | 0.660926i | 0.955598 | − | 0.294672i | \(-0.0952105\pi\) |
−0.294672 | + | 0.955598i | \(0.595211\pi\) | |||||||
\(278\) | 2.82843 | + | 2.82843i | 0.169638 | + | 0.169638i | ||||
\(279\) | 12.7990 | − | 26.7990i | 0.766255 | − | 1.60441i | ||||
\(280\) | − | 2.00000i | − | 0.119523i | ||||||
\(281\) | 12.7279 | + | 12.7279i | 0.759284 | + | 0.759284i | 0.976192 | − | 0.216908i | \(-0.0695971\pi\) |
−0.216908 | + | 0.976192i | \(0.569597\pi\) | |||||||
\(282\) | −0.828427 | − | 4.82843i | −0.0493321 | − | 0.287529i | ||||
\(283\) | 3.00000 | + | 3.00000i | 0.178331 | + | 0.178331i | 0.790628 | − | 0.612297i | \(-0.209754\pi\) |
−0.612297 | + | 0.790628i | \(0.709754\pi\) | |||||||
\(284\) | 2.82843 | 0.167836 | ||||||||
\(285\) | −6.00000 | − | 4.24264i | −0.355409 | − | 0.251312i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3137 | 0.667827 | ||||||||
\(288\) | −2.70711 | − | 1.29289i | −0.159518 | − | 0.0761845i | ||||
\(289\) | 19.0000i | 1.11765i | ||||||||
\(290\) | 4.24264 | − | 4.24264i | 0.249136 | − | 0.249136i | ||||
\(291\) | 16.8995 | − | 2.89949i | 0.990666 | − | 0.169971i | ||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | − | 22.6274i | − | 1.32191i | −0.750426 | − | 0.660954i | \(-0.770152\pi\) | ||
0.750426 | − | 0.660954i | \(-0.229848\pi\) | |||||||
\(294\) | −5.12132 | + | 0.878680i | −0.298681 | + | 0.0512456i | ||||
\(295\) | 8.00000i | 0.465778i | ||||||||
\(296\) | 4.94975 | − | 3.53553i | 0.287698 | − | 0.205499i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.0000 | − | 14.0000i | −0.810998 | − | 0.810998i | ||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 1.41421 | + | 1.00000i | 0.0816497 | + | 0.0577350i | ||||
\(301\) | 14.0000 | − | 14.0000i | 0.806947 | − | 0.806947i | ||||
\(302\) | −12.7279 | − | 12.7279i | −0.732410 | − | 0.732410i | ||||
\(303\) | −4.00000 | − | 2.82843i | −0.229794 | − | 0.162489i | ||||
\(304\) | 3.00000 | − | 3.00000i | 0.172062 | − | 0.172062i | ||||
\(305\) | − | 12.7279i | − | 0.728799i | ||||||
\(306\) | 6.00000 | + | 16.9706i | 0.342997 | + | 0.970143i | ||||
\(307\) | − | 10.0000i | − | 0.570730i | −0.958419 | − | 0.285365i | \(-0.907885\pi\) | ||
0.958419 | − | 0.285365i | \(-0.0921148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.07107 | − | 12.0711i | −0.117819 | − | 0.686699i | ||||
\(310\) | −7.00000 | − | 7.00000i | −0.397573 | − | 0.397573i | ||||
\(311\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(312\) | −2.00000 | − | 1.41421i | −0.113228 | − | 0.0800641i | ||||
\(313\) | 1.00000 | − | 1.00000i | 0.0565233 | − | 0.0565233i | −0.678280 | − | 0.734803i | \(-0.737274\pi\) |
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | −2.82843 | + | 2.82843i | −0.159617 | + | 0.159617i | ||||
\(315\) | −2.58579 | + | 5.41421i | −0.145693 | + | 0.305056i | ||||
\(316\) | −3.00000 | − | 3.00000i | −0.168763 | − | 0.168763i | ||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 1.65685 | + | 9.65685i | 0.0929118 | + | 0.541529i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | 11.3137 | − | 16.0000i | 0.631470 | − | 0.893033i | ||||
\(322\) | −8.00000 | −0.445823 | ||||||||
\(323\) | −25.4558 | −1.41640 | ||||||||
\(324\) | 5.65685 | + | 7.00000i | 0.314270 | + | 0.388889i | ||||
\(325\) | 1.00000 | + | 1.00000i | 0.0554700 | + | 0.0554700i | ||||
\(326\) | −21.2132 | −1.17489 | ||||||||
\(327\) | −7.24264 | + | 1.24264i | −0.400519 | + | 0.0687182i | ||||
\(328\) | −4.00000 | − | 4.00000i | −0.220863 | − | 0.220863i | ||||
\(329\) | − | 5.65685i | − | 0.311872i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0000 | − | 15.0000i | 0.824475 | − | 0.824475i | −0.162272 | − | 0.986746i | \(-0.551882\pi\) |
0.986746 | + | 0.162272i | \(0.0518821\pi\) | |||||||
\(332\) | 2.82843 | 0.155230 | ||||||||
\(333\) | −17.9706 | + | 3.17157i | −0.984781 | + | 0.173801i | ||||
\(334\) | 16.0000 | 0.875481 | ||||||||
\(335\) | −2.82843 | + | 2.82843i | −0.154533 | + | 0.154533i | ||||
\(336\) | −2.82843 | − | 2.00000i | −0.154303 | − | 0.109109i | ||||
\(337\) | 20.0000i | 1.08947i | 0.838608 | + | 0.544735i | \(0.183370\pi\) | ||||
−0.838608 | + | 0.544735i | \(0.816630\pi\) | |||||||
\(338\) | 7.77817 | + | 7.77817i | 0.423077 | + | 0.423077i | ||||
\(339\) | −3.41421 | + | 0.585786i | −0.185435 | + | 0.0318156i | ||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −12.0000 | + | 4.24264i | −0.648886 | + | 0.229416i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −9.89949 | −0.533745 | ||||||||
\(345\) | 4.00000 | − | 5.65685i | 0.215353 | − | 0.304555i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.65685 | + | 5.65685i | −0.303676 | + | 0.303676i | −0.842450 | − | 0.538774i | \(-0.818888\pi\) |
0.538774 | + | 0.842450i | \(0.318888\pi\) | |||||||
\(348\) | −1.75736 | − | 10.2426i | −0.0942043 | − | 0.549063i | ||||
\(349\) | 32.0000 | 1.71292 | 0.856460 | − | 0.516213i | \(-0.172659\pi\) | ||||
0.856460 | + | 0.516213i | \(0.172659\pi\) | |||||||
\(350\) | 1.41421 | + | 1.41421i | 0.0755929 | + | 0.0755929i | ||||
\(351\) | 3.58579 | + | 6.41421i | 0.191395 | + | 0.342365i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.3848 | + | 18.3848i | −0.978523 | + | 0.978523i | −0.999774 | − | 0.0212513i | \(-0.993235\pi\) |
0.0212513 | + | 0.999774i | \(0.493235\pi\) | |||||||
\(354\) | 11.3137 | + | 8.00000i | 0.601317 | + | 0.425195i | ||||
\(355\) | −2.00000 | + | 2.00000i | −0.106149 | + | 0.106149i | ||||
\(356\) | 1.41421 | + | 1.41421i | 0.0749532 | + | 0.0749532i | ||||
\(357\) | 3.51472 | + | 20.4853i | 0.186019 | + | 1.08420i | ||||
\(358\) | − | 16.0000i | − | 0.845626i | ||||||
\(359\) | 5.65685i | 0.298557i | 0.988795 | + | 0.149279i | \(0.0476951\pi\) | ||||
−0.988795 | + | 0.149279i | \(0.952305\pi\) | |||||||
\(360\) | 2.82843 | − | 1.00000i | 0.149071 | − | 0.0527046i | ||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.5563 | − | 11.0000i | −0.816497 | − | 0.577350i | ||||
\(364\) | −2.00000 | − | 2.00000i | −0.104828 | − | 0.104828i | ||||
\(365\) | 4.24264 | − | 4.24264i | 0.222070 | − | 0.222070i | ||||
\(366\) | −18.0000 | − | 12.7279i | −0.940875 | − | 0.665299i | ||||
\(367\) | 32.0000 | 1.67039 | 0.835193 | − | 0.549957i | \(-0.185356\pi\) | ||||
0.835193 | + | 0.549957i | \(0.185356\pi\) | |||||||
\(368\) | 2.82843 | + | 2.82843i | 0.147442 | + | 0.147442i | ||||
