Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(1,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("945.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.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: | \(7.54586299101\) |
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 | \(\chi\) | \(=\) | 945.1 |
$q$-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 | \(0.570119\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.618034 | 0.195440 | ||||||||
\(11\) | 3.23607 | 0.975711 | 0.487856 | − | 0.872924i | \(-0.337779\pi\) | ||||
0.487856 | + | 0.872924i | \(0.337779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.47214 | 0.685647 | 0.342824 | − | 0.939400i | \(-0.388617\pi\) | ||||
0.342824 | + | 0.939400i | \(0.388617\pi\) | |||||||
\(14\) | 0.618034 | 0.165177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −4.23607 | −1.02740 | −0.513699 | − | 0.857971i | \(-0.671725\pi\) | ||||
−0.513699 | + | 0.857971i | \(0.671725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.47214 | −1.71423 | −0.857113 | − | 0.515129i | \(-0.827744\pi\) | ||||
−0.857113 | + | 0.515129i | \(0.827744\pi\) | |||||||
\(20\) | 1.61803 | 0.361803 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 6.23607 | 1.30031 | 0.650155 | − | 0.759802i | \(-0.274704\pi\) | ||||
0.650155 | + | 0.759802i | \(0.274704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.52786 | −0.299639 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.61803 | 0.305780 | ||||||||
\(29\) | 7.70820 | 1.43138 | 0.715689 | − | 0.698419i | \(-0.246113\pi\) | ||||
0.715689 | + | 0.698419i | \(0.246113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.00000 | −1.61645 | −0.808224 | − | 0.588875i | \(-0.799571\pi\) | ||||
−0.808224 | + | 0.588875i | \(0.799571\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.61803 | 0.448989 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.70820 | −1.59602 | −0.798009 | − | 0.602645i | \(-0.794114\pi\) | ||||
−0.798009 | + | 0.602645i | \(0.794114\pi\) | |||||||
\(38\) | 4.61803 | 0.749144 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | −8.47214 | −1.32313 | −0.661563 | − | 0.749890i | \(-0.730106\pi\) | ||||
−0.661563 | + | 0.749890i | \(0.730106\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.47214 | −1.29199 | −0.645994 | − | 0.763342i | \(-0.723557\pi\) | ||||
−0.645994 | + | 0.763342i | \(0.723557\pi\) | |||||||
\(44\) | −5.23607 | −0.789367 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.85410 | −0.568256 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.618034 | −0.0874032 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | −7.94427 | −1.09123 | −0.545615 | − | 0.838036i | \(-0.683704\pi\) | ||||
−0.545615 | + | 0.838036i | \(0.683704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23607 | −0.436351 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.76393 | −0.625535 | ||||||||
\(59\) | −11.7082 | −1.52428 | −0.762139 | − | 0.647413i | \(-0.775851\pi\) | ||||
−0.762139 | + | 0.647413i | \(0.775851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.708204 | 0.0906762 | 0.0453381 | − | 0.998972i | \(-0.485563\pi\) | ||||
0.0453381 | + | 0.998972i | \(0.485563\pi\) | |||||||
\(62\) | 5.56231 | 0.706414 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −2.47214 | −0.306631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9443 | 1.33706 | 0.668528 | − | 0.743687i | \(-0.266925\pi\) | ||||
0.668528 | + | 0.743687i | \(0.266925\pi\) | |||||||
\(68\) | 6.85410 | 0.831182 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.618034 | −0.0738692 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.472136 | 0.0552593 | 0.0276297 | − | 0.999618i | \(-0.491204\pi\) | ||||
0.0276297 | + | 0.999618i | \(0.491204\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.0902 | 1.38684 | ||||||||
\(77\) | −3.23607 | −0.368784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.1803 | −1.93294 | −0.966470 | − | 0.256781i | \(-0.917338\pi\) | ||||
−0.966470 | + | 0.256781i | \(0.917338\pi\) | |||||||
\(80\) | −1.85410 | −0.207295 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.23607 | 0.578227 | ||||||||
\(83\) | 11.0000 | 1.20741 | 0.603703 | − | 0.797209i | \(-0.293691\pi\) | ||||
0.603703 | + | 0.797209i | \(0.293691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.23607 | 0.459466 | ||||||||
\(86\) | 5.23607 | 0.564620 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.23607 | 0.771367 | ||||||||
\(89\) | 8.18034 | 0.867114 | 0.433557 | − | 0.901126i | \(-0.357258\pi\) | ||||
0.433557 | + | 0.901126i | \(0.357258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.47214 | −0.259150 | ||||||||
\(92\) | −10.0902 | −1.05197 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.47214 | −0.254981 | ||||||||
\(95\) | 7.47214 | 0.766625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.23607 | −0.531642 | −0.265821 | − | 0.964022i | \(-0.585643\pi\) | ||||
−0.265821 | + | 0.964022i | \(0.585643\pi\) | |||||||
\(98\) | −0.618034 | −0.0624309 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.61803 | −0.161803 | ||||||||
\(101\) | −6.18034 | −0.614967 | −0.307483 | − | 0.951553i | \(-0.599487\pi\) | ||||
−0.307483 | + | 0.951553i | \(0.599487\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.7639 | −1.06060 | −0.530301 | − | 0.847810i | \(-0.677921\pi\) | ||||
−0.530301 | + | 0.847810i | \(0.677921\pi\) | |||||||
\(104\) | 5.52786 | 0.542052 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.90983 | 0.476885 | ||||||||
\(107\) | −11.4164 | −1.10367 | −0.551833 | − | 0.833955i | \(-0.686071\pi\) | ||||
−0.551833 | + | 0.833955i | \(0.686071\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | 0.0957826 | 0.0478913 | − | 0.998853i | \(-0.484750\pi\) | ||||
0.0478913 | + | 0.998853i | \(0.484750\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.85410 | −0.175196 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.23607 | −0.581516 | ||||||||
\(116\) | −12.4721 | −1.15801 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.23607 | 0.666134 | ||||||||
\(119\) | 4.23607 | 0.388320 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | −0.437694 | −0.0396270 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.5623 | 1.30773 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1803 | 1.43577 | 0.717886 | − | 0.696160i | \(-0.245110\pi\) | ||||
0.717886 | + | 0.696160i | \(0.245110\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.52786 | 0.134003 | ||||||||
