Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(69,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("170.69");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.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: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 69.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.69 |
Dual form | 170.2.c.a.69.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | 0.957427 | + | 0.288675i | \(0.0932147\pi\) | ||||
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | + | 2.00000i | 0.447214 | + | 0.894427i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | −2.00000 | + | 1.00000i | −0.632456 | + | 0.316228i | ||||
\(11\) | −6.00000 | −1.80907 | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 3.00000i | 0.832050i | 0.909353 | + | 0.416025i | \(0.136577\pi\) | ||||
−0.909353 | + | 0.416025i | \(0.863423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 1.00000i | − | 0.242536i | ||||||
\(18\) | 2.00000i | 0.471405i | ||||||||
\(19\) | 7.00000 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | − | 8.00000i | − | 1.66812i | −0.551677 | − | 0.834058i | \(-0.686012\pi\) | ||
0.551677 | − | 0.834058i | \(-0.313988\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | −1.00000 | − | 2.00000i | −0.182574 | − | 0.365148i | ||||
\(31\) | 5.00000 | 0.898027 | 0.449013 | − | 0.893525i | \(-0.351776\pi\) | ||||
0.449013 | + | 0.893525i | \(0.351776\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 6.00000i | − | 1.04447i | ||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | − | 8.00000i | − | 1.31519i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) | ||
0.753371 | − | 0.657596i | \(-0.228427\pi\) | |||||||
\(38\) | 7.00000i | 1.13555i | ||||||||
\(39\) | −3.00000 | −0.480384 | ||||||||
\(40\) | 2.00000 | − | 1.00000i | 0.316228 | − | 0.158114i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 2.00000 | + | 4.00000i | 0.298142 | + | 0.596285i | ||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | − | 3.00000i | − | 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | − | 3.00000i | − | 0.416025i | ||||||
\(53\) | 9.00000i | 1.23625i | 0.786082 | + | 0.618123i | \(0.212106\pi\) | ||||
−0.786082 | + | 0.618123i | \(0.787894\pi\) | |||||||
\(54\) | −5.00000 | −0.680414 | ||||||||
\(55\) | −6.00000 | − | 12.0000i | −0.809040 | − | 1.61808i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000i | 0.927173i | ||||||||
\(58\) | 5.00000i | 0.656532i | ||||||||
\(59\) | −5.00000 | −0.650945 | −0.325472 | − | 0.945552i | \(-0.605523\pi\) | ||||
−0.325472 | + | 0.945552i | \(0.605523\pi\) | |||||||
\(60\) | 2.00000 | − | 1.00000i | 0.258199 | − | 0.129099i | ||||
\(61\) | −3.00000 | −0.384111 | −0.192055 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(62\) | 5.00000i | 0.635001i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.00000 | + | 3.00000i | −0.744208 | + | 0.372104i | ||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | 1.00000i | 0.121268i | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0000 | −1.78017 | −0.890086 | − | 0.455792i | \(-0.849356\pi\) | ||||
−0.890086 | + | 0.455792i | \(0.849356\pi\) | |||||||
\(72\) | − | 2.00000i | − | 0.235702i | ||||||
\(73\) | − | 11.0000i | − | 1.28745i | −0.765256 | − | 0.643726i | \(-0.777388\pi\) | ||
0.765256 | − | 0.643726i | \(-0.222612\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 3.00000i | − | 0.339683i | ||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 1.00000i | 0.216930 | − | 0.108465i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 5.00000i | 0.536056i | ||||||||
\(88\) | 6.00000i | 0.639602i | ||||||||
\(89\) | 1.00000 | 0.106000 | 0.0529999 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | −4.00000 | + | 2.00000i | −0.421637 | + | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | 5.00000i | 0.518476i | ||||||||
\(94\) | 3.00000 | 0.309426 | ||||||||
\(95\) | 7.00000 | + | 14.0000i | 0.718185 | + | 1.43637i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 9.00000i | 0.913812i | 0.889515 | + | 0.456906i | \(0.151042\pi\) | ||||
−0.889515 | + | 0.456906i | \(0.848958\pi\) | |||||||
\(98\) | 7.00000i | 0.707107i | ||||||||
\(99\) | −12.0000 | −1.20605 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 1.00000i | 0.0990148i | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 3.00000 | 0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | − | 5.00000i | − | 0.481125i | ||||||
\(109\) | −9.00000 | −0.862044 | −0.431022 | − | 0.902342i | \(-0.641847\pi\) | ||||
−0.431022 | + | 0.902342i | \(0.641847\pi\) | |||||||
\(110\) | 12.0000 | − | 6.00000i | 1.14416 | − | 0.572078i | ||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.0000i | − | 1.22294i | −0.791269 | − | 0.611469i | \(-0.790579\pi\) | ||
0.791269 | − | 0.611469i | \(-0.209421\pi\) | |||||||
\(114\) | −7.00000 | −0.655610 | ||||||||
\(115\) | 16.0000 | − | 8.00000i | 1.49201 | − | 0.746004i | ||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | 6.00000i | 0.554700i | ||||||||
\(118\) | − | 5.00000i | − | 0.460287i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | + | 2.00000i | 0.0912871 | + | 0.182574i | ||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | − | 3.00000i | − | 0.271607i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.00000 | −0.449013 | ||||||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.00000i | − | 0.0887357i | −0.999015 | − | 0.0443678i | \(-0.985873\pi\) | ||
0.999015 | − | 0.0443678i | \(-0.0141274\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | −3.00000 | − | 6.00000i | −0.263117 | − | 0.526235i | ||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | −10.0000 | + | 5.00000i | −0.860663 | + | 0.430331i | ||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | − | 12.0000i | − | 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 8.00000i | 0.681005i | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | − | 15.0000i | − | 1.25877i | ||||||
\(143\) | − | 18.0000i | − | 1.50524i | ||||||
\(144\) | 2.00000 | 0.166667 | ||||||||
\(145\) | 5.00000 | + | 10.0000i | 0.415227 | + | 0.830455i | ||||
\(146\) | 11.0000 | 0.910366 | ||||||||
\(147\) | 7.00000i | 0.577350i | ||||||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | 2.00000 | 0.163846 | 0.0819232 | − | 0.996639i | \(-0.473894\pi\) | ||||
0.0819232 | + | 0.996639i | \(0.473894\pi\) | |||||||
