Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,4,Mod(145,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, 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("288.145");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.d (of order \(2\), degree \(1\), not 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: | \(16.9925500817\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.8248384.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + x^{4} - 12x^{3} + 4x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 145.5 | ||
Root | \(-0.641412 + 1.89436i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.145 |
Dual form | 288.4.d.d.145.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 9.15486i | 0.818836i | 0.912347 | + | 0.409418i | \(0.134268\pi\) | ||||
−0.912347 | + | 0.409418i | \(0.865732\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −27.4175 | −1.48040 | −0.740202 | − | 0.672385i | \(-0.765270\pi\) | ||||
−0.740202 | + | 0.672385i | \(0.765270\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 20.5252i | − 0.562598i | −0.959620 | − | 0.281299i | \(-0.909235\pi\) | ||||
0.959620 | − | 0.281299i | \(-0.0907652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 32.0471i | − 0.683713i | −0.939752 | − | 0.341857i | \(-0.888944\pi\) | ||||
0.939752 | − | 0.341857i | \(-0.111056\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 111.764 | 1.59452 | 0.797258 | − | 0.603639i | \(-0.206283\pi\) | ||||
0.797258 | + | 0.603639i | \(0.206283\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 129.764i | − 1.56684i | −0.621494 | − | 0.783419i | \(-0.713474\pi\) | ||||
0.621494 | − | 0.783419i | \(-0.286526\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.16510 | 0.0830893 | 0.0415447 | − | 0.999137i | \(-0.486772\pi\) | ||||
0.0415447 | + | 0.999137i | \(0.486772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 41.1885 | 0.329508 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.0606i | 0.262923i | 0.991321 | + | 0.131461i | \(0.0419669\pi\) | ||||
−0.991321 | + | 0.131461i | \(0.958033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 187.606 | 1.08694 | 0.543468 | − | 0.839430i | \(-0.317111\pi\) | ||||
0.543468 | + | 0.839430i | \(0.317111\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 251.003i | − 1.21221i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 114.127i | − 0.507093i | −0.967323 | − | 0.253546i | \(-0.918403\pi\) | ||||
0.967323 | − | 0.253546i | \(-0.0815970\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −282.915 | −1.07766 | −0.538828 | − | 0.842416i | \(-0.681133\pi\) | ||||
−0.538828 | + | 0.842416i | \(0.681133\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 89.3870i | − 0.317009i | −0.987358 | − | 0.158505i | \(-0.949333\pi\) | ||||
0.987358 | − | 0.158505i | \(-0.0506673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −54.6464 | −0.169596 | −0.0847978 | − | 0.996398i | \(-0.527024\pi\) | ||||
−0.0847978 | + | 0.996398i | \(0.527024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 408.717 | 1.19159 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 726.878i | − 1.88386i | −0.335815 | − | 0.941928i | \(-0.609012\pi\) | ||||
0.335815 | − | 0.941928i | \(-0.390988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 187.905 | 0.460675 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 216.579i | 0.477900i | 0.971032 | + | 0.238950i | \(0.0768033\pi\) | ||||
−0.971032 | + | 0.238950i | \(0.923197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 754.222i | − 1.58309i | −0.611114 | − | 0.791543i | \(-0.709278\pi\) | ||||
0.611114 | − | 0.791543i | \(-0.290722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 293.387 | 0.559849 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 379.433i | − 0.691868i | −0.938259 | − | 0.345934i | \(-0.887562\pi\) | ||||
0.938259 | − | 0.345934i | \(-0.112438\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 302.080 | 0.504933 | 0.252467 | − | 0.967606i | \(-0.418758\pi\) | ||||
0.252467 | + | 0.967606i | \(0.418758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −504.396 | −0.808700 | −0.404350 | − | 0.914604i | \(-0.632502\pi\) | ||||
−0.404350 | + | 0.914604i | \(0.632502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 562.748i | 0.832872i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −301.780 | −0.429784 | −0.214892 | − | 0.976638i | \(-0.568940\pi\) | ||||
−0.214892 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 599.003i | 0.792158i | 0.918216 | + | 0.396079i | \(0.129629\pi\) | ||||
−0.918216 | + | 0.396079i | \(0.870371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1023.18i | 1.30565i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 277.528 | 0.330538 | 0.165269 | − | 0.986248i | \(-0.447151\pi\) | ||||
0.165269 | + | 0.986248i | \(0.447151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 878.651i | 1.01217i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1187.97 | 1.28298 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −765.905 | −0.801710 | −0.400855 | − | 0.916141i | \(-0.631287\pi\) | ||||
−0.400855 | + | 0.916141i | \(0.631287\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 201.253i | 0.198272i | 0.995074 | + | 0.0991360i | \(0.0316079\pi\) | ||||
