Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(34,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.p (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
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 | 34.2 | ||
Root | \(1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.34 |
Dual form | 273.2.p.b.265.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 0.581139 | − | 0.581139i | 0.259893 | − | 0.259893i | −0.565117 | − | 0.825011i | \(-0.691169\pi\) |
0.825011 | + | 0.565117i | \(0.191169\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.581139 | + | 2.58114i | 0.219650 | + | 0.975579i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.16228 | − | 4.16228i | 1.25497 | − | 1.25497i | 0.301511 | − | 0.953463i | \(-0.402509\pi\) |
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 3.58114 | + | 0.418861i | 0.993229 | + | 0.116171i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.581139 | + | 0.581139i | 0.150049 | + | 0.150049i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 1.16228 | 0.281894 | 0.140947 | − | 0.990017i | \(-0.454985\pi\) | ||||
0.140947 | + | 0.990017i | \(0.454985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.418861 | − | 0.418861i | 0.0960933 | − | 0.0960933i | −0.657426 | − | 0.753519i | \(-0.728355\pi\) |
0.753519 | + | 0.657426i | \(0.228355\pi\) | |||||||
\(20\) | −1.16228 | − | 1.16228i | −0.259893 | − | 0.259893i | ||||
\(21\) | −2.58114 | + | 0.581139i | −0.563251 | + | 0.126815i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.16228i | − | 0.867895i | −0.900938 | − | 0.433947i | \(-0.857120\pi\) | ||
0.900938 | − | 0.433947i | \(-0.142880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.32456i | 0.864911i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 5.16228 | − | 1.16228i | 0.975579 | − | 0.219650i | ||||
\(29\) | 1.83772 | 0.341256 | 0.170628 | − | 0.985335i | \(-0.445420\pi\) | ||||
0.170628 | + | 0.985335i | \(0.445420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.58114 | + | 5.58114i | −1.00240 | + | 1.00240i | −0.00240502 | + | 0.999997i | \(0.500766\pi\) |
−0.999997 | + | 0.00240502i | \(0.999234\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.16228 | + | 4.16228i | 0.724560 | + | 0.724560i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.83772 | + | 1.16228i | 0.310632 | + | 0.196461i | ||||
\(36\) | 2.00000i | 0.333333i | ||||||||
\(37\) | 4.32456 | − | 4.32456i | 0.710953 | − | 0.710953i | −0.255782 | − | 0.966734i | \(-0.582333\pi\) |
0.966734 | + | 0.255782i | \(0.0823329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.418861 | + | 3.58114i | −0.0670715 | + | 0.573441i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.16228 | + | 7.16228i | −1.11856 | + | 1.11856i | −0.126607 | + | 0.991953i | \(0.540409\pi\) |
−0.991953 | + | 0.126607i | \(0.959591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.32456i | 0.811987i | 0.913876 | + | 0.405994i | \(0.133074\pi\) | ||||
−0.913876 | + | 0.405994i | \(0.866926\pi\) | |||||||
\(44\) | −8.32456 | − | 8.32456i | −1.25497 | − | 1.25497i | ||||
\(45\) | −0.581139 | + | 0.581139i | −0.0866311 | + | 0.0866311i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.58114 | − | 6.58114i | −0.959958 | − | 0.959958i | 0.0392708 | − | 0.999229i | \(-0.487496\pi\) |
−0.999229 | + | 0.0392708i | \(0.987496\pi\) | |||||||
\(48\) | − | 4.00000i | − | 0.577350i | ||||||
\(49\) | −6.32456 | + | 3.00000i | −0.903508 | + | 0.428571i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.16228i | 0.162751i | ||||||||
\(52\) | 0.837722 | − | 7.16228i | 0.116171 | − | 0.993229i | ||||
\(53\) | −4.16228 | −0.571733 | −0.285866 | − | 0.958269i | \(-0.592281\pi\) | ||||
−0.285866 | + | 0.958269i | \(0.592281\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.83772i | − | 0.652318i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.418861 | + | 0.418861i | 0.0554795 | + | 0.0554795i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.32456 | − | 8.32456i | −1.08376 | − | 1.08376i | −0.996155 | − | 0.0876099i | \(-0.972077\pi\) |
−0.0876099 | − | 0.996155i | \(-0.527923\pi\) | |||||||
\(60\) | 1.16228 | − | 1.16228i | 0.150049 | − | 0.150049i | ||||
\(61\) | 3.16228i | 0.404888i | 0.979294 | + | 0.202444i | \(0.0648884\pi\) | ||||
−0.979294 | + | 0.202444i | \(0.935112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.581139 | − | 2.58114i | −0.0732166 | − | 0.325193i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 2.32456 | − | 1.83772i | 0.288326 | − | 0.227941i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.32456 | − | 6.32456i | −0.772667 | − | 0.772667i | 0.205905 | − | 0.978572i | \(-0.433986\pi\) |
−0.978572 | + | 0.205905i | \(0.933986\pi\) | |||||||
\(68\) | − | 2.32456i | − | 0.281894i | ||||||
\(69\) | 4.16228 | 0.501079 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | + | 6.00000i | 0.712069 | + | 0.712069i | 0.966968 | − | 0.254899i | \(-0.0820421\pi\) |
−0.254899 | + | 0.966968i | \(0.582042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.58114 | + | 5.58114i | 0.653223 | + | 0.653223i | 0.953768 | − | 0.300545i | \(-0.0971685\pi\) |
−0.300545 | + | 0.953768i | \(0.597168\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.32456 | −0.499357 | ||||||||
\(76\) | −0.837722 | − | 0.837722i | −0.0960933 | − | 0.0960933i | ||||
\(77\) | 13.1623 | + | 8.32456i | 1.49998 | + | 0.948671i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3246 | −1.27411 | −0.637056 | − | 0.770818i | \(-0.719848\pi\) | ||||
−0.637056 | + | 0.770818i | \(0.719848\pi\) | |||||||
\(80\) | −2.32456 | + | 2.32456i | −0.259893 | + | 0.259893i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.58114 | + | 6.58114i | −0.722374 | + | 0.722374i | −0.969088 | − | 0.246714i | \(-0.920649\pi\) |
0.246714 | + | 0.969088i | \(0.420649\pi\) | |||||||
\(84\) | 1.16228 | + | 5.16228i | 0.126815 | + | 0.563251i | ||||
\(85\) | 0.675445 | − | 0.675445i | 0.0732623 | − | 0.0732623i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.83772i | 0.197025i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.41886 | − | 5.41886i | −0.574398 | − | 0.574398i | 0.358956 | − | 0.933354i | \(-0.383133\pi\) |
−0.933354 | + | 0.358956i | \(0.883133\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | + | 9.48683i | 0.104828 | + | 0.994490i | ||||
\(92\) | −8.32456 | −0.867895 | ||||||||
\(93\) | −5.58114 | − | 5.58114i | −0.578737 | − | 0.578737i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.486833i | − | 0.0499480i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.418861 | + | 0.418861i | −0.0425289 | + | 0.0425289i | −0.728051 | − | 0.685523i | \(-0.759574\pi\) |
0.685523 | + | 0.728051i | \(0.259574\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.16228 | + | 4.16228i | −0.418325 | + | 0.418325i | ||||
\(100\) | 8.64911 | 0.864911 | ||||||||
\(101\) | 17.8114 | 1.77230 | 0.886150 | − | 0.463399i | \(-0.153370\pi\) | ||||
0.886150 | + | 0.463399i | \(0.153370\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.16228 | + | 1.83772i | −0.113427 | + | 0.179343i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6491 | 1.02949 | 0.514744 | − | 0.857344i | \(-0.327887\pi\) | ||||
0.514744 | + | 0.857344i | \(0.327887\pi\) | |||||||
\(108\) | −2.00000 | −0.192450 | ||||||||
\(109\) | −2.00000 | − | 2.00000i | −0.191565 | − | 0.191565i | 0.604807 | − | 0.796372i | \(-0.293250\pi\) |
−0.796372 | + | 0.604807i | \(0.793250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.32456 | + | 4.32456i | 0.410469 | + | 0.410469i | ||||
\(112\) | −2.32456 | − | 10.3246i | −0.219650 | − | 0.975579i | ||||
\(113\) | 14.8114 | 1.39334 | 0.696669 | − | 0.717393i | \(-0.254665\pi\) | ||||
0.696669 | + | 0.717393i | \(0.254665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.41886 | − | 2.41886i | −0.225560 | − | 0.225560i | ||||
\(116\) | − | 3.67544i | − | 0.341256i | ||||||
\(117\) | −3.58114 | − | 0.418861i | −0.331076 | − | 0.0387237i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.675445 | + | 3.00000i | 0.0619179 | + | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 23.6491i | − | 2.14992i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.16228 | − | 7.16228i | −0.645801 | − | 0.645801i | ||||
