Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(577,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.577");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(67.9702003266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(-2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.577 |
Dual form | 1152.4.d.o.577.4 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 18.4222i | − 1.64773i | −0.566785 | − | 0.823866i | \(-0.691813\pi\) | ||||
0.566785 | − | 0.823866i | \(-0.308187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.4222 | 1.21069 | 0.605343 | − | 0.795965i | \(-0.293036\pi\) | ||||
0.605343 | + | 0.795965i | \(0.293036\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 53.6888i | 1.47162i | 0.677190 | + | 0.735809i | \(0.263198\pi\) | ||||
−0.677190 | + | 0.735809i | \(0.736802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.15559i | 0.152662i | 0.997083 | + | 0.0763309i | \(0.0243205\pi\) | ||||
−0.997083 | + | 0.0763309i | \(0.975679\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −39.6888 | −0.566233 | −0.283116 | − | 0.959086i | \(-0.591368\pi\) | ||||
−0.283116 | + | 0.959086i | \(0.591368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 125.689i | 1.51763i | 0.651306 | + | 0.758816i | \(0.274222\pi\) | ||||
−0.651306 | + | 0.758816i | \(0.725778\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −99.1556 | −0.898929 | −0.449465 | − | 0.893298i | \(-0.648385\pi\) | ||||
−0.449465 | + | 0.893298i | \(0.648385\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −214.378 | −1.71502 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 205.800i | − 1.31780i | −0.752232 | − | 0.658898i | \(-0.771023\pi\) | ||||
0.752232 | − | 0.658898i | \(-0.228977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −147.489 | −0.854508 | −0.427254 | − | 0.904132i | \(-0.640519\pi\) | ||||
−0.427254 | + | 0.904132i | \(0.640519\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 413.066i | − 1.99489i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 125.689i | − 0.558463i | −0.960224 | − | 0.279231i | \(-0.909920\pi\) | ||||
0.960224 | − | 0.279231i | \(-0.0900796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −506.444 | −1.92910 | −0.964552 | − | 0.263892i | \(-0.914994\pi\) | ||||
−0.964552 | + | 0.263892i | \(0.914994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 413.689i | 1.46714i | 0.679615 | + | 0.733569i | \(0.262147\pi\) | ||||
−0.679615 | + | 0.733569i | \(0.737853\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −313.911 | −0.974226 | −0.487113 | − | 0.873339i | \(-0.661950\pi\) | ||||
−0.487113 | + | 0.873339i | \(0.661950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 159.755 | 0.465759 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 44.3331i | − 0.114898i | −0.998348 | − | 0.0574492i | \(-0.981703\pi\) | ||||
0.998348 | − | 0.0574492i | \(-0.0182967\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 989.066 | 2.42483 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 324.000i | − 0.714936i | −0.933925 | − | 0.357468i | \(-0.883640\pi\) | ||||
0.933925 | − | 0.357468i | \(-0.116360\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 324.000i | 0.680065i | 0.940414 | + | 0.340032i | \(0.110438\pi\) | ||||
−0.940414 | + | 0.340032i | \(0.889562\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 131.822 | 0.251546 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 464.266i | − 0.846554i | −0.906000 | − | 0.423277i | \(-0.860880\pi\) | ||||
0.906000 | − | 0.423277i | \(-0.139120\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1052.84 | −1.75985 | −0.879927 | − | 0.475109i | \(-0.842409\pi\) | ||||
−0.879927 | + | 0.475109i | \(0.842409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1022.27 | −1.63900 | −0.819501 | − | 0.573078i | \(-0.805749\pi\) | ||||
−0.819501 | + | 0.573078i | \(0.805749\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1203.82i | 1.78167i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 602.910 | 0.858642 | 0.429321 | − | 0.903152i | \(-0.358753\pi\) | ||||
0.429321 | + | 0.903152i | \(0.358753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.8217i | 0.0209236i | 0.999945 | + | 0.0104618i | \(0.00333016\pi\) | ||||
−0.999945 | + | 0.0104618i | \(0.996670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 731.156i | 0.933000i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 381.378 | 0.454224 | 0.227112 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227112 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 160.444i | 0.184825i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2315.47 | 2.50065 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 659.154 | 0.689969 | 0.344984 | − | 0.938608i | \(-0.387884\pi\) | ||||
0.344984 | + | 0.938608i | \(0.387884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 498.510i | 0.491125i | 0.969381 | + | 0.245562i | \(0.0789726\pi\) | ||||
−0.969381 | + | 0.245562i | \(0.921027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −196.821 | −0.188285 | −0.0941425 | − | 0.995559i | \(-0.530011\pi\) | ||||
−0.0941425 | + | 0.995559i | \(0.530011\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 359.378i | − 0.324695i | −0.986734 | − | 0.162347i | \(-0.948093\pi\) | ||||
