Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(364,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.4 | ||
Root | \(1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.364 |
Dual form | 605.2.b.d.364.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93185i | 1.36603i | 0.730406 | + | 0.683013i | \(0.239331\pi\) | ||||
−0.730406 | + | 0.683013i | \(0.760669\pi\) | |||||||
\(3\) | 0.517638i | 0.298858i | 0.988772 | + | 0.149429i | \(0.0477436\pi\) | ||||
−0.988772 | + | 0.149429i | \(0.952256\pi\) | |||||||
\(4\) | −1.73205 | −0.866025 | ||||||||
\(5\) | −1.73205 | + | 1.41421i | −0.774597 | + | 0.632456i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.896575i | 0.338874i | 0.985541 | + | 0.169437i | \(0.0541949\pi\) | ||||
−0.985541 | + | 0.169437i | \(0.945805\pi\) | |||||||
\(8\) | 0.517638i | 0.183013i | ||||||||
\(9\) | 2.73205 | 0.910684 | ||||||||
\(10\) | −2.73205 | − | 3.34607i | −0.863950 | − | 1.05812i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 0.896575i | − | 0.258819i | ||||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | −1.73205 | −0.462910 | ||||||||
\(15\) | −0.732051 | − | 0.896575i | −0.189015 | − | 0.231495i | ||||
\(16\) | −4.46410 | −1.11603 | ||||||||
\(17\) | 1.03528i | 0.251091i | 0.992088 | + | 0.125546i | \(0.0400682\pi\) | ||||
−0.992088 | + | 0.125546i | \(0.959932\pi\) | |||||||
\(18\) | 5.27792i | 1.24402i | ||||||||
\(19\) | −6.19615 | −1.42149 | −0.710747 | − | 0.703447i | \(-0.751643\pi\) | ||||
−0.710747 | + | 0.703447i | \(0.751643\pi\) | |||||||
\(20\) | 3.00000 | − | 2.44949i | 0.670820 | − | 0.547723i | ||||
\(21\) | −0.464102 | −0.101275 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.31319i | − | 1.31639i | −0.752847 | − | 0.658196i | \(-0.771320\pi\) | ||
0.752847 | − | 0.658196i | \(-0.228680\pi\) | |||||||
\(24\) | −0.267949 | −0.0546949 | ||||||||
\(25\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(26\) | −8.19615 | −1.60740 | ||||||||
\(27\) | 2.96713i | 0.571024i | ||||||||
\(28\) | − | 1.55291i | − | 0.293473i | ||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 1.73205 | − | 1.41421i | 0.316228 | − | 0.258199i | ||||
\(31\) | −5.26795 | −0.946152 | −0.473076 | − | 0.881022i | \(-0.656856\pi\) | ||||
−0.473076 | + | 0.881022i | \(0.656856\pi\) | |||||||
\(32\) | − | 7.58871i | − | 1.34151i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −1.26795 | − | 1.55291i | −0.214323 | − | 0.262490i | ||||
\(36\) | −4.73205 | −0.788675 | ||||||||
\(37\) | − | 6.69213i | − | 1.10018i | −0.835106 | − | 0.550090i | \(-0.814594\pi\) | ||
0.835106 | − | 0.550090i | \(-0.185406\pi\) | |||||||
\(38\) | − | 11.9700i | − | 1.94180i | ||||||
\(39\) | −2.19615 | −0.351666 | ||||||||
\(40\) | −0.732051 | − | 0.896575i | −0.115747 | − | 0.141761i | ||||
\(41\) | −1.73205 | −0.270501 | −0.135250 | − | 0.990811i | \(-0.543184\pi\) | ||||
−0.135250 | + | 0.990811i | \(0.543184\pi\) | |||||||
\(42\) | − | 0.896575i | − | 0.138345i | ||||||
\(43\) | 10.6945i | 1.63090i | 0.578827 | + | 0.815451i | \(0.303511\pi\) | ||||
−0.578827 | + | 0.815451i | \(0.696489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.73205 | + | 3.86370i | −0.705412 | + | 0.575967i | ||||
\(46\) | 12.1962 | 1.79822 | ||||||||
\(47\) | − | 4.10394i | − | 0.598621i | −0.954156 | − | 0.299311i | \(-0.903243\pi\) | ||
0.954156 | − | 0.299311i | \(-0.0967567\pi\) | |||||||
\(48\) | − | 2.31079i | − | 0.333534i | ||||||
\(49\) | 6.19615 | 0.885165 | ||||||||
\(50\) | 9.46410 | + | 1.93185i | 1.33843 | + | 0.273205i | ||||
\(51\) | −0.535898 | −0.0750408 | ||||||||
\(52\) | − | 7.34847i | − | 1.01905i | ||||||
\(53\) | 11.9700i | 1.64421i | 0.569334 | + | 0.822106i | \(0.307201\pi\) | ||||
−0.569334 | + | 0.822106i | \(0.692799\pi\) | |||||||
\(54\) | −5.73205 | −0.780033 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.464102 | −0.0620182 | ||||||||
\(57\) | − | 3.20736i | − | 0.424826i | ||||||
\(58\) | 13.3843i | 1.75744i | ||||||||
\(59\) | 4.73205 | 0.616061 | 0.308030 | − | 0.951377i | \(-0.400330\pi\) | ||||
0.308030 | + | 0.951377i | \(0.400330\pi\) | |||||||
\(60\) | 1.26795 | + | 1.55291i | 0.163692 | + | 0.200480i | ||||
\(61\) | −8.26795 | −1.05860 | −0.529301 | − | 0.848434i | \(-0.677546\pi\) | ||||
−0.529301 | + | 0.848434i | \(0.677546\pi\) | |||||||
\(62\) | − | 10.1769i | − | 1.29247i | ||||||
\(63\) | 2.44949i | 0.308607i | ||||||||
\(64\) | 5.73205 | 0.716506 | ||||||||
\(65\) | −6.00000 | − | 7.34847i | −0.744208 | − | 0.911465i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.9372i | 1.82487i | 0.409226 | + | 0.912433i | \(0.365799\pi\) | ||||
−0.409226 | + | 0.912433i | \(0.634201\pi\) | |||||||
\(68\) | − | 1.79315i | − | 0.217451i | ||||||
\(69\) | 3.26795 | 0.393415 | ||||||||
\(70\) | 3.00000 | − | 2.44949i | 0.358569 | − | 0.292770i | ||||
\(71\) | 2.19615 | 0.260635 | 0.130318 | − | 0.991472i | \(-0.458400\pi\) | ||||
0.130318 | + | 0.991472i | \(0.458400\pi\) | |||||||
\(72\) | 1.41421i | 0.166667i | ||||||||
\(73\) | 4.89898i | 0.573382i | 0.958023 | + | 0.286691i | \(0.0925553\pi\) | ||||
−0.958023 | + | 0.286691i | \(0.907445\pi\) | |||||||
\(74\) | 12.9282 | 1.50287 | ||||||||
\(75\) | 2.53590 | + | 0.517638i | 0.292820 | + | 0.0597717i | ||||
\(76\) | 10.7321 | 1.23105 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 4.24264i | − | 0.480384i | ||||||
\(79\) | 5.46410 | 0.614759 | 0.307380 | − | 0.951587i | \(-0.400548\pi\) | ||||
0.307380 | + | 0.951587i | \(0.400548\pi\) | |||||||
\(80\) | 7.73205 | − | 6.31319i | 0.864470 | − | 0.705836i | ||||
\(81\) | 6.66025 | 0.740028 | ||||||||
\(82\) | − | 3.34607i | − | 0.369511i | ||||||
\(83\) | − | 9.89949i | − | 1.08661i | −0.839535 | − | 0.543305i | \(-0.817173\pi\) | ||
0.839535 | − | 0.543305i | \(-0.182827\pi\) | |||||||
\(84\) | 0.803848 | 0.0877070 | ||||||||
\(85\) | −1.46410 | − | 1.79315i | −0.158804 | − | 0.194495i | ||||
\(86\) | −20.6603 | −2.22785 | ||||||||
\(87\) | 3.58630i | 0.384492i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.46410 | 0.685193 | 0.342597 | − | 0.939483i | \(-0.388694\pi\) | ||||
0.342597 | + | 0.939483i | \(0.388694\pi\) | |||||||
\(90\) | −7.46410 | − | 9.14162i | −0.786785 | − | 0.963611i | ||||
\(91\) | −3.80385 | −0.398752 | ||||||||
\(92\) | 10.9348i | 1.14003i | ||||||||
\(93\) | − | 2.72689i | − | 0.282765i | ||||||
\(94\) | 7.92820 | 0.817732 | ||||||||
\(95\) | 10.7321 | − | 8.76268i | 1.10109 | − | 0.899032i | ||||
\(96\) | 3.92820 | 0.400921 | ||||||||
\(97\) | − | 0.656339i | − | 0.0666411i | −0.999445 | − | 0.0333206i | \(-0.989392\pi\) | ||
0.999445 | − | 0.0333206i | \(-0.0106082\pi\) | |||||||
\(98\) | 11.9700i | 1.20916i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.73205 | + | 8.48528i | −0.173205 | + | 0.848528i | ||||
\(101\) | −1.39230 | −0.138540 | −0.0692698 | − | 0.997598i | \(-0.522067\pi\) | ||||
−0.0692698 | + | 0.997598i | \(0.522067\pi\) | |||||||
\(102\) | − | 1.03528i | − | 0.102508i | ||||||
\(103\) | 4.24264i | 0.418040i | 0.977911 | + | 0.209020i | \(0.0670273\pi\) | ||||
−0.977911 | + | 0.209020i | \(0.932973\pi\) | |||||||
\(104\) | −2.19615 | −0.215350 | ||||||||
\(105\) | 0.803848 | − | 0.656339i | 0.0784475 | − | 0.0640521i | ||||
\(106\) | −23.1244 | −2.24604 | ||||||||
\(107\) | 4.38134i | 0.423560i | 0.977317 | + | 0.211780i | \(0.0679261\pi\) | ||||
−0.977317 | + | 0.211780i | \(0.932074\pi\) | |||||||
\(108\) | − | 5.13922i | − | 0.494521i | ||||||
\(109\) | 1.19615 | 0.114571 | 0.0572853 | − | 0.998358i | \(-0.481756\pi\) | ||||
0.0572853 | + | 0.998358i | \(0.481756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.46410 | 0.328798 | ||||||||
\(112\) | − | 4.00240i | − | 0.378192i | ||||||
\(113\) | 2.82843i | 0.266076i | 0.991111 | + | 0.133038i | \(0.0424732\pi\) | ||||
−0.991111 | + | 0.133038i | \(0.957527\pi\) | |||||||
\(114\) | 6.19615 | 0.580323 | ||||||||
\(115\) | 8.92820 | + | 10.9348i | 0.832559 | + | 1.01967i | ||||
\(116\) | −12.0000 | −1.11417 | ||||||||
\(117\) | 11.5911i | 1.07160i | ||||||||
