Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(99,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, 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("490.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(3.91266969904\) |
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: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.2.c.c.99.1 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | + | 2.00000i | 0.447214 | + | 0.894427i | ||||
\(6\) | −3.00000 | −1.22474 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −6.00000 | −2.00000 | ||||||||
\(10\) | −2.00000 | + | 1.00000i | −0.632456 | + | 0.316228i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | − | 3.00000i | − | 0.866025i | ||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.00000 | + | 3.00000i | −1.54919 | + | 0.774597i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | − | 6.00000i | − | 1.41421i | ||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | 0.994550 | + | 0.104257i | \(0.0332465\pi\) | ||||
−0.994550 | + | 0.104257i | \(0.966753\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | − | 9.00000i | − | 1.73205i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | −3.00000 | − | 6.00000i | −0.547723 | − | 1.09545i | ||||
\(31\) | 10.0000 | 1.79605 | 0.898027 | − | 0.439941i | \(-0.145001\pi\) | ||||
0.898027 | + | 0.439941i | \(0.145001\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | − | 8.00000i | − | 1.31519i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) | ||
0.753371 | − | 0.657596i | \(-0.228427\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 2.00000 | − | 1.00000i | 0.316228 | − | 0.158114i | ||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.00000i | − | 0.762493i | −0.924473 | − | 0.381246i | \(-0.875495\pi\) | ||
0.924473 | − | 0.381246i | \(-0.124505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | − | 12.0000i | −0.894427 | − | 1.78885i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 3.00000i | 0.433013i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | − | 2.00000i | − | 0.277350i | ||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 9.00000 | 1.22474 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 1.00000i | 0.131306i | ||||||||
\(59\) | −2.00000 | −0.260378 | −0.130189 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130189 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(60\) | 6.00000 | − | 3.00000i | 0.774597 | − | 0.387298i | ||||
\(61\) | −9.00000 | −1.15233 | −0.576166 | − | 0.817333i | \(-0.695452\pi\) | ||||
−0.576166 | + | 0.817333i | \(0.695452\pi\) | |||||||
\(62\) | 10.0000i | 1.27000i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.00000 | + | 2.00000i | −0.496139 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.00000i | − | 0.855186i | −0.903971 | − | 0.427593i | \(-0.859362\pi\) | ||
0.903971 | − | 0.427593i | \(-0.140638\pi\) | |||||||
\(68\) | 2.00000i | 0.242536i | ||||||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 6.00000i | 0.707107i | ||||||||
\(73\) | 10.0000i | 1.17041i | 0.810885 | + | 0.585206i | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | −12.0000 | − | 9.00000i | −1.38564 | − | 1.03923i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 6.00000i | − | 0.679366i | ||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | − | 3.00000i | − | 0.331295i | ||||||
\(83\) | 9.00000i | 0.987878i | 0.869496 | + | 0.493939i | \(0.164443\pi\) | ||||
−0.869496 | + | 0.493939i | \(0.835557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 2.00000i | 0.433861 | − | 0.216930i | ||||
\(86\) | 5.00000 | 0.539164 | ||||||||
\(87\) | 3.00000i | 0.321634i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.00000 | 0.741999 | 0.370999 | − | 0.928633i | \(-0.379015\pi\) | ||||
0.370999 | + | 0.928633i | \(0.379015\pi\) | |||||||
\(90\) | 12.0000 | − | 6.00000i | 1.26491 | − | 0.632456i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | 30.0000i | 3.11086i | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 2.00000 | + | 4.00000i | 0.205196 | + | 0.410391i | ||||
\(96\) | −3.00000 | −0.306186 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | −15.0000 | −1.49256 | −0.746278 | − | 0.665635i | \(-0.768161\pi\) | ||||
−0.746278 | + | 0.665635i | \(0.768161\pi\) | |||||||
\(102\) | 6.00000i | 0.594089i | ||||||||
\(103\) | 11.0000i | 1.08386i | 0.840423 | + | 0.541931i | \(0.182307\pi\) | ||||
−0.840423 | + | 0.541931i | \(0.817693\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 7.00000i | − | 0.676716i | −0.941018 | − | 0.338358i | \(-0.890129\pi\) | ||
0.941018 | − | 0.338358i | \(-0.109871\pi\) | |||||||
\(108\) | 9.00000i | 0.866025i | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0000 | 2.27798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000i | 0.940721i | 0.882474 | + | 0.470360i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | −2.00000 | + | 1.00000i | −0.186501 | + | 0.0932505i | ||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | − | 12.0000i | − | 1.10940i | ||||||
\(118\) | − | 2.00000i | − | 0.184115i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.00000 | + | 6.00000i | 0.273861 | + | 0.547723i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 9.00000i | − | 0.814822i | ||||||
\(123\) | − | 9.00000i | − | 0.811503i | ||||||
\(124\) | −10.0000 | −0.898027 | ||||||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 15.0000 | 1.32068 | ||||||||
\(130\) | −2.00000 | − | 4.00000i | −0.175412 | − | 0.350823i | ||||
\(131\) | 20.0000 | 1.74741 | 0.873704 | − | 0.486458i | \(-0.161711\pi\) | ||||
0.873704 | + | 0.486458i | \(0.161711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.00000 | 0.604708 | ||||||||
\(135\) | 18.0000 | − | 9.00000i | 1.54919 | − | 0.774597i | ||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 16.0000i | 1.36697i | 0.729964 | + | 0.683486i | \(0.239537\pi\) | ||||
−0.729964 | + | 0.683486i | \(0.760463\pi\) | |||||||
\(138\) | − | 3.00000i | − | 0.255377i | ||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.0000 | −2.02116 | ||||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.00000 | −0.500000 | ||||||||
\(145\) | 1.00000 | + | 2.00000i | 0.0830455 | + | 0.166091i | ||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | 9.00000 | − | 12.0000i | 0.734847 | − | 0.979796i | ||||
\(151\) | 6.00000 | 0.488273 | 0.244137 | − | 0.969741i | \(-0.421495\pi\) | ||||
0.244137 | + | 0.969741i | \(0.421495\pi\) | |||||||
