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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 21x^{10} + 164x^{8} + 589x^{6} + 965x^{4} + 576x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.11 | ||
Root | \(2.42911i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.364 |
Dual form | 1815.2.c.i.364.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).
\(n\) | \(727\) | \(1211\) | \(1696\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.42911i | 1.71764i | 0.512280 | + | 0.858819i | \(0.328801\pi\) | ||||
−0.512280 | + | 0.858819i | \(0.671199\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −3.90056 | −1.95028 | ||||||||
\(5\) | 2.04405 | + | 0.906565i | 0.914127 | + | 0.405428i | ||||
\(6\) | −2.42911 | −0.991678 | ||||||||
\(7\) | − | 1.34168i | − | 0.507108i | −0.967321 | − | 0.253554i | \(-0.918400\pi\) | ||
0.967321 | − | 0.253554i | \(-0.0815995\pi\) | |||||||
\(8\) | − | 4.61665i | − | 1.63223i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.20214 | + | 4.96521i | −0.696379 | + | 1.57014i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 3.90056i | − | 1.12599i | ||||||
\(13\) | 4.12932i | 1.14527i | 0.819812 | + | 0.572633i | \(0.194078\pi\) | ||||
−0.819812 | + | 0.572633i | \(0.805922\pi\) | |||||||
\(14\) | 3.25908 | 0.871027 | ||||||||
\(15\) | −0.906565 | + | 2.04405i | −0.234074 | + | 0.527771i | ||||
\(16\) | 3.41322 | 0.853305 | ||||||||
\(17\) | 5.87573i | 1.42508i | 0.701634 | + | 0.712538i | \(0.252454\pi\) | ||||
−0.701634 | + | 0.712538i | \(0.747546\pi\) | |||||||
\(18\) | − | 2.42911i | − | 0.572546i | ||||||
\(19\) | 3.51653 | 0.806748 | 0.403374 | − | 0.915035i | \(-0.367837\pi\) | ||||
0.403374 | + | 0.915035i | \(0.367837\pi\) | |||||||
\(20\) | −7.97293 | − | 3.53611i | −1.78280 | − | 0.790698i | ||||
\(21\) | 1.34168 | 0.292779 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.37088i | 1.32842i | 0.747546 | + | 0.664210i | \(0.231232\pi\) | ||||
−0.747546 | + | 0.664210i | \(0.768768\pi\) | |||||||
\(24\) | 4.61665 | 0.942370 | ||||||||
\(25\) | 3.35628 | + | 3.70613i | 0.671256 | + | 0.741226i | ||||
\(26\) | −10.0305 | −1.96715 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 5.23330i | 0.989001i | ||||||||
\(29\) | −6.39637 | −1.18778 | −0.593888 | − | 0.804548i | \(-0.702408\pi\) | ||||
−0.593888 | + | 0.804548i | \(0.702408\pi\) | |||||||
\(30\) | −4.96521 | − | 2.20214i | −0.906520 | − | 0.402054i | ||||
\(31\) | 9.40429 | 1.68906 | 0.844530 | − | 0.535509i | \(-0.179880\pi\) | ||||
0.844530 | + | 0.535509i | \(0.179880\pi\) | |||||||
\(32\) | − | 0.942224i | − | 0.166563i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.2728 | −2.44776 | ||||||||
\(35\) | 1.21632 | − | 2.74246i | 0.205596 | − | 0.463561i | ||||
\(36\) | 3.90056 | 0.650093 | ||||||||
\(37\) | − | 7.01348i | − | 1.15301i | −0.817094 | − | 0.576504i | \(-0.804416\pi\) | ||
0.817094 | − | 0.576504i | \(-0.195584\pi\) | |||||||
\(38\) | 8.54203i | 1.38570i | ||||||||
\(39\) | −4.12932 | −0.661220 | ||||||||
\(40\) | 4.18529 | − | 9.43666i | 0.661753 | − | 1.49207i | ||||
\(41\) | −8.63013 | −1.34780 | −0.673900 | − | 0.738823i | \(-0.735382\pi\) | ||||
−0.673900 | + | 0.738823i | \(0.735382\pi\) | |||||||
\(42\) | 3.25908i | 0.502888i | ||||||||
\(43\) | 5.31799i | 0.810985i | 0.914098 | + | 0.405493i | \(0.132900\pi\) | ||||
−0.914098 | + | 0.405493i | \(0.867100\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.04405 | − | 0.906565i | −0.304709 | − | 0.135143i | ||||
\(46\) | −15.4755 | −2.28174 | ||||||||
\(47\) | − | 3.74642i | − | 0.546471i | −0.961947 | − | 0.273236i | \(-0.911906\pi\) | ||
0.961947 | − | 0.273236i | \(-0.0880939\pi\) | |||||||
\(48\) | 3.41322i | 0.492656i | ||||||||
\(49\) | 5.19989 | 0.742842 | ||||||||
\(50\) | −9.00258 | + | 8.15276i | −1.27316 | + | 1.15297i | ||||
\(51\) | −5.87573 | −0.822767 | ||||||||
\(52\) | − | 16.1066i | − | 2.23359i | ||||||
\(53\) | − | 6.41776i | − | 0.881547i | −0.897618 | − | 0.440774i | \(-0.854704\pi\) | ||
0.897618 | − | 0.440774i | \(-0.145296\pi\) | |||||||
\(54\) | 2.42911 | 0.330559 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.19407 | −0.827718 | ||||||||
\(57\) | 3.51653i | 0.465776i | ||||||||
\(58\) | − | 15.5375i | − | 2.04017i | ||||||
\(59\) | −8.97551 | −1.16851 | −0.584256 | − | 0.811570i | \(-0.698614\pi\) | ||||
−0.584256 | + | 0.811570i | \(0.698614\pi\) | |||||||
\(60\) | 3.53611 | − | 7.97293i | 0.456510 | − | 1.02930i | ||||
\(61\) | −6.52203 | −0.835061 | −0.417530 | − | 0.908663i | \(-0.637104\pi\) | ||||
−0.417530 | + | 0.908663i | \(0.637104\pi\) | |||||||
\(62\) | 22.8440i | 2.90119i | ||||||||
\(63\) | 1.34168i | 0.169036i | ||||||||
\(64\) | 9.11521 | 1.13940 | ||||||||
\(65\) | −3.74349 | + | 8.44053i | −0.464323 | + | 1.04692i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.83452i | − | 1.07931i | −0.841887 | − | 0.539654i | \(-0.818555\pi\) | ||
0.841887 | − | 0.539654i | \(-0.181445\pi\) | |||||||
\(68\) | − | 22.9186i | − | 2.77929i | ||||||
\(69\) | −6.37088 | −0.766964 | ||||||||
\(70\) | 6.66173 | + | 2.95457i | 0.796229 | + | 0.353139i | ||||
\(71\) | −7.17440 | −0.851444 | −0.425722 | − | 0.904854i | \(-0.639980\pi\) | ||||
−0.425722 | + | 0.904854i | \(0.639980\pi\) | |||||||
\(72\) | 4.61665i | 0.544077i | ||||||||
\(73\) | − | 4.08569i | − | 0.478194i | −0.970996 | − | 0.239097i | \(-0.923149\pi\) | ||
0.970996 | − | 0.239097i | \(-0.0768514\pi\) | |||||||
\(74\) | 17.0365 | 1.98045 | ||||||||
\(75\) | −3.70613 | + | 3.35628i | −0.427947 | + | 0.387550i | ||||
\(76\) | −13.7164 | −1.57338 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 10.0305i | − | 1.13574i | ||||||
\(79\) | −9.97344 | −1.12210 | −0.561050 | − | 0.827782i | \(-0.689603\pi\) | ||||
−0.561050 | + | 0.827782i | \(0.689603\pi\) | |||||||
\(80\) | 6.97679 | + | 3.09431i | 0.780029 | + | 0.345954i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 20.9635i | − | 2.31503i | ||||||
\(83\) | 3.06020i | 0.335900i | 0.985796 | + | 0.167950i | \(0.0537147\pi\) | ||||
−0.985796 | + | 0.167950i | \(0.946285\pi\) | |||||||
\(84\) | −5.23330 | −0.571000 | ||||||||
\(85\) | −5.32674 | + | 12.0103i | −0.577766 | + | 1.30270i | ||||
\(86\) | −12.9180 | −1.39298 | ||||||||
\(87\) | − | 6.39637i | − | 0.685763i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8382 | 1.25485 | 0.627424 | − | 0.778677i | \(-0.284109\pi\) | ||||
0.627424 | + | 0.778677i | \(0.284109\pi\) | |||||||
\(90\) | 2.20214 | − | 4.96521i | 0.232126 | − | 0.523379i | ||||
\(91\) | 5.54022 | 0.580773 | ||||||||
\(92\) | − | 24.8500i | − | 2.59079i | ||||||
\(93\) | 9.40429i | 0.975179i | ||||||||
\(94\) | 9.10045 | 0.938640 | ||||||||
\(95\) | 7.18796 | + | 3.18796i | 0.737470 | + | 0.327078i | ||||
\(96\) | 0.942224 | 0.0961654 | ||||||||
\(97\) | 2.55370i | 0.259289i | 0.991561 | + | 0.129644i | \(0.0413836\pi\) | ||||
−0.991561 | + | 0.129644i | \(0.958616\pi\) | |||||||
\(98\) | 12.6311i | 1.27593i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.0914 | − | 14.4560i | −1.30914 | − | 1.44560i | ||||
\(101\) | −15.7436 | −1.56654 | −0.783271 | − | 0.621680i | \(-0.786450\pi\) | ||||
−0.783271 | + | 0.621680i | \(0.786450\pi\) | |||||||
\(102\) | − | 14.2728i | − | 1.41322i | ||||||
\(103\) | 16.7498i | 1.65041i | 0.564833 | + | 0.825205i | \(0.308940\pi\) | ||||
−0.564833 | + | 0.825205i | \(0.691060\pi\) | |||||||
\(104\) | 19.0636 | 1.86934 | ||||||||
\(105\) | 2.74246 | + | 1.21632i | 0.267637 | + | 0.118701i | ||||
\(106\) | 15.5894 | 1.51418 | ||||||||
\(107\) | 4.51221i | 0.436212i | 0.975925 | + | 0.218106i | \(0.0699879\pi\) | ||||
−0.975925 | + | 0.218106i | \(0.930012\pi\) | |||||||
\(108\) | 3.90056i | 0.375331i | ||||||||
\(109\) | 5.59672 | 0.536068 | 0.268034 | − | 0.963409i | \(-0.413626\pi\) | ||||
0.268034 | + | 0.963409i | \(0.413626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.01348 | 0.665690 | ||||||||
