Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 | \(-0.209785\pi\) | ||||
0.790569 | + | 0.612372i | \(0.209785\pi\) | |||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | 3.00000 | 1.50000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.38197 | 0.564185 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | −2.23607 | −0.707107 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.85410 | 0.535233 | ||||||||
\(13\) | −4.61803 | −1.28081 | −0.640406 | − | 0.768036i | \(-0.721234\pi\) | ||||
−0.640406 | + | 0.768036i | \(0.721234\pi\) | |||||||
\(14\) | 2.23607 | 0.597614 | ||||||||
\(15\) | −0.618034 | −0.159576 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.61803 | −1.36257 | −0.681287 | − | 0.732017i | \(-0.738579\pi\) | ||||
−0.681287 | + | 0.732017i | \(0.738579\pi\) | |||||||
\(18\) | −5.85410 | −1.37983 | ||||||||
\(19\) | 3.23607 | 0.742405 | 0.371202 | − | 0.928552i | \(-0.378946\pi\) | ||||
0.371202 | + | 0.928552i | \(0.378946\pi\) | |||||||
\(20\) | −3.00000 | −0.670820 | ||||||||
\(21\) | 0.618034 | 0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.47214 | −0.932505 | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | 1.38197 | 0.282093 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −10.3262 | −2.02514 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | 3.00000 | 0.566947 | ||||||||
\(29\) | −0.854102 | −0.158603 | −0.0793014 | − | 0.996851i | \(-0.525269\pi\) | ||||
−0.0793014 | + | 0.996851i | \(0.525269\pi\) | |||||||
\(30\) | −1.38197 | −0.252311 | ||||||||
\(31\) | 3.23607 | 0.581215 | 0.290607 | − | 0.956842i | \(-0.406143\pi\) | ||||
0.290607 | + | 0.956842i | \(0.406143\pi\) | |||||||
\(32\) | −6.70820 | −1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.5623 | −2.15442 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −7.85410 | −1.30902 | ||||||||
\(37\) | −7.23607 | −1.18960 | −0.594801 | − | 0.803873i | \(-0.702769\pi\) | ||||
−0.594801 | + | 0.803873i | \(0.702769\pi\) | |||||||
\(38\) | 7.23607 | 1.17385 | ||||||||
\(39\) | −2.85410 | −0.457022 | ||||||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | −2.47214 | −0.386083 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(42\) | 1.38197 | 0.213242 | ||||||||
\(43\) | 5.23607 | 0.798493 | 0.399246 | − | 0.916844i | \(-0.369272\pi\) | ||||
0.399246 | + | 0.916844i | \(0.369272\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.61803 | 0.390273 | ||||||||
\(46\) | −10.0000 | −1.47442 | ||||||||
\(47\) | −1.14590 | −0.167146 | −0.0835732 | − | 0.996502i | \(-0.526633\pi\) | ||||
−0.0835732 | + | 0.996502i | \(0.526633\pi\) | |||||||
\(48\) | −0.618034 | −0.0892055 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.23607 | 0.316228 | ||||||||
\(51\) | −3.47214 | −0.486196 | ||||||||
\(52\) | −13.8541 | −1.92122 | ||||||||
\(53\) | −1.52786 | −0.209868 | −0.104934 | − | 0.994479i | \(-0.533463\pi\) | ||||
−0.104934 | + | 0.994479i | \(0.533463\pi\) | |||||||
\(54\) | −7.76393 | −1.05654 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −1.90983 | −0.250773 | ||||||||
\(59\) | −9.23607 | −1.20243 | −0.601217 | − | 0.799086i | \(-0.705317\pi\) | ||||
−0.601217 | + | 0.799086i | \(0.705317\pi\) | |||||||
\(60\) | −1.85410 | −0.239364 | ||||||||
\(61\) | 4.76393 | 0.609959 | 0.304979 | − | 0.952359i | \(-0.401350\pi\) | ||||
0.304979 | + | 0.952359i | \(0.401350\pi\) | |||||||
\(62\) | 7.23607 | 0.918982 | ||||||||
\(63\) | −2.61803 | −0.329841 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 4.61803 | 0.572797 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.18034 | 0.999388 | 0.499694 | − | 0.866202i | \(-0.333446\pi\) | ||||
0.499694 | + | 0.866202i | \(0.333446\pi\) | |||||||
\(68\) | −16.8541 | −2.04386 | ||||||||
\(69\) | −2.76393 | −0.332738 | ||||||||
\(70\) | −2.23607 | −0.267261 | ||||||||
\(71\) | 16.3262 | 1.93757 | 0.968784 | − | 0.247906i | \(-0.0797425\pi\) | ||||
0.968784 | + | 0.247906i | \(0.0797425\pi\) | |||||||
\(72\) | −5.85410 | −0.689913 | ||||||||
\(73\) | −6.38197 | −0.746953 | −0.373476 | − | 0.927640i | \(-0.621834\pi\) | ||||
−0.373476 | + | 0.927640i | \(0.621834\pi\) | |||||||
\(74\) | −16.1803 | −1.88093 | ||||||||
\(75\) | 0.618034 | 0.0713644 | ||||||||
\(76\) | 9.70820 | 1.11361 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.38197 | −0.722615 | ||||||||
\(79\) | −10.7984 | −1.21491 | −0.607456 | − | 0.794353i | \(-0.707810\pi\) | ||||
−0.607456 | + | 0.794353i | \(0.707810\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | −5.52786 | −0.610450 | ||||||||
\(83\) | −9.56231 | −1.04960 | −0.524800 | − | 0.851226i | \(-0.675860\pi\) | ||||
−0.524800 | + | 0.851226i | \(0.675860\pi\) | |||||||
\(84\) | 1.85410 | 0.202299 | ||||||||
\(85\) | 5.61803 | 0.609361 | ||||||||
\(86\) | 11.7082 | 1.26253 | ||||||||
\(87\) | −0.527864 | −0.0565930 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7639 | 1.35297 | 0.676487 | − | 0.736455i | \(-0.263501\pi\) | ||||
0.676487 | + | 0.736455i | \(0.263501\pi\) | |||||||
\(90\) | 5.85410 | 0.617077 | ||||||||
\(91\) | −4.61803 | −0.484102 | ||||||||
\(92\) | −13.4164 | −1.39876 | ||||||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | −2.56231 | −0.264282 | ||||||||
\(95\) | −3.23607 | −0.332014 | ||||||||
\(96\) | −4.14590 | −0.423139 | ||||||||
\(97\) | −15.3262 | −1.55614 | −0.778072 | − | 0.628175i | \(-0.783802\pi\) | ||||
−0.778072 | + | 0.628175i | \(0.783802\pi\) | |||||||
\(98\) | 2.23607 | 0.225877 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 13.7082 | 1.36402 | 0.682009 | − | 0.731344i | \(-0.261107\pi\) | ||||
0.682009 | + | 0.731344i | \(0.261107\pi\) | |||||||
\(102\) | −7.76393 | −0.768744 | ||||||||
\(103\) | −17.3262 | −1.70720 | −0.853602 | − | 0.520925i | \(-0.825587\pi\) | ||||
−0.853602 | + | 0.520925i | \(0.825587\pi\) | |||||||
\(104\) | −10.3262 | −1.01257 | ||||||||
\(105\) | −0.618034 | −0.0603139 | ||||||||
\(106\) | −3.41641 | −0.331831 | ||||||||
\(107\) | 7.23607 | 0.699537 | 0.349769 | − | 0.936836i | \(-0.386260\pi\) | ||||
0.349769 | + | 0.936836i | \(0.386260\pi\) | |||||||
\(108\) | −10.4164 | −1.00232 | ||||||||
\(109\) | 11.5279 | 1.10417 | 0.552085 | − | 0.833788i | \(-0.313833\pi\) | ||||
0.552085 | + | 0.833788i | \(0.313833\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.47214 | −0.424476 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 10.4721 | 0.985136 | 0.492568 | − | 0.870274i | \(-0.336058\pi\) | ||||
0.492568 | + | 0.870274i | \(0.336058\pi\) | |||||||
\(114\) | 4.47214 | 0.418854 | ||||||||
\(115\) | 4.47214 | 0.417029 | ||||||||
\(116\) | −2.56231 | −0.237904 | ||||||||
\(117\) | 12.0902 | 1.11774 | ||||||||
\(118\) | −20.6525 | −1.90121 | ||||||||
\(119\) | −5.61803 | −0.515004 | ||||||||
\(120\) | −1.38197 | −0.126156 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.6525 | 0.964430 | ||||||||
