Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(364,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.c (of order \(2\), degree \(1\), 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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.364 |
Dual form | 1815.2.c.g.364.7 |
$q$-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 \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).
\(n\) | \(727\) | \(1211\) | \(1696\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22474 | − | 0.224745i | −0.994936 | − | 0.100509i | ||||
\(6\) | −1.41421 | −0.577350 | ||||||||
\(7\) | 1.73205i | 0.654654i | 0.944911 | + | 0.327327i | \(0.106148\pi\) | ||||
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.317837 | + | 3.14626i | −0.100509 | + | 0.994936i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.635674i | 0.176304i | 0.996107 | + | 0.0881522i | \(0.0280962\pi\) | ||||
−0.996107 | + | 0.0881522i | \(0.971904\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | −0.224745 | + | 2.22474i | −0.0580289 | + | 0.574427i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | − | 4.87832i | − | 1.18317i | −0.806244 | − | 0.591583i | \(-0.798503\pi\) | ||
0.806244 | − | 0.591583i | \(-0.201497\pi\) | |||||||
\(18\) | 1.41421i | 0.333333i | ||||||||
\(19\) | −1.73205 | −0.397360 | −0.198680 | − | 0.980064i | \(-0.563665\pi\) | ||||
−0.198680 | + | 0.980064i | \(0.563665\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205 | 0.377964 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.00000i | − | 0.417029i | −0.978019 | − | 0.208514i | \(-0.933137\pi\) | ||
0.978019 | − | 0.208514i | \(-0.0668628\pi\) | |||||||
\(24\) | −2.82843 | −0.577350 | ||||||||
\(25\) | 4.89898 | + | 1.00000i | 0.979796 | + | 0.200000i | ||||
\(26\) | 0.898979 | 0.176304 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.34242 | −1.54915 | −0.774574 | − | 0.632483i | \(-0.782036\pi\) | ||||
−0.774574 | + | 0.632483i | \(0.782036\pi\) | |||||||
\(30\) | 3.14626 | + | 0.317837i | 0.574427 | + | 0.0580289i | ||||
\(31\) | −7.89898 | −1.41870 | −0.709349 | − | 0.704857i | \(-0.751011\pi\) | ||||
−0.709349 | + | 0.704857i | \(0.751011\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.89898 | −1.18317 | ||||||||
\(35\) | 0.389270 | − | 3.85337i | 0.0657986 | − | 0.651339i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.89898i | 0.969786i | 0.874573 | + | 0.484893i | \(0.161142\pi\) | ||||
−0.874573 | + | 0.484893i | \(0.838858\pi\) | |||||||
\(38\) | 2.44949i | 0.397360i | ||||||||
\(39\) | 0.635674 | 0.101789 | ||||||||
\(40\) | −0.635674 | + | 6.29253i | −0.100509 | + | 0.994936i | ||||
\(41\) | −9.12096 | −1.42445 | −0.712227 | − | 0.701949i | \(-0.752313\pi\) | ||||
−0.712227 | + | 0.701949i | \(0.752313\pi\) | |||||||
\(42\) | − | 2.44949i | − | 0.377964i | ||||||
\(43\) | 5.65685i | 0.862662i | 0.902194 | + | 0.431331i | \(0.141956\pi\) | ||||
−0.902194 | + | 0.431331i | \(0.858044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.22474 | + | 0.224745i | 0.331645 | + | 0.0335030i | ||||
\(46\) | −2.82843 | −0.417029 | ||||||||
\(47\) | 7.34847i | 1.07188i | 0.844255 | + | 0.535942i | \(0.180044\pi\) | ||||
−0.844255 | + | 0.535942i | \(0.819956\pi\) | |||||||
\(48\) | 4.00000i | 0.577350i | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 1.41421 | − | 6.92820i | 0.200000 | − | 0.979796i | ||||
\(51\) | −4.87832 | −0.683101 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000i | 1.37361i | 0.726844 | + | 0.686803i | \(0.240986\pi\) | ||||
−0.726844 | + | 0.686803i | \(0.759014\pi\) | |||||||
\(54\) | 1.41421 | 0.192450 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.89898 | 0.654654 | ||||||||
\(57\) | 1.73205i | 0.229416i | ||||||||
\(58\) | 11.7980i | 1.54915i | ||||||||
\(59\) | 12.2474 | 1.59448 | 0.797241 | − | 0.603661i | \(-0.206292\pi\) | ||||
0.797241 | + | 0.603661i | \(0.206292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.28913 | −0.421130 | −0.210565 | − | 0.977580i | \(-0.567530\pi\) | ||||
−0.210565 | + | 0.977580i | \(0.567530\pi\) | |||||||
\(62\) | 11.1708i | 1.41870i | ||||||||
\(63\) | − | 1.73205i | − | 0.218218i | ||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0.142865 | − | 1.41421i | 0.0177202 | − | 0.175412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.10102i | − | 0.501019i | −0.968114 | − | 0.250510i | \(-0.919402\pi\) | ||
0.968114 | − | 0.250510i | \(-0.0805982\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | −5.44949 | − | 0.550510i | −0.651339 | − | 0.0657986i | ||||
\(71\) | −3.55051 | −0.421368 | −0.210684 | − | 0.977554i | \(-0.567569\pi\) | ||||
−0.210684 | + | 0.977554i | \(0.567569\pi\) | |||||||
\(72\) | 2.82843i | 0.333333i | ||||||||
\(73\) | − | 3.28913i | − | 0.384963i | −0.981301 | − | 0.192482i | \(-0.938346\pi\) | ||
0.981301 | − | 0.192482i | \(-0.0616536\pi\) | |||||||
\(74\) | 8.34242 | 0.969786 | ||||||||
\(75\) | 1.00000 | − | 4.89898i | 0.115470 | − | 0.565685i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 0.898979i | − | 0.101789i | ||||||
\(79\) | −6.75323 | −0.759798 | −0.379899 | − | 0.925028i | \(-0.624041\pi\) | ||||
−0.379899 | + | 0.925028i | \(0.624041\pi\) | |||||||
\(80\) | 8.89898 | + | 0.898979i | 0.994936 | + | 0.100509i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.8990i | 1.42445i | ||||||||
\(83\) | − | 12.7279i | − | 1.39707i | −0.715575 | − | 0.698535i | \(-0.753835\pi\) | ||
0.715575 | − | 0.698535i | \(-0.246165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.09638 | + | 10.8530i | −0.118919 | + | 1.17717i | ||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 8.34242i | 0.894401i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.34847 | −0.142937 | −0.0714687 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714687 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(90\) | 0.317837 | − | 3.14626i | 0.0335030 | − | 0.331645i | ||||
\(91\) | −1.10102 | −0.115418 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.89898i | 0.819086i | ||||||||
\(94\) | 10.3923 | 1.07188 | ||||||||
\(95\) | 3.85337 | + | 0.389270i | 0.395348 | + | 0.0399382i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.00000i | − | 0.507673i | −0.967247 | − | 0.253837i | \(-0.918307\pi\) | ||
0.967247 | − | 0.253837i | \(-0.0816925\pi\) | |||||||
\(98\) | − | 5.65685i | − | 0.571429i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.142865 | 0.0142156 | 0.00710778 | − | 0.999975i | \(-0.497738\pi\) | ||||
0.00710778 | + | 0.999975i | \(0.497738\pi\) | |||||||
\(102\) | 6.89898i | 0.683101i | ||||||||
\(103\) | 17.8990i | 1.76364i | 0.471587 | + | 0.881819i | \(0.343681\pi\) | ||||
−0.471587 | + | 0.881819i | \(0.656319\pi\) | |||||||
\(104\) | 1.79796 | 0.176304 | ||||||||
\(105\) | −3.85337 | − | 0.389270i | −0.376051 | − | 0.0379888i | ||||
\(106\) | 14.1421 | 1.37361 | ||||||||
\(107\) | 8.34242i | 0.806492i | 0.915092 | + | 0.403246i | \(0.132118\pi\) | ||||
−0.915092 | + | 0.403246i | \(0.867882\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3383 | −1.85227 | −0.926136 | − | 0.377190i | \(-0.876890\pi\) | ||||
−0.926136 | + | 0.377190i | \(0.876890\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.89898 | 0.559906 | ||||||||
\(112\) | − | 6.92820i | − | 0.654654i | ||||||
\(113\) | 13.5505i | 1.27472i | 0.770564 | + | 0.637362i | \(0.219975\pi\) | ||||
−0.770564 | + | 0.637362i | \(0.780025\pi\) | |||||||
\(114\) | 2.44949 | 0.229416 | ||||||||
