Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [341,2,Mod(1,341)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(341, 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("341.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 341 = 11 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 341.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: | \(2.72289870893\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 341.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | 3.85410 | 1.45671 | 0.728357 | − | 0.685198i | \(-0.240284\pi\) | ||||
0.728357 | + | 0.685198i | \(0.240284\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0.236068 | 0.0746512 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | −5.47214 | −1.51770 | −0.758849 | − | 0.651267i | \(-0.774238\pi\) | ||||
−0.758849 | + | 0.651267i | \(0.774238\pi\) | |||||||
\(14\) | −2.38197 | −0.636607 | ||||||||
\(15\) | 0.381966 | 0.0986232 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −4.23607 | −1.02740 | −0.513699 | − | 0.857971i | \(-0.671725\pi\) | ||||
−0.513699 | + | 0.857971i | \(0.671725\pi\) | |||||||
\(18\) | 1.23607 | 0.291344 | ||||||||
\(19\) | −7.23607 | −1.66007 | −0.830034 | − | 0.557713i | \(-0.811679\pi\) | ||||
−0.830034 | + | 0.557713i | \(0.811679\pi\) | |||||||
\(20\) | 0.618034 | 0.138197 | ||||||||
\(21\) | −3.85410 | −0.841034 | ||||||||
\(22\) | −0.618034 | −0.131765 | ||||||||
\(23\) | −3.23607 | −0.674767 | −0.337383 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337383 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 3.38197 | 0.663258 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −6.23607 | −1.17851 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −0.236068 | −0.0430999 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 2.61803 | 0.448989 | ||||||||
\(35\) | −1.47214 | −0.248836 | ||||||||
\(36\) | 3.23607 | 0.539345 | ||||||||
\(37\) | 0.236068 | 0.0388093 | 0.0194047 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194047 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(38\) | 4.47214 | 0.725476 | ||||||||
\(39\) | 5.47214 | 0.876243 | ||||||||
\(40\) | −0.854102 | −0.135045 | ||||||||
\(41\) | 10.0902 | 1.57582 | 0.787910 | − | 0.615791i | \(-0.211163\pi\) | ||||
0.787910 | + | 0.615791i | \(0.211163\pi\) | |||||||
\(42\) | 2.38197 | 0.367545 | ||||||||
\(43\) | −7.38197 | −1.12574 | −0.562870 | − | 0.826546i | \(-0.690303\pi\) | ||||
−0.562870 | + | 0.826546i | \(0.690303\pi\) | |||||||
\(44\) | −1.61803 | −0.243928 | ||||||||
\(45\) | 0.763932 | 0.113880 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | 1.09017 | 0.159018 | 0.0795088 | − | 0.996834i | \(-0.474665\pi\) | ||||
0.0795088 | + | 0.996834i | \(0.474665\pi\) | |||||||
\(48\) | −1.85410 | −0.267617 | ||||||||
\(49\) | 7.85410 | 1.12201 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | 4.23607 | 0.593168 | ||||||||
\(52\) | 8.85410 | 1.22784 | ||||||||
\(53\) | −4.09017 | −0.561828 | −0.280914 | − | 0.959733i | \(-0.590638\pi\) | ||||
−0.280914 | + | 0.959733i | \(0.590638\pi\) | |||||||
\(54\) | −3.09017 | −0.420519 | ||||||||
\(55\) | −0.381966 | −0.0515043 | ||||||||
\(56\) | 8.61803 | 1.15163 | ||||||||
\(57\) | 7.23607 | 0.958441 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.23607 | 0.291111 | 0.145556 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145556 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(60\) | −0.618034 | −0.0797878 | ||||||||
\(61\) | −11.0902 | −1.41995 | −0.709975 | − | 0.704226i | \(-0.751294\pi\) | ||||
−0.709975 | + | 0.704226i | \(0.751294\pi\) | |||||||
\(62\) | −0.618034 | −0.0784904 | ||||||||
\(63\) | −7.70820 | −0.971142 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 2.09017 | 0.259254 | ||||||||
\(66\) | 0.618034 | 0.0760747 | ||||||||
\(67\) | −7.00000 | −0.855186 | −0.427593 | − | 0.903971i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(68\) | 6.85410 | 0.831182 | ||||||||
\(69\) | 3.23607 | 0.389577 | ||||||||
\(70\) | 0.909830 | 0.108745 | ||||||||
\(71\) | −11.0902 | −1.31616 | −0.658081 | − | 0.752948i | \(-0.728631\pi\) | ||||
−0.658081 | + | 0.752948i | \(0.728631\pi\) | |||||||
\(72\) | −4.47214 | −0.527046 | ||||||||
\(73\) | 10.7082 | 1.25330 | 0.626650 | − | 0.779301i | \(-0.284425\pi\) | ||||
0.626650 | + | 0.779301i | \(0.284425\pi\) | |||||||
\(74\) | −0.145898 | −0.0169603 | ||||||||
\(75\) | 4.85410 | 0.560503 | ||||||||
\(76\) | 11.7082 | 1.34302 | ||||||||
\(77\) | 3.85410 | 0.439216 | ||||||||
\(78\) | −3.38197 | −0.382932 | ||||||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | −0.708204 | −0.0791796 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.23607 | −0.688659 | ||||||||
\(83\) | 10.3820 | 1.13957 | 0.569784 | − | 0.821794i | \(-0.307027\pi\) | ||||
0.569784 | + | 0.821794i | \(0.307027\pi\) | |||||||
\(84\) | 6.23607 | 0.680411 | ||||||||
\(85\) | 1.61803 | 0.175500 | ||||||||
\(86\) | 4.56231 | 0.491966 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.23607 | 0.238366 | ||||||||
\(89\) | −10.3262 | −1.09458 | −0.547290 | − | 0.836943i | \(-0.684340\pi\) | ||||
−0.547290 | + | 0.836943i | \(0.684340\pi\) | |||||||
\(90\) | −0.472136 | −0.0497675 | ||||||||
\(91\) | −21.0902 | −2.21085 | ||||||||
\(92\) | 5.23607 | 0.545898 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −0.673762 | −0.0694933 | ||||||||
\(95\) | 2.76393 | 0.283573 | ||||||||
\(96\) | 5.61803 | 0.573388 | ||||||||
\(97\) | −0.944272 | −0.0958763 | −0.0479381 | − | 0.998850i | \(-0.515265\pi\) | ||||
−0.0479381 | + | 0.998850i | \(0.515265\pi\) | |||||||
\(98\) | −4.85410 | −0.490338 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 7.85410 | 0.785410 | ||||||||
\(101\) | 18.1803 | 1.80901 | 0.904506 | − | 0.426461i | \(-0.140240\pi\) | ||||
0.904506 | + | 0.426461i | \(0.140240\pi\) | |||||||
\(102\) | −2.61803 | −0.259224 | ||||||||
\(103\) | 9.00000 | 0.886796 | 0.443398 | − | 0.896325i | \(-0.353773\pi\) | ||||
0.443398 | + | 0.896325i | \(0.353773\pi\) | |||||||
\(104\) | −12.2361 | −1.19985 | ||||||||
\(105\) | 1.47214 | 0.143666 | ||||||||
\(106\) | 2.52786 | 0.245528 | ||||||||
\(107\) | 8.32624 | 0.804928 | 0.402464 | − | 0.915436i | \(-0.368154\pi\) | ||||
0.402464 | + | 0.915436i | \(0.368154\pi\) | |||||||
\(108\) | −8.09017 | −0.778477 | ||||||||
\(109\) | −3.29180 | −0.315297 | −0.157648 | − | 0.987495i | \(-0.550391\pi\) | ||||
−0.157648 | + | 0.987495i | \(0.550391\pi\) | |||||||
\(110\) | 0.236068 | 0.0225082 | ||||||||
\(111\) | −0.236068 | −0.0224066 | ||||||||
\(112\) | 7.14590 | 0.675224 | ||||||||
\(113\) | 12.9443 | 1.21769 | 0.608847 | − | 0.793287i | \(-0.291632\pi\) | ||||
0.608847 | + | 0.793287i | \(0.291632\pi\) | |||||||
\(114\) | −4.47214 | −0.418854 | ||||||||
\(115\) | 1.23607 | 0.115264 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.9443 | 1.01180 | ||||||||
\(118\) | −1.38197 | −0.127220 | ||||||||
\(119\) | −16.3262 | −1.49662 | ||||||||
\(120\) | 0.854102 | 0.0779685 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.85410 | 0.620541 | ||||||||
