Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(881,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.4 | ||
Root | \(0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.881 |
Dual form | 4410.2.b.f.881.5 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.00000i | − 0.316228i | ||||||||
\(11\) | 5.37849i | 1.62168i | 0.585270 | + | 0.810838i | \(0.300988\pi\) | ||||
−0.585270 | + | 0.810838i | \(0.699012\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.19891i | − 0.332518i | −0.986082 | − | 0.166259i | \(-0.946831\pi\) | ||||
0.986082 | − | 0.166259i | \(-0.0531689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.17958 | −0.528626 | −0.264313 | − | 0.964437i | \(-0.585145\pi\) | ||||
−0.264313 | + | 0.964437i | \(0.585145\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.71191i | − 0.622154i | −0.950385 | − | 0.311077i | \(-0.899310\pi\) | ||||
0.950385 | − | 0.311077i | \(-0.100690\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.37849 | 1.14670 | ||||||||
\(23\) | − 0.496606i | − 0.103549i | −0.998659 | − | 0.0517747i | \(-0.983512\pi\) | ||||
0.998659 | − | 0.0517747i | \(-0.0164878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.19891 | −0.235126 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.12453i | − 1.32299i | −0.749949 | − | 0.661496i | \(-0.769922\pi\) | ||||
0.749949 | − | 0.661496i | \(-0.230078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.550066i | − 0.0987947i | −0.998779 | − | 0.0493974i | \(-0.984270\pi\) | ||||
0.998779 | − | 0.0493974i | \(-0.0157301\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.17958i | 0.373795i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.10814 | −0.675374 | −0.337687 | − | 0.941258i | \(-0.609645\pi\) | ||||
−0.337687 | + | 0.941258i | \(0.609645\pi\) | |||||||
\(38\) | −2.71191 | −0.439929 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 1.04373 | 0.163003 | 0.0815015 | − | 0.996673i | \(-0.474028\pi\) | ||||
0.0815015 | + | 0.996673i | \(0.474028\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.03988 | 0.921074 | 0.460537 | − | 0.887641i | \(-0.347657\pi\) | ||||
0.460537 | + | 0.887641i | \(0.347657\pi\) | |||||||
\(44\) | − 5.37849i | − 0.810838i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.496606 | −0.0732205 | ||||||||
\(47\) | 7.42676 | 1.08330 | 0.541652 | − | 0.840603i | \(-0.317799\pi\) | ||||
0.541652 | + | 0.840603i | \(0.317799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.19891i | 0.166259i | ||||||||
\(53\) | 5.13707i | 0.705631i | 0.935693 | + | 0.352815i | \(0.114776\pi\) | ||||
−0.935693 | + | 0.352815i | \(0.885224\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.37849i | 0.725236i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.12453 | −0.935496 | ||||||||
\(59\) | 11.1097 | 1.44636 | 0.723182 | − | 0.690658i | \(-0.242679\pi\) | ||||
0.723182 | + | 0.690658i | \(0.242679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.88348i | 0.241155i | 0.992704 | + | 0.120577i | \(0.0384746\pi\) | ||||
−0.992704 | + | 0.120577i | \(0.961525\pi\) | |||||||
\(62\) | −0.550066 | −0.0698584 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 1.19891i | − 0.148707i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.25518 | 0.519853 | 0.259927 | − | 0.965628i | \(-0.416302\pi\) | ||||
0.259927 | + | 0.965628i | \(0.416302\pi\) | |||||||
\(68\) | 2.17958 | 0.264313 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8052i | 1.28235i | 0.767396 | + | 0.641174i | \(0.221552\pi\) | ||||
−0.767396 | + | 0.641174i | \(0.778448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.5349i | 1.81822i | 0.416554 | + | 0.909111i | \(0.363238\pi\) | ||||
−0.416554 | + | 0.909111i | \(0.636762\pi\) | |||||||
\(74\) | 4.10814i | 0.477561i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.71191i | 0.311077i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4525 | −1.17600 | −0.587999 | − | 0.808861i | \(-0.700084\pi\) | ||||
−0.587999 | + | 0.808861i | \(0.700084\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 1.04373i | − 0.115261i | ||||||||
\(83\) | 14.5400 | 1.59597 | 0.797984 | − | 0.602679i | \(-0.205900\pi\) | ||||
0.797984 | + | 0.602679i | \(0.205900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.17958 | −0.236409 | ||||||||
\(86\) | − 6.03988i | − 0.651297i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.37849 | −0.573349 | ||||||||
\(89\) | 15.8899 | 1.68433 | 0.842163 | − | 0.539223i | \(-0.181282\pi\) | ||||
0.842163 | + | 0.539223i | \(0.181282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.496606i | 0.0517747i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 7.42676i | − 0.766011i | ||||||||
\(95\) | − 2.71191i | − 0.278236i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.65685i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 0.0618412 | 0.00615343 | 0.00307671 | − | 0.999995i | \(-0.499021\pi\) | ||||
0.00307671 | + | 0.999995i | \(0.499021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 7.44155i | − 0.733238i | −0.930371 | − | 0.366619i | \(-0.880515\pi\) | ||||
0.930371 | − | 0.366619i | \(-0.119485\pi\) | |||||||
\(104\) | 1.19891 | 0.117563 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.13707 | 0.498956 | ||||||||
\(107\) | 4.05052i | 0.391578i | 0.980646 | + | 0.195789i | \(0.0627268\pi\) | ||||
−0.980646 | + | 0.195789i | \(0.937273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.01414 | 0.863398 | 0.431699 | − | 0.902018i | \(-0.357914\pi\) | ||||
0.431699 | + | 0.902018i | \(0.357914\pi\) | |||||||
\(110\) | 5.37849 | 0.512819 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.9082i | 1.77873i | 0.457195 | + | 0.889367i | \(0.348854\pi\) | ||||
−0.457195 | + | 0.889367i | \(0.651146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.496606i | − 0.0463087i | ||||||||
\(116\) | 7.12453i | 0.661496i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 11.1097i | − 1.02273i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.9282 | −1.62983 | ||||||||
\(122\) | 1.88348 | 0.170522 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.550066i | 0.0493974i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0251 | 1.06705 | 0.533527 | − | 0.845783i | \(-0.320866\pi\) | ||||
