Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2366.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.a (trivial) |
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: | yes |
Analytic conductor: | \(18.8926051182\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1384.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 10x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.30590\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.30590 | −1.90866 | −0.954330 | − | 0.298753i | \(-0.903429\pi\) | ||||
−0.954330 | + | 0.298753i | \(0.903429\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.376939 | −0.168572 | −0.0842861 | − | 0.996442i | \(-0.526861\pi\) | ||||
−0.0842861 | + | 0.996442i | \(0.526861\pi\) | |||||||
\(6\) | 3.30590 | 1.34963 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.92896 | 2.64299 | ||||||||
\(10\) | 0.376939 | 0.119199 | ||||||||
\(11\) | −5.68284 | −1.71344 | −0.856720 | − | 0.515782i | \(-0.827501\pi\) | ||||
−0.856720 | + | 0.515782i | \(0.827501\pi\) | |||||||
\(12\) | −3.30590 | −0.954330 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.24612 | 0.321747 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.24612 | 0.302229 | 0.151114 | − | 0.988516i | \(-0.451714\pi\) | ||||
0.151114 | + | 0.988516i | \(0.451714\pi\) | |||||||
\(18\) | −7.92896 | −1.86887 | ||||||||
\(19\) | −1.62306 | −0.372356 | −0.186178 | − | 0.982516i | \(-0.559610\pi\) | ||||
−0.186178 | + | 0.982516i | \(0.559610\pi\) | |||||||
\(20\) | −0.376939 | −0.0842861 | ||||||||
\(21\) | 3.30590 | 0.721406 | ||||||||
\(22\) | 5.68284 | 1.21158 | ||||||||
\(23\) | 4.92896 | 1.02776 | 0.513879 | − | 0.857862i | \(-0.328208\pi\) | ||||
0.513879 | + | 0.857862i | \(0.328208\pi\) | |||||||
\(24\) | 3.30590 | 0.674814 | ||||||||
\(25\) | −4.85792 | −0.971583 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.2946 | −3.13590 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −4.61180 | −0.856389 | −0.428194 | − | 0.903687i | \(-0.640850\pi\) | ||||
−0.428194 | + | 0.903687i | \(0.640850\pi\) | |||||||
\(30\) | −1.24612 | −0.227510 | ||||||||
\(31\) | 5.68284 | 1.02067 | 0.510334 | − | 0.859976i | \(-0.329522\pi\) | ||||
0.510334 | + | 0.859976i | \(0.329522\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 18.7869 | 3.27038 | ||||||||
\(34\) | −1.24612 | −0.213708 | ||||||||
\(35\) | 0.376939 | 0.0637143 | ||||||||
\(36\) | 7.92896 | 1.32149 | ||||||||
\(37\) | −6.92896 | −1.13911 | −0.569557 | − | 0.821952i | \(-0.692885\pi\) | ||||
−0.569557 | + | 0.821952i | \(0.692885\pi\) | |||||||
\(38\) | 1.62306 | 0.263295 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.376939 | 0.0595993 | ||||||||
\(41\) | 1.07104 | 0.167269 | 0.0836343 | − | 0.996497i | \(-0.473347\pi\) | ||||
0.0836343 | + | 0.996497i | \(0.473347\pi\) | |||||||
\(42\) | −3.30590 | −0.510111 | ||||||||
\(43\) | −3.24612 | −0.495029 | −0.247514 | − | 0.968884i | \(-0.579614\pi\) | ||||
−0.247514 | + | 0.968884i | \(0.579614\pi\) | |||||||
\(44\) | −5.68284 | −0.856720 | ||||||||
\(45\) | −2.98873 | −0.445534 | ||||||||
\(46\) | −4.92896 | −0.726735 | ||||||||
\(47\) | −2.31716 | −0.337993 | −0.168997 | − | 0.985617i | \(-0.554053\pi\) | ||||
−0.168997 | + | 0.985617i | \(0.554053\pi\) | |||||||
\(48\) | −3.30590 | −0.477165 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.85792 | 0.687013 | ||||||||
\(51\) | −4.11955 | −0.576853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 16.2946 | 2.21742 | ||||||||
\(55\) | 2.14208 | 0.288838 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 5.36567 | 0.710701 | ||||||||
\(58\) | 4.61180 | 0.605558 | ||||||||
\(59\) | −11.4810 | −1.49470 | −0.747348 | − | 0.664433i | \(-0.768673\pi\) | ||||
−0.747348 | + | 0.664433i | \(0.768673\pi\) | |||||||
\(60\) | 1.24612 | 0.160874 | ||||||||
\(61\) | 5.30590 | 0.679351 | 0.339675 | − | 0.940543i | \(-0.389683\pi\) | ||||
0.339675 | + | 0.940543i | \(0.389683\pi\) | |||||||
\(62\) | −5.68284 | −0.721721 | ||||||||
\(63\) | −7.92896 | −0.998955 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −18.7869 | −2.31250 | ||||||||
\(67\) | −8.92896 | −1.09085 | −0.545423 | − | 0.838161i | \(-0.683631\pi\) | ||||
−0.545423 | + | 0.838161i | \(0.683631\pi\) | |||||||
\(68\) | 1.24612 | 0.151114 | ||||||||
\(69\) | −16.2946 | −1.96164 | ||||||||
\(70\) | −0.376939 | −0.0450528 | ||||||||
\(71\) | −13.2236 | −1.56935 | −0.784676 | − | 0.619906i | \(-0.787171\pi\) | ||||
−0.784676 | + | 0.619906i | \(0.787171\pi\) | |||||||
\(72\) | −7.92896 | −0.934437 | ||||||||
\(73\) | 0.317163 | 0.0371212 | 0.0185606 | − | 0.999828i | \(-0.494092\pi\) | ||||
0.0185606 | + | 0.999828i | \(0.494092\pi\) | |||||||
\(74\) | 6.92896 | 0.805475 | ||||||||
\(75\) | 16.0598 | 1.85442 | ||||||||
\(76\) | −1.62306 | −0.186178 | ||||||||
\(77\) | 5.68284 | 0.647619 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.17508 | 0.244716 | 0.122358 | − | 0.992486i | \(-0.460954\pi\) | ||||
0.122358 | + | 0.992486i | \(0.460954\pi\) | |||||||
\(80\) | −0.376939 | −0.0421431 | ||||||||
\(81\) | 30.0815 | 3.34239 | ||||||||
\(82\) | −1.07104 | −0.118277 | ||||||||
\(83\) | −9.74261 | −1.06939 | −0.534695 | − | 0.845045i | \(-0.679574\pi\) | ||||
−0.534695 | + | 0.845045i | \(0.679574\pi\) | |||||||
\(84\) | 3.30590 | 0.360703 | ||||||||
\(85\) | −0.469712 | −0.0509474 | ||||||||
\(86\) | 3.24612 | 0.350038 | ||||||||
\(87\) | 15.2461 | 1.63456 | ||||||||
\(88\) | 5.68284 | 0.605792 | ||||||||
\(89\) | 9.24612 | 0.980087 | 0.490043 | − | 0.871698i | \(-0.336981\pi\) | ||||
0.490043 | + | 0.871698i | \(0.336981\pi\) | |||||||
\(90\) | 2.98873 | 0.315040 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.92896 | 0.513879 | ||||||||
\(93\) | −18.7869 | −1.94811 | ||||||||
\(94\) | 2.31716 | 0.238997 | ||||||||
\(95\) | 0.611795 | 0.0627688 | ||||||||
\(96\) | 3.30590 | 0.337407 | ||||||||
\(97\) | 10.9290 | 1.10967 | 0.554834 | − | 0.831961i | \(-0.312782\pi\) | ||||
0.554834 | + | 0.831961i | \(0.312782\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −45.0590 | −4.52860 | ||||||||
\(100\) | −4.85792 | −0.485792 | ||||||||
\(101\) | 3.44798 | 0.343087 | 0.171543 | − | 0.985177i | \(-0.445125\pi\) | ||||
0.171543 | + | 0.985177i | \(0.445125\pi\) | |||||||
\(102\) | 4.11955 | 0.407896 | ||||||||
\(103\) | −7.24612 | −0.713982 | −0.356991 | − | 0.934108i | \(-0.616197\pi\) | ||||
−0.356991 | + | 0.934108i | \(0.616197\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.24612 | −0.121609 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −9.85792 | −0.953001 | −0.476500 | − | 0.879174i | \(-0.658095\pi\) | ||||
−0.476500 | + | 0.879174i | \(0.658095\pi\) | |||||||
\(108\) | −16.2946 | −1.56795 | ||||||||
\(109\) | 11.2236 | 1.07502 | 0.537512 | − | 0.843256i | \(-0.319364\pi\) | ||||
0.537512 | + | 0.843256i | \(0.319364\pi\) | |||||||
\(110\) | −2.14208 | −0.204240 | ||||||||
\(111\) | 22.9064 | 2.17418 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −4.92896 | −0.463677 | −0.231839 | − | 0.972754i | \(-0.574474\pi\) | ||||
−0.231839 | + | 0.972754i | \(0.574474\pi\) | |||||||
\(114\) | −5.36567 | −0.502541 | ||||||||
\(115\) | −1.85792 | −0.173252 | ||||||||
