Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(107,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.f (of order \(4\), degree \(2\), 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.593 |
Dual form | 675.2.f.b.107.1 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 1.22474i | −0.866025 | − | 0.866025i | 0.126004 | − | 0.992030i | \(-0.459785\pi\) |
−0.992030 | + | 0.126004i | \(0.959785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.22474 | − | 1.22474i | 0.462910 | − | 0.462910i | −0.436698 | − | 0.899608i | \(-0.643852\pi\) |
0.899608 | + | 0.436698i | \(0.143852\pi\) | |||||||
\(8\) | −1.22474 | + | 1.22474i | −0.433013 | + | 0.433013i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.00000i | 1.80907i | 0.426401 | + | 0.904534i | \(0.359781\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 1.25000 | ||||||||
\(17\) | −2.44949 | − | 2.44949i | −0.594089 | − | 0.594089i | 0.344645 | − | 0.938733i | \(-0.387999\pi\) |
−0.938733 | + | 0.344645i | \(0.887999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000i | 1.60591i | 0.596040 | + | 0.802955i | \(0.296740\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.34847 | − | 7.34847i | 1.56670 | − | 1.56670i | ||||
\(23\) | −4.89898 | + | 4.89898i | −1.02151 | + | 1.02151i | −0.0217443 | + | 0.999764i | \(0.506922\pi\) |
−0.999764 | + | 0.0217443i | \(0.993078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.22474 | + | 1.22474i | 0.231455 | + | 0.231455i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | −3.67423 | − | 3.67423i | −0.649519 | − | 0.649519i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000i | 1.02899i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.22474 | + | 1.22474i | −0.201347 | + | 0.201347i | −0.800577 | − | 0.599230i | \(-0.795473\pi\) |
0.599230 | + | 0.800577i | \(0.295473\pi\) | |||||||
\(38\) | 8.57321 | − | 8.57321i | 1.39076 | − | 1.39076i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.12372 | + | 6.12372i | 0.933859 | + | 0.933859i | 0.997944 | − | 0.0640852i | \(-0.0204129\pi\) |
−0.0640852 | + | 0.997944i | \(0.520413\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | 7.34847 | + | 7.34847i | 1.07188 | + | 1.07188i | 0.997208 | + | 0.0746766i | \(0.0237924\pi\) |
0.0746766 | + | 0.997208i | \(0.476208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000i | 0.571429i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | + | 2.44949i | −0.336463 | + | 0.336463i | −0.855034 | − | 0.518571i | \(-0.826464\pi\) |
0.518571 | + | 0.855034i | \(0.326464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000i | 0.400892i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.34847 | − | 7.34847i | −0.964901 | − | 0.964901i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 6.12372 | + | 6.12372i | 0.777714 | + | 0.777714i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34847 | − | 7.34847i | 0.897758 | − | 0.897758i | −0.0974792 | − | 0.995238i | \(-0.531078\pi\) |
0.995238 | + | 0.0974792i | \(0.0310779\pi\) | |||||||
\(68\) | 2.44949 | − | 2.44949i | 0.297044 | − | 0.297044i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.12372 | + | 6.12372i | 0.716728 | + | 0.716728i | 0.967934 | − | 0.251206i | \(-0.0808271\pi\) |
−0.251206 | + | 0.967934i | \(0.580827\pi\) | |||||||
\(74\) | 3.00000 | 0.348743 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | 7.34847 | + | 7.34847i | 0.837436 | + | 0.837436i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.00000i | − | 0.112509i | −0.998416 | − | 0.0562544i | \(-0.982084\pi\) | ||
0.998416 | − | 0.0562544i | \(-0.0179158\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.34847 | + | 7.34847i | −0.811503 | + | 0.811503i | ||||
\(83\) | 2.44949 | − | 2.44949i | 0.268866 | − | 0.268866i | −0.559777 | − | 0.828643i | \(-0.689113\pi\) |
0.828643 | + | 0.559777i | \(0.189113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 15.0000i | − | 1.61749i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.34847 | − | 7.34847i | −0.783349 | − | 0.783349i | ||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.89898 | − | 4.89898i | −0.510754 | − | 0.510754i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 18.0000i | − | 1.85656i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.57321 | + | 8.57321i | −0.870478 | + | 0.870478i | −0.992524 | − | 0.122046i | \(-0.961054\pi\) |
0.122046 | + | 0.992524i | \(0.461054\pi\) | |||||||
\(98\) | 4.89898 | − | 4.89898i | 0.494872 | − | 0.494872i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000i | 0.597022i | 0.954406 | + | 0.298511i | \(0.0964900\pi\) | ||||
−0.954406 | + | 0.298511i | \(0.903510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.12372 | − | 6.12372i | −0.603388 | − | 0.603388i | 0.337822 | − | 0.941210i | \(-0.390310\pi\) |
−0.941210 | + | 0.337822i | \(0.890310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.00000i | − | 0.670478i | −0.942133 | − | 0.335239i | \(-0.891183\pi\) | ||
0.942133 | − | 0.335239i | \(-0.108817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.12372 | − | 6.12372i | 0.578638 | − | 0.578638i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000i | 0.557086i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | −0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −25.0000 | −2.27273 | ||||||||
\(122\) | 1.22474 | + | 1.22474i | 0.110883 | + | 0.110883i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.00000i | − | 0.449013i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | + | 7.34847i | −0.652071 | + | 0.652071i | −0.953491 | − | 0.301420i | \(-0.902539\pi\) |
0.301420 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(128\) | −8.57321 | + | 8.57321i | −0.757772 | + | 0.757772i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0000i | 1.57267i | 0.617802 | + | 0.786334i | \(0.288023\pi\) | ||||
−0.617802 | + | 0.786334i | \(0.711977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.57321 | + | 8.57321i | 0.743392 | + | 0.743392i | ||||