\(150\) | 3.00000 | − | 4.00000i | 0.244949 | − | 0.326599i | ||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | − | 7.00000i | − | 0.567775i | ||||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | + | 10.0000i | 0.401610 | + | 0.803219i | ||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | − | 14.0000i | − | 1.11732i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | − | 8.00000i | − | 0.636446i | ||||||
\(159\) | −9.00000 | −0.713746 | ||||||||
\(160\) | −2.00000 | + | 1.00000i | −0.158114 | + | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.0000 | − | 6.00000i | 0.934199 | − | 0.467099i | ||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 6.00000i | 0.464294i | 0.972681 | + | 0.232147i | \(0.0745750\pi\) | ||||
−0.972681 | + | 0.232147i | \(0.925425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 1.00000 | + | 2.00000i | 0.0766965 | + | 0.153393i | ||||
\(171\) | 14.0000 | 1.07061 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | − | 5.00000i | − | 0.375823i | ||||||
\(178\) | 1.00000i | 0.0749532i | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | −2.00000 | − | 4.00000i | −0.149071 | − | 0.298142i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.00000i | − | 0.221766i | ||||||
\(184\) | −8.00000 | −0.589768 | ||||||||
\(185\) | 16.0000 | − | 8.00000i | 1.17634 | − | 0.588172i | ||||
\(186\) | −5.00000 | −0.366618 | ||||||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | 3.00000i | 0.218797i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.0000 | + | 7.00000i | −1.01567 | + | 0.507833i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 26.0000i | 1.87152i | 0.352636 | + | 0.935760i | \(0.385285\pi\) | ||||
−0.352636 | + | 0.935760i | \(0.614715\pi\) | |||||||
\(194\) | −9.00000 | −0.646162 | ||||||||
\(195\) | −3.00000 | − | 6.00000i | −0.214834 | − | 0.429669i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | − | 12.0000i | − | 0.852803i | ||||||
\(199\) | −7.00000 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | − | 12.0000i | − | 0.844317i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 16.0000i | − | 1.11208i | ||||||
\(208\) | 3.00000i | 0.208013i | ||||||||
\(209\) | −42.0000 | −2.90520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | − | 9.00000i | − | 0.618123i | ||||||
\(213\) | − | 15.0000i | − | 1.02778i | ||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 8.00000 | − | 4.00000i | 0.545595 | − | 0.272798i | ||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 9.00000i | − | 0.609557i | ||||||
\(219\) | 11.0000 | 0.743311 | ||||||||
\(220\) | 6.00000 | + | 12.0000i | 0.404520 | + | 0.809040i | ||||
\(221\) | 3.00000 | 0.201802 | ||||||||
\(222\) | 8.00000i | 0.536925i | ||||||||
\(223\) | − | 15.0000i | − | 1.00447i | −0.864730 | − | 0.502237i | \(-0.832510\pi\) | ||
0.864730 | − | 0.502237i | \(-0.167490\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | + | 8.00000i | −0.400000 | + | 0.533333i | ||||
\(226\) | 13.0000 | 0.864747 | ||||||||
\(227\) | 9.00000i | 0.597351i | 0.954355 | + | 0.298675i | \(0.0965448\pi\) | ||||
−0.954355 | + | 0.298675i | \(0.903455\pi\) | |||||||
\(228\) | − | 7.00000i | − | 0.463586i | ||||||
\(229\) | −18.0000 | −1.18947 | −0.594737 | − | 0.803921i | \(-0.702744\pi\) | ||||
−0.594737 | + | 0.803921i | \(0.702744\pi\) | |||||||
\(230\) | 8.00000 | + | 16.0000i | 0.527504 | + | 1.05501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 5.00000i | − | 0.328266i | ||||||
\(233\) | 27.0000i | 1.76883i | 0.466702 | + | 0.884414i | \(0.345442\pi\) | ||||
−0.466702 | + | 0.884414i | \(0.654558\pi\) | |||||||
\(234\) | −6.00000 | −0.392232 | ||||||||
\(235\) | 6.00000 | − | 3.00000i | 0.391397 | − | 0.195698i | ||||
\(236\) | 5.00000 | 0.325472 | ||||||||
\(237\) | − | 8.00000i | − | 0.519656i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0000 | −0.646846 | −0.323423 | − | 0.946254i | \(-0.604834\pi\) | ||||
−0.323423 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(240\) | −2.00000 | + | 1.00000i | −0.129099 | + | 0.0645497i | ||||
\(241\) | −20.0000 | −1.28831 | −0.644157 | − | 0.764894i | \(-0.722792\pi\) | ||||
−0.644157 | + | 0.764894i | \(0.722792\pi\) | |||||||
\(242\) | 25.0000i | 1.60706i | ||||||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | 3.00000 | 0.192055 | ||||||||
\(245\) | 7.00000 | + | 14.0000i | 0.447214 | + | 0.894427i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.0000i | 1.33620i | ||||||||
\(248\) | − | 5.00000i | − | 0.317500i | ||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 2.00000 | − | 11.0000i | 0.126491 | − | 0.695701i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.0000i | 3.01773i | ||||||||
\(254\) | 1.00000 | 0.0627456 | ||||||||
\(255\) | 1.00000 | + | 2.00000i | 0.0626224 | + | 0.125245i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 28.0000i | − | 1.74659i | −0.487190 | − | 0.873296i | \(-0.661978\pi\) | ||
0.487190 | − | 0.873296i | \(-0.338022\pi\) | |||||||
\(258\) | 4.00000i | 0.249029i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | − | 3.00000i | 0.372104 | − | 0.186052i | ||||
\(261\) | 10.0000 | 0.618984 | ||||||||
\(262\) | 6.00000i | 0.370681i | ||||||||
\(263\) | 27.0000i | 1.66489i | 0.554107 | + | 0.832446i | \(0.313060\pi\) | ||||
−0.554107 | + | 0.832446i | \(0.686940\pi\) | |||||||
\(264\) | −6.00000 | −0.369274 | ||||||||
\(265\) | −18.0000 | + | 9.00000i | −1.10573 | + | 0.552866i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.00000i | 0.0611990i | ||||||||
\(268\) | − | 2.00000i | − | 0.122169i | ||||||
\(269\) | 19.0000 | 1.15845 | 0.579225 | − | 0.815168i | \(-0.303355\pi\) | ||||
0.579225 | + | 0.815168i | \(0.303355\pi\) | |||||||
\(270\) | −5.00000 | − | 10.0000i | −0.304290 | − | 0.608581i | ||||
\(271\) | −6.00000 | −0.364474 | −0.182237 | − | 0.983255i | \(-0.558334\pi\) | ||||
−0.182237 | + | 0.983255i | \(0.558334\pi\) | |||||||
\(272\) | − | 1.00000i | − | 0.0606339i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 18.0000 | − | 24.0000i | 1.08544 | − | 1.44725i | ||||
\(276\) | −8.00000 | −0.481543 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.0000 | 0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −33.0000 | −1.96861 | −0.984307 | − | 0.176462i | \(-0.943535\pi\) | ||||
−0.984307 | + | 0.176462i | \(0.943535\pi\) | |||||||
\(282\) | 3.00000i | 0.178647i | ||||||||
\(283\) | 11.0000i | 0.653882i | 0.945045 | + | 0.326941i | \(0.106018\pi\) | ||||
−0.945045 | + | 0.326941i | \(0.893982\pi\) | |||||||
\(284\) | 15.0000 | 0.890086 | ||||||||
\(285\) | −14.0000 | + | 7.00000i | −0.829288 | + | 0.414644i | ||||