\(152\) | − | 2.00000i | − | 0.162221i | ||||||
\(153\) | 12.0000i | 0.970143i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0000 | + | 20.0000i | 0.803219 | + | 1.60644i | ||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | − | 12.0000i | − | 0.957704i | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||
0.877896 | − | 0.478852i | \(-0.158947\pi\) | |||||||
\(158\) | 10.0000i | 0.795557i | ||||||||
\(159\) | −18.0000 | −1.42749 | ||||||||
\(160\) | −2.00000 | + | 1.00000i | −0.158114 | + | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | − | 12.0000i | − | 0.939913i | −0.882690 | − | 0.469956i | \(-0.844270\pi\) | ||
0.882690 | − | 0.469956i | \(-0.155730\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00000 | −0.698535 | ||||||||
\(167\) | − | 9.00000i | − | 0.696441i | −0.937413 | − | 0.348220i | \(-0.886786\pi\) | ||
0.937413 | − | 0.348220i | \(-0.113214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 2.00000 | + | 4.00000i | 0.153393 | + | 0.306786i | ||||
\(171\) | −12.0000 | −0.917663 | ||||||||
\(172\) | 5.00000i | 0.381246i | ||||||||
\(173\) | − | 12.0000i | − | 0.912343i | −0.889892 | − | 0.456172i | \(-0.849220\pi\) | ||
0.889892 | − | 0.456172i | \(-0.150780\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.00000i | − | 0.450988i | ||||||
\(178\) | 7.00000i | 0.524672i | ||||||||
\(179\) | 26.0000 | 1.94333 | 0.971666 | − | 0.236360i | \(-0.0759544\pi\) | ||||
0.971666 | + | 0.236360i | \(0.0759544\pi\) | |||||||
\(180\) | 6.00000 | + | 12.0000i | 0.447214 | + | 0.894427i | ||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 27.0000i | − | 1.99590i | ||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 16.0000 | − | 8.00000i | 1.17634 | − | 0.588172i | ||||
\(186\) | −30.0000 | −2.19971 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 8.00000i | − | 0.583460i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | + | 2.00000i | −0.290191 | + | 0.145095i | ||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | − | 3.00000i | − | 0.216506i | ||||||
\(193\) | − | 20.0000i | − | 1.43963i | −0.694165 | − | 0.719816i | \(-0.744226\pi\) | ||
0.694165 | − | 0.719816i | \(-0.255774\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | − | 12.0000i | −0.429669 | − | 0.859338i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.00000i | − | 0.569976i | −0.958531 | − | 0.284988i | \(-0.908010\pi\) | ||
0.958531 | − | 0.284988i | \(-0.0919897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | −0.850657 | −0.425329 | − | 0.905039i | \(-0.639842\pi\) | ||||
−0.425329 | + | 0.905039i | \(0.639842\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | 21.0000 | 1.48123 | ||||||||
\(202\) | − | 15.0000i | − | 1.05540i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | −3.00000 | − | 6.00000i | −0.209529 | − | 0.419058i | ||||
\(206\) | −11.0000 | −0.766406 | ||||||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0000 | −1.23917 | −0.619586 | − | 0.784929i | \(-0.712699\pi\) | ||||
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | 18.0000i | 1.23334i | ||||||||
\(214\) | 7.00000 | 0.478510 | ||||||||
\(215\) | 10.0000 | − | 5.00000i | 0.681994 | − | 0.340997i | ||||
\(216\) | −9.00000 | −0.612372 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 5.00000i | − | 0.338643i | ||||||
\(219\) | −30.0000 | −2.02721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 24.0000i | 1.61077i | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.0000 | − | 24.0000i | 1.20000 | − | 1.60000i | ||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | − | 6.00000i | − | 0.397360i | ||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | −1.00000 | − | 2.00000i | −0.0659380 | − | 0.131876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.00000i | − | 0.0656532i | ||||||
\(233\) | 14.0000i | 0.917170i | 0.888650 | + | 0.458585i | \(0.151644\pi\) | ||||
−0.888650 | + | 0.458585i | \(0.848356\pi\) | |||||||
\(234\) | 12.0000 | 0.784465 | ||||||||
\(235\) | −16.0000 | + | 8.00000i | −1.04372 | + | 0.521862i | ||||
\(236\) | 2.00000 | 0.130189 | ||||||||
\(237\) | 30.0000i | 1.94871i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0000 | 0.646846 | 0.323423 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323423 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(240\) | −6.00000 | + | 3.00000i | −0.387298 | + | 0.193649i | ||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | − | 11.0000i | − | 0.707107i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.00000 | 0.576166 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | − | 10.0000i | − | 0.635001i | ||||||
\(249\) | −27.0000 | −1.71106 | ||||||||
\(250\) | 2.00000 | − | 11.0000i | 0.126491 | − | 0.695701i | ||||
\(251\) | −10.0000 | −0.631194 | −0.315597 | − | 0.948893i | \(-0.602205\pi\) | ||||
−0.315597 | + | 0.948893i | \(0.602205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | 6.00000 | + | 12.0000i | 0.375735 | + | 0.751469i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.0000i | 0.748539i | 0.927320 | + | 0.374270i | \(0.122107\pi\) | ||||
−0.927320 | + | 0.374270i | \(0.877893\pi\) | |||||||
\(258\) | 15.0000i | 0.933859i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | − | 2.00000i | 0.248069 | − | 0.124035i | ||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 20.0000i | 1.23560i | ||||||||
\(263\) | − | 21.0000i | − | 1.29492i | −0.762101 | − | 0.647458i | \(-0.775832\pi\) | ||
0.762101 | − | 0.647458i | \(-0.224168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | + | 6.00000i | −0.737154 | + | 0.368577i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.0000i | 1.28518i | ||||||||
\(268\) | 7.00000i | 0.427593i | ||||||||
\(269\) | −5.00000 | −0.304855 | −0.152428 | − | 0.988315i | \(-0.548709\pi\) | ||||
−0.152428 | + | 0.988315i | \(0.548709\pi\) | |||||||
\(270\) | 9.00000 | + | 18.0000i | 0.547723 | + | 1.09545i | ||||
\(271\) | 6.00000 | 0.364474 | 0.182237 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182237 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | 0.180579 | ||||||||
\(277\) | − | 26.0000i | − | 1.56219i | −0.624413 | − | 0.781094i | \(-0.714662\pi\) | ||
0.624413 | − | 0.781094i | \(-0.285338\pi\) | |||||||
\(278\) | 8.00000i | 0.479808i | ||||||||
\(279\) | −60.0000 | −3.59211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | − | 24.0000i | − | 1.42918i | ||||||
\(283\) | − | 8.00000i | − | 0.475551i | −0.971320 | − | 0.237775i | \(-0.923582\pi\) | ||