\(115\) | −0.449490 | + | 4.44949i | −0.0419151 | + | 0.414917i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.635674i | − | 0.0587681i | ||||||
\(118\) | − | 17.3205i | − | 1.59448i | ||||||
\(119\) | 8.44949 | 0.774563 | ||||||||
\(120\) | 6.29253 | + | 0.635674i | 0.574427 | + | 0.0580289i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.65153i | 0.421130i | ||||||||
\(123\) | 9.12096i | 0.822409i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6742 | − | 3.32577i | −0.954733 | − | 0.297465i | ||||
\(126\) | −2.44949 | −0.218218 | ||||||||
\(127\) | − | 18.7026i | − | 1.65959i | −0.558069 | − | 0.829794i | \(-0.688458\pi\) | ||
0.558069 | − | 0.829794i | \(-0.311542\pi\) | |||||||
\(128\) | 11.3137i | 1.00000i | ||||||||
\(129\) | 5.65685 | 0.498058 | ||||||||
\(130\) | −2.00000 | − | 0.202041i | −0.175412 | − | 0.0177202i | ||||
\(131\) | 10.6780 | 0.932944 | 0.466472 | − | 0.884536i | \(-0.345525\pi\) | ||||
0.466472 | + | 0.884536i | \(0.345525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.00000i | − | 0.260133i | ||||||
\(134\) | −5.79972 | −0.501019 | ||||||||
\(135\) | 0.224745 | − | 2.22474i | 0.0193430 | − | 0.191476i | ||||
\(136\) | −13.7980 | −1.18317 | ||||||||
\(137\) | − | 21.7980i | − | 1.86233i | −0.364604 | − | 0.931163i | \(-0.618796\pi\) | ||
0.364604 | − | 0.931163i | \(-0.381204\pi\) | |||||||
\(138\) | 2.82843i | 0.240772i | ||||||||
\(139\) | 12.5851 | 1.06745 | 0.533725 | − | 0.845658i | \(-0.320792\pi\) | ||||
0.533725 | + | 0.845658i | \(0.320792\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.34847 | 0.618853 | ||||||||
\(142\) | 5.02118i | 0.421368i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 18.5597 | + | 1.87492i | 1.54130 | + | 0.155703i | ||||
\(146\) | −4.65153 | −0.384963 | ||||||||
\(147\) | − | 4.00000i | − | 0.329914i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.8065 | −0.967228 | −0.483614 | − | 0.875281i | \(-0.660676\pi\) | ||||
−0.483614 | + | 0.875281i | \(0.660676\pi\) | |||||||
\(150\) | −6.92820 | − | 1.41421i | −0.565685 | − | 0.115470i | ||||
\(151\) | −16.0492 | −1.30606 | −0.653031 | − | 0.757331i | \(-0.726503\pi\) | ||||
−0.653031 | + | 0.757331i | \(0.726503\pi\) | |||||||
\(152\) | 4.89898i | 0.397360i | ||||||||
\(153\) | 4.87832i | 0.394388i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.5732 | + | 1.77526i | 1.41151 | + | 0.142592i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.5959i | − | 1.48412i | −0.670336 | − | 0.742058i | \(-0.733850\pi\) | ||
0.670336 | − | 0.742058i | \(-0.266150\pi\) | |||||||
\(158\) | 9.55051i | 0.759798i | ||||||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | 0.273009 | ||||||||
\(162\) | − | 1.41421i | − | 0.111111i | ||||||
\(163\) | − | 1.00000i | − | 0.0783260i | −0.999233 | − | 0.0391630i | \(-0.987531\pi\) | ||
0.999233 | − | 0.0391630i | \(-0.0124692\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.0000 | −1.39707 | ||||||||
\(167\) | − | 13.2207i | − | 1.02305i | −0.859268 | − | 0.511525i | \(-0.829081\pi\) | ||
0.859268 | − | 0.511525i | \(-0.170919\pi\) | |||||||
\(168\) | − | 4.89898i | − | 0.377964i | ||||||
\(169\) | 12.5959 | 0.968917 | ||||||||
\(170\) | 15.3485 | + | 1.55051i | 1.17717 | + | 0.118919i | ||||
\(171\) | 1.73205 | 0.132453 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 14.6349i | − | 1.11267i | −0.830957 | − | 0.556337i | \(-0.812206\pi\) | ||
0.830957 | − | 0.556337i | \(-0.187794\pi\) | |||||||
\(174\) | 11.7980 | 0.894401 | ||||||||
\(175\) | −1.73205 | + | 8.48528i | −0.130931 | + | 0.641427i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.2474i | − | 0.920575i | ||||||
\(178\) | 1.90702i | 0.142937i | ||||||||
\(179\) | −26.0454 | −1.94673 | −0.973363 | − | 0.229271i | \(-0.926366\pi\) | ||||
−0.973363 | + | 0.229271i | \(0.926366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 1.55708i | 0.115418i | ||||||||
\(183\) | 3.28913i | 0.243139i | ||||||||
\(184\) | −5.65685 | −0.417029 | ||||||||
\(185\) | 1.32577 | − | 13.1237i | 0.0974722 | − | 0.964875i | ||||
\(186\) | 11.1708 | 0.819086 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.73205 | −0.125988 | ||||||||
\(190\) | 0.550510 | − | 5.44949i | 0.0399382 | − | 0.395348i | ||||
\(191\) | −5.79796 | −0.419526 | −0.209763 | − | 0.977752i | \(-0.567269\pi\) | ||||
−0.209763 | + | 0.977752i | \(0.567269\pi\) | |||||||
\(192\) | 8.00000i | 0.577350i | ||||||||
\(193\) | 17.7812i | 1.27992i | 0.768408 | + | 0.639960i | \(0.221049\pi\) | ||||
−0.768408 | + | 0.639960i | \(0.778951\pi\) | |||||||
\(194\) | −7.07107 | −0.507673 | ||||||||
\(195\) | −1.41421 | − | 0.142865i | −0.101274 | − | 0.0102307i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.82843i | − | 0.201517i | −0.994911 | − | 0.100759i | \(-0.967873\pi\) | ||
0.994911 | − | 0.100759i | \(-0.0321270\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5959 | −1.17645 | −0.588227 | − | 0.808696i | \(-0.700174\pi\) | ||||
−0.588227 | + | 0.808696i | \(0.700174\pi\) | |||||||
\(200\) | 2.82843 | − | 13.8564i | 0.200000 | − | 0.979796i | ||||
\(201\) | −4.10102 | −0.289264 | ||||||||
\(202\) | − | 0.202041i | − | 0.0142156i | ||||||
\(203\) | − | 14.4495i | − | 1.01416i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.2918 | + | 2.04989i | 1.41724 | + | 0.143170i | ||||
\(206\) | 25.3130 | 1.76364 | ||||||||
\(207\) | 2.00000i | 0.139010i | ||||||||
\(208\) | − | 2.54270i | − | 0.176304i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.550510 | + | 5.44949i | −0.0379888 | + | 0.376051i | ||||
\(211\) | 12.4101 | 0.854345 | 0.427173 | − | 0.904170i | \(-0.359510\pi\) | ||||
0.427173 | + | 0.904170i | \(0.359510\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.55051i | 0.243277i | ||||||||
\(214\) | 11.7980 | 0.806492 | ||||||||
\(215\) | 1.27135 | − | 12.5851i | 0.0867053 | − | 0.858294i | ||||
\(216\) | 2.82843 | 0.192450 | ||||||||
\(217\) | − | 13.6814i | − | 0.928756i | ||||||
\(218\) | 27.3485i | 1.85227i | ||||||||
\(219\) | −3.28913 | −0.222259 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.10102 | 0.208597 | ||||||||
\(222\) | − | 8.34242i | − | 0.559906i | ||||||
\(223\) | 11.0000i | 0.736614i | 0.929704 | + | 0.368307i | \(0.120063\pi\) | ||||
−0.929704 | + | 0.368307i | \(0.879937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.89898 | − | 1.00000i | −0.326599 | − | 0.0666667i | ||||
\(226\) | 19.1633 | 1.27472 | ||||||||
\(227\) | − | 4.09978i | − | 0.272112i | −0.990701 | − | 0.136056i | \(-0.956557\pi\) | ||
0.990701 | − | 0.136056i | \(-0.0434427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.10102 | 0.204921 | 0.102461 | − | 0.994737i | \(-0.467328\pi\) | ||||
0.102461 | + | 0.994737i | \(0.467328\pi\) | |||||||
\(230\) | 6.29253 | + | 0.635674i | 0.414917 | + | 0.0419151i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23.5959i | 1.54915i | ||||||||
\(233\) | 23.7559i | 1.55630i | 0.628078 | + | 0.778150i | \(0.283842\pi\) | ||||
−0.628078 | + | 0.778150i | \(0.716158\pi\) | |||||||
\(234\) | −0.898979 | −0.0587681 | ||||||||
\(235\) | 1.65153 | − | 16.3485i | 0.107734 | − | 1.06646i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.75323i | 0.438669i | ||||||||
\(238\) | − | 11.9494i | − | 0.774563i | ||||||
\(239\) | 9.89949 | 0.640345 | 0.320173 | − | 0.947359i | \(-0.396259\pi\) | ||||
0.320173 | + | 0.947359i | \(0.396259\pi\) | |||||||
\(240\) | 0.898979 | − | 8.89898i | 0.0580289 | − | 0.574427i | ||||