\(118\) | 9.14162i | 0.841554i | ||||||||
\(119\) | −0.928203 | −0.0850883 | ||||||||
\(120\) | 0.464102 | − | 0.378937i | 0.0423665 | − | 0.0345921i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 15.9725i | − | 1.44608i | ||||||
\(123\) | − | 0.896575i | − | 0.0808415i | ||||||
\(124\) | 9.12436 | 0.819391 | ||||||||
\(125\) | 5.19615 | + | 9.89949i | 0.464758 | + | 0.885438i | ||||
\(126\) | −4.73205 | −0.421565 | ||||||||
\(127\) | 3.34607i | 0.296915i | 0.988919 | + | 0.148458i | \(0.0474309\pi\) | ||||
−0.988919 | + | 0.148458i | \(0.952569\pi\) | |||||||
\(128\) | − | 4.10394i | − | 0.362740i | ||||||
\(129\) | −5.53590 | −0.487409 | ||||||||
\(130\) | 14.1962 | − | 11.5911i | 1.24508 | − | 1.01661i | ||||
\(131\) | 21.1244 | 1.84564 | 0.922822 | − | 0.385227i | \(-0.125877\pi\) | ||||
0.922822 | + | 0.385227i | \(0.125877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.55532i | − | 0.481707i | ||||||
\(134\) | −28.8564 | −2.49281 | ||||||||
\(135\) | −4.19615 | − | 5.13922i | −0.361147 | − | 0.442313i | ||||
\(136\) | −0.535898 | −0.0459529 | ||||||||
\(137\) | 13.7632i | 1.17587i | 0.808908 | + | 0.587935i | \(0.200059\pi\) | ||||
−0.808908 | + | 0.587935i | \(0.799941\pi\) | |||||||
\(138\) | 6.31319i | 0.537415i | ||||||||
\(139\) | −16.5885 | −1.40701 | −0.703507 | − | 0.710688i | \(-0.748384\pi\) | ||||
−0.703507 | + | 0.710688i | \(0.748384\pi\) | |||||||
\(140\) | 2.19615 | + | 2.68973i | 0.185609 | + | 0.227323i | ||||
\(141\) | 2.12436 | 0.178903 | ||||||||
\(142\) | 4.24264i | 0.356034i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.1962 | −1.01635 | ||||||||
\(145\) | −12.0000 | + | 9.79796i | −0.996546 | + | 0.813676i | ||||
\(146\) | −9.46410 | −0.783255 | ||||||||
\(147\) | 3.20736i | 0.264539i | ||||||||
\(148\) | 11.5911i | 0.952783i | ||||||||
\(149\) | 13.7321 | 1.12497 | 0.562487 | − | 0.826806i | \(-0.309845\pi\) | ||||
0.562487 | + | 0.826806i | \(0.309845\pi\) | |||||||
\(150\) | −1.00000 | + | 4.89898i | −0.0816497 | + | 0.400000i | ||||
\(151\) | −6.19615 | −0.504236 | −0.252118 | − | 0.967697i | \(-0.581127\pi\) | ||||
−0.252118 | + | 0.967697i | \(0.581127\pi\) | |||||||
\(152\) | − | 3.20736i | − | 0.260152i | ||||||
\(153\) | 2.82843i | 0.228665i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.12436 | − | 7.45001i | 0.732886 | − | 0.598399i | ||||
\(156\) | 3.80385 | 0.304552 | ||||||||
\(157\) | 12.0716i | 0.963417i | 0.876331 | + | 0.481709i | \(0.159984\pi\) | ||||
−0.876331 | + | 0.481709i | \(0.840016\pi\) | |||||||
\(158\) | 10.5558i | 0.839777i | ||||||||
\(159\) | −6.19615 | −0.491387 | ||||||||
\(160\) | 10.7321 | + | 13.1440i | 0.848443 | + | 1.03913i | ||||
\(161\) | 5.66025 | 0.446091 | ||||||||
\(162\) | 12.8666i | 1.01090i | ||||||||
\(163\) | − | 7.58871i | − | 0.594393i | −0.954816 | − | 0.297197i | \(-0.903948\pi\) | ||
0.954816 | − | 0.297197i | \(-0.0960517\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.1244 | 1.48434 | ||||||||
\(167\) | 1.93185i | 0.149491i | 0.997203 | + | 0.0747456i | \(0.0238145\pi\) | ||||
−0.997203 | + | 0.0747456i | \(0.976186\pi\) | |||||||
\(168\) | − | 0.240237i | − | 0.0185347i | ||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 3.46410 | − | 2.82843i | 0.265684 | − | 0.216930i | ||||
\(171\) | −16.9282 | −1.29453 | ||||||||
\(172\) | − | 18.5235i | − | 1.41240i | ||||||
\(173\) | − | 7.62587i | − | 0.579784i | −0.957059 | − | 0.289892i | \(-0.906381\pi\) | ||
0.957059 | − | 0.289892i | \(-0.0936194\pi\) | |||||||
\(174\) | −6.92820 | −0.525226 | ||||||||
\(175\) | 4.39230 | + | 0.896575i | 0.332027 | + | 0.0677747i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.44949i | 0.184115i | ||||||||
\(178\) | 12.4877i | 0.935992i | ||||||||
\(179\) | 8.53590 | 0.638003 | 0.319002 | − | 0.947754i | \(-0.396652\pi\) | ||||
0.319002 | + | 0.947754i | \(0.396652\pi\) | |||||||
\(180\) | 8.19615 | − | 6.69213i | 0.610905 | − | 0.498802i | ||||
\(181\) | 3.39230 | 0.252148 | 0.126074 | − | 0.992021i | \(-0.459762\pi\) | ||||
0.126074 | + | 0.992021i | \(0.459762\pi\) | |||||||
\(182\) | − | 7.34847i | − | 0.544705i | ||||||
\(183\) | − | 4.27981i | − | 0.316372i | ||||||
\(184\) | 3.26795 | 0.240916 | ||||||||
\(185\) | 9.46410 | + | 11.5911i | 0.695815 | + | 0.852195i | ||||
\(186\) | 5.26795 | 0.386265 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.10823i | 0.518421i | ||||||||
\(189\) | −2.66025 | −0.193505 | ||||||||
\(190\) | 16.9282 | + | 20.7327i | 1.22810 | + | 1.50411i | ||||
\(191\) | −10.7321 | −0.776544 | −0.388272 | − | 0.921545i | \(-0.626928\pi\) | ||||
−0.388272 | + | 0.921545i | \(0.626928\pi\) | |||||||
\(192\) | 2.96713i | 0.214134i | ||||||||
\(193\) | 10.2784i | 0.739858i | 0.929060 | + | 0.369929i | \(0.120618\pi\) | ||||
−0.929060 | + | 0.369929i | \(0.879382\pi\) | |||||||
\(194\) | 1.26795 | 0.0910334 | ||||||||
\(195\) | 3.80385 | − | 3.10583i | 0.272399 | − | 0.222413i | ||||
\(196\) | −10.7321 | −0.766575 | ||||||||
\(197\) | − | 2.55103i | − | 0.181753i | −0.995862 | − | 0.0908765i | \(-0.971033\pi\) | ||
0.995862 | − | 0.0908765i | \(-0.0289669\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 2.53590 | + | 0.517638i | 0.179315 | + | 0.0366025i | ||||
\(201\) | −7.73205 | −0.545377 | ||||||||
\(202\) | − | 2.68973i | − | 0.189248i | ||||||
\(203\) | 6.21166i | 0.435973i | ||||||||
\(204\) | 0.928203 | 0.0649872 | ||||||||
\(205\) | 3.00000 | − | 2.44949i | 0.209529 | − | 0.171080i | ||||
\(206\) | −8.19615 | −0.571053 | ||||||||
\(207\) | − | 17.2480i | − | 1.19882i | ||||||
\(208\) | − | 18.9396i | − | 1.31322i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.26795 | + | 1.55291i | 0.0874968 | + | 0.107161i | ||||
\(211\) | 11.1244 | 0.765832 | 0.382916 | − | 0.923783i | \(-0.374920\pi\) | ||||
0.382916 | + | 0.923783i | \(0.374920\pi\) | |||||||
\(212\) | − | 20.7327i | − | 1.42393i | ||||||
\(213\) | 1.13681i | 0.0778931i | ||||||||
\(214\) | −8.46410 | −0.578594 | ||||||||
\(215\) | −15.1244 | − | 18.5235i | −1.03147 | − | 1.26329i | ||||
\(216\) | −1.53590 | −0.104505 | ||||||||
\(217\) | − | 4.72311i | − | 0.320626i | ||||||
\(218\) | 2.31079i | 0.156506i | ||||||||
\(219\) | −2.53590 | −0.171360 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.39230 | −0.295458 | ||||||||
\(222\) | 6.69213i | 0.449146i | ||||||||
\(223\) | − | 5.79555i | − | 0.388099i | −0.980992 | − | 0.194050i | \(-0.937838\pi\) | ||
0.980992 | − | 0.194050i | \(-0.0621623\pi\) | |||||||
\(224\) | 6.80385 | 0.454601 | ||||||||
\(225\) | 2.73205 | − | 13.3843i | 0.182137 | − | 0.892284i | ||||
\(226\) | −5.46410 | −0.363467 | ||||||||
\(227\) | 21.5278i | 1.42885i | 0.699713 | + | 0.714424i | \(0.253311\pi\) | ||||
−0.699713 | + | 0.714424i | \(0.746689\pi\) | |||||||
\(228\) | 5.55532i | 0.367910i | ||||||||
\(229\) | 17.9282 | 1.18473 | 0.592365 | − | 0.805670i | \(-0.298195\pi\) | ||||
0.592365 | + | 0.805670i | \(0.298195\pi\) | |||||||
\(230\) | −21.1244 | + | 17.2480i | −1.39290 | + | 1.13730i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.58630i | 0.235452i | ||||||||
\(233\) | − | 13.0053i | − | 0.852007i | −0.904721 | − | 0.426004i | \(-0.859921\pi\) | ||
0.904721 | − | 0.426004i | \(-0.140079\pi\) | |||||||
\(234\) | −22.3923 | −1.46383 | ||||||||
\(235\) | 5.80385 | + | 7.10823i | 0.378601 | + | 0.463690i | ||||
\(236\) | −8.19615 | −0.533524 | ||||||||
\(237\) | 2.82843i | 0.183726i | ||||||||
\(238\) | − | 1.79315i | − | 0.116233i | ||||||
\(239\) | 11.6603 | 0.754239 | 0.377120 | − | 0.926165i | \(-0.376915\pi\) | ||||
0.377120 | + | 0.926165i | \(0.376915\pi\) | |||||||
\(240\) | 3.26795 | + | 4.00240i | 0.210945 | + | 0.258354i | ||||
\(241\) | −10.1244 | −0.652167 | −0.326084 | − | 0.945341i | \(-0.605729\pi\) | ||||
−0.326084 | + | 0.945341i | \(0.605729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3490i | 0.792188i | ||||||||
\(244\) | 14.3205 | 0.916777 | ||||||||
\(245\) | −10.7321 | + | 8.76268i | −0.685646 | + | 0.559827i | ||||
\(246\) | 1.73205 | 0.110432 | ||||||||
\(247\) | − | 26.2880i | − | 1.67267i | ||||||
