Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 361) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23607 | −1.58114 | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | 2.00000 | 1.15470 | 0.577350 | − | 0.816497i | \(-0.304087\pi\) | ||||
0.577350 | + | 0.816497i | \(0.304087\pi\) | |||||||
\(4\) | 3.00000 | 1.50000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.47214 | −1.82574 | ||||||||
\(7\) | −1.23607 | −0.467190 | −0.233595 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233595 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23607 | 1.57873 | 0.789367 | − | 0.613922i | \(-0.210409\pi\) | ||||
0.789367 | + | 0.613922i | \(0.210409\pi\) | |||||||
\(12\) | 6.00000 | 1.73205 | ||||||||
\(13\) | −1.85410 | −0.514235 | −0.257118 | − | 0.966380i | \(-0.582773\pi\) | ||||
−0.257118 | + | 0.966380i | \(0.582773\pi\) | |||||||
\(14\) | 2.76393 | 0.738692 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.618034 | −0.149895 | −0.0749476 | − | 0.997187i | \(-0.523879\pi\) | ||||
−0.0749476 | + | 0.997187i | \(0.523879\pi\) | |||||||
\(18\) | −2.23607 | −0.527046 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.47214 | −0.539464 | ||||||||
\(22\) | −11.7082 | −2.49620 | ||||||||
\(23\) | 4.47214 | 0.932505 | 0.466252 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466252 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(24\) | −4.47214 | −0.912871 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.14590 | 0.813077 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | −3.70820 | −0.700785 | ||||||||
\(29\) | −7.09017 | −1.31661 | −0.658306 | − | 0.752751i | \(-0.728727\pi\) | ||||
−0.658306 | + | 0.752751i | \(0.728727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | 10.4721 | 1.82296 | ||||||||
\(34\) | 1.38197 | 0.237005 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 8.85410 | 1.45561 | 0.727803 | − | 0.685787i | \(-0.240542\pi\) | ||||
0.727803 | + | 0.685787i | \(0.240542\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.70820 | −0.593788 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.09017 | −0.638777 | −0.319389 | − | 0.947624i | \(-0.603478\pi\) | ||||
−0.319389 | + | 0.947624i | \(0.603478\pi\) | |||||||
\(42\) | 5.52786 | 0.852968 | ||||||||
\(43\) | 0.472136 | 0.0720001 | 0.0360000 | − | 0.999352i | \(-0.488538\pi\) | ||||
0.0360000 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(44\) | 15.7082 | 2.36810 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.0000 | −1.47442 | ||||||||
\(47\) | −4.76393 | −0.694891 | −0.347445 | − | 0.937700i | \(-0.612951\pi\) | ||||
−0.347445 | + | 0.937700i | \(0.612951\pi\) | |||||||
\(48\) | −2.00000 | −0.288675 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23607 | −0.173084 | ||||||||
\(52\) | −5.56231 | −0.771353 | ||||||||
\(53\) | −0.0901699 | −0.0123858 | −0.00619290 | − | 0.999981i | \(-0.501971\pi\) | ||||
−0.00619290 | + | 0.999981i | \(0.501971\pi\) | |||||||
\(54\) | 8.94427 | 1.21716 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.76393 | 0.369346 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.8541 | 2.08175 | ||||||||
\(59\) | −3.23607 | −0.421300 | −0.210650 | − | 0.977562i | \(-0.567558\pi\) | ||||
−0.210650 | + | 0.977562i | \(0.567558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.85410 | 1.26169 | 0.630844 | − | 0.775909i | \(-0.282709\pi\) | ||||
0.630844 | + | 0.775909i | \(0.282709\pi\) | |||||||
\(62\) | −13.4164 | −1.70389 | ||||||||
\(63\) | −1.23607 | −0.155730 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −23.4164 | −2.88236 | ||||||||
\(67\) | −0.472136 | −0.0576806 | −0.0288403 | − | 0.999584i | \(-0.509181\pi\) | ||||
−0.0288403 | + | 0.999584i | \(0.509181\pi\) | |||||||
\(68\) | −1.85410 | −0.224843 | ||||||||
\(69\) | 8.94427 | 1.07676 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.23607 | 0.384051 | 0.192025 | − | 0.981390i | \(-0.438494\pi\) | ||||
0.192025 | + | 0.981390i | \(0.438494\pi\) | |||||||
\(72\) | −2.23607 | −0.263523 | ||||||||
\(73\) | 14.5623 | 1.70439 | 0.852194 | − | 0.523225i | \(-0.175271\pi\) | ||||
0.852194 | + | 0.523225i | \(0.175271\pi\) | |||||||
\(74\) | −19.7984 | −2.30151 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.47214 | −0.737568 | ||||||||
\(78\) | 8.29180 | 0.938861 | ||||||||
\(79\) | −2.00000 | −0.225018 | −0.112509 | − | 0.993651i | \(-0.535889\pi\) | ||||
−0.112509 | + | 0.993651i | \(0.535889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 9.14590 | 1.01000 | ||||||||
\(83\) | 9.70820 | 1.06561 | 0.532807 | − | 0.846237i | \(-0.321137\pi\) | ||||
0.532807 | + | 0.846237i | \(0.321137\pi\) | |||||||
\(84\) | −7.41641 | −0.809196 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.05573 | −0.113842 | ||||||||
\(87\) | −14.1803 | −1.52029 | ||||||||
\(88\) | −11.7082 | −1.24810 | ||||||||
\(89\) | 7.32624 | 0.776580 | 0.388290 | − | 0.921537i | \(-0.373066\pi\) | ||||
0.388290 | + | 0.921537i | \(0.373066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.29180 | 0.240246 | ||||||||
\(92\) | 13.4164 | 1.39876 | ||||||||
\(93\) | 12.0000 | 1.24434 | ||||||||
\(94\) | 10.6525 | 1.09872 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 13.4164 | 1.36931 | ||||||||
\(97\) | −11.0902 | −1.12604 | −0.563018 | − | 0.826445i | \(-0.690360\pi\) | ||||
−0.563018 | + | 0.826445i | \(0.690360\pi\) | |||||||
\(98\) | 12.2361 | 1.23603 | ||||||||
\(99\) | 5.23607 | 0.526245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.673762 | 0.0670418 | 0.0335209 | − | 0.999438i | \(-0.489328\pi\) | ||||
0.0335209 | + | 0.999438i | \(0.489328\pi\) | |||||||
\(102\) | 2.76393 | 0.273670 | ||||||||
\(103\) | 7.70820 | 0.759512 | 0.379756 | − | 0.925087i | \(-0.376008\pi\) | ||||
0.379756 | + | 0.925087i | \(0.376008\pi\) | |||||||
\(104\) | 4.14590 | 0.406539 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.201626 | 0.0195837 | ||||||||
\(107\) | 0.763932 | 0.0738521 | 0.0369260 | − | 0.999318i | \(-0.488243\pi\) | ||||
0.0369260 | + | 0.999318i | \(0.488243\pi\) | |||||||
\(108\) | −12.0000 | −1.15470 | ||||||||
\(109\) | 12.0902 | 1.15803 | 0.579014 | − | 0.815318i | \(-0.303438\pi\) | ||||
0.579014 | + | 0.815318i | \(0.303438\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.7082 | 1.68079 | ||||||||
\(112\) | 1.23607 | 0.116797 | ||||||||
\(113\) | −10.1459 | −0.954446 | −0.477223 | − | 0.878782i | \(-0.658357\pi\) | ||||
−0.477223 | + | 0.878782i | \(0.658357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −21.2705 | −1.97492 | ||||||||
\(117\) | −1.85410 | −0.171412 | ||||||||
\(118\) | 7.23607 | 0.666134 | ||||||||
\(119\) | 0.763932 | 0.0700295 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | −22.0344 | −1.99490 | ||||||||
\(123\) | −8.18034 | −0.737596 | ||||||||
