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 | 107.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.107 |
Dual form | 675.2.f.e.593.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | \(-0.540215\pi\) |
0.992030 | + | 0.126004i | \(0.0402153\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.22474 | + | 1.22474i | 0.462910 | + | 0.462910i | 0.899608 | − | 0.436698i | \(-0.143852\pi\) |
−0.436698 | + | 0.899608i | \(0.643852\pi\) | |||||||
\(8\) | 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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 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 | \(-0.612001\pi\) |
0.938733 | + | 0.344645i | \(0.112001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.00000i | − | 1.60591i | −0.596040 | − | 0.802955i | \(-0.703260\pi\) | ||
0.596040 | − | 0.802955i | \(-0.296740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.34847 | + | 7.34847i | 1.56670 | + | 1.56670i | ||||
\(23\) | 4.89898 | + | 4.89898i | 1.02151 | + | 1.02151i | 0.999764 | + | 0.0217443i | \(0.00692196\pi\) |
0.0217443 | + | 0.999764i | \(0.493078\pi\) | |||||||
\(24\) | 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 | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 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 | 0.599230 | − | 0.800577i | \(-0.295473\pi\) |
−0.800577 | + | 0.599230i | \(0.795473\pi\) | |||||||
\(38\) | −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 | −0.0640852 | − | 0.997944i | \(-0.520413\pi\) |
0.997944 | + | 0.0640852i | \(0.0204129\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | −7.34847 | + | 7.34847i | −1.07188 | + | 1.07188i | −0.0746766 | + | 0.997208i | \(0.523792\pi\) |
−0.997208 | + | 0.0746766i | \(0.976208\pi\) | |||||||
\(48\) | 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 | \(-0.173536\pi\) |
−0.518571 | + | 0.855034i | \(0.673536\pi\) | |||||||
\(54\) | 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 | 0.995238 | − | 0.0974792i | \(-0.0310779\pi\) |
−0.0974792 | + | 0.995238i | \(0.531078\pi\) | |||||||
\(68\) | −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 | −0.251206 | − | 0.967934i | \(-0.580827\pi\) |
0.967934 | + | 0.251206i | \(0.0808271\pi\) | |||||||
\(74\) | −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 | \(0.0179158\pi\) | ||||
−0.998416 | + | 0.0562544i | \(0.982084\pi\) | |||||||
\(80\) | 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 | \(-0.310887\pi\) |
−0.828643 | + | 0.559777i | \(0.810887\pi\) | |||||||
\(84\) | 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 | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 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 | 0.122046 | − | 0.992524i | \(-0.461054\pi\) |
−0.992524 | + | 0.122046i | \(0.961054\pi\) | |||||||
\(98\) | −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 | −0.941210 | − | 0.337822i | \(-0.890310\pi\) |
0.337822 | + | 0.941210i | \(0.390310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000i | 0.670478i | 0.942133 | + | 0.335239i | \(0.108817\pi\) | ||||
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.12372 | + | 6.12372i | 0.578638 | + | 0.578638i | ||||
\(113\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 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 | 0.301420 | − | 0.953491i | \(-0.402539\pi\) |
−0.953491 | + | 0.301420i | \(0.902539\pi\) | |||||||
\(128\) | 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 | \(-0.702723\pi\) |
0.803959 | + | 0.594685i | \(0.202723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.00000i | − | 0.593732i | −0.954919 | − | 0.296866i | \(-0.904058\pi\) | ||
0.954919 | − | 0.296866i | \(-0.0959415\pi\) | |||||||
\(140\) | 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 | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 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 | −0.996933 | − | 0.0782656i | \(-0.975062\pi\) |
−0.0782656 | − | 0.996933i | \(-0.524938\pi\) | |||||||