\(123\) | −10.0902 | −0.909800 | ||||||||
\(124\) | −1.61803 | −0.145304 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | 4.76393 | 0.424405 | ||||||||
\(127\) | −5.29180 | −0.469571 | −0.234785 | − | 0.972047i | \(-0.575439\pi\) | ||||
−0.234785 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 7.38197 | 0.649946 | ||||||||
\(130\) | −1.29180 | −0.113298 | ||||||||
\(131\) | −16.0902 | −1.40580 | −0.702902 | − | 0.711286i | \(-0.748113\pi\) | ||||
−0.702902 | + | 0.711286i | \(0.748113\pi\) | |||||||
\(132\) | 1.61803 | 0.140832 | ||||||||
\(133\) | −27.8885 | −2.41824 | ||||||||
\(134\) | 4.32624 | 0.373730 | ||||||||
\(135\) | −1.90983 | −0.164372 | ||||||||
\(136\) | −9.47214 | −0.812229 | ||||||||
\(137\) | 9.70820 | 0.829428 | 0.414714 | − | 0.909952i | \(-0.363882\pi\) | ||||
0.414714 | + | 0.909952i | \(0.363882\pi\) | |||||||
\(138\) | −2.00000 | −0.170251 | ||||||||
\(139\) | 8.41641 | 0.713870 | 0.356935 | − | 0.934129i | \(-0.383822\pi\) | ||||
0.356935 | + | 0.934129i | \(0.383822\pi\) | |||||||
\(140\) | 2.38197 | 0.201313 | ||||||||
\(141\) | −1.09017 | −0.0918089 | ||||||||
\(142\) | 6.85410 | 0.575183 | ||||||||
\(143\) | −5.47214 | −0.457603 | ||||||||
\(144\) | −3.70820 | −0.309017 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.61803 | −0.547712 | ||||||||
\(147\) | −7.85410 | −0.647795 | ||||||||
\(148\) | −0.381966 | −0.0313974 | ||||||||
\(149\) | 2.23607 | 0.183186 | 0.0915929 | − | 0.995797i | \(-0.470804\pi\) | ||||
0.0915929 | + | 0.995797i | \(0.470804\pi\) | |||||||
\(150\) | −3.00000 | −0.244949 | ||||||||
\(151\) | −17.2705 | −1.40545 | −0.702727 | − | 0.711460i | \(-0.748034\pi\) | ||||
−0.702727 | + | 0.711460i | \(0.748034\pi\) | |||||||
\(152\) | −16.1803 | −1.31240 | ||||||||
\(153\) | 8.47214 | 0.684932 | ||||||||
\(154\) | −2.38197 | −0.191944 | ||||||||
\(155\) | −0.381966 | −0.0306802 | ||||||||
\(156\) | −8.85410 | −0.708896 | ||||||||
\(157\) | −9.56231 | −0.763155 | −0.381578 | − | 0.924337i | \(-0.624619\pi\) | ||||
−0.381578 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(158\) | 3.09017 | 0.245841 | ||||||||
\(159\) | 4.09017 | 0.324372 | ||||||||
\(160\) | 2.14590 | 0.169648 | ||||||||
\(161\) | −12.4721 | −0.982942 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | −11.0000 | −0.861586 | −0.430793 | − | 0.902451i | \(-0.641766\pi\) | ||||
−0.430793 | + | 0.902451i | \(0.641766\pi\) | |||||||
\(164\) | −16.3262 | −1.27486 | ||||||||
\(165\) | 0.381966 | 0.0297360 | ||||||||
\(166\) | −6.41641 | −0.498010 | ||||||||
\(167\) | 9.38197 | 0.725998 | 0.362999 | − | 0.931789i | \(-0.381753\pi\) | ||||
0.362999 | + | 0.931789i | \(0.381753\pi\) | |||||||
\(168\) | −8.61803 | −0.664896 | ||||||||
\(169\) | 16.9443 | 1.30341 | ||||||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | 14.4721 | 1.10671 | ||||||||
\(172\) | 11.9443 | 0.910742 | ||||||||
\(173\) | 10.9098 | 0.829459 | 0.414730 | − | 0.909945i | \(-0.363876\pi\) | ||||
0.414730 | + | 0.909945i | \(0.363876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.7082 | −1.41421 | ||||||||
\(176\) | 1.85410 | 0.139758 | ||||||||
\(177\) | −2.23607 | −0.168073 | ||||||||
\(178\) | 6.38197 | 0.478349 | ||||||||
\(179\) | −17.7639 | −1.32774 | −0.663869 | − | 0.747849i | \(-0.731087\pi\) | ||||
−0.663869 | + | 0.747849i | \(0.731087\pi\) | |||||||
\(180\) | −1.23607 | −0.0921311 | ||||||||
\(181\) | −6.09017 | −0.452679 | −0.226339 | − | 0.974049i | \(-0.572676\pi\) | ||||
−0.226339 | + | 0.974049i | \(0.572676\pi\) | |||||||
\(182\) | 13.0344 | 0.966177 | ||||||||
\(183\) | 11.0902 | 0.819809 | ||||||||
\(184\) | −7.23607 | −0.533450 | ||||||||
\(185\) | −0.0901699 | −0.00662943 | ||||||||
\(186\) | 0.618034 | 0.0453165 | ||||||||
\(187\) | −4.23607 | −0.309772 | ||||||||
\(188\) | −1.76393 | −0.128648 | ||||||||
\(189\) | 19.2705 | 1.40172 | ||||||||
\(190\) | −1.70820 | −0.123926 | ||||||||
\(191\) | 8.18034 | 0.591909 | 0.295954 | − | 0.955202i | \(-0.404362\pi\) | ||||
0.295954 | + | 0.955202i | \(0.404362\pi\) | |||||||
\(192\) | 0.236068 | 0.0170367 | ||||||||
\(193\) | 2.81966 | 0.202964 | 0.101482 | − | 0.994837i | \(-0.467642\pi\) | ||||
0.101482 | + | 0.994837i | \(0.467642\pi\) | |||||||
\(194\) | 0.583592 | 0.0418995 | ||||||||
\(195\) | −2.09017 | −0.149680 | ||||||||
\(196\) | −12.7082 | −0.907729 | ||||||||
\(197\) | 9.70820 | 0.691681 | 0.345840 | − | 0.938293i | \(-0.387594\pi\) | ||||
0.345840 | + | 0.938293i | \(0.387594\pi\) | |||||||
\(198\) | 1.23607 | 0.0878435 | ||||||||
\(199\) | 22.8885 | 1.62253 | 0.811263 | − | 0.584682i | \(-0.198781\pi\) | ||||
0.811263 | + | 0.584682i | \(0.198781\pi\) | |||||||
\(200\) | −10.8541 | −0.767501 | ||||||||
\(201\) | 7.00000 | 0.493742 | ||||||||
\(202\) | −11.2361 | −0.790567 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.85410 | −0.479883 | ||||||||
\(205\) | −3.85410 | −0.269182 | ||||||||
\(206\) | −5.56231 | −0.387544 | ||||||||
\(207\) | 6.47214 | 0.449845 | ||||||||
\(208\) | −10.1459 | −0.703491 | ||||||||
\(209\) | −7.23607 | −0.500529 | ||||||||
\(210\) | −0.909830 | −0.0627842 | ||||||||
\(211\) | −18.0000 | −1.23917 | −0.619586 | − | 0.784929i | \(-0.712699\pi\) | ||||
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(212\) | 6.61803 | 0.454528 | ||||||||
\(213\) | 11.0902 | 0.759886 | ||||||||
\(214\) | −5.14590 | −0.351766 | ||||||||
\(215\) | 2.81966 | 0.192299 | ||||||||
\(216\) | 11.1803 | 0.760726 | ||||||||
\(217\) | 3.85410 | 0.261633 | ||||||||
\(218\) | 2.03444 | 0.137790 | ||||||||
\(219\) | −10.7082 | −0.723593 | ||||||||
\(220\) | 0.618034 | 0.0416678 | ||||||||
\(221\) | 23.1803 | 1.55928 | ||||||||
\(222\) | 0.145898 | 0.00979203 | ||||||||
\(223\) | −9.29180 | −0.622225 | −0.311112 | − | 0.950373i | \(-0.600702\pi\) | ||||
−0.311112 | + | 0.950373i | \(0.600702\pi\) | |||||||
\(224\) | −21.6525 | −1.44672 | ||||||||
\(225\) | 9.70820 | 0.647214 | ||||||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | −29.3607 | −1.94874 | −0.974368 | − | 0.224958i | \(-0.927775\pi\) | ||||
−0.974368 | + | 0.224958i | \(0.927775\pi\) | |||||||
\(228\) | −11.7082 | −0.775395 | ||||||||
\(229\) | −25.8541 | −1.70849 | −0.854244 | − | 0.519873i | \(-0.825979\pi\) | ||||
−0.854244 | + | 0.519873i | \(0.825979\pi\) | |||||||
\(230\) | −0.763932 | −0.0503722 | ||||||||
\(231\) | −3.85410 | −0.253581 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.4721 | −1.34117 | −0.670587 | − | 0.741831i | \(-0.733958\pi\) | ||||
−0.670587 | + | 0.741831i | \(0.733958\pi\) | |||||||
\(234\) | −6.76393 | −0.442172 | ||||||||
\(235\) | −0.416408 | −0.0271635 | ||||||||
\(236\) | −3.61803 | −0.235514 | ||||||||
\(237\) | 5.00000 | 0.324785 | ||||||||
\(238\) | 10.0902 | 0.654049 | ||||||||
\(239\) | 18.6180 | 1.20430 | 0.602150 | − | 0.798383i | \(-0.294311\pi\) | ||||
0.602150 | + | 0.798383i | \(0.294311\pi\) | |||||||
\(240\) | 0.708204 | 0.0457144 | ||||||||
\(241\) | 3.90983 | 0.251854 | 0.125927 | − | 0.992039i | \(-0.459809\pi\) | ||||
0.125927 | + | 0.992039i | \(0.459809\pi\) | |||||||
