Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1324,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1324.2 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1324 |
Dual form | 1575.2.d.d.1324.3 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.23607i | − 1.58114i | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
0.612372 | − | 0.790569i | \(-0.290215\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.00000 | −1.50000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47214 | 0.745377 | 0.372689 | − | 0.927957i | \(-0.378436\pi\) | ||||
0.372689 | + | 0.927957i | \(0.378436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214i | 1.24035i | 0.784465 | + | 0.620174i | \(0.212938\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | 2.23607 | 0.597614 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 5.52786i | − 1.17854i | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.0000 | 1.96116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 3.00000i | − 0.566947i | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4721 | 1.88085 | 0.940426 | − | 0.340000i | \(-0.110427\pi\) | ||||
0.940426 | + | 0.340000i | \(0.110427\pi\) | |||||||
\(32\) | 6.70820i | 1.18585i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.47214 | 0.766965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9443i | 1.79923i | 0.436687 | + | 0.899614i | \(0.356152\pi\) | ||||
−0.436687 | + | 0.899614i | \(0.643848\pi\) | |||||||
\(38\) | 14.4721i | 2.34769i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.94427i | 1.36399i | 0.731357 | + | 0.681994i | \(0.238887\pi\) | ||||
−0.731357 | + | 0.681994i | \(0.761113\pi\) | |||||||
\(44\) | −7.41641 | −1.11807 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.94427 | 1.31876 | ||||||||
\(47\) | 4.94427i | 0.721196i | 0.932721 | + | 0.360598i | \(0.117427\pi\) | ||||
−0.932721 | + | 0.360598i | \(0.882573\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 13.4164i | − 1.86052i | ||||||||
\(53\) | − 12.4721i | − 1.71318i | −0.515998 | − | 0.856590i | \(-0.672579\pi\) | ||||
0.515998 | − | 0.856590i | \(-0.327421\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.47214i | 0.587220i | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | − 23.4164i | − 2.97389i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | − 6.00000i | − 0.727607i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4721 | −1.71753 | −0.858763 | − | 0.512373i | \(-0.828767\pi\) | ||||
−0.858763 | + | 0.512373i | \(0.828767\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.52786i | 0.412905i | 0.978457 | + | 0.206453i | \(0.0661919\pi\) | ||||
−0.978457 | + | 0.206453i | \(0.933808\pi\) | |||||||
\(74\) | 24.4721 | 2.84483 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.4164 | 2.22721 | ||||||||
\(77\) | 2.47214i | 0.281726i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94427 | 0.556274 | 0.278137 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278137 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 4.47214i | − 0.493865i | ||||||||
\(83\) | 0.944272i | 0.103647i | 0.998656 | + | 0.0518237i | \(0.0165034\pi\) | ||||
−0.998656 | + | 0.0518237i | \(0.983497\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 20.0000 | 2.15666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.52786i | 0.589272i | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | − 12.0000i | − 1.25109i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.0557 | 1.14031 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 0.472136i | − 0.0479381i | −0.999713 | − | 0.0239691i | \(-0.992370\pi\) | ||||
0.999713 | − | 0.0239691i | \(-0.00763032\pi\) | |||||||
\(98\) | 2.23607i | 0.225877i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0000 | 1.39305 | 0.696526 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696526 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | −10.0000 | −0.980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.8885 | −2.70877 | ||||||||
\(107\) | − 4.94427i | − 0.477981i | −0.971022 | − | 0.238990i | \(-0.923184\pi\) | ||||
0.971022 | − | 0.238990i | \(-0.0768164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 1.00000i | − 0.0944911i | ||||||||
\(113\) | − 8.47214i | − 0.796992i | −0.917170 | − | 0.398496i | \(-0.869532\pi\) | ||||
0.917170 | − | 0.398496i | \(-0.130468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 20.0000i | − 1.84115i | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.88854 | −0.444413 | ||||||||
\(122\) | 4.47214i | 0.404888i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −31.4164 | −2.82128 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9443i | 1.14862i | 0.818638 | + | 0.574309i | \(0.194729\pi\) | ||||
−0.818638 | + | 0.574309i | \(0.805271\pi\) | |||||||
\(128\) | − 15.6525i | − 1.38350i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 6.47214i | − 0.561205i | ||||||||
\(134\) | −8.94427 | −0.772667 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.47214 | −0.383482 | ||||||||
\(137\) | − 12.4721i | − 1.06557i | −0.846252 | − | 0.532783i | \(-0.821146\pi\) | ||||
0.846252 | − | 0.532783i | \(-0.178854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4164 | 1.64688 | 0.823439 | − | 0.567405i | \(-0.192052\pi\) | ||||
0.823439 | + | 0.567405i | \(0.192052\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 32.3607i | 2.71565i | ||||||||
\(143\) | 11.0557i | 0.924526i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.88854 | 0.652861 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 32.8328i | − 2.69884i | ||||||||
\(149\) | 2.94427 | 0.241204 | 0.120602 | − | 0.992701i | \(-0.461517\pi\) | ||||
