Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.84109\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.67352 | 0.966208 | 0.483104 | − | 0.875563i | \(-0.339509\pi\) | ||||
0.483104 | + | 0.875563i | \(0.339509\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.566489 | −0.253342 | −0.126671 | − | 0.991945i | \(-0.540429\pi\) | ||||
−0.126671 | + | 0.991945i | \(0.540429\pi\) | |||||||
\(6\) | 1.67352 | 0.683212 | ||||||||
\(7\) | 3.40033 | 1.28520 | 0.642602 | − | 0.766200i | \(-0.277855\pi\) | ||||
0.642602 | + | 0.766200i | \(0.277855\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.199325 | −0.0664418 | ||||||||
\(10\) | −0.566489 | −0.179140 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.67352 | 0.483104 | ||||||||
\(13\) | 1.35442 | 0.375647 | 0.187824 | − | 0.982203i | \(-0.439857\pi\) | ||||
0.187824 | + | 0.982203i | \(0.439857\pi\) | |||||||
\(14\) | 3.40033 | 0.908777 | ||||||||
\(15\) | −0.948032 | −0.244781 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.30453 | 1.04400 | 0.522002 | − | 0.852945i | \(-0.325186\pi\) | ||||
0.522002 | + | 0.852945i | \(0.325186\pi\) | |||||||
\(18\) | −0.199325 | −0.0469814 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.566489 | −0.126671 | ||||||||
\(21\) | 5.69053 | 1.24178 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.71065 | −0.565210 | −0.282605 | − | 0.959236i | \(-0.591199\pi\) | ||||
−0.282605 | + | 0.959236i | \(0.591199\pi\) | |||||||
\(24\) | 1.67352 | 0.341606 | ||||||||
\(25\) | −4.67909 | −0.935818 | ||||||||
\(26\) | 1.35442 | 0.265623 | ||||||||
\(27\) | −5.35414 | −1.03040 | ||||||||
\(28\) | 3.40033 | 0.642602 | ||||||||
\(29\) | 5.64462 | 1.04818 | 0.524089 | − | 0.851663i | \(-0.324406\pi\) | ||||
0.524089 | + | 0.851663i | \(0.324406\pi\) | |||||||
\(30\) | −0.948032 | −0.173086 | ||||||||
\(31\) | 9.62449 | 1.72861 | 0.864305 | − | 0.502968i | \(-0.167759\pi\) | ||||
0.864305 | + | 0.502968i | \(0.167759\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.30453 | 0.738222 | ||||||||
\(35\) | −1.92625 | −0.325596 | ||||||||
\(36\) | −0.199325 | −0.0332209 | ||||||||
\(37\) | 3.63304 | 0.597269 | 0.298634 | − | 0.954368i | \(-0.403469\pi\) | ||||
0.298634 | + | 0.954368i | \(0.403469\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.26664 | 0.362953 | ||||||||
\(40\) | −0.566489 | −0.0895698 | ||||||||
\(41\) | −3.64782 | −0.569694 | −0.284847 | − | 0.958573i | \(-0.591943\pi\) | ||||
−0.284847 | + | 0.958573i | \(0.591943\pi\) | |||||||
\(42\) | 5.69053 | 0.878068 | ||||||||
\(43\) | −7.94488 | −1.21158 | −0.605791 | − | 0.795624i | \(-0.707143\pi\) | ||||
−0.605791 | + | 0.795624i | \(0.707143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.112916 | 0.0168325 | ||||||||
\(46\) | −2.71065 | −0.399664 | ||||||||
\(47\) | 13.5117 | 1.97088 | 0.985440 | − | 0.170023i | \(-0.0543841\pi\) | ||||
0.985440 | + | 0.170023i | \(0.0543841\pi\) | |||||||
\(48\) | 1.67352 | 0.241552 | ||||||||
\(49\) | 4.56226 | 0.651752 | ||||||||
\(50\) | −4.67909 | −0.661723 | ||||||||
\(51\) | 7.20373 | 1.00872 | ||||||||
\(52\) | 1.35442 | 0.187824 | ||||||||
\(53\) | 4.25789 | 0.584867 | 0.292433 | − | 0.956286i | \(-0.405535\pi\) | ||||
0.292433 | + | 0.956286i | \(0.405535\pi\) | |||||||
\(54\) | −5.35414 | −0.728606 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.40033 | 0.454389 | ||||||||
\(57\) | −1.67352 | −0.221663 | ||||||||
\(58\) | 5.64462 | 0.741174 | ||||||||
\(59\) | 7.97498 | 1.03825 | 0.519127 | − | 0.854697i | \(-0.326257\pi\) | ||||
0.519127 | + | 0.854697i | \(0.326257\pi\) | |||||||
\(60\) | −0.948032 | −0.122390 | ||||||||
\(61\) | 9.37992 | 1.20098 | 0.600488 | − | 0.799634i | \(-0.294973\pi\) | ||||
0.600488 | + | 0.799634i | \(0.294973\pi\) | |||||||
\(62\) | 9.62449 | 1.22231 | ||||||||
\(63\) | −0.677772 | −0.0853913 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.767262 | −0.0951671 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.01003 | 0.123395 | 0.0616973 | − | 0.998095i | \(-0.480349\pi\) | ||||
0.0616973 | + | 0.998095i | \(0.480349\pi\) | |||||||
\(68\) | 4.30453 | 0.522002 | ||||||||
\(69\) | −4.53633 | −0.546110 | ||||||||
\(70\) | −1.92625 | −0.230231 | ||||||||
\(71\) | 6.30982 | 0.748838 | 0.374419 | − | 0.927260i | \(-0.377842\pi\) | ||||
0.374419 | + | 0.927260i | \(0.377842\pi\) | |||||||
\(72\) | −0.199325 | −0.0234907 | ||||||||
\(73\) | −14.0378 | −1.64300 | −0.821498 | − | 0.570211i | \(-0.806861\pi\) | ||||
−0.821498 | + | 0.570211i | \(0.806861\pi\) | |||||||
\(74\) | 3.63304 | 0.422333 | ||||||||
\(75\) | −7.83056 | −0.904195 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.26664 | 0.256647 | ||||||||
\(79\) | −7.11185 | −0.800145 | −0.400073 | − | 0.916483i | \(-0.631015\pi\) | ||||
−0.400073 | + | 0.916483i | \(0.631015\pi\) | |||||||
\(80\) | −0.566489 | −0.0633354 | ||||||||
\(81\) | −8.36229 | −0.929144 | ||||||||
\(82\) | −3.64782 | −0.402835 | ||||||||
\(83\) | −1.02452 | −0.112456 | −0.0562280 | − | 0.998418i | \(-0.517907\pi\) | ||||
−0.0562280 | + | 0.998418i | \(0.517907\pi\) | |||||||
\(84\) | 5.69053 | 0.620888 | ||||||||
\(85\) | −2.43847 | −0.264489 | ||||||||
\(86\) | −7.94488 | −0.856718 | ||||||||
\(87\) | 9.44639 | 1.01276 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1613 | −1.60710 | −0.803548 | − | 0.595239i | \(-0.797057\pi\) | ||||
−0.803548 | + | 0.595239i | \(0.797057\pi\) | |||||||
\(90\) | 0.112916 | 0.0119024 | ||||||||
\(91\) | 4.60546 | 0.482784 | ||||||||
\(92\) | −2.71065 | −0.282605 | ||||||||
\(93\) | 16.1068 | 1.67020 | ||||||||
\(94\) | 13.5117 | 1.39362 | ||||||||
\(95\) | 0.566489 | 0.0581206 | ||||||||
\(96\) | 1.67352 | 0.170803 | ||||||||
\(97\) | 7.04118 | 0.714923 | 0.357462 | − | 0.933928i | \(-0.383642\pi\) | ||||
0.357462 | + | 0.933928i | \(0.383642\pi\) | |||||||
\(98\) | 4.56226 | 0.460858 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.67909 | −0.467909 | ||||||||
\(101\) | −8.12037 | −0.808007 | −0.404003 | − | 0.914758i | \(-0.632382\pi\) | ||||
−0.404003 | + | 0.914758i | \(0.632382\pi\) | |||||||
\(102\) | 7.20373 | 0.713276 | ||||||||
\(103\) | −3.00499 | −0.296091 | −0.148045 | − | 0.988981i | \(-0.547298\pi\) | ||||
−0.148045 | + | 0.988981i | \(0.547298\pi\) | |||||||
\(104\) | 1.35442 | 0.132811 | ||||||||
\(105\) | −3.22362 | −0.314593 | ||||||||
\(106\) | 4.25789 | 0.413563 | ||||||||
\(107\) | −7.33334 | −0.708941 | −0.354471 | − | 0.935067i | \(-0.615339\pi\) | ||||
