Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(1,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(7.54586299101\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 945.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.61803 | −0.511667 | ||||||||
\(11\) | −4.23607 | −1.27722 | −0.638611 | − | 0.769529i | \(-0.720491\pi\) | ||||
−0.638611 | + | 0.769529i | \(0.720491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.38197 | 0.383288 | 0.191644 | − | 0.981464i | \(-0.438618\pi\) | ||||
0.191644 | + | 0.981464i | \(0.438618\pi\) | |||||||
\(14\) | −1.61803 | −0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −1.61803 | −0.392431 | −0.196215 | − | 0.980561i | \(-0.562865\pi\) | ||||
−0.196215 | + | 0.980561i | \(0.562865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.09017 | −1.62660 | −0.813298 | − | 0.581847i | \(-0.802330\pi\) | ||||
−0.813298 | + | 0.581847i | \(0.802330\pi\) | |||||||
\(20\) | −0.618034 | −0.138197 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.85410 | −1.46130 | ||||||||
\(23\) | −5.38197 | −1.12222 | −0.561109 | − | 0.827742i | \(-0.689625\pi\) | ||||
−0.561109 | + | 0.827742i | \(0.689625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.23607 | 0.438529 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.618034 | −0.116797 | ||||||||
\(29\) | 9.56231 | 1.77568 | 0.887838 | − | 0.460157i | \(-0.152207\pi\) | ||||
0.887838 | + | 0.460157i | \(0.152207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.70820 | 1.20483 | 0.602414 | − | 0.798183i | \(-0.294205\pi\) | ||||
0.602414 | + | 0.798183i | \(0.294205\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.61803 | −0.448989 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.70820 | 1.10282 | 0.551411 | − | 0.834234i | \(-0.314090\pi\) | ||||
0.551411 | + | 0.834234i | \(0.314090\pi\) | |||||||
\(38\) | −11.4721 | −1.86103 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.23607 | 0.353553 | ||||||||
\(41\) | −8.09017 | −1.26347 | −0.631736 | − | 0.775183i | \(-0.717657\pi\) | ||||
−0.631736 | + | 0.775183i | \(0.717657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.94427 | −1.51649 | −0.758244 | − | 0.651971i | \(-0.773942\pi\) | ||||
−0.758244 | + | 0.651971i | \(0.773942\pi\) | |||||||
\(44\) | −2.61803 | −0.394683 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.70820 | −1.28395 | ||||||||
\(47\) | −11.0000 | −1.60451 | −0.802257 | − | 0.596978i | \(-0.796368\pi\) | ||||
−0.802257 | + | 0.596978i | \(0.796368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.61803 | 0.228825 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.854102 | 0.118443 | ||||||||
\(53\) | 4.38197 | 0.601909 | 0.300955 | − | 0.953638i | \(-0.402695\pi\) | ||||
0.300955 | + | 0.953638i | \(0.402695\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.23607 | 0.571191 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.4721 | 2.03159 | ||||||||
\(59\) | −1.29180 | −0.168178 | −0.0840888 | − | 0.996458i | \(-0.526798\pi\) | ||||
−0.0840888 | + | 0.996458i | \(0.526798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8541 | −1.77384 | −0.886918 | − | 0.461927i | \(-0.847158\pi\) | ||||
−0.886918 | + | 0.461927i | \(0.847158\pi\) | |||||||
\(62\) | 10.8541 | 1.37847 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −1.38197 | −0.171412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3262 | 1.38372 | 0.691860 | − | 0.722032i | \(-0.256791\pi\) | ||||
0.691860 | + | 0.722032i | \(0.256791\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.61803 | 0.193392 | ||||||||
\(71\) | −3.85410 | −0.457398 | −0.228699 | − | 0.973497i | \(-0.573447\pi\) | ||||
−0.228699 | + | 0.973497i | \(0.573447\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9443 | 1.63205 | 0.816027 | − | 0.578014i | \(-0.196172\pi\) | ||||
0.816027 | + | 0.578014i | \(0.196172\pi\) | |||||||
\(74\) | 10.8541 | 1.26176 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.38197 | −0.502646 | ||||||||
\(77\) | 4.23607 | 0.482745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.61803 | 0.632078 | 0.316039 | − | 0.948746i | \(-0.397647\pi\) | ||||
0.316039 | + | 0.948746i | \(0.397647\pi\) | |||||||
\(80\) | 4.85410 | 0.542705 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.0902 | −1.44557 | ||||||||
\(83\) | −10.7082 | −1.17538 | −0.587689 | − | 0.809087i | \(-0.699962\pi\) | ||||
−0.587689 | + | 0.809087i | \(0.699962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.61803 | 0.175500 | ||||||||
\(86\) | −16.0902 | −1.73505 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.47214 | 1.00973 | ||||||||
\(89\) | −1.47214 | −0.156046 | −0.0780230 | − | 0.996952i | \(-0.524861\pi\) | ||||
−0.0780230 | + | 0.996952i | \(0.524861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.38197 | −0.144869 | ||||||||
\(92\) | −3.32624 | −0.346784 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.7984 | −1.83576 | ||||||||
\(95\) | 7.09017 | 0.727436 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.32624 | −0.337728 | −0.168864 | − | 0.985639i | \(-0.554010\pi\) | ||||
−0.168864 | + | 0.985639i | \(0.554010\pi\) | |||||||
\(98\) | 1.61803 | 0.163446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.618034 | 0.0618034 | ||||||||
\(101\) | −5.52786 | −0.550043 | −0.275022 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275022 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6180 | 1.04623 | 0.523113 | − | 0.852263i | \(-0.324771\pi\) | ||||
0.523113 | + | 0.852263i | \(0.324771\pi\) | |||||||
\(104\) | −3.09017 | −0.303016 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.09017 | 0.688658 | ||||||||
\(107\) | 2.70820 | 0.261812 | 0.130906 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130906 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5623 | 1.20325 | 0.601625 | − | 0.798778i | \(-0.294520\pi\) | ||||
0.601625 | + | 0.798778i | \(0.294520\pi\) | |||||||
\(110\) | 6.85410 | 0.653513 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.85410 | 0.458670 | ||||||||
\(113\) | −5.85410 | −0.550708 | −0.275354 | − | 0.961343i | \(-0.588795\pi\) | ||||
−0.275354 | + | 0.961343i | \(0.588795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.38197 | 0.501871 | ||||||||
\(116\) | 5.90983 | 0.548714 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.09017 | −0.192416 | ||||||||
\(119\) | 1.61803 | 0.148325 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.94427 | 0.631297 | ||||||||