0.120602 | + | 0.992701i | \(0.461517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | − 14.4721i | − 1.17385i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.52786 | 0.445448 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.47214i | 0.676150i | 0.941119 | + | 0.338075i | \(0.109776\pi\) | ||||
−0.941119 | + | 0.338075i | \(0.890224\pi\) | |||||||
\(158\) | − 11.0557i | − 0.879547i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 0.944272i | − 0.0739611i | −0.999316 | − | 0.0369805i | \(-0.988226\pi\) | ||||
0.999316 | − | 0.0369805i | \(-0.0117740\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.11146 | 0.163881 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 26.8328i | − 2.04598i | ||||||||
\(173\) | 14.9443i | 1.13619i | 0.822962 | + | 0.568096i | \(0.192320\pi\) | ||||
−0.822962 | + | 0.568096i | \(0.807680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.47214 | −0.186344 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.47214i | 0.335201i | ||||||||
\(179\) | −2.47214 | −0.184776 | −0.0923881 | − | 0.995723i | \(-0.529450\pi\) | ||||
−0.0923881 | + | 0.995723i | \(0.529450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.9443 | 1.40812 | 0.704058 | − | 0.710142i | \(-0.251369\pi\) | ||||
0.704058 | + | 0.710142i | \(0.251369\pi\) | |||||||
\(182\) | 10.0000i | 0.741249i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.94427 | −0.659380 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.94427i | 0.361561i | ||||||||
\(188\) | − 14.8328i | − 1.08179i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.4164 | −1.98378 | −0.991891 | − | 0.127093i | \(-0.959435\pi\) | ||||
−0.991891 | + | 0.127093i | \(0.959435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000i | 1.00774i | 0.863779 | + | 0.503871i | \(0.168091\pi\) | ||||
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | −1.05573 | −0.0757969 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | − 24.4721i | − 1.74357i | −0.489891 | − | 0.871784i | \(-0.662963\pi\) | ||||
0.489891 | − | 0.871784i | \(-0.337037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.583592 | −0.0413697 | −0.0206849 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206849 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 31.3050i | − 2.20261i | ||||||||
\(203\) | − 2.00000i | − 0.140372i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 4.47214i | − 0.310087i | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.944272 | 0.0650064 | 0.0325032 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325032 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(212\) | 37.4164i | 2.56977i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.0557 | −0.755754 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4721i | 0.710895i | ||||||||
\(218\) | − 4.47214i | − 0.302891i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.94427 | −0.601657 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4.94427i | − 0.331093i | −0.986202 | − | 0.165546i | \(-0.947061\pi\) | ||||
0.986202 | − | 0.165546i | \(-0.0529388\pi\) | |||||||
\(224\) | −6.70820 | −0.448211 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.9443 | −1.26015 | ||||||||
\(227\) | 16.9443i | 1.12463i | 0.826923 | + | 0.562315i | \(0.190089\pi\) | ||||
−0.826923 | + | 0.562315i | \(0.809911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.8885 | 0.785617 | 0.392809 | − | 0.919620i | \(-0.371504\pi\) | ||||
0.392809 | + | 0.919620i | \(0.371504\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 4.47214i | − 0.293610i | ||||||||
\(233\) | 17.4164i | 1.14099i | 0.821302 | + | 0.570493i | \(0.193248\pi\) | ||||
−0.821302 | + | 0.570493i | \(0.806752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −26.8328 | −1.74667 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.47214i | 0.289886i | ||||||||
\(239\) | −1.52786 | −0.0988293 | −0.0494147 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494147 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.05573 | −0.0680054 | −0.0340027 | − | 0.999422i | \(-0.510825\pi\) | ||||
−0.0340027 | + | 0.999422i | \(0.510825\pi\) | |||||||
\(242\) | 10.9311i | 0.702679i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 28.9443i | − 1.84168i | ||||||||
\(248\) | 23.4164i | 1.48694i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.944272 | 0.0596019 | 0.0298010 | − | 0.999556i | \(-0.490513\pi\) | ||||
0.0298010 | + | 0.999556i | \(0.490513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.88854i | 0.621687i | ||||||||
\(254\) | 28.9443 | 1.81613 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | − 1.05573i | − 0.0658545i | −0.999458 | − | 0.0329273i | \(-0.989517\pi\) | ||||
0.999458 | − | 0.0329273i | \(-0.0104830\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.9443 | −0.680044 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.94427i | 0.552579i | ||||||||
\(263\) | 24.9443i | 1.53813i | 0.639171 | + | 0.769065i | \(0.279278\pi\) | ||||
−0.639171 | + | 0.769065i | \(0.720722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.4721 | −0.887344 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | −23.8885 | −1.45651 | −0.728255 | − | 0.685306i | \(-0.759668\pi\) | ||||
−0.728255 | + | 0.685306i | \(0.759668\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4721 | −0.636137 | −0.318068 | − | 0.948068i | \(-0.603034\pi\) | ||||
−0.318068 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(272\) | − 2.00000i | − 0.121268i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −27.8885 | −1.68481 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.05573i | 0.0634326i | 0.999497 | + | 0.0317163i | \(0.0100973\pi\) | ||||