\(112\) | − | 4.57945i | − | 0.432718i | ||||||
\(113\) | 3.19237i | 0.300313i | 0.988662 | + | 0.150157i | \(0.0479778\pi\) | ||||
−0.988662 | + | 0.150157i | \(0.952022\pi\) | |||||||
\(114\) | −8.54203 | −0.800034 | ||||||||
\(115\) | −5.77562 | + | 13.0224i | −0.538579 | + | 1.21434i | ||||
\(116\) | 24.9494 | 2.31649 | ||||||||
\(117\) | − | 4.12932i | − | 0.381755i | ||||||
\(118\) | − | 21.8025i | − | 2.00708i | ||||||
\(119\) | 7.88336 | 0.722667 | ||||||||
\(120\) | 9.43666 | + | 4.18529i | 0.861446 | + | 0.382063i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 15.8427i | − | 1.43433i | ||||||
\(123\) | − | 8.63013i | − | 0.778152i | ||||||
\(124\) | −36.6819 | −3.29414 | ||||||||
\(125\) | 3.50055 | + | 10.6182i | 0.313099 | + | 0.949720i | ||||
\(126\) | −3.25908 | −0.290342 | ||||||||
\(127\) | − | 13.9500i | − | 1.23786i | −0.785445 | − | 0.618932i | \(-0.787566\pi\) | ||
0.785445 | − | 0.618932i | \(-0.212434\pi\) | |||||||
\(128\) | 20.2574i | 1.79051i | ||||||||
\(129\) | −5.31799 | −0.468223 | ||||||||
\(130\) | −20.5029 | − | 9.09334i | −1.79823 | − | 0.797539i | ||||
\(131\) | 18.4618 | 1.61301 | 0.806507 | − | 0.591225i | \(-0.201355\pi\) | ||||
0.806507 | + | 0.591225i | \(0.201355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.71806i | − | 0.409108i | ||||||
\(134\) | 21.4600 | 1.85386 | ||||||||
\(135\) | 0.906565 | − | 2.04405i | 0.0780247 | − | 0.175924i | ||||
\(136\) | 27.1262 | 2.32605 | ||||||||
\(137\) | − | 7.56366i | − | 0.646207i | −0.946364 | − | 0.323103i | \(-0.895274\pi\) | ||
0.946364 | − | 0.323103i | \(-0.104726\pi\) | |||||||
\(138\) | − | 15.4755i | − | 1.31737i | ||||||
\(139\) | 0.572021 | 0.0485182 | 0.0242591 | − | 0.999706i | \(-0.492277\pi\) | ||||
0.0242591 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(140\) | −4.74433 | + | 10.6971i | −0.400969 | + | 0.904072i | ||||
\(141\) | 3.74642 | 0.315505 | ||||||||
\(142\) | − | 17.4274i | − | 1.46247i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.41322 | −0.284435 | ||||||||
\(145\) | −13.0745 | − | 5.79873i | −1.08578 | − | 0.481558i | ||||
\(146\) | 9.92457 | 0.821364 | ||||||||
\(147\) | 5.19989i | 0.428880i | ||||||||
\(148\) | 27.3564i | 2.24869i | ||||||||
\(149\) | 9.20494 | 0.754098 | 0.377049 | − | 0.926193i | \(-0.376939\pi\) | ||||
0.377049 | + | 0.926193i | \(0.376939\pi\) | |||||||
\(150\) | −8.15276 | − | 9.00258i | −0.665670 | − | 0.735057i | ||||
\(151\) | −0.453311 | −0.0368899 | −0.0184450 | − | 0.999830i | \(-0.505872\pi\) | ||||
−0.0184450 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(152\) | − | 16.2346i | − | 1.31680i | ||||||
\(153\) | − | 5.87573i | − | 0.475025i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.2228 | + | 8.52560i | 1.54401 | + | 0.684792i | ||||
\(156\) | 16.1066 | 1.28956 | ||||||||
\(157\) | − | 3.14144i | − | 0.250714i | −0.992112 | − | 0.125357i | \(-0.959992\pi\) | ||
0.992112 | − | 0.125357i | \(-0.0400077\pi\) | |||||||
\(158\) | − | 24.2266i | − | 1.92736i | ||||||
\(159\) | 6.41776 | 0.508962 | ||||||||
\(160\) | 0.854188 | − | 1.92595i | 0.0675295 | − | 0.152260i | ||||
\(161\) | 8.54768 | 0.673652 | ||||||||
\(162\) | 2.42911i | 0.190849i | ||||||||
\(163\) | − | 0.374743i | − | 0.0293521i | −0.999892 | − | 0.0146761i | \(-0.995328\pi\) | ||
0.999892 | − | 0.0146761i | \(-0.00467170\pi\) | |||||||
\(164\) | 33.6623 | 2.62858 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.43354 | −0.576955 | ||||||||
\(167\) | 20.0873i | 1.55440i | 0.629252 | + | 0.777201i | \(0.283361\pi\) | ||||
−0.629252 | + | 0.777201i | \(0.716639\pi\) | |||||||
\(168\) | − | 6.19407i | − | 0.477883i | ||||||
\(169\) | −4.05125 | −0.311635 | ||||||||
\(170\) | −29.1743 | − | 12.9392i | −2.23756 | − | 0.992392i | ||||
\(171\) | −3.51653 | −0.268916 | ||||||||
\(172\) | − | 20.7431i | − | 1.58165i | ||||||
\(173\) | 2.71823i | 0.206663i | 0.994647 | + | 0.103331i | \(0.0329502\pi\) | ||||
−0.994647 | + | 0.103331i | \(0.967050\pi\) | |||||||
\(174\) | 15.5375 | 1.17789 | ||||||||
\(175\) | 4.97244 | − | 4.50306i | 0.375881 | − | 0.340399i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 8.97551i | − | 0.674641i | ||||||
\(178\) | 28.7563i | 2.15538i | ||||||||
\(179\) | −14.5157 | −1.08496 | −0.542478 | − | 0.840070i | \(-0.682514\pi\) | ||||
−0.542478 | + | 0.840070i | \(0.682514\pi\) | |||||||
\(180\) | 7.97293 | + | 3.53611i | 0.594267 | + | 0.263566i | ||||
\(181\) | −20.5147 | −1.52484 | −0.762422 | − | 0.647080i | \(-0.775990\pi\) | ||||
−0.762422 | + | 0.647080i | \(0.775990\pi\) | |||||||
\(182\) | 13.4578i | 0.997558i | ||||||||
\(183\) | − | 6.52203i | − | 0.482123i | ||||||
\(184\) | 29.4121 | 2.16829 | ||||||||
\(185\) | 6.35817 | − | 14.3359i | 0.467462 | − | 1.05400i | ||||
\(186\) | −22.8440 | −1.67500 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 14.6131i | 1.06577i | ||||||||
\(189\) | −1.34168 | −0.0975929 | ||||||||
\(190\) | −7.74390 | + | 17.4603i | −0.561802 | + | 1.26671i | ||||
\(191\) | 14.4836 | 1.04799 | 0.523997 | − | 0.851720i | \(-0.324440\pi\) | ||||
0.523997 | + | 0.851720i | \(0.324440\pi\) | |||||||
\(192\) | 9.11521i | 0.657833i | ||||||||
\(193\) | 11.8730i | 0.854640i | 0.904100 | + | 0.427320i | \(0.140542\pi\) | ||||
−0.904100 | + | 0.427320i | \(0.859458\pi\) | |||||||
\(194\) | −6.20321 | −0.445364 | ||||||||
\(195\) | −8.44053 | − | 3.74349i | −0.604439 | − | 0.268077i | ||||
\(196\) | −20.2825 | −1.44875 | ||||||||
\(197\) | 7.58073i | 0.540104i | 0.962846 | + | 0.270052i | \(0.0870410\pi\) | ||||
−0.962846 | + | 0.270052i | \(0.912959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8804 | 1.19662 | 0.598310 | − | 0.801265i | \(-0.295839\pi\) | ||||
0.598310 | + | 0.801265i | \(0.295839\pi\) | |||||||
\(200\) | 17.1099 | − | 15.4948i | 1.20985 | − | 1.09565i | ||||
\(201\) | 8.83452 | 0.623139 | ||||||||
\(202\) | − | 38.2428i | − | 2.69075i | ||||||
\(203\) | 8.58189i | 0.602331i | ||||||||
\(204\) | 22.9186 | 1.60463 | ||||||||
\(205\) | −17.6404 | − | 7.82377i | −1.23206 | − | 0.546436i | ||||
\(206\) | −40.6871 | −2.83481 | ||||||||
\(207\) | − | 6.37088i | − | 0.442807i | ||||||
\(208\) | 14.0943i | 0.977262i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.95457 | + | 6.66173i | −0.203885 | + | 0.459703i | ||||
\(211\) | 23.8041 | 1.63874 | 0.819370 | − | 0.573265i | \(-0.194324\pi\) | ||||
0.819370 | + | 0.573265i | \(0.194324\pi\) | |||||||
\(212\) | 25.0328i | 1.71926i | ||||||||
\(213\) | − | 7.17440i | − | 0.491582i | ||||||
\(214\) | −10.9606 | −0.749254 | ||||||||
\(215\) | −4.82110 | + | 10.8702i | −0.328796 | + | 0.741344i | ||||
\(216\) | −4.61665 | −0.314123 | ||||||||
\(217\) | − | 12.6175i | − | 0.856535i | ||||||
\(218\) | 13.5950i | 0.920771i | ||||||||
\(219\) | 4.08569 | 0.276085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.2628 | −1.63209 | ||||||||
\(222\) | 17.0365i | 1.14341i | ||||||||
\(223\) | 21.6870i | 1.45227i | 0.687552 | + | 0.726135i | \(0.258685\pi\) | ||||
−0.687552 | + | 0.726135i | \(0.741315\pi\) | |||||||
\(224\) | −1.26416 | −0.0844655 | ||||||||
\(225\) | −3.35628 | − | 3.70613i | −0.223752 | − | 0.247075i | ||||
\(226\) | −7.75461 | −0.515829 | ||||||||
\(227\) | − | 1.05996i | − | 0.0703522i | −0.999381 | − | 0.0351761i | \(-0.988801\pi\) | ||
0.999381 | − | 0.0351761i | \(-0.0111992\pi\) | |||||||
\(228\) | − | 13.7164i | − | 0.908392i | ||||||
\(229\) | 14.0678 | 0.929624 | 0.464812 | − | 0.885409i | \(-0.346122\pi\) | ||||
0.464812 | + | 0.885409i | \(0.346122\pi\) | |||||||
\(230\) | −31.6328 | − | 14.0296i | −2.08580 | − | 0.925083i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 29.5298i | 1.93873i | ||||||||
\(233\) | − | 0.300464i | − | 0.0196841i | −0.999952 | − | 0.00984204i | \(-0.996867\pi\) | ||
0.999952 | − | 0.00984204i | \(-0.00313287\pi\) | |||||||
\(234\) | 10.0305 | 0.655717 | ||||||||
\(235\) | 3.39637 | − | 7.65787i | 0.221555 | − | 0.499544i | ||||