\(116\) | −4.61180 | −0.428194 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.4810 | 1.05691 | ||||||||
\(119\) | −1.24612 | −0.114232 | ||||||||
\(120\) | −1.24612 | −0.113755 | ||||||||
\(121\) | 21.2946 | 1.93588 | ||||||||
\(122\) | −5.30590 | −0.480373 | ||||||||
\(123\) | −3.54075 | −0.319259 | ||||||||
\(124\) | 5.68284 | 0.510334 | ||||||||
\(125\) | 3.71583 | 0.332354 | ||||||||
\(126\) | 7.92896 | 0.706368 | ||||||||
\(127\) | −8.29463 | −0.736030 | −0.368015 | − | 0.929820i | \(-0.619962\pi\) | ||||
−0.368015 | + | 0.929820i | \(0.619962\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.7313 | 0.944842 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3544 | 1.42889 | 0.714446 | − | 0.699691i | \(-0.246679\pi\) | ||||
0.714446 | + | 0.699691i | \(0.246679\pi\) | |||||||
\(132\) | 18.7869 | 1.63519 | ||||||||
\(133\) | 1.62306 | 0.140737 | ||||||||
\(134\) | 8.92896 | 0.771345 | ||||||||
\(135\) | 6.14208 | 0.528626 | ||||||||
\(136\) | −1.24612 | −0.106854 | ||||||||
\(137\) | −13.2236 | −1.12977 | −0.564884 | − | 0.825170i | \(-0.691079\pi\) | ||||
−0.564884 | + | 0.825170i | \(0.691079\pi\) | |||||||
\(138\) | 16.2946 | 1.38709 | ||||||||
\(139\) | 1.62306 | 0.137666 | 0.0688331 | − | 0.997628i | \(-0.478072\pi\) | ||||
0.0688331 | + | 0.997628i | \(0.478072\pi\) | |||||||
\(140\) | 0.376939 | 0.0318572 | ||||||||
\(141\) | 7.66030 | 0.645114 | ||||||||
\(142\) | 13.2236 | 1.10970 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.92896 | 0.660747 | ||||||||
\(145\) | 1.73837 | 0.144363 | ||||||||
\(146\) | −0.317163 | −0.0262486 | ||||||||
\(147\) | −3.30590 | −0.272666 | ||||||||
\(148\) | −6.92896 | −0.569557 | ||||||||
\(149\) | 9.54075 | 0.781609 | 0.390804 | − | 0.920474i | \(-0.372197\pi\) | ||||
0.390804 | + | 0.920474i | \(0.372197\pi\) | |||||||
\(150\) | −16.0598 | −1.31128 | ||||||||
\(151\) | 2.75388 | 0.224107 | 0.112054 | − | 0.993702i | \(-0.464257\pi\) | ||||
0.112054 | + | 0.993702i | \(0.464257\pi\) | |||||||
\(152\) | 1.62306 | 0.131648 | ||||||||
\(153\) | 9.88045 | 0.798787 | ||||||||
\(154\) | −5.68284 | −0.457936 | ||||||||
\(155\) | −2.14208 | −0.172056 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.5295 | 1.79805 | 0.899024 | − | 0.437898i | \(-0.144277\pi\) | ||||
0.899024 | + | 0.437898i | \(0.144277\pi\) | |||||||
\(158\) | −2.17508 | −0.173040 | ||||||||
\(159\) | 19.8354 | 1.57305 | ||||||||
\(160\) | 0.376939 | 0.0297996 | ||||||||
\(161\) | −4.92896 | −0.388456 | ||||||||
\(162\) | −30.0815 | −2.36343 | ||||||||
\(163\) | 8.46971 | 0.663399 | 0.331700 | − | 0.943385i | \(-0.392378\pi\) | ||||
0.331700 | + | 0.943385i | \(0.392378\pi\) | |||||||
\(164\) | 1.07104 | 0.0836343 | ||||||||
\(165\) | −7.08151 | −0.551295 | ||||||||
\(166\) | 9.74261 | 0.756173 | ||||||||
\(167\) | −5.97747 | −0.462550 | −0.231275 | − | 0.972888i | \(-0.574290\pi\) | ||||
−0.231275 | + | 0.972888i | \(0.574290\pi\) | |||||||
\(168\) | −3.30590 | −0.255056 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.469712 | 0.0360253 | ||||||||
\(171\) | −12.8692 | −0.984131 | ||||||||
\(172\) | −3.24612 | −0.247514 | ||||||||
\(173\) | 0.846651 | 0.0643697 | 0.0321848 | − | 0.999482i | \(-0.489753\pi\) | ||||
0.0321848 | + | 0.999482i | \(0.489753\pi\) | |||||||
\(174\) | −15.2461 | −1.15581 | ||||||||
\(175\) | 4.85792 | 0.367224 | ||||||||
\(176\) | −5.68284 | −0.428360 | ||||||||
\(177\) | 37.9549 | 2.85287 | ||||||||
\(178\) | −9.24612 | −0.693026 | ||||||||
\(179\) | 18.7313 | 1.40005 | 0.700023 | − | 0.714120i | \(-0.253173\pi\) | ||||
0.700023 | + | 0.714120i | \(0.253173\pi\) | |||||||
\(180\) | −2.98873 | −0.222767 | ||||||||
\(181\) | 17.6561 | 1.31236 | 0.656182 | − | 0.754602i | \(-0.272170\pi\) | ||||
0.656182 | + | 0.754602i | \(0.272170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.5408 | −1.29665 | ||||||||
\(184\) | −4.92896 | −0.363368 | ||||||||
\(185\) | 2.61180 | 0.192023 | ||||||||
\(186\) | 18.7869 | 1.37752 | ||||||||
\(187\) | −7.08151 | −0.517851 | ||||||||
\(188\) | −2.31716 | −0.168997 | ||||||||
\(189\) | 16.2946 | 1.18526 | ||||||||
\(190\) | −0.611795 | −0.0443843 | ||||||||
\(191\) | 16.6118 | 1.20199 | 0.600994 | − | 0.799254i | \(-0.294772\pi\) | ||||
0.600994 | + | 0.799254i | \(0.294772\pi\) | |||||||
\(192\) | −3.30590 | −0.238583 | ||||||||
\(193\) | 3.85792 | 0.277699 | 0.138849 | − | 0.990313i | \(-0.455660\pi\) | ||||
0.138849 | + | 0.990313i | \(0.455660\pi\) | |||||||
\(194\) | −10.9290 | −0.784653 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −6.17508 | −0.439956 | −0.219978 | − | 0.975505i | \(-0.570599\pi\) | ||||
−0.219978 | + | 0.975505i | \(0.570599\pi\) | |||||||
\(198\) | 45.0590 | 3.20220 | ||||||||
\(199\) | 4.75388 | 0.336993 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(200\) | 4.85792 | 0.343507 | ||||||||
\(201\) | 29.5182 | 2.08205 | ||||||||
\(202\) | −3.44798 | −0.242599 | ||||||||
\(203\) | 4.61180 | 0.323685 | ||||||||
\(204\) | −4.11955 | −0.288426 | ||||||||
\(205\) | −0.403717 | −0.0281968 | ||||||||
\(206\) | 7.24612 | 0.504861 | ||||||||
\(207\) | 39.0815 | 2.71635 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.22359 | 0.638009 | ||||||||
\(210\) | 1.24612 | 0.0859906 | ||||||||
\(211\) | 27.7158 | 1.90804 | 0.954018 | − | 0.299748i | \(-0.0969027\pi\) | ||||
0.954018 | + | 0.299748i | \(0.0969027\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 43.7158 | 2.99536 | ||||||||
\(214\) | 9.85792 | 0.673873 | ||||||||
\(215\) | 1.22359 | 0.0834482 | ||||||||
\(216\) | 16.2946 | 1.10871 | ||||||||
\(217\) | −5.68284 | −0.385776 | ||||||||
\(218\) | −11.2236 | −0.760157 | ||||||||
\(219\) | −1.04851 | −0.0708517 | ||||||||
\(220\) | 2.14208 | 0.144419 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −22.9064 | −1.53738 | ||||||||
\(223\) | 8.29463 | 0.555450 | 0.277725 | − | 0.960661i | \(-0.410420\pi\) | ||||
0.277725 | + | 0.960661i | \(0.410420\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −38.5182 | −2.56788 | ||||||||
\(226\) | 4.92896 | 0.327869 | ||||||||
\(227\) | −0.234856 | −0.0155879 | −0.00779397 | − | 0.999970i | \(-0.502481\pi\) | ||||
−0.00779397 | + | 0.999970i | \(0.502481\pi\) | |||||||
\(228\) | 5.36567 | 0.355350 | ||||||||
\(229\) | 19.4584 | 1.28585 | 0.642925 | − | 0.765929i | \(-0.277721\pi\) | ||||
0.642925 | + | 0.765929i | \(0.277721\pi\) | |||||||
\(230\) | 1.85792 | 0.122507 | ||||||||
\(231\) | −18.7869 | −1.23609 | ||||||||
\(232\) | 4.61180 | 0.302779 | ||||||||
\(233\) | −20.1525 | −1.32024 | −0.660119 | − | 0.751161i | \(-0.729494\pi\) | ||||
−0.660119 | + | 0.751161i | \(0.729494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.873429 | 0.0569763 | ||||||||
\(236\) | −11.4810 | −0.747348 | ||||||||
\(237\) | −7.19059 | −0.467079 | ||||||||
\(238\) | 1.24612 | 0.0807741 | ||||||||
\(239\) | 12.9620 | 0.838439 | 0.419220 | − | 0.907885i | \(-0.362304\pi\) | ||||
0.419220 | + | 0.907885i | \(0.362304\pi\) | |||||||
\(240\) | 1.24612 | 0.0804368 | ||||||||
\(241\) | −8.73135 | −0.562435 | −0.281218 | − | 0.959644i | \(-0.590738\pi\) | ||||
−0.281218 | + | 0.959644i | \(0.590738\pi\) | |||||||
\(242\) | −21.2946 | −1.36887 | ||||||||
\(243\) | −50.5625 | −3.24358 | ||||||||