\(134\) | −18.0000 | −1.55496 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | −2.44949 | − | 2.44949i | −0.209274 | − | 0.209274i | 0.594685 | − | 0.803959i | \(-0.297277\pi\) |
−0.803959 | + | 0.594685i | \(0.797277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.00000i | 0.593732i | 0.954919 | + | 0.296866i | \(0.0959415\pi\) | ||||
−0.954919 | + | 0.296866i | \(0.904058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.6969 | + | 14.6969i | −1.23334 | + | 1.23334i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 15.0000i | − | 1.24141i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.22474 | − | 1.22474i | −0.100673 | − | 0.100673i | ||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | −8.57321 | − | 8.57321i | −0.695379 | − | 0.695379i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 18.0000i | − | 1.45048i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.4722 | + | 13.4722i | −1.07520 | + | 1.07520i | −0.0782656 | + | 0.996933i | \(0.524938\pi\) |
−0.996933 | + | 0.0782656i | \(0.975062\pi\) | |||||||
\(158\) | −1.22474 | + | 1.22474i | −0.0974355 | + | 0.0974355i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000i | 0.945732i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.34847 | + | 7.34847i | 0.575577 | + | 0.575577i | 0.933681 | − | 0.358105i | \(-0.116577\pi\) |
−0.358105 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | −12.2474 | − | 12.2474i | −0.947736 | − | 0.947736i | 0.0509644 | − | 0.998700i | \(-0.483770\pi\) |
−0.998700 | + | 0.0509644i | \(0.983770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.12372 | + | 6.12372i | −0.466930 | + | 0.466930i | ||||
\(173\) | −9.79796 | + | 9.79796i | −0.744925 | + | 0.744925i | −0.973521 | − | 0.228596i | \(-0.926586\pi\) |
0.228596 | + | 0.973521i | \(0.426586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30.0000i | 2.26134i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.6969 | − | 14.6969i | −1.10158 | − | 1.10158i | ||||
\(179\) | 24.0000 | 1.79384 | 0.896922 | − | 0.442189i | \(-0.145798\pi\) | ||||
0.896922 | + | 0.442189i | \(0.145798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 12.0000i | − | 0.884652i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.6969 | − | 14.6969i | 1.07475 | − | 1.07475i | ||||
\(188\) | −7.34847 | + | 7.34847i | −0.535942 | + | 0.535942i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.0000i | − | 1.30243i | −0.758891 | − | 0.651217i | \(-0.774259\pi\) | ||
0.758891 | − | 0.651217i | \(-0.225741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.22474 | − | 1.22474i | −0.0881591 | − | 0.0881591i | 0.661652 | − | 0.749811i | \(-0.269856\pi\) |
−0.749811 | + | 0.661652i | \(0.769856\pi\) | |||||||
\(194\) | 21.0000 | 1.50771 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.00000 | −0.285714 | ||||||||
\(197\) | −12.2474 | − | 12.2474i | −0.872595 | − | 0.872595i | 0.120160 | − | 0.992755i | \(-0.461659\pi\) |
−0.992755 | + | 0.120160i | \(0.961659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000i | 1.41776i | 0.705328 | + | 0.708881i | \(0.250800\pi\) | ||||
−0.705328 | + | 0.708881i | \(0.749200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.34847 | − | 7.34847i | 0.517036 | − | 0.517036i | ||||
\(203\) | 7.34847 | − | 7.34847i | 0.515761 | − | 0.515761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.0000i | 1.04510i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −42.0000 | −2.90520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −2.44949 | − | 2.44949i | −0.168232 | − | 0.168232i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.12372 | + | 6.12372i | −0.415705 | + | 0.415705i | ||||
\(218\) | −8.57321 | + | 8.57321i | −0.580651 | + | 0.580651i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.57321 | + | 8.57321i | 0.574105 | + | 0.574105i | 0.933273 | − | 0.359168i | \(-0.116940\pi\) |
−0.359168 | + | 0.933273i | \(0.616940\pi\) | |||||||
\(224\) | −9.00000 | −0.601338 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.89898 | − | 4.89898i | −0.325157 | − | 0.325157i | 0.525585 | − | 0.850741i | \(-0.323847\pi\) |
−0.850741 | + | 0.525585i | \(0.823847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.00000i | − | 0.330409i | −0.986259 | − | 0.165205i | \(-0.947172\pi\) | ||
0.986259 | − | 0.165205i | \(-0.0528285\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.34847 | + | 7.34847i | −0.482451 | + | 0.482451i | ||||
\(233\) | 7.34847 | − | 7.34847i | 0.481414 | − | 0.481414i | −0.424169 | − | 0.905583i | \(-0.639434\pi\) |
0.905583 | + | 0.424169i | \(0.139434\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.34847 | + | 7.34847i | 0.476331 | + | 0.476331i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 30.6186 | + | 30.6186i | 1.96824 | + | 1.96824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1.00000i | − | 0.0640184i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.12372 | − | 6.12372i | 0.388857 | − | 0.388857i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.00000i | − | 0.378717i | −0.981908 | − | 0.189358i | \(-0.939359\pi\) | ||
0.981908 | − | 0.189358i | \(-0.0606408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.3939 | − | 29.3939i | −1.84798 | − | 1.84798i | ||||
\(254\) | 18.0000 | 1.12942 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 12.2474 | + | 12.2474i | 0.763975 | + | 0.763975i | 0.977038 | − | 0.213063i | \(-0.0683441\pi\) |
−0.213063 | + | 0.977038i | \(0.568344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000i | 0.186411i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.0454 | − | 22.0454i | 1.36197 | − | 1.36197i | ||||
\(263\) | −7.34847 | + | 7.34847i | −0.453126 | + | 0.453126i | −0.896391 | − | 0.443265i | \(-0.853820\pi\) |