\(123\) | −1.52786 | −0.137763 | ||||||||
\(124\) | 9.70820 | 0.871822 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.85410 | −0.521525 | ||||||||
\(127\) | −9.23607 | −0.819569 | −0.409784 | − | 0.912182i | \(-0.634396\pi\) | ||||
−0.409784 | + | 0.912182i | \(0.634396\pi\) | |||||||
\(128\) | −15.6525 | −1.38350 | ||||||||
\(129\) | 3.23607 | 0.284920 | ||||||||
\(130\) | 10.3262 | 0.905671 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23607 | 0.280603 | ||||||||
\(134\) | 18.2918 | 1.58017 | ||||||||
\(135\) | 3.47214 | 0.298834 | ||||||||
\(136\) | −12.5623 | −1.07721 | ||||||||
\(137\) | −11.4164 | −0.975370 | −0.487685 | − | 0.873020i | \(-0.662158\pi\) | ||||
−0.487685 | + | 0.873020i | \(0.662158\pi\) | |||||||
\(138\) | −6.18034 | −0.526105 | ||||||||
\(139\) | −5.52786 | −0.468867 | −0.234434 | − | 0.972132i | \(-0.575324\pi\) | ||||
−0.234434 | + | 0.972132i | \(0.575324\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | −0.708204 | −0.0596415 | ||||||||
\(142\) | 36.5066 | 3.06356 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.61803 | 0.218169 | ||||||||
\(145\) | 0.854102 | 0.0709293 | ||||||||
\(146\) | −14.2705 | −1.18104 | ||||||||
\(147\) | 0.618034 | 0.0509746 | ||||||||
\(148\) | −21.7082 | −1.78440 | ||||||||
\(149\) | 17.8541 | 1.46267 | 0.731333 | − | 0.682021i | \(-0.238899\pi\) | ||||
0.731333 | + | 0.682021i | \(0.238899\pi\) | |||||||
\(150\) | 1.38197 | 0.112837 | ||||||||
\(151\) | 0.381966 | 0.0310840 | 0.0155420 | − | 0.999879i | \(-0.495053\pi\) | ||||
0.0155420 | + | 0.999879i | \(0.495053\pi\) | |||||||
\(152\) | 7.23607 | 0.586923 | ||||||||
\(153\) | 14.7082 | 1.18909 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.23607 | −0.259927 | ||||||||
\(156\) | −8.56231 | −0.685533 | ||||||||
\(157\) | −16.0902 | −1.28414 | −0.642068 | − | 0.766648i | \(-0.721923\pi\) | ||||
−0.642068 | + | 0.766648i | \(0.721923\pi\) | |||||||
\(158\) | −24.1459 | −1.92094 | ||||||||
\(159\) | −0.944272 | −0.0748856 | ||||||||
\(160\) | 6.70820 | 0.530330 | ||||||||
\(161\) | −4.47214 | −0.352454 | ||||||||
\(162\) | 12.7639 | 1.00283 | ||||||||
\(163\) | −22.1803 | −1.73730 | −0.868649 | − | 0.495428i | \(-0.835011\pi\) | ||||
−0.868649 | + | 0.495428i | \(0.835011\pi\) | |||||||
\(164\) | −7.41641 | −0.579124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.3820 | −1.65956 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 1.38197 | 0.106621 | ||||||||
\(169\) | 8.32624 | 0.640480 | ||||||||
\(170\) | 12.5623 | 0.963485 | ||||||||
\(171\) | −8.47214 | −0.647880 | ||||||||
\(172\) | 15.7082 | 1.19774 | ||||||||
\(173\) | 1.56231 | 0.118780 | 0.0593900 | − | 0.998235i | \(-0.481084\pi\) | ||||
0.0593900 | + | 0.998235i | \(0.481084\pi\) | |||||||
\(174\) | −1.18034 | −0.0894813 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.70820 | −0.429055 | ||||||||
\(178\) | 28.5410 | 2.13924 | ||||||||
\(179\) | 19.6180 | 1.46632 | 0.733160 | − | 0.680056i | \(-0.238044\pi\) | ||||
0.733160 | + | 0.680056i | \(0.238044\pi\) | |||||||
\(180\) | 7.85410 | 0.585410 | ||||||||
\(181\) | 5.52786 | 0.410883 | 0.205441 | − | 0.978669i | \(-0.434137\pi\) | ||||
0.205441 | + | 0.978669i | \(0.434137\pi\) | |||||||
\(182\) | −10.3262 | −0.765432 | ||||||||
\(183\) | 2.94427 | 0.217647 | ||||||||
\(184\) | −10.0000 | −0.737210 | ||||||||
\(185\) | 7.23607 | 0.532006 | ||||||||
\(186\) | 4.47214 | 0.327913 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.43769 | −0.250720 | ||||||||
\(189\) | −3.47214 | −0.252561 | ||||||||
\(190\) | −7.23607 | −0.524960 | ||||||||
\(191\) | 23.0902 | 1.67075 | 0.835373 | − | 0.549683i | \(-0.185252\pi\) | ||||
0.835373 | + | 0.549683i | \(0.185252\pi\) | |||||||
\(192\) | −8.03444 | −0.579836 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | −34.2705 | −2.46048 | ||||||||
\(195\) | 2.85410 | 0.204386 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 2.23607 | 0.158114 | ||||||||
\(201\) | 5.05573 | 0.356604 | ||||||||
\(202\) | 30.6525 | 2.15670 | ||||||||
\(203\) | −0.854102 | −0.0599462 | ||||||||
\(204\) | −10.4164 | −0.729294 | ||||||||
\(205\) | 2.47214 | 0.172661 | ||||||||
\(206\) | −38.7426 | −2.69933 | ||||||||
\(207\) | 11.7082 | 0.813776 | ||||||||
\(208\) | 4.61803 | 0.320203 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.38197 | −0.0953647 | ||||||||
\(211\) | −7.67376 | −0.528284 | −0.264142 | − | 0.964484i | \(-0.585089\pi\) | ||||
−0.264142 | + | 0.964484i | \(0.585089\pi\) | |||||||
\(212\) | −4.58359 | −0.314802 | ||||||||
\(213\) | 10.0902 | 0.691367 | ||||||||
\(214\) | 16.1803 | 1.10607 | ||||||||
\(215\) | −5.23607 | −0.357097 | ||||||||
\(216\) | −7.76393 | −0.528269 | ||||||||
\(217\) | 3.23607 | 0.219679 | ||||||||
\(218\) | 25.7771 | 1.74584 | ||||||||
\(219\) | −3.94427 | −0.266529 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.9443 | 1.74520 | ||||||||
\(222\) | −10.0000 | −0.671156 | ||||||||
\(223\) | 1.52786 | 0.102313 | 0.0511567 | − | 0.998691i | \(-0.483709\pi\) | ||||
0.0511567 | + | 0.998691i | \(0.483709\pi\) | |||||||
\(224\) | −6.70820 | −0.448211 | ||||||||
\(225\) | −2.61803 | −0.174536 | ||||||||
\(226\) | 23.4164 | 1.55764 | ||||||||
\(227\) | 10.7984 | 0.716713 | 0.358357 | − | 0.933585i | \(-0.383337\pi\) | ||||
0.358357 | + | 0.933585i | \(0.383337\pi\) | |||||||
\(228\) | 6.00000 | 0.397360 | ||||||||
\(229\) | −24.7639 | −1.63645 | −0.818223 | − | 0.574900i | \(-0.805041\pi\) | ||||
−0.818223 | + | 0.574900i | \(0.805041\pi\) | |||||||
\(230\) | 10.0000 | 0.659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.90983 | −0.125386 | ||||||||
\(233\) | −6.65248 | −0.435818 | −0.217909 | − | 0.975969i | \(-0.569924\pi\) | ||||
−0.217909 | + | 0.975969i | \(0.569924\pi\) | |||||||
\(234\) | 27.0344 | 1.76730 | ||||||||
\(235\) | 1.14590 | 0.0747501 | ||||||||
\(236\) | −27.7082 | −1.80365 | ||||||||
\(237\) | −6.67376 | −0.433507 | ||||||||
\(238\) | −12.5623 | −0.814293 | ||||||||
\(239\) | −24.9787 | −1.61574 | −0.807869 | − | 0.589362i | \(-0.799379\pi\) | ||||
−0.807869 | + | 0.589362i | \(0.799379\pi\) | |||||||
\(240\) | 0.618034 | 0.0398939 | ||||||||
\(241\) | 17.1246 | 1.10309 | 0.551547 | − | 0.834144i | \(-0.314038\pi\) | ||||
0.551547 | + | 0.834144i | \(0.314038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 14.2918 | 0.914938 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −3.41641 | −0.217822 | ||||||||
\(247\) | −14.9443 | −0.950881 | ||||||||
\(248\) | 7.23607 | 0.459491 | ||||||||
\(249\) | −5.90983 | −0.374520 | ||||||||
\(250\) | −2.23607 | −0.141421 | ||||||||
\(251\) | −7.70820 | −0.486538 | −0.243269 | − | 0.969959i | \(-0.578220\pi\) | ||||
−0.243269 | + | 0.969959i | \(0.578220\pi\) | |||||||
\(252\) | −7.85410 | −0.494762 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −20.6525 | −1.29585 | ||||||||