−0.354471 | + | 0.935067i | \(0.615339\pi\) | |||||||
\(108\) | −5.35414 | −0.515202 | ||||||||
\(109\) | 3.90465 | 0.373998 | 0.186999 | − | 0.982360i | \(-0.440124\pi\) | ||||
0.186999 | + | 0.982360i | \(0.440124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.07998 | 0.577086 | ||||||||
\(112\) | 3.40033 | 0.321301 | ||||||||
\(113\) | −6.36327 | −0.598606 | −0.299303 | − | 0.954158i | \(-0.596754\pi\) | ||||
−0.299303 | + | 0.954158i | \(0.596754\pi\) | |||||||
\(114\) | −1.67352 | −0.156740 | ||||||||
\(115\) | 1.53555 | 0.143191 | ||||||||
\(116\) | 5.64462 | 0.524089 | ||||||||
\(117\) | −0.269969 | −0.0249587 | ||||||||
\(118\) | 7.97498 | 0.734156 | ||||||||
\(119\) | 14.6369 | 1.34176 | ||||||||
\(120\) | −0.948032 | −0.0865431 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.37992 | 0.849218 | ||||||||
\(123\) | −6.10471 | −0.550443 | ||||||||
\(124\) | 9.62449 | 0.864305 | ||||||||
\(125\) | 5.48310 | 0.490423 | ||||||||
\(126\) | −0.677772 | −0.0603808 | ||||||||
\(127\) | 17.3575 | 1.54023 | 0.770115 | − | 0.637905i | \(-0.220199\pi\) | ||||
0.770115 | + | 0.637905i | \(0.220199\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −13.2959 | −1.17064 | ||||||||
\(130\) | −0.767262 | −0.0672933 | ||||||||
\(131\) | −3.39115 | −0.296286 | −0.148143 | − | 0.988966i | \(-0.547330\pi\) | ||||
−0.148143 | + | 0.988966i | \(0.547330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.40033 | −0.294846 | ||||||||
\(134\) | 1.01003 | 0.0872531 | ||||||||
\(135\) | 3.03306 | 0.261044 | ||||||||
\(136\) | 4.30453 | 0.369111 | ||||||||
\(137\) | 0.0612122 | 0.00522971 | 0.00261486 | − | 0.999997i | \(-0.499168\pi\) | ||||
0.00261486 | + | 0.999997i | \(0.499168\pi\) | |||||||
\(138\) | −4.53633 | −0.386158 | ||||||||
\(139\) | −16.7756 | −1.42289 | −0.711443 | − | 0.702744i | \(-0.751958\pi\) | ||||
−0.711443 | + | 0.702744i | \(0.751958\pi\) | |||||||
\(140\) | −1.92625 | −0.162798 | ||||||||
\(141\) | 22.6121 | 1.90428 | ||||||||
\(142\) | 6.30982 | 0.529508 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.199325 | −0.0166104 | ||||||||
\(145\) | −3.19761 | −0.265547 | ||||||||
\(146\) | −14.0378 | −1.16177 | ||||||||
\(147\) | 7.63504 | 0.629728 | ||||||||
\(148\) | 3.63304 | 0.298634 | ||||||||
\(149\) | 8.95206 | 0.733382 | 0.366691 | − | 0.930343i | \(-0.380491\pi\) | ||||
0.366691 | + | 0.930343i | \(0.380491\pi\) | |||||||
\(150\) | −7.83056 | −0.639362 | ||||||||
\(151\) | −8.51404 | −0.692862 | −0.346431 | − | 0.938075i | \(-0.612607\pi\) | ||||
−0.346431 | + | 0.938075i | \(0.612607\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −0.858003 | −0.0693654 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.45217 | −0.437929 | ||||||||
\(156\) | 2.26664 | 0.181477 | ||||||||
\(157\) | 12.0876 | 0.964698 | 0.482349 | − | 0.875979i | \(-0.339784\pi\) | ||||
0.482349 | + | 0.875979i | \(0.339784\pi\) | |||||||
\(158\) | −7.11185 | −0.565788 | ||||||||
\(159\) | 7.12568 | 0.565103 | ||||||||
\(160\) | −0.566489 | −0.0447849 | ||||||||
\(161\) | −9.21711 | −0.726410 | ||||||||
\(162\) | −8.36229 | −0.657004 | ||||||||
\(163\) | 13.6320 | 1.06774 | 0.533870 | − | 0.845566i | \(-0.320737\pi\) | ||||
0.533870 | + | 0.845566i | \(0.320737\pi\) | |||||||
\(164\) | −3.64782 | −0.284847 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.02452 | −0.0795184 | ||||||||
\(167\) | −3.77640 | −0.292226 | −0.146113 | − | 0.989268i | \(-0.546676\pi\) | ||||
−0.146113 | + | 0.989268i | \(0.546676\pi\) | |||||||
\(168\) | 5.69053 | 0.439034 | ||||||||
\(169\) | −11.1656 | −0.858889 | ||||||||
\(170\) | −2.43847 | −0.187022 | ||||||||
\(171\) | 0.199325 | 0.0152428 | ||||||||
\(172\) | −7.94488 | −0.605791 | ||||||||
\(173\) | −1.92088 | −0.146042 | −0.0730210 | − | 0.997330i | \(-0.523264\pi\) | ||||
−0.0730210 | + | 0.997330i | \(0.523264\pi\) | |||||||
\(174\) | 9.44639 | 0.716129 | ||||||||
\(175\) | −15.9105 | −1.20272 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.3463 | 1.00317 | ||||||||
\(178\) | −15.1613 | −1.13639 | ||||||||
\(179\) | −12.9182 | −0.965548 | −0.482774 | − | 0.875745i | \(-0.660371\pi\) | ||||
−0.482774 | + | 0.875745i | \(0.660371\pi\) | |||||||
\(180\) | 0.112916 | 0.00841623 | ||||||||
\(181\) | 17.7782 | 1.32144 | 0.660722 | − | 0.750630i | \(-0.270250\pi\) | ||||
0.660722 | + | 0.750630i | \(0.270250\pi\) | |||||||
\(182\) | 4.60546 | 0.341380 | ||||||||
\(183\) | 15.6975 | 1.16039 | ||||||||
\(184\) | −2.71065 | −0.199832 | ||||||||
\(185\) | −2.05808 | −0.151313 | ||||||||
\(186\) | 16.1068 | 1.18101 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 13.5117 | 0.985440 | ||||||||
\(189\) | −18.2059 | −1.32428 | ||||||||
\(190\) | 0.566489 | 0.0410974 | ||||||||
\(191\) | −20.7230 | −1.49947 | −0.749733 | − | 0.661741i | \(-0.769818\pi\) | ||||
−0.749733 | + | 0.661741i | \(0.769818\pi\) | |||||||
\(192\) | 1.67352 | 0.120776 | ||||||||
\(193\) | 12.1336 | 0.873396 | 0.436698 | − | 0.899608i | \(-0.356148\pi\) | ||||
0.436698 | + | 0.899608i | \(0.356148\pi\) | |||||||
\(194\) | 7.04118 | 0.505527 | ||||||||
\(195\) | −1.28403 | −0.0919512 | ||||||||
\(196\) | 4.56226 | 0.325876 | ||||||||
\(197\) | −14.2097 | −1.01240 | −0.506199 | − | 0.862417i | \(-0.668950\pi\) | ||||
−0.506199 | + | 0.862417i | \(0.668950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.976956 | −0.0692545 | −0.0346273 | − | 0.999400i | \(-0.511024\pi\) | ||||
−0.0346273 | + | 0.999400i | \(0.511024\pi\) | |||||||
\(200\) | −4.67909 | −0.330862 | ||||||||
\(201\) | 1.69030 | 0.119225 | ||||||||
\(202\) | −8.12037 | −0.571347 | ||||||||
\(203\) | 19.1936 | 1.34712 | ||||||||
\(204\) | 7.20373 | 0.504362 | ||||||||
\(205\) | 2.06645 | 0.144327 | ||||||||
\(206\) | −3.00499 | −0.209368 | ||||||||
\(207\) | 0.540301 | 0.0375535 | ||||||||
\(208\) | 1.35442 | 0.0939118 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.22362 | −0.222451 | ||||||||
\(211\) | −8.44427 | −0.581327 | −0.290664 | − | 0.956825i | \(-0.593876\pi\) | ||||
−0.290664 | + | 0.956825i | \(0.593876\pi\) | |||||||
\(212\) | 4.25789 | 0.292433 | ||||||||
\(213\) | 10.5596 | 0.723533 | ||||||||
\(214\) | −7.33334 | −0.501297 | ||||||||
\(215\) | 4.50069 | 0.306944 | ||||||||
\(216\) | −5.35414 | −0.364303 | ||||||||
\(217\) | 32.7265 | 2.22162 | ||||||||
\(218\) | 3.90465 | 0.264456 | ||||||||
\(219\) | −23.4925 | −1.58748 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.83013 | 0.392177 | ||||||||