−0.999497 | + | 0.0317163i | \(0.989903\pi\) | |||||||
\(278\) | − 43.4164i | − 2.60394i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.94427 | −0.414261 | −0.207130 | − | 0.978313i | \(-0.566412\pi\) | ||||
−0.207130 | + | 0.978313i | \(0.566412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 12.0000i | − 0.713326i | −0.934233 | − | 0.356663i | \(-0.883914\pi\) | ||||
0.934233 | − | 0.356663i | \(-0.116086\pi\) | |||||||
\(284\) | 43.4164 | 2.57629 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.7214 | 1.46180 | ||||||||
\(287\) | 2.00000i | 0.118056i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 10.5836i | − 0.619358i | ||||||||
\(293\) | 22.9443i | 1.34042i | 0.742172 | + | 0.670209i | \(0.233796\pi\) | ||||
−0.742172 | + | 0.670209i | \(0.766204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −24.4721 | −1.42241 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 6.58359i | − 0.381377i | ||||||||
\(299\) | −17.8885 | −1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.94427 | −0.515539 | ||||||||
\(302\) | 35.7771i | 2.05874i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.47214 | 0.371202 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 32.9443i | − 1.88023i | −0.340859 | − | 0.940114i | \(-0.610718\pi\) | ||||
0.340859 | − | 0.940114i | \(-0.389282\pi\) | |||||||
\(308\) | − 7.41641i | − 0.422589i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.88854 | 0.560728 | 0.280364 | − | 0.959894i | \(-0.409545\pi\) | ||||
0.280364 | + | 0.959894i | \(0.409545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 9.41641i | − 0.532247i | −0.963939 | − | 0.266123i | \(-0.914257\pi\) | ||||
0.963939 | − | 0.266123i | \(-0.0857429\pi\) | |||||||
\(314\) | 18.9443 | 1.06909 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.8328 | −0.834411 | ||||||||
\(317\) | 30.3607i | 1.70523i | 0.522543 | + | 0.852613i | \(0.324983\pi\) | ||||
−0.522543 | + | 0.852613i | \(0.675017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.94427 | −0.276826 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.94427i | 0.498445i | ||||||||
\(323\) | − 12.9443i | − 0.720239i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.11146 | −0.116943 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.47214i | 0.246932i | ||||||||
\(329\) | −4.94427 | −0.272587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9443 | −0.931341 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(332\) | − 2.83282i | − 0.155471i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.8885 | 0.978818 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8885i | 0.647610i | 0.946124 | + | 0.323805i | \(0.104962\pi\) | ||||
−0.946124 | + | 0.323805i | \(0.895038\pi\) | |||||||
\(338\) | 15.6525i | 0.851382i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.8885 | 1.40194 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 33.4164 | 1.79648 | ||||||||
\(347\) | 8.00000i | 0.429463i | 0.976673 | + | 0.214731i | \(0.0688876\pi\) | ||||
−0.976673 | + | 0.214731i | \(0.931112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.8885 | −1.27872 | −0.639362 | − | 0.768906i | \(-0.720802\pi\) | ||||
−0.639362 | + | 0.768906i | \(0.720802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.5836i | 0.883908i | ||||||||
\(353\) | − 27.8885i | − 1.48436i | −0.670202 | − | 0.742179i | \(-0.733793\pi\) | ||||
0.670202 | − | 0.742179i | \(-0.266207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.52786i | 0.292157i | ||||||||
\(359\) | 9.52786 | 0.502861 | 0.251431 | − | 0.967875i | \(-0.419099\pi\) | ||||
0.251431 | + | 0.967875i | \(0.419099\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | − 42.3607i | − 2.22643i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.4164 | 0.703211 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.9443i | 1.09328i | 0.837367 | + | 0.546641i | \(0.184094\pi\) | ||||
−0.837367 | + | 0.546641i | \(0.815906\pi\) | |||||||
\(368\) | − 4.00000i | − 0.208514i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.4721 | 0.647521 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6.00000i | − 0.310668i | −0.987862 | − | 0.155334i | \(-0.950355\pi\) | ||||
0.987862 | − | 0.155334i | \(-0.0496454\pi\) | |||||||
\(374\) | 11.0557 | 0.571678 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.0557 | −0.570156 | ||||||||
\(377\) | − 8.94427i | − 0.460653i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.11146 | 0.108458 | 0.0542291 | − | 0.998529i | \(-0.482730\pi\) | ||||
0.0542291 | + | 0.998529i | \(0.482730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 61.3050i | 3.13663i | ||||||||
\(383\) | − 8.00000i | − 0.408781i | −0.978889 | − | 0.204390i | \(-0.934479\pi\) | ||||
0.978889 | − | 0.204390i | \(-0.0655212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.3050 | 1.59338 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.41641i | 0.0719072i | ||||||||
\(389\) | 10.9443 | 0.554897 | 0.277448 | − | 0.960741i | \(-0.410511\pi\) | ||||
0.277448 | + | 0.960741i | \(0.410511\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | − 2.23607i | − 0.112938i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −54.7214 | −2.75682 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4164i | 0.673350i | 0.941621 | + | 0.336675i | \(0.109302\pi\) | ||||
−0.941621 | + | 0.336675i | \(0.890698\pi\) | |||||||
\(398\) | 1.30495i | 0.0654113i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 46.8328i | 2.33291i | ||||||||