0.533527 | + | 0.845783i | \(0.320866\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.19891 | −0.105152 | ||||||||
\(131\) | 9.21077 | 0.804748 | 0.402374 | − | 0.915475i | \(-0.368185\pi\) | ||||
0.402374 | + | 0.915475i | \(0.368185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 4.25518i | − 0.367592i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 2.17958i | − 0.186897i | ||||||||
\(137\) | 16.6195i | 1.41990i | 0.704250 | + | 0.709952i | \(0.251283\pi\) | ||||
−0.704250 | + | 0.709952i | \(0.748717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.13932i | 0.775187i | 0.921830 | + | 0.387594i | \(0.126694\pi\) | ||||
−0.921830 | + | 0.387594i | \(0.873306\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.8052 | 0.906756 | ||||||||
\(143\) | 6.44834 | 0.539237 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 7.12453i | − 0.591660i | ||||||||
\(146\) | 15.5349 | 1.28568 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.10814 | 0.337687 | ||||||||
\(149\) | − 14.6762i | − 1.20232i | −0.799129 | − | 0.601160i | \(-0.794705\pi\) | ||||
0.799129 | − | 0.601160i | \(-0.205295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.74150 | −0.548615 | −0.274308 | − | 0.961642i | \(-0.588449\pi\) | ||||
−0.274308 | + | 0.961642i | \(0.588449\pi\) | |||||||
\(152\) | 2.71191 | 0.219965 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.550066i | − 0.0441823i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.62726i | 0.768339i | 0.923263 | + | 0.384170i | \(0.125512\pi\) | ||||
−0.923263 | + | 0.384170i | \(0.874488\pi\) | |||||||
\(158\) | 10.4525i | 0.831557i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.00000i | − 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.15866 | −0.325731 | −0.162866 | − | 0.986648i | \(-0.552074\pi\) | ||||
−0.162866 | + | 0.986648i | \(0.552074\pi\) | |||||||
\(164\) | −1.04373 | −0.0815015 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 14.5400i | − 1.12852i | ||||||||
\(167\) | −12.4764 | −0.965451 | −0.482725 | − | 0.875772i | \(-0.660353\pi\) | ||||
−0.482725 | + | 0.875772i | \(0.660353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5626 | 0.889431 | ||||||||
\(170\) | 2.17958i | 0.167166i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.03988 | −0.460537 | ||||||||
\(173\) | −1.02869 | −0.0782098 | −0.0391049 | − | 0.999235i | \(-0.512451\pi\) | ||||
−0.0391049 | + | 0.999235i | \(0.512451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.37849i | 0.405419i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 15.8899i | − 1.19100i | ||||||||
\(179\) | − 9.99480i | − 0.747047i | −0.927621 | − | 0.373523i | \(-0.878150\pi\) | ||||
0.927621 | − | 0.373523i | \(-0.121850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.08014i | 0.228945i | 0.993426 | + | 0.114472i | \(0.0365178\pi\) | ||||
−0.993426 | + | 0.114472i | \(0.963482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.496606 | 0.0366103 | ||||||||
\(185\) | −4.10814 | −0.302036 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 11.7229i | − 0.857260i | ||||||||
\(188\) | −7.42676 | −0.541652 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.71191 | −0.196742 | ||||||||
\(191\) | 5.82805i | 0.421703i | 0.977518 | + | 0.210852i | \(0.0676237\pi\) | ||||
−0.977518 | + | 0.210852i | \(0.932376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.75789 | −0.414462 | −0.207231 | − | 0.978292i | \(-0.566445\pi\) | ||||
−0.207231 | + | 0.978292i | \(0.566445\pi\) | |||||||
\(194\) | 7.65685 | 0.549730 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.9259i | 1.06343i | 0.846924 | + | 0.531714i | \(0.178452\pi\) | ||||
−0.846924 | + | 0.531714i | \(0.821548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 26.6163i | − 1.88678i | −0.331691 | − | 0.943388i | \(-0.607619\pi\) | ||||
0.331691 | − | 0.943388i | \(-0.392381\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 0.0618412i | − 0.00435113i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.04373 | 0.0728971 | ||||||||
\(206\) | −7.44155 | −0.518478 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1.19891i | − 0.0831296i | ||||||||
\(209\) | 14.5860 | 1.00893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.65269 | −0.526833 | −0.263417 | − | 0.964682i | \(-0.584849\pi\) | ||||
−0.263417 | + | 0.964682i | \(0.584849\pi\) | |||||||
\(212\) | − 5.13707i | − 0.352815i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.05052 | 0.276888 | ||||||||
\(215\) | 6.03988 | 0.411917 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 9.01414i | − 0.610514i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 5.37849i | − 0.362618i | ||||||||
\(221\) | 2.61313i | 0.175778i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.25715i | 0.151150i | 0.997140 | + | 0.0755750i | \(0.0240792\pi\) | ||||
−0.997140 | + | 0.0755750i | \(0.975921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.9082 | 1.25775 | ||||||||
\(227\) | 17.5011 | 1.16159 | 0.580796 | − | 0.814049i | \(-0.302741\pi\) | ||||
0.580796 | + | 0.814049i | \(0.302741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4840i | 1.61795i | 0.587844 | + | 0.808974i | \(0.299977\pi\) | ||||
−0.587844 | + | 0.808974i | \(0.700023\pi\) | |||||||
\(230\) | −0.496606 | −0.0327452 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.12453 | 0.467748 | ||||||||
\(233\) | − 17.7366i | − 1.16196i | −0.813916 | − | 0.580982i | \(-0.802669\pi\) | ||||
0.813916 | − | 0.580982i | \(-0.197331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.42676 | 0.484468 | ||||||||
\(236\) | −11.1097 | −0.723182 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8111i | 0.958053i | 0.877801 | + | 0.479026i | \(0.159010\pi\) | ||||
−0.877801 | + | 0.479026i | \(0.840990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 9.93938i | − 0.640252i | −0.947375 | − | 0.320126i | \(-0.896275\pi\) | ||||
0.947375 | − | 0.320126i | \(-0.103725\pi\) | |||||||
\(242\) | 17.9282i | 1.15247i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 1.88348i | − 0.120577i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.25134 | −0.206878 | ||||||||