\(369\) | 5.65685 | + | 16.0000i | 0.294484 | + | 0.832927i | ||||
\(370\) | −1.00000 | + | 6.00000i | −0.0519875 | + | 0.311925i | ||||
\(371\) | 11.3137i | 0.587378i | ||||||||
\(372\) | −16.8995 | + | 2.89949i | −0.876198 | + | 0.150332i | ||||
\(373\) | 10.0000i | 0.517780i | 0.965907 | + | 0.258890i | \(0.0833568\pi\) | ||||
−0.965907 | + | 0.258890i | \(0.916643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.70711 | + | 0.292893i | −0.0881546 | + | 0.0151249i | ||||
\(376\) | −2.00000 | + | 2.00000i | −0.103142 | + | 0.103142i | ||||
\(377\) | − | 8.48528i | − | 0.437014i | ||||||
\(378\) | 5.07107 | + | 9.07107i | 0.260828 | + | 0.466565i | ||||
\(379\) | −6.00000 | −0.308199 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(380\) | 4.24264i | 0.217643i | ||||||||
\(381\) | −22.6274 | − | 16.0000i | −1.15924 | − | 0.819705i | ||||
\(382\) | −8.00000 | −0.409316 | ||||||||
\(383\) | −25.4558 | − | 25.4558i | −1.30073 | − | 1.30073i | −0.927898 | − | 0.372835i | \(-0.878386\pi\) |
−0.372835 | − | 0.927898i | \(-0.621614\pi\) | |||||||
\(384\) | 0.292893 | + | 1.70711i | 0.0149466 | + | 0.0871154i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.41421i | 0.0719816i | ||||||||
\(387\) | 26.7990 | + | 12.7990i | 1.36227 | + | 0.650609i | ||||
\(388\) | −7.00000 | − | 7.00000i | −0.355371 | − | 0.355371i | ||||
\(389\) | 18.3848 | + | 18.3848i | 0.932145 | + | 0.932145i | 0.997840 | − | 0.0656946i | \(-0.0209263\pi\) |
−0.0656946 | + | 0.997840i | \(0.520926\pi\) | |||||||
\(390\) | 2.41421 | − | 0.414214i | 0.122248 | − | 0.0209745i | ||||
\(391\) | − | 24.0000i | − | 1.21373i | ||||||
\(392\) | 2.12132 | + | 2.12132i | 0.107143 | + | 0.107143i | ||||
\(393\) | −27.3137 | + | 4.68629i | −1.37779 | + | 0.236392i | ||||
\(394\) | 2.00000 | + | 2.00000i | 0.100759 | + | 0.100759i | ||||
\(395\) | 4.24264 | 0.213470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000i | 0.903394i | 0.892171 | + | 0.451697i | \(0.149181\pi\) | ||||
−0.892171 | + | 0.451697i | \(0.850819\pi\) | |||||||
\(398\) | 1.41421 | 0.0708881 | ||||||||
\(399\) | −14.4853 | + | 2.48528i | −0.725171 | + | 0.124420i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | 12.7279 | − | 12.7279i | 0.635602 | − | 0.635602i | −0.313865 | − | 0.949467i | \(-0.601624\pi\) |
0.949467 | + | 0.313865i | \(0.101624\pi\) | |||||||
\(402\) | 1.17157 | + | 6.82843i | 0.0584327 | + | 0.340571i | ||||
\(403\) | −14.0000 | −0.697390 | ||||||||
\(404\) | 2.82843i | 0.140720i | ||||||||
\(405\) | −8.94975 | − | 0.949747i | −0.444717 | − | 0.0471933i | ||||
\(406\) | − | 12.0000i | − | 0.595550i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.00000 | − | 8.48528i | 0.297044 | − | 0.420084i | ||||
\(409\) | −5.00000 | − | 5.00000i | −0.247234 | − | 0.247234i | 0.572600 | − | 0.819835i | \(-0.305935\pi\) |
−0.819835 | + | 0.572600i | \(0.805935\pi\) | |||||||
\(410\) | 5.65685 | 0.279372 | ||||||||
\(411\) | −2.82843 | + | 4.00000i | −0.139516 | + | 0.197305i | ||||
\(412\) | −5.00000 | + | 5.00000i | −0.246332 | + | 0.246332i | ||||
\(413\) | 11.3137 | + | 11.3137i | 0.556711 | + | 0.556711i | ||||
\(414\) | −4.00000 | − | 11.3137i | −0.196589 | − | 0.556038i | ||||
\(415\) | −2.00000 | + | 2.00000i | −0.0981761 | + | 0.0981761i | ||||
\(416\) | 1.41421i | 0.0693375i | ||||||||
\(417\) | −4.00000 | + | 5.65685i | −0.195881 | + | 0.277017i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4558i | 1.24360i | 0.783176 | + | 0.621800i | \(0.213598\pi\) | ||||
−0.783176 | + | 0.621800i | \(0.786402\pi\) | |||||||
\(420\) | 3.41421 | − | 0.585786i | 0.166597 | − | 0.0285835i | ||||
\(421\) | 9.00000 | + | 9.00000i | 0.438633 | + | 0.438633i | 0.891552 | − | 0.452919i | \(-0.149617\pi\) |
−0.452919 | + | 0.891552i | \(0.649617\pi\) | |||||||
\(422\) | 14.1421 | − | 14.1421i | 0.688428 | − | 0.688428i | ||||
\(423\) | 8.00000 | − | 2.82843i | 0.388973 | − | 0.137523i | ||||
\(424\) | 4.00000 | − | 4.00000i | 0.194257 | − | 0.194257i | ||||
\(425\) | −4.24264 | + | 4.24264i | −0.205798 | + | 0.205798i | ||||
\(426\) | 0.828427 | + | 4.82843i | 0.0401374 | + | 0.233938i | ||||
\(427\) | −18.0000 | − | 18.0000i | −0.871081 | − | 0.871081i | ||||
\(428\) | −11.3137 | −0.546869 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.00000 | − | 7.00000i | 0.337570 | − | 0.337570i | ||||
\(431\) | 5.65685 | − | 5.65685i | 0.272481 | − | 0.272481i | −0.557617 | − | 0.830098i | \(-0.688284\pi\) |
0.830098 | + | 0.557617i | \(0.188284\pi\) | |||||||
\(432\) | 1.41421 | − | 5.00000i | 0.0680414 | − | 0.240563i | ||||
\(433\) | −24.0000 | −1.15337 | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||||
−0.576683 | + | 0.816968i | \(0.695653\pi\) | |||||||
\(434\) | −19.7990 | −0.950382 | ||||||||
\(435\) | 8.48528 | + | 6.00000i | 0.406838 | + | 0.287678i | ||||
\(436\) | 3.00000 | + | 3.00000i | 0.143674 | + | 0.143674i | ||||
\(437\) | 16.9706 | 0.811812 | ||||||||
\(438\) | −1.75736 | − | 10.2426i | −0.0839699 | − | 0.489412i | ||||
\(439\) | 27.0000 | + | 27.0000i | 1.28864 | + | 1.28864i | 0.935613 | + | 0.353026i | \(0.114847\pi\) |
0.353026 | + | 0.935613i | \(0.385153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 8.48528i | −0.142857 | − | 0.404061i | ||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | 14.1421 | 0.671913 | 0.335957 | − | 0.941877i | \(-0.390940\pi\) | ||||
0.335957 | + | 0.941877i | \(0.390940\pi\) | |||||||
\(444\) | 7.48528 | + | 7.41421i | 0.355236 | + | 0.351863i | ||||
\(445\) | −2.00000 | −0.0948091 | ||||||||
\(446\) | −16.9706 | + | 16.9706i | −0.803579 | + | 0.803579i | ||||
\(447\) | 19.7990 | − | 28.0000i | 0.936460 | − | 1.32435i | ||||
\(448\) | 2.00000i | 0.0944911i | ||||||||
\(449\) | 18.3848 | + | 18.3848i | 0.867631 | + | 0.867631i | 0.992210 | − | 0.124579i | \(-0.0397579\pi\) |
−0.124579 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(450\) | −1.29289 | + | 2.70711i | −0.0609476 | + | 0.127614i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.41421 | + | 1.41421i | 0.0665190 | + | 0.0665190i | ||||
\(453\) | 18.0000 | − | 25.4558i | 0.845714 | − | 1.19602i | ||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | 2.82843 | 0.132599 | ||||||||
\(456\) | 6.00000 | + | 4.24264i | 0.280976 | + | 0.198680i | ||||
\(457\) | −7.00000 | + | 7.00000i | −0.327446 | + | 0.327446i | −0.851615 | − | 0.524168i | \(-0.824376\pi\) |