\(248\) | − | 2.72689i | − | 0.173158i | ||||||
\(249\) | 5.12436 | 0.324743 | ||||||||
\(250\) | −19.1244 | + | 10.0382i | −1.20953 | + | 0.634871i | ||||
\(251\) | −14.1962 | −0.896053 | −0.448027 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448027 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(252\) | − | 4.24264i | − | 0.267261i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.46410 | −0.405594 | ||||||||
\(255\) | 0.928203 | − | 0.757875i | 0.0581263 | − | 0.0474600i | ||||
\(256\) | 19.3923 | 1.21202 | ||||||||
\(257\) | − | 5.00052i | − | 0.311924i | −0.987763 | − | 0.155962i | \(-0.950152\pi\) | ||
0.987763 | − | 0.155962i | \(-0.0498477\pi\) | |||||||
\(258\) | − | 10.6945i | − | 0.665813i | ||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 10.3923 | + | 12.7279i | 0.644503 | + | 0.789352i | ||||
\(261\) | 18.9282 | 1.17163 | ||||||||
\(262\) | 40.8091i | 2.52120i | ||||||||
\(263\) | − | 21.4906i | − | 1.32517i | −0.748988 | − | 0.662584i | \(-0.769460\pi\) | ||
0.748988 | − | 0.662584i | \(-0.230540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.9282 | − | 20.7327i | −1.03989 | − | 1.27360i | ||||
\(266\) | 10.7321 | 0.658024 | ||||||||
\(267\) | 3.34607i | 0.204776i | ||||||||
\(268\) | − | 25.8719i | − | 1.58038i | ||||||
\(269\) | 19.7321 | 1.20308 | 0.601542 | − | 0.798841i | \(-0.294553\pi\) | ||||
0.601542 | + | 0.798841i | \(0.294553\pi\) | |||||||
\(270\) | 9.92820 | − | 8.10634i | 0.604211 | − | 0.493336i | ||||
\(271\) | 4.53590 | 0.275536 | 0.137768 | − | 0.990465i | \(-0.456007\pi\) | ||||
0.137768 | + | 0.990465i | \(0.456007\pi\) | |||||||
\(272\) | − | 4.62158i | − | 0.280224i | ||||||
\(273\) | − | 1.96902i | − | 0.119170i | ||||||
\(274\) | −26.5885 | −1.60627 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.66025 | −0.340707 | ||||||||
\(277\) | − | 22.7017i | − | 1.36402i | −0.731345 | − | 0.682008i | \(-0.761107\pi\) | ||
0.731345 | − | 0.682008i | \(-0.238893\pi\) | |||||||
\(278\) | − | 32.0464i | − | 1.92202i | ||||||
\(279\) | −14.3923 | −0.861645 | ||||||||
\(280\) | 0.803848 | − | 0.656339i | 0.0480391 | − | 0.0392237i | ||||
\(281\) | 17.3205 | 1.03325 | 0.516627 | − | 0.856210i | \(-0.327187\pi\) | ||||
0.516627 | + | 0.856210i | \(0.327187\pi\) | |||||||
\(282\) | 4.10394i | 0.244386i | ||||||||
\(283\) | − | 30.1146i | − | 1.79013i | −0.445939 | − | 0.895063i | \(-0.647130\pi\) | ||
0.445939 | − | 0.895063i | \(-0.352870\pi\) | |||||||
\(284\) | −3.80385 | −0.225717 | ||||||||
\(285\) | 4.53590 | + | 5.55532i | 0.268683 | + | 0.329069i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.55291i | − | 0.0916656i | ||||||
\(288\) | − | 20.7327i | − | 1.22169i | ||||||
\(289\) | 15.9282 | 0.936953 | ||||||||
\(290\) | −18.9282 | − | 23.1822i | −1.11150 | − | 1.36131i | ||||
\(291\) | 0.339746 | 0.0199163 | ||||||||
\(292\) | − | 8.48528i | − | 0.496564i | ||||||
\(293\) | − | 9.41902i | − | 0.550265i | −0.961406 | − | 0.275133i | \(-0.911278\pi\) | ||
0.961406 | − | 0.275133i | \(-0.0887217\pi\) | |||||||
\(294\) | −6.19615 | −0.361367 | ||||||||
\(295\) | −8.19615 | + | 6.69213i | −0.477198 | + | 0.389631i | ||||
\(296\) | 3.46410 | 0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.5283i | 1.53674i | ||||||||
\(299\) | 26.7846 | 1.54899 | ||||||||
\(300\) | −4.39230 | − | 0.896575i | −0.253590 | − | 0.0517638i | ||||
\(301\) | −9.58846 | −0.552669 | ||||||||
\(302\) | − | 11.9700i | − | 0.688799i | ||||||
\(303\) | − | 0.720710i | − | 0.0414037i | ||||||
\(304\) | 27.6603 | 1.58642 | ||||||||
\(305\) | 14.3205 | − | 11.6926i | 0.819990 | − | 0.669519i | ||||
\(306\) | −5.46410 | −0.312362 | ||||||||
\(307\) | 17.6269i | 1.00602i | 0.864280 | + | 0.503010i | \(0.167774\pi\) | ||||
−0.864280 | + | 0.503010i | \(0.832226\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.19615 | −0.124935 | ||||||||
\(310\) | 14.3923 | + | 17.6269i | 0.817428 | + | 1.00114i | ||||
\(311\) | −28.0526 | −1.59071 | −0.795357 | − | 0.606141i | \(-0.792717\pi\) | ||||
−0.795357 | + | 0.606141i | \(0.792717\pi\) | |||||||
\(312\) | − | 1.13681i | − | 0.0643593i | ||||||
\(313\) | 17.1464i | 0.969173i | 0.874743 | + | 0.484587i | \(0.161030\pi\) | ||||
−0.874743 | + | 0.484587i | \(0.838970\pi\) | |||||||
\(314\) | −23.3205 | −1.31605 | ||||||||
\(315\) | −3.46410 | − | 4.24264i | −0.195180 | − | 0.239046i | ||||
\(316\) | −9.46410 | −0.532397 | ||||||||
\(317\) | − | 6.96953i | − | 0.391448i | −0.980659 | − | 0.195724i | \(-0.937294\pi\) | ||
0.980659 | − | 0.195724i | \(-0.0627057\pi\) | |||||||
\(318\) | − | 11.9700i | − | 0.671247i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −9.92820 | + | 8.10634i | −0.555003 | + | 0.453158i | ||||
\(321\) | −2.26795 | −0.126585 | ||||||||
\(322\) | 10.9348i | 0.609371i | ||||||||
\(323\) | − | 6.41473i | − | 0.356925i | ||||||
\(324\) | −11.5359 | −0.640883 | ||||||||
\(325\) | 20.7846 | + | 4.24264i | 1.15292 | + | 0.235339i | ||||
\(326\) | 14.6603 | 0.811956 | ||||||||
\(327\) | 0.619174i | 0.0342404i | ||||||||
\(328\) | − | 0.896575i | − | 0.0495051i | ||||||
\(329\) | 3.67949 | 0.202857 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.80385 | −0.428938 | −0.214469 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214469 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(332\) | 17.1464i | 0.941033i | ||||||||
\(333\) | − | 18.2832i | − | 1.00192i | ||||||
\(334\) | −3.73205 | −0.204209 | ||||||||
\(335\) | −21.1244 | − | 25.8719i | −1.15415 | − | 1.41354i | ||||
\(336\) | 2.07180 | 0.113026 | ||||||||
\(337\) | 7.82894i | 0.426470i | 0.977001 | + | 0.213235i | \(0.0683999\pi\) | ||||
−0.977001 | + | 0.213235i | \(0.931600\pi\) | |||||||
\(338\) | − | 9.65926i | − | 0.525394i | ||||||
\(339\) | −1.46410 | −0.0795191 | ||||||||
\(340\) | 2.53590 | + | 3.10583i | 0.137528 | + | 0.168437i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 32.7028i | − | 1.76836i | ||||||
\(343\) | 11.8313i | 0.638833i | ||||||||
\(344\) | −5.53590 | −0.298476 | ||||||||
\(345\) | −5.66025 | + | 4.62158i | −0.304738 | + | 0.248817i | ||||
\(346\) | 14.7321 | 0.792000 | ||||||||
\(347\) | − | 2.96713i | − | 0.159284i | −0.996824 | − | 0.0796419i | \(-0.974622\pi\) | ||
0.996824 | − | 0.0796419i | \(-0.0253777\pi\) | |||||||
\(348\) | − | 6.21166i | − | 0.332980i | ||||||
\(349\) | −27.3205 | −1.46243 | −0.731217 | − | 0.682145i | \(-0.761047\pi\) | ||||
−0.731217 | + | 0.682145i | \(0.761047\pi\) | |||||||
\(350\) | −1.73205 | + | 8.48528i | −0.0925820 | + | 0.453557i | ||||
\(351\) | −12.5885 | −0.671922 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.69161i | 0.0900356i | 0.998986 | + | 0.0450178i | \(0.0143345\pi\) | ||||
−0.998986 | + | 0.0450178i | \(0.985666\pi\) | |||||||
\(354\) | −4.73205 | −0.251506 | ||||||||
\(355\) | −3.80385 | + | 3.10583i | −0.201887 | + | 0.164840i | ||||
\(356\) | −11.1962 | −0.593395 | ||||||||
\(357\) | − | 0.480473i | − | 0.0254293i | ||||||
\(358\) | 16.4901i | 0.871528i | ||||||||
\(359\) | −18.3397 | −0.967935 | −0.483967 | − | 0.875086i | \(-0.660805\pi\) | ||||
−0.483967 | + | 0.875086i | \(0.660805\pi\) | |||||||
\(360\) | −2.00000 | − | 2.44949i | −0.105409 | − | 0.129099i | ||||
\(361\) | 19.3923 | 1.02065 | ||||||||
\(362\) | 6.55343i | 0.344441i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.58846 | 0.345329 | ||||||||
\(365\) | −6.92820 | − | 8.48528i | −0.362639 | − | 0.444140i | ||||
\(366\) | 8.26795 | 0.432173 | ||||||||
\(367\) | − | 29.6341i | − | 1.54689i | −0.633865 | − | 0.773444i | \(-0.718532\pi\) | ||
0.633865 | − | 0.773444i | \(-0.281468\pi\) | |||||||
\(368\) | 28.1827i | 1.46913i | ||||||||
\(369\) | −4.73205 | −0.246341 | ||||||||
\(370\) | −22.3923 | + | 18.2832i | −1.16412 | + | 0.950500i | ||||
\(371\) | −10.7321 | −0.557180 | ||||||||
\(372\) | 4.72311i | 0.244882i | ||||||||
\(373\) | − | 34.1170i | − | 1.76651i | −0.468892 | − | 0.883255i | \(-0.655347\pi\) | ||
0.468892 | − | 0.883255i | \(-0.344653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.12436 | + | 2.68973i | −0.264621 | + | 0.138897i | ||||
