Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2175,2,Mod(349,2175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2175.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2175 = 3 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2175.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.3674624396\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 9x^{2} + 16 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 435) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.2 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2175.349 |
Dual form | 2175.2.c.h.349.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2175\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1451\) | \(2002\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.56155i | − 1.10418i | −0.833783 | − | 0.552092i | \(-0.813830\pi\) | ||||
0.833783 | − | 0.552092i | \(-0.186170\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −0.438447 | −0.219224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.56155 | −0.637501 | ||||||||
\(7\) | 5.12311i | 1.93635i | 0.250270 | + | 0.968176i | \(0.419480\pi\) | ||||
−0.250270 | + | 0.968176i | \(0.580520\pi\) | |||||||
\(8\) | − 2.43845i | − 0.862121i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.43845 | −0.433708 | −0.216854 | − | 0.976204i | \(-0.569580\pi\) | ||||
−0.216854 | + | 0.976204i | \(0.569580\pi\) | |||||||
\(12\) | 0.438447i | 0.126569i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 8.00000 | 2.13809 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | − 7.12311i | − 1.72761i | −0.503829 | − | 0.863803i | \(-0.668076\pi\) | ||||
0.503829 | − | 0.863803i | \(-0.331924\pi\) | |||||||
\(18\) | 1.56155i | 0.368062i | ||||||||
\(19\) | −5.12311 | −1.17532 | −0.587661 | − | 0.809108i | \(-0.699951\pi\) | ||||
−0.587661 | + | 0.809108i | \(0.699951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.12311 | 1.11795 | ||||||||
\(22\) | 2.24621i | 0.478894i | ||||||||
\(23\) | − 6.56155i | − 1.36818i | −0.729398 | − | 0.684089i | \(-0.760200\pi\) | ||||
0.729398 | − | 0.684089i | \(-0.239800\pi\) | |||||||
\(24\) | −2.43845 | −0.497746 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.12311 | 0.612491 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 2.24621i | − 0.424494i | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 2.43845i | 0.431061i | ||||||||
\(33\) | 1.43845i | 0.250402i | ||||||||
\(34\) | −11.1231 | −1.90760 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.438447 | 0.0730745 | ||||||||
\(37\) | − 1.68466i | − 0.276956i | −0.990366 | − | 0.138478i | \(-0.955779\pi\) | ||||
0.990366 | − | 0.138478i | \(-0.0442210\pi\) | |||||||
\(38\) | 8.00000i | 1.29777i | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.68466 | −0.263099 | −0.131550 | − | 0.991310i | \(-0.541995\pi\) | ||||
−0.131550 | + | 0.991310i | \(0.541995\pi\) | |||||||
\(42\) | − 8.00000i | − 1.23443i | ||||||||
\(43\) | − 7.68466i | − 1.17190i | −0.810347 | − | 0.585950i | \(-0.800722\pi\) | ||||
0.810347 | − | 0.585950i | \(-0.199278\pi\) | |||||||
\(44\) | 0.630683 | 0.0950791 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.2462 | −1.51072 | ||||||||
\(47\) | − 13.1231i | − 1.91420i | −0.289755 | − | 0.957101i | \(-0.593574\pi\) | ||||
0.289755 | − | 0.957101i | \(-0.406426\pi\) | |||||||
\(48\) | 4.68466i | 0.676172i | ||||||||
\(49\) | −19.2462 | −2.74946 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.12311 | −0.997434 | ||||||||
\(52\) | − 0.876894i | − 0.121603i | ||||||||
\(53\) | 3.43845i | 0.472307i | 0.971716 | + | 0.236154i | \(0.0758868\pi\) | ||||
−0.971716 | + | 0.236154i | \(0.924113\pi\) | |||||||
\(54\) | 1.56155 | 0.212500 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.4924 | 1.66937 | ||||||||
\(57\) | 5.12311i | 0.678572i | ||||||||
\(58\) | 1.56155i | 0.205042i | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.876894 | 0.112275 | 0.0561374 | − | 0.998423i | \(-0.482122\pi\) | ||||
0.0561374 | + | 0.998423i | \(0.482122\pi\) | |||||||
\(62\) | − 6.24621i | − 0.793270i | ||||||||
\(63\) | − 5.12311i | − 0.645451i | ||||||||
\(64\) | −5.56155 | −0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.24621 | 0.276489 | ||||||||
\(67\) | − 11.3693i | − 1.38898i | −0.719501 | − | 0.694492i | \(-0.755629\pi\) | ||||
0.719501 | − | 0.694492i | \(-0.244371\pi\) | |||||||
\(68\) | 3.12311i | 0.378732i | ||||||||
\(69\) | −6.56155 | −0.789918 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.87689 | −0.341425 | −0.170712 | − | 0.985321i | \(-0.554607\pi\) | ||||
−0.170712 | + | 0.985321i | \(0.554607\pi\) | |||||||
\(72\) | 2.43845i | 0.287374i | ||||||||
\(73\) | − 1.68466i | − 0.197174i | −0.995128 | − | 0.0985872i | \(-0.968568\pi\) | ||||
0.995128 | − | 0.0985872i | \(-0.0314323\pi\) | |||||||
\(74\) | −2.63068 | −0.305811 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.24621 | 0.257658 | ||||||||
\(77\) | − 7.36932i | − 0.839812i | ||||||||
\(78\) | − 3.12311i | − 0.353622i | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.63068i | 0.290510i | ||||||||
\(83\) | 2.56155i | 0.281167i | 0.990069 | + | 0.140583i | \(0.0448978\pi\) | ||||
−0.990069 | + | 0.140583i | \(0.955102\pi\) | |||||||
\(84\) | −2.24621 | −0.245082 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | 1.00000i | 0.107211i | ||||||||
\(88\) | 3.50758i | 0.373909i | ||||||||
\(89\) | −12.2462 | −1.29810 | −0.649048 | − | 0.760748i | \(-0.724833\pi\) | ||||
−0.649048 | + | 0.760748i | \(0.724833\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2462 | −1.07409 | ||||||||
\(92\) | 2.87689i | 0.299937i | ||||||||
\(93\) | − 4.00000i | − 0.414781i | ||||||||
\(94\) | −20.4924 | −2.11363 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.43845 | 0.248873 | ||||||||
\(97\) | − 5.68466i | − 0.577190i | −0.957451 | − | 0.288595i | \(-0.906812\pi\) | ||||
0.957451 | − | 0.288595i | \(-0.0931880\pi\) | |||||||
\(98\) | 30.0540i | 3.03591i | ||||||||
\(99\) | 1.43845 | 0.144569 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.56155 | −0.851906 | −0.425953 | − | 0.904745i | \(-0.640061\pi\) | ||||
−0.425953 | + | 0.904745i | \(0.640061\pi\) | |||||||
\(102\) | 11.1231i | 1.10135i | ||||||||
\(103\) | 2.87689i | 0.283469i | 0.989905 | + | 0.141734i | \(0.0452679\pi\) | ||||
−0.989905 | + | 0.141734i | \(0.954732\pi\) | |||||||
\(104\) | 4.87689 | 0.478219 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.36932 | 0.521514 | ||||||||
\(107\) | 16.4924i | 1.59438i | 0.603727 | + | 0.797191i | \(0.293682\pi\) | ||||
−0.603727 | + | 0.797191i | \(0.706318\pi\) | |||||||
\(108\) | − 0.438447i | − 0.0421896i | ||||||||
\(109\) | 5.68466 | 0.544492 | 0.272246 | − | 0.962228i | \(-0.412234\pi\) | ||||
0.272246 | + | 0.962228i | \(0.412234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.68466 | −0.159901 | ||||||||
\(112\) | − 24.0000i | − 2.26779i | ||||||||