\(241\) | 0.635674 | 0.0409474 | 0.0204737 | − | 0.999790i | \(-0.493483\pi\) | ||||
0.0204737 | + | 0.999790i | \(0.493483\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.89898 | − | 0.898979i | −0.568535 | − | 0.0574337i | ||||
\(246\) | 12.8990 | 0.822409 | ||||||||
\(247\) | − | 1.10102i | − | 0.0700563i | ||||||
\(248\) | 22.3417i | 1.41870i | ||||||||
\(249\) | −12.7279 | −0.806599 | ||||||||
\(250\) | −4.70334 | + | 15.0956i | −0.297465 | + | 0.954733i | ||||
\(251\) | 2.00000 | 0.126239 | 0.0631194 | − | 0.998006i | \(-0.479895\pi\) | ||||
0.0631194 | + | 0.998006i | \(0.479895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −26.4495 | −1.65959 | ||||||||
\(255\) | 10.8530 | + | 1.09638i | 0.679642 | + | 0.0686577i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.69694i | − | 0.542500i | −0.962509 | − | 0.271250i | \(-0.912563\pi\) | ||
0.962509 | − | 0.271250i | \(-0.0874370\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | −10.2173 | −0.634874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.34242 | 0.516383 | ||||||||
\(262\) | − | 15.1010i | − | 0.932944i | ||||||
\(263\) | − | 16.0492i | − | 0.989634i | −0.868997 | − | 0.494817i | \(-0.835235\pi\) | ||
0.868997 | − | 0.494817i | \(-0.164765\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.24745 | − | 22.2474i | 0.138060 | − | 1.36665i | ||||
\(266\) | −4.24264 | −0.260133 | ||||||||
\(267\) | 1.34847i | 0.0825250i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4495 | −0.637117 | −0.318558 | − | 0.947903i | \(-0.603199\pi\) | ||||
−0.318558 | + | 0.947903i | \(0.603199\pi\) | |||||||
\(270\) | −3.14626 | − | 0.317837i | −0.191476 | − | 0.0193430i | ||||
\(271\) | 8.19955 | 0.498087 | 0.249044 | − | 0.968492i | \(-0.419884\pi\) | ||||
0.249044 | + | 0.968492i | \(0.419884\pi\) | |||||||
\(272\) | 19.5133i | 1.18317i | ||||||||
\(273\) | 1.10102i | 0.0666368i | ||||||||
\(274\) | −30.8270 | −1.86233 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1667i | 1.33187i | 0.746010 | + | 0.665934i | \(0.231967\pi\) | ||||
−0.746010 | + | 0.665934i | \(0.768033\pi\) | |||||||
\(278\) | − | 17.7980i | − | 1.06745i | ||||||
\(279\) | 7.89898 | 0.472900 | ||||||||
\(280\) | −10.8990 | − | 1.10102i | −0.651339 | − | 0.0657986i | ||||
\(281\) | 2.04989 | 0.122286 | 0.0611430 | − | 0.998129i | \(-0.480525\pi\) | ||||
0.0611430 | + | 0.998129i | \(0.480525\pi\) | |||||||
\(282\) | − | 10.3923i | − | 0.618853i | ||||||
\(283\) | 11.1387i | 0.662129i | 0.943608 | + | 0.331065i | \(0.107408\pi\) | ||||
−0.943608 | + | 0.331065i | \(0.892592\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.389270 | − | 3.85337i | 0.0230583 | − | 0.228254i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 15.7980i | − | 0.932524i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.79796 | −0.399880 | ||||||||
\(290\) | 2.65153 | − | 26.2474i | 0.155703 | − | 1.54130i | ||||
\(291\) | −5.00000 | −0.293105 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.8345i | − | 1.33401i | −0.745055 | − | 0.667003i | \(-0.767577\pi\) | ||
0.745055 | − | 0.667003i | \(-0.232423\pi\) | |||||||
\(294\) | −5.65685 | −0.329914 | ||||||||
\(295\) | −27.2474 | − | 2.75255i | −1.58641 | − | 0.160260i | ||||
\(296\) | 16.6848 | 0.969786 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.6969i | 0.967228i | ||||||||
\(299\) | 1.27135 | 0.0735240 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.79796 | −0.564745 | ||||||||
\(302\) | 22.6969i | 1.30606i | ||||||||
\(303\) | − | 0.142865i | − | 0.00820736i | ||||||
\(304\) | 6.92820 | 0.397360 | ||||||||
\(305\) | 7.31747 | + | 0.739215i | 0.418997 | + | 0.0423273i | ||||
\(306\) | 6.89898 | 0.394388 | ||||||||
\(307\) | 1.44632i | 0.0825459i | 0.999148 | + | 0.0412730i | \(0.0131413\pi\) | ||||
−0.999148 | + | 0.0412730i | \(0.986859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.8990 | 1.01824 | ||||||||
\(310\) | 2.51059 | − | 24.8523i | 0.142592 | − | 1.41151i | ||||
\(311\) | 5.75255 | 0.326197 | 0.163099 | − | 0.986610i | \(-0.447851\pi\) | ||||
0.163099 | + | 0.986610i | \(0.447851\pi\) | |||||||
\(312\) | − | 1.79796i | − | 0.101789i | ||||||
\(313\) | − | 22.6969i | − | 1.28291i | −0.767162 | − | 0.641453i | \(-0.778332\pi\) | ||
0.767162 | − | 0.641453i | \(-0.221668\pi\) | |||||||
\(314\) | −26.2986 | −1.48412 | ||||||||
\(315\) | −0.389270 | + | 3.85337i | −0.0219329 | + | 0.217113i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.44949i | − | 0.474571i | −0.971440 | − | 0.237285i | \(-0.923742\pi\) | ||
0.971440 | − | 0.237285i | \(-0.0762576\pi\) | |||||||
\(318\) | − | 14.1421i | − | 0.793052i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 17.7980 | + | 1.79796i | 0.994936 | + | 0.100509i | ||||
\(321\) | 8.34242 | 0.465628 | ||||||||
\(322\) | − | 4.89898i | − | 0.273009i | ||||||
\(323\) | 8.44949i | 0.470142i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.635674 | + | 3.11416i | −0.0352609 | + | 0.172742i | ||||
\(326\) | −1.41421 | −0.0783260 | ||||||||
\(327\) | 19.3383i | 1.06941i | ||||||||
\(328\) | 25.7980i | 1.42445i | ||||||||
\(329\) | −12.7279 | −0.701713 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.5959 | −1.02212 | −0.511062 | − | 0.859544i | \(-0.670748\pi\) | ||||
−0.511062 | + | 0.859544i | \(0.670748\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.89898i | − | 0.323262i | ||||||
\(334\) | −18.6969 | −1.02305 | ||||||||
\(335\) | −0.921683 | + | 9.12372i | −0.0503569 | + | 0.498482i | ||||
\(336\) | −6.92820 | −0.377964 | ||||||||
\(337\) | − | 11.1387i | − | 0.606766i | −0.952869 | − | 0.303383i | \(-0.901884\pi\) | ||
0.952869 | − | 0.303383i | \(-0.0981161\pi\) | |||||||
\(338\) | − | 17.8133i | − | 0.968917i | ||||||
\(339\) | 13.5505 | 0.735963 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 2.44949i | − | 0.132453i | ||||||
\(343\) | 19.0526i | 1.02874i | ||||||||
\(344\) | 16.0000 | 0.862662 | ||||||||
\(345\) | 4.44949 | + | 0.449490i | 0.239552 | + | 0.0241997i | ||||
\(346\) | −20.6969 | −1.11267 | ||||||||
\(347\) | 13.2207i | 0.709726i | 0.934918 | + | 0.354863i | \(0.115473\pi\) | ||||
−0.934918 | + | 0.354863i | \(0.884527\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.19615 | −0.278144 | −0.139072 | − | 0.990282i | \(-0.544412\pi\) | ||||
−0.139072 | + | 0.990282i | \(0.544412\pi\) | |||||||
\(350\) | 12.0000 | + | 2.44949i | 0.641427 | + | 0.130931i | ||||
\(351\) | −0.635674 | −0.0339298 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.55051i | 0.401873i | 0.979604 | + | 0.200937i | \(0.0643985\pi\) | ||||
−0.979604 | + | 0.200937i | \(0.935601\pi\) | |||||||
\(354\) | −17.3205 | −0.920575 | ||||||||
\(355\) | 7.89898 | + | 0.797959i | 0.419234 | + | 0.0423513i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 8.44949i | − | 0.447194i | ||||||
\(358\) | 36.8338i | 1.94673i | ||||||||
\(359\) | −25.9487 | −1.36952 | −0.684759 | − | 0.728770i | \(-0.740092\pi\) | ||||
−0.684759 | + | 0.728770i | \(0.740092\pi\) | |||||||
\(360\) | 0.635674 | − | 6.29253i | 0.0335030 | − | 0.331645i | ||||
\(361\) | −16.0000 | −0.842105 | ||||||||
\(362\) | − | 7.07107i | − | 0.371647i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.739215 | + | 7.31747i | −0.0386923 | + | 0.383014i | ||||
\(366\) | 4.65153 | 0.243139 | ||||||||
\(367\) | − | 35.7980i | − | 1.86864i | −0.356438 | − | 0.934319i | \(-0.616009\pi\) | ||
0.356438 | − | 0.934319i | \(-0.383991\pi\) | |||||||
\(368\) | 8.00000i | 0.417029i | ||||||||