\(122\) | −22.4164 | −2.02949 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.14590 | 0.372313 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0901699 | 0.00800129 | 0.00400064 | − | 0.999992i | \(-0.498727\pi\) | ||||
0.00400064 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.23607 | −0.196116 | ||||||||
\(131\) | −4.38197 | −0.382854 | −0.191427 | − | 0.981507i | \(-0.561312\pi\) | ||||
−0.191427 | + | 0.981507i | \(0.561312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.09017 | 0.614796 | ||||||||
\(134\) | 18.3262 | 1.58315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.61803 | 0.310244 | ||||||||
\(137\) | −13.8885 | −1.18658 | −0.593289 | − | 0.804989i | \(-0.702171\pi\) | ||||
−0.593289 | + | 0.804989i | \(0.702171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.18034 | 0.269753 | 0.134876 | − | 0.990862i | \(-0.456936\pi\) | ||||
0.134876 | + | 0.990862i | \(0.456936\pi\) | |||||||
\(140\) | 0.618034 | 0.0522334 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.23607 | −0.523319 | ||||||||
\(143\) | −5.85410 | −0.489545 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.56231 | −0.794106 | ||||||||
\(146\) | 22.5623 | 1.86727 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.14590 | 0.340791 | ||||||||
\(149\) | 15.7984 | 1.29425 | 0.647127 | − | 0.762383i | \(-0.275971\pi\) | ||||
0.647127 | + | 0.762383i | \(0.275971\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0557281 | −0.00453509 | −0.00226754 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226754 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(152\) | 15.8541 | 1.28594 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.85410 | 0.552319 | ||||||||
\(155\) | −6.70820 | −0.538816 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.23607 | −0.417884 | −0.208942 | − | 0.977928i | \(-0.567002\pi\) | ||||
−0.208942 | + | 0.977928i | \(0.567002\pi\) | |||||||
\(158\) | 9.09017 | 0.723175 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.38197 | 0.267368 | ||||||||
\(161\) | 5.38197 | 0.424158 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.94427 | −0.230613 | −0.115307 | − | 0.993330i | \(-0.536785\pi\) | ||||
−0.115307 | + | 0.993330i | \(0.536785\pi\) | |||||||
\(164\) | −5.00000 | −0.390434 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.3262 | −1.34478 | ||||||||
\(167\) | 7.47214 | 0.578211 | 0.289106 | − | 0.957297i | \(-0.406642\pi\) | ||||
0.289106 | + | 0.957297i | \(0.406642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0902 | −0.853090 | ||||||||
\(170\) | 2.61803 | 0.200794 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.14590 | −0.468620 | ||||||||
\(173\) | −11.4721 | −0.872210 | −0.436105 | − | 0.899896i | \(-0.643642\pi\) | ||||
−0.436105 | + | 0.899896i | \(0.643642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 20.5623 | 1.54994 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.38197 | −0.178536 | ||||||||
\(179\) | 7.00000 | 0.523205 | 0.261602 | − | 0.965176i | \(-0.415749\pi\) | ||||
0.261602 | + | 0.965176i | \(0.415749\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4721 | −1.44735 | −0.723676 | − | 0.690140i | \(-0.757549\pi\) | ||||
−0.723676 | + | 0.690140i | \(0.757549\pi\) | |||||||
\(182\) | −2.23607 | −0.165748 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0344 | 0.887191 | ||||||||
\(185\) | −6.70820 | −0.493197 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.85410 | 0.501222 | ||||||||
\(188\) | −6.79837 | −0.495822 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.4721 | 0.832276 | ||||||||
\(191\) | −18.7984 | −1.36020 | −0.680101 | − | 0.733118i | \(-0.738064\pi\) | ||||
−0.680101 | + | 0.733118i | \(0.738064\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.854102 | −0.0614796 | −0.0307398 | − | 0.999527i | \(-0.509786\pi\) | ||||
−0.0307398 | + | 0.999527i | \(0.509786\pi\) | |||||||
\(194\) | −5.38197 | −0.386403 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | 19.4721 | 1.38733 | 0.693666 | − | 0.720297i | \(-0.255994\pi\) | ||||
0.693666 | + | 0.720297i | \(0.255994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.61803 | 0.114699 | 0.0573497 | − | 0.998354i | \(-0.481735\pi\) | ||||
0.0573497 | + | 0.998354i | \(0.481735\pi\) | |||||||
\(200\) | −2.23607 | −0.158114 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.94427 | −0.629317 | ||||||||
\(203\) | −9.56231 | −0.671142 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.09017 | 0.565042 | ||||||||
\(206\) | 17.1803 | 1.19701 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.70820 | −0.465130 | ||||||||
\(209\) | 30.0344 | 2.07753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.1246 | −1.17891 | −0.589453 | − | 0.807802i | \(-0.700657\pi\) | ||||
−0.589453 | + | 0.807802i | \(0.700657\pi\) | |||||||
\(212\) | 2.70820 | 0.186000 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.38197 | 0.299545 | ||||||||
\(215\) | 9.94427 | 0.678194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.70820 | −0.455383 | ||||||||
\(218\) | 20.3262 | 1.37667 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.61803 | 0.176508 | ||||||||
\(221\) | −2.23607 | −0.150414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.47214 | 0.500371 | 0.250186 | − | 0.968198i | \(-0.419508\pi\) | ||||
0.250186 | + | 0.968198i | \(0.419508\pi\) | |||||||
\(224\) | 3.38197 | 0.225967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.47214 | −0.630077 | ||||||||
\(227\) | −7.43769 | −0.493657 | −0.246829 | − | 0.969059i | \(-0.579388\pi\) | ||||
−0.246829 | + | 0.969059i | \(0.579388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.9443 | −1.18579 | −0.592895 | − | 0.805279i | \(-0.702015\pi\) | ||||
−0.592895 | + | 0.805279i | \(0.702015\pi\) | |||||||
\(230\) | 8.70820 | 0.574202 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.3820 | −1.40379 | ||||||||
\(233\) | −17.0902 | −1.11961 | −0.559807 | − | 0.828623i | \(-0.689125\pi\) | ||||
−0.559807 | + | 0.828623i | \(0.689125\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0000 | 0.717561 | ||||||||
\(236\) | −0.798374 | −0.0519697 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.61803 | 0.169702 | ||||||||
\(239\) | −11.6525 | −0.753736 | −0.376868 | − | 0.926267i | \(-0.622999\pi\) | ||||
−0.376868 | + | 0.926267i | \(0.622999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.61803 | −0.490721 | −0.245360 | − | 0.969432i | \(-0.578906\pi\) | ||||
−0.245360 | + | 0.969432i | \(0.578906\pi\) | |||||||
\(242\) | 11.2361 | 0.722282 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.56231 | −0.548145 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.79837 | −0.623456 | ||||||||