\(242\) | −0.618034 | −0.0397287 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 17.9443 | 1.14876 | ||||||||
\(245\) | −3.00000 | −0.191663 | ||||||||
\(246\) | 6.23607 | 0.397597 | ||||||||
\(247\) | 39.5967 | 2.51948 | ||||||||
\(248\) | 2.23607 | 0.141990 | ||||||||
\(249\) | −10.3820 | −0.657930 | ||||||||
\(250\) | −2.32624 | −0.147124 | ||||||||
\(251\) | 15.0902 | 0.952483 | 0.476242 | − | 0.879315i | \(-0.341999\pi\) | ||||
0.476242 | + | 0.879315i | \(0.341999\pi\) | |||||||
\(252\) | 12.4721 | 0.785671 | ||||||||
\(253\) | −3.23607 | −0.203450 | ||||||||
\(254\) | 3.27051 | 0.205210 | ||||||||
\(255\) | −1.61803 | −0.101325 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 27.0689 | 1.68851 | 0.844255 | − | 0.535941i | \(-0.180043\pi\) | ||||
0.844255 | + | 0.535941i | \(0.180043\pi\) | |||||||
\(258\) | −4.56231 | −0.284037 | ||||||||
\(259\) | 0.909830 | 0.0565341 | ||||||||
\(260\) | −3.38197 | −0.209741 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.94427 | 0.614359 | ||||||||
\(263\) | 20.3820 | 1.25681 | 0.628403 | − | 0.777888i | \(-0.283709\pi\) | ||||
0.628403 | + | 0.777888i | \(0.283709\pi\) | |||||||
\(264\) | −2.23607 | −0.137620 | ||||||||
\(265\) | 1.56231 | 0.0959717 | ||||||||
\(266\) | 17.2361 | 1.05681 | ||||||||
\(267\) | 10.3262 | 0.631955 | ||||||||
\(268\) | 11.3262 | 0.691860 | ||||||||
\(269\) | −13.7426 | −0.837904 | −0.418952 | − | 0.908008i | \(-0.637602\pi\) | ||||
−0.418952 | + | 0.908008i | \(0.637602\pi\) | |||||||
\(270\) | 1.18034 | 0.0718332 | ||||||||
\(271\) | −22.2705 | −1.35284 | −0.676419 | − | 0.736517i | \(-0.736469\pi\) | ||||
−0.676419 | + | 0.736517i | \(0.736469\pi\) | |||||||
\(272\) | −7.85410 | −0.476225 | ||||||||
\(273\) | 21.0902 | 1.27644 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −4.85410 | −0.292713 | ||||||||
\(276\) | −5.23607 | −0.315174 | ||||||||
\(277\) | −13.7082 | −0.823646 | −0.411823 | − | 0.911264i | \(-0.635108\pi\) | ||||
−0.411823 | + | 0.911264i | \(0.635108\pi\) | |||||||
\(278\) | −5.20163 | −0.311973 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | −3.29180 | −0.196722 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 0.673762 | 0.0401219 | ||||||||
\(283\) | 22.2148 | 1.32053 | 0.660266 | − | 0.751032i | \(-0.270444\pi\) | ||||
0.660266 | + | 0.751032i | \(0.270444\pi\) | |||||||
\(284\) | 17.9443 | 1.06480 | ||||||||
\(285\) | −2.76393 | −0.163721 | ||||||||
\(286\) | 3.38197 | 0.199980 | ||||||||
\(287\) | 38.8885 | 2.29552 | ||||||||
\(288\) | 11.2361 | 0.662092 | ||||||||
\(289\) | 0.944272 | 0.0555454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.944272 | 0.0553542 | ||||||||
\(292\) | −17.3262 | −1.01394 | ||||||||
\(293\) | 0.0557281 | 0.00325567 | 0.00162783 | − | 0.999999i | \(-0.499482\pi\) | ||||
0.00162783 | + | 0.999999i | \(0.499482\pi\) | |||||||
\(294\) | 4.85410 | 0.283097 | ||||||||
\(295\) | −0.854102 | −0.0497277 | ||||||||
\(296\) | 0.527864 | 0.0306815 | ||||||||
\(297\) | 5.00000 | 0.290129 | ||||||||
\(298\) | −1.38197 | −0.0800551 | ||||||||
\(299\) | 17.7082 | 1.02409 | ||||||||
\(300\) | −7.85410 | −0.453457 | ||||||||
\(301\) | −28.4508 | −1.63988 | ||||||||
\(302\) | 10.6738 | 0.614206 | ||||||||
\(303\) | −18.1803 | −1.04443 | ||||||||
\(304\) | −13.4164 | −0.769484 | ||||||||
\(305\) | 4.23607 | 0.242557 | ||||||||
\(306\) | −5.23607 | −0.299326 | ||||||||
\(307\) | 25.6869 | 1.46603 | 0.733015 | − | 0.680213i | \(-0.238113\pi\) | ||||
0.733015 | + | 0.680213i | \(0.238113\pi\) | |||||||
\(308\) | −6.23607 | −0.355333 | ||||||||
\(309\) | −9.00000 | −0.511992 | ||||||||
\(310\) | 0.236068 | 0.0134078 | ||||||||
\(311\) | −28.4508 | −1.61330 | −0.806650 | − | 0.591030i | \(-0.798722\pi\) | ||||
−0.806650 | + | 0.591030i | \(0.798722\pi\) | |||||||
\(312\) | 12.2361 | 0.692731 | ||||||||
\(313\) | −11.1246 | −0.628800 | −0.314400 | − | 0.949291i | \(-0.601803\pi\) | ||||
−0.314400 | + | 0.949291i | \(0.601803\pi\) | |||||||
\(314\) | 5.90983 | 0.333511 | ||||||||
\(315\) | 2.94427 | 0.165891 | ||||||||
\(316\) | 8.09017 | 0.455108 | ||||||||
\(317\) | −17.1246 | −0.961814 | −0.480907 | − | 0.876772i | \(-0.659693\pi\) | ||||
−0.480907 | + | 0.876772i | \(0.659693\pi\) | |||||||
\(318\) | −2.52786 | −0.141756 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.0901699 | 0.00504065 | ||||||||
\(321\) | −8.32624 | −0.464725 | ||||||||
\(322\) | 7.70820 | 0.429561 | ||||||||
\(323\) | 30.6525 | 1.70555 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 26.5623 | 1.47341 | ||||||||
\(326\) | 6.79837 | 0.376527 | ||||||||
\(327\) | 3.29180 | 0.182037 | ||||||||
\(328\) | 22.5623 | 1.24579 | ||||||||
\(329\) | 4.20163 | 0.231643 | ||||||||
\(330\) | −0.236068 | −0.0129951 | ||||||||
\(331\) | −11.8197 | −0.649667 | −0.324834 | − | 0.945771i | \(-0.605308\pi\) | ||||
−0.324834 | + | 0.945771i | \(0.605308\pi\) | |||||||
\(332\) | −16.7984 | −0.921931 | ||||||||
\(333\) | −0.472136 | −0.0258729 | ||||||||
\(334\) | −5.79837 | −0.317273 | ||||||||
\(335\) | 2.67376 | 0.146083 | ||||||||
\(336\) | −7.14590 | −0.389841 | ||||||||
\(337\) | 28.8541 | 1.57178 | 0.785892 | − | 0.618364i | \(-0.212204\pi\) | ||||
0.785892 | + | 0.618364i | \(0.212204\pi\) | |||||||
\(338\) | −10.4721 | −0.569609 | ||||||||
\(339\) | −12.9443 | −0.703036 | ||||||||
\(340\) | −2.61803 | −0.141983 | ||||||||
\(341\) | 1.00000 | 0.0541530 | ||||||||
\(342\) | −8.94427 | −0.483651 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | −16.5066 | −0.889975 | ||||||||
\(345\) | −1.23607 | −0.0665477 | ||||||||
\(346\) | −6.74265 | −0.362487 | ||||||||
\(347\) | −4.88854 | −0.262431 | −0.131215 | − | 0.991354i | \(-0.541888\pi\) | ||||
−0.131215 | + | 0.991354i | \(0.541888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.9787 | 1.39061 | 0.695304 | − | 0.718715i | \(-0.255270\pi\) | ||||
0.695304 | + | 0.718715i | \(0.255270\pi\) | |||||||
\(350\) | 11.5623 | 0.618031 | ||||||||
\(351\) | −27.3607 | −1.46041 | ||||||||
\(352\) | −5.61803 | −0.299442 | ||||||||
\(353\) | −29.7426 | −1.58304 | −0.791521 | − | 0.611142i | \(-0.790710\pi\) | ||||
−0.791521 | + | 0.611142i | \(0.790710\pi\) | |||||||
\(354\) | 1.38197 | 0.0734507 | ||||||||
\(355\) | 4.23607 | 0.224827 | ||||||||
\(356\) | 16.7082 | 0.885533 | ||||||||
\(357\) | 16.3262 | 0.864076 | ||||||||
\(358\) | 10.9787 | 0.580243 | ||||||||
\(359\) | −20.1246 | −1.06214 | −0.531068 | − | 0.847329i | \(-0.678209\pi\) | ||||
−0.531068 | + | 0.847329i | \(0.678209\pi\) | |||||||
\(360\) | 1.70820 | 0.0900303 | ||||||||
\(361\) | 33.3607 | 1.75583 | ||||||||
\(362\) | 3.76393 | 0.197828 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 34.1246 | 1.78862 | ||||||||
\(365\) | −4.09017 | −0.214089 | ||||||||
\(366\) | −6.85410 | −0.358270 | ||||||||
\(367\) | 7.14590 | 0.373013 | 0.186506 | − | 0.982454i | \(-0.440283\pi\) | ||||
0.186506 | + | 0.982454i | \(0.440283\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | −20.1803 | −1.05055 | ||||||||
\(370\) | 0.0557281 | 0.00289717 | ||||||||
\(371\) | −15.7639 | −0.818423 | ||||||||