\(369\) | 9.12096 | 0.474818 | ||||||||
\(370\) | −18.5597 | − | 1.87492i | −0.964875 | − | 0.0974722i | ||||
\(371\) | −17.3205 | −0.899236 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.9022i | − | 1.39294i | −0.717585 | − | 0.696471i | \(-0.754753\pi\) | ||
0.717585 | − | 0.696471i | \(-0.245247\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.32577 | + | 10.6742i | −0.171742 | + | 0.551215i | ||||
\(376\) | 20.7846 | 1.07188 | ||||||||
\(377\) | − | 5.30306i | − | 0.273122i | ||||||
\(378\) | 2.44949i | 0.125988i | ||||||||
\(379\) | −1.79796 | −0.0923549 | −0.0461775 | − | 0.998933i | \(-0.514704\pi\) | ||||
−0.0461775 | + | 0.998933i | \(0.514704\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.7026 | −0.958164 | ||||||||
\(382\) | 8.19955i | 0.419526i | ||||||||
\(383\) | − | 22.4949i | − | 1.14944i | −0.818352 | − | 0.574718i | \(-0.805112\pi\) | ||
0.818352 | − | 0.574718i | \(-0.194888\pi\) | |||||||
\(384\) | 11.3137 | 0.577350 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.1464 | 1.27992 | ||||||||
\(387\) | − | 5.65685i | − | 0.287554i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.8990 | 0.552600 | 0.276300 | − | 0.961071i | \(-0.410892\pi\) | ||||
0.276300 | + | 0.961071i | \(0.410892\pi\) | |||||||
\(390\) | −0.202041 | + | 2.00000i | −0.0102307 | + | 0.101274i | ||||
\(391\) | −9.75663 | −0.493414 | ||||||||
\(392\) | − | 11.3137i | − | 0.571429i | ||||||
\(393\) | − | 10.6780i | − | 0.538636i | ||||||
\(394\) | −4.00000 | −0.201517 | ||||||||
\(395\) | 15.0242 | + | 1.51775i | 0.755950 | + | 0.0763665i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.3939i | 1.22429i | 0.790744 | + | 0.612147i | \(0.209694\pi\) | ||||
−0.790744 | + | 0.612147i | \(0.790306\pi\) | |||||||
\(398\) | 23.4702i | 1.17645i | ||||||||
\(399\) | −3.00000 | −0.150188 | ||||||||
\(400\) | −19.5959 | − | 4.00000i | −0.979796 | − | 0.200000i | ||||
\(401\) | 10.6515 | 0.531912 | 0.265956 | − | 0.963985i | \(-0.414312\pi\) | ||||
0.265956 | + | 0.963985i | \(0.414312\pi\) | |||||||
\(402\) | 5.79972i | 0.289264i | ||||||||
\(403\) | − | 5.02118i | − | 0.250123i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.22474 | − | 0.224745i | −0.110548 | − | 0.0111677i | ||||
\(406\) | −20.4347 | −1.01416 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 13.7980i | 0.683101i | ||||||||
\(409\) | −28.8092 | −1.42452 | −0.712261 | − | 0.701914i | \(-0.752329\pi\) | ||||
−0.712261 | + | 0.701914i | \(0.752329\pi\) | |||||||
\(410\) | 2.89898 | − | 28.6969i | 0.143170 | − | 1.41724i | ||||
\(411\) | −21.7980 | −1.07521 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.2132i | 1.04383i | ||||||||
\(414\) | 2.82843 | 0.139010 | ||||||||
\(415\) | −2.86054 | + | 28.3164i | −0.140418 | + | 1.39000i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12.5851i | − | 0.616293i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.55051 | −0.466573 | −0.233286 | − | 0.972408i | \(-0.574948\pi\) | ||||
−0.233286 | + | 0.972408i | \(0.574948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.6969 | 1.69103 | 0.845513 | − | 0.533955i | \(-0.179295\pi\) | ||||
0.845513 | + | 0.533955i | \(0.179295\pi\) | |||||||
\(422\) | − | 17.5505i | − | 0.854345i | ||||||
\(423\) | − | 7.34847i | − | 0.357295i | ||||||
\(424\) | 28.2843 | 1.37361 | ||||||||
\(425\) | 4.87832 | − | 23.8988i | 0.236633 | − | 1.15926i | ||||
\(426\) | 5.02118 | 0.243277 | ||||||||
\(427\) | − | 5.69694i | − | 0.275694i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.7980 | − | 1.79796i | −0.858294 | − | 0.0867053i | ||||
\(431\) | −22.9774 | −1.10678 | −0.553390 | − | 0.832922i | \(-0.686666\pi\) | ||||
−0.553390 | + | 0.832922i | \(0.686666\pi\) | |||||||
\(432\) | − | 4.00000i | − | 0.192450i | ||||||
\(433\) | 19.0000i | 0.913082i | 0.889702 | + | 0.456541i | \(0.150912\pi\) | ||||
−0.889702 | + | 0.456541i | \(0.849088\pi\) | |||||||
\(434\) | −19.3485 | −0.928756 | ||||||||
\(435\) | 1.87492 | − | 18.5597i | 0.0898953 | − | 0.889872i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.46410i | 0.165710i | ||||||||
\(438\) | 4.65153i | 0.222259i | ||||||||
\(439\) | 21.2453 | 1.01398 | 0.506992 | − | 0.861951i | \(-0.330757\pi\) | ||||
0.506992 | + | 0.861951i | \(0.330757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.00000 | −0.190476 | ||||||||
\(442\) | − | 4.38551i | − | 0.208597i | ||||||
\(443\) | 1.34847i | 0.0640677i | 0.999487 | + | 0.0320339i | \(0.0101984\pi\) | ||||
−0.999487 | + | 0.0320339i | \(0.989802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | + | 0.303062i | 0.142214 | + | 0.0143665i | ||||
\(446\) | 15.5563 | 0.736614 | ||||||||
\(447\) | 11.8065i | 0.558429i | ||||||||
\(448\) | − | 13.8564i | − | 0.654654i | ||||||
\(449\) | −31.5505 | −1.48896 | −0.744480 | − | 0.667644i | \(-0.767303\pi\) | ||||
−0.744480 | + | 0.667644i | \(0.767303\pi\) | |||||||
\(450\) | −1.41421 | + | 6.92820i | −0.0666667 | + | 0.326599i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0492i | 0.754055i | ||||||||
\(454\) | −5.79796 | −0.272112 | ||||||||
\(455\) | 2.44949 | + | 0.247449i | 0.114834 | + | 0.0116006i | ||||
\(456\) | 4.89898 | 0.229416 | ||||||||
\(457\) | − | 23.8988i | − | 1.11794i | −0.829189 | − | 0.558969i | \(-0.811197\pi\) | ||
0.829189 | − | 0.558969i | \(-0.188803\pi\) | |||||||
\(458\) | − | 4.38551i | − | 0.204921i | ||||||
\(459\) | 4.87832 | 0.227700 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.57826 | −0.306380 | −0.153190 | − | 0.988197i | \(-0.548955\pi\) | ||||
−0.153190 | + | 0.988197i | \(0.548955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.6969i | − | 1.70545i | −0.522359 | − | 0.852726i | \(-0.674948\pi\) | ||
0.522359 | − | 0.852726i | \(-0.325052\pi\) | |||||||
\(464\) | 33.3697 | 1.54915 | ||||||||
\(465\) | 1.77526 | − | 17.5732i | 0.0823255 | − | 0.814938i | ||||
\(466\) | 33.5959 | 1.55630 | ||||||||
\(467\) | − | 10.2474i | − | 0.474195i | −0.971486 | − | 0.237098i | \(-0.923804\pi\) | ||
0.971486 | − | 0.237098i | \(-0.0761961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.10318 | 0.327994 | ||||||||
\(470\) | −23.1202 | − | 2.33562i | −1.06646 | − | 0.107734i | ||||
\(471\) | −18.5959 | −0.856855 | ||||||||
\(472\) | − | 34.6410i | − | 1.59448i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.55051 | 0.438669 | ||||||||
\(475\) | −8.48528 | − | 1.73205i | −0.389331 | − | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 10.0000i | − | 0.457869i | ||||||
\(478\) | − | 14.0000i | − | 0.640345i | ||||||
\(479\) | 8.34242 | 0.381175 | 0.190587 | − | 0.981670i | \(-0.438961\pi\) | ||||
0.190587 | + | 0.981670i | \(0.438961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.74983 | −0.170978 | ||||||||
\(482\) | − | 0.898979i | − | 0.0409474i | ||||||
\(483\) | − | 3.46410i | − | 0.157622i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.12372 | + | 11.1237i | −0.0510257 | + | 0.505102i | ||||
\(486\) | −1.41421 | −0.0641500 | ||||||||
\(487\) | − | 38.4949i | − | 1.74437i | −0.489176 | − | 0.872185i | \(-0.662702\pi\) | ||
0.489176 | − | 0.872185i | \(-0.337298\pi\) | |||||||
\(488\) | 9.30306i | 0.421130i | ||||||||
\(489\) | −1.00000 | −0.0452216 | ||||||||
\(490\) | −1.27135 | + | 12.5851i | −0.0574337 | + | 0.568535i | ||||
\(491\) | −30.1913 | −1.36251 | −0.681257 | − | 0.732044i | \(-0.738566\pi\) | ||||
−0.681257 | + | 0.732044i | \(0.738566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.6969i | 1.83290i | ||||||||