\(248\) | 0.550066 | 0.0349292 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.00000i | − 0.0632456i | ||||||||
\(251\) | −5.66593 | −0.357630 | −0.178815 | − | 0.983883i | \(-0.557226\pi\) | ||||
−0.178815 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.67099 | 0.167924 | ||||||||
\(254\) | − 12.0251i | − 0.754521i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.4814 | 1.71424 | 0.857122 | − | 0.515113i | \(-0.172250\pi\) | ||||
0.857122 | + | 0.515113i | \(0.172250\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.19891i | 0.0743534i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 9.21077i | − 0.569043i | ||||||||
\(263\) | − 4.06150i | − 0.250443i | −0.992129 | − | 0.125221i | \(-0.960036\pi\) | ||||
0.992129 | − | 0.125221i | \(-0.0399641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.13707i | 0.315568i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.25518 | −0.259927 | ||||||||
\(269\) | −0.0637508 | −0.00388696 | −0.00194348 | − | 0.999998i | \(-0.500619\pi\) | ||||
−0.00194348 | + | 0.999998i | \(0.500619\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 28.8200i | − 1.75069i | −0.483496 | − | 0.875347i | \(-0.660633\pi\) | ||||
0.483496 | − | 0.875347i | \(-0.339367\pi\) | |||||||
\(272\) | −2.17958 | −0.132156 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.6195 | 1.00402 | ||||||||
\(275\) | 5.37849i | 0.324335i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.49141 | 0.390031 | 0.195016 | − | 0.980800i | \(-0.437524\pi\) | ||||
0.195016 | + | 0.980800i | \(0.437524\pi\) | |||||||
\(278\) | 9.13932 | 0.548140 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7666i | 0.761591i | 0.924659 | + | 0.380795i | \(0.124350\pi\) | ||||
−0.924659 | + | 0.380795i | \(0.875650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.3637i | 0.794389i | 0.917734 | + | 0.397195i | \(0.130016\pi\) | ||||
−0.917734 | + | 0.397195i | \(0.869984\pi\) | |||||||
\(284\) | − 10.8052i | − 0.641174i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 6.44834i | − 0.381298i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2494 | −0.720555 | ||||||||
\(290\) | −7.12453 | −0.418367 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 15.5349i | − 0.909111i | ||||||||
\(293\) | 5.76377 | 0.336723 | 0.168362 | − | 0.985725i | \(-0.446152\pi\) | ||||
0.168362 | + | 0.985725i | \(0.446152\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1097 | 0.646834 | ||||||||
\(296\) | − 4.10814i | − 0.238781i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.6762 | −0.850169 | ||||||||
\(299\) | −0.595387 | −0.0344321 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.74150i | 0.387930i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 2.71191i | − 0.155539i | ||||||||
\(305\) | 1.88348i | 0.107848i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 24.5978i | − 1.40387i | −0.712240 | − | 0.701936i | \(-0.752319\pi\) | ||||
0.712240 | − | 0.701936i | \(-0.247681\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.550066 | −0.0312416 | ||||||||
\(311\) | 25.3356 | 1.43665 | 0.718325 | − | 0.695707i | \(-0.244909\pi\) | ||||
0.718325 | + | 0.695707i | \(0.244909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 25.5213i | − 1.44255i | −0.692649 | − | 0.721275i | \(-0.743556\pi\) | ||||
0.692649 | − | 0.721275i | \(-0.256444\pi\) | |||||||
\(314\) | 9.62726 | 0.543298 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4525 | 0.587999 | ||||||||
\(317\) | 21.4206i | 1.20310i | 0.798834 | + | 0.601551i | \(0.205450\pi\) | ||||
−0.798834 | + | 0.601551i | \(0.794550\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.3192 | 2.14546 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.91082i | 0.328887i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.19891i | − 0.0665037i | ||||||||
\(326\) | 4.15866i | 0.230327i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.04373i | 0.0576303i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.3430 | −1.83269 | −0.916347 | − | 0.400384i | \(-0.868877\pi\) | ||||
−0.916347 | + | 0.400384i | \(0.868877\pi\) | |||||||
\(332\) | −14.5400 | −0.797984 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4764i | 0.682677i | ||||||||
\(335\) | 4.25518 | 0.232486 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.4776 | −0.897592 | −0.448796 | − | 0.893634i | \(-0.648147\pi\) | ||||
−0.448796 | + | 0.893634i | \(0.648147\pi\) | |||||||
\(338\) | − 11.5626i | − 0.628923i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.17958 | 0.118204 | ||||||||
\(341\) | 2.95852 | 0.160213 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.03988i | 0.325649i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.02869i | 0.0553027i | ||||||||
\(347\) | − 8.71832i | − 0.468024i | −0.972234 | − | 0.234012i | \(-0.924814\pi\) | ||||
0.972234 | − | 0.234012i | \(-0.0751855\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 10.6141i | − 0.568158i | −0.958801 | − | 0.284079i | \(-0.908312\pi\) | ||||
0.958801 | − | 0.284079i | \(-0.0916877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.37849 | 0.286675 | ||||||||
\(353\) | 35.0073 | 1.86325 | 0.931624 | − | 0.363423i | \(-0.118392\pi\) | ||||
0.931624 | + | 0.363423i | \(0.118392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8052i | 0.573483i | ||||||||
\(356\) | −15.8899 | −0.842163 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.99480 | −0.528242 | ||||||||
\(359\) | − 6.19703i | − 0.327067i | −0.986538 | − | 0.163533i | \(-0.947711\pi\) | ||||
0.986538 | − | 0.163533i | \(-0.0522892\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.6456 | 0.612924 | ||||||||
\(362\) | 3.08014 | 0.161889 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5349i | 0.813134i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.5641i | 1.75203i | 0.482280 | + | 0.876017i | \(0.339809\pi\) | ||||
−0.482280 | + | 0.876017i | \(0.660191\pi\) | |||||||
\(368\) | − 0.496606i | − 0.0258874i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.10814i | 0.213572i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.38547 | −0.434183 | −0.217092 | − | 0.976151i | \(-0.569657\pi\) | ||||