0.524168 | + | 0.851615i | \(0.324376\pi\) | |||||||
\(458\) | −18.3848 | + | 18.3848i | −0.859064 | + | 0.859064i | ||||
\(459\) | −27.2132 | + | 15.2132i | −1.27020 | + | 0.710092i | ||||
\(460\) | −4.00000 | −0.186501 | ||||||||
\(461\) | 21.2132 | + | 21.2132i | 0.987997 | + | 0.987997i | 0.999929 | − | 0.0119314i | \(-0.00379798\pi\) |
−0.0119314 | + | 0.999929i | \(0.503798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | − | 11.0000i | 0.511213 | − | 0.511213i | −0.403685 | − | 0.914898i | \(-0.632271\pi\) |
0.914898 | + | 0.403685i | \(0.132271\pi\) | |||||||
\(464\) | −4.24264 | + | 4.24264i | −0.196960 | + | 0.196960i | ||||
\(465\) | 9.89949 | − | 14.0000i | 0.459078 | − | 0.649234i | ||||
\(466\) | 20.0000 | − | 20.0000i | 0.926482 | − | 0.926482i | ||||
\(467\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | 1.82843 | − | 3.82843i | 0.0845191 | − | 0.176969i | ||||
\(469\) | 8.00000i | 0.369406i | ||||||||
\(470\) | − | 2.82843i | − | 0.130466i | ||||||
\(471\) | −5.65685 | − | 4.00000i | −0.260654 | − | 0.184310i | ||||
\(472\) | − | 8.00000i | − | 0.368230i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.24264 | − | 6.00000i | 0.194871 | − | 0.275589i | ||||
\(475\) | −3.00000 | − | 3.00000i | −0.137649 | − | 0.137649i | ||||
\(476\) | 8.48528 | − | 8.48528i | 0.388922 | − | 0.388922i | ||||
\(477\) | −16.0000 | + | 5.65685i | −0.732590 | + | 0.259010i | ||||
\(478\) | 20.0000 | 0.914779 | ||||||||
\(479\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(480\) | −1.41421 | − | 1.00000i | −0.0645497 | − | 0.0456435i | ||||
\(481\) | 5.00000 | + | 7.00000i | 0.227980 | + | 0.319173i | ||||
\(482\) | 15.5563i | 0.708572i | ||||||||
\(483\) | −2.34315 | − | 13.6569i | −0.106617 | − | 0.621408i | ||||
\(484\) | 11.0000i | 0.500000i | ||||||||
\(485\) | 9.89949 | 0.449513 | ||||||||
\(486\) | −10.2929 | + | 11.7071i | −0.466895 | + | 0.531045i | ||||
\(487\) | 17.0000 | − | 17.0000i | 0.770344 | − | 0.770344i | −0.207823 | − | 0.978166i | \(-0.566638\pi\) |
0.978166 | + | 0.207823i | \(0.0666378\pi\) | |||||||
\(488\) | 12.7279i | 0.576166i | ||||||||
\(489\) | −6.21320 | − | 36.2132i | −0.280971 | − | 1.63762i | ||||
\(490\) | −3.00000 | −0.135526 | ||||||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | 5.65685 | − | 8.00000i | 0.255031 | − | 0.360668i | ||||
\(493\) | 36.0000 | 1.62136 | ||||||||
\(494\) | 4.24264 | + | 4.24264i | 0.190885 | + | 0.190885i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.00000 | + | 7.00000i | 0.314309 | + | 0.314309i | ||||
\(497\) | 5.65685i | 0.253745i | ||||||||
\(498\) | 0.828427 | + | 4.82843i | 0.0371227 | + | 0.216367i | ||||
\(499\) | 3.00000 | + | 3.00000i | 0.134298 | + | 0.134298i | 0.771060 | − | 0.636762i | \(-0.219727\pi\) |
−0.636762 | + | 0.771060i | \(0.719727\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | 4.68629 | + | 27.3137i | 0.209368 | + | 1.22029i | ||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 2.58579 | − | 5.41421i | 0.115180 | − | 0.241168i | ||||
\(505\) | −2.00000 | − | 2.00000i | −0.0889988 | − | 0.0889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | + | 15.5563i | −0.488527 | + | 0.690882i | ||||
\(508\) | 16.0000i | 0.709885i | ||||||||
\(509\) | −5.65685 | −0.250736 | −0.125368 | − | 0.992110i | \(-0.540011\pi\) | ||||
−0.125368 | + | 0.992110i | \(0.540011\pi\) | |||||||
\(510\) | 1.75736 | + | 10.2426i | 0.0778172 | + | 0.453552i | ||||
\(511\) | − | 12.0000i | − | 0.530849i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −10.7574 | − | 19.2426i | −0.474949 | − | 0.849583i | ||||
\(514\) | −14.0000 | −0.617514 | ||||||||
\(515\) | − | 7.07107i | − | 0.311588i | ||||||
\(516\) | −2.89949 | − | 16.8995i | −0.127643 | − | 0.743959i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.07107 | + | 9.89949i | 0.310685 | + | 0.434959i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.00000 | − | 1.00000i | −0.0438529 | − | 0.0438529i | ||||
\(521\) | −16.9706 | −0.743494 | −0.371747 | − | 0.928334i | \(-0.621241\pi\) | ||||
−0.371747 | + | 0.928334i | \(0.621241\pi\) | |||||||
\(522\) | 16.9706 | − | 6.00000i | 0.742781 | − | 0.262613i | ||||
\(523\) | 3.00000 | − | 3.00000i | 0.131181 | − | 0.131181i | −0.638468 | − | 0.769649i | \(-0.720431\pi\) |
0.769649 | + | 0.638468i | \(0.220431\pi\) | |||||||
\(524\) | 11.3137 | + | 11.3137i | 0.494242 | + | 0.494242i | ||||
\(525\) | −2.00000 | + | 2.82843i | −0.0872872 | + | 0.123443i | ||||
\(526\) | −22.0000 | + | 22.0000i | −0.959246 | + | 0.959246i | ||||
\(527\) | − | 59.3970i | − | 2.58737i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 5.65685i | 0.245718i | ||||||||
\(531\) | −10.3431 | + | 21.6569i | −0.448854 | + | 0.939827i | ||||
\(532\) | 6.00000 | + | 6.00000i | 0.260133 | + | 0.260133i | ||||
\(533\) | 5.65685 | − | 5.65685i | 0.245026 | − | 0.245026i | ||||
\(534\) | −2.00000 | + | 2.82843i | −0.0865485 | + | 0.122398i | ||||
\(535\) | 8.00000 | − | 8.00000i | 0.345870 | − | 0.345870i | ||||
\(536\) | 2.82843 | − | 2.82843i | 0.122169 | − | 0.122169i | ||||
\(537\) | 27.3137 | − | 4.68629i | 1.17867 | − | 0.202228i | ||||
\(538\) | 14.0000 | + | 14.0000i | 0.603583 | + | 0.603583i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.53553 | + | 4.53553i | 0.109112 | + | 0.195178i | ||||
\(541\) | 21.0000 | − | 21.0000i | 0.902861 | − | 0.902861i | −0.0928222 | − | 0.995683i | \(-0.529589\pi\) |
0.995683 | + | 0.0928222i | \(0.0295888\pi\) | |||||||
\(542\) | 7.07107 | − | 7.07107i | 0.303728 | − | 0.303728i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | −4.24264 | −0.181735 | ||||||||
\(546\) | 2.82843 | − | 4.00000i | 0.121046 | − | 0.171184i | ||||
\(547\) | 7.00000 | + | 7.00000i | 0.299298 | + | 0.299298i | 0.840739 | − | 0.541441i | \(-0.182121\pi\) |
−0.541441 | + | 0.840739i | \(0.682121\pi\) | |||||||
\(548\) | 2.82843 | 0.120824 | ||||||||
\(549\) | 16.4558 | − | 34.4558i | 0.702318 | − | 1.47054i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.4558i | 1.08446i | ||||||||
\(552\) | −4.00000 | + | 5.65685i | −0.170251 | + | 0.240772i | ||||
\(553\) | 6.00000 | − | 6.00000i | 0.255146 | − | 0.255146i | ||||
\(554\) | 15.5563 | 0.660926 | ||||||||
\(555\) | −10.5355 | + | 0.0502525i | −0.447209 | + | 0.00213310i | ||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 7.07107 | − | 7.07107i | 0.299611 | − | 0.299611i | −0.541251 | − | 0.840861i | \(-0.682049\pi\) |