\(372\) | 1.61803 | 0.0838912 | ||||||||
\(373\) | 17.0902 | 0.884895 | 0.442448 | − | 0.896794i | \(-0.354110\pi\) | ||||
0.442448 | + | 0.896794i | \(0.354110\pi\) | |||||||
\(374\) | 2.61803 | 0.135375 | ||||||||
\(375\) | −3.76393 | −0.194369 | ||||||||
\(376\) | 2.43769 | 0.125714 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −11.9098 | −0.612576 | ||||||||
\(379\) | 14.2705 | 0.733027 | 0.366513 | − | 0.930413i | \(-0.380551\pi\) | ||||
0.366513 | + | 0.930413i | \(0.380551\pi\) | |||||||
\(380\) | −4.47214 | −0.229416 | ||||||||
\(381\) | 5.29180 | 0.271107 | ||||||||
\(382\) | −5.05573 | −0.258674 | ||||||||
\(383\) | −6.52786 | −0.333558 | −0.166779 | − | 0.985994i | \(-0.553337\pi\) | ||||
−0.166779 | + | 0.985994i | \(0.553337\pi\) | |||||||
\(384\) | −11.3820 | −0.580834 | ||||||||
\(385\) | −1.47214 | −0.0750270 | ||||||||
\(386\) | −1.74265 | −0.0886983 | ||||||||
\(387\) | 14.7639 | 0.750493 | ||||||||
\(388\) | 1.52786 | 0.0775655 | ||||||||
\(389\) | −32.2361 | −1.63443 | −0.817217 | − | 0.576330i | \(-0.804484\pi\) | ||||
−0.817217 | + | 0.576330i | \(0.804484\pi\) | |||||||
\(390\) | 1.29180 | 0.0654126 | ||||||||
\(391\) | 13.7082 | 0.693254 | ||||||||
\(392\) | 17.5623 | 0.887030 | ||||||||
\(393\) | 16.0902 | 0.811642 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 1.90983 | 0.0960940 | ||||||||
\(396\) | 3.23607 | 0.162619 | ||||||||
\(397\) | 13.0000 | 0.652451 | 0.326226 | − | 0.945292i | \(-0.394223\pi\) | ||||
0.326226 | + | 0.945292i | \(0.394223\pi\) | |||||||
\(398\) | −14.1459 | −0.709070 | ||||||||
\(399\) | 27.8885 | 1.39617 | ||||||||
\(400\) | −9.00000 | −0.450000 | ||||||||
\(401\) | −29.1803 | −1.45720 | −0.728598 | − | 0.684941i | \(-0.759828\pi\) | ||||
−0.728598 | + | 0.684941i | \(0.759828\pi\) | |||||||
\(402\) | −4.32624 | −0.215773 | ||||||||
\(403\) | −5.47214 | −0.272587 | ||||||||
\(404\) | −29.4164 | −1.46352 | ||||||||
\(405\) | −0.381966 | −0.0189800 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.236068 | 0.0117015 | ||||||||
\(408\) | 9.47214 | 0.468941 | ||||||||
\(409\) | 30.1246 | 1.48957 | 0.744783 | − | 0.667307i | \(-0.232553\pi\) | ||||
0.744783 | + | 0.667307i | \(0.232553\pi\) | |||||||
\(410\) | 2.38197 | 0.117637 | ||||||||
\(411\) | −9.70820 | −0.478870 | ||||||||
\(412\) | −14.5623 | −0.717433 | ||||||||
\(413\) | 8.61803 | 0.424066 | ||||||||
\(414\) | −4.00000 | −0.196589 | ||||||||
\(415\) | −3.96556 | −0.194662 | ||||||||
\(416\) | 30.7426 | 1.50728 | ||||||||
\(417\) | −8.41641 | −0.412153 | ||||||||
\(418\) | 4.47214 | 0.218739 | ||||||||
\(419\) | −14.4721 | −0.707010 | −0.353505 | − | 0.935433i | \(-0.615010\pi\) | ||||
−0.353505 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(420\) | −2.38197 | −0.116228 | ||||||||
\(421\) | −3.00000 | −0.146211 | −0.0731055 | − | 0.997324i | \(-0.523291\pi\) | ||||
−0.0731055 | + | 0.997324i | \(0.523291\pi\) | |||||||
\(422\) | 11.1246 | 0.541538 | ||||||||
\(423\) | −2.18034 | −0.106012 | ||||||||
\(424\) | −9.14590 | −0.444164 | ||||||||
\(425\) | 20.5623 | 0.997418 | ||||||||
\(426\) | −6.85410 | −0.332082 | ||||||||
\(427\) | −42.7426 | −2.06846 | ||||||||
\(428\) | −13.4721 | −0.651200 | ||||||||
\(429\) | 5.47214 | 0.264197 | ||||||||
\(430\) | −1.74265 | −0.0840378 | ||||||||
\(431\) | −26.0902 | −1.25672 | −0.628360 | − | 0.777923i | \(-0.716273\pi\) | ||||
−0.628360 | + | 0.777923i | \(0.716273\pi\) | |||||||
\(432\) | 9.27051 | 0.446028 | ||||||||
\(433\) | −8.43769 | −0.405490 | −0.202745 | − | 0.979232i | \(-0.564986\pi\) | ||||
−0.202745 | + | 0.979232i | \(0.564986\pi\) | |||||||
\(434\) | −2.38197 | −0.114338 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.32624 | 0.255081 | ||||||||
\(437\) | 23.4164 | 1.12016 | ||||||||
\(438\) | 6.61803 | 0.316222 | ||||||||
\(439\) | 6.18034 | 0.294972 | 0.147486 | − | 0.989064i | \(-0.452882\pi\) | ||||
0.147486 | + | 0.989064i | \(0.452882\pi\) | |||||||
\(440\) | −0.854102 | −0.0407177 | ||||||||
\(441\) | −15.7082 | −0.748010 | ||||||||
\(442\) | −14.3262 | −0.681430 | ||||||||
\(443\) | 20.8328 | 0.989797 | 0.494898 | − | 0.868951i | \(-0.335205\pi\) | ||||
0.494898 | + | 0.868951i | \(0.335205\pi\) | |||||||
\(444\) | 0.381966 | 0.0181273 | ||||||||
\(445\) | 3.94427 | 0.186976 | ||||||||
\(446\) | 5.74265 | 0.271922 | ||||||||
\(447\) | −2.23607 | −0.105762 | ||||||||
\(448\) | −0.909830 | −0.0429854 | ||||||||
\(449\) | −19.7984 | −0.934343 | −0.467172 | − | 0.884167i | \(-0.654727\pi\) | ||||
−0.467172 | + | 0.884167i | \(0.654727\pi\) | |||||||
\(450\) | −6.00000 | −0.282843 | ||||||||
\(451\) | 10.0902 | 0.475128 | ||||||||
\(452\) | −20.9443 | −0.985136 | ||||||||
\(453\) | 17.2705 | 0.811439 | ||||||||
\(454\) | 18.1459 | 0.851629 | ||||||||
\(455\) | 8.05573 | 0.377658 | ||||||||
\(456\) | 16.1803 | 0.757714 | ||||||||
\(457\) | −28.5066 | −1.33348 | −0.666741 | − | 0.745290i | \(-0.732311\pi\) | ||||
−0.666741 | + | 0.745290i | \(0.732311\pi\) | |||||||
\(458\) | 15.9787 | 0.746636 | ||||||||
\(459\) | −21.1803 | −0.988614 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | −14.1803 | −0.660444 | −0.330222 | − | 0.943903i | \(-0.607124\pi\) | ||||
−0.330222 | + | 0.943903i | \(0.607124\pi\) | |||||||
\(462\) | 2.38197 | 0.110819 | ||||||||
\(463\) | −0.472136 | −0.0219420 | −0.0109710 | − | 0.999940i | \(-0.503492\pi\) | ||||
−0.0109710 | + | 0.999940i | \(0.503492\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.381966 | 0.0177132 | ||||||||
\(466\) | 12.6525 | 0.586115 | ||||||||
\(467\) | −7.85410 | −0.363444 | −0.181722 | − | 0.983350i | \(-0.558167\pi\) | ||||
−0.181722 | + | 0.983350i | \(0.558167\pi\) | |||||||
\(468\) | −17.7082 | −0.818562 | ||||||||
\(469\) | −26.9787 | −1.24576 | ||||||||
\(470\) | 0.257354 | 0.0118709 | ||||||||
\(471\) | 9.56231 | 0.440608 | ||||||||
\(472\) | 5.00000 | 0.230144 | ||||||||
\(473\) | −7.38197 | −0.339423 | ||||||||
\(474\) | −3.09017 | −0.141936 | ||||||||
\(475\) | 35.1246 | 1.61163 | ||||||||
\(476\) | 26.4164 | 1.21079 | ||||||||
\(477\) | 8.18034 | 0.374552 | ||||||||
\(478\) | −11.5066 | −0.526299 | ||||||||
\(479\) | 6.38197 | 0.291599 | 0.145800 | − | 0.989314i | \(-0.453424\pi\) | ||||
0.145800 | + | 0.989314i | \(0.453424\pi\) | |||||||
\(480\) | −2.14590 | −0.0979464 | ||||||||
\(481\) | −1.29180 | −0.0589008 | ||||||||
\(482\) | −2.41641 | −0.110064 | ||||||||
\(483\) | 12.4721 | 0.567502 | ||||||||
\(484\) | −1.61803 | −0.0735470 | ||||||||
\(485\) | 0.360680 | 0.0163776 | ||||||||
\(486\) | 9.88854 | 0.448553 | ||||||||
\(487\) | −14.0344 | −0.635961 | −0.317981 | − | 0.948097i | \(-0.603005\pi\) | ||||
−0.317981 | + | 0.948097i | \(0.603005\pi\) | |||||||
\(488\) | −24.7984 | −1.12257 | ||||||||
\(489\) | 11.0000 | 0.497437 | ||||||||
\(490\) | 1.85410 | 0.0837598 | ||||||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | 16.3262 | 0.736044 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −24.4721 | −1.10105 | ||||||||
\(495\) | 0.763932 | 0.0343362 | ||||||||
\(496\) | 1.85410 | 0.0832516 | ||||||||