\(286\) | 18.0000 | 1.06436 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.00000i | 0.117851i | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −10.0000 | + | 5.00000i | −0.587220 | + | 0.293610i | ||||
\(291\) | −9.00000 | −0.527589 | ||||||||
\(292\) | 11.0000i | 0.643726i | ||||||||
\(293\) | − | 19.0000i | − | 1.10999i | −0.831853 | − | 0.554996i | \(-0.812720\pi\) | ||
0.831853 | − | 0.554996i | \(-0.187280\pi\) | |||||||
\(294\) | −7.00000 | −0.408248 | ||||||||
\(295\) | −5.00000 | − | 10.0000i | −0.291111 | − | 0.582223i | ||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | − | 30.0000i | − | 1.74078i | ||||||
\(298\) | 2.00000i | 0.115857i | ||||||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 4.00000 | + | 3.00000i | 0.230940 | + | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | − | 12.0000i | − | 0.689382i | ||||||
\(304\) | 7.00000 | 0.401478 | ||||||||
\(305\) | −3.00000 | − | 6.00000i | −0.171780 | − | 0.343559i | ||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | 24.0000i | 1.36975i | 0.728659 | + | 0.684876i | \(0.240144\pi\) | ||||
−0.728659 | + | 0.684876i | \(0.759856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.0000 | + | 5.00000i | −0.567962 | + | 0.283981i | ||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | 3.00000i | 0.169842i | ||||||||
\(313\) | − | 22.0000i | − | 1.24351i | −0.783210 | − | 0.621757i | \(-0.786419\pi\) | ||
0.783210 | − | 0.621757i | \(-0.213581\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(318\) | − | 9.00000i | − | 0.504695i | ||||||
\(319\) | −30.0000 | −1.67968 | ||||||||
\(320\) | −1.00000 | − | 2.00000i | −0.0559017 | − | 0.111803i | ||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.00000i | − | 0.389490i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −12.0000 | − | 9.00000i | −0.665640 | − | 0.499230i | ||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | − | 9.00000i | − | 0.497701i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.00000 | + | 12.0000i | 0.330289 | + | 0.660578i | ||||
\(331\) | 7.00000 | 0.384755 | 0.192377 | − | 0.981321i | \(-0.438380\pi\) | ||||
0.192377 | + | 0.981321i | \(0.438380\pi\) | |||||||
\(332\) | − | 4.00000i | − | 0.219529i | ||||||
\(333\) | − | 16.0000i | − | 0.876795i | ||||||
\(334\) | −6.00000 | −0.328305 | ||||||||
\(335\) | −4.00000 | + | 2.00000i | −0.218543 | + | 0.109272i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.0000i | − | 0.708155i | −0.935216 | − | 0.354078i | \(-0.884795\pi\) | ||
0.935216 | − | 0.354078i | \(-0.115205\pi\) | |||||||
\(338\) | 4.00000i | 0.217571i | ||||||||
\(339\) | 13.0000 | 0.706063 | ||||||||
\(340\) | −2.00000 | + | 1.00000i | −0.108465 | + | 0.0542326i | ||||
\(341\) | −30.0000 | −1.62459 | ||||||||
\(342\) | 14.0000i | 0.757033i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 8.00000 | + | 16.0000i | 0.430706 | + | 0.861411i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5.00000i | − | 0.268414i | −0.990953 | − | 0.134207i | \(-0.957151\pi\) | ||
0.990953 | − | 0.134207i | \(-0.0428487\pi\) | |||||||
\(348\) | − | 5.00000i | − | 0.268028i | ||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0000 | −0.800641 | ||||||||
\(352\) | − | 6.00000i | − | 0.319801i | ||||||
\(353\) | − | 8.00000i | − | 0.425797i | −0.977074 | − | 0.212899i | \(-0.931710\pi\) | ||
0.977074 | − | 0.212899i | \(-0.0682904\pi\) | |||||||
\(354\) | 5.00000 | 0.265747 | ||||||||
\(355\) | −15.0000 | − | 30.0000i | −0.796117 | − | 1.59223i | ||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000i | 0.634220i | ||||||||
\(359\) | 28.0000 | 1.47778 | 0.738892 | − | 0.673824i | \(-0.235349\pi\) | ||||
0.738892 | + | 0.673824i | \(0.235349\pi\) | |||||||
\(360\) | 4.00000 | − | 2.00000i | 0.210819 | − | 0.105409i | ||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 2.00000i | 0.105118i | ||||||||
\(363\) | 25.0000i | 1.31216i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.0000 | − | 11.0000i | 1.15153 | − | 0.575766i | ||||
\(366\) | 3.00000 | 0.156813 | ||||||||
\(367\) | 10.0000i | 0.521996i | 0.965339 | + | 0.260998i | \(0.0840516\pi\) | ||||
−0.965339 | + | 0.260998i | \(0.915948\pi\) | |||||||
\(368\) | − | 8.00000i | − | 0.417029i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | + | 16.0000i | 0.415900 | + | 0.831800i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 5.00000i | − | 0.259238i | ||||||
\(373\) | − | 14.0000i | − | 0.724893i | −0.932005 | − | 0.362446i | \(-0.881942\pi\) | ||
0.932005 | − | 0.362446i | \(-0.118058\pi\) | |||||||
\(374\) | −6.00000 | −0.310253 | ||||||||
\(375\) | 2.00000 | − | 11.0000i | 0.103280 | − | 0.568038i | ||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | 15.0000i | 0.772539i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −7.00000 | − | 14.0000i | −0.359092 | − | 0.718185i | ||||
\(381\) | 1.00000 | 0.0512316 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 27.0000i | − | 1.37964i | −0.723983 | − | 0.689818i | \(-0.757691\pi\) | ||
0.723983 | − | 0.689818i | \(-0.242309\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.0000 | −1.32337 | ||||||||
\(387\) | − | 8.00000i | − | 0.406663i | ||||||
\(388\) | − | 9.00000i | − | 0.456906i | ||||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 6.00000 | − | 3.00000i | 0.303822 | − | 0.151911i | ||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | − | 7.00000i | − | 0.353553i | ||||||
\(393\) | 6.00000i | 0.302660i | ||||||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | −8.00000 | − | 16.0000i | −0.402524 | − | 0.805047i | ||||
\(396\) | 12.0000 | 0.603023 | ||||||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | − | 7.00000i | − | 0.350878i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | − | 2.00000i | − | 0.0997509i | ||||||
\(403\) | 15.0000i | 0.747203i | ||||||||
\(404\) | 12.0000 | 0.597022 | ||||||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.0000i | 2.37927i | ||||||||
\(408\) | − | 1.00000i | − | 0.0495074i | ||||||
\(409\) | 31.0000 | 1.53285 | 0.766426 | − | 0.642333i | \(-0.222033\pi\) | ||||
0.766426 | + | 0.642333i | \(0.222033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.0000 | 0.786357 | ||||||||
\(415\) | −8.00000 | + | 4.00000i | −0.392705 | + | 0.196352i | ||||
\(416\) | −3.00000 | −0.147087 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 42.0000i | − | 2.05429i | ||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 16.0000i | 0.778868i | ||||||||
\(423\) | − | 6.00000i | − | 0.291730i | ||||||
\(424\) | 9.00000 | 0.437079 | ||||||||