0.443265 | + | 0.896391i | \(0.353820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 21.0000i | − | 1.28759i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.34847 | + | 7.34847i | 0.448879 | + | 0.448879i | ||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0000 | 0.668202 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(272\) | −12.2474 | − | 12.2474i | −0.742611 | − | 0.742611i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000i | 0.362473i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.12372 | − | 6.12372i | 0.367939 | − | 0.367939i | −0.498786 | − | 0.866725i | \(-0.666221\pi\) |
0.866725 | + | 0.498786i | \(0.166221\pi\) | |||||||
\(278\) | 8.57321 | − | 8.57321i | 0.514187 | − | 0.514187i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.22474 | + | 1.22474i | 0.0728035 | + | 0.0728035i | 0.742571 | − | 0.669767i | \(-0.233606\pi\) |
−0.669767 | + | 0.742571i | \(0.733606\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.34847 | − | 7.34847i | −0.433766 | − | 0.433766i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 5.00000i | − | 0.294118i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.12372 | + | 6.12372i | −0.358364 | + | 0.358364i | ||||
\(293\) | 19.5959 | − | 19.5959i | 1.14481 | − | 1.14481i | 0.157246 | − | 0.987559i | \(-0.449738\pi\) |
0.987559 | − | 0.157246i | \(-0.0502617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.00000i | − | 0.174371i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.34847 | + | 7.34847i | 0.425685 | + | 0.425685i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.0000 | 0.864586 | ||||||||
\(302\) | 6.12372 | + | 6.12372i | 0.352381 | + | 0.352381i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 35.0000i | 2.00739i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.22474 | − | 1.22474i | 0.0698999 | − | 0.0698999i | −0.671293 | − | 0.741192i | \(-0.734261\pi\) |
0.741192 | + | 0.671293i | \(0.234261\pi\) | |||||||
\(308\) | −7.34847 | + | 7.34847i | −0.418718 | + | 0.418718i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.00000i | − | 0.340229i | −0.985424 | − | 0.170114i | \(-0.945586\pi\) | ||
0.985424 | − | 0.170114i | \(-0.0544137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6969 | + | 14.6969i | 0.830720 | + | 0.830720i | 0.987615 | − | 0.156895i | \(-0.0501485\pi\) |
−0.156895 | + | 0.987615i | \(0.550148\pi\) | |||||||
\(314\) | 33.0000 | 1.86230 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00000 | 0.0562544 | ||||||||
\(317\) | 17.1464 | + | 17.1464i | 0.963039 | + | 0.963039i | 0.999341 | − | 0.0363015i | \(-0.0115577\pi\) |
−0.0363015 | + | 0.999341i | \(0.511558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0000i | 2.01561i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.6969 | − | 14.6969i | 0.819028 | − | 0.819028i | ||||
\(323\) | 17.1464 | − | 17.1464i | 0.954053 | − | 0.954053i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 18.0000i | − | 0.996928i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.34847 | + | 7.34847i | 0.405751 | + | 0.405751i | ||||
\(329\) | 18.0000 | 0.992372 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | 0.274825 | 0.137412 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137412 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(332\) | 2.44949 | + | 2.44949i | 0.134433 | + | 0.134433i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 30.0000i | 1.64153i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | −15.9217 | + | 15.9217i | −0.866025 | + | 0.866025i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 30.0000i | − | 1.62459i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4722 | + | 13.4722i | 0.727430 | + | 0.727430i | ||||
\(344\) | −15.0000 | −0.808746 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0000 | 1.29025 | ||||||||
\(347\) | 14.6969 | + | 14.6969i | 0.788973 | + | 0.788973i | 0.981326 | − | 0.192353i | \(-0.0616118\pi\) |
−0.192353 | + | 0.981326i | \(0.561612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 35.0000i | − | 1.87351i | −0.349990 | − | 0.936754i | \(-0.613815\pi\) | ||
0.349990 | − | 0.936754i | \(-0.386185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.0454 | − | 22.0454i | 1.17502 | − | 1.17502i | ||||
\(353\) | 14.6969 | − | 14.6969i | 0.782239 | − | 0.782239i | −0.197969 | − | 0.980208i | \(-0.563435\pi\) |
0.980208 | + | 0.197969i | \(0.0634346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.0000i | 0.635999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.3939 | − | 29.3939i | −1.55351 | − | 1.55351i | ||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.0000 | −1.57895 | ||||||||
\(362\) | 17.1464 | + | 17.1464i | 0.901196 | + | 0.901196i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0454 | − | 22.0454i | 1.15076 | − | 1.15076i | 0.164361 | − | 0.986400i | \(-0.447444\pi\) |
0.986400 | − | 0.164361i | \(-0.0525561\pi\) | |||||||
\(368\) | −24.4949 | + | 24.4949i | −1.27688 | + | 1.27688i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000i | 0.311504i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.22474 | + | 1.22474i | 0.0634149 | + | 0.0634149i | 0.738103 | − | 0.674688i | \(-0.235722\pi\) |
−0.674688 | + | 0.738103i | \(0.735722\pi\) | |||||||
\(374\) | −36.0000 | −1.86152 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.0000 | −0.928279 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000i | 0.205466i | 0.994709 | + | 0.102733i | \(0.0327588\pi\) | ||||
−0.994709 | + | 0.102733i | \(0.967241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −22.0454 | + | 22.0454i | −1.12794 | + | 1.12794i | ||||
\(383\) | −2.44949 | + | 2.44949i | −0.125163 | + | 0.125163i | −0.766914 | − | 0.641750i | \(-0.778208\pi\) |
0.641750 | + | 0.766914i | \(0.278208\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.00000i | 0.152696i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.57321 | − | 8.57321i | −0.435239 | − | 0.435239i | ||||