−0.217092 | + | 0.976151i | \(0.569657\pi\) | |||||||
\(374\) | −11.7229 | −0.606175 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.42676i | 0.383006i | ||||||||
\(377\) | −8.54168 | −0.439919 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.33954 | 0.0688077 | 0.0344038 | − | 0.999408i | \(-0.489047\pi\) | ||||
0.0344038 | + | 0.999408i | \(0.489047\pi\) | |||||||
\(380\) | 2.71191i | 0.139118i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.82805 | 0.298189 | ||||||||
\(383\) | −21.2686 | −1.08677 | −0.543387 | − | 0.839483i | \(-0.682858\pi\) | ||||
−0.543387 | + | 0.839483i | \(0.682858\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.75789i | 0.293069i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 7.65685i | − 0.388718i | ||||||||
\(389\) | − 27.8774i | − 1.41344i | −0.707494 | − | 0.706719i | \(-0.750175\pi\) | ||||
0.707494 | − | 0.706719i | \(-0.249825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08239i | 0.0547389i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.9259 | 0.751958 | ||||||||
\(395\) | −10.4525 | −0.525923 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.789763i | 0.0396371i | 0.999804 | + | 0.0198185i | \(0.00630885\pi\) | ||||
−0.999804 | + | 0.0198185i | \(0.993691\pi\) | |||||||
\(398\) | −26.6163 | −1.33415 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − 10.8599i | − 0.542319i | −0.962534 | − | 0.271159i | \(-0.912593\pi\) | ||||
0.962534 | − | 0.271159i | \(-0.0874071\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.659481 | −0.0328511 | ||||||||
\(404\) | −0.0618412 | −0.00307671 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 22.0956i | − 1.09524i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.9507i | 1.23373i | 0.787068 | + | 0.616866i | \(0.211598\pi\) | ||||
−0.787068 | + | 0.616866i | \(0.788402\pi\) | |||||||
\(410\) | − 1.04373i | − 0.0515461i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.44155i | 0.366619i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.5400 | 0.713739 | ||||||||
\(416\) | −1.19891 | −0.0587815 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 14.5860i | − 0.713423i | ||||||||
\(419\) | 38.9552 | 1.90309 | 0.951543 | − | 0.307517i | \(-0.0994981\pi\) | ||||
0.951543 | + | 0.307517i | \(0.0994981\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.1818 | −1.86087 | −0.930433 | − | 0.366462i | \(-0.880569\pi\) | ||||
−0.930433 | + | 0.366462i | \(0.880569\pi\) | |||||||
\(422\) | 7.65269i | 0.372527i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.13707 | −0.249478 | ||||||||
\(425\) | −2.17958 | −0.105725 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 4.05052i | − 0.195789i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 6.03988i | − 0.291269i | ||||||||
\(431\) | 3.01639i | 0.145294i | 0.997358 | + | 0.0726472i | \(0.0231447\pi\) | ||||
−0.997358 | + | 0.0726472i | \(0.976855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 37.7167i | − 1.81255i | −0.422691 | − | 0.906274i | \(-0.638914\pi\) | ||||
0.422691 | − | 0.906274i | \(-0.361086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.01414 | −0.431699 | ||||||||
\(437\) | −1.34675 | −0.0644237 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3683i | 1.01985i | 0.860217 | + | 0.509927i | \(0.170328\pi\) | ||||
−0.860217 | + | 0.509927i | \(0.829672\pi\) | |||||||
\(440\) | −5.37849 | −0.256410 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.61313 | 0.124294 | ||||||||
\(443\) | − 1.59629i | − 0.0758420i | −0.999281 | − | 0.0379210i | \(-0.987926\pi\) | ||||
0.999281 | − | 0.0379210i | \(-0.0120735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8899 | 0.753253 | ||||||||
\(446\) | 2.25715 | 0.106879 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.9895i | 0.707398i | 0.935359 | + | 0.353699i | \(0.115076\pi\) | ||||
−0.935359 | + | 0.353699i | \(0.884924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.61369i | 0.264338i | ||||||||
\(452\) | − 18.9082i | − 0.889367i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 17.5011i | − 0.821369i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.5650 | 1.05555 | 0.527774 | − | 0.849385i | \(-0.323027\pi\) | ||||
0.527774 | + | 0.849385i | \(0.323027\pi\) | |||||||
\(458\) | 24.4840 | 1.14406 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.496606i | 0.0231544i | ||||||||
\(461\) | −7.03506 | −0.327655 | −0.163828 | − | 0.986489i | \(-0.552384\pi\) | ||||
−0.163828 | + | 0.986489i | \(0.552384\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.8845 | −1.34238 | −0.671188 | − | 0.741287i | \(-0.734216\pi\) | ||||
−0.671188 | + | 0.741287i | \(0.734216\pi\) | |||||||
\(464\) | − 7.12453i | − 0.330748i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.7366 | −0.821633 | ||||||||
\(467\) | 26.5709 | 1.22956 | 0.614778 | − | 0.788700i | \(-0.289246\pi\) | ||||
0.614778 | + | 0.788700i | \(0.289246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 7.42676i | − 0.342571i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.1097i | 0.511367i | ||||||||
\(473\) | 32.4855i | 1.49368i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.71191i | − 0.124431i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.8111 | 0.677446 | ||||||||
\(479\) | −28.6410 | −1.30864 | −0.654320 | − | 0.756218i | \(-0.727045\pi\) | ||||
−0.654320 | + | 0.756218i | \(0.727045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.92530i | 0.224574i | ||||||||
\(482\) | −9.93938 | −0.452726 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.9282 | 0.814917 | ||||||||
\(485\) | 7.65685i | 0.347680i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7266 | 0.848585 | 0.424293 | − | 0.905525i | \(-0.360523\pi\) | ||||
0.424293 | + | 0.905525i | \(0.360523\pi\) | |||||||
\(488\) | −1.88348 | −0.0852611 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 24.0927i | − 1.08729i | −0.839317 | − | 0.543643i | \(-0.817045\pi\) | ||||
0.839317 | − | 0.543643i | \(-0.182955\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5285i | 0.699368i | ||||||||