\(222\) | 6.07998 | 0.408061 | ||||||||
\(223\) | −0.309593 | −0.0207319 | −0.0103659 | − | 0.999946i | \(-0.503300\pi\) | ||||
−0.0103659 | + | 0.999946i | \(0.503300\pi\) | |||||||
\(224\) | 3.40033 | 0.227194 | ||||||||
\(225\) | 0.932661 | 0.0621774 | ||||||||
\(226\) | −6.36327 | −0.423278 | ||||||||
\(227\) | 17.8942 | 1.18768 | 0.593840 | − | 0.804583i | \(-0.297611\pi\) | ||||
0.593840 | + | 0.804583i | \(0.297611\pi\) | |||||||
\(228\) | −1.67352 | −0.110832 | ||||||||
\(229\) | −4.77162 | −0.315318 | −0.157659 | − | 0.987494i | \(-0.550395\pi\) | ||||
−0.157659 | + | 0.987494i | \(0.550395\pi\) | |||||||
\(230\) | 1.53555 | 0.101251 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.64462 | 0.370587 | ||||||||
\(233\) | −12.5120 | −0.819686 | −0.409843 | − | 0.912156i | \(-0.634417\pi\) | ||||
−0.409843 | + | 0.912156i | \(0.634417\pi\) | |||||||
\(234\) | −0.269969 | −0.0176484 | ||||||||
\(235\) | −7.65422 | −0.499306 | ||||||||
\(236\) | 7.97498 | 0.519127 | ||||||||
\(237\) | −11.9018 | −0.773107 | ||||||||
\(238\) | 14.6369 | 0.948766 | ||||||||
\(239\) | 11.2492 | 0.727653 | 0.363826 | − | 0.931467i | \(-0.381470\pi\) | ||||
0.363826 | + | 0.931467i | \(0.381470\pi\) | |||||||
\(240\) | −0.948032 | −0.0611952 | ||||||||
\(241\) | 23.4105 | 1.50801 | 0.754003 | − | 0.656871i | \(-0.228121\pi\) | ||||
0.754003 | + | 0.656871i | \(0.228121\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.06794 | 0.132658 | ||||||||
\(244\) | 9.37992 | 0.600488 | ||||||||
\(245\) | −2.58447 | −0.165116 | ||||||||
\(246\) | −6.10471 | −0.389222 | ||||||||
\(247\) | −1.35442 | −0.0861794 | ||||||||
\(248\) | 9.62449 | 0.611156 | ||||||||
\(249\) | −1.71456 | −0.108656 | ||||||||
\(250\) | 5.48310 | 0.346782 | ||||||||
\(251\) | −27.2448 | −1.71967 | −0.859837 | − | 0.510568i | \(-0.829435\pi\) | ||||
−0.859837 | + | 0.510568i | \(0.829435\pi\) | |||||||
\(252\) | −0.677772 | −0.0426956 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 17.3575 | 1.08911 | ||||||||
\(255\) | −4.08084 | −0.255552 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.9406 | 1.18148 | 0.590742 | − | 0.806861i | \(-0.298835\pi\) | ||||
0.590742 | + | 0.806861i | \(0.298835\pi\) | |||||||
\(258\) | −13.2959 | −0.827768 | ||||||||
\(259\) | 12.3536 | 0.767613 | ||||||||
\(260\) | −0.767262 | −0.0475835 | ||||||||
\(261\) | −1.12511 | −0.0696428 | ||||||||
\(262\) | −3.39115 | −0.209506 | ||||||||
\(263\) | −28.1414 | −1.73527 | −0.867637 | − | 0.497198i | \(-0.834362\pi\) | ||||
−0.867637 | + | 0.497198i | \(0.834362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.41205 | −0.148171 | ||||||||
\(266\) | −3.40033 | −0.208488 | ||||||||
\(267\) | −25.3728 | −1.55279 | ||||||||
\(268\) | 1.01003 | 0.0616973 | ||||||||
\(269\) | −0.144365 | −0.00880207 | −0.00440104 | − | 0.999990i | \(-0.501401\pi\) | ||||
−0.00440104 | + | 0.999990i | \(0.501401\pi\) | |||||||
\(270\) | 3.03306 | 0.184586 | ||||||||
\(271\) | 7.88292 | 0.478853 | 0.239427 | − | 0.970914i | \(-0.423041\pi\) | ||||
0.239427 | + | 0.970914i | \(0.423041\pi\) | |||||||
\(272\) | 4.30453 | 0.261001 | ||||||||
\(273\) | 7.70734 | 0.466469 | ||||||||
\(274\) | 0.0612122 | 0.00369797 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.53633 | −0.273055 | ||||||||
\(277\) | −16.4244 | −0.986846 | −0.493423 | − | 0.869790i | \(-0.664254\pi\) | ||||
−0.493423 | + | 0.869790i | \(0.664254\pi\) | |||||||
\(278\) | −16.7756 | −1.00613 | ||||||||
\(279\) | −1.91841 | −0.114852 | ||||||||
\(280\) | −1.92625 | −0.115116 | ||||||||
\(281\) | 1.71799 | 0.102487 | 0.0512435 | − | 0.998686i | \(-0.483682\pi\) | ||||
0.0512435 | + | 0.998686i | \(0.483682\pi\) | |||||||
\(282\) | 22.6121 | 1.34653 | ||||||||
\(283\) | 5.05430 | 0.300447 | 0.150223 | − | 0.988652i | \(-0.452001\pi\) | ||||
0.150223 | + | 0.988652i | \(0.452001\pi\) | |||||||
\(284\) | 6.30982 | 0.374419 | ||||||||
\(285\) | 0.948032 | 0.0561566 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.4038 | −0.732174 | ||||||||
\(288\) | −0.199325 | −0.0117454 | ||||||||
\(289\) | 1.52902 | 0.0899424 | ||||||||
\(290\) | −3.19761 | −0.187770 | ||||||||
\(291\) | 11.7836 | 0.690765 | ||||||||
\(292\) | −14.0378 | −0.821498 | ||||||||
\(293\) | −19.2526 | −1.12475 | −0.562376 | − | 0.826882i | \(-0.690112\pi\) | ||||
−0.562376 | + | 0.826882i | \(0.690112\pi\) | |||||||
\(294\) | 7.63504 | 0.445285 | ||||||||
\(295\) | −4.51774 | −0.263033 | ||||||||
\(296\) | 3.63304 | 0.211166 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.95206 | 0.518579 | ||||||||
\(299\) | −3.67135 | −0.212319 | ||||||||
\(300\) | −7.83056 | −0.452097 | ||||||||
\(301\) | −27.0152 | −1.55713 | ||||||||
\(302\) | −8.51404 | −0.489928 | ||||||||
\(303\) | −13.5896 | −0.780703 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −5.31362 | −0.304257 | ||||||||
\(306\) | −0.858003 | −0.0490487 | ||||||||
\(307\) | −12.2585 | −0.699629 | −0.349814 | − | 0.936819i | \(-0.613755\pi\) | ||||
−0.349814 | + | 0.936819i | \(0.613755\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.02892 | −0.286085 | ||||||||
\(310\) | −5.45217 | −0.309663 | ||||||||
\(311\) | −5.48085 | −0.310791 | −0.155395 | − | 0.987852i | \(-0.549665\pi\) | ||||
−0.155395 | + | 0.987852i | \(0.549665\pi\) | |||||||
\(312\) | 2.26664 | 0.128323 | ||||||||
\(313\) | 8.75492 | 0.494858 | 0.247429 | − | 0.968906i | \(-0.420414\pi\) | ||||
0.247429 | + | 0.968906i | \(0.420414\pi\) | |||||||
\(314\) | 12.0876 | 0.682144 | ||||||||
\(315\) | 0.383951 | 0.0216332 | ||||||||
\(316\) | −7.11185 | −0.400073 | ||||||||
\(317\) | −18.4394 | −1.03566 | −0.517829 | − | 0.855484i | \(-0.673260\pi\) | ||||
−0.517829 | + | 0.855484i | \(0.673260\pi\) | |||||||
\(318\) | 7.12568 | 0.399588 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.566489 | −0.0316677 | ||||||||
\(321\) | −12.2725 | −0.684985 | ||||||||
\(322\) | −9.21711 | −0.513650 | ||||||||
\(323\) | −4.30453 | −0.239511 | ||||||||
\(324\) | −8.36229 | −0.464572 | ||||||||
\(325\) | −6.33743 | −0.351537 | ||||||||
\(326\) | 13.6320 | 0.755007 | ||||||||
\(327\) | 6.53452 | 0.361360 | ||||||||
\(328\) | −3.64782 | −0.201417 | ||||||||
\(329\) | 45.9442 | 2.53298 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.57096 | 0.361172 | 0.180586 | − | 0.983559i | \(-0.442201\pi\) | ||||
0.180586 | + | 0.983559i | \(0.442201\pi\) | |||||||