\(404\) | −42.0000 | −2.08958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | 27.0557i | 1.34110i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.8885 | 1.18121 | 0.590606 | − | 0.806960i | \(-0.298889\pi\) | ||||
0.590606 | + | 0.806960i | \(0.298889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.94427i | 0.440119i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −30.0000 | −1.47087 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 35.7771i | 1.74991i | ||||||||
\(419\) | 5.88854 | 0.287674 | 0.143837 | − | 0.989601i | \(-0.454056\pi\) | ||||
0.143837 | + | 0.989601i | \(0.454056\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | − 2.11146i | − 0.102784i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27.8885 | 1.35439 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.00000i | − 0.0967868i | ||||||||
\(428\) | 14.8328i | 0.716971i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.52786 | 0.458941 | 0.229471 | − | 0.973316i | \(-0.426301\pi\) | ||||
0.229471 | + | 0.973316i | \(0.426301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7.52786i | − 0.361766i | −0.983505 | − | 0.180883i | \(-0.942104\pi\) | ||||
0.983505 | − | 0.180883i | \(-0.0578955\pi\) | |||||||
\(434\) | 23.4164 | 1.12402 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.00000 | −0.287348 | ||||||||
\(437\) | − 25.8885i | − 1.23842i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4721 | −0.499808 | −0.249904 | − | 0.968271i | \(-0.580399\pi\) | ||||
−0.249904 | + | 0.968271i | \(0.580399\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.0000i | 0.951303i | ||||||||
\(443\) | − 8.00000i | − 0.380091i | −0.981775 | − | 0.190046i | \(-0.939136\pi\) | ||||
0.981775 | − | 0.190046i | \(-0.0608636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.0557 | −0.523504 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.0000i | 0.614192i | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.94427 | 0.232817 | ||||||||
\(452\) | 25.4164i | 1.19549i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 37.8885 | 1.77820 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 10.9443i | − 0.511951i | −0.966683 | − | 0.255976i | \(-0.917603\pi\) | ||||
0.966683 | − | 0.255976i | \(-0.0823967\pi\) | |||||||
\(458\) | − 26.5836i | − 1.24217i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8885 | 1.48520 | 0.742599 | − | 0.669737i | \(-0.233593\pi\) | ||||
0.742599 | + | 0.669737i | \(0.233593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3.05573i | − 0.142012i | −0.997476 | − | 0.0710059i | \(-0.977379\pi\) | ||||
0.997476 | − | 0.0710059i | \(-0.0226209\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38.9443 | 1.80406 | ||||||||
\(467\) | − 8.94427i | − 0.413892i | −0.978352 | − | 0.206946i | \(-0.933648\pi\) | ||||
0.978352 | − | 0.206946i | \(-0.0663524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.0000i | 0.920575i | ||||||||
\(473\) | 22.1115i | 1.01669i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.41641i | 0.156263i | ||||||||
\(479\) | 17.8885 | 0.817348 | 0.408674 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408674 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.9443 | −2.23167 | ||||||||
\(482\) | 2.36068i | 0.107526i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.6656 | 0.666620 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3.05573i | − 0.138468i | −0.997600 | − | 0.0692341i | \(-0.977944\pi\) | ||||
0.997600 | − | 0.0692341i | \(-0.0220556\pi\) | |||||||
\(488\) | − 4.47214i | − 0.202444i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.3050 | −1.86407 | −0.932033 | − | 0.362373i | \(-0.881967\pi\) | ||||
−0.932033 | + | 0.362373i | \(0.881967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.00000i | − 0.180151i | ||||||||
\(494\) | −64.7214 | −2.91195 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.4721 | −0.470213 | ||||||||
\(497\) | − 14.4721i | − 0.649164i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.8885 | −0.979866 | −0.489933 | − | 0.871760i | \(-0.662979\pi\) | ||||
−0.489933 | + | 0.871760i | \(0.662979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 2.11146i | − 0.0942389i | ||||||||
\(503\) | 32.0000i | 1.42681i | 0.700752 | + | 0.713405i | \(0.252848\pi\) | ||||
−0.700752 | + | 0.713405i | \(0.747152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.1115 | 0.982974 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 38.8328i | − 1.72293i | ||||||||
\(509\) | 11.8885 | 0.526950 | 0.263475 | − | 0.964666i | \(-0.415131\pi\) | ||||
0.263475 | + | 0.964666i | \(0.415131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.52786 | −0.156064 | ||||||||
\(512\) | − 11.1803i | − 0.494106i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.36068 | −0.104125 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2229i | 0.537563i | ||||||||
\(518\) | 24.4721i | 1.07524i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.8885 | −0.696090 | −0.348045 | − | 0.937478i | \(-0.613154\pi\) | ||||
−0.348045 | + | 0.937478i | \(0.613154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.94427i | − 0.391106i | −0.980693 | − | 0.195553i | \(-0.937350\pi\) | ||||
0.980693 | − | 0.195553i | \(-0.0626501\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 55.7771 | 2.43200 | ||||||||
\(527\) | 20.9443i | 0.912347i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.4164i | 0.841808i | ||||||||
\(533\) | 8.94427i | 0.387419i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.94427 | 0.386334 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 53.4164i | 2.30294i | ||||||||
\(539\) | −2.47214 | −0.106482 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.8885 | 1.02705 | 0.513524 | − | 0.858075i | \(-0.328340\pi\) | ||||
