Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(109,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.k (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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.109 |
Dual form | 432.2.k.b.325.1 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 1.00000i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | −0.531089 | − | 0.847316i | \(-0.678217\pi\) |
0.847316 | + | 0.531089i | \(0.178217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000i | 1.13389i | 0.823754 | + | 0.566947i | \(0.191875\pi\) | ||||
−0.823754 | + | 0.566947i | \(0.808125\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 1.00000i | 0.316228 | + | 0.316228i | ||||
\(11\) | −3.53553 | + | 3.53553i | −1.06600 | + | 1.06600i | −0.0683416 | + | 0.997662i | \(0.521771\pi\) |
−0.997662 | + | 0.0683416i | \(0.978229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.00000i | 0.277350 | + | 0.277350i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −4.24264 | −1.13389 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −4.24264 | −1.02899 | −0.514496 | − | 0.857493i | \(-0.672021\pi\) | ||||
−0.514496 | + | 0.857493i | \(0.672021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | + | 4.00000i | 0.917663 | + | 0.917663i | 0.996859 | − | 0.0791961i | \(-0.0252353\pi\) |
−0.0791961 | + | 0.996859i | \(0.525235\pi\) | |||||||
\(20\) | −1.41421 | + | 1.41421i | −0.316228 | + | 0.316228i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.00000 | − | 5.00000i | −1.06600 | − | 1.06600i | ||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000i | 0.800000i | ||||||||
\(26\) | −1.41421 | + | 1.41421i | −0.277350 | + | 0.277350i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 6.00000i | − | 1.13389i | ||||||
\(29\) | −2.82843 | − | 2.82843i | −0.525226 | − | 0.525226i | 0.393919 | − | 0.919145i | \(-0.371119\pi\) |
−0.919145 | + | 0.393919i | \(0.871119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 5.65685i | 1.00000i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.00000i | − | 1.02899i | ||||||
\(35\) | 2.12132 | + | 2.12132i | 0.358569 | + | 0.358569i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | + | 2.00000i | −0.328798 | + | 0.328798i | −0.852129 | − | 0.523331i | \(-0.824689\pi\) |
0.523331 | + | 0.852129i | \(0.324689\pi\) | |||||||
\(38\) | −5.65685 | + | 5.65685i | −0.917663 | + | 0.917663i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | − | 2.00000i | −0.316228 | − | 0.316228i | ||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00000 | − | 7.00000i | 1.06749 | − | 1.06749i | 0.0699387 | − | 0.997551i | \(-0.477720\pi\) |
0.997551 | − | 0.0699387i | \(-0.0222804\pi\) | |||||||
\(44\) | 7.07107 | − | 7.07107i | 1.06600 | − | 1.06600i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 4.24264 | 0.618853 | 0.309426 | − | 0.950923i | \(-0.399863\pi\) | ||||
0.309426 | + | 0.950923i | \(0.399863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | −5.65685 | −0.800000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | − | 2.00000i | −0.277350 | − | 0.277350i | ||||
\(53\) | 0.707107 | − | 0.707107i | 0.0971286 | − | 0.0971286i | −0.656873 | − | 0.754001i | \(-0.728121\pi\) |
0.754001 | + | 0.656873i | \(0.228121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000i | 0.674200i | ||||||||
\(56\) | 8.48528 | 1.13389 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | − | 4.00000i | 0.525226 | − | 0.525226i | ||||
\(59\) | 7.07107 | − | 7.07107i | 0.920575 | − | 0.920575i | −0.0764953 | − | 0.997070i | \(-0.524373\pi\) |
0.997070 | + | 0.0764953i | \(0.0243730\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | + | 10.0000i | 1.28037 | + | 1.28037i | 0.940457 | + | 0.339911i | \(0.110397\pi\) |
0.339911 | + | 0.940457i | \(0.389603\pi\) | |||||||
\(62\) | − | 9.89949i | − | 1.25724i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 1.41421 | 0.175412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | + | 1.00000i | 0.122169 | + | 0.122169i | 0.765548 | − | 0.643379i | \(-0.222468\pi\) |
−0.643379 | + | 0.765548i | \(0.722468\pi\) | |||||||
\(68\) | 8.48528 | 1.02899 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | + | 3.00000i | −0.358569 | + | 0.358569i | ||||
\(71\) | 15.5563i | 1.84620i | 0.384561 | + | 0.923099i | \(0.374353\pi\) | ||||
−0.384561 | + | 0.923099i | \(0.625647\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.0000i | − | 1.75562i | −0.479012 | − | 0.877809i | \(-0.659005\pi\) | ||
0.479012 | − | 0.877809i | \(-0.340995\pi\) | |||||||
\(74\) | −2.82843 | − | 2.82843i | −0.328798 | − | 0.328798i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00000 | − | 8.00000i | −0.917663 | − | 0.917663i | ||||
\(77\) | −10.6066 | − | 10.6066i | −1.20873 | − | 1.20873i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | 2.82843 | − | 2.82843i | 0.316228 | − | 0.316228i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.00000 | 0.883452 | ||||||||
\(83\) | 7.77817 | + | 7.77817i | 0.853766 | + | 0.853766i | 0.990595 | − | 0.136829i | \(-0.0436911\pi\) |
−0.136829 | + | 0.990595i | \(0.543691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | + | 3.00000i | −0.325396 | + | 0.325396i | ||||
\(86\) | 9.89949 | + | 9.89949i | 1.06749 | + | 1.06749i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.0000 | + | 10.0000i | 1.06600 | + | 1.06600i | ||||
\(89\) | − | 1.41421i | − | 0.149906i | −0.997187 | − | 0.0749532i | \(-0.976119\pi\) | ||
0.997187 | − | 0.0749532i | \(-0.0238807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 3.00000i | −0.314485 | + | 0.314485i | ||||
\(92\) | − | 5.65685i | − | 0.589768i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000i | 0.618853i | ||||||||
\(95\) | 5.65685 | 0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | − | 2.82843i | − | 0.285714i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | − | 8.00000i | − | 0.800000i | ||||||
\(101\) | 4.94975 | − | 4.94975i | 0.492518 | − | 0.492518i | −0.416581 | − | 0.909099i | \(-0.636772\pi\) |
0.909099 | + | 0.416581i | \(0.136772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 2.82843 | − | 2.82843i | 0.277350 | − | 0.277350i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | + | 1.00000i | 0.0971286 | + | 0.0971286i | ||||
\(107\) | −7.77817 | + | 7.77817i | −0.751945 | + | 0.751945i | −0.974842 | − | 0.222897i | \(-0.928449\pi\) |
0.222897 | + | 0.974842i | \(0.428449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | + | 10.0000i | 0.957826 | + | 0.957826i | 0.999146 | − | 0.0413197i | \(-0.0131562\pi\) |
−0.0413197 | + | 0.999146i | \(0.513156\pi\) | |||||||
\(110\) | −7.07107 | −0.674200 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.0000i | 1.13389i | ||||||||
\(113\) | 8.48528 | 0.798228 | 0.399114 | − | 0.916901i | \(-0.369318\pi\) | ||||
0.399114 | + | 0.916901i | \(0.369318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | + | 2.00000i | 0.186501 | + | 0.186501i | ||||
\(116\) | 5.65685 | + | 5.65685i | 0.525226 | + | 0.525226i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.0000 | + | 10.0000i | 0.920575 | + | 0.920575i | ||||
\(119\) | − | 12.7279i | − | 1.16677i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 14.0000i | − | 1.27273i | ||||||
\(122\) | −14.1421 | + | 14.1421i | −1.28037 | + | 1.28037i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.0000 | 1.25724 | ||||||||
\(125\) | 6.36396 | + | 6.36396i | 0.569210 | + | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | − | 11.3137i | − | 1.00000i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000i | 0.175412i | ||||||||