\(244\) | 5.30590 | 0.339675 | ||||||||
\(245\) | −0.376939 | −0.0240818 | ||||||||
\(246\) | 3.54075 | 0.225750 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.68284 | −0.360860 | ||||||||
\(249\) | 32.2081 | 2.04110 | ||||||||
\(250\) | −3.71583 | −0.235010 | ||||||||
\(251\) | −5.04426 | −0.318391 | −0.159196 | − | 0.987247i | \(-0.550890\pi\) | ||||
−0.159196 | + | 0.987247i | \(0.550890\pi\) | |||||||
\(252\) | −7.92896 | −0.499477 | ||||||||
\(253\) | −28.0105 | −1.76100 | ||||||||
\(254\) | 8.29463 | 0.520451 | ||||||||
\(255\) | 1.55282 | 0.0972413 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.2236 | −1.44865 | −0.724324 | − | 0.689460i | \(-0.757848\pi\) | ||||
−0.724324 | + | 0.689460i | \(0.757848\pi\) | |||||||
\(258\) | −10.7313 | −0.668104 | ||||||||
\(259\) | 6.92896 | 0.430545 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −36.5667 | −2.26342 | ||||||||
\(262\) | −16.3544 | −1.01038 | ||||||||
\(263\) | −11.1040 | −0.684704 | −0.342352 | − | 0.939572i | \(-0.611224\pi\) | ||||
−0.342352 | + | 0.939572i | \(0.611224\pi\) | |||||||
\(264\) | −18.7869 | −1.15625 | ||||||||
\(265\) | 2.26163 | 0.138931 | ||||||||
\(266\) | −1.62306 | −0.0995163 | ||||||||
\(267\) | −30.5667 | −1.87065 | ||||||||
\(268\) | −8.92896 | −0.545423 | ||||||||
\(269\) | 11.5675 | 0.705285 | 0.352642 | − | 0.935758i | \(-0.385283\pi\) | ||||
0.352642 | + | 0.935758i | \(0.385283\pi\) | |||||||
\(270\) | −6.14208 | −0.373795 | ||||||||
\(271\) | −26.1525 | −1.58865 | −0.794327 | − | 0.607490i | \(-0.792176\pi\) | ||||
−0.794327 | + | 0.607490i | \(0.792176\pi\) | |||||||
\(272\) | 1.24612 | 0.0755572 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.2236 | 0.798866 | ||||||||
\(275\) | 27.6067 | 1.66475 | ||||||||
\(276\) | −16.2946 | −0.980822 | ||||||||
\(277\) | 23.2236 | 1.39537 | 0.697685 | − | 0.716405i | \(-0.254213\pi\) | ||||
0.697685 | + | 0.716405i | \(0.254213\pi\) | |||||||
\(278\) | −1.62306 | −0.0973447 | ||||||||
\(279\) | 45.0590 | 2.69761 | ||||||||
\(280\) | −0.376939 | −0.0225264 | ||||||||
\(281\) | −17.2236 | −1.02747 | −0.513737 | − | 0.857948i | \(-0.671739\pi\) | ||||
−0.513737 | + | 0.857948i | \(0.671739\pi\) | |||||||
\(282\) | −7.66030 | −0.456165 | ||||||||
\(283\) | −19.7756 | −1.17554 | −0.587769 | − | 0.809029i | \(-0.699994\pi\) | ||||
−0.587769 | + | 0.809029i | \(0.699994\pi\) | |||||||
\(284\) | −13.2236 | −0.784676 | ||||||||
\(285\) | −2.02253 | −0.119804 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.07104 | −0.0632216 | ||||||||
\(288\) | −7.92896 | −0.467218 | ||||||||
\(289\) | −15.4472 | −0.908658 | ||||||||
\(290\) | −1.73837 | −0.102080 | ||||||||
\(291\) | −36.1300 | −2.11798 | ||||||||
\(292\) | 0.317163 | 0.0185606 | ||||||||
\(293\) | 1.13082 | 0.0660630 | 0.0330315 | − | 0.999454i | \(-0.489484\pi\) | ||||
0.0330315 | + | 0.999454i | \(0.489484\pi\) | |||||||
\(294\) | 3.30590 | 0.192804 | ||||||||
\(295\) | 4.32763 | 0.251964 | ||||||||
\(296\) | 6.92896 | 0.402738 | ||||||||
\(297\) | 92.5997 | 5.37318 | ||||||||
\(298\) | −9.54075 | −0.552681 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 16.0598 | 0.927212 | ||||||||
\(301\) | 3.24612 | 0.187103 | ||||||||
\(302\) | −2.75388 | −0.158468 | ||||||||
\(303\) | −11.3987 | −0.654837 | ||||||||
\(304\) | −1.62306 | −0.0930889 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | −9.88045 | −0.564828 | ||||||||
\(307\) | 30.9662 | 1.76733 | 0.883667 | − | 0.468116i | \(-0.155067\pi\) | ||||
0.883667 | + | 0.468116i | \(0.155067\pi\) | |||||||
\(308\) | 5.68284 | 0.323810 | ||||||||
\(309\) | 23.9549 | 1.36275 | ||||||||
\(310\) | 2.14208 | 0.121662 | ||||||||
\(311\) | 9.50776 | 0.539135 | 0.269568 | − | 0.962981i | \(-0.413119\pi\) | ||||
0.269568 | + | 0.962981i | \(0.413119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.38820 | 0.191513 | 0.0957563 | − | 0.995405i | \(-0.469473\pi\) | ||||
0.0957563 | + | 0.995405i | \(0.469473\pi\) | |||||||
\(314\) | −22.5295 | −1.27141 | ||||||||
\(315\) | 2.98873 | 0.168396 | ||||||||
\(316\) | 2.17508 | 0.122358 | ||||||||
\(317\) | 29.5408 | 1.65917 | 0.829587 | − | 0.558377i | \(-0.188576\pi\) | ||||
0.829587 | + | 0.558377i | \(0.188576\pi\) | |||||||
\(318\) | −19.8354 | −1.11231 | ||||||||
\(319\) | 26.2081 | 1.46737 | ||||||||
\(320\) | −0.376939 | −0.0210715 | ||||||||
\(321\) | 32.5893 | 1.81896 | ||||||||
\(322\) | 4.92896 | 0.274680 | ||||||||
\(323\) | −2.02253 | −0.112537 | ||||||||
\(324\) | 30.0815 | 1.67119 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.46971 | −0.469094 | ||||||||
\(327\) | −37.1040 | −2.05186 | ||||||||
\(328\) | −1.07104 | −0.0591384 | ||||||||
\(329\) | 2.31716 | 0.127749 | ||||||||
\(330\) | 7.08151 | 0.389824 | ||||||||
\(331\) | −0.175080 | −0.00962329 | −0.00481164 | − | 0.999988i | \(-0.501532\pi\) | ||||
−0.00481164 | + | 0.999988i | \(0.501532\pi\) | |||||||
\(332\) | −9.74261 | −0.534695 | ||||||||
\(333\) | −54.9394 | −3.01066 | ||||||||
\(334\) | 5.97747 | 0.327073 | ||||||||
\(335\) | 3.36567 | 0.183886 | ||||||||
\(336\) | 3.30590 | 0.180351 | ||||||||
\(337\) | −19.3761 | −1.05549 | −0.527743 | − | 0.849404i | \(-0.676961\pi\) | ||||
−0.527743 | + | 0.849404i | \(0.676961\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.2946 | 0.885003 | ||||||||
\(340\) | −0.469712 | −0.0254737 | ||||||||
\(341\) | −32.2946 | −1.74885 | ||||||||
\(342\) | 12.8692 | 0.695886 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.24612 | 0.175019 | ||||||||
\(345\) | 6.14208 | 0.330679 | ||||||||
\(346\) | −0.846651 | −0.0455162 | ||||||||
\(347\) | 24.4697 | 1.31360 | 0.656801 | − | 0.754064i | \(-0.271909\pi\) | ||||
0.656801 | + | 0.754064i | \(0.271909\pi\) | |||||||
\(348\) | 15.2461 | 0.817278 | ||||||||
\(349\) | 11.8622 | 0.634967 | 0.317484 | − | 0.948264i | \(-0.397162\pi\) | ||||
0.317484 | + | 0.948264i | \(0.397162\pi\) | |||||||
\(350\) | −4.85792 | −0.259667 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.68284 | 0.302896 | ||||||||
\(353\) | 1.82492 | 0.0971307 | 0.0485653 | − | 0.998820i | \(-0.484535\pi\) | ||||
0.0485653 | + | 0.998820i | \(0.484535\pi\) | |||||||
\(354\) | −37.9549 | −2.01728 | ||||||||
\(355\) | 4.98449 | 0.264549 | ||||||||
\(356\) | 9.24612 | 0.490043 | ||||||||
\(357\) | 4.11955 | 0.218030 | ||||||||
\(358\) | −18.7313 | −0.989982 | ||||||||
\(359\) | −7.62731 | −0.402554 | −0.201277 | − | 0.979534i | \(-0.564509\pi\) | ||||
−0.201277 | + | 0.979534i | \(0.564509\pi\) | |||||||
\(360\) | 2.98873 | 0.157520 | ||||||||
\(361\) | −16.3657 | −0.861351 | ||||||||
\(362\) | −17.6561 | −0.927982 | ||||||||
\(363\) | −70.3979 | −3.69493 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.119551 | −0.00625760 | ||||||||
\(366\) | 17.5408 | 0.916870 | ||||||||
\(367\) | 17.2236 | 0.899064 | 0.449532 | − | 0.893264i | \(-0.351591\pi\) | ||||
0.449532 | + | 0.893264i | \(0.351591\pi\) | |||||||
\(368\) | 4.92896 | 0.256940 | ||||||||
\(369\) | 8.49224 | 0.442089 | ||||||||
\(370\) | −2.61180 | −0.135781 | ||||||||
\(371\) | 6.00000 | 0.311504 | ||||||||
\(372\) | −18.7869 | −0.974054 | ||||||||
\(373\) | −8.77641 | −0.454425 | −0.227213 | − | 0.973845i | \(-0.572961\pi\) | ||||