−0.995074 | + | 0.0991360i | \(0.968392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −682.440 | −0.652843 | −0.326421 | − | 0.945224i | \(-0.605843\pi\) | ||||
−0.326421 | + | 0.945224i | \(0.605843\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 457.252i | − 0.413123i | −0.978434 | − | 0.206562i | \(-0.933773\pi\) | ||||
0.978434 | − | 0.206562i | \(-0.0662274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 625.812i | − 0.549926i | −0.961455 | − | 0.274963i | \(-0.911334\pi\) | ||||
0.961455 | − | 0.274963i | \(-0.0886655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −981.151 | −0.816805 | −0.408402 | − | 0.912802i | \(-0.633914\pi\) | ||||
−0.408402 | + | 0.912802i | \(0.633914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.9052i | 0.0680365i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3064.29 | −2.36053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 909.717 | 0.683484 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1521.43i | 1.08865i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 808.055 | 0.564593 | 0.282296 | − | 0.959327i | \(-0.408904\pi\) | ||||
0.282296 | + | 0.959327i | \(0.408904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1110.85i | − 0.740884i | −0.928856 | − | 0.370442i | \(-0.879206\pi\) | ||||
0.928856 | − | 0.370442i | \(-0.120794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3557.80i | 2.31955i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 466.765 | 0.291084 | 0.145542 | − | 0.989352i | \(-0.453507\pi\) | ||||
0.145542 | + | 0.989352i | \(0.453507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 351.773i | 0.214654i | 0.994224 | + | 0.107327i | \(0.0342292\pi\) | ||||
−0.994224 | + | 0.107327i | \(0.965771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −657.773 | −0.384656 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −375.904 | −0.215291 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1290.49i | − 0.709540i | −0.934954 | − | 0.354770i | \(-0.884559\pi\) | ||||
0.934954 | − | 0.354770i | \(-0.115441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1175.51 | −0.633521 | −0.316761 | − | 0.948505i | \(-0.602595\pi\) | ||||
−0.316761 | + | 0.948505i | \(0.602595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1717.51i | 0.890022i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1092.09i | 0.555148i | 0.960704 | + | 0.277574i | \(0.0895303\pi\) | ||||
−0.960704 | + | 0.277574i | \(0.910470\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −251.284 | −0.123006 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3626.97i | 1.74286i | 0.490519 | + | 0.871430i | \(0.336807\pi\) | ||||
−0.490519 | + | 0.871430i | \(0.663193\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 45.8012 | 0.0212228 | 0.0106114 | − | 0.999944i | \(-0.496622\pi\) | ||||
0.0106114 | + | 0.999944i | \(0.496622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1169.98 | 0.532536 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2455.02i | 1.07891i | 0.842014 | + | 0.539455i | \(0.181370\pi\) | ||||
−0.842014 | + | 0.539455i | \(0.818630\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1129.28 | −0.487805 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1026.28i | 0.428533i | 0.976775 | + | 0.214267i | \(0.0687362\pi\) | ||||
−0.976775 | + | 0.214267i | \(0.931264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3699.05i | − 1.51905i | −0.650477 | − | 0.759526i | \(-0.725431\pi\) | ||||
0.650477 | − | 0.759526i | \(-0.274569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1044.82 | 0.415226 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2293.98i | − 0.897071i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5108.93 | 1.93544 | 0.967721 | − | 0.252023i | \(-0.0810960\pi\) | ||||
0.967721 | + | 0.252023i | \(0.0810960\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1414.13 | −0.527417 | −0.263709 | − | 0.964602i | \(-0.584946\pi\) | ||||
−0.263709 | + | 0.964602i | \(0.584946\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2816.66i | − 1.01867i | −0.860567 | − | 0.509337i | \(-0.829891\pi\) | ||||
0.860567 | − | 0.509337i | \(-0.170109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 948.556 | 0.337896 | 0.168948 | − | 0.985625i | \(-0.445963\pi\) | ||||
0.168948 | + | 0.985625i | \(0.445963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1125.78i | − 0.389232i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2590.05i | − 0.882424i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2663.43 | −0.881499 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 4487.28i | − 1.46406i | −0.681271 | − | 0.732032i | \(-0.738572\pi\) | ||||
0.681271 | − | 0.732032i | \(-0.261428\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 818.326 | 0.259578 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5143.68 | −1.60910 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3581.72i | − 1.09019i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4590.98 | 1.37863 | 0.689315 | − | 0.724462i | \(-0.257912\pi\) | ||||
0.689315 | + | 0.724462i | \(0.257912\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2897.47i | 0.847189i | 0.905852 | + | 0.423594i | \(0.139232\pi\) | ||||