\(236\) | 35.0095 | 2.27892 | ||||||||
\(237\) | − | 9.97344i | − | 0.647845i | ||||||
\(238\) | 19.1495i | 1.24128i | ||||||||
\(239\) | 10.3905 | 0.672107 | 0.336054 | − | 0.941843i | \(-0.390908\pi\) | ||||
0.336054 | + | 0.941843i | \(0.390908\pi\) | |||||||
\(240\) | −3.09431 | + | 6.97679i | −0.199737 | + | 0.450350i | ||||
\(241\) | 5.73625 | 0.369504 | 0.184752 | − | 0.982785i | \(-0.440852\pi\) | ||||
0.184752 | + | 0.982785i | \(0.440852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 25.4396 | 1.62860 | ||||||||
\(245\) | 10.6288 | + | 4.71404i | 0.679052 | + | 0.301169i | ||||
\(246\) | 20.9635 | 1.33658 | ||||||||
\(247\) | 14.5209i | 0.923941i | ||||||||
\(248\) | − | 43.4163i | − | 2.75694i | ||||||
\(249\) | −3.06020 | −0.193932 | ||||||||
\(250\) | −25.7927 | + | 8.50322i | −1.63128 | + | 0.537791i | ||||
\(251\) | −2.09242 | −0.132072 | −0.0660361 | − | 0.997817i | \(-0.521035\pi\) | ||||
−0.0660361 | + | 0.997817i | \(0.521035\pi\) | |||||||
\(252\) | − | 5.23330i | − | 0.329667i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 33.8861 | 2.12620 | ||||||||
\(255\) | −12.0103 | − | 5.32674i | −0.752114 | − | 0.333573i | ||||
\(256\) | −30.9768 | −1.93605 | ||||||||
\(257\) | 23.2533i | 1.45050i | 0.688486 | + | 0.725250i | \(0.258276\pi\) | ||||
−0.688486 | + | 0.725250i | \(0.741724\pi\) | |||||||
\(258\) | − | 12.9180i | − | 0.804237i | ||||||
\(259\) | −9.40985 | −0.584699 | ||||||||
\(260\) | 14.6017 | − | 32.9227i | 0.905559 | − | 2.04178i | ||||
\(261\) | 6.39637 | 0.395926 | ||||||||
\(262\) | 44.8456i | 2.77057i | ||||||||
\(263\) | 3.71929i | 0.229341i | 0.993404 | + | 0.114670i | \(0.0365812\pi\) | ||||
−0.993404 | + | 0.114670i | \(0.963419\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.81812 | − | 13.1182i | 0.357404 | − | 0.805846i | ||||
\(266\) | 11.4607 | 0.702699 | ||||||||
\(267\) | 11.8382i | 0.724487i | ||||||||
\(268\) | 34.4595i | 2.10495i | ||||||||
\(269\) | −12.0991 | −0.737696 | −0.368848 | − | 0.929490i | \(-0.620248\pi\) | ||||
−0.368848 | + | 0.929490i | \(0.620248\pi\) | |||||||
\(270\) | 4.96521 | + | 2.20214i | 0.302173 | + | 0.134018i | ||||
\(271\) | 3.26311 | 0.198220 | 0.0991100 | − | 0.995076i | \(-0.468400\pi\) | ||||
0.0991100 | + | 0.995076i | \(0.468400\pi\) | |||||||
\(272\) | 20.0552i | 1.21602i | ||||||||
\(273\) | 5.54022i | 0.335310i | ||||||||
\(274\) | 18.3729 | 1.10995 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 24.8500 | 1.49579 | ||||||||
\(277\) | − | 23.6465i | − | 1.42078i | −0.703808 | − | 0.710390i | \(-0.748518\pi\) | ||
0.703808 | − | 0.710390i | \(-0.251482\pi\) | |||||||
\(278\) | 1.38950i | 0.0833367i | ||||||||
\(279\) | −9.40429 | −0.563020 | ||||||||
\(280\) | −12.6610 | − | 5.61533i | −0.756639 | − | 0.335580i | ||||
\(281\) | 30.2948 | 1.80724 | 0.903619 | − | 0.428336i | \(-0.140900\pi\) | ||||
0.903619 | + | 0.428336i | \(0.140900\pi\) | |||||||
\(282\) | 9.10045i | 0.541924i | ||||||||
\(283\) | 12.6940i | 0.754581i | 0.926095 | + | 0.377291i | \(0.123144\pi\) | ||||
−0.926095 | + | 0.377291i | \(0.876856\pi\) | |||||||
\(284\) | 27.9841 | 1.66055 | ||||||||
\(285\) | −3.18796 | + | 7.18796i | −0.188839 | + | 0.425778i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.5789i | 0.683479i | ||||||||
\(288\) | 0.942224i | 0.0555211i | ||||||||
\(289\) | −17.5243 | −1.03084 | ||||||||
\(290\) | 14.0857 | − | 31.7594i | 0.827142 | − | 1.86497i | ||||
\(291\) | −2.55370 | −0.149701 | ||||||||
\(292\) | 15.9365i | 0.932611i | ||||||||
\(293\) | − | 2.10292i | − | 0.122854i | −0.998112 | − | 0.0614271i | \(-0.980435\pi\) | ||
0.998112 | − | 0.0614271i | \(-0.0195652\pi\) | |||||||
\(294\) | −12.6311 | −0.736660 | ||||||||
\(295\) | −18.3464 | − | 8.13688i | −1.06817 | − | 0.473748i | ||||
\(296\) | −32.3788 | −1.88198 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.3598i | 1.29527i | ||||||||
\(299\) | −26.3074 | −1.52139 | ||||||||
\(300\) | 14.4560 | − | 13.0914i | 0.834615 | − | 0.755830i | ||||
\(301\) | 7.13504 | 0.411257 | ||||||||
\(302\) | − | 1.10114i | − | 0.0633635i | ||||||
\(303\) | − | 15.7436i | − | 0.904444i | ||||||
\(304\) | 12.0027 | 0.688402 | ||||||||
\(305\) | −13.3314 | − | 5.91265i | −0.763352 | − | 0.338557i | ||||
\(306\) | 14.2728 | 0.815921 | ||||||||
\(307\) | 13.5435i | 0.772967i | 0.922296 | + | 0.386484i | \(0.126310\pi\) | ||||
−0.922296 | + | 0.386484i | \(0.873690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.7498 | −0.952865 | ||||||||
\(310\) | −20.7096 | + | 46.6943i | −1.17623 | + | 2.65206i | ||||
\(311\) | 7.20000 | 0.408274 | 0.204137 | − | 0.978942i | \(-0.434561\pi\) | ||||
0.204137 | + | 0.978942i | \(0.434561\pi\) | |||||||
\(312\) | 19.0636i | 1.07926i | ||||||||
\(313\) | − | 3.59811i | − | 0.203377i | −0.994816 | − | 0.101689i | \(-0.967575\pi\) | ||
0.994816 | − | 0.101689i | \(-0.0324246\pi\) | |||||||
\(314\) | 7.63090 | 0.430636 | ||||||||
\(315\) | −1.21632 | + | 2.74246i | −0.0685319 | + | 0.154520i | ||||
\(316\) | 38.9020 | 2.18841 | ||||||||
\(317\) | − | 24.7458i | − | 1.38986i | −0.719077 | − | 0.694931i | \(-0.755435\pi\) | ||
0.719077 | − | 0.694931i | \(-0.244565\pi\) | |||||||
\(318\) | 15.5894i | 0.874211i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 18.6319 | + | 8.26353i | 1.04156 | + | 0.461945i | ||||
\(321\) | −4.51221 | −0.251847 | ||||||||
\(322\) | 20.7632i | 1.15709i | ||||||||
\(323\) | 20.6622i | 1.14968i | ||||||||
\(324\) | −3.90056 | −0.216698 | ||||||||
\(325\) | −15.3038 | + | 13.8591i | −0.848901 | + | 0.768767i | ||||
\(326\) | 0.910290 | 0.0504163 | ||||||||
\(327\) | 5.59672i | 0.309499i | ||||||||
\(328\) | 39.8423i | 2.19992i | ||||||||
\(329\) | −5.02650 | −0.277120 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.3411 | 0.733292 | 0.366646 | − | 0.930361i | \(-0.380506\pi\) | ||||
0.366646 | + | 0.930361i | \(0.380506\pi\) | |||||||
\(332\) | − | 11.9365i | − | 0.655098i | ||||||
\(333\) | 7.01348i | 0.384336i | ||||||||
\(334\) | −48.7942 | −2.66990 | ||||||||
\(335\) | 8.00907 | − | 18.0582i | 0.437582 | − | 0.986625i | ||||
\(336\) | 4.57945 | 0.249830 | ||||||||
\(337\) | − | 26.1890i | − | 1.42661i | −0.700855 | − | 0.713304i | \(-0.747198\pi\) | ||
0.700855 | − | 0.713304i | \(-0.252802\pi\) | |||||||
\(338\) | − | 9.84092i | − | 0.535275i | ||||||
\(339\) | −3.19237 | −0.173386 | ||||||||
\(340\) | 20.7772 | − | 46.8468i | 1.12680 | − | 2.54063i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 8.54203i | − | 0.461900i | ||||||
\(343\) | − | 16.3684i | − | 0.883808i | ||||||
\(344\) | 24.5513 | 1.32372 | ||||||||
\(345\) | −13.0224 | − | 5.77562i | −0.701102 | − | 0.310949i | ||||
\(346\) | −6.60286 | −0.354972 | ||||||||
\(347\) | − | 2.23005i | − | 0.119715i | −0.998207 | − | 0.0598577i | \(-0.980935\pi\) | ||
0.998207 | − | 0.0598577i | \(-0.0190647\pi\) | |||||||
\(348\) | 24.9494i | 1.33743i | ||||||||
\(349\) | 19.5128 | 1.04449 | 0.522247 | − | 0.852794i | \(-0.325094\pi\) | ||||
0.522247 | + | 0.852794i | \(0.325094\pi\) | |||||||
\(350\) | 10.9384 | + | 12.0786i | 0.584682 | + | 0.645628i | ||||
\(351\) | 4.12932 | 0.220407 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 0.606483i | − | 0.0322798i | −0.999870 | − | 0.0161399i | \(-0.994862\pi\) | ||
0.999870 | − | 0.0161399i | \(-0.00513772\pi\) | |||||||
\(354\) | 21.8025 | 1.15879 | ||||||||
\(355\) | −14.6648 | − | 6.50406i | −0.778328 | − | 0.345200i | ||||
\(356\) | −46.1756 | −2.44730 | ||||||||
\(357\) | 7.88336i | 0.417232i | ||||||||
\(358\) | − | 35.2603i | − | 1.86356i | ||||||
\(359\) | −1.92548 | −0.101623 | −0.0508115 | − | 0.998708i | \(-0.516181\pi\) | ||||
−0.0508115 | + | 0.998708i | \(0.516181\pi\) | |||||||
\(360\) | −4.18529 | + | 9.43666i | −0.220584 | + | 0.497356i | ||||
\(361\) | −6.63401 | −0.349158 | ||||||||
\(362\) | − | 49.8323i | − | 2.61913i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.6100 | −1.13267 | ||||||||