0.513524 | + | 0.858075i | \(0.328340\pi\) | |||||||
\(542\) | 23.4164i | 1.00582i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.4164 | −0.575224 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 29.8885i | − 1.27794i | −0.769231 | − | 0.638971i | \(-0.779360\pi\) | ||||
0.769231 | − | 0.638971i | \(-0.220640\pi\) | |||||||
\(548\) | 37.4164i | 1.59835i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.9443 | 0.551445 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.94427i | 0.210252i | ||||||||
\(554\) | 2.36068 | 0.100296 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −58.2492 | −2.47032 | ||||||||
\(557\) | − 11.5279i | − 0.488451i | −0.969718 | − | 0.244226i | \(-0.921466\pi\) | ||||
0.969718 | − | 0.244226i | \(-0.0785338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.0000 | −1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.5279i | 0.655003i | ||||||||
\(563\) | − 21.8885i | − 0.922492i | −0.887272 | − | 0.461246i | \(-0.847403\pi\) | ||||
0.887272 | − | 0.461246i | \(-0.152597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.8328 | −1.12787 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 32.3607i | − 1.35782i | ||||||||
\(569\) | −4.11146 | −0.172361 | −0.0861806 | − | 0.996280i | \(-0.527466\pi\) | ||||
−0.0861806 | + | 0.996280i | \(0.527466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | − 33.1672i | − 1.38679i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.47214 | 0.186663 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 34.3607i | − 1.43045i | −0.698892 | − | 0.715227i | \(-0.746323\pi\) | ||||
0.698892 | − | 0.715227i | \(-0.253677\pi\) | |||||||
\(578\) | − 29.0689i | − 1.20911i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.944272 | −0.0391750 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 30.8328i | − 1.27696i | ||||||||
\(584\) | −7.88854 | −0.326430 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.3050 | 2.11939 | ||||||||
\(587\) | 4.00000i | 0.165098i | 0.996587 | + | 0.0825488i | \(0.0263060\pi\) | ||||
−0.996587 | + | 0.0825488i | \(0.973694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −67.7771 | −2.79271 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 10.9443i | − 0.449807i | ||||||||
\(593\) | − 11.8885i | − 0.488204i | −0.969750 | − | 0.244102i | \(-0.921507\pi\) | ||||
0.969750 | − | 0.244102i | \(-0.0784932\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.83282 | −0.361806 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 40.0000i | 1.63572i | ||||||||
\(599\) | −32.3607 | −1.32222 | −0.661111 | − | 0.750288i | \(-0.729915\pi\) | ||||
−0.661111 | + | 0.750288i | \(0.729915\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0557 | 0.858881 | 0.429441 | − | 0.903095i | \(-0.358711\pi\) | ||||
0.429441 | + | 0.903095i | \(0.358711\pi\) | |||||||
\(602\) | 20.0000i | 0.815139i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 48.0000 | 1.95309 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 14.8328i | − 0.602045i | −0.953617 | − | 0.301023i | \(-0.902672\pi\) | ||||
0.953617 | − | 0.301023i | \(-0.0973280\pi\) | |||||||
\(608\) | − 43.4164i | − 1.76077i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.1115 | −0.894534 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 10.9443i | − 0.442035i | −0.975270 | − | 0.221017i | \(-0.929062\pi\) | ||||
0.975270 | − | 0.221017i | \(-0.0709378\pi\) | |||||||
\(614\) | −73.6656 | −2.97290 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.52786 | −0.222724 | ||||||||
\(617\) | − 7.52786i | − 0.303060i | −0.988453 | − | 0.151530i | \(-0.951580\pi\) | ||||
0.988453 | − | 0.151530i | \(-0.0484201\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5836 | −0.505777 | −0.252889 | − | 0.967495i | \(-0.581381\pi\) | ||||
−0.252889 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 22.1115i | − 0.886589i | ||||||||
\(623\) | − 2.00000i | − 0.0801283i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21.0557 | −0.841556 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 25.4164i | − 1.01423i | ||||||||
\(629\) | −21.8885 | −0.872753 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.8328 | −0.908960 | −0.454480 | − | 0.890757i | \(-0.650175\pi\) | ||||
−0.454480 | + | 0.890757i | \(0.650175\pi\) | |||||||
\(632\) | 11.0557i | 0.439773i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 67.8885 | 2.69620 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.47214i | − 0.177192i | ||||||||
\(638\) | 11.0557i | 0.437700i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.8328 | 1.45481 | 0.727404 | − | 0.686209i | \(-0.240726\pi\) | ||||
0.727404 | + | 0.686209i | \(0.240726\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.9443i | 1.29920i | 0.760278 | + | 0.649598i | \(0.225063\pi\) | ||||
−0.760278 | + | 0.649598i | \(0.774937\pi\) | |||||||
\(644\) | 12.0000 | 0.472866 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.9443 | −1.13880 | ||||||||
\(647\) | − 33.8885i | − 1.33230i | −0.745820 | − | 0.666148i | \(-0.767942\pi\) | ||||
0.745820 | − | 0.666148i | \(-0.232058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.1115 | 0.867951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.83282i | 0.110942i | ||||||||
\(653\) | − 49.4164i | − 1.93381i | −0.255130 | − | 0.966907i | \(-0.582118\pi\) | ||||
0.255130 | − | 0.966907i | \(-0.417882\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.0557i | 0.430997i | ||||||||
\(659\) | −41.3050 | −1.60901 | −0.804506 | − | 0.593944i | \(-0.797570\pi\) | ||||
−0.804506 | + | 0.593944i | \(0.797570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.111456 | −0.00433514 | −0.00216757 | − | 0.999998i | \(-0.500690\pi\) | ||||