\(425\) | 4.00000 | + | 3.00000i | 0.194029 | + | 0.145521i | ||||
\(426\) | 15.0000 | 0.726752 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 4.00000i | − | 0.193347i | ||||||
\(429\) | 18.0000 | 0.869048 | ||||||||
\(430\) | 4.00000 | + | 8.00000i | 0.192897 | + | 0.385794i | ||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 5.00000i | 0.240563i | ||||||||
\(433\) | 20.0000i | 0.961139i | 0.876957 | + | 0.480569i | \(0.159570\pi\) | ||||
−0.876957 | + | 0.480569i | \(0.840430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.0000 | + | 5.00000i | −0.479463 | + | 0.239732i | ||||
\(436\) | 9.00000 | 0.431022 | ||||||||
\(437\) | − | 56.0000i | − | 2.67884i | ||||||
\(438\) | 11.0000i | 0.525600i | ||||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | −12.0000 | + | 6.00000i | −0.572078 | + | 0.286039i | ||||
\(441\) | 14.0000 | 0.666667 | ||||||||
\(442\) | 3.00000i | 0.142695i | ||||||||
\(443\) | 10.0000i | 0.475114i | 0.971374 | + | 0.237557i | \(0.0763467\pi\) | ||||
−0.971374 | + | 0.237557i | \(0.923653\pi\) | |||||||
\(444\) | −8.00000 | −0.379663 | ||||||||
\(445\) | 1.00000 | + | 2.00000i | 0.0474045 | + | 0.0948091i | ||||
\(446\) | 15.0000 | 0.710271 | ||||||||
\(447\) | 2.00000i | 0.0945968i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | −8.00000 | − | 6.00000i | −0.377124 | − | 0.282843i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.0000i | 0.611469i | ||||||||
\(453\) | − | 8.00000i | − | 0.375873i | ||||||
\(454\) | −9.00000 | −0.422391 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.00000 | 0.327805 | ||||||||
\(457\) | 12.0000i | 0.561336i | 0.959805 | + | 0.280668i | \(0.0905560\pi\) | ||||
−0.959805 | + | 0.280668i | \(0.909444\pi\) | |||||||
\(458\) | − | 18.0000i | − | 0.841085i | ||||||
\(459\) | 5.00000 | 0.233380 | ||||||||
\(460\) | −16.0000 | + | 8.00000i | −0.746004 | + | 0.373002i | ||||
\(461\) | −20.0000 | −0.931493 | −0.465746 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465746 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.0000i | 1.44069i | 0.693615 | + | 0.720346i | \(0.256017\pi\) | ||||
−0.693615 | + | 0.720346i | \(0.743983\pi\) | |||||||
\(464\) | 5.00000 | 0.232119 | ||||||||
\(465\) | −10.0000 | + | 5.00000i | −0.463739 | + | 0.231869i | ||||
\(466\) | −27.0000 | −1.25075 | ||||||||
\(467\) | 14.0000i | 0.647843i | 0.946084 | + | 0.323921i | \(0.105001\pi\) | ||||
−0.946084 | + | 0.323921i | \(0.894999\pi\) | |||||||
\(468\) | − | 6.00000i | − | 0.277350i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.00000 | + | 6.00000i | 0.138380 | + | 0.276759i | ||||
\(471\) | 14.0000 | 0.645086 | ||||||||
\(472\) | 5.00000i | 0.230144i | ||||||||
\(473\) | 24.0000i | 1.10352i | ||||||||
\(474\) | 8.00000 | 0.367452 | ||||||||
\(475\) | −21.0000 | + | 28.0000i | −0.963546 | + | 1.28473i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000i | 0.824163i | ||||||||
\(478\) | − | 10.0000i | − | 0.457389i | ||||||
\(479\) | 37.0000 | 1.69057 | 0.845287 | − | 0.534313i | \(-0.179430\pi\) | ||||
0.845287 | + | 0.534313i | \(0.179430\pi\) | |||||||
\(480\) | −1.00000 | − | 2.00000i | −0.0456435 | − | 0.0912871i | ||||
\(481\) | 24.0000 | 1.09431 | ||||||||
\(482\) | − | 20.0000i | − | 0.910975i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.0000 | −1.13636 | ||||||||
\(485\) | −18.0000 | + | 9.00000i | −0.817338 | + | 0.408669i | ||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | 2.00000i | 0.0906287i | 0.998973 | + | 0.0453143i | \(0.0144289\pi\) | ||||
−0.998973 | + | 0.0453143i | \(0.985571\pi\) | |||||||
\(488\) | 3.00000i | 0.135804i | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | −14.0000 | + | 7.00000i | −0.632456 | + | 0.316228i | ||||
\(491\) | −13.0000 | −0.586682 | −0.293341 | − | 0.956008i | \(-0.594767\pi\) | ||||
−0.293341 | + | 0.956008i | \(0.594767\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.00000i | − | 0.225189i | ||||||
\(494\) | −21.0000 | −0.944835 | ||||||||
\(495\) | −12.0000 | − | 24.0000i | −0.539360 | − | 1.07872i | ||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 4.00000i | − | 0.179244i | ||||||
\(499\) | 28.0000 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(500\) | 11.0000 | + | 2.00000i | 0.491935 | + | 0.0894427i | ||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | − | 42.0000i | − | 1.87269i | −0.351085 | − | 0.936344i | \(-0.614187\pi\) | ||
0.351085 | − | 0.936344i | \(-0.385813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | − | 24.0000i | −0.533993 | − | 1.06799i | ||||
\(506\) | −48.0000 | −2.13386 | ||||||||
\(507\) | 4.00000i | 0.177646i | ||||||||
\(508\) | 1.00000i | 0.0443678i | ||||||||
\(509\) | 12.0000 | 0.531891 | 0.265945 | − | 0.963988i | \(-0.414316\pi\) | ||||
0.265945 | + | 0.963988i | \(0.414316\pi\) | |||||||
\(510\) | −2.00000 | + | 1.00000i | −0.0885615 | + | 0.0442807i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 35.0000i | 1.54529i | ||||||||
\(514\) | 28.0000 | 1.23503 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | −0.176090 | ||||||||
\(517\) | 18.0000i | 0.791639i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | + | 6.00000i | 0.131559 | + | 0.263117i | ||||
\(521\) | 28.0000 | 1.22670 | 0.613351 | − | 0.789810i | \(-0.289821\pi\) | ||||
0.613351 | + | 0.789810i | \(0.289821\pi\) | |||||||
\(522\) | 10.0000i | 0.437688i | ||||||||
\(523\) | 14.0000i | 0.612177i | 0.952003 | + | 0.306089i | \(0.0990204\pi\) | ||||
−0.952003 | + | 0.306089i | \(0.900980\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.0000 | −1.17726 | ||||||||
\(527\) | − | 5.00000i | − | 0.217803i | ||||||
\(528\) | − | 6.00000i | − | 0.261116i | ||||||
\(529\) | −41.0000 | −1.78261 | ||||||||
\(530\) | −9.00000 | − | 18.0000i | −0.390935 | − | 0.781870i | ||||
\(531\) | −10.0000 | −0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.00000 | −0.0432742 | ||||||||
\(535\) | −8.00000 | + | 4.00000i | −0.345870 | + | 0.172935i | ||||
\(536\) | 2.00000 | 0.0863868 | ||||||||
\(537\) | 12.0000i | 0.517838i | ||||||||
\(538\) | 19.0000i | 0.819148i | ||||||||
\(539\) | −42.0000 | −1.80907 | ||||||||
\(540\) | 10.0000 | − | 5.00000i | 0.430331 | − | 0.215166i | ||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | − | 6.00000i | − | 0.257722i | ||||||
\(543\) | 2.00000i | 0.0858282i | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −9.00000 | − | 18.0000i | −0.385518 | − | 0.771035i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 13.0000i | − | 0.555840i | −0.960604 | − | 0.277920i | \(-0.910355\pi\) | ||