0.986734 | − | 0.162347i | \(-0.0519065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1969.73i | 1.73088i | 0.501011 | + | 0.865441i | \(0.332962\pi\) | ||||
−0.501011 | + | 0.865441i | \(0.667038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 693.643 | 0.577456 | 0.288728 | − | 0.957411i | \(-0.406768\pi\) | ||||
0.288728 | + | 0.957411i | \(0.406768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1826.66i | 1.48119i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −889.911 | −0.685529 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1551.49 | −1.16566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1646.53i | 1.17816i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2656.78 | −1.85631 | −0.928153 | − | 0.372199i | \(-0.878604\pi\) | ||||
−0.928153 | + | 0.372199i | \(0.878604\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 615.734i | 0.410664i | 0.978692 | + | 0.205332i | \(0.0658274\pi\) | ||||
−0.978692 | + | 0.205332i | \(0.934173\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2818.22i | 1.83737i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −613.290 | −0.382459 | −0.191230 | − | 0.981545i | \(-0.561247\pi\) | ||||
−0.191230 | + | 0.981545i | \(0.561247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1899.29i | − 1.15896i | −0.814987 | − | 0.579480i | \(-0.803256\pi\) | ||||
0.814987 | − | 0.579480i | \(-0.196744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −384.175 | −0.224660 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3791.29 | −2.17137 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 976.377i | − 0.536832i | −0.963303 | − | 0.268416i | \(-0.913500\pi\) | ||||
0.963303 | − | 0.268416i | \(-0.0865001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 683.132 | 0.368162 | 0.184081 | − | 0.982911i | \(-0.441069\pi\) | ||||
0.184081 | + | 0.982911i | \(0.441069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2717.07i | 1.40800i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 511.109i | − 0.259815i | −0.991526 | − | 0.129907i | \(-0.958532\pi\) | ||||
0.991526 | − | 0.129907i | \(-0.0414680\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2223.29 | −1.08832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2425.95i | − 1.16574i | −0.812566 | − | 0.582869i | \(-0.801930\pi\) | ||||
0.812566 | − | 0.582869i | \(-0.198070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −337.332 | −0.156309 | −0.0781544 | − | 0.996941i | \(-0.524903\pi\) | ||||
−0.0781544 | + | 0.996941i | \(0.524903\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2145.80 | 0.976694 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2648.29i | 1.16385i | 0.813243 | + | 0.581924i | \(0.197700\pi\) | ||||
−0.813243 | + | 0.581924i | \(0.802300\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4806.82 | −2.07635 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2907.29i | 1.21397i | 0.794713 | + | 0.606986i | \(0.207621\pi\) | ||||
−0.794713 | + | 0.606986i | \(0.792379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3682.80i | − 1.51238i | −0.654354 | − | 0.756188i | \(-0.727060\pi\) | ||||
0.654354 | − | 0.756188i | \(-0.272940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2315.47 | −0.920197 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2130.85i | − 0.833277i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1279.56 | 0.484740 | 0.242370 | − | 0.970184i | \(-0.422075\pi\) | ||||
0.242370 | + | 0.970184i | \(0.422075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4836.84 | −1.80396 | −0.901978 | − | 0.431783i | \(-0.857885\pi\) | ||||
−0.901978 | + | 0.431783i | \(0.857885\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2869.31i | − 1.03771i | −0.854861 | − | 0.518857i | \(-0.826358\pi\) | ||||
0.854861 | − | 0.518857i | \(-0.173642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 652.242 | 0.232343 | 0.116171 | − | 0.993229i | \(-0.462938\pi\) | ||||
0.116171 | + | 0.993229i | \(0.462938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4614.49i | − 1.59544i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9329.82i | 3.17865i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6748.08 | −2.23337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 537.511i | − 0.175373i | −0.996148 | − | 0.0876866i | \(-0.972053\pi\) | ||||
0.996148 | − | 0.0876866i | \(-0.0279474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7621.06 | 2.41745 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3307.02 | −1.03454 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 283.997i | − 0.0864421i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4041.98 | 1.21377 | 0.606885 | − | 0.794790i | \(-0.292419\pi\) | ||||
0.606885 | + | 0.794790i | \(0.292419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3070.22i | 0.897699i | 0.893607 | + | 0.448850i | \(0.148166\pi\) | ||||
−0.893607 | + | 0.448850i | \(0.851834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 205.110i | 0.0591881i | 0.999562 | + | 0.0295940i | \(0.00942145\pi\) | ||||