−0.905852 | + | 0.423594i | \(0.860768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 34.6293i | 0.00999288i | 0.999988 | + | 0.00499644i | \(0.00159042\pi\) | ||||
−0.999988 | + | 0.00499644i | \(0.998410\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1054.02 | 0.296355 | 0.148178 | − | 0.988961i | \(-0.452659\pi\) | ||||
0.148178 | + | 0.988961i | \(0.452659\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 500.280i | − 0.138871i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −654.700 | −0.177192 | −0.0885962 | − | 0.996068i | \(-0.528238\pi\) | ||||
−0.0885962 | + | 0.996068i | \(0.528238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3194.00 | 0.853707 | 0.426854 | − | 0.904321i | \(-0.359622\pi\) | ||||
0.426854 | + | 0.904321i | \(0.359622\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3741.74i | 0.975719i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4158.57 | −1.07127 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 5042.90i | − 1.26815i | −0.773273 | − | 0.634074i | \(-0.781382\pi\) | ||||
0.773273 | − | 0.634074i | \(-0.218618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 188.115i | − 0.0467459i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5166.64 | 1.25403 | 0.627016 | − | 0.779007i | \(-0.284276\pi\) | ||||
0.627016 | + | 0.779007i | \(0.284276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3129.08i | 0.750702i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7366.11 | −1.72705 | −0.863524 | − | 0.504308i | \(-0.831748\pi\) | ||||
−0.863524 | + | 0.504308i | \(0.831748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6654.47 | 1.54257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 7877.80i | − 1.78557i | −0.450484 | − | 0.892784i | \(-0.648749\pi\) | ||||
0.450484 | − | 0.892784i | \(-0.351251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5399.92 | 1.21041 | 0.605206 | − | 0.796069i | \(-0.293091\pi\) | ||||
0.605206 | + | 0.796069i | \(0.293091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 845.402i | − 0.185381i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4416.07i | − 0.957892i | −0.877844 | − | 0.478946i | \(-0.841019\pi\) | ||||
0.877844 | − | 0.478946i | \(-0.158981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8068.94 | −1.71300 | −0.856499 | − | 0.516148i | \(-0.827365\pi\) | ||||
−0.856499 | + | 0.516148i | \(0.827365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5241.13i | − 1.10089i | −0.834870 | − | 0.550447i | \(-0.814457\pi\) | ||||
0.834870 | − | 0.550447i | \(-0.185543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7756.81 | 1.59537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7578.21 | 1.54248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6372.75i | 1.27065i | 0.772246 | + | 0.635324i | \(0.219133\pi\) | ||||
−0.772246 | + | 0.635324i | \(0.780867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1982.75 | −0.391322 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 293.715i | − 0.0568093i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2450.76i | 0.469301i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6904.79 | 1.29629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3810.22i | − 0.708342i | −0.935181 | − | 0.354171i | \(-0.884763\pi\) | ||||
0.935181 | − | 0.354171i | \(-0.115237\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8106.73 | −1.47810 | −0.739052 | − | 0.673648i | \(-0.764726\pi\) | ||||
−0.739052 | + | 0.673648i | \(0.764726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −559.983 | −0.101125 | −0.0505625 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505625 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5828.98i | 1.03277i | 0.856357 | + | 0.516385i | \(0.172723\pi\) | ||||
−0.856357 | + | 0.516385i | \(0.827277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 842.776 | 0.147920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 14503.0i | − 2.49835i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1319.97i | − 0.225289i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1498.26 | 0.251070 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2847.98i | 0.472928i | 0.971640 | + | 0.236464i | \(0.0759885\pi\) | ||||
−0.971640 | + | 0.236464i | \(0.924011\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3473.66 | 0.566526 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10127.8 | −1.63707 | −0.818537 | − | 0.574454i | \(-0.805214\pi\) | ||||
−0.818537 | + | 0.574454i | \(0.805214\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3850.65i | − 0.611508i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1801.78 | −0.283636 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10148.2i | 1.56999i | 0.619505 | + | 0.784993i | \(0.287333\pi\) | ||||
−0.619505 | + | 0.784993i | \(0.712667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9515.96i | 1.45954i | 0.683695 | + | 0.729768i | \(0.260372\pi\) | ||||
−0.683695 | + | 0.729768i | \(0.739628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2813.56 | −0.424223 | −0.212111 | − | 0.977245i | \(-0.568034\pi\) | ||||