\(497\) | −42.7426 | −1.91727 | ||||||||
\(498\) | 6.41641 | 0.287526 | ||||||||
\(499\) | −39.3951 | −1.76357 | −0.881784 | − | 0.471654i | \(-0.843657\pi\) | ||||
−0.881784 | + | 0.471654i | \(0.843657\pi\) | |||||||
\(500\) | −6.09017 | −0.272361 | ||||||||
\(501\) | −9.38197 | −0.419155 | ||||||||
\(502\) | −9.32624 | −0.416250 | ||||||||
\(503\) | 6.76393 | 0.301589 | 0.150794 | − | 0.988565i | \(-0.451817\pi\) | ||||
0.150794 | + | 0.988565i | \(0.451817\pi\) | |||||||
\(504\) | −17.2361 | −0.767755 | ||||||||
\(505\) | −6.94427 | −0.309016 | ||||||||
\(506\) | 2.00000 | 0.0889108 | ||||||||
\(507\) | −16.9443 | −0.752522 | ||||||||
\(508\) | 8.56231 | 0.379891 | ||||||||
\(509\) | −3.81966 | −0.169303 | −0.0846517 | − | 0.996411i | \(-0.526978\pi\) | ||||
−0.0846517 | + | 0.996411i | \(0.526978\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | 41.2705 | 1.82570 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | −36.1803 | −1.59740 | ||||||||
\(514\) | −16.7295 | −0.737906 | ||||||||
\(515\) | −3.43769 | −0.151483 | ||||||||
\(516\) | −11.9443 | −0.525817 | ||||||||
\(517\) | 1.09017 | 0.0479456 | ||||||||
\(518\) | −0.562306 | −0.0247063 | ||||||||
\(519\) | −10.9098 | −0.478888 | ||||||||
\(520\) | 4.67376 | 0.204958 | ||||||||
\(521\) | 17.4508 | 0.764536 | 0.382268 | − | 0.924052i | \(-0.375143\pi\) | ||||
0.382268 | + | 0.924052i | \(0.375143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2705 | 0.798914 | 0.399457 | − | 0.916752i | \(-0.369199\pi\) | ||||
0.399457 | + | 0.916752i | \(0.369199\pi\) | |||||||
\(524\) | 26.0344 | 1.13732 | ||||||||
\(525\) | 18.7082 | 0.816493 | ||||||||
\(526\) | −12.5967 | −0.549244 | ||||||||
\(527\) | −4.23607 | −0.184526 | ||||||||
\(528\) | −1.85410 | −0.0806894 | ||||||||
\(529\) | −12.5279 | −0.544690 | ||||||||
\(530\) | −0.965558 | −0.0419412 | ||||||||
\(531\) | −4.47214 | −0.194074 | ||||||||
\(532\) | 45.1246 | 1.95640 | ||||||||
\(533\) | −55.2148 | −2.39162 | ||||||||
\(534\) | −6.38197 | −0.276175 | ||||||||
\(535\) | −3.18034 | −0.137498 | ||||||||
\(536\) | −15.6525 | −0.676084 | ||||||||
\(537\) | 17.7639 | 0.766570 | ||||||||
\(538\) | 8.49342 | 0.366177 | ||||||||
\(539\) | 7.85410 | 0.338300 | ||||||||
\(540\) | 3.09017 | 0.132980 | ||||||||
\(541\) | 39.3607 | 1.69225 | 0.846124 | − | 0.532986i | \(-0.178930\pi\) | ||||
0.846124 | + | 0.532986i | \(0.178930\pi\) | |||||||
\(542\) | 13.7639 | 0.591212 | ||||||||
\(543\) | 6.09017 | 0.261354 | ||||||||
\(544\) | 23.7984 | 1.02035 | ||||||||
\(545\) | 1.25735 | 0.0538591 | ||||||||
\(546\) | −13.0344 | −0.557823 | ||||||||
\(547\) | 4.38197 | 0.187359 | 0.0936797 | − | 0.995602i | \(-0.470137\pi\) | ||||
0.0936797 | + | 0.995602i | \(0.470137\pi\) | |||||||
\(548\) | −15.7082 | −0.671021 | ||||||||
\(549\) | 22.1803 | 0.946634 | ||||||||
\(550\) | 3.00000 | 0.127920 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 7.23607 | 0.307988 | ||||||||
\(553\) | −19.2705 | −0.819465 | ||||||||
\(554\) | 8.47214 | 0.359947 | ||||||||
\(555\) | 0.0901699 | 0.00382750 | ||||||||
\(556\) | −13.6180 | −0.577533 | ||||||||
\(557\) | 1.41641 | 0.0600151 | 0.0300076 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300076 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(558\) | 1.23607 | 0.0523269 | ||||||||
\(559\) | 40.3951 | 1.70853 | ||||||||
\(560\) | −2.72949 | −0.115342 | ||||||||
\(561\) | 4.23607 | 0.178847 | ||||||||
\(562\) | −7.41641 | −0.312842 | ||||||||
\(563\) | −41.1246 | −1.73320 | −0.866598 | − | 0.499007i | \(-0.833698\pi\) | ||||
−0.866598 | + | 0.499007i | \(0.833698\pi\) | |||||||
\(564\) | 1.76393 | 0.0742749 | ||||||||
\(565\) | −4.94427 | −0.208007 | ||||||||
\(566\) | −13.7295 | −0.577094 | ||||||||
\(567\) | 3.85410 | 0.161857 | ||||||||
\(568\) | −24.7984 | −1.04052 | ||||||||
\(569\) | 28.4164 | 1.19128 | 0.595639 | − | 0.803252i | \(-0.296899\pi\) | ||||
0.595639 | + | 0.803252i | \(0.296899\pi\) | |||||||
\(570\) | 1.70820 | 0.0715488 | ||||||||
\(571\) | −12.2705 | −0.513505 | −0.256752 | − | 0.966477i | \(-0.582652\pi\) | ||||
−0.256752 | + | 0.966477i | \(0.582652\pi\) | |||||||
\(572\) | 8.85410 | 0.370209 | ||||||||
\(573\) | −8.18034 | −0.341739 | ||||||||
\(574\) | −24.0344 | −1.00318 | ||||||||
\(575\) | 15.7082 | 0.655077 | ||||||||
\(576\) | 0.472136 | 0.0196723 | ||||||||
\(577\) | −24.0344 | −1.00057 | −0.500283 | − | 0.865862i | \(-0.666771\pi\) | ||||
−0.500283 | + | 0.865862i | \(0.666771\pi\) | |||||||
\(578\) | −0.583592 | −0.0242742 | ||||||||
\(579\) | −2.81966 | −0.117181 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.0132 | 1.66003 | ||||||||
\(582\) | −0.583592 | −0.0241907 | ||||||||
\(583\) | −4.09017 | −0.169398 | ||||||||
\(584\) | 23.9443 | 0.990821 | ||||||||
\(585\) | −4.18034 | −0.172836 | ||||||||
\(586\) | −0.0344419 | −0.00142278 | ||||||||
\(587\) | −18.9098 | −0.780492 | −0.390246 | − | 0.920711i | \(-0.627610\pi\) | ||||
−0.390246 | + | 0.920711i | \(0.627610\pi\) | |||||||
\(588\) | 12.7082 | 0.524077 | ||||||||
\(589\) | −7.23607 | −0.298157 | ||||||||
\(590\) | 0.527864 | 0.0217318 | ||||||||
\(591\) | −9.70820 | −0.399342 | ||||||||
\(592\) | 0.437694 | 0.0179891 | ||||||||
\(593\) | 25.5066 | 1.04743 | 0.523715 | − | 0.851894i | \(-0.324546\pi\) | ||||
0.523715 | + | 0.851894i | \(0.324546\pi\) | |||||||
\(594\) | −3.09017 | −0.126791 | ||||||||
\(595\) | 6.23607 | 0.255654 | ||||||||
\(596\) | −3.61803 | −0.148200 | ||||||||
\(597\) | −22.8885 | −0.936766 | ||||||||
\(598\) | −10.9443 | −0.447545 | ||||||||
\(599\) | −15.6525 | −0.639543 | −0.319771 | − | 0.947495i | \(-0.603606\pi\) | ||||
−0.319771 | + | 0.947495i | \(0.603606\pi\) | |||||||
\(600\) | 10.8541 | 0.443117 | ||||||||
\(601\) | −18.0000 | −0.734235 | −0.367118 | − | 0.930175i | \(-0.619655\pi\) | ||||
−0.367118 | + | 0.930175i | \(0.619655\pi\) | |||||||
\(602\) | 17.5836 | 0.716654 | ||||||||
\(603\) | 14.0000 | 0.570124 | ||||||||
\(604\) | 27.9443 | 1.13704 | ||||||||
\(605\) | −0.381966 | −0.0155291 | ||||||||
\(606\) | 11.2361 | 0.456434 | ||||||||
\(607\) | 33.1246 | 1.34449 | 0.672243 | − | 0.740330i | \(-0.265331\pi\) | ||||
0.672243 | + | 0.740330i | \(0.265331\pi\) | |||||||
\(608\) | 40.6525 | 1.64868 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.61803 | −0.106001 | ||||||||
\(611\) | −5.96556 | −0.241341 | ||||||||
\(612\) | −13.7082 | −0.554121 | ||||||||
\(613\) | −28.2361 | −1.14044 | −0.570222 | − | 0.821491i | \(-0.693143\pi\) | ||||
−0.570222 | + | 0.821491i | \(0.693143\pi\) | |||||||
\(614\) | −15.8754 | −0.640679 | ||||||||
\(615\) | 3.85410 | 0.155412 | ||||||||
\(616\) | 8.61803 | 0.347230 | ||||||||
\(617\) | −33.3050 | −1.34081 | −0.670403 | − | 0.741997i | \(-0.733879\pi\) | ||||
−0.670403 | + | 0.741997i | \(0.733879\pi\) | |||||||
\(618\) | 5.56231 | 0.223749 | ||||||||
\(619\) | −13.6180 | −0.547355 | −0.273677 | − | 0.961822i | \(-0.588240\pi\) | ||||
−0.273677 | + | 0.961822i | \(0.588240\pi\) | |||||||
\(620\) | 0.618034 | 0.0248208 | ||||||||
\(621\) | −16.1803 | −0.649295 | ||||||||
\(622\) | 17.5836 | 0.705038 | ||||||||