\(255\) | 3.47214 | 0.217434 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −2.38197 | −0.148583 | −0.0742915 | − | 0.997237i | \(-0.523670\pi\) | ||||
−0.0742915 | + | 0.997237i | \(0.523670\pi\) | |||||||
\(258\) | 7.23607 | 0.450498 | ||||||||
\(259\) | −7.23607 | −0.449627 | ||||||||
\(260\) | 13.8541 | 0.859195 | ||||||||
\(261\) | 2.23607 | 0.138409 | ||||||||
\(262\) | −17.8885 | −1.10516 | ||||||||
\(263\) | −14.1803 | −0.874397 | −0.437199 | − | 0.899365i | \(-0.644029\pi\) | ||||
−0.437199 | + | 0.899365i | \(0.644029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.52786 | 0.0938559 | ||||||||
\(266\) | 7.23607 | 0.443672 | ||||||||
\(267\) | 7.88854 | 0.482771 | ||||||||
\(268\) | 24.5410 | 1.49908 | ||||||||
\(269\) | −18.6525 | −1.13726 | −0.568631 | − | 0.822593i | \(-0.692527\pi\) | ||||
−0.568631 | + | 0.822593i | \(0.692527\pi\) | |||||||
\(270\) | 7.76393 | 0.472498 | ||||||||
\(271\) | −23.2361 | −1.41149 | −0.705745 | − | 0.708466i | \(-0.749388\pi\) | ||||
−0.705745 | + | 0.708466i | \(0.749388\pi\) | |||||||
\(272\) | 5.61803 | 0.340643 | ||||||||
\(273\) | −2.85410 | −0.172738 | ||||||||
\(274\) | −25.5279 | −1.54219 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.29180 | −0.499107 | ||||||||
\(277\) | 9.41641 | 0.565777 | 0.282889 | − | 0.959153i | \(-0.408707\pi\) | ||||
0.282889 | + | 0.959153i | \(0.408707\pi\) | |||||||
\(278\) | −12.3607 | −0.741344 | ||||||||
\(279\) | −8.47214 | −0.507214 | ||||||||
\(280\) | −2.23607 | −0.133631 | ||||||||
\(281\) | 8.47214 | 0.505405 | 0.252703 | − | 0.967544i | \(-0.418681\pi\) | ||||
0.252703 | + | 0.967544i | \(0.418681\pi\) | |||||||
\(282\) | −1.58359 | −0.0943015 | ||||||||
\(283\) | 7.43769 | 0.442125 | 0.221063 | − | 0.975260i | \(-0.429048\pi\) | ||||
0.221063 | + | 0.975260i | \(0.429048\pi\) | |||||||
\(284\) | 48.9787 | 2.90635 | ||||||||
\(285\) | −2.00000 | −0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.47214 | −0.145926 | ||||||||
\(288\) | 17.5623 | 1.03487 | ||||||||
\(289\) | 14.5623 | 0.856606 | ||||||||
\(290\) | 1.90983 | 0.112149 | ||||||||
\(291\) | −9.47214 | −0.555266 | ||||||||
\(292\) | −19.1459 | −1.12043 | ||||||||
\(293\) | 9.41641 | 0.550112 | 0.275056 | − | 0.961428i | \(-0.411304\pi\) | ||||
0.275056 | + | 0.961428i | \(0.411304\pi\) | |||||||
\(294\) | 1.38197 | 0.0805979 | ||||||||
\(295\) | 9.23607 | 0.537745 | ||||||||
\(296\) | −16.1803 | −0.940463 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 39.9230 | 2.31268 | ||||||||
\(299\) | 20.6525 | 1.19436 | ||||||||
\(300\) | 1.85410 | 0.107047 | ||||||||
\(301\) | 5.23607 | 0.301802 | ||||||||
\(302\) | 0.854102 | 0.0491480 | ||||||||
\(303\) | 8.47214 | 0.486711 | ||||||||
\(304\) | −3.23607 | −0.185601 | ||||||||
\(305\) | −4.76393 | −0.272782 | ||||||||
\(306\) | 32.8885 | 1.88011 | ||||||||
\(307\) | 20.5623 | 1.17355 | 0.586776 | − | 0.809749i | \(-0.300397\pi\) | ||||
0.586776 | + | 0.809749i | \(0.300397\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.7082 | −0.609168 | ||||||||
\(310\) | −7.23607 | −0.410981 | ||||||||
\(311\) | 13.1246 | 0.744228 | 0.372114 | − | 0.928187i | \(-0.378633\pi\) | ||||
0.372114 | + | 0.928187i | \(0.378633\pi\) | |||||||
\(312\) | −6.38197 | −0.361308 | ||||||||
\(313\) | −18.0000 | −1.01742 | −0.508710 | − | 0.860938i | \(-0.669877\pi\) | ||||
−0.508710 | + | 0.860938i | \(0.669877\pi\) | |||||||
\(314\) | −35.9787 | −2.03040 | ||||||||
\(315\) | 2.61803 | 0.147510 | ||||||||
\(316\) | −32.3951 | −1.82237 | ||||||||
\(317\) | −21.5279 | −1.20913 | −0.604563 | − | 0.796558i | \(-0.706652\pi\) | ||||
−0.604563 | + | 0.796558i | \(0.706652\pi\) | |||||||
\(318\) | −2.11146 | −0.118405 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 13.0000 | 0.726722 | ||||||||
\(321\) | 4.47214 | 0.249610 | ||||||||
\(322\) | −10.0000 | −0.557278 | ||||||||
\(323\) | −18.1803 | −1.01158 | ||||||||
\(324\) | 17.1246 | 0.951367 | ||||||||
\(325\) | −4.61803 | −0.256162 | ||||||||
\(326\) | −49.5967 | −2.74691 | ||||||||
\(327\) | 7.12461 | 0.393992 | ||||||||
\(328\) | −5.52786 | −0.305225 | ||||||||
\(329\) | −1.14590 | −0.0631754 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.5066 | −1.01721 | −0.508607 | − | 0.860999i | \(-0.669839\pi\) | ||||
−0.508607 | + | 0.860999i | \(0.669839\pi\) | |||||||
\(332\) | −28.6869 | −1.57440 | ||||||||
\(333\) | 18.9443 | 1.03814 | ||||||||
\(334\) | 26.8328 | 1.46823 | ||||||||
\(335\) | −8.18034 | −0.446940 | ||||||||
\(336\) | −0.618034 | −0.0337165 | ||||||||
\(337\) | 31.4164 | 1.71136 | 0.855680 | − | 0.517505i | \(-0.173139\pi\) | ||||
0.855680 | + | 0.517505i | \(0.173139\pi\) | |||||||
\(338\) | 18.6180 | 1.01269 | ||||||||
\(339\) | 6.47214 | 0.351518 | ||||||||
\(340\) | 16.8541 | 0.914042 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −18.9443 | −1.02439 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.7082 | 0.631264 | ||||||||
\(345\) | 2.76393 | 0.148805 | ||||||||
\(346\) | 3.49342 | 0.187808 | ||||||||
\(347\) | 1.52786 | 0.0820200 | 0.0410100 | − | 0.999159i | \(-0.486942\pi\) | ||||
0.0410100 | + | 0.999159i | \(0.486942\pi\) | |||||||
\(348\) | −1.58359 | −0.0848894 | ||||||||
\(349\) | −3.88854 | −0.208149 | −0.104074 | − | 0.994570i | \(-0.533188\pi\) | ||||
−0.104074 | + | 0.994570i | \(0.533188\pi\) | |||||||
\(350\) | 2.23607 | 0.119523 | ||||||||
\(351\) | 16.0344 | 0.855855 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.5623 | −0.721849 | −0.360924 | − | 0.932595i | \(-0.617539\pi\) | ||||
−0.360924 | + | 0.932595i | \(0.617539\pi\) | |||||||
\(354\) | −12.7639 | −0.678395 | ||||||||
\(355\) | −16.3262 | −0.866507 | ||||||||
\(356\) | 38.2918 | 2.02946 | ||||||||
\(357\) | −3.47214 | −0.183765 | ||||||||
\(358\) | 43.8673 | 2.31846 | ||||||||
\(359\) | 12.9787 | 0.684990 | 0.342495 | − | 0.939520i | \(-0.388728\pi\) | ||||
0.342495 | + | 0.939520i | \(0.388728\pi\) | |||||||
\(360\) | 5.85410 | 0.308538 | ||||||||
\(361\) | −8.52786 | −0.448835 | ||||||||
\(362\) | 12.3607 | 0.649663 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.8541 | −0.726152 | ||||||||
\(365\) | 6.38197 | 0.334047 | ||||||||
\(366\) | 6.58359 | 0.344130 | ||||||||
\(367\) | −31.4508 | −1.64172 | −0.820860 | − | 0.571129i | \(-0.806506\pi\) | ||||
−0.820860 | + | 0.571129i | \(0.806506\pi\) | |||||||
\(368\) | 4.47214 | 0.233126 | ||||||||
\(369\) | 6.47214 | 0.336926 | ||||||||
\(370\) | 16.1803 | 0.841176 | ||||||||
\(371\) | −1.52786 | −0.0793227 | ||||||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | −11.1246 | −0.576011 | −0.288005 | − | 0.957629i | \(-0.592992\pi\) | ||||
−0.288005 | + | 0.957629i | \(0.592992\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.618034 | −0.0319151 | ||||||||
\(376\) | −2.56231 | −0.132141 | ||||||||
\(377\) | 3.94427 | 0.203140 | ||||||||
\(378\) | −7.76393 | −0.399334 | ||||||||