\(131\) | −0.707107 | − | 0.707107i | −0.0617802 | − | 0.0617802i | 0.675542 | − | 0.737322i | \(-0.263910\pi\) |
−0.737322 | + | 0.675542i | \(0.763910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | + | 12.0000i | −1.04053 | + | 1.04053i | ||||
\(134\) | −1.41421 | + | 1.41421i | −0.122169 | + | 0.122169i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000i | 1.02899i | ||||||||
\(137\) | − | 18.3848i | − | 1.57072i | −0.619041 | − | 0.785359i | \(-0.712479\pi\) | ||
0.619041 | − | 0.785359i | \(-0.287521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | − | 10.0000i | 0.848189 | − | 0.848189i | −0.141718 | − | 0.989907i | \(-0.545263\pi\) |
0.989907 | + | 0.141718i | \(0.0452627\pi\) | |||||||
\(140\) | −4.24264 | − | 4.24264i | −0.358569 | − | 0.358569i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.0000 | −1.84620 | ||||||||
\(143\) | −7.07107 | −0.591312 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 21.2132 | 1.75562 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00000 | − | 4.00000i | 0.328798 | − | 0.328798i | ||||
\(149\) | 4.94975 | − | 4.94975i | 0.405499 | − | 0.405499i | −0.474667 | − | 0.880166i | \(-0.657431\pi\) |
0.880166 | + | 0.474667i | \(0.157431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 21.0000i | − | 1.70896i | −0.519488 | − | 0.854478i | \(-0.673877\pi\) | ||
0.519488 | − | 0.854478i | \(-0.326123\pi\) | |||||||
\(152\) | 11.3137 | − | 11.3137i | 0.917663 | − | 0.917663i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.0000 | − | 15.0000i | 1.20873 | − | 1.20873i | ||||
\(155\) | −4.94975 | + | 4.94975i | −0.397573 | + | 0.397573i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | − | 2.00000i | −0.159617 | − | 0.159617i | 0.622780 | − | 0.782397i | \(-0.286003\pi\) |
−0.782397 | + | 0.622780i | \(0.786003\pi\) | |||||||
\(158\) | 2.82843i | 0.225018i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.00000 | + | 4.00000i | 0.316228 | + | 0.316228i | ||||
\(161\) | −8.48528 | −0.668734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.00000 | − | 5.00000i | −0.391630 | − | 0.391630i | 0.483638 | − | 0.875268i | \(-0.339315\pi\) |
−0.875268 | + | 0.483638i | \(0.839315\pi\) | |||||||
\(164\) | 11.3137i | 0.883452i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.0000 | + | 11.0000i | −0.853766 | + | 0.853766i | ||||
\(167\) | 7.07107i | 0.547176i | 0.961847 | + | 0.273588i | \(0.0882104\pi\) | ||||
−0.961847 | + | 0.273588i | \(0.911790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | −4.24264 | − | 4.24264i | −0.325396 | − | 0.325396i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.0000 | + | 14.0000i | −1.06749 | + | 1.06749i | ||||
\(173\) | 7.77817 | + | 7.77817i | 0.591364 | + | 0.591364i | 0.938000 | − | 0.346636i | \(-0.112676\pi\) |
−0.346636 | + | 0.938000i | \(0.612676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0000 | −0.907115 | ||||||||
\(176\) | −14.1421 | + | 14.1421i | −1.06600 | + | 1.06600i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.00000 | 0.149906 | ||||||||
\(179\) | 7.77817 | + | 7.77817i | 0.581368 | + | 0.581368i | 0.935279 | − | 0.353911i | \(-0.115148\pi\) |
−0.353911 | + | 0.935279i | \(0.615148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000 | − | 16.0000i | 1.18927 | − | 1.18927i | 0.212001 | − | 0.977269i | \(-0.432002\pi\) |
0.977269 | − | 0.212001i | \(-0.0679981\pi\) | |||||||
\(182\) | −4.24264 | − | 4.24264i | −0.314485 | − | 0.314485i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | 2.82843i | 0.207950i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0000 | − | 15.0000i | 1.09691 | − | 1.09691i | ||||
\(188\) | −8.48528 | −0.618853 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000i | 0.580381i | ||||||||
\(191\) | 4.24264 | 0.306987 | 0.153493 | − | 0.988150i | \(-0.450948\pi\) | ||||
0.153493 | + | 0.988150i | \(0.450948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(194\) | − | 9.89949i | − | 0.710742i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | 0.285714 | ||||||||
\(197\) | −16.2635 | + | 16.2635i | −1.15872 | + | 1.15872i | −0.173973 | + | 0.984750i | \(0.555660\pi\) |
−0.984750 | + | 0.173973i | \(0.944340\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0000i | 1.06332i | 0.846957 | + | 0.531661i | \(0.178432\pi\) | ||||
−0.846957 | + | 0.531661i | \(0.821568\pi\) | |||||||
\(200\) | 11.3137 | 0.800000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.00000 | + | 7.00000i | 0.492518 | + | 0.492518i | ||||
\(203\) | 8.48528 | − | 8.48528i | 0.595550 | − | 0.595550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | − | 4.00000i | −0.279372 | − | 0.279372i | ||||
\(206\) | −8.48528 | −0.591198 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000 | + | 4.00000i | 0.277350 | + | 0.277350i | ||||
\(209\) | −28.2843 | −1.95646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | + | 4.00000i | 0.275371 | + | 0.275371i | 0.831258 | − | 0.555887i | \(-0.187621\pi\) |
−0.555887 | + | 0.831258i | \(0.687621\pi\) | |||||||
\(212\) | −1.41421 | + | 1.41421i | −0.0971286 | + | 0.0971286i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.0000 | − | 11.0000i | −0.751945 | − | 0.751945i | ||||
\(215\) | − | 9.89949i | − | 0.675140i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 21.0000i | − | 1.42557i | ||||||
\(218\) | −14.1421 | + | 14.1421i | −0.957826 | + | 0.957826i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 10.0000i | − | 0.674200i | ||||||
\(221\) | −4.24264 | − | 4.24264i | −0.285391 | − | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.0000 | −1.47323 | −0.736614 | − | 0.676313i | \(-0.763577\pi\) | ||||
−0.736614 | + | 0.676313i | \(0.763577\pi\) | |||||||
\(224\) | −16.9706 | −1.13389 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000i | 0.798228i | ||||||||
\(227\) | −7.07107 | − | 7.07107i | −0.469323 | − | 0.469323i | 0.432372 | − | 0.901695i | \(-0.357677\pi\) |
−0.901695 | + | 0.432372i | \(0.857677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | − | 7.00000i | 0.462573 | − | 0.462573i | −0.436925 | − | 0.899498i | \(-0.643932\pi\) |
0.899498 | + | 0.436925i | \(0.143932\pi\) | |||||||
\(230\) | −2.82843 | + | 2.82843i | −0.186501 | + | 0.186501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.00000 | + | 8.00000i | −0.525226 | + | 0.525226i | ||||
\(233\) | 15.5563i | 1.01913i | 0.860432 | + | 0.509565i | \(0.170194\pi\) | ||||
−0.860432 | + | 0.509565i | \(0.829806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | − | 3.00000i | 0.195698 | − | 0.195698i | ||||
\(236\) | −14.1421 | + | 14.1421i | −0.920575 | + | 0.920575i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.0000 | 1.16677 | ||||||||
\(239\) | −25.4558 | −1.64660 | −0.823301 | − | 0.567605i | \(-0.807870\pi\) | ||||
−0.823301 | + | 0.567605i | \(0.807870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | −0.257663 | −0.128831 | − | 0.991667i | \(-0.541123\pi\) | ||||
−0.128831 | + | 0.991667i | \(0.541123\pi\) | |||||||
\(242\) | 19.7990 | 1.27273 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.0000 | − | 20.0000i | −1.28037 | − | 1.28037i | ||||
\(245\) | −1.41421 | + | 1.41421i | −0.0903508 | + | 0.0903508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000i | 0.509028i | ||||||||
\(248\) | 19.7990i | 1.25724i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.00000 | + | 9.00000i | −0.569210 | + | 0.569210i | ||||
\(251\) | −1.41421 | + | 1.41421i | −0.0892644 | + | 0.0892644i | −0.750329 | − | 0.661065i | \(-0.770105\pi\) |
