Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8450,2,Mod(1,8450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8450, 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("8450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8450.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: | \(67.4735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8450.1 |
$q$-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 | ||||||||
\(3\) | 3.16228 | 1.82574 | 0.912871 | − | 0.408248i | \(-0.133860\pi\) | ||||
0.912871 | + | 0.408248i | \(0.133860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.16228 | 1.29099 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.00000 | 2.33333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.16228 | 1.25497 | 0.627487 | − | 0.778627i | \(-0.284084\pi\) | ||||
0.627487 | + | 0.778627i | \(0.284084\pi\) | |||||||
\(12\) | 3.16228 | 0.912871 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.16228 | −0.281894 | −0.140947 | − | 0.990017i | \(-0.545015\pi\) | ||||
−0.140947 | + | 0.990017i | \(0.545015\pi\) | |||||||
\(18\) | 7.00000 | 1.64992 | ||||||||
\(19\) | 8.16228 | 1.87255 | 0.936277 | − | 0.351261i | \(-0.114247\pi\) | ||||
0.936277 | + | 0.351261i | \(0.114247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.16228 | −0.690066 | ||||||||
\(22\) | 4.16228 | 0.887401 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 3.16228 | 0.645497 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.6491 | 2.43432 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.32456 | −0.431659 | −0.215830 | − | 0.976431i | \(-0.569246\pi\) | ||||
−0.215830 | + | 0.976431i | \(0.569246\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.837722 | −0.150459 | −0.0752297 | − | 0.997166i | \(-0.523969\pi\) | ||||
−0.0752297 | + | 0.997166i | \(0.523969\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 13.1623 | 2.29126 | ||||||||
\(34\) | −1.16228 | −0.199329 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.00000 | 1.16667 | ||||||||
\(37\) | 6.16228 | 1.01307 | 0.506536 | − | 0.862219i | \(-0.330926\pi\) | ||||
0.506536 | + | 0.862219i | \(0.330926\pi\) | |||||||
\(38\) | 8.16228 | 1.32410 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.32456 | −0.363035 | −0.181517 | − | 0.983388i | \(-0.558101\pi\) | ||||
−0.181517 | + | 0.983388i | \(0.558101\pi\) | |||||||
\(42\) | −3.16228 | −0.487950 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 4.16228 | 0.627487 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 3.16228 | 0.456435 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.67544 | −0.514665 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.16228 | −0.571733 | −0.285866 | − | 0.958269i | \(-0.592281\pi\) | ||||
−0.285866 | + | 0.958269i | \(0.592281\pi\) | |||||||
\(54\) | 12.6491 | 1.72133 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 25.8114 | 3.41880 | ||||||||
\(58\) | −2.32456 | −0.305229 | ||||||||
\(59\) | −2.32456 | −0.302631 | −0.151316 | − | 0.988485i | \(-0.548351\pi\) | ||||
−0.151316 | + | 0.988485i | \(0.548351\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4868 | 1.47074 | 0.735369 | − | 0.677667i | \(-0.237009\pi\) | ||||
0.735369 | + | 0.677667i | \(0.237009\pi\) | |||||||
\(62\) | −0.837722 | −0.106391 | ||||||||
\(63\) | −7.00000 | −0.881917 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.1623 | 1.62016 | ||||||||
\(67\) | 10.3246 | 1.26135 | 0.630673 | − | 0.776049i | \(-0.282779\pi\) | ||||
0.630673 | + | 0.776049i | \(0.282779\pi\) | |||||||
\(68\) | −1.16228 | −0.140947 | ||||||||
\(69\) | −18.9737 | −2.28416 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.32456 | −0.987943 | −0.493971 | − | 0.869478i | \(-0.664455\pi\) | ||||
−0.493971 | + | 0.869478i | \(0.664455\pi\) | |||||||
\(72\) | 7.00000 | 0.824958 | ||||||||
\(73\) | 9.16228 | 1.07236 | 0.536182 | − | 0.844103i | \(-0.319866\pi\) | ||||
0.536182 | + | 0.844103i | \(0.319866\pi\) | |||||||
\(74\) | 6.16228 | 0.716350 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.16228 | 0.936277 | ||||||||
\(77\) | −4.16228 | −0.474336 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.48683 | 0.617317 | 0.308658 | − | 0.951173i | \(-0.400120\pi\) | ||||
0.308658 | + | 0.951173i | \(0.400120\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 19.0000 | 2.11111 | ||||||||
\(82\) | −2.32456 | −0.256704 | ||||||||
\(83\) | −9.48683 | −1.04132 | −0.520658 | − | 0.853766i | \(-0.674313\pi\) | ||||
−0.520658 | + | 0.853766i | \(0.674313\pi\) | |||||||
\(84\) | −3.16228 | −0.345033 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −7.35089 | −0.788098 | ||||||||
\(88\) | 4.16228 | 0.443700 | ||||||||
\(89\) | −5.32456 | −0.564402 | −0.282201 | − | 0.959355i | \(-0.591064\pi\) | ||||
−0.282201 | + | 0.959355i | \(0.591064\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | −2.64911 | −0.274700 | ||||||||
\(94\) | −3.00000 | −0.309426 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.16228 | 0.322749 | ||||||||
\(97\) | 11.4868 | 1.16631 | 0.583156 | − | 0.812360i | \(-0.301818\pi\) | ||||
0.583156 | + | 0.812360i | \(0.301818\pi\) | |||||||
\(98\) | −6.00000 | −0.606092 | ||||||||
\(99\) | 29.1359 | 2.92827 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.83772 | −0.481371 | −0.240686 | − | 0.970603i | \(-0.577372\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577372\pi\) | |||||||
\(102\) | −3.67544 | −0.363923 | ||||||||
\(103\) | −13.3246 | −1.31291 | −0.656454 | − | 0.754366i | \(-0.727944\pi\) | ||||
−0.656454 | + | 0.754366i | \(0.727944\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.16228 | −0.404276 | ||||||||
\(107\) | −15.4868 | −1.49717 | −0.748584 | − | 0.663040i | \(-0.769266\pi\) | ||||
−0.748584 | + | 0.663040i | \(0.769266\pi\) | |||||||
\(108\) | 12.6491 | 1.21716 | ||||||||
\(109\) | 14.6491 | 1.40313 | 0.701565 | − | 0.712605i | \(-0.252485\pi\) | ||||
0.701565 | + | 0.712605i | \(0.252485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.4868 | 1.84961 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −16.6491 | −1.56622 | −0.783108 | − | 0.621885i | \(-0.786367\pi\) | ||||
−0.783108 | + | 0.621885i | \(0.786367\pi\) | |||||||
\(114\) | 25.8114 | 2.41746 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.32456 | −0.215830 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.32456 | −0.213993 | ||||||||
\(119\) | 1.16228 | 0.106546 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.32456 | 0.574960 | ||||||||
\(122\) | 11.4868 | 1.03997 | ||||||||
\(123\) | −7.35089 | −0.662807 | ||||||||
\(124\) | −0.837722 | −0.0752297 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.00000 | −0.623610 | ||||||||