\(124\) | 11.1623 | + | 11.1623i | 1.00240 | + | 1.00240i | ||||
\(125\) | 5.41886 | + | 5.41886i | 0.484678 | + | 0.484678i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.32456 | −0.468801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1623i | 1.14999i | 0.818156 | + | 0.574997i | \(0.194997\pi\) | ||||
−0.818156 | + | 0.574997i | \(0.805003\pi\) | |||||||
\(132\) | 8.32456 | − | 8.32456i | 0.724560 | − | 0.724560i | ||||
\(133\) | 1.32456 | + | 0.837722i | 0.114854 | + | 0.0726397i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.581139 | − | 0.581139i | −0.0500165 | − | 0.0500165i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.0000 | + | 12.0000i | −1.02523 | + | 1.02523i | −0.0255558 | + | 0.999673i | \(0.508136\pi\) |
−0.999673 | + | 0.0255558i | \(0.991864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.16228i | − | 0.607496i | −0.952752 | − | 0.303748i | \(-0.901762\pi\) | ||
0.952752 | − | 0.303748i | \(-0.0982382\pi\) | |||||||
\(140\) | 2.32456 | − | 3.67544i | 0.196461 | − | 0.310632i | ||||
\(141\) | 6.58114 | − | 6.58114i | 0.554232 | − | 0.554232i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.6491 | − | 13.1623i | 1.39227 | − | 1.10068i | ||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 1.06797 | − | 1.06797i | 0.0886902 | − | 0.0886902i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00000 | − | 6.32456i | −0.247436 | − | 0.521641i | ||||
\(148\) | −8.64911 | − | 8.64911i | −0.710953 | − | 0.710953i | ||||
\(149\) | −10.1623 | − | 10.1623i | −0.832526 | − | 0.832526i | 0.155336 | − | 0.987862i | \(-0.450354\pi\) |
−0.987862 | + | 0.155336i | \(0.950354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 4.00000i | −0.325515 | + | 0.325515i | −0.850878 | − | 0.525363i | \(-0.823930\pi\) |
0.525363 | + | 0.850878i | \(0.323930\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.16228 | −0.0939646 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.48683i | 0.521035i | ||||||||
\(156\) | 7.16228 | + | 0.837722i | 0.573441 | + | 0.0670715i | ||||
\(157\) | 2.51317i | 0.200573i | 0.994959 | + | 0.100286i | \(0.0319759\pi\) | ||||
−0.994959 | + | 0.100286i | \(0.968024\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 4.16228i | − | 0.330090i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7434 | − | 2.41886i | 0.846700 | − | 0.190633i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.32456 | + | 1.32456i | −0.103747 | + | 0.103747i | −0.757075 | − | 0.653328i | \(-0.773372\pi\) |
0.653328 | + | 0.757075i | \(0.273372\pi\) | |||||||
\(164\) | 14.3246 | + | 14.3246i | 1.11856 | + | 1.11856i | ||||
\(165\) | 4.83772 | 0.376616 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.90569 | − | 2.90569i | −0.224849 | − | 0.224849i | 0.585688 | − | 0.810537i | \(-0.300825\pi\) |
−0.810537 | + | 0.585688i | \(0.800825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6491 | + | 3.00000i | 0.973009 | + | 0.230769i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.418861 | + | 0.418861i | −0.0320311 | + | 0.0320311i | ||||
\(172\) | 10.6491 | 0.811987 | ||||||||
\(173\) | −2.32456 | −0.176733 | −0.0883663 | − | 0.996088i | \(-0.528165\pi\) | ||||
−0.0883663 | + | 0.996088i | \(0.528165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1623 | + | 2.51317i | −0.843789 | + | 0.189978i | ||||
\(176\) | −16.6491 | + | 16.6491i | −1.25497 | + | 1.25497i | ||||
\(177\) | 8.32456 | − | 8.32456i | 0.625712 | − | 0.625712i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.486833i | 0.0363876i | 0.999834 | + | 0.0181938i | \(0.00579159\pi\) | ||||
−0.999834 | + | 0.0181938i | \(0.994208\pi\) | |||||||
\(180\) | 1.16228 | + | 1.16228i | 0.0866311 | + | 0.0866311i | ||||
\(181\) | 15.1623 | 1.12700 | 0.563502 | − | 0.826115i | \(-0.309454\pi\) | ||||
0.563502 | + | 0.826115i | \(0.309454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.16228 | −0.233762 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.02633i | − | 0.369543i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.83772 | − | 4.83772i | 0.353769 | − | 0.353769i | ||||
\(188\) | −13.1623 | + | 13.1623i | −0.959958 | + | 0.959958i | ||||
\(189\) | 2.58114 | − | 0.581139i | 0.187750 | − | 0.0422716i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.3246 | −1.03649 | −0.518244 | − | 0.855233i | \(-0.673414\pi\) | ||||
−0.518244 | + | 0.855233i | \(0.673414\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | 6.32456 | − | 6.32456i | 0.455251 | − | 0.455251i | −0.441842 | − | 0.897093i | \(-0.645675\pi\) |
0.897093 | + | 0.441842i | \(0.145675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.83772 | + | 2.32456i | 0.131602 | + | 0.166465i | ||||
\(196\) | 6.00000 | + | 12.6491i | 0.428571 | + | 0.903508i | ||||
\(197\) | −1.83772 | − | 1.83772i | −0.130932 | − | 0.130932i | 0.638604 | − | 0.769536i | \(-0.279512\pi\) |
−0.769536 | + | 0.638604i | \(0.779512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.48683 | −0.672504 | −0.336252 | − | 0.941772i | \(-0.609159\pi\) | ||||
−0.336252 | + | 0.941772i | \(0.609159\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.32456 | − | 6.32456i | 0.446100 | − | 0.446100i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.06797 | + | 4.74342i | 0.0749569 | + | 0.332923i | ||||
\(204\) | 2.32456 | 0.162751 | ||||||||
\(205\) | 8.32456i | 0.581412i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.16228i | 0.289298i | ||||||||
\(208\) | −14.3246 | − | 1.67544i | −0.993229 | − | 0.116171i | ||||
\(209\) | − | 3.48683i | − | 0.241189i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.6491 | 1.35270 | 0.676350 | − | 0.736580i | \(-0.263561\pi\) | ||||
0.676350 | + | 0.736580i | \(0.263561\pi\) | |||||||
\(212\) | 8.32456i | 0.571733i | ||||||||
\(213\) | −6.00000 | + | 6.00000i | −0.411113 | + | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.09431 | + | 3.09431i | 0.211030 | + | 0.211030i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.6491 | − | 11.1623i | −1.19810 | − | 0.757745i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.58114 | + | 5.58114i | −0.377138 | + | 0.377138i | ||||
\(220\) | −9.67544 | −0.652318 | ||||||||
\(221\) | 4.16228 | + | 0.486833i | 0.279985 | + | 0.0327479i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.25658 | − | 5.25658i | 0.352007 | − | 0.352007i | −0.508849 | − | 0.860856i | \(-0.669929\pi\) |
0.860856 | + | 0.508849i | \(0.169929\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 4.32456i | − | 0.288304i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.83772 | − | 4.83772i | 0.321091 | − | 0.321091i | −0.528095 | − | 0.849186i | \(-0.677093\pi\) |
0.849186 | + | 0.528095i | \(0.177093\pi\) | |||||||
\(228\) | 0.837722 | − | 0.837722i | 0.0554795 | − | 0.0554795i | ||||
\(229\) | −18.3246 | − | 18.3246i | −1.21092 | − | 1.21092i | −0.970724 | − | 0.240196i | \(-0.922788\pi\) |
−0.240196 | − | 0.970724i | \(-0.577212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.32456 | + | 13.1623i | −0.547716 | + | 0.866014i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.1623i | 1.45190i | 0.687748 | + | 0.725950i | \(0.258599\pi\) | ||||
−0.687748 | + | 0.725950i | \(0.741401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.64911 | −0.498973 | ||||||||
\(236\) | −16.6491 | + | 16.6491i | −1.08376 | + | 1.08376i | ||||
\(237\) | − | 11.3246i | − | 0.735609i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.48683 | − | 6.48683i | −0.419598 | − | 0.419598i | 0.465467 | − | 0.885065i | \(-0.345886\pi\) |
−0.885065 | + | 0.465467i | \(0.845886\pi\) | |||||||
\(240\) | −2.32456 | − | 2.32456i | −0.150049 | − | 0.150049i | ||||
\(241\) | 3.90569 | + | 3.90569i | 0.251588 | + | 0.251588i | 0.821621 | − | 0.570034i | \(-0.193070\pi\) |
−0.570034 | + | 0.821621i | \(0.693070\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 6.32456 | 0.404888 | ||||||||
