Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.107 |
Dual form | 225.4.f.b.143.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12132 | + | 2.12132i | −0.750000 | + | 0.750000i | −0.974479 | − | 0.224479i | \(-0.927932\pi\) |
0.224479 | + | 0.974479i | \(0.427932\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.125000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.00000 | + | 9.00000i | 0.485954 | + | 0.485954i | 0.907027 | − | 0.421073i | \(-0.138346\pi\) |
−0.421073 | + | 0.907027i | \(0.638346\pi\) | |||||||
\(8\) | −14.8492 | − | 14.8492i | −0.656250 | − | 0.656250i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 38.1838i | − | 1.04662i | −0.852142 | − | 0.523311i | \(-0.824697\pi\) | ||
0.852142 | − | 0.523311i | \(-0.175303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −63.0000 | + | 63.0000i | −1.34408 | + | 1.34408i | −0.452128 | + | 0.891953i | \(0.649335\pi\) |
−0.891953 | + | 0.452128i | \(0.850665\pi\) | |||||||
\(14\) | −38.1838 | −0.728931 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 71.0000 | 1.10938 | ||||||||
\(17\) | −29.6985 | + | 29.6985i | −0.423702 | + | 0.423702i | −0.886476 | − | 0.462774i | \(-0.846854\pi\) |
0.462774 | + | 0.886476i | \(0.346854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 70.0000i | − | 0.845216i | −0.906313 | − | 0.422608i | \(-0.861115\pi\) | ||
0.906313 | − | 0.422608i | \(-0.138885\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 81.0000 | + | 81.0000i | 0.784966 | + | 0.784966i | ||||
\(23\) | −72.1249 | − | 72.1249i | −0.653873 | − | 0.653873i | 0.300050 | − | 0.953923i | \(-0.402997\pi\) |
−0.953923 | + | 0.300050i | \(0.902997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 267.286i | − | 2.01612i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.00000 | − | 9.00000i | 0.0607443 | − | 0.0607443i | ||||
\(29\) | −229.103 | −1.46701 | −0.733505 | − | 0.679684i | \(-0.762117\pi\) | ||||
−0.733505 | + | 0.679684i | \(0.762117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 196.000 | 1.13557 | 0.567785 | − | 0.823177i | \(-0.307801\pi\) | ||||
0.567785 | + | 0.823177i | \(0.307801\pi\) | |||||||
\(32\) | −31.8198 | + | 31.8198i | −0.175781 | + | 0.175781i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 126.000i | − | 0.635554i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −207.000 | − | 207.000i | −0.919746 | − | 0.919746i | 0.0772649 | − | 0.997011i | \(-0.475381\pi\) |
−0.997011 | + | 0.0772649i | \(0.975381\pi\) | |||||||
\(38\) | 148.492 | + | 148.492i | 0.633912 | + | 0.633912i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 267.286i | − | 1.01812i | −0.860730 | − | 0.509062i | \(-0.829992\pi\) | ||
0.860730 | − | 0.509062i | \(-0.170008\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 144.000 | − | 144.000i | 0.510693 | − | 0.510693i | −0.404046 | − | 0.914739i | \(-0.632396\pi\) |
0.914739 | + | 0.404046i | \(0.132396\pi\) | |||||||
\(44\) | −38.1838 | −0.130828 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 306.000 | 0.980810 | ||||||||
\(47\) | 356.382 | − | 356.382i | 1.10603 | − | 1.10603i | 0.112368 | − | 0.993667i | \(-0.464156\pi\) |
0.993667 | − | 0.112368i | \(-0.0358436\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 181.000i | − | 0.527697i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 63.0000 | + | 63.0000i | 0.168010 | + | 0.168010i | ||||
\(53\) | 224.860 | + | 224.860i | 0.582772 | + | 0.582772i | 0.935664 | − | 0.352892i | \(-0.114802\pi\) |
−0.352892 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 267.286i | − | 0.637815i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 486.000 | − | 486.000i | 1.10026 | − | 1.10026i | ||||
\(59\) | −267.286 | −0.589792 | −0.294896 | − | 0.955529i | \(-0.595285\pi\) | ||||
−0.294896 | + | 0.955529i | \(0.595285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −322.000 | −0.675867 | −0.337933 | − | 0.941170i | \(-0.609728\pi\) | ||||
−0.337933 | + | 0.941170i | \(0.609728\pi\) | |||||||
\(62\) | −415.779 | + | 415.779i | −0.851677 | + | 0.851677i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000i | 0.845703i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −378.000 | − | 378.000i | −0.689254 | − | 0.689254i | 0.272813 | − | 0.962067i | \(-0.412046\pi\) |
−0.962067 | + | 0.272813i | \(0.912046\pi\) | |||||||
\(68\) | 29.6985 | + | 29.6985i | 0.0529628 | + | 0.0529628i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 840.043i | 1.40415i | 0.712102 | + | 0.702076i | \(0.247743\pi\) | ||||
−0.712102 | + | 0.702076i | \(0.752257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −378.000 | + | 378.000i | −0.606049 | + | 0.606049i | −0.941911 | − | 0.335862i | \(-0.890972\pi\) |
0.335862 | + | 0.941911i | \(0.390972\pi\) | |||||||
\(74\) | 878.227 | 1.37962 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −70.0000 | −0.105652 | ||||||||
\(77\) | 343.654 | − | 343.654i | 0.508610 | − | 0.508610i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 488.000i | − | 0.694991i | −0.937682 | − | 0.347496i | \(-0.887032\pi\) | ||
0.937682 | − | 0.347496i | \(-0.112968\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 567.000 | + | 567.000i | 0.763594 | + | 0.763594i | ||||
\(83\) | −772.161 | − | 772.161i | −1.02115 | − | 1.02115i | −0.999771 | − | 0.0213809i | \(-0.993194\pi\) |
−0.0213809 | − | 0.999771i | \(-0.506806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 610.940i | 0.766039i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −567.000 | + | 567.000i | −0.686845 | + | 0.686845i | ||||
\(89\) | −267.286 | −0.318340 | −0.159170 | − | 0.987251i | \(-0.550882\pi\) | ||||
−0.159170 | + | 0.987251i | \(0.550882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1134.00 | −1.30632 | ||||||||
\(92\) | −72.1249 | + | 72.1249i | −0.0817341 | + | 0.0817341i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1512.00i | 1.65905i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 252.000 | + | 252.000i | 0.263781 | + | 0.263781i | 0.826588 | − | 0.562807i | \(-0.190279\pi\) |
−0.562807 | + | 0.826588i | \(0.690279\pi\) | |||||||
\(98\) | 383.959 | + | 383.959i | 0.395773 | + | 0.395773i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1603.72i | 1.57996i | 0.613133 | + | 0.789980i | \(0.289909\pi\) | ||||
−0.613133 | + | 0.789980i | \(0.710091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −945.000 | + | 945.000i | −0.904016 | + | 0.904016i | −0.995781 | − | 0.0917650i | \(-0.970749\pi\) |
0.0917650 | + | 0.995781i | \(0.470749\pi\) | |||||||
\(104\) | 1871.00 | 1.76411 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −954.000 | −0.874157 | ||||||||
\(107\) | −1323.70 | + | 1323.70i | −1.19596 | + | 1.19596i | −0.220589 | + | 0.975367i | \(0.570798\pi\) |
−0.975367 | + | 0.220589i | \(0.929202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70.0000i | 0.0615118i | 0.999527 | + | 0.0307559i | \(0.00979145\pi\) | ||||
−0.999527 | + | 0.0307559i | \(0.990209\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 639.000 | + | 639.000i | 0.539106 | + | 0.539106i | ||||