0.661065 | + | 0.750329i | \(0.270105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0000 | − | 10.0000i | −0.628695 | − | 0.628695i | ||||
\(254\) | − | 18.3848i | − | 1.15356i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 29.6985 | 1.85254 | 0.926270 | − | 0.376860i | \(-0.122996\pi\) | ||||
0.926270 | + | 0.376860i | \(0.122996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | − | 6.00000i | −0.372822 | − | 0.372822i | ||||
\(260\) | −2.82843 | −0.175412 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.00000 | − | 1.00000i | 0.0617802 | − | 0.0617802i | ||||
\(263\) | − | 5.65685i | − | 0.348817i | −0.984673 | − | 0.174408i | \(-0.944199\pi\) | ||
0.984673 | − | 0.174408i | \(-0.0558013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.00000i | − | 0.0614295i | ||||||
\(266\) | −16.9706 | − | 16.9706i | −1.04053 | − | 1.04053i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00000 | − | 2.00000i | −0.122169 | − | 0.122169i | ||||
\(269\) | −11.3137 | − | 11.3137i | −0.689809 | − | 0.689809i | 0.272381 | − | 0.962190i | \(-0.412189\pi\) |
−0.962190 | + | 0.272381i | \(0.912189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0000 | −0.789694 | −0.394847 | − | 0.918747i | \(-0.629202\pi\) | ||||
−0.394847 | + | 0.918747i | \(0.629202\pi\) | |||||||
\(272\) | −16.9706 | −1.02899 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.0000 | 1.57072 | ||||||||
\(275\) | −14.1421 | − | 14.1421i | −0.852803 | − | 0.852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.0000 | + | 20.0000i | −1.20168 | + | 1.20168i | −0.228029 | + | 0.973654i | \(0.573228\pi\) |
−0.973654 | + | 0.228029i | \(0.926772\pi\) | |||||||
\(278\) | 14.1421 | + | 14.1421i | 0.848189 | + | 0.848189i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.00000 | − | 6.00000i | 0.358569 | − | 0.358569i | ||||
\(281\) | 24.0416i | 1.43420i | 0.696969 | + | 0.717102i | \(0.254532\pi\) | ||||
−0.696969 | + | 0.717102i | \(0.745468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | − | 4.00000i | 0.237775 | − | 0.237775i | −0.578153 | − | 0.815928i | \(-0.696226\pi\) |
0.815928 | + | 0.578153i | \(0.196226\pi\) | |||||||
\(284\) | − | 31.1127i | − | 1.84620i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 10.0000i | − | 0.591312i | ||||||
\(287\) | 16.9706 | 1.00174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | − | 5.65685i | − | 0.332182i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.0000i | 1.75562i | ||||||||
\(293\) | −14.1421 | + | 14.1421i | −0.826192 | + | 0.826192i | −0.986988 | − | 0.160795i | \(-0.948594\pi\) |
0.160795 | + | 0.986988i | \(0.448594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 10.0000i | − | 0.582223i | ||||||
\(296\) | 5.65685 | + | 5.65685i | 0.328798 | + | 0.328798i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.00000 | + | 7.00000i | 0.405499 | + | 0.405499i | ||||
\(299\) | −2.82843 | + | 2.82843i | −0.163572 | + | 0.163572i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.0000 | + | 21.0000i | 1.21042 | + | 1.21042i | ||||
\(302\) | 29.6985 | 1.70896 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000 | + | 16.0000i | 0.917663 | + | 0.917663i | ||||
\(305\) | 14.1421 | 0.809776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | + | 7.00000i | 0.399511 | + | 0.399511i | 0.878061 | − | 0.478549i | \(-0.158837\pi\) |
−0.478549 | + | 0.878061i | \(0.658837\pi\) | |||||||
\(308\) | 21.2132 | + | 21.2132i | 1.20873 | + | 1.20873i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.00000 | − | 7.00000i | −0.397573 | − | 0.397573i | ||||
\(311\) | 19.7990i | 1.12270i | 0.827579 | + | 0.561349i | \(0.189717\pi\) | ||||
−0.827579 | + | 0.561349i | \(0.810283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0000i | 1.52613i | 0.646322 | + | 0.763065i | \(0.276306\pi\) | ||||
−0.646322 | + | 0.763065i | \(0.723694\pi\) | |||||||
\(314\) | 2.82843 | − | 2.82843i | 0.159617 | − | 0.159617i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 24.7487 | + | 24.7487i | 1.39003 | + | 1.39003i | 0.825228 | + | 0.564799i | \(0.191046\pi\) |
0.564799 | + | 0.825228i | \(0.308954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.0000 | 1.11979 | ||||||||
\(320\) | −5.65685 | + | 5.65685i | −0.316228 | + | 0.316228i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 12.0000i | − | 0.668734i | ||||||
\(323\) | −16.9706 | − | 16.9706i | −0.944267 | − | 0.944267i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | + | 4.00000i | −0.221880 | + | 0.221880i | ||||
\(326\) | 7.07107 | − | 7.07107i | 0.391630 | − | 0.391630i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.0000 | −0.883452 | ||||||||
\(329\) | 12.7279i | 0.701713i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00000 | − | 7.00000i | 0.384755 | − | 0.384755i | −0.488057 | − | 0.872812i | \(-0.662294\pi\) |
0.872812 | + | 0.488057i | \(0.162294\pi\) | |||||||
\(332\) | −15.5563 | − | 15.5563i | −0.853766 | − | 0.853766i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.0000 | −0.547176 | ||||||||
\(335\) | 1.41421 | 0.0772667 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 15.5563 | 0.846154 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | − | 6.00000i | 0.325396 | − | 0.325396i | ||||
\(341\) | 24.7487 | − | 24.7487i | 1.34022 | − | 1.34022i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | −19.7990 | − | 19.7990i | −1.06749 | − | 1.06749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0000 | + | 11.0000i | −0.591364 | + | 0.591364i | ||||
\(347\) | 17.6777 | − | 17.6777i | 0.948987 | − | 0.948987i | −0.0497735 | − | 0.998761i | \(-0.515850\pi\) |
0.998761 | + | 0.0497735i | \(0.0158499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00000 | + | 4.00000i | 0.214115 | + | 0.214115i | 0.806013 | − | 0.591898i | \(-0.201621\pi\) |
−0.591898 | + | 0.806013i | \(0.701621\pi\) | |||||||
\(350\) | − | 16.9706i | − | 0.907115i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.0000 | − | 20.0000i | −1.06600 | − | 1.06600i | ||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.0000 | + | 11.0000i | 0.583819 | + | 0.583819i | ||||
\(356\) | 2.82843i | 0.149906i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.0000 | + | 11.0000i | −0.581368 | + | 0.581368i | ||||
\(359\) | − | 35.3553i | − | 1.86598i | −0.359898 | − | 0.932992i | \(-0.617188\pi\) | ||
0.359898 | − | 0.932992i | \(-0.382812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000i | 0.684211i | ||||||||
\(362\) | 22.6274 | + | 22.6274i | 1.18927 | + | 1.18927i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.00000 | − | 6.00000i | 0.314485 | − | 0.314485i | ||||
\(365\) | −10.6066 | − | 10.6066i | −0.555175 | − | 0.555175i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | 0.574195 | 0.287098 | − | 0.957901i | \(-0.407310\pi\) | ||||
0.287098 | + | 0.957901i | \(0.407310\pi\) | |||||||
\(368\) | 11.3137i | 0.589768i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 2.12132 | + | 2.12132i | 0.110133 | + | 0.110133i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00000 | − | 1.00000i | 0.0517780 | − | 0.0517780i | −0.680744 | − | 0.732522i | \(-0.738343\pi\) |
0.732522 | + | 0.680744i | \(0.238343\pi\) | |||||||
\(374\) | 21.2132 | + | 21.2132i | 1.09691 | + | 1.09691i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 12.0000i | − | 0.618853i | ||||||
\(377\) | − | 5.65685i | − | 0.291343i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00000 | + | 2.00000i | −0.102733 | + | 0.102733i | −0.756605 | − | 0.653872i | \(-0.773143\pi\) |
0.653872 | + | 0.756605i | \(0.273143\pi\) | |||||||
\(380\) | −11.3137 | −0.580381 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.00000i | 0.306987i | ||||||||