\(494\) | 3.25134i | 0.146285i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 0.550066i | − 0.0246987i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.7333 | −0.659552 | −0.329776 | − | 0.944059i | \(-0.606973\pi\) | ||||
−0.329776 | + | 0.944059i | \(0.606973\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.66593i | 0.252883i | ||||||||
\(503\) | −29.6758 | −1.32318 | −0.661590 | − | 0.749866i | \(-0.730118\pi\) | ||||
−0.661590 | + | 0.749866i | \(0.730118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0618412 | 0.00275190 | ||||||||
\(506\) | − 2.67099i | − 0.118740i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.0251 | −0.533527 | ||||||||
\(509\) | 2.69833 | 0.119601 | 0.0598007 | − | 0.998210i | \(-0.480953\pi\) | ||||
0.0598007 | + | 0.998210i | \(0.480953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 27.4814i | − 1.21215i | ||||||||
\(515\) | − 7.44155i | − 0.327914i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.9448i | 1.75677i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.19891 | 0.0525758 | ||||||||
\(521\) | 20.9210 | 0.916567 | 0.458283 | − | 0.888806i | \(-0.348465\pi\) | ||||
0.458283 | + | 0.888806i | \(0.348465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 15.7615i | − 0.689203i | −0.938749 | − | 0.344602i | \(-0.888014\pi\) | ||||
0.938749 | − | 0.344602i | \(-0.111986\pi\) | |||||||
\(524\) | −9.21077 | −0.402374 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.06150 | −0.177090 | ||||||||
\(527\) | 1.19891i | 0.0522254i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7534 | 0.989278 | ||||||||
\(530\) | 5.13707 | 0.223140 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.25134i | − 0.0542015i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.05052i | 0.175119i | ||||||||
\(536\) | 4.25518i | 0.183796i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.0637508i | 0.00274849i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.9865 | 1.76215 | 0.881074 | − | 0.472979i | \(-0.156821\pi\) | ||||
0.881074 | + | 0.472979i | \(0.156821\pi\) | |||||||
\(542\) | −28.8200 | −1.23793 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.17958i | 0.0934487i | ||||||||
\(545\) | 9.01414 | 0.386123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.8878 | 0.807583 | 0.403791 | − | 0.914851i | \(-0.367692\pi\) | ||||
0.403791 | + | 0.914851i | \(0.367692\pi\) | |||||||
\(548\) | − 16.6195i | − 0.709952i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.37849 | 0.229340 | ||||||||
\(551\) | −19.3211 | −0.823105 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 6.49141i | − 0.275794i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 9.13932i | − 0.387594i | ||||||||
\(557\) | − 14.3256i | − 0.606997i | −0.952832 | − | 0.303498i | \(-0.901845\pi\) | ||||
0.952832 | − | 0.303498i | \(-0.0981547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 7.24129i | − 0.306274i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.7666 | 0.538526 | ||||||||
\(563\) | −8.49754 | −0.358129 | −0.179064 | − | 0.983837i | \(-0.557307\pi\) | ||||
−0.179064 | + | 0.983837i | \(0.557307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.9082i | 0.795474i | ||||||||
\(566\) | 13.3637 | 0.561718 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.8052 | −0.453378 | ||||||||
\(569\) | − 20.8380i | − 0.873576i | −0.899565 | − | 0.436788i | \(-0.856116\pi\) | ||||
0.899565 | − | 0.436788i | \(-0.143884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.87346 | −0.203948 | −0.101974 | − | 0.994787i | \(-0.532516\pi\) | ||||
−0.101974 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(572\) | −6.44834 | −0.269619 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 0.496606i | − 0.0207099i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 32.6863i | − 1.36075i | −0.732866 | − | 0.680373i | \(-0.761818\pi\) | ||||
0.732866 | − | 0.680373i | \(-0.238182\pi\) | |||||||
\(578\) | 12.2494i | 0.509509i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.12453i | 0.295830i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.6297 | −1.14431 | ||||||||
\(584\) | −15.5349 | −0.642839 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 5.76377i | − 0.238099i | ||||||||
\(587\) | −43.5641 | −1.79808 | −0.899042 | − | 0.437862i | \(-0.855736\pi\) | ||||
−0.899042 | + | 0.437862i | \(0.855736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.49173 | −0.0614655 | ||||||||
\(590\) | − 11.1097i | − 0.457380i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.10814 | −0.168843 | ||||||||
\(593\) | −20.7978 | −0.854065 | −0.427033 | − | 0.904236i | \(-0.640441\pi\) | ||||
−0.427033 | + | 0.904236i | \(0.640441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.6762i | 0.601160i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.595387i | 0.0243472i | ||||||||
\(599\) | − 20.1486i | − 0.823247i | −0.911354 | − | 0.411624i | \(-0.864962\pi\) | ||||
0.911354 | − | 0.411624i | \(-0.135038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 20.4515i | − 0.834233i | −0.908853 | − | 0.417116i | \(-0.863041\pi\) | ||||
0.908853 | − | 0.417116i | \(-0.136959\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.74150 | 0.274308 | ||||||||
\(605\) | −17.9282 | −0.728884 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.3111i | − 0.986756i | −0.869815 | − | 0.493378i | \(-0.835762\pi\) | ||||
0.869815 | − | 0.493378i | \(-0.164238\pi\) | |||||||
\(608\) | −2.71191 | −0.109982 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.88348 | 0.0762599 | ||||||||
\(611\) | − 8.90403i | − 0.360219i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.4497 | −1.75492 | −0.877459 | − | 0.479652i | \(-0.840763\pi\) | ||||
−0.877459 | + | 0.479652i | \(0.840763\pi\) | |||||||
\(614\) | −24.5978 | −0.992687 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.0693i | 0.848220i | 0.905611 | + | 0.424110i | \(0.139413\pi\) | ||||
−0.905611 | + | 0.424110i | \(0.860587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 27.6215i | − 1.11020i | −0.831783 | − | 0.555101i | \(-0.812680\pi\) | ||||
0.831783 | − | 0.555101i | \(-0.187320\pi\) | |||||||