\(113\) | −521.845 | − | 521.845i | −0.434434 | − | 0.434434i | 0.455700 | − | 0.890134i | \(-0.349389\pi\) |
−0.890134 | + | 0.455700i | \(0.849389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 229.103i | 0.183376i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 567.000 | − | 567.000i | 0.442344 | − | 0.442344i | ||||
\(119\) | −534.573 | −0.411800 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −127.000 | −0.0954170 | ||||||||
\(122\) | 683.065 | − | 683.065i | 0.506900 | − | 0.506900i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 196.000i | − | 0.141946i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −315.000 | − | 315.000i | −0.220092 | − | 0.220092i | 0.588445 | − | 0.808537i | \(-0.299740\pi\) |
−0.808537 | + | 0.588445i | \(0.799740\pi\) | |||||||
\(128\) | −1173.09 | − | 1173.09i | −0.810059 | − | 0.810059i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1336.43i | 0.891333i | 0.895199 | + | 0.445666i | \(0.147033\pi\) | ||||
−0.895199 | + | 0.445666i | \(0.852967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 630.000 | − | 630.000i | 0.410736 | − | 0.410736i | ||||
\(134\) | 1603.72 | 1.03388 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 882.000 | 0.556109 | ||||||||
\(137\) | 1294.01 | − | 1294.01i | 0.806966 | − | 0.806966i | −0.177208 | − | 0.984174i | \(-0.556706\pi\) |
0.984174 | + | 0.177208i | \(0.0567064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 308.000i | 0.187944i | 0.995575 | + | 0.0939720i | \(0.0299564\pi\) | ||||
−0.995575 | + | 0.0939720i | \(0.970044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1782.00 | − | 1782.00i | −1.05311 | − | 1.05311i | ||||
\(143\) | 2405.58 | + | 2405.58i | 1.40674 | + | 1.40674i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 1603.72i | − | 0.909073i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −207.000 | + | 207.000i | −0.114968 | + | 0.114968i | ||||
\(149\) | −2443.76 | −1.34363 | −0.671814 | − | 0.740719i | \(-0.734485\pi\) | ||||
−0.671814 | + | 0.740719i | \(0.734485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2072.00 | −1.11667 | −0.558334 | − | 0.829616i | \(-0.688559\pi\) | ||||
−0.558334 | + | 0.829616i | \(0.688559\pi\) | |||||||
\(152\) | −1039.45 | + | 1039.45i | −0.554673 | + | 0.554673i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1458.00i | 0.762916i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 315.000 | + | 315.000i | 0.160126 | + | 0.160126i | 0.782622 | − | 0.622497i | \(-0.213882\pi\) |
−0.622497 | + | 0.782622i | \(0.713882\pi\) | |||||||
\(158\) | 1035.20 | + | 1035.20i | 0.521243 | + | 0.521243i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1298.25i | − | 0.635505i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2394.00 | − | 2394.00i | 1.15038 | − | 1.15038i | 0.163908 | − | 0.986476i | \(-0.447590\pi\) |
0.986476 | − | 0.163908i | \(-0.0524101\pi\) | |||||||
\(164\) | −267.286 | −0.127266 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3276.00 | 1.53173 | ||||||||
\(167\) | 742.462 | − | 742.462i | 0.344033 | − | 0.344033i | −0.513848 | − | 0.857881i | \(-0.671781\pi\) |
0.857881 | + | 0.513848i | \(0.171781\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5741.00i | − | 2.61311i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −144.000 | − | 144.000i | −0.0638366 | − | 0.0638366i | ||||
\(173\) | 326.683 | + | 326.683i | 0.143568 | + | 0.143568i | 0.775238 | − | 0.631670i | \(-0.217630\pi\) |
−0.631670 | + | 0.775238i | \(0.717630\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2711.05i | − | 1.16110i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 567.000 | − | 567.000i | 0.238755 | − | 0.238755i | ||||
\(179\) | −1565.53 | −0.653707 | −0.326853 | − | 0.945075i | \(-0.605988\pi\) | ||||
−0.326853 | + | 0.945075i | \(0.605988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3094.00 | 1.27058 | 0.635291 | − | 0.772273i | \(-0.280880\pi\) | ||||
0.635291 | + | 0.772273i | \(0.280880\pi\) | |||||||
\(182\) | 2405.58 | − | 2405.58i | 0.979743 | − | 0.979743i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2142.00i | 0.858208i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1134.00 | + | 1134.00i | 0.443456 | + | 0.443456i | ||||
\(188\) | −356.382 | − | 356.382i | −0.138254 | − | 0.138254i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 840.043i | − | 0.318238i | −0.987259 | − | 0.159119i | \(-0.949135\pi\) | ||
0.987259 | − | 0.159119i | \(-0.0508653\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1242.00 | − | 1242.00i | 0.463218 | − | 0.463218i | −0.436491 | − | 0.899709i | \(-0.643779\pi\) |
0.899709 | + | 0.436491i | \(0.143779\pi\) | |||||||
\(194\) | −1069.15 | −0.395671 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −181.000 | −0.0659621 | ||||||||
\(197\) | −3725.04 | + | 3725.04i | −1.34720 | + | 1.34720i | −0.458507 | + | 0.888691i | \(0.651616\pi\) |
−0.888691 | + | 0.458507i | \(0.848384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 700.000i | 0.249355i | 0.992197 | + | 0.124678i | \(0.0397897\pi\) | ||||
−0.992197 | + | 0.124678i | \(0.960210\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3402.00 | − | 3402.00i | −1.18497 | − | 1.18497i | ||||
\(203\) | −2061.92 | − | 2061.92i | −0.712900 | − | 0.712900i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 4009.30i | − | 1.35602i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4473.00 | + | 4473.00i | −1.49109 | + | 1.49109i | ||||
\(209\) | −2672.86 | −0.884621 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1316.00 | 0.429371 | 0.214685 | − | 0.976683i | \(-0.431127\pi\) | ||||
0.214685 | + | 0.976683i | \(0.431127\pi\) | |||||||
\(212\) | 224.860 | − | 224.860i | 0.0728464 | − | 0.0728464i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 5616.00i | − | 1.79393i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1764.00 | + | 1764.00i | 0.551835 | + | 0.551835i | ||||
\(218\) | −148.492 | − | 148.492i | −0.0461338 | − | 0.0461338i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3742.01i | − | 1.13898i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2205.00 | + | 2205.00i | −0.662142 | + | 0.662142i | −0.955885 | − | 0.293742i | \(-0.905099\pi\) |
0.293742 | + | 0.955885i | \(0.405099\pi\) | |||||||
\(224\) | −572.756 | −0.170843 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2214.00 | 0.651651 | ||||||||
\(227\) | 653.367 | − | 653.367i | 0.191037 | − | 0.191037i | −0.605107 | − | 0.796144i | \(-0.706870\pi\) |
0.796144 | + | 0.605107i | \(0.206870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3206.00i | 0.925146i | 0.886581 | + | 0.462573i | \(0.153074\pi\) | ||||
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3402.00 | + | 3402.00i | 0.962725 | + | 0.962725i | ||||
\(233\) | 12.7279 | + | 12.7279i | 0.00357869 | + | 0.00357869i | 0.708894 | − | 0.705315i | \(-0.249195\pi\) |
−0.705315 | + | 0.708894i | \(0.749195\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 267.286i | 0.0737240i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1134.00 | − | 1134.00i | 0.308850 | − | 0.308850i | ||||