\(365\) | 3.70394 | − | 8.35135i | 0.193873 | − | 0.437130i | ||||
\(366\) | 15.8427 | 0.828112 | ||||||||
\(367\) | 21.6704i | 1.13118i | 0.824685 | + | 0.565592i | \(0.191352\pi\) | ||||
−0.824685 | + | 0.565592i | \(0.808648\pi\) | |||||||
\(368\) | 21.7452i | 1.13355i | ||||||||
\(369\) | 8.63013 | 0.449266 | ||||||||
\(370\) | 34.8234 | + | 15.4447i | 1.81038 | + | 0.802930i | ||||
\(371\) | −8.61059 | −0.447039 | ||||||||
\(372\) | − | 36.6819i | − | 1.90187i | ||||||
\(373\) | 3.79920i | 0.196715i | 0.995151 | + | 0.0983576i | \(0.0313589\pi\) | ||||
−0.995151 | + | 0.0983576i | \(0.968641\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.6182 | + | 3.50055i | −0.548321 | + | 0.180768i | ||||
\(376\) | −17.2959 | −0.891968 | ||||||||
\(377\) | − | 26.4126i | − | 1.36032i | ||||||
\(378\) | − | 3.25908i | − | 0.167629i | ||||||
\(379\) | 3.37217 | 0.173217 | 0.0866084 | − | 0.996242i | \(-0.472397\pi\) | ||||
0.0866084 | + | 0.996242i | \(0.472397\pi\) | |||||||
\(380\) | −28.0371 | − | 12.4348i | −1.43827 | − | 0.637893i | ||||
\(381\) | 13.9500 | 0.714681 | ||||||||
\(382\) | 35.1821i | 1.80007i | ||||||||
\(383\) | 12.1412i | 0.620384i | 0.950674 | + | 0.310192i | \(0.100393\pi\) | ||||
−0.950674 | + | 0.310192i | \(0.899607\pi\) | |||||||
\(384\) | −20.2574 | −1.03375 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.8409 | −1.46796 | ||||||||
\(387\) | − | 5.31799i | − | 0.270328i | ||||||
\(388\) | − | 9.96085i | − | 0.505685i | ||||||
\(389\) | 29.9203 | 1.51702 | 0.758509 | − | 0.651663i | \(-0.225928\pi\) | ||||
0.758509 | + | 0.651663i | \(0.225928\pi\) | |||||||
\(390\) | 9.09334 | − | 20.5029i | 0.460459 | − | 1.03821i | ||||
\(391\) | −37.4336 | −1.89310 | ||||||||
\(392\) | − | 24.0061i | − | 1.21249i | ||||||
\(393\) | 18.4618i | 0.931274i | ||||||||
\(394\) | −18.4144 | −0.927703 | ||||||||
\(395\) | −20.3862 | − | 9.04158i | −1.02574 | − | 0.454931i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3735i | 1.32365i | 0.749658 | + | 0.661825i | \(0.230218\pi\) | ||||
−0.749658 | + | 0.661825i | \(0.769782\pi\) | |||||||
\(398\) | 41.0043i | 2.05536i | ||||||||
\(399\) | 4.71806 | 0.236199 | ||||||||
\(400\) | 11.4557 | + | 12.6498i | 0.572786 | + | 0.632492i | ||||
\(401\) | −3.39283 | −0.169430 | −0.0847148 | − | 0.996405i | \(-0.526998\pi\) | ||||
−0.0847148 | + | 0.996405i | \(0.526998\pi\) | |||||||
\(402\) | 21.4600i | 1.07033i | ||||||||
\(403\) | 38.8333i | 1.93442i | ||||||||
\(404\) | 61.4086 | 3.05519 | ||||||||
\(405\) | 2.04405 | + | 0.906565i | 0.101570 | + | 0.0450476i | ||||
\(406\) | −20.8463 | −1.03459 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 27.1262i | 1.34295i | ||||||||
\(409\) | −12.3786 | −0.612084 | −0.306042 | − | 0.952018i | \(-0.599005\pi\) | ||||
−0.306042 | + | 0.952018i | \(0.599005\pi\) | |||||||
\(410\) | 19.0048 | − | 42.8504i | 0.938579 | − | 2.11623i | ||||
\(411\) | 7.56366 | 0.373088 | ||||||||
\(412\) | − | 65.3336i | − | 3.21876i | ||||||
\(413\) | 12.0423i | 0.592561i | ||||||||
\(414\) | 15.4755 | 0.760581 | ||||||||
\(415\) | −2.77427 | + | 6.25519i | −0.136183 | + | 0.307055i | ||||
\(416\) | 3.89074 | 0.190759 | ||||||||
\(417\) | 0.572021i | 0.0280120i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.92515 | −0.289463 | −0.144731 | − | 0.989471i | \(-0.546232\pi\) | ||||
−0.144731 | + | 0.989471i | \(0.546232\pi\) | |||||||
\(420\) | −10.6971 | − | 4.74433i | −0.521966 | − | 0.231499i | ||||
\(421\) | 25.2177 | 1.22904 | 0.614518 | − | 0.788903i | \(-0.289350\pi\) | ||||
0.614518 | + | 0.788903i | \(0.289350\pi\) | |||||||
\(422\) | 57.8226i | 2.81476i | ||||||||
\(423\) | 3.74642i | 0.182157i | ||||||||
\(424\) | −29.6286 | −1.43889 | ||||||||
\(425\) | −21.7762 | + | 19.7206i | −1.05630 | + | 0.956590i | ||||
\(426\) | 17.4274 | 0.844359 | ||||||||
\(427\) | 8.75049i | 0.423466i | ||||||||
\(428\) | − | 17.6001i | − | 0.850735i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.4049 | − | 11.7110i | −1.27336 | − | 0.564753i | ||||
\(431\) | 7.51462 | 0.361967 | 0.180983 | − | 0.983486i | \(-0.442072\pi\) | ||||
0.180983 | + | 0.983486i | \(0.442072\pi\) | |||||||
\(432\) | − | 3.41322i | − | 0.164219i | ||||||
\(433\) | − | 15.0318i | − | 0.722382i | −0.932492 | − | 0.361191i | \(-0.882370\pi\) | ||
0.932492 | − | 0.361191i | \(-0.117630\pi\) | |||||||
\(434\) | 30.6494 | 1.47122 | ||||||||
\(435\) | 5.79873 | − | 13.0745i | 0.278028 | − | 0.626875i | ||||
\(436\) | −21.8303 | −1.04548 | ||||||||
\(437\) | 22.4034i | 1.07170i | ||||||||
\(438\) | 9.92457i | 0.474215i | ||||||||
\(439\) | −23.9302 | −1.14213 | −0.571063 | − | 0.820906i | \(-0.693469\pi\) | ||||
−0.571063 | + | 0.820906i | \(0.693469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.19989 | −0.247614 | ||||||||
\(442\) | − | 58.9368i | − | 2.80334i | ||||||
\(443\) | − | 38.2368i | − | 1.81668i | −0.418228 | − | 0.908342i | \(-0.637349\pi\) | ||
0.418228 | − | 0.908342i | \(-0.362651\pi\) | |||||||
\(444\) | −27.3564 | −1.29828 | ||||||||
\(445\) | 24.1979 | + | 10.7321i | 1.14709 | + | 0.508751i | ||||
\(446\) | −52.6800 | −2.49447 | ||||||||
\(447\) | 9.20494i | 0.435379i | ||||||||
\(448\) | − | 12.2297i | − | 0.577799i | ||||||
\(449\) | 0.0371096 | 0.00175131 | 0.000875656 | − | 1.00000i | \(-0.499721\pi\) | ||||
0.000875656 | 1.00000i | \(0.499721\pi\) | ||||||||
\(450\) | 9.00258 | − | 8.15276i | 0.424386 | − | 0.384325i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 12.4520i | − | 0.585694i | ||||||
\(453\) | − | 0.453311i | − | 0.0212984i | ||||||
\(454\) | 2.57476 | 0.120840 | ||||||||
\(455\) | 11.3245 | + | 5.02257i | 0.530900 | + | 0.235462i | ||||
\(456\) | 16.2346 | 0.760254 | ||||||||
\(457\) | − | 6.66208i | − | 0.311639i | −0.987786 | − | 0.155819i | \(-0.950198\pi\) | ||
0.987786 | − | 0.155819i | \(-0.0498018\pi\) | |||||||
\(458\) | 34.1721i | 1.59676i | ||||||||
\(459\) | 5.87573 | 0.274256 | ||||||||
\(460\) | 22.5281 | − | 50.7946i | 1.05038 | − | 2.36831i | ||||
\(461\) | 41.4711 | 1.93150 | 0.965751 | − | 0.259469i | \(-0.0835476\pi\) | ||||
0.965751 | + | 0.259469i | \(0.0835476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.90915i | − | 0.460517i | −0.973129 | − | 0.230259i | \(-0.926043\pi\) | ||
0.973129 | − | 0.230259i | \(-0.0739572\pi\) | |||||||
\(464\) | −21.8322 | −1.01354 | ||||||||
\(465\) | −8.52560 | + | 19.2228i | −0.395365 | + | 0.891437i | ||||
\(466\) | 0.729860 | 0.0338101 | ||||||||
\(467\) | 20.2241i | 0.935862i | 0.883765 | + | 0.467931i | \(0.155000\pi\) | ||||
−0.883765 | + | 0.467931i | \(0.845000\pi\) | |||||||
\(468\) | 16.1066i | 0.744529i | ||||||||
\(469\) | −11.8531 | −0.547325 | ||||||||
\(470\) | 18.6018 | + | 8.25015i | 0.858036 | + | 0.380551i | ||||
\(471\) | 3.14144 | 0.144750 | ||||||||
\(472\) | 41.4368i | 1.90728i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 24.2266 | 1.11276 | ||||||||
\(475\) | 11.8025 | + | 13.0327i | 0.541534 | + | 0.597982i | ||||
\(476\) | −30.7495 | −1.40940 | ||||||||
\(477\) | 6.41776i | 0.293849i | ||||||||
\(478\) | 25.2397i | 1.15444i | ||||||||
\(479\) | −14.6210 | −0.668050 | −0.334025 | − | 0.942564i | \(-0.608407\pi\) | ||||
−0.334025 | + | 0.942564i | \(0.608407\pi\) | |||||||
\(480\) | 1.92595 | + | 0.854188i | 0.0879074 | + | 0.0389882i | ||||
\(481\) | 28.9609 | 1.32050 | ||||||||
\(482\) | 13.9340i | 0.634675i | ||||||||
\(483\) | 8.54768i | 0.388933i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.31510 | + | 5.21989i | −0.105123 | + | 0.237023i | ||||
\(486\) | −2.42911 | −0.110186 | ||||||||
\(487\) | − | 8.06456i | − | 0.365440i | −0.983165 | − | 0.182720i | \(-0.941510\pi\) | ||
0.983165 | − | 0.182720i | \(-0.0584902\pi\) | |||||||
\(488\) | 30.1100i | 1.36301i | ||||||||
\(489\) | 0.374743 | 0.0169464 | ||||||||
\(490\) | −11.4509 | + | 25.8186i | −0.517299 | + | 1.16636i | ||||