\(332\) | −1.02452 | −0.0562280 | ||||||||
\(333\) | −0.724158 | −0.0396836 | ||||||||
\(334\) | −3.77640 | −0.206635 | ||||||||
\(335\) | −0.572170 | −0.0312610 | ||||||||
\(336\) | 5.69053 | 0.310444 | ||||||||
\(337\) | −23.5185 | −1.28114 | −0.640568 | − | 0.767902i | \(-0.721301\pi\) | ||||
−0.640568 | + | 0.767902i | \(0.721301\pi\) | |||||||
\(338\) | −11.1656 | −0.607326 | ||||||||
\(339\) | −10.6491 | −0.578378 | ||||||||
\(340\) | −2.43847 | −0.132245 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.199325 | 0.0107783 | ||||||||
\(343\) | −8.28912 | −0.447571 | ||||||||
\(344\) | −7.94488 | −0.428359 | ||||||||
\(345\) | 2.56978 | 0.138352 | ||||||||
\(346\) | −1.92088 | −0.103267 | ||||||||
\(347\) | −6.22613 | −0.334236 | −0.167118 | − | 0.985937i | \(-0.553446\pi\) | ||||
−0.167118 | + | 0.985937i | \(0.553446\pi\) | |||||||
\(348\) | 9.44639 | 0.506379 | ||||||||
\(349\) | 22.3550 | 1.19664 | 0.598319 | − | 0.801258i | \(-0.295836\pi\) | ||||
0.598319 | + | 0.801258i | \(0.295836\pi\) | |||||||
\(350\) | −15.9105 | −0.850450 | ||||||||
\(351\) | −7.25173 | −0.387069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.4241 | 1.93866 | 0.969329 | − | 0.245768i | \(-0.0790402\pi\) | ||||
0.969329 | + | 0.245768i | \(0.0790402\pi\) | |||||||
\(354\) | 13.3463 | 0.709348 | ||||||||
\(355\) | −3.57444 | −0.189712 | ||||||||
\(356\) | −15.1613 | −0.803548 | ||||||||
\(357\) | 24.4951 | 1.29642 | ||||||||
\(358\) | −12.9182 | −0.682746 | ||||||||
\(359\) | 7.54684 | 0.398307 | 0.199153 | − | 0.979968i | \(-0.436181\pi\) | ||||
0.199153 | + | 0.979968i | \(0.436181\pi\) | |||||||
\(360\) | 0.112916 | 0.00595118 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 17.7782 | 0.934403 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.60546 | 0.241392 | ||||||||
\(365\) | 7.95224 | 0.416240 | ||||||||
\(366\) | 15.6975 | 0.820521 | ||||||||
\(367\) | 25.7229 | 1.34273 | 0.671363 | − | 0.741129i | \(-0.265709\pi\) | ||||
0.671363 | + | 0.741129i | \(0.265709\pi\) | |||||||
\(368\) | −2.71065 | −0.141302 | ||||||||
\(369\) | 0.727103 | 0.0378515 | ||||||||
\(370\) | −2.05808 | −0.106995 | ||||||||
\(371\) | 14.4783 | 0.751674 | ||||||||
\(372\) | 16.1068 | 0.835099 | ||||||||
\(373\) | −7.13854 | −0.369619 | −0.184810 | − | 0.982774i | \(-0.559167\pi\) | ||||
−0.184810 | + | 0.982774i | \(0.559167\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.17609 | 0.473851 | ||||||||
\(376\) | 13.5117 | 0.696811 | ||||||||
\(377\) | 7.64515 | 0.393745 | ||||||||
\(378\) | −18.2059 | −0.936408 | ||||||||
\(379\) | −27.1836 | −1.39633 | −0.698165 | − | 0.715937i | \(-0.746000\pi\) | ||||
−0.698165 | + | 0.715937i | \(0.746000\pi\) | |||||||
\(380\) | 0.566489 | 0.0290603 | ||||||||
\(381\) | 29.0482 | 1.48818 | ||||||||
\(382\) | −20.7230 | −1.06028 | ||||||||
\(383\) | −30.3425 | −1.55043 | −0.775215 | − | 0.631698i | \(-0.782358\pi\) | ||||
−0.775215 | + | 0.631698i | \(0.782358\pi\) | |||||||
\(384\) | 1.67352 | 0.0854015 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.1336 | 0.617584 | ||||||||
\(387\) | 1.58362 | 0.0804997 | ||||||||
\(388\) | 7.04118 | 0.357462 | ||||||||
\(389\) | 5.82380 | 0.295278 | 0.147639 | − | 0.989041i | \(-0.452833\pi\) | ||||
0.147639 | + | 0.989041i | \(0.452833\pi\) | |||||||
\(390\) | −1.28403 | −0.0650193 | ||||||||
\(391\) | −11.6681 | −0.590081 | ||||||||
\(392\) | 4.56226 | 0.230429 | ||||||||
\(393\) | −5.67516 | −0.286274 | ||||||||
\(394\) | −14.2097 | −0.715874 | ||||||||
\(395\) | 4.02878 | 0.202710 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.13644 | 0.107225 | 0.0536124 | − | 0.998562i | \(-0.482926\pi\) | ||||
0.0536124 | + | 0.998562i | \(0.482926\pi\) | |||||||
\(398\) | −0.976956 | −0.0489704 | ||||||||
\(399\) | −5.69053 | −0.284883 | ||||||||
\(400\) | −4.67909 | −0.233954 | ||||||||
\(401\) | 3.52506 | 0.176033 | 0.0880164 | − | 0.996119i | \(-0.471947\pi\) | ||||
0.0880164 | + | 0.996119i | \(0.471947\pi\) | |||||||
\(402\) | 1.69030 | 0.0843047 | ||||||||
\(403\) | 13.0356 | 0.649347 | ||||||||
\(404\) | −8.12037 | −0.404003 | ||||||||
\(405\) | 4.73715 | 0.235391 | ||||||||
\(406\) | 19.1936 | 0.952561 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.20373 | 0.356638 | ||||||||
\(409\) | 13.0620 | 0.645874 | 0.322937 | − | 0.946421i | \(-0.395330\pi\) | ||||
0.322937 | + | 0.946421i | \(0.395330\pi\) | |||||||
\(410\) | 2.06645 | 0.102055 | ||||||||
\(411\) | 0.102440 | 0.00505299 | ||||||||
\(412\) | −3.00499 | −0.148045 | ||||||||
\(413\) | 27.1176 | 1.33437 | ||||||||
\(414\) | 0.540301 | 0.0265544 | ||||||||
\(415\) | 0.580381 | 0.0284898 | ||||||||
\(416\) | 1.35442 | 0.0664057 | ||||||||
\(417\) | −28.0743 | −1.37480 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4288 | 1.19342 | 0.596712 | − | 0.802456i | \(-0.296474\pi\) | ||||
0.596712 | + | 0.802456i | \(0.296474\pi\) | |||||||
\(420\) | −3.22362 | −0.157297 | ||||||||
\(421\) | −11.0083 | −0.536514 | −0.268257 | − | 0.963347i | \(-0.586448\pi\) | ||||
−0.268257 | + | 0.963347i | \(0.586448\pi\) | |||||||
\(422\) | −8.44427 | −0.411061 | ||||||||
\(423\) | −2.69322 | −0.130949 | ||||||||
\(424\) | 4.25789 | 0.206782 | ||||||||
\(425\) | −20.1413 | −0.976997 | ||||||||
\(426\) | 10.5596 | 0.511615 | ||||||||
\(427\) | 31.8948 | 1.54350 | ||||||||
\(428\) | −7.33334 | −0.354471 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.50069 | 0.217042 | ||||||||
\(431\) | −13.5147 | −0.650978 | −0.325489 | − | 0.945546i | \(-0.605529\pi\) | ||||
−0.325489 | + | 0.945546i | \(0.605529\pi\) | |||||||
\(432\) | −5.35414 | −0.257601 | ||||||||
\(433\) | 22.8978 | 1.10040 | 0.550199 | − | 0.835033i | \(-0.314552\pi\) | ||||
0.550199 | + | 0.835033i | \(0.314552\pi\) | |||||||
\(434\) | 32.7265 | 1.57092 | ||||||||
\(435\) | −5.35128 | −0.256574 | ||||||||
\(436\) | 3.90465 | 0.186999 | ||||||||
\(437\) | 2.71065 | 0.129668 | ||||||||
\(438\) | −23.4925 | −1.12252 | ||||||||
\(439\) | −4.19717 | −0.200320 | −0.100160 | − | 0.994971i | \(-0.531935\pi\) | ||||
−0.100160 | + | 0.994971i | \(0.531935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.909374 | −0.0433035 | ||||||||
\(442\) | 5.83013 | 0.277311 | ||||||||
\(443\) | −31.0222 | −1.47391 | −0.736954 | − | 0.675943i | \(-0.763737\pi\) | ||||
−0.736954 | + | 0.675943i | \(0.763737\pi\) | |||||||
\(444\) | 6.07998 | 0.288543 | ||||||||
\(445\) | 8.58873 | 0.407145 | ||||||||
\(446\) | −0.309593 | −0.0146596 | ||||||||