\(239\) | 1298.25 | 0.351367 | 0.175683 | − | 0.984447i | \(-0.443786\pi\) | ||||
0.175683 | + | 0.984447i | \(0.443786\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −700.000 | −0.187099 | −0.0935497 | − | 0.995615i | \(-0.529821\pi\) | ||||
−0.0935497 | + | 0.995615i | \(0.529821\pi\) | |||||||
\(242\) | 269.408 | − | 269.408i | 0.0715627 | − | 0.0715627i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 322.000i | 0.0844834i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4410.00 | + | 4410.00i | 1.13604 | + | 1.13604i | ||||
\(248\) | −2910.45 | − | 2910.45i | −0.745217 | − | 0.745217i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5078.44i | 1.27709i | 0.769587 | + | 0.638543i | \(0.220462\pi\) | ||||
−0.769587 | + | 0.638543i | \(0.779538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2754.00 | + | 2754.00i | −0.684358 | + | 0.684358i | ||||
\(254\) | 1336.43 | 0.330139 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | −2880.75 | + | 2880.75i | −0.699208 | + | 0.699208i | −0.964240 | − | 0.265032i | \(-0.914618\pi\) |
0.265032 | + | 0.964240i | \(0.414618\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3726.00i | − | 0.893909i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2835.00 | − | 2835.00i | −0.668500 | − | 0.668500i | ||||
\(263\) | 1412.80 | + | 1412.80i | 0.331243 | + | 0.331243i | 0.853058 | − | 0.521815i | \(-0.174745\pi\) |
−0.521815 | + | 0.853058i | \(0.674745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2672.86i | 0.616104i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −378.000 | + | 378.000i | −0.0861568 | + | 0.0861568i | ||||
\(269\) | −1603.72 | −0.363496 | −0.181748 | − | 0.983345i | \(-0.558176\pi\) | ||||
−0.181748 | + | 0.983345i | \(0.558176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2716.00 | −0.608802 | −0.304401 | − | 0.952544i | \(-0.598456\pi\) | ||||
−0.304401 | + | 0.952544i | \(0.598456\pi\) | |||||||
\(272\) | −2108.59 | + | 2108.59i | −0.470045 | + | 0.470045i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5490.00i | 1.21045i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3843.00 | − | 3843.00i | −0.833587 | − | 0.833587i | 0.154419 | − | 0.988005i | \(-0.450649\pi\) |
−0.988005 | + | 0.154419i | \(0.950649\pi\) | |||||||
\(278\) | −653.367 | − | 653.367i | −0.140958 | − | 0.140958i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3780.19i | − | 0.802517i | −0.915965 | − | 0.401259i | \(-0.868573\pi\) | ||
0.915965 | − | 0.401259i | \(-0.131427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −126.000 | + | 126.000i | −0.0264662 | + | 0.0264662i | −0.720216 | − | 0.693750i | \(-0.755957\pi\) |
0.693750 | + | 0.720216i | \(0.255957\pi\) | |||||||
\(284\) | 840.043 | 0.175519 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10206.0 | −2.11012 | ||||||||
\(287\) | 2405.58 | − | 2405.58i | 0.494762 | − | 0.494762i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3149.00i | 0.640953i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 378.000 | + | 378.000i | 0.0757561 | + | 0.0757561i | ||||
\(293\) | 772.161 | + | 772.161i | 0.153959 | + | 0.153959i | 0.779884 | − | 0.625924i | \(-0.215278\pi\) |
−0.625924 | + | 0.779884i | \(0.715278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6147.59i | 1.20717i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5184.00 | − | 5184.00i | 1.00772 | − | 1.00772i | ||||
\(299\) | 9087.74 | 1.75772 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2592.00 | 0.496347 | ||||||||
\(302\) | 4395.38 | − | 4395.38i | 0.837501 | − | 0.837501i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4970.00i | − | 0.937661i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3024.00 | − | 3024.00i | −0.562178 | − | 0.562178i | 0.367747 | − | 0.929926i | \(-0.380129\pi\) |
−0.929926 | + | 0.367747i | \(0.880129\pi\) | |||||||
\(308\) | −343.654 | − | 343.654i | −0.0635763 | − | 0.0635763i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10156.9i | 1.85191i | 0.377634 | + | 0.925955i | \(0.376738\pi\) | ||||
−0.377634 | + | 0.925955i | \(0.623262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5418.00 | − | 5418.00i | 0.978414 | − | 0.978414i | −0.0213583 | − | 0.999772i | \(-0.506799\pi\) |
0.999772 | + | 0.0213583i | \(0.00679906\pi\) | |||||||
\(314\) | −1336.43 | −0.240189 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −488.000 | −0.0868739 | ||||||||
\(317\) | 1977.07 | − | 1977.07i | 0.350294 | − | 0.350294i | −0.509925 | − | 0.860219i | \(-0.670327\pi\) |
0.860219 | + | 0.509925i | \(0.170327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8748.00i | 1.53540i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2754.00 | + | 2754.00i | 0.476629 | + | 0.476629i | ||||
\(323\) | 2078.89 | + | 2078.89i | 0.358120 | + | 0.358120i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10156.9i | 1.72558i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3969.00 | + | 3969.00i | −0.668144 | + | 0.668144i | ||||
\(329\) | 6414.87 | 1.07496 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6622.00 | −1.09963 | −0.549816 | − | 0.835286i | \(-0.685302\pi\) | ||||
−0.549816 | + | 0.835286i | \(0.685302\pi\) | |||||||
\(332\) | −772.161 | + | 772.161i | −0.127644 | + | 0.127644i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3150.00i | 0.516049i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2790.00 | − | 2790.00i | −0.450982 | − | 0.450982i | 0.444698 | − | 0.895680i | \(-0.353311\pi\) |
−0.895680 | + | 0.444698i | \(0.853311\pi\) | |||||||
\(338\) | 12178.5 | + | 12178.5i | 1.95983 | + | 1.95983i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7484.02i | − | 1.18851i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4716.00 | − | 4716.00i | 0.742391 | − | 0.742391i | ||||
\(344\) | −4276.58 | −0.670284 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1386.00 | −0.215352 | ||||||||
\(347\) | −1858.28 | + | 1858.28i | −0.287486 | + | 0.287486i | −0.836085 | − | 0.548600i | \(-0.815161\pi\) |
0.548600 | + | 0.836085i | \(0.315161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5614.00i | − | 0.861062i | −0.902576 | − | 0.430531i | \(-0.858326\pi\) | ||
0.902576 | − | 0.430531i | \(-0.141674\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1215.00 | + | 1215.00i | 0.183976 | + | 0.183976i | ||||
\(353\) | −1514.62 | − | 1514.62i | −0.228372 | − | 0.228372i | 0.583640 | − | 0.812012i | \(-0.301628\pi\) |
−0.812012 | + | 0.583640i | \(0.801628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 267.286i | 0.0397926i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3321.00 | − | 3321.00i | 0.490280 | − | 0.490280i | ||||
\(359\) | 11455.1 | 1.68406 | 0.842032 | − | 0.539428i | \(-0.181360\pi\) | ||||
0.842032 | + | 0.539428i | \(0.181360\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1959.00 | 0.285610 | ||||||||
\(362\) | −6563.37 | + | 6563.37i | −0.952936 | + | 0.952936i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1134.00i | 0.163291i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5481.00 | − | 5481.00i | −0.779580 | − | 0.779580i | 0.200179 | − | 0.979759i | \(-0.435848\pi\) |