\(379\) | 24.7426 | 1.27094 | 0.635472 | − | 0.772124i | \(-0.280805\pi\) | ||||
0.635472 | + | 0.772124i | \(0.280805\pi\) | |||||||
\(380\) | −9.70820 | −0.498020 | ||||||||
\(381\) | −5.70820 | −0.292440 | ||||||||
\(382\) | 51.6312 | 2.64168 | ||||||||
\(383\) | 26.7984 | 1.36933 | 0.684666 | − | 0.728857i | \(-0.259948\pi\) | ||||
0.684666 | + | 0.728857i | \(0.259948\pi\) | |||||||
\(384\) | −9.67376 | −0.493662 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.94427 | −0.455251 | ||||||||
\(387\) | −13.7082 | −0.696827 | ||||||||
\(388\) | −45.9787 | −2.33422 | ||||||||
\(389\) | −33.5623 | −1.70168 | −0.850838 | − | 0.525428i | \(-0.823905\pi\) | ||||
−0.850838 | + | 0.525428i | \(0.823905\pi\) | |||||||
\(390\) | 6.38197 | 0.323163 | ||||||||
\(391\) | 25.1246 | 1.27061 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | −4.94427 | −0.249406 | ||||||||
\(394\) | 26.8328 | 1.35182 | ||||||||
\(395\) | 10.7984 | 0.543325 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.1591 | 1.76458 | 0.882291 | − | 0.470704i | \(-0.156000\pi\) | ||||
0.882291 | + | 0.470704i | \(0.156000\pi\) | |||||||
\(398\) | −40.2492 | −2.01751 | ||||||||
\(399\) | 2.00000 | 0.100125 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 15.5066 | 0.774362 | 0.387181 | − | 0.922004i | \(-0.373449\pi\) | ||||
0.387181 | + | 0.922004i | \(0.373449\pi\) | |||||||
\(402\) | 11.3050 | 0.563840 | ||||||||
\(403\) | −14.9443 | −0.744427 | ||||||||
\(404\) | 41.1246 | 2.04603 | ||||||||
\(405\) | −5.70820 | −0.283643 | ||||||||
\(406\) | −1.90983 | −0.0947833 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.76393 | −0.384372 | ||||||||
\(409\) | 3.23607 | 0.160013 | 0.0800066 | − | 0.996794i | \(-0.474506\pi\) | ||||
0.0800066 | + | 0.996794i | \(0.474506\pi\) | |||||||
\(410\) | 5.52786 | 0.273002 | ||||||||
\(411\) | −7.05573 | −0.348033 | ||||||||
\(412\) | −51.9787 | −2.56081 | ||||||||
\(413\) | −9.23607 | −0.454477 | ||||||||
\(414\) | 26.1803 | 1.28669 | ||||||||
\(415\) | 9.56231 | 0.469395 | ||||||||
\(416\) | 30.9787 | 1.51886 | ||||||||
\(417\) | −3.41641 | −0.167302 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.3050 | −1.72476 | −0.862380 | − | 0.506262i | \(-0.831027\pi\) | ||||
−0.862380 | + | 0.506262i | \(0.831027\pi\) | |||||||
\(420\) | −1.85410 | −0.0904709 | ||||||||
\(421\) | −34.5066 | −1.68175 | −0.840874 | − | 0.541231i | \(-0.817958\pi\) | ||||
−0.840874 | + | 0.541231i | \(0.817958\pi\) | |||||||
\(422\) | −17.1591 | −0.835290 | ||||||||
\(423\) | 3.00000 | 0.145865 | ||||||||
\(424\) | −3.41641 | −0.165915 | ||||||||
\(425\) | −5.61803 | −0.272515 | ||||||||
\(426\) | 22.5623 | 1.09315 | ||||||||
\(427\) | 4.76393 | 0.230543 | ||||||||
\(428\) | 21.7082 | 1.04931 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.7082 | −0.564620 | ||||||||
\(431\) | 5.32624 | 0.256556 | 0.128278 | − | 0.991738i | \(-0.459055\pi\) | ||||
0.128278 | + | 0.991738i | \(0.459055\pi\) | |||||||
\(432\) | 3.47214 | 0.167053 | ||||||||
\(433\) | 12.0344 | 0.578338 | 0.289169 | − | 0.957278i | \(-0.406621\pi\) | ||||
0.289169 | + | 0.957278i | \(0.406621\pi\) | |||||||
\(434\) | 7.23607 | 0.347342 | ||||||||
\(435\) | 0.527864 | 0.0253091 | ||||||||
\(436\) | 34.5836 | 1.65625 | ||||||||
\(437\) | −14.4721 | −0.692296 | ||||||||
\(438\) | −8.81966 | −0.421420 | ||||||||
\(439\) | −4.29180 | −0.204836 | −0.102418 | − | 0.994741i | \(-0.532658\pi\) | ||||
−0.102418 | + | 0.994741i | \(0.532658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | 58.0132 | 2.75940 | ||||||||
\(443\) | −3.34752 | −0.159046 | −0.0795228 | − | 0.996833i | \(-0.525340\pi\) | ||||
−0.0795228 | + | 0.996833i | \(0.525340\pi\) | |||||||
\(444\) | −13.4164 | −0.636715 | ||||||||
\(445\) | −12.7639 | −0.605068 | ||||||||
\(446\) | 3.41641 | 0.161772 | ||||||||
\(447\) | 11.0344 | 0.521911 | ||||||||
\(448\) | −13.0000 | −0.614192 | ||||||||
\(449\) | −9.27051 | −0.437502 | −0.218751 | − | 0.975781i | \(-0.570198\pi\) | ||||
−0.218751 | + | 0.975781i | \(0.570198\pi\) | |||||||
\(450\) | −5.85410 | −0.275965 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 31.4164 | 1.47770 | ||||||||
\(453\) | 0.236068 | 0.0110914 | ||||||||
\(454\) | 24.1459 | 1.13322 | ||||||||
\(455\) | 4.61803 | 0.216497 | ||||||||
\(456\) | 4.47214 | 0.209427 | ||||||||
\(457\) | 37.7771 | 1.76714 | 0.883569 | − | 0.468301i | \(-0.155134\pi\) | ||||
0.883569 | + | 0.468301i | \(0.155134\pi\) | |||||||
\(458\) | −55.3738 | −2.58745 | ||||||||
\(459\) | 19.5066 | 0.910489 | ||||||||
\(460\) | 13.4164 | 0.625543 | ||||||||
\(461\) | −16.2918 | −0.758785 | −0.379392 | − | 0.925236i | \(-0.623867\pi\) | ||||
−0.379392 | + | 0.925236i | \(0.623867\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.1246 | −0.795848 | −0.397924 | − | 0.917418i | \(-0.630269\pi\) | ||||
−0.397924 | + | 0.917418i | \(0.630269\pi\) | |||||||
\(464\) | 0.854102 | 0.0396507 | ||||||||
\(465\) | −2.00000 | −0.0927478 | ||||||||
\(466\) | −14.8754 | −0.689089 | ||||||||
\(467\) | −32.3262 | −1.49588 | −0.747940 | − | 0.663766i | \(-0.768957\pi\) | ||||
−0.747940 | + | 0.663766i | \(0.768957\pi\) | |||||||
\(468\) | 36.2705 | 1.67660 | ||||||||
\(469\) | 8.18034 | 0.377733 | ||||||||
\(470\) | 2.56231 | 0.118190 | ||||||||
\(471\) | −9.94427 | −0.458208 | ||||||||
\(472\) | −20.6525 | −0.950607 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −14.9230 | −0.685435 | ||||||||
\(475\) | 3.23607 | 0.148481 | ||||||||
\(476\) | −16.8541 | −0.772506 | ||||||||
\(477\) | 4.00000 | 0.183147 | ||||||||
\(478\) | −55.8541 | −2.55471 | ||||||||
\(479\) | −22.6525 | −1.03502 | −0.517509 | − | 0.855678i | \(-0.673141\pi\) | ||||
−0.517509 | + | 0.855678i | \(0.673141\pi\) | |||||||
\(480\) | 4.14590 | 0.189233 | ||||||||
\(481\) | 33.4164 | 1.52366 | ||||||||
\(482\) | 38.2918 | 1.74414 | ||||||||
\(483\) | −2.76393 | −0.125763 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.3262 | 0.695929 | ||||||||
\(486\) | 31.1803 | 1.41437 | ||||||||
\(487\) | −1.81966 | −0.0824567 | −0.0412283 | − | 0.999150i | \(-0.513127\pi\) | ||||
−0.0412283 | + | 0.999150i | \(0.513127\pi\) | |||||||
\(488\) | 10.6525 | 0.482215 | ||||||||
\(489\) | −13.7082 | −0.619906 | ||||||||
\(490\) | −2.23607 | −0.101015 | ||||||||
\(491\) | −2.11146 | −0.0952887 | −0.0476443 | − | 0.998864i | \(-0.515171\pi\) | ||||
−0.0476443 | + | 0.998864i | \(0.515171\pi\) | |||||||
\(492\) | −4.58359 | −0.206644 | ||||||||
\(493\) | 4.79837 | 0.216108 | ||||||||
\(494\) | −33.4164 | −1.50348 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.23607 | −0.145304 | ||||||||
\(497\) | 16.3262 | 0.732332 | ||||||||
\(498\) | −13.2148 | −0.592169 | ||||||||
\(499\) | −23.0344 | −1.03116 | −0.515582 | − | 0.856840i | \(-0.672424\pi\) | ||||
−0.515582 | + | 0.856840i | \(0.672424\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | 7.41641 | 0.331341 | ||||||||
