Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(73,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.w (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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.73 |
Dual form | 585.2.w.c.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00000i | − | 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 1.00000i | 0.632456 | + | 0.316228i | ||||
\(11\) | 2.00000 | − | 2.00000i | 0.603023 | − | 0.603023i | −0.338091 | − | 0.941113i | \(-0.609781\pi\) |
0.941113 | + | 0.338091i | \(0.109781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 2.00000i | 0.832050 | − | 0.554700i | ||||
\(14\) | − | 4.00000i | − | 1.06904i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.00000 | + | 1.00000i | 0.242536 | + | 0.242536i | 0.817898 | − | 0.575363i | \(-0.195139\pi\) |
−0.575363 | + | 0.817898i | \(0.695139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | + | 2.00000i | −0.458831 | + | 0.458831i | −0.898272 | − | 0.439440i | \(-0.855177\pi\) |
0.439440 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | − | 2.00000i | 0.426401 | − | 0.426401i | ||||
\(23\) | 6.00000 | − | 6.00000i | 1.25109 | − | 1.25109i | 0.295853 | − | 0.955233i | \(-0.404396\pi\) |
0.955233 | − | 0.295853i | \(-0.0956039\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 3.00000 | − | 2.00000i | 0.588348 | − | 0.392232i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 4.00000i | −0.718421 | − | 0.718421i | 0.249861 | − | 0.968282i | \(-0.419615\pi\) |
−0.968282 | + | 0.249861i | \(0.919615\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | + | 1.00000i | 0.171499 | + | 0.171499i | ||||
\(35\) | 4.00000 | − | 8.00000i | 0.676123 | − | 1.35225i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | −2.00000 | + | 2.00000i | −0.324443 | + | 0.324443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | − | 3.00000i | −0.948683 | − | 0.474342i | ||||
\(41\) | 5.00000 | + | 5.00000i | 0.780869 | + | 0.780869i | 0.979977 | − | 0.199109i | \(-0.0638047\pi\) |
−0.199109 | + | 0.979977i | \(0.563805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | + | 4.00000i | −0.609994 | + | 0.609994i | −0.942944 | − | 0.332950i | \(-0.891956\pi\) |
0.332950 | + | 0.942944i | \(0.391956\pi\) | |||||||
\(44\) | −2.00000 | + | 2.00000i | −0.301511 | + | 0.301511i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | − | 6.00000i | 0.884652 | − | 0.884652i | ||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 3.00000 | + | 4.00000i | 0.424264 | + | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | + | 2.00000i | −0.416025 | + | 0.277350i | ||||
\(53\) | −7.00000 | − | 7.00000i | −0.961524 | − | 0.961524i | 0.0377628 | − | 0.999287i | \(-0.487977\pi\) |
−0.999287 | + | 0.0377628i | \(0.987977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | − | 2.00000i | 0.809040 | − | 0.269680i | ||||
\(56\) | 12.0000i | 1.60357i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 2.00000i | 0.260378 | + | 0.260378i | 0.825208 | − | 0.564830i | \(-0.191058\pi\) |
−0.564830 | + | 0.825208i | \(0.691058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | −4.00000 | − | 4.00000i | −0.508001 | − | 0.508001i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 8.00000 | − | 1.00000i | 0.992278 | − | 0.124035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | −1.00000 | − | 1.00000i | −0.121268 | − | 0.121268i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.00000 | − | 8.00000i | 0.478091 | − | 0.956183i | ||||
\(71\) | −8.00000 | − | 8.00000i | −0.949425 | − | 0.949425i | 0.0493559 | − | 0.998781i | \(-0.484283\pi\) |
−0.998781 | + | 0.0493559i | \(0.984283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 6.00000i | 0.697486i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 2.00000i | 0.229416 | − | 0.229416i | ||||
\(77\) | −8.00000 | − | 8.00000i | −0.911685 | − | 0.911685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000i | 0.900070i | 0.893011 | + | 0.450035i | \(0.148589\pi\) | ||||
−0.893011 | + | 0.450035i | \(0.851411\pi\) | |||||||
\(80\) | −2.00000 | − | 1.00000i | −0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.00000 | + | 5.00000i | 0.552158 | + | 0.552158i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | + | 3.00000i | 0.108465 | + | 0.325396i | ||||
\(86\) | −4.00000 | + | 4.00000i | −0.431331 | + | 0.431331i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.00000 | + | 6.00000i | −0.639602 | + | 0.639602i | ||||
\(89\) | 5.00000 | + | 5.00000i | 0.529999 | + | 0.529999i | 0.920572 | − | 0.390573i | \(-0.127723\pi\) |
−0.390573 | + | 0.920572i | \(0.627723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | − | 12.0000i | −0.838628 | − | 1.25794i | ||||
\(92\) | −6.00000 | + | 6.00000i | −0.625543 | + | 0.625543i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00000 | + | 2.00000i | −0.615587 | + | 0.205196i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | −9.00000 | −0.909137 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | − | 6.00000i | − | 0.597022i | −0.954406 | − | 0.298511i | \(-0.903510\pi\) | ||
0.954406 | − | 0.298511i | \(-0.0964900\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | + | 14.0000i | −1.37946 | + | 1.37946i | −0.533936 | + | 0.845525i | \(0.679288\pi\) |
−0.845525 | + | 0.533936i | \(0.820712\pi\) | |||||||
\(104\) | −9.00000 | + | 6.00000i | −0.882523 | + | 0.588348i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.00000 | − | 7.00000i | −0.679900 | − | 0.679900i | ||||
\(107\) | −8.00000 | + | 8.00000i | −0.773389 | + | 0.773389i | −0.978697 | − | 0.205308i | \(-0.934180\pi\) |
0.205308 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.00000 | + | 9.00000i | −0.862044 | + | 0.862044i | −0.991575 | − | 0.129532i | \(-0.958653\pi\) |
0.129532 | + | 0.991575i | \(0.458653\pi\) | |||||||
\(110\) | 6.00000 | − | 2.00000i | 0.572078 | − | 0.190693i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | 11.0000 | + | 11.0000i | 1.03479 | + | 1.03479i | 0.999372 | + | 0.0354205i | \(0.0112770\pi\) |
0.0354205 | + | 0.999372i | \(0.488723\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.0000 | − | 6.00000i | 1.67851 | − | 0.559503i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | + | 2.00000i | 0.184115 | + | 0.184115i | ||||
\(119\) | 4.00000 | − | 4.00000i | 0.366679 | − | 0.366679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000i | 0.272727i | ||||||||
\(122\) | −8.00000 | −0.724286 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000 | + | 4.00000i | 0.359211 | + | 0.359211i | ||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | + | 6.00000i | 0.532414 | + | 0.532414i | 0.921290 | − | 0.388876i | \(-0.127137\pi\) |
−0.388876 | + | 0.921290i | \(0.627137\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.00000 | − | 1.00000i | 0.701646 | − | 0.0877058i | ||||
\(131\) | 16.0000 | 1.39793 | 0.698963 | − | 0.715158i | \(-0.253645\pi\) | ||||