\(245\) | −1.93203 | + | 5.41886i | −0.123433 | + | 0.346198i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.67544 | − | 1.32456i | 0.106606 | − | 0.0842794i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.58114 | − | 6.58114i | −0.417063 | − | 0.417063i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4868 | −1.73495 | −0.867477 | − | 0.497478i | \(-0.834260\pi\) | ||||
−0.867477 | + | 0.497478i | \(0.834260\pi\) | |||||||
\(252\) | −5.16228 | + | 1.16228i | −0.325193 | + | 0.0732166i | ||||
\(253\) | −17.3246 | − | 17.3246i | −1.08919 | − | 1.08919i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.675445 | + | 0.675445i | 0.0422980 | + | 0.0422980i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 27.4868 | 1.71458 | 0.857291 | − | 0.514833i | \(-0.172146\pi\) | ||||
0.857291 | + | 0.514833i | \(0.172146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.6754 | + | 8.64911i | 0.849751 | + | 0.537430i | ||||
\(260\) | −3.67544 | − | 4.64911i | −0.227941 | − | 0.288326i | ||||
\(261\) | −1.83772 | −0.113752 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.4868 | 1.13995 | 0.569973 | − | 0.821663i | \(-0.306953\pi\) | ||||
0.569973 | + | 0.821663i | \(0.306953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.41886 | + | 2.41886i | −0.148589 | + | 0.148589i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.41886 | − | 5.41886i | 0.331629 | − | 0.331629i | ||||
\(268\) | −12.6491 | + | 12.6491i | −0.772667 | + | 0.772667i | ||||
\(269\) | − | 3.48683i | − | 0.212596i | −0.994334 | − | 0.106298i | \(-0.966100\pi\) | ||
0.994334 | − | 0.106298i | \(-0.0338997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.4868 | − | 13.4868i | −0.819267 | − | 0.819267i | 0.166735 | − | 0.986002i | \(-0.446678\pi\) |
−0.986002 | + | 0.166735i | \(0.946678\pi\) | |||||||
\(272\) | −4.64911 | −0.281894 | ||||||||
\(273\) | −9.48683 | + | 1.00000i | −0.574169 | + | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.0000 | + | 18.0000i | 1.08544 | + | 1.08544i | ||||
\(276\) | − | 8.32456i | − | 0.501079i | ||||||
\(277\) | 4.35089i | 0.261420i | 0.991421 | + | 0.130710i | \(0.0417256\pi\) | ||||
−0.991421 | + | 0.130710i | \(0.958274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.58114 | − | 5.58114i | 0.334134 | − | 0.334134i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.67544 | − | 9.67544i | 0.577189 | − | 0.577189i | −0.356939 | − | 0.934128i | \(-0.616180\pi\) |
0.934128 | + | 0.356939i | \(0.116180\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.2982 | −1.26605 | −0.633024 | − | 0.774132i | \(-0.718187\pi\) | ||||
−0.633024 | + | 0.774132i | \(0.718187\pi\) | |||||||
\(284\) | 12.0000 | − | 12.0000i | 0.712069 | − | 0.712069i | ||||
\(285\) | 0.486833 | 0.0288375 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.6491 | − | 14.3246i | −1.33693 | − | 0.845552i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6491 | −0.920536 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.418861 | − | 0.418861i | −0.0245541 | − | 0.0245541i | ||||
\(292\) | 11.1623 | − | 11.1623i | 0.653223 | − | 0.653223i | ||||
\(293\) | −22.0680 | − | 22.0680i | −1.28922 | − | 1.28922i | −0.935258 | − | 0.353967i | \(-0.884833\pi\) |
−0.353967 | − | 0.935258i | \(-0.615167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.67544 | −0.563326 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.16228 | − | 4.16228i | −0.241520 | − | 0.241520i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.74342 | − | 14.9057i | 0.100824 | − | 0.862019i | ||||
\(300\) | 8.64911i | 0.499357i | ||||||||
\(301\) | −13.7434 | + | 3.09431i | −0.792157 | + | 0.178353i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.8114i | 1.02324i | ||||||||
\(304\) | −1.67544 | + | 1.67544i | −0.0960933 | + | 0.0960933i | ||||
\(305\) | 1.83772 | + | 1.83772i | 0.105228 | + | 0.105228i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0680 | + | 11.0680i | 0.631683 | + | 0.631683i | 0.948490 | − | 0.316807i | \(-0.102611\pi\) |
−0.316807 | + | 0.948490i | \(0.602611\pi\) | |||||||
\(308\) | 16.6491 | − | 26.3246i | 0.948671 | − | 1.49998i | ||||
\(309\) | 4.00000i | 0.227552i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.3246 | −0.812271 | −0.406136 | − | 0.913813i | \(-0.633124\pi\) | ||||
−0.406136 | + | 0.913813i | \(0.633124\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8114i | 1.11981i | 0.828558 | + | 0.559903i | \(0.189162\pi\) | ||||
−0.828558 | + | 0.559903i | \(0.810838\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.83772 | − | 1.16228i | −0.103544 | − | 0.0654869i | ||||
\(316\) | 22.6491i | 1.27411i | ||||||||
\(317\) | −1.83772 | − | 1.83772i | −0.103217 | − | 0.103217i | 0.653613 | − | 0.756829i | \(-0.273253\pi\) |
−0.756829 | + | 0.653613i | \(0.773253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.64911 | − | 7.64911i | 0.428268 | − | 0.428268i | ||||
\(320\) | 4.64911 | + | 4.64911i | 0.259893 | + | 0.259893i | ||||
\(321\) | 10.6491i | 0.594375i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.486833 | − | 0.486833i | 0.0270881 | − | 0.0270881i | ||||
\(324\) | − | 2.00000i | − | 0.111111i | ||||||
\(325\) | −1.81139 | + | 15.4868i | −0.100478 | + | 0.859055i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | − | 2.00000i | 0.110600 | − | 0.110600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.1623 | − | 20.8114i | 0.725660 | − | 1.14737i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.6491 | + | 23.6491i | 1.29987 | + | 1.29987i | 0.928473 | + | 0.371400i | \(0.121122\pi\) |
0.371400 | + | 0.928473i | \(0.378878\pi\) | |||||||
\(332\) | 13.1623 | + | 13.1623i | 0.722374 | + | 0.722374i | ||||
\(333\) | −4.32456 | + | 4.32456i | −0.236984 | + | 0.236984i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.35089 | −0.401622 | ||||||||
\(336\) | 10.3246 | − | 2.32456i | 0.563251 | − | 0.126815i | ||||
\(337\) | − | 13.0000i | − | 0.708155i | −0.935216 | − | 0.354078i | \(-0.884795\pi\) | ||
0.935216 | − | 0.354078i | \(-0.115205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.8114i | 0.804444i | ||||||||
\(340\) | −1.35089 | − | 1.35089i | −0.0732623 | − | 0.0732623i | ||||
\(341\) | 46.4605i | 2.51598i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4189 | − | 14.5811i | −0.616561 | − | 0.787307i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.41886 | − | 2.41886i | 0.130227 | − | 0.130227i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.9737 | −1.66275 | −0.831377 | − | 0.555709i | \(-0.812447\pi\) | ||||
−0.831377 | + | 0.555709i | \(0.812447\pi\) | |||||||
\(348\) | 3.67544 | 0.197025 | ||||||||
\(349\) | 12.7434 | + | 12.7434i | 0.682139 | + | 0.682139i | 0.960482 | − | 0.278342i | \(-0.0897850\pi\) |
−0.278342 | + | 0.960482i | \(0.589785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.418861 | − | 3.58114i | 0.0223572 | − | 0.191147i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.48683 | − | 9.48683i | 0.504933 | − | 0.504933i | −0.408034 | − | 0.912967i | \(-0.633785\pi\) |
0.912967 | + | 0.408034i | \(0.133785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.97367 | 0.370124 | ||||||||
\(356\) | −10.8377 | + | 10.8377i | −0.574398 | + | 0.574398i | ||||
\(357\) | −3.00000 | + | 0.675445i | −0.158777 | + | 0.0357483i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.1623 | − | 10.1623i | 0.536345 | − | 0.536345i | −0.386109 | − | 0.922453i | \(-0.626181\pi\) |
0.922453 | + | 0.386109i | \(0.126181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6491i | 0.981532i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 23.6491 | 1.24126 | ||||||||
\(364\) | 18.9737 | − | 2.00000i | 0.994490 | − | 0.104828i | ||||
\(365\) | 6.48683 | 0.339536 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.2982i | − | 1.73815i | −0.494678 | − | 0.869077i | \(-0.664714\pi\) | ||
0.494678 | − | 0.869077i | \(-0.335286\pi\) | |||||||
\(368\) | 16.6491i | 0.867895i | ||||||||
\(369\) | 7.16228 | − | 7.16228i | 0.372853 | − | 0.372853i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.41886 | − | 10.7434i | −0.125581 | − | 0.557770i | ||||