\(383\) | −4.24264 | −0.216789 | −0.108394 | − | 0.994108i | \(-0.534571\pi\) | ||||
−0.108394 | + | 0.994108i | \(0.534571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.0000 | −0.764471 | ||||||||
\(386\) | − | 9.89949i | − | 0.503871i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.0000 | 0.710742 | ||||||||
\(389\) | 9.19239 | − | 9.19239i | 0.466073 | − | 0.466073i | −0.434567 | − | 0.900640i | \(-0.643099\pi\) |
0.900640 | + | 0.434567i | \(0.143099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | 5.65685i | 0.285714i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.0000 | − | 23.0000i | −1.15872 | − | 1.15872i | ||||
\(395\) | 1.41421 | − | 1.41421i | 0.0711568 | − | 0.0711568i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.00000 | − | 5.00000i | −0.250943 | − | 0.250943i | 0.570414 | − | 0.821357i | \(-0.306783\pi\) |
−0.821357 | + | 0.570414i | \(0.806783\pi\) | |||||||
\(398\) | −21.2132 | −1.06332 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0000i | 0.800000i | ||||||||
\(401\) | 8.48528 | 0.423735 | 0.211867 | − | 0.977298i | \(-0.432046\pi\) | ||||
0.211867 | + | 0.977298i | \(0.432046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.00000 | − | 7.00000i | −0.348695 | − | 0.348695i | ||||
\(404\) | −9.89949 | + | 9.89949i | −0.492518 | + | 0.492518i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | + | 12.0000i | 0.595550 | + | 0.595550i | ||||
\(407\) | − | 14.1421i | − | 0.701000i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.00000i | 0.148340i | 0.997246 | + | 0.0741702i | \(0.0236308\pi\) | ||||
−0.997246 | + | 0.0741702i | \(0.976369\pi\) | |||||||
\(410\) | 5.65685 | − | 5.65685i | 0.279372 | − | 0.279372i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.0000i | − | 0.591198i | ||||||
\(413\) | 21.2132 | + | 21.2132i | 1.04383 | + | 1.04383i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0000 | 0.539969 | ||||||||
\(416\) | −5.65685 | + | 5.65685i | −0.277350 | + | 0.277350i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 40.0000i | − | 1.95646i | ||||||
\(419\) | −7.07107 | − | 7.07107i | −0.345444 | − | 0.345444i | 0.512965 | − | 0.858409i | \(-0.328547\pi\) |
−0.858409 | + | 0.512965i | \(0.828547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | − | 16.0000i | 0.779792 | − | 0.779792i | −0.200003 | − | 0.979795i | \(-0.564095\pi\) |
0.979795 | + | 0.200003i | \(0.0640952\pi\) | |||||||
\(422\) | −5.65685 | + | 5.65685i | −0.275371 | + | 0.275371i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | − | 2.00000i | −0.0971286 | − | 0.0971286i | ||||
\(425\) | − | 16.9706i | − | 0.823193i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.0000 | + | 30.0000i | −1.45180 | + | 1.45180i | ||||
\(428\) | 15.5563 | − | 15.5563i | 0.751945 | − | 0.751945i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.0000 | 0.675140 | ||||||||
\(431\) | −4.24264 | −0.204361 | −0.102180 | − | 0.994766i | \(-0.532582\pi\) | ||||
−0.102180 | + | 0.994766i | \(0.532582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 29.6985 | 1.42557 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.0000 | − | 20.0000i | −0.957826 | − | 0.957826i | ||||
\(437\) | −11.3137 | + | 11.3137i | −0.541208 | + | 0.541208i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0000i | 0.715911i | 0.933739 | + | 0.357955i | \(0.116526\pi\) | ||||
−0.933739 | + | 0.357955i | \(0.883474\pi\) | |||||||
\(440\) | 14.1421 | 0.674200 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | −9.89949 | + | 9.89949i | −0.470339 | + | 0.470339i | −0.902024 | − | 0.431685i | \(-0.857919\pi\) |
0.431685 | + | 0.902024i | \(0.357919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | − | 1.00000i | −0.0474045 | − | 0.0474045i | ||||
\(446\) | − | 31.1127i | − | 1.47323i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 24.0000i | − | 1.13389i | ||||||
\(449\) | 16.9706 | 0.800890 | 0.400445 | − | 0.916321i | \(-0.368855\pi\) | ||||
0.400445 | + | 0.916321i | \(0.368855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0000 | + | 20.0000i | 0.941763 | + | 0.941763i | ||||
\(452\) | −16.9706 | −0.798228 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.0000 | − | 10.0000i | 0.469323 | − | 0.469323i | ||||
\(455\) | 4.24264i | 0.198898i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.00000i | − | 0.140334i | −0.997535 | − | 0.0701670i | \(-0.977647\pi\) | ||
0.997535 | − | 0.0701670i | \(-0.0223532\pi\) | |||||||
\(458\) | 9.89949 | + | 9.89949i | 0.462573 | + | 0.462573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | − | 4.00000i | −0.186501 | − | 0.186501i | ||||
\(461\) | 24.7487 | + | 24.7487i | 1.15266 | + | 1.15266i | 0.986017 | + | 0.166647i | \(0.0532940\pi\) |
0.166647 | + | 0.986017i | \(0.446706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00000 | −0.325318 | −0.162659 | − | 0.986682i | \(-0.552007\pi\) | ||||
−0.162659 | + | 0.986682i | \(0.552007\pi\) | |||||||
\(464\) | −11.3137 | − | 11.3137i | −0.525226 | − | 0.525226i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.0000 | −1.01913 | ||||||||
\(467\) | 3.53553 | + | 3.53553i | 0.163605 | + | 0.163605i | 0.784162 | − | 0.620557i | \(-0.213093\pi\) |
−0.620557 | + | 0.784162i | \(0.713093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.00000 | + | 3.00000i | −0.138527 | + | 0.138527i | ||||
\(470\) | 4.24264 | + | 4.24264i | 0.195698 | + | 0.195698i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.0000 | − | 20.0000i | −0.920575 | − | 0.920575i | ||||
\(473\) | 49.4975i | 2.27590i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | + | 16.0000i | −0.734130 | + | 0.734130i | ||||
\(476\) | 25.4558i | 1.16677i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 36.0000i | − | 1.64660i | ||||||
\(479\) | −4.24264 | −0.193851 | −0.0969256 | − | 0.995292i | \(-0.530901\pi\) | ||||
−0.0969256 | + | 0.995292i | \(0.530901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | − | 5.65685i | − | 0.257663i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.0000i | 1.27273i | ||||||||
\(485\) | −4.94975 | + | 4.94975i | −0.224756 | + | 0.224756i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.0000i | − | 0.543772i | −0.962329 | − | 0.271886i | \(-0.912353\pi\) | ||
0.962329 | − | 0.271886i | \(-0.0876473\pi\) | |||||||
\(488\) | 28.2843 | − | 28.2843i | 1.28037 | − | 1.28037i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.00000 | − | 2.00000i | −0.0903508 | − | 0.0903508i | ||||
\(491\) | 4.94975 | − | 4.94975i | 0.223379 | − | 0.223379i | −0.586541 | − | 0.809920i | \(-0.699511\pi\) |
0.809920 | + | 0.586541i | \(0.199511\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | + | 12.0000i | 0.540453 | + | 0.540453i | ||||
\(494\) | −11.3137 | −0.509028 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.0000 | −1.25724 | ||||||||
\(497\) | −46.6690 | −2.09339 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.0000 | − | 23.0000i | −1.02962 | − | 1.02962i | −0.999548 | − | 0.0300737i | \(-0.990426\pi\) |
−0.0300737 | − | 0.999548i | \(-0.509574\pi\) | |||||||
\(500\) | −12.7279 | − | 12.7279i | −0.569210 | − | 0.569210i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.00000 | − | 2.00000i | −0.0892644 | − | 0.0892644i | ||||
\(503\) | − | 22.6274i | − | 1.00891i | −0.863439 | − | 0.504453i | \(-0.831694\pi\) | ||
0.863439 | − | 0.504453i | \(-0.168306\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.00000i | − | 0.311496i | ||||||
\(506\) | 14.1421 | − | 14.1421i | 0.628695 | − | 0.628695i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.0000 | 1.15356 | ||||||||