−0.999562 | + | 0.0295940i | \(0.990579\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3776 | 0.00376137 | 0.00188068 | − | 0.999998i | \(-0.499401\pi\) | ||||
0.00188068 | + | 0.999998i | \(0.499401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5782.93i | 1.60526i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4327.99 | 1.17136 | 0.585679 | − | 0.810543i | \(-0.300828\pi\) | ||||
0.585679 | + | 0.810543i | \(0.300828\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1508.31 | −0.403150 | −0.201575 | − | 0.979473i | \(-0.564606\pi\) | ||||
−0.201575 | + | 0.979473i | \(0.564606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2943.04i | − 0.767446i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −899.378 | −0.231684 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4871.47i | 1.22504i | 0.790456 | + | 0.612518i | \(0.209843\pi\) | ||||
−0.790456 | + | 0.612518i | \(0.790157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5323.55i | − 1.32288i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1665.55 | 0.404258 | 0.202129 | − | 0.979359i | \(-0.435214\pi\) | ||||
0.202129 | + | 0.979359i | \(0.435214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2818.22i | − 0.676122i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7167.64 | −1.68052 | −0.840258 | − | 0.542188i | \(-0.817596\pi\) | ||||
−0.840258 | + | 0.542188i | \(0.817596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −816.713 | −0.189322 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5453.84i | 1.23616i | 0.786116 | + | 0.618079i | \(0.212089\pi\) | ||||
−0.786116 | + | 0.618079i | \(0.787911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5416.20 | 1.21406 | 0.607031 | − | 0.794678i | \(-0.292360\pi\) | ||||
0.607031 | + | 0.794678i | \(0.292360\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 11509.7i | − 2.52385i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2648.75i | 0.574542i | 0.957849 | + | 0.287271i | \(0.0927479\pi\) | ||||
−0.957849 | + | 0.287271i | \(0.907252\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6664.57 | 1.41486 | 0.707429 | − | 0.706784i | \(-0.249855\pi\) | ||||
0.707429 | + | 0.706784i | \(0.249855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5630.84i | − 1.18275i | −0.806396 | − | 0.591376i | \(-0.798585\pi\) | ||||
0.806396 | − | 0.591376i | \(-0.201415\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11355.6 | −2.33554 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3337.80 | −0.679381 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 908.374i | 0.181119i | 0.995891 | + | 0.0905593i | \(0.0288655\pi\) | ||||
−0.995891 | + | 0.0905593i | \(0.971135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5968.79 | −1.17802 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 709.517i | − 0.137232i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9275.82i | 1.77624i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5968.79 | 1.12056 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 414.671i | 0.0770896i | 0.999257 | + | 0.0385448i | \(0.0122722\pi\) | ||||
−0.999257 | + | 0.0385448i | \(0.987728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1615.91 | −0.294629 | −0.147315 | − | 0.989090i | \(-0.547063\pi\) | ||||
−0.147315 | + | 0.989090i | \(0.547063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8479.33 | 1.53125 | 0.765623 | − | 0.643289i | \(-0.222431\pi\) | ||||
0.765623 | + | 0.643289i | \(0.222431\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6774.73i | 1.20034i | 0.799873 | + | 0.600169i | \(0.204900\pi\) | ||||
−0.799873 | + | 0.600169i | \(0.795100\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11049.2 | 1.93929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4988.44i | − 0.859332i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1534.00i | − 0.261818i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7038.57 | −1.17948 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9292.36i | 1.54306i | 0.636191 | + | 0.771532i | \(0.280509\pi\) | ||||
−0.636191 | + | 0.771532i | \(0.719491\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8552.80 | −1.39489 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6563.78 | 1.06098 | 0.530492 | − | 0.847690i | \(-0.322007\pi\) | ||||
0.530492 | + | 0.847690i | \(0.322007\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7918.49i | − 1.25751i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4108.75 | −0.646798 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3870.93i | 0.598855i | 0.954119 | + | 0.299427i | \(0.0967956\pi\) | ||||
−0.954119 | + | 0.299427i | \(0.903204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3474.57i | 0.532922i | 0.963846 | + | 0.266461i | \(0.0858543\pi\) | ||||
−0.963846 | + | 0.266461i | \(0.914146\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4308.58 | 0.649639 | 0.324820 | − | 0.945776i | \(-0.394696\pi\) | ||||
0.324820 | + | 0.945776i | \(0.394696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19395.7i | 2.89977i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8161.19 | 1.19981 | 0.599904 | − | 0.800072i | \(-0.295205\pi\) | ||||