\(389\) | 30.0000 | 1.52106 | 0.760530 | − | 0.649303i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649303i | \(0.224939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | −4.89898 | − | 4.89898i | −0.247436 | − | 0.247436i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 30.0000i | 1.51138i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4722 | − | 13.4722i | 0.676150 | − | 0.676150i | −0.282977 | − | 0.959127i | \(-0.591322\pi\) |
0.959127 | + | 0.282977i | \(0.0913219\pi\) | |||||||
\(398\) | 24.4949 | − | 24.4949i | 1.22782 | − | 1.22782i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000i | 0.599251i | 0.954057 | + | 0.299626i | \(0.0968618\pi\) | ||||
−0.954057 | + | 0.299626i | \(0.903138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.0000 | −0.893325 | ||||||||
\(407\) | −7.34847 | − | 7.34847i | −0.364250 | − | 0.364250i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000i | 0.494468i | 0.968956 | + | 0.247234i | \(0.0795217\pi\) | ||||
−0.968956 | + | 0.247234i | \(0.920478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.12372 | − | 6.12372i | 0.301694 | − | 0.301694i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 51.4393 | + | 51.4393i | 2.51598 | + | 2.51598i | ||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | −9.79796 | − | 9.79796i | −0.476957 | − | 0.476957i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 6.00000i | − | 0.291386i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.22474 | + | 1.22474i | −0.0592696 | + | 0.0592696i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000i | 1.44505i | 0.691345 | + | 0.722525i | \(0.257018\pi\) | ||||
−0.691345 | + | 0.722525i | \(0.742982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.4722 | − | 13.4722i | −0.647432 | − | 0.647432i | 0.304939 | − | 0.952372i | \(-0.401364\pi\) |
−0.952372 | + | 0.304939i | \(0.901364\pi\) | |||||||
\(434\) | 15.0000 | 0.720023 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.00000 | 0.335239 | ||||||||
\(437\) | −34.2929 | − | 34.2929i | −1.64045 | − | 1.64045i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0000i | 0.811366i | 0.914014 | + | 0.405683i | \(0.132966\pi\) | ||||
−0.914014 | + | 0.405683i | \(0.867034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.89898 | − | 4.89898i | 0.232758 | − | 0.232758i | −0.581085 | − | 0.813843i | \(-0.697372\pi\) |
0.813843 | + | 0.581085i | \(0.197372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 21.0000i | − | 0.994379i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.22474 | − | 1.22474i | −0.0578638 | − | 0.0578638i | ||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000i | 0.563188i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6969 | + | 14.6969i | −0.687494 | + | 0.687494i | −0.961677 | − | 0.274184i | \(-0.911592\pi\) |
0.274184 | + | 0.961677i | \(0.411592\pi\) | |||||||
\(458\) | −6.12372 | + | 6.12372i | −0.286143 | + | 0.286143i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0000i | 1.11779i | 0.829238 | + | 0.558896i | \(0.188775\pi\) | ||||
−0.829238 | + | 0.558896i | \(0.811225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.2702 | − | 23.2702i | −1.08146 | − | 1.08146i | −0.996374 | − | 0.0850817i | \(-0.972885\pi\) |
−0.0850817 | − | 0.996374i | \(-0.527115\pi\) | |||||||
\(464\) | 30.0000 | 1.39272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.0000 | −0.833834 | ||||||||
\(467\) | −4.89898 | − | 4.89898i | −0.226698 | − | 0.226698i | 0.584614 | − | 0.811312i | \(-0.301246\pi\) |
−0.811312 | + | 0.584614i | \(0.801246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 18.0000i | − | 0.831163i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.7423 | + | 36.7423i | −1.68941 | + | 1.68941i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 6.00000i | − | 0.275010i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.34847 | + | 7.34847i | 0.336111 | + | 0.336111i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.44949 | − | 2.44949i | −0.111571 | − | 0.111571i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 25.0000i | − | 1.13636i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0454 | − | 22.0454i | 0.998973 | − | 0.998973i | −0.00102669 | − | 0.999999i | \(-0.500327\pi\) |
0.999999 | + | 0.00102669i | \(0.000326807\pi\) | |||||||
\(488\) | 1.22474 | − | 1.22474i | 0.0554416 | − | 0.0554416i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 30.0000i | − | 1.35388i | −0.736038 | − | 0.676941i | \(-0.763305\pi\) | ||
0.736038 | − | 0.676941i | \(-0.236695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.6969 | − | 14.6969i | −0.661917 | − | 0.661917i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.0000 | −1.12253 | ||||||||
\(497\) | −14.6969 | − | 14.6969i | −0.659248 | − | 0.659248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.0000i | − | 0.581960i | −0.956729 | − | 0.290980i | \(-0.906019\pi\) | ||
0.956729 | − | 0.290980i | \(-0.0939813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.34847 | + | 7.34847i | −0.327978 | + | 0.327978i | ||||
\(503\) | −12.2474 | + | 12.2474i | −0.546087 | + | 0.546087i | −0.925307 | − | 0.379220i | \(-0.876192\pi\) |
0.379220 | + | 0.925307i | \(0.376192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 72.0000i | 3.20079i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.34847 | − | 7.34847i | −0.326036 | − | 0.326036i | ||||
\(509\) | −24.0000 | −1.06378 | −0.531891 | − | 0.846813i | \(-0.678518\pi\) | ||||
−0.531891 | + | 0.846813i | \(0.678518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0000 | 0.663561 | ||||||||
\(512\) | −6.12372 | − | 6.12372i | −0.270633 | − | 0.270633i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 30.0000i | − | 1.32324i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.0908 | + | 44.0908i | −1.93911 | + | 1.93911i | ||||
\(518\) | 3.67423 | − | 3.67423i | 0.161437 | − | 0.161437i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.0000i | − | 0.525730i | −0.964833 | − | 0.262865i | \(-0.915333\pi\) | ||