\(124\) | 18.0000 | 1.61645 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.76393 | 0.246231 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 15.6525 | 1.38350 | ||||||||
\(129\) | 0.944272 | 0.0831385 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.7082 | 1.89665 | 0.948327 | − | 0.317294i | \(-0.102774\pi\) | ||||
0.948327 | + | 0.317294i | \(0.102774\pi\) | |||||||
\(132\) | 31.4164 | 2.73445 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.05573 | 0.0912010 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.38197 | 0.118503 | ||||||||
\(137\) | −1.79837 | −0.153645 | −0.0768227 | − | 0.997045i | \(-0.524478\pi\) | ||||
−0.0768227 | + | 0.997045i | \(0.524478\pi\) | |||||||
\(138\) | −20.0000 | −1.70251 | ||||||||
\(139\) | 13.7082 | 1.16271 | 0.581357 | − | 0.813648i | \(-0.302522\pi\) | ||||
0.581357 | + | 0.813648i | \(0.302522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.52786 | −0.802391 | ||||||||
\(142\) | −7.23607 | −0.607237 | ||||||||
\(143\) | −9.70820 | −0.811841 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −32.5623 | −2.69488 | ||||||||
\(147\) | −10.9443 | −0.902668 | ||||||||
\(148\) | 26.5623 | 2.18341 | ||||||||
\(149\) | 1.85410 | 0.151894 | 0.0759470 | − | 0.997112i | \(-0.475802\pi\) | ||||
0.0759470 | + | 0.997112i | \(0.475802\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.618034 | −0.0499651 | ||||||||
\(154\) | 14.4721 | 1.16620 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.1246 | −0.890682 | ||||||||
\(157\) | 8.03444 | 0.641218 | 0.320609 | − | 0.947212i | \(-0.396112\pi\) | ||||
0.320609 | + | 0.947212i | \(0.396112\pi\) | |||||||
\(158\) | 4.47214 | 0.355784 | ||||||||
\(159\) | −0.180340 | −0.0143019 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.52786 | −0.435657 | ||||||||
\(162\) | 24.5967 | 1.93250 | ||||||||
\(163\) | 8.29180 | 0.649464 | 0.324732 | − | 0.945806i | \(-0.394726\pi\) | ||||
0.324732 | + | 0.945806i | \(0.394726\pi\) | |||||||
\(164\) | −12.2705 | −0.958166 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.7082 | −1.68488 | ||||||||
\(167\) | −4.76393 | −0.368644 | −0.184322 | − | 0.982866i | \(-0.559009\pi\) | ||||
−0.184322 | + | 0.982866i | \(0.559009\pi\) | |||||||
\(168\) | 5.52786 | 0.426484 | ||||||||
\(169\) | −9.56231 | −0.735562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.41641 | 0.108000 | ||||||||
\(173\) | −5.61803 | −0.427131 | −0.213566 | − | 0.976929i | \(-0.568508\pi\) | ||||
−0.213566 | + | 0.976929i | \(0.568508\pi\) | |||||||
\(174\) | 31.7082 | 2.40379 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.23607 | −0.394683 | ||||||||
\(177\) | −6.47214 | −0.486476 | ||||||||
\(178\) | −16.3820 | −1.22788 | ||||||||
\(179\) | 20.9443 | 1.56545 | 0.782724 | − | 0.622369i | \(-0.213830\pi\) | ||||
0.782724 | + | 0.622369i | \(0.213830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4164 | −1.59187 | −0.795935 | − | 0.605383i | \(-0.793020\pi\) | ||||
−0.795935 | + | 0.605383i | \(0.793020\pi\) | |||||||
\(182\) | −5.12461 | −0.379861 | ||||||||
\(183\) | 19.7082 | 1.45687 | ||||||||
\(184\) | −10.0000 | −0.737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −26.8328 | −1.96748 | ||||||||
\(187\) | −3.23607 | −0.236645 | ||||||||
\(188\) | −14.2918 | −1.04234 | ||||||||
\(189\) | 4.94427 | 0.359643 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.76393 | −0.344706 | −0.172353 | − | 0.985035i | \(-0.555137\pi\) | ||||
−0.172353 | + | 0.985035i | \(0.555137\pi\) | |||||||
\(192\) | −26.0000 | −1.87639 | ||||||||
\(193\) | −11.5279 | −0.829794 | −0.414897 | − | 0.909868i | \(-0.636182\pi\) | ||||
−0.414897 | + | 0.909868i | \(0.636182\pi\) | |||||||
\(194\) | 24.7984 | 1.78042 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.4164 | −1.17260 | ||||||||
\(197\) | 24.0344 | 1.71238 | 0.856192 | − | 0.516659i | \(-0.172824\pi\) | ||||
0.856192 | + | 0.516659i | \(0.172824\pi\) | |||||||
\(198\) | −11.7082 | −0.832066 | ||||||||
\(199\) | −12.9443 | −0.917595 | −0.458798 | − | 0.888541i | \(-0.651720\pi\) | ||||
−0.458798 | + | 0.888541i | \(0.651720\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.944272 | −0.0666038 | ||||||||
\(202\) | −1.50658 | −0.106002 | ||||||||
\(203\) | 8.76393 | 0.615107 | ||||||||
\(204\) | −3.70820 | −0.259626 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −17.2361 | −1.20089 | ||||||||
\(207\) | 4.47214 | 0.310835 | ||||||||
\(208\) | 1.85410 | 0.128559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.7082 | −1.90751 | −0.953756 | − | 0.300583i | \(-0.902819\pi\) | ||||
−0.953756 | + | 0.300583i | \(0.902819\pi\) | |||||||
\(212\) | −0.270510 | −0.0185787 | ||||||||
\(213\) | 6.47214 | 0.443463 | ||||||||
\(214\) | −1.70820 | −0.116770 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.94427 | 0.608581 | ||||||||
\(217\) | −7.41641 | −0.503459 | ||||||||
\(218\) | −27.0344 | −1.83100 | ||||||||
\(219\) | 29.1246 | 1.96806 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.14590 | 0.0770814 | ||||||||
\(222\) | −39.5967 | −2.65756 | ||||||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | −8.29180 | −0.554019 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22.6869 | 1.50911 | ||||||||
\(227\) | 13.5279 | 0.897876 | 0.448938 | − | 0.893563i | \(-0.351802\pi\) | ||||
0.448938 | + | 0.893563i | \(0.351802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.9787 | 1.71672 | 0.858361 | − | 0.513046i | \(-0.171483\pi\) | ||||
0.858361 | + | 0.513046i | \(0.171483\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.9443 | −0.851671 | ||||||||
\(232\) | 15.8541 | 1.04087 | ||||||||
\(233\) | −7.09017 | −0.464492 | −0.232246 | − | 0.972657i | \(-0.574608\pi\) | ||||
−0.232246 | + | 0.972657i | \(0.574608\pi\) | |||||||
\(234\) | 4.14590 | 0.271026 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.70820 | −0.631950 | ||||||||
\(237\) | −4.00000 | −0.259828 | ||||||||
\(238\) | −1.70820 | −0.110726 | ||||||||
\(239\) | 1.05573 | 0.0682894 | 0.0341447 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341447 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.05573 | 0.0680054 | 0.0340027 | − | 0.999422i | \(-0.489175\pi\) | ||||
0.0340027 | + | 0.999422i | \(0.489175\pi\) | |||||||
\(242\) | −36.7082 | −2.35969 | ||||||||
\(243\) | −10.0000 | −0.641500 | ||||||||
\(244\) | 29.5623 | 1.89253 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.2918 | 1.16624 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −13.4164 | −0.851943 | ||||||||
\(249\) | 19.4164 | 1.23046 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.2361 | 0.835453 | 0.417727 | − | 0.908573i | \(-0.362827\pi\) | ||||
0.417727 | + | 0.908573i | \(0.362827\pi\) | |||||||
\(252\) | −3.70820 | −0.233595 | ||||||||
\(253\) | 23.4164 | 1.47218 | ||||||||