0.960604 | − | 0.277920i | \(-0.0896450\pi\) | |||||||
\(548\) | 12.0000i | 0.512615i | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 24.0000 | + | 18.0000i | 1.02336 | + | 0.767523i | ||||
\(551\) | 35.0000 | 1.49105 | ||||||||
\(552\) | − | 8.00000i | − | 0.340503i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 8.00000 | + | 16.0000i | 0.339581 | + | 0.679162i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 11.0000i | − | 0.466085i | −0.972467 | − | 0.233042i | \(-0.925132\pi\) | ||
0.972467 | − | 0.233042i | \(-0.0748681\pi\) | |||||||
\(558\) | 10.0000i | 0.423334i | ||||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | − | 33.0000i | − | 1.39202i | ||||||
\(563\) | 32.0000i | 1.34864i | 0.738440 | + | 0.674320i | \(0.235563\pi\) | ||||
−0.738440 | + | 0.674320i | \(0.764437\pi\) | |||||||
\(564\) | −3.00000 | −0.126323 | ||||||||
\(565\) | 26.0000 | − | 13.0000i | 1.09383 | − | 0.546914i | ||||
\(566\) | −11.0000 | −0.462364 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.0000i | 0.629386i | ||||||||
\(569\) | 21.0000 | 0.880366 | 0.440183 | − | 0.897908i | \(-0.354914\pi\) | ||||
0.440183 | + | 0.897908i | \(0.354914\pi\) | |||||||
\(570\) | −7.00000 | − | 14.0000i | −0.293198 | − | 0.586395i | ||||
\(571\) | −10.0000 | −0.418487 | −0.209243 | − | 0.977864i | \(-0.567100\pi\) | ||||
−0.209243 | + | 0.977864i | \(0.567100\pi\) | |||||||
\(572\) | 18.0000i | 0.752618i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.0000 | + | 24.0000i | 1.33449 | + | 1.00087i | ||||
\(576\) | −2.00000 | −0.0833333 | ||||||||
\(577\) | − | 16.0000i | − | 0.666089i | −0.942911 | − | 0.333044i | \(-0.891924\pi\) | ||
0.942911 | − | 0.333044i | \(-0.108076\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | −26.0000 | −1.08052 | ||||||||
\(580\) | −5.00000 | − | 10.0000i | −0.207614 | − | 0.415227i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 9.00000i | − | 0.373062i | ||||||
\(583\) | − | 54.0000i | − | 2.23645i | ||||||
\(584\) | −11.0000 | −0.455183 | ||||||||
\(585\) | −12.0000 | + | 6.00000i | −0.496139 | + | 0.248069i | ||||
\(586\) | 19.0000 | 0.784883 | ||||||||
\(587\) | − | 36.0000i | − | 1.48588i | −0.669359 | − | 0.742940i | \(-0.733431\pi\) | ||
0.669359 | − | 0.742940i | \(-0.266569\pi\) | |||||||
\(588\) | − | 7.00000i | − | 0.288675i | ||||||
\(589\) | 35.0000 | 1.44215 | ||||||||
\(590\) | 10.0000 | − | 5.00000i | 0.411693 | − | 0.205847i | ||||
\(591\) | 2.00000 | 0.0822690 | ||||||||
\(592\) | − | 8.00000i | − | 0.328798i | ||||||
\(593\) | 22.0000i | 0.903432i | 0.892162 | + | 0.451716i | \(0.149188\pi\) | ||||
−0.892162 | + | 0.451716i | \(0.850812\pi\) | |||||||
\(594\) | 30.0000 | 1.23091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.00000 | −0.0819232 | ||||||||
\(597\) | − | 7.00000i | − | 0.286491i | ||||||
\(598\) | 24.0000i | 0.981433i | ||||||||
\(599\) | 32.0000 | 1.30748 | 0.653742 | − | 0.756717i | \(-0.273198\pi\) | ||||
0.653742 | + | 0.756717i | \(0.273198\pi\) | |||||||
\(600\) | −3.00000 | + | 4.00000i | −0.122474 | + | 0.163299i | ||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 25.0000 | + | 50.0000i | 1.01639 | + | 2.03279i | ||||
\(606\) | 12.0000 | 0.487467 | ||||||||
\(607\) | 12.0000i | 0.487065i | 0.969893 | + | 0.243532i | \(0.0783062\pi\) | ||||
−0.969893 | + | 0.243532i | \(0.921694\pi\) | |||||||
\(608\) | 7.00000i | 0.283887i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | − | 3.00000i | 0.242933 | − | 0.121466i | ||||
\(611\) | 9.00000 | 0.364101 | ||||||||
\(612\) | 2.00000i | 0.0808452i | ||||||||
\(613\) | − | 17.0000i | − | 0.686624i | −0.939222 | − | 0.343312i | \(-0.888451\pi\) | ||
0.939222 | − | 0.343312i | \(-0.111549\pi\) | |||||||
\(614\) | −24.0000 | −0.968561 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.0000i | 1.16750i | 0.811935 | + | 0.583748i | \(0.198414\pi\) | ||||
−0.811935 | + | 0.583748i | \(0.801586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0000 | −0.562708 | −0.281354 | − | 0.959604i | \(-0.590783\pi\) | ||||
−0.281354 | + | 0.959604i | \(0.590783\pi\) | |||||||
\(620\) | −5.00000 | − | 10.0000i | −0.200805 | − | 0.401610i | ||||
\(621\) | 40.0000 | 1.60514 | ||||||||
\(622\) | − | 4.00000i | − | 0.160385i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 22.0000 | 0.879297 | ||||||||
\(627\) | − | 42.0000i | − | 1.67732i | ||||||
\(628\) | 14.0000i | 0.558661i | ||||||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0000 | −1.67199 | −0.835997 | − | 0.548734i | \(-0.815110\pi\) | ||||
−0.835997 | + | 0.548734i | \(0.815110\pi\) | |||||||
\(632\) | 8.00000i | 0.318223i | ||||||||
\(633\) | 16.0000i | 0.635943i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.00000 | − | 1.00000i | 0.0793676 | − | 0.0396838i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | 21.0000i | 0.832050i | ||||||||
\(638\) | − | 30.0000i | − | 1.18771i | ||||||
\(639\) | −30.0000 | −1.18678 | ||||||||
\(640\) | 2.00000 | − | 1.00000i | 0.0790569 | − | 0.0395285i | ||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | − | 4.00000i | − | 0.157867i | ||||||
\(643\) | − | 44.0000i | − | 1.73519i | −0.497271 | − | 0.867595i | \(-0.665665\pi\) | ||
0.497271 | − | 0.867595i | \(-0.334335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | + | 8.00000i | 0.157500 | + | 0.315000i | ||||
\(646\) | 7.00000 | 0.275411 | ||||||||
\(647\) | − | 17.0000i | − | 0.668339i | −0.942513 | − | 0.334169i | \(-0.891544\pi\) | ||
0.942513 | − | 0.334169i | \(-0.108456\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 30.0000 | 1.17760 | ||||||||
\(650\) | 9.00000 | − | 12.0000i | 0.353009 | − | 0.470679i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | 30.0000i | 1.17399i | 0.809590 | + | 0.586995i | \(0.199689\pi\) | ||||
−0.809590 | + | 0.586995i | \(0.800311\pi\) | |||||||
\(654\) | 9.00000 | 0.351928 | ||||||||
\(655\) | 6.00000 | + | 12.0000i | 0.234439 | + | 0.468879i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 22.0000i | − | 0.858302i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.0000 | −0.740135 | −0.370067 | − | 0.929005i | \(-0.620665\pi\) | ||||
−0.370067 | + | 0.929005i | \(0.620665\pi\) | |||||||
\(660\) | −12.0000 | + | 6.00000i | −0.467099 | + | 0.233550i | ||||
\(661\) | −16.0000 | −0.622328 | −0.311164 | − | 0.950356i | \(-0.600719\pi\) | ||||
−0.311164 | + | 0.950356i | \(0.600719\pi\) | |||||||
\(662\) | 7.00000i | 0.272063i | ||||||||
\(663\) | 3.00000i | 0.116510i | ||||||||
\(664\) | 4.00000 | 0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.0000 | 0.619987 | ||||||||