\(113\) | 4.87689i | 0.458780i | 0.973335 | + | 0.229390i | \(0.0736731\pi\) | ||||
−0.973335 | + | 0.229390i | \(0.926327\pi\) | |||||||
\(114\) | 8.00000 | 0.749269 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.438447 | 0.0407088 | ||||||||
\(117\) | − 2.00000i | − 0.184900i | ||||||||
\(118\) | 18.7386i | 1.72503i | ||||||||
\(119\) | 36.4924 | 3.34525 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.93087 | −0.811897 | ||||||||
\(122\) | − 1.36932i | − 0.123972i | ||||||||
\(123\) | 1.68466i | 0.151901i | ||||||||
\(124\) | −1.75379 | −0.157495 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.00000 | −0.712697 | ||||||||
\(127\) | 4.31534i | 0.382925i | 0.981500 | + | 0.191462i | \(0.0613230\pi\) | ||||
−0.981500 | + | 0.191462i | \(0.938677\pi\) | |||||||
\(128\) | 13.5616i | 1.19868i | ||||||||
\(129\) | −7.68466 | −0.676596 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2462 | 0.895216 | 0.447608 | − | 0.894230i | \(-0.352276\pi\) | ||||
0.447608 | + | 0.894230i | \(0.352276\pi\) | |||||||
\(132\) | − 0.630683i | − 0.0548939i | ||||||||
\(133\) | − 26.2462i | − 2.27584i | ||||||||
\(134\) | −17.7538 | −1.53369 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.3693 | −1.48941 | ||||||||
\(137\) | − 15.1231i | − 1.29205i | −0.763315 | − | 0.646027i | \(-0.776429\pi\) | ||||
0.763315 | − | 0.646027i | \(-0.223571\pi\) | |||||||
\(138\) | 10.2462i | 0.872215i | ||||||||
\(139\) | 17.9309 | 1.52088 | 0.760438 | − | 0.649410i | \(-0.224984\pi\) | ||||
0.760438 | + | 0.649410i | \(0.224984\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.1231 | −1.10516 | ||||||||
\(142\) | 4.49242i | 0.376996i | ||||||||
\(143\) | − 2.87689i | − 0.240578i | ||||||||
\(144\) | 4.68466 | 0.390388 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.63068 | −0.217717 | ||||||||
\(147\) | 19.2462i | 1.58740i | ||||||||
\(148\) | 0.738634i | 0.0607153i | ||||||||
\(149\) | −0.246211 | −0.0201704 | −0.0100852 | − | 0.999949i | \(-0.503210\pi\) | ||||
−0.0100852 | + | 0.999949i | \(0.503210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.31534 | 0.351178 | 0.175589 | − | 0.984464i | \(-0.443817\pi\) | ||||
0.175589 | + | 0.984464i | \(0.443817\pi\) | |||||||
\(152\) | 12.4924i | 1.01327i | ||||||||
\(153\) | 7.12311i | 0.575869i | ||||||||
\(154\) | −11.5076 | −0.927307 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.876894 | −0.0702077 | ||||||||
\(157\) | − 14.0000i | − 1.11732i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||||
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | − 18.7386i | − 1.49077i | ||||||||
\(159\) | 3.43845 | 0.272687 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 33.6155 | 2.64927 | ||||||||
\(162\) | − 1.56155i | − 0.122687i | ||||||||
\(163\) | 17.9309i | 1.40445i | 0.711953 | + | 0.702227i | \(0.247811\pi\) | ||||
−0.711953 | + | 0.702227i | \(0.752189\pi\) | |||||||
\(164\) | 0.738634 | 0.0576776 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | − 12.4924i | − 0.963811i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.12311 | 0.391774 | ||||||||
\(172\) | 3.36932i | 0.256908i | ||||||||
\(173\) | − 12.5616i | − 0.955037i | −0.878622 | − | 0.477519i | \(-0.841536\pi\) | ||||
0.878622 | − | 0.477519i | \(-0.158464\pi\) | |||||||
\(174\) | 1.56155 | 0.118381 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.73863 | 0.507944 | ||||||||
\(177\) | 12.0000i | 0.901975i | ||||||||
\(178\) | 19.1231i | 1.43334i | ||||||||
\(179\) | −1.12311 | −0.0839449 | −0.0419724 | − | 0.999119i | \(-0.513364\pi\) | ||||
−0.0419724 | + | 0.999119i | \(0.513364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.6847 | 1.90913 | 0.954563 | − | 0.298010i | \(-0.0963228\pi\) | ||||
0.954563 | + | 0.298010i | \(0.0963228\pi\) | |||||||
\(182\) | 16.0000i | 1.18600i | ||||||||
\(183\) | − 0.876894i | − 0.0648219i | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.24621 | −0.457994 | ||||||||
\(187\) | 10.2462i | 0.749277i | ||||||||
\(188\) | 5.75379i | 0.419638i | ||||||||
\(189\) | −5.12311 | −0.372651 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.93087 | −0.718573 | −0.359286 | − | 0.933227i | \(-0.616980\pi\) | ||||
−0.359286 | + | 0.933227i | \(0.616980\pi\) | |||||||
\(192\) | 5.56155i | 0.401371i | ||||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | −8.87689 | −0.637324 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.43845 | 0.602746 | ||||||||
\(197\) | 4.56155i | 0.324997i | 0.986709 | + | 0.162499i | \(0.0519553\pi\) | ||||
−0.986709 | + | 0.162499i | \(0.948045\pi\) | |||||||
\(198\) | − 2.24621i | − 0.159631i | ||||||||
\(199\) | 11.0540 | 0.783596 | 0.391798 | − | 0.920051i | \(-0.371853\pi\) | ||||
0.391798 | + | 0.920051i | \(0.371853\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3693 | −0.801930 | ||||||||
\(202\) | 13.3693i | 0.940662i | ||||||||
\(203\) | − 5.12311i | − 0.359572i | ||||||||
\(204\) | 3.12311 | 0.218661 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.49242 | 0.313002 | ||||||||
\(207\) | 6.56155i | 0.456059i | ||||||||
\(208\) | − 9.36932i | − 0.649645i | ||||||||
\(209\) | 7.36932 | 0.509746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.87689 | −0.198054 | −0.0990268 | − | 0.995085i | \(-0.531573\pi\) | ||||
−0.0990268 | + | 0.995085i | \(0.531573\pi\) | |||||||
\(212\) | − 1.50758i | − 0.103541i | ||||||||
\(213\) | 2.87689i | 0.197122i | ||||||||
\(214\) | 25.7538 | 1.76049 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.43845 | 0.165915 | ||||||||
\(217\) | 20.4924i | 1.39112i | ||||||||
\(218\) | − 8.87689i | − 0.601219i | ||||||||
\(219\) | −1.68466 | −0.113839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.2462 | 0.958304 | ||||||||
\(222\) | 2.63068i | 0.176560i | ||||||||
\(223\) | 18.2462i | 1.22186i | 0.791686 | + | 0.610928i | \(0.209204\pi\) | ||||
−0.791686 | + | 0.610928i | \(0.790796\pi\) | |||||||
\(224\) | −12.4924 | −0.834685 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.61553 | 0.506577 | ||||||||
\(227\) | − 3.19224i | − 0.211876i | −0.994373 | − | 0.105938i | \(-0.966215\pi\) | ||||
0.994373 | − | 0.105938i | \(-0.0337845\pi\) | |||||||
\(228\) | − 2.24621i | − 0.148759i | ||||||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.36932 | −0.484865 | ||||||||
\(232\) | 2.43845i | 0.160092i | ||||||||
\(233\) | 10.3153i | 0.675780i | 0.941186 | + | 0.337890i | \(0.109713\pi\) | ||||
−0.941186 | + | 0.337890i | \(0.890287\pi\) | |||||||
\(234\) | −3.12311 | −0.204164 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.26137 | 0.342486 | ||||||||
\(237\) | − 12.0000i | − 0.779484i | ||||||||
\(238\) | − 56.9848i | − 3.69378i | ||||||||
\(239\) | 13.1231 | 0.848863 | 0.424432 | − | 0.905460i | \(-0.360474\pi\) | ||||
0.424432 | + | 0.905460i | \(0.360474\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.0540 | −1.61387 | −0.806934 | − | 0.590641i | \(-0.798875\pi\) | ||||