\(447\) | 14.9815 | 0.708599 | ||||||||
\(448\) | 3.40033 | 0.160651 | ||||||||
\(449\) | −30.0246 | −1.41695 | −0.708474 | − | 0.705737i | \(-0.750616\pi\) | ||||
−0.708474 | + | 0.705737i | \(0.750616\pi\) | |||||||
\(450\) | 0.932661 | 0.0439661 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.36327 | −0.299303 | ||||||||
\(453\) | −14.2484 | −0.669449 | ||||||||
\(454\) | 17.8942 | 0.839817 | ||||||||
\(455\) | −2.60894 | −0.122309 | ||||||||
\(456\) | −1.67352 | −0.0783698 | ||||||||
\(457\) | −9.16793 | −0.428858 | −0.214429 | − | 0.976740i | \(-0.568789\pi\) | ||||
−0.214429 | + | 0.976740i | \(0.568789\pi\) | |||||||
\(458\) | −4.77162 | −0.222963 | ||||||||
\(459\) | −23.0471 | −1.07575 | ||||||||
\(460\) | 1.53555 | 0.0715956 | ||||||||
\(461\) | −30.4549 | −1.41843 | −0.709213 | − | 0.704995i | \(-0.750949\pi\) | ||||
−0.709213 | + | 0.704995i | \(0.750949\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.4686 | 0.765359 | 0.382679 | − | 0.923881i | \(-0.375001\pi\) | ||||
0.382679 | + | 0.923881i | \(0.375001\pi\) | |||||||
\(464\) | 5.64462 | 0.262045 | ||||||||
\(465\) | −9.12433 | −0.423131 | ||||||||
\(466\) | −12.5120 | −0.579606 | ||||||||
\(467\) | −36.8201 | −1.70383 | −0.851916 | − | 0.523679i | \(-0.824559\pi\) | ||||
−0.851916 | + | 0.523679i | \(0.824559\pi\) | |||||||
\(468\) | −0.269969 | −0.0124793 | ||||||||
\(469\) | 3.43443 | 0.158587 | ||||||||
\(470\) | −7.65422 | −0.353063 | ||||||||
\(471\) | 20.2289 | 0.932099 | ||||||||
\(472\) | 7.97498 | 0.367078 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −11.9018 | −0.546669 | ||||||||
\(475\) | 4.67909 | 0.214691 | ||||||||
\(476\) | 14.6369 | 0.670879 | ||||||||
\(477\) | −0.848706 | −0.0388596 | ||||||||
\(478\) | 11.2492 | 0.514528 | ||||||||
\(479\) | −31.1691 | −1.42415 | −0.712077 | − | 0.702102i | \(-0.752245\pi\) | ||||
−0.712077 | + | 0.702102i | \(0.752245\pi\) | |||||||
\(480\) | −0.948032 | −0.0432715 | ||||||||
\(481\) | 4.92065 | 0.224362 | ||||||||
\(482\) | 23.4105 | 1.06632 | ||||||||
\(483\) | −15.4250 | −0.701864 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.98875 | −0.181120 | ||||||||
\(486\) | 2.06794 | 0.0938037 | ||||||||
\(487\) | 40.4109 | 1.83119 | 0.915597 | − | 0.402097i | \(-0.131718\pi\) | ||||
0.915597 | + | 0.402097i | \(0.131718\pi\) | |||||||
\(488\) | 9.37992 | 0.424609 | ||||||||
\(489\) | 22.8134 | 1.03166 | ||||||||
\(490\) | −2.58447 | −0.116755 | ||||||||
\(491\) | −9.86715 | −0.445298 | −0.222649 | − | 0.974899i | \(-0.571470\pi\) | ||||
−0.222649 | + | 0.974899i | \(0.571470\pi\) | |||||||
\(492\) | −6.10471 | −0.275222 | ||||||||
\(493\) | 24.2974 | 1.09430 | ||||||||
\(494\) | −1.35442 | −0.0609380 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.62449 | 0.432153 | ||||||||
\(497\) | 21.4555 | 0.962410 | ||||||||
\(498\) | −1.71456 | −0.0768313 | ||||||||
\(499\) | −13.4498 | −0.602094 | −0.301047 | − | 0.953609i | \(-0.597336\pi\) | ||||
−0.301047 | + | 0.953609i | \(0.597336\pi\) | |||||||
\(500\) | 5.48310 | 0.245212 | ||||||||
\(501\) | −6.31988 | −0.282352 | ||||||||
\(502\) | −27.2448 | −1.21599 | ||||||||
\(503\) | −22.5378 | −1.00491 | −0.502456 | − | 0.864603i | \(-0.667570\pi\) | ||||
−0.502456 | + | 0.864603i | \(0.667570\pi\) | |||||||
\(504\) | −0.677772 | −0.0301904 | ||||||||
\(505\) | 4.60010 | 0.204702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.6858 | −0.829866 | ||||||||
\(508\) | 17.3575 | 0.770115 | ||||||||
\(509\) | 4.87076 | 0.215893 | 0.107946 | − | 0.994157i | \(-0.465573\pi\) | ||||
0.107946 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(510\) | −4.08084 | −0.180702 | ||||||||
\(511\) | −47.7331 | −2.11159 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.35414 | 0.236391 | ||||||||
\(514\) | 18.9406 | 0.835435 | ||||||||
\(515\) | 1.70230 | 0.0750121 | ||||||||
\(516\) | −13.2959 | −0.585321 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 12.3536 | 0.542784 | ||||||||
\(519\) | −3.21464 | −0.141107 | ||||||||
\(520\) | −0.767262 | −0.0336466 | ||||||||
\(521\) | 6.08484 | 0.266582 | 0.133291 | − | 0.991077i | \(-0.457446\pi\) | ||||
0.133291 | + | 0.991077i | \(0.457446\pi\) | |||||||
\(522\) | −1.12511 | −0.0492449 | ||||||||
\(523\) | 40.9388 | 1.79013 | 0.895065 | − | 0.445936i | \(-0.147129\pi\) | ||||
0.895065 | + | 0.445936i | \(0.147129\pi\) | |||||||
\(524\) | −3.39115 | −0.148143 | ||||||||
\(525\) | −26.6265 | −1.16208 | ||||||||
\(526\) | −28.1414 | −1.22702 | ||||||||
\(527\) | 41.4290 | 1.80467 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.6524 | −0.680538 | ||||||||
\(530\) | −2.41205 | −0.104773 | ||||||||
\(531\) | −1.58961 | −0.0689834 | ||||||||
\(532\) | −3.40033 | −0.147423 | ||||||||
\(533\) | −4.94067 | −0.214004 | ||||||||
\(534\) | −25.3728 | −1.09799 | ||||||||
\(535\) | 4.15426 | 0.179604 | ||||||||
\(536\) | 1.01003 | 0.0436266 | ||||||||
\(537\) | −21.6188 | −0.932921 | ||||||||
\(538\) | −0.144365 | −0.00622400 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.03306 | 0.130522 | ||||||||
\(541\) | 20.1046 | 0.864366 | 0.432183 | − | 0.901786i | \(-0.357743\pi\) | ||||
0.432183 | + | 0.901786i | \(0.357743\pi\) | |||||||
\(542\) | 7.88292 | 0.338601 | ||||||||
\(543\) | 29.7522 | 1.27679 | ||||||||
\(544\) | 4.30453 | 0.184555 | ||||||||
\(545\) | −2.21194 | −0.0947493 | ||||||||
\(546\) | 7.70734 | 0.329844 | ||||||||
\(547\) | 30.7418 | 1.31442 | 0.657212 | − | 0.753706i | \(-0.271736\pi\) | ||||
0.657212 | + | 0.753706i | \(0.271736\pi\) | |||||||
\(548\) | 0.0612122 | 0.00261486 | ||||||||
\(549\) | −1.86965 | −0.0797949 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.64462 | −0.240469 | ||||||||
\(552\) | −4.53633 | −0.193079 | ||||||||
\(553\) | −24.1826 | −1.02835 | ||||||||
\(554\) | −16.4244 | −0.697805 | ||||||||
\(555\) | −3.44424 | −0.146200 | ||||||||
\(556\) | −16.7756 | −0.711443 | ||||||||
\(557\) | 9.53569 | 0.404040 | 0.202020 | − | 0.979381i | \(-0.435249\pi\) | ||||
0.202020 | + | 0.979381i | \(0.435249\pi\) | |||||||
\(558\) | −1.91841 | −0.0812126 | ||||||||
\(559\) | −10.7607 | −0.455128 | ||||||||
\(560\) | −1.92625 | −0.0813990 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.71799 | 0.0724692 | ||||||||
\(563\) | −38.1065 | −1.60600 | −0.802998 | − | 0.595981i | \(-0.796763\pi\) | ||||
−0.802998 | + | 0.595981i | \(0.796763\pi\) | |||||||
\(564\) | 22.6121 | 0.952140 | ||||||||