\(376\) | 2.12436 | 0.109555 | ||||||||
\(377\) | 29.3939i | 1.51386i | ||||||||
\(378\) | − | 5.13922i | − | 0.264333i | ||||||
\(379\) | 5.46410 | 0.280672 | 0.140336 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140336 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(380\) | −18.5885 | + | 15.1774i | −0.953568 | + | 0.778585i | ||||
\(381\) | −1.73205 | −0.0887357 | ||||||||
\(382\) | − | 20.7327i | − | 1.06078i | ||||||
\(383\) | − | 23.7642i | − | 1.21430i | −0.794589 | − | 0.607148i | \(-0.792314\pi\) | ||
0.794589 | − | 0.607148i | \(-0.207686\pi\) | |||||||
\(384\) | 2.12436 | 0.108408 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.8564 | −1.01066 | ||||||||
\(387\) | 29.2180i | 1.48523i | ||||||||
\(388\) | 1.13681i | 0.0577129i | ||||||||
\(389\) | 18.1244 | 0.918941 | 0.459471 | − | 0.888193i | \(-0.348039\pi\) | ||||
0.459471 | + | 0.888193i | \(0.348039\pi\) | |||||||
\(390\) | 6.00000 | + | 7.34847i | 0.303822 | + | 0.372104i | ||||
\(391\) | 6.53590 | 0.330535 | ||||||||
\(392\) | 3.20736i | 0.161996i | ||||||||
\(393\) | 10.9348i | 0.551586i | ||||||||
\(394\) | 4.92820 | 0.248279 | ||||||||
\(395\) | −9.46410 | + | 7.72741i | −0.476191 | + | 0.388808i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.0096i | 0.803500i | 0.915749 | + | 0.401750i | \(0.131598\pi\) | ||||
−0.915749 | + | 0.401750i | \(0.868402\pi\) | |||||||
\(398\) | 3.86370i | 0.193670i | ||||||||
\(399\) | 2.87564 | 0.143962 | ||||||||
\(400\) | −4.46410 | + | 21.8695i | −0.223205 | + | 1.09348i | ||||
\(401\) | −32.3205 | −1.61401 | −0.807005 | − | 0.590545i | \(-0.798913\pi\) | ||||
−0.807005 | + | 0.590545i | \(0.798913\pi\) | |||||||
\(402\) | − | 14.9372i | − | 0.744999i | ||||||
\(403\) | − | 22.3500i | − | 1.11333i | ||||||
\(404\) | 2.41154 | 0.119979 | ||||||||
\(405\) | −11.5359 | + | 9.41902i | −0.573223 | + | 0.468035i | ||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 0.277401i | − | 0.0137334i | ||||||
\(409\) | 1.87564 | 0.0927446 | 0.0463723 | − | 0.998924i | \(-0.485234\pi\) | ||||
0.0463723 | + | 0.998924i | \(0.485234\pi\) | |||||||
\(410\) | 4.73205 | + | 5.79555i | 0.233699 | + | 0.286222i | ||||
\(411\) | −7.12436 | −0.351419 | ||||||||
\(412\) | − | 7.34847i | − | 0.362033i | ||||||
\(413\) | 4.24264i | 0.208767i | ||||||||
\(414\) | 33.3205 | 1.63761 | ||||||||
\(415\) | 14.0000 | + | 17.1464i | 0.687233 | + | 0.841685i | ||||
\(416\) | 32.1962 | 1.57855 | ||||||||
\(417\) | − | 8.58682i | − | 0.420498i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.6603 | 1.44900 | 0.724499 | − | 0.689276i | \(-0.242071\pi\) | ||||
0.724499 | + | 0.689276i | \(0.242071\pi\) | |||||||
\(420\) | −1.39230 | + | 1.13681i | −0.0679375 | + | 0.0554708i | ||||
\(421\) | 21.0526 | 1.02604 | 0.513019 | − | 0.858377i | \(-0.328527\pi\) | ||||
0.513019 | + | 0.858377i | \(0.328527\pi\) | |||||||
\(422\) | 21.4906i | 1.04615i | ||||||||
\(423\) | − | 11.2122i | − | 0.545154i | ||||||
\(424\) | −6.19615 | −0.300912 | ||||||||
\(425\) | 5.07180 | + | 1.03528i | 0.246018 | + | 0.0502183i | ||||
\(426\) | −2.19615 | −0.106404 | ||||||||
\(427\) | − | 7.41284i | − | 0.358732i | ||||||
\(428\) | − | 7.58871i | − | 0.366814i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 35.7846 | − | 29.2180i | 1.72569 | − | 1.40902i | ||||
\(431\) | −18.9282 | −0.911739 | −0.455870 | − | 0.890047i | \(-0.650672\pi\) | ||||
−0.455870 | + | 0.890047i | \(0.650672\pi\) | |||||||
\(432\) | − | 13.2456i | − | 0.637277i | ||||||
\(433\) | 20.2523i | 0.973261i | 0.873608 | + | 0.486631i | \(0.161774\pi\) | ||||
−0.873608 | + | 0.486631i | \(0.838226\pi\) | |||||||
\(434\) | 9.12436 | 0.437983 | ||||||||
\(435\) | −5.07180 | − | 6.21166i | −0.243174 | − | 0.297826i | ||||
\(436\) | −2.07180 | −0.0992211 | ||||||||
\(437\) | 39.1175i | 1.87124i | ||||||||
\(438\) | − | 4.89898i | − | 0.234082i | ||||||
\(439\) | 20.2487 | 0.966418 | 0.483209 | − | 0.875505i | \(-0.339471\pi\) | ||||
0.483209 | + | 0.875505i | \(0.339471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.9282 | 0.806105 | ||||||||
\(442\) | − | 8.48528i | − | 0.403604i | ||||||
\(443\) | − | 9.17878i | − | 0.436097i | −0.975938 | − | 0.218049i | \(-0.930031\pi\) | ||
0.975938 | − | 0.218049i | \(-0.0699691\pi\) | |||||||
\(444\) | −6.00000 | −0.284747 | ||||||||
\(445\) | −11.1962 | + | 9.14162i | −0.530749 | + | 0.433354i | ||||
\(446\) | 11.1962 | 0.530153 | ||||||||
\(447\) | 7.10823i | 0.336208i | ||||||||
\(448\) | 5.13922i | 0.242805i | ||||||||
\(449\) | 10.5167 | 0.496312 | 0.248156 | − | 0.968720i | \(-0.420175\pi\) | ||||
0.248156 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(450\) | 25.8564 | + | 5.27792i | 1.21888 | + | 0.248803i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 4.89898i | − | 0.230429i | ||||||
\(453\) | − | 3.20736i | − | 0.150695i | ||||||
\(454\) | −41.5885 | −1.95184 | ||||||||
\(455\) | 6.58846 | − | 5.37945i | 0.308872 | − | 0.252193i | ||||
\(456\) | 1.66025 | 0.0777485 | ||||||||
\(457\) | 21.2132i | 0.992312i | 0.868233 | + | 0.496156i | \(0.165256\pi\) | ||||
−0.868233 | + | 0.496156i | \(0.834744\pi\) | |||||||
\(458\) | 34.6346i | 1.61837i | ||||||||
\(459\) | −3.07180 | −0.143379 | ||||||||
\(460\) | −15.4641 | − | 18.9396i | −0.721017 | − | 0.883062i | ||||
\(461\) | −33.0000 | −1.53696 | −0.768482 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768482 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.8671i | − | 0.830356i | −0.909740 | − | 0.415178i | \(-0.863719\pi\) | ||
0.909740 | − | 0.415178i | \(-0.136281\pi\) | |||||||
\(464\) | −30.9282 | −1.43581 | ||||||||
\(465\) | 3.85641 | + | 4.72311i | 0.178837 | + | 0.219029i | ||||
\(466\) | 25.1244 | 1.16386 | ||||||||
\(467\) | 17.7656i | 0.822094i | 0.911614 | + | 0.411047i | \(0.134837\pi\) | ||||
−0.911614 | + | 0.411047i | \(0.865163\pi\) | |||||||
\(468\) | − | 20.0764i | − | 0.928032i | ||||||
\(469\) | −13.3923 | −0.618399 | ||||||||
\(470\) | −13.7321 | + | 11.2122i | −0.633412 | + | 0.517179i | ||||
\(471\) | −6.24871 | −0.287925 | ||||||||
\(472\) | 2.44949i | 0.112747i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.46410 | −0.250974 | ||||||||
\(475\) | −6.19615 | + | 30.3548i | −0.284299 | + | 1.39277i | ||||
\(476\) | 1.60770 | 0.0736886 | ||||||||
\(477\) | 32.7028i | 1.49736i | ||||||||
\(478\) | 22.5259i | 1.03031i | ||||||||
\(479\) | −9.46410 | −0.432426 | −0.216213 | − | 0.976346i | \(-0.569371\pi\) | ||||
−0.216213 | + | 0.976346i | \(0.569371\pi\) | |||||||
\(480\) | −6.80385 | + | 5.55532i | −0.310552 | + | 0.253564i | ||||
\(481\) | 28.3923 | 1.29458 | ||||||||
\(482\) | − | 19.5588i | − | 0.890877i | ||||||
\(483\) | 2.92996i | 0.133318i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.928203 | + | 1.13681i | 0.0421475 | + | 0.0516200i | ||||
\(486\) | −23.8564 | −1.08215 | ||||||||
\(487\) | − | 12.7279i | − | 0.576757i | −0.957516 | − | 0.288379i | \(-0.906884\pi\) | ||
0.957516 | − | 0.288379i | \(-0.0931162\pi\) | |||||||
\(488\) | − | 4.27981i | − | 0.193738i | ||||||
\(489\) | 3.92820 | 0.177639 | ||||||||
\(490\) | −16.9282 | − | 20.7327i | −0.764738 | − | 0.936609i | ||||
\(491\) | −15.7128 | −0.709109 | −0.354555 | − | 0.935035i | \(-0.615368\pi\) | ||||
−0.354555 | + | 0.935035i | \(0.615368\pi\) | |||||||
\(492\) | 1.55291i | 0.0700108i | ||||||||
\(493\) | 7.17260i | 0.323038i | ||||||||
\(494\) | 50.7846 | 2.28491 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.5167 | 1.05593 | ||||||||
\(497\) | 1.96902i | 0.0883225i | ||||||||
\(498\) | 9.89949i | 0.443607i | ||||||||
\(499\) | −38.3923 | −1.71868 | −0.859338 | − | 0.511408i | \(-0.829124\pi\) | ||||
−0.859338 | + | 0.511408i | \(0.829124\pi\) | |||||||
\(500\) | −9.00000 | − | 17.1464i | −0.402492 | − | 0.766812i | ||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | − | 27.4249i | − | 1.22403i | ||||||
\(503\) | 34.2557i | 1.52739i | 0.645580 | + | 0.763693i | \(0.276616\pi\) | ||||
−0.645580 | + | 0.763693i | \(0.723384\pi\) | |||||||