0.840861 | + | 0.541251i | \(0.182049\pi\) | |||||||
\(558\) | −9.89949 | − | 28.0000i | −0.419079 | − | 1.18533i | ||||
\(559\) | − | 14.0000i | − | 0.592137i | ||||||
\(560\) | −1.41421 | − | 1.41421i | −0.0597614 | − | 0.0597614i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | 0.759284 | ||||||||
\(563\) | −8.48528 | − | 8.48528i | −0.357612 | − | 0.357612i | 0.505320 | − | 0.862932i | \(-0.331374\pi\) |
−0.862932 | + | 0.505320i | \(0.831374\pi\) | |||||||
\(564\) | −4.00000 | − | 2.82843i | −0.168430 | − | 0.119098i | ||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 4.24264 | 0.178331 | ||||||||
\(567\) | −14.0000 | + | 11.3137i | −0.587945 | + | 0.475131i | ||||
\(568\) | 2.00000 | − | 2.00000i | 0.0839181 | − | 0.0839181i | ||||
\(569\) | 32.5269 | − | 32.5269i | 1.36360 | − | 1.36360i | 0.494318 | − | 0.869281i | \(-0.335418\pi\) |
0.869281 | − | 0.494318i | \(-0.164582\pi\) | |||||||
\(570\) | −7.24264 | + | 1.24264i | −0.303361 | + | 0.0520485i | ||||
\(571\) | 30.0000 | 1.25546 | 0.627730 | − | 0.778431i | \(-0.283984\pi\) | ||||
0.627730 | + | 0.778431i | \(0.283984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.34315 | − | 13.6569i | −0.0978863 | − | 0.570523i | ||||
\(574\) | 8.00000 | − | 8.00000i | 0.333914 | − | 0.333914i | ||||
\(575\) | 2.82843 | − | 2.82843i | 0.117954 | − | 0.117954i | ||||
\(576\) | −2.82843 | + | 1.00000i | −0.117851 | + | 0.0416667i | ||||
\(577\) | 27.0000 | − | 27.0000i | 1.12402 | − | 1.12402i | 0.132895 | − | 0.991130i | \(-0.457573\pi\) |
0.991130 | − | 0.132895i | \(-0.0424272\pi\) | |||||||
\(578\) | 13.4350 | + | 13.4350i | 0.558824 | + | 0.558824i | ||||
\(579\) | −2.41421 | + | 0.414214i | −0.100331 | + | 0.0172141i | ||||
\(580\) | − | 6.00000i | − | 0.249136i | ||||||
\(581\) | 5.65685i | 0.234686i | ||||||||
\(582\) | 9.89949 | − | 14.0000i | 0.410347 | − | 0.580319i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4.24264 | + | 4.24264i | −0.175562 | + | 0.175562i | ||||
\(585\) | 1.41421 | + | 4.00000i | 0.0584705 | + | 0.165380i | ||||
\(586\) | −16.0000 | − | 16.0000i | −0.660954 | − | 0.660954i | ||||
\(587\) | 25.4558 | − | 25.4558i | 1.05068 | − | 1.05068i | 0.0520296 | − | 0.998646i | \(-0.483431\pi\) |
0.998646 | − | 0.0520296i | \(-0.0165690\pi\) | |||||||
\(588\) | −3.00000 | + | 4.24264i | −0.123718 | + | 0.174964i | ||||
\(589\) | 42.0000 | 1.73058 | ||||||||
\(590\) | 5.65685 | + | 5.65685i | 0.232889 | + | 0.232889i | ||||
\(591\) | −2.82843 | + | 4.00000i | −0.116346 | + | 0.164538i | ||||
\(592\) | 1.00000 | − | 6.00000i | 0.0410997 | − | 0.246598i | ||||
\(593\) | 39.5980i | 1.62609i | 0.582198 | + | 0.813047i | \(0.302193\pi\) | ||||
−0.582198 | + | 0.813047i | \(0.697807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000i | 0.491952i | ||||||||
\(596\) | −19.7990 | −0.810998 | ||||||||
\(597\) | 0.414214 | + | 2.41421i | 0.0169526 | + | 0.0988072i | ||||
\(598\) | −4.00000 | + | 4.00000i | −0.163572 | + | 0.163572i | ||||
\(599\) | 8.48528i | 0.346699i | 0.984860 | + | 0.173350i | \(0.0554591\pi\) | ||||
−0.984860 | + | 0.173350i | \(0.944541\pi\) | |||||||
\(600\) | 1.70711 | − | 0.292893i | 0.0696923 | − | 0.0119573i | ||||
\(601\) | 12.0000 | 0.489490 | 0.244745 | − | 0.969587i | \(-0.421296\pi\) | ||||
0.244745 | + | 0.969587i | \(0.421296\pi\) | |||||||
\(602\) | − | 19.7990i | − | 0.806947i | ||||||
\(603\) | −11.3137 | + | 4.00000i | −0.460730 | + | 0.162893i | ||||
\(604\) | −18.0000 | −0.732410 | ||||||||
\(605\) | −7.77817 | − | 7.77817i | −0.316228 | − | 0.316228i | ||||
\(606\) | −4.82843 | + | 0.828427i | −0.196141 | + | 0.0336526i | ||||
\(607\) | −9.00000 | − | 9.00000i | −0.365299 | − | 0.365299i | 0.500461 | − | 0.865759i | \(-0.333164\pi\) |
−0.865759 | + | 0.500461i | \(0.833164\pi\) | |||||||
\(608\) | − | 4.24264i | − | 0.172062i | ||||||
\(609\) | 20.4853 | − | 3.51472i | 0.830105 | − | 0.142424i | ||||
\(610\) | −9.00000 | − | 9.00000i | −0.364399 | − | 0.364399i | ||||
\(611\) | −2.82843 | − | 2.82843i | −0.114426 | − | 0.114426i | ||||
\(612\) | 16.2426 | + | 7.75736i | 0.656570 | + | 0.313573i | ||||
\(613\) | − | 4.00000i | − | 0.161558i | −0.996732 | − | 0.0807792i | \(-0.974259\pi\) | ||
0.996732 | − | 0.0807792i | \(-0.0257409\pi\) | |||||||
\(614\) | −7.07107 | − | 7.07107i | −0.285365 | − | 0.285365i | ||||
\(615\) | 1.65685 | + | 9.65685i | 0.0668108 | + | 0.389402i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1421 | −0.569341 | −0.284670 | − | 0.958625i | \(-0.591884\pi\) | ||||
−0.284670 | + | 0.958625i | \(0.591884\pi\) | |||||||
\(618\) | −10.0000 | − | 7.07107i | −0.402259 | − | 0.284440i | ||||
\(619\) | 14.0000i | 0.562708i | 0.959604 | + | 0.281354i | \(0.0907834\pi\) | ||||
−0.959604 | + | 0.281354i | \(0.909217\pi\) | |||||||
\(620\) | −9.89949 | −0.397573 | ||||||||
\(621\) | 18.1421 | − | 10.1421i | 0.728019 | − | 0.406990i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.82843 | + | 2.82843i | −0.113319 | + | 0.113319i | ||||
\(624\) | −2.41421 | + | 0.414214i | −0.0966459 | + | 0.0165818i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | − | 1.41421i | − | 0.0565233i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000i | 0.159617i | ||||||||
\(629\) | −29.6985 | + | 21.2132i | −1.18416 | + | 0.845826i | ||||
\(630\) | 2.00000 | + | 5.65685i | 0.0796819 | + | 0.225374i | ||||
\(631\) | −19.0000 | − | 19.0000i | −0.756378 | − | 0.756378i | 0.219283 | − | 0.975661i | \(-0.429628\pi\) |
−0.975661 | + | 0.219283i | \(0.929628\pi\) | |||||||
\(632\) | −4.24264 | −0.168763 | ||||||||
\(633\) | 28.2843 | + | 20.0000i | 1.12420 | + | 0.794929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.3137 | − | 11.3137i | −0.448971 | − | 0.448971i | ||||
\(636\) | 8.00000 | + | 5.65685i | 0.317221 | + | 0.224309i | ||||
\(637\) | −3.00000 | + | 3.00000i | −0.118864 | + | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | + | 2.82843i | −0.316475 | + | 0.111891i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 22.6274i | 0.893729i | 0.894602 | + | 0.446865i | \(0.147459\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(642\) | −3.31371 | − | 19.3137i | −0.130782 | − | 0.762251i | ||||
\(643\) | 27.0000 | + | 27.0000i | 1.06478 | + | 1.06478i | 0.997751 | + | 0.0670247i | \(0.0213506\pi\) |