0.599904 | + | 0.800072i | \(0.295205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8938.68 | −1.30320 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18832.4i | 2.70064i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4427.66 | −0.629760 | −0.314880 | − | 0.949132i | \(-0.601964\pi\) | ||||
−0.314880 | + | 0.949132i | \(0.601964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 994.045i | − 0.139106i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 11278.5i | − 1.56562i | −0.622258 | − | 0.782812i | \(-0.713785\pi\) | ||||
0.622258 | − | 0.782812i | \(-0.286215\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1472.62 | 0.201177 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 709.683i | 0.0961846i | 0.998843 | + | 0.0480923i | \(0.0153142\pi\) | ||||
−0.998843 | + | 0.0480923i | \(0.984686\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1233.69 | −0.164592 | −0.0822962 | − | 0.996608i | \(-0.526225\pi\) | ||||
−0.0822962 | + | 0.996608i | \(0.526225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22177.1 | 2.93571 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6830.06i | − 0.890226i | −0.895474 | − | 0.445113i | \(-0.853164\pi\) | ||||
0.895474 | − | 0.445113i | \(-0.146836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3935.37 | 0.509003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 11106.9i | − 1.41481i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11289.7i | − 1.42724i | −0.700535 | − | 0.713618i | \(-0.747055\pi\) | ||||
0.700535 | − | 0.713618i | \(-0.252945\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3055.59 | 0.380521 | 0.190261 | − | 0.981734i | \(-0.439067\pi\) | ||||
0.190261 | + | 0.981734i | \(0.439067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1055.37i | − 0.130451i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6748.08 | 0.821843 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4089.01 | −0.494349 | −0.247175 | − | 0.968971i | \(-0.579502\pi\) | ||||
−0.247175 | + | 0.968971i | \(0.579502\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7264.79i | − 0.865562i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 291.471 | 0.0344765 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15397.0i | 1.79520i | 0.440806 | + | 0.897602i | \(0.354693\pi\) | ||||
−0.440806 | + | 0.897602i | \(0.645307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1034.45i | − 0.119753i | −0.998206 | − | 0.0598766i | \(-0.980929\pi\) | ||||
0.998206 | − | 0.0598766i | \(-0.0190707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8508.40 | 0.971101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7264.79i | 0.823344i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4943.86 | −0.552523 | −0.276261 | − | 0.961083i | \(-0.589096\pi\) | ||||
−0.276261 | + | 0.961083i | \(0.589096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 337.202 | 0.0374247 | 0.0187124 | − | 0.999825i | \(-0.494043\pi\) | ||||
0.0187124 | + | 0.999825i | \(0.494043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 12462.7i | − 1.36424i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4493.93 | 0.488573 | 0.244286 | − | 0.969703i | \(-0.421446\pi\) | ||||
0.244286 | + | 0.969703i | \(0.421446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4292.26i | − 0.460341i | −0.973150 | − | 0.230171i | \(-0.926072\pi\) | ||||
0.973150 | − | 0.230171i | \(-0.0739285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 7025.82i | − 0.748440i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4167.96 | 0.438081 | 0.219040 | − | 0.975716i | \(-0.429707\pi\) | ||||
0.219040 | + | 0.975716i | \(0.429707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 27190.4i | − 2.83890i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2955.73 | 0.304543 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −301.643 | −0.0308759 | −0.0154380 | − | 0.999881i | \(-0.504914\pi\) | ||||
−0.0154380 | + | 0.999881i | \(0.504914\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 9611.88i | − 0.971085i | −0.874213 | − | 0.485542i | \(-0.838622\pi\) | ||||
0.874213 | − | 0.485542i | \(-0.161378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13251.0 | 1.33008 | 0.665041 | − | 0.746807i | \(-0.268414\pi\) | ||||
0.665041 | + | 0.746807i | \(0.268414\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4432.00i | 0.439161i | 0.975594 | + | 0.219581i | \(0.0704689\pi\) | ||||
−0.975594 | + | 0.219581i | \(0.929531\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10409.9i | − 1.02491i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22210.5 | −2.15907 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 26944.9i | − 2.60277i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9076.49 | 0.865794 | 0.432897 | − | 0.901443i | \(-0.357491\pi\) | ||||
0.432897 | + | 0.901443i | \(0.357491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 899.378 | 0.0852559 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 12143.1i | − 1.13688i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3343.89 | −0.311142 | −0.155571 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155571 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2423.73i | − 0.222773i | −0.993777 | − | 0.111386i | \(-0.964471\pi\) | ||||