\(504\) | −1.26795 | −0.0564789 | ||||||||
\(505\) | 2.41154 | − | 1.96902i | 0.107312 | − | 0.0876201i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 2.58819i | − | 0.114946i | ||||||
\(508\) | − | 5.79555i | − | 0.257136i | ||||||
\(509\) | 21.9282 | 0.971951 | 0.485975 | − | 0.873973i | \(-0.338465\pi\) | ||||
0.485975 | + | 0.873973i | \(0.338465\pi\) | |||||||
\(510\) | 1.46410 | + | 1.79315i | 0.0648315 | + | 0.0794021i | ||||
\(511\) | −4.39230 | −0.194304 | ||||||||
\(512\) | 29.2552i | 1.29291i | ||||||||
\(513\) | − | 18.3848i | − | 0.811708i | ||||||
\(514\) | 9.66025 | 0.426096 | ||||||||
\(515\) | −6.00000 | − | 7.34847i | −0.264392 | − | 0.323812i | ||||
\(516\) | 9.58846 | 0.422108 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.5911i | 0.509284i | ||||||||
\(519\) | 3.94744 | 0.173273 | ||||||||
\(520\) | 3.80385 | − | 3.10583i | 0.166810 | − | 0.136200i | ||||
\(521\) | 39.2487 | 1.71952 | 0.859759 | − | 0.510701i | \(-0.170614\pi\) | ||||
0.859759 | + | 0.510701i | \(0.170614\pi\) | |||||||
\(522\) | 36.5665i | 1.60047i | ||||||||
\(523\) | − | 8.66115i | − | 0.378726i | −0.981907 | − | 0.189363i | \(-0.939358\pi\) | ||
0.981907 | − | 0.189363i | \(-0.0606422\pi\) | |||||||
\(524\) | −36.5885 | −1.59837 | ||||||||
\(525\) | −0.464102 | + | 2.27362i | −0.0202551 | + | 0.0992291i | ||||
\(526\) | 41.5167 | 1.81021 | ||||||||
\(527\) | − | 5.45378i | − | 0.237570i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8564 | −0.732887 | ||||||||
\(530\) | 40.0526 | − | 32.7028i | 1.73977 | − | 1.42052i | ||||
\(531\) | 12.9282 | 0.561036 | ||||||||
\(532\) | 9.62209i | 0.417171i | ||||||||
\(533\) | − | 7.34847i | − | 0.318298i | ||||||
\(534\) | −6.46410 | −0.279729 | ||||||||
\(535\) | −6.19615 | − | 7.58871i | −0.267883 | − | 0.328088i | ||||
\(536\) | −7.73205 | −0.333974 | ||||||||
\(537\) | 4.41851i | 0.190673i | ||||||||
\(538\) | 38.1194i | 1.64344i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.26795 | + | 8.90138i | 0.312763 | + | 0.383055i | ||||
\(541\) | −23.3923 | −1.00571 | −0.502857 | − | 0.864370i | \(-0.667718\pi\) | ||||
−0.502857 | + | 0.864370i | \(0.667718\pi\) | |||||||
\(542\) | 8.76268i | 0.376389i | ||||||||
\(543\) | 1.75599i | 0.0753566i | ||||||||
\(544\) | 7.85641 | 0.336841 | ||||||||
\(545\) | −2.07180 | + | 1.69161i | −0.0887460 | + | 0.0724608i | ||||
\(546\) | 3.80385 | 0.162790 | ||||||||
\(547\) | − | 20.2523i | − | 0.865924i | −0.901412 | − | 0.432962i | \(-0.857468\pi\) | ||
0.901412 | − | 0.432962i | \(-0.142532\pi\) | |||||||
\(548\) | − | 23.8386i | − | 1.01833i | ||||||
\(549\) | −22.5885 | −0.964052 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.9282 | −1.82880 | ||||||||
\(552\) | 1.69161i | 0.0719999i | ||||||||
\(553\) | 4.89898i | 0.208326i | ||||||||
\(554\) | 43.8564 | 1.86328 | ||||||||
\(555\) | −6.00000 | + | 4.89898i | −0.254686 | + | 0.207950i | ||||
\(556\) | 28.7321 | 1.21851 | ||||||||
\(557\) | − | 6.48906i | − | 0.274950i | −0.990505 | − | 0.137475i | \(-0.956101\pi\) | ||
0.990505 | − | 0.137475i | \(-0.0438987\pi\) | |||||||
\(558\) | − | 27.8038i | − | 1.17703i | ||||||
\(559\) | −45.3731 | −1.91908 | ||||||||
\(560\) | 5.66025 | + | 6.93237i | 0.239189 | + | 0.292946i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.4607i | 1.41145i | ||||||||
\(563\) | − | 6.07296i | − | 0.255945i | −0.991778 | − | 0.127972i | \(-0.959153\pi\) | ||
0.991778 | − | 0.127972i | \(-0.0408469\pi\) | |||||||
\(564\) | −3.67949 | −0.154935 | ||||||||
\(565\) | −4.00000 | − | 4.89898i | −0.168281 | − | 0.206102i | ||||
\(566\) | 58.1769 | 2.44536 | ||||||||
\(567\) | 5.97142i | 0.250776i | ||||||||
\(568\) | 1.13681i | 0.0476996i | ||||||||
\(569\) | −5.87564 | −0.246320 | −0.123160 | − | 0.992387i | \(-0.539303\pi\) | ||||
−0.123160 | + | 0.992387i | \(0.539303\pi\) | |||||||
\(570\) | −10.7321 | + | 8.76268i | −0.449516 | + | 0.367028i | ||||
\(571\) | 35.7128 | 1.49453 | 0.747267 | − | 0.664524i | \(-0.231365\pi\) | ||||
0.747267 | + | 0.664524i | \(0.231365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.55532i | − | 0.232077i | ||||||
\(574\) | 3.00000 | 0.125218 | ||||||||
\(575\) | −30.9282 | − | 6.31319i | −1.28980 | − | 0.263278i | ||||
\(576\) | 15.6603 | 0.652511 | ||||||||
\(577\) | − | 20.7327i | − | 0.863115i | −0.902085 | − | 0.431557i | \(-0.857964\pi\) | ||
0.902085 | − | 0.431557i | \(-0.142036\pi\) | |||||||
\(578\) | 30.7709i | 1.27990i | ||||||||
\(579\) | −5.32051 | −0.221113 | ||||||||
\(580\) | 20.7846 | − | 16.9706i | 0.863034 | − | 0.704664i | ||||
\(581\) | 8.87564 | 0.368224 | ||||||||
\(582\) | 0.656339i | 0.0272061i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.53590 | −0.104936 | ||||||||
\(585\) | −16.3923 | − | 20.0764i | −0.677738 | − | 0.830057i | ||||
\(586\) | 18.1962 | 0.751676 | ||||||||
\(587\) | − | 35.9473i | − | 1.48370i | −0.670564 | − | 0.741852i | \(-0.733948\pi\) | ||
0.670564 | − | 0.741852i | \(-0.266052\pi\) | |||||||
\(588\) | − | 5.55532i | − | 0.229097i | ||||||
\(589\) | 32.6410 | 1.34495 | ||||||||
\(590\) | −12.9282 | − | 15.8338i | −0.532246 | − | 0.651865i | ||||
\(591\) | 1.32051 | 0.0543184 | ||||||||
\(592\) | 29.8744i | 1.22783i | ||||||||
\(593\) | 30.2533i | 1.24235i | 0.783670 | + | 0.621177i | \(0.213345\pi\) | ||||
−0.783670 | + | 0.621177i | \(0.786655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.60770 | − | 1.31268i | 0.0659091 | − | 0.0538145i | ||||
\(596\) | −23.7846 | −0.974256 | ||||||||
\(597\) | 1.03528i | 0.0423710i | ||||||||
\(598\) | 51.7439i | 2.11597i | ||||||||
\(599\) | −20.4449 | −0.835354 | −0.417677 | − | 0.908595i | \(-0.637156\pi\) | ||||
−0.417677 | + | 0.908595i | \(0.637156\pi\) | |||||||
\(600\) | −0.267949 | + | 1.31268i | −0.0109390 | + | 0.0535898i | ||||
\(601\) | 20.0000 | 0.815817 | 0.407909 | − | 0.913023i | \(-0.366258\pi\) | ||||
0.407909 | + | 0.913023i | \(0.366258\pi\) | |||||||
\(602\) | − | 18.5235i | − | 0.754961i | ||||||
\(603\) | 40.8091i | 1.66188i | ||||||||
\(604\) | 10.7321 | 0.436681 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.39230 | 0.0565585 | ||||||||
\(607\) | − | 31.4916i | − | 1.27821i | −0.769121 | − | 0.639103i | \(-0.779306\pi\) | ||
0.769121 | − | 0.639103i | \(-0.220694\pi\) | |||||||
\(608\) | 47.0208i | 1.90694i | ||||||||
\(609\) | −3.21539 | −0.130294 | ||||||||
\(610\) | 22.5885 | + | 27.6651i | 0.914580 | + | 1.12013i | ||||
\(611\) | 17.4115 | 0.704396 | ||||||||
\(612\) | − | 4.89898i | − | 0.198030i | ||||||
\(613\) | 6.69213i | 0.270293i | 0.990826 | + | 0.135146i | \(0.0431504\pi\) | ||||
−0.990826 | + | 0.135146i | \(0.956850\pi\) | |||||||
\(614\) | −34.0526 | −1.37425 | ||||||||
\(615\) | 1.26795 | + | 1.55291i | 0.0511286 | + | 0.0626195i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.69161i | 0.0681019i | 0.999420 | + | 0.0340509i | \(0.0108408\pi\) | ||||
−0.999420 | + | 0.0340509i | \(0.989159\pi\) | |||||||
\(618\) | − | 4.24264i | − | 0.170664i | ||||||
\(619\) | 28.7846 | 1.15695 | 0.578476 | − | 0.815700i | \(-0.303648\pi\) | ||||
0.578476 | + | 0.815700i | \(0.303648\pi\) | |||||||
\(620\) | −15.8038 | + | 12.9038i | −0.634698 | + | 0.518229i | ||||
\(621\) | 18.7321 | 0.751691 | ||||||||
\(622\) | − | 54.1934i | − | 2.17296i | ||||||
\(623\) | 5.79555i | 0.232194i | ||||||||
\(624\) | 9.80385 | 0.392468 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | −33.1244 | −1.32392 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 20.9086i | − | 0.834344i | ||||||
\(629\) | 6.92820 | 0.276246 | ||||||||
\(630\) | 8.19615 | − | 6.69213i | 0.326543 | − | 0.266621i | ||||
\(631\) | 19.3205 | 0.769137 | 0.384569 | − | 0.923096i | \(-0.374350\pi\) | ||||
0.384569 | + | 0.923096i | \(0.374350\pi\) | |||||||
\(632\) | 2.82843i | 0.112509i | ||||||||
\(633\) | 5.75839i | 0.228875i | ||||||||
\(634\) | 13.4641 | 0.534728 | ||||||||
\(635\) | −4.73205 | − | 5.79555i | −0.187786 | − | 0.229990i | ||||
\(636\) | 10.7321 | 0.425553 | ||||||||