0.0670247 | + | 0.997751i | \(0.478649\pi\) | |||||||
\(644\) | −5.65685 | + | 5.65685i | −0.222911 | + | 0.222911i | ||||
\(645\) | 14.0000 | + | 9.89949i | 0.551249 | + | 0.389792i | ||||
\(646\) | −18.0000 | + | 18.0000i | −0.708201 | + | 0.708201i | ||||
\(647\) | 25.4558 | − | 25.4558i | 1.00077 | − | 1.00077i | 0.000772798 | − | 1.00000i | \(-0.499754\pi\) |
1.00000 | 0.000772798i | \(-0.000245989\pi\) | ||||||||
\(648\) | 8.94975 | + | 0.949747i | 0.351579 | + | 0.0373096i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.41421 | 0.0554700 | ||||||||
\(651\) | −5.79899 | − | 33.7990i | −0.227280 | − | 1.32469i | ||||
\(652\) | −15.0000 | + | 15.0000i | −0.587445 | + | 0.587445i | ||||
\(653\) | 24.0416 | − | 24.0416i | 0.940822 | − | 0.940822i | −0.0575225 | − | 0.998344i | \(-0.518320\pi\) |
0.998344 | + | 0.0575225i | \(0.0183201\pi\) | |||||||
\(654\) | −4.24264 | + | 6.00000i | −0.165900 | + | 0.234619i | ||||
\(655\) | −16.0000 | −0.625172 | ||||||||
\(656\) | −5.65685 | −0.220863 | ||||||||
\(657\) | 16.9706 | − | 6.00000i | 0.662085 | − | 0.234082i | ||||
\(658\) | −4.00000 | − | 4.00000i | −0.155936 | − | 0.155936i | ||||
\(659\) | 16.9706 | 0.661079 | 0.330540 | − | 0.943792i | \(-0.392769\pi\) | ||||
0.330540 | + | 0.943792i | \(0.392769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0000 | + | 11.0000i | 0.427850 | + | 0.427850i | 0.887896 | − | 0.460045i | \(-0.152167\pi\) |
−0.460045 | + | 0.887896i | \(0.652167\pi\) | |||||||
\(662\) | − | 21.2132i | − | 0.824475i | ||||||
\(663\) | 12.0000 | + | 8.48528i | 0.466041 | + | 0.329541i | ||||
\(664\) | 2.00000 | − | 2.00000i | 0.0776151 | − | 0.0776151i | ||||
\(665\) | −8.48528 | −0.329045 | ||||||||
\(666\) | −10.4645 | + | 14.9497i | −0.405490 | + | 0.579291i | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | 11.3137 | − | 11.3137i | 0.437741 | − | 0.437741i | ||||
\(669\) | −33.9411 | − | 24.0000i | −1.31224 | − | 0.927894i | ||||
\(670\) | 4.00000i | 0.154533i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.41421 | + | 0.585786i | −0.131706 | + | 0.0225972i | ||||
\(673\) | −4.00000 | −0.154189 | −0.0770943 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770943 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(674\) | 14.1421 | + | 14.1421i | 0.544735 | + | 0.544735i | ||||
\(675\) | −5.00000 | − | 1.41421i | −0.192450 | − | 0.0544331i | ||||
\(676\) | 11.0000 | 0.423077 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | −2.00000 | + | 2.82843i | −0.0768095 | + | 0.108625i | ||||
\(679\) | 14.0000 | − | 14.0000i | 0.537271 | − | 0.537271i | ||||
\(680\) | 4.24264 | − | 4.24264i | 0.162698 | − | 0.162698i | ||||
\(681\) | −7.02944 | − | 40.9706i | −0.269369 | − | 1.57000i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.82843 | + | 2.82843i | 0.108227 | + | 0.108227i | 0.759147 | − | 0.650920i | \(-0.225617\pi\) |
−0.650920 | + | 0.759147i | \(0.725617\pi\) | |||||||
\(684\) | −5.48528 | + | 11.4853i | −0.209735 | + | 0.439151i | ||||
\(685\) | −2.00000 | + | 2.00000i | −0.0764161 | + | 0.0764161i | ||||
\(686\) | −14.1421 | + | 14.1421i | −0.539949 | + | 0.539949i | ||||
\(687\) | −36.7696 | − | 26.0000i | −1.40285 | − | 0.991962i | ||||
\(688\) | −7.00000 | + | 7.00000i | −0.266872 | + | 0.266872i | ||||
\(689\) | 5.65685 | + | 5.65685i | 0.215509 | + | 0.215509i | ||||
\(690\) | −1.17157 | − | 6.82843i | −0.0446010 | − | 0.259954i | ||||
\(691\) | 20.0000i | 0.760836i | 0.924815 | + | 0.380418i | \(0.124220\pi\) | ||||
−0.924815 | + | 0.380418i | \(0.875780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.00000i | 0.303676i | ||||||||
\(695\) | −2.82843 | + | 2.82843i | −0.107288 | + | 0.107288i | ||||
\(696\) | −8.48528 | − | 6.00000i | −0.321634 | − | 0.227429i | ||||
\(697\) | 24.0000 | + | 24.0000i | 0.909065 | + | 0.909065i | ||||
\(698\) | 22.6274 | − | 22.6274i | 0.856460 | − | 0.856460i | ||||
\(699\) | 40.0000 | + | 28.2843i | 1.51294 | + | 1.06981i | ||||
\(700\) | 2.00000 | 0.0755929 | ||||||||
\(701\) | 18.3848 | + | 18.3848i | 0.694383 | + | 0.694383i | 0.963193 | − | 0.268810i | \(-0.0866303\pi\) |
−0.268810 | + | 0.963193i | \(0.586630\pi\) | |||||||
\(702\) | 7.07107 | + | 2.00000i | 0.266880 | + | 0.0754851i | ||||
\(703\) | −15.0000 | − | 21.0000i | −0.565736 | − | 0.792030i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.82843 | − | 0.828427i | 0.181849 | − | 0.0312004i | ||||
\(706\) | 26.0000i | 0.978523i | ||||||||
\(707\) | −5.65685 | −0.212748 | ||||||||
\(708\) | 13.6569 | − | 2.34315i | 0.513256 | − | 0.0880608i | ||||
\(709\) | 15.0000 | − | 15.0000i | 0.563337 | − | 0.563337i | −0.366917 | − | 0.930254i | \(-0.619587\pi\) |
0.930254 | + | 0.366917i | \(0.119587\pi\) | |||||||
\(710\) | 2.82843i | 0.106149i | ||||||||
\(711\) | 11.4853 | + | 5.48528i | 0.430732 | + | 0.205714i | ||||
\(712\) | 2.00000 | 0.0749532 | ||||||||
\(713\) | 39.5980i | 1.48296i | ||||||||
\(714\) | 16.9706 | + | 12.0000i | 0.635107 | + | 0.449089i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.3137 | − | 11.3137i | −0.422813 | − | 0.422813i | ||||
\(717\) | 5.85786 | + | 34.1421i | 0.218766 | + | 1.27506i | ||||
\(718\) | 4.00000 | + | 4.00000i | 0.149279 | + | 0.149279i | ||||
\(719\) | 11.3137i | 0.421930i | 0.977494 | + | 0.210965i | \(0.0676606\pi\) | ||||
−0.977494 | + | 0.210965i | \(0.932339\pi\) | |||||||
\(720\) | 1.29289 | − | 2.70711i | 0.0481833 | − | 0.100888i | ||||
\(721\) | −10.0000 | − | 10.0000i | −0.372419 | − | 0.372419i | ||||
\(722\) | 0.707107 | + | 0.707107i | 0.0263158 | + | 0.0263158i | ||||
\(723\) | −26.5563 | + | 4.55635i | −0.987641 | + | 0.169452i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.24264 | + | 4.24264i | 0.157568 | + | 0.157568i | ||||
\(726\) | −18.7782 | + | 3.22183i | −0.696923 | + | 0.119573i | ||||
\(727\) | −27.0000 | − | 27.0000i | −1.00137 | − | 1.00137i | −0.999999 | − | 0.00137552i | \(-0.999562\pi\) |
−0.00137552 | − | 0.999999i | \(-0.500438\pi\) | |||||||
\(728\) | −2.82843 | −0.104828 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | − | 6.00000i | − | 0.222070i | ||||||
\(731\) | 59.3970 | 2.19688 | ||||||||
\(732\) | −21.7279 | + | 3.72792i | −0.803087 | + | 0.137788i | ||||
\(733\) | − | 4.00000i | − | 0.147743i | −0.997268 | − | 0.0738717i | \(-0.976464\pi\) | ||