−0.00216757 | + | 0.999998i | \(0.500690\pi\) | |||||||
\(662\) | 37.8885i | 1.47258i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.11146 | −0.0819404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.00000i | − 0.309761i | ||||||||
\(668\) | − 24.0000i | − 0.928588i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.94427 | −0.190872 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.8328i | 1.72818i | 0.503339 | + | 0.864089i | \(0.332105\pi\) | ||||
−0.503339 | + | 0.864089i | \(0.667895\pi\) | |||||||
\(674\) | 26.5836 | 1.02396 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | − 38.9443i | − 1.49675i | −0.663276 | − | 0.748375i | \(-0.730834\pi\) | ||||
0.663276 | − | 0.748375i | \(-0.269166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.472136 | 0.0181189 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 57.8885i | − 2.21667i | ||||||||
\(683\) | 33.8885i | 1.29671i | 0.761339 | + | 0.648355i | \(0.224543\pi\) | ||||
−0.761339 | + | 0.648355i | \(0.775457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.23607 | −0.0853735 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 8.94427i | − 0.340997i | ||||||||
\(689\) | 55.7771 | 2.12494 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.360680 | −0.0137209 | −0.00686045 | − | 0.999976i | \(-0.502184\pi\) | ||||
−0.00686045 | + | 0.999976i | \(0.502184\pi\) | |||||||
\(692\) | − 44.8328i | − 1.70429i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.8885 | 0.679040 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000i | 0.151511i | ||||||||
\(698\) | 53.4164i | 2.02184i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0000 | 1.28416 | 0.642081 | − | 0.766637i | \(-0.278071\pi\) | ||||
0.642081 | + | 0.766637i | \(0.278071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 70.8328i | − 2.67151i | ||||||||
\(704\) | 32.1378 | 1.21124 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −62.3607 | −2.34698 | ||||||||
\(707\) | 14.0000i | 0.526524i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.7771 | 1.71919 | 0.859597 | − | 0.510972i | \(-0.170714\pi\) | ||||
0.859597 | + | 0.510972i | \(0.170714\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 4.47214i | − 0.167600i | ||||||||
\(713\) | 41.8885i | 1.56874i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.41641 | 0.277164 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 21.3050i | − 0.795094i | ||||||||
\(719\) | 46.8328 | 1.74657 | 0.873285 | − | 0.487210i | \(-0.161985\pi\) | ||||
0.873285 | + | 0.487210i | \(0.161985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 51.1803i | − 1.90474i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −56.8328 | −2.11217 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.8328i | 0.550119i | 0.961427 | + | 0.275059i | \(0.0886975\pi\) | ||||
−0.961427 | + | 0.275059i | \(0.911302\pi\) | |||||||
\(728\) | − 10.0000i | − 0.370625i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 37.4164i | − 1.38201i | −0.722852 | − | 0.691003i | \(-0.757169\pi\) | ||||
0.722852 | − | 0.691003i | \(-0.242831\pi\) | |||||||
\(734\) | 46.8328 | 1.72863 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.8328 | −0.989071 | ||||||||
\(737\) | − 9.88854i | − 0.364249i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.8885 | −1.09947 | −0.549734 | − | 0.835340i | \(-0.685271\pi\) | ||||
−0.549734 | + | 0.835340i | \(0.685271\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 27.8885i | − 1.02382i | ||||||||
\(743\) | − 18.8328i | − 0.690909i | −0.938436 | − | 0.345455i | \(-0.887725\pi\) | ||||
0.938436 | − | 0.345455i | \(-0.112275\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.4164 | −0.491210 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 14.8328i | − 0.542341i | ||||||||
\(749\) | 4.94427 | 0.180660 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.05573 | −0.111505 | −0.0557526 | − | 0.998445i | \(-0.517756\pi\) | ||||
−0.0557526 | + | 0.998445i | \(0.517756\pi\) | |||||||
\(752\) | − 4.94427i | − 0.180299i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.0000 | −0.728357 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.88854i | − 0.141332i | −0.997500 | − | 0.0706658i | \(-0.977488\pi\) | ||||
0.997500 | − | 0.0706658i | \(-0.0225124\pi\) | |||||||
\(758\) | − 4.72136i | − 0.171488i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.88854 | −0.285959 | −0.142980 | − | 0.989726i | \(-0.545668\pi\) | ||||
−0.142980 | + | 0.989726i | \(0.545668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.00000i | 0.0724049i | ||||||||
\(764\) | 82.2492 | 2.97567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.8885 | −0.646339 | ||||||||
\(767\) | 40.0000i | 1.44432i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.832816 | −0.0300321 | −0.0150161 | − | 0.999887i | \(-0.504780\pi\) | ||||
−0.0150161 | + | 0.999887i | \(0.504780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 42.0000i | − 1.51161i | ||||||||
\(773\) | − 25.0557i | − 0.901192i | −0.892728 | − | 0.450596i | \(-0.851212\pi\) | ||||
0.892728 | − | 0.450596i | \(-0.148788\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.05573 | 0.0378984 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 24.4721i | − 0.877369i | ||||||||
\(779\) | −12.9443 | −0.463777 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.7771 | −1.28020 | ||||||||
\(782\) | 17.8885i | 0.639693i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.9443i | 1.74467i | 0.488904 | + | 0.872337i | \(0.337397\pi\) | ||||
−0.488904 | + | 0.872337i | \(0.662603\pi\) | |||||||