0.964833 | − | 0.262865i | \(-0.0846673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.12372 | − | 6.12372i | −0.267772 | − | 0.267772i | 0.560430 | − | 0.828202i | \(-0.310636\pi\) |
−0.828202 | + | 0.560430i | \(0.810636\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0000 | 0.784837 | ||||||||
\(527\) | 12.2474 | + | 12.2474i | 0.533507 | + | 0.533507i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 25.0000i | − | 1.08696i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.57321 | + | 8.57321i | −0.371696 | + | 0.371696i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18.0000i | 0.777482i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.6969 | + | 14.6969i | 0.633630 | + | 0.633630i | ||||
\(539\) | −24.0000 | −1.03375 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0000 | −0.816874 | −0.408437 | − | 0.912787i | \(-0.633926\pi\) | ||||
−0.408437 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(542\) | −13.4722 | − | 13.4722i | −0.578680 | − | 0.578680i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.0000i | 0.771744i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.57321 | − | 8.57321i | 0.366564 | − | 0.366564i | −0.499658 | − | 0.866223i | \(-0.666541\pi\) |
0.866223 | + | 0.499658i | \(0.166541\pi\) | |||||||
\(548\) | 2.44949 | − | 2.44949i | 0.104637 | − | 0.104637i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.0000i | 1.78926i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.22474 | − | 1.22474i | −0.0520814 | − | 0.0520814i | ||||
\(554\) | −15.0000 | −0.637289 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.00000 | −0.296866 | ||||||||
\(557\) | 7.34847 | + | 7.34847i | 0.311365 | + | 0.311365i | 0.845438 | − | 0.534073i | \(-0.179339\pi\) |
−0.534073 | + | 0.845438i | \(0.679339\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.34847 | + | 7.34847i | −0.309976 | + | 0.309976i | ||||
\(563\) | −14.6969 | + | 14.6969i | −0.619402 | + | 0.619402i | −0.945378 | − | 0.325976i | \(-0.894307\pi\) |
0.325976 | + | 0.945378i | \(0.394307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 3.00000i | − | 0.126099i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.6969 | + | 14.6969i | 0.616670 | + | 0.616670i | ||||
\(569\) | 36.0000 | 1.50920 | 0.754599 | − | 0.656186i | \(-0.227831\pi\) | ||||
0.754599 | + | 0.656186i | \(0.227831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.00000 | 0.209243 | 0.104622 | − | 0.994512i | \(-0.466637\pi\) | ||||
0.104622 | + | 0.994512i | \(0.466637\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.0000i | 0.751305i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.22474 | + | 1.22474i | −0.0509868 | + | 0.0509868i | −0.732140 | − | 0.681154i | \(-0.761479\pi\) |
0.681154 | + | 0.732140i | \(0.261479\pi\) | |||||||
\(578\) | −6.12372 | + | 6.12372i | −0.254713 | + | 0.254713i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.00000i | − | 0.248922i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.6969 | − | 14.6969i | −0.608685 | − | 0.608685i | ||||
\(584\) | −15.0000 | −0.620704 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.0000 | −1.98286 | ||||||||
\(587\) | 12.2474 | + | 12.2474i | 0.505506 | + | 0.505506i | 0.913144 | − | 0.407638i | \(-0.133647\pi\) |
−0.407638 | + | 0.913144i | \(0.633647\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 35.0000i | − | 1.44215i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.12372 | + | 6.12372i | −0.251684 | + | 0.251684i | ||||
\(593\) | −19.5959 | + | 19.5959i | −0.804708 | + | 0.804708i | −0.983827 | − | 0.179119i | \(-0.942675\pi\) |
0.179119 | + | 0.983827i | \(0.442675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.00000i | − | 0.245770i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0000 | 1.47092 | 0.735460 | − | 0.677568i | \(-0.236966\pi\) | ||||
0.735460 | + | 0.677568i | \(0.236966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.0000 | −1.42768 | −0.713840 | − | 0.700309i | \(-0.753046\pi\) | ||||
−0.713840 | + | 0.700309i | \(0.753046\pi\) | |||||||
\(602\) | −18.3712 | − | 18.3712i | −0.748753 | − | 0.748753i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 5.00000i | − | 0.203447i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.12372 | − | 6.12372i | 0.248554 | − | 0.248554i | −0.571823 | − | 0.820377i | \(-0.693764\pi\) |
0.820377 | + | 0.571823i | \(0.193764\pi\) | |||||||
\(608\) | 25.7196 | − | 25.7196i | 1.04307 | − | 1.04307i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.4722 | − | 13.4722i | −0.544137 | − | 0.544137i | 0.380602 | − | 0.924739i | \(-0.375717\pi\) |
−0.924739 | + | 0.380602i | \(0.875717\pi\) | |||||||
\(614\) | −3.00000 | −0.121070 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.0000 | −0.725241 | ||||||||
\(617\) | −9.79796 | − | 9.79796i | −0.394451 | − | 0.394451i | 0.481820 | − | 0.876270i | \(-0.339976\pi\) |
−0.876270 | + | 0.481820i | \(0.839976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 31.0000i | − | 1.24600i | −0.782224 | − | 0.622998i | \(-0.785915\pi\) | ||
0.782224 | − | 0.622998i | \(-0.214085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.34847 | + | 7.34847i | −0.294647 | + | 0.294647i | ||||
\(623\) | 14.6969 | − | 14.6969i | 0.588820 | − | 0.588820i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 36.0000i | − | 1.43885i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.4722 | − | 13.4722i | −0.537599 | − | 0.537599i | ||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 1.22474 | + | 1.22474i | 0.0487177 | + | 0.0487177i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 42.0000i | − | 1.66803i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 44.0908 | − | 44.0908i | 1.74557 | − | 1.74557i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 24.0000i | − | 0.947943i | −0.880540 | − | 0.473972i | \(-0.842820\pi\) | ||