−0.979759 | + | 0.200179i | \(0.935848\pi\) | |||||||
\(368\) | −5120.87 | − | 5120.87i | −0.725390 | − | 0.725390i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4047.48i | 0.566401i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2709.00 | + | 2709.00i | −0.376050 | + | 0.376050i | −0.869675 | − | 0.493625i | \(-0.835672\pi\) |
0.493625 | + | 0.869675i | \(0.335672\pi\) | |||||||
\(374\) | −4811.15 | −0.665184 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10584.0 | −1.45167 | ||||||||
\(377\) | 14433.5 | − | 14433.5i | 1.97178 | − | 1.97178i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13916.0i | 1.88606i | 0.332707 | + | 0.943030i | \(0.392038\pi\) | ||||
−0.332707 | + | 0.943030i | \(0.607962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1782.00 | + | 1782.00i | 0.238678 | + | 0.238678i | ||||
\(383\) | −6890.05 | − | 6890.05i | −0.919230 | − | 0.919230i | 0.0777435 | − | 0.996973i | \(-0.475228\pi\) |
−0.996973 | + | 0.0777435i | \(0.975228\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5269.36i | 0.694827i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 252.000 | − | 252.000i | 0.0329726 | − | 0.0329726i | ||||
\(389\) | −6720.34 | −0.875925 | −0.437963 | − | 0.898993i | \(-0.644300\pi\) | ||||
−0.437963 | + | 0.898993i | \(0.644300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4284.00 | 0.554095 | ||||||||
\(392\) | −2687.71 | + | 2687.71i | −0.346301 | + | 0.346301i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 15804.0i | − | 2.02080i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5607.00 | + | 5607.00i | 0.708834 | + | 0.708834i | 0.966290 | − | 0.257456i | \(-0.0828841\pi\) |
−0.257456 | + | 0.966290i | \(0.582884\pi\) | |||||||
\(398\) | −1484.92 | − | 1484.92i | −0.187016 | − | 0.187016i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8056.77i | − | 1.00333i | −0.865061 | − | 0.501666i | \(-0.832721\pi\) | ||
0.865061 | − | 0.501666i | \(-0.167279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12348.0 | + | 12348.0i | −1.52630 | + | 1.52630i | ||||
\(404\) | 1603.72 | 0.197495 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8748.00 | 1.06935 | ||||||||
\(407\) | −7904.04 | + | 7904.04i | −0.962626 | + | 0.962626i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1694.00i | 0.204799i | 0.994743 | + | 0.102400i | \(0.0326521\pi\) | ||||
−0.994743 | + | 0.102400i | \(0.967348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 945.000 | + | 945.000i | 0.113002 | + | 0.113002i | ||||
\(413\) | −2405.58 | − | 2405.58i | −0.286612 | − | 0.286612i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4009.30i | − | 0.472529i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5670.00 | − | 5670.00i | 0.663466 | − | 0.663466i | ||||
\(419\) | −267.286 | −0.0311642 | −0.0155821 | − | 0.999879i | \(-0.504960\pi\) | ||||
−0.0155821 | + | 0.999879i | \(0.504960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12850.0 | 1.48758 | 0.743789 | − | 0.668414i | \(-0.233027\pi\) | ||||
0.743789 | + | 0.668414i | \(0.233027\pi\) | |||||||
\(422\) | −2791.66 | + | 2791.66i | −0.322028 | + | 0.322028i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 6678.00i | − | 0.764888i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2898.00 | − | 2898.00i | −0.328440 | − | 0.328440i | ||||
\(428\) | 1323.70 | + | 1323.70i | 0.149494 | + | 0.149494i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7178.55i | − | 0.802270i | −0.916019 | − | 0.401135i | \(-0.868616\pi\) | ||
0.916019 | − | 0.401135i | \(-0.131384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11214.0 | + | 11214.0i | −1.24460 | + | 1.24460i | −0.286524 | + | 0.958073i | \(0.592500\pi\) |
−0.958073 | + | 0.286524i | \(0.907500\pi\) | |||||||
\(434\) | −7484.02 | −0.827752 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 70.0000 | 0.00768897 | ||||||||
\(437\) | −5048.74 | + | 5048.74i | −0.552664 | + | 0.552664i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2324.00i | − | 0.252662i | −0.991988 | − | 0.126331i | \(-0.959680\pi\) | ||
0.991988 | − | 0.126331i | \(-0.0403201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7938.00 | + | 7938.00i | 0.854236 | + | 0.854236i | ||||
\(443\) | 5685.14 | + | 5685.14i | 0.609727 | + | 0.609727i | 0.942875 | − | 0.333148i | \(-0.108111\pi\) |
−0.333148 | + | 0.942875i | \(0.608111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 9355.02i | − | 0.993213i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3897.00 | + | 3897.00i | −0.410973 | + | 0.410973i | ||||
\(449\) | −3703.83 | −0.389297 | −0.194648 | − | 0.980873i | \(-0.562357\pi\) | ||||
−0.194648 | + | 0.980873i | \(0.562357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10206.0 | −1.06559 | ||||||||
\(452\) | −521.845 | + | 521.845i | −0.0543042 | + | 0.0543042i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2772.00i | 0.286556i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7200.00 | + | 7200.00i | 0.736984 | + | 0.736984i | 0.971993 | − | 0.235009i | \(-0.0755120\pi\) |
−0.235009 | + | 0.971993i | \(0.575512\pi\) | |||||||
\(458\) | −6800.95 | − | 6800.95i | −0.693860 | − | 0.693860i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13898.9i | − | 1.40420i | −0.712079 | − | 0.702100i | \(-0.752246\pi\) | ||
0.712079 | − | 0.702100i | \(-0.247754\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4095.00 | − | 4095.00i | 0.411038 | − | 0.411038i | −0.471062 | − | 0.882100i | \(-0.656129\pi\) |
0.882100 | + | 0.471062i | \(0.156129\pi\) | |||||||
\(464\) | −16266.3 | −1.62746 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −54.0000 | −0.00536803 | ||||||||
\(467\) | 9919.29 | − | 9919.29i | 0.982891 | − | 0.982891i | −0.0169649 | − | 0.999856i | \(-0.505400\pi\) |
0.999856 | + | 0.0169649i | \(0.00540036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6804.00i | − | 0.669892i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3969.00 | + | 3969.00i | 0.387051 | + | 0.387051i | ||||
\(473\) | −5498.46 | − | 5498.46i | −0.534502 | − | 0.534502i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 534.573i | 0.0514750i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2754.00 | + | 2754.00i | −0.263525 | + | 0.263525i | ||||
\(479\) | 15502.6 | 1.47877 | 0.739387 | − | 0.673281i | \(-0.235116\pi\) | ||||
0.739387 | + | 0.673281i | \(0.235116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26082.0 | 2.47243 | ||||||||
\(482\) | 1484.92 | − | 1484.92i | 0.140325 | − | 0.140325i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 127.000i | 0.0119271i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6975.00 | − | 6975.00i | −0.649009 | − | 0.649009i | 0.303744 | − | 0.952754i | \(-0.401763\pi\) |
−0.952754 | + | 0.303744i | \(0.901763\pi\) | |||||||
\(488\) | 4781.46 | + | 4781.46i | 0.443538 | + | 0.443538i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2100.11i | − | 0.193028i | −0.995332 | − | 0.0965138i | \(-0.969231\pi\) | ||