\(158\) | 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 | −0.358105 | − | 0.933681i | \(-0.616577\pi\) |
0.933681 | + | 0.358105i | \(0.116577\pi\) | |||||||
\(164\) | −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 | \(-0.516230\pi\) |
0.998700 | + | 0.0509644i | \(0.0162295\pi\) | |||||||
\(168\) | 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 | \(-0.0734136\pi\) |
−0.228596 | + | 0.973521i | \(0.573414\pi\) | |||||||
\(174\) | 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 | \(-0.854202\pi\) | ||||
−0.896922 | + | 0.442189i | \(0.854202\pi\) | |||||||
\(180\) | 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 | −0.749811 | − | 0.661652i | \(-0.769856\pi\) |
0.661652 | + | 0.749811i | \(0.269856\pi\) | |||||||
\(194\) | −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 | \(-0.538341\pi\) |
0.992755 | + | 0.120160i | \(0.0383407\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.0000i | − | 1.41776i | −0.705328 | − | 0.708881i | \(-0.749200\pi\) | ||
0.705328 | − | 0.708881i | \(-0.250800\pi\) | |||||||
\(200\) | 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 | −0.359168 | − | 0.933273i | \(-0.616940\pi\) |
0.933273 | + | 0.359168i | \(0.116940\pi\) | |||||||
\(224\) | 9.00000 | 0.601338 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.89898 | − | 4.89898i | 0.325157 | − | 0.325157i | −0.525585 | − | 0.850741i | \(-0.676153\pi\) |
0.850741 | + | 0.525585i | \(0.176153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000i | 0.330409i | 0.986259 | + | 0.165205i | \(0.0528285\pi\) | ||||
−0.986259 | + | 0.165205i | \(0.947172\pi\) | |||||||
\(230\) | 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 | \(-0.360566\pi\) |
−0.905583 | + | 0.424169i | \(0.860566\pi\) | |||||||
\(234\) | 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 | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 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 | \(-0.931656\pi\) |
0.213063 | + | 0.977038i | \(0.431656\pi\) | |||||||
\(258\) | 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 | \(-0.146180\pi\) |
−0.443265 | + | 0.896391i | \(0.646180\pi\) | |||||||
\(264\) | 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 | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(270\) | 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 | 0.866725 | − | 0.498786i | \(-0.166221\pi\) |
−0.498786 | + | 0.866725i | \(0.666221\pi\) | |||||||
\(278\) | −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 | −0.669767 | − | 0.742571i | \(-0.733606\pi\) |
0.742571 | + | 0.669767i | \(0.233606\pi\) | |||||||
\(284\) | −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 | −0.987559 | − | 0.157246i | \(-0.949738\pi\) |
−0.157246 | − | 0.987559i | \(-0.550262\pi\) | |||||||
\(294\) | 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 | 0.741192 | − | 0.671293i | \(-0.234261\pi\) |
−0.671293 | + | 0.741192i | \(0.734261\pi\) | |||||||
\(308\) | 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 | −0.156895 | − | 0.987615i | \(-0.550148\pi\) |
0.987615 | + | 0.156895i | \(0.0501485\pi\) | |||||||
\(314\) | −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 | \(-0.988442\pi\) |
0.0363015 | + | 0.999341i | \(0.488442\pi\) | |||||||
\(318\) | 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 | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(338\) | 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 | \(-0.938388\pi\) |
0.192353 | + | 0.981326i | \(0.438388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.0000i | 1.87351i | 0.349990 | + | 0.936754i | \(0.386185\pi\) | ||||
−0.349990 | + | 0.936754i | \(0.613815\pi\) | |||||||
\(350\) | 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 | \(-0.436565\pi\) |
−0.980208 | + | 0.197969i | \(0.936565\pi\) | |||||||
\(354\) | 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 | \(-0.342447\pi\) | ||||
0.475002 | + | 0.879985i | \(0.342447\pi\) | |||||||