\(494\) | −1.55708 | −0.0700563 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.5959 | 1.41870 | ||||||||
\(497\) | − | 6.14966i | − | 0.275850i | ||||||
\(498\) | 18.0000i | 0.806599i | ||||||||
\(499\) | 10.3031 | 0.461228 | 0.230614 | − | 0.973045i | \(-0.425926\pi\) | ||||
0.230614 | + | 0.973045i | \(0.425926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.2207 | −0.590659 | ||||||||
\(502\) | − | 2.82843i | − | 0.126239i | ||||||
\(503\) | − | 15.4135i | − | 0.687253i | −0.939106 | − | 0.343627i | \(-0.888345\pi\) | ||
0.939106 | − | 0.343627i | \(-0.111655\pi\) | |||||||
\(504\) | −4.89898 | −0.218218 | ||||||||
\(505\) | −0.317837 | − | 0.0321081i | −0.0141436 | − | 0.00142879i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.5959i | − | 0.559404i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.1464 | 0.582705 | 0.291353 | − | 0.956616i | \(-0.405895\pi\) | ||||
0.291353 | + | 0.956616i | \(0.405895\pi\) | |||||||
\(510\) | 1.55051 | − | 15.3485i | 0.0686577 | − | 0.679642i | ||||
\(511\) | 5.69694 | 0.252018 | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | − | 1.73205i | − | 0.0764719i | ||||||
\(514\) | −12.2993 | −0.542500 | ||||||||
\(515\) | 4.02270 | − | 39.8207i | 0.177262 | − | 1.75471i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 14.4495i | 0.634874i | ||||||||
\(519\) | −14.6349 | −0.642403 | ||||||||
\(520\) | −4.00000 | − | 0.404082i | −0.175412 | − | 0.0177202i | ||||
\(521\) | −9.14643 | −0.400712 | −0.200356 | − | 0.979723i | \(-0.564210\pi\) | ||||
−0.200356 | + | 0.979723i | \(0.564210\pi\) | |||||||
\(522\) | − | 11.7980i | − | 0.516383i | ||||||
\(523\) | − | 0.810647i | − | 0.0354471i | −0.999843 | − | 0.0177236i | \(-0.994358\pi\) | ||
0.999843 | − | 0.0177236i | \(-0.00564188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.48528 | + | 1.73205i | 0.370328 | + | 0.0755929i | ||||
\(526\) | −22.6969 | −0.989634 | ||||||||
\(527\) | 38.5337i | 1.67855i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | −31.4626 | − | 3.17837i | −1.36665 | − | 0.138060i | ||||
\(531\) | −12.2474 | −0.531494 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.79796i | − | 0.251137i | ||||||
\(534\) | 1.90702 | 0.0825250 | ||||||||
\(535\) | 1.87492 | − | 18.5597i | 0.0810597 | − | 0.802408i | ||||
\(536\) | −11.5994 | −0.501019 | ||||||||
\(537\) | 26.0454i | 1.12394i | ||||||||
\(538\) | 14.7778i | 0.637117i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.1489 | −0.866270 | −0.433135 | − | 0.901329i | \(-0.642593\pi\) | ||||
−0.433135 | + | 0.901329i | \(0.642593\pi\) | |||||||
\(542\) | − | 11.5959i | − | 0.498087i | ||||||
\(543\) | − | 5.00000i | − | 0.214571i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 43.0228 | + | 4.34618i | 1.84289 | + | 0.186170i | ||||
\(546\) | 1.55708 | 0.0666368 | ||||||||
\(547\) | − | 29.5556i | − | 1.26371i | −0.775088 | − | 0.631854i | \(-0.782294\pi\) | ||
0.775088 | − | 0.631854i | \(-0.217706\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.28913 | 0.140377 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4495 | 0.615569 | ||||||||
\(552\) | 5.65685i | 0.240772i | ||||||||
\(553\) | − | 11.6969i | − | 0.497404i | ||||||
\(554\) | 31.3485 | 1.33187 | ||||||||
\(555\) | −13.1237 | − | 1.32577i | −0.557071 | − | 0.0562756i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.70674i | − | 0.326545i | −0.986581 | − | 0.163273i | \(-0.947795\pi\) | ||
0.986581 | − | 0.163273i | \(-0.0522050\pi\) | |||||||
\(558\) | − | 11.1708i | − | 0.472900i | ||||||
\(559\) | −3.59592 | −0.152091 | ||||||||
\(560\) | −1.55708 | + | 15.4135i | −0.0657986 | + | 0.651339i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 2.89898i | − | 0.122286i | ||||||
\(563\) | 2.54270i | 0.107162i | 0.998564 | + | 0.0535810i | \(0.0170635\pi\) | ||||
−0.998564 | + | 0.0535810i | \(0.982936\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.04541 | − | 30.1464i | 0.128121 | − | 1.26827i | ||||
\(566\) | 15.7526 | 0.662129 | ||||||||
\(567\) | 1.73205i | 0.0727393i | ||||||||
\(568\) | 10.0424i | 0.421368i | ||||||||
\(569\) | 17.9562 | 0.752762 | 0.376381 | − | 0.926465i | \(-0.377168\pi\) | ||||
0.376381 | + | 0.926465i | \(0.377168\pi\) | |||||||
\(570\) | −5.44949 | − | 0.550510i | −0.228254 | − | 0.0230583i | ||||
\(571\) | −15.3027 | −0.640399 | −0.320200 | − | 0.947350i | \(-0.603750\pi\) | ||||
−0.320200 | + | 0.947350i | \(0.603750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.79796i | 0.242213i | ||||||||
\(574\) | −22.3417 | −0.932524 | ||||||||
\(575\) | 2.00000 | − | 9.79796i | 0.0834058 | − | 0.408603i | ||||
\(576\) | 8.00000 | 0.333333 | ||||||||
\(577\) | − | 23.4949i | − | 0.978105i | −0.872254 | − | 0.489053i | \(-0.837343\pi\) | ||
0.872254 | − | 0.489053i | \(-0.162657\pi\) | |||||||
\(578\) | 9.61377i | 0.399880i | ||||||||
\(579\) | 17.7812 | 0.738962 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.0454 | 0.914598 | ||||||||
\(582\) | 7.07107i | 0.293105i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.30306 | −0.384963 | ||||||||
\(585\) | −0.142865 | + | 1.41421i | −0.00590672 | + | 0.0584705i | ||||
\(586\) | −32.2929 | −1.33401 | ||||||||
\(587\) | 10.6969i | 0.441510i | 0.975329 | + | 0.220755i | \(0.0708521\pi\) | ||||
−0.975329 | + | 0.220755i | \(0.929148\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.6814 | 0.563734 | ||||||||
\(590\) | −3.89270 | + | 38.5337i | −0.160260 | + | 1.58641i | ||||
\(591\) | −2.82843 | −0.116346 | ||||||||
\(592\) | − | 23.5959i | − | 0.969786i | ||||||
\(593\) | 10.6780i | 0.438494i | 0.975669 | + | 0.219247i | \(0.0703601\pi\) | ||||
−0.975669 | + | 0.219247i | \(0.929640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.7980 | − | 1.89898i | −0.770641 | − | 0.0778506i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.5959i | 0.679226i | ||||||||
\(598\) | − | 1.79796i | − | 0.0735240i | ||||||
\(599\) | −29.3485 | −1.19915 | −0.599573 | − | 0.800320i | \(-0.704663\pi\) | ||||
−0.599573 | + | 0.800320i | \(0.704663\pi\) | |||||||
\(600\) | −13.8564 | − | 2.82843i | −0.565685 | − | 0.115470i | ||||
\(601\) | −4.56048 | −0.186026 | −0.0930129 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930129 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(602\) | 13.8564i | 0.564745i | ||||||||
\(603\) | 4.10102i | 0.167006i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.202041 | −0.00820736 | ||||||||
\(607\) | − | 30.5412i | − | 1.23963i | −0.784748 | − | 0.619815i | \(-0.787207\pi\) | ||
0.784748 | − | 0.619815i | \(-0.212793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.4495 | −0.585523 | ||||||||
\(610\) | 1.04541 | − | 10.3485i | 0.0423273 | − | 0.418997i | ||||
\(611\) | −4.67123 | −0.188978 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 0.174973i | − | 0.00706708i | −0.999994 | − | 0.00353354i | \(-0.998875\pi\) | ||
0.999994 | − | 0.00353354i | \(-0.00112476\pi\) | |||||||
\(614\) | 2.04541 | 0.0825459 | ||||||||
\(615\) | 2.04989 | − | 20.2918i | 0.0826595 | − | 0.818244i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 40.0454i | − | 1.61217i | −0.591802 | − | 0.806084i | \(-0.701583\pi\) | ||
0.591802 | − | 0.806084i | \(-0.298417\pi\) | |||||||
\(618\) | − | 25.3130i | − | 1.01824i | ||||||
\(619\) | 28.6969 | 1.15343 | 0.576714 | − | 0.816946i | \(-0.304335\pi\) | ||||
0.576714 | + | 0.816946i | \(0.304335\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | 0.0802572 | ||||||||