0.993777 | − | 0.111386i | \(-0.0355291\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8167.95i | 0.746179i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23607.1 | −2.13063 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 811.819i | 0.0728296i | 0.999337 | + | 0.0364148i | \(0.0115938\pi\) | ||||
−0.999337 | + | 0.0364148i | \(0.988406\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18192.4 | −1.61264 | −0.806320 | − | 0.591479i | \(-0.798544\pi\) | ||||
−0.806320 | + | 0.591479i | \(0.798544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9183.65 | 0.809242 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 5645.44i | − 0.491610i | −0.969319 | − | 0.245805i | \(-0.920948\pi\) | ||||
0.969319 | − | 0.245805i | \(-0.0790523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22921.5 | −1.98432 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3625.88i | 0.310243i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16853.5i | − 1.43369i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12338.7 | 1.03756 | 0.518780 | − | 0.854908i | \(-0.326386\pi\) | ||||
0.518780 | + | 0.854908i | \(0.326386\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10609.8i | 0.887062i | 0.896259 | + | 0.443531i | \(0.146274\pi\) | ||||
−0.896259 | + | 0.443531i | \(0.853726\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5853.65 | 0.483850 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2335.17 | −0.191926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3623.91i | − 0.294501i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6620.53 | −0.535010 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8577.07i | 0.685419i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4035.42i | − 0.320696i | −0.987061 | − | 0.160348i | \(-0.948738\pi\) | ||||
0.987061 | − | 0.160348i | \(-0.0512616\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36286.8 | 2.85203 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7407.45i | 0.579012i | 0.957176 | + | 0.289506i | \(0.0934911\pi\) | ||||
−0.957176 | + | 0.289506i | \(0.906509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25866.7 | 1.99993 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13518.6 | 1.03954 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9500.77i | − 0.722730i | −0.932424 | − | 0.361365i | \(-0.882311\pi\) | ||||
0.932424 | − | 0.361365i | \(-0.117689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2960.19 | −0.223976 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2700.26i | − 0.202136i | −0.994880 | − | 0.101068i | \(-0.967774\pi\) | ||||
0.994880 | − | 0.101068i | \(-0.0322259\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 12778.4i | − 0.951492i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15904.9 | 1.17183 | 0.585913 | − | 0.810374i | \(-0.300736\pi\) | ||||
0.585913 | + | 0.810374i | \(0.300736\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 18234.0i | − 1.33638i | −0.743992 | − | 0.668188i | \(-0.767070\pi\) | ||||
0.743992 | − | 0.668188i | \(-0.232930\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21256.7 | 1.54168 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4869.57 | 0.351339 | 0.175670 | − | 0.984449i | \(-0.443791\pi\) | ||||
0.175670 | + | 0.984449i | \(0.443791\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 354.758i | 0.0253319i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2380.19 | 0.169086 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1616.99i | − 0.113697i | −0.998383 | − | 0.0568485i | \(-0.981895\pi\) | ||||
0.998383 | − | 0.0568485i | \(-0.0181052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 18537.7i | − 1.29683i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8117.01 | −0.562101 | −0.281050 | − | 0.959693i | \(-0.590683\pi\) | ||||
−0.281050 | + | 0.959693i | \(0.590683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16394.1i | 1.12957i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9536.40 | −0.650495 | −0.325248 | − | 0.945629i | \(-0.605448\pi\) | ||||
−0.325248 | + | 0.945629i | \(0.605448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16247.8 | 1.10276 | 0.551381 | − | 0.834253i | \(-0.314101\pi\) | ||||
0.551381 | + | 0.834253i | \(0.314101\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28581.9i | 1.92069i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27725.7 | −1.85396 | −0.926980 | − | 0.375111i | \(-0.877605\pi\) | ||||
−0.926980 | + | 0.375111i | \(0.877605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2246.22i | − 0.148727i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 927.190i | 0.0610911i | 0.999533 | + | 0.0305456i | \(0.00972447\pi\) | ||||
−0.999533 | + | 0.0305456i | \(0.990276\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18727.8 | −1.22196 | −0.610982 | − | 0.791644i | \(-0.709225\pi\) | ||||
−0.610982 | + | 0.791644i | \(0.709225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 3210.22i | − 0.208449i | −0.994554 | − | 0.104224i | \(-0.966764\pi\) | ||||
0.994554 | − | 0.104224i | \(-0.0332360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8551.33 | 0.549922 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3535.57 | 0.226276 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4988.44i | 0.316220i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11911.2 | −0.751468 | −0.375734 | − | 0.926728i | \(-0.622609\pi\) | ||||