\(127\) | 9.32456 | 0.827420 | 0.413710 | − | 0.910409i | \(-0.364233\pi\) | ||||
0.413710 | + | 0.910409i | \(0.364233\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.32456 | −0.556846 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.8114 | 1.81830 | 0.909150 | − | 0.416469i | \(-0.136733\pi\) | ||||
0.909150 | + | 0.416469i | \(0.136733\pi\) | |||||||
\(132\) | 13.1623 | 1.14563 | ||||||||
\(133\) | −8.16228 | −0.707759 | ||||||||
\(134\) | 10.3246 | 0.891906 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.16228 | −0.0996645 | ||||||||
\(137\) | −3.48683 | −0.297900 | −0.148950 | − | 0.988845i | \(-0.547589\pi\) | ||||
−0.148950 | + | 0.988845i | \(0.547589\pi\) | |||||||
\(138\) | −18.9737 | −1.61515 | ||||||||
\(139\) | −5.83772 | −0.495149 | −0.247575 | − | 0.968869i | \(-0.579634\pi\) | ||||
−0.247575 | + | 0.968869i | \(0.579634\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.48683 | −0.798935 | ||||||||
\(142\) | −8.32456 | −0.698581 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.00000 | 0.583333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.16228 | 0.758275 | ||||||||
\(147\) | −18.9737 | −1.56492 | ||||||||
\(148\) | 6.16228 | 0.506536 | ||||||||
\(149\) | −3.67544 | −0.301104 | −0.150552 | − | 0.988602i | \(-0.548105\pi\) | ||||
−0.150552 | + | 0.988602i | \(0.548105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1623 | 0.908373 | 0.454187 | − | 0.890907i | \(-0.349930\pi\) | ||||
0.454187 | + | 0.890907i | \(0.349930\pi\) | |||||||
\(152\) | 8.16228 | 0.662048 | ||||||||
\(153\) | −8.13594 | −0.657752 | ||||||||
\(154\) | −4.16228 | −0.335406 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.83772 | 0.465901 | 0.232950 | − | 0.972489i | \(-0.425162\pi\) | ||||
0.232950 | + | 0.972489i | \(0.425162\pi\) | |||||||
\(158\) | 5.48683 | 0.436509 | ||||||||
\(159\) | −13.1623 | −1.04384 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 19.0000 | 1.49278 | ||||||||
\(163\) | −1.48683 | −0.116458 | −0.0582289 | − | 0.998303i | \(-0.518545\pi\) | ||||
−0.0582289 | + | 0.998303i | \(0.518545\pi\) | |||||||
\(164\) | −2.32456 | −0.181517 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.48683 | −0.736321 | ||||||||
\(167\) | 0.675445 | 0.0522675 | 0.0261337 | − | 0.999658i | \(-0.491680\pi\) | ||||
0.0261337 | + | 0.999658i | \(0.491680\pi\) | |||||||
\(168\) | −3.16228 | −0.243975 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 57.1359 | 4.36929 | ||||||||
\(172\) | −2.00000 | −0.152499 | ||||||||
\(173\) | 4.16228 | 0.316452 | 0.158226 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158226 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(174\) | −7.35089 | −0.557269 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.16228 | 0.313743 | ||||||||
\(177\) | −7.35089 | −0.552527 | ||||||||
\(178\) | −5.32456 | −0.399092 | ||||||||
\(179\) | 9.67544 | 0.723177 | 0.361588 | − | 0.932338i | \(-0.382235\pi\) | ||||
0.361588 | + | 0.932338i | \(0.382235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8114 | −1.62123 | −0.810614 | − | 0.585581i | \(-0.800866\pi\) | ||||
−0.810614 | + | 0.585581i | \(0.800866\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 36.3246 | 2.68519 | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.64911 | −0.194242 | ||||||||
\(187\) | −4.83772 | −0.353769 | ||||||||
\(188\) | −3.00000 | −0.218797 | ||||||||
\(189\) | −12.6491 | −0.920087 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.48683 | −0.686443 | −0.343222 | − | 0.939254i | \(-0.611518\pi\) | ||||
−0.343222 | + | 0.939254i | \(0.611518\pi\) | |||||||
\(192\) | 3.16228 | 0.228218 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 11.4868 | 0.824707 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 0.486833 | 0.0346854 | 0.0173427 | − | 0.999850i | \(-0.494479\pi\) | ||||
0.0173427 | + | 0.999850i | \(0.494479\pi\) | |||||||
\(198\) | 29.1359 | 2.07060 | ||||||||
\(199\) | −26.6491 | −1.88911 | −0.944553 | − | 0.328360i | \(-0.893504\pi\) | ||||
−0.944553 | + | 0.328360i | \(0.893504\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.6491 | 2.30289 | ||||||||
\(202\) | −4.83772 | −0.340381 | ||||||||
\(203\) | 2.32456 | 0.163152 | ||||||||
\(204\) | −3.67544 | −0.257333 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.3246 | −0.928366 | ||||||||
\(207\) | −42.0000 | −2.91920 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.9737 | 2.35001 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1623 | 1.25034 | 0.625171 | − | 0.780488i | \(-0.285029\pi\) | ||||
0.625171 | + | 0.780488i | \(0.285029\pi\) | |||||||
\(212\) | −4.16228 | −0.285866 | ||||||||
\(213\) | −26.3246 | −1.80373 | ||||||||
\(214\) | −15.4868 | −1.05866 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.6491 | 0.860663 | ||||||||
\(217\) | 0.837722 | 0.0568683 | ||||||||
\(218\) | 14.6491 | 0.992163 | ||||||||
\(219\) | 28.9737 | 1.95786 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 19.4868 | 1.30787 | ||||||||
\(223\) | −9.32456 | −0.624418 | −0.312209 | − | 0.950013i | \(-0.601069\pi\) | ||||
−0.312209 | + | 0.950013i | \(0.601069\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.6491 | −1.10748 | ||||||||
\(227\) | −2.32456 | −0.154286 | −0.0771431 | − | 0.997020i | \(-0.524580\pi\) | ||||
−0.0771431 | + | 0.997020i | \(0.524580\pi\) | |||||||
\(228\) | 25.8114 | 1.70940 | ||||||||
\(229\) | −9.16228 | −0.605460 | −0.302730 | − | 0.953076i | \(-0.597898\pi\) | ||||
−0.302730 | + | 0.953076i | \(0.597898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.1623 | −0.866014 | ||||||||
\(232\) | −2.32456 | −0.152615 | ||||||||
\(233\) | 9.48683 | 0.621503 | 0.310752 | − | 0.950491i | \(-0.399419\pi\) | ||||
0.310752 | + | 0.950491i | \(0.399419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.32456 | −0.151316 | ||||||||
\(237\) | 17.3509 | 1.12706 | ||||||||
\(238\) | 1.16228 | 0.0753393 | ||||||||
\(239\) | −4.83772 | −0.312926 | −0.156463 | − | 0.987684i | \(-0.550009\pi\) | ||||
−0.156463 | + | 0.987684i | \(0.550009\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9737 | −0.771292 | −0.385646 | − | 0.922647i | \(-0.626021\pi\) | ||||
−0.385646 | + | 0.922647i | \(0.626021\pi\) | |||||||
\(242\) | 6.32456 | 0.406558 | ||||||||
\(243\) | 22.1359 | 1.42002 | ||||||||
\(244\) | 11.4868 | 0.735369 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.35089 | −0.468676 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.837722 | −0.0531954 | ||||||||
\(249\) | −30.0000 | −1.90117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.48683 | −0.409445 | −0.204723 | − | 0.978820i | \(-0.565629\pi\) | ||||
−0.204723 | + | 0.978820i | \(0.565629\pi\) | |||||||