−0.227213 | + | 0.973845i | \(0.572961\pi\) | |||||||
\(374\) | 7.08151 | 0.366176 | ||||||||
\(375\) | −12.2842 | −0.634352 | ||||||||
\(376\) | 2.31716 | 0.119499 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −16.2946 | −0.838105 | ||||||||
\(379\) | −17.7384 | −0.911159 | −0.455579 | − | 0.890195i | \(-0.650568\pi\) | ||||
−0.455579 | + | 0.890195i | \(0.650568\pi\) | |||||||
\(380\) | 0.611795 | 0.0313844 | ||||||||
\(381\) | 27.4212 | 1.40483 | ||||||||
\(382\) | −16.6118 | −0.849933 | ||||||||
\(383\) | 32.7643 | 1.67418 | 0.837090 | − | 0.547065i | \(-0.184255\pi\) | ||||
0.837090 | + | 0.547065i | \(0.184255\pi\) | |||||||
\(384\) | 3.30590 | 0.168703 | ||||||||
\(385\) | −2.14208 | −0.109171 | ||||||||
\(386\) | −3.85792 | −0.196363 | ||||||||
\(387\) | −25.7384 | −1.30835 | ||||||||
\(388\) | 10.9290 | 0.554834 | ||||||||
\(389\) | −12.2616 | −0.621690 | −0.310845 | − | 0.950461i | \(-0.600612\pi\) | ||||
−0.310845 | + | 0.950461i | \(0.600612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.14208 | 0.310618 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −54.0660 | −2.72727 | ||||||||
\(394\) | 6.17508 | 0.311096 | ||||||||
\(395\) | −0.819873 | −0.0412523 | ||||||||
\(396\) | −45.0590 | −2.26430 | ||||||||
\(397\) | −22.5850 | −1.13351 | −0.566755 | − | 0.823887i | \(-0.691801\pi\) | ||||
−0.566755 | + | 0.823887i | \(0.691801\pi\) | |||||||
\(398\) | −4.75388 | −0.238290 | ||||||||
\(399\) | −5.36567 | −0.268620 | ||||||||
\(400\) | −4.85792 | −0.242896 | ||||||||
\(401\) | 27.8579 | 1.39116 | 0.695579 | − | 0.718450i | \(-0.255148\pi\) | ||||
0.695579 | + | 0.718450i | \(0.255148\pi\) | |||||||
\(402\) | −29.5182 | −1.47224 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.44798 | 0.171543 | ||||||||
\(405\) | −11.3389 | −0.563434 | ||||||||
\(406\) | −4.61180 | −0.228880 | ||||||||
\(407\) | 39.3761 | 1.95180 | ||||||||
\(408\) | 4.11955 | 0.203948 | ||||||||
\(409\) | −16.7313 | −0.827312 | −0.413656 | − | 0.910433i | \(-0.635748\pi\) | ||||
−0.413656 | + | 0.910433i | \(0.635748\pi\) | |||||||
\(410\) | 0.403717 | 0.0199382 | ||||||||
\(411\) | 43.7158 | 2.15634 | ||||||||
\(412\) | −7.24612 | −0.356991 | ||||||||
\(413\) | 11.4810 | 0.564942 | ||||||||
\(414\) | −39.0815 | −1.92075 | ||||||||
\(415\) | 3.67237 | 0.180270 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.36567 | −0.262758 | ||||||||
\(418\) | −9.22359 | −0.451141 | ||||||||
\(419\) | −11.7756 | −0.575276 | −0.287638 | − | 0.957739i | \(-0.592870\pi\) | ||||
−0.287638 | + | 0.957739i | \(0.592870\pi\) | |||||||
\(420\) | −1.24612 | −0.0608045 | ||||||||
\(421\) | −12.3172 | −0.600302 | −0.300151 | − | 0.953892i | \(-0.597037\pi\) | ||||
−0.300151 | + | 0.953892i | \(0.597037\pi\) | |||||||
\(422\) | −27.7158 | −1.34919 | ||||||||
\(423\) | −18.3727 | −0.893311 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | −6.05356 | −0.293641 | ||||||||
\(426\) | −43.7158 | −2.11804 | ||||||||
\(427\) | −5.30590 | −0.256770 | ||||||||
\(428\) | −9.85792 | −0.476500 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.22359 | −0.0590068 | ||||||||
\(431\) | −0.611795 | −0.0294691 | −0.0147346 | − | 0.999891i | \(-0.504690\pi\) | ||||
−0.0147346 | + | 0.999891i | \(0.504690\pi\) | |||||||
\(432\) | −16.2946 | −0.783976 | ||||||||
\(433\) | 25.2011 | 1.21109 | 0.605543 | − | 0.795813i | \(-0.292956\pi\) | ||||
0.605543 | + | 0.795813i | \(0.292956\pi\) | |||||||
\(434\) | 5.68284 | 0.272785 | ||||||||
\(435\) | −5.74686 | −0.275541 | ||||||||
\(436\) | 11.2236 | 0.537512 | ||||||||
\(437\) | −8.00000 | −0.382692 | ||||||||
\(438\) | 1.04851 | 0.0500997 | ||||||||
\(439\) | 36.9394 | 1.76302 | 0.881511 | − | 0.472163i | \(-0.156527\pi\) | ||||
0.881511 | + | 0.472163i | \(0.156527\pi\) | |||||||
\(440\) | −2.14208 | −0.102120 | ||||||||
\(441\) | 7.92896 | 0.377569 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.77641 | 0.131911 | 0.0659556 | − | 0.997823i | \(-0.478990\pi\) | ||||
0.0659556 | + | 0.997823i | \(0.478990\pi\) | |||||||
\(444\) | 22.9064 | 1.08709 | ||||||||
\(445\) | −3.48522 | −0.165215 | ||||||||
\(446\) | −8.29463 | −0.392762 | ||||||||
\(447\) | −31.5408 | −1.49183 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −4.35016 | −0.205297 | −0.102648 | − | 0.994718i | \(-0.532732\pi\) | ||||
−0.102648 | + | 0.994718i | \(0.532732\pi\) | |||||||
\(450\) | 38.5182 | 1.81577 | ||||||||
\(451\) | −6.08655 | −0.286605 | ||||||||
\(452\) | −4.92896 | −0.231839 | ||||||||
\(453\) | −9.10404 | −0.427745 | ||||||||
\(454\) | 0.234856 | 0.0110223 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.36567 | −0.251271 | ||||||||
\(457\) | 29.6048 | 1.38485 | 0.692426 | − | 0.721488i | \(-0.256542\pi\) | ||||
0.692426 | + | 0.721488i | \(0.256542\pi\) | |||||||
\(458\) | −19.4584 | −0.909233 | ||||||||
\(459\) | −20.3051 | −0.947761 | ||||||||
\(460\) | −1.85792 | −0.0866258 | ||||||||
\(461\) | −30.2349 | −1.40818 | −0.704089 | − | 0.710112i | \(-0.748644\pi\) | ||||
−0.704089 | + | 0.710112i | \(0.748644\pi\) | |||||||
\(462\) | 18.7869 | 0.874045 | ||||||||
\(463\) | −4.87343 | −0.226487 | −0.113244 | − | 0.993567i | \(-0.536124\pi\) | ||||
−0.113244 | + | 0.993567i | \(0.536124\pi\) | |||||||
\(464\) | −4.61180 | −0.214097 | ||||||||
\(465\) | 7.08151 | 0.328397 | ||||||||
\(466\) | 20.1525 | 0.933549 | ||||||||
\(467\) | −15.8847 | −0.735056 | −0.367528 | − | 0.930012i | \(-0.619796\pi\) | ||||
−0.367528 | + | 0.930012i | \(0.619796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.92896 | 0.412301 | ||||||||
\(470\) | −0.873429 | −0.0402883 | ||||||||
\(471\) | −74.4802 | −3.43187 | ||||||||
\(472\) | 11.4810 | 0.528455 | ||||||||
\(473\) | 18.4472 | 0.848202 | ||||||||
\(474\) | 7.19059 | 0.330275 | ||||||||
\(475\) | 7.88470 | 0.361775 | ||||||||
\(476\) | −1.24612 | −0.0571159 | ||||||||
\(477\) | −47.5738 | −2.17825 | ||||||||
\(478\) | −12.9620 | −0.592866 | ||||||||
\(479\) | 3.53029 | 0.161303 | 0.0806515 | − | 0.996742i | \(-0.474300\pi\) | ||||
0.0806515 | + | 0.996742i | \(0.474300\pi\) | |||||||
\(480\) | −1.24612 | −0.0568774 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8.73135 | 0.397702 | ||||||||
\(483\) | 16.2946 | 0.741431 | ||||||||
\(484\) | 21.2946 | 0.967938 | ||||||||
\(485\) | −4.11955 | −0.187059 | ||||||||
\(486\) | 50.5625 | 2.29356 | ||||||||
\(487\) | 16.6118 | 0.752752 | 0.376376 | − | 0.926467i | \(-0.377170\pi\) | ||||
0.376376 | + | 0.926467i | \(0.377170\pi\) | |||||||
\(488\) | −5.30590 | −0.240187 | ||||||||
\(489\) | −28.0000 | −1.26620 | ||||||||
\(490\) | 0.376939 | 0.0170284 | ||||||||
\(491\) | −10.3812 | −0.468496 | −0.234248 | − | 0.972177i | \(-0.575263\pi\) | ||||
−0.234248 | + | 0.972177i | \(0.575263\pi\) | |||||||
\(492\) | −3.54075 | −0.159629 | ||||||||
\(493\) | −5.74686 | −0.258826 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.9845 | 0.763396 | ||||||||
\(496\) | 5.68284 | 0.255167 | ||||||||
\(497\) | 13.2236 | 0.593159 | ||||||||
\(498\) | −32.2081 | −1.44328 | ||||||||
\(499\) | −9.80239 | −0.438815 | −0.219408 | − | 0.975633i | \(-0.570412\pi\) | ||||
−0.219408 | + | 0.975633i | \(0.570412\pi\) | |||||||
\(500\) | 3.71583 | 0.166177 | ||||||||