−0.375734 | + | 0.926728i | \(0.622609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 48943.7i | 3.05869i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1143.14i | 0.0711036i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17232.6 | −1.06185 | −0.530924 | − | 0.847419i | \(-0.678155\pi\) | ||||
−0.530924 | + | 0.847419i | \(0.678155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 12754.6i | − 0.782262i | −0.920335 | − | 0.391131i | \(-0.872084\pi\) | ||||
0.920335 | − | 0.391131i | \(-0.127916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9441.73 | −0.573714 | −0.286857 | − | 0.957973i | \(-0.592610\pi\) | ||||
−0.286857 | + | 0.957973i | \(0.592610\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17395.2 | 1.05211 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5198.99i | − 0.311565i | −0.987791 | − | 0.155783i | \(-0.950210\pi\) | ||||
0.987791 | − | 0.155783i | \(-0.0497900\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11343.2 | 0.676664 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6508.01i | − 0.384698i | −0.981327 | − | 0.192349i | \(-0.938389\pi\) | ||||
0.981327 | − | 0.192349i | \(-0.0616105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25280.2i | 1.48757i | 0.668419 | + | 0.743785i | \(0.266972\pi\) | ||||
−0.668419 | + | 0.743785i | \(0.733028\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 51917.8 | 3.02750 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20406.2i | 1.18460i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17395.2 | −1.00079 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5525.89 | −0.316504 | −0.158252 | − | 0.987399i | \(-0.550586\pi\) | ||||
−0.158252 | + | 0.987399i | \(0.550586\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6293.21i | 0.357264i | 0.983916 | + | 0.178632i | \(0.0571671\pi\) | ||||
−0.983916 | + | 0.178632i | \(0.942833\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14779.7 | 0.835335 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5675.91i | − 0.317984i | −0.987280 | − | 0.158992i | \(-0.949176\pi\) | ||||
0.987280 | − | 0.158992i | \(-0.0508243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11298.2i | 0.630190i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 317.229 | 0.0175406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 3617.79i | − 0.199171i | −0.995029 | − | 0.0995854i | \(-0.968248\pi\) | ||||
0.995029 | − | 0.0995854i | \(-0.0317517\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34989.1 | −1.90966 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20100.2 | 1.09232 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 7938.43i | − 0.427718i | −0.976865 | − | 0.213859i | \(-0.931397\pi\) | ||||
0.976865 | − | 0.213859i | \(-0.0686033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15797.7 | 0.847540 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11177.7i | 0.594597i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 25691.6i | − 1.36088i | −0.732802 | − | 0.680442i | \(-0.761788\pi\) | ||||
0.732802 | − | 0.680442i | \(-0.238212\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14624.3 | 0.768142 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7077.35i | 0.370179i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36803.3 | 1.90895 | 0.954473 | − | 0.298298i | \(-0.0964190\pi\) | ||||
0.954473 | + | 0.298298i | \(0.0964190\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4413.16 | −0.227954 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44118.9i | 2.26005i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28333.2 | 1.44542 | 0.722709 | − | 0.691152i | \(-0.242897\pi\) | ||||
0.722709 | + | 0.691152i | \(0.242897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 16418.8i | − 0.830742i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10767.9i | 0.542592i | 0.962496 | + | 0.271296i | \(0.0874522\pi\) | ||||
−0.962496 | + | 0.271296i | \(0.912548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24925.9 | 1.24580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 17301.4i | − 0.861221i | −0.902538 | − | 0.430610i | \(-0.858298\pi\) | ||||
0.902538 | − | 0.430610i | \(-0.141702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24110.8 | −1.19050 | −0.595248 | − | 0.803542i | \(-0.702946\pi\) | ||||
−0.595248 | + | 0.803542i | \(0.702946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17987.0 | −0.884555 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 8058.04i | − 0.393103i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30052.8 | −1.46024 | −0.730121 | − | 0.683318i | \(-0.760536\pi\) | ||||
−0.730121 | + | 0.683318i | \(0.760536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 12584.8i | − 0.606633i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25599.4i | 1.22910i | 0.788879 | + | 0.614549i | \(0.210662\pi\) | ||||
−0.788879 | + | 0.614549i | \(0.789338\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28904.5 | −1.37685 | −0.688427 | − | 0.725306i | \(-0.741698\pi\) | ||||