\(131\) | −16.7639 | −1.46467 | −0.732336 | − | 0.680944i | \(-0.761570\pi\) | ||||
−0.732336 | + | 0.680944i | \(0.761570\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.47214 | 0.647916 | ||||||||
\(134\) | −6.76393 | −0.584315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.47214 | −0.812229 | ||||||||
\(137\) | −1.94427 | −0.166110 | −0.0830552 | − | 0.996545i | \(-0.526468\pi\) | ||||
−0.0830552 | + | 0.996545i | \(0.526468\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.52786 | 0.468867 | 0.234434 | − | 0.972132i | \(-0.424676\pi\) | ||||
0.234434 | + | 0.972132i | \(0.424676\pi\) | |||||||
\(140\) | −1.61803 | −0.136749 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.23607 | 0.103729 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.70820 | −0.640131 | ||||||||
\(146\) | −0.291796 | −0.0241492 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.7082 | 1.29121 | ||||||||
\(149\) | −6.94427 | −0.568897 | −0.284448 | − | 0.958691i | \(-0.591810\pi\) | ||||
−0.284448 | + | 0.958691i | \(0.591810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8885 | 1.45575 | 0.727875 | − | 0.685710i | \(-0.240508\pi\) | ||||
0.727875 | + | 0.685710i | \(0.240508\pi\) | |||||||
\(152\) | −16.7082 | −1.35521 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 9.00000 | 0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.763932 | −0.0609684 | −0.0304842 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304842 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(158\) | 10.6180 | 0.844725 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.61803 | 0.444145 | ||||||||
\(161\) | −6.23607 | −0.491471 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2361 | 0.880077 | 0.440038 | − | 0.897979i | \(-0.354965\pi\) | ||||
0.440038 | + | 0.897979i | \(0.354965\pi\) | |||||||
\(164\) | 13.7082 | 1.07043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.79837 | −0.527656 | ||||||||
\(167\) | 5.94427 | 0.459982 | 0.229991 | − | 0.973193i | \(-0.426130\pi\) | ||||
0.229991 | + | 0.973193i | \(0.426130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.88854 | −0.529888 | ||||||||
\(170\) | −2.61803 | −0.200794 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.7082 | 1.04524 | ||||||||
\(173\) | 13.1803 | 1.00208 | 0.501041 | − | 0.865423i | \(-0.332950\pi\) | ||||
0.501041 | + | 0.865423i | \(0.332950\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.05573 | −0.378943 | ||||||||
\(179\) | −15.4164 | −1.15228 | −0.576138 | − | 0.817352i | \(-0.695441\pi\) | ||||
−0.576138 | + | 0.817352i | \(0.695441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.76393 | 0.279771 | 0.139885 | − | 0.990168i | \(-0.455327\pi\) | ||||
0.139885 | + | 0.990168i | \(0.455327\pi\) | |||||||
\(182\) | 1.52786 | 0.113253 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.9443 | 1.02799 | ||||||||
\(185\) | 9.70820 | 0.713761 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7082 | −1.00244 | ||||||||
\(188\) | −6.47214 | −0.472029 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.61803 | −0.335027 | ||||||||
\(191\) | −20.7639 | −1.50243 | −0.751213 | − | 0.660060i | \(-0.770531\pi\) | ||||
−0.751213 | + | 0.660060i | \(0.770531\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.41641 | −0.245918 | −0.122959 | − | 0.992412i | \(-0.539238\pi\) | ||||
−0.122959 | + | 0.992412i | \(0.539238\pi\) | |||||||
\(194\) | 3.23607 | 0.232336 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61803 | −0.115574 | ||||||||
\(197\) | −0.0557281 | −0.00397046 | −0.00198523 | − | 0.999998i | \(-0.500632\pi\) | ||||
−0.00198523 | + | 0.999998i | \(0.500632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.4721 | −1.87656 | −0.938280 | − | 0.345877i | \(-0.887582\pi\) | ||||
−0.938280 | + | 0.345877i | \(0.887582\pi\) | |||||||
\(200\) | 2.23607 | 0.158114 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.81966 | 0.268750 | ||||||||
\(203\) | −7.70820 | −0.541010 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.47214 | 0.591720 | ||||||||
\(206\) | 6.65248 | 0.463500 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.58359 | 0.317815 | ||||||||
\(209\) | −24.1803 | −1.67259 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.708204 | 0.0487548 | 0.0243774 | − | 0.999703i | \(-0.492240\pi\) | ||||
0.0243774 | + | 0.999703i | \(0.492240\pi\) | |||||||
\(212\) | 12.8541 | 0.882823 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.05573 | 0.482320 | ||||||||
\(215\) | 8.47214 | 0.577795 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.00000 | 0.610960 | ||||||||
\(218\) | −0.618034 | −0.0418585 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.23607 | 0.353016 | ||||||||
\(221\) | −10.4721 | −0.704432 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.6525 | 1.24906 | 0.624531 | − | 0.781000i | \(-0.285290\pi\) | ||||
0.624531 | + | 0.781000i | \(0.285290\pi\) | |||||||
\(224\) | 5.61803 | 0.375371 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.23607 | −0.0822220 | ||||||||
\(227\) | 11.0000 | 0.730096 | 0.365048 | − | 0.930989i | \(-0.381053\pi\) | ||||
0.365048 | + | 0.930989i | \(0.381053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.23607 | 0.544255 | 0.272127 | − | 0.962261i | \(-0.412273\pi\) | ||||
0.272127 | + | 0.962261i | \(0.412273\pi\) | |||||||
\(230\) | 3.85410 | 0.254132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.2361 | 1.13160 | ||||||||
\(233\) | 18.3607 | 1.20285 | 0.601424 | − | 0.798930i | \(-0.294600\pi\) | ||||
0.601424 | + | 0.798930i | \(0.294600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | −0.260931 | ||||||||
\(236\) | 18.9443 | 1.23317 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.61803 | −0.169702 | ||||||||
\(239\) | −12.4721 | −0.806755 | −0.403378 | − | 0.915034i | \(-0.632164\pi\) | ||||
−0.403378 | + | 0.915034i | \(0.632164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.65248 | −0.364108 | −0.182054 | − | 0.983289i | \(-0.558275\pi\) | ||||
−0.182054 | + | 0.983289i | \(0.558275\pi\) | |||||||
\(242\) | 0.326238 | 0.0209714 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.14590 | −0.0733586 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.4721 | −1.17535 | ||||||||
\(248\) | −20.1246 | −1.27791 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.618034 | 0.0390879 | ||||||||
\(251\) | −2.76393 | −0.174458 | −0.0872289 | − | 0.996188i | \(-0.527801\pi\) | ||||