0.997268 | − | 0.0738717i | \(-0.0235355\pi\) | |||||||
\(734\) | 22.6274 | − | 22.6274i | 0.835193 | − | 0.835193i | ||||
\(735\) | −0.878680 | − | 5.12132i | −0.0324106 | − | 0.188903i | ||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 15.3137 | + | 7.31371i | 0.563705 | + | 0.269221i | ||||
\(739\) | 22.0000i | 0.809283i | 0.914475 | + | 0.404642i | \(0.132604\pi\) | ||||
−0.914475 | + | 0.404642i | \(0.867396\pi\) | |||||||
\(740\) | 3.53553 | + | 4.94975i | 0.129969 | + | 0.181956i | ||||
\(741\) | −6.00000 | + | 8.48528i | −0.220416 | + | 0.311715i | ||||
\(742\) | 8.00000 | + | 8.00000i | 0.293689 | + | 0.293689i | ||||
\(743\) | −31.1127 | −1.14141 | −0.570707 | − | 0.821154i | \(-0.693331\pi\) | ||||
−0.570707 | + | 0.821154i | \(0.693331\pi\) | |||||||
\(744\) | −9.89949 | + | 14.0000i | −0.362933 | + | 0.513265i | ||||
\(745\) | 14.0000 | − | 14.0000i | 0.512920 | − | 0.512920i | ||||
\(746\) | 7.07107 | + | 7.07107i | 0.258890 | + | 0.258890i | ||||
\(747\) | −8.00000 | + | 2.82843i | −0.292705 | + | 0.103487i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 22.6274i | − | 0.826788i | ||||||
\(750\) | −1.00000 | + | 1.41421i | −0.0365148 | + | 0.0516398i | ||||
\(751\) | 40.0000i | 1.45962i | 0.683650 | + | 0.729810i | \(0.260392\pi\) | ||||
−0.683650 | + | 0.729810i | \(0.739608\pi\) | |||||||
\(752\) | 2.82843i | 0.103142i | ||||||||
\(753\) | −20.4853 | + | 3.51472i | −0.746525 | + | 0.128083i | ||||
\(754\) | −6.00000 | − | 6.00000i | −0.218507 | − | 0.218507i | ||||
\(755\) | 12.7279 | − | 12.7279i | 0.463217 | − | 0.463217i | ||||
\(756\) | 10.0000 | + | 2.82843i | 0.363696 | + | 0.102869i | ||||
\(757\) | 3.00000 | − | 3.00000i | 0.109037 | − | 0.109037i | −0.650484 | − | 0.759520i | \(-0.725434\pi\) |
0.759520 | + | 0.650484i | \(0.225434\pi\) | |||||||
\(758\) | −4.24264 | + | 4.24264i | −0.154100 | + | 0.154100i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.00000 | + | 3.00000i | 0.108821 | + | 0.108821i | ||||
\(761\) | 2.82843 | 0.102530 | 0.0512652 | − | 0.998685i | \(-0.483675\pi\) | ||||
0.0512652 | + | 0.998685i | \(0.483675\pi\) | |||||||
\(762\) | −27.3137 | + | 4.68629i | −0.989471 | + | 0.169766i | ||||
\(763\) | −6.00000 | + | 6.00000i | −0.217215 | + | 0.217215i | ||||
\(764\) | −5.65685 | + | 5.65685i | −0.204658 | + | 0.204658i | ||||
\(765\) | −16.9706 | + | 6.00000i | −0.613572 | + | 0.216930i | ||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | 11.3137 | 0.408514 | ||||||||
\(768\) | 1.41421 | + | 1.00000i | 0.0510310 | + | 0.0360844i | ||||
\(769\) | 3.00000 | + | 3.00000i | 0.108183 | + | 0.108183i | 0.759126 | − | 0.650943i | \(-0.225627\pi\) |
−0.650943 | + | 0.759126i | \(0.725627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.10051 | − | 23.8995i | −0.147676 | − | 0.860719i | ||||
\(772\) | 1.00000 | + | 1.00000i | 0.0359908 | + | 0.0359908i | ||||
\(773\) | 8.48528i | 0.305194i | 0.988288 | + | 0.152597i | \(0.0487637\pi\) | ||||
−0.988288 | + | 0.152597i | \(0.951236\pi\) | |||||||
\(774\) | 28.0000 | − | 9.89949i | 1.00644 | − | 0.355830i | ||||
\(775\) | 7.00000 | − | 7.00000i | 0.251447 | − | 0.251447i | ||||
\(776\) | −9.89949 | −0.355371 | ||||||||
\(777\) | −14.8284 | + | 14.9706i | −0.531967 | + | 0.537066i | ||||
\(778\) | 26.0000 | 0.932145 | ||||||||
\(779\) | −16.9706 | + | 16.9706i | −0.608034 | + | 0.608034i | ||||
\(780\) | 1.41421 | − | 2.00000i | 0.0506370 | − | 0.0716115i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −16.9706 | − | 16.9706i | −0.606866 | − | 0.606866i | ||||
\(783\) | 15.2132 | + | 27.2132i | 0.543676 | + | 0.972521i | ||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | −2.82843 | − | 2.82843i | −0.100951 | − | 0.100951i | ||||
\(786\) | −16.0000 | + | 22.6274i | −0.570701 | + | 0.807093i | ||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | 2.82843 | 0.100759 | ||||||||
\(789\) | −44.0000 | − | 31.1127i | −1.56644 | − | 1.10764i | ||||
\(790\) | 3.00000 | − | 3.00000i | 0.106735 | − | 0.106735i | ||||
\(791\) | −2.82843 | + | 2.82843i | −0.100567 | + | 0.100567i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | −0.639199 | ||||||||
\(794\) | 12.7279 | + | 12.7279i | 0.451697 | + | 0.451697i | ||||
\(795\) | −9.65685 | + | 1.65685i | −0.342493 | + | 0.0587626i | ||||
\(796\) | 1.00000 | − | 1.00000i | 0.0354441 | − | 0.0354441i | ||||
\(797\) | −15.5563 | + | 15.5563i | −0.551034 | + | 0.551034i | −0.926739 | − | 0.375705i | \(-0.877401\pi\) |
0.375705 | + | 0.926739i | \(0.377401\pi\) | |||||||
\(798\) | −8.48528 | + | 12.0000i | −0.300376 | + | 0.424795i | ||||
\(799\) | 12.0000 | − | 12.0000i | 0.424529 | − | 0.424529i | ||||
\(800\) | −0.707107 | − | 0.707107i | −0.0250000 | − | 0.0250000i | ||||
\(801\) | −5.41421 | − | 2.58579i | −0.191302 | − | 0.0913643i | ||||
\(802\) | − | 18.0000i | − | 0.635602i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.65685 | + | 4.00000i | 0.199502 | + | 0.141069i | ||||
\(805\) | − | 8.00000i | − | 0.281963i | ||||||
\(806\) | −9.89949 | + | 9.89949i | −0.348695 | + | 0.348695i | ||||
\(807\) | −19.7990 | + | 28.0000i | −0.696957 | + | 0.985647i | ||||
\(808\) | 2.00000 | + | 2.00000i | 0.0703598 | + | 0.0703598i | ||||
\(809\) | −15.5563 | + | 15.5563i | −0.546932 | + | 0.546932i | −0.925552 | − | 0.378620i | \(-0.876399\pi\) |
0.378620 | + | 0.925552i | \(0.376399\pi\) | |||||||
\(810\) | −7.00000 | + | 5.65685i | −0.245955 | + | 0.198762i | ||||
\(811\) | −30.0000 | −1.05344 | −0.526721 | − | 0.850038i | \(-0.676579\pi\) | ||||
−0.526721 | + | 0.850038i | \(0.676579\pi\) | |||||||
\(812\) | −8.48528 | − | 8.48528i | −0.297775 | − | 0.297775i | ||||
\(813\) | 14.1421 | + | 10.0000i | 0.495986 | + | 0.350715i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 21.2132i | − | 0.743066i | ||||||
\(816\) | −1.75736 | − | 10.2426i | −0.0615199 | − | 0.358564i | ||||
\(817\) | 42.0000i | 1.46939i | ||||||||
\(818\) | −7.07107 | −0.247234 | ||||||||
\(819\) | 7.65685 | + | 3.65685i | 0.267552 | + | 0.127781i | ||||
\(820\) | 4.00000 | − | 4.00000i | 0.139686 | − | 0.139686i | ||||
\(821\) | − | 28.2843i | − | 0.987128i | −0.869710 | − | 0.493564i | \(-0.835694\pi\) | ||
0.869710 | − | 0.493564i | \(-0.164306\pi\) | |||||||
\(822\) | 0.828427 | + | 4.82843i | 0.0288947 | + | 0.168411i | ||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | 7.07107i | 0.246332i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.0000 | 0.556711 | ||||||||