0.995332 | − | 0.0965138i | \(-0.0307692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6804.00 | − | 6804.00i | 0.621576 | − | 0.621576i | ||||
\(494\) | −18710.0 | −1.70406 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13916.0 | 1.25977 | ||||||||
\(497\) | −7560.39 | + | 7560.39i | −0.682353 | + | 0.682353i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 574.000i | 0.0514945i | 0.999668 | + | 0.0257473i | \(0.00819651\pi\) | ||||
−0.999668 | + | 0.0257473i | \(0.991803\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10773.0 | − | 10773.0i | −0.957814 | − | 0.957814i | ||||
\(503\) | −8077.99 | − | 8077.99i | −0.716063 | − | 0.716063i | 0.251734 | − | 0.967797i | \(-0.418999\pi\) |
−0.967797 | + | 0.251734i | \(0.918999\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 11684.2i | − | 1.02654i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −315.000 | + | 315.000i | −0.0275115 | + | 0.0275115i | ||||
\(509\) | 4811.15 | 0.418960 | 0.209480 | − | 0.977813i | \(-0.432823\pi\) | ||||
0.209480 | + | 0.977813i | \(0.432823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6804.00 | −0.589024 | ||||||||
\(512\) | 6175.16 | − | 6175.16i | 0.533020 | − | 0.533020i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 12222.0i | − | 1.04881i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13608.0 | − | 13608.0i | −1.15760 | − | 1.15760i | ||||
\(518\) | 7904.04 | + | 7904.04i | 0.670432 | + | 0.670432i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14166.2i | − | 1.19123i | −0.803270 | − | 0.595616i | \(-0.796908\pi\) | ||
0.803270 | − | 0.595616i | \(-0.203092\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8694.00 | − | 8694.00i | 0.726887 | − | 0.726887i | −0.243111 | − | 0.969998i | \(-0.578168\pi\) |
0.969998 | + | 0.243111i | \(0.0781680\pi\) | |||||||
\(524\) | 1336.43 | 0.111417 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5994.00 | −0.496865 | ||||||||
\(527\) | −5820.90 | + | 5820.90i | −0.481143 | + | 0.481143i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1763.00i | − | 0.144900i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −630.000 | − | 630.000i | −0.0513420 | − | 0.0513420i | ||||
\(533\) | 16839.0 | + | 16839.0i | 1.36844 | + | 1.36844i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11226.0i | 0.904647i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3402.00 | − | 3402.00i | 0.272622 | − | 0.272622i | ||||
\(539\) | −6911.26 | −0.552299 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −646.000 | −0.0513377 | −0.0256689 | − | 0.999671i | \(-0.508172\pi\) | ||||
−0.0256689 | + | 0.999671i | \(0.508172\pi\) | |||||||
\(542\) | 5761.51 | − | 5761.51i | 0.456601 | − | 0.456601i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1890.00i | − | 0.148958i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11340.0 | + | 11340.0i | 0.886405 | + | 0.886405i | 0.994176 | − | 0.107771i | \(-0.0343713\pi\) |
−0.107771 | + | 0.994176i | \(0.534371\pi\) | |||||||
\(548\) | −1294.01 | − | 1294.01i | −0.100871 | − | 0.100871i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16037.2i | 1.23994i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4392.00 | − | 4392.00i | 0.337734 | − | 0.337734i | ||||
\(554\) | 16304.5 | 1.25038 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 308.000 | 0.0234930 | ||||||||
\(557\) | 5867.57 | − | 5867.57i | 0.446350 | − | 0.446350i | −0.447789 | − | 0.894139i | \(-0.647788\pi\) |
0.894139 | + | 0.447789i | \(0.147788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18144.0i | 1.37283i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8019.00 | + | 8019.00i | 0.601888 | + | 0.601888i | ||||
\(563\) | 2672.86 | + | 2672.86i | 0.200085 | + | 0.200085i | 0.800036 | − | 0.599952i | \(-0.204813\pi\) |
−0.599952 | + | 0.800036i | \(0.704813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 534.573i | − | 0.0396992i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12474.0 | − | 12474.0i | 0.921474 | − | 0.921474i | ||||
\(569\) | −20886.5 | −1.53885 | −0.769427 | − | 0.638734i | \(-0.779458\pi\) | ||||
−0.769427 | + | 0.638734i | \(0.779458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12238.0 | −0.896925 | −0.448463 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448463 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(572\) | 2405.58 | − | 2405.58i | 0.175843 | − | 0.175843i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10206.0i | 0.742143i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4536.00 | − | 4536.00i | −0.327272 | − | 0.327272i | 0.524276 | − | 0.851548i | \(-0.324336\pi\) |
−0.851548 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(578\) | −6680.04 | − | 6680.04i | −0.480714 | − | 0.480714i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 13898.9i | − | 0.992467i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8586.00 | − | 8586.00i | 0.609941 | − | 0.609941i | ||||
\(584\) | 11226.0 | 0.795439 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3276.00 | −0.230939 | ||||||||
\(587\) | 9147.13 | − | 9147.13i | 0.643173 | − | 0.643173i | −0.308161 | − | 0.951334i | \(-0.599714\pi\) |
0.951334 | + | 0.308161i | \(0.0997136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 13720.0i | − | 0.959801i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14697.0 | − | 14697.0i | −1.02034 | − | 1.02034i | ||||
\(593\) | 14285.0 | + | 14285.0i | 0.989230 | + | 0.989230i | 0.999943 | − | 0.0107125i | \(-0.00340996\pi\) |
−0.0107125 | + | 0.999943i | \(0.503410\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2443.76i | 0.167954i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19278.0 | + | 19278.0i | −1.31829 | + | 1.31829i | ||||
\(599\) | 7789.49 | 0.531335 | 0.265668 | − | 0.964065i | \(-0.414408\pi\) | ||||
0.265668 | + | 0.964065i | \(0.414408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6748.00 | 0.457998 | 0.228999 | − | 0.973427i | \(-0.426455\pi\) | ||||
0.228999 | + | 0.973427i | \(0.426455\pi\) | |||||||
\(602\) | −5498.46 | + | 5498.46i | −0.372260 | + | 0.372260i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2072.00i | 0.139584i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13671.0 | + | 13671.0i | 0.914150 | + | 0.914150i | 0.996596 | − | 0.0824460i | \(-0.0262732\pi\) |
−0.0824460 | + | 0.996596i | \(0.526273\pi\) | |||||||
\(608\) | 2227.39 | + | 2227.39i | 0.148573 | + | 0.148573i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44904.1i | 2.97320i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3213.00 | + | 3213.00i | −0.211700 | + | 0.211700i | −0.804989 | − | 0.593290i | \(-0.797829\pi\) |
0.593290 | + | 0.804989i | \(0.297829\pi\) | |||||||
\(614\) | 12829.7 | 0.843268 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10206.0 | −0.667551 | ||||||||
\(617\) | −9906.57 | + | 9906.57i | −0.646391 | + | 0.646391i | −0.952119 | − | 0.305728i | \(-0.901100\pi\) |
0.305728 | + | 0.952119i | \(0.401100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2828.00i | − | 0.183630i | −0.995776 | − | 0.0918150i | \(-0.970733\pi\) | ||