−0.0872289 | + | 0.996188i | \(0.527801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1803 | 1.26873 | ||||||||
\(254\) | −10.0000 | −0.627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 24.5967 | 1.53430 | 0.767151 | − | 0.641466i | \(-0.221673\pi\) | ||||
0.767151 | + | 0.641466i | \(0.221673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.70820 | 0.603238 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.3607 | 0.640085 | ||||||||
\(263\) | 9.52786 | 0.587513 | 0.293757 | − | 0.955880i | \(-0.405094\pi\) | ||||
0.293757 | + | 0.955880i | \(0.405094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.94427 | 0.488013 | ||||||||
\(266\) | −4.61803 | −0.283150 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.7082 | −1.08170 | ||||||||
\(269\) | 5.70820 | 0.348035 | 0.174018 | − | 0.984743i | \(-0.444325\pi\) | ||||
0.174018 | + | 0.984743i | \(0.444325\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.41641 | 0.389769 | 0.194885 | − | 0.980826i | \(-0.437567\pi\) | ||||
0.194885 | + | 0.980826i | \(0.437567\pi\) | |||||||
\(272\) | −7.85410 | −0.476225 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.20163 | 0.0725929 | ||||||||
\(275\) | 3.23607 | 0.195142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3607 | −0.862850 | −0.431425 | − | 0.902149i | \(-0.641989\pi\) | ||||
−0.431425 | + | 0.902149i | \(0.641989\pi\) | |||||||
\(278\) | −3.41641 | −0.204903 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.23607 | 0.133631 | ||||||||
\(281\) | 20.6525 | 1.23202 | 0.616012 | − | 0.787737i | \(-0.288747\pi\) | ||||
0.616012 | + | 0.787737i | \(0.288747\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0000 | −1.30776 | −0.653882 | − | 0.756596i | \(-0.726861\pi\) | ||||
−0.653882 | + | 0.756596i | \(0.726861\pi\) | |||||||
\(284\) | 3.23607 | 0.192025 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.94427 | −0.292361 | ||||||||
\(287\) | 8.47214 | 0.500094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.944272 | 0.0555454 | ||||||||
\(290\) | 4.76393 | 0.279748 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.763932 | −0.0447057 | ||||||||
\(293\) | 22.7082 | 1.32663 | 0.663314 | − | 0.748341i | \(-0.269150\pi\) | ||||
0.663314 | + | 0.748341i | \(0.269150\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7082 | 0.681678 | ||||||||
\(296\) | −21.7082 | −1.26176 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.29180 | 0.248617 | ||||||||
\(299\) | 15.4164 | 0.891554 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.47214 | 0.488326 | ||||||||
\(302\) | −11.0557 | −0.636186 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.8541 | −0.794587 | ||||||||
\(305\) | −0.708204 | −0.0405516 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.1246 | −0.977353 | −0.488677 | − | 0.872465i | \(-0.662520\pi\) | ||||
−0.488677 | + | 0.872465i | \(0.662520\pi\) | |||||||
\(308\) | 5.23607 | 0.298353 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.56231 | −0.315918 | ||||||||
\(311\) | −16.9443 | −0.960822 | −0.480411 | − | 0.877044i | \(-0.659512\pi\) | ||||
−0.480411 | + | 0.877044i | \(0.659512\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.52786 | −0.0863600 | −0.0431800 | − | 0.999067i | \(-0.513749\pi\) | ||||
−0.0431800 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(314\) | 0.472136 | 0.0266442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.7984 | 1.56378 | ||||||||
\(317\) | 5.94427 | 0.333864 | 0.166932 | − | 0.985968i | \(-0.446614\pi\) | ||||
0.166932 | + | 0.985968i | \(0.446614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9443 | 1.39661 | ||||||||
\(320\) | 0.236068 | 0.0131966 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.85410 | 0.214781 | ||||||||
\(323\) | 31.6525 | 1.76119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.47214 | 0.137129 | ||||||||
\(326\) | −6.94427 | −0.384608 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.9443 | −1.04602 | ||||||||
\(329\) | −4.00000 | −0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.41641 | 0.407643 | 0.203821 | − | 0.979008i | \(-0.434664\pi\) | ||||
0.203821 | + | 0.979008i | \(0.434664\pi\) | |||||||
\(332\) | −17.7984 | −0.976813 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.67376 | −0.201019 | ||||||||
\(335\) | −10.9443 | −0.597949 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.05573 | 0.166456 | 0.0832281 | − | 0.996531i | \(-0.473477\pi\) | ||||
0.0832281 | + | 0.996531i | \(0.473477\pi\) | |||||||
\(338\) | 4.25735 | 0.231570 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.85410 | −0.371716 | ||||||||
\(341\) | −29.1246 | −1.57719 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −18.9443 | −1.02141 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.14590 | −0.437926 | ||||||||
\(347\) | −3.05573 | −0.164040 | −0.0820200 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820200 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.1803 | 0.598470 | 0.299235 | − | 0.954179i | \(-0.403269\pi\) | ||||
0.299235 | + | 0.954179i | \(0.403269\pi\) | |||||||
\(350\) | 0.618034 | 0.0330353 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.1803 | −0.969015 | ||||||||
\(353\) | −4.47214 | −0.238028 | −0.119014 | − | 0.992893i | \(-0.537973\pi\) | ||||
−0.119014 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00000 | 0.106149 | ||||||||
\(356\) | −13.2361 | −0.701510 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.52786 | 0.503563 | ||||||||
\(359\) | −9.41641 | −0.496979 | −0.248489 | − | 0.968635i | \(-0.579934\pi\) | ||||
−0.248489 | + | 0.968635i | \(0.579934\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.8328 | 1.93857 | ||||||||
\(362\) | −2.32624 | −0.122264 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −0.472136 | −0.0247127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.4164 | −1.22233 | −0.611163 | − | 0.791505i | \(-0.709298\pi\) | ||||
−0.611163 | + | 0.791505i | \(0.709298\pi\) | |||||||
\(368\) | 11.5623 | 0.602727 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 7.94427 | 0.412446 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4164 | −0.591119 | −0.295560 | − | 0.955324i | \(-0.595506\pi\) | ||||
−0.295560 | + | 0.955324i | \(0.595506\pi\) | |||||||
\(374\) | 8.47214 | 0.438084 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.94427 | 0.461266 | ||||||||
\(377\) | 19.0557 | 0.981420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.34752 | −0.120584 | −0.0602921 | − | 0.998181i | \(-0.519203\pi\) | ||||