\(827\) | −2.82843 | − | 2.82843i | −0.0983540 | − | 0.0983540i | 0.656218 | − | 0.754572i | \(-0.272155\pi\) |
−0.754572 | + | 0.656218i | \(0.772155\pi\) | |||||||
\(828\) | −10.8284 | − | 5.17157i | −0.376314 | − | 0.179725i | ||||
\(829\) | 21.0000 | + | 21.0000i | 0.729360 | + | 0.729360i | 0.970492 | − | 0.241132i | \(-0.0775187\pi\) |
−0.241132 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(830\) | 2.82843i | 0.0981761i | ||||||||
\(831\) | 4.55635 | + | 26.5563i | 0.158058 | + | 0.921230i | ||||
\(832\) | 1.00000 | + | 1.00000i | 0.0346688 | + | 0.0346688i | ||||
\(833\) | −12.7279 | − | 12.7279i | −0.440996 | − | 0.440996i | ||||
\(834\) | 1.17157 | + | 6.82843i | 0.0405683 | + | 0.236449i | ||||
\(835\) | 16.0000i | 0.553703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 44.8995 | − | 25.1005i | 1.55195 | − | 0.867600i | ||||
\(838\) | 18.0000 | + | 18.0000i | 0.621800 | + | 0.621800i | ||||
\(839\) | −36.7696 | −1.26943 | −0.634713 | − | 0.772748i | \(-0.718882\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(840\) | 2.00000 | − | 2.82843i | 0.0690066 | − | 0.0975900i | ||||
\(841\) | − | 7.00000i | − | 0.241379i | ||||||
\(842\) | 12.7279 | 0.438633 | ||||||||
\(843\) | 5.27208 | + | 30.7279i | 0.181580 | + | 1.05833i | ||||
\(844\) | − | 20.0000i | − | 0.688428i | ||||||
\(845\) | −7.77817 | + | 7.77817i | −0.267577 | + | 0.267577i | ||||
\(846\) | 3.65685 | − | 7.65685i | 0.125725 | − | 0.263248i | ||||
\(847\) | −22.0000 | −0.755929 | ||||||||
\(848\) | − | 5.65685i | − | 0.194257i | ||||||
\(849\) | 1.24264 | + | 7.24264i | 0.0426473 | + | 0.248567i | ||||
\(850\) | 6.00000i | 0.205798i | ||||||||
\(851\) | 19.7990 | − | 14.1421i | 0.678701 | − | 0.484786i | ||||
\(852\) | 4.00000 | + | 2.82843i | 0.137038 | + | 0.0969003i | ||||
\(853\) | 21.0000 | + | 21.0000i | 0.719026 | + | 0.719026i | 0.968406 | − | 0.249380i | \(-0.0802267\pi\) |
−0.249380 | + | 0.968406i | \(0.580227\pi\) | |||||||
\(854\) | −25.4558 | −0.871081 | ||||||||
\(855\) | −4.24264 | − | 12.0000i | −0.145095 | − | 0.410391i | ||||
\(856\) | −8.00000 | + | 8.00000i | −0.273434 | + | 0.273434i | ||||
\(857\) | 29.6985 | + | 29.6985i | 1.01448 | + | 1.01448i | 0.999894 | + | 0.0145873i | \(0.00464345\pi\) |
0.0145873 | + | 0.999894i | \(0.495357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.0000 | + | 15.0000i | −0.511793 | + | 0.511793i | −0.915076 | − | 0.403282i | \(-0.867869\pi\) |
0.403282 | + | 0.915076i | \(0.367869\pi\) | |||||||
\(860\) | − | 9.89949i | − | 0.337570i | ||||||
\(861\) | 16.0000 | + | 11.3137i | 0.545279 | + | 0.385570i | ||||
\(862\) | − | 8.00000i | − | 0.272481i | ||||||
\(863\) | − | 28.2843i | − | 0.962808i | −0.876499 | − | 0.481404i | \(-0.840127\pi\) | ||
0.876499 | − | 0.481404i | \(-0.159873\pi\) | |||||||
\(864\) | −2.53553 | − | 4.53553i | −0.0862606 | − | 0.154302i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.9706 | + | 16.9706i | −0.576683 | + | 0.576683i | ||||
\(867\) | −19.0000 | + | 26.8701i | −0.645274 | + | 0.912555i | ||||
\(868\) | −14.0000 | + | 14.0000i | −0.475191 | + | 0.475191i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 10.2426 | − | 1.75736i | 0.347258 | − | 0.0595801i | ||||
\(871\) | 4.00000 | + | 4.00000i | 0.135535 | + | 0.135535i | ||||
\(872\) | 4.24264 | 0.143674 | ||||||||
\(873\) | 26.7990 | + | 12.7990i | 0.907008 | + | 0.433180i | ||||
\(874\) | 12.0000 | − | 12.0000i | 0.405906 | − | 0.405906i | ||||
\(875\) | −1.41421 | + | 1.41421i | −0.0478091 | + | 0.0478091i | ||||
\(876\) | −8.48528 | − | 6.00000i | −0.286691 | − | 0.202721i | ||||
\(877\) | 28.0000 | 0.945493 | 0.472746 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472746 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(878\) | 38.1838 | 1.28864 | ||||||||
\(879\) | 22.6274 | − | 32.0000i | 0.763204 | − | 1.07933i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1127 | 1.04821 | 0.524107 | − | 0.851653i | \(-0.324399\pi\) | ||||
0.524107 | + | 0.851653i | \(0.324399\pi\) | |||||||
\(882\) | −8.12132 | − | 3.87868i | −0.273459 | − | 0.130602i | ||||
\(883\) | 35.0000 | + | 35.0000i | 1.17784 | + | 1.17784i | 0.980293 | + | 0.197551i | \(0.0632989\pi\) |
0.197551 | + | 0.980293i | \(0.436701\pi\) | |||||||
\(884\) | − | 8.48528i | − | 0.285391i | ||||||
\(885\) | −8.00000 | + | 11.3137i | −0.268917 | + | 0.380306i | ||||
\(886\) | 10.0000 | − | 10.0000i | 0.335957 | − | 0.335957i | ||||
\(887\) | 2.82843 | 0.0949693 | 0.0474846 | − | 0.998872i | \(-0.484879\pi\) | ||||
0.0474846 | + | 0.998872i | \(0.484879\pi\) | |||||||
\(888\) | 10.5355 | − | 0.0502525i | 0.353549 | − | 0.00168636i | ||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | −1.41421 | + | 1.41421i | −0.0474045 | + | 0.0474045i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.0000i | 0.803579i | ||||||||
\(893\) | 8.48528 | + | 8.48528i | 0.283949 | + | 0.283949i | ||||
\(894\) | −5.79899 | − | 33.7990i | −0.193947 | − | 1.13041i | ||||
\(895\) | 16.0000 | 0.534821 | ||||||||
\(896\) | 1.41421 | + | 1.41421i | 0.0472456 | + | 0.0472456i | ||||
\(897\) | −8.00000 | − | 5.65685i | −0.267112 | − | 0.188877i | ||||
\(898\) | 26.0000 | 0.867631 | ||||||||
\(899\) | −59.3970 | −1.98100 | ||||||||
\(900\) | 1.00000 | + | 2.82843i | 0.0333333 | + | 0.0942809i | ||||
\(901\) | −24.0000 | + | 24.0000i | −0.799556 | + | 0.799556i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.7990 | − | 5.79899i | 1.12476 | − | 0.192978i | ||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.27208 | − | 30.7279i | −0.175153 | − | 1.02087i | ||||
\(907\) | −13.0000 | + | 13.0000i | −0.431658 | + | 0.431658i | −0.889192 | − | 0.457534i | \(-0.848733\pi\) |
0.457534 | + | 0.889192i | \(0.348733\pi\) | |||||||
\(908\) | −16.9706 | + | 16.9706i | −0.563188 | + | 0.563188i | ||||
\(909\) | −2.82843 | − | 8.00000i | −0.0938130 | − | 0.265343i | ||||
\(910\) | 2.00000 | − | 2.00000i | 0.0662994 | − | 0.0662994i | ||||
\(911\) | −25.4558 | − | 25.4558i | −0.843390 | − | 0.843390i | 0.145908 | − | 0.989298i | \(-0.453390\pi\) |
−0.989298 | + | 0.145908i | \(0.953390\pi\) | |||||||
\(912\) | 7.24264 | − | 1.24264i | 0.239828 | − | 0.0411479i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.89949i | 0.327446i | ||||||||