\(667\) | − | 40.0000i | − | 1.54881i | ||||||
\(668\) | − | 6.00000i | − | 0.232147i | ||||||
\(669\) | 15.0000 | 0.579934 | ||||||||
\(670\) | −2.00000 | − | 4.00000i | −0.0772667 | − | 0.154533i | ||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 35.0000i | − | 1.34915i | −0.738206 | − | 0.674575i | \(-0.764327\pi\) | ||
0.738206 | − | 0.674575i | \(-0.235673\pi\) | |||||||
\(674\) | 13.0000 | 0.500741 | ||||||||
\(675\) | −20.0000 | − | 15.0000i | −0.769800 | − | 0.577350i | ||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 24.0000i | 0.922395i | 0.887298 | + | 0.461197i | \(0.152580\pi\) | ||||
−0.887298 | + | 0.461197i | \(0.847420\pi\) | |||||||
\(678\) | 13.0000i | 0.499262i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.00000 | − | 2.00000i | −0.0383482 | − | 0.0766965i | ||||
\(681\) | −9.00000 | −0.344881 | ||||||||
\(682\) | − | 30.0000i | − | 1.14876i | ||||||
\(683\) | 45.0000i | 1.72188i | 0.508709 | + | 0.860939i | \(0.330123\pi\) | ||||
−0.508709 | + | 0.860939i | \(0.669877\pi\) | |||||||
\(684\) | −14.0000 | −0.535303 | ||||||||
\(685\) | 24.0000 | − | 12.0000i | 0.916993 | − | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 18.0000i | − | 0.686743i | ||||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | −27.0000 | −1.02862 | ||||||||
\(690\) | −16.0000 | + | 8.00000i | −0.609110 | + | 0.304555i | ||||
\(691\) | −16.0000 | −0.608669 | −0.304334 | − | 0.952565i | \(-0.598434\pi\) | ||||
−0.304334 | + | 0.952565i | \(0.598434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.00000 | 0.189797 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.00000 | 0.189525 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.00000i | 0.0757011i | ||||||||
\(699\) | −27.0000 | −1.02123 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0000 | −0.453234 | −0.226617 | − | 0.973984i | \(-0.572767\pi\) | ||||
−0.226617 | + | 0.973984i | \(0.572767\pi\) | |||||||
\(702\) | − | 15.0000i | − | 0.566139i | ||||||
\(703\) | − | 56.0000i | − | 2.11208i | ||||||
\(704\) | 6.00000 | 0.226134 | ||||||||
\(705\) | 3.00000 | + | 6.00000i | 0.112987 | + | 0.225973i | ||||
\(706\) | 8.00000 | 0.301084 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.00000i | 0.187912i | ||||||||
\(709\) | −23.0000 | −0.863783 | −0.431892 | − | 0.901926i | \(-0.642154\pi\) | ||||
−0.431892 | + | 0.901926i | \(0.642154\pi\) | |||||||
\(710\) | 30.0000 | − | 15.0000i | 1.12588 | − | 0.562940i | ||||
\(711\) | −16.0000 | −0.600047 | ||||||||
\(712\) | − | 1.00000i | − | 0.0374766i | ||||||
\(713\) | − | 40.0000i | − | 1.49801i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | − | 18.0000i | 1.34632 | − | 0.673162i | ||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | − | 10.0000i | − | 0.373457i | ||||||
\(718\) | 28.0000i | 1.04495i | ||||||||
\(719\) | 27.0000 | 1.00693 | 0.503465 | − | 0.864016i | \(-0.332058\pi\) | ||||
0.503465 | + | 0.864016i | \(0.332058\pi\) | |||||||
\(720\) | 2.00000 | + | 4.00000i | 0.0745356 | + | 0.149071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30.0000i | 1.11648i | ||||||||
\(723\) | − | 20.0000i | − | 0.743808i | ||||||
\(724\) | −2.00000 | −0.0743294 | ||||||||
\(725\) | −15.0000 | + | 20.0000i | −0.557086 | + | 0.742781i | ||||
\(726\) | −25.0000 | −0.927837 | ||||||||
\(727\) | 29.0000i | 1.07555i | 0.843088 | + | 0.537775i | \(0.180735\pi\) | ||||
−0.843088 | + | 0.537775i | \(0.819265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 11.0000 | + | 22.0000i | 0.407128 | + | 0.814257i | ||||
\(731\) | −4.00000 | −0.147945 | ||||||||
\(732\) | 3.00000i | 0.110883i | ||||||||
\(733\) | − | 14.0000i | − | 0.517102i | −0.965998 | − | 0.258551i | \(-0.916755\pi\) | ||
0.965998 | − | 0.258551i | \(-0.0832450\pi\) | |||||||
\(734\) | −10.0000 | −0.369107 | ||||||||
\(735\) | −14.0000 | + | 7.00000i | −0.516398 | + | 0.258199i | ||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | − | 12.0000i | − | 0.442026i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.00000 | 0.0367856 | 0.0183928 | − | 0.999831i | \(-0.494145\pi\) | ||||
0.0183928 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(740\) | −16.0000 | + | 8.00000i | −0.588172 | + | 0.294086i | ||||
\(741\) | −21.0000 | −0.771454 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | 5.00000 | 0.183309 | ||||||||
\(745\) | 2.00000 | + | 4.00000i | 0.0732743 | + | 0.146549i | ||||
\(746\) | 14.0000 | 0.512576 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | − | 6.00000i | − | 0.219382i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.0000 | + | 2.00000i | 0.401663 | + | 0.0730297i | ||||
\(751\) | 11.0000 | 0.401396 | 0.200698 | − | 0.979653i | \(-0.435679\pi\) | ||||
0.200698 | + | 0.979653i | \(0.435679\pi\) | |||||||
\(752\) | − | 3.00000i | − | 0.109399i | ||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | −15.0000 | −0.546268 | ||||||||
\(755\) | −8.00000 | − | 16.0000i | −0.291150 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.0000i | 1.63555i | 0.575536 | + | 0.817776i | \(0.304793\pi\) | ||||
−0.575536 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(758\) | 20.0000i | 0.726433i | ||||||||
\(759\) | −48.0000 | −1.74229 | ||||||||
\(760\) | 14.0000 | − | 7.00000i | 0.507833 | − | 0.253917i | ||||
\(761\) | 14.0000 | 0.507500 | 0.253750 | − | 0.967270i | \(-0.418336\pi\) | ||||
0.253750 | + | 0.967270i | \(0.418336\pi\) | |||||||
\(762\) | 1.00000i | 0.0362262i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.00000 | − | 2.00000i | 0.144620 | − | 0.0723102i | ||||
\(766\) | 27.0000 | 0.975550 | ||||||||
\(767\) | − | 15.0000i | − | 0.541619i | ||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −37.0000 | −1.33425 | −0.667127 | − | 0.744944i | \(-0.732476\pi\) | ||||
−0.667127 | + | 0.744944i | \(0.732476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.0000 | 1.00840 | ||||||||
\(772\) | − | 26.0000i | − | 0.935760i | ||||||
\(773\) | − | 6.00000i | − | 0.215805i | −0.994161 | − | 0.107903i | \(-0.965587\pi\) | ||
0.994161 | − | 0.107903i | \(-0.0344134\pi\) | |||||||
\(774\) | 8.00000 | 0.287554 | ||||||||
\(775\) | −15.0000 | + | 20.0000i | −0.538816 | + | 0.718421i | ||||
\(776\) | 9.00000 | 0.323081 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 30.0000i | − | 1.07555i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3.00000 | + | 6.00000i | 0.107417 | + | 0.214834i | ||||
\(781\) | 90.0000 | 3.22045 | ||||||||
\(782\) | − | 8.00000i | − | 0.286079i | ||||||