0.698963 | + | 0.715158i | \(0.253645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | + | 8.00000i | 0.693688 | + | 0.693688i | ||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | − | 3.00000i | −0.257248 | − | 0.257248i | ||||
\(137\) | 22.0000i | 1.87959i | 0.341743 | + | 0.939793i | \(0.388983\pi\) | ||||
−0.341743 | + | 0.939793i | \(0.611017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.0000i | − | 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | −4.00000 | + | 8.00000i | −0.338062 | + | 0.676123i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.00000 | − | 8.00000i | −0.671345 | − | 0.671345i | ||||
\(143\) | 2.00000 | − | 10.0000i | 0.167248 | − | 0.836242i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | −15.0000 | + | 15.0000i | −1.22885 | + | 1.22885i | −0.264448 | + | 0.964400i | \(0.585190\pi\) |
−0.964400 | + | 0.264448i | \(0.914810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 4.00000i | 0.325515 | − | 0.325515i | −0.525363 | − | 0.850878i | \(-0.676070\pi\) |
0.850878 | + | 0.525363i | \(0.176070\pi\) | |||||||
\(152\) | 6.00000 | − | 6.00000i | 0.486664 | − | 0.486664i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.00000 | − | 8.00000i | −0.644658 | − | 0.644658i | ||||
\(155\) | −4.00000 | − | 12.0000i | −0.321288 | − | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000 | − | 7.00000i | 0.558661 | − | 0.558661i | −0.370265 | − | 0.928926i | \(-0.620733\pi\) |
0.928926 | + | 0.370265i | \(0.120733\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.0000 | + | 5.00000i | 0.790569 | + | 0.395285i | ||||
\(161\) | −24.0000 | − | 24.0000i | −1.89146 | − | 1.89146i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | −5.00000 | − | 5.00000i | −0.390434 | − | 0.390434i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | − | 12.0000i | 0.384615 | − | 0.923077i | ||||
\(170\) | 1.00000 | + | 3.00000i | 0.0766965 | + | 0.230089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | − | 4.00000i | 0.304997 | − | 0.304997i | ||||
\(173\) | 7.00000 | − | 7.00000i | 0.532200 | − | 0.532200i | −0.389026 | − | 0.921227i | \(-0.627189\pi\) |
0.921227 | + | 0.389026i | \(0.127189\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.0000 | − | 12.0000i | 1.20949 | − | 0.907115i | ||||
\(176\) | −2.00000 | + | 2.00000i | −0.150756 | + | 0.150756i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.00000 | + | 5.00000i | 0.374766 | + | 0.374766i | ||||
\(179\) | −8.00000 | −0.597948 | −0.298974 | − | 0.954261i | \(-0.596644\pi\) | ||||
−0.298974 | + | 0.954261i | \(0.596644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.0000i | − | 1.63525i | −0.575753 | − | 0.817624i | \(-0.695291\pi\) | ||
0.575753 | − | 0.817624i | \(-0.304709\pi\) | |||||||
\(182\) | −8.00000 | − | 12.0000i | −0.592999 | − | 0.889499i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.0000 | + | 18.0000i | −1.32698 | + | 1.32698i | ||||
\(185\) | −6.00000 | + | 12.0000i | −0.441129 | + | 0.882258i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | + | 2.00000i | −0.435286 | + | 0.145095i | ||||
\(191\) | 20.0000 | 1.44715 | 0.723575 | − | 0.690246i | \(-0.242498\pi\) | ||||
0.723575 | + | 0.690246i | \(0.242498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0000 | 1.29567 | 0.647834 | − | 0.761781i | \(-0.275675\pi\) | ||||
0.647834 | + | 0.761781i | \(0.275675\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | −9.00000 | − | 12.0000i | −0.636396 | − | 0.848528i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00000 | + | 15.0000i | 0.349215 | + | 1.04765i | ||||
\(206\) | −14.0000 | + | 14.0000i | −0.975426 | + | 0.975426i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | + | 2.00000i | −0.208013 | + | 0.138675i | ||||
\(209\) | 8.00000i | 0.553372i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 7.00000 | + | 7.00000i | 0.480762 | + | 0.480762i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00000 | + | 8.00000i | −0.546869 | + | 0.546869i | ||||
\(215\) | −12.0000 | + | 4.00000i | −0.818393 | + | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | + | 16.0000i | −1.08615 | + | 1.08615i | ||||
\(218\) | −9.00000 | + | 9.00000i | −0.609557 | + | 0.609557i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00000 | + | 2.00000i | −0.404520 | + | 0.134840i | ||||
\(221\) | 5.00000 | + | 1.00000i | 0.336336 | + | 0.0672673i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | − | 20.0000i | − | 1.33631i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.0000 | + | 11.0000i | 0.731709 | + | 0.731709i | ||||
\(227\) | 24.0000 | 1.59294 | 0.796468 | − | 0.604681i | \(-0.206699\pi\) | ||||
0.796468 | + | 0.604681i | \(0.206699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.00000 | − | 9.00000i | −0.594737 | − | 0.594737i | 0.344170 | − | 0.938907i | \(-0.388160\pi\) |
−0.938907 | + | 0.344170i | \(0.888160\pi\) | |||||||
\(230\) | 18.0000 | − | 6.00000i | 1.18688 | − | 0.395628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00000 | − | 7.00000i | 0.458585 | − | 0.458585i | −0.439606 | − | 0.898191i | \(-0.644882\pi\) |
0.898191 | + | 0.439606i | \(0.144882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | − | 2.00000i | −0.130189 | − | 0.130189i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000 | − | 4.00000i | 0.259281 | − | 0.259281i | ||||
\(239\) | 12.0000 | − | 12.0000i | 0.776215 | − | 0.776215i | −0.202970 | − | 0.979185i | \(-0.565059\pi\) |
0.979185 | + | 0.202970i | \(0.0650593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | + | 13.0000i | −0.837404 | + | 0.837404i | −0.988517 | − | 0.151113i | \(-0.951714\pi\) |
0.151113 | + | 0.988517i | \(0.451714\pi\) | |||||||
\(242\) | 3.00000i | 0.192847i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | −18.0000 | − | 9.00000i | −1.14998 | − | 0.574989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | + | 10.0000i | −0.127257 | + | 0.636285i | ||||
\(248\) | 12.0000 | + | 12.0000i | 0.762001 | + | 0.762001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.00000 | + | 11.0000i | 0.126491 | + | 0.695701i | ||||
\(251\) | 28.0000i | 1.76734i | 0.468106 | + | 0.883672i | \(0.344936\pi\) | ||||
−0.468106 | + | 0.883672i | \(0.655064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 24.0000i | − | 1.50887i | ||||||
\(254\) | 6.00000 | + | 6.00000i | 0.376473 | + | 0.376473i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −5.00000 | − | 5.00000i | −0.311891 | − | 0.311891i | 0.533751 | − | 0.845642i | \(-0.320782\pi\) |
−0.845642 | + | 0.533751i | \(0.820782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.0000 | 1.49129 | ||||||||
\(260\) | −8.00000 | + | 1.00000i | −0.496139 | + | 0.0620174i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.0000 | 0.988483 | ||||||||
\(263\) | 10.0000 | + | 10.0000i | 0.616626 | + | 0.616626i | 0.944664 | − | 0.328038i | \(-0.106387\pi\) |