\(372\) | −11.1623 | + | 11.1623i | −0.578737 | + | 0.578737i | ||||
\(373\) | 24.0000 | 1.24267 | 0.621336 | − | 0.783544i | \(-0.286590\pi\) | ||||
0.621336 | + | 0.783544i | \(0.286590\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.41886 | + | 5.41886i | −0.279829 | + | 0.279829i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.58114 | + | 0.769751i | 0.338946 | + | 0.0396442i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.00000 | − | 7.00000i | −0.359566 | − | 0.359566i | 0.504087 | − | 0.863653i | \(-0.331829\pi\) |
−0.863653 | + | 0.504087i | \(0.831829\pi\) | |||||||
\(380\) | −0.973666 | −0.0499480 | ||||||||
\(381\) | −2.00000 | −0.102463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.67544 | − | 3.67544i | 0.187806 | − | 0.187806i | −0.606941 | − | 0.794747i | \(-0.707603\pi\) |
0.794747 | + | 0.606941i | \(0.207603\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4868 | − | 2.81139i | 0.636388 | − | 0.143282i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 5.32456i | − | 0.270662i | ||||||
\(388\) | 0.837722 | + | 0.837722i | 0.0425289 | + | 0.0425289i | ||||
\(389\) | 6.00000i | 0.304212i | 0.988364 | + | 0.152106i | \(0.0486055\pi\) | ||||
−0.988364 | + | 0.152106i | \(0.951394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.83772i | − | 0.244654i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1623 | −0.663949 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.58114 | + | 6.58114i | −0.331133 | + | 0.331133i | ||||
\(396\) | 8.32456 | + | 8.32456i | 0.418325 | + | 0.418325i | ||||
\(397\) | 5.25658 | + | 5.25658i | 0.263820 | + | 0.263820i | 0.826604 | − | 0.562784i | \(-0.190270\pi\) |
−0.562784 | + | 0.826604i | \(0.690270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.837722 | + | 1.32456i | −0.0419386 | + | 0.0663107i | ||||
\(400\) | − | 17.2982i | − | 0.864911i | ||||||
\(401\) | 7.83772 | − | 7.83772i | 0.391397 | − | 0.391397i | −0.483788 | − | 0.875185i | \(-0.660739\pi\) |
0.875185 | + | 0.483788i | \(0.160739\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.3246 | + | 17.6491i | −1.11207 | + | 0.879165i | ||||
\(404\) | − | 35.6228i | − | 1.77230i | ||||||
\(405\) | 0.581139 | − | 0.581139i | 0.0288770 | − | 0.0288770i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 36.0000i | − | 1.78445i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3925 | − | 19.3925i | 0.958899 | − | 0.958899i | −0.0402893 | − | 0.999188i | \(-0.512828\pi\) |
0.999188 | + | 0.0402893i | \(0.0128280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0000 | − | 12.0000i | −0.591916 | − | 0.591916i | ||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | 16.6491 | − | 26.3246i | 0.819249 | − | 1.29535i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.64911i | 0.375480i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.16228 | 0.350738 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.4868i | 0.756581i | 0.925687 | + | 0.378291i | \(0.123488\pi\) | ||||
−0.925687 | + | 0.378291i | \(0.876512\pi\) | |||||||
\(420\) | 3.67544 | + | 2.32456i | 0.179343 | + | 0.113427i | ||||
\(421\) | 7.32456 | + | 7.32456i | 0.356977 | + | 0.356977i | 0.862697 | − | 0.505720i | \(-0.168773\pi\) |
−0.505720 | + | 0.862697i | \(0.668773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.58114 | + | 6.58114i | 0.319986 | + | 0.319986i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.02633i | 0.243813i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.16228 | + | 1.83772i | −0.395000 | + | 0.0889336i | ||||
\(428\) | − | 21.2982i | − | 1.02949i | ||||||
\(429\) | 13.1623 | + | 16.6491i | 0.635481 | + | 0.803827i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8114 | − | 14.8114i | −0.713439 | − | 0.713439i | 0.253814 | − | 0.967253i | \(-0.418315\pi\) |
−0.967253 | + | 0.253814i | \(0.918315\pi\) | |||||||
\(432\) | 4.00000i | 0.192450i | ||||||||
\(433\) | 7.16228 | 0.344197 | 0.172099 | − | 0.985080i | \(-0.444945\pi\) | ||||
0.172099 | + | 0.985080i | \(0.444945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.06797 | + | 1.06797i | 0.0512053 | + | 0.0512053i | ||||
\(436\) | −4.00000 | + | 4.00000i | −0.191565 | + | 0.191565i | ||||
\(437\) | −1.74342 | − | 1.74342i | −0.0833989 | − | 0.0833989i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.4868 | 1.40733 | 0.703665 | − | 0.710532i | \(-0.251546\pi\) | ||||
0.703665 | + | 0.710532i | \(0.251546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.32456 | − | 3.00000i | 0.301169 | − | 0.142857i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.8377 | 1.22759 | 0.613794 | − | 0.789467i | \(-0.289643\pi\) | ||||
0.613794 | + | 0.789467i | \(0.289643\pi\) | |||||||
\(444\) | 8.64911 | − | 8.64911i | 0.410469 | − | 0.410469i | ||||
\(445\) | −6.29822 | −0.298564 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1623 | − | 10.1623i | 0.480659 | − | 0.480659i | ||||
\(448\) | −20.6491 | + | 4.64911i | −0.975579 | + | 0.219650i | ||||
\(449\) | 2.81139 | − | 2.81139i | 0.132678 | − | 0.132678i | −0.637649 | − | 0.770327i | \(-0.720093\pi\) |
0.770327 | + | 0.637649i | \(0.220093\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 59.6228i | 2.80753i | ||||||||
\(452\) | − | 29.6228i | − | 1.39334i | ||||||
\(453\) | −4.00000 | − | 4.00000i | −0.187936 | − | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.09431 | + | 4.93203i | 0.285705 | + | 0.231217i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.32456 | + | 1.32456i | 0.0619601 | + | 0.0619601i | 0.737408 | − | 0.675448i | \(-0.236050\pi\) |
−0.675448 | + | 0.737408i | \(0.736050\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1.16228i | − | 0.0542505i | ||||||
\(460\) | −4.83772 | + | 4.83772i | −0.225560 | + | 0.225560i | ||||
\(461\) | −20.3246 | + | 20.3246i | −0.946609 | + | 0.946609i | −0.998645 | − | 0.0520363i | \(-0.983429\pi\) |
0.0520363 | + | 0.998645i | \(0.483429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.64911 | − | 2.64911i | 0.123115 | − | 0.123115i | −0.642865 | − | 0.765980i | \(-0.722254\pi\) |
0.765980 | + | 0.642865i | \(0.222254\pi\) | |||||||
\(464\) | −7.35089 | −0.341256 | ||||||||
\(465\) | −6.48683 | −0.300820 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.9737 | −1.43329 | −0.716645 | − | 0.697438i | \(-0.754323\pi\) | ||||
−0.716645 | + | 0.697438i | \(0.754323\pi\) | |||||||
\(468\) | −0.837722 | + | 7.16228i | −0.0387237 | + | 0.331076i | ||||
\(469\) | 12.6491 | − | 20.0000i | 0.584082 | − | 0.923514i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.51317 | −0.115801 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.1623 | + | 22.1623i | 1.01902 | + | 1.01902i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.81139 | + | 1.81139i | 0.0831122 | + | 0.0831122i | ||||
\(476\) | 6.00000 | − | 1.35089i | 0.275010 | − | 0.0619179i | ||||
\(477\) | 4.16228 | 0.190578 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.41886 | − | 5.41886i | −0.247594 | − | 0.247594i | 0.572388 | − | 0.819983i | \(-0.306017\pi\) |
−0.819983 | + | 0.572388i | \(0.806017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2982 | − | 13.6754i | 0.788731 | − | 0.623547i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.41886 | + | 10.7434i | 0.110062 | + | 0.488842i | ||||
\(484\) | −47.2982 | −2.14992 | ||||||||
\(485\) | 0.486833i | 0.0221059i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.32456 | + | 1.32456i | 0.0600213 | + | 0.0600213i | 0.736480 | − | 0.676459i | \(-0.236486\pi\) |
−0.676459 | + | 0.736480i | \(0.736486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.32456 | − | 1.32456i | −0.0598985 | − | 0.0598985i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.3246i | − | 1.18801i | −0.804461 | − | 0.594005i | \(-0.797546\pi\) | ||
0.804461 | − | 0.594005i | \(-0.202454\pi\) | |||||||
\(492\) | −14.3246 | + | 14.3246i | −0.645801 | + | 0.645801i | ||||
\(493\) | 2.13594 | 0.0961981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.83772i | 0.217439i | ||||||||
\(496\) | 22.3246 | − | 22.3246i | 1.00240 | − | 1.00240i | ||||