−0.212111 | + | 0.977245i | \(0.568034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2765.50i | 0.413457i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2427.25 | −0.356839 | −0.178419 | − | 0.983955i | \(-0.557098\pi\) | ||||
−0.178419 | + | 0.983955i | \(0.557098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9979.71 | −1.45498 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4617.67i | − 0.662192i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5021.46 | −0.714219 | −0.357109 | − | 0.934063i | \(-0.616238\pi\) | ||||
−0.357109 | + | 0.934063i | \(0.616238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19929.1i | 2.78887i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3182.40i | − 0.441765i | −0.975300 | − | 0.220882i | \(-0.929106\pi\) | ||||
0.975300 | − | 0.220882i | \(-0.0708937\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1315.87 | 0.179764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5868.93i | 0.795426i | 0.917510 | + | 0.397713i | \(0.130196\pi\) | ||||
−0.917510 | + | 0.397713i | \(0.869804\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7350.18 | 0.980618 | 0.490309 | − | 0.871549i | \(-0.336884\pi\) | ||||
0.490309 | + | 0.871549i | \(0.336884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5151.88 | −0.681985 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13009.1i | 1.69560i | 0.530317 | + | 0.847800i | \(0.322073\pi\) | ||||
−0.530317 | + | 0.847800i | \(0.677927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1024.33 | 0.132487 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2762.76i | − 0.351923i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4877.88i | 0.616659i | 0.951280 | + | 0.308330i | \(0.0997700\pi\) | ||||
−0.951280 | + | 0.308330i | \(0.900230\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5552.33 | −0.691446 | −0.345723 | − | 0.938337i | \(-0.612366\pi\) | ||||
−0.345723 | + | 0.938337i | \(0.612366\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6012.23i | − 0.743153i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2342.49 | −0.285289 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6989.27 | 0.844981 | 0.422491 | − | 0.906367i | \(-0.361156\pi\) | ||||
0.422491 | + | 0.906367i | \(0.361156\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5938.03i | − 0.707485i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5483.79 | −0.648647 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 10461.0i | − 1.21970i | −0.792518 | − | 0.609849i | \(-0.791230\pi\) | ||||
0.792518 | − | 0.609849i | \(-0.208770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4648.55i | − 0.538139i | −0.963121 | − | 0.269070i | \(-0.913284\pi\) | ||||
0.963121 | − | 0.269070i | \(-0.0867162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4603.40 | 0.525406 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20678.8i | 2.34360i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12490.7 | 1.39595 | 0.697975 | − | 0.716122i | \(-0.254085\pi\) | ||||
0.697975 | + | 0.716122i | \(0.254085\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9446.37 | 1.04842 | 0.524208 | − | 0.851590i | \(-0.324362\pi\) | ||||
0.524208 | + | 0.851590i | \(0.324362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1189.30i | − 0.130188i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2793.60 | −0.303716 | −0.151858 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151858 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7601.37i | 0.815241i | 0.913151 | + | 0.407621i | \(0.133641\pi\) | ||||
−0.913151 | + | 0.407621i | \(0.866359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2540.73i | 0.270657i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10708.8 | −1.12557 | −0.562785 | − | 0.826603i | \(-0.690270\pi\) | ||||
−0.562785 | + | 0.826603i | \(0.690270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5806.89i | 0.606287i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8043.92 | −0.828802 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 233.840 | 0.0239356 | 0.0119678 | − | 0.999928i | \(-0.496190\pi\) | ||||
0.0119678 | + | 0.999928i | \(0.496190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 981.307i | − 0.0991410i | −0.998771 | − | 0.0495705i | \(-0.984215\pi\) | ||||
0.998771 | − | 0.0495705i | \(-0.0157853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14082.7 | 1.41356 | 0.706782 | − | 0.707431i | \(-0.250146\pi\) | ||||
0.706782 | + | 0.707431i | \(0.250146\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9286.49i | 0.920188i | 0.887870 | + | 0.460094i | \(0.152184\pi\) | ||||
−0.887870 | + | 0.460094i | \(0.847816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10403.1i | 1.02424i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1834.68 | −0.178349 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5344.79i | − 0.516286i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19409.3 | −1.85143 | −0.925715 | − | 0.378222i | \(-0.876536\pi\) | ||||
−0.925715 | + | 0.378222i | \(0.876536\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3657.46 | −0.346706 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 7011.76i | − 0.656469i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12124.8 | −1.12818 | −0.564091 | − | 0.825712i | \(-0.690773\pi\) | ||||