0.971320 | − | 0.237775i | \(-0.0764182\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | −12.0000 | + | 6.00000i | −0.710819 | + | 0.355409i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 6.00000i | − | 0.353553i | ||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −2.00000 | + | 1.00000i | −0.117444 | + | 0.0587220i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 10.0000i | − | 0.585206i | ||||||
\(293\) | − | 24.0000i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | − | 4.00000i | −0.116445 | − | 0.232889i | ||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.0000i | 0.868927i | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 12.0000 | + | 9.00000i | 0.692820 | + | 0.519615i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.00000i | 0.345261i | ||||||||
\(303\) | − | 45.0000i | − | 2.58518i | ||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | −9.00000 | − | 18.0000i | −0.515339 | − | 1.03068i | ||||
\(306\) | −12.0000 | −0.685994 | ||||||||
\(307\) | − | 19.0000i | − | 1.08439i | −0.840254 | − | 0.542194i | \(-0.817594\pi\) | ||
0.840254 | − | 0.542194i | \(-0.182406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.0000 | −1.87730 | ||||||||
\(310\) | −20.0000 | + | 10.0000i | −1.13592 | + | 0.567962i | ||||
\(311\) | 6.00000 | 0.340229 | 0.170114 | − | 0.985424i | \(-0.445586\pi\) | ||||
0.170114 | + | 0.985424i | \(0.445586\pi\) | |||||||
\(312\) | 6.00000i | 0.339683i | ||||||||
\(313\) | − | 8.00000i | − | 0.452187i | −0.974106 | − | 0.226093i | \(-0.927405\pi\) | ||
0.974106 | − | 0.226093i | \(-0.0725954\pi\) | |||||||
\(314\) | 12.0000 | 0.677199 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 22.0000i | 1.23564i | 0.786318 | + | 0.617822i | \(0.211985\pi\) | ||||
−0.786318 | + | 0.617822i | \(0.788015\pi\) | |||||||
\(318\) | − | 18.0000i | − | 1.00939i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | − | 2.00000i | −0.0559017 | − | 0.111803i | ||||
\(321\) | 21.0000 | 1.17211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | −8.00000 | − | 6.00000i | −0.443760 | − | 0.332820i | ||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | − | 15.0000i | − | 0.829502i | ||||||
\(328\) | 3.00000i | 0.165647i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | 0.769510 | 0.384755 | − | 0.923019i | \(-0.374286\pi\) | ||||
0.384755 | + | 0.923019i | \(0.374286\pi\) | |||||||
\(332\) | − | 9.00000i | − | 0.493939i | ||||||
\(333\) | 48.0000i | 2.63038i | ||||||||
\(334\) | 9.00000 | 0.492458 | ||||||||
\(335\) | 14.0000 | − | 7.00000i | 0.764902 | − | 0.382451i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.00000i | − | 0.108947i | −0.998515 | − | 0.0544735i | \(-0.982652\pi\) | ||
0.998515 | − | 0.0544735i | \(-0.0173480\pi\) | |||||||
\(338\) | 9.00000i | 0.489535i | ||||||||
\(339\) | −30.0000 | −1.62938 | ||||||||
\(340\) | −4.00000 | + | 2.00000i | −0.216930 | + | 0.108465i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 12.0000i | − | 0.648886i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.00000 | −0.269582 | ||||||||
\(345\) | −3.00000 | − | 6.00000i | −0.161515 | − | 0.323029i | ||||
\(346\) | 12.0000 | 0.645124 | ||||||||
\(347\) | 21.0000i | 1.12734i | 0.826000 | + | 0.563670i | \(0.190611\pi\) | ||||
−0.826000 | + | 0.563670i | \(0.809389\pi\) | |||||||
\(348\) | − | 3.00000i | − | 0.160817i | ||||||
\(349\) | 9.00000 | 0.481759 | 0.240879 | − | 0.970555i | \(-0.422564\pi\) | ||||
0.240879 | + | 0.970555i | \(0.422564\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | 0.960769 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | 6.00000 | + | 12.0000i | 0.318447 | + | 0.636894i | ||||
\(356\) | −7.00000 | −0.370999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.0000i | 1.37414i | ||||||||
\(359\) | 14.0000 | 0.738892 | 0.369446 | − | 0.929252i | \(-0.379548\pi\) | ||||
0.369446 | + | 0.929252i | \(0.379548\pi\) | |||||||
\(360\) | −12.0000 | + | 6.00000i | −0.632456 | + | 0.316228i | ||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 5.00000i | 0.262794i | ||||||||
\(363\) | − | 33.0000i | − | 1.73205i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0000 | + | 10.0000i | −1.04685 | + | 0.523424i | ||||
\(366\) | 27.0000 | 1.41131 | ||||||||
\(367\) | − | 23.0000i | − | 1.20059i | −0.799779 | − | 0.600295i | \(-0.795050\pi\) | ||
0.799779 | − | 0.600295i | \(-0.204950\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | 8.00000 | + | 16.0000i | 0.415900 | + | 0.831800i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 30.0000i | − | 1.55543i | ||||||
\(373\) | − | 8.00000i | − | 0.414224i | −0.978317 | − | 0.207112i | \(-0.933593\pi\) | ||
0.978317 | − | 0.207112i | \(-0.0664065\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.00000 | − | 33.0000i | 0.309839 | − | 1.70411i | ||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 2.00000i | 0.103005i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | −2.00000 | − | 4.00000i | −0.102598 | − | 0.205196i | ||||
\(381\) | 24.0000 | 1.22956 | ||||||||
\(382\) | − | 20.0000i | − | 1.02329i | ||||||
\(383\) | 9.00000i | 0.459879i | 0.973205 | + | 0.229939i | \(0.0738528\pi\) | ||||
−0.973205 | + | 0.229939i | \(0.926147\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 30.0000i | 1.52499i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 12.0000 | − | 6.00000i | 0.607644 | − | 0.303822i | ||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 60.0000i | 3.02660i | ||||||||
\(394\) | 8.00000 | 0.403034 | ||||||||
\(395\) | 10.0000 | + | 20.0000i | 0.503155 | + | 1.00631i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.0000i | − | 1.60603i | −0.595956 | − | 0.803017i | \(-0.703227\pi\) | ||
0.595956 | − | 0.803017i | \(-0.296773\pi\) | |||||||
\(398\) | − | 12.0000i | − | 0.601506i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 3.00000 | 0.149813 | 0.0749064 | − | 0.997191i | \(-0.476134\pi\) | ||||
0.0749064 | + | 0.997191i | \(0.476134\pi\) | |||||||
\(402\) | 21.0000i | 1.04738i | ||||||||
\(403\) | 20.0000i | 0.996271i | ||||||||
\(404\) | 15.0000 | 0.746278 | ||||||||
\(405\) | 9.00000 | + | 18.0000i | 0.447214 | + | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | 17.0000 | 0.840596 | 0.420298 | − | 0.907386i | \(-0.361926\pi\) | ||||
0.420298 | + | 0.907386i | \(0.361926\pi\) | |||||||
\(410\) | 6.00000 | − | 3.00000i | 0.296319 | − | 0.148159i | ||||
\(411\) | −48.0000 | −2.36767 | ||||||||