\(497\) | −12.0000 | + | 18.9737i | −0.538274 | + | 0.851085i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.3246 | + | 19.3246i | 0.865086 | + | 0.865086i | 0.991923 | − | 0.126838i | \(-0.0404827\pi\) |
−0.126838 | + | 0.991923i | \(0.540483\pi\) | |||||||
\(500\) | 10.8377 | − | 10.8377i | 0.484678 | − | 0.484678i | ||||
\(501\) | 2.90569 | − | 2.90569i | 0.129817 | − | 0.129817i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 34.4605i | − | 1.53652i | −0.640139 | − | 0.768259i | \(-0.721123\pi\) | ||
0.640139 | − | 0.768259i | \(-0.278877\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3509 | − | 10.3509i | 0.460609 | − | 0.460609i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.00000 | + | 12.6491i | −0.133235 | + | 0.561767i | ||||
\(508\) | 4.00000 | 0.177471 | ||||||||
\(509\) | −20.9057 | + | 20.9057i | −0.926629 | + | 0.926629i | −0.997486 | − | 0.0708578i | \(-0.977426\pi\) |
0.0708578 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1623 | + | 17.6491i | −0.493790 | + | 0.780751i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.418861 | − | 0.418861i | −0.0184932 | − | 0.0184932i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.32456 | − | 2.32456i | 0.102432 | − | 0.102432i | ||||
\(516\) | 10.6491i | 0.468801i | ||||||||
\(517\) | −54.7851 | −2.40944 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.32456i | − | 0.102037i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.35089i | − | 0.322048i | −0.986950 | − | 0.161024i | \(-0.948520\pi\) | ||
0.986950 | − | 0.161024i | \(-0.0514797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5132i | 0.634616i | 0.948322 | + | 0.317308i | \(0.102779\pi\) | ||||
−0.948322 | + | 0.317308i | \(0.897221\pi\) | |||||||
\(524\) | 26.3246 | 1.14999 | ||||||||
\(525\) | −2.51317 | − | 11.1623i | −0.109684 | − | 0.487162i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.48683 | + | 6.48683i | −0.282571 | + | 0.282571i | ||||
\(528\) | −16.6491 | − | 16.6491i | −0.724560 | − | 0.724560i | ||||
\(529\) | 5.67544 | 0.246758 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.32456 | + | 8.32456i | 0.361255 | + | 0.361255i | ||||
\(532\) | 1.67544 | − | 2.64911i | 0.0726397 | − | 0.114854i | ||||
\(533\) | −28.6491 | + | 22.6491i | −1.24093 | + | 0.981042i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.18861 | − | 6.18861i | 0.267557 | − | 0.267557i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.486833 | −0.0210084 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.8377 | + | 38.8114i | −0.596033 | + | 1.67172i | ||||
\(540\) | −1.16228 | + | 1.16228i | −0.0500165 | + | 0.0500165i | ||||
\(541\) | −4.00000 | + | 4.00000i | −0.171973 | + | 0.171973i | −0.787846 | − | 0.615872i | \(-0.788804\pi\) |
0.615872 | + | 0.787846i | \(0.288804\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1623i | 0.650676i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.32456 | −0.0995730 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.6491 | 0.669108 | 0.334554 | − | 0.942377i | \(-0.391414\pi\) | ||||
0.334554 | + | 0.942377i | \(0.391414\pi\) | |||||||
\(548\) | 24.0000 | + | 24.0000i | 1.02523 | + | 1.02523i | ||||
\(549\) | − | 3.16228i | − | 0.134963i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.769751 | − | 0.769751i | 0.0327925 | − | 0.0327925i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.58114 | − | 29.2302i | −0.279858 | − | 1.24300i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.02633 | 0.213356 | ||||||||
\(556\) | −14.3246 | −0.607496 | ||||||||
\(557\) | −4.64911 | + | 4.64911i | −0.196989 | + | 0.196989i | −0.798708 | − | 0.601719i | \(-0.794483\pi\) |
0.601719 | + | 0.798708i | \(0.294483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.23025 | + | 19.0680i | −0.0943295 | + | 0.806489i | ||||
\(560\) | −7.35089 | − | 4.64911i | −0.310632 | − | 0.196461i | ||||
\(561\) | 4.83772 | + | 4.83772i | 0.204249 | + | 0.204249i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.4605 | 0.946597 | 0.473299 | − | 0.880902i | \(-0.343063\pi\) | ||||
0.473299 | + | 0.880902i | \(0.343063\pi\) | |||||||
\(564\) | −13.1623 | − | 13.1623i | −0.554232 | − | 0.554232i | ||||
\(565\) | 8.60747 | − | 8.60747i | 0.362119 | − | 0.362119i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.581139 | + | 2.58114i | 0.0244055 | + | 0.108398i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.4868i | 1.27807i | 0.769176 | + | 0.639037i | \(0.220667\pi\) | ||||
−0.769176 | + | 0.639037i | \(0.779333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 21.3246i | − | 0.892405i | −0.894932 | − | 0.446202i | \(-0.852776\pi\) | ||
0.894932 | − | 0.446202i | \(-0.147224\pi\) | |||||||
\(572\) | −26.3246 | − | 33.2982i | −1.10068 | − | 1.39227i | ||||
\(573\) | − | 14.3246i | − | 0.598417i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.0000 | 0.750652 | ||||||||
\(576\) | − | 8.00000i | − | 0.333333i | ||||||
\(577\) | 8.00000 | − | 8.00000i | 0.333044 | − | 0.333044i | −0.520697 | − | 0.853741i | \(-0.674328\pi\) |
0.853741 | + | 0.520697i | \(0.174328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.32456 | + | 6.32456i | 0.262840 | + | 0.262840i | ||||
\(580\) | −2.13594 | − | 2.13594i | −0.0886902 | − | 0.0886902i | ||||
\(581\) | −20.8114 | − | 13.1623i | −0.863402 | − | 0.546063i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.3246 | + | 17.3246i | −0.717510 | + | 0.717510i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.32456 | + | 1.83772i | −0.0961085 | + | 0.0759805i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.74342 | + | 1.74342i | −0.0719585 | + | 0.0719585i | −0.742170 | − | 0.670212i | \(-0.766203\pi\) |
0.670212 | + | 0.742170i | \(0.266203\pi\) | |||||||
\(588\) | −12.6491 | + | 6.00000i | −0.521641 | + | 0.247436i | ||||
\(589\) | 4.67544i | 0.192648i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.83772 | − | 1.83772i | 0.0755938 | − | 0.0755938i | ||||
\(592\) | −17.2982 | + | 17.2982i | −0.710953 | + | 0.710953i | ||||
\(593\) | −3.09431 | − | 3.09431i | −0.127068 | − | 0.127068i | 0.640713 | − | 0.767781i | \(-0.278639\pi\) |
−0.767781 | + | 0.640713i | \(0.778639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.13594 | + | 1.35089i | 0.0875652 | + | 0.0553811i | ||||
\(596\) | −20.3246 | + | 20.3246i | −0.832526 | + | 0.832526i | ||||
\(597\) | − | 9.48683i | − | 0.388270i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.18861 | −0.375436 | −0.187718 | − | 0.982223i | \(-0.560109\pi\) | ||||
−0.187718 | + | 0.982223i | \(0.560109\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 31.6228i | − | 1.28992i | −0.764216 | − | 0.644960i | \(-0.776874\pi\) | ||
0.764216 | − | 0.644960i | \(-0.223126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.32456 | + | 6.32456i | 0.257556 | + | 0.257556i | ||||
\(604\) | 8.00000 | + | 8.00000i | 0.325515 | + | 0.325515i | ||||
\(605\) | −13.7434 | − | 13.7434i | −0.558749 | − | 0.558749i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.8377i | 1.17049i | 0.810858 | + | 0.585244i | \(0.199001\pi\) | ||||
−0.810858 | + | 0.585244i | \(0.800999\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.74342 | + | 1.06797i | −0.192213 | + | 0.0432764i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.8114 | − | 26.3246i | −0.841939 | − | 1.06498i | ||||
\(612\) | 2.32456i | 0.0939646i | ||||||||
\(613\) | −7.32456 | − | 7.32456i | −0.295836 | − | 0.295836i | 0.543544 | − | 0.839380i | \(-0.317082\pi\) |
−0.839380 | + | 0.543544i | \(0.817082\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.32456 | −0.335678 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4868 | + | 24.4868i | 0.985803 | + | 0.985803i | 0.999901 | − | 0.0140978i | \(-0.00448763\pi\) |
−0.0140978 | + | 0.999901i | \(0.504488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.67544 | − | 5.67544i | −0.228115 | − | 0.228115i | 0.583790 | − | 0.811905i | \(-0.301569\pi\) |
−0.811905 | + | 0.583790i | \(0.801569\pi\) | |||||||
\(620\) | 12.9737 | 0.521035 | ||||||||