0.880540 | − | 0.473972i | \(-0.157180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.34847 | + | 7.34847i | 0.289795 | + | 0.289795i | 0.836999 | − | 0.547204i | \(-0.184308\pi\) |
−0.547204 | + | 0.836999i | \(0.684308\pi\) | |||||||
\(644\) | −12.0000 | −0.472866 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −42.0000 | −1.65247 | ||||||||
\(647\) | 24.4949 | + | 24.4949i | 0.962994 | + | 0.962994i | 0.999339 | − | 0.0363455i | \(-0.0115717\pi\) |
−0.0363455 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.34847 | + | 7.34847i | −0.287788 | + | 0.287788i | ||||
\(653\) | 4.89898 | − | 4.89898i | 0.191712 | − | 0.191712i | −0.604724 | − | 0.796435i | \(-0.706716\pi\) |
0.796435 | + | 0.604724i | \(0.206716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 30.0000i | − | 1.17130i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.0454 | − | 22.0454i | −0.859419 | − | 0.859419i | ||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.0000 | 0.972387 | 0.486194 | − | 0.873851i | \(-0.338385\pi\) | ||||
0.486194 | + | 0.873851i | \(0.338385\pi\) | |||||||
\(662\) | −6.12372 | − | 6.12372i | −0.238005 | − | 0.238005i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000i | 0.232845i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.3939 | + | 29.3939i | −1.13814 | + | 1.13814i | ||||
\(668\) | 12.2474 | − | 12.2474i | 0.473868 | − | 0.473868i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.00000i | − | 0.231627i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.1691 | + | 28.1691i | 1.08584 | + | 1.08584i | 0.995952 | + | 0.0898884i | \(0.0286510\pi\) |
0.0898884 | + | 0.995952i | \(0.471349\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | 0.500000 | ||||||||
\(677\) | 7.34847 | + | 7.34847i | 0.282425 | + | 0.282425i | 0.834075 | − | 0.551651i | \(-0.186002\pi\) |
−0.551651 | + | 0.834075i | \(0.686002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.0000i | 0.805906i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.7423 | + | 36.7423i | −1.40694 | + | 1.40694i | ||||
\(683\) | −31.8434 | + | 31.8434i | −1.21845 | + | 1.21845i | −0.250279 | + | 0.968174i | \(0.580522\pi\) |
−0.968174 | + | 0.250279i | \(0.919478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 33.0000i | − | 1.25995i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.6186 | + | 30.6186i | 1.16732 | + | 1.16732i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | −9.79796 | − | 9.79796i | −0.372463 | − | 0.372463i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 36.0000i | − | 1.36654i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.6969 | + | 14.6969i | −0.556686 | + | 0.556686i | ||||
\(698\) | −42.8661 | + | 42.8661i | −1.62250 | + | 1.62250i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.0000i | 0.906467i | 0.891392 | + | 0.453234i | \(0.149730\pi\) | ||||
−0.891392 | + | 0.453234i | \(0.850270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.57321 | − | 8.57321i | −0.323345 | − | 0.323345i | ||||
\(704\) | 6.00000 | 0.226134 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.0000 | −1.35488 | ||||||||
\(707\) | 7.34847 | + | 7.34847i | 0.276368 | + | 0.276368i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.00000i | − | 0.187779i | −0.995583 | − | 0.0938895i | \(-0.970070\pi\) | ||
0.995583 | − | 0.0938895i | \(-0.0299300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.6969 | + | 14.6969i | −0.550791 | + | 0.550791i | ||||
\(713\) | 24.4949 | − | 24.4949i | 0.917341 | − | 0.917341i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0000i | 0.896922i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.0454 | + | 22.0454i | 0.822727 | + | 0.822727i | ||||
\(719\) | 30.0000 | 1.11881 | 0.559406 | − | 0.828894i | \(-0.311029\pi\) | ||||
0.559406 | + | 0.828894i | \(0.311029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0000 | −0.558629 | ||||||||
\(722\) | 36.7423 | + | 36.7423i | 1.36741 | + | 1.36741i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 14.0000i | − | 0.520306i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.2702 | − | 23.2702i | 0.863042 | − | 0.863042i | −0.128648 | − | 0.991690i | \(-0.541064\pi\) |
0.991690 | + | 0.128648i | \(0.0410638\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 30.0000i | − | 1.10959i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.3939 | − | 29.3939i | −1.08569 | − | 1.08569i | −0.995967 | − | 0.0897206i | \(-0.971403\pi\) |
−0.0897206 | − | 0.995967i | \(-0.528597\pi\) | |||||||
\(734\) | −54.0000 | −1.99318 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.0000 | 1.32698 | ||||||||
\(737\) | 44.0908 | + | 44.0908i | 1.62411 | + | 1.62411i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0000i | 1.47142i | 0.677295 | + | 0.735712i | \(0.263152\pi\) | ||||
−0.677295 | + | 0.735712i | \(0.736848\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.34847 | − | 7.34847i | 0.269771 | − | 0.269771i | ||||
\(743\) | 29.3939 | − | 29.3939i | 1.07836 | − | 1.07836i | 0.0816998 | − | 0.996657i | \(-0.473965\pi\) |
0.996657 | − | 0.0816998i | \(-0.0260349\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 3.00000i | − | 0.109838i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.6969 | + | 14.6969i | 0.537373 | + | 0.537373i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0000 | −0.839282 | −0.419641 | − | 0.907690i | \(-0.637844\pi\) | ||||
−0.419641 | + | 0.907690i | \(0.637844\pi\) | |||||||
\(752\) | 36.7423 | + | 36.7423i | 1.33986 | + | 1.33986i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.57321 | − | 8.57321i | 0.311599 | − | 0.311599i | −0.533930 | − | 0.845529i | \(-0.679285\pi\) |
0.845529 | + | 0.533930i | \(0.179285\pi\) | |||||||
\(758\) | 4.89898 | − | 4.89898i | 0.177939 | − | 0.177939i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000i | 0.652499i | 0.945284 | + | 0.326250i | \(0.105785\pi\) | ||||