\(491\) | −9.09215 | −0.410323 | −0.205161 | − | 0.978728i | \(-0.565772\pi\) | ||||
−0.205161 | + | 0.978728i | \(0.565772\pi\) | |||||||
\(492\) | 33.6623i | 1.51761i | ||||||||
\(493\) | − | 37.5834i | − | 1.69267i | ||||||
\(494\) | −35.2727 | −1.58699 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0989 | 1.44128 | ||||||||
\(497\) | 9.62575i | 0.431774i | ||||||||
\(498\) | − | 7.43354i | − | 0.333105i | ||||||
\(499\) | 4.36117 | 0.195233 | 0.0976164 | − | 0.995224i | \(-0.468878\pi\) | ||||
0.0976164 | + | 0.995224i | \(0.468878\pi\) | |||||||
\(500\) | −13.6541 | − | 41.4169i | −0.610630 | − | 1.85222i | ||||
\(501\) | −20.0873 | −0.897434 | ||||||||
\(502\) | − | 5.08270i | − | 0.226852i | ||||||
\(503\) | − | 10.3116i | − | 0.459771i | −0.973218 | − | 0.229885i | \(-0.926165\pi\) | ||
0.973218 | − | 0.229885i | \(-0.0738351\pi\) | |||||||
\(504\) | 6.19407 | 0.275906 | ||||||||
\(505\) | −32.1806 | − | 14.2726i | −1.43202 | − | 0.635121i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.05125i | − | 0.179922i | ||||||
\(508\) | 54.4128i | 2.41418i | ||||||||
\(509\) | −7.38429 | −0.327303 | −0.163652 | − | 0.986518i | \(-0.552327\pi\) | ||||
−0.163652 | + | 0.986518i | \(0.552327\pi\) | |||||||
\(510\) | 12.9392 | − | 29.1743i | 0.572958 | − | 1.29186i | ||||
\(511\) | −5.48169 | −0.242496 | ||||||||
\(512\) | − | 34.7313i | − | 1.53492i | ||||||
\(513\) | − | 3.51653i | − | 0.155259i | ||||||
\(514\) | −56.4847 | −2.49143 | ||||||||
\(515\) | −15.1848 | + | 34.2375i | −0.669123 | + | 1.50868i | ||||
\(516\) | 20.7431 | 0.913164 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 22.8575i | − | 1.00430i | ||||||
\(519\) | −2.71823 | −0.119317 | ||||||||
\(520\) | 38.9670 | + | 17.2824i | 1.70881 | + | 0.757883i | ||||
\(521\) | −43.3169 | −1.89775 | −0.948874 | − | 0.315655i | \(-0.897776\pi\) | ||||
−0.948874 | + | 0.315655i | \(0.897776\pi\) | |||||||
\(522\) | 15.5375i | 0.680056i | ||||||||
\(523\) | − | 17.9584i | − | 0.785268i | −0.919695 | − | 0.392634i | \(-0.871564\pi\) | ||
0.919695 | − | 0.392634i | \(-0.128436\pi\) | |||||||
\(524\) | −72.0112 | −3.14582 | ||||||||
\(525\) | 4.50306 | + | 4.97244i | 0.196529 | + | 0.217015i | ||||
\(526\) | −9.03454 | −0.393925 | ||||||||
\(527\) | 55.2571i | 2.40704i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5881 | −0.764699 | ||||||||
\(530\) | 31.8656 | + | 14.1328i | 1.38415 | + | 0.613891i | ||||
\(531\) | 8.97551 | 0.389504 | ||||||||
\(532\) | 18.4031i | 0.797874i | ||||||||
\(533\) | − | 35.6365i | − | 1.54359i | ||||||
\(534\) | −28.7563 | −1.24441 | ||||||||
\(535\) | −4.09062 | + | 9.22319i | −0.176853 | + | 0.398753i | ||||
\(536\) | −40.7859 | −1.76168 | ||||||||
\(537\) | − | 14.5157i | − | 0.626400i | ||||||
\(538\) | − | 29.3900i | − | 1.26709i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.53611 | + | 7.97293i | −0.152170 | + | 0.343100i | ||||
\(541\) | −25.6681 | −1.10356 | −0.551780 | − | 0.833990i | \(-0.686051\pi\) | ||||
−0.551780 | + | 0.833990i | \(0.686051\pi\) | |||||||
\(542\) | 7.92645i | 0.340470i | ||||||||
\(543\) | − | 20.5147i | − | 0.880369i | ||||||
\(544\) | 5.53626 | 0.237365 | ||||||||
\(545\) | 11.4400 | + | 5.07379i | 0.490034 | + | 0.217337i | ||||
\(546\) | −13.4578 | −0.575940 | ||||||||
\(547\) | − | 6.31838i | − | 0.270154i | −0.990835 | − | 0.135077i | \(-0.956872\pi\) | ||
0.990835 | − | 0.135077i | \(-0.0431282\pi\) | |||||||
\(548\) | 29.5025i | 1.26028i | ||||||||
\(549\) | 6.52203 | 0.278354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.4930 | −0.958236 | ||||||||
\(552\) | 29.4121i | 1.25186i | ||||||||
\(553\) | 13.3812i | 0.569026i | ||||||||
\(554\) | 57.4399 | 2.44039 | ||||||||
\(555\) | 14.3359 | + | 6.35817i | 0.608525 | + | 0.269889i | ||||
\(556\) | −2.23120 | −0.0946240 | ||||||||
\(557\) | − | 41.0505i | − | 1.73936i | −0.493612 | − | 0.869682i | \(-0.664324\pi\) | ||
0.493612 | − | 0.869682i | \(-0.335676\pi\) | |||||||
\(558\) | − | 22.8440i | − | 0.967064i | ||||||
\(559\) | −21.9597 | −0.928794 | ||||||||
\(560\) | 4.15157 | − | 9.36063i | 0.175436 | − | 0.395559i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 73.5894i | 3.10418i | ||||||||
\(563\) | 8.99298i | 0.379009i | 0.981880 | + | 0.189505i | \(0.0606882\pi\) | ||||
−0.981880 | + | 0.189505i | \(0.939312\pi\) | |||||||
\(564\) | −14.6131 | −0.615323 | ||||||||
\(565\) | −2.89409 | + | 6.52537i | −0.121755 | + | 0.274524i | ||||
\(566\) | −30.8351 | −1.29610 | ||||||||
\(567\) | − | 1.34168i | − | 0.0563453i | ||||||
\(568\) | 33.1217i | 1.38975i | ||||||||
\(569\) | −1.86723 | −0.0782785 | −0.0391393 | − | 0.999234i | \(-0.512462\pi\) | ||||
−0.0391393 | + | 0.999234i | \(0.512462\pi\) | |||||||
\(570\) | −17.4603 | − | 7.74390i | −0.731333 | − | 0.324356i | ||||
\(571\) | 1.74298 | 0.0729414 | 0.0364707 | − | 0.999335i | \(-0.488388\pi\) | ||||
0.0364707 | + | 0.999335i | \(0.488388\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.4836i | 0.605060i | ||||||||
\(574\) | −28.1263 | −1.17397 | ||||||||
\(575\) | −23.6113 | + | 21.3824i | −0.984659 | + | 0.891710i | ||||
\(576\) | −9.11521 | −0.379800 | ||||||||
\(577\) | − | 14.6183i | − | 0.608566i | −0.952582 | − | 0.304283i | \(-0.901583\pi\) | ||
0.952582 | − | 0.304283i | \(-0.0984169\pi\) | |||||||
\(578\) | − | 42.5683i | − | 1.77061i | ||||||
\(579\) | −11.8730 | −0.493427 | ||||||||
\(580\) | 50.9978 | + | 22.6183i | 2.11757 | + | 0.939172i | ||||
\(581\) | 4.10581 | 0.170338 | ||||||||
\(582\) | − | 6.20321i | − | 0.257131i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −18.8622 | −0.780524 | ||||||||
\(585\) | 3.74349 | − | 8.44053i | 0.154774 | − | 0.348973i | ||||
\(586\) | 5.10823 | 0.211019 | ||||||||
\(587\) | 20.3498i | 0.839924i | 0.907542 | + | 0.419962i | \(0.137957\pi\) | ||||
−0.907542 | + | 0.419962i | \(0.862043\pi\) | |||||||
\(588\) | − | 20.2825i | − | 0.836435i | ||||||
\(589\) | 33.0705 | 1.36264 | ||||||||
\(590\) | 19.7654 | − | 44.5653i | 0.813727 | − | 1.83472i | ||||
\(591\) | −7.58073 | −0.311829 | ||||||||
\(592\) | − | 23.9385i | − | 0.983868i | ||||||
\(593\) | 22.6138i | 0.928637i | 0.885668 | + | 0.464318i | \(0.153701\pi\) | ||||
−0.885668 | + | 0.464318i | \(0.846299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.1140 | + | 7.14678i | 0.660609 | + | 0.292989i | ||||
\(596\) | −35.9044 | −1.47070 | ||||||||
\(597\) | 16.8804i | 0.690868i | ||||||||
\(598\) | − | 63.9034i | − | 2.61320i | ||||||
\(599\) | 23.2627 | 0.950488 | 0.475244 | − | 0.879854i | \(-0.342360\pi\) | ||||
0.475244 | + | 0.879854i | \(0.342360\pi\) | |||||||
\(600\) | 15.4948 | + | 17.1099i | 0.632571 | + | 0.698509i | ||||
\(601\) | 21.6032 | 0.881214 | 0.440607 | − | 0.897700i | \(-0.354763\pi\) | ||||
0.440607 | + | 0.897700i | \(0.354763\pi\) | |||||||
\(602\) | 17.3318i | 0.706390i | ||||||||
\(603\) | 8.83452i | 0.359769i | ||||||||
\(604\) | 1.76816 | 0.0719456 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 38.2428 | 1.55351 | ||||||||
\(607\) | − | 17.3433i | − | 0.703945i | −0.936010 | − | 0.351972i | \(-0.885511\pi\) | ||
0.936010 | − | 0.351972i | \(-0.114489\pi\) | |||||||
\(608\) | − | 3.31336i | − | 0.134375i | ||||||
\(609\) | −8.58189 | −0.347756 | ||||||||
\(610\) | 14.3625 | − | 32.3833i | 0.581519 | − | 1.31116i | ||||
\(611\) | 15.4701 | 0.625855 | ||||||||
\(612\) | 22.9186i | 0.926431i | ||||||||
\(613\) | − | 26.2287i | − | 1.05937i | −0.848195 | − | 0.529684i | \(-0.822311\pi\) | ||
0.848195 | − | 0.529684i | \(-0.177689\pi\) | |||||||
\(614\) | −32.8986 | −1.32768 | ||||||||
\(615\) | 7.82377 | − | 17.6404i | 0.315485 | − | 0.711330i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.3468i | − | 0.980164i | −0.871676 | − | 0.490082i | \(-0.836967\pi\) | ||
0.871676 | − | 0.490082i | \(-0.163033\pi\) | |||||||
\(618\) | − | 40.6871i | − | 1.63668i | ||||||
\(619\) | 23.1100 | 0.928868 | 0.464434 | − | 0.885608i | \(-0.346258\pi\) | ||||