\(252\) | −7.00000 | −0.440959 | ||||||||
\(253\) | −24.9737 | −1.57008 | ||||||||
\(254\) | 9.32456 | 0.585075 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | −6.32456 | −0.393750 | ||||||||
\(259\) | −6.16228 | −0.382905 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.2719 | −1.00720 | ||||||||
\(262\) | 20.8114 | 1.28573 | ||||||||
\(263\) | −13.6491 | −0.841640 | −0.420820 | − | 0.907144i | \(-0.638258\pi\) | ||||
−0.420820 | + | 0.907144i | \(0.638258\pi\) | |||||||
\(264\) | 13.1623 | 0.810082 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.16228 | −0.500461 | ||||||||
\(267\) | −16.8377 | −1.03045 | ||||||||
\(268\) | 10.3246 | 0.630673 | ||||||||
\(269\) | 21.4868 | 1.31008 | 0.655038 | − | 0.755596i | \(-0.272653\pi\) | ||||
0.655038 | + | 0.755596i | \(0.272653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32456 | 0.384189 | 0.192095 | − | 0.981376i | \(-0.438472\pi\) | ||||
0.192095 | + | 0.981376i | \(0.438472\pi\) | |||||||
\(272\) | −1.16228 | −0.0704734 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.48683 | −0.210647 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −18.9737 | −1.14208 | ||||||||
\(277\) | −20.4868 | −1.23093 | −0.615467 | − | 0.788162i | \(-0.711033\pi\) | ||||
−0.615467 | + | 0.788162i | \(0.711033\pi\) | |||||||
\(278\) | −5.83772 | −0.350123 | ||||||||
\(279\) | −5.86406 | −0.351072 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.9737 | −1.13187 | −0.565937 | − | 0.824448i | \(-0.691485\pi\) | ||||
−0.565937 | + | 0.824448i | \(0.691485\pi\) | |||||||
\(282\) | −9.48683 | −0.564933 | ||||||||
\(283\) | 22.0000 | 1.30776 | 0.653882 | − | 0.756596i | \(-0.273139\pi\) | ||||
0.653882 | + | 0.756596i | \(0.273139\pi\) | |||||||
\(284\) | −8.32456 | −0.493971 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.32456 | 0.137214 | ||||||||
\(288\) | 7.00000 | 0.412479 | ||||||||
\(289\) | −15.6491 | −0.920536 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.3246 | 2.12938 | ||||||||
\(292\) | 9.16228 | 0.536182 | ||||||||
\(293\) | −28.1623 | −1.64526 | −0.822629 | − | 0.568579i | \(-0.807494\pi\) | ||||
−0.822629 | + | 0.568579i | \(0.807494\pi\) | |||||||
\(294\) | −18.9737 | −1.10657 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.16228 | 0.358175 | ||||||||
\(297\) | 52.6491 | 3.05501 | ||||||||
\(298\) | −3.67544 | −0.212913 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | 11.1623 | 0.642317 | ||||||||
\(303\) | −15.2982 | −0.878860 | ||||||||
\(304\) | 8.16228 | 0.468139 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.13594 | −0.465101 | ||||||||
\(307\) | 28.3246 | 1.61657 | 0.808284 | − | 0.588793i | \(-0.200397\pi\) | ||||
0.808284 | + | 0.588793i | \(0.200397\pi\) | |||||||
\(308\) | −4.16228 | −0.237168 | ||||||||
\(309\) | −42.1359 | −2.39703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4868 | 0.878178 | 0.439089 | − | 0.898444i | \(-0.355301\pi\) | ||||
0.439089 | + | 0.898444i | \(0.355301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.32456 | −0.244438 | −0.122219 | − | 0.992503i | \(-0.539001\pi\) | ||||
−0.122219 | + | 0.992503i | \(0.539001\pi\) | |||||||
\(314\) | 5.83772 | 0.329442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.48683 | 0.308658 | ||||||||
\(317\) | −6.48683 | −0.364337 | −0.182168 | − | 0.983267i | \(-0.558312\pi\) | ||||
−0.182168 | + | 0.983267i | \(0.558312\pi\) | |||||||
\(318\) | −13.1623 | −0.738104 | ||||||||
\(319\) | −9.67544 | −0.541721 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −48.9737 | −2.73344 | ||||||||
\(322\) | 6.00000 | 0.334367 | ||||||||
\(323\) | −9.48683 | −0.527862 | ||||||||
\(324\) | 19.0000 | 1.05556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.48683 | −0.0823481 | ||||||||
\(327\) | 46.3246 | 2.56175 | ||||||||
\(328\) | −2.32456 | −0.128352 | ||||||||
\(329\) | 3.00000 | 0.165395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.649111 | −0.0356783 | −0.0178392 | − | 0.999841i | \(-0.505679\pi\) | ||||
−0.0178392 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(332\) | −9.48683 | −0.520658 | ||||||||
\(333\) | 43.1359 | 2.36384 | ||||||||
\(334\) | 0.675445 | 0.0369587 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.16228 | −0.172516 | ||||||||
\(337\) | 1.48683 | 0.0809930 | 0.0404965 | − | 0.999180i | \(-0.487106\pi\) | ||||
0.0404965 | + | 0.999180i | \(0.487106\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −52.6491 | −2.85951 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.48683 | −0.188823 | ||||||||
\(342\) | 57.1359 | 3.08956 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.16228 | 0.223765 | ||||||||
\(347\) | −21.4868 | −1.15347 | −0.576737 | − | 0.816930i | \(-0.695674\pi\) | ||||
−0.576737 | + | 0.816930i | \(0.695674\pi\) | |||||||
\(348\) | −7.35089 | −0.394049 | ||||||||
\(349\) | 1.48683 | 0.0795883 | 0.0397942 | − | 0.999208i | \(-0.487330\pi\) | ||||
0.0397942 | + | 0.999208i | \(0.487330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.16228 | 0.221850 | ||||||||
\(353\) | −1.16228 | −0.0618618 | −0.0309309 | − | 0.999522i | \(-0.509847\pi\) | ||||
−0.0309309 | + | 0.999522i | \(0.509847\pi\) | |||||||
\(354\) | −7.35089 | −0.390695 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.32456 | −0.282201 | ||||||||
\(357\) | 3.67544 | 0.194525 | ||||||||
\(358\) | 9.67544 | 0.511363 | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.6228 | 2.50646 | ||||||||
\(362\) | −21.8114 | −1.14638 | ||||||||
\(363\) | 20.0000 | 1.04973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 36.3246 | 1.89871 | ||||||||
\(367\) | 20.6491 | 1.07787 | 0.538937 | − | 0.842346i | \(-0.318826\pi\) | ||||
0.538937 | + | 0.842346i | \(0.318826\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | −16.2719 | −0.847081 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.16228 | 0.216095 | ||||||||
\(372\) | −2.64911 | −0.137350 | ||||||||
\(373\) | 5.35089 | 0.277059 | 0.138529 | − | 0.990358i | \(-0.455762\pi\) | ||||
0.138529 | + | 0.990358i | \(0.455762\pi\) | |||||||
\(374\) | −4.83772 | −0.250153 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −12.6491 | −0.650600 | ||||||||
\(379\) | 7.18861 | 0.369254 | 0.184627 | − | 0.982809i | \(-0.440892\pi\) | ||||
0.184627 | + | 0.982809i | \(0.440892\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.4868 | 1.51066 | ||||||||
\(382\) | −9.48683 | −0.485389 | ||||||||
\(383\) | 30.0000 | 1.53293 | 0.766464 | − | 0.642287i | \(-0.222014\pi\) | ||||
0.766464 | + | 0.642287i | \(0.222014\pi\) | |||||||
\(384\) | 3.16228 | 0.161374 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | −14.0000 | −0.711660 | ||||||||