\(783\) | 25.0000i | 0.893427i | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | 28.0000 | − | 14.0000i | 0.999363 | − | 0.499681i | ||||
\(786\) | −6.00000 | −0.214013 | ||||||||
\(787\) | 47.0000i | 1.67537i | 0.546154 | + | 0.837685i | \(0.316091\pi\) | ||||
−0.546154 | + | 0.837685i | \(0.683909\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | −27.0000 | −0.961225 | ||||||||
\(790\) | 16.0000 | − | 8.00000i | 0.569254 | − | 0.284627i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.0000i | 0.426401i | ||||||||
\(793\) | − | 9.00000i | − | 0.319599i | ||||||
\(794\) | −2.00000 | −0.0709773 | ||||||||
\(795\) | −9.00000 | − | 18.0000i | −0.319197 | − | 0.638394i | ||||
\(796\) | 7.00000 | 0.248108 | ||||||||
\(797\) | − | 54.0000i | − | 1.91278i | −0.292096 | − | 0.956389i | \(-0.594353\pi\) | ||
0.292096 | − | 0.956389i | \(-0.405647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00000 | −0.106132 | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | − | 10.0000i | − | 0.353112i | ||||||
\(803\) | 66.0000i | 2.32909i | ||||||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.0000 | −0.528352 | ||||||||
\(807\) | 19.0000i | 0.668832i | ||||||||
\(808\) | 12.0000i | 0.422159i | ||||||||
\(809\) | −10.0000 | −0.351581 | −0.175791 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | −2.00000 | + | 1.00000i | −0.0702728 | + | 0.0351364i | ||||
\(811\) | −32.0000 | −1.12367 | −0.561836 | − | 0.827249i | \(-0.689905\pi\) | ||||
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 6.00000i | − | 0.210429i | ||||||
\(814\) | −48.0000 | −1.68240 | ||||||||
\(815\) | 8.00000 | − | 4.00000i | 0.280228 | − | 0.140114i | ||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | − | 28.0000i | − | 0.979596i | ||||||
\(818\) | 31.0000i | 1.08389i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0000 | −0.942306 | −0.471153 | − | 0.882051i | \(-0.656162\pi\) | ||||
−0.471153 | + | 0.882051i | \(0.656162\pi\) | |||||||
\(822\) | 12.0000i | 0.418548i | ||||||||
\(823\) | − | 54.0000i | − | 1.88232i | −0.337959 | − | 0.941161i | \(-0.609737\pi\) | ||
0.337959 | − | 0.941161i | \(-0.390263\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.0000 | + | 18.0000i | 0.835573 | + | 0.626680i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.0000i | 1.11275i | 0.830932 | + | 0.556375i | \(0.187808\pi\) | ||||
−0.830932 | + | 0.556375i | \(0.812192\pi\) | |||||||
\(828\) | 16.0000i | 0.556038i | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | −4.00000 | − | 8.00000i | −0.138842 | − | 0.277684i | ||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | − | 3.00000i | − | 0.104006i | ||||||
\(833\) | − | 7.00000i | − | 0.242536i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | + | 6.00000i | −0.415277 | + | 0.207639i | ||||
\(836\) | 42.0000 | 1.45260 | ||||||||
\(837\) | 25.0000i | 0.864126i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.0000 | −1.07024 | −0.535119 | − | 0.844776i | \(-0.679733\pi\) | ||||
−0.535119 | + | 0.844776i | \(0.679733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 20.0000i | 0.689246i | ||||||||
\(843\) | − | 33.0000i | − | 1.13658i | ||||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | 4.00000 | + | 8.00000i | 0.137604 | + | 0.275208i | ||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.00000i | 0.309061i | ||||||||
\(849\) | −11.0000 | −0.377519 | ||||||||
\(850\) | −3.00000 | + | 4.00000i | −0.102899 | + | 0.137199i | ||||
\(851\) | −64.0000 | −2.19389 | ||||||||
\(852\) | 15.0000i | 0.513892i | ||||||||
\(853\) | 30.0000i | 1.02718i | 0.858036 | + | 0.513590i | \(0.171685\pi\) | ||||
−0.858036 | + | 0.513590i | \(0.828315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.0000 | + | 28.0000i | 0.478790 | + | 0.957580i | ||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | 57.0000i | 1.94708i | 0.228510 | + | 0.973541i | \(0.426614\pi\) | ||||
−0.228510 | + | 0.973541i | \(0.573386\pi\) | |||||||
\(858\) | 18.0000i | 0.614510i | ||||||||
\(859\) | −33.0000 | −1.12595 | −0.562973 | − | 0.826475i | \(-0.690342\pi\) | ||||
−0.562973 | + | 0.826475i | \(0.690342\pi\) | |||||||
\(860\) | −8.00000 | + | 4.00000i | −0.272798 | + | 0.136399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 16.0000i | − | 0.544962i | ||||||
\(863\) | − | 8.00000i | − | 0.272323i | −0.990687 | − | 0.136162i | \(-0.956523\pi\) | ||
0.990687 | − | 0.136162i | \(-0.0434766\pi\) | |||||||
\(864\) | −5.00000 | −0.170103 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.0000 | −0.679628 | ||||||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.0000 | 1.62829 | ||||||||
\(870\) | −5.00000 | − | 10.0000i | −0.169516 | − | 0.339032i | ||||
\(871\) | −6.00000 | −0.203302 | ||||||||
\(872\) | 9.00000i | 0.304778i | ||||||||
\(873\) | 18.0000i | 0.609208i | ||||||||
\(874\) | 56.0000 | 1.89423 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.0000 | −0.371656 | ||||||||
\(877\) | 10.0000i | 0.337676i | 0.985644 | + | 0.168838i | \(0.0540015\pi\) | ||||
−0.985644 | + | 0.168838i | \(0.945999\pi\) | |||||||
\(878\) | − | 16.0000i | − | 0.539974i | ||||||
\(879\) | 19.0000 | 0.640854 | ||||||||
\(880\) | −6.00000 | − | 12.0000i | −0.202260 | − | 0.404520i | ||||
\(881\) | 38.0000 | 1.28025 | 0.640126 | − | 0.768270i | \(-0.278882\pi\) | ||||
0.640126 | + | 0.768270i | \(0.278882\pi\) | |||||||
\(882\) | 14.0000i | 0.471405i | ||||||||
\(883\) | − | 26.0000i | − | 0.874970i | −0.899226 | − | 0.437485i | \(-0.855869\pi\) | ||
0.899226 | − | 0.437485i | \(-0.144131\pi\) | |||||||
\(884\) | −3.00000 | −0.100901 | ||||||||
\(885\) | 10.0000 | − | 5.00000i | 0.336146 | − | 0.168073i | ||||
\(886\) | −10.0000 | −0.335957 | ||||||||
\(887\) | 14.0000i | 0.470074i | 0.971986 | + | 0.235037i | \(0.0755211\pi\) | ||||
−0.971986 | + | 0.235037i | \(0.924479\pi\) | |||||||
\(888\) | − | 8.00000i | − | 0.268462i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.00000 | + | 1.00000i | −0.0670402 | + | 0.0335201i | ||||
\(891\) | −6.00000 | −0.201008 | ||||||||
\(892\) | 15.0000i | 0.502237i | ||||||||
\(893\) | − | 21.0000i | − | 0.702738i | ||||||
\(894\) | −2.00000 | −0.0668900 | ||||||||
\(895\) | 12.0000 | + | 24.0000i | 0.401116 | + | 0.802232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000i | 0.801337i | ||||||||
\(898\) | 6.00000i | 0.200223i | ||||||||
\(899\) | 25.0000 | 0.833797 | ||||||||
\(900\) | 6.00000 | − | 8.00000i | 0.200000 | − | 0.266667i | ||||
\(901\) | 9.00000 | 0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.0000 | −0.432374 | ||||||||