\(637\) | 26.2880i | 1.04157i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 5.80385 | + | 7.10823i | 0.229417 | + | 0.280978i | ||||
\(641\) | 19.8564 | 0.784281 | 0.392140 | − | 0.919905i | \(-0.371735\pi\) | ||||
0.392140 | + | 0.919905i | \(0.371735\pi\) | |||||||
\(642\) | − | 4.38134i | − | 0.172918i | ||||||
\(643\) | − | 27.6651i | − | 1.09100i | −0.838109 | − | 0.545502i | \(-0.816339\pi\) | ||
0.838109 | − | 0.545502i | \(-0.183661\pi\) | |||||||
\(644\) | −9.80385 | −0.386326 | ||||||||
\(645\) | 9.58846 | − | 7.82894i | 0.377545 | − | 0.308264i | ||||
\(646\) | 12.3923 | 0.487569 | ||||||||
\(647\) | − | 18.9767i | − | 0.746053i | −0.927821 | − | 0.373026i | \(-0.878320\pi\) | ||
0.927821 | − | 0.373026i | \(-0.121680\pi\) | |||||||
\(648\) | 3.44760i | 0.135435i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −8.19615 | + | 40.1528i | −0.321480 | + | 1.57492i | ||||
\(651\) | 2.44486 | 0.0958218 | ||||||||
\(652\) | 13.1440i | 0.514760i | ||||||||
\(653\) | − | 31.9449i | − | 1.25010i | −0.780584 | − | 0.625050i | \(-0.785078\pi\) | ||
0.780584 | − | 0.625050i | \(-0.214922\pi\) | |||||||
\(654\) | −1.19615 | −0.0467733 | ||||||||
\(655\) | −36.5885 | + | 29.8744i | −1.42963 | + | 1.16729i | ||||
\(656\) | 7.73205 | 0.301886 | ||||||||
\(657\) | 13.3843i | 0.522170i | ||||||||
\(658\) | 7.10823i | 0.277108i | ||||||||
\(659\) | −11.3205 | −0.440984 | −0.220492 | − | 0.975389i | \(-0.570766\pi\) | ||||
−0.220492 | + | 0.975389i | \(0.570766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.58846 | −0.0617838 | −0.0308919 | − | 0.999523i | \(-0.509835\pi\) | ||||
−0.0308919 | + | 0.999523i | \(0.509835\pi\) | |||||||
\(662\) | − | 15.0759i | − | 0.585941i | ||||||
\(663\) | − | 2.27362i | − | 0.0883003i | ||||||
\(664\) | 5.12436 | 0.198864 | ||||||||
\(665\) | 7.85641 | + | 9.62209i | 0.304658 | + | 0.373129i | ||||
\(666\) | 35.3205 | 1.36864 | ||||||||
\(667\) | − | 43.7391i | − | 1.69358i | ||||||
\(668\) | − | 3.34607i | − | 0.129463i | ||||||
\(669\) | 3.00000 | 0.115987 | ||||||||
\(670\) | 49.9808 | − | 40.8091i | 1.93093 | − | 1.57659i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.52193i | 0.135861i | ||||||||
\(673\) | − | 1.61729i | − | 0.0623418i | −0.999514 | − | 0.0311709i | \(-0.990076\pi\) | ||
0.999514 | − | 0.0311709i | \(-0.00992361\pi\) | |||||||
\(674\) | −15.1244 | −0.582568 | ||||||||
\(675\) | 14.5359 | + | 2.96713i | 0.559487 | + | 0.114205i | ||||
\(676\) | 8.66025 | 0.333087 | ||||||||
\(677\) | 9.04008i | 0.347439i | 0.984795 | + | 0.173719i | \(0.0555786\pi\) | ||||
−0.984795 | + | 0.173719i | \(0.944421\pi\) | |||||||
\(678\) | − | 2.82843i | − | 0.108625i | ||||||
\(679\) | 0.588457 | 0.0225829 | ||||||||
\(680\) | 0.928203 | − | 0.757875i | 0.0355950 | − | 0.0290632i | ||||
\(681\) | −11.1436 | −0.427023 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.4887i | 0.860507i | 0.902708 | + | 0.430253i | \(0.141576\pi\) | ||||
−0.902708 | + | 0.430253i | \(0.858424\pi\) | |||||||
\(684\) | 29.3205 | 1.12110 | ||||||||
\(685\) | −19.4641 | − | 23.8386i | −0.743685 | − | 0.910825i | ||||
\(686\) | −22.8564 | −0.872662 | ||||||||
\(687\) | 9.28032i | 0.354066i | ||||||||
\(688\) | − | 47.7415i | − | 1.82013i | ||||||
\(689\) | −50.7846 | −1.93474 | ||||||||
\(690\) | −8.92820 | − | 10.9348i | −0.339891 | − | 0.416280i | ||||
\(691\) | −27.9090 | −1.06171 | −0.530854 | − | 0.847464i | \(-0.678129\pi\) | ||||
−0.530854 | + | 0.847464i | \(0.678129\pi\) | |||||||
\(692\) | 13.2084i | 0.502108i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.73205 | 0.217586 | ||||||||
\(695\) | 28.7321 | − | 23.4596i | 1.08987 | − | 0.889874i | ||||
\(696\) | −1.85641 | −0.0703669 | ||||||||
\(697\) | − | 1.79315i | − | 0.0679204i | ||||||
\(698\) | − | 52.7792i | − | 1.99772i | ||||||
\(699\) | 6.73205 | 0.254630 | ||||||||
\(700\) | −7.60770 | − | 1.55291i | −0.287544 | − | 0.0586946i | ||||
\(701\) | 10.1436 | 0.383118 | 0.191559 | − | 0.981481i | \(-0.438646\pi\) | ||||
0.191559 | + | 0.981481i | \(0.438646\pi\) | |||||||
\(702\) | − | 24.3190i | − | 0.917863i | ||||||
\(703\) | 41.4655i | 1.56390i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.67949 | + | 3.00429i | −0.138578 | + | 0.113148i | ||||
\(706\) | −3.26795 | −0.122991 | ||||||||
\(707\) | − | 1.24831i | − | 0.0469474i | ||||||
\(708\) | − | 4.24264i | − | 0.159448i | ||||||
\(709\) | −23.3923 | −0.878516 | −0.439258 | − | 0.898361i | \(-0.644759\pi\) | ||||
−0.439258 | + | 0.898361i | \(0.644759\pi\) | |||||||
\(710\) | −6.00000 | − | 7.34847i | −0.225176 | − | 0.275783i | ||||
\(711\) | 14.9282 | 0.559851 | ||||||||
\(712\) | 3.34607i | 0.125399i | ||||||||
\(713\) | 33.2576i | 1.24551i | ||||||||
\(714\) | 0.928203 | 0.0347371 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.7846 | −0.552527 | ||||||||
\(717\) | 6.03579i | 0.225411i | ||||||||
\(718\) | − | 35.4297i | − | 1.32222i | ||||||
\(719\) | 39.8038 | 1.48443 | 0.742217 | − | 0.670160i | \(-0.233775\pi\) | ||||
0.742217 | + | 0.670160i | \(0.233775\pi\) | |||||||
\(720\) | 21.1244 | − | 17.2480i | 0.787258 | − | 0.642794i | ||||
\(721\) | −3.80385 | −0.141663 | ||||||||
\(722\) | 37.4631i | 1.39423i | ||||||||
\(723\) | − | 5.24075i | − | 0.194906i | ||||||
\(724\) | −5.87564 | −0.218367 | ||||||||
\(725\) | 6.92820 | − | 33.9411i | 0.257307 | − | 1.26054i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.00240i | − | 0.148441i | −0.997242 | − | 0.0742205i | \(-0.976353\pi\) | ||
0.997242 | − | 0.0742205i | \(-0.0236469\pi\) | |||||||
\(728\) | − | 1.96902i | − | 0.0729766i | ||||||
\(729\) | 13.5885 | 0.503276 | ||||||||
\(730\) | 16.3923 | − | 13.3843i | 0.606706 | − | 0.495374i | ||||
\(731\) | −11.0718 | −0.409505 | ||||||||
\(732\) | 7.41284i | 0.273986i | ||||||||
\(733\) | 34.7733i | 1.28438i | 0.766545 | + | 0.642191i | \(0.221974\pi\) | ||||
−0.766545 | + | 0.642191i | \(0.778026\pi\) | |||||||
\(734\) | 57.2487 | 2.11309 | ||||||||
\(735\) | −4.53590 | − | 5.55532i | −0.167309 | − | 0.204911i | ||||
\(736\) | −47.9090 | −1.76595 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 9.14162i | − | 0.336508i | ||||||
\(739\) | 25.0718 | 0.922281 | 0.461140 | − | 0.887327i | \(-0.347440\pi\) | ||||
0.461140 | + | 0.887327i | \(0.347440\pi\) | |||||||
\(740\) | −16.3923 | − | 20.0764i | −0.602593 | − | 0.738023i | ||||
\(741\) | 13.6077 | 0.499891 | ||||||||
\(742\) | − | 20.7327i | − | 0.761122i | ||||||
\(743\) | − | 8.04197i | − | 0.295031i | −0.989060 | − | 0.147516i | \(-0.952872\pi\) | ||
0.989060 | − | 0.147516i | \(-0.0471277\pi\) | |||||||
\(744\) | 1.41154 | 0.0517497 | ||||||||
\(745\) | −23.7846 | + | 19.4201i | −0.871401 | + | 0.711496i | ||||
\(746\) | 65.9090 | 2.41310 | ||||||||
\(747\) | − | 27.0459i | − | 0.989559i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.92820 | −0.143533 | ||||||||
\(750\) | −5.19615 | − | 9.89949i | −0.189737 | − | 0.361478i | ||||
\(751\) | −20.6410 | −0.753201 | −0.376601 | − | 0.926376i | \(-0.622907\pi\) | ||||
−0.376601 | + | 0.926376i | \(0.622907\pi\) | |||||||
\(752\) | 18.3204i | 0.668076i | ||||||||
\(753\) | − | 7.34847i | − | 0.267793i | ||||||
\(754\) | −56.7846 | −2.06797 | ||||||||
\(755\) | 10.7321 | − | 8.76268i | 0.390579 | − | 0.318907i | ||||
\(756\) | 4.60770 | 0.167580 | ||||||||
\(757\) | 35.0779i | 1.27493i | 0.770480 | + | 0.637465i | \(0.220017\pi\) | ||||
−0.770480 | + | 0.637465i | \(0.779983\pi\) | |||||||
\(758\) | 10.5558i | 0.383405i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.53590 | + | 5.55532i | 0.164534 | + | 0.201513i | ||||
\(761\) | 7.85641 | 0.284795 | 0.142397 | − | 0.989810i | \(-0.454519\pi\) | ||||
0.142397 | + | 0.989810i | \(0.454519\pi\) | |||||||
\(762\) | − | 3.34607i | − | 0.121215i | ||||||
\(763\) | 1.07244i | 0.0388250i | ||||||||
\(764\) | 18.5885 | 0.672507 | ||||||||
\(765\) | −4.00000 | − | 4.89898i | −0.144620 | − | 0.177123i | ||||
\(766\) | 45.9090 | 1.65876 | ||||||||
\(767\) | 20.0764i | 0.724916i | ||||||||
\(768\) | 10.0382i | 0.362222i | ||||||||
\(769\) | −17.8564 | −0.643918 | −0.321959 | − | 0.946754i | \(-0.604341\pi\) | ||||