\(620\) | 0.550066i | 0.0220912i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 25.3356i | − 1.01587i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −25.5213 | −1.02004 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 9.62726i | − 0.384170i | ||||||||
\(629\) | 8.95402 | 0.357020 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.81204 | −0.390611 | −0.195306 | − | 0.980742i | \(-0.562570\pi\) | ||||
−0.195306 | + | 0.980742i | \(0.562570\pi\) | |||||||
\(632\) | − 10.4525i | − 0.415778i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.4206 | 0.850722 | ||||||||
\(635\) | 12.0251 | 0.477201 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 38.3192i | − 1.51707i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | − 22.3931i | − 0.884474i | −0.896898 | − | 0.442237i | \(-0.854185\pi\) | ||||
0.896898 | − | 0.442237i | \(-0.145815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 19.1699i | − 0.755987i | −0.925808 | − | 0.377993i | \(-0.876614\pi\) | ||||
0.925808 | − | 0.377993i | \(-0.123386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.91082 | 0.232558 | ||||||||
\(647\) | −8.27465 | −0.325310 | −0.162655 | − | 0.986683i | \(-0.552006\pi\) | ||||
−0.162655 | + | 0.986683i | \(0.552006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 59.7536i | 2.34553i | ||||||||
\(650\) | −1.19891 | −0.0470252 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.15866 | 0.162866 | ||||||||
\(653\) | 29.7566i | 1.16446i | 0.813023 | + | 0.582232i | \(0.197821\pi\) | ||||
−0.813023 | + | 0.582232i | \(0.802179\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.21077 | 0.359894 | ||||||||
\(656\) | 1.04373 | 0.0407507 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 30.2145i | − 1.17699i | −0.808501 | − | 0.588495i | \(-0.799721\pi\) | ||||
0.808501 | − | 0.588495i | \(-0.200279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.0803i | 1.71452i | 0.514880 | + | 0.857262i | \(0.327837\pi\) | ||||
−0.514880 | + | 0.857262i | \(0.672163\pi\) | |||||||
\(662\) | 33.3430i | 1.29591i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.5400i | 0.564260i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.53808 | −0.136995 | ||||||||
\(668\) | 12.4764 | 0.482725 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 4.25518i | − 0.164392i | ||||||||
\(671\) | −10.1303 | −0.391075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.793211 | −0.0305760 | −0.0152880 | − | 0.999883i | \(-0.504867\pi\) | ||||
−0.0152880 | + | 0.999883i | \(0.504867\pi\) | |||||||
\(674\) | 16.4776i | 0.634693i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5626 | −0.444716 | ||||||||
\(677\) | −44.0480 | −1.69290 | −0.846452 | − | 0.532465i | \(-0.821266\pi\) | ||||
−0.846452 | + | 0.532465i | \(0.821266\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 2.17958i | − 0.0835831i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 2.95852i | − 0.113288i | ||||||||
\(683\) | 16.5254i | 0.632327i | 0.948705 | + | 0.316164i | \(0.102395\pi\) | ||||
−0.948705 | + | 0.316164i | \(0.897605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.6195i | 0.635000i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.03988 | 0.230268 | ||||||||
\(689\) | 6.15890 | 0.234635 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 22.4248i | − 0.853080i | −0.904469 | − | 0.426540i | \(-0.859732\pi\) | ||||
0.904469 | − | 0.426540i | \(-0.140268\pi\) | |||||||
\(692\) | 1.02869 | 0.0391049 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.71832 | −0.330943 | ||||||||
\(695\) | 9.13932i | 0.346674i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.27489 | −0.0861676 | ||||||||
\(698\) | −10.6141 | −0.401748 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 14.1136i | − 0.533062i | −0.963826 | − | 0.266531i | \(-0.914122\pi\) | ||||
0.963826 | − | 0.266531i | \(-0.0858775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.1409i | 0.420187i | ||||||||
\(704\) | − 5.37849i | − 0.202710i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 35.0073i | − 1.31752i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.3349 | 1.25192 | 0.625959 | − | 0.779856i | \(-0.284708\pi\) | ||||
0.625959 | + | 0.779856i | \(0.284708\pi\) | |||||||
\(710\) | 10.8052 | 0.405514 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.8899i | 0.595499i | ||||||||
\(713\) | −0.273166 | −0.0102301 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.44834 | 0.241154 | ||||||||
\(716\) | 9.99480i | 0.373523i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.19703 | −0.231271 | ||||||||
\(719\) | −16.2049 | −0.604341 | −0.302171 | − | 0.953254i | \(-0.597711\pi\) | ||||
−0.302171 | + | 0.953254i | \(0.597711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 11.6456i | − 0.433403i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 3.08014i | − 0.114472i | ||||||||
\(725\) | − 7.12453i | − 0.264598i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2759i | 0.529463i | 0.964322 | + | 0.264731i | \(0.0852833\pi\) | ||||
−0.964322 | + | 0.264731i | \(0.914717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.5349 | 0.574972 | ||||||||
\(731\) | −13.1644 | −0.486903 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.3899i | 1.78732i | 0.448744 | + | 0.893660i | \(0.351872\pi\) | ||||
−0.448744 | + | 0.893660i | \(0.648128\pi\) | |||||||
\(734\) | 33.5641 | 1.23888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.496606 | −0.0183051 | ||||||||
\(737\) | 22.8865i | 0.843034i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.6546 | 1.12765 | 0.563823 | − | 0.825895i | \(-0.309330\pi\) | ||||
0.563823 | + | 0.825895i | \(0.309330\pi\) | |||||||
\(740\) | 4.10814 | 0.151018 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5113i | 0.862545i | 0.902222 | + | 0.431272i | \(0.141935\pi\) | ||||
−0.902222 | + | 0.431272i | \(0.858065\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 14.6762i | − 0.537694i | ||||||||
\(746\) | 8.38547i | 0.307014i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.7229i | 0.428630i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.5805 | −0.969937 | −0.484969 | − | 0.874531i | \(-0.661169\pi\) | ||||