−0.328038 | + | 0.944664i | \(0.606387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.00000 | − | 21.0000i | −0.430007 | − | 1.29002i | ||||
\(266\) | 8.00000 | + | 8.00000i | 0.490511 | + | 0.490511i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | − | 18.0000i | − | 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(272\) | −1.00000 | − | 1.00000i | −0.0606339 | − | 0.0606339i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.0000i | 1.32907i | ||||||||
\(275\) | 14.0000 | + | 2.00000i | 0.844232 | + | 0.120605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.00000 | − | 3.00000i | −0.180253 | − | 0.180253i | 0.611213 | − | 0.791466i | \(-0.290682\pi\) |
−0.791466 | + | 0.611213i | \(0.790682\pi\) | |||||||
\(278\) | − | 16.0000i | − | 0.959616i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.0000 | + | 24.0000i | −0.717137 | + | 1.43427i | ||||
\(281\) | 13.0000 | − | 13.0000i | 0.775515 | − | 0.775515i | −0.203550 | − | 0.979065i | \(-0.565248\pi\) |
0.979065 | + | 0.203550i | \(0.0652478\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(284\) | 8.00000 | + | 8.00000i | 0.474713 | + | 0.474713i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | − | 10.0000i | 0.118262 | − | 0.591312i | ||||
\(287\) | 20.0000 | − | 20.0000i | 1.18056 | − | 1.18056i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.0000i | − | 0.882353i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.00000 | 0.234082 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | + | 6.00000i | 0.116445 | + | 0.349334i | ||||
\(296\) | − | 18.0000i | − | 1.04623i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.0000 | + | 15.0000i | −0.868927 | + | 0.868927i | ||||
\(299\) | 6.00000 | − | 30.0000i | 0.346989 | − | 1.73494i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | + | 16.0000i | 0.922225 | + | 0.922225i | ||||
\(302\) | 4.00000 | − | 4.00000i | 0.230174 | − | 0.230174i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 2.00000i | 0.114708 | − | 0.114708i | ||||
\(305\) | −16.0000 | − | 8.00000i | −0.916157 | − | 0.458079i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000i | 0.684876i | 0.939540 | + | 0.342438i | \(0.111253\pi\) | ||||
−0.939540 | + | 0.342438i | \(0.888747\pi\) | |||||||
\(308\) | 8.00000 | + | 8.00000i | 0.455842 | + | 0.455842i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.00000 | − | 12.0000i | −0.227185 | − | 0.681554i | ||||
\(311\) | − | 12.0000i | − | 0.680458i | −0.940343 | − | 0.340229i | \(-0.889495\pi\) | ||
0.940343 | − | 0.340229i | \(-0.110505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00000 | + | 9.00000i | 0.508710 | + | 0.508710i | 0.914130 | − | 0.405420i | \(-0.132875\pi\) |
−0.405420 | + | 0.914130i | \(0.632875\pi\) | |||||||
\(314\) | 7.00000 | − | 7.00000i | 0.395033 | − | 0.395033i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.00000i | − | 0.450035i | ||||||
\(317\) | −26.0000 | −1.46031 | −0.730153 | − | 0.683284i | \(-0.760551\pi\) | ||||
−0.730153 | + | 0.683284i | \(0.760551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 14.0000 | + | 7.00000i | 0.782624 | + | 0.391312i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −24.0000 | − | 24.0000i | −1.33747 | − | 1.33747i | ||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0000 | + | 6.00000i | 0.942990 | + | 0.332820i | ||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.0000 | − | 15.0000i | −0.828236 | − | 0.828236i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | − | 6.00000i | −0.329790 | − | 0.329790i | 0.522717 | − | 0.852506i | \(-0.324919\pi\) |
−0.852506 | + | 0.522717i | \(0.824919\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.0000 | + | 8.00000i | 0.874173 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | + | 1.00000i | 0.0544735 | + | 0.0544735i | 0.733819 | − | 0.679345i | \(-0.237736\pi\) |
−0.679345 | + | 0.733819i | \(0.737736\pi\) | |||||||
\(338\) | 5.00000 | − | 12.0000i | 0.271964 | − | 0.652714i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.00000 | − | 3.00000i | −0.0542326 | − | 0.162698i | ||||
\(341\) | −16.0000 | −0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 12.0000 | − | 12.0000i | 0.646997 | − | 0.646997i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.00000 | − | 7.00000i | 0.376322 | − | 0.376322i | ||||
\(347\) | 24.0000 | − | 24.0000i | 1.28839 | − | 1.28839i | 0.352621 | − | 0.935766i | \(-0.385290\pi\) |
0.935766 | − | 0.352621i | \(-0.114710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.00000 | + | 3.00000i | 0.160586 | + | 0.160586i | 0.782826 | − | 0.622240i | \(-0.213777\pi\) |
−0.622240 | + | 0.782826i | \(0.713777\pi\) | |||||||
\(350\) | 16.0000 | − | 12.0000i | 0.855236 | − | 0.641427i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.0000 | − | 10.0000i | 0.533002 | − | 0.533002i | ||||
\(353\) | 36.0000i | 1.91609i | 0.286623 | + | 0.958043i | \(0.407467\pi\) | ||||
−0.286623 | + | 0.958043i | \(0.592533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | − | 24.0000i | −0.424596 | − | 1.27379i | ||||
\(356\) | −5.00000 | − | 5.00000i | −0.264999 | − | 0.264999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.00000 | −0.422813 | ||||||||
\(359\) | 4.00000 | + | 4.00000i | 0.211112 | + | 0.211112i | 0.804740 | − | 0.593628i | \(-0.202305\pi\) |
−0.593628 | + | 0.804740i | \(0.702305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000i | 0.578947i | ||||||||
\(362\) | − | 22.0000i | − | 1.15629i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | + | 12.0000i | 0.419314 | + | 0.628971i | ||||
\(365\) | −8.00000 | − | 4.00000i | −0.418739 | − | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0000 | + | 10.0000i | −0.521996 | + | 0.521996i | −0.918174 | − | 0.396178i | \(-0.870336\pi\) |
0.396178 | + | 0.918174i | \(0.370336\pi\) | |||||||
\(368\) | −6.00000 | + | 6.00000i | −0.312772 | + | 0.312772i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | + | 12.0000i | −0.311925 | + | 0.623850i | ||||
\(371\) | −28.0000 | + | 28.0000i | −1.45369 | + | 1.45369i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00000 | + | 3.00000i | 0.155334 | + | 0.155334i | 0.780496 | − | 0.625161i | \(-0.214967\pi\) |
−0.625161 | + | 0.780496i | \(0.714967\pi\) | |||||||
\(374\) | 4.00000 | 0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0000 | − | 14.0000i | 0.719132 | − | 0.719132i | −0.249296 | − | 0.968427i | \(-0.580199\pi\) |
0.968427 | + | 0.249296i | \(0.0801991\pi\) | |||||||
\(380\) | 6.00000 | − | 2.00000i | 0.307794 | − | 0.102598i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.0000 | 1.02329 | ||||||||
\(383\) | 12.0000i | 0.613171i | 0.951843 | + | 0.306586i | \(0.0991866\pi\) | ||||
−0.951843 | + | 0.306586i | \(0.900813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | − | 24.0000i | −0.407718 | − | 1.22315i | ||||