−0.564091 | + | 0.825712i | \(0.690773\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 5100.69i | − 0.468820i | −0.972138 | − | 0.234410i | \(-0.924684\pi\) | ||||
0.972138 | − | 0.234410i | \(-0.0753159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4589.10i | 0.419235i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8282.26 | −0.747505 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 85.2797i | 0.00765058i | 0.999993 | + | 0.00382529i | \(0.00121763\pi\) | ||||
−0.999993 | + | 0.00382529i | \(0.998782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12287.2 | −1.08918 | −0.544592 | − | 0.838701i | \(-0.683316\pi\) | ||||
−0.544592 | + | 0.838701i | \(0.683316\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1842.45 | −0.162352 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 450.441i | 0.0392248i | 0.999808 | + | 0.0196124i | \(0.00624322\pi\) | ||||
−0.999808 | + | 0.0196124i | \(0.993757\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13829.2 | 1.19720 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 6247.64i | − 0.534571i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1121.63i | 0.0954141i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15088.1 | 1.26876 | 0.634378 | − | 0.773023i | \(-0.281256\pi\) | ||||
0.634378 | + | 0.773023i | \(0.281256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 17719.4i | − 1.48149i | −0.671789 | − | 0.740743i | \(-0.734474\pi\) | ||||
0.671789 | − | 0.740743i | \(-0.265526\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20967.6 | 1.73314 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12083.0 | −0.993096 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9066.62i | 0.736808i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4186.08 | 0.338280 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 8388.98i | − 0.670388i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 12244.5i | − 0.973074i | −0.873660 | − | 0.486537i | \(-0.838260\pi\) | ||||
0.873660 | − | 0.486537i | \(-0.161740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5729.22 | 0.450299 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7822.46i | 0.611452i | 0.952119 | + | 0.305726i | \(0.0988992\pi\) | ||||
−0.952119 | + | 0.305726i | \(0.901101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5328.19 | 0.411957 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8274.05 | 0.636254 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16555.5i | 1.25938i | 0.776845 | + | 0.629692i | \(0.216819\pi\) | ||||
−0.776845 | + | 0.629692i | \(0.783181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2864.60 | −0.216743 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 12580.7i | − 0.941766i | −0.882196 | − | 0.470883i | \(-0.843935\pi\) | ||||
0.882196 | − | 0.470883i | \(-0.156065\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 8982.30i | − 0.668829i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2657.93 | −0.195828 | −0.0979141 | − | 0.995195i | \(-0.531217\pi\) | ||||
−0.0979141 | + | 0.995195i | \(0.531217\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 17669.0i | − 1.29496i | −0.762081 | − | 0.647481i | \(-0.775822\pi\) | ||||
0.762081 | − | 0.647481i | \(-0.224178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 377.497 | 0.0273786 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14617.7 | 1.05467 | 0.527334 | − | 0.849658i | \(-0.323192\pi\) | ||||
0.527334 | + | 0.849658i | \(0.323192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 16423.1i | − 1.17271i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14919.3 | −1.05985 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4096.53i | − 0.288044i | −0.989574 | − | 0.144022i | \(-0.953996\pi\) | ||||
0.989574 | − | 0.144022i | \(-0.0460036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 24344.5i | − 1.70305i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21988.3 | 1.52269 | 0.761343 | − | 0.648349i | \(-0.224540\pi\) | ||||
0.761343 | + | 0.648349i | \(0.224540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 28053.1i | − 1.93288i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20767.7 | 1.41660 | 0.708302 | − | 0.705909i | \(-0.249461\pi\) | ||||
0.708302 | + | 0.705909i | \(0.249461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5382.61 | 0.365326 | 0.182663 | − | 0.983176i | \(-0.441528\pi\) | ||||
0.182663 | + | 0.983176i | \(0.441528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8328.33i | 0.559661i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11165.4 | −0.746607 | −0.373304 | − | 0.927709i | \(-0.621775\pi\) | ||||
−0.373304 | + | 0.927709i | \(0.621775\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1751.26i | 0.115955i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16413.5i | 1.08146i | 0.841195 | + | 0.540731i | \(0.181852\pi\) | ||||
−0.841195 | + | 0.540731i | \(0.818148\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 51.5882 | 0.00336607 | 0.00168303 | − | 0.999999i | \(-0.499464\pi\) | ||||
0.00168303 | + | 0.999999i | \(0.499464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6349.55i | 0.412294i | 0.978521 | + | 0.206147i | \(0.0660925\pi\) | ||||