−0.484969 | + | 0.874531i | \(0.661169\pi\) | |||||||
\(752\) | 7.42676 | 0.270826 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.54168i | 0.311070i | ||||||||
\(755\) | −6.74150 | −0.245348 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.7997 | −1.73731 | −0.868655 | − | 0.495417i | \(-0.835015\pi\) | ||||
−0.868655 | + | 0.495417i | \(0.835015\pi\) | |||||||
\(758\) | − 1.33954i | − 0.0486544i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.71191 | 0.0983712 | ||||||||
\(761\) | 14.8528 | 0.538412 | 0.269206 | − | 0.963083i | \(-0.413239\pi\) | ||||
0.269206 | + | 0.963083i | \(0.413239\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 5.82805i | − 0.210852i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.2686i | 0.768465i | ||||||||
\(767\) | − 13.3196i | − 0.480943i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.4756i | 1.27928i | 0.768674 | + | 0.639641i | \(0.220917\pi\) | ||||
−0.768674 | + | 0.639641i | \(0.779083\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.75789 | 0.207231 | ||||||||
\(773\) | −3.06221 | −0.110140 | −0.0550701 | − | 0.998482i | \(-0.517538\pi\) | ||||
−0.0550701 | + | 0.998482i | \(0.517538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 0.550066i | − 0.0197589i | ||||||||
\(776\) | −7.65685 | −0.274865 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −27.8774 | −0.999451 | ||||||||
\(779\) | − 2.83049i | − 0.101413i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −58.1160 | −2.07955 | ||||||||
\(782\) | 1.08239 | 0.0387063 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.62726i | 0.343612i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.8957i | 1.24390i | 0.783058 | + | 0.621948i | \(0.213659\pi\) | ||||
−0.783058 | + | 0.621948i | \(0.786341\pi\) | |||||||
\(788\) | − 14.9259i | − 0.531714i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.4525i | 0.371883i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.25813 | 0.0801885 | ||||||||
\(794\) | 0.789763 | 0.0280276 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.6163i | 0.943388i | ||||||||
\(797\) | 2.52920 | 0.0895888 | 0.0447944 | − | 0.998996i | \(-0.485737\pi\) | ||||
0.0447944 | + | 0.998996i | \(0.485737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.1872 | −0.572662 | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.8599 | −0.383477 | ||||||||
\(803\) | −83.5543 | −2.94857 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.659481i | 0.0232292i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.0618412i | 0.00217557i | ||||||||
\(809\) | − 43.4977i | − 1.52930i | −0.644446 | − | 0.764649i | \(-0.722912\pi\) | ||||
0.644446 | − | 0.764649i | \(-0.277088\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6495i | 1.21671i | 0.793665 | + | 0.608355i | \(0.208170\pi\) | ||||
−0.793665 | + | 0.608355i | \(0.791830\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.0956 | −0.774450 | ||||||||
\(815\) | −4.15866 | −0.145671 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 16.3796i | − 0.573050i | ||||||||
\(818\) | 24.9507 | 0.872380 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.04373 | −0.0364486 | ||||||||
\(821\) | 19.9704i | 0.696970i | 0.937314 | + | 0.348485i | \(0.113304\pi\) | ||||
−0.937314 | + | 0.348485i | \(0.886696\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.24587 | 0.287433 | 0.143716 | − | 0.989619i | \(-0.454095\pi\) | ||||
0.143716 | + | 0.989619i | \(0.454095\pi\) | |||||||
\(824\) | 7.44155 | 0.259239 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 16.3355i | − 0.568039i | −0.958818 | − | 0.284020i | \(-0.908332\pi\) | ||||
0.958818 | − | 0.284020i | \(-0.0916681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 36.8032i | − 1.27823i | −0.769112 | − | 0.639114i | \(-0.779301\pi\) | ||||
0.769112 | − | 0.639114i | \(-0.220699\pi\) | |||||||
\(830\) | − 14.5400i | − 0.504689i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.19891i | 0.0415648i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.4764 | −0.431763 | ||||||||
\(836\) | −14.5860 | −0.504466 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 38.9552i | − 1.34568i | ||||||||
\(839\) | 0.712840 | 0.0246100 | 0.0123050 | − | 0.999924i | \(-0.496083\pi\) | ||||
0.0123050 | + | 0.999924i | \(0.496083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.7589 | −0.750307 | ||||||||
\(842\) | 38.1818i | 1.31583i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.65269 | 0.263417 | ||||||||
\(845\) | 11.5626 | 0.397766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.13707i | 0.176408i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.17958i | 0.0747590i | ||||||||
\(851\) | 2.04013i | 0.0699346i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 26.8405i | − 0.919002i | −0.888177 | − | 0.459501i | \(-0.848028\pi\) | ||||
0.888177 | − | 0.459501i | \(-0.151972\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.05052 | −0.138444 | ||||||||
\(857\) | 4.27465 | 0.146019 | 0.0730096 | − | 0.997331i | \(-0.476740\pi\) | ||||
0.0730096 | + | 0.997331i | \(0.476740\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7201i | 0.399884i | 0.979808 | + | 0.199942i | \(0.0640754\pi\) | ||||
−0.979808 | + | 0.199942i | \(0.935925\pi\) | |||||||
\(860\) | −6.03988 | −0.205958 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.01639 | 0.102739 | ||||||||
\(863\) | 48.4744i | 1.65009i | 0.565069 | + | 0.825044i | \(0.308850\pi\) | ||||
−0.565069 | + | 0.825044i | \(0.691150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.02869 | −0.0349765 | ||||||||
\(866\) | −37.7167 | −1.28166 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 56.2187i | − 1.90709i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 5.10159i | − 0.172861i | ||||||||
\(872\) | 9.01414i | 0.305257i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.34675i | 0.0455545i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.53874 | −0.153262 | −0.0766312 | − | 0.997060i | \(-0.524416\pi\) | ||||
−0.0766312 | + | 0.997060i | \(0.524416\pi\) | |||||||
\(878\) | 21.3683 | 0.721146 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.37849i | 0.181309i | ||||||||