\(623\) | −39.7984 | −1.59449 | ||||||||
\(624\) | 10.1459 | 0.406161 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 6.87539 | 0.274796 | ||||||||
\(627\) | 7.23607 | 0.288981 | ||||||||
\(628\) | 15.4721 | 0.617405 | ||||||||
\(629\) | −1.00000 | −0.0398726 | ||||||||
\(630\) | −1.81966 | −0.0724970 | ||||||||
\(631\) | −27.2705 | −1.08562 | −0.542811 | − | 0.839855i | \(-0.682640\pi\) | ||||
−0.542811 | + | 0.839855i | \(0.682640\pi\) | |||||||
\(632\) | −11.1803 | −0.444730 | ||||||||
\(633\) | 18.0000 | 0.715436 | ||||||||
\(634\) | 10.5836 | 0.420328 | ||||||||
\(635\) | 2.02129 | 0.0802123 | ||||||||
\(636\) | −6.61803 | −0.262422 | ||||||||
\(637\) | −42.9787 | −1.70288 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.1803 | 0.877441 | ||||||||
\(640\) | −4.34752 | −0.171851 | ||||||||
\(641\) | 13.9098 | 0.549405 | 0.274703 | − | 0.961529i | \(-0.411421\pi\) | ||||
0.274703 | + | 0.961529i | \(0.411421\pi\) | |||||||
\(642\) | 5.14590 | 0.203092 | ||||||||
\(643\) | −28.5623 | −1.12639 | −0.563194 | − | 0.826325i | \(-0.690428\pi\) | ||||
−0.563194 | + | 0.826325i | \(0.690428\pi\) | |||||||
\(644\) | 20.1803 | 0.795217 | ||||||||
\(645\) | −2.81966 | −0.111024 | ||||||||
\(646\) | −18.9443 | −0.745352 | ||||||||
\(647\) | 34.5066 | 1.35659 | 0.678297 | − | 0.734788i | \(-0.262718\pi\) | ||||
0.678297 | + | 0.734788i | \(0.262718\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 2.23607 | 0.0877733 | ||||||||
\(650\) | −16.4164 | −0.643904 | ||||||||
\(651\) | −3.85410 | −0.151054 | ||||||||
\(652\) | 17.7984 | 0.697038 | ||||||||
\(653\) | 19.4508 | 0.761171 | 0.380585 | − | 0.924746i | \(-0.375723\pi\) | ||||
0.380585 | + | 0.924746i | \(0.375723\pi\) | |||||||
\(654\) | −2.03444 | −0.0795530 | ||||||||
\(655\) | 6.14590 | 0.240140 | ||||||||
\(656\) | 18.7082 | 0.730433 | ||||||||
\(657\) | −21.4164 | −0.835534 | ||||||||
\(658\) | −2.59675 | −0.101232 | ||||||||
\(659\) | −5.12461 | −0.199627 | −0.0998133 | − | 0.995006i | \(-0.531825\pi\) | ||||
−0.0998133 | + | 0.995006i | \(0.531825\pi\) | |||||||
\(660\) | −0.618034 | −0.0240569 | ||||||||
\(661\) | 20.5410 | 0.798953 | 0.399477 | − | 0.916743i | \(-0.369192\pi\) | ||||
0.399477 | + | 0.916743i | \(0.369192\pi\) | |||||||
\(662\) | 7.30495 | 0.283915 | ||||||||
\(663\) | −23.1803 | −0.900250 | ||||||||
\(664\) | 23.2148 | 0.900908 | ||||||||
\(665\) | 10.6525 | 0.413085 | ||||||||
\(666\) | 0.291796 | 0.0113069 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −15.1803 | −0.587345 | ||||||||
\(669\) | 9.29180 | 0.359242 | ||||||||
\(670\) | −1.65248 | −0.0638407 | ||||||||
\(671\) | −11.0902 | −0.428131 | ||||||||
\(672\) | 21.6525 | 0.835262 | ||||||||
\(673\) | −3.36068 | −0.129545 | −0.0647723 | − | 0.997900i | \(-0.520632\pi\) | ||||
−0.0647723 | + | 0.997900i | \(0.520632\pi\) | |||||||
\(674\) | −17.8328 | −0.686894 | ||||||||
\(675\) | −24.2705 | −0.934172 | ||||||||
\(676\) | −27.4164 | −1.05448 | ||||||||
\(677\) | 1.74265 | 0.0669753 | 0.0334877 | − | 0.999439i | \(-0.489339\pi\) | ||||
0.0334877 | + | 0.999439i | \(0.489339\pi\) | |||||||
\(678\) | 8.00000 | 0.307238 | ||||||||
\(679\) | −3.63932 | −0.139664 | ||||||||
\(680\) | 3.61803 | 0.138745 | ||||||||
\(681\) | 29.3607 | 1.12510 | ||||||||
\(682\) | −0.618034 | −0.0236657 | ||||||||
\(683\) | 31.3607 | 1.19998 | 0.599992 | − | 0.800006i | \(-0.295171\pi\) | ||||
0.599992 | + | 0.800006i | \(0.295171\pi\) | |||||||
\(684\) | −23.4164 | −0.895349 | ||||||||
\(685\) | −3.70820 | −0.141683 | ||||||||
\(686\) | −2.03444 | −0.0776754 | ||||||||
\(687\) | 25.8541 | 0.986396 | ||||||||
\(688\) | −13.6869 | −0.521809 | ||||||||
\(689\) | 22.3820 | 0.852685 | ||||||||
\(690\) | 0.763932 | 0.0290824 | ||||||||
\(691\) | −34.1803 | −1.30028 | −0.650141 | − | 0.759814i | \(-0.725290\pi\) | ||||
−0.650141 | + | 0.759814i | \(0.725290\pi\) | |||||||
\(692\) | −17.6525 | −0.671046 | ||||||||
\(693\) | −7.70820 | −0.292810 | ||||||||
\(694\) | 3.02129 | 0.114686 | ||||||||
\(695\) | −3.21478 | −0.121944 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.7426 | −1.61899 | ||||||||
\(698\) | −16.0557 | −0.607718 | ||||||||
\(699\) | 20.4721 | 0.774327 | ||||||||
\(700\) | 30.2705 | 1.14412 | ||||||||
\(701\) | −31.0902 | −1.17426 | −0.587130 | − | 0.809493i | \(-0.699742\pi\) | ||||
−0.587130 | + | 0.809493i | \(0.699742\pi\) | |||||||
\(702\) | 16.9098 | 0.638220 | ||||||||
\(703\) | −1.70820 | −0.0644261 | ||||||||
\(704\) | −0.236068 | −0.00889715 | ||||||||
\(705\) | 0.416408 | 0.0156828 | ||||||||
\(706\) | 18.3820 | 0.691814 | ||||||||
\(707\) | 70.0689 | 2.63521 | ||||||||
\(708\) | 3.61803 | 0.135974 | ||||||||
\(709\) | 33.5410 | 1.25966 | 0.629830 | − | 0.776733i | \(-0.283125\pi\) | ||||
0.629830 | + | 0.776733i | \(0.283125\pi\) | |||||||
\(710\) | −2.61803 | −0.0982531 | ||||||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | −23.0902 | −0.865341 | ||||||||
\(713\) | −3.23607 | −0.121192 | ||||||||
\(714\) | −10.0902 | −0.377615 | ||||||||
\(715\) | 2.09017 | 0.0781679 | ||||||||
\(716\) | 28.7426 | 1.07416 | ||||||||
\(717\) | −18.6180 | −0.695303 | ||||||||
\(718\) | 12.4377 | 0.464171 | ||||||||
\(719\) | 22.8885 | 0.853599 | 0.426799 | − | 0.904346i | \(-0.359641\pi\) | ||||
0.426799 | + | 0.904346i | \(0.359641\pi\) | |||||||
\(720\) | 1.41641 | 0.0527864 | ||||||||
\(721\) | 34.6869 | 1.29181 | ||||||||
\(722\) | −20.6180 | −0.767324 | ||||||||
\(723\) | −3.90983 | −0.145408 | ||||||||
\(724\) | 9.85410 | 0.366225 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.618034 | 0.0229374 | ||||||||
\(727\) | 11.2918 | 0.418790 | 0.209395 | − | 0.977831i | \(-0.432851\pi\) | ||||
0.209395 | + | 0.977831i | \(0.432851\pi\) | |||||||
\(728\) | −47.1591 | −1.74783 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 2.52786 | 0.0935604 | ||||||||
\(731\) | 31.2705 | 1.15658 | ||||||||
\(732\) | −17.9443 | −0.663239 | ||||||||
\(733\) | −27.8328 | −1.02803 | −0.514014 | − | 0.857782i | \(-0.671842\pi\) | ||||
−0.514014 | + | 0.857782i | \(0.671842\pi\) | |||||||
\(734\) | −4.41641 | −0.163013 | ||||||||
\(735\) | 3.00000 | 0.110657 | ||||||||
\(736\) | 18.1803 | 0.670136 | ||||||||
\(737\) | −7.00000 | −0.257848 | ||||||||
\(738\) | 12.4721 | 0.459106 | ||||||||
\(739\) | −28.4164 | −1.04531 | −0.522657 | − | 0.852543i | \(-0.675059\pi\) | ||||
−0.522657 | + | 0.852543i | \(0.675059\pi\) | |||||||
\(740\) | 0.145898 | 0.00536332 | ||||||||
\(741\) | −39.5967 | −1.45462 | ||||||||
\(742\) | 9.74265 | 0.357664 | ||||||||
\(743\) | 4.85410 | 0.178080 | 0.0890399 | − | 0.996028i | \(-0.471620\pi\) | ||||
0.0890399 | + | 0.996028i | \(0.471620\pi\) | |||||||
\(744\) | −2.23607 | −0.0819782 | ||||||||
\(745\) | −0.854102 | −0.0312919 | ||||||||
\(746\) | −10.5623 | −0.386713 | ||||||||
\(747\) | −20.7639 | −0.759713 | ||||||||
\(748\) | 6.85410 | 0.250611 | ||||||||
\(749\) | 32.0902 | 1.17255 | ||||||||
\(750\) | 2.32624 | 0.0849422 | ||||||||
\(751\) | 40.5410 | 1.47936 | 0.739681 | − | 0.672957i | \(-0.234976\pi\) | ||||