−0.688427 | + | 0.725306i | \(0.741698\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44165.7i | 2.09555i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2318.41 | 0.109143 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8756.13 | −0.410603 | −0.205302 | − | 0.978699i | \(-0.565818\pi\) | ||||
−0.205302 | + | 0.978699i | \(0.565818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 28289.8i | − 1.31632i | −0.752879 | − | 0.658159i | \(-0.771335\pi\) | ||||
0.752879 | − | 0.658159i | \(-0.228665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31618.3 | 1.46550 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 63654.4i | − 2.92767i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 56526.0i | − 2.58983i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9415.75 | −0.428105 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4859.74i | 0.220116i | 0.993925 | + | 0.110058i | \(0.0351036\pi\) | ||||
−0.993925 | + | 0.110058i | \(0.964896\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15553.0 | 0.699117 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2318.41 | −0.103820 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17361.7i | 0.771623i | 0.922578 | + | 0.385811i | \(0.126078\pi\) | ||||
−0.922578 | + | 0.385811i | \(0.873922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12458.8 | 0.551638 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 54884.2i | − 2.41198i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40957.8i | 1.79326i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24475.3 | −1.06367 | −0.531833 | − | 0.846849i | \(-0.678497\pi\) | ||||
−0.531833 | + | 0.846849i | \(0.678497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 19875.4i | − 0.860566i | −0.902694 | − | 0.430283i | \(-0.858414\pi\) | ||||
0.902694 | − | 0.430283i | \(-0.141586\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −44691.4 | −1.92083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51996.1 | −2.22658 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 21682.1i | − 0.921693i | −0.887480 | − | 0.460846i | \(-0.847546\pi\) | ||||
0.887480 | − | 0.460846i | \(-0.152454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6698.17 | 0.283698 | 0.141849 | − | 0.989888i | \(-0.454695\pi\) | ||||
0.141849 | + | 0.989888i | \(0.454695\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3390.85i | − 0.142577i | −0.997456 | − | 0.0712886i | \(-0.977289\pi\) | ||||
0.997456 | − | 0.0712886i | \(-0.0227111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40093.4i | 1.67974i | 0.542789 | + | 0.839869i | \(0.317368\pi\) | ||||
−0.542789 | + | 0.839869i | \(0.682632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6340.50 | −0.263728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6214.40i | 0.257555i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6172.12 | 0.253975 | 0.126988 | − | 0.991904i | \(-0.459469\pi\) | ||||
0.126988 | + | 0.991904i | \(0.459469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17964.6 | −0.736585 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 39530.3i | − 1.60933i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34787.8 | −1.41124 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12462.7i | 0.502018i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 276.632i | − 0.0111040i | −0.999985 | − | 0.00555198i | \(-0.998233\pi\) | ||||
0.999985 | − | 0.00555198i | \(-0.00176726\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3704.41 | 0.147655 | 0.0738274 | − | 0.997271i | \(-0.476479\pi\) | ||||
0.0738274 | + | 0.997271i | \(0.476479\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 26915.5i | − 1.06909i | −0.845141 | − | 0.534544i | \(-0.820484\pi\) | ||||
0.845141 | − | 0.534544i | \(-0.179516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23623.9 | −0.931828 | −0.465914 | − | 0.884830i | \(-0.654274\pi\) | ||||
−0.465914 | + | 0.884830i | \(0.654274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48787.3 | 1.91771 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32369.5i | 1.26359i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3322.10 | 0.129236 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36918.9i | 1.42638i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 14094.0i | − 0.542667i | −0.962485 | − | 0.271333i | \(-0.912535\pi\) | ||||
0.962485 | − | 0.271333i | \(-0.0874646\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18967.3 | −0.725341 | −0.362671 | − | 0.931917i | \(-0.618135\pi\) | ||||
−0.362671 | + | 0.931917i | \(0.618135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32886.0i | 1.25334i | 0.779283 | + | 0.626672i | \(0.215583\pi\) | ||||
−0.779283 | + | 0.626672i | \(0.784417\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27945.6 | 1.05786 | 0.528929 | − | 0.848666i | \(-0.322594\pi\) | ||||
0.528929 | + | 0.848666i | \(0.322594\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59570.8 | −2.24740 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 39455.1i | − 1.47852i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53558.6 | 2.00030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30353.1i | 1.12607i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1759.53i | 0.0650592i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −67845.2 | −2.49199 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5544.89i | 0.202993i | 0.994836 | + | 0.101497i | \(0.0323631\pi\) | ||||