\(388\) | 11.4868 | 0.583156 | ||||||||
\(389\) | 19.1623 | 0.971566 | 0.485783 | − | 0.874079i | \(-0.338535\pi\) | ||||
0.485783 | + | 0.874079i | \(0.338535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.97367 | 0.352673 | ||||||||
\(392\) | −6.00000 | −0.303046 | ||||||||
\(393\) | 65.8114 | 3.31975 | ||||||||
\(394\) | 0.486833 | 0.0245263 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 29.1359 | 1.46414 | ||||||||
\(397\) | 19.5132 | 0.979338 | 0.489669 | − | 0.871908i | \(-0.337118\pi\) | ||||
0.489669 | + | 0.871908i | \(0.337118\pi\) | |||||||
\(398\) | −26.6491 | −1.33580 | ||||||||
\(399\) | −25.8114 | −1.29219 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.9737 | 0.797687 | 0.398843 | − | 0.917019i | \(-0.369412\pi\) | ||||
0.398843 | + | 0.917019i | \(0.369412\pi\) | |||||||
\(402\) | 32.6491 | 1.62839 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.83772 | −0.240686 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.32456 | 0.115366 | ||||||||
\(407\) | 25.6491 | 1.27138 | ||||||||
\(408\) | −3.67544 | −0.181962 | ||||||||
\(409\) | −3.64911 | −0.180437 | −0.0902185 | − | 0.995922i | \(-0.528757\pi\) | ||||
−0.0902185 | + | 0.995922i | \(0.528757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.0263 | −0.543889 | ||||||||
\(412\) | −13.3246 | −0.656454 | ||||||||
\(413\) | 2.32456 | 0.114384 | ||||||||
\(414\) | −42.0000 | −2.06419 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.4605 | −0.904015 | ||||||||
\(418\) | 33.9737 | 1.66171 | ||||||||
\(419\) | −10.6491 | −0.520243 | −0.260122 | − | 0.965576i | \(-0.583763\pi\) | ||||
−0.260122 | + | 0.965576i | \(0.583763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.16228 | −0.154120 | −0.0770600 | − | 0.997026i | \(-0.524553\pi\) | ||||
−0.0770600 | + | 0.997026i | \(0.524553\pi\) | |||||||
\(422\) | 18.1623 | 0.884126 | ||||||||
\(423\) | −21.0000 | −1.02105 | ||||||||
\(424\) | −4.16228 | −0.202138 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −26.3246 | −1.27543 | ||||||||
\(427\) | −11.4868 | −0.555887 | ||||||||
\(428\) | −15.4868 | −0.748584 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.48683 | 0.167955 | 0.0839774 | − | 0.996468i | \(-0.473238\pi\) | ||||
0.0839774 | + | 0.996468i | \(0.473238\pi\) | |||||||
\(432\) | 12.6491 | 0.608581 | ||||||||
\(433\) | 6.32456 | 0.303939 | 0.151969 | − | 0.988385i | \(-0.451438\pi\) | ||||
0.151969 | + | 0.988385i | \(0.451438\pi\) | |||||||
\(434\) | 0.837722 | 0.0402120 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.6491 | 0.701565 | ||||||||
\(437\) | −48.9737 | −2.34273 | ||||||||
\(438\) | 28.9737 | 1.38442 | ||||||||
\(439\) | −27.8114 | −1.32737 | −0.663683 | − | 0.748014i | \(-0.731007\pi\) | ||||
−0.663683 | + | 0.748014i | \(0.731007\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.0000 | −2.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.35089 | −0.0641827 | −0.0320913 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320913 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(444\) | 19.4868 | 0.924804 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.32456 | −0.441530 | ||||||||
\(447\) | −11.6228 | −0.549738 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 39.9737 | 1.88647 | 0.943237 | − | 0.332120i | \(-0.107764\pi\) | ||||
0.943237 | + | 0.332120i | \(0.107764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.67544 | −0.455599 | ||||||||
\(452\) | −16.6491 | −0.783108 | ||||||||
\(453\) | 35.2982 | 1.65846 | ||||||||
\(454\) | −2.32456 | −0.109097 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 25.8114 | 1.20873 | ||||||||
\(457\) | −32.4605 | −1.51844 | −0.759219 | − | 0.650835i | \(-0.774419\pi\) | ||||
−0.759219 | + | 0.650835i | \(0.774419\pi\) | |||||||
\(458\) | −9.16228 | −0.428125 | ||||||||
\(459\) | −14.7018 | −0.686220 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.51317 | −0.117050 | −0.0585249 | − | 0.998286i | \(-0.518640\pi\) | ||||
−0.0585249 | + | 0.998286i | \(0.518640\pi\) | |||||||
\(462\) | −13.1623 | −0.612365 | ||||||||
\(463\) | −0.324555 | −0.0150834 | −0.00754168 | − | 0.999972i | \(-0.502401\pi\) | ||||
−0.00754168 | + | 0.999972i | \(0.502401\pi\) | |||||||
\(464\) | −2.32456 | −0.107915 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.48683 | 0.439469 | ||||||||
\(467\) | −7.35089 | −0.340159 | −0.170079 | − | 0.985430i | \(-0.554402\pi\) | ||||
−0.170079 | + | 0.985430i | \(0.554402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.3246 | −0.476744 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.4605 | 0.850615 | ||||||||
\(472\) | −2.32456 | −0.106996 | ||||||||
\(473\) | −8.32456 | −0.382763 | ||||||||
\(474\) | 17.3509 | 0.796953 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.16228 | 0.0532729 | ||||||||
\(477\) | −29.1359 | −1.33404 | ||||||||
\(478\) | −4.83772 | −0.221272 | ||||||||
\(479\) | −32.1359 | −1.46833 | −0.734164 | − | 0.678972i | \(-0.762426\pi\) | ||||
−0.734164 | + | 0.678972i | \(0.762426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11.9737 | −0.545386 | ||||||||
\(483\) | 18.9737 | 0.863332 | ||||||||
\(484\) | 6.32456 | 0.287480 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.1359 | 1.00411 | ||||||||
\(487\) | −1.00000 | −0.0453143 | −0.0226572 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226572 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(488\) | 11.4868 | 0.519984 | ||||||||
\(489\) | −4.70178 | −0.212622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.4868 | 1.64663 | 0.823314 | − | 0.567586i | \(-0.192123\pi\) | ||||
0.823314 | + | 0.567586i | \(0.192123\pi\) | |||||||
\(492\) | −7.35089 | −0.331404 | ||||||||
\(493\) | 2.70178 | 0.121682 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.837722 | −0.0376148 | ||||||||
\(497\) | 8.32456 | 0.373407 | ||||||||
\(498\) | −30.0000 | −1.34433 | ||||||||
\(499\) | 22.0000 | 0.984855 | 0.492428 | − | 0.870353i | \(-0.336110\pi\) | ||||
0.492428 | + | 0.870353i | \(0.336110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.13594 | 0.0954269 | ||||||||
\(502\) | −6.48683 | −0.289522 | ||||||||
\(503\) | −36.2982 | −1.61846 | −0.809229 | − | 0.587494i | \(-0.800115\pi\) | ||||
−0.809229 | + | 0.587494i | \(0.800115\pi\) | |||||||
\(504\) | −7.00000 | −0.311805 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −24.9737 | −1.11021 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.32456 | 0.413710 | ||||||||
\(509\) | −36.9737 | −1.63883 | −0.819414 | − | 0.573201i | \(-0.805701\pi\) | ||||
−0.819414 | + | 0.573201i | \(0.805701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.16228 | −0.405315 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 103.246 | 4.55840 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.32456 | −0.278423 | ||||||||