\(502\) | −17.2361 | −0.769283 | ||||||||
\(503\) | −3.09017 | −0.137784 | −0.0688919 | − | 0.997624i | \(-0.521946\pi\) | ||||
−0.0688919 | + | 0.997624i | \(0.521946\pi\) | |||||||
\(504\) | −5.85410 | −0.260762 | ||||||||
\(505\) | −13.7082 | −0.610007 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.14590 | 0.228537 | ||||||||
\(508\) | −27.7082 | −1.22935 | ||||||||
\(509\) | 26.3607 | 1.16842 | 0.584208 | − | 0.811604i | \(-0.301405\pi\) | ||||
0.584208 | + | 0.811604i | \(0.301405\pi\) | |||||||
\(510\) | 7.76393 | 0.343793 | ||||||||
\(511\) | −6.38197 | −0.282322 | ||||||||
\(512\) | 11.1803 | 0.494106 | ||||||||
\(513\) | −11.2361 | −0.496085 | ||||||||
\(514\) | −5.32624 | −0.234930 | ||||||||
\(515\) | 17.3262 | 0.763485 | ||||||||
\(516\) | 9.70820 | 0.427380 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −16.1803 | −0.710923 | ||||||||
\(519\) | 0.965558 | 0.0423833 | ||||||||
\(520\) | 10.3262 | 0.452835 | ||||||||
\(521\) | −14.1803 | −0.621252 | −0.310626 | − | 0.950532i | \(-0.600539\pi\) | ||||
−0.310626 | + | 0.950532i | \(0.600539\pi\) | |||||||
\(522\) | 5.00000 | 0.218844 | ||||||||
\(523\) | −1.14590 | −0.0501066 | −0.0250533 | − | 0.999686i | \(-0.507976\pi\) | ||||
−0.0250533 | + | 0.999686i | \(0.507976\pi\) | |||||||
\(524\) | −24.0000 | −1.04844 | ||||||||
\(525\) | 0.618034 | 0.0269732 | ||||||||
\(526\) | −31.7082 | −1.38254 | ||||||||
\(527\) | −18.1803 | −0.791948 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 3.41641 | 0.148399 | ||||||||
\(531\) | 24.1803 | 1.04934 | ||||||||
\(532\) | 9.70820 | 0.420904 | ||||||||
\(533\) | 11.4164 | 0.494500 | ||||||||
\(534\) | 17.6393 | 0.763328 | ||||||||
\(535\) | −7.23607 | −0.312842 | ||||||||
\(536\) | 18.2918 | 0.790085 | ||||||||
\(537\) | 12.1246 | 0.523216 | ||||||||
\(538\) | −41.7082 | −1.79817 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.4164 | 0.448251 | ||||||||
\(541\) | −6.14590 | −0.264233 | −0.132116 | − | 0.991234i | \(-0.542177\pi\) | ||||
−0.132116 | + | 0.991234i | \(0.542177\pi\) | |||||||
\(542\) | −51.9574 | −2.23176 | ||||||||
\(543\) | 3.41641 | 0.146612 | ||||||||
\(544\) | 37.6869 | 1.61581 | ||||||||
\(545\) | −11.5279 | −0.493799 | ||||||||
\(546\) | −6.38197 | −0.273123 | ||||||||
\(547\) | 18.0689 | 0.772570 | 0.386285 | − | 0.922380i | \(-0.373758\pi\) | ||||
0.386285 | + | 0.922380i | \(0.373758\pi\) | |||||||
\(548\) | −34.2492 | −1.46305 | ||||||||
\(549\) | −12.4721 | −0.532298 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.76393 | −0.117747 | ||||||||
\(552\) | −6.18034 | −0.263053 | ||||||||
\(553\) | −10.7984 | −0.459194 | ||||||||
\(554\) | 21.0557 | 0.894572 | ||||||||
\(555\) | 4.47214 | 0.189832 | ||||||||
\(556\) | −16.5836 | −0.703301 | ||||||||
\(557\) | 17.7082 | 0.750321 | 0.375160 | − | 0.926960i | \(-0.377588\pi\) | ||||
0.375160 | + | 0.926960i | \(0.377588\pi\) | |||||||
\(558\) | −18.9443 | −0.801975 | ||||||||
\(559\) | −24.1803 | −1.02272 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.9443 | 0.799116 | ||||||||
\(563\) | 23.6180 | 0.995381 | 0.497691 | − | 0.867355i | \(-0.334181\pi\) | ||||
0.497691 | + | 0.867355i | \(0.334181\pi\) | |||||||
\(564\) | −2.12461 | −0.0894623 | ||||||||
\(565\) | −10.4721 | −0.440566 | ||||||||
\(566\) | 16.6312 | 0.699061 | ||||||||
\(567\) | 5.70820 | 0.239722 | ||||||||
\(568\) | 36.5066 | 1.53178 | ||||||||
\(569\) | 37.7984 | 1.58459 | 0.792295 | − | 0.610138i | \(-0.208886\pi\) | ||||
0.792295 | + | 0.610138i | \(0.208886\pi\) | |||||||
\(570\) | −4.47214 | −0.187317 | ||||||||
\(571\) | 35.9787 | 1.50566 | 0.752831 | − | 0.658214i | \(-0.228688\pi\) | ||||
0.752831 | + | 0.658214i | \(0.228688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.2705 | 0.596159 | ||||||||
\(574\) | −5.52786 | −0.230729 | ||||||||
\(575\) | −4.47214 | −0.186501 | ||||||||
\(576\) | 34.0344 | 1.41810 | ||||||||
\(577\) | 33.2148 | 1.38275 | 0.691375 | − | 0.722496i | \(-0.257005\pi\) | ||||
0.691375 | + | 0.722496i | \(0.257005\pi\) | |||||||
\(578\) | 32.5623 | 1.35441 | ||||||||
\(579\) | −2.47214 | −0.102738 | ||||||||
\(580\) | 2.56231 | 0.106394 | ||||||||
\(581\) | −9.56231 | −0.396711 | ||||||||
\(582\) | −21.1803 | −0.877953 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.2705 | −0.590518 | ||||||||
\(585\) | −12.0902 | −0.499867 | ||||||||
\(586\) | 21.0557 | 0.869804 | ||||||||
\(587\) | 6.72949 | 0.277756 | 0.138878 | − | 0.990310i | \(-0.455650\pi\) | ||||
0.138878 | + | 0.990310i | \(0.455650\pi\) | |||||||
\(588\) | 1.85410 | 0.0764619 | ||||||||
\(589\) | 10.4721 | 0.431497 | ||||||||
\(590\) | 20.6525 | 0.850249 | ||||||||
\(591\) | 7.41641 | 0.305070 | ||||||||
\(592\) | 7.23607 | 0.297401 | ||||||||
\(593\) | −9.79837 | −0.402371 | −0.201185 | − | 0.979553i | \(-0.564479\pi\) | ||||
−0.201185 | + | 0.979553i | \(0.564479\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.61803 | 0.230317 | ||||||||
\(596\) | 53.5623 | 2.19400 | ||||||||
\(597\) | −11.1246 | −0.455300 | ||||||||
\(598\) | 46.1803 | 1.88845 | ||||||||
\(599\) | 26.2705 | 1.07338 | 0.536692 | − | 0.843778i | \(-0.319674\pi\) | ||||
0.536692 | + | 0.843778i | \(0.319674\pi\) | |||||||
\(600\) | 1.38197 | 0.0564185 | ||||||||
\(601\) | 15.4164 | 0.628848 | 0.314424 | − | 0.949283i | \(-0.398189\pi\) | ||||
0.314424 | + | 0.949283i | \(0.398189\pi\) | |||||||
\(602\) | 11.7082 | 0.477191 | ||||||||
\(603\) | −21.4164 | −0.872144 | ||||||||
\(604\) | 1.14590 | 0.0466259 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.9443 | 0.769558 | ||||||||
\(607\) | 1.90983 | 0.0775176 | 0.0387588 | − | 0.999249i | \(-0.487660\pi\) | ||||
0.0387588 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(608\) | −21.7082 | −0.880384 | ||||||||
\(609\) | −0.527864 | −0.0213901 | ||||||||
\(610\) | −10.6525 | −0.431306 | ||||||||
\(611\) | 5.29180 | 0.214083 | ||||||||
\(612\) | 44.1246 | 1.78363 | ||||||||
\(613\) | 40.8328 | 1.64922 | 0.824611 | − | 0.565700i | \(-0.191394\pi\) | ||||
0.824611 | + | 0.565700i | \(0.191394\pi\) | |||||||
\(614\) | 45.9787 | 1.85555 | ||||||||
\(615\) | 1.52786 | 0.0616094 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.76393 | −0.111272 | −0.0556359 | − | 0.998451i | \(-0.517719\pi\) | ||||
−0.0556359 | + | 0.998451i | \(0.517719\pi\) | |||||||
\(618\) | −23.9443 | −0.963180 | ||||||||
\(619\) | −22.4721 | −0.903231 | −0.451616 | − | 0.892213i | \(-0.649152\pi\) | ||||
−0.451616 | + | 0.892213i | \(0.649152\pi\) | |||||||
\(620\) | −9.70820 | −0.389891 | ||||||||
\(621\) | 15.5279 | 0.623112 | ||||||||
\(622\) | 29.3475 | 1.17673 | ||||||||
\(623\) | 12.7639 | 0.511376 | ||||||||
\(624\) | 2.85410 | 0.114256 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −40.2492 | −1.60868 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −48.2705 | −1.92620 | ||||||||