\(412\) | − | 11.0000i | − | 0.541931i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | −18.0000 | + | 9.00000i | −0.883585 | + | 0.441793i | ||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 24.0000i | 1.17529i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.0000 | 1.95413 | 0.977064 | − | 0.212946i | \(-0.0683059\pi\) | ||||
0.977064 | + | 0.212946i | \(0.0683059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.0000 | 1.51085 | 0.755424 | − | 0.655237i | \(-0.227431\pi\) | ||||
0.755424 | + | 0.655237i | \(0.227431\pi\) | |||||||
\(422\) | − | 18.0000i | − | 0.876226i | ||||||
\(423\) | − | 48.0000i | − | 2.33384i | ||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 8.00000 | + | 6.00000i | 0.388057 | + | 0.291043i | ||||
\(426\) | −18.0000 | −0.872103 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.00000i | 0.338358i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.00000 | + | 10.0000i | 0.241121 | + | 0.482243i | ||||
\(431\) | 32.0000 | 1.54139 | 0.770693 | − | 0.637207i | \(-0.219910\pi\) | ||||
0.770693 | + | 0.637207i | \(0.219910\pi\) | |||||||
\(432\) | − | 9.00000i | − | 0.433013i | ||||||
\(433\) | 14.0000i | 0.672797i | 0.941720 | + | 0.336399i | \(0.109209\pi\) | ||||
−0.941720 | + | 0.336399i | \(0.890791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.00000 | + | 3.00000i | −0.287678 | + | 0.143839i | ||||
\(436\) | 5.00000 | 0.239457 | ||||||||
\(437\) | 2.00000i | 0.0956730i | ||||||||
\(438\) | − | 30.0000i | − | 1.43346i | ||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000i | 0.190261i | ||||||||
\(443\) | 3.00000i | 0.142534i | 0.997457 | + | 0.0712672i | \(0.0227043\pi\) | ||||
−0.997457 | + | 0.0712672i | \(0.977296\pi\) | |||||||
\(444\) | −24.0000 | −1.13899 | ||||||||
\(445\) | 7.00000 | + | 14.0000i | 0.331832 | + | 0.663664i | ||||
\(446\) | −8.00000 | −0.378811 | ||||||||
\(447\) | 45.0000i | 2.12843i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.0000 | −1.08544 | −0.542719 | − | 0.839915i | \(-0.682605\pi\) | ||||
−0.542719 | + | 0.839915i | \(0.682605\pi\) | |||||||
\(450\) | 24.0000 | + | 18.0000i | 1.13137 | + | 0.848528i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 10.0000i | − | 0.470360i | ||||||
\(453\) | 18.0000i | 0.845714i | ||||||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | 32.0000i | 1.49690i | 0.663193 | + | 0.748448i | \(0.269201\pi\) | ||||
−0.663193 | + | 0.748448i | \(0.730799\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | −18.0000 | −0.840168 | ||||||||
\(460\) | 2.00000 | − | 1.00000i | 0.0932505 | − | 0.0466252i | ||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.0000i | − | 1.16185i | −0.813958 | − | 0.580924i | \(-0.802691\pi\) | ||
0.813958 | − | 0.580924i | \(-0.197309\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −60.0000 | + | 30.0000i | −2.78243 | + | 1.39122i | ||||
\(466\) | −14.0000 | −0.648537 | ||||||||
\(467\) | 1.00000i | 0.0462745i | 0.999732 | + | 0.0231372i | \(0.00736547\pi\) | ||||
−0.999732 | + | 0.0231372i | \(0.992635\pi\) | |||||||
\(468\) | 12.0000i | 0.554700i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.00000 | − | 16.0000i | −0.369012 | − | 0.738025i | ||||
\(471\) | 36.0000 | 1.65879 | ||||||||
\(472\) | 2.00000i | 0.0920575i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −30.0000 | −1.37795 | ||||||||
\(475\) | −6.00000 | + | 8.00000i | −0.275299 | + | 0.367065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 36.0000i | − | 1.64833i | ||||||
\(478\) | 10.0000i | 0.457389i | ||||||||
\(479\) | −18.0000 | −0.822441 | −0.411220 | − | 0.911536i | \(-0.634897\pi\) | ||||
−0.411220 | + | 0.911536i | \(0.634897\pi\) | |||||||
\(480\) | −3.00000 | − | 6.00000i | −0.136931 | − | 0.273861i | ||||
\(481\) | 16.0000 | 0.729537 | ||||||||
\(482\) | 18.0000i | 0.819878i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000i | 0.181257i | 0.995885 | + | 0.0906287i | \(0.0288876\pi\) | ||||
−0.995885 | + | 0.0906287i | \(0.971112\pi\) | |||||||
\(488\) | 9.00000i | 0.407411i | ||||||||
\(489\) | 36.0000 | 1.62798 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | 9.00000i | 0.405751i | ||||||||
\(493\) | − | 2.00000i | − | 0.0900755i | ||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.0000 | 0.449013 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 27.0000i | − | 1.20990i | ||||||
\(499\) | −16.0000 | −0.716258 | −0.358129 | − | 0.933672i | \(-0.616585\pi\) | ||||
−0.358129 | + | 0.933672i | \(0.616585\pi\) | |||||||
\(500\) | 11.0000 | + | 2.00000i | 0.491935 | + | 0.0894427i | ||||
\(501\) | 27.0000 | 1.20627 | ||||||||
\(502\) | − | 10.0000i | − | 0.446322i | ||||||
\(503\) | 5.00000i | 0.222939i | 0.993768 | + | 0.111469i | \(0.0355557\pi\) | ||||
−0.993768 | + | 0.111469i | \(0.964444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.0000 | − | 30.0000i | −0.667491 | − | 1.33498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.0000i | 1.19911i | ||||||||
\(508\) | 8.00000i | 0.354943i | ||||||||
\(509\) | −35.0000 | −1.55135 | −0.775674 | − | 0.631134i | \(-0.782590\pi\) | ||||
−0.775674 | + | 0.631134i | \(0.782590\pi\) | |||||||
\(510\) | −12.0000 | + | 6.00000i | −0.531369 | + | 0.265684i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 18.0000i | − | 0.794719i | ||||||
\(514\) | −12.0000 | −0.529297 | ||||||||
\(515\) | −22.0000 | + | 11.0000i | −0.969436 | + | 0.484718i | ||||
\(516\) | −15.0000 | −0.660338 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.0000 | 1.58022 | ||||||||
\(520\) | 2.00000 | + | 4.00000i | 0.0877058 | + | 0.175412i | ||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | − | 6.00000i | − | 0.262613i | ||||||
\(523\) | − | 4.00000i | − | 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | −20.0000 | −0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.0000 | 0.915644 | ||||||||
\(527\) | − | 20.0000i | − | 0.871214i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | −6.00000 | − | 12.0000i | −0.260623 | − | 0.521247i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.00000i | − | 0.259889i | ||||||
\(534\) | −21.0000 | −0.908759 | ||||||||
\(535\) | 14.0000 | − | 7.00000i | 0.605273 | − | 0.302636i | ||||
\(536\) | −7.00000 | −0.302354 | ||||||||
\(537\) | 78.0000i | 3.36595i | ||||||||
\(538\) | − | 5.00000i | − | 0.215565i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18.0000 | + | 9.00000i | −0.774597 | + | 0.387298i | ||||