\(881\) | −13.4827 | −0.454242 | −0.227121 | − | 0.973867i | \(-0.572931\pi\) | ||||
−0.227121 | + | 0.973867i | \(0.572931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.6089 | 0.457977 | 0.228989 | − | 0.973429i | \(-0.426458\pi\) | ||||
0.228989 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(884\) | − 2.61313i | − 0.0878889i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.59629 | −0.0536284 | ||||||||
\(887\) | −17.7194 | −0.594959 | −0.297479 | − | 0.954728i | \(-0.596146\pi\) | ||||
−0.297479 | + | 0.954728i | \(0.596146\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 15.8899i | − 0.532630i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 2.25715i | − 0.0755750i | ||||||||
\(893\) | − 20.1407i | − 0.673982i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 9.99480i | − 0.334089i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.9895 | 0.500206 | ||||||||
\(899\) | −3.91896 | −0.130705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 11.1967i | − 0.373015i | ||||||||
\(902\) | 5.61369 | 0.186915 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.9082 | −0.628877 | ||||||||
\(905\) | 3.08014i | 0.102387i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.2895 | −1.30459 | −0.652293 | − | 0.757967i | \(-0.726193\pi\) | ||||
−0.652293 | + | 0.757967i | \(0.726193\pi\) | |||||||
\(908\) | −17.5011 | −0.580796 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 41.2365i | − 1.36623i | −0.730313 | − | 0.683113i | \(-0.760626\pi\) | ||||
0.730313 | − | 0.683113i | \(-0.239374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 78.2031i | 2.58814i | ||||||||
\(914\) | − 22.5650i | − 0.746385i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 24.4840i | − 0.808974i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.16123 | 0.0383053 | 0.0191526 | − | 0.999817i | \(-0.493903\pi\) | ||||
0.0191526 | + | 0.999817i | \(0.493903\pi\) | |||||||
\(920\) | 0.496606 | 0.0163726 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.03506i | 0.231687i | ||||||||
\(923\) | 12.9545 | 0.426404 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.10814 | −0.135075 | ||||||||
\(926\) | 28.8845i | 0.949203i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.12453 | −0.233874 | ||||||||
\(929\) | 52.9648 | 1.73772 | 0.868860 | − | 0.495058i | \(-0.164853\pi\) | ||||
0.868860 | + | 0.495058i | \(0.164853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.7366i | 0.580982i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 26.5709i | − 0.869428i | ||||||||
\(935\) | − 11.7229i | − 0.383378i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9970i | 0.881955i | 0.897518 | + | 0.440977i | \(0.145368\pi\) | ||||
−0.897518 | + | 0.440977i | \(0.854632\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.42676 | −0.242234 | ||||||||
\(941\) | 47.6026 | 1.55180 | 0.775900 | − | 0.630856i | \(-0.217296\pi\) | ||||
0.775900 | + | 0.630856i | \(0.217296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 0.518321i | − 0.0168789i | ||||||||
\(944\) | 11.1097 | 0.361591 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.4855 | 1.05619 | ||||||||
\(947\) | 41.7275i | 1.35596i | 0.735080 | + | 0.677980i | \(0.237145\pi\) | ||||
−0.735080 | + | 0.677980i | \(0.762855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.6250 | 0.604592 | ||||||||
\(950\) | −2.71191 | −0.0879859 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.5279i | 1.70155i | 0.525534 | + | 0.850773i | \(0.323866\pi\) | ||||
−0.525534 | + | 0.850773i | \(0.676134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.82805i | 0.188591i | ||||||||
\(956\) | − 14.8111i | − 0.479026i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.6410i | 0.925349i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6974 | 0.990240 | ||||||||
\(962\) | 4.92530 | 0.158798 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.93938i | 0.320126i | ||||||||
\(965\) | −5.75789 | −0.185353 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.6987 | −0.569152 | −0.284576 | − | 0.958653i | \(-0.591853\pi\) | ||||
−0.284576 | + | 0.958653i | \(0.591853\pi\) | |||||||
\(968\) | − 17.9282i | − 0.576234i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.65685 | 0.245847 | ||||||||
\(971\) | −44.1003 | −1.41525 | −0.707623 | − | 0.706590i | \(-0.750232\pi\) | ||||
−0.707623 | + | 0.706590i | \(0.750232\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 18.7266i | − 0.600040i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.88348i | 0.0602887i | ||||||||
\(977\) | 31.1015i | 0.995026i | 0.867457 | + | 0.497513i | \(0.165753\pi\) | ||||
−0.867457 | + | 0.497513i | \(0.834247\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 85.4637i | 2.73143i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.0927 | −0.768827 | ||||||||
\(983\) | −30.4697 | −0.971834 | −0.485917 | − | 0.874005i | \(-0.661514\pi\) | ||||
−0.485917 | + | 0.874005i | \(0.661514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.9259i | 0.475580i | ||||||||
\(986\) | 15.5285 | 0.494528 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.25134 | 0.103439 | ||||||||
\(989\) | − 2.99944i | − 0.0953767i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.6020 | 0.622677 | 0.311338 | − | 0.950299i | \(-0.399223\pi\) | ||||
0.311338 | + | 0.950299i | \(0.399223\pi\) | |||||||
\(992\) | −0.550066 | −0.0174646 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 26.6163i | − 0.843792i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.69192i | 0.148594i | 0.997236 | + | 0.0742972i | \(0.0236714\pi\) | ||||
−0.997236 | + | 0.0742972i | \(0.976329\pi\) | |||||||
\(998\) | 14.7333i | 0.466374i | ||||||||
\(999\) | 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 | 4410.2.b.f.881.4 | yes | 8 | |
3.2 | odd | 2 | 4410.2.b.c.881.5 | yes | 8 | ||
7.6 | odd | 2 | 4410.2.b.c.881.4 | ✓ | 8 | ||
21.20 | even | 2 | inner | 4410.2.b.f.881.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.b.c.881.4 | ✓ | 8 | 7.6 | odd | 2 | ||
4410.2.b.c.881.5 | yes | 8 | 3.2 | odd | 2 | ||
4410.2.b.f.881.4 | yes | 8 | 1.1 | even | 1 | trivial | |
4410.2.b.f.881.5 | yes | 8 | 21.20 | even | 2 | inner |