\(517\) | −12.4868 | −0.549170 | ||||||||
\(518\) | −6.16228 | −0.270755 | ||||||||
\(519\) | 13.1623 | 0.577760 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.3246 | 1.54760 | 0.773798 | − | 0.633432i | \(-0.218354\pi\) | ||||
0.773798 | + | 0.633432i | \(0.218354\pi\) | |||||||
\(522\) | −16.2719 | −0.712201 | ||||||||
\(523\) | −11.2982 | −0.494037 | −0.247018 | − | 0.969011i | \(-0.579451\pi\) | ||||
−0.247018 | + | 0.969011i | \(0.579451\pi\) | |||||||
\(524\) | 20.8114 | 0.909150 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6491 | −0.595130 | ||||||||
\(527\) | 0.973666 | 0.0424136 | ||||||||
\(528\) | 13.1623 | 0.572815 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.2719 | −0.706140 | ||||||||
\(532\) | −8.16228 | −0.353880 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −16.8377 | −0.728640 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.3246 | 0.445953 | ||||||||
\(537\) | 30.5964 | 1.32033 | ||||||||
\(538\) | 21.4868 | 0.926363 | ||||||||
\(539\) | −24.9737 | −1.07569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.1623 | −1.42576 | −0.712879 | − | 0.701287i | \(-0.752609\pi\) | ||||
−0.712879 | + | 0.701287i | \(0.752609\pi\) | |||||||
\(542\) | 6.32456 | 0.271663 | ||||||||
\(543\) | −68.9737 | −2.95994 | ||||||||
\(544\) | −1.16228 | −0.0498322 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.6491 | −0.797378 | −0.398689 | − | 0.917086i | \(-0.630535\pi\) | ||||
−0.398689 | + | 0.917086i | \(0.630535\pi\) | |||||||
\(548\) | −3.48683 | −0.148950 | ||||||||
\(549\) | 80.4078 | 3.43172 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.9737 | −0.808305 | ||||||||
\(552\) | −18.9737 | −0.807573 | ||||||||
\(553\) | −5.48683 | −0.233324 | ||||||||
\(554\) | −20.4868 | −0.870402 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.83772 | −0.247575 | ||||||||
\(557\) | 22.1623 | 0.939046 | 0.469523 | − | 0.882920i | \(-0.344426\pi\) | ||||
0.469523 | + | 0.882920i | \(0.344426\pi\) | |||||||
\(558\) | −5.86406 | −0.248245 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.2982 | −0.645891 | ||||||||
\(562\) | −18.9737 | −0.800356 | ||||||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | −9.48683 | −0.399468 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | −19.0000 | −0.797925 | ||||||||
\(568\) | −8.32456 | −0.349291 | ||||||||
\(569\) | 3.97367 | 0.166585 | 0.0832924 | − | 0.996525i | \(-0.473456\pi\) | ||||
0.0832924 | + | 0.996525i | \(0.473456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.1359 | 0.800814 | 0.400407 | − | 0.916337i | \(-0.368869\pi\) | ||||
0.400407 | + | 0.916337i | \(0.368869\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.0000 | −1.25327 | ||||||||
\(574\) | 2.32456 | 0.0970251 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | 0.837722 | 0.0348748 | 0.0174374 | − | 0.999848i | \(-0.494449\pi\) | ||||
0.0174374 | + | 0.999848i | \(0.494449\pi\) | |||||||
\(578\) | −15.6491 | −0.650917 | ||||||||
\(579\) | −12.6491 | −0.525679 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.48683 | 0.393580 | ||||||||
\(582\) | 36.3246 | 1.50570 | ||||||||
\(583\) | −17.3246 | −0.717510 | ||||||||
\(584\) | 9.16228 | 0.379138 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.1623 | −1.16337 | ||||||||
\(587\) | −24.9737 | −1.03077 | −0.515387 | − | 0.856958i | \(-0.672352\pi\) | ||||
−0.515387 | + | 0.856958i | \(0.672352\pi\) | |||||||
\(588\) | −18.9737 | −0.782461 | ||||||||
\(589\) | −6.83772 | −0.281743 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.53950 | 0.0633266 | ||||||||
\(592\) | 6.16228 | 0.253268 | ||||||||
\(593\) | −28.6491 | −1.17648 | −0.588239 | − | 0.808687i | \(-0.700179\pi\) | ||||
−0.588239 | + | 0.808687i | \(0.700179\pi\) | |||||||
\(594\) | 52.6491 | 2.16022 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.67544 | −0.150552 | ||||||||
\(597\) | −84.2719 | −3.44902 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.9473 | −1.30533 | −0.652666 | − | 0.757646i | \(-0.726350\pi\) | ||||
−0.652666 | + | 0.757646i | \(0.726350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2982 | −0.664818 | −0.332409 | − | 0.943135i | \(-0.607861\pi\) | ||||
−0.332409 | + | 0.943135i | \(0.607861\pi\) | |||||||
\(602\) | 2.00000 | 0.0815139 | ||||||||
\(603\) | 72.2719 | 2.94314 | ||||||||
\(604\) | 11.1623 | 0.454187 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.2982 | −0.621448 | ||||||||
\(607\) | −5.00000 | −0.202944 | −0.101472 | − | 0.994838i | \(-0.532355\pi\) | ||||
−0.101472 | + | 0.994838i | \(0.532355\pi\) | |||||||
\(608\) | 8.16228 | 0.331024 | ||||||||
\(609\) | 7.35089 | 0.297873 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8.13594 | −0.328876 | ||||||||
\(613\) | 1.51317 | 0.0611162 | 0.0305581 | − | 0.999533i | \(-0.490272\pi\) | ||||
0.0305581 | + | 0.999533i | \(0.490272\pi\) | |||||||
\(614\) | 28.3246 | 1.14309 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.16228 | −0.167703 | ||||||||
\(617\) | 43.9473 | 1.76925 | 0.884626 | − | 0.466300i | \(-0.154413\pi\) | ||||
0.884626 | + | 0.466300i | \(0.154413\pi\) | |||||||
\(618\) | −42.1359 | −1.69496 | ||||||||
\(619\) | −27.4605 | −1.10373 | −0.551865 | − | 0.833933i | \(-0.686084\pi\) | ||||
−0.551865 | + | 0.833933i | \(0.686084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −75.8947 | −3.04555 | ||||||||
\(622\) | 15.4868 | 0.620965 | ||||||||
\(623\) | 5.32456 | 0.213324 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.32456 | −0.172844 | ||||||||
\(627\) | 107.434 | 4.29051 | ||||||||
\(628\) | 5.83772 | 0.232950 | ||||||||
\(629\) | −7.16228 | −0.285579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.67544 | 0.0666984 | 0.0333492 | − | 0.999444i | \(-0.489383\pi\) | ||||
0.0333492 | + | 0.999444i | \(0.489383\pi\) | |||||||
\(632\) | 5.48683 | 0.218254 | ||||||||
\(633\) | 57.4342 | 2.28280 | ||||||||
\(634\) | −6.48683 | −0.257625 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.1623 | −0.521918 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.67544 | −0.383055 | ||||||||
\(639\) | −58.2719 | −2.30520 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.9737 | 1.10489 | 0.552447 | − | 0.833548i | \(-0.313694\pi\) | ||||
0.552447 | + | 0.833548i | \(0.313694\pi\) | |||||||
\(642\) | −48.9737 | −1.93284 | ||||||||
\(643\) | −44.4605 | −1.75335 | −0.876675 | − | 0.481082i | \(-0.840244\pi\) | ||||
−0.876675 | + | 0.481082i | \(0.840244\pi\) | |||||||
\(644\) | 6.00000 | 0.236433 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.48683 | −0.373254 | ||||||||