−0.0602921 | + | 0.998181i | \(0.519203\pi\) | |||||||
\(380\) | −12.0902 | −0.620213 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.8328 | 0.656584 | ||||||||
\(383\) | −27.9443 | −1.42789 | −0.713943 | − | 0.700204i | \(-0.753092\pi\) | ||||
−0.713943 | + | 0.700204i | \(0.753092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.23607 | 0.164925 | ||||||||
\(386\) | 2.11146 | 0.107470 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.47214 | 0.430108 | ||||||||
\(389\) | 6.65248 | 0.337294 | 0.168647 | − | 0.985677i | \(-0.446060\pi\) | ||||
0.168647 | + | 0.985677i | \(0.446060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.4164 | −1.33594 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.0344419 | 0.00173516 | ||||||||
\(395\) | 17.1803 | 0.864437 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.76393 | −0.339472 | −0.169736 | − | 0.985490i | \(-0.554292\pi\) | ||||
−0.169736 | + | 0.985490i | \(0.554292\pi\) | |||||||
\(398\) | 16.3607 | 0.820087 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.85410 | 0.0927051 | ||||||||
\(401\) | 24.4721 | 1.22208 | 0.611040 | − | 0.791600i | \(-0.290751\pi\) | ||||
0.611040 | + | 0.791600i | \(0.290751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.2492 | −1.10831 | ||||||||
\(404\) | 10.0000 | 0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.76393 | 0.236430 | ||||||||
\(407\) | −31.4164 | −1.55725 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.236068 | −0.0116728 | −0.00583641 | − | 0.999983i | \(-0.501858\pi\) | ||||
−0.00583641 | + | 0.999983i | \(0.501858\pi\) | |||||||
\(410\) | −5.23607 | −0.258591 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.4164 | 0.858045 | ||||||||
\(413\) | 11.7082 | 0.576123 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.0000 | −0.539969 | ||||||||
\(416\) | −13.8885 | −0.680942 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.9443 | 0.730948 | ||||||||
\(419\) | −18.6525 | −0.911233 | −0.455617 | − | 0.890176i | \(-0.650581\pi\) | ||||
−0.455617 | + | 0.890176i | \(0.650581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.8328 | −1.35649 | −0.678244 | − | 0.734837i | \(-0.737259\pi\) | ||||
−0.678244 | + | 0.734837i | \(0.737259\pi\) | |||||||
\(422\) | −0.437694 | −0.0213066 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.7639 | −0.862693 | ||||||||
\(425\) | −4.23607 | −0.205479 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.708204 | −0.0342724 | ||||||||
\(428\) | 18.4721 | 0.892884 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.23607 | −0.252506 | ||||||||
\(431\) | 18.4721 | 0.889771 | 0.444886 | − | 0.895587i | \(-0.353244\pi\) | ||||
0.444886 | + | 0.895587i | \(0.353244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.23607 | 0.251629 | 0.125815 | − | 0.992054i | \(-0.459846\pi\) | ||||
0.125815 | + | 0.992054i | \(0.459846\pi\) | |||||||
\(434\) | −5.56231 | −0.266999 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.61803 | −0.0774898 | ||||||||
\(437\) | −46.5967 | −2.22902 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.0000 | −1.00228 | −0.501138 | − | 0.865368i | \(-0.667085\pi\) | ||||
−0.501138 | + | 0.865368i | \(0.667085\pi\) | |||||||
\(440\) | −7.23607 | −0.344966 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.47214 | 0.307848 | ||||||||
\(443\) | −17.2918 | −0.821558 | −0.410779 | − | 0.911735i | \(-0.634743\pi\) | ||||
−0.410779 | + | 0.911735i | \(0.634743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.18034 | −0.387785 | ||||||||
\(446\) | −11.5279 | −0.545860 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.236068 | 0.0111532 | ||||||||
\(449\) | −24.9443 | −1.17719 | −0.588596 | − | 0.808427i | \(-0.700319\pi\) | ||||
−0.588596 | + | 0.808427i | \(0.700319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.4164 | −1.29099 | ||||||||
\(452\) | −3.23607 | −0.152212 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.79837 | −0.319063 | ||||||||
\(455\) | 2.47214 | 0.115896 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.0689 | 1.87434 | 0.937172 | − | 0.348869i | \(-0.113434\pi\) | ||||
0.937172 | + | 0.348869i | \(0.113434\pi\) | |||||||
\(458\) | −5.09017 | −0.237848 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.0902 | 0.470457 | ||||||||
\(461\) | −19.5279 | −0.909503 | −0.454752 | − | 0.890618i | \(-0.650272\pi\) | ||||
−0.454752 | + | 0.890618i | \(0.650272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.5279 | −1.09343 | −0.546716 | − | 0.837318i | \(-0.684122\pi\) | ||||
−0.546716 | + | 0.837318i | \(0.684122\pi\) | |||||||
\(464\) | 14.2918 | 0.663480 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.3475 | −0.525664 | ||||||||
\(467\) | 32.5279 | 1.50521 | 0.752605 | − | 0.658472i | \(-0.228797\pi\) | ||||
0.752605 | + | 0.658472i | \(0.228797\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.9443 | −0.505360 | ||||||||
\(470\) | 2.47214 | 0.114031 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −26.1803 | −1.20505 | ||||||||
\(473\) | −27.4164 | −1.26061 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.47214 | −0.342845 | ||||||||
\(476\) | −6.85410 | −0.314157 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.70820 | 0.352565 | ||||||||
\(479\) | 27.5967 | 1.26093 | 0.630464 | − | 0.776219i | \(-0.282865\pi\) | ||||
0.630464 | + | 0.776219i | \(0.282865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 3.49342 | 0.159121 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.854102 | 0.0388228 | ||||||||
\(485\) | 5.23607 | 0.237758 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.23607 | 0.146640 | 0.0733201 | − | 0.997308i | \(-0.476641\pi\) | ||||
0.0733201 | + | 0.997308i | \(0.476641\pi\) | |||||||
\(488\) | 1.58359 | 0.0716858 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.618034 | 0.0279199 | ||||||||
\(491\) | 31.8885 | 1.43911 | 0.719555 | − | 0.694436i | \(-0.244346\pi\) | ||||
0.719555 | + | 0.694436i | \(0.244346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.6525 | −1.47059 | ||||||||
\(494\) | 11.4164 | 0.513648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.6869 | −0.749265 | ||||||||
\(497\) | 2.00000 | 0.0897123 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.76393 | 0.258029 | 0.129015 | − | 0.991643i | \(-0.458819\pi\) | ||||
0.129015 | + | 0.991643i | \(0.458819\pi\) | |||||||