\(248\) | −15.0000 | −0.952501 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.61803 | −0.102333 | ||||||||
\(251\) | −1.23607 | −0.0780199 | −0.0390100 | − | 0.999239i | \(-0.512420\pi\) | ||||
−0.0390100 | + | 0.999239i | \(0.512420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.7984 | 1.43332 | ||||||||
\(254\) | 0.145898 | 0.00915446 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 8.94427 | 0.557928 | 0.278964 | − | 0.960302i | \(-0.410009\pi\) | ||||
0.278964 | + | 0.960302i | \(0.410009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.70820 | −0.416828 | ||||||||
\(260\) | −0.854102 | −0.0529692 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.09017 | −0.438032 | ||||||||
\(263\) | 30.7426 | 1.89567 | 0.947836 | − | 0.318757i | \(-0.103265\pi\) | ||||
0.947836 | + | 0.318757i | \(0.103265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.38197 | −0.269182 | ||||||||
\(266\) | 11.4721 | 0.703402 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.00000 | 0.427593 | ||||||||
\(269\) | −10.7082 | −0.652891 | −0.326445 | − | 0.945216i | \(-0.605851\pi\) | ||||
−0.326445 | + | 0.945216i | \(0.605851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.5623 | −1.49205 | −0.746027 | − | 0.665916i | \(-0.768041\pi\) | ||||
−0.746027 | + | 0.665916i | \(0.768041\pi\) | |||||||
\(272\) | 7.85410 | 0.476225 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.4721 | −1.35759 | ||||||||
\(275\) | −4.23607 | −0.255445 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.67376 | 0.280819 | 0.140410 | − | 0.990094i | \(-0.455158\pi\) | ||||
0.140410 | + | 0.990094i | \(0.455158\pi\) | |||||||
\(278\) | 5.14590 | 0.308630 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.23607 | −0.133631 | ||||||||
\(281\) | 13.6180 | 0.812384 | 0.406192 | − | 0.913788i | \(-0.366856\pi\) | ||||
0.406192 | + | 0.913788i | \(0.366856\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.1459 | 1.25699 | 0.628497 | − | 0.777812i | \(-0.283671\pi\) | ||||
0.628497 | + | 0.777812i | \(0.283671\pi\) | |||||||
\(284\) | −2.38197 | −0.141344 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.47214 | −0.560099 | ||||||||
\(287\) | 8.09017 | 0.477548 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3820 | −0.845998 | ||||||||
\(290\) | −15.4721 | −0.908555 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.61803 | 0.504332 | ||||||||
\(293\) | 6.29180 | 0.367571 | 0.183785 | − | 0.982966i | \(-0.441165\pi\) | ||||
0.183785 | + | 0.982966i | \(0.441165\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.29180 | 0.0752113 | ||||||||
\(296\) | −15.0000 | −0.871857 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.5623 | 1.48078 | ||||||||
\(299\) | −7.43769 | −0.430133 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.94427 | 0.573178 | ||||||||
\(302\) | −0.0901699 | −0.00518870 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 34.4164 | 1.97392 | ||||||||
\(305\) | 13.8541 | 0.793284 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.4164 | 1.10815 | 0.554076 | − | 0.832466i | \(-0.313072\pi\) | ||||
0.554076 | + | 0.832466i | \(0.313072\pi\) | |||||||
\(308\) | 2.61803 | 0.149176 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.8541 | −0.616472 | ||||||||
\(311\) | −14.3262 | −0.812366 | −0.406183 | − | 0.913792i | \(-0.633141\pi\) | ||||
−0.406183 | + | 0.913792i | \(0.633141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.1803 | −1.31023 | −0.655115 | − | 0.755529i | \(-0.727380\pi\) | ||||
−0.655115 | + | 0.755529i | \(0.727380\pi\) | |||||||
\(314\) | −8.47214 | −0.478110 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.47214 | 0.195323 | ||||||||
\(317\) | 6.05573 | 0.340124 | 0.170062 | − | 0.985433i | \(-0.445603\pi\) | ||||
0.170062 | + | 0.985433i | \(0.445603\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −40.5066 | −2.26793 | ||||||||
\(320\) | −4.23607 | −0.236803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.70820 | 0.485289 | ||||||||
\(323\) | 11.4721 | 0.638327 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.38197 | 0.0766577 | ||||||||
\(326\) | −4.76393 | −0.263850 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.0902 | 0.998863 | ||||||||
\(329\) | 11.0000 | 0.606450 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.8541 | −1.75086 | −0.875430 | − | 0.483345i | \(-0.839422\pi\) | ||||
−0.875430 | + | 0.483345i | \(0.839422\pi\) | |||||||
\(332\) | −6.61803 | −0.363212 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0902 | 0.661545 | ||||||||
\(335\) | −11.3262 | −0.618818 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.7426 | −1.72913 | −0.864566 | − | 0.502519i | \(-0.832407\pi\) | ||||
−0.864566 | + | 0.502519i | \(0.832407\pi\) | |||||||
\(338\) | −17.9443 | −0.976040 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | −28.4164 | −1.53883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 22.2361 | 1.19889 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.5623 | −0.997916 | ||||||||
\(347\) | 12.7639 | 0.685204 | 0.342602 | − | 0.939481i | \(-0.388692\pi\) | ||||
0.342602 | + | 0.939481i | \(0.388692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.3607 | 1.67870 | 0.839349 | − | 0.543592i | \(-0.182936\pi\) | ||||
0.839349 | + | 0.543592i | \(0.182936\pi\) | |||||||
\(350\) | −1.61803 | −0.0864876 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.3262 | 0.763591 | ||||||||
\(353\) | −11.6738 | −0.621332 | −0.310666 | − | 0.950519i | \(-0.600552\pi\) | ||||
−0.310666 | + | 0.950519i | \(0.600552\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.85410 | 0.204554 | ||||||||
\(356\) | −0.909830 | −0.0482209 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.3262 | 0.598610 | ||||||||
\(359\) | −36.4164 | −1.92198 | −0.960992 | − | 0.276575i | \(-0.910800\pi\) | ||||
−0.960992 | + | 0.276575i | \(0.910800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.2705 | 1.64582 | ||||||||
\(362\) | −31.5066 | −1.65595 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.854102 | −0.0447671 | ||||||||
\(365\) | −13.9443 | −0.729877 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.8541 | −0.775378 | −0.387689 | − | 0.921790i | \(-0.626727\pi\) | ||||
−0.387689 | + | 0.921790i | \(0.626727\pi\) | |||||||
\(368\) | 26.1246 | 1.36184 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.8541 | −0.564278 | ||||||||
\(371\) | −4.38197 | −0.227500 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.9787 | −0.879124 | −0.439562 | − | 0.898212i | \(-0.644866\pi\) | ||||