0.464434 | + | 0.885608i | \(0.346258\pi\) | |||||||
\(620\) | −74.9797 | − | 33.2546i | −3.01126 | − | 1.33554i | ||||
\(621\) | 6.37088 | 0.255655 | ||||||||
\(622\) | 17.4896i | 0.701267i | ||||||||
\(623\) | − | 15.8831i | − | 0.636343i | ||||||
\(624\) | −14.0943 | −0.564222 | ||||||||
\(625\) | −2.47078 | + | 24.8776i | −0.0988312 | + | 0.995104i | ||||
\(626\) | 8.74020 | 0.349329 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.2534i | 0.488963i | ||||||||
\(629\) | 41.2093 | 1.64312 | ||||||||
\(630\) | −6.66173 | − | 2.95457i | −0.265410 | − | 0.117713i | ||||
\(631\) | 4.85469 | 0.193262 | 0.0966311 | − | 0.995320i | \(-0.469193\pi\) | ||||
0.0966311 | + | 0.995320i | \(0.469193\pi\) | |||||||
\(632\) | 46.0439i | 1.83153i | ||||||||
\(633\) | 23.8041i | 0.946127i | ||||||||
\(634\) | 60.1101 | 2.38728 | ||||||||
\(635\) | 12.6466 | − | 28.5145i | 0.501865 | − | 1.13156i | ||||
\(636\) | −25.0328 | −0.992616 | ||||||||
\(637\) | 21.4720i | 0.850752i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.17440 | 0.283815 | ||||||||
\(640\) | −18.3646 | + | 41.4070i | −0.725925 | + | 1.63676i | ||||
\(641\) | 21.8725 | 0.863911 | 0.431956 | − | 0.901895i | \(-0.357824\pi\) | ||||
0.431956 | + | 0.901895i | \(0.357824\pi\) | |||||||
\(642\) | − | 10.9606i | − | 0.432582i | ||||||
\(643\) | 34.5523i | 1.36261i | 0.732000 | + | 0.681305i | \(0.238587\pi\) | ||||
−0.732000 | + | 0.681305i | \(0.761413\pi\) | |||||||
\(644\) | −33.3407 | −1.31381 | ||||||||
\(645\) | −10.8702 | − | 4.82110i | −0.428015 | − | 0.189831i | ||||
\(646\) | −50.1907 | −1.97473 | ||||||||
\(647\) | 19.5511i | 0.768632i | 0.923202 | + | 0.384316i | \(0.125563\pi\) | ||||
−0.923202 | + | 0.384316i | \(0.874437\pi\) | |||||||
\(648\) | − | 4.61665i | − | 0.181359i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −33.6653 | − | 37.1745i | −1.32046 | − | 1.45810i | ||||
\(651\) | 12.6175 | 0.494521 | ||||||||
\(652\) | 1.46170i | 0.0572448i | ||||||||
\(653\) | 34.6776i | 1.35704i | 0.734582 | + | 0.678520i | \(0.237379\pi\) | ||||
−0.734582 | + | 0.678520i | \(0.762621\pi\) | |||||||
\(654\) | −13.5950 | −0.531607 | ||||||||
\(655\) | 37.7368 | + | 16.7368i | 1.47450 | + | 0.653961i | ||||
\(656\) | −29.4565 | −1.15008 | ||||||||
\(657\) | 4.08569i | 0.159398i | ||||||||
\(658\) | − | 12.2099i | − | 0.475991i | ||||||
\(659\) | 33.0024 | 1.28559 | 0.642796 | − | 0.766037i | \(-0.277774\pi\) | ||||
0.642796 | + | 0.766037i | \(0.277774\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8988 | 0.773974 | 0.386987 | − | 0.922085i | \(-0.373516\pi\) | ||||
0.386987 | + | 0.922085i | \(0.373516\pi\) | |||||||
\(662\) | 32.4069i | 1.25953i | ||||||||
\(663\) | − | 24.2628i | − | 0.942288i | ||||||
\(664\) | 14.1279 | 0.548267 | ||||||||
\(665\) | 4.27723 | − | 9.64395i | 0.165864 | − | 0.373976i | ||||
\(666\) | −17.0365 | −0.660150 | ||||||||
\(667\) | − | 40.7505i | − | 1.57787i | ||||||
\(668\) | − | 78.3516i | − | 3.03152i | ||||||
\(669\) | −21.6870 | −0.838468 | ||||||||
\(670\) | 43.8653 | + | 19.4549i | 1.69466 | + | 0.751607i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 1.26416i | − | 0.0487662i | ||||||
\(673\) | − | 11.9694i | − | 0.461388i | −0.973026 | − | 0.230694i | \(-0.925900\pi\) | ||
0.973026 | − | 0.230694i | \(-0.0740996\pi\) | |||||||
\(674\) | 63.6159 | 2.45039 | ||||||||
\(675\) | 3.70613 | − | 3.35628i | 0.142649 | − | 0.129183i | ||||
\(676\) | 15.8021 | 0.607774 | ||||||||
\(677\) | 14.3812i | 0.552714i | 0.961055 | + | 0.276357i | \(0.0891273\pi\) | ||||
−0.961055 | + | 0.276357i | \(0.910873\pi\) | |||||||
\(678\) | − | 7.75461i | − | 0.297814i | ||||||
\(679\) | 3.42625 | 0.131487 | ||||||||
\(680\) | 55.4473 | + | 24.5917i | 2.12631 | + | 0.943048i | ||||
\(681\) | 1.05996 | 0.0406179 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0922i | 1.15144i | 0.817645 | + | 0.575722i | \(0.195279\pi\) | ||||
−0.817645 | + | 0.575722i | \(0.804721\pi\) | |||||||
\(684\) | 13.7164 | 0.524461 | ||||||||
\(685\) | 6.85695 | − | 15.4605i | 0.261990 | − | 0.590715i | ||||
\(686\) | 39.7605 | 1.51806 | ||||||||
\(687\) | 14.0678i | 0.536719i | ||||||||
\(688\) | 18.1515i | 0.692018i | ||||||||
\(689\) | 26.5010 | 1.00961 | ||||||||
\(690\) | 14.0296 | − | 31.6328i | 0.534097 | − | 1.20424i | ||||
\(691\) | 36.0306 | 1.37067 | 0.685334 | − | 0.728229i | \(-0.259656\pi\) | ||||
0.685334 | + | 0.728229i | \(0.259656\pi\) | |||||||
\(692\) | − | 10.6026i | − | 0.403050i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.41703 | 0.205628 | ||||||||
\(695\) | 1.16924 | + | 0.518575i | 0.0443518 | + | 0.0196707i | ||||
\(696\) | −29.5298 | −1.11932 | ||||||||
\(697\) | − | 50.7083i | − | 1.92071i | ||||||
\(698\) | 47.3986i | 1.79406i | ||||||||
\(699\) | 0.300464 | 0.0113646 | ||||||||
\(700\) | −19.3953 | + | 17.5644i | −0.733073 | + | 0.663873i | ||||
\(701\) | 20.9413 | 0.790942 | 0.395471 | − | 0.918478i | \(-0.370581\pi\) | ||||
0.395471 | + | 0.918478i | \(0.370581\pi\) | |||||||
\(702\) | 10.0305i | 0.378579i | ||||||||
\(703\) | − | 24.6631i | − | 0.930187i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.65787 | + | 3.39637i | 0.288412 | + | 0.127915i | ||||
\(706\) | 1.47321 | 0.0554451 | ||||||||
\(707\) | 21.1228i | 0.794406i | ||||||||
\(708\) | 35.0095i | 1.31574i | ||||||||
\(709\) | 11.1784 | 0.419815 | 0.209907 | − | 0.977721i | \(-0.432684\pi\) | ||||
0.209907 | + | 0.977721i | \(0.432684\pi\) | |||||||
\(710\) | 15.7990 | − | 35.6224i | 0.592928 | − | 1.33689i | ||||
\(711\) | 9.97344 | 0.374033 | ||||||||
\(712\) | − | 54.6529i | − | 2.04820i | ||||||
\(713\) | 59.9136i | 2.24378i | ||||||||
\(714\) | −19.1495 | −0.716653 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 56.6194 | 2.11597 | ||||||||
\(717\) | 10.3905i | 0.388041i | ||||||||
\(718\) | − | 4.67719i | − | 0.174551i | ||||||
\(719\) | 3.91415 | 0.145973 | 0.0729865 | − | 0.997333i | \(-0.476747\pi\) | ||||
0.0729865 | + | 0.997333i | \(0.476747\pi\) | |||||||
\(720\) | −6.97679 | − | 3.09431i | −0.260010 | − | 0.115318i | ||||
\(721\) | 22.4729 | 0.836936 | ||||||||
\(722\) | − | 16.1147i | − | 0.599728i | ||||||
\(723\) | 5.73625i | 0.213334i | ||||||||
\(724\) | 80.0186 | 2.97387 | ||||||||
\(725\) | −21.4680 | − | 23.7058i | −0.797302 | − | 0.880411i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.7446i | 0.583934i | 0.956428 | + | 0.291967i | \(0.0943098\pi\) | ||||
−0.956428 | + | 0.291967i | \(0.905690\pi\) | |||||||
\(728\) | − | 25.5773i | − | 0.947957i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 20.2863 | + | 8.99727i | 0.750831 | + | 0.333004i | ||||
\(731\) | −31.2471 | −1.15572 | ||||||||
\(732\) | 25.4396i | 0.940273i | ||||||||
\(733\) | − | 41.4651i | − | 1.53155i | −0.643109 | − | 0.765775i | \(-0.722356\pi\) | ||
0.643109 | − | 0.765775i | \(-0.277644\pi\) | |||||||
\(734\) | −52.6397 | −1.94297 | ||||||||
\(735\) | −4.71404 | + | 10.6288i | −0.173880 | + | 0.392051i | ||||
\(736\) | 6.00280 | 0.221266 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 20.9635i | 0.771677i | ||||||||
\(739\) | 38.5029 | 1.41635 | 0.708177 | − | 0.706035i | \(-0.249518\pi\) | ||||
0.708177 | + | 0.706035i | \(0.249518\pi\) | |||||||
\(740\) | −24.8004 | + | 55.9179i | −0.911681 | + | 2.05558i | ||||
\(741\) | −14.5209 | −0.533437 | ||||||||
\(742\) | − | 20.9160i | − | 0.767851i | ||||||
\(743\) | 22.4806i | 0.824733i | 0.911018 | + | 0.412366i | \(0.135298\pi\) | ||||
−0.911018 | + | 0.412366i | \(0.864702\pi\) | |||||||
\(744\) | 43.4163 | 1.59172 | ||||||||
\(745\) | 18.8154 | + | 8.34488i | 0.689342 | + | 0.305733i | ||||
\(746\) | −9.22866 | −0.337885 | ||||||||
\(747\) | − | 3.06020i | − | 0.111967i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.05395 | 0.221207 | ||||||||
\(750\) | −8.50322 | − | 25.7927i | −0.310494 | − | 0.941817i | ||||
\(751\) | 27.3369 | 0.997537 | 0.498769 | − | 0.866735i | \(-0.333786\pi\) | ||||