\(386\) | 18.0000 | 0.916176 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | −24.0000 | −1.21685 | −0.608424 | − | 0.793612i | \(-0.708198\pi\) | ||||
−0.608424 | + | 0.793612i | \(0.708198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 27.0000 | 1.36371 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | 0.604551 | ||||||||
\(395\) | −8.00000 | + | 16.0000i | −0.402524 | + | 0.805047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.0000i | − | 1.10415i | −0.833795 | − | 0.552074i | \(-0.813837\pi\) | ||
0.833795 | − | 0.552074i | \(-0.186163\pi\) | |||||||
\(398\) | −20.0000 | −1.00251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | −5.00000 | + | 5.00000i | −0.249688 | + | 0.249688i | −0.820843 | − | 0.571154i | \(-0.806496\pi\) |
0.571154 | + | 0.820843i | \(0.306496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0000 | − | 4.00000i | −0.996271 | − | 0.199254i | ||||
\(404\) | 6.00000i | 0.298511i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | + | 12.0000i | 0.594818 | + | 0.594818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | + | 13.0000i | −0.642809 | + | 0.642809i | −0.951245 | − | 0.308436i | \(-0.900194\pi\) |
0.308436 | + | 0.951245i | \(0.400194\pi\) | |||||||
\(410\) | 5.00000 | + | 15.0000i | 0.246932 | + | 0.740797i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.0000 | − | 14.0000i | 0.689730 | − | 0.689730i | ||||
\(413\) | 8.00000 | − | 8.00000i | 0.393654 | − | 0.393654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.0000 | − | 10.0000i | 0.735436 | − | 0.490290i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000i | 0.391293i | ||||||||
\(419\) | − | 16.0000i | − | 0.781651i | −0.920465 | − | 0.390826i | \(-0.872190\pi\) | ||
0.920465 | − | 0.390826i | \(-0.127810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.00000 | + | 7.00000i | 0.341159 | + | 0.341159i | 0.856803 | − | 0.515644i | \(-0.172447\pi\) |
−0.515644 | + | 0.856803i | \(0.672447\pi\) | |||||||
\(422\) | −20.0000 | −0.973585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.0000 | + | 21.0000i | 1.01985 | + | 1.01985i | ||||
\(425\) | −1.00000 | + | 7.00000i | −0.0485071 | + | 0.339550i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.0000i | 1.54859i | ||||||||
\(428\) | 8.00000 | − | 8.00000i | 0.386695 | − | 0.386695i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.0000 | + | 4.00000i | −0.578691 | + | 0.192897i | ||||
\(431\) | 4.00000 | + | 4.00000i | 0.192673 | + | 0.192673i | 0.796850 | − | 0.604177i | \(-0.206498\pi\) |
−0.604177 | + | 0.796850i | \(0.706498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | − | 5.00000i | 0.240285 | − | 0.240285i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) |
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | −16.0000 | + | 16.0000i | −0.768025 | + | 0.768025i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | − | 9.00000i | 0.431022 | − | 0.431022i | ||||
\(437\) | 24.0000i | 1.14808i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −18.0000 | + | 6.00000i | −0.858116 | + | 0.286039i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.00000 | + | 1.00000i | 0.237826 | + | 0.0475651i | ||||
\(443\) | −8.00000 | − | 8.00000i | −0.380091 | − | 0.380091i | 0.491044 | − | 0.871135i | \(-0.336616\pi\) |
−0.871135 | + | 0.491044i | \(0.836616\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.00000 | + | 15.0000i | 0.237023 | + | 0.711068i | ||||
\(446\) | 8.00000i | 0.378811i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 28.0000i | − | 1.32288i | ||||||
\(449\) | 3.00000 | + | 3.00000i | 0.141579 | + | 0.141579i | 0.774344 | − | 0.632765i | \(-0.218080\pi\) |
−0.632765 | + | 0.774344i | \(0.718080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0000 | 0.941763 | ||||||||
\(452\) | −11.0000 | − | 11.0000i | −0.517396 | − | 0.517396i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | −4.00000 | − | 32.0000i | −0.187523 | − | 1.50018i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | −9.00000 | − | 9.00000i | −0.420542 | − | 0.420542i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18.0000 | + | 6.00000i | −0.839254 | + | 0.279751i | ||||
\(461\) | 11.0000 | + | 11.0000i | 0.512321 | + | 0.512321i | 0.915237 | − | 0.402916i | \(-0.132003\pi\) |
−0.402916 | + | 0.915237i | \(0.632003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0000 | 0.557687 | 0.278844 | − | 0.960337i | \(-0.410049\pi\) | ||||
0.278844 | + | 0.960337i | \(0.410049\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.00000 | − | 7.00000i | 0.324269 | − | 0.324269i | ||||
\(467\) | 12.0000 | + | 12.0000i | 0.555294 | + | 0.555294i | 0.927964 | − | 0.372670i | \(-0.121558\pi\) |
−0.372670 | + | 0.927964i | \(0.621558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 32.0000i | − | 1.47762i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.00000 | − | 6.00000i | −0.276172 | − | 0.276172i | ||||
\(473\) | 16.0000i | 0.735681i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0000 | − | 2.00000i | −0.642364 | − | 0.0917663i | ||||
\(476\) | −4.00000 | + | 4.00000i | −0.183340 | + | 0.183340i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | − | 12.0000i | 0.548867 | − | 0.548867i | ||||
\(479\) | 8.00000 | + | 8.00000i | 0.365529 | + | 0.365529i | 0.865844 | − | 0.500314i | \(-0.166782\pi\) |
−0.500314 | + | 0.865844i | \(0.666782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 18.0000i | 0.547153 | + | 0.820729i | ||||
\(482\) | −13.0000 | + | 13.0000i | −0.592134 | + | 0.592134i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 3.00000i | − | 0.136364i | ||||||
\(485\) | 4.00000 | + | 2.00000i | 0.181631 | + | 0.0908153i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0000 | −1.45006 | −0.725029 | − | 0.688718i | \(-0.758174\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(488\) | 24.0000 | 1.08643 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.0000 | − | 9.00000i | −0.813157 | − | 0.406579i | ||||
\(491\) | − | 32.0000i | − | 1.44414i | −0.691820 | − | 0.722070i | \(-0.743191\pi\) | ||
0.691820 | − | 0.722070i | \(-0.256809\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.00000 | + | 10.0000i | −0.0899843 | + | 0.449921i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | + | 4.00000i | 0.179605 | + | 0.179605i | ||||
\(497\) | −32.0000 | + | 32.0000i | −1.43540 | + | 1.43540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0000 | + | 18.0000i | −0.805791 | + | 0.805791i | −0.983994 | − | 0.178203i | \(-0.942972\pi\) |
0.178203 | + | 0.983994i | \(0.442972\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.0000i | 1.24970i | ||||||||
\(503\) | −6.00000 | − | 6.00000i | −0.267527 | − | 0.267527i | 0.560576 | − | 0.828103i | \(-0.310580\pi\) |
−0.828103 | + | 0.560576i | \(0.810580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | − | 12.0000i | 0.266996 | − | 0.533993i | ||||