\(621\) | −4.16228 | −0.167026 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.8377 | − | 17.1359i | 0.434204 | − | 0.686537i | ||||
\(624\) | 1.67544 | − | 14.3246i | 0.0670715 | − | 0.573441i | ||||
\(625\) | −15.3246 | −0.612982 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.48683 | 0.139251 | ||||||||
\(628\) | 5.02633 | 0.200573 | ||||||||
\(629\) | 5.02633 | − | 5.02633i | 0.200413 | − | 0.200413i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.64911 | − | 3.64911i | 0.145269 | − | 0.145269i | −0.630732 | − | 0.776001i | \(-0.717245\pi\) |
0.776001 | + | 0.630732i | \(0.217245\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.6491i | 0.780982i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.16228 | + | 1.16228i | 0.0461236 | + | 0.0461236i | ||||
\(636\) | −8.32456 | −0.330090 | ||||||||
\(637\) | −23.9057 | + | 8.09431i | −0.947178 | + | 0.320708i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | − | 6.00000i | −0.237356 | − | 0.237356i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.4868i | 0.967172i | 0.875297 | + | 0.483586i | \(0.160666\pi\) | ||||
−0.875297 | + | 0.483586i | \(0.839334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.18861 | + | 4.18861i | −0.165183 | + | 0.165183i | −0.784858 | − | 0.619675i | \(-0.787264\pi\) |
0.619675 | + | 0.784858i | \(0.287264\pi\) | |||||||
\(644\) | −4.83772 | − | 21.4868i | −0.190633 | − | 0.846700i | ||||
\(645\) | −3.09431 | + | 3.09431i | −0.121838 | + | 0.121838i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.97367 | 0.274163 | 0.137082 | − | 0.990560i | \(-0.456228\pi\) | ||||
0.137082 | + | 0.990560i | \(0.456228\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −69.2982 | −2.72019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1623 | − | 17.6491i | 0.437484 | − | 0.691723i | ||||
\(652\) | 2.64911 | + | 2.64911i | 0.103747 | + | 0.103747i | ||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.64911 | + | 7.64911i | 0.298875 | + | 0.298875i | ||||
\(656\) | 28.6491 | − | 28.6491i | 1.11856 | − | 1.11856i | ||||
\(657\) | −5.58114 | − | 5.58114i | −0.217741 | − | 0.217741i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4605 | −0.524347 | −0.262173 | − | 0.965021i | \(-0.584439\pi\) | ||||
−0.262173 | + | 0.965021i | \(0.584439\pi\) | |||||||
\(660\) | − | 9.67544i | − | 0.376616i | ||||||
\(661\) | 3.90569 | + | 3.90569i | 0.151914 | + | 0.151914i | 0.778972 | − | 0.627058i | \(-0.215741\pi\) |
−0.627058 | + | 0.778972i | \(0.715741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.486833 | + | 4.16228i | −0.0189070 | + | 0.161649i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.25658 | − | 0.282918i | 0.0487282 | − | 0.0109711i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.64911i | − | 0.296175i | ||||||
\(668\) | −5.81139 | + | 5.81139i | −0.224849 | + | 0.224849i | ||||
\(669\) | 5.25658 | + | 5.25658i | 0.203231 | + | 0.203231i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1623 | + | 13.1623i | 0.508124 | + | 0.508124i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6228i | 0.794950i | 0.917613 | + | 0.397475i | \(0.130113\pi\) | ||||
−0.917613 | + | 0.397475i | \(0.869887\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.32456 | 0.166452 | ||||||||
\(676\) | 6.00000 | − | 25.2982i | 0.230769 | − | 0.973009i | ||||
\(677\) | 12.0000i | 0.461197i | 0.973049 | + | 0.230599i | \(0.0740685\pi\) | ||||
−0.973049 | + | 0.230599i | \(0.925932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.32456 | − | 0.837722i | −0.0508318 | − | 0.0321488i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.83772 | + | 4.83772i | 0.185382 | + | 0.185382i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.6491 | − | 22.6491i | 0.866644 | − | 0.866644i | −0.125455 | − | 0.992099i | \(-0.540039\pi\) |
0.992099 | + | 0.125455i | \(0.0400391\pi\) | |||||||
\(684\) | 0.837722 | + | 0.837722i | 0.0320311 | + | 0.0320311i | ||||
\(685\) | 13.9473i | 0.532900i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.3246 | − | 18.3246i | 0.699125 | − | 0.699125i | ||||
\(688\) | − | 21.2982i | − | 0.811987i | ||||||
\(689\) | −14.9057 | − | 1.74342i | −0.567862 | − | 0.0664189i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.4189 | + | 12.4189i | −0.472436 | + | 0.472436i | −0.902702 | − | 0.430266i | \(-0.858420\pi\) |
0.430266 | + | 0.902702i | \(0.358420\pi\) | |||||||
\(692\) | 4.64911i | 0.176733i | ||||||||
\(693\) | −13.1623 | − | 8.32456i | −0.499994 | − | 0.316224i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.16228 | − | 4.16228i | −0.157884 | − | 0.157884i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.32456 | + | 8.32456i | −0.315315 | + | 0.315315i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.1623 | −0.838254 | ||||||||
\(700\) | 5.02633 | + | 22.3246i | 0.189978 | + | 0.843789i | ||||
\(701\) | 1.83772i | 0.0694098i | 0.999398 | + | 0.0347049i | \(0.0110491\pi\) | ||||
−0.999398 | + | 0.0347049i | \(0.988951\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.62278i | − | 0.136636i | ||||||
\(704\) | 33.2982 | + | 33.2982i | 1.25497 | + | 1.25497i | ||||
\(705\) | − | 7.64911i | − | 0.288082i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3509 | + | 45.9737i | 0.389285 | + | 1.72902i | ||||
\(708\) | −16.6491 | − | 16.6491i | −0.625712 | − | 0.625712i | ||||
\(709\) | 32.2982 | − | 32.2982i | 1.21299 | − | 1.21299i | 0.242945 | − | 0.970040i | \(-0.421887\pi\) |
0.970040 | − | 0.242945i | \(-0.0781135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3246 | 0.424704 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.2302 | + | 23.2302i | 0.869980 | + | 0.869980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.02633 | − | 17.3246i | 0.0757806 | − | 0.647902i | ||||
\(716\) | 0.973666 | 0.0363876 | ||||||||
\(717\) | 6.48683 | − | 6.48683i | 0.242255 | − | 0.242255i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.9737 | 0.707598 | 0.353799 | − | 0.935321i | \(-0.384890\pi\) | ||||
0.353799 | + | 0.935321i | \(0.384890\pi\) | |||||||
\(720\) | 2.32456 | − | 2.32456i | 0.0866311 | − | 0.0866311i | ||||
\(721\) | 2.32456 | + | 10.3246i | 0.0865710 | + | 0.384507i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.90569 | + | 3.90569i | −0.145254 | + | 0.145254i | ||||
\(724\) | − | 30.3246i | − | 1.12700i | ||||||
\(725\) | 7.94733i | 0.295156i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.2982 | 1.23496 | 0.617481 | − | 0.786586i | \(-0.288153\pi\) | ||||
0.617481 | + | 0.786586i | \(0.288153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.18861i | 0.228894i | ||||||||
\(732\) | 6.32456i | 0.233762i | ||||||||
\(733\) | 27.9057 | − | 27.9057i | 1.03072 | − | 1.03072i | 0.0312074 | − | 0.999513i | \(-0.490065\pi\) |
0.999513 | − | 0.0312074i | \(-0.00993524\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.41886 | − | 1.93203i | −0.199878 | − | 0.0712639i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −52.6491 | −1.93935 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.64911 | + | 5.64911i | −0.207806 | + | 0.207806i | −0.803334 | − | 0.595528i | \(-0.796943\pi\) |
0.595528 | + | 0.803334i | \(0.296943\pi\) | |||||||
\(740\) | −10.0527 | −0.369543 | ||||||||
\(741\) | 1.32456 | + | 1.67544i | 0.0486588 | + | 0.0615490i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.83772 | − | 7.83772i | −0.287538 | − | 0.287538i | 0.548568 | − | 0.836106i | \(-0.315173\pi\) |
−0.836106 | + | 0.548568i | \(0.815173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.8114 | −0.432736 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.58114 | − | 6.58114i | 0.240791 | − | 0.240791i | ||||
\(748\) | −9.67544 | − | 9.67544i | −0.353769 | − | 0.353769i | ||||
\(749\) | 6.18861 | + | 27.4868i | 0.226127 | + | 1.00435i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.3246i | − | 0.413239i | −0.978421 | − | 0.206619i | \(-0.933754\pi\) | ||
0.978421 | − | 0.206619i | \(-0.0662462\pi\) | |||||||
\(752\) | 26.3246 | + | 26.3246i | 0.959958 | + | 0.959958i | ||||
\(753\) | − | 27.4868i | − | 1.00168i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.64911i | 0.169198i | ||||||||