\(500\) | 1.61803 | 0.0723607 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.70820 | 0.0762409 | ||||||||
\(503\) | −7.94427 | −0.354218 | −0.177109 | − | 0.984191i | \(-0.556674\pi\) | ||||
−0.177109 | + | 0.984191i | \(0.556674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.18034 | 0.275022 | ||||||||
\(506\) | −12.4721 | −0.554454 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −26.1803 | −1.16156 | ||||||||
\(509\) | −8.36068 | −0.370581 | −0.185290 | − | 0.982684i | \(-0.559323\pi\) | ||||
−0.185290 | + | 0.982684i | \(0.559323\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.472136 | −0.0208861 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.2016 | −0.670515 | ||||||||
\(515\) | 10.7639 | 0.474316 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.9443 | 0.569288 | ||||||||
\(518\) | −6.00000 | −0.263625 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.52786 | −0.242413 | ||||||||
\(521\) | 41.7082 | 1.82727 | 0.913635 | − | 0.406536i | \(-0.133263\pi\) | ||||
0.913635 | + | 0.406536i | \(0.133263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0689 | −0.877551 | −0.438776 | − | 0.898597i | \(-0.644588\pi\) | ||||
−0.438776 | + | 0.898597i | \(0.644588\pi\) | |||||||
\(524\) | 27.1246 | 1.18494 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.88854 | −0.256753 | ||||||||
\(527\) | 38.1246 | 1.66073 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.8885 | 0.690806 | ||||||||
\(530\) | −4.90983 | −0.213269 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0902 | −0.524175 | ||||||||
\(533\) | −20.9443 | −0.907197 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4164 | 0.493574 | ||||||||
\(536\) | 24.4721 | 1.05704 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.52786 | −0.152097 | ||||||||
\(539\) | 3.23607 | 0.139387 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.472136 | −0.0202987 | −0.0101494 | − | 0.999948i | \(-0.503231\pi\) | ||||
−0.0101494 | + | 0.999948i | \(0.503231\pi\) | |||||||
\(542\) | −3.96556 | −0.170335 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.7984 | 1.02035 | ||||||||
\(545\) | −1.00000 | −0.0428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2361 | −0.480420 | −0.240210 | − | 0.970721i | \(-0.577216\pi\) | ||||
−0.240210 | + | 0.970721i | \(0.577216\pi\) | |||||||
\(548\) | 3.14590 | 0.134386 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | −57.5967 | −2.45370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1803 | 0.730582 | ||||||||
\(554\) | 8.87539 | 0.377079 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.94427 | −0.379322 | ||||||||
\(557\) | −2.94427 | −0.124753 | −0.0623764 | − | 0.998053i | \(-0.519868\pi\) | ||||
−0.0623764 | + | 0.998053i | \(0.519868\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.9443 | −0.885848 | ||||||||
\(560\) | 1.85410 | 0.0783501 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.7639 | −0.538414 | ||||||||
\(563\) | −0.583592 | −0.0245955 | −0.0122977 | − | 0.999924i | \(-0.503915\pi\) | ||||
−0.0122977 | + | 0.999924i | \(0.503915\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 13.5967 | 0.571514 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.47214 | −0.187647 | ||||||||
\(569\) | −42.4721 | −1.78052 | −0.890262 | − | 0.455448i | \(-0.849479\pi\) | ||||
−0.890262 | + | 0.455448i | \(0.849479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.1803 | 0.718975 | 0.359487 | − | 0.933150i | \(-0.382952\pi\) | ||||
0.359487 | + | 0.933150i | \(0.382952\pi\) | |||||||
\(572\) | −12.9443 | −0.541227 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.23607 | −0.218549 | ||||||||
\(575\) | 6.23607 | 0.260062 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5410 | −1.18818 | −0.594089 | − | 0.804399i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804399i | \(0.702487\pi\) | |||||||
\(578\) | −0.583592 | −0.0242742 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.4721 | 0.517877 | ||||||||
\(581\) | −11.0000 | −0.456357 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.7082 | −1.06473 | ||||||||
\(584\) | 1.05573 | 0.0436863 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0344 | −0.579757 | ||||||||
\(587\) | −16.3050 | −0.672977 | −0.336489 | − | 0.941688i | \(-0.609239\pi\) | ||||
−0.336489 | + | 0.941688i | \(0.609239\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 67.2492 | 2.77096 | ||||||||
\(590\) | −7.23607 | −0.297904 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18.0000 | −0.739795 | ||||||||
\(593\) | 0.819660 | 0.0336594 | 0.0168297 | − | 0.999858i | \(-0.494643\pi\) | ||||
0.0168297 | + | 0.999858i | \(0.494643\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.23607 | −0.173662 | ||||||||
\(596\) | 11.2361 | 0.460247 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.52786 | −0.389623 | ||||||||
\(599\) | −6.11146 | −0.249707 | −0.124854 | − | 0.992175i | \(-0.539846\pi\) | ||||
−0.124854 | + | 0.992175i | \(0.539846\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.236068 | −0.00962941 | −0.00481471 | − | 0.999988i | \(-0.501533\pi\) | ||||
−0.00481471 | + | 0.999988i | \(0.501533\pi\) | |||||||
\(602\) | −5.23607 | −0.213406 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −28.9443 | −1.17773 | ||||||||
\(605\) | 0.527864 | 0.0214607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.4164 | −1.19398 | −0.596988 | − | 0.802250i | \(-0.703636\pi\) | ||||
−0.596988 | + | 0.802250i | \(0.703636\pi\) | |||||||
\(608\) | 41.9787 | 1.70246 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.437694 | 0.0177217 | ||||||||
\(611\) | 9.88854 | 0.400048 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2918 | 0.496461 | 0.248230 | − | 0.968701i | \(-0.420151\pi\) | ||||
0.248230 | + | 0.968701i | \(0.420151\pi\) | |||||||
\(614\) | 10.5836 | 0.427119 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.23607 | −0.291549 | ||||||||
\(617\) | 26.8885 | 1.08249 | 0.541246 | − | 0.840864i | \(-0.317953\pi\) | ||||
0.541246 | + | 0.840864i | \(0.317953\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.8328 | 1.72160 | 0.860798 | − | 0.508947i | \(-0.169965\pi\) | ||||
0.860798 | + | 0.508947i | \(0.169965\pi\) | |||||||
\(620\) | −14.5623 | −0.584836 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.4721 | 0.419894 | ||||||||
\(623\) | −8.18034 | −0.327738 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.944272 | 0.0377407 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.23607 | 0.0493245 | ||||||||