\(254\) | 26.8328 | 1.68364 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −11.9098 | −0.742915 | −0.371457 | − | 0.928450i | \(-0.621142\pi\) | ||||
−0.371457 | + | 0.928450i | \(0.621142\pi\) | |||||||
\(258\) | −2.11146 | −0.131454 | ||||||||
\(259\) | −10.9443 | −0.680044 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.09017 | −0.438871 | ||||||||
\(262\) | −48.5410 | −2.99887 | ||||||||
\(263\) | −7.81966 | −0.482181 | −0.241090 | − | 0.970503i | \(-0.577505\pi\) | ||||
−0.241090 | + | 0.970503i | \(0.577505\pi\) | |||||||
\(264\) | −23.4164 | −1.44118 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6525 | 0.896717 | ||||||||
\(268\) | −1.41641 | −0.0865209 | ||||||||
\(269\) | −1.20163 | −0.0732644 | −0.0366322 | − | 0.999329i | \(-0.511663\pi\) | ||||
−0.0366322 | + | 0.999329i | \(0.511663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6525 | 0.890075 | 0.445037 | − | 0.895512i | \(-0.353190\pi\) | ||||
0.445037 | + | 0.895512i | \(0.353190\pi\) | |||||||
\(272\) | 0.618034 | 0.0374738 | ||||||||
\(273\) | 4.58359 | 0.277412 | ||||||||
\(274\) | 4.02129 | 0.242935 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 26.8328 | 1.61515 | ||||||||
\(277\) | 10.3820 | 0.623792 | 0.311896 | − | 0.950116i | \(-0.399036\pi\) | ||||
0.311896 | + | 0.950116i | \(0.399036\pi\) | |||||||
\(278\) | −30.6525 | −1.83841 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0902 | 1.13882 | 0.569412 | − | 0.822052i | \(-0.307171\pi\) | ||||
0.569412 | + | 0.822052i | \(0.307171\pi\) | |||||||
\(282\) | 21.3050 | 1.26869 | ||||||||
\(283\) | 31.4164 | 1.86751 | 0.933756 | − | 0.357911i | \(-0.116511\pi\) | ||||
0.933756 | + | 0.357911i | \(0.116511\pi\) | |||||||
\(284\) | 9.70820 | 0.576076 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.7082 | 1.28363 | ||||||||
\(287\) | 5.05573 | 0.298430 | ||||||||
\(288\) | 6.70820 | 0.395285 | ||||||||
\(289\) | −16.6180 | −0.977531 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.1803 | −1.30023 | ||||||||
\(292\) | 43.6869 | 2.55658 | ||||||||
\(293\) | 25.4164 | 1.48484 | 0.742421 | − | 0.669933i | \(-0.233677\pi\) | ||||
0.742421 | + | 0.669933i | \(0.233677\pi\) | |||||||
\(294\) | 24.4721 | 1.42724 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −19.7984 | −1.15076 | ||||||||
\(297\) | −20.9443 | −1.21531 | ||||||||
\(298\) | −4.14590 | −0.240165 | ||||||||
\(299\) | −8.29180 | −0.479527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.583592 | −0.0336377 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.34752 | 0.0774132 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.38197 | 0.0790017 | ||||||||
\(307\) | 15.5279 | 0.886222 | 0.443111 | − | 0.896467i | \(-0.353875\pi\) | ||||
0.443111 | + | 0.896467i | \(0.353875\pi\) | |||||||
\(308\) | −19.4164 | −1.10635 | ||||||||
\(309\) | 15.4164 | 0.877009 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.7639 | 0.837186 | 0.418593 | − | 0.908174i | \(-0.362523\pi\) | ||||
0.418593 | + | 0.908174i | \(0.362523\pi\) | |||||||
\(312\) | 8.29180 | 0.469431 | ||||||||
\(313\) | 25.9787 | 1.46840 | 0.734202 | − | 0.678931i | \(-0.237557\pi\) | ||||
0.734202 | + | 0.678931i | \(0.237557\pi\) | |||||||
\(314\) | −17.9656 | −1.01386 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | 10.3820 | 0.583109 | 0.291555 | − | 0.956554i | \(-0.405827\pi\) | ||||
0.291555 | + | 0.956554i | \(0.405827\pi\) | |||||||
\(318\) | 0.403252 | 0.0226133 | ||||||||
\(319\) | −37.1246 | −2.07858 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.52786 | 0.0852771 | ||||||||
\(322\) | 12.3607 | 0.688834 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −33.0000 | −1.83333 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.5410 | −1.02689 | ||||||||
\(327\) | 24.1803 | 1.33718 | ||||||||
\(328\) | 9.14590 | 0.504998 | ||||||||
\(329\) | 5.88854 | 0.324646 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.81966 | 0.319877 | 0.159939 | − | 0.987127i | \(-0.448870\pi\) | ||||
0.159939 | + | 0.987127i | \(0.448870\pi\) | |||||||
\(332\) | 29.1246 | 1.59842 | ||||||||
\(333\) | 8.85410 | 0.485202 | ||||||||
\(334\) | 10.6525 | 0.582878 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.47214 | 0.134866 | ||||||||
\(337\) | 13.9787 | 0.761469 | 0.380735 | − | 0.924684i | \(-0.375671\pi\) | ||||
0.380735 | + | 0.924684i | \(0.375671\pi\) | |||||||
\(338\) | 21.3820 | 1.16303 | ||||||||
\(339\) | −20.2918 | −1.10210 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.4164 | 1.70129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4164 | 0.832408 | ||||||||
\(344\) | −1.05573 | −0.0569210 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.5623 | 0.675354 | ||||||||
\(347\) | −25.5967 | −1.37411 | −0.687053 | − | 0.726608i | \(-0.741096\pi\) | ||||
−0.687053 | + | 0.726608i | \(0.741096\pi\) | |||||||
\(348\) | −42.5410 | −2.28044 | ||||||||
\(349\) | −2.14590 | −0.114867 | −0.0574336 | − | 0.998349i | \(-0.518292\pi\) | ||||
−0.0574336 | + | 0.998349i | \(0.518292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.41641 | 0.395859 | ||||||||
\(352\) | 35.1246 | 1.87215 | ||||||||
\(353\) | −30.5066 | −1.62370 | −0.811851 | − | 0.583865i | \(-0.801540\pi\) | ||||
−0.811851 | + | 0.583865i | \(0.801540\pi\) | |||||||
\(354\) | 14.4721 | 0.769185 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 21.9787 | 1.16487 | ||||||||
\(357\) | 1.52786 | 0.0808631 | ||||||||
\(358\) | −46.8328 | −2.47519 | ||||||||
\(359\) | 21.7082 | 1.14572 | 0.572858 | − | 0.819655i | \(-0.305835\pi\) | ||||
0.572858 | + | 0.819655i | \(0.305835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 47.8885 | 2.51697 | ||||||||
\(363\) | 32.8328 | 1.72328 | ||||||||
\(364\) | 6.87539 | 0.360368 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −44.0689 | −2.30352 | ||||||||
\(367\) | −31.4164 | −1.63992 | −0.819962 | − | 0.572419i | \(-0.806005\pi\) | ||||
−0.819962 | + | 0.572419i | \(0.806005\pi\) | |||||||
\(368\) | −4.47214 | −0.233126 | ||||||||
\(369\) | −4.09017 | −0.212926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.111456 | 0.00578652 | ||||||||
\(372\) | 36.0000 | 1.86651 | ||||||||
\(373\) | 1.56231 | 0.0808931 | 0.0404466 | − | 0.999182i | \(-0.487122\pi\) | ||||
0.0404466 | + | 0.999182i | \(0.487122\pi\) | |||||||
\(374\) | 7.23607 | 0.374168 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6525 | 0.549359 | ||||||||
\(377\) | 13.1459 | 0.677048 | ||||||||
\(378\) | −11.0557 | −0.568645 | ||||||||
\(379\) | −21.8885 | −1.12434 | −0.562169 | − | 0.827022i | \(-0.690033\pi\) | ||||
−0.562169 | + | 0.827022i | \(0.690033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.0000 | −1.22956 | ||||||||
\(382\) | 10.6525 | 0.545028 | ||||||||
\(383\) | −29.2361 | −1.49389 | −0.746947 | − | 0.664884i | \(-0.768481\pi\) | ||||