\(629\) | 40.6525 | 1.62092 | ||||||||
\(630\) | 5.85410 | 0.233233 | ||||||||
\(631\) | −9.50658 | −0.378451 | −0.189225 | − | 0.981934i | \(-0.560598\pi\) | ||||
−0.189225 | + | 0.981934i | \(0.560598\pi\) | |||||||
\(632\) | −24.1459 | −0.960472 | ||||||||
\(633\) | −4.74265 | −0.188503 | ||||||||
\(634\) | −48.1378 | −1.91179 | ||||||||
\(635\) | 9.23607 | 0.366522 | ||||||||
\(636\) | −2.83282 | −0.112328 | ||||||||
\(637\) | −4.61803 | −0.182973 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −42.7426 | −1.69087 | ||||||||
\(640\) | 15.6525 | 0.618718 | ||||||||
\(641\) | 20.9787 | 0.828609 | 0.414305 | − | 0.910138i | \(-0.364025\pi\) | ||||
0.414305 | + | 0.910138i | \(0.364025\pi\) | |||||||
\(642\) | 10.0000 | 0.394669 | ||||||||
\(643\) | 10.7984 | 0.425846 | 0.212923 | − | 0.977069i | \(-0.431702\pi\) | ||||
0.212923 | + | 0.977069i | \(0.431702\pi\) | |||||||
\(644\) | −13.4164 | −0.528681 | ||||||||
\(645\) | −3.23607 | −0.127420 | ||||||||
\(646\) | −40.6525 | −1.59945 | ||||||||
\(647\) | −46.8541 | −1.84202 | −0.921012 | − | 0.389533i | \(-0.872636\pi\) | ||||
−0.921012 | + | 0.389533i | \(0.872636\pi\) | |||||||
\(648\) | 12.7639 | 0.501415 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −10.3262 | −0.405028 | ||||||||
\(651\) | 2.00000 | 0.0783862 | ||||||||
\(652\) | −66.5410 | −2.60595 | ||||||||
\(653\) | −38.1803 | −1.49411 | −0.747056 | − | 0.664761i | \(-0.768533\pi\) | ||||
−0.747056 | + | 0.664761i | \(0.768533\pi\) | |||||||
\(654\) | 15.9311 | 0.622956 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | 2.47214 | 0.0965207 | ||||||||
\(657\) | 16.7082 | 0.651849 | ||||||||
\(658\) | −2.56231 | −0.0998891 | ||||||||
\(659\) | 4.03444 | 0.157160 | 0.0785798 | − | 0.996908i | \(-0.474961\pi\) | ||||
0.0785798 | + | 0.996908i | \(0.474961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.58359 | −0.256072 | −0.128036 | − | 0.991770i | \(-0.540867\pi\) | ||||
−0.128036 | + | 0.991770i | \(0.540867\pi\) | |||||||
\(662\) | −41.3820 | −1.60836 | ||||||||
\(663\) | 16.0344 | 0.622726 | ||||||||
\(664\) | −21.3820 | −0.829781 | ||||||||
\(665\) | −3.23607 | −0.125489 | ||||||||
\(666\) | 42.3607 | 1.64144 | ||||||||
\(667\) | 3.81966 | 0.147898 | ||||||||
\(668\) | 36.0000 | 1.39288 | ||||||||
\(669\) | 0.944272 | 0.0365077 | ||||||||
\(670\) | −18.2918 | −0.706674 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.14590 | −0.159931 | ||||||||
\(673\) | −21.8885 | −0.843741 | −0.421871 | − | 0.906656i | \(-0.638626\pi\) | ||||
−0.421871 | + | 0.906656i | \(0.638626\pi\) | |||||||
\(674\) | 70.2492 | 2.70590 | ||||||||
\(675\) | −3.47214 | −0.133643 | ||||||||
\(676\) | 24.9787 | 0.960720 | ||||||||
\(677\) | −48.8541 | −1.87762 | −0.938808 | − | 0.344441i | \(-0.888068\pi\) | ||||
−0.938808 | + | 0.344441i | \(0.888068\pi\) | |||||||
\(678\) | 14.4721 | 0.555799 | ||||||||
\(679\) | −15.3262 | −0.588167 | ||||||||
\(680\) | 12.5623 | 0.481742 | ||||||||
\(681\) | 6.67376 | 0.255739 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.7639 | 1.33020 | 0.665102 | − | 0.746752i | \(-0.268388\pi\) | ||||
0.665102 | + | 0.746752i | \(0.268388\pi\) | |||||||
\(684\) | −25.4164 | −0.971821 | ||||||||
\(685\) | 11.4164 | 0.436199 | ||||||||
\(686\) | 2.23607 | 0.0853735 | ||||||||
\(687\) | −15.3050 | −0.583920 | ||||||||
\(688\) | −5.23607 | −0.199623 | ||||||||
\(689\) | 7.05573 | 0.268802 | ||||||||
\(690\) | 6.18034 | 0.235282 | ||||||||
\(691\) | −26.8328 | −1.02077 | −0.510384 | − | 0.859946i | \(-0.670497\pi\) | ||||
−0.510384 | + | 0.859946i | \(0.670497\pi\) | |||||||
\(692\) | 4.68692 | 0.178170 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.41641 | 0.129685 | ||||||||
\(695\) | 5.52786 | 0.209684 | ||||||||
\(696\) | −1.18034 | −0.0447407 | ||||||||
\(697\) | 13.8885 | 0.526066 | ||||||||
\(698\) | −8.69505 | −0.329112 | ||||||||
\(699\) | −4.11146 | −0.155510 | ||||||||
\(700\) | 3.00000 | 0.113389 | ||||||||
\(701\) | 51.3050 | 1.93776 | 0.968881 | − | 0.247528i | \(-0.0796184\pi\) | ||||
0.968881 | + | 0.247528i | \(0.0796184\pi\) | |||||||
\(702\) | 35.8541 | 1.35323 | ||||||||
\(703\) | −23.4164 | −0.883167 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.708204 | 0.0266725 | ||||||||
\(706\) | −30.3262 | −1.14134 | ||||||||
\(707\) | 13.7082 | 0.515550 | ||||||||
\(708\) | −17.1246 | −0.643582 | ||||||||
\(709\) | 0.257354 | 0.00966514 | 0.00483257 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483257 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(710\) | −36.5066 | −1.37007 | ||||||||
\(711\) | 28.2705 | 1.06023 | ||||||||
\(712\) | 28.5410 | 1.06962 | ||||||||
\(713\) | −14.4721 | −0.541986 | ||||||||
\(714\) | −7.76393 | −0.290558 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 58.8541 | 2.19948 | ||||||||
\(717\) | −15.4377 | −0.576531 | ||||||||
\(718\) | 29.0213 | 1.08306 | ||||||||
\(719\) | 21.8885 | 0.816305 | 0.408152 | − | 0.912914i | \(-0.366173\pi\) | ||||
0.408152 | + | 0.912914i | \(0.366173\pi\) | |||||||
\(720\) | −2.61803 | −0.0975684 | ||||||||
\(721\) | −17.3262 | −0.645263 | ||||||||
\(722\) | −19.0689 | −0.709670 | ||||||||
\(723\) | 10.5836 | 0.393608 | ||||||||
\(724\) | 16.5836 | 0.616324 | ||||||||
\(725\) | −0.854102 | −0.0317206 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.5623 | −1.54146 | −0.770730 | − | 0.637162i | \(-0.780108\pi\) | ||||
−0.770730 | + | 0.637162i | \(0.780108\pi\) | |||||||
\(728\) | −10.3262 | −0.382716 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 14.2705 | 0.528175 | ||||||||
\(731\) | −29.4164 | −1.08801 | ||||||||
\(732\) | 8.83282 | 0.326470 | ||||||||
\(733\) | −34.8673 | −1.28785 | −0.643926 | − | 0.765088i | \(-0.722695\pi\) | ||||
−0.643926 | + | 0.765088i | \(0.722695\pi\) | |||||||
\(734\) | −70.3262 | −2.59579 | ||||||||
\(735\) | −0.618034 | −0.0227965 | ||||||||
\(736\) | 30.0000 | 1.10581 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 14.4721 | 0.532727 | ||||||||
\(739\) | −12.0000 | −0.441427 | −0.220714 | − | 0.975339i | \(-0.570839\pi\) | ||||
−0.220714 | + | 0.975339i | \(0.570839\pi\) | |||||||
\(740\) | 21.7082 | 0.798009 | ||||||||
\(741\) | −9.23607 | −0.339295 | ||||||||
\(742\) | −3.41641 | −0.125420 | ||||||||
\(743\) | −5.34752 | −0.196182 | −0.0980908 | − | 0.995177i | \(-0.531274\pi\) | ||||
−0.0980908 | + | 0.995177i | \(0.531274\pi\) | |||||||
\(744\) | 4.47214 | 0.163956 | ||||||||
\(745\) | −17.8541 | −0.654124 | ||||||||
\(746\) | −24.8754 | −0.910753 | ||||||||
\(747\) | 25.0344 | 0.915962 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.23607 | 0.264400 | ||||||||
\(750\) | −1.38197 | −0.0504623 | ||||||||
\(751\) | 37.3262 | 1.36205 | 0.681027 | − | 0.732258i | \(-0.261534\pi\) | ||||
0.681027 | + | 0.732258i | \(0.261534\pi\) | |||||||
\(752\) | 1.14590 | 0.0417866 | ||||||||