\(541\) | 5.00000 | 0.214967 | 0.107483 | − | 0.994207i | \(-0.465721\pi\) | ||||
0.107483 | + | 0.994207i | \(0.465721\pi\) | |||||||
\(542\) | 6.00000i | 0.257722i | ||||||||
\(543\) | 15.0000i | 0.643712i | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | −5.00000 | − | 10.0000i | −0.214176 | − | 0.428353i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.0000i | 1.58201i | 0.611812 | + | 0.791003i | \(0.290441\pi\) | ||||
−0.611812 | + | 0.791003i | \(0.709559\pi\) | |||||||
\(548\) | − | 16.0000i | − | 0.683486i | ||||||
\(549\) | 54.0000 | 2.30466 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 3.00000i | 0.127688i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.0000 | 1.10463 | ||||||||
\(555\) | 24.0000 | + | 48.0000i | 1.01874 | + | 2.03749i | ||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | − | 4.00000i | − | 0.169485i | −0.996403 | − | 0.0847427i | \(-0.972993\pi\) | ||
0.996403 | − | 0.0847427i | \(-0.0270068\pi\) | |||||||
\(558\) | − | 60.0000i | − | 2.54000i | ||||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000i | 0.759284i | ||||||||
\(563\) | − | 11.0000i | − | 0.463595i | −0.972764 | − | 0.231797i | \(-0.925539\pi\) | ||
0.972764 | − | 0.231797i | \(-0.0744606\pi\) | |||||||
\(564\) | 24.0000 | 1.01058 | ||||||||
\(565\) | −20.0000 | + | 10.0000i | −0.841406 | + | 0.420703i | ||||
\(566\) | 8.00000 | 0.336265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | −6.00000 | − | 12.0000i | −0.251312 | − | 0.502625i | ||||
\(571\) | −10.0000 | −0.418487 | −0.209243 | − | 0.977864i | \(-0.567100\pi\) | ||||
−0.209243 | + | 0.977864i | \(0.567100\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 60.0000i | − | 2.50654i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | − | 3.00000i | −0.166812 | − | 0.125109i | ||||
\(576\) | 6.00000 | 0.250000 | ||||||||
\(577\) | − | 16.0000i | − | 0.666089i | −0.942911 | − | 0.333044i | \(-0.891924\pi\) | ||
0.942911 | − | 0.333044i | \(-0.108076\pi\) | |||||||
\(578\) | 13.0000i | 0.540729i | ||||||||
\(579\) | 60.0000 | 2.49351 | ||||||||
\(580\) | −1.00000 | − | 2.00000i | −0.0415227 | − | 0.0830455i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 24.0000 | − | 12.0000i | 0.992278 | − | 0.496139i | ||||
\(586\) | 24.0000 | 0.991431 | ||||||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000 | 0.824086 | ||||||||
\(590\) | 4.00000 | − | 2.00000i | 0.164677 | − | 0.0823387i | ||||
\(591\) | 24.0000 | 0.987228 | ||||||||
\(592\) | − | 8.00000i | − | 0.328798i | ||||||
\(593\) | − | 42.0000i | − | 1.72473i | −0.506284 | − | 0.862367i | \(-0.668981\pi\) | ||
0.506284 | − | 0.862367i | \(-0.331019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.0000 | −0.614424 | ||||||||
\(597\) | − | 36.0000i | − | 1.47338i | ||||||
\(598\) | − | 2.00000i | − | 0.0817861i | ||||||
\(599\) | −36.0000 | −1.47092 | −0.735460 | − | 0.677568i | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(600\) | −9.00000 | + | 12.0000i | −0.367423 | + | 0.489898i | ||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 42.0000i | 1.71037i | ||||||||
\(604\) | −6.00000 | −0.244137 | ||||||||
\(605\) | −11.0000 | − | 22.0000i | −0.447214 | − | 0.894427i | ||||
\(606\) | 45.0000 | 1.82800 | ||||||||
\(607\) | 5.00000i | 0.202944i | 0.994838 | + | 0.101472i | \(0.0323552\pi\) | ||||
−0.994838 | + | 0.101472i | \(0.967645\pi\) | |||||||
\(608\) | 2.00000i | 0.0811107i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.0000 | − | 9.00000i | 0.728799 | − | 0.364399i | ||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | − | 12.0000i | − | 0.485071i | ||||||
\(613\) | − | 18.0000i | − | 0.727013i | −0.931592 | − | 0.363507i | \(-0.881579\pi\) | ||
0.931592 | − | 0.363507i | \(-0.118421\pi\) | |||||||
\(614\) | 19.0000 | 0.766778 | ||||||||
\(615\) | 18.0000 | − | 9.00000i | 0.725830 | − | 0.362915i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.0000i | 0.805170i | 0.915383 | + | 0.402585i | \(0.131888\pi\) | ||||
−0.915383 | + | 0.402585i | \(0.868112\pi\) | |||||||
\(618\) | − | 33.0000i | − | 1.32745i | ||||||
\(619\) | 20.0000 | 0.803868 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | −10.0000 | − | 20.0000i | −0.401610 | − | 0.803219i | ||||
\(621\) | 9.00000 | 0.361158 | ||||||||
\(622\) | 6.00000i | 0.240578i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 8.00000 | 0.319744 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.0000i | 0.478852i | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(632\) | − | 10.0000i | − | 0.397779i | ||||||
\(633\) | − | 54.0000i | − | 2.14631i | ||||||
\(634\) | −22.0000 | −0.873732 | ||||||||
\(635\) | 16.0000 | − | 8.00000i | 0.634941 | − | 0.317470i | ||||
\(636\) | 18.0000 | 0.713746 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.0000 | −1.42414 | ||||||||
\(640\) | 2.00000 | − | 1.00000i | 0.0790569 | − | 0.0395285i | ||||
\(641\) | −35.0000 | −1.38242 | −0.691208 | − | 0.722655i | \(-0.742921\pi\) | ||||
−0.691208 | + | 0.722655i | \(0.742921\pi\) | |||||||
\(642\) | 21.0000i | 0.828804i | ||||||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0000 | + | 30.0000i | 0.590624 | + | 1.18125i | ||||
\(646\) | 4.00000 | 0.157378 | ||||||||
\(647\) | 21.0000i | 0.825595i | 0.910823 | + | 0.412798i | \(0.135448\pi\) | ||||
−0.910823 | + | 0.412798i | \(0.864552\pi\) | |||||||
\(648\) | − | 9.00000i | − | 0.353553i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.00000 | − | 8.00000i | 0.235339 | − | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000i | 0.469956i | ||||||||
\(653\) | − | 42.0000i | − | 1.64359i | −0.569785 | − | 0.821794i | \(-0.692974\pi\) | ||
0.569785 | − | 0.821794i | \(-0.307026\pi\) | |||||||
\(654\) | 15.0000 | 0.586546 | ||||||||
\(655\) | 20.0000 | + | 40.0000i | 0.781465 | + | 1.56293i | ||||
\(656\) | −3.00000 | −0.117130 | ||||||||
\(657\) | − | 60.0000i | − | 2.34082i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.0000 | −1.59472 | −0.797358 | − | 0.603507i | \(-0.793769\pi\) | ||||
−0.797358 | + | 0.603507i | \(0.793769\pi\) | |||||||
\(662\) | 14.0000i | 0.544125i | ||||||||
\(663\) | 12.0000i | 0.466041i | ||||||||
\(664\) | 9.00000 | 0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −48.0000 | −1.85996 | ||||||||
\(667\) | 1.00000i | 0.0387202i | ||||||||
\(668\) | 9.00000i | 0.348220i | ||||||||
\(669\) | −24.0000 | −0.927894 | ||||||||
\(670\) | 7.00000 | + | 14.0000i | 0.270434 | + | 0.540867i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20.0000i | − | 0.770943i | −0.922720 | − | 0.385472i | \(-0.874039\pi\) | ||