\(647\) | −21.9737 | −0.863874 | −0.431937 | − | 0.901904i | \(-0.642170\pi\) | ||||
−0.431937 | + | 0.901904i | \(0.642170\pi\) | |||||||
\(648\) | 19.0000 | 0.746390 | ||||||||
\(649\) | −9.67544 | −0.379794 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.64911 | 0.103827 | ||||||||
\(652\) | −1.48683 | −0.0582289 | ||||||||
\(653\) | −36.4868 | −1.42784 | −0.713920 | − | 0.700227i | \(-0.753082\pi\) | ||||
−0.713920 | + | 0.700227i | \(0.753082\pi\) | |||||||
\(654\) | 46.3246 | 1.81143 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.32456 | −0.0907586 | ||||||||
\(657\) | 64.1359 | 2.50218 | ||||||||
\(658\) | 3.00000 | 0.116952 | ||||||||
\(659\) | −27.2982 | −1.06339 | −0.531694 | − | 0.846937i | \(-0.678444\pi\) | ||||
−0.531694 | + | 0.846937i | \(0.678444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.1623 | 0.667535 | 0.333768 | − | 0.942655i | \(-0.391680\pi\) | ||||
0.333768 | + | 0.942655i | \(0.391680\pi\) | |||||||
\(662\) | −0.649111 | −0.0252284 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.48683 | −0.368161 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 43.1359 | 1.67148 | ||||||||
\(667\) | 13.9473 | 0.540043 | ||||||||
\(668\) | 0.675445 | 0.0261337 | ||||||||
\(669\) | −29.4868 | −1.14003 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.8114 | 1.84574 | ||||||||
\(672\) | −3.16228 | −0.121988 | ||||||||
\(673\) | 22.9737 | 0.885570 | 0.442785 | − | 0.896628i | \(-0.353991\pi\) | ||||
0.442785 | + | 0.896628i | \(0.353991\pi\) | |||||||
\(674\) | 1.48683 | 0.0572707 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.9737 | −0.959816 | −0.479908 | − | 0.877319i | \(-0.659330\pi\) | ||||
−0.479908 | + | 0.877319i | \(0.659330\pi\) | |||||||
\(678\) | −52.6491 | −2.02198 | ||||||||
\(679\) | −11.4868 | −0.440824 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.35089 | −0.281687 | ||||||||
\(682\) | −3.48683 | −0.133518 | ||||||||
\(683\) | 32.3246 | 1.23686 | 0.618432 | − | 0.785838i | \(-0.287768\pi\) | ||||
0.618432 | + | 0.785838i | \(0.287768\pi\) | |||||||
\(684\) | 57.1359 | 2.18465 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.0000 | 0.496342 | ||||||||
\(687\) | −28.9737 | −1.10541 | ||||||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.13594 | −0.271464 | −0.135732 | − | 0.990746i | \(-0.543339\pi\) | ||||
−0.135732 | + | 0.990746i | \(0.543339\pi\) | |||||||
\(692\) | 4.16228 | 0.158226 | ||||||||
\(693\) | −29.1359 | −1.10678 | ||||||||
\(694\) | −21.4868 | −0.815629 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.35089 | −0.278635 | ||||||||
\(697\) | 2.70178 | 0.102337 | ||||||||
\(698\) | 1.48683 | 0.0562775 | ||||||||
\(699\) | 30.0000 | 1.13470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.8377 | −0.635952 | −0.317976 | − | 0.948099i | \(-0.603003\pi\) | ||||
−0.317976 | + | 0.948099i | \(0.603003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.2982 | 1.89703 | ||||||||
\(704\) | 4.16228 | 0.156872 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.16228 | −0.0437429 | ||||||||
\(707\) | 4.83772 | 0.181941 | ||||||||
\(708\) | −7.35089 | −0.276263 | ||||||||
\(709\) | −22.5132 | −0.845500 | −0.422750 | − | 0.906246i | \(-0.638935\pi\) | ||||
−0.422750 | + | 0.906246i | \(0.638935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 38.4078 | 1.44041 | ||||||||
\(712\) | −5.32456 | −0.199546 | ||||||||
\(713\) | 5.02633 | 0.188238 | ||||||||
\(714\) | 3.67544 | 0.137550 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.67544 | 0.361588 | ||||||||
\(717\) | −15.2982 | −0.571323 | ||||||||
\(718\) | 6.00000 | 0.223918 | ||||||||
\(719\) | 12.0000 | 0.447524 | 0.223762 | − | 0.974644i | \(-0.428166\pi\) | ||||
0.223762 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.3246 | 0.496232 | ||||||||
\(722\) | 47.6228 | 1.77234 | ||||||||
\(723\) | −37.8641 | −1.40818 | ||||||||
\(724\) | −21.8114 | −0.810614 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.0000 | 0.742270 | ||||||||
\(727\) | 33.3246 | 1.23594 | 0.617970 | − | 0.786202i | \(-0.287955\pi\) | ||||
0.617970 | + | 0.786202i | \(0.287955\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.32456 | 0.0859768 | ||||||||
\(732\) | 36.3246 | 1.34259 | ||||||||
\(733\) | −10.4868 | −0.387340 | −0.193670 | − | 0.981067i | \(-0.562039\pi\) | ||||
−0.193670 | + | 0.981067i | \(0.562039\pi\) | |||||||
\(734\) | 20.6491 | 0.762173 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 42.9737 | 1.58296 | ||||||||
\(738\) | −16.2719 | −0.598976 | ||||||||
\(739\) | 13.1886 | 0.485151 | 0.242575 | − | 0.970133i | \(-0.422008\pi\) | ||||
0.242575 | + | 0.970133i | \(0.422008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.16228 | 0.152802 | ||||||||
\(743\) | −18.0000 | −0.660356 | −0.330178 | − | 0.943919i | \(-0.607109\pi\) | ||||
−0.330178 | + | 0.943919i | \(0.607109\pi\) | |||||||
\(744\) | −2.64911 | −0.0971211 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.35089 | 0.195910 | ||||||||
\(747\) | −66.4078 | −2.42974 | ||||||||
\(748\) | −4.83772 | −0.176885 | ||||||||
\(749\) | 15.4868 | 0.565877 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.97367 | 0.108511 | 0.0542553 | − | 0.998527i | \(-0.482722\pi\) | ||||
0.0542553 | + | 0.998527i | \(0.482722\pi\) | |||||||
\(752\) | −3.00000 | −0.109399 | ||||||||
\(753\) | −20.5132 | −0.747541 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.6491 | −0.460044 | ||||||||
\(757\) | −27.8377 | −1.01178 | −0.505890 | − | 0.862598i | \(-0.668836\pi\) | ||||
−0.505890 | + | 0.862598i | \(0.668836\pi\) | |||||||
\(758\) | 7.18861 | 0.261102 | ||||||||
\(759\) | −78.9737 | −2.86656 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.2982 | −1.53331 | −0.766655 | − | 0.642060i | \(-0.778080\pi\) | ||||
−0.766655 | + | 0.642060i | \(0.778080\pi\) | |||||||
\(762\) | 29.4868 | 1.06820 | ||||||||
\(763\) | −14.6491 | −0.530333 | ||||||||
\(764\) | −9.48683 | −0.343222 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0000 | 1.08394 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.16228 | 0.114109 | ||||||||
\(769\) | 6.32456 | 0.228069 | 0.114035 | − | 0.993477i | \(-0.463623\pi\) | ||||
0.114035 | + | 0.993477i | \(0.463623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.00000 | −0.143963 | ||||||||
\(773\) | −21.7851 | −0.783554 | −0.391777 | − | 0.920060i | \(-0.628140\pi\) | ||||
−0.391777 | + | 0.920060i | \(0.628140\pi\) | |||||||
\(774\) | −14.0000 | −0.503220 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.4868 | 0.412353 | ||||||||
\(777\) | −19.4868 | −0.699086 | ||||||||
\(778\) | 19.1623 | 0.687001 | ||||||||