−0.439562 | + | 0.898212i | \(0.644866\pi\) | |||||||
\(374\) | 11.0902 | 0.573459 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.5967 | 1.26848 | ||||||||
\(377\) | 13.2148 | 0.680596 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8885 | 0.610673 | 0.305337 | − | 0.952244i | \(-0.401231\pi\) | ||||
0.305337 | + | 0.952244i | \(0.401231\pi\) | |||||||
\(380\) | 4.38197 | 0.224790 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −30.4164 | −1.55624 | ||||||||
\(383\) | 11.6525 | 0.595414 | 0.297707 | − | 0.954657i | \(-0.403778\pi\) | ||||
0.297707 | + | 0.954657i | \(0.403778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.23607 | −0.215890 | ||||||||
\(386\) | −1.38197 | −0.0703402 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.05573 | −0.104364 | ||||||||
\(389\) | −25.7984 | −1.30803 | −0.654015 | − | 0.756482i | \(-0.726917\pi\) | ||||
−0.654015 | + | 0.756482i | \(0.726917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.70820 | 0.440393 | ||||||||
\(392\) | −2.23607 | −0.112938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 31.5066 | 1.58728 | ||||||||
\(395\) | −5.61803 | −0.282674 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.05573 | 0.454494 | 0.227247 | − | 0.973837i | \(-0.427028\pi\) | ||||
0.227247 | + | 0.973837i | \(0.427028\pi\) | |||||||
\(398\) | 2.61803 | 0.131230 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.85410 | −0.242705 | ||||||||
\(401\) | 17.3820 | 0.868014 | 0.434007 | − | 0.900910i | \(-0.357099\pi\) | ||||
0.434007 | + | 0.900910i | \(0.357099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.27051 | 0.461797 | ||||||||
\(404\) | −3.41641 | −0.169973 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.4721 | −0.767869 | ||||||||
\(407\) | −28.4164 | −1.40855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0557 | −0.645564 | −0.322782 | − | 0.946473i | \(-0.604618\pi\) | ||||
−0.322782 | + | 0.946473i | \(0.604618\pi\) | |||||||
\(410\) | 13.0902 | 0.646477 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.56231 | 0.323302 | ||||||||
\(413\) | 1.29180 | 0.0635651 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.7082 | 0.525645 | ||||||||
\(416\) | −4.67376 | −0.229150 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 48.5967 | 2.37694 | ||||||||
\(419\) | −7.47214 | −0.365038 | −0.182519 | − | 0.983202i | \(-0.558425\pi\) | ||||
−0.182519 | + | 0.983202i | \(0.558425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.43769 | 0.411228 | 0.205614 | − | 0.978633i | \(-0.434081\pi\) | ||||
0.205614 | + | 0.978633i | \(0.434081\pi\) | |||||||
\(422\) | −27.7082 | −1.34881 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.79837 | −0.475851 | ||||||||
\(425\) | −1.61803 | −0.0784862 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8541 | 0.670447 | ||||||||
\(428\) | 1.67376 | 0.0809043 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.0902 | 0.775937 | ||||||||
\(431\) | −30.4508 | −1.46677 | −0.733383 | − | 0.679816i | \(-0.762060\pi\) | ||||
−0.733383 | + | 0.679816i | \(0.762060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.2148 | −1.01952 | −0.509759 | − | 0.860317i | \(-0.670265\pi\) | ||||
−0.509759 | + | 0.860317i | \(0.670265\pi\) | |||||||
\(434\) | −10.8541 | −0.521014 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.76393 | 0.371825 | ||||||||
\(437\) | 38.1591 | 1.82540 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2918 | 0.538928 | 0.269464 | − | 0.963010i | \(-0.413153\pi\) | ||||
0.269464 | + | 0.963010i | \(0.413153\pi\) | |||||||
\(440\) | −9.47214 | −0.451566 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.61803 | −0.172092 | ||||||||
\(443\) | 40.6869 | 1.93309 | 0.966547 | − | 0.256490i | \(-0.0825661\pi\) | ||||
0.966547 | + | 0.256490i | \(0.0825661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.47214 | 0.0697859 | ||||||||
\(446\) | 12.0902 | 0.572486 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.23607 | −0.200135 | ||||||||
\(449\) | −20.4721 | −0.966140 | −0.483070 | − | 0.875582i | \(-0.660478\pi\) | ||||
−0.483070 | + | 0.875582i | \(0.660478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.2705 | 1.61374 | ||||||||
\(452\) | −3.61803 | −0.170178 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.0344 | −0.564804 | ||||||||
\(455\) | 1.38197 | 0.0647876 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3262 | 0.810487 | 0.405244 | − | 0.914209i | \(-0.367187\pi\) | ||||
0.405244 | + | 0.914209i | \(0.367187\pi\) | |||||||
\(458\) | −29.0344 | −1.35669 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.32624 | 0.155087 | ||||||||
\(461\) | 22.7984 | 1.06183 | 0.530913 | − | 0.847426i | \(-0.321849\pi\) | ||||
0.530913 | + | 0.847426i | \(0.321849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.618034 | −0.0287225 | −0.0143612 | − | 0.999897i | \(-0.504571\pi\) | ||||
−0.0143612 | + | 0.999897i | \(0.504571\pi\) | |||||||
\(464\) | −46.4164 | −2.15483 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.6525 | −1.28098 | ||||||||
\(467\) | −16.9443 | −0.784087 | −0.392044 | − | 0.919947i | \(-0.628232\pi\) | ||||
−0.392044 | + | 0.919947i | \(0.628232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.3262 | −0.522997 | ||||||||
\(470\) | 17.7984 | 0.820978 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.88854 | 0.132956 | ||||||||
\(473\) | 42.1246 | 1.93689 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.09017 | −0.325319 | ||||||||
\(476\) | 1.00000 | 0.0458349 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.8541 | −0.862367 | ||||||||
\(479\) | −25.9098 | −1.18385 | −0.591925 | − | 0.805993i | \(-0.701632\pi\) | ||||
−0.591925 | + | 0.805993i | \(0.701632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.27051 | 0.422699 | ||||||||
\(482\) | −12.3262 | −0.561445 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.29180 | 0.195082 | ||||||||
\(485\) | 3.32624 | 0.151037 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.5279 | −0.703635 | −0.351817 | − | 0.936069i | \(-0.614436\pi\) | ||||
−0.351817 | + | 0.936069i | \(0.614436\pi\) | |||||||
\(488\) | 30.9787 | 1.40234 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.61803 | −0.0730953 | ||||||||
\(491\) | 19.5066 | 0.880320 | 0.440160 | − | 0.897919i | \(-0.354922\pi\) | ||||
0.440160 | + | 0.897919i | \(0.354922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.4721 | −0.696830 | ||||||||
\(494\) | −15.8541 | −0.713310 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −32.5623 | −1.46209 | ||||||||