\(905\) | 2.00000 | + | 4.00000i | 0.0664822 | + | 0.132964i | ||||
\(906\) | 8.00000 | 0.265782 | ||||||||
\(907\) | − | 27.0000i | − | 0.896520i | −0.893903 | − | 0.448260i | \(-0.852044\pi\) | ||
0.893903 | − | 0.448260i | \(-0.147956\pi\) | |||||||
\(908\) | − | 9.00000i | − | 0.298675i | ||||||
\(909\) | −24.0000 | −0.796030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 7.00000i | 0.231793i | ||||||||
\(913\) | − | 24.0000i | − | 0.794284i | ||||||
\(914\) | −12.0000 | −0.396925 | ||||||||
\(915\) | 6.00000 | − | 3.00000i | 0.198354 | − | 0.0991769i | ||||
\(916\) | 18.0000 | 0.594737 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.00000i | 0.165025i | ||||||||
\(919\) | 6.00000 | 0.197922 | 0.0989609 | − | 0.995091i | \(-0.468448\pi\) | ||||
0.0989609 | + | 0.995091i | \(0.468448\pi\) | |||||||
\(920\) | −8.00000 | − | 16.0000i | −0.263752 | − | 0.527504i | ||||
\(921\) | −24.0000 | −0.790827 | ||||||||
\(922\) | − | 20.0000i | − | 0.658665i | ||||||
\(923\) | − | 45.0000i | − | 1.48119i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | + | 24.0000i | 1.05215 | + | 0.789115i | ||||
\(926\) | −31.0000 | −1.01872 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.00000i | 0.164133i | ||||||||
\(929\) | 34.0000 | 1.11550 | 0.557752 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(930\) | −5.00000 | − | 10.0000i | −0.163956 | − | 0.327913i | ||||
\(931\) | 49.0000 | 1.60591 | ||||||||
\(932\) | − | 27.0000i | − | 0.884414i | ||||||
\(933\) | − | 4.00000i | − | 0.130954i | ||||||
\(934\) | −14.0000 | −0.458094 | ||||||||
\(935\) | −12.0000 | + | 6.00000i | −0.392442 | + | 0.196221i | ||||
\(936\) | 6.00000 | 0.196116 | ||||||||
\(937\) | 44.0000i | 1.43742i | 0.695311 | + | 0.718709i | \(0.255266\pi\) | ||||
−0.695311 | + | 0.718709i | \(0.744734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.0000 | 0.717943 | ||||||||
\(940\) | −6.00000 | + | 3.00000i | −0.195698 | + | 0.0978492i | ||||
\(941\) | −5.00000 | −0.162995 | −0.0814977 | − | 0.996674i | \(-0.525970\pi\) | ||||
−0.0814977 | + | 0.996674i | \(0.525970\pi\) | |||||||
\(942\) | 14.0000i | 0.456145i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −5.00000 | −0.162736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | 9.00000i | 0.292461i | 0.989251 | + | 0.146230i | \(0.0467141\pi\) | ||||
−0.989251 | + | 0.146230i | \(0.953286\pi\) | |||||||
\(948\) | 8.00000i | 0.259828i | ||||||||
\(949\) | 33.0000 | 1.07123 | ||||||||
\(950\) | −28.0000 | − | 21.0000i | −0.908440 | − | 0.681330i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.0000i | − | 1.42530i | −0.701520 | − | 0.712650i | \(-0.747495\pi\) | ||
0.701520 | − | 0.712650i | \(-0.252505\pi\) | |||||||
\(954\) | −18.0000 | −0.582772 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.0000 | 0.323423 | ||||||||
\(957\) | − | 30.0000i | − | 0.969762i | ||||||
\(958\) | 37.0000i | 1.19542i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00000 | − | 1.00000i | 0.0645497 | − | 0.0322749i | ||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 24.0000i | 0.773791i | ||||||||
\(963\) | 8.00000i | 0.257796i | ||||||||
\(964\) | 20.0000 | 0.644157 | ||||||||
\(965\) | −52.0000 | + | 26.0000i | −1.67394 | + | 0.836970i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000i | 0.514525i | 0.966342 | + | 0.257263i | \(0.0828206\pi\) | ||||
−0.966342 | + | 0.257263i | \(0.917179\pi\) | |||||||
\(968\) | − | 25.0000i | − | 0.803530i | ||||||
\(969\) | 7.00000 | 0.224872 | ||||||||
\(970\) | −9.00000 | − | 18.0000i | −0.288973 | − | 0.577945i | ||||
\(971\) | 37.0000 | 1.18739 | 0.593693 | − | 0.804691i | \(-0.297669\pi\) | ||||
0.593693 | + | 0.804691i | \(0.297669\pi\) | |||||||
\(972\) | − | 16.0000i | − | 0.513200i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.00000 | −0.0640841 | ||||||||
\(975\) | 9.00000 | − | 12.0000i | 0.288231 | − | 0.384308i | ||||
\(976\) | −3.00000 | −0.0960277 | ||||||||
\(977\) | − | 38.0000i | − | 1.21573i | −0.794041 | − | 0.607864i | \(-0.792027\pi\) | ||
0.794041 | − | 0.607864i | \(-0.207973\pi\) | |||||||
\(978\) | 4.00000i | 0.127906i | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | −7.00000 | − | 14.0000i | −0.223607 | − | 0.447214i | ||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | − | 13.0000i | − | 0.414847i | ||||||
\(983\) | 30.0000i | 0.956851i | 0.878128 | + | 0.478426i | \(0.158792\pi\) | ||||
−0.878128 | + | 0.478426i | \(0.841208\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00000 | − | 2.00000i | 0.127451 | − | 0.0637253i | ||||
\(986\) | 5.00000 | 0.159232 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 21.0000i | − | 0.668099i | ||||||
\(989\) | −32.0000 | −1.01754 | ||||||||
\(990\) | 24.0000 | − | 12.0000i | 0.762770 | − | 0.381385i | ||||
\(991\) | −19.0000 | −0.603555 | −0.301777 | − | 0.953378i | \(-0.597580\pi\) | ||||
−0.301777 | + | 0.953378i | \(0.597580\pi\) | |||||||
\(992\) | 5.00000i | 0.158750i | ||||||||
\(993\) | 7.00000i | 0.222138i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.00000 | − | 14.0000i | −0.221915 | − | 0.443830i | ||||
\(996\) | 4.00000 | 0.126745 | ||||||||
\(997\) | − | 28.0000i | − | 0.886769i | −0.896332 | − | 0.443384i | \(-0.853778\pi\) | ||
0.896332 | − | 0.443384i | \(-0.146222\pi\) | |||||||
\(998\) | 28.0000i | 0.886325i | ||||||||
\(999\) | 40.0000 | 1.26554 |
(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 | 170.2.c.a.69.2 | yes | 2 | |
3.2 | odd | 2 | 1530.2.d.b.919.1 | 2 | |||
4.3 | odd | 2 | 1360.2.e.b.1089.1 | 2 | |||
5.2 | odd | 4 | 850.2.a.d.1.1 | 1 | |||
5.3 | odd | 4 | 850.2.a.h.1.1 | 1 | |||
5.4 | even | 2 | inner | 170.2.c.a.69.1 | ✓ | 2 | |
15.2 | even | 4 | 7650.2.a.cb.1.1 | 1 | |||
15.8 | even | 4 | 7650.2.a.s.1.1 | 1 | |||
15.14 | odd | 2 | 1530.2.d.b.919.2 | 2 | |||
20.3 | even | 4 | 6800.2.a.r.1.1 | 1 | |||
20.7 | even | 4 | 6800.2.a.g.1.1 | 1 | |||
20.19 | odd | 2 | 1360.2.e.b.1089.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.c.a.69.1 | ✓ | 2 | 5.4 | even | 2 | inner | |
170.2.c.a.69.2 | yes | 2 | 1.1 | even | 1 | trivial | |
850.2.a.d.1.1 | 1 | 5.2 | odd | 4 | |||
850.2.a.h.1.1 | 1 | 5.3 | odd | 4 | |||
1360.2.e.b.1089.1 | 2 | 4.3 | odd | 2 | |||
1360.2.e.b.1089.2 | 2 | 20.19 | odd | 2 | |||
1530.2.d.b.919.1 | 2 | 3.2 | odd | 2 | |||
1530.2.d.b.919.2 | 2 | 15.14 | odd | 2 | |||
6800.2.a.g.1.1 | 1 | 20.7 | even | 4 | |||
6800.2.a.r.1.1 | 1 | 20.3 | even | 4 | |||
7650.2.a.s.1.1 | 1 | 15.8 | even | 4 | |||
7650.2.a.cb.1.1 | 1 | 15.2 | even | 4 |