−0.978521 | + | 0.206147i | \(0.933907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7609.11 | −0.489330 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8779.94 | −0.561916 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 12755.3i | − 0.808567i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13379.1 | 0.844078 | 0.422039 | − | 0.906578i | \(-0.361315\pi\) | ||||
0.422039 | + | 0.906578i | \(0.361315\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7397.63i | 0.462309i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 13098.2i | − 0.814709i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20406.3 | 1.25741 | 0.628705 | − | 0.777644i | \(-0.283585\pi\) | ||||
0.628705 | + | 0.777644i | \(0.283585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19415.1i | 1.19076i | 0.803446 | + | 0.595378i | \(0.202998\pi\) | ||||
−0.803446 | + | 0.595378i | \(0.797002\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8167.12 | −0.496264 | −0.248132 | − | 0.968726i | \(-0.579817\pi\) | ||||
−0.248132 | + | 0.968726i | \(0.579817\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4445.31 | 0.268866 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7444.93i | 0.446160i | 0.974800 | + | 0.223080i | \(0.0716111\pi\) | ||||
−0.974800 | + | 0.223080i | \(0.928389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10169.7 | 0.606662 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23780.4i | 1.40569i | 0.711342 | + | 0.702846i | \(0.248088\pi\) | ||||
−0.711342 | + | 0.702846i | \(0.751912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2528.90i | − 0.148809i | −0.997228 | − | 0.0744046i | \(-0.976294\pi\) | ||||
0.997228 | − | 0.0744046i | \(-0.0237056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −32571.2 | −1.89933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 376.324i | 0.0218461i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15480.5 | −0.890640 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16733.7 | 0.958447 | 0.479224 | − | 0.877693i | \(-0.340918\pi\) | ||||
0.479224 | + | 0.877693i | \(0.340918\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 24191.5i | − 1.37335i | −0.726966 | − | 0.686673i | \(-0.759070\pi\) | ||||
0.726966 | − | 0.686673i | \(-0.240930\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20999.2 | 1.18685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 13965.2i | − 0.782376i | −0.920311 | − | 0.391188i | \(-0.872064\pi\) | ||||
0.920311 | − | 0.391188i | \(-0.127936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4273.17i | 0.238350i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23294.4 | −1.28802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 8685.63i | − 0.478172i | −0.970998 | − | 0.239086i | \(-0.923152\pi\) | ||||
0.970998 | − | 0.239086i | \(-0.0768479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3220.43 | −0.175767 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31619.7 | −1.71834 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 25942.2i | − 1.39775i | −0.715243 | − | 0.698876i | \(-0.753684\pi\) | ||||
0.715243 | − | 0.698876i | \(-0.246316\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14809.6 | −0.794532 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5517.86i | − 0.293522i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5487.75i | 0.290687i | 0.989381 | + | 0.145343i | \(0.0464287\pi\) | ||||
−0.989381 | + | 0.145343i | \(0.953571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1719.43 | 0.0903128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 6021.82i | − 0.314970i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17141.2 | 0.889094 | 0.444547 | − | 0.895756i | \(-0.353365\pi\) | ||||
0.444547 | + | 0.895756i | \(0.353365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18710.8 | 0.966470 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1691.23i | 0.0866352i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15946.4 | 0.813508 | 0.406754 | − | 0.913538i | \(-0.366661\pi\) | ||||
0.406754 | + | 0.913538i | \(0.366661\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 9990.26i | − 0.505476i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 15914.2i | − 0.801917i | −0.916096 | − | 0.400958i | \(-0.868677\pi\) | ||||
0.916096 | − | 0.400958i | \(-0.131323\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7787.94 | −0.389243 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13555.4i | 0.674755i | 0.941369 | + | 0.337377i | \(0.109540\pi\) | ||||
−0.941369 | + | 0.337377i | \(0.890460\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1772.73 | −0.0875303 | −0.0437652 | − | 0.999042i | \(-0.513935\pi\) | ||||
−0.0437652 | + | 0.999042i | \(0.513935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11814.3 | 0.580997 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12536.7i | 0.611589i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1006.65 | 0.0489124 | 0.0244562 | − | 0.999701i | \(-0.492215\pi\) | ||||
0.0244562 | + | 0.999701i | \(0.492215\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 10761.6i | − 0.518750i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28774.0i | 1.38152i | 0.723086 | + | 0.690758i | \(0.242723\pi\) | ||||