\(360\) | 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 | 0.986400 | + | 0.164361i | \(0.0525561\pi\) |
0.164361 | + | 0.986400i | \(0.447444\pi\) | |||||||
\(368\) | 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 | −0.674688 | − | 0.738103i | \(-0.735722\pi\) |
0.738103 | + | 0.674688i | \(0.235722\pi\) | |||||||
\(374\) | 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 | \(-0.967241\pi\) | ||
0.994709 | − | 0.102733i | \(-0.0327588\pi\) | |||||||
\(380\) | 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 | \(-0.221792\pi\) |
−0.641750 | + | 0.766914i | \(0.721792\pi\) | |||||||
\(384\) | 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 | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 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 | 0.959127 | − | 0.282977i | \(-0.0913219\pi\) |
−0.282977 | + | 0.959127i | \(0.591322\pi\) | |||||||
\(398\) | −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 | \(-0.920478\pi\) | ||
0.968956 | − | 0.247234i | \(-0.0795217\pi\) | |||||||
\(410\) | 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 | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 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 | −0.952372 | − | 0.304939i | \(-0.901364\pi\) |
0.304939 | + | 0.952372i | \(0.401364\pi\) | |||||||
\(434\) | −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 | \(-0.867034\pi\) | ||
0.914014 | − | 0.405683i | \(-0.132966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.89898 | − | 4.89898i | −0.232758 | − | 0.232758i | 0.581085 | − | 0.813843i | \(-0.302628\pi\) |
−0.813843 | + | 0.581085i | \(0.802628\pi\) | |||||||
\(444\) | 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 | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 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 | 0.274184 | − | 0.961677i | \(-0.411592\pi\) |
−0.961677 | + | 0.274184i | \(0.911592\pi\) | |||||||
\(458\) | 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 | −0.0850817 | + | 0.996374i | \(0.527115\pi\) |
−0.996374 | + | 0.0850817i | \(0.972885\pi\) | |||||||
\(464\) | −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 | \(-0.698754\pi\) |
0.811312 | + | 0.584614i | \(0.198754\pi\) | |||||||
\(468\) | 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 | 0.999999 | − | 0.00102669i | \(-0.000326807\pi\) |
−0.00102669 | + | 0.999999i | \(0.500327\pi\) | |||||||
\(488\) | −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 | \(0.0939813\pi\) | ||||
−0.956729 | + | 0.290980i | \(0.906019\pi\) | |||||||
\(500\) | 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 | \(-0.123808\pi\) |
−0.379220 | + | 0.925307i | \(0.623808\pi\) | |||||||
\(504\) | 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 | \(-0.321482\pi\) | ||||
0.531891 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(510\) | 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 | −0.828202 | − | 0.560430i | \(-0.810636\pi\) |
0.560430 | + | 0.828202i | \(0.310636\pi\) | |||||||
\(524\) | 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 | 0.866223 | − | 0.499658i | \(-0.166541\pi\) |
−0.499658 | + | 0.866223i | \(0.666541\pi\) | |||||||
\(548\) | −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 | \(-0.820661\pi\) |
0.534073 | + | 0.845438i | \(0.320661\pi\) | |||||||
\(558\) | 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 | \(-0.105693\pi\) |
−0.325976 | + | 0.945378i | \(0.605693\pi\) | |||||||
\(564\) | 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 | \(-0.772169\pi\) | ||||
−0.754599 | + | 0.656186i | \(0.772169\pi\) | |||||||
\(570\) | 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 | 0.681154 | − | 0.732140i | \(-0.261479\pi\) |
−0.732140 | + | 0.681154i | \(0.761479\pi\) | |||||||
\(578\) | 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 | \(-0.866353\pi\) |
0.407638 | + | 0.913144i | \(0.366353\pi\) | |||||||
\(588\) | 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 | \(-0.0573249\pi\) |