−0.746947 | + | 0.664884i | \(0.768481\pi\) | |||||||
\(384\) | 31.3050 | 1.59752 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.7771 | 1.31202 | ||||||||
\(387\) | 0.472136 | 0.0240000 | ||||||||
\(388\) | −33.2705 | −1.68905 | ||||||||
\(389\) | 25.8541 | 1.31086 | 0.655428 | − | 0.755258i | \(-0.272488\pi\) | ||||
0.655428 | + | 0.755258i | \(0.272488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.76393 | −0.139778 | ||||||||
\(392\) | 12.2361 | 0.618015 | ||||||||
\(393\) | 43.4164 | 2.19007 | ||||||||
\(394\) | −53.7426 | −2.70752 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.7082 | 0.789367 | ||||||||
\(397\) | −1.41641 | −0.0710875 | −0.0355437 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355437 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(398\) | 28.9443 | 1.45085 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.4164 | 1.26923 | 0.634617 | − | 0.772826i | \(-0.281158\pi\) | ||||
0.634617 | + | 0.772826i | \(0.281158\pi\) | |||||||
\(402\) | 2.11146 | 0.105310 | ||||||||
\(403\) | −11.1246 | −0.554156 | ||||||||
\(404\) | 2.02129 | 0.100563 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.5967 | −0.972570 | ||||||||
\(407\) | 46.3607 | 2.29801 | ||||||||
\(408\) | 2.76393 | 0.136835 | ||||||||
\(409\) | 20.2705 | 1.00231 | 0.501156 | − | 0.865357i | \(-0.332908\pi\) | ||||
0.501156 | + | 0.865357i | \(0.332908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.59675 | −0.177414 | ||||||||
\(412\) | 23.1246 | 1.13927 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | −10.0000 | −0.491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.4377 | −0.609808 | ||||||||
\(417\) | 27.4164 | 1.34259 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.58359 | 0.223923 | 0.111962 | − | 0.993713i | \(-0.464287\pi\) | ||||
0.111962 | + | 0.993713i | \(0.464287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7984 | −1.06239 | −0.531194 | − | 0.847250i | \(-0.678256\pi\) | ||||
−0.531194 | + | 0.847250i | \(0.678256\pi\) | |||||||
\(422\) | 61.9574 | 3.01604 | ||||||||
\(423\) | −4.76393 | −0.231630 | ||||||||
\(424\) | 0.201626 | 0.00979183 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4721 | −0.701177 | ||||||||
\(427\) | −12.1803 | −0.589448 | ||||||||
\(428\) | 2.29180 | 0.110778 | ||||||||
\(429\) | −19.4164 | −0.937433 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.7639 | 0.903827 | 0.451913 | − | 0.892062i | \(-0.350742\pi\) | ||||
0.451913 | + | 0.892062i | \(0.350742\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −9.43769 | −0.453547 | −0.226773 | − | 0.973948i | \(-0.572818\pi\) | ||||
−0.226773 | + | 0.973948i | \(0.572818\pi\) | |||||||
\(434\) | 16.5836 | 0.796038 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 36.2705 | 1.73704 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −65.1246 | −3.11177 | ||||||||
\(439\) | −10.0000 | −0.477274 | −0.238637 | − | 0.971109i | \(-0.576701\pi\) | ||||
−0.238637 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.47214 | −0.260578 | ||||||||
\(442\) | −2.56231 | −0.121876 | ||||||||
\(443\) | 1.41641 | 0.0672956 | 0.0336478 | − | 0.999434i | \(-0.489288\pi\) | ||||
0.0336478 | + | 0.999434i | \(0.489288\pi\) | |||||||
\(444\) | 53.1246 | 2.52118 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.3607 | 1.05881 | ||||||||
\(447\) | 3.70820 | 0.175392 | ||||||||
\(448\) | 16.0689 | 0.759183 | ||||||||
\(449\) | 35.4508 | 1.67303 | 0.836515 | − | 0.547945i | \(-0.184590\pi\) | ||||
0.836515 | + | 0.547945i | \(0.184590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.4164 | −1.00846 | ||||||||
\(452\) | −30.4377 | −1.43167 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.2492 | −1.41967 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0901699 | 0.00421797 | 0.00210899 | − | 0.999998i | \(-0.499329\pi\) | ||||
0.00210899 | + | 0.999998i | \(0.499329\pi\) | |||||||
\(458\) | −58.0902 | −2.71438 | ||||||||
\(459\) | 2.47214 | 0.115389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.472136 | −0.0219896 | −0.0109948 | − | 0.999940i | \(-0.503500\pi\) | ||||
−0.0109948 | + | 0.999940i | \(0.503500\pi\) | |||||||
\(462\) | 28.9443 | 1.34661 | ||||||||
\(463\) | −25.7082 | −1.19476 | −0.597381 | − | 0.801958i | \(-0.703792\pi\) | ||||
−0.597381 | + | 0.801958i | \(0.703792\pi\) | |||||||
\(464\) | 7.09017 | 0.329153 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.8541 | 0.734427 | ||||||||
\(467\) | 9.88854 | 0.457587 | 0.228794 | − | 0.973475i | \(-0.426522\pi\) | ||||
0.228794 | + | 0.973475i | \(0.426522\pi\) | |||||||
\(468\) | −5.56231 | −0.257118 | ||||||||
\(469\) | 0.583592 | 0.0269478 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0689 | 0.740415 | ||||||||
\(472\) | 7.23607 | 0.333067 | ||||||||
\(473\) | 2.47214 | 0.113669 | ||||||||
\(474\) | 8.94427 | 0.410824 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.29180 | 0.105044 | ||||||||
\(477\) | −0.0901699 | −0.00412860 | ||||||||
\(478\) | −2.36068 | −0.107975 | ||||||||
\(479\) | 9.05573 | 0.413767 | 0.206883 | − | 0.978366i | \(-0.433668\pi\) | ||||
0.206883 | + | 0.978366i | \(0.433668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4164 | −0.748524 | ||||||||
\(482\) | −2.36068 | −0.107526 | ||||||||
\(483\) | −11.0557 | −0.503053 | ||||||||
\(484\) | 49.2492 | 2.23860 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.3607 | 1.01430 | ||||||||
\(487\) | 25.2361 | 1.14356 | 0.571778 | − | 0.820409i | \(-0.306254\pi\) | ||||
0.571778 | + | 0.820409i | \(0.306254\pi\) | |||||||
\(488\) | −22.0344 | −0.997452 | ||||||||
\(489\) | 16.5836 | 0.749936 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | −24.5410 | −1.10639 | ||||||||
\(493\) | 4.38197 | 0.197354 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | −4.00000 | −0.179425 | ||||||||
\(498\) | −43.4164 | −1.94554 | ||||||||
\(499\) | −7.23607 | −0.323931 | −0.161965 | − | 0.986796i | \(-0.551783\pi\) | ||||
−0.161965 | + | 0.986796i | \(0.551783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.52786 | −0.425674 | ||||||||
\(502\) | −29.5967 | −1.32097 | ||||||||
\(503\) | 10.3607 | 0.461960 | 0.230980 | − | 0.972959i | \(-0.425807\pi\) | ||||
0.230980 | + | 0.972959i | \(0.425807\pi\) | |||||||
\(504\) | 2.76393 | 0.123115 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −52.3607 | −2.32772 | ||||||||
\(507\) | −19.1246 | −0.849354 | ||||||||
\(508\) | −36.0000 | −1.59724 | ||||||||
\(509\) | −23.0902 | −1.02345 | −0.511727 | − | 0.859148i | \(-0.670994\pi\) | ||||
−0.511727 | + | 0.859148i | \(0.670994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0000 | −0.796273 | ||||||||
\(512\) | −11.1803 | −0.494106 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.6312 | 1.17465 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.83282 | 0.124708 | ||||||||