\(501\) | 19.7609 | 0.882852 | ||||||||
\(502\) | 5.04426 | 0.225136 | ||||||||
\(503\) | −12.3502 | −0.550666 | −0.275333 | − | 0.961349i | \(-0.588788\pi\) | ||||
−0.275333 | + | 0.961349i | \(0.588788\pi\) | |||||||
\(504\) | 7.92896 | 0.353184 | ||||||||
\(505\) | −1.29968 | −0.0578349 | ||||||||
\(506\) | 28.0105 | 1.24522 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.29463 | −0.368015 | ||||||||
\(509\) | −10.1153 | −0.448353 | −0.224176 | − | 0.974549i | \(-0.571969\pi\) | ||||
−0.224176 | + | 0.974549i | \(0.571969\pi\) | |||||||
\(510\) | −1.55282 | −0.0687600 | ||||||||
\(511\) | −0.317163 | −0.0140305 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 26.4472 | 1.16767 | ||||||||
\(514\) | 23.2236 | 1.02435 | ||||||||
\(515\) | 2.73135 | 0.120357 | ||||||||
\(516\) | 10.7313 | 0.472421 | ||||||||
\(517\) | 13.1681 | 0.579131 | ||||||||
\(518\) | −6.92896 | −0.304441 | ||||||||
\(519\) | −2.79894 | −0.122860 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.6118 | −1.42875 | −0.714374 | − | 0.699764i | \(-0.753289\pi\) | ||||
−0.714374 | + | 0.699764i | \(0.753289\pi\) | |||||||
\(522\) | 36.5667 | 1.60048 | ||||||||
\(523\) | 32.4099 | 1.41719 | 0.708594 | − | 0.705617i | \(-0.249330\pi\) | ||||
0.708594 | + | 0.705617i | \(0.249330\pi\) | |||||||
\(524\) | 16.3544 | 0.714446 | ||||||||
\(525\) | −16.0598 | −0.700906 | ||||||||
\(526\) | 11.1040 | 0.484159 | ||||||||
\(527\) | 7.08151 | 0.308475 | ||||||||
\(528\) | 18.7869 | 0.817594 | ||||||||
\(529\) | 1.29463 | 0.0562883 | ||||||||
\(530\) | −2.26163 | −0.0982391 | ||||||||
\(531\) | −91.0322 | −3.95046 | ||||||||
\(532\) | 1.62306 | 0.0703686 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 30.5667 | 1.32275 | ||||||||
\(535\) | 3.71583 | 0.160650 | ||||||||
\(536\) | 8.92896 | 0.385672 | ||||||||
\(537\) | −61.9239 | −2.67221 | ||||||||
\(538\) | −11.5675 | −0.498712 | ||||||||
\(539\) | −5.68284 | −0.244777 | ||||||||
\(540\) | 6.14208 | 0.264313 | ||||||||
\(541\) | −23.4542 | −1.00837 | −0.504187 | − | 0.863594i | \(-0.668208\pi\) | ||||
−0.504187 | + | 0.863594i | \(0.668208\pi\) | |||||||
\(542\) | 26.1525 | 1.12335 | ||||||||
\(543\) | −58.3691 | −2.50486 | ||||||||
\(544\) | −1.24612 | −0.0534270 | ||||||||
\(545\) | −4.23061 | −0.181219 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.3882 | 0.572438 | 0.286219 | − | 0.958164i | \(-0.407601\pi\) | ||||
0.286219 | + | 0.958164i | \(0.407601\pi\) | |||||||
\(548\) | −13.2236 | −0.564884 | ||||||||
\(549\) | 42.0702 | 1.79551 | ||||||||
\(550\) | −27.6067 | −1.17716 | ||||||||
\(551\) | 7.48522 | 0.318881 | ||||||||
\(552\) | 16.2946 | 0.693546 | ||||||||
\(553\) | −2.17508 | −0.0924938 | ||||||||
\(554\) | −23.2236 | −0.986676 | ||||||||
\(555\) | −8.63433 | −0.366507 | ||||||||
\(556\) | 1.62306 | 0.0688331 | ||||||||
\(557\) | 23.0485 | 0.976597 | 0.488298 | − | 0.872677i | \(-0.337618\pi\) | ||||
0.488298 | + | 0.872677i | \(0.337618\pi\) | |||||||
\(558\) | −45.0590 | −1.90750 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.376939 | 0.0159286 | ||||||||
\(561\) | 23.4107 | 0.988402 | ||||||||
\(562\) | 17.2236 | 0.726533 | ||||||||
\(563\) | −0.858717 | −0.0361906 | −0.0180953 | − | 0.999836i | \(-0.505760\pi\) | ||||
−0.0180953 | + | 0.999836i | \(0.505760\pi\) | |||||||
\(564\) | 7.66030 | 0.322557 | ||||||||
\(565\) | 1.85792 | 0.0781632 | ||||||||
\(566\) | 19.7756 | 0.831231 | ||||||||
\(567\) | −30.0815 | −1.26330 | ||||||||
\(568\) | 13.2236 | 0.554850 | ||||||||
\(569\) | 3.31014 | 0.138768 | 0.0693842 | − | 0.997590i | \(-0.477897\pi\) | ||||
0.0693842 | + | 0.997590i | \(0.477897\pi\) | |||||||
\(570\) | 2.02253 | 0.0847145 | ||||||||
\(571\) | 21.6273 | 0.905075 | 0.452537 | − | 0.891745i | \(-0.350519\pi\) | ||||
0.452537 | + | 0.891745i | \(0.350519\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.9169 | −2.29419 | ||||||||
\(574\) | 1.07104 | 0.0447044 | ||||||||
\(575\) | −23.9445 | −0.998553 | ||||||||
\(576\) | 7.92896 | 0.330373 | ||||||||
\(577\) | −9.48522 | −0.394875 | −0.197438 | − | 0.980315i | \(-0.563262\pi\) | ||||
−0.197438 | + | 0.980315i | \(0.563262\pi\) | |||||||
\(578\) | 15.4472 | 0.642518 | ||||||||
\(579\) | −12.7539 | −0.530033 | ||||||||
\(580\) | 1.73837 | 0.0721817 | ||||||||
\(581\) | 9.74261 | 0.404192 | ||||||||
\(582\) | 36.1300 | 1.49764 | ||||||||
\(583\) | 34.0970 | 1.41215 | ||||||||
\(584\) | −0.317163 | −0.0131243 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.13082 | −0.0467136 | ||||||||
\(587\) | 36.4204 | 1.50323 | 0.751615 | − | 0.659602i | \(-0.229275\pi\) | ||||
0.751615 | + | 0.659602i | \(0.229275\pi\) | |||||||
\(588\) | −3.30590 | −0.136333 | ||||||||
\(589\) | −9.22359 | −0.380051 | ||||||||
\(590\) | −4.32763 | −0.178166 | ||||||||
\(591\) | 20.4142 | 0.839727 | ||||||||
\(592\) | −6.92896 | −0.284778 | ||||||||
\(593\) | 21.4852 | 0.882292 | 0.441146 | − | 0.897435i | \(-0.354572\pi\) | ||||
0.441146 | + | 0.897435i | \(0.354572\pi\) | |||||||
\(594\) | −92.5997 | −3.79941 | ||||||||
\(595\) | 0.469712 | 0.0192563 | ||||||||
\(596\) | 9.54075 | 0.390804 | ||||||||
\(597\) | −15.7158 | −0.643206 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.89091 | 0.0772607 | 0.0386303 | − | 0.999254i | \(-0.487701\pi\) | ||||
0.0386303 | + | 0.999254i | \(0.487701\pi\) | |||||||
\(600\) | −16.0598 | −0.655638 | ||||||||
\(601\) | −2.35016 | −0.0958651 | −0.0479325 | − | 0.998851i | \(-0.515263\pi\) | ||||
−0.0479325 | + | 0.998851i | \(0.515263\pi\) | |||||||
\(602\) | −3.24612 | −0.132302 | ||||||||
\(603\) | −70.7973 | −2.88309 | ||||||||
\(604\) | 2.75388 | 0.112054 | ||||||||
\(605\) | −8.02678 | −0.326335 | ||||||||
\(606\) | 11.3987 | 0.463039 | ||||||||
\(607\) | −28.3502 | −1.15070 | −0.575349 | − | 0.817908i | \(-0.695134\pi\) | ||||
−0.575349 | + | 0.817908i | \(0.695134\pi\) | |||||||
\(608\) | 1.62306 | 0.0658238 | ||||||||
\(609\) | −15.2461 | −0.617804 | ||||||||
\(610\) | 2.00000 | 0.0809776 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 9.88045 | 0.399393 | ||||||||
\(613\) | −21.3101 | −0.860709 | −0.430354 | − | 0.902660i | \(-0.641611\pi\) | ||||
−0.430354 | + | 0.902660i | \(0.641611\pi\) | |||||||
\(614\) | −30.9662 | −1.24969 | ||||||||
\(615\) | 1.33465 | 0.0538182 | ||||||||
\(616\) | −5.68284 | −0.228968 | ||||||||
\(617\) | −7.85792 | −0.316348 | −0.158174 | − | 0.987411i | \(-0.550561\pi\) | ||||
−0.158174 | + | 0.987411i | \(0.550561\pi\) | |||||||
\(618\) | −23.9549 | −0.963609 | ||||||||
\(619\) | 32.3544 | 1.30043 | 0.650217 | − | 0.759749i | \(-0.274678\pi\) | ||||
0.650217 | + | 0.759749i | \(0.274678\pi\) | |||||||
\(620\) | −2.14208 | −0.0860281 | ||||||||
\(621\) | −80.3156 | −3.22295 | ||||||||
\(622\) | −9.50776 | −0.381226 | ||||||||
\(623\) | −9.24612 | −0.370438 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.8889 | 0.915558 | ||||||||
\(626\) | −3.38820 | −0.135420 | ||||||||
\(627\) | −30.4922 | −1.21774 | ||||||||
\(628\) | 22.5295 | 0.899024 | ||||||||
\(629\) | −8.63433 | −0.344273 | ||||||||
\(630\) | −2.98873 | −0.119074 | ||||||||
\(631\) | 27.9549 | 1.11287 | 0.556434 | − | 0.830892i | \(-0.312169\pi\) | ||||
0.556434 | + | 0.830892i | \(0.312169\pi\) | |||||||