\(622\) | − | 8.13534i | − | 0.326197i | ||||||
\(623\) | − | 2.33562i | − | 0.0935745i | ||||||
\(624\) | −2.54270 | −0.101789 | ||||||||
\(625\) | 23.0000 | + | 9.79796i | 0.920000 | + | 0.391918i | ||||
\(626\) | −32.0983 | −1.28291 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.7771 | 1.14742 | ||||||||
\(630\) | 5.44949 | + | 0.550510i | 0.217113 | + | 0.0219329i | ||||
\(631\) | −18.8990 | −0.752356 | −0.376178 | − | 0.926547i | \(-0.622762\pi\) | ||||
−0.376178 | + | 0.926547i | \(0.622762\pi\) | |||||||
\(632\) | 19.1010i | 0.759798i | ||||||||
\(633\) | − | 12.4101i | − | 0.493257i | ||||||
\(634\) | −11.9494 | −0.474571 | ||||||||
\(635\) | −4.20332 | + | 41.6085i | −0.166804 | + | 1.65118i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.54270i | 0.100745i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.55051 | 0.140456 | ||||||||
\(640\) | 2.54270 | − | 25.1701i | 0.100509 | − | 0.994936i | ||||
\(641\) | 8.44949 | 0.333735 | 0.166867 | − | 0.985979i | \(-0.446635\pi\) | ||||
0.166867 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(642\) | − | 11.7980i | − | 0.465628i | ||||||
\(643\) | 29.6969i | 1.17113i | 0.810624 | + | 0.585566i | \(0.199128\pi\) | ||||
−0.810624 | + | 0.585566i | \(0.800872\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.5851 | − | 1.27135i | −0.495536 | − | 0.0500593i | ||||
\(646\) | 11.9494 | 0.470142 | ||||||||
\(647\) | − | 22.2020i | − | 0.872852i | −0.899740 | − | 0.436426i | \(-0.856244\pi\) | ||
0.899740 | − | 0.436426i | \(-0.143756\pi\) | |||||||
\(648\) | − | 2.82843i | − | 0.111111i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.40408 | + | 0.898979i | 0.172742 | + | 0.0352609i | ||||
\(651\) | −13.6814 | −0.536218 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.6969i | 1.43606i | 0.696011 | + | 0.718031i | \(0.254956\pi\) | ||||
−0.696011 | + | 0.718031i | \(0.745044\pi\) | |||||||
\(654\) | 27.3485 | 1.06941 | ||||||||
\(655\) | −23.7559 | − | 2.39983i | −0.928220 | − | 0.0937692i | ||||
\(656\) | 36.4838 | 1.42445 | ||||||||
\(657\) | 3.28913i | 0.128321i | ||||||||
\(658\) | 18.0000i | 0.701713i | ||||||||
\(659\) | 36.8338 | 1.43484 | 0.717420 | − | 0.696641i | \(-0.245323\pi\) | ||||
0.717420 | + | 0.696641i | \(0.245323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.2020 | −0.591291 | −0.295645 | − | 0.955298i | \(-0.595535\pi\) | ||||
−0.295645 | + | 0.955298i | \(0.595535\pi\) | |||||||
\(662\) | 26.2986i | 1.02212i | ||||||||
\(663\) | − | 3.10102i | − | 0.120434i | ||||||
\(664\) | −36.0000 | −1.39707 | ||||||||
\(665\) | −0.674235 | + | 6.67423i | −0.0261457 | + | 0.258816i | ||||
\(666\) | −8.34242 | −0.323262 | ||||||||
\(667\) | 16.6848i | 0.646039i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.0000 | 0.425285 | ||||||||
\(670\) | 12.9029 | + | 1.30346i | 0.498482 | + | 0.0503569i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.1441i | 1.74018i | 0.492896 | + | 0.870088i | \(0.335938\pi\) | ||||
−0.492896 | + | 0.870088i | \(0.664062\pi\) | |||||||
\(674\) | −15.7526 | −0.606766 | ||||||||
\(675\) | −1.00000 | + | 4.89898i | −0.0384900 | + | 0.188562i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.5556i | 1.13591i | 0.823058 | + | 0.567957i | \(0.192266\pi\) | ||||
−0.823058 | + | 0.567957i | \(0.807734\pi\) | |||||||
\(678\) | − | 19.1633i | − | 0.735963i | ||||||
\(679\) | 8.66025 | 0.332350 | ||||||||
\(680\) | 30.6969 | + | 3.10102i | 1.17717 | + | 0.118919i | ||||
\(681\) | −4.09978 | −0.157104 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000i | 0.229584i | 0.993390 | + | 0.114792i | \(0.0366201\pi\) | ||||
−0.993390 | + | 0.114792i | \(0.963380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.89898 | + | 48.4949i | −0.187180 | + | 1.85289i | ||||
\(686\) | 26.9444 | 1.02874 | ||||||||
\(687\) | − | 3.10102i | − | 0.118311i | ||||||
\(688\) | − | 22.6274i | − | 0.862662i | ||||||
\(689\) | −6.35674 | −0.242173 | ||||||||
\(690\) | 0.635674 | − | 6.29253i | 0.0241997 | − | 0.239552i | ||||
\(691\) | 28.1010 | 1.06901 | 0.534507 | − | 0.845164i | \(-0.320497\pi\) | ||||
0.534507 | + | 0.845164i | \(0.320497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.6969 | 0.709726 | ||||||||
\(695\) | −27.9985 | − | 2.82843i | −1.06205 | − | 0.107288i | ||||
\(696\) | 23.5959 | 0.894401 | ||||||||
\(697\) | 44.4949i | 1.68536i | ||||||||
\(698\) | 7.34847i | 0.278144i | ||||||||
\(699\) | 23.7559 | 0.898531 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.73545 | 0.178856 | 0.0894278 | − | 0.995993i | \(-0.471496\pi\) | ||||
0.0894278 | + | 0.995993i | \(0.471496\pi\) | |||||||
\(702\) | 0.898979i | 0.0339298i | ||||||||
\(703\) | − | 10.2173i | − | 0.385354i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.3485 | − | 1.65153i | −0.615719 | − | 0.0622002i | ||||
\(706\) | 10.6780 | 0.401873 | ||||||||
\(707\) | 0.247449i | 0.00930627i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0000 | 0.901339 | 0.450669 | − | 0.892691i | \(-0.351185\pi\) | ||||
0.450669 | + | 0.892691i | \(0.351185\pi\) | |||||||
\(710\) | 1.12848 | − | 11.1708i | 0.0423513 | − | 0.419234i | ||||
\(711\) | 6.75323 | 0.253266 | ||||||||
\(712\) | 3.81405i | 0.142937i | ||||||||
\(713\) | 15.7980i | 0.591638i | ||||||||
\(714\) | −11.9494 | −0.447194 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 9.89949i | − | 0.369703i | ||||||
\(718\) | 36.6969i | 1.36952i | ||||||||
\(719\) | −46.5403 | −1.73566 | −0.867830 | − | 0.496861i | \(-0.834486\pi\) | ||||
−0.867830 | + | 0.496861i | \(0.834486\pi\) | |||||||
\(720\) | −8.89898 | − | 0.898979i | −0.331645 | − | 0.0335030i | ||||
\(721\) | −31.0019 | −1.15457 | ||||||||
\(722\) | 22.6274i | 0.842105i | ||||||||
\(723\) | − | 0.635674i | − | 0.0236410i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.8693 | − | 8.34242i | −1.51785 | − | 0.309830i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.3939i | 1.60939i | 0.593689 | + | 0.804695i | \(0.297671\pi\) | ||||
−0.593689 | + | 0.804695i | \(0.702329\pi\) | |||||||
\(728\) | 3.11416i | 0.115418i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 10.3485 | + | 1.04541i | 0.383014 | + | 0.0386923i | ||||
\(731\) | 27.5959 | 1.02067 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.73545i | − | 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278731\pi\) | |||||||
\(734\) | −50.6260 | −1.86864 | ||||||||
\(735\) | −0.898979 | + | 8.89898i | −0.0331594 | + | 0.328244i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 12.8990i | − | 0.474818i | ||||||
\(739\) | 24.9951 | 0.919461 | 0.459731 | − | 0.888058i | \(-0.347946\pi\) | ||||
0.459731 | + | 0.888058i | \(0.347946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.10102 | −0.0404470 | ||||||||
\(742\) | 24.4949i | 0.899236i | ||||||||
\(743\) | 3.81405i | 0.139924i | 0.997550 | + | 0.0699619i | \(0.0222878\pi\) | ||||
−0.997550 | + | 0.0699619i | \(0.977712\pi\) | |||||||
\(744\) | 22.3417 | 0.819086 | ||||||||
\(745\) | 26.2665 | + | 2.65345i | 0.962330 | + | 0.0972150i | ||||
\(746\) | −38.0454 | −1.39294 | ||||||||
\(747\) | 12.7279i | 0.465690i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.4495 | −0.527973 | ||||||||
\(750\) | 15.0956 | + | 4.70334i | 0.551215 | + | 0.171742i | ||||
\(751\) | −4.10102 | −0.149648 | −0.0748242 | − | 0.997197i | \(-0.523840\pi\) | ||||
−0.0748242 | + | 0.997197i | \(0.523840\pi\) | |||||||