\(506\) | − | 24.0000i | − | 1.06693i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.00000 | − | 6.00000i | −0.266207 | − | 0.266207i | ||||
\(509\) | −23.0000 | + | 23.0000i | −1.01946 | + | 1.01946i | −0.0196502 | + | 0.999807i | \(0.506255\pi\) |
−0.999807 | + | 0.0196502i | \(0.993745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0000i | 0.707798i | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.00000 | − | 5.00000i | −0.220541 | − | 0.220541i | ||||
\(515\) | −42.0000 | + | 14.0000i | −1.85074 | + | 0.616914i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 24.0000 | 1.05450 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.0000 | + | 3.00000i | −1.05247 | + | 0.131559i | ||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0000 | + | 12.0000i | 0.524723 | + | 0.524723i | 0.918994 | − | 0.394271i | \(-0.129003\pi\) |
−0.394271 | + | 0.918994i | \(0.629003\pi\) | |||||||
\(524\) | −16.0000 | −0.698963 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0000 | + | 10.0000i | 0.436021 | + | 0.436021i | ||||
\(527\) | − | 8.00000i | − | 0.348485i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 49.0000i | − | 2.13043i | ||||||
\(530\) | −7.00000 | − | 21.0000i | −0.304061 | − | 0.912182i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.00000 | − | 8.00000i | −0.346844 | − | 0.346844i | ||||
\(533\) | 25.0000 | + | 5.00000i | 1.08287 | + | 0.216574i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0000 | + | 8.00000i | −1.03761 | + | 0.345870i | ||||
\(536\) | −24.0000 | −1.03664 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 18.0000i | − | 0.776035i | ||||||
\(539\) | −18.0000 | + | 18.0000i | −0.775315 | + | 0.775315i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | + | 9.00000i | −0.386940 | + | 0.386940i | −0.873595 | − | 0.486654i | \(-0.838217\pi\) |
0.486654 | + | 0.873595i | \(0.338217\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.00000 | + | 5.00000i | 0.214373 | + | 0.214373i | ||||
\(545\) | −27.0000 | + | 9.00000i | −1.15655 | + | 0.385518i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | − | 12.0000i | 0.513083 | − | 0.513083i | −0.402387 | − | 0.915470i | \(-0.631819\pi\) |
0.915470 | + | 0.402387i | \(0.131819\pi\) | |||||||
\(548\) | − | 22.0000i | − | 0.939793i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.0000 | + | 2.00000i | 0.596962 | + | 0.0852803i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000 | 1.36078 | ||||||||
\(554\) | −3.00000 | − | 3.00000i | −0.127458 | − | 0.127458i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.0000i | 0.678551i | ||||||||
\(557\) | 12.0000i | 0.508456i | 0.967144 | + | 0.254228i | \(0.0818214\pi\) | ||||
−0.967144 | + | 0.254228i | \(0.918179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | + | 20.0000i | −0.169182 | + | 0.845910i | ||||
\(560\) | −4.00000 | + | 8.00000i | −0.169031 | + | 0.338062i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.0000 | − | 13.0000i | 0.548372 | − | 0.548372i | ||||
\(563\) | −24.0000 | + | 24.0000i | −1.01148 | + | 1.01148i | −0.0115461 | + | 0.999933i | \(0.503675\pi\) |
−0.999933 | + | 0.0115461i | \(0.996325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0000 | + | 33.0000i | 0.462773 | + | 1.38832i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.0000 | + | 24.0000i | 1.00702 | + | 1.00702i | ||||
\(569\) | 42.0000 | 1.76073 | 0.880366 | − | 0.474295i | \(-0.157297\pi\) | ||||
0.880366 | + | 0.474295i | \(0.157297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000i | 0.502184i | 0.967963 | + | 0.251092i | \(0.0807897\pi\) | ||||
−0.967963 | + | 0.251092i | \(0.919210\pi\) | |||||||
\(572\) | −2.00000 | + | 10.0000i | −0.0836242 | + | 0.418121i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.0000 | − | 20.0000i | 0.834784 | − | 0.834784i | ||||
\(575\) | 42.0000 | + | 6.00000i | 1.75152 | + | 0.250217i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.0000 | −1.83174 | −0.915872 | − | 0.401470i | \(-0.868499\pi\) | ||||
−0.915872 | + | 0.401470i | \(0.868499\pi\) | |||||||
\(578\) | − | 15.0000i | − | 0.623918i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.0000 | −1.15964 | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 2.00000 | + | 6.00000i | 0.0823387 | + | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 6.00000i | − | 0.246598i | ||||||
\(593\) | 4.00000 | 0.164260 | 0.0821302 | − | 0.996622i | \(-0.473828\pi\) | ||||
0.0821302 | + | 0.996622i | \(0.473828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | − | 4.00000i | 0.491952 | − | 0.163984i | ||||
\(596\) | 15.0000 | − | 15.0000i | 0.614424 | − | 0.614424i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.00000 | − | 30.0000i | 0.245358 | − | 1.22679i | ||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 16.0000 | + | 16.0000i | 0.652111 | + | 0.652111i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.00000 | + | 4.00000i | −0.162758 | + | 0.162758i | ||||
\(605\) | −3.00000 | + | 6.00000i | −0.121967 | + | 0.243935i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000 | − | 14.0000i | 0.568242 | − | 0.568242i | −0.363393 | − | 0.931636i | \(-0.618382\pi\) |
0.931636 | + | 0.363393i | \(0.118382\pi\) | |||||||
\(608\) | −10.0000 | + | 10.0000i | −0.405554 | + | 0.405554i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.0000 | − | 8.00000i | −0.647821 | − | 0.323911i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.0000i | − | 1.77714i | −0.458738 | − | 0.888572i | \(-0.651698\pi\) | ||
0.458738 | − | 0.888572i | \(-0.348302\pi\) | |||||||
\(614\) | 12.0000i | 0.484281i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.0000 | + | 24.0000i | 0.966988 | + | 0.966988i | ||||
\(617\) | −4.00000 | −0.161034 | −0.0805170 | − | 0.996753i | \(-0.525657\pi\) | ||||
−0.0805170 | + | 0.996753i | \(0.525657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0000 | − | 14.0000i | −0.562708 | − | 0.562708i | 0.367368 | − | 0.930076i | \(-0.380259\pi\) |
−0.930076 | + | 0.367368i | \(0.880259\pi\) | |||||||
\(620\) | 4.00000 | + | 12.0000i | 0.160644 | + | 0.481932i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 12.0000i | − | 0.481156i | ||||||
\(623\) | 20.0000 | − | 20.0000i | 0.801283 | − | 0.801283i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 9.00000 | + | 9.00000i | 0.359712 | + | 0.359712i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.00000 | + | 7.00000i | −0.279330 | + | 0.279330i | ||||
\(629\) | −6.00000 | + | 6.00000i | −0.239236 | + | 0.239236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | + | 16.0000i | −0.636950 | + | 0.636950i | −0.949802 | − | 0.312852i | \(-0.898716\pi\) |
0.312852 | + | 0.949802i | \(0.398716\pi\) | |||||||
\(632\) | − | 24.0000i | − | 0.954669i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.0000 | −1.03259 | ||||||||