\(632\) | −2.17508 | −0.0865201 | ||||||||
\(633\) | −91.6257 | −3.64179 | ||||||||
\(634\) | −29.5408 | −1.17321 | ||||||||
\(635\) | 3.12657 | 0.124074 | ||||||||
\(636\) | 19.8354 | 0.786524 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −26.2081 | −1.03759 | ||||||||
\(639\) | −104.849 | −4.14777 | ||||||||
\(640\) | 0.376939 | 0.0148998 | ||||||||
\(641\) | −15.0260 | −0.593490 | −0.296745 | − | 0.954957i | \(-0.595901\pi\) | ||||
−0.296745 | + | 0.954957i | \(0.595901\pi\) | |||||||
\(642\) | −32.5893 | −1.28620 | ||||||||
\(643\) | 9.27290 | 0.365687 | 0.182844 | − | 0.983142i | \(-0.441470\pi\) | ||||
0.182844 | + | 0.983142i | \(0.441470\pi\) | |||||||
\(644\) | −4.92896 | −0.194228 | ||||||||
\(645\) | −4.04506 | −0.159274 | ||||||||
\(646\) | 2.02253 | 0.0795754 | ||||||||
\(647\) | −20.1196 | −0.790981 | −0.395491 | − | 0.918470i | \(-0.629425\pi\) | ||||
−0.395491 | + | 0.918470i | \(0.629425\pi\) | |||||||
\(648\) | −30.0815 | −1.18171 | ||||||||
\(649\) | 65.2445 | 2.56107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.7869 | 0.736316 | ||||||||
\(652\) | 8.46971 | 0.331700 | ||||||||
\(653\) | 25.3121 | 0.990540 | 0.495270 | − | 0.868739i | \(-0.335069\pi\) | ||||
0.495270 | + | 0.868739i | \(0.335069\pi\) | |||||||
\(654\) | 37.1040 | 1.45088 | ||||||||
\(655\) | −6.16461 | −0.240871 | ||||||||
\(656\) | 1.07104 | 0.0418171 | ||||||||
\(657\) | 2.51478 | 0.0981107 | ||||||||
\(658\) | −2.31716 | −0.0903324 | ||||||||
\(659\) | −15.2461 | −0.593905 | −0.296952 | − | 0.954892i | \(-0.595970\pi\) | ||||
−0.296952 | + | 0.954892i | \(0.595970\pi\) | |||||||
\(660\) | −7.08151 | −0.275647 | ||||||||
\(661\) | −29.4359 | −1.14492 | −0.572462 | − | 0.819931i | \(-0.694012\pi\) | ||||
−0.572462 | + | 0.819931i | \(0.694012\pi\) | |||||||
\(662\) | 0.175080 | 0.00680469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.74261 | 0.378087 | ||||||||
\(665\) | −0.611795 | −0.0237244 | ||||||||
\(666\) | 54.9394 | 2.12886 | ||||||||
\(667\) | −22.7313 | −0.880161 | ||||||||
\(668\) | −5.97747 | −0.231275 | ||||||||
\(669\) | −27.4212 | −1.06016 | ||||||||
\(670\) | −3.36567 | −0.130027 | ||||||||
\(671\) | −30.1525 | −1.16403 | ||||||||
\(672\) | −3.30590 | −0.127528 | ||||||||
\(673\) | −26.6448 | −1.02708 | −0.513541 | − | 0.858065i | \(-0.671666\pi\) | ||||
−0.513541 | + | 0.858065i | \(0.671666\pi\) | |||||||
\(674\) | 19.3761 | 0.746341 | ||||||||
\(675\) | 79.1580 | 3.04679 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.1188 | 1.50346 | 0.751728 | − | 0.659473i | \(-0.229221\pi\) | ||||
0.751728 | + | 0.659473i | \(0.229221\pi\) | |||||||
\(678\) | −16.2946 | −0.625792 | ||||||||
\(679\) | −10.9290 | −0.419415 | ||||||||
\(680\) | 0.469712 | 0.0180126 | ||||||||
\(681\) | 0.776410 | 0.0297521 | ||||||||
\(682\) | 32.2946 | 1.23663 | ||||||||
\(683\) | 12.0105 | 0.459568 | 0.229784 | − | 0.973242i | \(-0.426198\pi\) | ||||
0.229784 | + | 0.973242i | \(0.426198\pi\) | |||||||
\(684\) | −12.8692 | −0.492066 | ||||||||
\(685\) | 4.98449 | 0.190447 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −64.3276 | −2.45425 | ||||||||
\(688\) | −3.24612 | −0.123757 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.14208 | −0.233825 | ||||||||
\(691\) | 50.2123 | 1.91017 | 0.955083 | − | 0.296337i | \(-0.0957652\pi\) | ||||
0.955083 | + | 0.296337i | \(0.0957652\pi\) | |||||||
\(692\) | 0.846651 | 0.0321848 | ||||||||
\(693\) | 45.0590 | 1.71165 | ||||||||
\(694\) | −24.4697 | −0.928858 | ||||||||
\(695\) | −0.611795 | −0.0232067 | ||||||||
\(696\) | −15.2461 | −0.577903 | ||||||||
\(697\) | 1.33465 | 0.0505534 | ||||||||
\(698\) | −11.8622 | −0.448990 | ||||||||
\(699\) | 66.6223 | 2.51989 | ||||||||
\(700\) | 4.85792 | 0.183612 | ||||||||
\(701\) | −31.6933 | −1.19704 | −0.598520 | − | 0.801108i | \(-0.704244\pi\) | ||||
−0.598520 | + | 0.801108i | \(0.704244\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2461 | 0.424156 | ||||||||
\(704\) | −5.68284 | −0.214180 | ||||||||
\(705\) | −2.88747 | −0.108748 | ||||||||
\(706\) | −1.82492 | −0.0686818 | ||||||||
\(707\) | −3.44798 | −0.129675 | ||||||||
\(708\) | 37.9549 | 1.42643 | ||||||||
\(709\) | 10.6448 | 0.399774 | 0.199887 | − | 0.979819i | \(-0.435943\pi\) | ||||
0.199887 | + | 0.979819i | \(0.435943\pi\) | |||||||
\(710\) | −4.98449 | −0.187064 | ||||||||
\(711\) | 17.2461 | 0.646780 | ||||||||
\(712\) | −9.24612 | −0.346513 | ||||||||
\(713\) | 28.0105 | 1.04900 | ||||||||
\(714\) | −4.11955 | −0.154170 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.7313 | 0.700023 | ||||||||
\(717\) | −42.8509 | −1.60030 | ||||||||
\(718\) | 7.62731 | 0.284649 | ||||||||
\(719\) | 19.5303 | 0.728357 | 0.364178 | − | 0.931329i | \(-0.381350\pi\) | ||||
0.364178 | + | 0.931329i | \(0.381350\pi\) | |||||||
\(720\) | −2.98873 | −0.111384 | ||||||||
\(721\) | 7.24612 | 0.269860 | ||||||||
\(722\) | 16.3657 | 0.609067 | ||||||||
\(723\) | 28.8649 | 1.07350 | ||||||||
\(724\) | 17.6561 | 0.656182 | ||||||||
\(725\) | 22.4037 | 0.832053 | ||||||||
\(726\) | 70.3979 | 2.61271 | ||||||||
\(727\) | 29.1040 | 1.07941 | 0.539705 | − | 0.841855i | \(-0.318536\pi\) | ||||
0.539705 | + | 0.841855i | \(0.318536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 76.9099 | 2.84851 | ||||||||
\(730\) | 0.119551 | 0.00442479 | ||||||||
\(731\) | −4.04506 | −0.149612 | ||||||||
\(732\) | −17.5408 | −0.648325 | ||||||||
\(733\) | 43.9282 | 1.62252 | 0.811262 | − | 0.584683i | \(-0.198781\pi\) | ||||
0.811262 | + | 0.584683i | \(0.198781\pi\) | |||||||
\(734\) | −17.2236 | −0.635734 | ||||||||
\(735\) | 1.24612 | 0.0459639 | ||||||||
\(736\) | −4.92896 | −0.181684 | ||||||||
\(737\) | 50.7418 | 1.86910 | ||||||||
\(738\) | −8.49224 | −0.312604 | ||||||||
\(739\) | −43.4852 | −1.59963 | −0.799815 | − | 0.600247i | \(-0.795069\pi\) | ||||
−0.799815 | + | 0.600247i | \(0.795069\pi\) | |||||||
\(740\) | 2.61180 | 0.0960115 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | 30.4697 | 1.11783 | 0.558913 | − | 0.829227i | \(-0.311219\pi\) | ||||
0.558913 | + | 0.829227i | \(0.311219\pi\) | |||||||
\(744\) | 18.7869 | 0.688760 | ||||||||
\(745\) | −3.59628 | −0.131758 | ||||||||
\(746\) | 8.77641 | 0.321327 | ||||||||
\(747\) | −77.2488 | −2.82638 | ||||||||
\(748\) | −7.08151 | −0.258926 | ||||||||
\(749\) | 9.85792 | 0.360200 | ||||||||
\(750\) | 12.2842 | 0.448554 | ||||||||
\(751\) | 11.6603 | 0.425491 | 0.212745 | − | 0.977108i | \(-0.431760\pi\) | ||||
0.212745 | + | 0.977108i | \(0.431760\pi\) | |||||||
\(752\) | −2.31716 | −0.0844983 | ||||||||
\(753\) | 16.6758 | 0.607701 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.03804 | −0.0377783 | ||||||||
\(756\) | 16.2946 | 0.592630 | ||||||||
\(757\) | −8.02253 | −0.291584 | −0.145792 | − | 0.989315i | \(-0.546573\pi\) | ||||
−0.145792 | + | 0.989315i | \(0.546573\pi\) | |||||||
\(758\) | 17.7384 | 0.644286 | ||||||||
\(759\) | 92.5997 | 3.36116 | ||||||||
\(760\) | −0.611795 | −0.0221921 | ||||||||
\(761\) | 0.831939 | 0.0301578 | 0.0150789 | − | 0.999886i | \(-0.495200\pi\) | ||||
0.0150789 | + | 0.999886i | \(0.495200\pi\) | |||||||
\(762\) | −27.4212 | −0.993365 | ||||||||
\(763\) | −11.2236 | −0.406321 | ||||||||