0.995776 | − | 0.0918150i | \(-0.0292668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21546.0 | − | 21546.0i | −1.38893 | − | 1.38893i | ||||
\(623\) | −2405.58 | − | 2405.58i | −0.154699 | − | 0.154699i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22986.6i | 1.46762i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 315.000 | − | 315.000i | 0.0200157 | − | 0.0200157i | ||||
\(629\) | 12295.2 | 0.779397 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12220.0 | −0.770952 | −0.385476 | − | 0.922718i | \(-0.625963\pi\) | ||||
−0.385476 | + | 0.922718i | \(0.625963\pi\) | |||||||
\(632\) | −7246.43 | + | 7246.43i | −0.456088 | + | 0.456088i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8388.00i | 0.525442i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11403.0 | + | 11403.0i | 0.709267 | + | 0.709267i | ||||
\(638\) | −18557.3 | − | 18557.3i | −1.15155 | − | 1.15155i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2176.47i | 0.134112i | 0.997749 | + | 0.0670558i | \(0.0213606\pi\) | ||||
−0.997749 | + | 0.0670558i | \(0.978639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4914.00 | + | 4914.00i | −0.301383 | + | 0.301383i | −0.841555 | − | 0.540172i | \(-0.818359\pi\) |
0.540172 | + | 0.841555i | \(0.318359\pi\) | |||||||
\(644\) | −1298.25 | −0.0794381 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8820.00 | −0.537180 | ||||||||
\(647\) | −2375.88 | + | 2375.88i | −0.144367 | + | 0.144367i | −0.775596 | − | 0.631229i | \(-0.782551\pi\) |
0.631229 | + | 0.775596i | \(0.282551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10206.0i | 0.617289i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2394.00 | − | 2394.00i | −0.143798 | − | 0.143798i | ||||
\(653\) | −21603.5 | − | 21603.5i | −1.29466 | − | 1.29466i | −0.931873 | − | 0.362784i | \(-0.881826\pi\) |
−0.362784 | − | 0.931873i | \(-0.618174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 18977.3i | − | 1.12948i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13608.0 | + | 13608.0i | −0.806224 | + | 0.806224i | ||||
\(659\) | 14395.3 | 0.850926 | 0.425463 | − | 0.904976i | \(-0.360111\pi\) | ||||
0.425463 | + | 0.904976i | \(0.360111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22610.0 | −1.33045 | −0.665225 | − | 0.746643i | \(-0.731664\pi\) | ||||
−0.665225 | + | 0.746643i | \(0.731664\pi\) | |||||||
\(662\) | 14047.4 | − | 14047.4i | 0.824724 | − | 0.824724i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22932.0i | 1.34026i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16524.0 | + | 16524.0i | 0.959238 | + | 0.959238i | ||||
\(668\) | −742.462 | − | 742.462i | −0.0430041 | − | 0.0430041i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12295.2i | 0.707377i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1278.00 | + | 1278.00i | −0.0731995 | + | 0.0731995i | −0.742759 | − | 0.669559i | \(-0.766483\pi\) |
0.669559 | + | 0.742759i | \(0.266483\pi\) | |||||||
\(674\) | 11837.0 | 0.676473 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5741.00 | −0.326639 | ||||||||
\(677\) | −7840.40 | + | 7840.40i | −0.445098 | + | 0.445098i | −0.893721 | − | 0.448623i | \(-0.851914\pi\) |
0.448623 | + | 0.893721i | \(0.351914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4536.00i | 0.256371i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15876.0 | + | 15876.0i | 0.891383 | + | 0.891383i | ||||
\(683\) | 5125.11 | + | 5125.11i | 0.287126 | + | 0.287126i | 0.835943 | − | 0.548817i | \(-0.184922\pi\) |
−0.548817 | + | 0.835943i | \(0.684922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20008.3i | 1.11359i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10224.0 | − | 10224.0i | 0.566550 | − | 0.566550i | ||||
\(689\) | −28332.4 | −1.56658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12418.0 | 0.683651 | 0.341826 | − | 0.939763i | \(-0.388955\pi\) | ||||
0.341826 | + | 0.939763i | \(0.388955\pi\) | |||||||
\(692\) | 326.683 | − | 326.683i | 0.0179460 | − | 0.0179460i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 7884.00i | − | 0.431228i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7938.00 | + | 7938.00i | 0.431382 | + | 0.431382i | ||||
\(698\) | 11909.1 | + | 11909.1i | 0.645796 | + | 0.645796i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7254.92i | 0.390891i | 0.980715 | + | 0.195445i | \(0.0626152\pi\) | ||||
−0.980715 | + | 0.195445i | \(0.937385\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14490.0 | + | 14490.0i | −0.777384 | + | 0.777384i | ||||
\(704\) | 16533.6 | 0.885131 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6426.00 | 0.342558 | ||||||||
\(707\) | −14433.5 | + | 14433.5i | −0.767788 | + | 0.767788i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2086.00i | − | 0.110496i | −0.998473 | − | 0.0552478i | \(-0.982405\pi\) | ||
0.998473 | − | 0.0552478i | \(-0.0175949\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3969.00 | + | 3969.00i | 0.208911 | + | 0.208911i | ||||
\(713\) | −14136.5 | − | 14136.5i | −0.742518 | − | 0.742518i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1565.53i | 0.0817134i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24300.0 | + | 24300.0i | −1.26305 | + | 1.26305i | ||||
\(719\) | 10691.5 | 0.554554 | 0.277277 | − | 0.960790i | \(-0.410568\pi\) | ||||
0.277277 | + | 0.960790i | \(0.410568\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17010.0 | −0.878621 | ||||||||
\(722\) | −4155.67 | + | 4155.67i | −0.214208 | + | 0.214208i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3094.00i | − | 0.158823i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14931.0 | − | 14931.0i | −0.761706 | − | 0.761706i | 0.214925 | − | 0.976631i | \(-0.431049\pi\) |
−0.976631 | + | 0.214925i | \(0.931049\pi\) | |||||||
\(728\) | 16839.0 | + | 16839.0i | 0.857275 | + | 0.857275i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8553.16i | 0.432764i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8757.00 | − | 8757.00i | 0.441265 | − | 0.441265i | −0.451172 | − | 0.892437i | \(-0.648994\pi\) |
0.892437 | + | 0.451172i | \(0.148994\pi\) | |||||||
\(734\) | 23253.9 | 1.16937 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4590.00 | 0.229877 | ||||||||
\(737\) | −14433.5 | + | 14433.5i | −0.721389 | + | 0.721389i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 33010.0i | − | 1.64316i | −0.570096 | − | 0.821578i | \(-0.693094\pi\) | ||
0.570096 | − | 0.821578i | \(-0.306906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8586.00 | − | 8586.00i | −0.424801 | − | 0.424801i | ||||
\(743\) | 4734.79 | + | 4734.79i | 0.233785 | + | 0.233785i | 0.814271 | − | 0.580485i | \(-0.197137\pi\) |
−0.580485 | + | 0.814271i | \(0.697137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 11493.3i | − | 0.564075i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1134.00 | − | 1134.00i | 0.0554320 | − | 0.0554320i | ||||
\(749\) | −23826.7 | −1.16236 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18704.0 | −0.908813 | −0.454407 | − | 0.890794i | \(-0.650149\pi\) | ||||
−0.454407 | + | 0.890794i | \(0.650149\pi\) | |||||||