0.739681 | + | 0.672957i | \(0.234976\pi\) | |||||||
\(752\) | 2.02129 | 0.0737087 | ||||||||
\(753\) | −15.0902 | −0.549916 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.59675 | 0.240080 | ||||||||
\(756\) | −31.1803 | −1.13402 | ||||||||
\(757\) | 19.5836 | 0.711778 | 0.355889 | − | 0.934528i | \(-0.384178\pi\) | ||||
0.355889 | + | 0.934528i | \(0.384178\pi\) | |||||||
\(758\) | −8.81966 | −0.320344 | ||||||||
\(759\) | 3.23607 | 0.117462 | ||||||||
\(760\) | 6.18034 | 0.224184 | ||||||||
\(761\) | −19.9098 | −0.721731 | −0.360865 | − | 0.932618i | \(-0.617519\pi\) | ||||
−0.360865 | + | 0.932618i | \(0.617519\pi\) | |||||||
\(762\) | −3.27051 | −0.118478 | ||||||||
\(763\) | −12.6869 | −0.459297 | ||||||||
\(764\) | −13.2361 | −0.478864 | ||||||||
\(765\) | −3.23607 | −0.117000 | ||||||||
\(766\) | 4.03444 | 0.145770 | ||||||||
\(767\) | −12.2361 | −0.441819 | ||||||||
\(768\) | 6.56231 | 0.236797 | ||||||||
\(769\) | 45.0000 | 1.62274 | 0.811371 | − | 0.584532i | \(-0.198722\pi\) | ||||
0.811371 | + | 0.584532i | \(0.198722\pi\) | |||||||
\(770\) | 0.909830 | 0.0327880 | ||||||||
\(771\) | −27.0689 | −0.974862 | ||||||||
\(772\) | −4.56231 | −0.164201 | ||||||||
\(773\) | 30.0557 | 1.08103 | 0.540515 | − | 0.841335i | \(-0.318230\pi\) | ||||
0.540515 | + | 0.841335i | \(0.318230\pi\) | |||||||
\(774\) | −9.12461 | −0.327977 | ||||||||
\(775\) | −4.85410 | −0.174364 | ||||||||
\(776\) | −2.11146 | −0.0757969 | ||||||||
\(777\) | −0.909830 | −0.0326400 | ||||||||
\(778\) | 19.9230 | 0.714274 | ||||||||
\(779\) | −73.0132 | −2.61597 | ||||||||
\(780\) | 3.38197 | 0.121094 | ||||||||
\(781\) | −11.0902 | −0.396837 | ||||||||
\(782\) | −8.47214 | −0.302963 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14.5623 | 0.520082 | ||||||||
\(785\) | 3.65248 | 0.130362 | ||||||||
\(786\) | −9.94427 | −0.354700 | ||||||||
\(787\) | −17.1246 | −0.610426 | −0.305213 | − | 0.952284i | \(-0.598728\pi\) | ||||
−0.305213 | + | 0.952284i | \(0.598728\pi\) | |||||||
\(788\) | −15.7082 | −0.559582 | ||||||||
\(789\) | −20.3820 | −0.725617 | ||||||||
\(790\) | −1.18034 | −0.0419946 | ||||||||
\(791\) | 49.8885 | 1.77383 | ||||||||
\(792\) | −4.47214 | −0.158910 | ||||||||
\(793\) | 60.6869 | 2.15506 | ||||||||
\(794\) | −8.03444 | −0.285132 | ||||||||
\(795\) | −1.56231 | −0.0554093 | ||||||||
\(796\) | −37.0344 | −1.31265 | ||||||||
\(797\) | 50.4853 | 1.78828 | 0.894140 | − | 0.447787i | \(-0.147788\pi\) | ||||
0.894140 | + | 0.447787i | \(0.147788\pi\) | |||||||
\(798\) | −17.2361 | −0.610150 | ||||||||
\(799\) | −4.61803 | −0.163374 | ||||||||
\(800\) | 27.2705 | 0.964158 | ||||||||
\(801\) | 20.6525 | 0.729719 | ||||||||
\(802\) | 18.0344 | 0.636818 | ||||||||
\(803\) | 10.7082 | 0.377884 | ||||||||
\(804\) | −11.3262 | −0.399446 | ||||||||
\(805\) | 4.76393 | 0.167907 | ||||||||
\(806\) | 3.38197 | 0.119125 | ||||||||
\(807\) | 13.7426 | 0.483764 | ||||||||
\(808\) | 40.6525 | 1.43015 | ||||||||
\(809\) | −24.5967 | −0.864776 | −0.432388 | − | 0.901688i | \(-0.642329\pi\) | ||||
−0.432388 | + | 0.901688i | \(0.642329\pi\) | |||||||
\(810\) | 0.236068 | 0.00829458 | ||||||||
\(811\) | −5.36068 | −0.188239 | −0.0941195 | − | 0.995561i | \(-0.530004\pi\) | ||||
−0.0941195 | + | 0.995561i | \(0.530004\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.2705 | 0.781061 | ||||||||
\(814\) | −0.145898 | −0.00511372 | ||||||||
\(815\) | 4.20163 | 0.147177 | ||||||||
\(816\) | 7.85410 | 0.274949 | ||||||||
\(817\) | 53.4164 | 1.86880 | ||||||||
\(818\) | −18.6180 | −0.650964 | ||||||||
\(819\) | 42.1803 | 1.47390 | ||||||||
\(820\) | 6.23607 | 0.217773 | ||||||||
\(821\) | 45.5410 | 1.58939 | 0.794696 | − | 0.607007i | \(-0.207630\pi\) | ||||
0.794696 | + | 0.607007i | \(0.207630\pi\) | |||||||
\(822\) | 6.00000 | 0.209274 | ||||||||
\(823\) | −36.4508 | −1.27060 | −0.635298 | − | 0.772267i | \(-0.719123\pi\) | ||||
−0.635298 | + | 0.772267i | \(0.719123\pi\) | |||||||
\(824\) | 20.1246 | 0.701074 | ||||||||
\(825\) | 4.85410 | 0.168998 | ||||||||
\(826\) | −5.32624 | −0.185324 | ||||||||
\(827\) | −11.3475 | −0.394592 | −0.197296 | − | 0.980344i | \(-0.563216\pi\) | ||||
−0.197296 | + | 0.980344i | \(0.563216\pi\) | |||||||
\(828\) | −10.4721 | −0.363932 | ||||||||
\(829\) | 30.1246 | 1.04627 | 0.523136 | − | 0.852250i | \(-0.324762\pi\) | ||||
0.523136 | + | 0.852250i | \(0.324762\pi\) | |||||||
\(830\) | 2.45085 | 0.0850702 | ||||||||
\(831\) | 13.7082 | 0.475532 | ||||||||
\(832\) | 1.29180 | 0.0447850 | ||||||||
\(833\) | −33.2705 | −1.15275 | ||||||||
\(834\) | 5.20163 | 0.180118 | ||||||||
\(835\) | −3.58359 | −0.124015 | ||||||||
\(836\) | 11.7082 | 0.404937 | ||||||||
\(837\) | 5.00000 | 0.172825 | ||||||||
\(838\) | 8.94427 | 0.308975 | ||||||||
\(839\) | −28.4164 | −0.981043 | −0.490522 | − | 0.871429i | \(-0.663194\pi\) | ||||
−0.490522 | + | 0.871429i | \(0.663194\pi\) | |||||||
\(840\) | 3.29180 | 0.113578 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 1.85410 | 0.0638966 | ||||||||
\(843\) | −12.0000 | −0.413302 | ||||||||
\(844\) | 29.1246 | 1.00251 | ||||||||
\(845\) | −6.47214 | −0.222648 | ||||||||
\(846\) | 1.34752 | 0.0463288 | ||||||||
\(847\) | 3.85410 | 0.132429 | ||||||||
\(848\) | −7.58359 | −0.260422 | ||||||||
\(849\) | −22.2148 | −0.762409 | ||||||||
\(850\) | −12.7082 | −0.435888 | ||||||||
\(851\) | −0.763932 | −0.0261873 | ||||||||
\(852\) | −17.9443 | −0.614761 | ||||||||
\(853\) | −4.94427 | −0.169289 | −0.0846443 | − | 0.996411i | \(-0.526975\pi\) | ||||
−0.0846443 | + | 0.996411i | \(0.526975\pi\) | |||||||
\(854\) | 26.4164 | 0.903951 | ||||||||
\(855\) | −5.52786 | −0.189049 | ||||||||
\(856\) | 18.6180 | 0.636351 | ||||||||
\(857\) | 43.2492 | 1.47737 | 0.738683 | − | 0.674053i | \(-0.235448\pi\) | ||||
0.738683 | + | 0.674053i | \(0.235448\pi\) | |||||||
\(858\) | −3.38197 | −0.115458 | ||||||||
\(859\) | −33.9443 | −1.15816 | −0.579082 | − | 0.815269i | \(-0.696589\pi\) | ||||
−0.579082 | + | 0.815269i | \(0.696589\pi\) | |||||||
\(860\) | −4.56231 | −0.155573 | ||||||||
\(861\) | −38.8885 | −1.32532 | ||||||||
\(862\) | 16.1246 | 0.549206 | ||||||||
\(863\) | 16.0344 | 0.545819 | 0.272909 | − | 0.962040i | \(-0.412014\pi\) | ||||
0.272909 | + | 0.962040i | \(0.412014\pi\) | |||||||
\(864\) | −28.0902 | −0.955647 | ||||||||
\(865\) | −4.16718 | −0.141689 | ||||||||
\(866\) | 5.21478 | 0.177205 | ||||||||
\(867\) | −0.944272 | −0.0320692 | ||||||||
\(868\) | −6.23607 | −0.211666 | ||||||||
\(869\) | −5.00000 | −0.169613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.3050 | 1.29791 | ||||||||
\(872\) | −7.36068 | −0.249264 | ||||||||
\(873\) | 1.88854 | 0.0639175 | ||||||||
\(874\) | −14.4721 | −0.489527 | ||||||||
\(875\) | 14.5066 | 0.490412 | ||||||||
\(876\) | 17.3262 | 0.585399 | ||||||||
\(877\) | 14.0557 | 0.474628 | 0.237314 | − | 0.971433i | \(-0.423733\pi\) | ||||
0.237314 | + | 0.971433i | \(0.423733\pi\) | |||||||
\(878\) | −3.81966 | −0.128907 | ||||||||
\(879\) | −0.0557281 | −0.00187966 | ||||||||
\(880\) | −0.708204 | −0.0238735 | ||||||||