\(788\) | 73.4164i | 2.61535i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.47214 | 0.301234 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 8.94427i | − 0.317620i | ||||||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.75078 | 0.0620546 | ||||||||
\(797\) | 1.05573i | 0.0373958i | 0.999825 | + | 0.0186979i | \(0.00595207\pi\) | ||||
−0.999825 | + | 0.0186979i | \(0.994048\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.88854 | −0.349832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.3607i | 0.789583i | ||||||||
\(803\) | 8.72136i | 0.307770i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 104.721 | 3.68865 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31.3050i | 1.10130i | ||||||||
\(809\) | 21.0557 | 0.740280 | 0.370140 | − | 0.928976i | \(-0.379310\pi\) | ||||
0.370140 | + | 0.928976i | \(0.379310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.5836 | 1.00371 | 0.501853 | − | 0.864953i | \(-0.332652\pi\) | ||||
0.501853 | + | 0.864953i | \(0.332652\pi\) | |||||||
\(812\) | 6.00000i | 0.210559i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 60.4984 | 2.12047 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 57.8885i | − 2.02526i | ||||||||
\(818\) | − 53.4164i | − 1.86766i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.7771 | 1.31843 | 0.659215 | − | 0.751955i | \(-0.270889\pi\) | ||||
0.659215 | + | 0.751955i | \(0.270889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 27.0557i | − 0.943103i | −0.881838 | − | 0.471552i | \(-0.843694\pi\) | ||||
0.881838 | − | 0.471552i | \(-0.156306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.0000 | 0.695889 | ||||||||
\(827\) | 4.94427i | 0.171929i | 0.996298 | + | 0.0859646i | \(0.0273972\pi\) | ||||
−0.996298 | + | 0.0859646i | \(0.972603\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.9443 | 1.07474 | 0.537369 | − | 0.843347i | \(-0.319418\pi\) | ||||
0.537369 | + | 0.843347i | \(0.319418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 58.1378i | 2.01556i | ||||||||
\(833\) | − 2.00000i | − 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 48.0000 | 1.66011 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 13.1672i | − 0.454853i | ||||||||
\(839\) | 1.16718 | 0.0402957 | 0.0201478 | − | 0.999797i | \(-0.493586\pi\) | ||||
0.0201478 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − 49.1935i | − 1.69532i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.83282 | −0.0975095 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 4.88854i | − 0.167972i | ||||||||
\(848\) | 12.4721i | 0.428295i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.7771 | −1.50066 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 31.3050i | − 1.07186i | −0.844262 | − | 0.535931i | \(-0.819961\pi\) | ||||
0.844262 | − | 0.535931i | \(-0.180039\pi\) | |||||||
\(854\) | −4.47214 | −0.153033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.0557 | 0.377877 | ||||||||
\(857\) | 16.8328i | 0.574998i | 0.957781 | + | 0.287499i | \(0.0928238\pi\) | ||||
−0.957781 | + | 0.287499i | \(0.907176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.5279 | −1.41691 | −0.708456 | − | 0.705755i | \(-0.750608\pi\) | ||||
−0.708456 | + | 0.705755i | \(0.750608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 21.3050i | − 0.725650i | ||||||||
\(863\) | − 13.8885i | − 0.472772i | −0.971659 | − | 0.236386i | \(-0.924037\pi\) | ||||
0.971659 | − | 0.236386i | \(-0.0759629\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.8328 | −0.572002 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 31.4164i | − 1.06634i | ||||||||
\(869\) | 12.2229 | 0.414634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.8885 | 0.606130 | ||||||||
\(872\) | 4.47214i | 0.151446i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −57.8885 | −1.95811 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.16718i | − 0.106948i | −0.998569 | − | 0.0534741i | \(-0.982971\pi\) | ||||
0.998569 | − | 0.0534741i | \(-0.0170295\pi\) | |||||||
\(878\) | 23.4164i | 0.790265i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.88854 | −0.265772 | −0.132886 | − | 0.991131i | \(-0.542424\pi\) | ||||
−0.132886 | + | 0.991131i | \(0.542424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.11146i | 0.0710562i | 0.999369 | + | 0.0355281i | \(0.0113113\pi\) | ||||
−0.999369 | + | 0.0355281i | \(0.988689\pi\) | |||||||
\(884\) | 26.8328 | 0.902485 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.8885 | −0.600977 | ||||||||
\(887\) | − 22.8328i | − 0.766651i | −0.923613 | − | 0.383325i | \(-0.874779\pi\) | ||||
0.923613 | − | 0.383325i | \(-0.125221\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9443 | −0.434137 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.8328i | 0.496639i | ||||||||
\(893\) | − 32.0000i | − 1.07084i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.6525 | 0.522913 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.3050i | 1.04466i | ||||||||
\(899\) | −20.9443 | −0.698531 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.9443 | 0.831014 | ||||||||
\(902\) | − 11.0557i | − 0.368115i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.9443 | 0.630077 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.1115i | 0.601381i | 0.953722 | + | 0.300691i | \(0.0972171\pi\) | ||||
−0.953722 | + | 0.300691i | \(0.902783\pi\) | |||||||
\(908\) | − 50.8328i | − 1.68695i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.2492 | 1.13473 | 0.567364 | − | 0.823467i | \(-0.307963\pi\) | ||||
0.567364 | + | 0.823467i | \(0.307963\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.33437i | 0.0772563i | ||||||||