\(565\) | 3.60472 | 0.151652 | ||||||||
\(566\) | 5.05430 | 0.212448 | ||||||||
\(567\) | −28.4346 | −1.19414 | ||||||||
\(568\) | 6.30982 | 0.264754 | ||||||||
\(569\) | −22.1572 | −0.928879 | −0.464439 | − | 0.885605i | \(-0.653744\pi\) | ||||
−0.464439 | + | 0.885605i | \(0.653744\pi\) | |||||||
\(570\) | 0.948032 | 0.0397087 | ||||||||
\(571\) | −19.3268 | −0.808801 | −0.404400 | − | 0.914582i | \(-0.632520\pi\) | ||||
−0.404400 | + | 0.914582i | \(0.632520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.6804 | −1.44880 | ||||||||
\(574\) | −12.4038 | −0.517725 | ||||||||
\(575\) | 12.6834 | 0.528933 | ||||||||
\(576\) | −0.199325 | −0.00830522 | ||||||||
\(577\) | 26.9783 | 1.12312 | 0.561560 | − | 0.827436i | \(-0.310201\pi\) | ||||
0.561560 | + | 0.827436i | \(0.310201\pi\) | |||||||
\(578\) | 1.52902 | 0.0635989 | ||||||||
\(579\) | 20.3058 | 0.843882 | ||||||||
\(580\) | −3.19761 | −0.132774 | ||||||||
\(581\) | −3.48372 | −0.144529 | ||||||||
\(582\) | 11.7836 | 0.488444 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.0378 | −0.580887 | ||||||||
\(585\) | 0.152935 | 0.00632307 | ||||||||
\(586\) | −19.2526 | −0.795319 | ||||||||
\(587\) | −27.5285 | −1.13622 | −0.568112 | − | 0.822951i | \(-0.692326\pi\) | ||||
−0.568112 | + | 0.822951i | \(0.692326\pi\) | |||||||
\(588\) | 7.63504 | 0.314864 | ||||||||
\(589\) | −9.62449 | −0.396570 | ||||||||
\(590\) | −4.51774 | −0.185992 | ||||||||
\(591\) | −23.7802 | −0.978188 | ||||||||
\(592\) | 3.63304 | 0.149317 | ||||||||
\(593\) | −0.523811 | −0.0215103 | −0.0107552 | − | 0.999942i | \(-0.503424\pi\) | ||||
−0.0107552 | + | 0.999942i | \(0.503424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.29162 | −0.339923 | ||||||||
\(596\) | 8.95206 | 0.366691 | ||||||||
\(597\) | −1.63496 | −0.0669143 | ||||||||
\(598\) | −3.67135 | −0.150133 | ||||||||
\(599\) | −2.50378 | −0.102302 | −0.0511508 | − | 0.998691i | \(-0.516289\pi\) | ||||
−0.0511508 | + | 0.998691i | \(0.516289\pi\) | |||||||
\(600\) | −7.83056 | −0.319681 | ||||||||
\(601\) | −19.0143 | −0.775608 | −0.387804 | − | 0.921742i | \(-0.626766\pi\) | ||||
−0.387804 | + | 0.921742i | \(0.626766\pi\) | |||||||
\(602\) | −27.0152 | −1.10106 | ||||||||
\(603\) | −0.201324 | −0.00819855 | ||||||||
\(604\) | −8.51404 | −0.346431 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.5896 | −0.552040 | ||||||||
\(607\) | −37.9481 | −1.54026 | −0.770132 | − | 0.637884i | \(-0.779810\pi\) | ||||
−0.770132 | + | 0.637884i | \(0.779810\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 32.1209 | 1.30160 | ||||||||
\(610\) | −5.31362 | −0.215142 | ||||||||
\(611\) | 18.3004 | 0.740356 | ||||||||
\(612\) | −0.858003 | −0.0346827 | ||||||||
\(613\) | −17.9322 | −0.724274 | −0.362137 | − | 0.932125i | \(-0.617953\pi\) | ||||
−0.362137 | + | 0.932125i | \(0.617953\pi\) | |||||||
\(614\) | −12.2585 | −0.494712 | ||||||||
\(615\) | 3.45825 | 0.139450 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.0578 | −1.61267 | −0.806333 | − | 0.591462i | \(-0.798551\pi\) | ||||
−0.806333 | + | 0.591462i | \(0.798551\pi\) | |||||||
\(618\) | −5.02892 | −0.202293 | ||||||||
\(619\) | −24.2014 | −0.972737 | −0.486368 | − | 0.873754i | \(-0.661679\pi\) | ||||
−0.486368 | + | 0.873754i | \(0.661679\pi\) | |||||||
\(620\) | −5.45217 | −0.218965 | ||||||||
\(621\) | 14.5132 | 0.582395 | ||||||||
\(622\) | −5.48085 | −0.219762 | ||||||||
\(623\) | −51.5535 | −2.06545 | ||||||||
\(624\) | 2.26664 | 0.0907383 | ||||||||
\(625\) | 20.2893 | 0.811573 | ||||||||
\(626\) | 8.75492 | 0.349917 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.0876 | 0.482349 | ||||||||
\(629\) | 15.6386 | 0.623550 | ||||||||
\(630\) | 0.383951 | 0.0152970 | ||||||||
\(631\) | 48.8748 | 1.94567 | 0.972837 | − | 0.231489i | \(-0.0743599\pi\) | ||||
0.972837 | + | 0.231489i | \(0.0743599\pi\) | |||||||
\(632\) | −7.11185 | −0.282894 | ||||||||
\(633\) | −14.1317 | −0.561683 | ||||||||
\(634\) | −18.4394 | −0.732320 | ||||||||
\(635\) | −9.83284 | −0.390204 | ||||||||
\(636\) | 7.12568 | 0.282552 | ||||||||
\(637\) | 6.17920 | 0.244829 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.25771 | −0.0497541 | ||||||||
\(640\) | −0.566489 | −0.0223925 | ||||||||
\(641\) | −13.6718 | −0.540002 | −0.270001 | − | 0.962860i | \(-0.587024\pi\) | ||||
−0.270001 | + | 0.962860i | \(0.587024\pi\) | |||||||
\(642\) | −12.2725 | −0.484357 | ||||||||
\(643\) | 35.5605 | 1.40237 | 0.701185 | − | 0.712980i | \(-0.252655\pi\) | ||||
0.701185 | + | 0.712980i | \(0.252655\pi\) | |||||||
\(644\) | −9.21711 | −0.363205 | ||||||||
\(645\) | 7.53200 | 0.296572 | ||||||||
\(646\) | −4.30453 | −0.169360 | ||||||||
\(647\) | −34.6366 | −1.36170 | −0.680852 | − | 0.732421i | \(-0.738391\pi\) | ||||
−0.680852 | + | 0.732421i | \(0.738391\pi\) | |||||||
\(648\) | −8.36229 | −0.328502 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.33743 | −0.248574 | ||||||||
\(651\) | 54.7685 | 2.14655 | ||||||||
\(652\) | 13.6320 | 0.533870 | ||||||||
\(653\) | 7.70803 | 0.301638 | 0.150819 | − | 0.988561i | \(-0.451809\pi\) | ||||
0.150819 | + | 0.988561i | \(0.451809\pi\) | |||||||
\(654\) | 6.53452 | 0.255520 | ||||||||
\(655\) | 1.92105 | 0.0750617 | ||||||||
\(656\) | −3.64782 | −0.142424 | ||||||||
\(657\) | 2.79808 | 0.109164 | ||||||||
\(658\) | 45.9442 | 1.79109 | ||||||||
\(659\) | −2.66717 | −0.103898 | −0.0519491 | − | 0.998650i | \(-0.516543\pi\) | ||||
−0.0519491 | + | 0.998650i | \(0.516543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.9320 | 1.43649 | 0.718244 | − | 0.695792i | \(-0.244946\pi\) | ||||
0.718244 | + | 0.695792i | \(0.244946\pi\) | |||||||
\(662\) | 6.57096 | 0.255387 | ||||||||
\(663\) | 9.75684 | 0.378924 | ||||||||
\(664\) | −1.02452 | −0.0397592 | ||||||||
\(665\) | 1.92625 | 0.0746968 | ||||||||
\(666\) | −0.724158 | −0.0280605 | ||||||||
\(667\) | −15.3006 | −0.592441 | ||||||||
\(668\) | −3.77640 | −0.146113 | ||||||||
\(669\) | −0.518110 | −0.0200313 | ||||||||
\(670\) | −0.572170 | −0.0221049 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.69053 | 0.219517 | ||||||||
\(673\) | −49.1070 | −1.89293 | −0.946467 | − | 0.322799i | \(-0.895376\pi\) | ||||
−0.946467 | + | 0.322799i | \(0.895376\pi\) | |||||||
\(674\) | −23.5185 | −0.905900 | ||||||||
\(675\) | 25.0525 | 0.964271 | ||||||||
\(676\) | −11.1656 | −0.429445 | ||||||||
\(677\) | −3.66330 | −0.140792 | −0.0703961 | − | 0.997519i | \(-0.522426\pi\) | ||||