\(509\) | −4.94975 | − | 4.94975i | −0.219394 | − | 0.219394i | 0.588849 | − | 0.808243i | \(-0.299581\pi\) |
−0.808243 | + | 0.588849i | \(0.799581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.0000 | 1.99068 | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 42.0000i | 1.85254i | ||||||||
\(515\) | 4.24264 | + | 4.24264i | 0.186953 | + | 0.186953i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0000 | + | 15.0000i | −0.659699 | + | 0.659699i | ||||
\(518\) | 8.48528 | − | 8.48528i | 0.372822 | − | 0.372822i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 4.00000i | − | 0.175412i | ||||||
\(521\) | − | 26.8701i | − | 1.17720i | −0.808425 | − | 0.588599i | \(-0.799680\pi\) | ||
0.808425 | − | 0.588599i | \(-0.200320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.0000 | + | 23.0000i | −1.00572 | + | 1.00572i | −0.00573623 | + | 0.999984i | \(0.501826\pi\) |
−0.999984 | + | 0.00573623i | \(0.998174\pi\) | |||||||
\(524\) | 1.41421 | + | 1.41421i | 0.0617802 | + | 0.0617802i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.00000 | 0.348817 | ||||||||
\(527\) | 29.6985 | 1.29369 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 1.41421 | 0.0614295 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.0000 | − | 24.0000i | 1.04053 | − | 1.04053i | ||||
\(533\) | 5.65685 | − | 5.65685i | 0.245026 | − | 0.245026i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0000i | 0.475571i | ||||||||
\(536\) | 2.82843 | − | 2.82843i | 0.122169 | − | 0.122169i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.0000 | − | 16.0000i | 0.689809 | − | 0.689809i | ||||
\(539\) | 7.07107 | − | 7.07107i | 0.304572 | − | 0.304572i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | − | 2.00000i | −0.0859867 | − | 0.0859867i | 0.662805 | − | 0.748792i | \(-0.269366\pi\) |
−0.748792 | + | 0.662805i | \(0.769366\pi\) | |||||||
\(542\) | − | 18.3848i | − | 0.789694i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 24.0000i | − | 1.02899i | ||||||
\(545\) | 14.1421 | 0.605783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | − | 5.00000i | −0.213785 | − | 0.213785i | 0.592088 | − | 0.805873i | \(-0.298304\pi\) |
−0.805873 | + | 0.592088i | \(0.798304\pi\) | |||||||
\(548\) | 36.7696i | 1.57072i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20.0000 | − | 20.0000i | 0.852803 | − | 0.852803i | ||||
\(551\) | − | 22.6274i | − | 0.963960i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000i | 0.255146i | ||||||||
\(554\) | −28.2843 | − | 28.2843i | −1.20168 | − | 1.20168i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0000 | + | 20.0000i | −0.848189 | + | 0.848189i | ||||
\(557\) | −9.19239 | − | 9.19239i | −0.389494 | − | 0.389494i | 0.485013 | − | 0.874507i | \(-0.338815\pi\) |
−0.874507 | + | 0.485013i | \(0.838815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0000 | 0.592137 | ||||||||
\(560\) | 8.48528 | + | 8.48528i | 0.358569 | + | 0.358569i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −34.0000 | −1.43420 | ||||||||
\(563\) | −0.707107 | − | 0.707107i | −0.0298010 | − | 0.0298010i | 0.692049 | − | 0.721850i | \(-0.256708\pi\) |
−0.721850 | + | 0.692049i | \(0.756708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | − | 6.00000i | 0.252422 | − | 0.252422i | ||||
\(566\) | 5.65685 | + | 5.65685i | 0.237775 | + | 0.237775i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 44.0000 | 1.84620 | ||||||||
\(569\) | − | 5.65685i | − | 0.237148i | −0.992945 | − | 0.118574i | \(-0.962168\pi\) | ||
0.992945 | − | 0.118574i | \(-0.0378322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | − | 7.00000i | 0.292941 | − | 0.292941i | −0.545300 | − | 0.838241i | \(-0.683584\pi\) |
0.838241 | + | 0.545300i | \(0.183584\pi\) | |||||||
\(572\) | 14.1421 | 0.591312 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.0000i | 1.00174i | ||||||||
\(575\) | −11.3137 | −0.471814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0000 | 1.33218 | 0.666089 | − | 0.745873i | \(-0.267967\pi\) | ||||
0.666089 | + | 0.745873i | \(0.267967\pi\) | |||||||
\(578\) | 1.41421i | 0.0588235i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.00000 | 0.332182 | ||||||||
\(581\) | −23.3345 | + | 23.3345i | −0.968079 | + | 0.968079i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.00000i | 0.207079i | ||||||||
\(584\) | −42.4264 | −1.75562 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.0000 | − | 20.0000i | −0.826192 | − | 0.826192i | ||||
\(587\) | −7.77817 | + | 7.77817i | −0.321040 | + | 0.321040i | −0.849166 | − | 0.528126i | \(-0.822895\pi\) |
0.528126 | + | 0.849166i | \(0.322895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.0000 | − | 28.0000i | −1.15372 | − | 1.15372i | ||||
\(590\) | 14.1421 | 0.582223 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.00000 | + | 8.00000i | −0.328798 | + | 0.328798i | ||||
\(593\) | −29.6985 | −1.21957 | −0.609785 | − | 0.792567i | \(-0.708744\pi\) | ||||
−0.609785 | + | 0.792567i | \(0.708744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00000 | − | 9.00000i | −0.368964 | − | 0.368964i | ||||
\(596\) | −9.89949 | + | 9.89949i | −0.405499 | + | 0.405499i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.00000 | − | 4.00000i | −0.163572 | − | 0.163572i | ||||
\(599\) | 41.0122i | 1.67571i | 0.545891 | + | 0.837856i | \(0.316191\pi\) | ||||
−0.545891 | + | 0.837856i | \(0.683809\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.0000i | 1.10135i | 0.834719 | + | 0.550676i | \(0.185630\pi\) | ||||
−0.834719 | + | 0.550676i | \(0.814370\pi\) | |||||||
\(602\) | −29.6985 | + | 29.6985i | −1.21042 | + | 1.21042i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 42.0000i | 1.70896i | ||||||||
\(605\) | −9.89949 | − | 9.89949i | −0.402472 | − | 0.402472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000 | 0.811775 | 0.405887 | − | 0.913923i | \(-0.366962\pi\) | ||||
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | −22.6274 | + | 22.6274i | −0.917663 | + | 0.917663i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.0000i | 0.809776i | ||||||||
\(611\) | 4.24264 | + | 4.24264i | 0.171639 | + | 0.171639i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00000 | − | 1.00000i | 0.0403896 | − | 0.0403896i | −0.686624 | − | 0.727013i | \(-0.740908\pi\) |
0.727013 | + | 0.686624i | \(0.240908\pi\) | |||||||
\(614\) | −9.89949 | + | 9.89949i | −0.399511 | + | 0.399511i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.0000 | + | 30.0000i | −1.20873 | + | 1.20873i | ||||
\(617\) | 2.82843i | 0.113868i | 0.998378 | + | 0.0569341i | \(0.0181325\pi\) | ||||
−0.998378 | + | 0.0569341i | \(0.981868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.00000 | − | 1.00000i | 0.0401934 | − | 0.0401934i | −0.686724 | − | 0.726918i | \(-0.740952\pi\) |
0.726918 | + | 0.686724i | \(0.240952\pi\) | |||||||
\(620\) | 9.89949 | − | 9.89949i | 0.397573 | − | 0.397573i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.0000 | −1.12270 | ||||||||
\(623\) | 4.24264 | 0.169978 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −38.1838 | −1.52613 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000 | + | 4.00000i | 0.159617 | + | 0.159617i | ||||
\(629\) | 8.48528 | − | 8.48528i | 0.338330 | − | 0.338330i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 15.0000i | − | 0.597141i | −0.954388 | − | 0.298570i | \(-0.903490\pi\) | ||
0.954388 | − | 0.298570i | \(-0.0965097\pi\) | |||||||
\(632\) | − | 5.65685i | − | 0.225018i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −35.0000 | + | 35.0000i | −1.39003 | + | 1.39003i | ||||