\(752\) | − | 29.3939i | − | 1.07188i | ||||||
\(753\) | − | 2.00000i | − | 0.0728841i | ||||||
\(754\) | −7.49966 | −0.273122 | ||||||||
\(755\) | 35.7053 | + | 3.60697i | 1.29945 | + | 0.131271i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13.8990i | − | 0.505167i | −0.967575 | − | 0.252584i | \(-0.918720\pi\) | ||
0.967575 | − | 0.252584i | \(-0.0812802\pi\) | |||||||
\(758\) | 2.54270i | 0.0923549i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.10102 | − | 10.8990i | 0.0399382 | − | 0.395348i | ||||
\(761\) | 48.2903 | 1.75052 | 0.875262 | − | 0.483650i | \(-0.160689\pi\) | ||||
0.875262 | + | 0.483650i | \(0.160689\pi\) | |||||||
\(762\) | 26.4495i | 0.958164i | ||||||||
\(763\) | − | 33.4949i | − | 1.21260i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.09638 | − | 10.8530i | 0.0396396 | − | 0.392391i | ||||
\(766\) | −31.8126 | −1.14944 | ||||||||
\(767\) | 7.78539i | 0.281114i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.8153 | 1.79639 | 0.898193 | − | 0.439601i | \(-0.144880\pi\) | ||||
0.898193 | + | 0.439601i | \(0.144880\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.69694 | −0.313213 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.5959i | 1.13643i | 0.822881 | + | 0.568213i | \(0.192365\pi\) | ||||
−0.822881 | + | 0.568213i | \(0.807635\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | −38.6969 | − | 7.89898i | −1.39004 | − | 0.283740i | ||||
\(776\) | −14.1421 | −0.507673 | ||||||||
\(777\) | 10.2173i | 0.366545i | ||||||||
\(778\) | − | 15.4135i | − | 0.552600i | ||||||
\(779\) | 15.7980 | 0.566021 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 13.7980i | 0.493414i | ||||||||
\(783\) | − | 8.34242i | − | 0.298134i | ||||||
\(784\) | −16.0000 | −0.571429 | ||||||||
\(785\) | −4.17934 | + | 41.3712i | −0.149167 | + | 1.47660i | ||||
\(786\) | −15.1010 | −0.538636 | ||||||||
\(787\) | − | 50.0545i | − | 1.78425i | −0.451788 | − | 0.892125i | \(-0.649214\pi\) | ||
0.451788 | − | 0.892125i | \(-0.350786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.0492 | −0.571365 | ||||||||
\(790\) | 2.14643 | − | 21.2474i | 0.0763665 | − | 0.755950i | ||||
\(791\) | −23.4702 | −0.834503 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.09082i | − | 0.0742470i | ||||||
\(794\) | 34.4982 | 1.22429 | ||||||||
\(795\) | −22.2474 | − | 2.24745i | −0.789036 | − | 0.0797088i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3939i | 0.828654i | 0.910128 | + | 0.414327i | \(0.135983\pi\) | ||||
−0.910128 | + | 0.414327i | \(0.864017\pi\) | |||||||
\(798\) | 4.24264i | 0.150188i | ||||||||
\(799\) | 35.8481 | 1.26822 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.34847 | 0.0476458 | ||||||||
\(802\) | − | 15.0635i | − | 0.531912i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.70674 | − | 0.778539i | −0.271627 | − | 0.0274399i | ||||
\(806\) | −7.10102 | −0.250123 | ||||||||
\(807\) | 10.4495i | 0.367839i | ||||||||
\(808\) | − | 0.404082i | − | 0.0142156i | ||||||
\(809\) | −35.4196 | −1.24529 | −0.622643 | − | 0.782506i | \(-0.713941\pi\) | ||||
−0.622643 | + | 0.782506i | \(0.713941\pi\) | |||||||
\(810\) | −0.317837 | + | 3.14626i | −0.0111677 | + | 0.110548i | ||||
\(811\) | 29.4449 | 1.03395 | 0.516975 | − | 0.856001i | \(-0.327058\pi\) | ||||
0.516975 | + | 0.856001i | \(0.327058\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.19955i | − | 0.287571i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.224745 | + | 2.22474i | −0.00787247 | + | 0.0779294i | ||||
\(816\) | 19.5133 | 0.683101 | ||||||||
\(817\) | − | 9.79796i | − | 0.342787i | ||||||
\(818\) | 40.7423i | 1.42452i | ||||||||
\(819\) | 1.10102 | 0.0384728 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00680 | 0.209639 | 0.104819 | − | 0.994491i | \(-0.466574\pi\) | ||||
0.104819 | + | 0.994491i | \(0.466574\pi\) | |||||||
\(822\) | 30.8270i | 1.07521i | ||||||||
\(823\) | 1.49490i | 0.0521088i | 0.999661 | + | 0.0260544i | \(0.00829432\pi\) | ||||
−0.999661 | + | 0.0260544i | \(0.991706\pi\) | |||||||
\(824\) | 50.6260 | 1.76364 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0000 | 1.04383 | ||||||||
\(827\) | − | 27.5699i | − | 0.958701i | −0.877624 | − | 0.479351i | \(-0.840872\pi\) | ||
0.877624 | − | 0.479351i | \(-0.159128\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7980 | 0.375029 | 0.187514 | − | 0.982262i | \(-0.439957\pi\) | ||||
0.187514 | + | 0.982262i | \(0.439957\pi\) | |||||||
\(830\) | 40.0454 | + | 4.04541i | 1.39000 | + | 0.140418i | ||||
\(831\) | 22.1667 | 0.768955 | ||||||||
\(832\) | − | 5.08540i | − | 0.176304i | ||||||
\(833\) | − | 19.5133i | − | 0.676094i | ||||||
\(834\) | −17.7980 | −0.616293 | ||||||||
\(835\) | −2.97129 | + | 29.4128i | −0.102826 | + | 1.01787i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.89898i | − | 0.273029i | ||||||
\(838\) | 13.5065i | 0.466573i | ||||||||
\(839\) | 0.898979 | 0.0310362 | 0.0155181 | − | 0.999880i | \(-0.495060\pi\) | ||||
0.0155181 | + | 0.999880i | \(0.495060\pi\) | |||||||
\(840\) | −1.10102 | + | 10.8990i | −0.0379888 | + | 0.376051i | ||||
\(841\) | 40.5959 | 1.39986 | ||||||||
\(842\) | − | 49.0689i | − | 1.69103i | ||||||
\(843\) | − | 2.04989i | − | 0.0706019i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.0227 | − | 2.83087i | −0.964010 | − | 0.0973848i | ||||
\(846\) | −10.3923 | −0.357295 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 40.0000i | − | 1.37361i | ||||||
\(849\) | 11.1387 | 0.382280 | ||||||||
\(850\) | −33.7980 | − | 6.89898i | −1.15926 | − | 0.236633i | ||||
\(851\) | 11.7980 | 0.404429 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.09638i | 0.0375392i | 0.999824 | + | 0.0187696i | \(0.00597490\pi\) | ||||
−0.999824 | + | 0.0187696i | \(0.994025\pi\) | |||||||
\(854\) | −8.05669 | −0.275694 | ||||||||
\(855\) | −3.85337 | − | 0.389270i | −0.131783 | − | 0.0133127i | ||||
\(856\) | 23.5959 | 0.806492 | ||||||||
\(857\) | 38.5337i | 1.31629i | 0.752893 | + | 0.658143i | \(0.228658\pi\) | ||||
−0.752893 | + | 0.658143i | \(0.771342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.2929 | 1.20418 | 0.602088 | − | 0.798429i | \(-0.294335\pi\) | ||||
0.602088 | + | 0.798429i | \(0.294335\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.7980 | −0.538393 | ||||||||
\(862\) | 32.4949i | 1.10678i | ||||||||
\(863\) | 15.8434i | 0.539314i | 0.962956 | + | 0.269657i | \(0.0869104\pi\) | ||||
−0.962956 | + | 0.269657i | \(0.913090\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.28913 | + | 32.5590i | −0.111834 | + | 1.10704i | ||||
\(866\) | 26.8701 | 0.913082 | ||||||||
\(867\) | 6.79796i | 0.230871i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −26.2474 | − | 2.65153i | −0.889872 | − | 0.0898953i | ||||
\(871\) | 2.60691 | 0.0883319 | ||||||||
\(872\) | 54.6969i | 1.85227i | ||||||||
\(873\) | 5.00000i | 0.169224i | ||||||||
\(874\) | 4.89898 | 0.165710 | ||||||||
\(875\) | 5.76039 | − | 18.4883i | 0.194737 | − | 0.625019i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 31.2877i | − | 1.05651i | −0.849086 | − | 0.528255i | \(-0.822847\pi\) | ||
0.849086 | − | 0.528255i | \(-0.177153\pi\) | |||||||
\(878\) | − | 30.0454i | − | 1.01398i | ||||||
\(879\) | −22.8345 | −0.770188 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.6413 | −1.53770 | −0.768848 | − | 0.639432i | \(-0.779170\pi\) | ||||
−0.768848 | + | 0.639432i | \(0.779170\pi\) | |||||||
\(882\) | 5.65685i | 0.190476i | ||||||||