\(915\) | 12.7279 | − | 18.0000i | 0.420772 | − | 0.595062i | ||||
\(916\) | 26.0000i | 0.859064i | ||||||||
\(917\) | −22.6274 | + | 22.6274i | −0.747223 | + | 0.747223i | ||||
\(918\) | −8.48528 | + | 30.0000i | −0.280056 | + | 0.990148i | ||||
\(919\) | −37.0000 | − | 37.0000i | −1.22052 | − | 1.22052i | −0.967448 | − | 0.253069i | \(-0.918560\pi\) |
−0.253069 | − | 0.967448i | \(-0.581440\pi\) | |||||||
\(920\) | −2.82843 | + | 2.82843i | −0.0932505 | + | 0.0932505i | ||||
\(921\) | 10.0000 | − | 14.1421i | 0.329511 | − | 0.465999i | ||||
\(922\) | 30.0000 | 0.987997 | ||||||||
\(923\) | 2.82843 | + | 2.82843i | 0.0930988 | + | 0.0930988i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | − | 1.00000i | −0.197279 | − | 0.0328798i | ||||
\(926\) | − | 15.5563i | − | 0.511213i | ||||||
\(927\) | 9.14214 | − | 19.1421i | 0.300267 | − | 0.628710i | ||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | −45.2548 | −1.48476 | −0.742381 | − | 0.669977i | \(-0.766304\pi\) | ||||
−0.742381 | + | 0.669977i | \(0.766304\pi\) | |||||||
\(930\) | −2.89949 | − | 16.8995i | −0.0950782 | − | 0.554156i | ||||
\(931\) | 9.00000 | − | 9.00000i | 0.294963 | − | 0.294963i | ||||
\(932\) | − | 28.2843i | − | 0.926482i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.41421 | − | 4.00000i | −0.0462250 | − | 0.130744i | ||||
\(937\) | −10.0000 | −0.326686 | −0.163343 | − | 0.986569i | \(-0.552228\pi\) | ||||
−0.163343 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(938\) | 5.65685 | + | 5.65685i | 0.184703 | + | 0.184703i | ||||
\(939\) | 2.41421 | − | 0.414214i | 0.0787849 | − | 0.0135173i | ||||
\(940\) | −2.00000 | − | 2.00000i | −0.0652328 | − | 0.0652328i | ||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | −6.82843 | + | 1.17157i | −0.222482 | + | 0.0381719i | ||||
\(943\) | −16.0000 | − | 16.0000i | −0.521032 | − | 0.521032i | ||||
\(944\) | −5.65685 | − | 5.65685i | −0.184115 | − | 0.184115i | ||||
\(945\) | −9.07107 | + | 5.07107i | −0.295082 | + | 0.164962i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7696 | − | 36.7696i | −1.19485 | − | 1.19485i | −0.975689 | − | 0.219161i | \(-0.929668\pi\) |
−0.219161 | − | 0.975689i | \(-0.570332\pi\) | |||||||
\(948\) | −1.24264 | − | 7.24264i | −0.0403591 | − | 0.235230i | ||||
\(949\) | −6.00000 | − | 6.00000i | −0.194768 | − | 0.194768i | ||||
\(950\) | −4.24264 | −0.137649 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 12.0000i | − | 0.388922i | ||||||
\(953\) | −48.0833 | −1.55757 | −0.778785 | − | 0.627291i | \(-0.784164\pi\) | ||||
−0.778785 | + | 0.627291i | \(0.784164\pi\) | |||||||
\(954\) | −7.31371 | + | 15.3137i | −0.236790 | + | 0.495800i | ||||
\(955\) | − | 8.00000i | − | 0.258874i | ||||||
\(956\) | 14.1421 | − | 14.1421i | 0.457389 | − | 0.457389i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.65685i | 0.182669i | ||||||||
\(960\) | −1.70711 | + | 0.292893i | −0.0550966 | + | 0.00945309i | ||||
\(961\) | 67.0000i | 2.16129i | ||||||||
\(962\) | 8.48528 | + | 1.41421i | 0.273576 | + | 0.0455961i | ||||
\(963\) | 32.0000 | − | 11.3137i | 1.03119 | − | 0.364579i | ||||
\(964\) | 11.0000 | + | 11.0000i | 0.354286 | + | 0.354286i | ||||
\(965\) | −1.41421 | −0.0455251 | ||||||||
\(966\) | −11.3137 | − | 8.00000i | −0.364013 | − | 0.257396i | ||||
\(967\) | −5.00000 | + | 5.00000i | −0.160789 | + | 0.160789i | −0.782916 | − | 0.622127i | \(-0.786269\pi\) |
0.622127 | + | 0.782916i | \(0.286269\pi\) | |||||||
\(968\) | 7.77817 | + | 7.77817i | 0.250000 | + | 0.250000i | ||||
\(969\) | −36.0000 | − | 25.4558i | −1.15649 | − | 0.817760i | ||||
\(970\) | 7.00000 | − | 7.00000i | 0.224756 | − | 0.224756i | ||||
\(971\) | − | 19.7990i | − | 0.635380i | −0.948195 | − | 0.317690i | \(-0.897093\pi\) | ||
0.948195 | − | 0.317690i | \(-0.102907\pi\) | |||||||
\(972\) | 1.00000 | + | 15.5563i | 0.0320750 | + | 0.498970i | ||||
\(973\) | 8.00000i | 0.256468i | ||||||||
\(974\) | − | 24.0416i | − | 0.770344i | ||||||
\(975\) | 0.414214 | + | 2.41421i | 0.0132655 | + | 0.0773167i | ||||
\(976\) | 9.00000 | + | 9.00000i | 0.288083 | + | 0.288083i | ||||
\(977\) | −18.3848 | + | 18.3848i | −0.588181 | + | 0.588181i | −0.937139 | − | 0.348957i | \(-0.886536\pi\) |
0.348957 | + | 0.937139i | \(0.386536\pi\) | |||||||
\(978\) | −30.0000 | − | 21.2132i | −0.959294 | − | 0.678323i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.12132 | + | 2.12132i | −0.0677631 | + | 0.0677631i | ||||
\(981\) | −11.4853 | − | 5.48528i | −0.366697 | − | 0.175132i | ||||
\(982\) | −10.0000 | − | 10.0000i | −0.319113 | − | 0.319113i | ||||
\(983\) | 48.0833 | 1.53362 | 0.766809 | − | 0.641875i | \(-0.221843\pi\) | ||||
0.766809 | + | 0.641875i | \(0.221843\pi\) | |||||||
\(984\) | −1.65685 | − | 9.65685i | −0.0528186 | − | 0.307849i | ||||
\(985\) | −2.00000 | + | 2.00000i | −0.0637253 | + | 0.0637253i | ||||
\(986\) | 25.4558 | − | 25.4558i | 0.810679 | − | 0.810679i | ||||
\(987\) | 5.65685 | − | 8.00000i | 0.180060 | − | 0.254643i | ||||
\(988\) | 6.00000 | 0.190885 | ||||||||
\(989\) | −39.5980 | −1.25914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.00000 | − | 9.00000i | −0.285894 | − | 0.285894i | 0.549560 | − | 0.835454i | \(-0.314795\pi\) |
−0.835454 | + | 0.549560i | \(0.814795\pi\) | |||||||
\(992\) | 9.89949 | 0.314309 | ||||||||
\(993\) | 36.2132 | − | 6.21320i | 1.14919 | − | 0.197170i | ||||
\(994\) | 4.00000 | + | 4.00000i | 0.126872 | + | 0.126872i | ||||
\(995\) | 1.41421i | 0.0448336i | ||||||||
\(996\) | 4.00000 | + | 2.82843i | 0.126745 | + | 0.0896221i | ||||
\(997\) | −11.0000 | + | 11.0000i | −0.348373 | + | 0.348373i | −0.859503 | − | 0.511130i | \(-0.829227\pi\) |
0.511130 | + | 0.859503i | \(0.329227\pi\) | |||||||
\(998\) | 4.24264 | 0.134298 | ||||||||
\(999\) | −28.5858 | − | 13.4853i | −0.904414 | − | 0.426655i |
(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 | 1110.2.u.d.401.2 | yes | 4 | |
3.2 | odd | 2 | inner | 1110.2.u.d.401.1 | yes | 4 | |
37.6 | odd | 4 | inner | 1110.2.u.d.191.1 | ✓ | 4 | |
111.80 | even | 4 | inner | 1110.2.u.d.191.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.d.191.1 | ✓ | 4 | 37.6 | odd | 4 | inner | |
1110.2.u.d.191.2 | yes | 4 | 111.80 | even | 4 | inner | |
1110.2.u.d.401.1 | yes | 4 | 3.2 | odd | 2 | inner | |
1110.2.u.d.401.2 | yes | 4 | 1.1 | even | 1 | trivial |