−0.0703961 | + | 0.997519i | \(0.522426\pi\) | |||||||
\(678\) | −10.6491 | −0.408975 | ||||||||
\(679\) | 23.9423 | 0.918823 | ||||||||
\(680\) | −2.43847 | −0.0935112 | ||||||||
\(681\) | 29.9463 | 1.14755 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.1273 | −0.884941 | −0.442471 | − | 0.896783i | \(-0.645898\pi\) | ||||
−0.442471 | + | 0.896783i | \(0.645898\pi\) | |||||||
\(684\) | 0.199325 | 0.00762139 | ||||||||
\(685\) | −0.0346761 | −0.00132490 | ||||||||
\(686\) | −8.28912 | −0.316480 | ||||||||
\(687\) | −7.98541 | −0.304662 | ||||||||
\(688\) | −7.94488 | −0.302896 | ||||||||
\(689\) | 5.76696 | 0.219704 | ||||||||
\(690\) | 2.56978 | 0.0978300 | ||||||||
\(691\) | 46.5289 | 1.77004 | 0.885021 | − | 0.465552i | \(-0.154144\pi\) | ||||
0.885021 | + | 0.465552i | \(0.154144\pi\) | |||||||
\(692\) | −1.92088 | −0.0730210 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.22613 | −0.236341 | ||||||||
\(695\) | 9.50319 | 0.360476 | ||||||||
\(696\) | 9.44639 | 0.358064 | ||||||||
\(697\) | −15.7022 | −0.594763 | ||||||||
\(698\) | 22.3550 | 0.846151 | ||||||||
\(699\) | −20.9390 | −0.791987 | ||||||||
\(700\) | −15.9105 | −0.601359 | ||||||||
\(701\) | −15.3125 | −0.578344 | −0.289172 | − | 0.957277i | \(-0.593380\pi\) | ||||
−0.289172 | + | 0.957277i | \(0.593380\pi\) | |||||||
\(702\) | −7.25173 | −0.273699 | ||||||||
\(703\) | −3.63304 | −0.137023 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.8095 | −0.482434 | ||||||||
\(706\) | 36.4241 | 1.37084 | ||||||||
\(707\) | −27.6119 | −1.03845 | ||||||||
\(708\) | 13.3463 | 0.501584 | ||||||||
\(709\) | 35.5773 | 1.33613 | 0.668067 | − | 0.744101i | \(-0.267122\pi\) | ||||
0.668067 | + | 0.744101i | \(0.267122\pi\) | |||||||
\(710\) | −3.57444 | −0.134147 | ||||||||
\(711\) | 1.41757 | 0.0531631 | ||||||||
\(712\) | −15.1613 | −0.568195 | ||||||||
\(713\) | −26.0886 | −0.977027 | ||||||||
\(714\) | 24.4951 | 0.916706 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.9182 | −0.482774 | ||||||||
\(717\) | 18.8258 | 0.703064 | ||||||||
\(718\) | 7.54684 | 0.281645 | ||||||||
\(719\) | 41.8647 | 1.56129 | 0.780646 | − | 0.624974i | \(-0.214890\pi\) | ||||
0.780646 | + | 0.624974i | \(0.214890\pi\) | |||||||
\(720\) | 0.112916 | 0.00420812 | ||||||||
\(721\) | −10.2180 | −0.380537 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 39.1780 | 1.45705 | ||||||||
\(724\) | 17.7782 | 0.660722 | ||||||||
\(725\) | −26.4117 | −0.980904 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6492 | 0.654574 | 0.327287 | − | 0.944925i | \(-0.393866\pi\) | ||||
0.327287 | + | 0.944925i | \(0.393866\pi\) | |||||||
\(728\) | 4.60546 | 0.170690 | ||||||||
\(729\) | 28.5476 | 1.05732 | ||||||||
\(730\) | 7.95224 | 0.294326 | ||||||||
\(731\) | −34.1990 | −1.26490 | ||||||||
\(732\) | 15.6975 | 0.580196 | ||||||||
\(733\) | −42.7110 | −1.57756 | −0.788782 | − | 0.614672i | \(-0.789288\pi\) | ||||
−0.788782 | + | 0.614672i | \(0.789288\pi\) | |||||||
\(734\) | 25.7229 | 0.949450 | ||||||||
\(735\) | −4.32517 | −0.159536 | ||||||||
\(736\) | −2.71065 | −0.0999159 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.727103 | 0.0267650 | ||||||||
\(739\) | −5.03814 | −0.185331 | −0.0926655 | − | 0.995697i | \(-0.529539\pi\) | ||||
−0.0926655 | + | 0.995697i | \(0.529539\pi\) | |||||||
\(740\) | −2.05808 | −0.0756565 | ||||||||
\(741\) | −2.26664 | −0.0832672 | ||||||||
\(742\) | 14.4783 | 0.531514 | ||||||||
\(743\) | 22.7649 | 0.835165 | 0.417583 | − | 0.908639i | \(-0.362877\pi\) | ||||
0.417583 | + | 0.908639i | \(0.362877\pi\) | |||||||
\(744\) | 16.1068 | 0.590504 | ||||||||
\(745\) | −5.07125 | −0.185796 | ||||||||
\(746\) | −7.13854 | −0.261360 | ||||||||
\(747\) | 0.204213 | 0.00747177 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.9358 | −0.911134 | ||||||||
\(750\) | 9.17609 | 0.335063 | ||||||||
\(751\) | −10.7708 | −0.393031 | −0.196515 | − | 0.980501i | \(-0.562963\pi\) | ||||
−0.196515 | + | 0.980501i | \(0.562963\pi\) | |||||||
\(752\) | 13.5117 | 0.492720 | ||||||||
\(753\) | −45.5947 | −1.66156 | ||||||||
\(754\) | 7.64515 | 0.278420 | ||||||||
\(755\) | 4.82311 | 0.175531 | ||||||||
\(756\) | −18.2059 | −0.662141 | ||||||||
\(757\) | −39.7209 | −1.44368 | −0.721841 | − | 0.692059i | \(-0.756704\pi\) | ||||
−0.721841 | + | 0.692059i | \(0.756704\pi\) | |||||||
\(758\) | −27.1836 | −0.987355 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.566489 | 0.0205487 | ||||||||
\(761\) | 50.5954 | 1.83408 | 0.917041 | − | 0.398794i | \(-0.130571\pi\) | ||||
0.917041 | + | 0.398794i | \(0.130571\pi\) | |||||||
\(762\) | 29.0482 | 1.05230 | ||||||||
\(763\) | 13.2771 | 0.480664 | ||||||||
\(764\) | −20.7230 | −0.749733 | ||||||||
\(765\) | 0.486049 | 0.0175731 | ||||||||
\(766\) | −30.3425 | −1.09632 | ||||||||
\(767\) | 10.8014 | 0.390017 | ||||||||
\(768\) | 1.67352 | 0.0603880 | ||||||||
\(769\) | −21.0614 | −0.759495 | −0.379748 | − | 0.925090i | \(-0.623989\pi\) | ||||
−0.379748 | + | 0.925090i | \(0.623989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.6976 | 1.14156 | ||||||||
\(772\) | 12.1336 | 0.436698 | ||||||||
\(773\) | −6.82724 | −0.245559 | −0.122779 | − | 0.992434i | \(-0.539181\pi\) | ||||
−0.122779 | + | 0.992434i | \(0.539181\pi\) | |||||||
\(774\) | 1.58362 | 0.0569219 | ||||||||
\(775\) | −45.0339 | −1.61766 | ||||||||
\(776\) | 7.04118 | 0.252764 | ||||||||
\(777\) | 20.6739 | 0.741674 | ||||||||
\(778\) | 5.82380 | 0.208793 | ||||||||
\(779\) | 3.64782 | 0.130697 | ||||||||
\(780\) | −1.28403 | −0.0459756 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −11.6681 | −0.417250 | ||||||||
\(783\) | −30.2221 | −1.08005 | ||||||||
\(784\) | 4.56226 | 0.162938 | ||||||||
\(785\) | −6.84751 | −0.244398 | ||||||||
\(786\) | −5.67516 | −0.202426 | ||||||||
\(787\) | −45.8465 | −1.63425 | −0.817125 | − | 0.576461i | \(-0.804433\pi\) | ||||
−0.817125 | + | 0.576461i | \(0.804433\pi\) | |||||||
\(788\) | −14.2097 | −0.506199 | ||||||||
\(789\) | −47.0953 | −1.67664 | ||||||||
\(790\) | 4.02878 | 0.143338 | ||||||||
\(791\) | −21.6372 | −0.769331 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7043 | 0.451143 | ||||||||
\(794\) | 2.13644 | 0.0758194 | ||||||||
\(795\) | −4.03662 | −0.143164 | ||||||||
\(796\) | −0.976956 | −0.0346273 | ||||||||
\(797\) | −39.1554 | −1.38696 | −0.693478 | − | 0.720478i | \(-0.743923\pi\) | ||||
−0.693478 | + | 0.720478i | \(0.743923\pi\) | |||||||