\(779\) | −18.9737 | −0.679802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.6491 | −1.23984 | ||||||||
\(782\) | 6.97367 | 0.249378 | ||||||||
\(783\) | −29.4036 | −1.05080 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 65.8114 | 2.34741 | ||||||||
\(787\) | −1.86406 | −0.0664464 | −0.0332232 | − | 0.999448i | \(-0.510577\pi\) | ||||
−0.0332232 | + | 0.999448i | \(0.510577\pi\) | |||||||
\(788\) | 0.486833 | 0.0173427 | ||||||||
\(789\) | −43.1623 | −1.53662 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.6491 | 0.591974 | ||||||||
\(792\) | 29.1359 | 1.03530 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 19.5132 | 0.692496 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.6491 | −0.944553 | ||||||||
\(797\) | 26.3246 | 0.932464 | 0.466232 | − | 0.884663i | \(-0.345611\pi\) | ||||
0.466232 | + | 0.884663i | \(0.345611\pi\) | |||||||
\(798\) | −25.8114 | −0.913713 | ||||||||
\(799\) | 3.48683 | 0.123355 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.2719 | −1.31694 | ||||||||
\(802\) | 15.9737 | 0.564050 | ||||||||
\(803\) | 38.1359 | 1.34579 | ||||||||
\(804\) | 32.6491 | 1.15145 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 67.9473 | 2.39186 | ||||||||
\(808\) | −4.83772 | −0.170190 | ||||||||
\(809\) | −2.32456 | −0.0817270 | −0.0408635 | − | 0.999165i | \(-0.513011\pi\) | ||||
−0.0408635 | + | 0.999165i | \(0.513011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.162278 | −0.00569834 | −0.00284917 | − | 0.999996i | \(-0.500907\pi\) | ||||
−0.00284917 | + | 0.999996i | \(0.500907\pi\) | |||||||
\(812\) | 2.32456 | 0.0815759 | ||||||||
\(813\) | 20.0000 | 0.701431 | ||||||||
\(814\) | 25.6491 | 0.899001 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.67544 | −0.128666 | ||||||||
\(817\) | −16.3246 | −0.571124 | ||||||||
\(818\) | −3.64911 | −0.127588 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.16228 | −0.0405638 | −0.0202819 | − | 0.999794i | \(-0.506456\pi\) | ||||
−0.0202819 | + | 0.999794i | \(0.506456\pi\) | |||||||
\(822\) | −11.0263 | −0.384588 | ||||||||
\(823\) | −47.0000 | −1.63832 | −0.819159 | − | 0.573567i | \(-0.805559\pi\) | ||||
−0.819159 | + | 0.573567i | \(0.805559\pi\) | |||||||
\(824\) | −13.3246 | −0.464183 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.32456 | 0.0808816 | ||||||||
\(827\) | −32.5132 | −1.13059 | −0.565297 | − | 0.824888i | \(-0.691238\pi\) | ||||
−0.565297 | + | 0.824888i | \(0.691238\pi\) | |||||||
\(828\) | −42.0000 | −1.45960 | ||||||||
\(829\) | 32.0000 | 1.11141 | 0.555703 | − | 0.831381i | \(-0.312449\pi\) | ||||
0.555703 | + | 0.831381i | \(0.312449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64.7851 | −2.24737 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.97367 | 0.241623 | ||||||||
\(834\) | −18.4605 | −0.639235 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 33.9737 | 1.17500 | ||||||||
\(837\) | −10.5964 | −0.366267 | ||||||||
\(838\) | −10.6491 | −0.367867 | ||||||||
\(839\) | 16.8377 | 0.581303 | 0.290651 | − | 0.956829i | \(-0.406128\pi\) | ||||
0.290651 | + | 0.956829i | \(0.406128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.5964 | −0.813670 | ||||||||
\(842\) | −3.16228 | −0.108979 | ||||||||
\(843\) | −60.0000 | −2.06651 | ||||||||
\(844\) | 18.1623 | 0.625171 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21.0000 | −0.721995 | ||||||||
\(847\) | −6.32456 | −0.217314 | ||||||||
\(848\) | −4.16228 | −0.142933 | ||||||||
\(849\) | 69.5701 | 2.38764 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.9737 | −1.26744 | ||||||||
\(852\) | −26.3246 | −0.901864 | ||||||||
\(853\) | −32.2719 | −1.10497 | −0.552484 | − | 0.833523i | \(-0.686320\pi\) | ||||
−0.552484 | + | 0.833523i | \(0.686320\pi\) | |||||||
\(854\) | −11.4868 | −0.393071 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.4868 | −0.529329 | ||||||||
\(857\) | 14.1359 | 0.482875 | 0.241437 | − | 0.970416i | \(-0.422381\pi\) | ||||
0.241437 | + | 0.970416i | \(0.422381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.86406 | 0.0977203 | 0.0488602 | − | 0.998806i | \(-0.484441\pi\) | ||||
0.0488602 | + | 0.998806i | \(0.484441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.35089 | 0.250518 | ||||||||
\(862\) | 3.48683 | 0.118762 | ||||||||
\(863\) | −18.0000 | −0.612727 | −0.306364 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306364 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(864\) | 12.6491 | 0.430331 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.32456 | 0.214917 | ||||||||
\(867\) | −49.4868 | −1.68066 | ||||||||
\(868\) | 0.837722 | 0.0284341 | ||||||||
\(869\) | 22.8377 | 0.774717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.6491 | 0.496081 | ||||||||
\(873\) | 80.4078 | 2.72139 | ||||||||
\(874\) | −48.9737 | −1.65656 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28.9737 | 0.978929 | ||||||||
\(877\) | −36.3246 | −1.22659 | −0.613297 | − | 0.789853i | \(-0.710157\pi\) | ||||
−0.613297 | + | 0.789853i | \(0.710157\pi\) | |||||||
\(878\) | −27.8114 | −0.938589 | ||||||||
\(879\) | −89.0569 | −3.00382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0263 | −0.674704 | −0.337352 | − | 0.941379i | \(-0.609531\pi\) | ||||
−0.337352 | + | 0.941379i | \(0.609531\pi\) | |||||||
\(882\) | −42.0000 | −1.41421 | ||||||||
\(883\) | −16.5132 | −0.555712 | −0.277856 | − | 0.960623i | \(-0.589624\pi\) | ||||
−0.277856 | + | 0.960623i | \(0.589624\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.35089 | −0.0453840 | ||||||||
\(887\) | 26.6228 | 0.893905 | 0.446953 | − | 0.894558i | \(-0.352509\pi\) | ||||
0.446953 | + | 0.894558i | \(0.352509\pi\) | |||||||
\(888\) | 19.4868 | 0.653935 | ||||||||
\(889\) | −9.32456 | −0.312736 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 79.0833 | 2.64939 | ||||||||
\(892\) | −9.32456 | −0.312209 | ||||||||
\(893\) | −24.4868 | −0.819421 | ||||||||
\(894\) | −11.6228 | −0.388724 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.9737 | 1.33394 | ||||||||
\(899\) | 1.94733 | 0.0649472 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.83772 | 0.161168 | ||||||||
\(902\) | −9.67544 | −0.322157 | ||||||||
\(903\) | 6.32456 | 0.210468 | ||||||||
\(904\) | −16.6491 | −0.553741 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35.2982 | 1.17270 | ||||||||
\(907\) | −28.1359 | −0.934239 | −0.467119 | − | 0.884194i | \(-0.654708\pi\) | ||||
−0.467119 | + | 0.884194i | \(0.654708\pi\) | |||||||
\(908\) | −2.32456 | −0.0771431 | ||||||||
\(909\) | −33.8641 | −1.12320 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.2982 | 1.10322 | 0.551610 | − | 0.834102i | \(-0.314014\pi\) | ||||
0.551610 | + | 0.834102i | \(0.314014\pi\) | |||||||