\(753\) | −4.76393 | −0.173607 | ||||||||
\(754\) | 8.81966 | 0.321193 | ||||||||
\(755\) | −0.381966 | −0.0139012 | ||||||||
\(756\) | −10.4164 | −0.378841 | ||||||||
\(757\) | 4.18034 | 0.151937 | 0.0759685 | − | 0.997110i | \(-0.475795\pi\) | ||||
0.0759685 | + | 0.997110i | \(0.475795\pi\) | |||||||
\(758\) | 55.3262 | 2.00954 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.23607 | −0.262480 | ||||||||
\(761\) | −48.8328 | −1.77019 | −0.885094 | − | 0.465412i | \(-0.845906\pi\) | ||||
−0.885094 | + | 0.465412i | \(0.845906\pi\) | |||||||
\(762\) | −12.7639 | −0.462388 | ||||||||
\(763\) | 11.5279 | 0.417337 | ||||||||
\(764\) | 69.2705 | 2.50612 | ||||||||
\(765\) | −14.7082 | −0.531776 | ||||||||
\(766\) | 59.9230 | 2.16511 | ||||||||
\(767\) | 42.6525 | 1.54009 | ||||||||
\(768\) | −5.56231 | −0.200712 | ||||||||
\(769\) | −11.7082 | −0.422209 | −0.211104 | − | 0.977464i | \(-0.567706\pi\) | ||||
−0.211104 | + | 0.977464i | \(0.567706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.47214 | −0.0530177 | ||||||||
\(772\) | −12.0000 | −0.431889 | ||||||||
\(773\) | −27.3820 | −0.984861 | −0.492430 | − | 0.870352i | \(-0.663891\pi\) | ||||
−0.492430 | + | 0.870352i | \(0.663891\pi\) | |||||||
\(774\) | −30.6525 | −1.10178 | ||||||||
\(775\) | 3.23607 | 0.116243 | ||||||||
\(776\) | −34.2705 | −1.23024 | ||||||||
\(777\) | −4.47214 | −0.160437 | ||||||||
\(778\) | −75.0476 | −2.69059 | ||||||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | 8.56231 | 0.306580 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 56.1803 | 2.00900 | ||||||||
\(783\) | 2.96556 | 0.105980 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 16.0902 | 0.574283 | ||||||||
\(786\) | −11.0557 | −0.394345 | ||||||||
\(787\) | −40.0344 | −1.42707 | −0.713537 | − | 0.700618i | \(-0.752908\pi\) | ||||
−0.713537 | + | 0.700618i | \(0.752908\pi\) | |||||||
\(788\) | 36.0000 | 1.28245 | ||||||||
\(789\) | −8.76393 | −0.312004 | ||||||||
\(790\) | 24.1459 | 0.859072 | ||||||||
\(791\) | 10.4721 | 0.372346 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.0000 | −0.781243 | ||||||||
\(794\) | 78.6180 | 2.79005 | ||||||||
\(795\) | 0.944272 | 0.0334899 | ||||||||
\(796\) | −54.0000 | −1.91398 | ||||||||
\(797\) | 44.1033 | 1.56222 | 0.781110 | − | 0.624393i | \(-0.214654\pi\) | ||||
0.781110 | + | 0.624393i | \(0.214654\pi\) | |||||||
\(798\) | 4.47214 | 0.158312 | ||||||||
\(799\) | 6.43769 | 0.227749 | ||||||||
\(800\) | −6.70820 | −0.237171 | ||||||||
\(801\) | −33.4164 | −1.18071 | ||||||||
\(802\) | 34.6738 | 1.22437 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.1672 | 0.534905 | ||||||||
\(805\) | 4.47214 | 0.157622 | ||||||||
\(806\) | −33.4164 | −1.17704 | ||||||||
\(807\) | −11.5279 | −0.405800 | ||||||||
\(808\) | 30.6525 | 1.07835 | ||||||||
\(809\) | 3.09017 | 0.108645 | 0.0543223 | − | 0.998523i | \(-0.482700\pi\) | ||||
0.0543223 | + | 0.998523i | \(0.482700\pi\) | |||||||
\(810\) | −12.7639 | −0.448479 | ||||||||
\(811\) | −31.4164 | −1.10318 | −0.551590 | − | 0.834116i | \(-0.685979\pi\) | ||||
−0.551590 | + | 0.834116i | \(0.685979\pi\) | |||||||
\(812\) | −2.56231 | −0.0899193 | ||||||||
\(813\) | −14.3607 | −0.503651 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.1803 | 0.776943 | ||||||||
\(816\) | 3.47214 | 0.121549 | ||||||||
\(817\) | 16.9443 | 0.592805 | ||||||||
\(818\) | 7.23607 | 0.253003 | ||||||||
\(819\) | 12.0902 | 0.422465 | ||||||||
\(820\) | 7.41641 | 0.258992 | ||||||||
\(821\) | −12.6738 | −0.442317 | −0.221159 | − | 0.975238i | \(-0.570984\pi\) | ||||
−0.221159 | + | 0.975238i | \(0.570984\pi\) | |||||||
\(822\) | −15.7771 | −0.550289 | ||||||||
\(823\) | −20.0000 | −0.697156 | −0.348578 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(824\) | −38.7426 | −1.34966 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.6525 | −0.718592 | ||||||||
\(827\) | 37.8885 | 1.31751 | 0.658757 | − | 0.752356i | \(-0.271083\pi\) | ||||
0.658757 | + | 0.752356i | \(0.271083\pi\) | |||||||
\(828\) | 35.1246 | 1.22066 | ||||||||
\(829\) | 33.8885 | 1.17700 | 0.588499 | − | 0.808498i | \(-0.299719\pi\) | ||||
0.588499 | + | 0.808498i | \(0.299719\pi\) | |||||||
\(830\) | 21.3820 | 0.742179 | ||||||||
\(831\) | 5.81966 | 0.201882 | ||||||||
\(832\) | 60.0344 | 2.08132 | ||||||||
\(833\) | −5.61803 | −0.194653 | ||||||||
\(834\) | −7.63932 | −0.264528 | ||||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.2361 | −0.388375 | ||||||||
\(838\) | −78.9443 | −2.72708 | ||||||||
\(839\) | 7.63932 | 0.263739 | 0.131869 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131869 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(840\) | −1.38197 | −0.0476824 | ||||||||
\(841\) | −28.2705 | −0.974845 | ||||||||
\(842\) | −77.1591 | −2.65908 | ||||||||
\(843\) | 5.23607 | 0.180340 | ||||||||
\(844\) | −23.0213 | −0.792425 | ||||||||
\(845\) | −8.32624 | −0.286431 | ||||||||
\(846\) | 6.70820 | 0.230633 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.52786 | 0.0524671 | ||||||||
\(849\) | 4.59675 | 0.157760 | ||||||||
\(850\) | −12.5623 | −0.430884 | ||||||||
\(851\) | 32.3607 | 1.10931 | ||||||||
\(852\) | 30.2705 | 1.03705 | ||||||||
\(853\) | −18.4377 | −0.631295 | −0.315647 | − | 0.948877i | \(-0.602222\pi\) | ||||
−0.315647 | + | 0.948877i | \(0.602222\pi\) | |||||||
\(854\) | 10.6525 | 0.364520 | ||||||||
\(855\) | 8.47214 | 0.289741 | ||||||||
\(856\) | 16.1803 | 0.553033 | ||||||||
\(857\) | 57.1935 | 1.95369 | 0.976846 | − | 0.213942i | \(-0.0686305\pi\) | ||||
0.976846 | + | 0.213942i | \(0.0686305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0557 | −0.377217 | −0.188608 | − | 0.982052i | \(-0.560398\pi\) | ||||
−0.188608 | + | 0.982052i | \(0.560398\pi\) | |||||||
\(860\) | −15.7082 | −0.535645 | ||||||||
\(861\) | −1.52786 | −0.0520695 | ||||||||
\(862\) | 11.9098 | 0.405650 | ||||||||
\(863\) | 3.05573 | 0.104018 | 0.0520091 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520091 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(864\) | 23.2918 | 0.792403 | ||||||||
\(865\) | −1.56231 | −0.0531200 | ||||||||
\(866\) | 26.9098 | 0.914433 | ||||||||
\(867\) | 9.00000 | 0.305656 | ||||||||
\(868\) | 9.70820 | 0.329518 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.18034 | 0.0400173 | ||||||||
\(871\) | −37.7771 | −1.28003 | ||||||||
\(872\) | 25.7771 | 0.872922 | ||||||||
\(873\) | 40.1246 | 1.35801 | ||||||||
\(874\) | −32.3607 | −1.09462 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −11.8328 | −0.399794 | ||||||||
\(877\) | −55.0132 | −1.85766 | −0.928831 | − | 0.370503i | \(-0.879185\pi\) | ||||
−0.928831 | + | 0.370503i | \(0.879185\pi\) | |||||||
\(878\) | −9.59675 | −0.323875 | ||||||||
\(879\) | 5.81966 | 0.196292 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.23607 | −0.176408 | −0.0882038 | − | 0.996102i | \(-0.528113\pi\) | ||||