\(635\) | −9.19239 | + | 9.19239i | −0.364789 | + | 0.364789i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00000 | − | 2.00000i | −0.0792429 | − | 0.0792429i | ||||
\(638\) | 28.2843i | 1.11979i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.00000 | − | 8.00000i | −0.316228 | − | 0.316228i | ||||
\(641\) | 42.4264 | 1.67574 | 0.837871 | − | 0.545868i | \(-0.183800\pi\) | ||||
0.837871 | + | 0.545868i | \(0.183800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0000 | + | 10.0000i | 0.394362 | + | 0.394362i | 0.876239 | − | 0.481877i | \(-0.160045\pi\) |
−0.481877 | + | 0.876239i | \(0.660045\pi\) | |||||||
\(644\) | 16.9706 | 0.668734 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | − | 24.0000i | 0.944267 | − | 0.944267i | ||||
\(647\) | 28.2843i | 1.11197i | 0.831193 | + | 0.555985i | \(0.187659\pi\) | ||||
−0.831193 | + | 0.555985i | \(0.812341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.0000i | 1.96267i | ||||||||
\(650\) | −5.65685 | − | 5.65685i | −0.221880 | − | 0.221880i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000 | + | 10.0000i | 0.391630 | + | 0.391630i | ||||
\(653\) | −21.9203 | − | 21.9203i | −0.857808 | − | 0.857808i | 0.133272 | − | 0.991080i | \(-0.457452\pi\) |
−0.991080 | + | 0.133272i | \(0.957452\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.00000 | −0.0390732 | ||||||||
\(656\) | − | 22.6274i | − | 0.883452i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.0000 | −0.701713 | ||||||||
\(659\) | −9.19239 | − | 9.19239i | −0.358085 | − | 0.358085i | 0.505022 | − | 0.863107i | \(-0.331484\pi\) |
−0.863107 | + | 0.505022i | \(0.831484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0000 | − | 16.0000i | 0.622328 | − | 0.622328i | −0.323798 | − | 0.946126i | \(-0.604960\pi\) |
0.946126 | + | 0.323798i | \(0.104960\pi\) | |||||||
\(662\) | 9.89949 | + | 9.89949i | 0.384755 | + | 0.384755i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.0000 | − | 22.0000i | 0.853766 | − | 0.853766i | ||||
\(665\) | 16.9706i | 0.658090i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | − | 8.00000i | 0.309761 | − | 0.309761i | ||||
\(668\) | − | 14.1421i | − | 0.547176i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.00000i | 0.0772667i | ||||||||
\(671\) | −70.7107 | −2.72976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | −0.269830 | −0.134915 | − | 0.990857i | \(-0.543076\pi\) | ||||
−0.134915 | + | 0.990857i | \(0.543076\pi\) | |||||||
\(674\) | 28.2843i | 1.08947i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.0000i | 0.846154i | ||||||||
\(677\) | −22.6274 | + | 22.6274i | −0.869642 | + | 0.869642i | −0.992433 | − | 0.122790i | \(-0.960816\pi\) |
0.122790 | + | 0.992433i | \(0.460816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 21.0000i | − | 0.805906i | ||||||
\(680\) | 8.48528 | + | 8.48528i | 0.325396 | + | 0.325396i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.0000 | + | 35.0000i | 1.34022 | + | 1.34022i | ||||
\(683\) | 11.3137 | − | 11.3137i | 0.432907 | − | 0.432907i | −0.456709 | − | 0.889616i | \(-0.650972\pi\) |
0.889616 | + | 0.456709i | \(0.150972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.0000 | − | 13.0000i | −0.496704 | − | 0.496704i | ||||
\(686\) | −21.2132 | −0.809924 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.0000 | − | 28.0000i | 1.06749 | − | 1.06749i | ||||
\(689\) | 1.41421 | 0.0538772 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0000 | + | 16.0000i | 0.608669 | + | 0.608669i | 0.942598 | − | 0.333929i | \(-0.108375\pi\) |
−0.333929 | + | 0.942598i | \(0.608375\pi\) | |||||||
\(692\) | −15.5563 | − | 15.5563i | −0.591364 | − | 0.591364i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.0000 | + | 25.0000i | 0.948987 | + | 0.948987i | ||||
\(695\) | − | 14.1421i | − | 0.536442i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000i | 0.909065i | ||||||||
\(698\) | −5.65685 | + | 5.65685i | −0.214115 | + | 0.214115i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.0000 | 0.907115 | ||||||||
\(701\) | −0.707107 | − | 0.707107i | −0.0267071 | − | 0.0267071i | 0.693627 | − | 0.720334i | \(-0.256012\pi\) |
−0.720334 | + | 0.693627i | \(0.756012\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0000 | −0.603451 | ||||||||
\(704\) | 28.2843 | − | 28.2843i | 1.06600 | − | 1.06600i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.8492 | + | 14.8492i | 0.558463 | + | 0.558463i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0000 | − | 22.0000i | 0.826227 | − | 0.826227i | −0.160765 | − | 0.986993i | \(-0.551396\pi\) |
0.986993 | + | 0.160765i | \(0.0513962\pi\) | |||||||
\(710\) | −15.5563 | + | 15.5563i | −0.583819 | + | 0.583819i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.00000 | −0.149906 | ||||||||
\(713\) | − | 19.7990i | − | 0.741478i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.00000 | + | 5.00000i | −0.186989 | + | 0.186989i | ||||
\(716\) | −15.5563 | − | 15.5563i | −0.581368 | − | 0.581368i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 50.0000 | 1.86598 | ||||||||
\(719\) | 16.9706 | 0.632895 | 0.316448 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316448 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | −18.3848 | −0.684211 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −32.0000 | + | 32.0000i | −1.18927 | + | 1.18927i | ||||
\(725\) | 11.3137 | − | 11.3137i | 0.420181 | − | 0.420181i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.00000i | − | 0.333792i | −0.985975 | − | 0.166896i | \(-0.946626\pi\) | ||
0.985975 | − | 0.166896i | \(-0.0533743\pi\) | |||||||
\(728\) | 8.48528 | + | 8.48528i | 0.314485 | + | 0.314485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.0000 | − | 15.0000i | 0.555175 | − | 0.555175i | ||||
\(731\) | −29.6985 | + | 29.6985i | −1.09844 | + | 1.09844i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.0000 | − | 26.0000i | −0.960332 | − | 0.960332i | 0.0389108 | − | 0.999243i | \(-0.487611\pi\) |
−0.999243 | + | 0.0389108i | \(0.987611\pi\) | |||||||
\(734\) | 15.5563i | 0.574195i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.0000 | −0.589768 | ||||||||
\(737\) | −7.07107 | −0.260466 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.0000 | − | 29.0000i | −1.06678 | − | 1.06678i | −0.997604 | − | 0.0691779i | \(-0.977962\pi\) |
−0.0691779 | − | 0.997604i | \(-0.522038\pi\) | |||||||
\(740\) | − | 5.65685i | − | 0.207950i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.00000 | + | 3.00000i | −0.110133 | + | 0.110133i | ||||
\(743\) | 41.0122i | 1.50459i | 0.658826 | + | 0.752296i | \(0.271054\pi\) | ||||
−0.658826 | + | 0.752296i | \(0.728946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.00000i | − | 0.256460i | ||||||
\(746\) | 1.41421 | + | 1.41421i | 0.0517780 | + | 0.0517780i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30.0000 | + | 30.0000i | −1.09691 | + | 1.09691i | ||||
\(749\) | −23.3345 | − | 23.3345i | −0.852625 | − | 0.852625i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | −0.0182453 | − | 0.999834i | \(-0.505808\pi\) | ||||
−0.0182453 | + | 0.999834i | \(0.505808\pi\) | |||||||
\(752\) | 16.9706 | 0.618853 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | −14.8492 | − | 14.8492i | −0.540419 | − | 0.540419i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.0000 | − | 13.0000i | 0.472493 | − | 0.472493i | −0.430227 | − | 0.902721i | \(-0.641567\pi\) |
0.902721 | + | 0.430227i | \(0.141567\pi\) | |||||||
\(758\) | −2.82843 | − | 2.82843i | −0.102733 | − | 0.102733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 16.0000i | − | 0.580381i | ||||||