\(517\) | −24.9443 | −1.09705 | ||||||||
\(518\) | 24.4721 | 1.07524 | ||||||||
\(519\) | −11.2361 | −0.493209 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.5623 | 0.769419 | 0.384709 | − | 0.923038i | \(-0.374302\pi\) | ||||
0.384709 | + | 0.923038i | \(0.374302\pi\) | |||||||
\(522\) | 15.8541 | 0.693915 | ||||||||
\(523\) | −11.4164 | −0.499205 | −0.249602 | − | 0.968348i | \(-0.580300\pi\) | ||||
−0.249602 | + | 0.968348i | \(0.580300\pi\) | |||||||
\(524\) | 65.1246 | 2.84498 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.4853 | 0.762395 | ||||||||
\(527\) | −3.70820 | −0.161532 | ||||||||
\(528\) | −10.4721 | −0.455741 | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.23607 | −0.140433 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.58359 | 0.328482 | ||||||||
\(534\) | −32.7639 | −1.41783 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.05573 | 0.0456005 | ||||||||
\(537\) | 41.8885 | 1.80762 | ||||||||
\(538\) | 2.68692 | 0.115841 | ||||||||
\(539\) | −28.6525 | −1.23415 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.8541 | 1.11155 | 0.555777 | − | 0.831331i | \(-0.312421\pi\) | ||||
0.555777 | + | 0.831331i | \(0.312421\pi\) | |||||||
\(542\) | −32.7639 | −1.40733 | ||||||||
\(543\) | −42.8328 | −1.83813 | ||||||||
\(544\) | −4.14590 | −0.177754 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.2492 | −0.438626 | ||||||||
\(547\) | −4.76393 | −0.203691 | −0.101846 | − | 0.994800i | \(-0.532475\pi\) | ||||
−0.101846 | + | 0.994800i | \(0.532475\pi\) | |||||||
\(548\) | −5.39512 | −0.230468 | ||||||||
\(549\) | 9.85410 | 0.420563 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −20.0000 | −0.851257 | ||||||||
\(553\) | 2.47214 | 0.105126 | ||||||||
\(554\) | −23.2148 | −0.986302 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 41.1246 | 1.74407 | ||||||||
\(557\) | 28.4721 | 1.20640 | 0.603202 | − | 0.797589i | \(-0.293891\pi\) | ||||
0.603202 | + | 0.797589i | \(0.293891\pi\) | |||||||
\(558\) | −13.4164 | −0.567962 | ||||||||
\(559\) | −0.875388 | −0.0370250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.47214 | −0.273254 | ||||||||
\(562\) | −42.6869 | −1.80064 | ||||||||
\(563\) | 3.34752 | 0.141081 | 0.0705407 | − | 0.997509i | \(-0.477528\pi\) | ||||
0.0705407 | + | 0.997509i | \(0.477528\pi\) | |||||||
\(564\) | −28.5836 | −1.20359 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −70.2492 | −2.95280 | ||||||||
\(567\) | 13.5967 | 0.571010 | ||||||||
\(568\) | −7.23607 | −0.303619 | ||||||||
\(569\) | 22.3820 | 0.938301 | 0.469150 | − | 0.883118i | \(-0.344560\pi\) | ||||
0.469150 | + | 0.883118i | \(0.344560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7082 | −0.657368 | −0.328684 | − | 0.944440i | \(-0.606605\pi\) | ||||
−0.328684 | + | 0.944440i | \(0.606605\pi\) | |||||||
\(572\) | −29.1246 | −1.21776 | ||||||||
\(573\) | −9.52786 | −0.398032 | ||||||||
\(574\) | −11.3050 | −0.471860 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.0000 | −0.541667 | ||||||||
\(577\) | −4.61803 | −0.192251 | −0.0961256 | − | 0.995369i | \(-0.530645\pi\) | ||||
−0.0961256 | + | 0.995369i | \(0.530645\pi\) | |||||||
\(578\) | 37.1591 | 1.54561 | ||||||||
\(579\) | −23.0557 | −0.958163 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 49.5967 | 2.05585 | ||||||||
\(583\) | −0.472136 | −0.0195539 | ||||||||
\(584\) | −32.5623 | −1.34744 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −56.8328 | −2.34774 | ||||||||
\(587\) | 2.76393 | 0.114080 | 0.0570398 | − | 0.998372i | \(-0.481834\pi\) | ||||
0.0570398 | + | 0.998372i | \(0.481834\pi\) | |||||||
\(588\) | −32.8328 | −1.35400 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 48.0689 | 1.97729 | ||||||||
\(592\) | −8.85410 | −0.363901 | ||||||||
\(593\) | −28.8541 | −1.18490 | −0.592448 | − | 0.805609i | \(-0.701838\pi\) | ||||
−0.592448 | + | 0.805609i | \(0.701838\pi\) | |||||||
\(594\) | 46.8328 | 1.92157 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.56231 | 0.227841 | ||||||||
\(597\) | −25.8885 | −1.05955 | ||||||||
\(598\) | 18.5410 | 0.758199 | ||||||||
\(599\) | −34.9443 | −1.42778 | −0.713892 | − | 0.700256i | \(-0.753069\pi\) | ||||
−0.713892 | + | 0.700256i | \(0.753069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.00000 | 0.244745 | 0.122373 | − | 0.992484i | \(-0.460950\pi\) | ||||
0.122373 | + | 0.992484i | \(0.460950\pi\) | |||||||
\(602\) | 1.30495 | 0.0531859 | ||||||||
\(603\) | −0.472136 | −0.0192269 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.01316 | −0.122401 | ||||||||
\(607\) | −35.4164 | −1.43751 | −0.718754 | − | 0.695265i | \(-0.755287\pi\) | ||||
−0.718754 | + | 0.695265i | \(0.755287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.5279 | 0.710265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.83282 | 0.357337 | ||||||||
\(612\) | −1.85410 | −0.0749476 | ||||||||
\(613\) | 20.2705 | 0.818718 | 0.409359 | − | 0.912373i | \(-0.365752\pi\) | ||||
0.409359 | + | 0.912373i | \(0.365752\pi\) | |||||||
\(614\) | −34.7214 | −1.40124 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.4721 | 0.583099 | ||||||||
\(617\) | −6.36068 | −0.256071 | −0.128036 | − | 0.991770i | \(-0.540867\pi\) | ||||
−0.128036 | + | 0.991770i | \(0.540867\pi\) | |||||||
\(618\) | −34.4721 | −1.38667 | ||||||||
\(619\) | −41.1246 | −1.65294 | −0.826469 | − | 0.562982i | \(-0.809654\pi\) | ||||
−0.826469 | + | 0.562982i | \(0.809654\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.8885 | −0.717843 | ||||||||
\(622\) | −33.0132 | −1.32371 | ||||||||
\(623\) | −9.05573 | −0.362810 | ||||||||
\(624\) | 3.70820 | 0.148447 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −58.0902 | −2.32175 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.1033 | 0.961827 | ||||||||
\(629\) | −5.47214 | −0.218188 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.3607 | −1.04940 | −0.524701 | − | 0.851287i | \(-0.675823\pi\) | ||||
−0.524701 | + | 0.851287i | \(0.675823\pi\) | |||||||
\(632\) | 4.47214 | 0.177892 | ||||||||
\(633\) | −55.4164 | −2.20260 | ||||||||
\(634\) | −23.2148 | −0.921977 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.541020 | −0.0214528 | ||||||||
\(637\) | 10.1459 | 0.401995 | ||||||||
\(638\) | 83.0132 | 3.28652 | ||||||||
\(639\) | 3.23607 | 0.128017 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.3820 | −1.23951 | −0.619757 | − | 0.784794i | \(-0.712769\pi\) | ||||
−0.619757 | + | 0.784794i | \(0.712769\pi\) | |||||||
\(642\) | −3.41641 | −0.134835 | ||||||||
\(643\) | −12.0000 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(644\) | −16.5836 | −0.653485 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.5967 | −1.63534 | −0.817668 | − | 0.575689i | \(-0.804734\pi\) | ||||