−0.0882038 | + | 0.996102i | \(0.528113\pi\) | |||||||
\(882\) | −5.85410 | −0.197118 | ||||||||
\(883\) | −10.1803 | −0.342596 | −0.171298 | − | 0.985219i | \(-0.554796\pi\) | ||||
−0.171298 | + | 0.985219i | \(0.554796\pi\) | |||||||
\(884\) | 77.8328 | 2.61780 | ||||||||
\(885\) | 5.70820 | 0.191879 | ||||||||
\(886\) | −7.48529 | −0.251473 | ||||||||
\(887\) | 21.1459 | 0.710010 | 0.355005 | − | 0.934864i | \(-0.384479\pi\) | ||||
0.355005 | + | 0.934864i | \(0.384479\pi\) | |||||||
\(888\) | −10.0000 | −0.335578 | ||||||||
\(889\) | −9.23607 | −0.309768 | ||||||||
\(890\) | −28.5410 | −0.956697 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.58359 | 0.153470 | ||||||||
\(893\) | −3.70820 | −0.124090 | ||||||||
\(894\) | 24.6738 | 0.825214 | ||||||||
\(895\) | −19.6180 | −0.655759 | ||||||||
\(896\) | −15.6525 | −0.522913 | ||||||||
\(897\) | 12.7639 | 0.426175 | ||||||||
\(898\) | −20.7295 | −0.691752 | ||||||||
\(899\) | −2.76393 | −0.0921823 | ||||||||
\(900\) | −7.85410 | −0.261803 | ||||||||
\(901\) | 8.58359 | 0.285961 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.23607 | 0.107690 | ||||||||
\(904\) | 23.4164 | 0.778818 | ||||||||
\(905\) | −5.52786 | −0.183752 | ||||||||
\(906\) | 0.527864 | 0.0175371 | ||||||||
\(907\) | 27.8885 | 0.926024 | 0.463012 | − | 0.886352i | \(-0.346769\pi\) | ||||
0.463012 | + | 0.886352i | \(0.346769\pi\) | |||||||
\(908\) | 32.3951 | 1.07507 | ||||||||
\(909\) | −35.8885 | −1.19035 | ||||||||
\(910\) | 10.3262 | 0.342311 | ||||||||
\(911\) | −1.50658 | −0.0499151 | −0.0249576 | − | 0.999689i | \(-0.507945\pi\) | ||||
−0.0249576 | + | 0.999689i | \(0.507945\pi\) | |||||||
\(912\) | −2.00000 | −0.0662266 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 84.4721 | 2.79409 | ||||||||
\(915\) | −2.94427 | −0.0973346 | ||||||||
\(916\) | −74.2918 | −2.45467 | ||||||||
\(917\) | −8.00000 | −0.264183 | ||||||||
\(918\) | 43.6180 | 1.43961 | ||||||||
\(919\) | −2.27051 | −0.0748972 | −0.0374486 | − | 0.999299i | \(-0.511923\pi\) | ||||
−0.0374486 | + | 0.999299i | \(0.511923\pi\) | |||||||
\(920\) | 10.0000 | 0.329690 | ||||||||
\(921\) | 12.7082 | 0.418750 | ||||||||
\(922\) | −36.4296 | −1.19974 | ||||||||
\(923\) | −75.3951 | −2.48166 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.23607 | −0.237920 | ||||||||
\(926\) | −38.2918 | −1.25835 | ||||||||
\(927\) | 45.3607 | 1.48984 | ||||||||
\(928\) | 5.72949 | 0.188080 | ||||||||
\(929\) | −17.8885 | −0.586904 | −0.293452 | − | 0.955974i | \(-0.594804\pi\) | ||||
−0.293452 | + | 0.955974i | \(0.594804\pi\) | |||||||
\(930\) | −4.47214 | −0.146647 | ||||||||
\(931\) | 3.23607 | 0.106058 | ||||||||
\(932\) | −19.9574 | −0.653727 | ||||||||
\(933\) | 8.11146 | 0.265557 | ||||||||
\(934\) | −72.2837 | −2.36519 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 27.0344 | 0.883648 | ||||||||
\(937\) | −0.549150 | −0.0179400 | −0.00896998 | − | 0.999960i | \(-0.502855\pi\) | ||||
−0.00896998 | + | 0.999960i | \(0.502855\pi\) | |||||||
\(938\) | 18.2918 | 0.597248 | ||||||||
\(939\) | −11.1246 | −0.363038 | ||||||||
\(940\) | 3.43769 | 0.112125 | ||||||||
\(941\) | 30.5410 | 0.995609 | 0.497804 | − | 0.867289i | \(-0.334140\pi\) | ||||
0.497804 | + | 0.867289i | \(0.334140\pi\) | |||||||
\(942\) | −22.2361 | −0.724490 | ||||||||
\(943\) | 11.0557 | 0.360024 | ||||||||
\(944\) | 9.23607 | 0.300608 | ||||||||
\(945\) | 3.47214 | 0.112949 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.0689 | 1.10709 | 0.553545 | − | 0.832819i | \(-0.313275\pi\) | ||||
0.553545 | + | 0.832819i | \(0.313275\pi\) | |||||||
\(948\) | −20.0213 | −0.650261 | ||||||||
\(949\) | 29.4721 | 0.956706 | ||||||||
\(950\) | 7.23607 | 0.234769 | ||||||||
\(951\) | −13.3050 | −0.431443 | ||||||||
\(952\) | −12.5623 | −0.407147 | ||||||||
\(953\) | −42.9443 | −1.39110 | −0.695551 | − | 0.718477i | \(-0.744840\pi\) | ||||
−0.695551 | + | 0.718477i | \(0.744840\pi\) | |||||||
\(954\) | 8.94427 | 0.289581 | ||||||||
\(955\) | −23.0902 | −0.747180 | ||||||||
\(956\) | −74.9361 | −2.42361 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50.6525 | −1.63651 | ||||||||
\(959\) | −11.4164 | −0.368655 | ||||||||
\(960\) | 8.03444 | 0.259310 | ||||||||
\(961\) | −20.5279 | −0.662189 | ||||||||
\(962\) | 74.7214 | 2.40911 | ||||||||
\(963\) | −18.9443 | −0.610471 | ||||||||
\(964\) | 51.3738 | 1.65464 | ||||||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | −6.18034 | −0.198849 | ||||||||
\(967\) | 16.7639 | 0.539092 | 0.269546 | − | 0.962988i | \(-0.413126\pi\) | ||||
0.269546 | + | 0.962988i | \(0.413126\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.2361 | −0.360955 | ||||||||
\(970\) | 34.2705 | 1.10036 | ||||||||
\(971\) | −2.58359 | −0.0829114 | −0.0414557 | − | 0.999140i | \(-0.513200\pi\) | ||||
−0.0414557 | + | 0.999140i | \(0.513200\pi\) | |||||||
\(972\) | 41.8328 | 1.34179 | ||||||||
\(973\) | −5.52786 | −0.177215 | ||||||||
\(974\) | −4.06888 | −0.130375 | ||||||||
\(975\) | −2.85410 | −0.0914044 | ||||||||
\(976\) | −4.76393 | −0.152490 | ||||||||
\(977\) | 41.2361 | 1.31926 | 0.659629 | − | 0.751591i | \(-0.270713\pi\) | ||||
0.659629 | + | 0.751591i | \(0.270713\pi\) | |||||||
\(978\) | −30.6525 | −0.980158 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.00000 | −0.0958315 | ||||||||
\(981\) | −30.1803 | −0.963584 | ||||||||
\(982\) | −4.72136 | −0.150665 | ||||||||
\(983\) | −27.9787 | −0.892382 | −0.446191 | − | 0.894938i | \(-0.647220\pi\) | ||||
−0.446191 | + | 0.894938i | \(0.647220\pi\) | |||||||
\(984\) | −3.41641 | −0.108911 | ||||||||
\(985\) | −12.0000 | −0.382352 | ||||||||
\(986\) | 10.7295 | 0.341697 | ||||||||
\(987\) | −0.708204 | −0.0225424 | ||||||||
\(988\) | −44.8328 | −1.42632 | ||||||||
\(989\) | −23.4164 | −0.744598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8541 | 0.440090 | 0.220045 | − | 0.975490i | \(-0.429380\pi\) | ||||
0.220045 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(992\) | −21.7082 | −0.689236 | ||||||||
\(993\) | −11.4377 | −0.362964 | ||||||||
\(994\) | 36.5066 | 1.15792 | ||||||||
\(995\) | 18.0000 | 0.570638 | ||||||||
\(996\) | −17.7295 | −0.561780 | ||||||||
\(997\) | 25.2148 | 0.798560 | 0.399280 | − | 0.916829i | \(-0.369260\pi\) | ||||
0.399280 | + | 0.916829i | \(0.369260\pi\) | |||||||
\(998\) | −51.5066 | −1.63041 | ||||||||
\(999\) | 25.1246 | 0.794908 |
(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 | 4235.2.a.k.1.2 | 2 | ||
11.2 | odd | 10 | 385.2.n.b.246.1 | yes | 4 | ||
11.6 | odd | 10 | 385.2.n.b.36.1 | ✓ | 4 | ||
11.10 | odd | 2 | 4235.2.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.n.b.36.1 | ✓ | 4 | 11.6 | odd | 10 | ||
385.2.n.b.246.1 | yes | 4 | 11.2 | odd | 10 | ||
4235.2.a.j.1.1 | 2 | 11.10 | odd | 2 | |||
4235.2.a.k.1.2 | 2 | 1.1 | even | 1 | trivial |