\(629\) | 41.1246 | 1.63975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.18034 | −0.206226 | −0.103113 | − | 0.994670i | \(-0.532880\pi\) | ||||
−0.103113 | + | 0.994670i | \(0.532880\pi\) | |||||||
\(632\) | −38.4164 | −1.52812 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.67376 | −0.145904 | ||||||||
\(635\) | −16.1803 | −0.642097 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.47214 | 0.0979496 | ||||||||
\(638\) | −15.4164 | −0.610341 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.3820 | −0.449912 | ||||||||
\(641\) | 27.1246 | 1.07136 | 0.535679 | − | 0.844422i | \(-0.320056\pi\) | ||||
0.535679 | + | 0.844422i | \(0.320056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.6525 | 0.656710 | 0.328355 | − | 0.944554i | \(-0.393506\pi\) | ||||
0.328355 | + | 0.944554i | \(0.393506\pi\) | |||||||
\(644\) | 10.0902 | 0.397608 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.5623 | −0.769669 | ||||||||
\(647\) | 2.52786 | 0.0993806 | 0.0496903 | − | 0.998765i | \(-0.484177\pi\) | ||||
0.0496903 | + | 0.998765i | \(0.484177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.8885 | −1.48726 | ||||||||
\(650\) | −1.52786 | −0.0599278 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.1803 | −0.711997 | ||||||||
\(653\) | 30.8885 | 1.20876 | 0.604381 | − | 0.796695i | \(-0.293420\pi\) | ||||
0.604381 | + | 0.796695i | \(0.293420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.7639 | 0.655021 | ||||||||
\(656\) | −15.7082 | −0.613302 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.47214 | 0.0963739 | ||||||||
\(659\) | −22.4721 | −0.875390 | −0.437695 | − | 0.899123i | \(-0.644205\pi\) | ||||
−0.437695 | + | 0.899123i | \(0.644205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.3607 | 0.714148 | 0.357074 | − | 0.934076i | \(-0.383774\pi\) | ||||
0.357074 | + | 0.934076i | \(0.383774\pi\) | |||||||
\(662\) | −4.58359 | −0.178146 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.5967 | 0.954539 | ||||||||
\(665\) | −7.47214 | −0.289757 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0689 | 1.86123 | ||||||||
\(668\) | −9.61803 | −0.372133 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.76393 | 0.261313 | ||||||||
\(671\) | 2.29180 | 0.0884738 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.7639 | 1.18586 | 0.592931 | − | 0.805253i | \(-0.297971\pi\) | ||||
0.592931 | + | 0.805253i | \(0.297971\pi\) | |||||||
\(674\) | −1.88854 | −0.0727440 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.1459 | 0.428688 | ||||||||
\(677\) | 24.4721 | 0.940541 | 0.470270 | − | 0.882522i | \(-0.344156\pi\) | ||||
0.470270 | + | 0.882522i | \(0.344156\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.23607 | 0.200942 | ||||||||
\(680\) | 9.47214 | 0.363240 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.0000 | 0.689256 | ||||||||
\(683\) | 2.12461 | 0.0812960 | 0.0406480 | − | 0.999174i | \(-0.487058\pi\) | ||||
0.0406480 | + | 0.999174i | \(0.487058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.94427 | 0.0742868 | ||||||||
\(686\) | 0.618034 | 0.0235966 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.7082 | −0.598870 | ||||||||
\(689\) | −19.6393 | −0.748199 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3607 | 0.660431 | 0.330216 | − | 0.943906i | \(-0.392879\pi\) | ||||
0.330216 | + | 0.943906i | \(0.392879\pi\) | |||||||
\(692\) | −21.3262 | −0.810702 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.88854 | 0.0716881 | ||||||||
\(695\) | −5.52786 | −0.209684 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.8885 | 1.35938 | ||||||||
\(698\) | −6.90983 | −0.261541 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.61803 | 0.0611559 | ||||||||
\(701\) | 29.0557 | 1.09742 | 0.548710 | − | 0.836013i | \(-0.315119\pi\) | ||||
0.548710 | + | 0.836013i | \(0.315119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 72.5410 | 2.73594 | ||||||||
\(704\) | −0.763932 | −0.0287918 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.76393 | 0.104022 | ||||||||
\(707\) | 6.18034 | 0.232436 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.0557 | 0.790764 | 0.395382 | − | 0.918517i | \(-0.370612\pi\) | ||||
0.395382 | + | 0.918517i | \(0.370612\pi\) | |||||||
\(710\) | −1.23607 | −0.0463888 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.2918 | 0.685514 | ||||||||
\(713\) | −56.1246 | −2.10188 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | −0.299183 | ||||||||
\(716\) | 24.9443 | 0.932211 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.81966 | 0.217188 | ||||||||
\(719\) | 33.7771 | 1.25967 | 0.629836 | − | 0.776728i | \(-0.283122\pi\) | ||||
0.629836 | + | 0.776728i | \(0.283122\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7639 | 0.400870 | ||||||||
\(722\) | −22.7639 | −0.847186 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.09017 | −0.226339 | ||||||||
\(725\) | 7.70820 | 0.286276 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.9443 | −1.22184 | −0.610918 | − | 0.791694i | \(-0.709199\pi\) | ||||
−0.610918 | + | 0.791694i | \(0.709199\pi\) | |||||||
\(728\) | −5.52786 | −0.204876 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.291796 | 0.0107999 | ||||||||
\(731\) | 35.8885 | 1.32739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.1246 | −0.558640 | −0.279320 | − | 0.960198i | \(-0.590109\pi\) | ||||
−0.279320 | + | 0.960198i | \(0.590109\pi\) | |||||||
\(734\) | 14.4721 | 0.534176 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.0344 | −1.29139 | ||||||||
\(737\) | 35.4164 | 1.30458 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.76393 | −0.212030 | −0.106015 | − | 0.994365i | \(-0.533809\pi\) | ||||
−0.106015 | + | 0.994365i | \(0.533809\pi\) | |||||||
\(740\) | −15.7082 | −0.577445 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.90983 | −0.180246 | ||||||||
\(743\) | −41.8885 | −1.53674 | −0.768371 | − | 0.640005i | \(-0.778932\pi\) | ||||
−0.768371 | + | 0.640005i | \(0.778932\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.94427 | 0.254418 | ||||||||
\(746\) | 7.05573 | 0.258329 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.1803 | 0.810994 | ||||||||
\(749\) | 11.4164 | 0.417146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.6525 | −1.44694 | −0.723470 | − | 0.690356i | \(-0.757454\pi\) | ||||
−0.723470 | + | 0.690356i | \(0.757454\pi\) | |||||||
\(752\) | 7.41641 | 0.270449 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.7771 | −0.428896 | ||||||||