0.922720 | − | 0.385472i | \(-0.125961\pi\) | |||||||
\(674\) | 2.00000 | 0.0770371 | ||||||||
\(675\) | 36.0000 | + | 27.0000i | 1.38564 | + | 1.03923i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | − | 2.00000i | − | 0.0768662i | −0.999261 | − | 0.0384331i | \(-0.987763\pi\) | ||
0.999261 | − | 0.0384331i | \(-0.0122367\pi\) | |||||||
\(678\) | − | 30.0000i | − | 1.15214i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.00000 | − | 4.00000i | −0.0766965 | − | 0.153393i | ||||
\(681\) | −36.0000 | −1.37952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.0000i | − | 0.956598i | −0.878197 | − | 0.478299i | \(-0.841253\pi\) | ||
0.878197 | − | 0.478299i | \(-0.158747\pi\) | |||||||
\(684\) | 12.0000 | 0.458831 | ||||||||
\(685\) | −32.0000 | + | 16.0000i | −1.22266 | + | 0.611329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 30.0000i | − | 1.14457i | ||||||
\(688\) | − | 5.00000i | − | 0.190623i | ||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 6.00000 | − | 3.00000i | 0.228416 | − | 0.114208i | ||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 12.0000i | 0.456172i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.0000 | −0.797149 | ||||||||
\(695\) | 8.00000 | + | 16.0000i | 0.303457 | + | 0.606915i | ||||
\(696\) | 3.00000 | 0.113715 | ||||||||
\(697\) | 6.00000i | 0.227266i | ||||||||
\(698\) | 9.00000i | 0.340655i | ||||||||
\(699\) | −42.0000 | −1.58859 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.00000 | −0.0377695 | −0.0188847 | − | 0.999822i | \(-0.506012\pi\) | ||||
−0.0188847 | + | 0.999822i | \(0.506012\pi\) | |||||||
\(702\) | 18.0000i | 0.679366i | ||||||||
\(703\) | − | 16.0000i | − | 0.603451i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.0000 | − | 48.0000i | −0.903892 | − | 1.80778i | ||||
\(706\) | −6.00000 | −0.225813 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.00000i | 0.225494i | ||||||||
\(709\) | 9.00000 | 0.338002 | 0.169001 | − | 0.985616i | \(-0.445946\pi\) | ||||
0.169001 | + | 0.985616i | \(0.445946\pi\) | |||||||
\(710\) | −12.0000 | + | 6.00000i | −0.450352 | + | 0.225176i | ||||
\(711\) | −60.0000 | −2.25018 | ||||||||
\(712\) | − | 7.00000i | − | 0.262336i | ||||||
\(713\) | 10.0000i | 0.374503i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −26.0000 | −0.971666 | ||||||||
\(717\) | 30.0000i | 1.12037i | ||||||||
\(718\) | 14.0000i | 0.522475i | ||||||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | −6.00000 | − | 12.0000i | −0.223607 | − | 0.447214i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 15.0000i | − | 0.558242i | ||||||
\(723\) | 54.0000i | 2.00828i | ||||||||
\(724\) | −5.00000 | −0.185824 | ||||||||
\(725\) | −3.00000 | + | 4.00000i | −0.111417 | + | 0.148556i | ||||
\(726\) | 33.0000 | 1.22474 | ||||||||
\(727\) | − | 29.0000i | − | 1.07555i | −0.843088 | − | 0.537775i | \(-0.819265\pi\) | ||
0.843088 | − | 0.537775i | \(-0.180735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −10.0000 | − | 20.0000i | −0.370117 | − | 0.740233i | ||||
\(731\) | −10.0000 | −0.369863 | ||||||||
\(732\) | 27.0000i | 0.997949i | ||||||||
\(733\) | 16.0000i | 0.590973i | 0.955347 | + | 0.295487i | \(0.0954818\pi\) | ||||
−0.955347 | + | 0.295487i | \(0.904518\pi\) | |||||||
\(734\) | 23.0000 | 0.848945 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 18.0000i | 0.662589i | ||||||||
\(739\) | 32.0000 | 1.17714 | 0.588570 | − | 0.808447i | \(-0.299691\pi\) | ||||
0.588570 | + | 0.808447i | \(0.299691\pi\) | |||||||
\(740\) | −16.0000 | + | 8.00000i | −0.588172 | + | 0.294086i | ||||
\(741\) | −12.0000 | −0.440831 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000i | 0.110059i | 0.998485 | + | 0.0550297i | \(0.0175253\pi\) | ||||
−0.998485 | + | 0.0550297i | \(0.982475\pi\) | |||||||
\(744\) | 30.0000 | 1.09985 | ||||||||
\(745\) | 15.0000 | + | 30.0000i | 0.549557 | + | 1.09911i | ||||
\(746\) | 8.00000 | 0.292901 | ||||||||
\(747\) | − | 54.0000i | − | 1.97576i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 33.0000 | + | 6.00000i | 1.20499 | + | 0.219089i | ||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | 8.00000i | 0.291730i | ||||||||
\(753\) | − | 30.0000i | − | 1.09326i | ||||||
\(754\) | −2.00000 | −0.0728357 | ||||||||
\(755\) | 6.00000 | + | 12.0000i | 0.218362 | + | 0.436725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.00000i | − | 0.218074i | −0.994038 | − | 0.109037i | \(-0.965223\pi\) | ||
0.994038 | − | 0.109037i | \(-0.0347767\pi\) | |||||||
\(758\) | 2.00000i | 0.0726433i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.00000 | − | 2.00000i | 0.145095 | − | 0.0725476i | ||||
\(761\) | −50.0000 | −1.81250 | −0.906249 | − | 0.422744i | \(-0.861067\pi\) | ||||
−0.906249 | + | 0.422744i | \(0.861067\pi\) | |||||||
\(762\) | 24.0000i | 0.869428i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | −24.0000 | + | 12.0000i | −0.867722 | + | 0.433861i | ||||
\(766\) | −9.00000 | −0.325183 | ||||||||
\(767\) | − | 4.00000i | − | 0.144432i | ||||||
\(768\) | 3.00000i | 0.108253i | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.0000 | −1.29651 | ||||||||
\(772\) | 20.0000i | 0.719816i | ||||||||
\(773\) | 18.0000i | 0.647415i | 0.946157 | + | 0.323708i | \(0.104929\pi\) | ||||
−0.946157 | + | 0.323708i | \(0.895071\pi\) | |||||||
\(774\) | −30.0000 | −1.07833 | ||||||||
\(775\) | −30.0000 | + | 40.0000i | −1.07763 | + | 1.43684i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.0000i | 0.645331i | ||||||||
\(779\) | −6.00000 | −0.214972 | ||||||||
\(780\) | 6.00000 | + | 12.0000i | 0.214834 | + | 0.429669i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.00000i | 0.0715199i | ||||||||
\(783\) | − | 9.00000i | − | 0.321634i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0000 | − | 12.0000i | 0.856597 | − | 0.428298i | ||||
\(786\) | −60.0000 | −2.14013 | ||||||||
\(787\) | 21.0000i | 0.748569i | 0.927314 | + | 0.374285i | \(0.122112\pi\) | ||||
−0.927314 | + | 0.374285i | \(0.877888\pi\) | |||||||
\(788\) | 8.00000i | 0.284988i | ||||||||
\(789\) | 63.0000 | 2.24286 | ||||||||
\(790\) | −20.0000 | + | 10.0000i | −0.711568 | + | 0.355784i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.0000i | − | 0.639199i | ||||||
\(794\) | 32.0000 | 1.13564 | ||||||||
\(795\) | −18.0000 | − | 36.0000i | −0.638394 | − | 1.27679i | ||||
\(796\) | 12.0000 | 0.425329 | ||||||||