\(764\) | 16.6118 | 0.600994 | ||||||||
\(765\) | −3.72433 | −0.134653 | ||||||||
\(766\) | −32.7643 | −1.18382 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.30590 | −0.119291 | ||||||||
\(769\) | 21.0710 | 0.759841 | 0.379921 | − | 0.925019i | \(-0.375951\pi\) | ||||
0.379921 | + | 0.925019i | \(0.375951\pi\) | |||||||
\(770\) | 2.14208 | 0.0771953 | ||||||||
\(771\) | 76.7748 | 2.76498 | ||||||||
\(772\) | 3.85792 | 0.138849 | ||||||||
\(773\) | −4.84665 | −0.174322 | −0.0871610 | − | 0.996194i | \(-0.527779\pi\) | ||||
−0.0871610 | + | 0.996194i | \(0.527779\pi\) | |||||||
\(774\) | 25.7384 | 0.925146 | ||||||||
\(775\) | −27.6067 | −0.991664 | ||||||||
\(776\) | −10.9290 | −0.392327 | ||||||||
\(777\) | −22.9064 | −0.821763 | ||||||||
\(778\) | 12.2616 | 0.439601 | ||||||||
\(779\) | −1.73837 | −0.0622834 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 75.1475 | 2.68899 | ||||||||
\(782\) | −6.14208 | −0.219640 | ||||||||
\(783\) | 75.1475 | 2.68555 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −8.49224 | −0.303101 | ||||||||
\(786\) | 54.0660 | 1.92847 | ||||||||
\(787\) | −35.6005 | −1.26902 | −0.634511 | − | 0.772914i | \(-0.718798\pi\) | ||||
−0.634511 | + | 0.772914i | \(0.718798\pi\) | |||||||
\(788\) | −6.17508 | −0.219978 | ||||||||
\(789\) | 36.7088 | 1.30687 | ||||||||
\(790\) | 0.819873 | 0.0291698 | ||||||||
\(791\) | 4.92896 | 0.175254 | ||||||||
\(792\) | 45.0590 | 1.60110 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 22.5850 | 0.801512 | ||||||||
\(795\) | −7.47673 | −0.265172 | ||||||||
\(796\) | 4.75388 | 0.168497 | ||||||||
\(797\) | −24.5520 | −0.869677 | −0.434839 | − | 0.900508i | \(-0.643195\pi\) | ||||
−0.434839 | + | 0.900508i | \(0.643195\pi\) | |||||||
\(798\) | 5.36567 | 0.189943 | ||||||||
\(799\) | −2.88747 | −0.102151 | ||||||||
\(800\) | 4.85792 | 0.171753 | ||||||||
\(801\) | 73.3121 | 2.59036 | ||||||||
\(802\) | −27.8579 | −0.983697 | ||||||||
\(803\) | −1.80239 | −0.0636049 | ||||||||
\(804\) | 29.5182 | 1.04103 | ||||||||
\(805\) | 1.85792 | 0.0654830 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.2411 | −1.34615 | ||||||||
\(808\) | −3.44798 | −0.121300 | ||||||||
\(809\) | 38.0970 | 1.33942 | 0.669710 | − | 0.742623i | \(-0.266418\pi\) | ||||
0.669710 | + | 0.742623i | \(0.266418\pi\) | |||||||
\(810\) | 11.3389 | 0.398408 | ||||||||
\(811\) | 36.3009 | 1.27470 | 0.637348 | − | 0.770576i | \(-0.280032\pi\) | ||||
0.637348 | + | 0.770576i | \(0.280032\pi\) | |||||||
\(812\) | 4.61180 | 0.161842 | ||||||||
\(813\) | 86.4576 | 3.03220 | ||||||||
\(814\) | −39.3761 | −1.38013 | ||||||||
\(815\) | −3.19257 | −0.111831 | ||||||||
\(816\) | −4.11955 | −0.144213 | ||||||||
\(817\) | 5.26865 | 0.184327 | ||||||||
\(818\) | 16.7313 | 0.584998 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.403717 | −0.0140984 | ||||||||
\(821\) | 34.4697 | 1.20300 | 0.601501 | − | 0.798872i | \(-0.294570\pi\) | ||||
0.601501 | + | 0.798872i | \(0.294570\pi\) | |||||||
\(822\) | −43.7158 | −1.52476 | ||||||||
\(823\) | 3.04851 | 0.106264 | 0.0531322 | − | 0.998587i | \(-0.483080\pi\) | ||||
0.0531322 | + | 0.998587i | \(0.483080\pi\) | |||||||
\(824\) | 7.24612 | 0.252431 | ||||||||
\(825\) | −91.2651 | −3.17744 | ||||||||
\(826\) | −11.4810 | −0.399474 | ||||||||
\(827\) | 23.6708 | 0.823113 | 0.411557 | − | 0.911384i | \(-0.364985\pi\) | ||||
0.411557 | + | 0.911384i | \(0.364985\pi\) | |||||||
\(828\) | 39.0815 | 1.35818 | ||||||||
\(829\) | 9.83114 | 0.341450 | 0.170725 | − | 0.985319i | \(-0.445389\pi\) | ||||
0.170725 | + | 0.985319i | \(0.445389\pi\) | |||||||
\(830\) | −3.67237 | −0.127470 | ||||||||
\(831\) | −76.7748 | −2.66329 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.24612 | 0.0431756 | ||||||||
\(834\) | 5.36567 | 0.185798 | ||||||||
\(835\) | 2.25314 | 0.0779732 | ||||||||
\(836\) | 9.22359 | 0.319005 | ||||||||
\(837\) | −92.5997 | −3.20071 | ||||||||
\(838\) | 11.7756 | 0.406782 | ||||||||
\(839\) | −25.6828 | −0.886670 | −0.443335 | − | 0.896356i | \(-0.646205\pi\) | ||||
−0.443335 | + | 0.896356i | \(0.646205\pi\) | |||||||
\(840\) | 1.24612 | 0.0429953 | ||||||||
\(841\) | −7.73135 | −0.266598 | ||||||||
\(842\) | 12.3172 | 0.424477 | ||||||||
\(843\) | 56.9394 | 1.96110 | ||||||||
\(844\) | 27.7158 | 0.954018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.3727 | 0.631666 | ||||||||
\(847\) | −21.2946 | −0.731692 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 65.3761 | 2.24370 | ||||||||
\(850\) | 6.05356 | 0.207635 | ||||||||
\(851\) | −34.1525 | −1.17073 | ||||||||
\(852\) | 43.7158 | 1.49768 | ||||||||
\(853\) | −23.1743 | −0.793472 | −0.396736 | − | 0.917933i | \(-0.629857\pi\) | ||||
−0.396736 | + | 0.917933i | \(0.629857\pi\) | |||||||
\(854\) | 5.30590 | 0.181564 | ||||||||
\(855\) | 4.85090 | 0.165897 | ||||||||
\(856\) | 9.85792 | 0.336937 | ||||||||
\(857\) | −26.8199 | −0.916149 | −0.458075 | − | 0.888914i | \(-0.651461\pi\) | ||||
−0.458075 | + | 0.888914i | \(0.651461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7756 | 0.401779 | 0.200889 | − | 0.979614i | \(-0.435617\pi\) | ||||
0.200889 | + | 0.979614i | \(0.435617\pi\) | |||||||
\(860\) | 1.22359 | 0.0417241 | ||||||||
\(861\) | 3.54075 | 0.120669 | ||||||||
\(862\) | 0.611795 | 0.0208378 | ||||||||
\(863\) | −8.91849 | −0.303589 | −0.151795 | − | 0.988412i | \(-0.548505\pi\) | ||||
−0.151795 | + | 0.988412i | \(0.548505\pi\) | |||||||
\(864\) | 16.2946 | 0.554355 | ||||||||
\(865\) | −0.319136 | −0.0108509 | ||||||||
\(866\) | −25.2011 | −0.856367 | ||||||||
\(867\) | 51.0668 | 1.73432 | ||||||||
\(868\) | −5.68284 | −0.192888 | ||||||||
\(869\) | −12.3606 | −0.419306 | ||||||||
\(870\) | 5.74686 | 0.194837 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.2236 | −0.380079 | ||||||||
\(873\) | 86.6553 | 2.93284 | ||||||||
\(874\) | 8.00000 | 0.270604 | ||||||||
\(875\) | −3.71583 | −0.125618 | ||||||||
\(876\) | −1.04851 | −0.0354259 | ||||||||
\(877\) | −34.2496 | −1.15653 | −0.578263 | − | 0.815851i | \(-0.696269\pi\) | ||||
−0.578263 | + | 0.815851i | \(0.696269\pi\) | |||||||
\(878\) | −36.9394 | −1.24665 | ||||||||
\(879\) | −3.73837 | −0.126092 | ||||||||
\(880\) | 2.14208 | 0.0722096 | ||||||||
\(881\) | 1.41074 | 0.0475289 | 0.0237645 | − | 0.999718i | \(-0.492435\pi\) | ||||
0.0237645 | + | 0.999718i | \(0.492435\pi\) | |||||||
\(882\) | −7.92896 | −0.266982 | ||||||||
\(883\) | 13.5078 | 0.454572 | 0.227286 | − | 0.973828i | \(-0.427015\pi\) | ||||
0.227286 | + | 0.973828i | \(0.427015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.3067 | −0.480914 | ||||||||
\(886\) | −2.77641 | −0.0932753 | ||||||||
\(887\) | −10.2616 | −0.344552 | −0.172276 | − | 0.985049i | \(-0.555112\pi\) | ||||
−0.172276 | + | 0.985049i | \(0.555112\pi\) | |||||||
\(888\) | −22.9064 | −0.768689 | ||||||||
\(889\) | 8.29463 | 0.278193 | ||||||||
\(890\) | 3.48522 | 0.116825 | ||||||||
\(891\) | −170.948 | −5.72698 | ||||||||
\(892\) | 8.29463 | 0.277725 | ||||||||
\(893\) | 3.76090 | 0.125854 | ||||||||
\(894\) | 31.5408 | 1.05488 | ||||||||
\(895\) | −7.06058 | −0.236009 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.35016 | 0.145167 | ||||||||