\(497\) | 3.85410 | 0.172880 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.36068 | 0.150445 | 0.0752223 | − | 0.997167i | \(-0.476033\pi\) | ||||
0.0752223 | + | 0.997167i | \(0.476033\pi\) | |||||||
\(500\) | −0.618034 | −0.0276393 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.00000 | −0.0892644 | ||||||||
\(503\) | −30.9098 | −1.37820 | −0.689101 | − | 0.724666i | \(-0.741994\pi\) | ||||
−0.689101 | + | 0.724666i | \(0.741994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.52786 | 0.245987 | ||||||||
\(506\) | 36.8885 | 1.63990 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.0557281 | 0.00247253 | ||||||||
\(509\) | −32.3050 | −1.43189 | −0.715946 | − | 0.698156i | \(-0.754004\pi\) | ||||
−0.715946 | + | 0.698156i | \(0.754004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.9443 | −0.616858 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.4721 | 0.638339 | ||||||||
\(515\) | −10.6180 | −0.467886 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.5967 | 2.04932 | ||||||||
\(518\) | −10.8541 | −0.476902 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.09017 | 0.135513 | ||||||||
\(521\) | 19.8328 | 0.868891 | 0.434446 | − | 0.900698i | \(-0.356944\pi\) | ||||
0.434446 | + | 0.900698i | \(0.356944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.20163 | −0.0525434 | −0.0262717 | − | 0.999655i | \(-0.508364\pi\) | ||||
−0.0262717 | + | 0.999655i | \(0.508364\pi\) | |||||||
\(524\) | −2.70820 | −0.118308 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.7426 | 2.16888 | ||||||||
\(527\) | −10.8541 | −0.472812 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.96556 | 0.259372 | ||||||||
\(530\) | −7.09017 | −0.307977 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.38197 | 0.189982 | ||||||||
\(533\) | −11.1803 | −0.484274 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.70820 | −0.117086 | ||||||||
\(536\) | −25.3262 | −1.09393 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.3262 | −0.746987 | ||||||||
\(539\) | −4.23607 | −0.182460 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5066 | −0.580693 | −0.290347 | − | 0.956922i | \(-0.593771\pi\) | ||||
−0.290347 | + | 0.956922i | \(0.593771\pi\) | |||||||
\(542\) | −39.7426 | −1.70709 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.47214 | 0.234616 | ||||||||
\(545\) | −12.5623 | −0.538110 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3607 | 0.827803 | 0.413901 | − | 0.910322i | \(-0.364166\pi\) | ||||
0.413901 | + | 0.910322i | \(0.364166\pi\) | |||||||
\(548\) | −8.58359 | −0.366673 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.85410 | −0.292260 | ||||||||
\(551\) | −67.7984 | −2.88831 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.61803 | −0.238903 | ||||||||
\(554\) | 7.56231 | 0.321292 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.96556 | 0.0833582 | ||||||||
\(557\) | 16.7984 | 0.711770 | 0.355885 | − | 0.934530i | \(-0.384179\pi\) | ||||
0.355885 | + | 0.934530i | \(0.384179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7426 | −0.581252 | ||||||||
\(560\) | −4.85410 | −0.205123 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.0344 | 0.929467 | ||||||||
\(563\) | −21.6869 | −0.913995 | −0.456997 | − | 0.889468i | \(-0.651075\pi\) | ||||
−0.456997 | + | 0.889468i | \(0.651075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.85410 | 0.246284 | ||||||||
\(566\) | 34.2148 | 1.43815 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.61803 | 0.361605 | ||||||||
\(569\) | 37.7639 | 1.58315 | 0.791573 | − | 0.611074i | \(-0.209262\pi\) | ||||
0.791573 | + | 0.611074i | \(0.209262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.25735 | 0.0526186 | 0.0263093 | − | 0.999654i | \(-0.491625\pi\) | ||||
0.0263093 | + | 0.999654i | \(0.491625\pi\) | |||||||
\(572\) | −3.61803 | −0.151278 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.0902 | 0.546373 | ||||||||
\(575\) | −5.38197 | −0.224443 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.1246 | 0.921060 | 0.460530 | − | 0.887644i | \(-0.347659\pi\) | ||||
0.460530 | + | 0.887644i | \(0.347659\pi\) | |||||||
\(578\) | −23.2705 | −0.967926 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.90983 | −0.245392 | ||||||||
\(581\) | 10.7082 | 0.444251 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.5623 | −0.768772 | ||||||||
\(584\) | −31.1803 | −1.29025 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.1803 | 0.420546 | ||||||||
\(587\) | 7.20163 | 0.297243 | 0.148621 | − | 0.988894i | \(-0.452516\pi\) | ||||
0.148621 | + | 0.988894i | \(0.452516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −47.5623 | −1.95977 | ||||||||
\(590\) | 2.09017 | 0.0860509 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −32.5623 | −1.33830 | ||||||||
\(593\) | 34.3050 | 1.40874 | 0.704368 | − | 0.709835i | \(-0.251231\pi\) | ||||
0.704368 | + | 0.709835i | \(0.251231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.61803 | −0.0663329 | ||||||||
\(596\) | 9.76393 | 0.399946 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.0344 | −0.492125 | ||||||||
\(599\) | 38.9443 | 1.59122 | 0.795610 | − | 0.605809i | \(-0.207151\pi\) | ||||
0.795610 | + | 0.605809i | \(0.207151\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.798374 | 0.0325663 | 0.0162832 | − | 0.999867i | \(-0.494817\pi\) | ||||
0.0162832 | + | 0.999867i | \(0.494817\pi\) | |||||||
\(602\) | 16.0902 | 0.655786 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.0344419 | −0.00140142 | ||||||||
\(605\) | −6.94427 | −0.282325 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4164 | 0.991031 | 0.495516 | − | 0.868599i | \(-0.334979\pi\) | ||||
0.495516 | + | 0.868599i | \(0.334979\pi\) | |||||||
\(608\) | 23.9787 | 0.972465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.4164 | 0.907614 | ||||||||
\(611\) | −15.2016 | −0.614992 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.29180 | −0.294513 | −0.147256 | − | 0.989098i | \(-0.547044\pi\) | ||||
−0.147256 | + | 0.989098i | \(0.547044\pi\) | |||||||
\(614\) | 31.4164 | 1.26786 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.47214 | −0.381643 | ||||||||
\(617\) | 37.7984 | 1.52171 | 0.760853 | − | 0.648925i | \(-0.224781\pi\) | ||||
0.760853 | + | 0.648925i | \(0.224781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.5410 | −1.91083 | −0.955417 | − | 0.295258i | \(-0.904594\pi\) | ||||
−0.955417 | + | 0.295258i | \(0.904594\pi\) | |||||||
\(620\) | −4.14590 | −0.166503 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.1803 | −0.929447 | ||||||||