−0.806934 | + | 0.590641i | \(0.798875\pi\) | |||||||
\(242\) | 13.9460i | 0.896484i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −0.384472 | −0.0246133 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.63068 | 0.167726 | ||||||||
\(247\) | − 10.2462i | − 0.651951i | ||||||||
\(248\) | − 9.75379i | − 0.619366i | ||||||||
\(249\) | 2.56155 | 0.162332 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.24621 | 0.141780 | 0.0708898 | − | 0.997484i | \(-0.477416\pi\) | ||||
0.0708898 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(252\) | 2.24621i | 0.141498i | ||||||||
\(253\) | 9.43845i | 0.593390i | ||||||||
\(254\) | 6.73863 | 0.422819 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 11.4384i | 0.713511i | 0.934198 | + | 0.356755i | \(0.116117\pi\) | ||||
−0.934198 | + | 0.356755i | \(0.883883\pi\) | |||||||
\(258\) | 12.0000i | 0.747087i | ||||||||
\(259\) | 8.63068 | 0.536285 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | − 16.0000i | − 0.988483i | ||||||||
\(263\) | 5.75379i | 0.354794i | 0.984139 | + | 0.177397i | \(0.0567676\pi\) | ||||
−0.984139 | + | 0.177397i | \(0.943232\pi\) | |||||||
\(264\) | 3.50758 | 0.215876 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −40.9848 | −2.51294 | ||||||||
\(267\) | 12.2462i | 0.749456i | ||||||||
\(268\) | 4.98485i | 0.304498i | ||||||||
\(269\) | −11.7538 | −0.716641 | −0.358321 | − | 0.933599i | \(-0.616651\pi\) | ||||
−0.358321 | + | 0.933599i | \(0.616651\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1231 | 1.04015 | 0.520077 | − | 0.854119i | \(-0.325903\pi\) | ||||
0.520077 | + | 0.854119i | \(0.325903\pi\) | |||||||
\(272\) | 33.3693i | 2.02331i | ||||||||
\(273\) | 10.2462i | 0.620129i | ||||||||
\(274\) | −23.6155 | −1.42667 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.87689 | 0.173169 | ||||||||
\(277\) | 0.876894i | 0.0526875i | 0.999653 | + | 0.0263437i | \(0.00838644\pi\) | ||||
−0.999653 | + | 0.0263437i | \(0.991614\pi\) | |||||||
\(278\) | − 28.0000i | − 1.67933i | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.6155 | −1.40878 | −0.704392 | − | 0.709811i | \(-0.748780\pi\) | ||||
−0.704392 | + | 0.709811i | \(0.748780\pi\) | |||||||
\(282\) | 20.4924i | 1.22031i | ||||||||
\(283\) | − 6.87689i | − 0.408789i | −0.978889 | − | 0.204394i | \(-0.934477\pi\) | ||||
0.978889 | − | 0.204394i | \(-0.0655225\pi\) | |||||||
\(284\) | 1.26137 | 0.0748483 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.49242 | −0.265643 | ||||||||
\(287\) | − 8.63068i | − 0.509453i | ||||||||
\(288\) | − 2.43845i | − 0.143687i | ||||||||
\(289\) | −33.7386 | −1.98463 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.68466 | −0.333241 | ||||||||
\(292\) | 0.738634i | 0.0432253i | ||||||||
\(293\) | 21.3693i | 1.24841i | 0.781261 | + | 0.624204i | \(0.214577\pi\) | ||||
−0.781261 | + | 0.624204i | \(0.785423\pi\) | |||||||
\(294\) | 30.0540 | 1.75278 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.10795 | −0.238770 | ||||||||
\(297\) | − 1.43845i | − 0.0834672i | ||||||||
\(298\) | 0.384472i | 0.0222719i | ||||||||
\(299\) | 13.1231 | 0.758929 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.3693 | 2.26921 | ||||||||
\(302\) | − 6.73863i | − 0.387765i | ||||||||
\(303\) | 8.56155i | 0.491848i | ||||||||
\(304\) | 24.0000 | 1.37649 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.1231 | 0.635866 | ||||||||
\(307\) | − 31.6847i | − 1.80834i | −0.427174 | − | 0.904169i | \(-0.640491\pi\) | ||||
0.427174 | − | 0.904169i | \(-0.359509\pi\) | |||||||
\(308\) | 3.23106i | 0.184107i | ||||||||
\(309\) | 2.87689 | 0.163661 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3153 | 0.925158 | 0.462579 | − | 0.886578i | \(-0.346924\pi\) | ||||
0.462579 | + | 0.886578i | \(0.346924\pi\) | |||||||
\(312\) | − 4.87689i | − 0.276100i | ||||||||
\(313\) | 21.3693i | 1.20787i | 0.797035 | + | 0.603933i | \(0.206400\pi\) | ||||
−0.797035 | + | 0.603933i | \(0.793600\pi\) | |||||||
\(314\) | −21.8617 | −1.23373 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.26137 | −0.295975 | ||||||||
\(317\) | 4.87689i | 0.273914i | 0.990577 | + | 0.136957i | \(0.0437322\pi\) | ||||
−0.990577 | + | 0.136957i | \(0.956268\pi\) | |||||||
\(318\) | − 5.36932i | − 0.301096i | ||||||||
\(319\) | 1.43845 | 0.0805376 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.4924 | 0.920517 | ||||||||
\(322\) | − 52.4924i | − 2.92529i | ||||||||
\(323\) | 36.4924i | 2.03049i | ||||||||
\(324\) | −0.438447 | −0.0243582 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 28.0000 | 1.55078 | ||||||||
\(327\) | − 5.68466i | − 0.314362i | ||||||||
\(328\) | 4.10795i | 0.226824i | ||||||||
\(329\) | 67.2311 | 3.70657 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2462 | 0.563183 | 0.281591 | − | 0.959534i | \(-0.409138\pi\) | ||||
0.281591 | + | 0.959534i | \(0.409138\pi\) | |||||||
\(332\) | − 1.12311i | − 0.0616384i | ||||||||
\(333\) | 1.68466i | 0.0923187i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −24.0000 | −1.30931 | ||||||||
\(337\) | − 7.75379i | − 0.422376i | −0.977445 | − | 0.211188i | \(-0.932267\pi\) | ||||
0.977445 | − | 0.211188i | \(-0.0677332\pi\) | |||||||
\(338\) | − 14.0540i | − 0.764435i | ||||||||
\(339\) | 4.87689 | 0.264877 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.75379 | −0.311585 | ||||||||
\(342\) | − 8.00000i | − 0.432590i | ||||||||
\(343\) | − 62.7386i | − 3.38757i | ||||||||
\(344\) | −18.7386 | −1.01032 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.6155 | −1.05454 | ||||||||
\(347\) | − 12.1771i | − 0.653700i | −0.945076 | − | 0.326850i | \(-0.894013\pi\) | ||||
0.945076 | − | 0.326850i | \(-0.105987\pi\) | |||||||
\(348\) | − 0.438447i | − 0.0235032i | ||||||||
\(349\) | −0.0691303 | −0.00370046 | −0.00185023 | − | 0.999998i | \(-0.500589\pi\) | ||||
−0.00185023 | + | 0.999998i | \(0.500589\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | − 3.50758i | − 0.186955i | ||||||||
\(353\) | − 30.4924i | − 1.62295i | −0.584389 | − | 0.811474i | \(-0.698666\pi\) | ||||
0.584389 | − | 0.811474i | \(-0.301334\pi\) | |||||||
\(354\) | 18.7386 | 0.995947 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.36932 | 0.284573 | ||||||||
\(357\) | − 36.4924i | − 1.93138i | ||||||||
\(358\) | 1.75379i | 0.0926906i | ||||||||
\(359\) | 3.19224 | 0.168480 | 0.0842399 | − | 0.996446i | \(-0.473154\pi\) | ||||
0.0842399 | + | 0.996446i | \(0.473154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | − 40.1080i | − 2.10803i | ||||||||
\(363\) | 8.93087i | 0.468749i | ||||||||
\(364\) | 4.49242 | 0.235467 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.36932 | −0.0715753 | ||||||||
\(367\) | − 19.6847i | − 1.02753i | −0.857931 | − | 0.513765i | \(-0.828250\pi\) | ||||
0.857931 | − | 0.513765i | \(-0.171750\pi\) | |||||||
\(368\) | 30.7386i | 1.60236i | ||||||||