−0.817668 | + | 0.575689i | \(0.804734\pi\) | |||||||
\(648\) | 24.5967 | 0.966252 | ||||||||
\(649\) | −16.9443 | −0.665121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.8328 | −0.581344 | ||||||||
\(652\) | 24.8754 | 0.974195 | ||||||||
\(653\) | 22.7426 | 0.889989 | 0.444994 | − | 0.895533i | \(-0.353206\pi\) | ||||
0.444994 | + | 0.895533i | \(0.353206\pi\) | |||||||
\(654\) | −54.0689 | −2.11426 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.09017 | 0.159694 | ||||||||
\(657\) | 14.5623 | 0.568130 | ||||||||
\(658\) | −13.1672 | −0.513310 | ||||||||
\(659\) | −8.29180 | −0.323003 | −0.161501 | − | 0.986873i | \(-0.551634\pi\) | ||||
−0.161501 | + | 0.986873i | \(0.551634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8885 | 0.773575 | 0.386787 | − | 0.922169i | \(-0.373585\pi\) | ||||
0.386787 | + | 0.922169i | \(0.373585\pi\) | |||||||
\(662\) | −13.0132 | −0.505771 | ||||||||
\(663\) | 2.29180 | 0.0890060 | ||||||||
\(664\) | −21.7082 | −0.842442 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19.7984 | −0.767171 | ||||||||
\(667\) | −31.7082 | −1.22775 | ||||||||
\(668\) | −14.2918 | −0.552966 | ||||||||
\(669\) | −20.0000 | −0.773245 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.5967 | 1.99187 | ||||||||
\(672\) | −16.5836 | −0.639726 | ||||||||
\(673\) | 19.1459 | 0.738020 | 0.369010 | − | 0.929425i | \(-0.379697\pi\) | ||||
0.369010 | + | 0.929425i | \(0.379697\pi\) | |||||||
\(674\) | −31.2574 | −1.20399 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.6869 | −1.10334 | ||||||||
\(677\) | 45.3394 | 1.74253 | 0.871267 | − | 0.490809i | \(-0.163299\pi\) | ||||
0.871267 | + | 0.490809i | \(0.163299\pi\) | |||||||
\(678\) | 45.3738 | 1.74257 | ||||||||
\(679\) | 13.7082 | 0.526073 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.0557 | 1.03678 | ||||||||
\(682\) | −70.2492 | −2.68998 | ||||||||
\(683\) | 37.0132 | 1.41627 | 0.708135 | − | 0.706078i | \(-0.249537\pi\) | ||||
0.708135 | + | 0.706078i | \(0.249537\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −34.4721 | −1.31615 | ||||||||
\(687\) | 51.9574 | 1.98230 | ||||||||
\(688\) | −0.472136 | −0.0180000 | ||||||||
\(689\) | 0.167184 | 0.00636921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5410 | 0.781417 | 0.390709 | − | 0.920514i | \(-0.372230\pi\) | ||||
0.390709 | + | 0.920514i | \(0.372230\pi\) | |||||||
\(692\) | −16.8541 | −0.640697 | ||||||||
\(693\) | −6.47214 | −0.245856 | ||||||||
\(694\) | 57.2361 | 2.17265 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 31.7082 | 1.20190 | ||||||||
\(697\) | 2.52786 | 0.0957497 | ||||||||
\(698\) | 4.79837 | 0.181621 | ||||||||
\(699\) | −14.1803 | −0.536350 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.85410 | −0.183337 | −0.0916685 | − | 0.995790i | \(-0.529220\pi\) | ||||
−0.0916685 | + | 0.995790i | \(0.529220\pi\) | |||||||
\(702\) | −16.5836 | −0.625907 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −68.0689 | −2.56544 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 68.2148 | 2.56730 | ||||||||
\(707\) | −0.832816 | −0.0313213 | ||||||||
\(708\) | −19.4164 | −0.729713 | ||||||||
\(709\) | 43.1591 | 1.62087 | 0.810436 | − | 0.585827i | \(-0.199230\pi\) | ||||
0.810436 | + | 0.585827i | \(0.199230\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.00000 | −0.0750059 | ||||||||
\(712\) | −16.3820 | −0.613940 | ||||||||
\(713\) | 26.8328 | 1.00490 | ||||||||
\(714\) | −3.41641 | −0.127856 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 62.8328 | 2.34817 | ||||||||
\(717\) | 2.11146 | 0.0788538 | ||||||||
\(718\) | −48.5410 | −1.81153 | ||||||||
\(719\) | 31.3050 | 1.16748 | 0.583739 | − | 0.811941i | \(-0.301589\pi\) | ||||
0.583739 | + | 0.811941i | \(0.301589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.52786 | −0.354836 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.11146 | 0.0785259 | ||||||||
\(724\) | −64.2492 | −2.38780 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −73.4164 | −2.72474 | ||||||||
\(727\) | 29.1246 | 1.08017 | 0.540086 | − | 0.841610i | \(-0.318392\pi\) | ||||
0.540086 | + | 0.841610i | \(0.318392\pi\) | |||||||
\(728\) | −5.12461 | −0.189931 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.291796 | −0.0107925 | ||||||||
\(732\) | 59.1246 | 2.18531 | ||||||||
\(733\) | −37.2705 | −1.37662 | −0.688309 | − | 0.725418i | \(-0.741647\pi\) | ||||
−0.688309 | + | 0.725418i | \(0.741647\pi\) | |||||||
\(734\) | 70.2492 | 2.59295 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.0000 | 1.10581 | ||||||||
\(737\) | −2.47214 | −0.0910623 | ||||||||
\(738\) | 9.14590 | 0.336665 | ||||||||
\(739\) | 24.2918 | 0.893588 | 0.446794 | − | 0.894637i | \(-0.352566\pi\) | ||||
0.446794 | + | 0.894637i | \(0.352566\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.249224 | −0.00914929 | ||||||||
\(743\) | 7.41641 | 0.272082 | 0.136041 | − | 0.990703i | \(-0.456562\pi\) | ||||
0.136041 | + | 0.990703i | \(0.456562\pi\) | |||||||
\(744\) | −26.8328 | −0.983739 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.49342 | −0.127903 | ||||||||
\(747\) | 9.70820 | 0.355205 | ||||||||
\(748\) | −9.70820 | −0.354967 | ||||||||
\(749\) | −0.944272 | −0.0345029 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.4164 | −0.781496 | −0.390748 | − | 0.920498i | \(-0.627784\pi\) | ||||
−0.390748 | + | 0.920498i | \(0.627784\pi\) | |||||||
\(752\) | 4.76393 | 0.173723 | ||||||||
\(753\) | 26.4721 | 0.964698 | ||||||||
\(754\) | −29.3951 | −1.07051 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.8328 | 0.539464 | ||||||||
\(757\) | 6.50658 | 0.236486 | 0.118243 | − | 0.992985i | \(-0.462274\pi\) | ||||
0.118243 | + | 0.992985i | \(0.462274\pi\) | |||||||
\(758\) | 48.9443 | 1.77774 | ||||||||
\(759\) | 46.8328 | 1.69992 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.8885 | −0.720959 | −0.360480 | − | 0.932767i | \(-0.617387\pi\) | ||||
−0.360480 | + | 0.932767i | \(0.617387\pi\) | |||||||
\(762\) | 53.6656 | 1.94410 | ||||||||
\(763\) | −14.9443 | −0.541019 | ||||||||
\(764\) | −14.2918 | −0.517059 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 65.3738 | 2.36205 | ||||||||
\(767\) | 6.00000 | 0.216647 | ||||||||
\(768\) | −18.0000 | −0.649519 | ||||||||
\(769\) | −31.1459 | −1.12315 | −0.561575 | − | 0.827426i | \(-0.689804\pi\) | ||||
−0.561575 | + | 0.827426i | \(0.689804\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.8197 | −0.857844 | ||||||||
\(772\) | −34.5836 | −1.24469 | ||||||||
\(773\) | −45.6312 | −1.64124 | −0.820620 | − | 0.571474i | \(-0.806372\pi\) | ||||
−0.820620 | + | 0.571474i | \(0.806372\pi\) | |||||||
\(774\) | −1.05573 | −0.0379474 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.7984 | 0.890210 | ||||||||
\(777\) | −21.8885 | −0.785247 | ||||||||