\(752\) | 25303.1 | − | 25303.1i | 1.22701 | − | 1.22701i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 61236.0i | 2.95767i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2187.00 | + | 2187.00i | 0.105004 | + | 0.105004i | 0.757657 | − | 0.652653i | \(-0.226344\pi\) |
−0.652653 | + | 0.757657i | \(0.726344\pi\) | |||||||
\(758\) | −29520.3 | − | 29520.3i | −1.41455 | − | 1.41455i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4543.87i | − | 0.216446i | −0.994127 | − | 0.108223i | \(-0.965484\pi\) | ||
0.994127 | − | 0.108223i | \(-0.0345160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −630.000 | + | 630.000i | −0.0298919 | + | 0.0298919i | ||||
\(764\) | −840.043 | −0.0397797 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29232.0 | 1.37884 | ||||||||
\(767\) | 16839.0 | − | 16839.0i | 0.792728 | − | 0.792728i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35336.0i | − | 1.65702i | −0.559974 | − | 0.828510i | \(-0.689189\pi\) | ||
0.559974 | − | 0.828510i | \(-0.310811\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1242.00 | − | 1242.00i | −0.0579023 | − | 0.0579023i | ||||
\(773\) | 9919.29 | + | 9919.29i | 0.461542 | + | 0.461542i | 0.899161 | − | 0.437618i | \(-0.144178\pi\) |
−0.437618 | + | 0.899161i | \(0.644178\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 7484.02i | − | 0.346212i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14256.0 | − | 14256.0i | 0.656944 | − | 0.656944i | ||||
\(779\) | −18710.0 | −0.860535 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32076.0 | 1.46962 | ||||||||
\(782\) | −9087.74 | + | 9087.74i | −0.415571 | + | 0.415571i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 12851.0i | − | 0.585414i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19278.0 | − | 19278.0i | −0.873172 | − | 0.873172i | 0.119645 | − | 0.992817i | \(-0.461824\pi\) |
−0.992817 | + | 0.119645i | \(0.961824\pi\) | |||||||
\(788\) | 3725.04 | + | 3725.04i | 0.168400 | + | 0.168400i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 9393.21i | − | 0.422230i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20286.0 | − | 20286.0i | 0.908420 | − | 0.908420i | ||||
\(794\) | −23788.5 | −1.06325 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 700.000 | 0.0311694 | ||||||||
\(797\) | 24441.9 | − | 24441.9i | 1.08629 | − | 1.08629i | 0.0903853 | − | 0.995907i | \(-0.471190\pi\) |
0.995907 | − | 0.0903853i | \(-0.0288098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21168.0i | 0.937259i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17091.0 | + | 17091.0i | 0.752499 | + | 0.752499i | ||||
\(803\) | 14433.5 | + | 14433.5i | 0.634304 | + | 0.634304i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 52388.1i | − | 2.28945i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23814.0 | − | 23814.0i | 1.03685 | − | 1.03685i | ||||
\(809\) | −28370.5 | −1.23295 | −0.616474 | − | 0.787375i | \(-0.711439\pi\) | ||||
−0.616474 | + | 0.787375i | \(0.711439\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37100.0 | −1.60636 | −0.803180 | − | 0.595737i | \(-0.796860\pi\) | ||||
−0.803180 | + | 0.595737i | \(0.796860\pi\) | |||||||
\(812\) | −2061.92 | + | 2061.92i | −0.0891125 | + | 0.0891125i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 33534.0i | − | 1.44394i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10080.0 | − | 10080.0i | −0.431646 | − | 0.431646i | ||||
\(818\) | −3593.52 | − | 3593.52i | −0.153599 | − | 0.153599i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 12600.6i | − | 0.535646i | −0.963468 | − | 0.267823i | \(-0.913696\pi\) | ||
0.963468 | − | 0.267823i | \(-0.0863043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1575.00 | − | 1575.00i | 0.0667084 | − | 0.0667084i | −0.672965 | − | 0.739674i | \(-0.734980\pi\) |
0.739674 | + | 0.672965i | \(0.234980\pi\) | |||||||
\(824\) | 28065.1 | 1.18652 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10206.0 | 0.429918 | ||||||||
\(827\) | −23181.8 | + | 23181.8i | −0.974740 | + | 0.974740i | −0.999689 | − | 0.0249490i | \(-0.992058\pi\) |
0.0249490 | + | 0.999689i | \(0.492058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1190.00i | 0.0498557i | 0.999689 | + | 0.0249279i | \(0.00793561\pi\) | ||||
−0.999689 | + | 0.0249279i | \(0.992064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27279.0 | − | 27279.0i | −1.13669 | − | 1.13669i | ||||
\(833\) | 5375.43 | + | 5375.43i | 0.223586 | + | 0.223586i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2672.86i | 0.110578i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 567.000 | − | 567.000i | 0.0233731 | − | 0.0233731i | ||||
\(839\) | −9622.31 | −0.395946 | −0.197973 | − | 0.980207i | \(-0.563436\pi\) | ||||
−0.197973 | + | 0.980207i | \(0.563436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28099.0 | 1.15212 | ||||||||
\(842\) | −27259.0 | + | 27259.0i | −1.11568 | + | 1.11568i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 1316.00i | − | 0.0536713i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1143.00 | − | 1143.00i | −0.0463683 | − | 0.0463683i | ||||
\(848\) | 15965.1 | + | 15965.1i | 0.646512 | + | 0.646512i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29859.7i | 1.20279i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3969.00 | + | 3969.00i | −0.159315 | + | 0.159315i | −0.782263 | − | 0.622948i | \(-0.785935\pi\) |
0.622948 | + | 0.782263i | \(0.285935\pi\) | |||||||
\(854\) | 12295.2 | 0.492661 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39312.0 | 1.56969 | ||||||||
\(857\) | 33292.0 | − | 33292.0i | 1.32699 | − | 1.32699i | 0.419013 | − | 0.907980i | \(-0.362376\pi\) |
0.907980 | − | 0.419013i | \(-0.137624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13412.0i | − | 0.532726i | −0.963873 | − | 0.266363i | \(-0.914178\pi\) | ||
0.963873 | − | 0.266363i | \(-0.0858220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15228.0 | + | 15228.0i | 0.601703 | + | 0.601703i | ||||
\(863\) | 33572.0 | + | 33572.0i | 1.32422 | + | 1.32422i | 0.910322 | + | 0.413902i | \(0.135834\pi\) |
0.413902 | + | 0.910322i | \(0.364166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 47577.0i | − | 1.86690i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1764.00 | − | 1764.00i | 0.0689793 | − | 0.0689793i | ||||
\(869\) | −18633.7 | −0.727393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47628.0 | 1.85283 | ||||||||
\(872\) | 1039.45 | − | 1039.45i | 0.0403671 | − | 0.0403671i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 21420.0i | − | 0.828996i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15939.0 | + | 15939.0i | 0.613708 | + | 0.613708i | 0.943910 | − | 0.330202i | \(-0.107117\pi\) |
−0.330202 | + | 0.943910i | \(0.607117\pi\) | |||||||
\(878\) | 4929.95 | + | 4929.95i | 0.189496 | + | 0.189496i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 30737.9i | − | 1.17547i | −0.809054 | − | 0.587734i | \(-0.800020\pi\) | ||
0.809054 | − | 0.587734i | \(-0.199980\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11574.0 | − | 11574.0i | 0.441105 | − | 0.441105i | −0.451278 | − | 0.892383i | \(-0.649032\pi\) |