\(369\) | 1.68466 | 0.0876998 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.6155 | −0.914553 | ||||||||
\(372\) | 1.75379i | 0.0909297i | ||||||||
\(373\) | − 13.3693i | − 0.692237i | −0.938191 | − | 0.346118i | \(-0.887500\pi\) | ||||
0.938191 | − | 0.346118i | \(-0.112500\pi\) | |||||||
\(374\) | 16.0000 | 0.827340 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.0000 | −1.65027 | ||||||||
\(377\) | − 2.00000i | − 0.103005i | ||||||||
\(378\) | 8.00000i | 0.411476i | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.31534 | 0.221082 | ||||||||
\(382\) | 15.5076i | 0.793437i | ||||||||
\(383\) | − 11.0540i | − 0.564832i | −0.959292 | − | 0.282416i | \(-0.908864\pi\) | ||||
0.959292 | − | 0.282416i | \(-0.0911358\pi\) | |||||||
\(384\) | 13.5616 | 0.692060 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.6155 | 0.794809 | ||||||||
\(387\) | 7.68466i | 0.390633i | ||||||||
\(388\) | 2.49242i | 0.126534i | ||||||||
\(389\) | −14.8078 | −0.750783 | −0.375392 | − | 0.926866i | \(-0.622492\pi\) | ||||
−0.375392 | + | 0.926866i | \(0.622492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −46.7386 | −2.36367 | ||||||||
\(392\) | 46.9309i | 2.37037i | ||||||||
\(393\) | − 10.2462i | − 0.516853i | ||||||||
\(394\) | 7.12311 | 0.358857 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.630683 | −0.0316930 | ||||||||
\(397\) | 24.2462i | 1.21688i | 0.793599 | + | 0.608441i | \(0.208205\pi\) | ||||
−0.793599 | + | 0.608441i | \(0.791795\pi\) | |||||||
\(398\) | − 17.2614i | − 0.865234i | ||||||||
\(399\) | −26.2462 | −1.31395 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.6155 | 1.77855 | 0.889277 | − | 0.457368i | \(-0.151208\pi\) | ||||
0.889277 | + | 0.457368i | \(0.151208\pi\) | |||||||
\(402\) | 17.7538i | 0.885479i | ||||||||
\(403\) | 8.00000i | 0.398508i | ||||||||
\(404\) | 3.75379 | 0.186758 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | 2.42329i | 0.120118i | ||||||||
\(408\) | 17.3693i | 0.859909i | ||||||||
\(409\) | −17.3693 | −0.858857 | −0.429429 | − | 0.903101i | \(-0.641285\pi\) | ||||
−0.429429 | + | 0.903101i | \(0.641285\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.1231 | −0.745968 | ||||||||
\(412\) | − 1.26137i | − 0.0621431i | ||||||||
\(413\) | − 61.4773i | − 3.02510i | ||||||||
\(414\) | 10.2462 | 0.503574 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.87689 | −0.239109 | ||||||||
\(417\) | − 17.9309i | − 0.878078i | ||||||||
\(418\) | − 11.5076i | − 0.562854i | ||||||||
\(419\) | 27.3693 | 1.33708 | 0.668539 | − | 0.743677i | \(-0.266920\pi\) | ||||
0.668539 | + | 0.743677i | \(0.266920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 4.49242i | 0.218688i | ||||||||
\(423\) | 13.1231i | 0.638067i | ||||||||
\(424\) | 8.38447 | 0.407186 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.49242 | 0.217659 | ||||||||
\(427\) | 4.49242i | 0.217404i | ||||||||
\(428\) | − 7.23106i | − 0.349526i | ||||||||
\(429\) | −2.87689 | −0.138898 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.1231 | −1.01746 | −0.508732 | − | 0.860925i | \(-0.669886\pi\) | ||||
−0.508732 | + | 0.860925i | \(0.669886\pi\) | |||||||
\(432\) | − 4.68466i | − 0.225391i | ||||||||
\(433\) | 4.06913i | 0.195550i | 0.995209 | + | 0.0977750i | \(0.0311725\pi\) | ||||
−0.995209 | + | 0.0977750i | \(0.968827\pi\) | |||||||
\(434\) | 32.0000 | 1.53605 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.49242 | −0.119365 | ||||||||
\(437\) | 33.6155i | 1.60805i | ||||||||
\(438\) | 2.63068i | 0.125699i | ||||||||
\(439\) | −12.4924 | −0.596231 | −0.298115 | − | 0.954530i | \(-0.596358\pi\) | ||||
−0.298115 | + | 0.954530i | \(0.596358\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.2462 | 0.916486 | ||||||||
\(442\) | − 22.2462i | − 1.05814i | ||||||||
\(443\) | − 6.24621i | − 0.296766i | −0.988930 | − | 0.148383i | \(-0.952593\pi\) | ||||
0.988930 | − | 0.148383i | \(-0.0474069\pi\) | |||||||
\(444\) | 0.738634 | 0.0350540 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.4924 | 1.34916 | ||||||||
\(447\) | 0.246211i | 0.0116454i | ||||||||
\(448\) | − 28.4924i | − 1.34614i | ||||||||
\(449\) | −11.4384 | −0.539814 | −0.269907 | − | 0.962886i | \(-0.586993\pi\) | ||||
−0.269907 | + | 0.962886i | \(0.586993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.42329 | 0.114108 | ||||||||
\(452\) | − 2.13826i | − 0.100575i | ||||||||
\(453\) | − 4.31534i | − 0.202752i | ||||||||
\(454\) | −4.98485 | −0.233950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.4924 | 0.585011 | ||||||||
\(457\) | − 8.87689i | − 0.415244i | −0.978209 | − | 0.207622i | \(-0.933428\pi\) | ||||
0.978209 | − | 0.207622i | \(-0.0665723\pi\) | |||||||
\(458\) | 34.3542i | 1.60526i | ||||||||
\(459\) | 7.12311 | 0.332478 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1771 | −0.846591 | −0.423296 | − | 0.905992i | \(-0.639127\pi\) | ||||
−0.423296 | + | 0.905992i | \(0.639127\pi\) | |||||||
\(462\) | 11.5076i | 0.535381i | ||||||||
\(463\) | − 25.6155i | − 1.19045i | −0.803557 | − | 0.595227i | \(-0.797062\pi\) | ||||
0.803557 | − | 0.595227i | \(-0.202938\pi\) | |||||||
\(464\) | 4.68466 | 0.217480 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.1080 | 0.746186 | ||||||||
\(467\) | − 3.36932i | − 0.155913i | −0.996957 | − | 0.0779567i | \(-0.975160\pi\) | ||||
0.996957 | − | 0.0779567i | \(-0.0248396\pi\) | |||||||
\(468\) | 0.876894i | 0.0405345i | ||||||||
\(469\) | 58.2462 | 2.68956 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.0000 | −0.645086 | ||||||||
\(472\) | 29.2614i | 1.34686i | ||||||||
\(473\) | 11.0540i | 0.508262i | ||||||||
\(474\) | −18.7386 | −0.860694 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.0000 | −0.733359 | ||||||||
\(477\) | − 3.43845i | − 0.157436i | ||||||||
\(478\) | − 20.4924i | − 0.937302i | ||||||||
\(479\) | 22.2462 | 1.01646 | 0.508228 | − | 0.861223i | \(-0.330301\pi\) | ||||
0.508228 | + | 0.861223i | \(0.330301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.36932 | 0.153628 | ||||||||
\(482\) | 39.1231i | 1.78201i | ||||||||
\(483\) | − 33.6155i | − 1.52956i | ||||||||
\(484\) | 3.91571 | 0.177987 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.56155 | −0.0708335 | ||||||||
\(487\) | 34.2462i | 1.55184i | 0.630829 | + | 0.775922i | \(0.282715\pi\) | ||||
−0.630829 | + | 0.775922i | \(0.717285\pi\) | |||||||
\(488\) | − 2.13826i | − 0.0967945i | ||||||||
\(489\) | 17.9309 | 0.810862 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.73863 | 0.304110 | 0.152055 | − | 0.988372i | \(-0.451411\pi\) | ||||
0.152055 | + | 0.988372i | \(0.451411\pi\) | |||||||
\(492\) | − 0.738634i | − 0.0333002i | ||||||||
\(493\) | 7.12311i | 0.320809i | ||||||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.7386 | −0.841389 | ||||||||
\(497\) | − 14.7386i | − 0.661118i | ||||||||
\(498\) | − 4.00000i | − 0.179244i | ||||||||