−0.723086 | + | 0.690758i | \(0.757277\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18393.5 | −0.876166 | −0.438083 | − | 0.898934i | \(-0.644342\pi\) | ||||
−0.438083 | + | 0.898934i | \(0.644342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17158.2i | 0.814112i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6940.72 | 0.326747 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14672.2 | −0.688027 | −0.344014 | − | 0.938965i | \(-0.611787\pi\) | ||||
−0.344014 | + | 0.938965i | \(0.611787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16256.4i | 0.756405i | 0.925723 | + | 0.378202i | \(0.123458\pi\) | ||||
−0.925723 | + | 0.378202i | \(0.876542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7727.21 | 0.358154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36712.2i | 1.68851i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 6200.24i | − 0.284074i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9997.92 | −0.454575 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23988.3i | 1.08652i | 0.839565 | + | 0.543259i | \(0.182810\pi\) | ||||
−0.839565 | + | 0.543259i | \(0.817190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26900.7 | 1.20920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24170.6 | −1.08238 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32966.9i | 1.46518i | 0.680672 | + | 0.732589i | \(0.261688\pi\) | ||||
−0.680672 | + | 0.732589i | \(0.738312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6107.50 | −0.270423 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10352.8i | 0.454973i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2300.47i | − 0.100721i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41700.3 | 1.81224 | 0.906122 | − | 0.423017i | \(-0.139029\pi\) | ||||
0.906122 | + | 0.423017i | \(0.139029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 5981.80i | − 0.259000i | −0.991579 | − | 0.129500i | \(-0.958663\pi\) | ||||
0.991579 | − | 0.129500i | \(-0.0413373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33204.4 | −1.42712 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11599.2 | −0.496702 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 9846.06i | − 0.418550i | −0.977857 | − | 0.209275i | \(-0.932890\pi\) | ||||
0.977857 | − | 0.209275i | \(-0.0671104\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47001.9 | −1.99074 | −0.995372 | − | 0.0960935i | \(-0.969365\pi\) | ||||
−0.995372 | + | 0.0960935i | \(0.969365\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21727.4i | 0.913587i | 0.889573 | + | 0.456794i | \(0.151002\pi\) | ||||
−0.889573 | + | 0.456794i | \(0.848998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22772.3i | 0.954058i | 0.878888 | + | 0.477029i | \(0.158286\pi\) | ||||
−0.878888 | + | 0.477029i | \(0.841714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45679.8 | 1.90002 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 419.304i | 0.0173780i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11010.4 | 0.453064 | 0.226532 | − | 0.974004i | \(-0.427261\pi\) | ||||
0.226532 | + | 0.974004i | \(0.427261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22703.0 | 0.930872 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10711.0i | 0.436059i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24942.1 | −1.01183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1045.99i | − 0.0421340i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38177.4i | 1.53244i | 0.642579 | + | 0.766219i | \(0.277864\pi\) | ||||
−0.642579 | + | 0.766219i | \(0.722136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8848.01 | −0.352675 | −0.176337 | − | 0.984330i | \(-0.556425\pi\) | ||||
−0.176337 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4347.66i | − 0.172690i | −0.996265 | − | 0.0863448i | \(-0.972481\pi\) | ||||
0.996265 | − | 0.0863448i | \(-0.0275187\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33669.9 | −1.32808 | −0.664042 | − | 0.747695i | \(-0.731161\pi\) | ||||
−0.664042 | + | 0.747695i | \(0.731161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22475.3 | −0.883450 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6194.10i | 0.241796i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12159.7 | −0.473039 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 41713.8i | − 1.61164i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50102.0i | 1.92910i | 0.263892 | + | 0.964552i | \(0.414994\pi\) | ||||
−0.263892 | + | 0.964552i | \(0.585006\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18716.9 | −0.715766 | −0.357883 | − | 0.933766i | \(-0.616501\pi\) | ||||
−0.357883 | + | 0.933766i | \(0.616501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7514.19i | 0.286379i | 0.989695 | + | 0.143189i | \(0.0457358\pi\) | ||||
−0.989695 | + | 0.143189i | \(0.954264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15544.6 | −0.588429 | −0.294215 | − | 0.955739i | \(-0.595058\pi\) | ||||