\(914\) | −24.4721 | −0.809466 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.6656 | −1.17843 | ||||||||
\(917\) | − 4.00000i | − 0.132092i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.9443 | 1.74647 | 0.873235 | − | 0.487299i | \(-0.162018\pi\) | ||||
0.873235 | + | 0.487299i | \(0.162018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 71.3050i | − 2.34830i | ||||||||
\(923\) | − 64.7214i | − 2.13033i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.83282 | −0.224540 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 13.4164i | − 0.440415i | ||||||||
\(929\) | −51.8885 | −1.70241 | −0.851204 | − | 0.524835i | \(-0.824127\pi\) | ||||
−0.851204 | + | 0.524835i | \(0.824127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.47214 | 0.212116 | ||||||||
\(932\) | − 52.2492i | − 1.71148i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.0000 | −0.654420 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 43.5279i | − 1.42199i | −0.703195 | − | 0.710997i | \(-0.748244\pi\) | ||||
0.703195 | − | 0.710997i | \(-0.251756\pi\) | |||||||
\(938\) | − 8.94427i | − 0.292041i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000i | 0.260516i | ||||||||
\(944\) | −8.94427 | −0.291111 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.4427 | 1.60752 | ||||||||
\(947\) | − 17.8885i | − 0.581300i | −0.956830 | − | 0.290650i | \(-0.906129\pi\) | ||||
0.956830 | − | 0.290650i | \(-0.0938715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.7771 | −0.512146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 4.47214i | − 0.144943i | ||||||||
\(953\) | − 6.58359i | − 0.213263i | −0.994299 | − | 0.106632i | \(-0.965993\pi\) | ||||
0.994299 | − | 0.106632i | \(-0.0340066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.58359 | 0.148244 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 40.0000i | − 1.29234i | ||||||||
\(959\) | 12.4721 | 0.402746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.6656 | 2.53760 | ||||||||
\(962\) | 109.443i | 3.52857i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.16718 | 0.102008 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 9.88854i | − 0.317994i | −0.987279 | − | 0.158997i | \(-0.949174\pi\) | ||||
0.987279 | − | 0.158997i | \(-0.0508260\pi\) | |||||||
\(968\) | − 10.9311i | − 0.351339i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.0557 | −0.739894 | −0.369947 | − | 0.929053i | \(-0.620624\pi\) | ||||
−0.369947 | + | 0.929053i | \(0.620624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.4164i | 0.622461i | ||||||||
\(974\) | −6.83282 | −0.218938 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | − 57.4164i | − 1.83691i | −0.395521 | − | 0.918457i | \(-0.629436\pi\) | ||||
0.395521 | − | 0.918457i | \(-0.370564\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.94427 | −0.158020 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 92.3607i | 2.94735i | ||||||||
\(983\) | 30.8328i | 0.983414i | 0.870761 | + | 0.491707i | \(0.163627\pi\) | ||||
−0.870761 | + | 0.491707i | \(0.836373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.94427 | −0.284844 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 86.8328i | 2.76252i | ||||||||
\(989\) | −35.7771 | −1.13765 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9443 | −0.411188 | −0.205594 | − | 0.978637i | \(-0.565913\pi\) | ||||
−0.205594 | + | 0.978637i | \(0.565913\pi\) | |||||||
\(992\) | 70.2492i | 2.23042i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.3607 | −1.02642 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.4164i | 0.678264i | 0.940739 | + | 0.339132i | \(0.110133\pi\) | ||||
−0.940739 | + | 0.339132i | \(0.889867\pi\) | |||||||
\(998\) | 48.9443i | 1.54930i | ||||||||
\(999\) | 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 | 1575.2.d.d.1324.2 | 4 | ||
3.2 | odd | 2 | 525.2.d.c.274.4 | 4 | |||
5.2 | odd | 4 | 1575.2.a.r.1.2 | 2 | |||
5.3 | odd | 4 | 315.2.a.d.1.1 | 2 | |||
5.4 | even | 2 | inner | 1575.2.d.d.1324.3 | 4 | ||
15.2 | even | 4 | 525.2.a.g.1.1 | 2 | |||
15.8 | even | 4 | 105.2.a.b.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 525.2.d.c.274.1 | 4 | |||
20.3 | even | 4 | 5040.2.a.bw.1.1 | 2 | |||
35.13 | even | 4 | 2205.2.a.w.1.1 | 2 | |||
60.23 | odd | 4 | 1680.2.a.v.1.2 | 2 | |||
60.47 | odd | 4 | 8400.2.a.cx.1.2 | 2 | |||
105.23 | even | 12 | 735.2.i.k.361.1 | 4 | |||
105.38 | odd | 12 | 735.2.i.i.226.1 | 4 | |||
105.53 | even | 12 | 735.2.i.k.226.1 | 4 | |||
105.62 | odd | 4 | 3675.2.a.y.1.1 | 2 | |||
105.68 | odd | 12 | 735.2.i.i.361.1 | 4 | |||
105.83 | odd | 4 | 735.2.a.k.1.2 | 2 | |||
120.53 | even | 4 | 6720.2.a.cx.1.2 | 2 | |||
120.83 | odd | 4 | 6720.2.a.cs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.a.b.1.2 | ✓ | 2 | 15.8 | even | 4 | ||
315.2.a.d.1.1 | 2 | 5.3 | odd | 4 | |||
525.2.a.g.1.1 | 2 | 15.2 | even | 4 | |||
525.2.d.c.274.1 | 4 | 15.14 | odd | 2 | |||
525.2.d.c.274.4 | 4 | 3.2 | odd | 2 | |||
735.2.a.k.1.2 | 2 | 105.83 | odd | 4 | |||
735.2.i.i.226.1 | 4 | 105.38 | odd | 12 | |||
735.2.i.i.361.1 | 4 | 105.68 | odd | 12 | |||
735.2.i.k.226.1 | 4 | 105.53 | even | 12 | |||
735.2.i.k.361.1 | 4 | 105.23 | even | 12 | |||
1575.2.a.r.1.2 | 2 | 5.2 | odd | 4 | |||
1575.2.d.d.1324.2 | 4 | 1.1 | even | 1 | trivial | ||
1575.2.d.d.1324.3 | 4 | 5.4 | even | 2 | inner | ||
1680.2.a.v.1.2 | 2 | 60.23 | odd | 4 | |||
2205.2.a.w.1.1 | 2 | 35.13 | even | 4 | |||
3675.2.a.y.1.1 | 2 | 105.62 | odd | 4 | |||
5040.2.a.bw.1.1 | 2 | 20.3 | even | 4 | |||
6720.2.a.cs.1.1 | 2 | 120.83 | odd | 4 | |||
6720.2.a.cx.1.2 | 2 | 120.53 | even | 4 | |||
8400.2.a.cx.1.2 | 2 | 60.47 | odd | 4 |