\(499\) | −42.7386 | −1.91324 | −0.956622 | − | 0.291332i | \(-0.905902\pi\) | ||||
−0.956622 | + | 0.291332i | \(0.905902\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 3.50758i | − 0.156551i | ||||||||
\(503\) | 39.3693i | 1.75539i | 0.479219 | + | 0.877696i | \(0.340920\pi\) | ||||
−0.479219 | + | 0.877696i | \(0.659080\pi\) | |||||||
\(504\) | −12.4924 | −0.556457 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.7386 | 0.655212 | ||||||||
\(507\) | − 9.00000i | − 0.399704i | ||||||||
\(508\) | − 1.89205i | − 0.0839461i | ||||||||
\(509\) | −18.4924 | −0.819662 | −0.409831 | − | 0.912161i | \(-0.634412\pi\) | ||||
−0.409831 | + | 0.912161i | \(0.634412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.63068 | 0.381799 | ||||||||
\(512\) | 11.4233i | 0.504843i | ||||||||
\(513\) | − 5.12311i | − 0.226191i | ||||||||
\(514\) | 17.8617 | 0.787848 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.36932 | 0.148326 | ||||||||
\(517\) | 18.8769i | 0.830205i | ||||||||
\(518\) | − 13.4773i | − 0.592157i | ||||||||
\(519\) | −12.5616 | −0.551391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.246211 | −0.0107867 | −0.00539336 | − | 0.999985i | \(-0.501717\pi\) | ||||
−0.00539336 | + | 0.999985i | \(0.501717\pi\) | |||||||
\(522\) | − 1.56155i | − 0.0683473i | ||||||||
\(523\) | − 18.7386i | − 0.819383i | −0.912224 | − | 0.409692i | \(-0.865636\pi\) | ||||
0.912224 | − | 0.409692i | \(-0.134364\pi\) | |||||||
\(524\) | −4.49242 | −0.196252 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.98485 | 0.391758 | ||||||||
\(527\) | − 28.4924i | − 1.24115i | ||||||||
\(528\) | − 6.73863i | − 0.293261i | ||||||||
\(529\) | −20.0540 | −0.871912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 11.5076i | 0.498917i | ||||||||
\(533\) | − 3.36932i | − 0.145941i | ||||||||
\(534\) | 19.1231 | 0.827538 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −27.7235 | −1.19747 | ||||||||
\(537\) | 1.12311i | 0.0484656i | ||||||||
\(538\) | 18.3542i | 0.791304i | ||||||||
\(539\) | 27.6847 | 1.19246 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.7386 | −1.75149 | −0.875745 | − | 0.482773i | \(-0.839629\pi\) | ||||
−0.875745 | + | 0.482773i | \(0.839629\pi\) | |||||||
\(542\) | − 26.7386i | − 1.14852i | ||||||||
\(543\) | − 25.6847i | − 1.10223i | ||||||||
\(544\) | 17.3693 | 0.744703 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.0000 | 0.684737 | ||||||||
\(547\) | − 42.7386i | − 1.82737i | −0.406421 | − | 0.913686i | \(-0.633223\pi\) | ||||
0.406421 | − | 0.913686i | \(-0.366777\pi\) | |||||||
\(548\) | 6.63068i | 0.283249i | ||||||||
\(549\) | −0.876894 | −0.0374249 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.12311 | 0.218252 | ||||||||
\(552\) | 16.0000i | 0.681005i | ||||||||
\(553\) | 61.4773i | 2.61428i | ||||||||
\(554\) | 1.36932 | 0.0581767 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.86174 | −0.333412 | ||||||||
\(557\) | − 20.4233i | − 0.865363i | −0.901547 | − | 0.432681i | \(-0.857568\pi\) | ||||
0.901547 | − | 0.432681i | \(-0.142432\pi\) | |||||||
\(558\) | 6.24621i | 0.264423i | ||||||||
\(559\) | 15.3693 | 0.650053 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.2462 | 0.432595 | ||||||||
\(562\) | 36.8769i | 1.55556i | ||||||||
\(563\) | − 9.12311i | − 0.384493i | −0.981347 | − | 0.192247i | \(-0.938423\pi\) | ||||
0.981347 | − | 0.192247i | \(-0.0615773\pi\) | |||||||
\(564\) | 5.75379 | 0.242278 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.7386 | −0.451378 | ||||||||
\(567\) | 5.12311i | 0.215150i | ||||||||
\(568\) | 7.01515i | 0.294349i | ||||||||
\(569\) | 16.2462 | 0.681077 | 0.340538 | − | 0.940231i | \(-0.389391\pi\) | ||||
0.340538 | + | 0.940231i | \(0.389391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.0540 | 1.63436 | 0.817179 | − | 0.576384i | \(-0.195537\pi\) | ||||
0.817179 | + | 0.576384i | \(0.195537\pi\) | |||||||
\(572\) | 1.26137i | 0.0527404i | ||||||||
\(573\) | 9.93087i | 0.414868i | ||||||||
\(574\) | −13.4773 | −0.562530 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.56155 | 0.231731 | ||||||||
\(577\) | − 30.4924i | − 1.26942i | −0.772752 | − | 0.634708i | \(-0.781120\pi\) | ||||
0.772752 | − | 0.634708i | \(-0.218880\pi\) | |||||||
\(578\) | 52.6847i | 2.19139i | ||||||||
\(579\) | 10.0000 | 0.415586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.1231 | −0.544438 | ||||||||
\(582\) | 8.87689i | 0.367959i | ||||||||
\(583\) | − 4.94602i | − 0.204843i | ||||||||
\(584\) | −4.10795 | −0.169988 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.3693 | 1.37847 | ||||||||
\(587\) | 24.4924i | 1.01091i | 0.862853 | + | 0.505455i | \(0.168675\pi\) | ||||
−0.862853 | + | 0.505455i | \(0.831325\pi\) | |||||||
\(588\) | − 8.43845i | − 0.347996i | ||||||||
\(589\) | −20.4924 | −0.844376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.56155 | 0.187637 | ||||||||
\(592\) | 7.89205i | 0.324361i | ||||||||
\(593\) | − 36.2462i | − 1.48845i | −0.667927 | − | 0.744227i | \(-0.732818\pi\) | ||||
0.667927 | − | 0.744227i | \(-0.267182\pi\) | |||||||
\(594\) | −2.24621 | −0.0921632 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.107951 | 0.00442183 | ||||||||
\(597\) | − 11.0540i | − 0.452409i | ||||||||
\(598\) | − 20.4924i | − 0.837997i | ||||||||
\(599\) | 20.9848 | 0.857418 | 0.428709 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428709 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.3693 | 1.68749 | 0.843745 | − | 0.536745i | \(-0.180346\pi\) | ||||
0.843745 | + | 0.536745i | \(0.180346\pi\) | |||||||
\(602\) | − 61.4773i | − 2.50563i | ||||||||
\(603\) | 11.3693i | 0.462994i | ||||||||
\(604\) | −1.89205 | −0.0769864 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.3693 | 0.543091 | ||||||||
\(607\) | − 16.0000i | − 0.649420i | −0.945814 | − | 0.324710i | \(-0.894733\pi\) | ||||
0.945814 | − | 0.324710i | \(-0.105267\pi\) | |||||||
\(608\) | − 12.4924i | − 0.506635i | ||||||||
\(609\) | −5.12311 | −0.207599 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.2462 | 1.06181 | ||||||||
\(612\) | − 3.12311i | − 0.126244i | ||||||||
\(613\) | 2.00000i | 0.0807792i | 0.999184 | + | 0.0403896i | \(0.0128599\pi\) | ||||
−0.999184 | + | 0.0403896i | \(0.987140\pi\) | |||||||
\(614\) | −49.4773 | −1.99674 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.9697 | −0.724019 | ||||||||
\(617\) | 8.24621i | 0.331980i | 0.986127 | + | 0.165990i | \(0.0530819\pi\) | ||||
−0.986127 | + | 0.165990i | \(0.946918\pi\) | |||||||
\(618\) | − 4.49242i | − 0.180712i | ||||||||
\(619\) | −29.1231 | −1.17056 | −0.585278 | − | 0.810833i | \(-0.699015\pi\) | ||||
−0.585278 | + | 0.810833i | \(0.699015\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.56155 | 0.263306 | ||||||||
\(622\) | − 25.4773i | − 1.02155i | ||||||||
\(623\) | − 62.7386i | − 2.51357i | ||||||||