\(623\) | 1.47214 | 0.0589799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −37.5066 | −1.49906 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.23607 | −0.129133 | ||||||||
\(629\) | −10.8541 | −0.432781 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.8885 | 1.66756 | 0.833778 | − | 0.552099i | \(-0.186173\pi\) | ||||
0.833778 | + | 0.552099i | \(0.186173\pi\) | |||||||
\(632\) | −12.5623 | −0.499702 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.79837 | 0.389143 | ||||||||
\(635\) | −0.0901699 | −0.00357829 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.38197 | 0.0547555 | ||||||||
\(638\) | −65.5410 | −2.59479 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.6180 | −0.538300 | ||||||||
\(641\) | 0.729490 | 0.0288131 | 0.0144066 | − | 0.999896i | \(-0.495414\pi\) | ||||
0.0144066 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.7426 | 1.64617 | 0.823085 | − | 0.567919i | \(-0.192251\pi\) | ||||
0.823085 | + | 0.567919i | \(0.192251\pi\) | |||||||
\(644\) | 3.32624 | 0.131072 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.5623 | 0.730324 | ||||||||
\(647\) | 13.0557 | 0.513274 | 0.256637 | − | 0.966508i | \(-0.417386\pi\) | ||||
0.256637 | + | 0.966508i | \(0.417386\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.47214 | 0.214800 | ||||||||
\(650\) | 2.23607 | 0.0877058 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.81966 | −0.0712634 | ||||||||
\(653\) | −6.03444 | −0.236146 | −0.118073 | − | 0.993005i | \(-0.537672\pi\) | ||||
−0.118073 | + | 0.993005i | \(0.537672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.38197 | 0.171218 | ||||||||
\(656\) | 39.2705 | 1.53326 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.7984 | 0.693853 | ||||||||
\(659\) | 0.763932 | 0.0297586 | 0.0148793 | − | 0.999889i | \(-0.495264\pi\) | ||||
0.0148793 | + | 0.999889i | \(0.495264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2148 | −0.630682 | −0.315341 | − | 0.948978i | \(-0.602119\pi\) | ||||
−0.315341 | + | 0.948978i | \(0.602119\pi\) | |||||||
\(662\) | −51.5410 | −2.00320 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.9443 | 0.929218 | ||||||||
\(665\) | −7.09017 | −0.274945 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51.4640 | −1.99269 | ||||||||
\(668\) | 4.61803 | 0.178677 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.3262 | −0.708004 | ||||||||
\(671\) | 58.6869 | 2.26558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.4721 | −1.79137 | −0.895685 | − | 0.444690i | \(-0.853314\pi\) | ||||
−0.895685 | + | 0.444690i | \(0.853314\pi\) | |||||||
\(674\) | −51.3607 | −1.97834 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.85410 | −0.263619 | ||||||||
\(677\) | 17.6525 | 0.678440 | 0.339220 | − | 0.940707i | \(-0.389837\pi\) | ||||
0.339220 | + | 0.940707i | \(0.389837\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.32624 | 0.127649 | ||||||||
\(680\) | −3.61803 | −0.138745 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −45.9787 | −1.76062 | ||||||||
\(683\) | 42.9787 | 1.64453 | 0.822267 | − | 0.569101i | \(-0.192709\pi\) | ||||
0.822267 | + | 0.569101i | \(0.192709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8885 | 0.530654 | ||||||||
\(686\) | −1.61803 | −0.0617768 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 48.2705 | 1.84030 | ||||||||
\(689\) | 6.05573 | 0.230705 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.5279 | −1.16133 | −0.580667 | − | 0.814141i | \(-0.697208\pi\) | ||||
−0.580667 | + | 0.814141i | \(0.697208\pi\) | |||||||
\(692\) | −7.09017 | −0.269528 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.6525 | 0.783957 | ||||||||
\(695\) | −3.18034 | −0.120637 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0902 | 0.495826 | ||||||||
\(698\) | 50.7426 | 1.92064 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.618034 | −0.0233595 | ||||||||
\(701\) | −6.88854 | −0.260177 | −0.130088 | − | 0.991502i | \(-0.541526\pi\) | ||||
−0.130088 | + | 0.991502i | \(0.541526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −47.5623 | −1.79385 | ||||||||
\(704\) | −17.9443 | −0.676300 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.8885 | −0.710880 | ||||||||
\(707\) | 5.52786 | 0.207897 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.59675 | −0.360413 | −0.180207 | − | 0.983629i | \(-0.557677\pi\) | ||||
−0.180207 | + | 0.983629i | \(0.557677\pi\) | |||||||
\(710\) | 6.23607 | 0.234035 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.29180 | 0.123365 | ||||||||
\(713\) | −36.1033 | −1.35208 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.85410 | 0.218931 | ||||||||
\(716\) | 4.32624 | 0.161679 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −58.9230 | −2.19899 | ||||||||
\(719\) | −12.9656 | −0.483534 | −0.241767 | − | 0.970334i | \(-0.577727\pi\) | ||||
−0.241767 | + | 0.970334i | \(0.577727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.6180 | −0.395436 | ||||||||
\(722\) | 50.5967 | 1.88302 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.0344 | −0.447257 | ||||||||
\(725\) | 9.56231 | 0.355135 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.4508 | −0.424689 | −0.212344 | − | 0.977195i | \(-0.568110\pi\) | ||||
−0.212344 | + | 0.977195i | \(0.568110\pi\) | |||||||
\(728\) | 3.09017 | 0.114529 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22.5623 | −0.835068 | ||||||||
\(731\) | 16.0902 | 0.595116 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5623 | 0.390128 | 0.195064 | − | 0.980791i | \(-0.437509\pi\) | ||||
0.195064 | + | 0.980791i | \(0.437509\pi\) | |||||||
\(734\) | −24.0344 | −0.887127 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.2016 | 0.670921 | ||||||||
\(737\) | −47.9787 | −1.76732 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6525 | −0.759714 | −0.379857 | − | 0.925045i | \(-0.624027\pi\) | ||||
−0.379857 | + | 0.925045i | \(0.624027\pi\) | |||||||
\(740\) | −4.14590 | −0.152406 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.09017 | −0.260288 | ||||||||
\(743\) | 3.32624 | 0.122028 | 0.0610139 | − | 0.998137i | \(-0.480567\pi\) | ||||
0.0610139 | + | 0.998137i | \(0.480567\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.7984 | −0.578808 | ||||||||
\(746\) | −27.4721 | −1.00583 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.23607 | 0.154886 | ||||||||
\(749\) | −2.70820 | −0.0989556 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.8885 | −1.74748 | −0.873739 | − | 0.486395i | \(-0.838312\pi\) | ||||