0.498769 | + | 0.866735i | \(0.333786\pi\) | |||||||
\(752\) | − | 12.7874i | − | 0.466307i | ||||||
\(753\) | − | 2.09242i | − | 0.0762519i | ||||||
\(754\) | 64.1591 | 2.33654 | ||||||||
\(755\) | −0.926590 | − | 0.410956i | −0.0337221 | − | 0.0149562i | ||||
\(756\) | 5.23330 | 0.190333 | ||||||||
\(757\) | − | 36.6287i | − | 1.33129i | −0.746267 | − | 0.665647i | \(-0.768156\pi\) | ||
0.746267 | − | 0.665647i | \(-0.231844\pi\) | |||||||
\(758\) | 8.19136i | 0.297524i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.7177 | − | 33.1843i | 0.533868 | − | 1.20372i | ||||
\(761\) | 53.6199 | 1.94372 | 0.971859 | − | 0.235562i | \(-0.0756932\pi\) | ||||
0.971859 | + | 0.235562i | \(0.0756932\pi\) | |||||||
\(762\) | 33.8861i | 1.22756i | ||||||||
\(763\) | − | 7.50901i | − | 0.271844i | ||||||
\(764\) | −56.4940 | −2.04388 | ||||||||
\(765\) | 5.32674 | − | 12.0103i | 0.192589 | − | 0.434233i | ||||
\(766\) | −29.4921 | −1.06559 | ||||||||
\(767\) | − | 37.0627i | − | 1.33826i | ||||||
\(768\) | − | 30.9768i | − | 1.11778i | ||||||
\(769\) | −51.8506 | −1.86978 | −0.934890 | − | 0.354939i | \(-0.884502\pi\) | ||||
−0.934890 | + | 0.354939i | \(0.884502\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.2533 | −0.837447 | ||||||||
\(772\) | − | 46.3114i | − | 1.66679i | ||||||
\(773\) | 1.50494i | 0.0541288i | 0.999634 | + | 0.0270644i | \(0.00861592\pi\) | ||||
−0.999634 | + | 0.0270644i | \(0.991384\pi\) | |||||||
\(774\) | 12.9180 | 0.464326 | ||||||||
\(775\) | 31.5634 | + | 34.8535i | 1.13379 | + | 1.25197i | ||||
\(776\) | 11.7895 | 0.423220 | ||||||||
\(777\) | − | 9.40985i | − | 0.337576i | ||||||
\(778\) | 72.6795i | 2.60569i | ||||||||
\(779\) | −30.3481 | −1.08733 | ||||||||
\(780\) | 32.9227 | + | 14.6017i | 1.17882 | + | 0.522825i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 90.9302i | − | 3.25166i | ||||||
\(783\) | 6.39637i | 0.228588i | ||||||||
\(784\) | 17.7484 | 0.633871 | ||||||||
\(785\) | 2.84792 | − | 6.42126i | 0.101647 | − | 0.229185i | ||||
\(786\) | −44.8456 | −1.59959 | ||||||||
\(787\) | − | 22.5259i | − | 0.802962i | −0.915867 | − | 0.401481i | \(-0.868496\pi\) | ||
0.915867 | − | 0.401481i | \(-0.131504\pi\) | |||||||
\(788\) | − | 29.5690i | − | 1.05335i | ||||||
\(789\) | −3.71929 | −0.132410 | ||||||||
\(790\) | 21.9629 | − | 49.5203i | 0.781407 | − | 1.76185i | ||||
\(791\) | 4.28315 | 0.152291 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 26.9315i | − | 0.956367i | ||||||
\(794\) | −64.0641 | −2.27355 | ||||||||
\(795\) | 13.1182 | + | 5.81812i | 0.465255 | + | 0.206347i | ||||
\(796\) | −65.8429 | −2.33374 | ||||||||
\(797\) | − | 44.3628i | − | 1.57141i | −0.618600 | − | 0.785706i | \(-0.712300\pi\) | ||
0.618600 | − | 0.785706i | \(-0.287700\pi\) | |||||||
\(798\) | 11.4607i | 0.405703i | ||||||||
\(799\) | 22.0130 | 0.778763 | ||||||||
\(800\) | 3.49200 | − | 3.16237i | 0.123461 | − | 0.111807i | ||||
\(801\) | −11.8382 | −0.418283 | ||||||||
\(802\) | − | 8.24153i | − | 0.291019i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −34.4595 | −1.21529 | ||||||||
\(805\) | 17.4719 | + | 7.74903i | 0.615803 | + | 0.273118i | ||||
\(806\) | −94.3301 | −3.32264 | ||||||||
\(807\) | − | 12.0991i | − | 0.425909i | ||||||
\(808\) | 72.6825i | 2.55696i | ||||||||
\(809\) | −7.69469 | −0.270531 | −0.135265 | − | 0.990809i | \(-0.543189\pi\) | ||||
−0.135265 | + | 0.990809i | \(0.543189\pi\) | |||||||
\(810\) | −2.20214 | + | 4.96521i | −0.0773754 | + | 0.174460i | ||||
\(811\) | 25.7414 | 0.903902 | 0.451951 | − | 0.892043i | \(-0.350728\pi\) | ||||
0.451951 | + | 0.892043i | \(0.350728\pi\) | |||||||
\(812\) | − | 33.4741i | − | 1.17471i | ||||||
\(813\) | 3.26311i | 0.114442i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.339729 | − | 0.765993i | 0.0119002 | − | 0.0268316i | ||||
\(816\) | −20.0552 | −0.702072 | ||||||||
\(817\) | 18.7009i | 0.654261i | ||||||||
\(818\) | − | 30.0690i | − | 1.05134i | ||||||
\(819\) | −5.54022 | −0.193591 | ||||||||
\(820\) | 68.8074 | + | 30.5171i | 2.40286 | + | 1.06570i | ||||
\(821\) | −18.3921 | −0.641887 | −0.320944 | − | 0.947098i | \(-0.604000\pi\) | ||||
−0.320944 | + | 0.947098i | \(0.604000\pi\) | |||||||
\(822\) | 18.3729i | 0.640829i | ||||||||
\(823\) | 3.49286i | 0.121753i | 0.998145 | + | 0.0608767i | \(0.0193896\pi\) | ||||
−0.998145 | + | 0.0608767i | \(0.980610\pi\) | |||||||
\(824\) | 77.3281 | 2.69385 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.2519 | −1.01781 | ||||||||
\(827\) | − | 0.466783i | − | 0.0162317i | −0.999967 | − | 0.00811583i | \(-0.997417\pi\) | ||
0.999967 | − | 0.00811583i | \(-0.00258338\pi\) | |||||||
\(828\) | 24.8500i | 0.863596i | ||||||||
\(829\) | 50.9521 | 1.76964 | 0.884820 | − | 0.465933i | \(-0.154281\pi\) | ||||
0.884820 | + | 0.465933i | \(0.154281\pi\) | |||||||
\(830\) | −15.1945 | − | 6.73899i | −0.527410 | − | 0.233914i | ||||
\(831\) | 23.6465 | 0.820288 | ||||||||
\(832\) | 37.6396i | 1.30492i | ||||||||
\(833\) | 30.5532i | 1.05861i | ||||||||
\(834\) | −1.38950 | −0.0481145 | ||||||||
\(835\) | −18.2104 | + | 41.0594i | −0.630199 | + | 1.42092i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.40429i | − | 0.325060i | ||||||
\(838\) | − | 14.3928i | − | 0.497192i | ||||||
\(839\) | −35.8479 | −1.23761 | −0.618804 | − | 0.785545i | \(-0.712383\pi\) | ||||
−0.618804 | + | 0.785545i | \(0.712383\pi\) | |||||||
\(840\) | 5.61533 | − | 12.6610i | 0.193747 | − | 0.436846i | ||||
\(841\) | 11.9136 | 0.410813 | ||||||||
\(842\) | 61.2565i | 2.11104i | ||||||||
\(843\) | 30.2948i | 1.04341i | ||||||||
\(844\) | −92.8491 | −3.19600 | ||||||||
\(845\) | −8.28096 | − | 3.67272i | −0.284874 | − | 0.126346i | ||||
\(846\) | −9.10045 | −0.312880 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 21.9052i | − | 0.752229i | ||||||
\(849\) | −12.6940 | −0.435658 | ||||||||
\(850\) | −47.9034 | − | 52.8968i | −1.64307 | − | 1.81434i | ||||
\(851\) | 44.6820 | 1.53168 | ||||||||
\(852\) | 27.9841i | 0.958721i | ||||||||
\(853\) | − | 39.0874i | − | 1.33833i | −0.743114 | − | 0.669164i | \(-0.766652\pi\) | ||
0.743114 | − | 0.669164i | \(-0.233348\pi\) | |||||||
\(854\) | −21.2559 | −0.727361 | ||||||||
\(855\) | −7.18796 | − | 3.18796i | −0.245823 | − | 0.109026i | ||||
\(856\) | 20.8313 | 0.712000 | ||||||||
\(857\) | − | 49.2657i | − | 1.68289i | −0.540346 | − | 0.841443i | \(-0.681707\pi\) | ||
0.540346 | − | 0.841443i | \(-0.318293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.27352 | −0.316408 | −0.158204 | − | 0.987406i | \(-0.550570\pi\) | ||||
−0.158204 | + | 0.987406i | \(0.550570\pi\) | |||||||
\(860\) | 18.8050 | − | 42.3999i | 0.641244 | − | 1.44583i | ||||
\(861\) | −11.5789 | −0.394607 | ||||||||
\(862\) | 18.2538i | 0.621727i | ||||||||
\(863\) | 11.8883i | 0.404683i | 0.979315 | + | 0.202341i | \(0.0648551\pi\) | ||||
−0.979315 | + | 0.202341i | \(0.935145\pi\) | |||||||
\(864\) | −0.942224 | −0.0320551 | ||||||||
\(865\) | −2.46425 | + | 5.55619i | −0.0837870 | + | 0.188916i | ||||
\(866\) | 36.5138 | 1.24079 | ||||||||
\(867\) | − | 17.5243i | − | 0.595155i | ||||||
\(868\) | 49.2154i | 1.67048i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 31.7594 | + | 14.0857i | 1.07674 | + | 0.477551i | ||||
\(871\) | 36.4805 | 1.23610 | ||||||||
\(872\) | − | 25.8381i | − | 0.874988i | ||||||
\(873\) | − | 2.55370i | − | 0.0864296i | ||||||
\(874\) | −54.4202 | −1.84079 | ||||||||
\(875\) | 14.2462 | − | 4.69663i | 0.481611 | − | 0.158775i | ||||
\(876\) | −15.9365 | −0.538443 | ||||||||
\(877\) | 29.9283i | 1.01061i | 0.862942 | + | 0.505303i | \(0.168619\pi\) | ||||
−0.862942 | + | 0.505303i | \(0.831381\pi\) | |||||||
\(878\) | − | 58.1290i | − | 1.96176i | ||||||
\(879\) | 2.10292 | 0.0709299 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.7852 | −1.23932 | −0.619662 | − | 0.784869i | \(-0.712730\pi\) | ||||