\(756\) | −1.16228 | − | 5.16228i | −0.0422716 | − | 0.187750i | ||||
\(757\) | 25.6491 | 0.932233 | 0.466116 | − | 0.884723i | \(-0.345653\pi\) | ||||
0.466116 | + | 0.884723i | \(0.345653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.3246 | − | 17.3246i | 0.628842 | − | 0.628842i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.76975 | + | 6.76975i | 0.245403 | + | 0.245403i | 0.819081 | − | 0.573678i | \(-0.194484\pi\) |
−0.573678 | + | 0.819081i | \(0.694484\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00000 | − | 6.32456i | 0.144810 | − | 0.228964i | ||||
\(764\) | 28.6491i | 1.03649i | ||||||||
\(765\) | −0.675445 | + | 0.675445i | −0.0244208 | + | 0.0244208i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.3246 | − | 33.2982i | −0.950525 | − | 1.20233i | ||||
\(768\) | 16.0000i | 0.577350i | ||||||||
\(769\) | −20.0943 | + | 20.0943i | −0.724619 | + | 0.724619i | −0.969542 | − | 0.244923i | \(-0.921237\pi\) |
0.244923 | + | 0.969542i | \(0.421237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.4868i | 0.989914i | ||||||||
\(772\) | −12.6491 | − | 12.6491i | −0.455251 | − | 0.455251i | ||||
\(773\) | −9.48683 | + | 9.48683i | −0.341218 | + | 0.341218i | −0.856825 | − | 0.515607i | \(-0.827566\pi\) |
0.515607 | + | 0.856825i | \(0.327566\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.1359 | − | 24.1359i | −0.866989 | − | 0.866989i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.64911 | + | 13.6754i | −0.310285 | + | 0.490604i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000i | 0.214972i | ||||||||
\(780\) | 4.64911 | − | 3.67544i | 0.166465 | − | 0.131602i | ||||
\(781\) | 49.9473 | 1.78726 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.83772i | − | 0.0656748i | ||||||
\(784\) | 25.2982 | − | 12.0000i | 0.903508 | − | 0.428571i | ||||
\(785\) | 1.46050 | + | 1.46050i | 0.0521274 | + | 0.0521274i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.0680 | + | 21.0680i | 0.750992 | + | 0.750992i | 0.974664 | − | 0.223672i | \(-0.0718045\pi\) |
−0.223672 | + | 0.974664i | \(0.571805\pi\) | |||||||
\(788\) | −3.67544 | + | 3.67544i | −0.130932 | + | 0.130932i | ||||
\(789\) | 18.4868i | 0.658149i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.60747 | + | 38.2302i | 0.306047 | + | 1.35931i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.32456 | + | 11.3246i | −0.0470363 | + | 0.402147i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.41886 | − | 2.41886i | −0.0857882 | − | 0.0857882i | ||||
\(796\) | 18.9737i | 0.672504i | ||||||||
\(797\) | 33.2982 | 1.17948 | 0.589742 | − | 0.807592i | \(-0.299230\pi\) | ||||
0.589742 | + | 0.807592i | \(0.299230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.64911 | − | 7.64911i | −0.270606 | − | 0.270606i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.41886 | + | 5.41886i | 0.191466 | + | 0.191466i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 46.4605 | 1.63956 | ||||||||
\(804\) | −12.6491 | − | 12.6491i | −0.446100 | − | 0.446100i | ||||
\(805\) | 4.83772 | − | 7.64911i | 0.170507 | − | 0.269596i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.48683 | 0.122742 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.4605 | −0.473246 | −0.236623 | − | 0.971602i | \(-0.576041\pi\) | ||||
−0.236623 | + | 0.971602i | \(0.576041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.8114 | − | 31.8114i | 1.11705 | − | 1.11705i | 0.124877 | − | 0.992172i | \(-0.460146\pi\) |
0.992172 | − | 0.124877i | \(-0.0398535\pi\) | |||||||
\(812\) | 9.48683 | − | 2.13594i | 0.332923 | − | 0.0749569i | ||||
\(813\) | 13.4868 | − | 13.4868i | 0.473004 | − | 0.473004i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.53950i | 0.0539264i | ||||||||
\(816\) | − | 4.64911i | − | 0.162751i | ||||||
\(817\) | 2.23025 | + | 2.23025i | 0.0780266 | + | 0.0780266i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | − | 9.48683i | −0.0349428 | − | 0.331497i | ||||
\(820\) | 16.6491 | 0.581412 | ||||||||
\(821\) | −20.3246 | − | 20.3246i | −0.709332 | − | 0.709332i | 0.257063 | − | 0.966395i | \(-0.417245\pi\) |
−0.966395 | + | 0.257063i | \(0.917245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 13.3509i | − | 0.465383i | −0.972551 | − | 0.232691i | \(-0.925247\pi\) | ||
0.972551 | − | 0.232691i | \(-0.0747532\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.0000 | + | 18.0000i | −0.626680 | + | 0.626680i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.1623 | − | 16.1623i | 0.562017 | − | 0.562017i | −0.367863 | − | 0.929880i | \(-0.619910\pi\) |
0.929880 | + | 0.367863i | \(0.119910\pi\) | |||||||
\(828\) | 8.32456 | 0.289298 | ||||||||
\(829\) | 33.6754 | 1.16960 | 0.584798 | − | 0.811179i | \(-0.301174\pi\) | ||||
0.584798 | + | 0.811179i | \(0.301174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.35089 | −0.150931 | ||||||||
\(832\) | −3.35089 | + | 28.6491i | −0.116171 | + | 0.993229i | ||||
\(833\) | −7.35089 | + | 3.48683i | −0.254693 | + | 0.120812i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.37722 | −0.116874 | ||||||||
\(836\) | −6.97367 | −0.241189 | ||||||||
\(837\) | 5.58114 | + | 5.58114i | 0.192912 | + | 0.192912i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.4868 | − | 21.4868i | −0.741808 | − | 0.741808i | 0.231118 | − | 0.972926i | \(-0.425762\pi\) |
−0.972926 | + | 0.231118i | \(0.925762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6228 | −0.883544 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.67544 | + | 9.67544i | 0.333240 | + | 0.333240i | ||||
\(844\) | − | 39.2982i | − | 1.35270i | ||||||
\(845\) | 9.09431 | − | 5.60747i | 0.312854 | − | 0.192903i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 61.0416 | − | 13.7434i | 2.09742 | − | 0.472229i | ||||
\(848\) | 16.6491 | 0.571733 | ||||||||
\(849\) | − | 21.2982i | − | 0.730953i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.0000 | − | 18.0000i | −0.617032 | − | 0.617032i | ||||
\(852\) | 12.0000 | + | 12.0000i | 0.411113 | + | 0.411113i | ||||
\(853\) | 1.90569 | + | 1.90569i | 0.0652497 | + | 0.0652497i | 0.738979 | − | 0.673729i | \(-0.235308\pi\) |
−0.673729 | + | 0.738979i | \(0.735308\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.486833i | 0.0166493i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.7851 | −1.25655 | −0.628277 | − | 0.777990i | \(-0.716239\pi\) | ||||
−0.628277 | + | 0.777990i | \(0.716239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.29822i | 0.0442947i | 0.999755 | + | 0.0221474i | \(0.00705030\pi\) | ||||
−0.999755 | + | 0.0221474i | \(0.992950\pi\) | |||||||
\(860\) | 6.18861 | − | 6.18861i | 0.211030 | − | 0.211030i | ||||
\(861\) | 14.3246 | − | 22.6491i | 0.488180 | − | 0.771880i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.29822 | + | 9.29822i | 0.316515 | + | 0.316515i | 0.847427 | − | 0.530912i | \(-0.178150\pi\) |
−0.530912 | + | 0.847427i | \(0.678150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.35089 | + | 1.35089i | −0.0459316 | + | 0.0459316i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 15.6491i | − | 0.531472i | ||||||
\(868\) | −22.3246 | + | 35.2982i | −0.757745 | + | 1.19810i | ||||
\(869\) | −47.1359 | + | 47.1359i | −1.59898 | + | 1.59898i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | − | 25.2982i | −0.677674 | − | 0.857198i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.418861 | − | 0.418861i | 0.0141763 | − | 0.0141763i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8377 | + | 17.1359i | −0.366382 | + | 0.579301i | ||||
\(876\) | 11.1623 | + | 11.1623i | 0.377138 | + | 0.377138i | ||||
\(877\) | −31.3246 | − | 31.3246i | −1.05776 | − | 1.05776i | −0.998227 | − | 0.0595285i | \(-0.981040\pi\) |
−0.0595285 | − | 0.998227i | \(-0.518960\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.0680 | − | 22.0680i | 0.744334 | − | 0.744334i | ||||
\(880\) | 19.3509i | 0.652318i | ||||||||
\(881\) | 23.6228 | 0.795872 | 0.397936 | − | 0.917413i | \(-0.369727\pi\) | ||||