\(761\) | − | 31.1127i | − | 1.12783i | −0.825831 | − | 0.563917i | \(-0.809294\pi\) | ||
0.825831 | − | 0.563917i | \(-0.190706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.0000 | + | 30.0000i | −1.08607 | + | 1.08607i | ||||
\(764\) | −8.48528 | −0.306987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 6.00000i | − | 0.216789i | ||||||
\(767\) | 14.1421 | 0.510643 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0000 | 0.396670 | 0.198335 | − | 0.980134i | \(-0.436447\pi\) | ||||
0.198335 | + | 0.980134i | \(0.436447\pi\) | |||||||
\(770\) | − | 21.2132i | − | 0.764471i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 7.07107 | − | 7.07107i | 0.254329 | − | 0.254329i | −0.568414 | − | 0.822743i | \(-0.692443\pi\) |
0.822743 | + | 0.568414i | \(0.192443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 28.0000i | − | 1.00579i | ||||||
\(776\) | 19.7990i | 0.710742i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.0000 | + | 13.0000i | 0.466073 | + | 0.466073i | ||||
\(779\) | 22.6274 | − | 22.6274i | 0.810711 | − | 0.810711i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.0000 | − | 55.0000i | −1.96805 | − | 1.96805i | ||||
\(782\) | 16.9706 | 0.606866 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | −0.285714 | ||||||||
\(785\) | −2.82843 | −0.100951 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.0000 | − | 26.0000i | −0.926800 | − | 0.926800i | 0.0706979 | − | 0.997498i | \(-0.477477\pi\) |
−0.997498 | + | 0.0706979i | \(0.977477\pi\) | |||||||
\(788\) | 32.5269 | − | 32.5269i | 1.15872 | − | 1.15872i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.00000 | + | 2.00000i | 0.0711568 | + | 0.0711568i | ||||
\(791\) | 25.4558i | 0.905106i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000i | 0.710221i | ||||||||
\(794\) | 7.07107 | − | 7.07107i | 0.250943 | − | 0.250943i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 30.0000i | − | 1.06332i | ||||||
\(797\) | 16.2635 | + | 16.2635i | 0.576081 | + | 0.576081i | 0.933821 | − | 0.357740i | \(-0.116453\pi\) |
−0.357740 | + | 0.933821i | \(0.616453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | −0.636794 | ||||||||
\(800\) | −22.6274 | −0.800000 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0000i | 0.423735i | ||||||||
\(803\) | 53.0330 | + | 53.0330i | 1.87149 | + | 1.87149i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.00000 | + | 6.00000i | −0.211472 | + | 0.211472i | ||||
\(806\) | 9.89949 | − | 9.89949i | 0.348695 | − | 0.348695i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.0000 | − | 14.0000i | −0.492518 | − | 0.492518i | ||||
\(809\) | − | 52.3259i | − | 1.83968i | −0.392293 | − | 0.919840i | \(-0.628318\pi\) | ||
0.392293 | − | 0.919840i | \(-0.371682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0000 | − | 10.0000i | 0.351147 | − | 0.351147i | −0.509389 | − | 0.860536i | \(-0.670129\pi\) |
0.860536 | + | 0.509389i | \(0.170129\pi\) | |||||||
\(812\) | −16.9706 | + | 16.9706i | −0.595550 | + | 0.595550i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.0000 | 0.701000 | ||||||||
\(815\) | −7.07107 | −0.247689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.0000 | 1.95919 | ||||||||
\(818\) | −4.24264 | −0.148340 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.00000 | + | 8.00000i | 0.279372 | + | 0.279372i | ||||
\(821\) | 32.5269 | − | 32.5269i | 1.13520 | − | 1.13520i | 0.145897 | − | 0.989300i | \(-0.453393\pi\) |
0.989300 | − | 0.145897i | \(-0.0466069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.00000i | − | 0.313720i | −0.987621 | − | 0.156860i | \(-0.949863\pi\) | ||
0.987621 | − | 0.156860i | \(-0.0501372\pi\) | |||||||
\(824\) | 16.9706 | 0.591198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.0000 | + | 30.0000i | −1.04383 | + | 1.04383i | ||||
\(827\) | 15.5563 | − | 15.5563i | 0.540947 | − | 0.540947i | −0.382859 | − | 0.923807i | \(-0.625061\pi\) |
0.923807 | + | 0.382859i | \(0.125061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0000 | − | 11.0000i | −0.382046 | − | 0.382046i | 0.489793 | − | 0.871839i | \(-0.337072\pi\) |
−0.871839 | + | 0.489793i | \(0.837072\pi\) | |||||||
\(830\) | 15.5563i | 0.539969i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.00000 | − | 8.00000i | −0.277350 | − | 0.277350i | ||||
\(833\) | 8.48528 | 0.293998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.00000 | + | 5.00000i | 0.173032 | + | 0.173032i | ||||
\(836\) | 56.5685 | 1.95646 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.0000 | − | 10.0000i | 0.345444 | − | 0.345444i | ||||
\(839\) | − | 9.89949i | − | 0.341769i | −0.985291 | − | 0.170884i | \(-0.945338\pi\) | ||
0.985291 | − | 0.170884i | \(-0.0546624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 13.0000i | − | 0.448276i | ||||||
\(842\) | 22.6274 | + | 22.6274i | 0.779792 | + | 0.779792i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.00000 | − | 8.00000i | −0.275371 | − | 0.275371i | ||||
\(845\) | −7.77817 | − | 7.77817i | −0.267577 | − | 0.267577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0000 | 1.44314 | ||||||||
\(848\) | 2.82843 | − | 2.82843i | 0.0971286 | − | 0.0971286i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.0000 | 0.823193 | ||||||||
\(851\) | −5.65685 | − | 5.65685i | −0.193914 | − | 0.193914i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.00000 | + | 5.00000i | −0.171197 | + | 0.171197i | −0.787505 | − | 0.616308i | \(-0.788628\pi\) |
0.616308 | + | 0.787505i | \(0.288628\pi\) | |||||||
\(854\) | −42.4264 | − | 42.4264i | −1.45180 | − | 1.45180i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.0000 | + | 22.0000i | 0.751945 | + | 0.751945i | ||||
\(857\) | 32.5269i | 1.11110i | 0.831484 | + | 0.555549i | \(0.187492\pi\) | ||||
−0.831484 | + | 0.555549i | \(0.812508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | − | 4.00000i | 0.136478 | − | 0.136478i | −0.635567 | − | 0.772046i | \(-0.719234\pi\) |
0.772046 | + | 0.635567i | \(0.219234\pi\) | |||||||
\(860\) | 19.7990i | 0.675140i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 6.00000i | − | 0.204361i | ||||||
\(863\) | 16.9706 | 0.577685 | 0.288842 | − | 0.957377i | \(-0.406730\pi\) | ||||
0.288842 | + | 0.957377i | \(0.406730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0000 | 0.374011 | ||||||||
\(866\) | 7.07107i | 0.240285i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 42.0000i | 1.42557i | ||||||||
\(869\) | −7.07107 | + | 7.07107i | −0.239870 | + | 0.239870i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000i | 0.0677674i | ||||||||
\(872\) | 28.2843 | − | 28.2843i | 0.957826 | − | 0.957826i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.0000 | − | 16.0000i | −0.541208 | − | 0.541208i | ||||
\(875\) | −19.0919 | + | 19.0919i | −0.645423 | + | 0.645423i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0000 | − | 11.0000i | −0.371444 | − | 0.371444i | 0.496559 | − | 0.868003i | \(-0.334597\pi\) |
−0.868003 | + | 0.496559i | \(0.834597\pi\) | |||||||
\(878\) | −21.2132 | −0.715911 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.0000i | 0.674200i | ||||||||
\(881\) | −12.7279 | −0.428815 | −0.214407 | − | 0.976744i | \(-0.568782\pi\) | ||||
−0.214407 | + | 0.976744i | \(0.568782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.0000 | − | 26.0000i | −0.874970 | − | 0.874970i | 0.118039 | − | 0.993009i | \(-0.462339\pi\) |
−0.993009 | + | 0.118039i | \(0.962339\pi\) | |||||||
\(884\) | 8.48528 | + | 8.48528i | 0.285391 | + | 0.285391i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.0000 | − | 14.0000i | −0.470339 | − | 0.470339i | ||||