\(755\) | −17.8885 | −0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.4164 | −0.923775 | −0.461888 | − | 0.886939i | \(-0.652828\pi\) | ||||
−0.461888 | + | 0.886939i | \(0.652828\pi\) | |||||||
\(758\) | 1.45085 | 0.0526972 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.7082 | 0.606070 | ||||||||
\(761\) | 6.47214 | 0.234615 | 0.117307 | − | 0.993096i | \(-0.462574\pi\) | ||||
0.117307 | + | 0.993096i | \(0.462574\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00000 | −0.0362024 | ||||||||
\(764\) | 33.5967 | 1.21549 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.2705 | 0.624009 | ||||||||
\(767\) | −28.9443 | −1.04512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.5967 | −0.742738 | −0.371369 | − | 0.928485i | \(-0.621111\pi\) | ||||
−0.371369 | + | 0.928485i | \(0.621111\pi\) | |||||||
\(770\) | −2.00000 | −0.0720750 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.52786 | 0.198952 | ||||||||
\(773\) | −24.8197 | −0.892701 | −0.446351 | − | 0.894858i | \(-0.647277\pi\) | ||||
−0.446351 | + | 0.894858i | \(0.647277\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.00000 | −0.323290 | ||||||||
\(776\) | −11.7082 | −0.420300 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.11146 | −0.147403 | ||||||||
\(779\) | 63.3050 | 2.26814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.47214 | −0.231591 | ||||||||
\(782\) | 16.3262 | 0.583825 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.85410 | 0.0662179 | ||||||||
\(785\) | 0.763932 | 0.0272659 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.8197 | 0.421325 | 0.210663 | − | 0.977559i | \(-0.432438\pi\) | ||||
0.210663 | + | 0.977559i | \(0.432438\pi\) | |||||||
\(788\) | 0.0901699 | 0.00321217 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.6180 | −0.377773 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.75078 | 0.0621719 | ||||||||
\(794\) | 4.18034 | 0.148355 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 42.8328 | 1.51817 | ||||||||
\(797\) | 38.7082 | 1.37111 | 0.685557 | − | 0.728019i | \(-0.259559\pi\) | ||||
0.685557 | + | 0.728019i | \(0.259559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.9443 | −0.599445 | ||||||||
\(800\) | −5.61803 | −0.198627 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.1246 | −0.534069 | ||||||||
\(803\) | 1.52786 | 0.0539172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.23607 | 0.219793 | ||||||||
\(806\) | 13.7508 | 0.484350 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.8197 | −0.486174 | ||||||||
\(809\) | 46.9443 | 1.65047 | 0.825236 | − | 0.564788i | \(-0.191042\pi\) | ||||
0.825236 | + | 0.564788i | \(0.191042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.9443 | 1.85912 | 0.929562 | − | 0.368665i | \(-0.120185\pi\) | ||||
0.929562 | + | 0.368665i | \(0.120185\pi\) | |||||||
\(812\) | 12.4721 | 0.437686 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.4164 | 0.680545 | ||||||||
\(815\) | −11.2361 | −0.393582 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 63.3050 | 2.21476 | ||||||||
\(818\) | 0.145898 | 0.00510121 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.7082 | −0.478711 | ||||||||
\(821\) | −21.4164 | −0.747438 | −0.373719 | − | 0.927542i | \(-0.621918\pi\) | ||||
−0.373719 | + | 0.927542i | \(0.621918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.3050 | −1.37008 | −0.685042 | − | 0.728503i | \(-0.740216\pi\) | ||||
−0.685042 | + | 0.728503i | \(0.740216\pi\) | |||||||
\(824\) | −24.0689 | −0.838479 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.23607 | −0.251775 | ||||||||
\(827\) | −34.7082 | −1.20692 | −0.603461 | − | 0.797392i | \(-0.706212\pi\) | ||||
−0.603461 | + | 0.797392i | \(0.706212\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.5279 | 0.678231 | 0.339115 | − | 0.940745i | \(-0.389872\pi\) | ||||
0.339115 | + | 0.940745i | \(0.389872\pi\) | |||||||
\(830\) | 6.79837 | 0.235975 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.583592 | −0.0202324 | ||||||||
\(833\) | −4.23607 | −0.146771 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.94427 | −0.205710 | ||||||||
\(836\) | 39.1246 | 1.35315 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.5279 | 0.398223 | ||||||||
\(839\) | −26.1803 | −0.903846 | −0.451923 | − | 0.892057i | \(-0.649262\pi\) | ||||
−0.451923 | + | 0.892057i | \(0.649262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.4164 | 1.04884 | ||||||||
\(842\) | 17.2016 | 0.592807 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.14590 | −0.0394434 | ||||||||
\(845\) | 6.88854 | 0.236973 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.527864 | 0.0181376 | ||||||||
\(848\) | −14.7295 | −0.505813 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.61803 | 0.0897978 | ||||||||
\(851\) | −60.5410 | −2.07532 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.2492 | 1.30963 | 0.654814 | − | 0.755790i | \(-0.272747\pi\) | ||||
0.654814 | + | 0.755790i | \(0.272747\pi\) | |||||||
\(854\) | 0.437694 | 0.0149776 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.5279 | −0.872524 | ||||||||
\(857\) | 23.1803 | 0.791825 | 0.395913 | − | 0.918288i | \(-0.370428\pi\) | ||||
0.395913 | + | 0.918288i | \(0.370428\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.94427 | 0.202816 | 0.101408 | − | 0.994845i | \(-0.467665\pi\) | ||||
0.101408 | + | 0.994845i | \(0.467665\pi\) | |||||||
\(860\) | −13.7082 | −0.467446 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.4164 | −0.388844 | ||||||||
\(863\) | 27.1803 | 0.925230 | 0.462615 | − | 0.886559i | \(-0.346911\pi\) | ||||
0.462615 | + | 0.886559i | \(0.346911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.1803 | −0.448145 | ||||||||
\(866\) | −3.23607 | −0.109966 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.5623 | −0.494277 | ||||||||
\(869\) | −55.5967 | −1.88599 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.0557 | 0.916748 | ||||||||
\(872\) | 2.23607 | 0.0757228 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 28.7984 | 0.974120 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.3475 | 0.720855 | 0.360427 | − | 0.932787i | \(-0.382631\pi\) | ||||
0.360427 | + | 0.932787i | \(0.382631\pi\) | |||||||
\(878\) | 12.9787 | 0.438010 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | −47.4853 | −1.59982 | −0.799910 | − | 0.600120i | \(-0.795120\pi\) | ||||