−0.873739 | + | 0.486395i | \(0.838312\pi\) | |||||||
\(752\) | 53.3951 | 1.94712 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.3820 | 0.778685 | ||||||||
\(755\) | 0.0557281 | 0.00202815 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.27051 | 0.227906 | 0.113953 | − | 0.993486i | \(-0.463649\pi\) | ||||
0.113953 | + | 0.993486i | \(0.463649\pi\) | |||||||
\(758\) | 19.2361 | 0.698685 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.8541 | −0.575089 | ||||||||
\(761\) | 9.96556 | 0.361251 | 0.180626 | − | 0.983552i | \(-0.442188\pi\) | ||||
0.180626 | + | 0.983552i | \(0.442188\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.5623 | −0.454786 | ||||||||
\(764\) | −11.6180 | −0.420326 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.8541 | 0.681226 | ||||||||
\(767\) | −1.78522 | −0.0644605 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.5967 | 0.814860 | 0.407430 | − | 0.913237i | \(-0.366425\pi\) | ||||
0.407430 | + | 0.913237i | \(0.366425\pi\) | |||||||
\(770\) | −6.85410 | −0.247005 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.527864 | −0.0189982 | ||||||||
\(773\) | 17.6738 | 0.635681 | 0.317841 | − | 0.948144i | \(-0.397042\pi\) | ||||
0.317841 | + | 0.948144i | \(0.397042\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.70820 | 0.240966 | ||||||||
\(776\) | 7.43769 | 0.266998 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.7426 | −1.49655 | ||||||||
\(779\) | 57.3607 | 2.05516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3262 | 0.584199 | ||||||||
\(782\) | 14.0902 | 0.503863 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | 5.23607 | 0.186883 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.23607 | −0.115353 | −0.0576767 | − | 0.998335i | \(-0.518369\pi\) | ||||
−0.0576767 | + | 0.998335i | \(0.518369\pi\) | |||||||
\(788\) | 12.0344 | 0.428709 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.09017 | −0.323414 | ||||||||
\(791\) | 5.85410 | 0.208148 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.1459 | −0.679891 | ||||||||
\(794\) | 14.6525 | 0.519997 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.00000 | 0.0354441 | ||||||||
\(797\) | −23.6869 | −0.839034 | −0.419517 | − | 0.907748i | \(-0.637800\pi\) | ||||
−0.419517 | + | 0.907748i | \(0.637800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.7984 | 0.629661 | ||||||||
\(800\) | −3.38197 | −0.119571 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.1246 | 0.993115 | ||||||||
\(803\) | −59.0689 | −2.08450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.38197 | −0.189689 | ||||||||
\(806\) | 15.0000 | 0.528352 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.3607 | 0.434847 | ||||||||
\(809\) | 6.63932 | 0.233426 | 0.116713 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116713 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.32624 | 0.292374 | 0.146187 | − | 0.989257i | \(-0.453300\pi\) | ||||
0.146187 | + | 0.989257i | \(0.453300\pi\) | |||||||
\(812\) | −5.90983 | −0.207394 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −45.9787 | −1.61155 | ||||||||
\(815\) | 2.94427 | 0.103133 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 70.5066 | 2.46671 | ||||||||
\(818\) | −21.1246 | −0.738605 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.00000 | 0.174608 | ||||||||
\(821\) | 29.5836 | 1.03247 | 0.516237 | − | 0.856446i | \(-0.327332\pi\) | ||||
0.516237 | + | 0.856446i | \(0.327332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.9443 | −1.32265 | −0.661327 | − | 0.750098i | \(-0.730006\pi\) | ||||
−0.661327 | + | 0.750098i | \(0.730006\pi\) | |||||||
\(824\) | −23.7426 | −0.827114 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.09017 | 0.0727263 | ||||||||
\(827\) | 11.5410 | 0.401321 | 0.200660 | − | 0.979661i | \(-0.435691\pi\) | ||||
0.200660 | + | 0.979661i | \(0.435691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.3607 | −0.464036 | −0.232018 | − | 0.972712i | \(-0.574533\pi\) | ||||
−0.232018 | + | 0.972712i | \(0.574533\pi\) | |||||||
\(830\) | 17.3262 | 0.601402 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.85410 | 0.202954 | ||||||||
\(833\) | −1.61803 | −0.0560616 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.47214 | −0.258584 | ||||||||
\(836\) | 18.5623 | 0.641991 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.0902 | −0.417648 | ||||||||
\(839\) | −0.381966 | −0.0131869 | −0.00659347 | − | 0.999978i | \(-0.502099\pi\) | ||||
−0.00659347 | + | 0.999978i | \(0.502099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.4377 | 2.15302 | ||||||||
\(842\) | 13.6525 | 0.470495 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.5836 | −0.364302 | ||||||||
\(845\) | 11.0902 | 0.381513 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.94427 | −0.238608 | ||||||||
\(848\) | −21.2705 | −0.730432 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.61803 | −0.0897978 | ||||||||
\(851\) | −36.1033 | −1.23761 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.16718 | −0.0742030 | −0.0371015 | − | 0.999312i | \(-0.511812\pi\) | ||||
−0.0371015 | + | 0.999312i | \(0.511812\pi\) | |||||||
\(854\) | 22.4164 | 0.767074 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.05573 | −0.206981 | ||||||||
\(857\) | 26.2361 | 0.896207 | 0.448104 | − | 0.893982i | \(-0.352100\pi\) | ||||
0.448104 | + | 0.893982i | \(0.352100\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.5967 | 0.736872 | 0.368436 | − | 0.929653i | \(-0.379893\pi\) | ||||
0.368436 | + | 0.929653i | \(0.379893\pi\) | |||||||
\(860\) | 6.14590 | 0.209573 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −49.2705 | −1.67816 | ||||||||
\(863\) | 51.7771 | 1.76251 | 0.881256 | − | 0.472639i | \(-0.156698\pi\) | ||||
0.881256 | + | 0.472639i | \(0.156698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.4721 | 0.390064 | ||||||||
\(866\) | −34.3262 | −1.16645 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.14590 | −0.140721 | ||||||||
\(869\) | −23.7984 | −0.807305 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.6525 | 0.530364 | ||||||||
\(872\) | −28.0902 | −0.951253 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 61.7426 | 2.08848 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9443 | 0.943611 | 0.471806 | − | 0.881703i | \(-0.343602\pi\) | ||||
0.471806 | + | 0.881703i | \(0.343602\pi\) | |||||||
\(878\) | 18.2705 | 0.616600 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.5623 | −0.693155 | ||||||||
\(881\) | −55.8885 | −1.88293 | −0.941466 | − | 0.337107i | \(-0.890552\pi\) | ||||