−0.945284 | + | 0.326250i | \(0.894215\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.57321 | − | 8.57321i | −0.310371 | − | 0.310371i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.00000 | 0.216789 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10.0000i | − | 0.360609i | −0.983611 | − | 0.180305i | \(-0.942292\pi\) | ||
0.983611 | − | 0.180305i | \(-0.0577084\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.22474 | − | 1.22474i | 0.0440795 | − | 0.0440795i | ||||
\(773\) | 17.1464 | − | 17.1464i | 0.616714 | − | 0.616714i | −0.327973 | − | 0.944687i | \(-0.606365\pi\) |
0.944687 | + | 0.327973i | \(0.106365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 21.0000i | − | 0.753856i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.7423 | − | 36.7423i | −1.31728 | − | 1.31728i | ||||
\(779\) | 42.0000 | 1.50481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 72.0000 | 2.57636 | ||||||||
\(782\) | −29.3939 | − | 29.3939i | −1.05112 | − | 1.05112i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.0000i | 0.714286i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.9671 | − | 37.9671i | 1.35338 | − | 1.35338i | 0.471531 | − | 0.881849i | \(-0.343701\pi\) |
0.881849 | − | 0.471531i | \(-0.156299\pi\) | |||||||
\(788\) | 12.2474 | − | 12.2474i | 0.436297 | − | 0.436297i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −33.0000 | −1.17113 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 9.79796 | + | 9.79796i | 0.347062 | + | 0.347062i | 0.859014 | − | 0.511952i | \(-0.171078\pi\) |
−0.511952 | + | 0.859014i | \(0.671078\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 36.0000i | − | 1.27359i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.6969 | − | 14.6969i | 0.518967 | − | 0.518967i | ||||
\(803\) | −36.7423 | + | 36.7423i | −1.29661 | + | 1.29661i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.34847 | − | 7.34847i | −0.258518 | − | 0.258518i | ||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.00000 | 0.0351147 | 0.0175574 | − | 0.999846i | \(-0.494411\pi\) | ||||
0.0175574 | + | 0.999846i | \(0.494411\pi\) | |||||||
\(812\) | 7.34847 | + | 7.34847i | 0.257881 | + | 0.257881i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.0000i | 0.630900i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.8661 | + | 42.8661i | −1.49969 | + | 1.49969i | ||||
\(818\) | 12.2474 | − | 12.2474i | 0.428222 | − | 0.428222i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 30.0000i | − | 1.04701i | −0.852023 | − | 0.523504i | \(-0.824625\pi\) | ||
0.852023 | − | 0.523504i | \(-0.175375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.34847 | + | 7.34847i | 0.256152 | + | 0.256152i | 0.823487 | − | 0.567335i | \(-0.192026\pi\) |
−0.567335 | + | 0.823487i | \(0.692026\pi\) | |||||||
\(824\) | 15.0000 | 0.522550 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.1464 | − | 17.1464i | −0.596240 | − | 0.596240i | 0.343070 | − | 0.939310i | \(-0.388533\pi\) |
−0.939310 | + | 0.343070i | \(0.888533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 53.0000i | − | 1.84077i | −0.391018 | − | 0.920383i | \(-0.627877\pi\) | ||
0.391018 | − | 0.920383i | \(-0.372123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.79796 | − | 9.79796i | 0.339479 | − | 0.339479i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 42.0000i | − | 1.45260i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.3939 | + | 29.3939i | 1.01539 | + | 1.01539i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −23.2702 | − | 23.2702i | −0.801942 | − | 0.801942i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000i | 0.275371i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.6186 | + | 30.6186i | −1.05207 | + | 1.05207i | ||||
\(848\) | −12.2474 | + | 12.2474i | −0.420579 | + | 0.420579i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 12.0000i | − | 0.411355i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.6969 | − | 14.6969i | −0.503214 | − | 0.503214i | 0.409221 | − | 0.912435i | \(-0.365800\pi\) |
−0.912435 | + | 0.409221i | \(0.865800\pi\) | |||||||
\(854\) | 3.00000 | 0.102658 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.4949 | − | 24.4949i | −0.836730 | − | 0.836730i | 0.151697 | − | 0.988427i | \(-0.451526\pi\) |
−0.988427 | + | 0.151697i | \(0.951526\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.00000i | 0.170598i | 0.996355 | + | 0.0852989i | \(0.0271845\pi\) | ||||
−0.996355 | + | 0.0852989i | \(0.972815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.7423 | − | 36.7423i | 1.25145 | − | 1.25145i | ||||
\(863\) | 12.2474 | − | 12.2474i | 0.416908 | − | 0.416908i | −0.467229 | − | 0.884137i | \(-0.654747\pi\) |
0.884137 | + | 0.467229i | \(0.154747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 33.0000i | 1.12139i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.12372 | − | 6.12372i | −0.207853 | − | 0.207853i | ||||
\(869\) | 6.00000 | 0.203536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.57321 | + | 8.57321i | 0.290326 | + | 0.290326i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 84.0000i | 2.84134i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.6186 | − | 30.6186i | 1.03392 | − | 1.03392i | 0.0345131 | − | 0.999404i | \(-0.489012\pi\) |
0.999404 | − | 0.0345131i | \(-0.0109881\pi\) | |||||||
\(878\) | 20.8207 | − | 20.8207i | 0.702663 | − | 0.702663i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000i | 0.606435i | 0.952921 | + | 0.303218i | \(0.0980609\pi\) | ||||
−0.952921 | + | 0.303218i | \(0.901939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.22474 | + | 1.22474i | 0.0412159 | + | 0.0412159i | 0.727414 | − | 0.686198i | \(-0.240722\pi\) |
−0.686198 | + | 0.727414i | \(0.740722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | −2.44949 | − | 2.44949i | −0.0822458 | − | 0.0822458i | 0.664787 | − | 0.747033i | \(-0.268522\pi\) |