\(635\) | 6.00000 | + | 18.0000i | 0.238103 | + | 0.714308i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.0000 | + | 18.0000i | −1.06978 | + | 0.713186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.00000 | − | 3.00000i | −0.237171 | − | 0.118585i | ||||
\(641\) | 18.0000i | 0.710957i | 0.934684 | + | 0.355479i | \(0.115682\pi\) | ||||
−0.934684 | + | 0.355479i | \(0.884318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.0000i | − | 0.630978i | −0.948929 | − | 0.315489i | \(-0.897831\pi\) | ||
0.948929 | − | 0.315489i | \(-0.102169\pi\) | |||||||
\(644\) | 24.0000 | + | 24.0000i | 0.945732 | + | 0.945732i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.00000 | −0.157378 | ||||||||
\(647\) | −14.0000 | − | 14.0000i | −0.550397 | − | 0.550397i | 0.376159 | − | 0.926555i | \(-0.377245\pi\) |
−0.926555 | + | 0.376159i | \(0.877245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | 17.0000 | + | 6.00000i | 0.666795 | + | 0.235339i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −17.0000 | − | 17.0000i | −0.665261 | − | 0.665261i | 0.291354 | − | 0.956615i | \(-0.405894\pi\) |
−0.956615 | + | 0.291354i | \(0.905894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.0000 | + | 16.0000i | 1.25034 | + | 0.625172i | ||||
\(656\) | −5.00000 | − | 5.00000i | −0.195217 | − | 0.195217i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.00000i | − | 0.311636i | −0.987786 | − | 0.155818i | \(-0.950199\pi\) | ||
0.987786 | − | 0.155818i | \(-0.0498013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.0000 | + | 31.0000i | −1.20576 | + | 1.20576i | −0.233373 | + | 0.972387i | \(0.574976\pi\) |
−0.972387 | + | 0.233373i | \(0.925024\pi\) | |||||||
\(662\) | −6.00000 | − | 6.00000i | −0.233197 | − | 0.233197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | + | 24.0000i | 0.310227 | + | 0.930680i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.0000 | + | 8.00000i | 0.618134 | + | 0.309067i | ||||
\(671\) | −16.0000 | + | 16.0000i | −0.617673 | + | 0.617673i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.0000 | − | 33.0000i | 1.27206 | − | 1.27206i | 0.327049 | − | 0.945007i | \(-0.393946\pi\) |
0.945007 | − | 0.327049i | \(-0.106054\pi\) | |||||||
\(674\) | 1.00000 | + | 1.00000i | 0.0385186 | + | 0.0385186i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | + | 12.0000i | −0.192308 | + | 0.461538i | ||||
\(677\) | 1.00000 | − | 1.00000i | 0.0384331 | − | 0.0384331i | −0.687629 | − | 0.726062i | \(-0.741348\pi\) |
0.726062 | + | 0.687629i | \(0.241348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.00000i | − | 0.307012i | ||||||
\(680\) | −3.00000 | − | 9.00000i | −0.115045 | − | 0.345134i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.0000 | −0.612672 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.0000 | + | 44.0000i | −0.840577 | + | 1.68115i | ||||
\(686\) | 8.00000i | 0.305441i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000 | − | 4.00000i | 0.152499 | − | 0.152499i | ||||
\(689\) | −35.0000 | − | 7.00000i | −1.33339 | − | 0.266679i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.0000 | − | 30.0000i | −1.14125 | − | 1.14125i | −0.988221 | − | 0.153033i | \(-0.951096\pi\) |
−0.153033 | − | 0.988221i | \(-0.548904\pi\) | |||||||
\(692\) | −7.00000 | + | 7.00000i | −0.266100 | + | 0.266100i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | − | 24.0000i | 0.911028 | − | 0.911028i | ||||
\(695\) | 16.0000 | − | 32.0000i | 0.606915 | − | 1.21383i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0000i | 0.378777i | ||||||||
\(698\) | 3.00000 | + | 3.00000i | 0.113552 | + | 0.113552i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −16.0000 | + | 12.0000i | −0.604743 | + | 0.453557i | ||||
\(701\) | 18.0000i | 0.679851i | 0.940452 | + | 0.339925i | \(0.110402\pi\) | ||||
−0.940452 | + | 0.339925i | \(0.889598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | − | 12.0000i | −0.452589 | − | 0.452589i | ||||
\(704\) | 14.0000 | − | 14.0000i | 0.527645 | − | 0.527645i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.0000i | 1.35488i | ||||||||
\(707\) | −24.0000 | −0.902613 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00000 | − | 1.00000i | −0.0375558 | − | 0.0375558i | 0.688080 | − | 0.725635i | \(-0.258454\pi\) |
−0.725635 | + | 0.688080i | \(0.758454\pi\) | |||||||
\(710\) | −8.00000 | − | 24.0000i | −0.300235 | − | 0.900704i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.0000 | − | 15.0000i | −0.562149 | − | 0.562149i | ||||
\(713\) | −48.0000 | −1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.0000 | − | 18.0000i | 0.523570 | − | 0.673162i | ||||
\(716\) | 8.00000 | 0.298974 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.00000 | + | 4.00000i | 0.149279 | + | 0.149279i | ||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.0000 | + | 56.0000i | 2.08555 | + | 2.08555i | ||||
\(722\) | 11.0000i | 0.409378i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.0000i | 0.817624i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0000 | + | 22.0000i | 0.815935 | + | 0.815935i | 0.985516 | − | 0.169581i | \(-0.0542416\pi\) |
−0.169581 | + | 0.985516i | \(0.554242\pi\) | |||||||
\(728\) | 24.0000 | + | 36.0000i | 0.889499 | + | 1.33425i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | − | 4.00000i | −0.296093 | − | 0.148047i | ||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.00000i | − | 0.147743i | −0.997268 | − | 0.0738717i | \(-0.976464\pi\) | ||
0.997268 | − | 0.0738717i | \(-0.0235355\pi\) | |||||||
\(734\) | −10.0000 | + | 10.0000i | −0.369107 | + | 0.369107i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.0000 | − | 30.0000i | 1.10581 | − | 1.10581i | ||||
\(737\) | 16.0000 | − | 16.0000i | 0.589368 | − | 0.589368i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.00000 | − | 6.00000i | −0.220714 | − | 0.220714i | 0.588085 | − | 0.808799i | \(-0.299882\pi\) |
−0.808799 | + | 0.588085i | \(0.799882\pi\) | |||||||
\(740\) | 6.00000 | − | 12.0000i | 0.220564 | − | 0.441129i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.0000 | + | 28.0000i | −1.02791 | + | 1.02791i | ||||
\(743\) | − | 44.0000i | − | 1.61420i | −0.590412 | − | 0.807102i | \(-0.701035\pi\) | ||
0.590412 | − | 0.807102i | \(-0.298965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45.0000 | + | 15.0000i | −1.64867 | + | 0.549557i | ||||
\(746\) | 3.00000 | + | 3.00000i | 0.109838 | + | 0.109838i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 32.0000 | + | 32.0000i | 1.16925 | + | 1.16925i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.00000i | − | 0.145962i | −0.997333 | − | 0.0729810i | \(-0.976749\pi\) | ||
0.997333 | − | 0.0729810i | \(-0.0232513\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | − | 4.00000i | 0.436725 | − | 0.145575i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0000 | − | 25.0000i | 0.908640 | − | 0.908640i | −0.0875221 | − | 0.996163i | \(-0.527895\pi\) |
0.996163 | + | 0.0875221i | \(0.0278948\pi\) | |||||||