\(883\) | 6.10102i | 0.205316i | 0.994717 | + | 0.102658i | \(0.0327347\pi\) | ||||
−0.994717 | + | 0.102658i | \(0.967265\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.75255 | + | 27.2474i | −0.0925260 | + | 0.915913i | ||||
\(886\) | 1.90702 | 0.0640677 | ||||||||
\(887\) | − | 13.2207i | − | 0.443909i | −0.975057 | − | 0.221954i | \(-0.928756\pi\) | ||
0.975057 | − | 0.221954i | \(-0.0712436\pi\) | |||||||
\(888\) | − | 16.6848i | − | 0.559906i | ||||||
\(889\) | 32.3939 | 1.08646 | ||||||||
\(890\) | 0.428594 | − | 4.24264i | 0.0143665 | − | 0.142214i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 12.7279i | − | 0.425924i | ||||||
\(894\) | 16.6969 | 0.558429 | ||||||||
\(895\) | 57.9444 | + | 5.85357i | 1.93687 | + | 0.195663i | ||||
\(896\) | −19.5959 | −0.654654 | ||||||||
\(897\) | − | 1.27135i | − | 0.0424491i | ||||||
\(898\) | 44.6192i | 1.48896i | ||||||||
\(899\) | 65.8966 | 2.19777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.7832 | 1.62520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.79796i | 0.326056i | ||||||||
\(904\) | 38.3266 | 1.27472 | ||||||||
\(905\) | −11.1237 | − | 1.12372i | −0.369765 | − | 0.0373539i | ||||
\(906\) | 22.6969 | 0.754055 | ||||||||
\(907\) | − | 12.3031i | − | 0.408516i | −0.978917 | − | 0.204258i | \(-0.934522\pi\) | ||
0.978917 | − | 0.204258i | \(-0.0654782\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.142865 | −0.00473852 | ||||||||
\(910\) | 0.349945 | − | 3.46410i | 0.0116006 | − | 0.114834i | ||||
\(911\) | 25.7980 | 0.854725 | 0.427362 | − | 0.904080i | \(-0.359443\pi\) | ||||
0.427362 | + | 0.904080i | \(0.359443\pi\) | |||||||
\(912\) | − | 6.92820i | − | 0.229416i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −33.7980 | −1.11794 | ||||||||
\(915\) | 0.739215 | − | 7.31747i | 0.0244377 | − | 0.241908i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.4949i | 0.610755i | ||||||||
\(918\) | − | 6.89898i | − | 0.227700i | ||||||
\(919\) | 7.45312 | 0.245856 | 0.122928 | − | 0.992416i | \(-0.460772\pi\) | ||||
0.122928 | + | 0.992416i | \(0.460772\pi\) | |||||||
\(920\) | 12.5851 | + | 1.27135i | 0.414917 | + | 0.0419151i | ||||
\(921\) | 1.44632 | 0.0476579 | ||||||||
\(922\) | 9.30306i | 0.306380i | ||||||||
\(923\) | − | 2.25697i | − | 0.0742890i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.89898 | + | 28.8990i | −0.193957 | + | 0.950193i | ||||
\(926\) | −51.8973 | −1.70545 | ||||||||
\(927\) | − | 17.8990i | − | 0.587880i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.8990 | −1.27623 | −0.638117 | − | 0.769939i | \(-0.720286\pi\) | ||||
−0.638117 | + | 0.769939i | \(0.720286\pi\) | |||||||
\(930\) | −24.8523 | − | 2.51059i | −0.814938 | − | 0.0823255i | ||||
\(931\) | −6.92820 | −0.227063 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 5.75255i | − | 0.188330i | ||||||
\(934\) | −14.4921 | −0.474195 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.79796 | −0.0587681 | ||||||||
\(937\) | 7.67463i | 0.250719i | 0.992111 | + | 0.125360i | \(0.0400085\pi\) | ||||
−0.992111 | + | 0.125360i | \(0.959992\pi\) | |||||||
\(938\) | − | 10.0454i | − | 0.327994i | ||||||
\(939\) | −22.6969 | −0.740687 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.4188 | 1.61101 | 0.805504 | − | 0.592591i | \(-0.201895\pi\) | ||||
0.805504 | + | 0.592591i | \(0.201895\pi\) | |||||||
\(942\) | 26.2986i | 0.856855i | ||||||||
\(943\) | 18.2419i | 0.594038i | ||||||||
\(944\) | −48.9898 | −1.59448 | ||||||||
\(945\) | 3.85337 | + | 0.389270i | 0.125350 | + | 0.0126629i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.55051i | 0.180367i | 0.995925 | + | 0.0901837i | \(0.0287454\pi\) | ||||
−0.995925 | + | 0.0901837i | \(0.971255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.09082 | 0.0678707 | ||||||||
\(950\) | −2.44949 | + | 12.0000i | −0.0794719 | + | 0.389331i | ||||
\(951\) | −8.44949 | −0.273993 | ||||||||
\(952\) | − | 23.8988i | − | 0.774563i | ||||||
\(953\) | − | 8.83523i | − | 0.286201i | −0.989708 | − | 0.143101i | \(-0.954293\pi\) | ||
0.989708 | − | 0.143101i | \(-0.0457072\pi\) | |||||||
\(954\) | −14.1421 | −0.457869 | ||||||||
\(955\) | 12.8990 | + | 1.30306i | 0.417401 | + | 0.0421661i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 11.7980i | − | 0.381175i | ||||||
\(959\) | 37.7552 | 1.21918 | ||||||||
\(960\) | 1.79796 | − | 17.7980i | 0.0580289 | − | 0.574427i | ||||
\(961\) | 31.3939 | 1.01271 | ||||||||
\(962\) | 5.30306i | 0.170978i | ||||||||
\(963\) | − | 8.34242i | − | 0.268831i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.99624 | − | 39.5587i | 0.128643 | − | 1.27344i | ||||
\(966\) | −4.89898 | −0.157622 | ||||||||
\(967\) | − | 6.11756i | − | 0.196727i | −0.995151 | − | 0.0983637i | \(-0.968639\pi\) | ||
0.995151 | − | 0.0983637i | \(-0.0313608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.44949 | 0.271437 | ||||||||
\(970\) | 15.7313 | + | 1.58919i | 0.505102 | + | 0.0510257i | ||||
\(971\) | −13.1010 | −0.420432 | −0.210216 | − | 0.977655i | \(-0.567417\pi\) | ||||
−0.210216 | + | 0.977655i | \(0.567417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.7980i | 0.698810i | ||||||||
\(974\) | −54.4400 | −1.74437 | ||||||||
\(975\) | 3.11416 | + | 0.635674i | 0.0997328 | + | 0.0203579i | ||||
\(976\) | 13.1565 | 0.421130 | ||||||||
\(977\) | 54.4949i | 1.74345i | 0.489999 | + | 0.871723i | \(0.336997\pi\) | ||||
−0.489999 | + | 0.871723i | \(0.663003\pi\) | |||||||
\(978\) | 1.41421i | 0.0452216i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.3383 | 0.617424 | ||||||||
\(982\) | 42.6969i | 1.36251i | ||||||||
\(983\) | − | 52.2929i | − | 1.66788i | −0.551853 | − | 0.833942i | \(-0.686079\pi\) | ||
0.551853 | − | 0.833942i | \(-0.313921\pi\) | |||||||
\(984\) | 25.7980 | 0.822409 | ||||||||
\(985\) | −0.635674 | + | 6.29253i | −0.0202543 | + | 0.200497i | ||||
\(986\) | 57.5542 | 1.83290 | ||||||||
\(987\) | 12.7279i | 0.405134i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3137 | 0.359755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.1918 | −1.56263 | −0.781315 | − | 0.624137i | \(-0.785451\pi\) | ||||
−0.781315 | + | 0.624137i | \(0.785451\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.5959i | 0.590124i | ||||||||
\(994\) | −8.69694 | −0.275850 | ||||||||
\(995\) | 36.9217 | + | 3.72985i | 1.17050 | + | 0.118244i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.5590i | 1.03115i | 0.856843 | + | 0.515577i | \(0.172422\pi\) | ||||
−0.856843 | + | 0.515577i | \(0.827578\pi\) | |||||||
\(998\) | − | 14.5707i | − | 0.461228i | ||||||
\(999\) | −5.89898 | −0.186635 |
(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 | 1815.2.c.g.364.1 | ✓ | 8 | |
5.2 | odd | 4 | 9075.2.a.cr.1.3 | 4 | |||
5.3 | odd | 4 | 9075.2.a.cy.1.2 | 4 | |||
5.4 | even | 2 | inner | 1815.2.c.g.364.7 | yes | 8 | |
11.10 | odd | 2 | inner | 1815.2.c.g.364.5 | yes | 8 | |
55.32 | even | 4 | 9075.2.a.cr.1.2 | 4 | |||
55.43 | even | 4 | 9075.2.a.cy.1.3 | 4 | |||
55.54 | odd | 2 | inner | 1815.2.c.g.364.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.c.g.364.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1815.2.c.g.364.3 | yes | 8 | 55.54 | odd | 2 | inner | |
1815.2.c.g.364.5 | yes | 8 | 11.10 | odd | 2 | inner | |
1815.2.c.g.364.7 | yes | 8 | 5.4 | even | 2 | inner | |
9075.2.a.cr.1.2 | 4 | 55.32 | even | 4 | |||
9075.2.a.cr.1.3 | 4 | 5.2 | odd | 4 | |||
9075.2.a.cy.1.2 | 4 | 5.3 | odd | 4 | |||
9075.2.a.cy.1.3 | 4 | 55.43 | even | 4 |