−0.179119 | + | 0.983827i | \(0.557325\pi\) | |||||||
\(594\) | 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 | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(600\) | 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 | 0.820377 | − | 0.571823i | \(-0.193764\pi\) |
−0.571823 | + | 0.820377i | \(0.693764\pi\) | |||||||
\(608\) | −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 | −0.924739 | − | 0.380602i | \(-0.875717\pi\) |
0.380602 | + | 0.924739i | \(0.375717\pi\) | |||||||
\(614\) | 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 | \(-0.660024\pi\) |
0.876270 | + | 0.481820i | \(0.160024\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.0000i | 1.24600i | 0.782224 | + | 0.622998i | \(0.214085\pi\) | ||||
−0.782224 | + | 0.622998i | \(0.785915\pi\) | |||||||
\(620\) | 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 | −0.547204 | − | 0.836999i | \(-0.684308\pi\) |
0.836999 | + | 0.547204i | \(0.184308\pi\) | |||||||
\(644\) | 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 | \(-0.988428\pi\) |
0.0363455 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(648\) | 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 | \(-0.293284\pi\) |
−0.796435 | + | 0.604724i | \(0.793284\pi\) | |||||||
\(654\) | 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 | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 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 | 0.0898884 | − | 0.995952i | \(-0.471349\pi\) |
0.995952 | − | 0.0898884i | \(-0.0286510\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | 0.500000 | ||||||||
\(677\) | −7.34847 | + | 7.34847i | −0.282425 | + | 0.282425i | −0.834075 | − | 0.551651i | \(-0.813998\pi\) |
0.551651 | + | 0.834075i | \(0.313998\pi\) | |||||||
\(678\) | 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 | 0.968174 | + | 0.250279i | \(0.0805223\pi\) |
0.250279 | + | 0.968174i | \(0.419478\pi\) | |||||||
\(684\) | 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 | \(0.0299300\pi\) | ||||
−0.995583 | + | 0.0938895i | \(0.970070\pi\) | |||||||
\(710\) | 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 | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | 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 | 0.991690 | − | 0.128648i | \(-0.0410638\pi\) |
−0.128648 | + | 0.991690i | \(0.541064\pi\) | |||||||
\(728\) | 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 | −0.0897206 | + | 0.995967i | \(0.528597\pi\) |
−0.995967 | + | 0.0897206i | \(0.971403\pi\) | |||||||
\(734\) | 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 | \(-0.736848\pi\) | ||
0.677295 | − | 0.735712i | \(-0.263152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.34847 | + | 7.34847i | 0.269771 | + | 0.269771i | ||||
\(743\) | −29.3939 | − | 29.3939i | −1.07836 | − | 1.07836i | −0.996657 | − | 0.0816998i | \(-0.973965\pi\) |
−0.0816998 | − | 0.996657i | \(-0.526035\pi\) | |||||||
\(744\) | 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 | 0.845529 | − | 0.533930i | \(-0.179285\pi\) |
−0.533930 | + | 0.845529i | \(0.679285\pi\) | |||||||
\(758\) | −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 | \(0.0577084\pi\) | ||||
−0.983611 | + | 0.180305i | \(0.942292\pi\) | |||||||
\(770\) | 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 | \(-0.393635\pi\) |
−0.944687 | + | 0.327973i | \(0.893635\pi\) | |||||||
\(774\) | 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 | 0.881849 | + | 0.471531i | \(0.156299\pi\) |
0.471531 | + | 0.881849i | \(0.343701\pi\) | |||||||
\(788\) | −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 | \(-0.828922\pi\) |
0.511952 | + | 0.859014i | \(0.328922\pi\) | |||||||
\(798\) | 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 | −0.567335 | − | 0.823487i | \(-0.692026\pi\) |
0.823487 | + | 0.567335i | \(0.192026\pi\) | |||||||
\(824\) | −15.0000 | −0.522550 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.1464 | − | 17.1464i | 0.596240 | − | 0.596240i | −0.343070 | − | 0.939310i | \(-0.611467\pi\) |