−0.294215 | + | 0.955739i | \(0.595058\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22154.8 | −0.835825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7091.14i | 0.265729i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9395.42 | −0.350898 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7703.21i | 0.285780i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 81238.8i | − 3.00384i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33864.3 | 1.24385 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8713.10i | 0.318979i | 0.987200 | + | 0.159489i | \(0.0509848\pi\) | ||||
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1975.97 | 0.0718627 | 0.0359313 | − | 0.999354i | \(-0.488560\pi\) | ||||
0.0359313 | + | 0.999354i | \(0.488560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12294.6 | 0.445666 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30456.8i | 1.09681i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18430.5 | 0.661552 | 0.330776 | − | 0.943709i | \(-0.392689\pi\) | ||||
0.330776 | + | 0.943709i | \(0.392689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 9680.79i | − 0.345230i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4700.74i | − 0.167091i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12506.8 | −0.441697 | −0.220848 | − | 0.975308i | \(-0.570883\pi\) | ||||
−0.220848 | + | 0.975308i | \(0.570883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 53036.7i | − 1.86703i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21001.0 | 0.734554 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39267.5 | 1.36906 | 0.684532 | − | 0.728982i | \(-0.260006\pi\) | ||||
0.684532 | + | 0.728982i | \(0.260006\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 23727.2i | − 0.821981i | −0.911640 | − | 0.410991i | \(-0.865183\pi\) | ||||
0.911640 | − | 0.410991i | \(-0.134817\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2592.94 | −0.0895418 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 23399.8i | − 0.802948i | −0.915870 | − | 0.401474i | \(-0.868498\pi\) | ||||
0.915870 | − | 0.401474i | \(-0.131502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16164.4i | 0.552919i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41497.1 | −1.41052 | −0.705258 | − | 0.708950i | \(-0.749169\pi\) | ||||
−0.705258 | + | 0.708950i | \(0.749169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46771.6i | 1.58481i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12797.5 | −0.430921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5405.00 | 0.181431 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 12946.2i | − 0.431868i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49123.6 | 1.63362 | 0.816808 | − | 0.576909i | \(-0.195741\pi\) | ||||
0.816808 | + | 0.576909i | \(0.195741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20346.8i | 0.672462i | 0.941780 | + | 0.336231i | \(0.109152\pi\) | ||||
−0.941780 | + | 0.336231i | \(0.890848\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9644.71i | − 0.317775i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40602.1 | −1.32955 | −0.664777 | − | 0.747042i | \(-0.731474\pi\) | ||||
−0.664777 | + | 0.747042i | \(0.731474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 5696.32i | − 0.185960i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50425.9 | 1.63615 | 0.818075 | − | 0.575112i | \(-0.195041\pi\) | ||||
0.818075 | + | 0.575112i | \(0.195041\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25786.2 | 0.834127 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 819.241i | − 0.0263401i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8511.62 | 0.272836 | 0.136418 | − | 0.990651i | \(-0.456441\pi\) | ||||
0.136418 | + | 0.990651i | \(0.456441\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8683.90i | 0.276681i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25302.1i | 0.803738i | 0.915697 | + | 0.401869i | \(0.131639\pi\) | ||||
−0.915697 | + | 0.401869i | \(0.868361\pi\) | |||||||
\(998\) | 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 | 288.4.d.d.145.5 | 6 | ||
3.2 | odd | 2 | 96.4.d.a.49.1 | 6 | |||
4.3 | odd | 2 | 72.4.d.d.37.3 | 6 | |||
8.3 | odd | 2 | 72.4.d.d.37.4 | 6 | |||
8.5 | even | 2 | inner | 288.4.d.d.145.2 | 6 | ||
12.11 | even | 2 | 24.4.d.a.13.4 | yes | 6 | ||
16.3 | odd | 4 | 2304.4.a.bt.1.3 | 3 | |||
16.5 | even | 4 | 2304.4.a.bw.1.1 | 3 | |||
16.11 | odd | 4 | 2304.4.a.bv.1.1 | 3 | |||
16.13 | even | 4 | 2304.4.a.bu.1.3 | 3 | |||
24.5 | odd | 2 | 96.4.d.a.49.6 | 6 | |||
24.11 | even | 2 | 24.4.d.a.13.3 | ✓ | 6 | ||
48.5 | odd | 4 | 768.4.a.q.1.3 | 3 | |||
48.11 | even | 4 | 768.4.a.s.1.3 | 3 | |||
48.29 | odd | 4 | 768.4.a.t.1.1 | 3 | |||
48.35 | even | 4 | 768.4.a.r.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.d.a.13.3 | ✓ | 6 | 24.11 | even | 2 | ||
24.4.d.a.13.4 | yes | 6 | 12.11 | even | 2 | ||
72.4.d.d.37.3 | 6 | 4.3 | odd | 2 | |||
72.4.d.d.37.4 | 6 | 8.3 | odd | 2 | |||
96.4.d.a.49.1 | 6 | 3.2 | odd | 2 | |||
96.4.d.a.49.6 | 6 | 24.5 | odd | 2 | |||
288.4.d.d.145.2 | 6 | 8.5 | even | 2 | inner | ||
288.4.d.d.145.5 | 6 | 1.1 | even | 1 | trivial | ||
768.4.a.q.1.3 | 3 | 48.5 | odd | 4 | |||
768.4.a.r.1.1 | 3 | 48.35 | even | 4 | |||
768.4.a.s.1.3 | 3 | 48.11 | even | 4 | |||
768.4.a.t.1.1 | 3 | 48.29 | odd | 4 | |||
2304.4.a.bt.1.3 | 3 | 16.3 | odd | 4 | |||
2304.4.a.bu.1.3 | 3 | 16.13 | even | 4 | |||
2304.4.a.bv.1.1 | 3 | 16.11 | odd | 4 | |||
2304.4.a.bw.1.1 | 3 | 16.5 | even | 4 |