\(758\) | 14.0000 | − | 14.0000i | 0.508503 | − | 0.508503i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.0000 | − | 6.00000i | 0.652929 | − | 0.217643i | ||||
\(761\) | 23.0000 | − | 23.0000i | 0.833749 | − | 0.833749i | −0.154278 | − | 0.988027i | \(-0.549305\pi\) |
0.988027 | + | 0.154278i | \(0.0493052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.0000 | + | 36.0000i | 1.30329 | + | 1.30329i | ||||
\(764\) | −20.0000 | −0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000i | 0.433578i | ||||||||
\(767\) | 10.0000 | + | 2.00000i | 0.361079 | + | 0.0722158i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.00000 | + | 3.00000i | −0.108183 | + | 0.108183i | −0.759126 | − | 0.650943i | \(-0.774373\pi\) |
0.650943 | + | 0.759126i | \(0.274373\pi\) | |||||||
\(770\) | −8.00000 | − | 24.0000i | −0.288300 | − | 0.864900i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.0000 | −0.647834 | ||||||||
\(773\) | − | 20.0000i | − | 0.719350i | −0.933078 | − | 0.359675i | \(-0.882888\pi\) | ||
0.933078 | − | 0.359675i | \(-0.117112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | − | 28.0000i | 0.143684 | − | 1.00579i | ||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | −20.0000 | −0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 12.0000 | 0.429119 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 21.0000 | − | 7.00000i | 0.749522 | − | 0.249841i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000i | 0.142585i | 0.997455 | + | 0.0712923i | \(0.0227123\pi\) | ||||
−0.997455 | + | 0.0712923i | \(0.977288\pi\) | |||||||
\(788\) | −12.0000 | −0.427482 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | + | 16.0000i | −0.284627 | + | 0.569254i | ||||
\(791\) | 44.0000 | − | 44.0000i | 1.56446 | − | 1.56446i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | + | 16.0000i | −0.852265 | + | 0.568177i | ||||
\(794\) | − | 22.0000i | − | 0.780751i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.0000 | 0.708881 | ||||||||
\(797\) | 5.00000 | + | 5.00000i | 0.177109 | + | 0.177109i | 0.790094 | − | 0.612985i | \(-0.210032\pi\) |
−0.612985 | + | 0.790094i | \(0.710032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 15.0000 | + | 20.0000i | 0.530330 | + | 0.707107i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.00000 | + | 5.00000i | −0.176556 | + | 0.176556i | ||||
\(803\) | −8.00000 | + | 8.00000i | −0.282314 | + | 0.282314i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0000 | − | 72.0000i | −0.845889 | − | 2.53767i | ||||
\(806\) | −20.0000 | − | 4.00000i | −0.704470 | − | 0.140894i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.0000i | 0.633238i | ||||||||
\(809\) | − | 16.0000i | − | 0.562530i | −0.959630 | − | 0.281265i | \(-0.909246\pi\) | ||
0.959630 | − | 0.281265i | \(-0.0907540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.0000 | − | 18.0000i | −0.632065 | − | 0.632065i | 0.316520 | − | 0.948586i | \(-0.397485\pi\) |
−0.948586 | + | 0.316520i | \(0.897485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | + | 12.0000i | 0.420600 | + | 0.420600i | ||||
\(815\) | 8.00000 | + | 4.00000i | 0.280228 | + | 0.140114i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 16.0000i | − | 0.559769i | ||||||
\(818\) | −13.0000 | + | 13.0000i | −0.454534 | + | 0.454534i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.00000 | − | 15.0000i | −0.174608 | − | 0.523823i | ||||
\(821\) | 27.0000 | + | 27.0000i | 0.942306 | + | 0.942306i | 0.998424 | − | 0.0561177i | \(-0.0178722\pi\) |
−0.0561177 | + | 0.998424i | \(0.517872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.0000 | − | 18.0000i | 0.627441 | − | 0.627441i | −0.319983 | − | 0.947423i | \(-0.603677\pi\) |
0.947423 | + | 0.319983i | \(0.103677\pi\) | |||||||
\(824\) | 42.0000 | − | 42.0000i | 1.46314 | − | 1.46314i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | − | 8.00000i | 0.278356 | − | 0.278356i | ||||
\(827\) | 4.00000i | 0.139094i | 0.997579 | + | 0.0695468i | \(0.0221553\pi\) | ||||
−0.997579 | + | 0.0695468i | \(0.977845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0000 | 0.555703 | 0.277851 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277851 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.0000 | − | 14.0000i | 0.728044 | − | 0.485363i | ||||
\(833\) | −9.00000 | − | 9.00000i | −0.311832 | − | 0.311832i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 8.00000i | − | 0.276686i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 16.0000i | − | 0.552711i | ||||||
\(839\) | −32.0000 | − | 32.0000i | −1.10476 | − | 1.10476i | −0.993828 | − | 0.110935i | \(-0.964615\pi\) |
−0.110935 | − | 0.993828i | \(-0.535385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 7.00000 | + | 7.00000i | 0.241236 | + | 0.241236i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | 22.0000 | − | 19.0000i | 0.756823 | − | 0.653620i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.0000 | 0.412325 | ||||||||
\(848\) | 7.00000 | + | 7.00000i | 0.240381 | + | 0.240381i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.00000 | + | 7.00000i | −0.0342997 | + | 0.240098i | ||||
\(851\) | 36.0000 | + | 36.0000i | 1.23406 | + | 1.23406i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.0000 | −0.958702 | −0.479351 | − | 0.877623i | \(-0.659128\pi\) | ||||
−0.479351 | + | 0.877623i | \(0.659128\pi\) | |||||||
\(854\) | 32.0000i | 1.09502i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.0000 | − | 24.0000i | 0.820303 | − | 0.820303i | ||||
\(857\) | 9.00000 | + | 9.00000i | 0.307434 | + | 0.307434i | 0.843913 | − | 0.536479i | \(-0.180246\pi\) |
−0.536479 | + | 0.843913i | \(0.680246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 36.0000i | − | 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | 12.0000 | − | 4.00000i | 0.409197 | − | 0.136399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.00000 | + | 4.00000i | 0.136241 | + | 0.136241i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.0000 | − | 7.00000i | 0.714021 | − | 0.238007i | ||||
\(866\) | 5.00000 | − | 5.00000i | 0.169907 | − | 0.169907i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0000 | − | 16.0000i | 0.543075 | − | 0.543075i | ||||
\(869\) | 16.0000 | + | 16.0000i | 0.542763 | + | 0.542763i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | − | 16.0000i | 0.813209 | − | 0.542139i | ||||
\(872\) | 27.0000 | − | 27.0000i | 0.914335 | − | 0.914335i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.0000i | 0.811812i | ||||||||
\(875\) | 44.0000 | − | 8.00000i | 1.48747 | − | 0.270449i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | + | 2.00000i | −0.202260 | + | 0.0674200i | ||||
\(881\) | 40.0000i | 1.34763i | 0.738898 | + | 0.673817i | \(0.235346\pi\) | ||||
−0.738898 | + | 0.673817i | \(0.764654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.0000 | + | 24.0000i | −0.807664 | + | 0.807664i | −0.984280 | − | 0.176616i | \(-0.943485\pi\) |