0.892383 | + | 0.451278i | \(0.149032\pi\) | |||||||
\(884\) | −3742.01 | −0.142373 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24120.0 | −0.914591 | ||||||||
\(887\) | 13512.8 | − | 13512.8i | 0.511517 | − | 0.511517i | −0.403474 | − | 0.914991i | \(-0.632197\pi\) |
0.914991 | + | 0.403474i | \(0.132197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5670.00i | − | 0.213910i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2205.00 | + | 2205.00i | 0.0827678 | + | 0.0827678i | ||||
\(893\) | −24946.7 | − | 24946.7i | −0.934838 | − | 0.934838i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 21115.6i | − | 0.787303i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7857.00 | − | 7857.00i | 0.291973 | − | 0.291973i | ||||
\(899\) | −44904.1 | −1.66589 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13356.0 | −0.493843 | ||||||||
\(902\) | 21650.2 | − | 21650.2i | 0.799194 | − | 0.799194i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15498.0i | 0.570194i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30600.0 | − | 30600.0i | −1.12024 | − | 1.12024i | −0.991705 | − | 0.128533i | \(-0.958973\pi\) |
−0.128533 | − | 0.991705i | \(-0.541027\pi\) | |||||||
\(908\) | −653.367 | − | 653.367i | −0.0238797 | − | 0.0238797i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15731.7i | − | 0.572135i | −0.958209 | − | 0.286067i | \(-0.907652\pi\) | ||
0.958209 | − | 0.286067i | \(-0.0923481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29484.0 | + | 29484.0i | −1.06876 | + | 1.06876i | ||||
\(914\) | −30547.0 | −1.10548 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3206.00 | 0.115643 | ||||||||
\(917\) | −12027.9 | + | 12027.9i | −0.433147 | + | 0.433147i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3724.00i | − | 0.133671i | −0.997764 | − | 0.0668354i | \(-0.978710\pi\) | ||
0.997764 | − | 0.0668354i | \(-0.0212902\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29484.0 | + | 29484.0i | 1.05315 | + | 1.05315i | ||||
\(923\) | −52922.7 | − | 52922.7i | −1.88729 | − | 1.88729i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17373.6i | 0.616558i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7290.00 | − | 7290.00i | 0.257873 | − | 0.257873i | ||||
\(929\) | 51586.3 | 1.82184 | 0.910921 | − | 0.412582i | \(-0.135373\pi\) | ||||
0.910921 | + | 0.412582i | \(0.135373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12670.0 | −0.446018 | ||||||||
\(932\) | 12.7279 | − | 12.7279i | 0.000447336 | − | 0.000447336i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 42084.0i | 1.47434i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30744.0 | − | 30744.0i | −1.07189 | − | 1.07189i | −0.997207 | − | 0.0746847i | \(-0.976205\pi\) |
−0.0746847 | − | 0.997207i | \(-0.523795\pi\) | |||||||
\(938\) | 14433.5 | + | 14433.5i | 0.502419 | + | 0.502419i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1069.15i | 0.0370384i | 0.999829 | + | 0.0185192i | \(0.00589518\pi\) | ||||
−0.999829 | + | 0.0185192i | \(0.994105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19278.0 | + | 19278.0i | −0.665724 | + | 0.665724i | ||||
\(944\) | −18977.3 | −0.654300 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23328.0 | 0.801753 | ||||||||
\(947\) | 2986.82 | − | 2986.82i | 0.102491 | − | 0.102491i | −0.654002 | − | 0.756493i | \(-0.726911\pi\) |
0.756493 | + | 0.654002i | \(0.226911\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 47628.0i | − | 1.62916i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7938.00 | + | 7938.00i | 0.270244 | + | 0.270244i | ||||
\(953\) | 3220.16 | + | 3220.16i | 0.109456 | + | 0.109456i | 0.759714 | − | 0.650258i | \(-0.225339\pi\) |
−0.650258 | + | 0.759714i | \(0.725339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1298.25i | − | 0.0439209i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32886.0 | + | 32886.0i | −1.10908 | + | 1.10908i | ||||
\(959\) | 23292.1 | 0.784297 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8625.00 | 0.289517 | ||||||||
\(962\) | −55328.3 | + | 55328.3i | −1.85432 | + | 1.85432i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 700.000i | 0.0233874i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30051.0 | + | 30051.0i | 0.999354 | + | 0.999354i | 1.00000 | 0.000646108i | \(-0.000205663\pi\) | |
−0.000646108 | 1.00000i | \(0.500206\pi\) | ||||||||
\(968\) | 1885.85 | + | 1885.85i | 0.0626174 | + | 0.0626174i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 10958.7i | − | 0.362186i | −0.983466 | − | 0.181093i | \(-0.942036\pi\) | ||
0.983466 | − | 0.181093i | \(-0.0579635\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2772.00 | + | 2772.00i | −0.0913322 | + | 0.0913322i | ||||
\(974\) | 29592.4 | 0.973514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22862.0 | −0.749790 | ||||||||
\(977\) | −19053.7 | + | 19053.7i | −0.623932 | + | 0.623932i | −0.946535 | − | 0.322602i | \(-0.895442\pi\) |
0.322602 | + | 0.946535i | \(0.395442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10206.0i | 0.333182i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4455.00 | + | 4455.00i | 0.144771 | + | 0.144771i | ||||
\(983\) | −20551.4 | − | 20551.4i | −0.666822 | − | 0.666822i | 0.290157 | − | 0.956979i | \(-0.406293\pi\) |
−0.956979 | + | 0.290157i | \(0.906293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 28866.9i | 0.932363i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4410.00 | − | 4410.00i | 0.142005 | − | 0.142005i | ||||
\(989\) | −20772.0 | −0.667857 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40516.0 | −1.29872 | −0.649361 | − | 0.760480i | \(-0.724963\pi\) | ||||
−0.649361 | + | 0.760480i | \(0.724963\pi\) | |||||||
\(992\) | −6236.68 | + | 6236.68i | −0.199612 | + | 0.199612i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 32076.0i | − | 1.02353i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 945.000 | + | 945.000i | 0.0300185 | + | 0.0300185i | 0.721957 | − | 0.691938i | \(-0.243243\pi\) |
−0.691938 | + | 0.721957i | \(0.743243\pi\) | |||||||
\(998\) | −1217.64 | − | 1217.64i | −0.0386209 | − | 0.0386209i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.4.f.b.107.1 | yes | 4 | |
3.2 | odd | 2 | inner | 225.4.f.b.107.2 | yes | 4 | |
5.2 | odd | 4 | 225.4.f.a.143.1 | yes | 4 | ||
5.3 | odd | 4 | inner | 225.4.f.b.143.2 | yes | 4 | |
5.4 | even | 2 | 225.4.f.a.107.2 | yes | 4 | ||
15.2 | even | 4 | 225.4.f.a.143.2 | yes | 4 | ||
15.8 | even | 4 | inner | 225.4.f.b.143.1 | yes | 4 | |
15.14 | odd | 2 | 225.4.f.a.107.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.f.a.107.1 | ✓ | 4 | 15.14 | odd | 2 | ||
225.4.f.a.107.2 | yes | 4 | 5.4 | even | 2 | ||
225.4.f.a.143.1 | yes | 4 | 5.2 | odd | 4 | ||
225.4.f.a.143.2 | yes | 4 | 15.2 | even | 4 | ||
225.4.f.b.107.1 | yes | 4 | 1.1 | even | 1 | trivial | |
225.4.f.b.107.2 | yes | 4 | 3.2 | odd | 2 | inner | |
225.4.f.b.143.1 | yes | 4 | 15.8 | even | 4 | inner | |
225.4.f.b.143.2 | yes | 4 | 5.3 | odd | 4 | inner |