\(778\) | −57.8115 | −2.07264 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9443 | 0.606314 | ||||||||
\(782\) | 6.18034 | 0.221009 | ||||||||
\(783\) | 28.3607 | 1.01353 | ||||||||
\(784\) | 5.47214 | 0.195433 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −97.0820 | −3.46280 | ||||||||
\(787\) | −3.23607 | −0.115353 | −0.0576767 | − | 0.998335i | \(-0.518369\pi\) | ||||
−0.0576767 | + | 0.998335i | \(0.518369\pi\) | |||||||
\(788\) | 72.1033 | 2.56857 | ||||||||
\(789\) | −15.6393 | −0.556775 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.5410 | 0.445907 | ||||||||
\(792\) | −11.7082 | −0.416033 | ||||||||
\(793\) | −18.2705 | −0.648805 | ||||||||
\(794\) | 3.16718 | 0.112399 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −38.8328 | −1.37639 | ||||||||
\(797\) | 18.5066 | 0.655537 | 0.327768 | − | 0.944758i | \(-0.393703\pi\) | ||||
0.327768 | + | 0.944758i | \(0.393703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.94427 | 0.104161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.32624 | 0.258860 | ||||||||
\(802\) | −56.8328 | −2.00684 | ||||||||
\(803\) | 76.2492 | 2.69078 | ||||||||
\(804\) | −2.83282 | −0.0999057 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.8754 | 0.876198 | ||||||||
\(807\) | −2.40325 | −0.0845985 | ||||||||
\(808\) | −1.50658 | −0.0530012 | ||||||||
\(809\) | −1.03444 | −0.0363690 | −0.0181845 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181845 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.0000 | −0.912983 | −0.456492 | − | 0.889728i | \(-0.650894\pi\) | ||||
−0.456492 | + | 0.889728i | \(0.650894\pi\) | |||||||
\(812\) | 26.2918 | 0.922661 | ||||||||
\(813\) | 29.3050 | 1.02777 | ||||||||
\(814\) | −103.666 | −3.63348 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.23607 | 0.0432710 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −45.3262 | −1.58479 | ||||||||
\(819\) | 2.29180 | 0.0800818 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.7426 | 1.10783 | 0.553913 | − | 0.832575i | \(-0.313134\pi\) | ||||
0.553913 | + | 0.832575i | \(0.313134\pi\) | |||||||
\(822\) | 8.04257 | 0.280517 | ||||||||
\(823\) | 13.3475 | 0.465265 | 0.232633 | − | 0.972565i | \(-0.425266\pi\) | ||||
0.232633 | + | 0.972565i | \(0.425266\pi\) | |||||||
\(824\) | −17.2361 | −0.600447 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.94427 | −0.311211 | ||||||||
\(827\) | −8.83282 | −0.307147 | −0.153574 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153574 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(828\) | 13.4164 | 0.466252 | ||||||||
\(829\) | 29.9787 | 1.04120 | 0.520602 | − | 0.853800i | \(-0.325708\pi\) | ||||
0.520602 | + | 0.853800i | \(0.325708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.7639 | 0.720293 | ||||||||
\(832\) | 24.1033 | 0.835632 | ||||||||
\(833\) | 3.38197 | 0.117178 | ||||||||
\(834\) | −61.3050 | −2.12282 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.0000 | −0.829561 | ||||||||
\(838\) | −10.2492 | −0.354054 | ||||||||
\(839\) | −17.1246 | −0.591207 | −0.295604 | − | 0.955311i | \(-0.595521\pi\) | ||||
−0.295604 | + | 0.955311i | \(0.595521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2705 | 0.733466 | ||||||||
\(842\) | 48.7426 | 1.67978 | ||||||||
\(843\) | 38.1803 | 1.31500 | ||||||||
\(844\) | −83.1246 | −2.86127 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.6525 | 0.366240 | ||||||||
\(847\) | −20.2918 | −0.697234 | ||||||||
\(848\) | 0.0901699 | 0.00309645 | ||||||||
\(849\) | 62.8328 | 2.15642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.5967 | 1.35736 | ||||||||
\(852\) | 19.4164 | 0.665195 | ||||||||
\(853\) | −7.38197 | −0.252754 | −0.126377 | − | 0.991982i | \(-0.540335\pi\) | ||||
−0.126377 | + | 0.991982i | \(0.540335\pi\) | |||||||
\(854\) | 27.2361 | 0.931999 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.70820 | −0.0583852 | ||||||||
\(857\) | 37.8541 | 1.29307 | 0.646536 | − | 0.762884i | \(-0.276217\pi\) | ||||
0.646536 | + | 0.762884i | \(0.276217\pi\) | |||||||
\(858\) | 43.4164 | 1.48221 | ||||||||
\(859\) | 22.5836 | 0.770542 | 0.385271 | − | 0.922803i | \(-0.374108\pi\) | ||||
0.385271 | + | 0.922803i | \(0.374108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.1115 | 0.344598 | ||||||||
\(862\) | −41.9574 | −1.42908 | ||||||||
\(863\) | 0.944272 | 0.0321434 | 0.0160717 | − | 0.999871i | \(-0.494884\pi\) | ||||
0.0160717 | + | 0.999871i | \(0.494884\pi\) | |||||||
\(864\) | −26.8328 | −0.912871 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21.1033 | 0.717120 | ||||||||
\(867\) | −33.2361 | −1.12876 | ||||||||
\(868\) | −22.2492 | −0.755188 | ||||||||
\(869\) | −10.4721 | −0.355243 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.875388 | 0.0296614 | ||||||||
\(872\) | −27.0344 | −0.915502 | ||||||||
\(873\) | −11.0902 | −0.375345 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 87.3738 | 2.95209 | ||||||||
\(877\) | 9.56231 | 0.322896 | 0.161448 | − | 0.986881i | \(-0.448384\pi\) | ||||
0.161448 | + | 0.986881i | \(0.448384\pi\) | |||||||
\(878\) | 22.3607 | 0.754636 | ||||||||
\(879\) | 50.8328 | 1.71455 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.32624 | 0.112064 | 0.0560319 | − | 0.998429i | \(-0.482155\pi\) | ||||
0.0560319 | + | 0.998429i | \(0.482155\pi\) | |||||||
\(882\) | 12.2361 | 0.412010 | ||||||||
\(883\) | −19.8885 | −0.669303 | −0.334651 | − | 0.942342i | \(-0.608619\pi\) | ||||
−0.334651 | + | 0.942342i | \(0.608619\pi\) | |||||||
\(884\) | 3.43769 | 0.115622 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.16718 | −0.106404 | ||||||||
\(887\) | 49.4853 | 1.66155 | 0.830777 | − | 0.556606i | \(-0.187897\pi\) | ||||
0.830777 | + | 0.556606i | \(0.187897\pi\) | |||||||
\(888\) | −39.5967 | −1.32878 | ||||||||
\(889\) | 14.8328 | 0.497477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −57.5967 | −1.92956 | ||||||||
\(892\) | −30.0000 | −1.00447 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −8.29180 | −0.277319 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.3475 | −0.646355 | ||||||||
\(897\) | −16.5836 | −0.553710 | ||||||||
\(898\) | −79.2705 | −2.64529 | ||||||||
\(899\) | −42.5410 | −1.41882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0557281 | 0.00185657 | ||||||||
\(902\) | 47.8885 | 1.59451 | ||||||||
\(903\) | −1.16718 | −0.0388415 | ||||||||
\(904\) | 22.6869 | 0.754556 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.4164 | 0.843938 | 0.421969 | − | 0.906610i | \(-0.361339\pi\) | ||||
0.421969 | + | 0.906610i | \(0.361339\pi\) | |||||||
\(908\) | 40.5836 | 1.34681 | ||||||||
\(909\) | 0.673762 | 0.0223473 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.8328 | −1.08780 | −0.543900 | − | 0.839150i | \(-0.683053\pi\) | ||||