0.176616 | + | 0.984280i | \(0.443485\pi\) | |||||||
\(884\) | −5.00000 | − | 1.00000i | −0.168168 | − | 0.0336336i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.00000 | − | 8.00000i | −0.268765 | − | 0.268765i | ||||
\(887\) | 14.0000 | − | 14.0000i | 0.470074 | − | 0.470074i | −0.431865 | − | 0.901938i | \(-0.642144\pi\) |
0.901938 | + | 0.431865i | \(0.142144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000 | − | 24.0000i | 0.804934 | − | 0.804934i | ||||
\(890\) | 5.00000 | + | 15.0000i | 0.167600 | + | 0.502801i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 8.00000i | − | 0.267860i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.0000 | − | 8.00000i | −0.534821 | − | 0.267411i | ||||
\(896\) | 12.0000i | 0.400892i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.00000 | + | 3.00000i | 0.100111 | + | 0.100111i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.0000i | − | 0.466408i | ||||||
\(902\) | 20.0000 | 0.665927 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.0000 | − | 33.0000i | −1.09756 | − | 1.09756i | ||||
\(905\) | 22.0000 | − | 44.0000i | 0.731305 | − | 1.46261i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.0000 | + | 12.0000i | 0.398453 | + | 0.398453i | 0.877687 | − | 0.479234i | \(-0.159085\pi\) |
−0.479234 | + | 0.877687i | \(0.659085\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | − | 32.0000i | −0.132599 | − | 1.06079i | ||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −10.0000 | −0.330771 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.00000 | + | 9.00000i | 0.297368 | + | 0.297368i | ||||
\(917\) | − | 64.0000i | − | 2.11347i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000i | 0.131948i | 0.997821 | + | 0.0659739i | \(0.0210154\pi\) | ||||
−0.997821 | + | 0.0659739i | \(0.978985\pi\) | |||||||
\(920\) | −54.0000 | + | 18.0000i | −1.78033 | + | 0.593442i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.0000 | + | 11.0000i | 0.362266 | + | 0.362266i | ||||
\(923\) | −40.0000 | − | 8.00000i | −1.31662 | − | 0.263323i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0000 | + | 18.0000i | −0.789115 | + | 0.591836i | ||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.00000 | − | 5.00000i | 0.164045 | − | 0.164045i | −0.620311 | − | 0.784356i | \(-0.712994\pi\) |
0.784356 | + | 0.620311i | \(0.212994\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | − | 18.0000i | 0.589926 | − | 0.589926i | ||||
\(932\) | −7.00000 | + | 7.00000i | −0.229293 | + | 0.229293i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.0000 | + | 12.0000i | 0.392652 | + | 0.392652i | ||||
\(935\) | 8.00000 | + | 4.00000i | 0.261628 | + | 0.130814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0000 | + | 19.0000i | −0.620703 | + | 0.620703i | −0.945711 | − | 0.325008i | \(-0.894633\pi\) |
0.325008 | + | 0.945711i | \(0.394633\pi\) | |||||||
\(938\) | − | 32.0000i | − | 1.04484i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0000 | − | 21.0000i | −0.684580 | − | 0.684580i | 0.276448 | − | 0.961029i | \(-0.410843\pi\) |
−0.961029 | + | 0.276448i | \(0.910843\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60.0000 | 1.95387 | ||||||||
\(944\) | −2.00000 | − | 2.00000i | −0.0650945 | − | 0.0650945i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000i | 0.520205i | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 8.00000i | −0.389536 | + | 0.259691i | ||||
\(950\) | −14.0000 | − | 2.00000i | −0.454220 | − | 0.0648886i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | + | 12.0000i | −0.388922 | + | 0.388922i | ||||
\(953\) | 31.0000 | − | 31.0000i | 1.00419 | − | 1.00419i | 0.00419731 | − | 0.999991i | \(-0.498664\pi\) |
0.999991 | − | 0.00419731i | \(-0.00133605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.0000 | + | 20.0000i | 1.29437 | + | 0.647185i | ||||
\(956\) | −12.0000 | + | 12.0000i | −0.388108 | + | 0.388108i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.00000 | + | 8.00000i | 0.258468 | + | 0.258468i | ||||
\(959\) | 88.0000 | 2.84167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000i | 0.0322581i | ||||||||
\(962\) | 12.0000 | + | 18.0000i | 0.386896 | + | 0.580343i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.0000 | − | 13.0000i | 0.418702 | − | 0.418702i | ||||
\(965\) | 36.0000 | + | 18.0000i | 1.15888 | + | 0.579441i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.0000 | −0.385894 | −0.192947 | − | 0.981209i | \(-0.561805\pi\) | ||||
−0.192947 | + | 0.981209i | \(0.561805\pi\) | |||||||
\(968\) | − | 9.00000i | − | 0.289271i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.00000 | + | 2.00000i | 0.128432 | + | 0.0642161i | ||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −64.0000 | −2.05175 | ||||||||
\(974\) | −32.0000 | −1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | −34.0000 | −1.08776 | −0.543878 | − | 0.839164i | \(-0.683045\pi\) | ||||
−0.543878 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000 | 0.639203 | ||||||||
\(980\) | 18.0000 | + | 9.00000i | 0.574989 | + | 0.287494i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 32.0000i | − | 1.02116i | ||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.0000 | + | 12.0000i | 0.764704 | + | 0.382352i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.00000 | − | 10.0000i | 0.0636285 | − | 0.318142i | ||||
\(989\) | 48.0000i | 1.52631i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0000 | −0.381193 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(992\) | −20.0000 | − | 20.0000i | −0.635001 | − | 0.635001i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.0000 | + | 32.0000i | −1.01498 | + | 1.01498i | ||||
\(995\) | −40.0000 | − | 20.0000i | −1.26809 | − | 0.634043i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.00000 | − | 9.00000i | 0.285033 | − | 0.285033i | −0.550079 | − | 0.835112i | \(-0.685403\pi\) |
0.835112 | + | 0.550079i | \(0.185403\pi\) | |||||||
\(998\) | −18.0000 | + | 18.0000i | −0.569780 | + | 0.569780i | ||||
\(999\) | 0 | 0 |
(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 | 585.2.w.c.73.1 | yes | 2 | |
3.2 | odd | 2 | 585.2.w.a.73.1 | yes | 2 | ||
5.2 | odd | 4 | 585.2.n.b.307.1 | yes | 2 | ||
13.5 | odd | 4 | 585.2.n.b.343.1 | yes | 2 | ||
15.2 | even | 4 | 585.2.n.a.307.1 | ✓ | 2 | ||
39.5 | even | 4 | 585.2.n.a.343.1 | yes | 2 | ||
65.57 | even | 4 | inner | 585.2.w.c.577.1 | yes | 2 | |
195.122 | odd | 4 | 585.2.w.a.577.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.n.a.307.1 | ✓ | 2 | 15.2 | even | 4 | ||
585.2.n.a.343.1 | yes | 2 | 39.5 | even | 4 | ||
585.2.n.b.307.1 | yes | 2 | 5.2 | odd | 4 | ||
585.2.n.b.343.1 | yes | 2 | 13.5 | odd | 4 | ||
585.2.w.a.73.1 | yes | 2 | 3.2 | odd | 2 | ||
585.2.w.a.577.1 | yes | 2 | 195.122 | odd | 4 | ||
585.2.w.c.73.1 | yes | 2 | 1.1 | even | 1 | trivial | |
585.2.w.c.577.1 | yes | 2 | 65.57 | even | 4 | inner |