\(899\) | −26.2081 | −0.874088 | ||||||||
\(900\) | −38.5182 | −1.28394 | ||||||||
\(901\) | −7.47673 | −0.249086 | ||||||||
\(902\) | 6.08655 | 0.202660 | ||||||||
\(903\) | −10.7313 | −0.357117 | ||||||||
\(904\) | 4.92896 | 0.163935 | ||||||||
\(905\) | −6.65526 | −0.221228 | ||||||||
\(906\) | 9.10404 | 0.302461 | ||||||||
\(907\) | −47.9549 | −1.59232 | −0.796159 | − | 0.605088i | \(-0.793138\pi\) | ||||
−0.796159 | + | 0.605088i | \(0.793138\pi\) | |||||||
\(908\) | −0.234856 | −0.00779397 | ||||||||
\(909\) | 27.3389 | 0.906774 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.4317 | −0.776326 | −0.388163 | − | 0.921591i | \(-0.626890\pi\) | ||||
−0.388163 | + | 0.921591i | \(0.626890\pi\) | |||||||
\(912\) | 5.36567 | 0.177675 | ||||||||
\(913\) | 55.3657 | 1.83234 | ||||||||
\(914\) | −29.6048 | −0.979239 | ||||||||
\(915\) | 6.61180 | 0.218579 | ||||||||
\(916\) | 19.4584 | 0.642925 | ||||||||
\(917\) | −16.3544 | −0.540070 | ||||||||
\(918\) | 20.3051 | 0.670168 | ||||||||
\(919\) | −41.2566 | −1.36093 | −0.680465 | − | 0.732781i | \(-0.738222\pi\) | ||||
−0.680465 | + | 0.732781i | \(0.738222\pi\) | |||||||
\(920\) | 1.85792 | 0.0612537 | ||||||||
\(921\) | −102.371 | −3.37324 | ||||||||
\(922\) | 30.2349 | 0.995732 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −18.7869 | −0.618043 | ||||||||
\(925\) | 33.6603 | 1.10674 | ||||||||
\(926\) | 4.87343 | 0.160151 | ||||||||
\(927\) | −57.4542 | −1.88704 | ||||||||
\(928\) | 4.61180 | 0.151390 | ||||||||
\(929\) | −51.5842 | −1.69242 | −0.846212 | − | 0.532847i | \(-0.821122\pi\) | ||||
−0.846212 | + | 0.532847i | \(0.821122\pi\) | |||||||
\(930\) | −7.08151 | −0.232212 | ||||||||
\(931\) | −1.62306 | −0.0531937 | ||||||||
\(932\) | −20.1525 | −0.660119 | ||||||||
\(933\) | −31.4317 | −1.02903 | ||||||||
\(934\) | 15.8847 | 0.519763 | ||||||||
\(935\) | 2.66930 | 0.0872953 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.28417 | 0.0746205 | 0.0373102 | − | 0.999304i | \(-0.488121\pi\) | ||||
0.0373102 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(938\) | −8.92896 | −0.291541 | ||||||||
\(939\) | −11.2011 | −0.365533 | ||||||||
\(940\) | 0.873429 | 0.0284881 | ||||||||
\(941\) | 6.51902 | 0.212514 | 0.106257 | − | 0.994339i | \(-0.466113\pi\) | ||||
0.106257 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(942\) | 74.4802 | 2.42670 | ||||||||
\(943\) | 5.27912 | 0.171912 | ||||||||
\(944\) | −11.4810 | −0.373674 | ||||||||
\(945\) | −6.14208 | −0.199802 | ||||||||
\(946\) | −18.4472 | −0.599770 | ||||||||
\(947\) | −23.9464 | −0.778155 | −0.389077 | − | 0.921205i | \(-0.627206\pi\) | ||||
−0.389077 | + | 0.921205i | \(0.627206\pi\) | |||||||
\(948\) | −7.19059 | −0.233540 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7.88470 | −0.255813 | ||||||||
\(951\) | −97.6587 | −3.16680 | ||||||||
\(952\) | 1.24612 | 0.0403870 | ||||||||
\(953\) | 6.28417 | 0.203564 | 0.101782 | − | 0.994807i | \(-0.467546\pi\) | ||||
0.101782 | + | 0.994807i | \(0.467546\pi\) | |||||||
\(954\) | 47.5738 | 1.54026 | ||||||||
\(955\) | −6.26163 | −0.202622 | ||||||||
\(956\) | 12.9620 | 0.419220 | ||||||||
\(957\) | −86.6412 | −2.80071 | ||||||||
\(958\) | −3.53029 | −0.114058 | ||||||||
\(959\) | 13.2236 | 0.427012 | ||||||||
\(960\) | 1.24612 | 0.0402184 | ||||||||
\(961\) | 1.29463 | 0.0417623 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −78.1630 | −2.51877 | ||||||||
\(964\) | −8.73135 | −0.281218 | ||||||||
\(965\) | −1.45420 | −0.0468123 | ||||||||
\(966\) | −16.2946 | −0.524271 | ||||||||
\(967\) | 57.2671 | 1.84158 | 0.920792 | − | 0.390054i | \(-0.127544\pi\) | ||||
0.920792 | + | 0.390054i | \(0.127544\pi\) | |||||||
\(968\) | −21.2946 | −0.684435 | ||||||||
\(969\) | 6.68628 | 0.214794 | ||||||||
\(970\) | 4.11955 | 0.132271 | ||||||||
\(971\) | −49.1188 | −1.57630 | −0.788148 | − | 0.615486i | \(-0.788960\pi\) | ||||
−0.788148 | + | 0.615486i | \(0.788960\pi\) | |||||||
\(972\) | −50.5625 | −1.62179 | ||||||||
\(973\) | −1.62306 | −0.0520329 | ||||||||
\(974\) | −16.6118 | −0.532276 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.30590 | 0.169838 | ||||||||
\(977\) | −12.0660 | −0.386025 | −0.193013 | − | 0.981196i | \(-0.561826\pi\) | ||||
−0.193013 | + | 0.981196i | \(0.561826\pi\) | |||||||
\(978\) | 28.0000 | 0.895341 | ||||||||
\(979\) | −52.5442 | −1.67932 | ||||||||
\(980\) | −0.376939 | −0.0120409 | ||||||||
\(981\) | 88.9914 | 2.84128 | ||||||||
\(982\) | 10.3812 | 0.331277 | ||||||||
\(983\) | 54.2166 | 1.72924 | 0.864620 | − | 0.502426i | \(-0.167559\pi\) | ||||
0.864620 | + | 0.502426i | \(0.167559\pi\) | |||||||
\(984\) | 3.54075 | 0.112875 | ||||||||
\(985\) | 2.32763 | 0.0741644 | ||||||||
\(986\) | 5.74686 | 0.183017 | ||||||||
\(987\) | −7.66030 | −0.243830 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | −0.508770 | ||||||||
\(990\) | −16.9845 | −0.539802 | ||||||||
\(991\) | 38.1751 | 1.21267 | 0.606336 | − | 0.795209i | \(-0.292639\pi\) | ||||
0.606336 | + | 0.795209i | \(0.292639\pi\) | |||||||
\(992\) | −5.68284 | −0.180430 | ||||||||
\(993\) | 0.578798 | 0.0183676 | ||||||||
\(994\) | −13.2236 | −0.419427 | ||||||||
\(995\) | −1.79192 | −0.0568078 | ||||||||
\(996\) | 32.2081 | 1.02055 | ||||||||
\(997\) | 6.05978 | 0.191915 | 0.0959575 | − | 0.995385i | \(-0.469409\pi\) | ||||
0.0959575 | + | 0.995385i | \(0.469409\pi\) | |||||||
\(998\) | 9.80239 | 0.310289 | ||||||||
\(999\) | 112.905 | 3.57215 |
(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 | 2366.2.a.x.1.1 | 3 | ||
13.5 | odd | 4 | 182.2.d.b.155.4 | yes | 6 | ||
13.8 | odd | 4 | 182.2.d.b.155.1 | ✓ | 6 | ||
13.12 | even | 2 | 2366.2.a.bc.1.1 | 3 | |||
39.5 | even | 4 | 1638.2.c.i.883.2 | 6 | |||
39.8 | even | 4 | 1638.2.c.i.883.5 | 6 | |||
52.31 | even | 4 | 1456.2.k.b.337.6 | 6 | |||
52.47 | even | 4 | 1456.2.k.b.337.5 | 6 | |||
91.5 | even | 12 | 1274.2.n.n.753.4 | 12 | |||
91.18 | odd | 12 | 1274.2.n.m.961.3 | 12 | |||
91.31 | even | 12 | 1274.2.n.n.961.1 | 12 | |||
91.34 | even | 4 | 1274.2.d.l.883.3 | 6 | |||
91.44 | odd | 12 | 1274.2.n.m.753.6 | 12 | |||
91.47 | even | 12 | 1274.2.n.n.753.1 | 12 | |||
91.60 | odd | 12 | 1274.2.n.m.961.6 | 12 | |||
91.73 | even | 12 | 1274.2.n.n.961.4 | 12 | |||
91.83 | even | 4 | 1274.2.d.l.883.6 | 6 | |||
91.86 | odd | 12 | 1274.2.n.m.753.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.d.b.155.1 | ✓ | 6 | 13.8 | odd | 4 | ||
182.2.d.b.155.4 | yes | 6 | 13.5 | odd | 4 | ||
1274.2.d.l.883.3 | 6 | 91.34 | even | 4 | |||
1274.2.d.l.883.6 | 6 | 91.83 | even | 4 | |||
1274.2.n.m.753.3 | 12 | 91.86 | odd | 12 | |||
1274.2.n.m.753.6 | 12 | 91.44 | odd | 12 | |||
1274.2.n.m.961.3 | 12 | 91.18 | odd | 12 | |||
1274.2.n.m.961.6 | 12 | 91.60 | odd | 12 | |||
1274.2.n.n.753.1 | 12 | 91.47 | even | 12 | |||
1274.2.n.n.753.4 | 12 | 91.5 | even | 12 | |||
1274.2.n.n.961.1 | 12 | 91.31 | even | 12 | |||
1274.2.n.n.961.4 | 12 | 91.73 | even | 12 | |||
1456.2.k.b.337.5 | 6 | 52.47 | even | 4 | |||
1456.2.k.b.337.6 | 6 | 52.31 | even | 4 | |||
1638.2.c.i.883.2 | 6 | 39.5 | even | 4 | |||
1638.2.c.i.883.5 | 6 | 39.8 | even | 4 | |||
2366.2.a.x.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2366.2.a.bc.1.1 | 3 | 13.12 | even | 2 |