−0.543900 | + | 0.839150i | \(0.683053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.8328 | 1.68232 | ||||||||
\(914\) | −0.201626 | −0.00666920 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 77.9361 | 2.57508 | ||||||||
\(917\) | −26.8328 | −0.886098 | ||||||||
\(918\) | −5.52786 | −0.182447 | ||||||||
\(919\) | −5.52786 | −0.182347 | −0.0911737 | − | 0.995835i | \(-0.529062\pi\) | ||||
−0.0911737 | + | 0.995835i | \(0.529062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.0557 | 1.02332 | ||||||||
\(922\) | 1.05573 | 0.0347686 | ||||||||
\(923\) | −6.00000 | −0.197492 | ||||||||
\(924\) | −38.8328 | −1.27751 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 57.4853 | 1.88908 | ||||||||
\(927\) | 7.70820 | 0.253171 | ||||||||
\(928\) | −47.5623 | −1.56131 | ||||||||
\(929\) | 30.8673 | 1.01272 | 0.506361 | − | 0.862322i | \(-0.330990\pi\) | ||||
0.506361 | + | 0.862322i | \(0.330990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.2705 | −0.696739 | ||||||||
\(933\) | 29.5279 | 0.966699 | ||||||||
\(934\) | −22.1115 | −0.723509 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.14590 | 0.135513 | ||||||||
\(937\) | 23.3050 | 0.761340 | 0.380670 | − | 0.924711i | \(-0.375693\pi\) | ||||
0.380670 | + | 0.924711i | \(0.375693\pi\) | |||||||
\(938\) | −1.30495 | −0.0426082 | ||||||||
\(939\) | 51.9574 | 1.69557 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.5279 | 0.897383 | 0.448691 | − | 0.893687i | \(-0.351890\pi\) | ||||
0.448691 | + | 0.893687i | \(0.351890\pi\) | |||||||
\(942\) | −35.9311 | −1.17070 | ||||||||
\(943\) | −18.2918 | −0.595663 | ||||||||
\(944\) | 3.23607 | 0.105325 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.52786 | −0.179726 | ||||||||
\(947\) | −13.5967 | −0.441835 | −0.220917 | − | 0.975293i | \(-0.570905\pi\) | ||||
−0.220917 | + | 0.975293i | \(0.570905\pi\) | |||||||
\(948\) | −12.0000 | −0.389742 | ||||||||
\(949\) | −27.0000 | −0.876457 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.7639 | 0.673317 | ||||||||
\(952\) | −1.70820 | −0.0553632 | ||||||||
\(953\) | 51.7426 | 1.67611 | 0.838054 | − | 0.545587i | \(-0.183693\pi\) | ||||
0.838054 | + | 0.545587i | \(0.183693\pi\) | |||||||
\(954\) | 0.201626 | 0.00652789 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.16718 | 0.102434 | ||||||||
\(957\) | −74.2492 | −2.40014 | ||||||||
\(958\) | −20.2492 | −0.654223 | ||||||||
\(959\) | 2.22291 | 0.0717816 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 36.7082 | 1.18352 | ||||||||
\(963\) | 0.763932 | 0.0246174 | ||||||||
\(964\) | 3.16718 | 0.102008 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 24.7214 | 0.795397 | ||||||||
\(967\) | −51.9574 | −1.67084 | −0.835419 | − | 0.549613i | \(-0.814775\pi\) | ||||
−0.835419 | + | 0.549613i | \(0.814775\pi\) | |||||||
\(968\) | −36.7082 | −1.17985 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.652476 | −0.0209389 | −0.0104695 | − | 0.999945i | \(-0.503333\pi\) | ||||
−0.0104695 | + | 0.999945i | \(0.503333\pi\) | |||||||
\(972\) | −30.0000 | −0.962250 | ||||||||
\(973\) | −16.9443 | −0.543208 | ||||||||
\(974\) | −56.4296 | −1.80812 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.85410 | −0.315422 | ||||||||
\(977\) | 27.5066 | 0.880013 | 0.440007 | − | 0.897994i | \(-0.354976\pi\) | ||||
0.440007 | + | 0.897994i | \(0.354976\pi\) | |||||||
\(978\) | −37.0820 | −1.18575 | ||||||||
\(979\) | 38.3607 | 1.22601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0902 | 0.386009 | ||||||||
\(982\) | −26.8328 | −0.856270 | ||||||||
\(983\) | 37.9574 | 1.21065 | 0.605327 | − | 0.795977i | \(-0.293042\pi\) | ||||
0.605327 | + | 0.795977i | \(0.293042\pi\) | |||||||
\(984\) | 18.2918 | 0.583121 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.79837 | −0.312044 | ||||||||
\(987\) | 11.7771 | 0.374869 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.11146 | 0.0671404 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.1246 | 1.62403 | 0.812013 | − | 0.583639i | \(-0.198372\pi\) | ||||
0.812013 | + | 0.583639i | \(0.198372\pi\) | |||||||
\(992\) | 40.2492 | 1.27791 | ||||||||
\(993\) | 11.6393 | 0.369363 | ||||||||
\(994\) | 8.94427 | 0.283695 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 58.2492 | 1.84570 | ||||||||
\(997\) | −0.0901699 | −0.00285571 | −0.00142786 | − | 0.999999i | \(-0.500455\pi\) | ||||
−0.00142786 | + | 0.999999i | \(0.500455\pi\) | |||||||
\(998\) | 16.1803 | 0.512180 | ||||||||
\(999\) | −35.4164 | −1.12053 |
(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 | 9025.2.a.r.1.1 | 2 | ||
5.4 | even | 2 | 361.2.a.d.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 3249.2.a.n.1.1 | 2 | |||
19.18 | odd | 2 | 9025.2.a.o.1.2 | 2 | |||
20.19 | odd | 2 | 5776.2.a.bh.1.2 | 2 | |||
95.4 | even | 18 | 361.2.e.l.54.2 | 12 | |||
95.9 | even | 18 | 361.2.e.l.62.1 | 12 | |||
95.14 | odd | 18 | 361.2.e.k.234.1 | 12 | |||
95.24 | even | 18 | 361.2.e.l.234.2 | 12 | |||
95.29 | odd | 18 | 361.2.e.k.62.2 | 12 | |||
95.34 | odd | 18 | 361.2.e.k.54.1 | 12 | |||
95.44 | even | 18 | 361.2.e.l.245.2 | 12 | |||
95.49 | even | 6 | 361.2.c.f.292.1 | 4 | |||
95.54 | even | 18 | 361.2.e.l.28.2 | 12 | |||
95.59 | odd | 18 | 361.2.e.k.99.2 | 12 | |||
95.64 | even | 6 | 361.2.c.f.68.1 | 4 | |||
95.69 | odd | 6 | 361.2.c.e.68.2 | 4 | |||
95.74 | even | 18 | 361.2.e.l.99.1 | 12 | |||
95.79 | odd | 18 | 361.2.e.k.28.1 | 12 | |||
95.84 | odd | 6 | 361.2.c.e.292.2 | 4 | |||
95.89 | odd | 18 | 361.2.e.k.245.1 | 12 | |||
95.94 | odd | 2 | 361.2.a.e.1.1 | yes | 2 | ||
285.284 | even | 2 | 3249.2.a.m.1.2 | 2 | |||
380.379 | even | 2 | 5776.2.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
361.2.a.d.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
361.2.a.e.1.1 | yes | 2 | 95.94 | odd | 2 | ||
361.2.c.e.68.2 | 4 | 95.69 | odd | 6 | |||
361.2.c.e.292.2 | 4 | 95.84 | odd | 6 | |||
361.2.c.f.68.1 | 4 | 95.64 | even | 6 | |||
361.2.c.f.292.1 | 4 | 95.49 | even | 6 | |||
361.2.e.k.28.1 | 12 | 95.79 | odd | 18 | |||
361.2.e.k.54.1 | 12 | 95.34 | odd | 18 | |||
361.2.e.k.62.2 | 12 | 95.29 | odd | 18 | |||
361.2.e.k.99.2 | 12 | 95.59 | odd | 18 | |||
361.2.e.k.234.1 | 12 | 95.14 | odd | 18 | |||
361.2.e.k.245.1 | 12 | 95.89 | odd | 18 | |||
361.2.e.l.28.2 | 12 | 95.54 | even | 18 | |||
361.2.e.l.54.2 | 12 | 95.4 | even | 18 | |||
361.2.e.l.62.1 | 12 | 95.9 | even | 18 | |||
361.2.e.l.99.1 | 12 | 95.74 | even | 18 | |||
361.2.e.l.234.2 | 12 | 95.24 | even | 18 | |||
361.2.e.l.245.2 | 12 | 95.44 | even | 18 | |||
3249.2.a.m.1.2 | 2 | 285.284 | even | 2 | |||
3249.2.a.n.1.1 | 2 | 15.14 | odd | 2 | |||
5776.2.a.r.1.2 | 2 | 380.379 | even | 2 | |||
5776.2.a.bh.1.2 | 2 | 20.19 | odd | 2 | |||
9025.2.a.o.1.2 | 2 | 19.18 | odd | 2 | |||
9025.2.a.r.1.1 | 2 | 1.1 | even | 1 | trivial |