\(912\) | 25.8114 | 0.854700 | ||||||||
\(913\) | −39.4868 | −1.30682 | ||||||||
\(914\) | −32.4605 | −1.07370 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.16228 | −0.302730 | ||||||||
\(917\) | −20.8114 | −0.687253 | ||||||||
\(918\) | −14.7018 | −0.485231 | ||||||||
\(919\) | −24.3246 | −0.802393 | −0.401197 | − | 0.915992i | \(-0.631406\pi\) | ||||
−0.401197 | + | 0.915992i | \(0.631406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 89.5701 | 2.95144 | ||||||||
\(922\) | −2.51317 | −0.0827667 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −13.1623 | −0.433007 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.324555 | −0.0106655 | ||||||||
\(927\) | −93.2719 | −3.06345 | ||||||||
\(928\) | −2.32456 | −0.0763073 | ||||||||
\(929\) | −54.0000 | −1.77168 | −0.885841 | − | 0.463988i | \(-0.846418\pi\) | ||||
−0.885841 | + | 0.463988i | \(0.846418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.9737 | −1.60505 | ||||||||
\(932\) | 9.48683 | 0.310752 | ||||||||
\(933\) | 48.9737 | 1.60333 | ||||||||
\(934\) | −7.35089 | −0.240528 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.3246 | −1.31735 | −0.658673 | − | 0.752429i | \(-0.728882\pi\) | ||||
−0.658673 | + | 0.752429i | \(0.728882\pi\) | |||||||
\(938\) | −10.3246 | −0.337109 | ||||||||
\(939\) | −13.6754 | −0.446281 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.67544 | −0.315410 | −0.157705 | − | 0.987486i | \(-0.550410\pi\) | ||||
−0.157705 | + | 0.987486i | \(0.550410\pi\) | |||||||
\(942\) | 18.4605 | 0.601476 | ||||||||
\(943\) | 13.9473 | 0.454188 | ||||||||
\(944\) | −2.32456 | −0.0756578 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.32456 | −0.270655 | ||||||||
\(947\) | 29.8114 | 0.968740 | 0.484370 | − | 0.874863i | \(-0.339049\pi\) | ||||
0.484370 | + | 0.874863i | \(0.339049\pi\) | |||||||
\(948\) | 17.3509 | 0.563531 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.5132 | −0.665185 | ||||||||
\(952\) | 1.16228 | 0.0376696 | ||||||||
\(953\) | 21.4868 | 0.696027 | 0.348013 | − | 0.937490i | \(-0.386856\pi\) | ||||
0.348013 | + | 0.937490i | \(0.386856\pi\) | |||||||
\(954\) | −29.1359 | −0.943311 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.83772 | −0.156463 | ||||||||
\(957\) | −30.5964 | −0.989043 | ||||||||
\(958\) | −32.1359 | −1.03827 | ||||||||
\(959\) | 3.48683 | 0.112596 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2982 | −0.977362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −108.408 | −3.49339 | ||||||||
\(964\) | −11.9737 | −0.385646 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 18.9737 | 0.610468 | ||||||||
\(967\) | 46.6228 | 1.49929 | 0.749644 | − | 0.661842i | \(-0.230225\pi\) | ||||
0.749644 | + | 0.661842i | \(0.230225\pi\) | |||||||
\(968\) | 6.32456 | 0.203279 | ||||||||
\(969\) | −30.0000 | −0.963739 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.78505 | −0.314017 | −0.157009 | − | 0.987597i | \(-0.550185\pi\) | ||||
−0.157009 | + | 0.987597i | \(0.550185\pi\) | |||||||
\(972\) | 22.1359 | 0.710011 | ||||||||
\(973\) | 5.83772 | 0.187149 | ||||||||
\(974\) | −1.00000 | −0.0320421 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.4868 | 0.367685 | ||||||||
\(977\) | −18.9737 | −0.607021 | −0.303511 | − | 0.952828i | \(-0.598159\pi\) | ||||
−0.303511 | + | 0.952828i | \(0.598159\pi\) | |||||||
\(978\) | −4.70178 | −0.150346 | ||||||||
\(979\) | −22.1623 | −0.708309 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 102.544 | 3.27397 | ||||||||
\(982\) | 36.4868 | 1.16434 | ||||||||
\(983\) | 55.6491 | 1.77493 | 0.887465 | − | 0.460874i | \(-0.152464\pi\) | ||||
0.887465 | + | 0.460874i | \(0.152464\pi\) | |||||||
\(984\) | −7.35089 | −0.234338 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.70178 | 0.0860422 | ||||||||
\(987\) | 9.48683 | 0.301969 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2982 | 0.358900 | 0.179450 | − | 0.983767i | \(-0.442568\pi\) | ||||
0.179450 | + | 0.983767i | \(0.442568\pi\) | |||||||
\(992\) | −0.837722 | −0.0265977 | ||||||||
\(993\) | −2.05267 | −0.0651395 | ||||||||
\(994\) | 8.32456 | 0.264039 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −30.0000 | −0.950586 | ||||||||
\(997\) | −18.1623 | −0.575205 | −0.287603 | − | 0.957750i | \(-0.592858\pi\) | ||||
−0.287603 | + | 0.957750i | \(0.592858\pi\) | |||||||
\(998\) | 22.0000 | 0.696398 | ||||||||
\(999\) | 77.9473 | 2.46614 |
(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 | 8450.2.a.bj.1.2 | 2 | ||
5.4 | even | 2 | 1690.2.a.k.1.1 | 2 | |||
13.4 | even | 6 | 650.2.e.h.601.1 | 4 | |||
13.10 | even | 6 | 650.2.e.h.451.1 | 4 | |||
13.12 | even | 2 | 8450.2.a.bc.1.2 | 2 | |||
65.4 | even | 6 | 130.2.e.c.81.2 | yes | 4 | ||
65.9 | even | 6 | 1690.2.e.m.991.2 | 4 | |||
65.17 | odd | 12 | 650.2.o.g.549.1 | 8 | |||
65.19 | odd | 12 | 1690.2.l.k.361.4 | 8 | |||
65.23 | odd | 12 | 650.2.o.g.399.1 | 8 | |||
65.24 | odd | 12 | 1690.2.l.k.1161.4 | 8 | |||
65.29 | even | 6 | 1690.2.e.m.191.2 | 4 | |||
65.34 | odd | 4 | 1690.2.d.g.1351.1 | 4 | |||
65.43 | odd | 12 | 650.2.o.g.549.4 | 8 | |||
65.44 | odd | 4 | 1690.2.d.g.1351.3 | 4 | |||
65.49 | even | 6 | 130.2.e.c.61.2 | ✓ | 4 | ||
65.54 | odd | 12 | 1690.2.l.k.1161.2 | 8 | |||
65.59 | odd | 12 | 1690.2.l.k.361.2 | 8 | |||
65.62 | odd | 12 | 650.2.o.g.399.4 | 8 | |||
65.64 | even | 2 | 1690.2.a.n.1.1 | 2 | |||
195.134 | odd | 6 | 1170.2.i.q.991.1 | 4 | |||
195.179 | odd | 6 | 1170.2.i.q.451.1 | 4 | |||
260.179 | odd | 6 | 1040.2.q.m.321.1 | 4 | |||
260.199 | odd | 6 | 1040.2.q.m.81.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.e.c.61.2 | ✓ | 4 | 65.49 | even | 6 | ||
130.2.e.c.81.2 | yes | 4 | 65.4 | even | 6 | ||
650.2.e.h.451.1 | 4 | 13.10 | even | 6 | |||
650.2.e.h.601.1 | 4 | 13.4 | even | 6 | |||
650.2.o.g.399.1 | 8 | 65.23 | odd | 12 | |||
650.2.o.g.399.4 | 8 | 65.62 | odd | 12 | |||
650.2.o.g.549.1 | 8 | 65.17 | odd | 12 | |||
650.2.o.g.549.4 | 8 | 65.43 | odd | 12 | |||
1040.2.q.m.81.1 | 4 | 260.199 | odd | 6 | |||
1040.2.q.m.321.1 | 4 | 260.179 | odd | 6 | |||
1170.2.i.q.451.1 | 4 | 195.179 | odd | 6 | |||
1170.2.i.q.991.1 | 4 | 195.134 | odd | 6 | |||
1690.2.a.k.1.1 | 2 | 5.4 | even | 2 | |||
1690.2.a.n.1.1 | 2 | 65.64 | even | 2 | |||
1690.2.d.g.1351.1 | 4 | 65.34 | odd | 4 | |||
1690.2.d.g.1351.3 | 4 | 65.44 | odd | 4 | |||
1690.2.e.m.191.2 | 4 | 65.29 | even | 6 | |||
1690.2.e.m.991.2 | 4 | 65.9 | even | 6 | |||
1690.2.l.k.361.2 | 8 | 65.59 | odd | 12 | |||
1690.2.l.k.361.4 | 8 | 65.19 | odd | 12 | |||
1690.2.l.k.1161.2 | 8 | 65.54 | odd | 12 | |||
1690.2.l.k.1161.4 | 8 | 65.24 | odd | 12 | |||
8450.2.a.bc.1.2 | 2 | 13.12 | even | 2 | |||
8450.2.a.bj.1.2 | 2 | 1.1 | even | 1 | trivial |