\(881\) | −26.0902 | −0.879000 | −0.439500 | − | 0.898243i | \(-0.644844\pi\) | ||||
−0.439500 | + | 0.898243i | \(0.644844\pi\) | |||||||
\(882\) | 9.70820 | 0.326892 | ||||||||
\(883\) | −6.00000 | −0.201916 | −0.100958 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100958 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(884\) | −37.5066 | −1.26148 | ||||||||
\(885\) | 0.854102 | 0.0287103 | ||||||||
\(886\) | −12.8754 | −0.432557 | ||||||||
\(887\) | −10.0902 | −0.338795 | −0.169397 | − | 0.985548i | \(-0.554182\pi\) | ||||
−0.169397 | + | 0.985548i | \(0.554182\pi\) | |||||||
\(888\) | −0.527864 | −0.0177140 | ||||||||
\(889\) | −20.3951 | −0.684030 | ||||||||
\(890\) | −2.43769 | −0.0817117 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 15.0344 | 0.503390 | ||||||||
\(893\) | −7.88854 | −0.263980 | ||||||||
\(894\) | 1.38197 | 0.0462199 | ||||||||
\(895\) | 6.78522 | 0.226805 | ||||||||
\(896\) | 43.8673 | 1.46550 | ||||||||
\(897\) | −17.7082 | −0.591260 | ||||||||
\(898\) | 12.2361 | 0.408323 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −15.7082 | −0.523607 | ||||||||
\(901\) | 17.3262 | 0.577221 | ||||||||
\(902\) | −6.23607 | −0.207638 | ||||||||
\(903\) | 28.4508 | 0.946785 | ||||||||
\(904\) | 28.9443 | 0.962672 | ||||||||
\(905\) | 2.32624 | 0.0773268 | ||||||||
\(906\) | −10.6738 | −0.354612 | ||||||||
\(907\) | −0.416408 | −0.0138266 | −0.00691330 | − | 0.999976i | \(-0.502201\pi\) | ||||
−0.00691330 | + | 0.999976i | \(0.502201\pi\) | |||||||
\(908\) | 47.5066 | 1.57656 | ||||||||
\(909\) | −36.3607 | −1.20601 | ||||||||
\(910\) | −4.97871 | −0.165043 | ||||||||
\(911\) | 10.8197 | 0.358471 | 0.179236 | − | 0.983806i | \(-0.442638\pi\) | ||||
0.179236 | + | 0.983806i | \(0.442638\pi\) | |||||||
\(912\) | 13.4164 | 0.444262 | ||||||||
\(913\) | 10.3820 | 0.343593 | ||||||||
\(914\) | 17.6180 | 0.582753 | ||||||||
\(915\) | −4.23607 | −0.140040 | ||||||||
\(916\) | 41.8328 | 1.38220 | ||||||||
\(917\) | −62.0132 | −2.04785 | ||||||||
\(918\) | 13.0902 | 0.432040 | ||||||||
\(919\) | −57.8115 | −1.90703 | −0.953513 | − | 0.301351i | \(-0.902562\pi\) | ||||
−0.953513 | + | 0.301351i | \(0.902562\pi\) | |||||||
\(920\) | 2.76393 | 0.0911241 | ||||||||
\(921\) | −25.6869 | −0.846413 | ||||||||
\(922\) | 8.76393 | 0.288625 | ||||||||
\(923\) | 60.6869 | 1.99753 | ||||||||
\(924\) | 6.23607 | 0.205152 | ||||||||
\(925\) | −1.14590 | −0.0376769 | ||||||||
\(926\) | 0.291796 | 0.00958901 | ||||||||
\(927\) | −18.0000 | −0.591198 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.0344 | −1.70719 | −0.853597 | − | 0.520933i | \(-0.825584\pi\) | ||||
−0.853597 | + | 0.520933i | \(0.825584\pi\) | |||||||
\(930\) | −0.236068 | −0.00774097 | ||||||||
\(931\) | −56.8328 | −1.86262 | ||||||||
\(932\) | 33.1246 | 1.08503 | ||||||||
\(933\) | 28.4508 | 0.931439 | ||||||||
\(934\) | 4.85410 | 0.158831 | ||||||||
\(935\) | 1.61803 | 0.0529154 | ||||||||
\(936\) | 24.4721 | 0.799897 | ||||||||
\(937\) | −37.8541 | −1.23664 | −0.618320 | − | 0.785927i | \(-0.712186\pi\) | ||||
−0.618320 | + | 0.785927i | \(0.712186\pi\) | |||||||
\(938\) | 16.6738 | 0.544418 | ||||||||
\(939\) | 11.1246 | 0.363038 | ||||||||
\(940\) | 0.673762 | 0.0219757 | ||||||||
\(941\) | 23.9098 | 0.779438 | 0.389719 | − | 0.920934i | \(-0.372572\pi\) | ||||
0.389719 | + | 0.920934i | \(0.372572\pi\) | |||||||
\(942\) | −5.90983 | −0.192553 | ||||||||
\(943\) | −32.6525 | −1.06331 | ||||||||
\(944\) | 4.14590 | 0.134937 | ||||||||
\(945\) | −7.36068 | −0.239443 | ||||||||
\(946\) | 4.56231 | 0.148333 | ||||||||
\(947\) | −53.4296 | −1.73623 | −0.868114 | − | 0.496365i | \(-0.834668\pi\) | ||||
−0.868114 | + | 0.496365i | \(0.834668\pi\) | |||||||
\(948\) | −8.09017 | −0.262757 | ||||||||
\(949\) | −58.5967 | −1.90213 | ||||||||
\(950\) | −21.7082 | −0.704307 | ||||||||
\(951\) | 17.1246 | 0.555304 | ||||||||
\(952\) | −36.5066 | −1.18318 | ||||||||
\(953\) | 32.8673 | 1.06467 | 0.532337 | − | 0.846532i | \(-0.321314\pi\) | ||||
0.532337 | + | 0.846532i | \(0.321314\pi\) | |||||||
\(954\) | −5.05573 | −0.163685 | ||||||||
\(955\) | −3.12461 | −0.101110 | ||||||||
\(956\) | −30.1246 | −0.974300 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.94427 | −0.127434 | ||||||||
\(959\) | 37.4164 | 1.20824 | ||||||||
\(960\) | −0.0901699 | −0.00291022 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0.798374 | 0.0257406 | ||||||||
\(963\) | −16.6525 | −0.536619 | ||||||||
\(964\) | −6.32624 | −0.203754 | ||||||||
\(965\) | −1.07701 | −0.0346703 | ||||||||
\(966\) | −7.70820 | −0.248007 | ||||||||
\(967\) | 13.0000 | 0.418052 | 0.209026 | − | 0.977910i | \(-0.432971\pi\) | ||||
0.209026 | + | 0.977910i | \(0.432971\pi\) | |||||||
\(968\) | 2.23607 | 0.0718699 | ||||||||
\(969\) | −30.6525 | −0.984699 | ||||||||
\(970\) | −0.222912 | −0.00715728 | ||||||||
\(971\) | −18.0000 | −0.577647 | −0.288824 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288824 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(972\) | 25.8885 | 0.830375 | ||||||||
\(973\) | 32.4377 | 1.03990 | ||||||||
\(974\) | 8.67376 | 0.277925 | ||||||||
\(975\) | −26.5623 | −0.850675 | ||||||||
\(976\) | −20.5623 | −0.658183 | ||||||||
\(977\) | −32.7771 | −1.04863 | −0.524316 | − | 0.851524i | \(-0.675679\pi\) | ||||
−0.524316 | + | 0.851524i | \(0.675679\pi\) | |||||||
\(978\) | −6.79837 | −0.217388 | ||||||||
\(979\) | −10.3262 | −0.330028 | ||||||||
\(980\) | 4.85410 | 0.155059 | ||||||||
\(981\) | 6.58359 | 0.210198 | ||||||||
\(982\) | 11.1246 | 0.355001 | ||||||||
\(983\) | −5.67376 | −0.180965 | −0.0904825 | − | 0.995898i | \(-0.528841\pi\) | ||||
−0.0904825 | + | 0.995898i | \(0.528841\pi\) | |||||||
\(984\) | −22.5623 | −0.719260 | ||||||||
\(985\) | −3.70820 | −0.118153 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.20163 | −0.133739 | ||||||||
\(988\) | −64.0689 | −2.03830 | ||||||||
\(989\) | 23.8885 | 0.759612 | ||||||||
\(990\) | −0.472136 | −0.0150055 | ||||||||
\(991\) | −26.8197 | −0.851955 | −0.425977 | − | 0.904734i | \(-0.640070\pi\) | ||||
−0.425977 | + | 0.904734i | \(0.640070\pi\) | |||||||
\(992\) | −5.61803 | −0.178373 | ||||||||
\(993\) | 11.8197 | 0.375086 | ||||||||
\(994\) | 26.4164 | 0.837878 | ||||||||
\(995\) | −8.74265 | −0.277161 | ||||||||
\(996\) | 16.7984 | 0.532277 | ||||||||
\(997\) | −14.7639 | −0.467578 | −0.233789 | − | 0.972287i | \(-0.575113\pi\) | ||||
−0.233789 | + | 0.972287i | \(0.575113\pi\) | |||||||
\(998\) | 24.3475 | 0.770707 | ||||||||
\(999\) | 1.18034 | 0.0373443 |
(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 | 341.2.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 3069.2.a.b.1.2 | 2 | |||
4.3 | odd | 2 | 5456.2.a.r.1.2 | 2 | |||
5.4 | even | 2 | 8525.2.a.d.1.2 | 2 | |||
11.10 | odd | 2 | 3751.2.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
341.2.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3069.2.a.b.1.2 | 2 | 3.2 | odd | 2 | |||
3751.2.a.a.1.2 | 2 | 11.10 | odd | 2 | |||
5456.2.a.r.1.2 | 2 | 4.3 | odd | 2 | |||
8525.2.a.d.1.2 | 2 | 5.4 | even | 2 |