\(624\) | −9.36932 | −0.375073 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 33.3693 | 1.33371 | ||||||||
\(627\) | − 7.36932i | − 0.294302i | ||||||||
\(628\) | 6.13826i | 0.244943i | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | − 29.2614i | − 1.16395i | ||||||||
\(633\) | 2.87689i | 0.114346i | ||||||||
\(634\) | 7.61553 | 0.302451 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.50758 | −0.0597793 | ||||||||
\(637\) | − 38.4924i | − 1.52513i | ||||||||
\(638\) | − 2.24621i | − 0.0889284i | ||||||||
\(639\) | 2.87689 | 0.113808 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.4384 | 0.767773 | 0.383886 | − | 0.923380i | \(-0.374585\pi\) | ||||
0.383886 | + | 0.923380i | \(0.374585\pi\) | |||||||
\(642\) | − 25.7538i | − 1.01642i | ||||||||
\(643\) | 18.7386i | 0.738980i | 0.929235 | + | 0.369490i | \(0.120468\pi\) | ||||
−0.929235 | + | 0.369490i | \(0.879532\pi\) | |||||||
\(644\) | −14.7386 | −0.580784 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 56.9848 | 2.24204 | ||||||||
\(647\) | 5.93087i | 0.233167i | 0.993181 | + | 0.116583i | \(0.0371942\pi\) | ||||
−0.993181 | + | 0.116583i | \(0.962806\pi\) | |||||||
\(648\) | − 2.43845i | − 0.0957913i | ||||||||
\(649\) | 17.2614 | 0.677568 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.4924 | 0.803161 | ||||||||
\(652\) | − 7.86174i | − 0.307889i | ||||||||
\(653\) | − 12.2462i | − 0.479231i | −0.970868 | − | 0.239616i | \(-0.922979\pi\) | ||||
0.970868 | − | 0.239616i | \(-0.0770214\pi\) | |||||||
\(654\) | −8.87689 | −0.347114 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.89205 | 0.308133 | ||||||||
\(657\) | 1.68466i | 0.0657248i | ||||||||
\(658\) | − 104.985i | − 4.09274i | ||||||||
\(659\) | −6.56155 | −0.255602 | −0.127801 | − | 0.991800i | \(-0.540792\pi\) | ||||
−0.127801 | + | 0.991800i | \(0.540792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.05398 | 0.0409949 | 0.0204974 | − | 0.999790i | \(-0.493475\pi\) | ||||
0.0204974 | + | 0.999790i | \(0.493475\pi\) | |||||||
\(662\) | − 16.0000i | − 0.621858i | ||||||||
\(663\) | − 14.2462i | − 0.553277i | ||||||||
\(664\) | 6.24621 | 0.242400 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.63068 | 0.101937 | ||||||||
\(667\) | 6.56155i | 0.254064i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.2462 | 0.705439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.26137 | −0.0486945 | ||||||||
\(672\) | 12.4924i | 0.481906i | ||||||||
\(673\) | 6.00000i | 0.231283i | 0.993291 | + | 0.115642i | \(0.0368924\pi\) | ||||
−0.993291 | + | 0.115642i | \(0.963108\pi\) | |||||||
\(674\) | −12.1080 | −0.466381 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.94602 | −0.151770 | ||||||||
\(677\) | 13.8617i | 0.532750i | 0.963869 | + | 0.266375i | \(0.0858259\pi\) | ||||
−0.963869 | + | 0.266375i | \(0.914174\pi\) | |||||||
\(678\) | − 7.61553i | − 0.292473i | ||||||||
\(679\) | 29.1231 | 1.11764 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.19224 | −0.122327 | ||||||||
\(682\) | 8.98485i | 0.344047i | ||||||||
\(683\) | 21.4384i | 0.820319i | 0.912014 | + | 0.410160i | \(0.134527\pi\) | ||||
−0.912014 | + | 0.410160i | \(0.865473\pi\) | |||||||
\(684\) | −2.24621 | −0.0858860 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −97.9697 | −3.74050 | ||||||||
\(687\) | 22.0000i | 0.839352i | ||||||||
\(688\) | 36.0000i | 1.37249i | ||||||||
\(689\) | −6.87689 | −0.261989 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | −0.152167 | −0.0760836 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760836 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(692\) | 5.50758i | 0.209367i | ||||||||
\(693\) | 7.36932i | 0.279937i | ||||||||
\(694\) | −19.0152 | −0.721805 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.43845 | 0.0924291 | ||||||||
\(697\) | 12.0000i | 0.454532i | ||||||||
\(698\) | 0.107951i | 0.00408599i | ||||||||
\(699\) | 10.3153 | 0.390162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.75379 | 0.141779 | 0.0708893 | − | 0.997484i | \(-0.477416\pi\) | ||||
0.0708893 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(702\) | 3.12311i | 0.117874i | ||||||||
\(703\) | 8.63068i | 0.325512i | ||||||||
\(704\) | 8.00000 | 0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −47.6155 | −1.79203 | ||||||||
\(707\) | − 43.8617i | − 1.64959i | ||||||||
\(708\) | − 5.26137i | − 0.197734i | ||||||||
\(709\) | 12.4233 | 0.466567 | 0.233283 | − | 0.972409i | \(-0.425053\pi\) | ||||
0.233283 | + | 0.972409i | \(0.425053\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | −0.450035 | ||||||||
\(712\) | 29.8617i | 1.11912i | ||||||||
\(713\) | − 26.2462i | − 0.982928i | ||||||||
\(714\) | −56.9848 | −2.13260 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.492423 | 0.0184027 | ||||||||
\(717\) | − 13.1231i | − 0.490091i | ||||||||
\(718\) | − 4.98485i | − 0.186033i | ||||||||
\(719\) | 4.49242 | 0.167539 | 0.0837695 | − | 0.996485i | \(-0.473304\pi\) | ||||
0.0837695 | + | 0.996485i | \(0.473304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.7386 | −0.548895 | ||||||||
\(722\) | − 11.3153i | − 0.421113i | ||||||||
\(723\) | 25.0540i | 0.931767i | ||||||||
\(724\) | −11.2614 | −0.418525 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.9460 | 0.517586 | ||||||||
\(727\) | − 38.7386i | − 1.43674i | −0.695663 | − | 0.718368i | \(-0.744889\pi\) | ||||
0.695663 | − | 0.718368i | \(-0.255111\pi\) | |||||||
\(728\) | 24.9848i | 0.926000i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.7386 | −2.02458 | ||||||||
\(732\) | 0.384472i | 0.0142105i | ||||||||
\(733\) | 22.9848i | 0.848965i | 0.905436 | + | 0.424482i | \(0.139544\pi\) | ||||
−0.905436 | + | 0.424482i | \(0.860456\pi\) | |||||||
\(734\) | −30.7386 | −1.13458 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | 0.589768 | ||||||||
\(737\) | 16.3542i | 0.602413i | ||||||||
\(738\) | − 2.63068i | − 0.0968368i | ||||||||
\(739\) | 24.0000 | 0.882854 | 0.441427 | − | 0.897297i | \(-0.354472\pi\) | ||||
0.441427 | + | 0.897297i | \(0.354472\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.2462 | −0.376404 | ||||||||
\(742\) | 27.5076i | 1.00983i | ||||||||
\(743\) | − 34.8769i | − 1.27951i | −0.768579 | − | 0.639755i | \(-0.779036\pi\) | ||||
0.768579 | − | 0.639755i | \(-0.220964\pi\) | |||||||
\(744\) | −9.75379 | −0.357591 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.8769 | −0.764357 | ||||||||
\(747\) | − 2.56155i | − 0.0937223i | ||||||||
\(748\) | − 4.49242i | − 0.164259i | ||||||||
\(749\) | −84.4924 | −3.08729 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.4924 | 1.76951 | 0.884757 | − | 0.466053i | \(-0.154324\pi\) | ||||
0.884757 | + | 0.466053i | \(0.154324\pi\) | |||||||
\(752\) | 61.4773i | 2.24185i | ||||||||
\(753\) | − 2.24621i | − 0.0818565i | ||||||||
\(754\) | −3.12311 | −0.113737 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.24621 | 0.0816939 | ||||||||