−0.747033 | + | 0.664787i | \(0.768522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000i | 0.603701i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.57321 | + | 8.57321i | −0.287052 | + | 0.287052i | ||||
\(893\) | −51.4393 | + | 51.4393i | −1.72135 | + | 1.72135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 21.0000i | 0.701561i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.34847 | − | 7.34847i | −0.245222 | − | 0.245222i | ||||
\(899\) | −30.0000 | −1.00056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −44.0908 | − | 44.0908i | −1.46806 | − | 1.46806i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.1691 | − | 28.1691i | 0.935341 | − | 0.935341i | −0.0626922 | − | 0.998033i | \(-0.519969\pi\) |
0.998033 | + | 0.0626922i | \(0.0199687\pi\) | |||||||
\(908\) | 4.89898 | − | 4.89898i | 0.162578 | − | 0.162578i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.0000i | − | 0.596367i | −0.954509 | − | 0.298183i | \(-0.903619\pi\) | ||
0.954509 | − | 0.298183i | \(-0.0963807\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6969 | + | 14.6969i | 0.486398 | + | 0.486398i | ||||
\(914\) | 36.0000 | 1.19077 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.00000 | 0.165205 | ||||||||
\(917\) | 22.0454 | + | 22.0454i | 0.728003 | + | 0.728003i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00000i | 0.0329870i | 0.999864 | + | 0.0164935i | \(0.00525028\pi\) | ||||
−0.999864 | + | 0.0164935i | \(0.994750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.3939 | − | 29.3939i | 0.968036 | − | 0.968036i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 57.0000i | 1.87314i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −22.0454 | − | 22.0454i | −0.723676 | − | 0.723676i | ||||
\(929\) | −24.0000 | −0.787414 | −0.393707 | − | 0.919236i | \(-0.628808\pi\) | ||||
−0.393707 | + | 0.919236i | \(0.628808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.0000 | −0.917663 | ||||||||
\(932\) | 7.34847 | + | 7.34847i | 0.240707 | + | 0.240707i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.0000i | 0.392652i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.6186 | − | 30.6186i | 1.00027 | − | 1.00027i | 0.000266809 | − | 1.00000i | \(-0.499915\pi\) |
1.00000 | 0.000266809i | \(-8.49279e-5\pi\) | ||||||||
\(938\) | −22.0454 | + | 22.0454i | −0.719808 | + | 0.719808i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000i | 0.977972i | 0.872292 | + | 0.488986i | \(0.162633\pi\) | ||||
−0.872292 | + | 0.488986i | \(0.837367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.3939 | + | 29.3939i | 0.957196 | + | 0.957196i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 90.0000 | 2.92615 | ||||||||
\(947\) | −31.8434 | − | 31.8434i | −1.03477 | − | 1.03477i | −0.999373 | − | 0.0353971i | \(-0.988730\pi\) |
−0.0353971 | − | 0.999373i | \(-0.511270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.34847 | − | 7.34847i | 0.238165 | − | 0.238165i | ||||
\(953\) | −7.34847 | + | 7.34847i | −0.238040 | + | 0.238040i | −0.816038 | − | 0.577998i | \(-0.803834\pi\) |
0.577998 | + | 0.816038i | \(0.303834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 6.00000i | − | 0.194054i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000i | 0.0644157i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.4722 | − | 13.4722i | 0.433237 | − | 0.433237i | −0.456491 | − | 0.889728i | \(-0.650894\pi\) |
0.889728 | + | 0.456491i | \(0.150894\pi\) | |||||||
\(968\) | 30.6186 | − | 30.6186i | 0.984120 | − | 0.984120i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0000i | 1.15529i | 0.816286 | + | 0.577647i | \(0.196029\pi\) | ||||
−0.816286 | + | 0.577647i | \(0.803971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.57321 | + | 8.57321i | 0.274845 | + | 0.274845i | ||||
\(974\) | −54.0000 | −1.73027 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.00000 | −0.160046 | ||||||||
\(977\) | 14.6969 | + | 14.6969i | 0.470197 | + | 0.470197i | 0.901978 | − | 0.431782i | \(-0.142115\pi\) |
−0.431782 | + | 0.901978i | \(0.642115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.0000i | 2.30113i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36.7423 | + | 36.7423i | −1.17250 | + | 1.17250i | ||||
\(983\) | 2.44949 | − | 2.44949i | 0.0781266 | − | 0.0781266i | −0.666964 | − | 0.745090i | \(-0.732406\pi\) |
0.745090 | + | 0.666964i | \(0.232406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.0000i | 1.14647i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.0000 | −1.90789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0000 | 1.49300 | 0.746502 | − | 0.665383i | \(-0.231732\pi\) | ||||
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(992\) | 18.3712 | + | 18.3712i | 0.583285 | + | 0.583285i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.0000i | 1.14185i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.3939 | + | 29.3939i | −0.930913 | + | 0.930913i | −0.997763 | − | 0.0668496i | \(-0.978705\pi\) |
0.0668496 | + | 0.997763i | \(0.478705\pi\) | |||||||
\(998\) | −15.9217 | + | 15.9217i | −0.503992 | + | 0.503992i | ||||
\(999\) | 0 | 0 |
(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 | 675.2.f.b.593.1 | yes | 4 | |
3.2 | odd | 2 | 675.2.f.e.593.2 | yes | 4 | ||
5.2 | odd | 4 | 675.2.f.e.107.2 | yes | 4 | ||
5.3 | odd | 4 | 675.2.f.e.107.1 | yes | 4 | ||
5.4 | even | 2 | inner | 675.2.f.b.593.2 | yes | 4 | |
15.2 | even | 4 | inner | 675.2.f.b.107.1 | ✓ | 4 | |
15.8 | even | 4 | inner | 675.2.f.b.107.2 | yes | 4 | |
15.14 | odd | 2 | 675.2.f.e.593.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.2.f.b.107.1 | ✓ | 4 | 15.2 | even | 4 | inner | |
675.2.f.b.107.2 | yes | 4 | 15.8 | even | 4 | inner | |
675.2.f.b.593.1 | yes | 4 | 1.1 | even | 1 | trivial | |
675.2.f.b.593.2 | yes | 4 | 5.4 | even | 2 | inner | |
675.2.f.e.107.1 | yes | 4 | 5.3 | odd | 4 | ||
675.2.f.e.107.2 | yes | 4 | 5.2 | odd | 4 | ||
675.2.f.e.593.1 | yes | 4 | 15.14 | odd | 2 | ||
675.2.f.e.593.2 | yes | 4 | 3.2 | odd | 2 |