−0.994836 | + | 0.101497i | \(0.967637\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19638.9 | 0.714233 | 0.357116 | − | 0.934060i | \(-0.383760\pi\) | ||||
0.357116 | + | 0.934060i | \(0.383760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −849.451 | −0.0307916 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13806.1i | 0.497184i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22128.7 | 0.794297 | 0.397149 | − | 0.917754i | \(-0.370000\pi\) | ||||
0.397149 | + | 0.917754i | \(0.370000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 7533.72i | − 0.268663i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26944.9i | 0.957775i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17599.3 | −0.621544 | −0.310772 | − | 0.950484i | \(-0.600588\pi\) | ||||
−0.310772 | + | 0.950484i | \(0.600588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20079.5i | 0.706850i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39254.9 | −1.37302 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −441.299 | −0.0153859 | −0.00769297 | − | 0.999970i | \(-0.502449\pi\) | ||||
−0.00769297 | + | 0.999970i | \(0.502449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5408.01i | 0.187350i | 0.995603 | + | 0.0936749i | \(0.0298614\pi\) | ||||
−0.995603 | + | 0.0936749i | \(0.970139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50216.8 | 1.73413 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34237.1i | 1.17482i | 0.809289 | + | 0.587410i | \(0.199852\pi\) | ||||
−0.809289 | + | 0.587410i | \(0.800148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 7314.92i | − 0.250213i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21410.7 | 0.727766 | 0.363883 | − | 0.931445i | \(-0.381451\pi\) | ||||
0.363883 | + | 0.931445i | \(0.381451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 23572.2i | − 0.798722i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13751.3 | −0.463038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8038.09 | −0.269816 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 89105.3i | 2.97243i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53874.6 | −1.79161 | −0.895806 | − | 0.444445i | \(-0.853401\pi\) | ||||
−0.895806 | + | 0.444445i | \(0.853401\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42901.5i | 1.41789i | 0.705262 | + | 0.708947i | \(0.250829\pi\) | ||||
−0.705262 | + | 0.708947i | \(0.749171\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 42586.2i | − 1.40314i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58636.5 | −1.92011 | −0.960055 | − | 0.279812i | \(-0.909728\pi\) | ||||
−0.960055 | + | 0.279812i | \(0.909728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20475.7i | 0.668444i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25296.7 | 0.820793 | 0.410396 | − | 0.911907i | \(-0.365390\pi\) | ||||
0.410396 | + | 0.911907i | \(0.365390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52859.0 | −1.70988 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 41019.6i | − 1.31885i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10605.2 | −0.339944 | −0.169972 | − | 0.985449i | \(-0.554368\pi\) | ||||
−0.169972 | + | 0.985449i | \(0.554368\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 12015.7i | − 0.382839i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5770.19i | − 0.183294i | −0.995792 | − | 0.0916469i | \(-0.970787\pi\) | ||||
0.995792 | − | 0.0916469i | \(-0.0292131\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1152.4.d.o.577.1 | 4 | ||
3.2 | odd | 2 | 384.4.d.e.193.2 | yes | 4 | ||
4.3 | odd | 2 | 1152.4.d.i.577.1 | 4 | |||
8.3 | odd | 2 | 1152.4.d.i.577.4 | 4 | |||
8.5 | even | 2 | inner | 1152.4.d.o.577.4 | 4 | ||
12.11 | even | 2 | 384.4.d.c.193.4 | yes | 4 | ||
16.3 | odd | 4 | 2304.4.a.t.1.1 | 2 | |||
16.5 | even | 4 | 2304.4.a.bp.1.2 | 2 | |||
16.11 | odd | 4 | 2304.4.a.bq.1.2 | 2 | |||
16.13 | even | 4 | 2304.4.a.s.1.1 | 2 | |||
24.5 | odd | 2 | 384.4.d.e.193.3 | yes | 4 | ||
24.11 | even | 2 | 384.4.d.c.193.1 | ✓ | 4 | ||
48.5 | odd | 4 | 768.4.a.e.1.1 | 2 | |||
48.11 | even | 4 | 768.4.a.k.1.1 | 2 | |||
48.29 | odd | 4 | 768.4.a.p.1.2 | 2 | |||
48.35 | even | 4 | 768.4.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.c.193.1 | ✓ | 4 | 24.11 | even | 2 | ||
384.4.d.c.193.4 | yes | 4 | 12.11 | even | 2 | ||
384.4.d.e.193.2 | yes | 4 | 3.2 | odd | 2 | ||
384.4.d.e.193.3 | yes | 4 | 24.5 | odd | 2 | ||
768.4.a.e.1.1 | 2 | 48.5 | odd | 4 | |||
768.4.a.j.1.2 | 2 | 48.35 | even | 4 | |||
768.4.a.k.1.1 | 2 | 48.11 | even | 4 | |||
768.4.a.p.1.2 | 2 | 48.29 | odd | 4 | |||
1152.4.d.i.577.1 | 4 | 4.3 | odd | 2 | |||
1152.4.d.i.577.4 | 4 | 8.3 | odd | 2 | |||
1152.4.d.o.577.1 | 4 | 1.1 | even | 1 | trivial | ||
1152.4.d.o.577.4 | 4 | 8.5 | even | 2 | inner | ||
2304.4.a.s.1.1 | 2 | 16.13 | even | 4 | |||
2304.4.a.t.1.1 | 2 | 16.3 | odd | 4 | |||
2304.4.a.bp.1.2 | 2 | 16.5 | even | 4 | |||
2304.4.a.bq.1.2 | 2 | 16.11 | odd | 4 |