0.939310 | + | 0.343070i | \(0.111467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.0000i | 1.84077i | 0.391018 | + | 0.920383i | \(0.372123\pi\) | ||||
−0.391018 | + | 0.920383i | \(0.627877\pi\) | |||||||
\(830\) | 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 | −0.912435 | − | 0.409221i | \(-0.865800\pi\) |
0.409221 | + | 0.912435i | \(0.365800\pi\) | |||||||
\(854\) | −3.00000 | −0.102658 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4949 | − | 24.4949i | 0.836730 | − | 0.836730i | −0.151697 | − | 0.988427i | \(-0.548474\pi\) |
0.988427 | + | 0.151697i | \(0.0484739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.00000i | − | 0.170598i | −0.996355 | − | 0.0852989i | \(-0.972815\pi\) | ||
0.996355 | − | 0.0852989i | \(-0.0271845\pi\) | |||||||
\(860\) | 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 | \(-0.345253\pi\) |
−0.884137 | + | 0.467229i | \(0.845253\pi\) | |||||||
\(864\) | 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 | 0.999404 | + | 0.0345131i | \(0.0109881\pi\) |
0.0345131 | + | 0.999404i | \(0.489012\pi\) | |||||||
\(878\) | −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 | −0.686198 | − | 0.727414i | \(-0.740722\pi\) |
0.727414 | + | 0.686198i | \(0.240722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | 2.44949 | − | 2.44949i | 0.0822458 | − | 0.0822458i | −0.664787 | − | 0.747033i | \(-0.731478\pi\) |
0.747033 | + | 0.664787i | \(0.231478\pi\) | |||||||
\(888\) | 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 | 0.998033 | − | 0.0626922i | \(-0.0199687\pi\) |
−0.0626922 | + | 0.998033i | \(0.519969\pi\) | |||||||
\(908\) | −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 | \(-0.994750\pi\) | ||
0.999864 | − | 0.0164935i | \(-0.00525028\pi\) | |||||||
\(920\) | 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 | \(-0.371192\pi\) | ||||
0.393707 | + | 0.919236i | \(0.371192\pi\) | |||||||
\(930\) | 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 | 1.00000 | 0.000266809i | \(8.49279e-5\pi\) | |
0.000266809 | 1.00000i | \(0.499915\pi\) | ||||||||
\(938\) | 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 | 0.0353971 | − | 0.999373i | \(-0.488730\pi\) |
0.999373 | − | 0.0353971i | \(-0.0112696\pi\) | |||||||
\(948\) | 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 | \(-0.196166\pi\) |
−0.577998 | + | 0.816038i | \(0.696166\pi\) | |||||||
\(954\) | 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 | 0.889728 | − | 0.456491i | \(-0.150894\pi\) |
−0.456491 | + | 0.889728i | \(0.650894\pi\) | |||||||
\(968\) | −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 | \(-0.857885\pi\) |
0.431782 | + | 0.901978i | \(0.357885\pi\) | |||||||
\(978\) | 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 | \(-0.267594\pi\) |
−0.745090 | + | 0.666964i | \(0.767594\pi\) | |||||||
\(984\) | 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 | 0.0668496 | − | 0.997763i | \(-0.478705\pi\) |
−0.997763 | + | 0.0668496i | \(0.978705\pi\) | |||||||
\(998\) | 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.e.107.2 | yes | 4 | |
3.2 | odd | 2 | 675.2.f.b.107.1 | ✓ | 4 | ||
5.2 | odd | 4 | 675.2.f.b.593.2 | yes | 4 | ||
5.3 | odd | 4 | 675.2.f.b.593.1 | yes | 4 | ||
5.4 | even | 2 | inner | 675.2.f.e.107.1 | yes | 4 | |
15.2 | even | 4 | inner | 675.2.f.e.593.1 | yes | 4 | |
15.8 | even | 4 | inner | 675.2.f.e.593.2 | yes | 4 | |
15.14 | odd | 2 | 675.2.f.b.107.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.2.f.b.107.1 | ✓ | 4 | 3.2 | odd | 2 | ||
675.2.f.b.107.2 | yes | 4 | 15.14 | odd | 2 | ||
675.2.f.b.593.1 | yes | 4 | 5.3 | odd | 4 | ||
675.2.f.b.593.2 | yes | 4 | 5.2 | odd | 4 | ||
675.2.f.e.107.1 | yes | 4 | 5.4 | even | 2 | inner | |
675.2.f.e.107.2 | yes | 4 | 1.1 | even | 1 | trivial | |
675.2.f.e.593.1 | yes | 4 | 15.2 | even | 4 | inner | |
675.2.f.e.593.2 | yes | 4 | 15.8 | even | 4 | inner |