−0.799910 | + | 0.600120i | \(0.795120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.34752 | −0.112653 | −0.0563266 | − | 0.998412i | \(-0.517939\pi\) | ||||
−0.0563266 | + | 0.998412i | \(0.517939\pi\) | |||||||
\(884\) | 16.9443 | 0.569898 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.6869 | 0.359034 | ||||||||
\(887\) | −51.7214 | −1.73663 | −0.868317 | − | 0.496010i | \(-0.834798\pi\) | ||||
−0.868317 | + | 0.496010i | \(0.834798\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.1803 | −0.542671 | ||||||||
\(890\) | 5.05573 | 0.169468 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.1803 | −1.01051 | ||||||||
\(893\) | −29.8885 | −1.00018 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4164 | 0.515314 | ||||||||
\(896\) | −11.3820 | −0.380245 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.4164 | 0.514452 | ||||||||
\(899\) | −69.3738 | −2.31375 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.6525 | 1.12113 | ||||||||
\(902\) | 16.9443 | 0.564183 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.47214 | 0.148741 | ||||||||
\(905\) | −3.76393 | −0.125117 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.1246 | 0.900658 | 0.450329 | − | 0.892863i | \(-0.351307\pi\) | ||||
0.450329 | + | 0.892863i | \(0.351307\pi\) | |||||||
\(908\) | −17.7984 | −0.590660 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.52786 | −0.0506482 | ||||||||
\(911\) | 54.7639 | 1.81441 | 0.907205 | − | 0.420689i | \(-0.138212\pi\) | ||||
0.907205 | + | 0.420689i | \(0.138212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.5967 | 1.17808 | ||||||||
\(914\) | −24.7639 | −0.819118 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.3262 | −0.440311 | ||||||||
\(917\) | 16.7639 | 0.553594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.3050 | −1.62642 | −0.813210 | − | 0.581970i | \(-0.802282\pi\) | ||||
−0.813210 | + | 0.581970i | \(0.802282\pi\) | |||||||
\(920\) | −13.9443 | −0.459729 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.0689 | 0.397468 | ||||||||
\(923\) | −4.94427 | −0.162743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.70820 | −0.319204 | ||||||||
\(926\) | 14.5410 | 0.477848 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −43.3050 | −1.42155 | ||||||||
\(929\) | −5.12461 | −0.168133 | −0.0840665 | − | 0.996460i | \(-0.526791\pi\) | ||||
−0.0840665 | + | 0.996460i | \(0.526791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.47214 | −0.244889 | ||||||||
\(932\) | −29.7082 | −0.973125 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.1033 | −0.657801 | ||||||||
\(935\) | 13.7082 | 0.448306 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.4721 | 0.734133 | 0.367066 | − | 0.930195i | \(-0.380362\pi\) | ||||
0.367066 | + | 0.930195i | \(0.380362\pi\) | |||||||
\(938\) | 6.76393 | 0.220850 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.47214 | 0.211098 | ||||||||
\(941\) | 35.2361 | 1.14866 | 0.574331 | − | 0.818623i | \(-0.305262\pi\) | ||||
0.574331 | + | 0.818623i | \(0.305262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52.8328 | −1.72047 | ||||||||
\(944\) | −21.7082 | −0.706542 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.9443 | 0.550906 | ||||||||
\(947\) | 41.5410 | 1.34990 | 0.674951 | − | 0.737863i | \(-0.264165\pi\) | ||||
0.674951 | + | 0.737863i | \(0.264165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.16718 | 0.0378884 | ||||||||
\(950\) | 4.61803 | 0.149829 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.47214 | 0.306994 | ||||||||
\(953\) | −57.7771 | −1.87158 | −0.935792 | − | 0.352553i | \(-0.885314\pi\) | ||||
−0.935792 | + | 0.352553i | \(0.885314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.7639 | 0.671905 | ||||||||
\(956\) | 20.1803 | 0.652679 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.0557 | −0.551046 | ||||||||
\(959\) | 1.94427 | 0.0627838 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.0000 | 1.61290 | ||||||||
\(962\) | 14.8328 | 0.478229 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.14590 | 0.294570 | ||||||||
\(965\) | 3.41641 | 0.109978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.5967 | −0.630189 | −0.315094 | − | 0.949060i | \(-0.602036\pi\) | ||||
−0.315094 | + | 0.949060i | \(0.602036\pi\) | |||||||
\(968\) | −1.18034 | −0.0379376 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.23607 | −0.103904 | ||||||||
\(971\) | 30.0000 | 0.962746 | 0.481373 | − | 0.876516i | \(-0.340138\pi\) | ||||
0.481373 | + | 0.876516i | \(0.340138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.52786 | −0.177215 | ||||||||
\(974\) | −2.00000 | −0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.31308 | 0.0420307 | ||||||||
\(977\) | 20.1115 | 0.643422 | 0.321711 | − | 0.946838i | \(-0.395742\pi\) | ||||
0.321711 | + | 0.946838i | \(0.395742\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.4721 | 0.846053 | ||||||||
\(980\) | 1.61803 | 0.0516862 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.7082 | −0.628914 | ||||||||
\(983\) | 41.0000 | 1.30770 | 0.653848 | − | 0.756626i | \(-0.273153\pi\) | ||||
0.653848 | + | 0.756626i | \(0.273153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0557281 | 0.00177564 | ||||||||
\(986\) | 20.1803 | 0.642673 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.8885 | 0.950881 | ||||||||
\(989\) | −52.8328 | −1.67999 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.0132 | 1.08046 | 0.540232 | − | 0.841516i | \(-0.318337\pi\) | ||||
0.540232 | + | 0.841516i | \(0.318337\pi\) | |||||||
\(992\) | 50.5623 | 1.60535 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.23607 | −0.0392057 | ||||||||
\(995\) | 26.4721 | 0.839223 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.58359 | 0.208504 | 0.104252 | − | 0.994551i | \(-0.466755\pi\) | ||||
0.104252 | + | 0.994551i | \(0.466755\pi\) | |||||||
\(998\) | −3.56231 | −0.112763 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.a.h.1.1 | yes | 2 | |
3.2 | odd | 2 | 945.2.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 4725.2.a.y.1.2 | 2 | |||
7.6 | odd | 2 | 6615.2.a.t.1.1 | 2 | |||
15.14 | odd | 2 | 4725.2.a.bd.1.1 | 2 | |||
21.20 | even | 2 | 6615.2.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.a.c.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
945.2.a.h.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
4725.2.a.y.1.2 | 2 | 5.4 | even | 2 | |||
4725.2.a.bd.1.1 | 2 | 15.14 | odd | 2 | |||
6615.2.a.n.1.2 | 2 | 21.20 | even | 2 | |||
6615.2.a.t.1.1 | 2 | 7.6 | odd | 2 |