\(757\) | 5.68466i | 0.206612i | 0.994650 | + | 0.103306i | \(0.0329422\pi\) | ||||
−0.994650 | + | 0.103306i | \(0.967058\pi\) | |||||||
\(758\) | 12.4924i | 0.453745i | ||||||||
\(759\) | 9.43845 | 0.342594 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8769 | −0.901787 | −0.450893 | − | 0.892578i | \(-0.648895\pi\) | ||||
−0.450893 | + | 0.892578i | \(0.648895\pi\) | |||||||
\(762\) | − 6.73863i | − 0.244115i | ||||||||
\(763\) | 29.1231i | 1.05433i | ||||||||
\(764\) | 4.35416 | 0.157528 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.2614 | −0.623679 | ||||||||
\(767\) | − 24.0000i | − 0.866590i | ||||||||
\(768\) | − 10.0540i | − 0.362792i | ||||||||
\(769\) | −43.6155 | −1.57282 | −0.786408 | − | 0.617707i | \(-0.788062\pi\) | ||||
−0.786408 | + | 0.617707i | \(0.788062\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4384 | 0.411946 | ||||||||
\(772\) | − 4.38447i | − 0.157801i | ||||||||
\(773\) | − 24.7386i | − 0.889787i | −0.895584 | − | 0.444893i | \(-0.853242\pi\) | ||||
0.895584 | − | 0.444893i | \(-0.146758\pi\) | |||||||
\(774\) | 12.0000 | 0.431331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.8617 | −0.497607 | ||||||||
\(777\) | − 8.63068i | − 0.309624i | ||||||||
\(778\) | 23.1231i | 0.829004i | ||||||||
\(779\) | 8.63068 | 0.309226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.13826 | 0.148079 | ||||||||
\(782\) | 72.9848i | 2.60993i | ||||||||
\(783\) | − 1.00000i | − 0.0357371i | ||||||||
\(784\) | 90.1619 | 3.22007 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.0000 | −0.570701 | ||||||||
\(787\) | − 31.2311i | − 1.11327i | −0.830758 | − | 0.556633i | \(-0.812093\pi\) | ||||
0.830758 | − | 0.556633i | \(-0.187907\pi\) | |||||||
\(788\) | − 2.00000i | − 0.0712470i | ||||||||
\(789\) | 5.75379 | 0.204840 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.9848 | −0.888359 | ||||||||
\(792\) | − 3.50758i | − 0.124636i | ||||||||
\(793\) | 1.75379i | 0.0622789i | ||||||||
\(794\) | 37.8617 | 1.34366 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.84658 | −0.171783 | ||||||||
\(797\) | 38.4924i | 1.36347i | 0.731598 | + | 0.681736i | \(0.238775\pi\) | ||||
−0.731598 | + | 0.681736i | \(0.761225\pi\) | |||||||
\(798\) | 40.9848i | 1.45085i | ||||||||
\(799\) | −93.4773 | −3.30699 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.2462 | 0.432699 | ||||||||
\(802\) | − 55.6155i | − 1.96385i | ||||||||
\(803\) | 2.42329i | 0.0855161i | ||||||||
\(804\) | 4.98485 | 0.175802 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.4924 | 0.440027 | ||||||||
\(807\) | 11.7538i | 0.413753i | ||||||||
\(808\) | 20.8769i | 0.734447i | ||||||||
\(809\) | 22.1771 | 0.779705 | 0.389852 | − | 0.920877i | \(-0.372526\pi\) | ||||
0.389852 | + | 0.920877i | \(0.372526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.1771 | 1.55127 | 0.775634 | − | 0.631183i | \(-0.217431\pi\) | ||||
0.775634 | + | 0.631183i | \(0.217431\pi\) | |||||||
\(812\) | 2.24621i | 0.0788266i | ||||||||
\(813\) | − 17.1231i | − 0.600534i | ||||||||
\(814\) | 3.78410 | 0.132633 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 33.3693 | 1.16816 | ||||||||
\(817\) | 39.3693i | 1.37736i | ||||||||
\(818\) | 27.1231i | 0.948337i | ||||||||
\(819\) | 10.2462 | 0.358032 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 55.6155 | 1.94100 | 0.970498 | − | 0.241111i | \(-0.0775116\pi\) | ||||
0.970498 | + | 0.241111i | \(0.0775116\pi\) | |||||||
\(822\) | 23.6155i | 0.823686i | ||||||||
\(823\) | − 16.0000i | − 0.557725i | −0.960331 | − | 0.278862i | \(-0.910043\pi\) | ||||
0.960331 | − | 0.278862i | \(-0.0899574\pi\) | |||||||
\(824\) | 7.01515 | 0.244385 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −96.0000 | −3.34027 | ||||||||
\(827\) | 53.6155i | 1.86439i | 0.361951 | + | 0.932197i | \(0.382111\pi\) | ||||
−0.361951 | + | 0.932197i | \(0.617889\pi\) | |||||||
\(828\) | − 2.87689i | − 0.0999790i | ||||||||
\(829\) | 4.24621 | 0.147477 | 0.0737385 | − | 0.997278i | \(-0.476507\pi\) | ||||
0.0737385 | + | 0.997278i | \(0.476507\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.876894 | 0.0304191 | ||||||||
\(832\) | − 11.1231i | − 0.385624i | ||||||||
\(833\) | 137.093i | 4.74998i | ||||||||
\(834\) | −28.0000 | −0.969561 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.23106 | −0.111748 | ||||||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | − 42.7386i | − 1.47638i | ||||||||
\(839\) | −42.7386 | −1.47550 | −0.737751 | − | 0.675073i | \(-0.764112\pi\) | ||||
−0.737751 | + | 0.675073i | \(0.764112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 15.6155i | 0.538147i | ||||||||
\(843\) | 23.6155i | 0.813362i | ||||||||
\(844\) | 1.26137 | 0.0434180 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 20.4924 | 0.704544 | ||||||||
\(847\) | − 45.7538i | − 1.57212i | ||||||||
\(848\) | − 16.1080i | − 0.553149i | ||||||||
\(849\) | −6.87689 | −0.236014 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0540 | −0.378925 | ||||||||
\(852\) | − 1.26137i | − 0.0432137i | ||||||||
\(853\) | − 19.4384i | − 0.665560i | −0.943005 | − | 0.332780i | \(-0.892013\pi\) | ||||
0.943005 | − | 0.332780i | \(-0.107987\pi\) | |||||||
\(854\) | 7.01515 | 0.240054 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 40.2159 | 1.37455 | ||||||||
\(857\) | − 15.4384i | − 0.527367i | −0.964609 | − | 0.263684i | \(-0.915062\pi\) | ||||
0.964609 | − | 0.263684i | \(-0.0849375\pi\) | |||||||
\(858\) | 4.49242i | 0.153369i | ||||||||
\(859\) | 23.3693 | 0.797351 | 0.398675 | − | 0.917092i | \(-0.369470\pi\) | ||||
0.398675 | + | 0.917092i | \(0.369470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.63068 | −0.294133 | ||||||||
\(862\) | 32.9848i | 1.12347i | ||||||||
\(863\) | − 40.9848i | − 1.39514i | −0.716516 | − | 0.697570i | \(-0.754265\pi\) | ||||
0.716516 | − | 0.697570i | \(-0.245735\pi\) | |||||||
\(864\) | −2.43845 | −0.0829577 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.35416 | 0.215923 | ||||||||
\(867\) | 33.7386i | 1.14582i | ||||||||
\(868\) | − 8.98485i | − 0.304966i | ||||||||
\(869\) | −17.2614 | −0.585552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.7386 | 0.770469 | ||||||||
\(872\) | − 13.8617i | − 0.469418i | ||||||||
\(873\) | 5.68466i | 0.192397i | ||||||||
\(874\) | 52.4924 | 1.77558 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.738634 | 0.0249561 | ||||||||
\(877\) | 8.87689i | 0.299751i | 0.988705 | + | 0.149876i | \(0.0478874\pi\) | ||||
−0.988705 | + | 0.149876i | \(0.952113\pi\) | |||||||
\(878\) | 19.5076i | 0.658349i | ||||||||
\(879\) | 21.3693 | 0.720769 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.06913 | −0.271856 | −0.135928 | − | 0.990719i | \(-0.543402\pi\) | ||||
−0.135928 | + | 0.990719i | \(0.543402\pi\) | |||||||
\(882\) | − 30.0540i | − 1.01197i | ||||||||
\(883\) | 42.7386i | 1.43827i | 0.694871 | + | 0.719135i | \(0.255462\pi\) | ||||