\(797\) | − | 8.00000i | − | 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | −42.0000 | −1.48400 | ||||||||
\(802\) | 3.00000i | 0.105934i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −21.0000 | −0.740613 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | − | 15.0000i | − | 0.528025i | ||||||
\(808\) | 15.0000i | 0.527698i | ||||||||
\(809\) | −25.0000 | −0.878953 | −0.439477 | − | 0.898254i | \(-0.644836\pi\) | ||||
−0.439477 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(810\) | −18.0000 | + | 9.00000i | −0.632456 | + | 0.316228i | ||||
\(811\) | 6.00000 | 0.210688 | 0.105344 | − | 0.994436i | \(-0.466406\pi\) | ||||
0.105344 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.0000i | 0.631288i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0000 | − | 12.0000i | 0.840683 | − | 0.420342i | ||||
\(816\) | 6.00000 | 0.210042 | ||||||||
\(817\) | − | 10.0000i | − | 0.349856i | ||||||
\(818\) | 17.0000i | 0.594391i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.00000 | + | 6.00000i | 0.104765 | + | 0.209529i | ||||
\(821\) | −42.0000 | −1.46581 | −0.732905 | − | 0.680331i | \(-0.761836\pi\) | ||||
−0.732905 | + | 0.680331i | \(0.761836\pi\) | |||||||
\(822\) | − | 48.0000i | − | 1.67419i | ||||||
\(823\) | 45.0000i | 1.56860i | 0.620381 | + | 0.784301i | \(0.286978\pi\) | ||||
−0.620381 | + | 0.784301i | \(0.713022\pi\) | |||||||
\(824\) | 11.0000 | 0.383203 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 37.0000i | − | 1.28662i | −0.765607 | − | 0.643308i | \(-0.777561\pi\) | ||
0.765607 | − | 0.643308i | \(-0.222439\pi\) | |||||||
\(828\) | 6.00000i | 0.208514i | ||||||||
\(829\) | −34.0000 | −1.18087 | −0.590434 | − | 0.807086i | \(-0.701044\pi\) | ||||
−0.590434 | + | 0.807086i | \(0.701044\pi\) | |||||||
\(830\) | −9.00000 | − | 18.0000i | −0.312395 | − | 0.624789i | ||||
\(831\) | 78.0000 | 2.70579 | ||||||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −24.0000 | −0.831052 | ||||||||
\(835\) | 18.0000 | − | 9.00000i | 0.622916 | − | 0.311458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 90.0000i | − | 3.11086i | ||||||
\(838\) | 40.0000i | 1.38178i | ||||||||
\(839\) | −32.0000 | −1.10476 | −0.552381 | − | 0.833592i | \(-0.686281\pi\) | ||||
−0.552381 | + | 0.833592i | \(0.686281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 31.0000i | 1.06833i | ||||||||
\(843\) | 54.0000i | 1.85986i | ||||||||
\(844\) | 18.0000 | 0.619586 | ||||||||
\(845\) | 9.00000 | + | 18.0000i | 0.309609 | + | 0.619219i | ||||
\(846\) | 48.0000 | 1.65027 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 24.0000 | 0.823678 | ||||||||
\(850\) | −6.00000 | + | 8.00000i | −0.205798 | + | 0.274398i | ||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | − | 18.0000i | − | 0.616670i | ||||||
\(853\) | 10.0000i | 0.342393i | 0.985237 | + | 0.171197i | \(0.0547634\pi\) | ||||
−0.985237 | + | 0.171197i | \(0.945237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | − | 24.0000i | −0.410391 | − | 0.820783i | ||||
\(856\) | −7.00000 | −0.239255 | ||||||||
\(857\) | − | 4.00000i | − | 0.136637i | −0.997664 | − | 0.0683187i | \(-0.978237\pi\) | ||
0.997664 | − | 0.0683187i | \(-0.0217635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | −10.0000 | + | 5.00000i | −0.340997 | + | 0.170499i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.0000i | 1.08992i | ||||||||
\(863\) | 11.0000i | 0.374444i | 0.982318 | + | 0.187222i | \(0.0599484\pi\) | ||||
−0.982318 | + | 0.187222i | \(0.940052\pi\) | |||||||
\(864\) | 9.00000 | 0.306186 | ||||||||
\(865\) | 24.0000 | − | 12.0000i | 0.816024 | − | 0.408012i | ||||
\(866\) | −14.0000 | −0.475739 | ||||||||
\(867\) | 39.0000i | 1.32451i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.00000 | − | 6.00000i | −0.101710 | − | 0.203419i | ||||
\(871\) | 14.0000 | 0.474372 | ||||||||
\(872\) | 5.00000i | 0.169321i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.00000 | −0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30.0000 | 1.01361 | ||||||||
\(877\) | − | 14.0000i | − | 0.472746i | −0.971662 | − | 0.236373i | \(-0.924041\pi\) | ||
0.971662 | − | 0.236373i | \(-0.0759588\pi\) | |||||||
\(878\) | − | 8.00000i | − | 0.269987i | ||||||
\(879\) | 72.0000 | 2.42850 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00000 | −0.101073 | −0.0505363 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505363 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.00000i | − | 0.134611i | −0.997732 | − | 0.0673054i | \(-0.978560\pi\) | ||
0.997732 | − | 0.0673054i | \(-0.0214402\pi\) | |||||||
\(884\) | −4.00000 | −0.134535 | ||||||||
\(885\) | 12.0000 | − | 6.00000i | 0.403376 | − | 0.201688i | ||||
\(886\) | −3.00000 | −0.100787 | ||||||||
\(887\) | 9.00000i | 0.302190i | 0.988519 | + | 0.151095i | \(0.0482800\pi\) | ||||
−0.988519 | + | 0.151095i | \(0.951720\pi\) | |||||||
\(888\) | − | 24.0000i | − | 0.805387i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.0000 | + | 7.00000i | −0.469281 | + | 0.234641i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 8.00000i | − | 0.267860i | ||||||
\(893\) | 16.0000i | 0.535420i | ||||||||
\(894\) | −45.0000 | −1.50503 | ||||||||
\(895\) | 26.0000 | + | 52.0000i | 0.869084 | + | 1.73817i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.00000i | − | 0.200334i | ||||||
\(898\) | − | 23.0000i | − | 0.767520i | ||||||
\(899\) | 10.0000 | 0.333519 | ||||||||
\(900\) | −18.0000 | + | 24.0000i | −0.600000 | + | 0.800000i | ||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.0000 | 0.332595 | ||||||||
\(905\) | 5.00000 | + | 10.0000i | 0.166206 | + | 0.332411i | ||||
\(906\) | −18.0000 | −0.598010 | ||||||||
\(907\) | − | 25.0000i | − | 0.830111i | −0.909796 | − | 0.415056i | \(-0.863762\pi\) | ||
0.909796 | − | 0.415056i | \(-0.136238\pi\) | |||||||
\(908\) | − | 12.0000i | − | 0.398234i | ||||||
\(909\) | 90.0000 | 2.98511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 6.00000i | 0.198680i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −32.0000 | −1.05847 | ||||||||
\(915\) | 54.0000 | − | 27.0000i | 1.78518 | − | 0.892592i | ||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 18.0000i | − | 0.594089i | ||||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 1.00000 | + | 2.00000i | 0.0329690 | + | 0.0659380i | ||||
\(921\) | 57.0000 | 1.87821 | ||||||||
\(922\) | − | 14.0000i | − | 0.461065i | ||||||
\(923\) | 12.0000i | 0.394985i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | + | 24.0000i | 1.05215 | + | 0.789115i | ||||