\(887\) | − | 9.89949i | − | 0.332393i | −0.986093 | − | 0.166196i | \(-0.946851\pi\) | ||
0.986093 | − | 0.166196i | \(-0.0531485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 39.0000i | − | 1.30802i | ||||||
\(890\) | 1.41421 | − | 1.41421i | 0.0474045 | − | 0.0474045i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 44.0000 | 1.47323 | ||||||||
\(893\) | 16.9706 | + | 16.9706i | 0.567898 | + | 0.567898i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0000 | 0.367689 | ||||||||
\(896\) | 33.9411 | 1.13389 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0000i | 0.800890i | ||||||||
\(899\) | 19.7990 | + | 19.7990i | 0.660333 | + | 0.660333i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.00000 | + | 3.00000i | −0.0999445 | + | 0.0999445i | ||||
\(902\) | −28.2843 | + | 28.2843i | −0.941763 | + | 0.941763i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 24.0000i | − | 0.798228i | ||||||
\(905\) | − | 22.6274i | − | 0.752161i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | + | 8.00000i | −0.265636 | + | 0.265636i | −0.827339 | − | 0.561703i | \(-0.810146\pi\) |
0.561703 | + | 0.827339i | \(0.310146\pi\) | |||||||
\(908\) | 14.1421 | + | 14.1421i | 0.469323 | + | 0.469323i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.00000 | −0.198898 | ||||||||
\(911\) | 38.1838 | 1.26508 | 0.632542 | − | 0.774526i | \(-0.282011\pi\) | ||||
0.632542 | + | 0.774526i | \(0.282011\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55.0000 | −1.82023 | ||||||||
\(914\) | 4.24264 | 0.140334 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | + | 14.0000i | −0.462573 | + | 0.462573i | ||||
\(917\) | 2.12132 | − | 2.12132i | 0.0700522 | − | 0.0700522i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 15.0000i | − | 0.494804i | −0.968913 | − | 0.247402i | \(-0.920423\pi\) | ||
0.968913 | − | 0.247402i | \(-0.0795769\pi\) | |||||||
\(920\) | 5.65685 | − | 5.65685i | 0.186501 | − | 0.186501i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −35.0000 | + | 35.0000i | −1.15266 | + | 1.15266i | ||||
\(923\) | −15.5563 | + | 15.5563i | −0.512043 | + | 0.512043i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | − | 8.00000i | −0.263038 | − | 0.263038i | ||||
\(926\) | − | 9.89949i | − | 0.325318i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.0000 | − | 16.0000i | 0.525226 | − | 0.525226i | ||||
\(929\) | −42.4264 | −1.39197 | −0.695983 | − | 0.718059i | \(-0.745031\pi\) | ||||
−0.695983 | + | 0.718059i | \(0.745031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.00000 | − | 8.00000i | −0.262189 | − | 0.262189i | ||||
\(932\) | − | 31.1127i | − | 1.01913i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.00000 | + | 5.00000i | −0.163605 | + | 0.163605i | ||||
\(935\) | − | 21.2132i | − | 0.693746i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.00000i | − | 0.0980057i | −0.998799 | − | 0.0490029i | \(-0.984396\pi\) | ||
0.998799 | − | 0.0490029i | \(-0.0156043\pi\) | |||||||
\(938\) | −4.24264 | − | 4.24264i | −0.138527 | − | 0.138527i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.00000 | + | 6.00000i | −0.195698 | + | 0.195698i | ||||
\(941\) | −21.9203 | − | 21.9203i | −0.714582 | − | 0.714582i | 0.252909 | − | 0.967490i | \(-0.418613\pi\) |
−0.967490 | + | 0.252909i | \(0.918613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | 28.2843 | − | 28.2843i | 0.920575 | − | 0.920575i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −70.0000 | −2.27590 | ||||||||
\(947\) | −9.19239 | − | 9.19239i | −0.298712 | − | 0.298712i | 0.541797 | − | 0.840509i | \(-0.317744\pi\) |
−0.840509 | + | 0.541797i | \(0.817744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.0000 | − | 15.0000i | 0.486921 | − | 0.486921i | ||||
\(950\) | −22.6274 | − | 22.6274i | −0.734130 | − | 0.734130i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −36.0000 | −1.16677 | ||||||||
\(953\) | − | 5.65685i | − | 0.183243i | −0.995794 | − | 0.0916217i | \(-0.970795\pi\) | ||
0.995794 | − | 0.0916217i | \(-0.0292051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00000 | − | 3.00000i | 0.0970777 | − | 0.0970777i | ||||
\(956\) | 50.9117 | 1.64660 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.00000i | − | 0.193851i | ||||||
\(959\) | 55.1543 | 1.78103 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | − | 5.65685i | − | 0.182384i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.00000 | 0.257663 | ||||||||
\(965\) | −4.94975 | + | 4.94975i | −0.159338 | + | 0.159338i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.0000i | − | 1.06121i | −0.847620 | − | 0.530604i | \(-0.821965\pi\) | ||
0.847620 | − | 0.530604i | \(-0.178035\pi\) | |||||||
\(968\) | −39.5980 | −1.27273 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.00000 | − | 7.00000i | −0.224756 | − | 0.224756i | ||||
\(971\) | −24.7487 | + | 24.7487i | −0.794225 | + | 0.794225i | −0.982178 | − | 0.187953i | \(-0.939815\pi\) |
0.187953 | + | 0.982178i | \(0.439815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0000 | + | 30.0000i | 0.961756 | + | 0.961756i | ||||
\(974\) | 16.9706 | 0.543772 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.0000 | + | 40.0000i | 1.28037 | + | 1.28037i | ||||
\(977\) | −38.1838 | −1.22161 | −0.610803 | − | 0.791782i | \(-0.709153\pi\) | ||||
−0.610803 | + | 0.791782i | \(0.709153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.00000 | + | 5.00000i | 0.159801 | + | 0.159801i | ||||
\(980\) | 2.82843 | − | 2.82843i | 0.0903508 | − | 0.0903508i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.00000 | + | 7.00000i | 0.223379 | + | 0.223379i | ||||
\(983\) | 32.5269i | 1.03745i | 0.854942 | + | 0.518724i | \(0.173593\pi\) | ||||
−0.854942 | + | 0.518724i | \(0.826407\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.0000i | 0.732841i | ||||||||
\(986\) | −16.9706 | + | 16.9706i | −0.540453 | + | 0.540453i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 16.0000i | − | 0.509028i | ||||||
\(989\) | 19.7990 | + | 19.7990i | 0.629571 | + | 0.629571i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.0000 | 1.68360 | 0.841800 | − | 0.539789i | \(-0.181496\pi\) | ||||
0.841800 | + | 0.539789i | \(0.181496\pi\) | |||||||
\(992\) | − | 39.5980i | − | 1.25724i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 66.0000i | − | 2.09339i | ||||||
\(995\) | 10.6066 | + | 10.6066i | 0.336252 | + | 0.336252i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.00000 | − | 7.00000i | 0.221692 | − | 0.221692i | −0.587519 | − | 0.809211i | \(-0.699895\pi\) |
0.809211 | + | 0.587519i | \(0.199895\pi\) | |||||||
\(998\) | 32.5269 | − | 32.5269i | 1.02962 | − | 1.02962i | ||||
\(999\) | 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 | 432.2.k.b.109.2 | yes | 4 | |
3.2 | odd | 2 | inner | 432.2.k.b.109.1 | ✓ | 4 | |
4.3 | odd | 2 | 1728.2.k.b.1297.2 | 4 | |||
12.11 | even | 2 | 1728.2.k.b.1297.1 | 4 | |||
16.5 | even | 4 | inner | 432.2.k.b.325.1 | yes | 4 | |
16.11 | odd | 4 | 1728.2.k.b.433.2 | 4 | |||
48.5 | odd | 4 | inner | 432.2.k.b.325.2 | yes | 4 | |
48.11 | even | 4 | 1728.2.k.b.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.k.b.109.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
432.2.k.b.109.2 | yes | 4 | 1.1 | even | 1 | trivial | |
432.2.k.b.325.1 | yes | 4 | 16.5 | even | 4 | inner | |
432.2.k.b.325.2 | yes | 4 | 48.5 | odd | 4 | inner | |
1728.2.k.b.433.1 | 4 | 48.11 | even | 4 | |||
1728.2.k.b.433.2 | 4 | 16.11 | odd | 4 | |||
1728.2.k.b.1297.1 | 4 | 12.11 | even | 2 | |||
1728.2.k.b.1297.2 | 4 | 4.3 | odd | 2 |