−0.321959 | + | 0.946754i | \(0.604341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.58846 | 0.0932210 | ||||||||
\(772\) | − | 17.8028i | − | 0.640736i | ||||||
\(773\) | 51.6424i | 1.85745i | 0.370774 | + | 0.928723i | \(0.379093\pi\) | ||||
−0.370774 | + | 0.928723i | \(0.620907\pi\) | |||||||
\(774\) | −56.4449 | −2.02887 | ||||||||
\(775\) | −5.26795 | + | 25.8076i | −0.189230 | + | 0.927035i | ||||
\(776\) | 0.339746 | 0.0121962 | ||||||||
\(777\) | 3.10583i | 0.111421i | ||||||||
\(778\) | 35.0136i | 1.25530i | ||||||||
\(779\) | 10.7321 | 0.384516 | ||||||||
\(780\) | −6.58846 | + | 5.37945i | −0.235905 | + | 0.192615i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.6264i | 0.451519i | ||||||||
\(783\) | 20.5569i | 0.734642i | ||||||||
\(784\) | −27.6603 | −0.987866 | ||||||||
\(785\) | −17.0718 | − | 20.9086i | −0.609319 | − | 0.746260i | ||||
\(786\) | −21.1244 | −0.753481 | ||||||||
\(787\) | − | 4.65874i | − | 0.166066i | −0.996547 | − | 0.0830331i | \(-0.973539\pi\) | ||
0.996547 | − | 0.0830331i | \(-0.0264607\pi\) | |||||||
\(788\) | 4.41851i | 0.157403i | ||||||||
\(789\) | 11.1244 | 0.396038 | ||||||||
\(790\) | −14.9282 | − | 18.2832i | −0.531122 | − | 0.650488i | ||||
\(791\) | −2.53590 | −0.0901662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.0779i | − | 1.24565i | ||||||
\(794\) | −30.9282 | −1.09760 | ||||||||
\(795\) | 10.7321 | − | 8.76268i | 0.380627 | − | 0.310780i | ||||
\(796\) | −3.46410 | −0.122782 | ||||||||
\(797\) | 7.90327i | 0.279948i | 0.990155 | + | 0.139974i | \(0.0447019\pi\) | ||||
−0.990155 | + | 0.139974i | \(0.955298\pi\) | |||||||
\(798\) | 5.55532i | 0.196656i | ||||||||
\(799\) | 4.24871 | 0.150309 | ||||||||
\(800\) | −37.1769 | − | 7.58871i | −1.31440 | − | 0.268301i | ||||
\(801\) | 17.6603 | 0.623994 | ||||||||
\(802\) | − | 62.4384i | − | 2.20478i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.3923 | 0.472310 | ||||||||
\(805\) | −9.80385 | + | 8.00481i | −0.345540 | + | 0.282132i | ||||
\(806\) | 43.1769 | 1.52084 | ||||||||
\(807\) | 10.2141i | 0.359552i | ||||||||
\(808\) | − | 0.720710i | − | 0.0253545i | ||||||
\(809\) | 21.4641 | 0.754638 | 0.377319 | − | 0.926083i | \(-0.376846\pi\) | ||||
0.377319 | + | 0.926083i | \(0.376846\pi\) | |||||||
\(810\) | −18.1962 | − | 22.2856i | −0.639348 | − | 0.783038i | ||||
\(811\) | −32.9808 | −1.15811 | −0.579056 | − | 0.815288i | \(-0.696579\pi\) | ||||
−0.579056 | + | 0.815288i | \(0.696579\pi\) | |||||||
\(812\) | − | 10.7589i | − | 0.377564i | ||||||
\(813\) | 2.34795i | 0.0823463i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.7321 | + | 13.1440i | 0.375927 | + | 0.460415i | ||||
\(816\) | 2.39230 | 0.0837474 | ||||||||
\(817\) | − | 66.2650i | − | 2.31832i | ||||||
\(818\) | 3.62347i | 0.126692i | ||||||||
\(819\) | −10.3923 | −0.363137 | ||||||||
\(820\) | −5.19615 | + | 4.24264i | −0.181458 | + | 0.148159i | ||||
\(821\) | 18.8038 | 0.656259 | 0.328129 | − | 0.944633i | \(-0.393582\pi\) | ||||
0.328129 | + | 0.944633i | \(0.393582\pi\) | |||||||
\(822\) | − | 13.7632i | − | 0.480047i | ||||||
\(823\) | − | 48.3978i | − | 1.68704i | −0.537096 | − | 0.843521i | \(-0.680479\pi\) | ||
0.537096 | − | 0.843521i | \(-0.319521\pi\) | |||||||
\(824\) | −2.19615 | −0.0765066 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.19615 | −0.285181 | ||||||||
\(827\) | 26.7314i | 0.929540i | 0.885431 | + | 0.464770i | \(0.153863\pi\) | ||||
−0.885431 | + | 0.464770i | \(0.846137\pi\) | |||||||
\(828\) | 29.8744i | 1.03821i | ||||||||
\(829\) | −41.9808 | −1.45805 | −0.729026 | − | 0.684486i | \(-0.760027\pi\) | ||||
−0.729026 | + | 0.684486i | \(0.760027\pi\) | |||||||
\(830\) | −33.1244 | + | 27.0459i | −1.14976 | + | 0.938778i | ||||
\(831\) | 11.7513 | 0.407648 | ||||||||
\(832\) | 24.3190i | 0.843111i | ||||||||
\(833\) | 6.41473i | 0.222257i | ||||||||
\(834\) | 16.5885 | 0.574411 | ||||||||
\(835\) | −2.73205 | − | 3.34607i | −0.0945465 | − | 0.115795i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 15.6307i | − | 0.540275i | ||||||
\(838\) | 57.2992i | 1.97937i | ||||||||
\(839\) | −2.78461 | −0.0961354 | −0.0480677 | − | 0.998844i | \(-0.515306\pi\) | ||||
−0.0480677 | + | 0.998844i | \(0.515306\pi\) | |||||||
\(840\) | 0.339746 | + | 0.416102i | 0.0117223 | + | 0.0143569i | ||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 40.6704i | 1.40160i | ||||||||
\(843\) | 8.96575i | 0.308797i | ||||||||
\(844\) | −19.2679 | −0.663230 | ||||||||
\(845\) | 8.66025 | − | 7.07107i | 0.297922 | − | 0.243252i | ||||
\(846\) | 21.6603 | 0.744695 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 53.4355i | − | 1.83498i | ||||||
\(849\) | 15.5885 | 0.534994 | ||||||||
\(850\) | −2.00000 | + | 9.79796i | −0.0685994 | + | 0.336067i | ||||
\(851\) | −42.2487 | −1.44827 | ||||||||
\(852\) | − | 1.96902i | − | 0.0674574i | ||||||
\(853\) | 12.4233i | 0.425366i | 0.977121 | + | 0.212683i | \(0.0682202\pi\) | ||||
−0.977121 | + | 0.212683i | \(0.931780\pi\) | |||||||
\(854\) | 14.3205 | 0.490038 | ||||||||
\(855\) | 29.3205 | − | 23.9401i | 1.00274 | − | 0.818734i | ||||
\(856\) | −2.26795 | −0.0775169 | ||||||||
\(857\) | − | 24.4206i | − | 0.834191i | −0.908863 | − | 0.417095i | \(-0.863048\pi\) | ||
0.908863 | − | 0.417095i | \(-0.136952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8038 | 0.402742 | 0.201371 | − | 0.979515i | \(-0.435460\pi\) | ||||
0.201371 | + | 0.979515i | \(0.435460\pi\) | |||||||
\(860\) | 26.1962 | + | 32.0836i | 0.893281 | + | 1.09404i | ||||
\(861\) | 0.803848 | 0.0273951 | ||||||||
\(862\) | − | 36.5665i | − | 1.24546i | ||||||
\(863\) | 9.76079i | 0.332261i | 0.986104 | + | 0.166131i | \(0.0531273\pi\) | ||||
−0.986104 | + | 0.166131i | \(0.946873\pi\) | |||||||
\(864\) | 22.5167 | 0.766032 | ||||||||
\(865\) | 10.7846 | + | 13.2084i | 0.366688 | + | 0.449099i | ||||
\(866\) | −39.1244 | −1.32950 | ||||||||
\(867\) | 8.24504i | 0.280016i | ||||||||
\(868\) | 8.18067i | 0.277670i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.0000 | − | 9.79796i | 0.406838 | − | 0.332182i | ||||
\(871\) | −63.3731 | −2.14731 | ||||||||
\(872\) | 0.619174i | 0.0209679i | ||||||||
\(873\) | − | 1.79315i | − | 0.0606890i | ||||||
\(874\) | −75.5692 | −2.55617 | ||||||||
\(875\) | −8.87564 | + | 4.65874i | −0.300052 | + | 0.157494i | ||||
\(876\) | 4.39230 | 0.148402 | ||||||||
\(877\) | − | 55.9865i | − | 1.89053i | −0.326302 | − | 0.945265i | \(-0.605803\pi\) | ||
0.326302 | − | 0.945265i | \(-0.394197\pi\) | |||||||
\(878\) | 39.1175i | 1.32015i | ||||||||
\(879\) | 4.87564 | 0.164451 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.9090 | 1.31088 | 0.655438 | − | 0.755249i | \(-0.272484\pi\) | ||||
0.655438 | + | 0.755249i | \(0.272484\pi\) | |||||||
\(882\) | 32.7028i | 1.10116i | ||||||||
\(883\) | 47.0208i | 1.58238i | 0.611574 | + | 0.791188i | \(0.290537\pi\) | ||||
−0.611574 | + | 0.791188i | \(0.709463\pi\) | |||||||
\(884\) | 7.60770 | 0.255874 | ||||||||
\(885\) | −3.46410 | − | 4.24264i | −0.116445 | − | 0.142615i | ||||
\(886\) | 17.7321 | 0.595720 | ||||||||
\(887\) | − | 8.34658i | − | 0.280251i | −0.990134 | − | 0.140125i | \(-0.955249\pi\) | ||
0.990134 | − | 0.140125i | \(-0.0447506\pi\) | |||||||
\(888\) | 1.79315i | 0.0601742i | ||||||||
\(889\) | −3.00000 | −0.100617 | ||||||||
\(890\) | −17.6603 | − | 21.6293i | −0.591973 | − | 0.725016i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.0382i | 0.336104i | ||||||||
\(893\) | 25.4286i | 0.850937i | ||||||||
\(894\) | −13.7321 | −0.459268 | ||||||||
\(895\) | −14.7846 | + | 12.0716i | −0.494195 | + | 0.403509i | ||||
\(896\) | 3.67949 | 0.122923 | ||||||||
\(897\) | 13.8647i | 0.462930i | ||||||||
\(898\) | 20.3166i | 0.677975i | ||||||||
\(899\) | −36.4974 | −1.21726 | ||||||||
\(900\) | −4.73205 | + | 23.1822i | −0.157735 | + | 0.772741i | ||||
\(901\) | −12.3923 | −0.412848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.96335i | − | 0.165170i | ||||||
\(904\) | −1.46410 | −0.0486953 | ||||||||