−0.694871 | + | 0.719135i | \(0.744538\pi\) | |||||||
\(884\) | −6.24621 | −0.210083 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.75379 | −0.327685 | ||||||||
\(887\) | − 43.8617i | − 1.47273i | −0.676583 | − | 0.736367i | \(-0.736540\pi\) | ||||
0.676583 | − | 0.736367i | \(-0.263460\pi\) | |||||||
\(888\) | 4.10795i | 0.137854i | ||||||||
\(889\) | −22.1080 | −0.741477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.43845 | −0.0481898 | ||||||||
\(892\) | − 8.00000i | − 0.267860i | ||||||||
\(893\) | 67.2311i | 2.24980i | ||||||||
\(894\) | 0.384472 | 0.0128587 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −69.4773 | −2.32107 | ||||||||
\(897\) | − 13.1231i | − 0.438168i | ||||||||
\(898\) | 17.8617i | 0.596054i | ||||||||
\(899\) | −4.00000 | −0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.4924 | 0.815961 | ||||||||
\(902\) | − 3.78410i | − 0.125997i | ||||||||
\(903\) | − 39.3693i | − 1.31013i | ||||||||
\(904\) | 11.8920 | 0.395524 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.73863 | −0.223876 | ||||||||
\(907\) | 31.0540i | 1.03113i | 0.856850 | + | 0.515565i | \(0.172418\pi\) | ||||
−0.856850 | + | 0.515565i | \(0.827582\pi\) | |||||||
\(908\) | 1.39963i | 0.0464482i | ||||||||
\(909\) | 8.56155 | 0.283969 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.5616 | −0.614972 | −0.307486 | − | 0.951553i | \(-0.599488\pi\) | ||||
−0.307486 | + | 0.951553i | \(0.599488\pi\) | |||||||
\(912\) | − 24.0000i | − 0.794719i | ||||||||
\(913\) | − 3.68466i | − 0.121944i | ||||||||
\(914\) | −13.8617 | −0.458506 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.64584 | 0.318707 | ||||||||
\(917\) | 52.4924i | 1.73345i | ||||||||
\(918\) | − 11.1231i | − 0.367117i | ||||||||
\(919\) | −30.7386 | −1.01397 | −0.506987 | − | 0.861954i | \(-0.669241\pi\) | ||||
−0.506987 | + | 0.861954i | \(0.669241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.6847 | −1.04404 | ||||||||
\(922\) | 28.3845i | 0.934793i | ||||||||
\(923\) | − 5.75379i | − 0.189388i | ||||||||
\(924\) | 3.23106 | 0.106294 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −40.0000 | −1.31448 | ||||||||
\(927\) | − 2.87689i | − 0.0944896i | ||||||||
\(928\) | − 2.43845i | − 0.0800460i | ||||||||
\(929\) | −4.87689 | −0.160006 | −0.0800029 | − | 0.996795i | \(-0.525493\pi\) | ||||
−0.0800029 | + | 0.996795i | \(0.525493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 98.6004 | 3.23150 | ||||||||
\(932\) | − 4.52273i | − 0.148147i | ||||||||
\(933\) | − 16.3153i | − 0.534140i | ||||||||
\(934\) | −5.26137 | −0.172157 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.87689 | −0.159406 | ||||||||
\(937\) | 39.1231i | 1.27810i | 0.769167 | + | 0.639048i | \(0.220672\pi\) | ||||
−0.769167 | + | 0.639048i | \(0.779328\pi\) | |||||||
\(938\) | − 90.9545i | − 2.96977i | ||||||||
\(939\) | 21.3693 | 0.697361 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.738634 | −0.0240788 | −0.0120394 | − | 0.999928i | \(-0.503832\pi\) | ||||
−0.0120394 | + | 0.999928i | \(0.503832\pi\) | |||||||
\(942\) | 21.8617i | 0.712294i | ||||||||
\(943\) | 11.0540i | 0.359967i | ||||||||
\(944\) | 56.2159 | 1.82967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.2614 | 0.561215 | ||||||||
\(947\) | − 3.36932i | − 0.109488i | −0.998500 | − | 0.0547440i | \(-0.982566\pi\) | ||||
0.998500 | − | 0.0547440i | \(-0.0174343\pi\) | |||||||
\(948\) | 5.26137i | 0.170881i | ||||||||
\(949\) | 3.36932 | 0.109373 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.87689 | 0.158144 | ||||||||
\(952\) | − 88.9848i | − 2.88402i | ||||||||
\(953\) | 34.4924i | 1.11732i | 0.829397 | + | 0.558660i | \(0.188684\pi\) | ||||
−0.829397 | + | 0.558660i | \(0.811316\pi\) | |||||||
\(954\) | −5.36932 | −0.173838 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.75379 | −0.186091 | ||||||||
\(957\) | − 1.43845i | − 0.0464984i | ||||||||
\(958\) | − 34.7386i | − 1.12235i | ||||||||
\(959\) | 77.4773 | 2.50187 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | − 5.26137i | − 0.169633i | ||||||||
\(963\) | − 16.4924i | − 0.531461i | ||||||||
\(964\) | 10.9848 | 0.353798 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −52.4924 | −1.68892 | ||||||||
\(967\) | 27.0540i | 0.869997i | 0.900431 | + | 0.434999i | \(0.143251\pi\) | ||||
−0.900431 | + | 0.434999i | \(0.856749\pi\) | |||||||
\(968\) | 21.7775i | 0.699954i | ||||||||
\(969\) | 36.4924 | 1.17231 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.6695 | −1.43351 | −0.716756 | − | 0.697324i | \(-0.754374\pi\) | ||||
−0.716756 | + | 0.697324i | \(0.754374\pi\) | |||||||
\(972\) | 0.438447i | 0.0140632i | ||||||||
\(973\) | 91.8617i | 2.94495i | ||||||||
\(974\) | 53.4773 | 1.71352 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.10795 | −0.131492 | ||||||||
\(977\) | − 7.43845i | − 0.237977i | −0.992896 | − | 0.118989i | \(-0.962035\pi\) | ||||
0.992896 | − | 0.118989i | \(-0.0379652\pi\) | |||||||
\(978\) | − 28.0000i | − 0.895341i | ||||||||
\(979\) | 17.6155 | 0.562995 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.68466 | −0.181497 | ||||||||
\(982\) | − 10.5227i | − 0.335794i | ||||||||
\(983\) | − 27.8617i | − 0.888651i | −0.895865 | − | 0.444326i | \(-0.853443\pi\) | ||||
0.895865 | − | 0.444326i | \(-0.146557\pi\) | |||||||
\(984\) | 4.10795 | 0.130957 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.1231 | 0.354232 | ||||||||
\(987\) | − 67.2311i | − 2.13999i | ||||||||
\(988\) | 4.49242i | 0.142923i | ||||||||
\(989\) | −50.4233 | −1.60337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.94602 | 0.157116 | 0.0785578 | − | 0.996910i | \(-0.474968\pi\) | ||||
0.0785578 | + | 0.996910i | \(0.474968\pi\) | |||||||
\(992\) | 9.75379i | 0.309683i | ||||||||
\(993\) | − 10.2462i | − 0.325154i | ||||||||
\(994\) | −23.0152 | −0.729996 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.12311 | −0.0355870 | ||||||||
\(997\) | 54.0388i | 1.71143i | 0.517450 | + | 0.855713i | \(0.326881\pi\) | ||||
−0.517450 | + | 0.855713i | \(0.673119\pi\) | |||||||
\(998\) | 66.7386i | 2.11257i | ||||||||
\(999\) | 1.68466 | 0.0533002 |
(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 | 2175.2.c.h.349.2 | 4 | ||
5.2 | odd | 4 | 2175.2.a.m.1.2 | 2 | |||
5.3 | odd | 4 | 435.2.a.h.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2175.2.c.h.349.3 | 4 | ||
15.2 | even | 4 | 6525.2.a.bc.1.1 | 2 | |||
15.8 | even | 4 | 1305.2.a.i.1.2 | 2 | |||
20.3 | even | 4 | 6960.2.a.bx.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.2.a.h.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
1305.2.a.i.1.2 | 2 | 15.8 | even | 4 | |||
2175.2.a.m.1.2 | 2 | 5.2 | odd | 4 | |||
2175.2.c.h.349.2 | 4 | 1.1 | even | 1 | trivial | ||
2175.2.c.h.349.3 | 4 | 5.4 | even | 2 | inner | ||
6525.2.a.bc.1.1 | 2 | 15.2 | even | 4 | |||
6960.2.a.bx.1.1 | 2 | 20.3 | even | 4 |