−0.619662 | + | 0.784869i | \(0.712730\pi\) | |||||||
\(882\) | − | 12.6311i | − | 0.425311i | ||||||
\(883\) | 21.6154i | 0.727418i | 0.931513 | + | 0.363709i | \(0.118490\pi\) | ||||
−0.931513 | + | 0.363709i | \(0.881510\pi\) | |||||||
\(884\) | 94.6383 | 3.18303 | ||||||||
\(885\) | 8.13688 | − | 18.3464i | 0.273518 | − | 0.616707i | ||||
\(886\) | 92.8812 | 3.12040 | ||||||||
\(887\) | 41.0937i | 1.37979i | 0.723909 | + | 0.689895i | \(0.242343\pi\) | ||||
−0.723909 | + | 0.689895i | \(0.757657\pi\) | |||||||
\(888\) | − | 32.3788i | − | 1.08656i | ||||||
\(889\) | −18.7165 | −0.627730 | ||||||||
\(890\) | −26.0695 | + | 58.7793i | −0.873850 | + | 1.97029i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 84.5914i | − | 2.83233i | ||||||
\(893\) | − | 13.1744i | − | 0.440864i | ||||||
\(894\) | −22.3598 | −0.747823 | ||||||||
\(895\) | −29.6709 | − | 13.1595i | −0.991788 | − | 0.439872i | ||||
\(896\) | 27.1789 | 0.907983 | ||||||||
\(897\) | − | 26.3074i | − | 0.878377i | ||||||
\(898\) | 0.0901432i | 0.00300812i | ||||||||
\(899\) | −60.1533 | −2.00623 | ||||||||
\(900\) | 13.0914 | + | 14.4560i | 0.436378 | + | 0.481865i | ||||
\(901\) | 37.7091 | 1.25627 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.13504i | 0.237439i | ||||||||
\(904\) | 14.7381 | 0.490181 | ||||||||
\(905\) | −41.9330 | − | 18.5979i | −1.39390 | − | 0.618215i | ||||
\(906\) | 1.10114 | 0.0365829 | ||||||||
\(907\) | − | 53.1355i | − | 1.76433i | −0.470936 | − | 0.882167i | \(-0.656084\pi\) | ||
0.470936 | − | 0.882167i | \(-0.343916\pi\) | |||||||
\(908\) | 4.13444i | 0.137206i | ||||||||
\(909\) | 15.7436 | 0.522181 | ||||||||
\(910\) | −12.2004 | + | 27.5084i | −0.404438 | + | 0.911894i | ||||
\(911\) | −9.05845 | −0.300120 | −0.150060 | − | 0.988677i | \(-0.547947\pi\) | ||||
−0.150060 | + | 0.988677i | \(0.547947\pi\) | |||||||
\(912\) | 12.0027i | 0.397449i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 16.1829 | 0.535283 | ||||||||
\(915\) | 5.91265 | − | 13.3314i | 0.195466 | − | 0.440721i | ||||
\(916\) | −54.8721 | −1.81302 | ||||||||
\(917\) | − | 24.7698i | − | 0.817971i | ||||||
\(918\) | 14.2728i | 0.471072i | ||||||||
\(919\) | −56.6136 | −1.86751 | −0.933755 | − | 0.357913i | \(-0.883489\pi\) | ||||
−0.933755 | + | 0.357913i | \(0.883489\pi\) | |||||||
\(920\) | 60.1198 | + | 26.6640i | 1.98209 | + | 0.879086i | ||||
\(921\) | −13.5435 | −0.446273 | ||||||||
\(922\) | 100.738i | 3.31762i | ||||||||
\(923\) | − | 29.6254i | − | 0.975130i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.9928 | − | 23.5392i | 0.854639 | − | 0.773964i | ||||
\(926\) | 24.0704 | 0.791001 | ||||||||
\(927\) | − | 16.7498i | − | 0.550137i | ||||||
\(928\) | 6.02682i | 0.197840i | ||||||||
\(929\) | 9.36897 | 0.307386 | 0.153693 | − | 0.988119i | \(-0.450883\pi\) | ||||
0.153693 | + | 0.988119i | \(0.450883\pi\) | |||||||
\(930\) | −46.6943 | − | 20.7096i | −1.53117 | − | 0.679094i | ||||
\(931\) | 18.2856 | 0.599286 | ||||||||
\(932\) | 1.17198i | 0.0383894i | ||||||||
\(933\) | 7.20000i | 0.235717i | ||||||||
\(934\) | −49.1266 | −1.60747 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −19.0636 | −0.623114 | ||||||||
\(937\) | 16.6027i | 0.542386i | 0.962525 | + | 0.271193i | \(0.0874182\pi\) | ||||
−0.962525 | + | 0.271193i | \(0.912582\pi\) | |||||||
\(938\) | − | 28.7924i | − | 0.940107i | ||||||
\(939\) | 3.59811 | 0.117420 | ||||||||
\(940\) | −13.2477 | + | 29.8699i | −0.432094 | + | 0.974250i | ||||
\(941\) | 11.1200 | 0.362501 | 0.181251 | − | 0.983437i | \(-0.441985\pi\) | ||||
0.181251 | + | 0.983437i | \(0.441985\pi\) | |||||||
\(942\) | 7.63090i | 0.248628i | ||||||||
\(943\) | − | 54.9815i | − | 1.79044i | ||||||
\(944\) | −30.6354 | −0.997097 | ||||||||
\(945\) | −2.74246 | − | 1.21632i | −0.0892123 | − | 0.0395669i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.1722i | 1.69537i | 0.530500 | + | 0.847685i | \(0.322004\pi\) | ||||
−0.530500 | + | 0.847685i | \(0.677996\pi\) | |||||||
\(948\) | 38.9020i | 1.26348i | ||||||||
\(949\) | 16.8711 | 0.547659 | ||||||||
\(950\) | −31.6578 | + | 28.6694i | −1.02712 | + | 0.930159i | ||||
\(951\) | 24.7458 | 0.802437 | ||||||||
\(952\) | − | 36.3947i | − | 1.17956i | ||||||
\(953\) | − | 0.0462258i | − | 0.00149740i | −1.00000 | 0.000748700i | \(-0.999762\pi\) | |||
1.00000 | 0.000748700i | \(-0.000238318\pi\) | ||||||||
\(954\) | −15.5894 | −0.504726 | ||||||||
\(955\) | 29.6051 | + | 13.1303i | 0.958000 | + | 0.424886i | ||||
\(956\) | −40.5288 | −1.31080 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 35.5159i | − | 1.14747i | ||||||
\(959\) | −10.1480 | −0.327696 | ||||||||
\(960\) | −8.26353 | + | 18.6319i | −0.266704 | + | 0.601343i | ||||
\(961\) | 57.4406 | 1.85292 | ||||||||
\(962\) | 70.3490i | 2.26814i | ||||||||
\(963\) | − | 4.51221i | − | 0.145404i | ||||||
\(964\) | −22.3746 | −0.720636 | ||||||||
\(965\) | −10.7637 | + | 24.2691i | −0.346495 | + | 0.781249i | ||||
\(966\) | −20.7632 | −0.668046 | ||||||||
\(967\) | 48.1618i | 1.54878i | 0.632709 | + | 0.774390i | \(0.281943\pi\) | ||||
−0.632709 | + | 0.774390i | \(0.718057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.6622 | −0.663766 | ||||||||
\(970\) | −12.6797 | − | 5.62361i | −0.407119 | − | 0.180563i | ||||
\(971\) | 5.42160 | 0.173988 | 0.0869938 | − | 0.996209i | \(-0.472274\pi\) | ||||
0.0869938 | + | 0.996209i | \(0.472274\pi\) | |||||||
\(972\) | − | 3.90056i | − | 0.125110i | ||||||
\(973\) | − | 0.767470i | − | 0.0246040i | ||||||
\(974\) | 19.5897 | 0.627694 | ||||||||
\(975\) | −13.8591 | − | 15.3038i | −0.443848 | − | 0.490113i | ||||
\(976\) | −22.2611 | −0.712562 | ||||||||
\(977\) | − | 17.0776i | − | 0.546360i | −0.961963 | − | 0.273180i | \(-0.911925\pi\) | ||
0.961963 | − | 0.273180i | \(-0.0880754\pi\) | |||||||
\(978\) | 0.910290i | 0.0291079i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −41.4584 | − | 18.3874i | −1.32434 | − | 0.587363i | ||||
\(981\) | −5.59672 | −0.178689 | ||||||||
\(982\) | − | 22.0858i | − | 0.704786i | ||||||
\(983\) | − | 4.68860i | − | 0.149543i | −0.997201 | − | 0.0747715i | \(-0.976177\pi\) | ||
0.997201 | − | 0.0747715i | \(-0.0238227\pi\) | |||||||
\(984\) | −39.8423 | −1.27013 | ||||||||
\(985\) | −6.87242 | + | 15.4954i | −0.218974 | + | 0.493724i | ||||
\(986\) | 91.2940 | 2.90739 | ||||||||
\(987\) | − | 5.02650i | − | 0.159995i | ||||||
\(988\) | − | 56.6394i | − | 1.80194i | ||||||
\(989\) | −33.8802 | −1.07733 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.7657 | −1.77145 | −0.885727 | − | 0.464206i | \(-0.846340\pi\) | ||||
−0.885727 | + | 0.464206i | \(0.846340\pi\) | |||||||
\(992\) | − | 8.86095i | − | 0.281335i | ||||||
\(993\) | 13.3411i | 0.423366i | ||||||||
\(994\) | −23.3820 | −0.741631 | ||||||||
\(995\) | 34.5044 | + | 15.3032i | 1.09386 | + | 0.485143i | ||||
\(996\) | 11.9365 | 0.378221 | ||||||||
\(997\) | 39.1950i | 1.24132i | 0.784081 | + | 0.620658i | \(0.213135\pi\) | ||||
−0.784081 | + | 0.620658i | \(0.786865\pi\) | |||||||
\(998\) | 10.5937i | 0.335339i | ||||||||
\(999\) | −7.01348 | −0.221897 |
(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.i.364.11 | yes | 12 | |
5.2 | odd | 4 | 9075.2.a.ds.1.1 | 6 | |||
5.3 | odd | 4 | 9075.2.a.do.1.6 | 6 | |||
5.4 | even | 2 | inner | 1815.2.c.i.364.2 | yes | 12 | |
11.10 | odd | 2 | 1815.2.c.h.364.2 | ✓ | 12 | ||
55.32 | even | 4 | 9075.2.a.dp.1.6 | 6 | |||
55.43 | even | 4 | 9075.2.a.dr.1.1 | 6 | |||
55.54 | odd | 2 | 1815.2.c.h.364.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.c.h.364.2 | ✓ | 12 | 11.10 | odd | 2 | ||
1815.2.c.h.364.11 | yes | 12 | 55.54 | odd | 2 | ||
1815.2.c.i.364.2 | yes | 12 | 5.4 | even | 2 | inner | |
1815.2.c.i.364.11 | yes | 12 | 1.1 | even | 1 | trivial | |
9075.2.a.do.1.6 | 6 | 5.3 | odd | 4 | |||
9075.2.a.dp.1.6 | 6 | 55.32 | even | 4 | |||
9075.2.a.dr.1.1 | 6 | 55.43 | even | 4 | |||
9075.2.a.ds.1.1 | 6 | 5.2 | odd | 4 |