\(926\) | 25.0000 | 0.821551 | ||||||||
\(927\) | − | 66.0000i | − | 2.16772i | ||||||
\(928\) | 1.00000i | 0.0328266i | ||||||||
\(929\) | −27.0000 | −0.885841 | −0.442921 | − | 0.896561i | \(-0.646058\pi\) | ||||
−0.442921 | + | 0.896561i | \(0.646058\pi\) | |||||||
\(930\) | −30.0000 | − | 60.0000i | −0.983739 | − | 1.96748i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 14.0000i | − | 0.458585i | ||||||
\(933\) | 18.0000i | 0.589294i | ||||||||
\(934\) | −1.00000 | −0.0327210 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.0000 | −0.392232 | ||||||||
\(937\) | − | 56.0000i | − | 1.82944i | −0.404088 | − | 0.914720i | \(-0.632411\pi\) | ||
0.404088 | − | 0.914720i | \(-0.367589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 16.0000 | − | 8.00000i | 0.521862 | − | 0.260931i | ||||
\(941\) | 14.0000 | 0.456387 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(942\) | 36.0000i | 1.17294i | ||||||||
\(943\) | − | 3.00000i | − | 0.0976934i | ||||||
\(944\) | −2.00000 | −0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.00000i | − | 0.0974869i | −0.998811 | − | 0.0487435i | \(-0.984478\pi\) | ||
0.998811 | − | 0.0487435i | \(-0.0155217\pi\) | |||||||
\(948\) | − | 30.0000i | − | 0.974355i | ||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | −8.00000 | − | 6.00000i | −0.259554 | − | 0.194666i | ||||
\(951\) | −66.0000 | −2.14020 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36.0000i | − | 1.16615i | −0.812417 | − | 0.583077i | \(-0.801849\pi\) | ||
0.812417 | − | 0.583077i | \(-0.198151\pi\) | |||||||
\(954\) | 36.0000 | 1.16554 | ||||||||
\(955\) | −20.0000 | − | 40.0000i | −0.647185 | − | 1.29437i | ||||
\(956\) | −10.0000 | −0.323423 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 18.0000i | − | 0.581554i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.00000 | − | 3.00000i | 0.193649 | − | 0.0968246i | ||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 16.0000i | 0.515861i | ||||||||
\(963\) | 42.0000i | 1.35343i | ||||||||
\(964\) | −18.0000 | −0.579741 | ||||||||
\(965\) | 40.0000 | − | 20.0000i | 1.28765 | − | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0000i | 0.546683i | 0.961917 | + | 0.273342i | \(0.0881289\pi\) | ||||
−0.961917 | + | 0.273342i | \(0.911871\pi\) | |||||||
\(968\) | 11.0000i | 0.353553i | ||||||||
\(969\) | 12.0000 | 0.385496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.00000 | −0.128168 | ||||||||
\(975\) | 18.0000 | − | 24.0000i | 0.576461 | − | 0.768615i | ||||
\(976\) | −9.00000 | −0.288083 | ||||||||
\(977\) | 36.0000i | 1.15174i | 0.817541 | + | 0.575871i | \(0.195337\pi\) | ||||
−0.817541 | + | 0.575871i | \(0.804663\pi\) | |||||||
\(978\) | 36.0000i | 1.15115i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.0000 | 0.957826 | ||||||||
\(982\) | − | 18.0000i | − | 0.574403i | ||||||
\(983\) | − | 25.0000i | − | 0.797376i | −0.917087 | − | 0.398688i | \(-0.869466\pi\) | ||
0.917087 | − | 0.398688i | \(-0.130534\pi\) | |||||||
\(984\) | −9.00000 | −0.286910 | ||||||||
\(985\) | 16.0000 | − | 8.00000i | 0.509802 | − | 0.254901i | ||||
\(986\) | 2.00000 | 0.0636930 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 4.00000i | − | 0.127257i | ||||||
\(989\) | 5.00000 | 0.158991 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.0000 | −0.825917 | −0.412959 | − | 0.910750i | \(-0.635505\pi\) | ||||
−0.412959 | + | 0.910750i | \(0.635505\pi\) | |||||||
\(992\) | 10.0000i | 0.317500i | ||||||||
\(993\) | 42.0000i | 1.33283i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0000 | − | 24.0000i | −0.380426 | − | 0.760851i | ||||
\(996\) | 27.0000 | 0.855528 | ||||||||
\(997\) | 34.0000i | 1.07679i | 0.842692 | + | 0.538395i | \(0.180969\pi\) | ||||
−0.842692 | + | 0.538395i | \(0.819031\pi\) | |||||||
\(998\) | − | 16.0000i | − | 0.506471i | ||||||
\(999\) | −72.0000 | −2.27798 |
(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 | 490.2.c.c.99.2 | 2 | ||
5.2 | odd | 4 | 2450.2.a.r.1.1 | 1 | |||
5.3 | odd | 4 | 2450.2.a.s.1.1 | 1 | |||
5.4 | even | 2 | inner | 490.2.c.c.99.1 | 2 | ||
7.2 | even | 3 | 70.2.i.a.39.2 | yes | 4 | ||
7.3 | odd | 6 | 490.2.i.b.79.1 | 4 | |||
7.4 | even | 3 | 70.2.i.a.9.1 | ✓ | 4 | ||
7.5 | odd | 6 | 490.2.i.b.459.2 | 4 | |||
7.6 | odd | 2 | 490.2.c.b.99.2 | 2 | |||
21.2 | odd | 6 | 630.2.u.b.109.1 | 4 | |||
21.11 | odd | 6 | 630.2.u.b.289.2 | 4 | |||
28.11 | odd | 6 | 560.2.bw.c.289.1 | 4 | |||
28.23 | odd | 6 | 560.2.bw.c.529.2 | 4 | |||
35.2 | odd | 12 | 350.2.e.g.151.1 | 2 | |||
35.4 | even | 6 | 70.2.i.a.9.2 | yes | 4 | ||
35.9 | even | 6 | 70.2.i.a.39.1 | yes | 4 | ||
35.13 | even | 4 | 2450.2.a.bh.1.1 | 1 | |||
35.18 | odd | 12 | 350.2.e.f.51.1 | 2 | |||
35.19 | odd | 6 | 490.2.i.b.459.1 | 4 | |||
35.23 | odd | 12 | 350.2.e.f.151.1 | 2 | |||
35.24 | odd | 6 | 490.2.i.b.79.2 | 4 | |||
35.27 | even | 4 | 2450.2.a.c.1.1 | 1 | |||
35.32 | odd | 12 | 350.2.e.g.51.1 | 2 | |||
35.34 | odd | 2 | 490.2.c.b.99.1 | 2 | |||
105.44 | odd | 6 | 630.2.u.b.109.2 | 4 | |||
105.74 | odd | 6 | 630.2.u.b.289.1 | 4 | |||
140.39 | odd | 6 | 560.2.bw.c.289.2 | 4 | |||
140.79 | odd | 6 | 560.2.bw.c.529.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.i.a.9.1 | ✓ | 4 | 7.4 | even | 3 | ||
70.2.i.a.9.2 | yes | 4 | 35.4 | even | 6 | ||
70.2.i.a.39.1 | yes | 4 | 35.9 | even | 6 | ||
70.2.i.a.39.2 | yes | 4 | 7.2 | even | 3 | ||
350.2.e.f.51.1 | 2 | 35.18 | odd | 12 | |||
350.2.e.f.151.1 | 2 | 35.23 | odd | 12 | |||
350.2.e.g.51.1 | 2 | 35.32 | odd | 12 | |||
350.2.e.g.151.1 | 2 | 35.2 | odd | 12 | |||
490.2.c.b.99.1 | 2 | 35.34 | odd | 2 | |||
490.2.c.b.99.2 | 2 | 7.6 | odd | 2 | |||
490.2.c.c.99.1 | 2 | 5.4 | even | 2 | inner | ||
490.2.c.c.99.2 | 2 | 1.1 | even | 1 | trivial | ||
490.2.i.b.79.1 | 4 | 7.3 | odd | 6 | |||
490.2.i.b.79.2 | 4 | 35.24 | odd | 6 | |||
490.2.i.b.459.1 | 4 | 35.19 | odd | 6 | |||
490.2.i.b.459.2 | 4 | 7.5 | odd | 6 | |||
560.2.bw.c.289.1 | 4 | 28.11 | odd | 6 | |||
560.2.bw.c.289.2 | 4 | 140.39 | odd | 6 | |||
560.2.bw.c.529.1 | 4 | 140.79 | odd | 6 | |||
560.2.bw.c.529.2 | 4 | 28.23 | odd | 6 | |||
630.2.u.b.109.1 | 4 | 21.2 | odd | 6 | |||
630.2.u.b.109.2 | 4 | 105.44 | odd | 6 | |||
630.2.u.b.289.1 | 4 | 105.74 | odd | 6 | |||
630.2.u.b.289.2 | 4 | 21.11 | odd | 6 | |||
2450.2.a.c.1.1 | 1 | 35.27 | even | 4 | |||
2450.2.a.r.1.1 | 1 | 5.2 | odd | 4 | |||
2450.2.a.s.1.1 | 1 | 5.3 | odd | 4 | |||
2450.2.a.bh.1.1 | 1 | 35.13 | even | 4 |