\(905\) | −5.87564 | + | 4.79744i | −0.195313 | + | 0.159472i | ||||
\(906\) | 6.19615 | 0.205853 | ||||||||
\(907\) | 8.06918i | 0.267933i | 0.990986 | + | 0.133966i | \(0.0427714\pi\) | ||||
−0.990986 | + | 0.133966i | \(0.957229\pi\) | |||||||
\(908\) | − | 37.2872i | − | 1.23742i | ||||||
\(909\) | −3.80385 | −0.126166 | ||||||||
\(910\) | 10.3923 | + | 12.7279i | 0.344502 | + | 0.421927i | ||||
\(911\) | 18.2487 | 0.604607 | 0.302303 | − | 0.953212i | \(-0.402244\pi\) | ||||
0.302303 | + | 0.953212i | \(0.402244\pi\) | |||||||
\(912\) | 14.3180i | 0.474116i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.9808 | −1.35552 | ||||||||
\(915\) | 6.05256 | + | 7.41284i | 0.200091 | + | 0.245061i | ||||
\(916\) | −31.0526 | −1.02601 | ||||||||
\(917\) | 18.9396i | 0.625440i | ||||||||
\(918\) | − | 5.93426i | − | 0.195860i | ||||||
\(919\) | −32.9808 | −1.08793 | −0.543967 | − | 0.839106i | \(-0.683079\pi\) | ||||
−0.543967 | + | 0.839106i | \(0.683079\pi\) | |||||||
\(920\) | −5.66025 | + | 4.62158i | −0.186613 | + | 0.152369i | ||||
\(921\) | −9.12436 | −0.300658 | ||||||||
\(922\) | − | 63.7511i | − | 2.09953i | ||||||
\(923\) | 9.31749i | 0.306689i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.7846 | − | 6.69213i | −1.07795 | − | 0.220036i | ||||
\(926\) | 34.5167 | 1.13429 | ||||||||
\(927\) | 11.5911i | 0.380702i | ||||||||
\(928\) | − | 52.5761i | − | 1.72589i | ||||||
\(929\) | 16.1436 | 0.529654 | 0.264827 | − | 0.964296i | \(-0.414685\pi\) | ||||
0.264827 | + | 0.964296i | \(0.414685\pi\) | |||||||
\(930\) | −9.12436 | + | 7.45001i | −0.299199 | + | 0.244295i | ||||
\(931\) | −38.3923 | −1.25826 | ||||||||
\(932\) | 22.5259i | 0.737860i | ||||||||
\(933\) | − | 14.5211i | − | 0.475399i | ||||||
\(934\) | −34.3205 | −1.12300 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | − | 22.7017i | − | 0.741634i | −0.928706 | − | 0.370817i | \(-0.879078\pi\) | ||
0.928706 | − | 0.370817i | \(-0.120922\pi\) | |||||||
\(938\) | − | 25.8719i | − | 0.844749i | ||||||
\(939\) | −8.87564 | −0.289646 | ||||||||
\(940\) | −10.0526 | − | 12.3118i | −0.327878 | − | 0.401567i | ||||
\(941\) | −27.0000 | −0.880175 | −0.440087 | − | 0.897955i | \(-0.645053\pi\) | ||||
−0.440087 | + | 0.897955i | \(0.645053\pi\) | |||||||
\(942\) | − | 12.0716i | − | 0.393313i | ||||||
\(943\) | 10.9348i | 0.356085i | ||||||||
\(944\) | −21.1244 | −0.687539 | ||||||||
\(945\) | 4.60770 | − | 3.76217i | 0.149888 | − | 0.122383i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.3180i | − | 0.465273i | −0.972564 | − | 0.232636i | \(-0.925265\pi\) | ||
0.972564 | − | 0.232636i | \(-0.0747352\pi\) | |||||||
\(948\) | − | 4.89898i | − | 0.159111i | ||||||
\(949\) | −20.7846 | −0.674697 | ||||||||
\(950\) | −58.6410 | − | 11.9700i | −1.90257 | − | 0.388360i | ||||
\(951\) | 3.60770 | 0.116988 | ||||||||
\(952\) | − | 0.480473i | − | 0.0155722i | ||||||
\(953\) | 31.3901i | 1.01683i | 0.861114 | + | 0.508413i | \(0.169767\pi\) | ||||
−0.861114 | + | 0.508413i | \(0.830233\pi\) | |||||||
\(954\) | −63.1769 | −2.04543 | ||||||||
\(955\) | 18.5885 | − | 15.1774i | 0.601508 | − | 0.491130i | ||||
\(956\) | −20.1962 | −0.653190 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 18.2832i | − | 0.590705i | ||||||
\(959\) | −12.3397 | −0.398471 | ||||||||
\(960\) | −4.19615 | − | 5.13922i | −0.135430 | − | 0.165867i | ||||
\(961\) | −3.24871 | −0.104797 | ||||||||
\(962\) | 54.8497i | 1.76843i | ||||||||
\(963\) | 11.9700i | 0.385729i | ||||||||
\(964\) | 17.5359 | 0.564793 | ||||||||
\(965\) | −14.5359 | − | 17.8028i | −0.467927 | − | 0.573091i | ||||
\(966\) | −5.66025 | −0.182116 | ||||||||
\(967\) | − | 4.24264i | − | 0.136434i | −0.997671 | − | 0.0682171i | \(-0.978269\pi\) | ||
0.997671 | − | 0.0682171i | \(-0.0217310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.32051 | 0.106670 | ||||||||
\(970\) | −2.19615 | + | 1.79315i | −0.0705142 | + | 0.0575746i | ||||
\(971\) | −11.0718 | −0.355311 | −0.177655 | − | 0.984093i | \(-0.556851\pi\) | ||||
−0.177655 | + | 0.984093i | \(0.556851\pi\) | |||||||
\(972\) | − | 21.3891i | − | 0.686055i | ||||||
\(973\) | − | 14.8728i | − | 0.476800i | ||||||
\(974\) | 24.5885 | 0.787865 | ||||||||
\(975\) | −2.19615 | + | 10.7589i | −0.0703332 | + | 0.344561i | ||||
\(976\) | 36.9090 | 1.18143 | ||||||||
\(977\) | − | 14.9743i | − | 0.479072i | −0.970888 | − | 0.239536i | \(-0.923005\pi\) | ||
0.970888 | − | 0.239536i | \(-0.0769952\pi\) | |||||||
\(978\) | 7.58871i | 0.242660i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 18.5885 | − | 15.1774i | 0.593786 | − | 0.484825i | ||||
\(981\) | 3.26795 | 0.104338 | ||||||||
\(982\) | − | 30.3548i | − | 0.968661i | ||||||
\(983\) | 15.0115i | 0.478793i | 0.970922 | + | 0.239396i | \(0.0769495\pi\) | ||||
−0.970922 | + | 0.239396i | \(0.923050\pi\) | |||||||
\(984\) | 0.464102 | 0.0147950 | ||||||||
\(985\) | 3.60770 | + | 4.41851i | 0.114951 | + | 0.140785i | ||||
\(986\) | −13.8564 | −0.441278 | ||||||||
\(987\) | 1.90465i | 0.0606255i | ||||||||
\(988\) | 45.5322i | 1.44857i | ||||||||
\(989\) | 67.5167 | 2.14690 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.9090 | −1.45835 | −0.729173 | − | 0.684329i | \(-0.760095\pi\) | ||||
−0.729173 | + | 0.684329i | \(0.760095\pi\) | |||||||
\(992\) | 39.9769i | 1.26927i | ||||||||
\(993\) | − | 4.03957i | − | 0.128192i | ||||||
\(994\) | −3.80385 | −0.120651 | ||||||||
\(995\) | −3.46410 | + | 2.82843i | −0.109819 | + | 0.0896672i | ||||
\(996\) | −8.87564 | −0.281236 | ||||||||
\(997\) | − | 0.175865i | − | 0.00556971i | −0.999996 | − | 0.00278486i | \(-0.999114\pi\) | ||
0.999996 | − | 0.00278486i | \(-0.000886449\pi\) | |||||||
\(998\) | − | 74.1682i | − | 2.34775i | ||||||
\(999\) | 19.8564 | 0.628229 |
(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 | 605.2.b.d.364.4 | yes | 4 | |
5.2 | odd | 4 | 3025.2.a.y.1.1 | 4 | |||
5.3 | odd | 4 | 3025.2.a.y.1.4 | 4 | |||
5.4 | even | 2 | inner | 605.2.b.d.364.1 | ✓ | 4 | |
11.2 | odd | 10 | 605.2.j.e.444.1 | 16 | |||
11.3 | even | 5 | 605.2.j.f.9.4 | 16 | |||
11.4 | even | 5 | 605.2.j.f.269.1 | 16 | |||
11.5 | even | 5 | 605.2.j.f.124.1 | 16 | |||
11.6 | odd | 10 | 605.2.j.e.124.4 | 16 | |||
11.7 | odd | 10 | 605.2.j.e.269.4 | 16 | |||
11.8 | odd | 10 | 605.2.j.e.9.1 | 16 | |||
11.9 | even | 5 | 605.2.j.f.444.4 | 16 | |||
11.10 | odd | 2 | 605.2.b.e.364.1 | yes | 4 | ||
55.4 | even | 10 | 605.2.j.f.269.4 | 16 | |||
55.9 | even | 10 | 605.2.j.f.444.1 | 16 | |||
55.14 | even | 10 | 605.2.j.f.9.1 | 16 | |||
55.19 | odd | 10 | 605.2.j.e.9.4 | 16 | |||
55.24 | odd | 10 | 605.2.j.e.444.4 | 16 | |||
55.29 | odd | 10 | 605.2.j.e.269.1 | 16 | |||
55.32 | even | 4 | 3025.2.a.z.1.4 | 4 | |||
55.39 | odd | 10 | 605.2.j.e.124.1 | 16 | |||
55.43 | even | 4 | 3025.2.a.z.1.1 | 4 | |||
55.49 | even | 10 | 605.2.j.f.124.4 | 16 | |||
55.54 | odd | 2 | 605.2.b.e.364.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.d.364.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
605.2.b.d.364.4 | yes | 4 | 1.1 | even | 1 | trivial | |
605.2.b.e.364.1 | yes | 4 | 11.10 | odd | 2 | ||
605.2.b.e.364.4 | yes | 4 | 55.54 | odd | 2 | ||
605.2.j.e.9.1 | 16 | 11.8 | odd | 10 | |||
605.2.j.e.9.4 | 16 | 55.19 | odd | 10 | |||
605.2.j.e.124.1 | 16 | 55.39 | odd | 10 | |||
605.2.j.e.124.4 | 16 | 11.6 | odd | 10 | |||
605.2.j.e.269.1 | 16 | 55.29 | odd | 10 | |||
605.2.j.e.269.4 | 16 | 11.7 | odd | 10 | |||
605.2.j.e.444.1 | 16 | 11.2 | odd | 10 | |||
605.2.j.e.444.4 | 16 | 55.24 | odd | 10 | |||
605.2.j.f.9.1 | 16 | 55.14 | even | 10 | |||
605.2.j.f.9.4 | 16 | 11.3 | even | 5 | |||
605.2.j.f.124.1 | 16 | 11.5 | even | 5 | |||
605.2.j.f.124.4 | 16 | 55.49 | even | 10 | |||
605.2.j.f.269.1 | 16 | 11.4 | even | 5 | |||
605.2.j.f.269.4 | 16 | 55.4 | even | 10 | |||
605.2.j.f.444.1 | 16 | 55.9 | even | 10 | |||
605.2.j.f.444.4 | 16 | 11.9 | even | 5 | |||
3025.2.a.y.1.1 | 4 | 5.2 | odd | 4 | |||
3025.2.a.y.1.4 | 4 | 5.3 | odd | 4 | |||
3025.2.a.z.1.1 | 4 | 55.43 | even | 4 | |||
3025.2.a.z.1.4 | 4 | 55.32 | even | 4 |