0.397936 | + | 0.917413i | \(0.369727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.6491i | − | 0.627593i | −0.949490 | − | 0.313796i | \(-0.898399\pi\) | ||
0.949490 | − | 0.313796i | \(-0.101601\pi\) | |||||||
\(884\) | 0.973666 | − | 8.32456i | 0.0327479 | − | 0.279985i | ||||
\(885\) | − | 9.67544i | − | 0.325237i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 27.4868i | − | 0.922918i | −0.887162 | − | 0.461459i | \(-0.847326\pi\) | ||
0.887162 | − | 0.461459i | \(-0.152674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.16228 | + | 1.16228i | −0.173137 | + | 0.0389815i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.16228 | − | 4.16228i | 0.139442 | − | 0.139442i | ||||
\(892\) | −10.5132 | − | 10.5132i | −0.352007 | − | 0.352007i | ||||
\(893\) | −5.51317 | −0.184491 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.282918 | + | 0.282918i | 0.00945689 | + | 0.00945689i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.9057 | + | 1.74342i | 0.497687 | + | 0.0582110i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.2566 | + | 10.2566i | −0.342076 | + | 0.342076i | ||||
\(900\) | −8.64911 | −0.288304 | ||||||||
\(901\) | −4.83772 | −0.161168 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.09431 | − | 13.7434i | −0.102972 | − | 0.457352i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.81139 | − | 8.81139i | 0.292900 | − | 0.292900i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 30.9473i | − | 1.02759i | −0.857913 | − | 0.513795i | \(-0.828239\pi\) | ||
0.857913 | − | 0.513795i | \(-0.171761\pi\) | |||||||
\(908\) | −9.67544 | − | 9.67544i | −0.321091 | − | 0.321091i | ||||
\(909\) | −17.8114 | −0.590766 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.5132 | 0.580237 | 0.290119 | − | 0.956991i | \(-0.406305\pi\) | ||||
0.290119 | + | 0.956991i | \(0.406305\pi\) | |||||||
\(912\) | −1.67544 | − | 1.67544i | −0.0554795 | − | 0.0554795i | ||||
\(913\) | 54.7851i | 1.81312i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.83772 | + | 1.83772i | −0.0607532 | + | 0.0607532i | ||||
\(916\) | −36.6491 | + | 36.6491i | −1.21092 | + | 1.21092i | ||||
\(917\) | −33.9737 | + | 7.64911i | −1.12191 | + | 0.252596i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2982 | −0.504642 | −0.252321 | − | 0.967644i | \(-0.581194\pi\) | ||||
−0.252321 | + | 0.967644i | \(0.581194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.0680 | + | 11.0680i | −0.364702 | + | 0.364702i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.9737 | + | 24.0000i | 0.624526 | + | 0.789970i | ||||
\(924\) | 26.3246 | + | 16.6491i | 0.866014 | + | 0.547716i | ||||
\(925\) | 18.7018 | + | 18.7018i | 0.614911 | + | 0.614911i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.2566 | − | 22.2566i | 0.730215 | − | 0.730215i | −0.240447 | − | 0.970662i | \(-0.577294\pi\) |
0.970662 | + | 0.240447i | \(0.0772941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.39253 | + | 3.90569i | −0.0456382 | + | 0.128004i | ||||
\(932\) | 44.3246 | 1.45190 | ||||||||
\(933\) | − | 14.3246i | − | 0.468965i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.62278i | − | 0.183884i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.9737i | − | 0.881191i | −0.897706 | − | 0.440596i | \(-0.854767\pi\) | ||
0.897706 | − | 0.440596i | \(-0.145233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.8114 | −0.646520 | ||||||||
\(940\) | 15.2982i | 0.498973i | ||||||||
\(941\) | 14.7171 | − | 14.7171i | 0.479763 | − | 0.479763i | −0.425293 | − | 0.905056i | \(-0.639829\pi\) |
0.905056 | + | 0.425293i | \(0.139829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.8114 | + | 29.8114i | 0.970792 | + | 0.970792i | ||||
\(944\) | 33.2982 | + | 33.2982i | 1.08376 | + | 1.08376i | ||||
\(945\) | 1.16228 | − | 1.83772i | 0.0378089 | − | 0.0597811i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.6754 | − | 21.6754i | 0.704357 | − | 0.704357i | −0.260985 | − | 0.965343i | \(-0.584047\pi\) |
0.965343 | + | 0.260985i | \(0.0840475\pi\) | |||||||
\(948\) | −22.6491 | −0.735609 | ||||||||
\(949\) | 17.6491 | + | 22.3246i | 0.572914 | + | 0.724686i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.83772 | − | 1.83772i | 0.0595922 | − | 0.0595922i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 0.486833i | − | 0.0157701i | −0.999969 | − | 0.00788503i | \(-0.997490\pi\) | ||
0.999969 | − | 0.00788503i | \(-0.00250991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.32456 | + | 8.32456i | −0.269376 | + | 0.269376i | ||||
\(956\) | −12.9737 | + | 12.9737i | −0.419598 | + | 0.419598i | ||||
\(957\) | 7.64911 | + | 7.64911i | 0.247261 | + | 0.247261i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.9473 | − | 24.0000i | −1.22538 | − | 0.775000i | ||||
\(960\) | −4.64911 | + | 4.64911i | −0.150049 | + | 0.150049i | ||||
\(961\) | − | 31.2982i | − | 1.00962i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.6491 | −0.343163 | ||||||||
\(964\) | 7.81139 | − | 7.81139i | 0.251588 | − | 0.251588i | ||||
\(965\) | − | 7.35089i | − | 0.236634i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.9473 | + | 42.9473i | 1.38109 | + | 1.38109i | 0.842683 | + | 0.538410i | \(0.180975\pi\) |
0.538410 | + | 0.842683i | \(0.319025\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.486833 | + | 0.486833i | 0.0156393 | + | 0.0156393i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.4868i | 1.26719i | 0.773664 | + | 0.633596i | \(0.218422\pi\) | ||||
−0.773664 | + | 0.633596i | \(0.781578\pi\) | |||||||
\(972\) | 2.00000 | 0.0641500 | ||||||||
\(973\) | 18.4868 | − | 4.16228i | 0.592661 | − | 0.133436i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.4868 | − | 1.81139i | −0.495976 | − | 0.0580109i | ||||
\(976\) | − | 12.6491i | − | 0.404888i | ||||||
\(977\) | 1.83772 | + | 1.83772i | 0.0587939 | + | 0.0587939i | 0.735892 | − | 0.677098i | \(-0.236763\pi\) |
−0.677098 | + | 0.735892i | \(0.736763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45.1096 | −1.44171 | ||||||||
\(980\) | 10.8377 | + | 3.86406i | 0.346198 | + | 0.123433i | ||||
\(981\) | 2.00000 | + | 2.00000i | 0.0638551 | + | 0.0638551i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.7434 | − | 25.7434i | −0.821087 | − | 0.821087i | 0.165177 | − | 0.986264i | \(-0.447181\pi\) |
−0.986264 | + | 0.165177i | \(0.947181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.13594 | −0.0680568 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.8114 | + | 13.1623i | 0.662434 | + | 0.418960i | ||||
\(988\) | −2.64911 | − | 3.35089i | −0.0842794 | − | 0.106606i | ||||
\(989\) | 22.1623 | 0.704719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.0000 | −1.20711 | −0.603555 | − | 0.797321i | \(-0.706250\pi\) | ||||
−0.603555 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.6491 | + | 23.6491i | −0.750482 | + | 0.750482i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.51317 | + | 5.51317i | −0.174779 | + | 0.174779i | ||||
\(996\) | −13.1623 | + | 13.1623i | −0.417063 | + | 0.417063i | ||||
\(997\) | − | 33.2982i | − | 1.05457i | −0.849690 | − | 0.527283i | \(-0.823211\pi\) | ||
0.849690 | − | 0.527283i | \(-0.176789\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.32456 | − | 4.32456i | −0.136823 | − | 0.136823i |
(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 | 273.2.p.b.34.2 | ✓ | 4 | |
3.2 | odd | 2 | 819.2.y.c.307.1 | 4 | |||
7.6 | odd | 2 | 273.2.p.c.34.1 | yes | 4 | ||
13.5 | odd | 4 | 273.2.p.c.265.1 | yes | 4 | ||
21.20 | even | 2 | 819.2.y.b.307.2 | 4 | |||
39.5 | even | 4 | 819.2.y.b.811.2 | 4 | |||
91.83 | even | 4 | inner | 273.2.p.b.265.2 | yes | 4 | |
273.83 | odd | 4 | 819.2.y.c.811.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.p.b.34.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
273.2.p.b.265.2 | yes | 4 | 91.83 | even | 4 | inner | |
273.2.p.c.34.1 | yes | 4 | 7.6 | odd | 2 | ||
273.2.p.c.265.1 | yes | 4 | 13.5 | odd | 4 | ||
819.2.y.b.307.2 | 4 | 21.20 | even | 2 | |||
819.2.y.b.811.2 | 4 | 39.5 | even | 4 | |||
819.2.y.c.307.1 | 4 | 3.2 | odd | 2 | |||
819.2.y.c.811.1 | 4 | 273.83 | odd | 4 |