−0.941466 | + | 0.337107i | \(0.890552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.6525 | −0.661358 | −0.330679 | − | 0.943743i | \(-0.607278\pi\) | ||||
−0.330679 | + | 0.943743i | \(0.607278\pi\) | |||||||
\(884\) | −1.38197 | −0.0464805 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 65.8328 | 2.21170 | ||||||||
\(887\) | 14.7639 | 0.495724 | 0.247862 | − | 0.968795i | \(-0.420272\pi\) | ||||
0.247862 | + | 0.968795i | \(0.420272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0901699 | −0.00302420 | ||||||||
\(890\) | 2.38197 | 0.0798437 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.61803 | 0.154623 | ||||||||
\(893\) | 77.9919 | 2.60990 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.00000 | −0.233984 | ||||||||
\(896\) | −13.6180 | −0.454947 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.1246 | −1.10538 | ||||||||
\(899\) | 64.1459 | 2.13939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.09017 | −0.236208 | ||||||||
\(902\) | 55.4508 | 1.84631 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.0902 | 0.435373 | ||||||||
\(905\) | 19.4721 | 0.647276 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.14590 | 0.270480 | 0.135240 | − | 0.990813i | \(-0.456819\pi\) | ||||
0.135240 | + | 0.990813i | \(0.456819\pi\) | |||||||
\(908\) | −4.59675 | −0.152548 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.23607 | 0.0741249 | ||||||||
\(911\) | −7.63932 | −0.253102 | −0.126551 | − | 0.991960i | \(-0.540391\pi\) | ||||
−0.126551 | + | 0.991960i | \(0.540391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.3607 | 1.50122 | ||||||||
\(914\) | 28.0344 | 0.927297 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.0902 | −0.366430 | ||||||||
\(917\) | 4.38197 | 0.144705 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1591 | 1.39070 | 0.695349 | − | 0.718672i | \(-0.255250\pi\) | ||||
0.695349 | + | 0.718672i | \(0.255250\pi\) | |||||||
\(920\) | −12.0344 | −0.396764 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.8885 | 1.21486 | ||||||||
\(923\) | −5.32624 | −0.175315 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.70820 | 0.220564 | ||||||||
\(926\) | −1.00000 | −0.0328620 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32.3394 | −1.06159 | ||||||||
\(929\) | 57.1033 | 1.87350 | 0.936750 | − | 0.350000i | \(-0.113818\pi\) | ||||
0.936750 | + | 0.350000i | \(0.113818\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.09017 | −0.232371 | ||||||||
\(932\) | −10.5623 | −0.345980 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.4164 | −0.897092 | ||||||||
\(935\) | −6.85410 | −0.224153 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9443 | 0.880231 | 0.440115 | − | 0.897941i | \(-0.354937\pi\) | ||||
0.440115 | + | 0.897941i | \(0.354937\pi\) | |||||||
\(938\) | −18.3262 | −0.598373 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.79837 | 0.221739 | ||||||||
\(941\) | 45.7639 | 1.49186 | 0.745931 | − | 0.666023i | \(-0.232005\pi\) | ||||
0.745931 | + | 0.666023i | \(0.232005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.5410 | 1.41789 | ||||||||
\(944\) | 6.27051 | 0.204088 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 68.1591 | 2.21604 | ||||||||
\(947\) | 5.43769 | 0.176701 | 0.0883507 | − | 0.996089i | \(-0.471840\pi\) | ||||
0.0883507 | + | 0.996089i | \(0.471840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.2705 | 0.625547 | ||||||||
\(950\) | −11.4721 | −0.372205 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.61803 | −0.117261 | ||||||||
\(953\) | 35.6525 | 1.15490 | 0.577448 | − | 0.816427i | \(-0.304048\pi\) | ||||
0.577448 | + | 0.816427i | \(0.304048\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.7984 | 0.608301 | ||||||||
\(956\) | −7.20163 | −0.232917 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −41.9230 | −1.35447 | ||||||||
\(959\) | 13.8885 | 0.448484 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | 15.0000 | 0.483619 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.70820 | −0.151641 | ||||||||
\(965\) | 0.854102 | 0.0274945 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.52786 | −0.274238 | −0.137119 | − | 0.990555i | \(-0.543784\pi\) | ||||
−0.137119 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(968\) | −15.5279 | −0.499084 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.38197 | 0.172805 | ||||||||
\(971\) | −22.2492 | −0.714012 | −0.357006 | − | 0.934102i | \(-0.616202\pi\) | ||||
−0.357006 | + | 0.934102i | \(0.616202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.18034 | −0.101957 | ||||||||
\(974\) | −25.1246 | −0.805044 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 67.2492 | 2.15260 | ||||||||
\(977\) | −14.3607 | −0.459439 | −0.229719 | − | 0.973257i | \(-0.573781\pi\) | ||||
−0.229719 | + | 0.973257i | \(0.573781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.23607 | 0.199306 | ||||||||
\(980\) | −0.618034 | −0.0197424 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.5623 | 1.00719 | ||||||||
\(983\) | −46.9787 | −1.49839 | −0.749194 | − | 0.662350i | \(-0.769559\pi\) | ||||
−0.749194 | + | 0.662350i | \(0.769559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.4721 | −0.620434 | ||||||||
\(986\) | −25.0344 | −0.797259 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.05573 | −0.192658 | ||||||||
\(989\) | 53.5197 | 1.70183 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.8885 | −1.36240 | −0.681200 | − | 0.732098i | \(-0.738541\pi\) | ||||
−0.681200 | + | 0.732098i | \(0.738541\pi\) | |||||||
\(992\) | −22.6869 | −0.720310 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.23607 | 0.197796 | ||||||||
\(995\) | −1.61803 | −0.0512951 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.7082 | 0.465813 | 0.232907 | − | 0.972499i | \(-0.425176\pi\) | ||||
0.232907 | + | 0.972499i | \(0.425176\pi\) | |||||||
\(998\) | 5.43769 | 0.172127 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.a.g.1.2 | yes | 2 | |
3.2 | odd | 2 | 945.2.a.e.1.1 | ✓ | 2 | ||
5.4 | even | 2 | 4725.2.a.w.1.1 | 2 | |||
7.6 | odd | 2 | 6615.2.a.r.1.2 | 2 | |||
15.14 | odd | 2 | 4725.2.a.be.1.2 | 2 | |||
21.20 | even | 2 | 6615.2.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.a.e.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
945.2.a.g.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
4725.2.a.w.1.1 | 2 | 5.4 | even | 2 | |||
4725.2.a.be.1.2 | 2 | 15.14 | odd | 2 | |||
6615.2.a.o.1.1 | 2 | 21.20 | even | 2 | |||
6615.2.a.r.1.2 | 2 | 7.6 | odd | 2 |