\(798\) | −5.69053 | −0.201443 | ||||||||
\(799\) | 58.1615 | 2.05761 | ||||||||
\(800\) | −4.67909 | −0.165431 | ||||||||
\(801\) | 3.02204 | 0.106778 | ||||||||
\(802\) | 3.52506 | 0.124474 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.69030 | 0.0596124 | ||||||||
\(805\) | 5.22140 | 0.184030 | ||||||||
\(806\) | 13.0356 | 0.459158 | ||||||||
\(807\) | −0.241597 | −0.00850463 | ||||||||
\(808\) | −8.12037 | −0.285674 | ||||||||
\(809\) | 29.0753 | 1.02223 | 0.511116 | − | 0.859512i | \(-0.329232\pi\) | ||||
0.511116 | + | 0.859512i | \(0.329232\pi\) | |||||||
\(810\) | 4.73715 | 0.166446 | ||||||||
\(811\) | −20.3401 | −0.714238 | −0.357119 | − | 0.934059i | \(-0.616241\pi\) | ||||
−0.357119 | + | 0.934059i | \(0.616241\pi\) | |||||||
\(812\) | 19.1936 | 0.673562 | ||||||||
\(813\) | 13.1922 | 0.462672 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.72238 | −0.270503 | ||||||||
\(816\) | 7.20373 | 0.252181 | ||||||||
\(817\) | 7.94488 | 0.277956 | ||||||||
\(818\) | 13.0620 | 0.456702 | ||||||||
\(819\) | −0.917985 | −0.0320770 | ||||||||
\(820\) | 2.06645 | 0.0721636 | ||||||||
\(821\) | −10.1130 | −0.352947 | −0.176474 | − | 0.984305i | \(-0.556469\pi\) | ||||
−0.176474 | + | 0.984305i | \(0.556469\pi\) | |||||||
\(822\) | 0.102440 | 0.00357301 | ||||||||
\(823\) | 17.1457 | 0.597662 | 0.298831 | − | 0.954306i | \(-0.403403\pi\) | ||||
0.298831 | + | 0.954306i | \(0.403403\pi\) | |||||||
\(824\) | −3.00499 | −0.104684 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.1176 | 0.943541 | ||||||||
\(827\) | 46.5796 | 1.61973 | 0.809866 | − | 0.586615i | \(-0.199540\pi\) | ||||
0.809866 | + | 0.586615i | \(0.199540\pi\) | |||||||
\(828\) | 0.540301 | 0.0187768 | ||||||||
\(829\) | −32.4293 | −1.12632 | −0.563158 | − | 0.826350i | \(-0.690414\pi\) | ||||
−0.563158 | + | 0.826350i | \(0.690414\pi\) | |||||||
\(830\) | 0.580381 | 0.0201453 | ||||||||
\(831\) | −27.4866 | −0.953498 | ||||||||
\(832\) | 1.35442 | 0.0469559 | ||||||||
\(833\) | 19.6384 | 0.680431 | ||||||||
\(834\) | −28.0743 | −0.972134 | ||||||||
\(835\) | 2.13929 | 0.0740331 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −51.5309 | −1.78117 | ||||||||
\(838\) | 24.4288 | 0.843878 | ||||||||
\(839\) | 44.9176 | 1.55073 | 0.775363 | − | 0.631516i | \(-0.217567\pi\) | ||||
0.775363 | + | 0.631516i | \(0.217567\pi\) | |||||||
\(840\) | −3.22362 | −0.111226 | ||||||||
\(841\) | 2.86168 | 0.0986786 | ||||||||
\(842\) | −11.0083 | −0.379373 | ||||||||
\(843\) | 2.87510 | 0.0990237 | ||||||||
\(844\) | −8.44427 | −0.290664 | ||||||||
\(845\) | 6.32517 | 0.217592 | ||||||||
\(846\) | −2.69322 | −0.0925948 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.25789 | 0.146217 | ||||||||
\(849\) | 8.45847 | 0.290294 | ||||||||
\(850\) | −20.1413 | −0.690841 | ||||||||
\(851\) | −9.84791 | −0.337582 | ||||||||
\(852\) | 10.5596 | 0.361767 | ||||||||
\(853\) | −41.7985 | −1.43115 | −0.715577 | − | 0.698534i | \(-0.753836\pi\) | ||||
−0.715577 | + | 0.698534i | \(0.753836\pi\) | |||||||
\(854\) | 31.8948 | 1.09142 | ||||||||
\(855\) | −0.112916 | −0.00386163 | ||||||||
\(856\) | −7.33334 | −0.250649 | ||||||||
\(857\) | 20.6115 | 0.704076 | 0.352038 | − | 0.935986i | \(-0.385489\pi\) | ||||
0.352038 | + | 0.935986i | \(0.385489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.0170 | 1.67244 | 0.836220 | − | 0.548394i | \(-0.184761\pi\) | ||||
0.836220 | + | 0.548394i | \(0.184761\pi\) | |||||||
\(860\) | 4.50069 | 0.153472 | ||||||||
\(861\) | −20.7580 | −0.707432 | ||||||||
\(862\) | −13.5147 | −0.460311 | ||||||||
\(863\) | −10.0126 | −0.340833 | −0.170416 | − | 0.985372i | \(-0.554511\pi\) | ||||
−0.170416 | + | 0.985372i | \(0.554511\pi\) | |||||||
\(864\) | −5.35414 | −0.182152 | ||||||||
\(865\) | 1.08816 | 0.0369985 | ||||||||
\(866\) | 22.8978 | 0.778099 | ||||||||
\(867\) | 2.55885 | 0.0869031 | ||||||||
\(868\) | 32.7265 | 1.11081 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −5.35128 | −0.181425 | ||||||||
\(871\) | 1.36800 | 0.0463528 | ||||||||
\(872\) | 3.90465 | 0.132228 | ||||||||
\(873\) | −1.40348 | −0.0475008 | ||||||||
\(874\) | 2.71065 | 0.0916891 | ||||||||
\(875\) | 18.6444 | 0.630295 | ||||||||
\(876\) | −23.4925 | −0.793738 | ||||||||
\(877\) | 40.9542 | 1.38293 | 0.691463 | − | 0.722412i | \(-0.256967\pi\) | ||||
0.691463 | + | 0.722412i | \(0.256967\pi\) | |||||||
\(878\) | −4.19717 | −0.141648 | ||||||||
\(879\) | −32.2197 | −1.08674 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.6017 | −1.60374 | −0.801870 | − | 0.597498i | \(-0.796161\pi\) | ||||
−0.801870 | + | 0.597498i | \(0.796161\pi\) | |||||||
\(882\) | −0.909374 | −0.0306202 | ||||||||
\(883\) | −18.8140 | −0.633142 | −0.316571 | − | 0.948569i | \(-0.602532\pi\) | ||||
−0.316571 | + | 0.948569i | \(0.602532\pi\) | |||||||
\(884\) | 5.83013 | 0.196088 | ||||||||
\(885\) | −7.56053 | −0.254145 | ||||||||
\(886\) | −31.0222 | −1.04221 | ||||||||
\(887\) | −36.2917 | −1.21856 | −0.609278 | − | 0.792957i | \(-0.708541\pi\) | ||||
−0.609278 | + | 0.792957i | \(0.708541\pi\) | |||||||
\(888\) | 6.07998 | 0.204031 | ||||||||
\(889\) | 59.0213 | 1.97951 | ||||||||
\(890\) | 8.58873 | 0.287895 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.309593 | −0.0103659 | ||||||||
\(893\) | −13.5117 | −0.452151 | ||||||||
\(894\) | 14.9815 | 0.501055 | ||||||||
\(895\) | 7.31800 | 0.244614 | ||||||||
\(896\) | 3.40033 | 0.113597 | ||||||||
\(897\) | −6.14408 | −0.205145 | ||||||||
\(898\) | −30.0246 | −1.00193 | ||||||||
\(899\) | 54.3266 | 1.81189 | ||||||||
\(900\) | 0.932661 | 0.0310887 | ||||||||
\(901\) | 18.3283 | 0.610603 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −45.2106 | −1.50451 | ||||||||
\(904\) | −6.36327 | −0.211639 | ||||||||
\(905\) | −10.0712 | −0.334777 | ||||||||
\(906\) | −14.2484 | −0.473372 | ||||||||
\(907\) | −44.4140 | −1.47474 | −0.737371 | − | 0.675488i | \(-0.763933\pi\) | ||||
−0.737371 | + | 0.675488i | \(0.763933\pi\) | |||||||
\(908\) | 17.8942 | 0.593840 | ||||||||
\(909\) | 1.61859 | 0.0536854 | ||||||||
\(910\) | −2.60894 | −0.0864857 | ||||||||
\(911\) | 14.7495 | 0.488674 | 0.244337 | − | 0.969690i | \(-0.421430\pi\) | ||||
0.244337 | + | 0.969690i | \(0.421430\pi\) | |||||||
\(912\) | −1.67352 | −0.0554158 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −9.16793 | −0.303248 | ||||||||
\(915\) | −8.89246 | −0.293976 | ||||||||
\(916\) | −4.77162 | −0.157659 | ||||||||
\(917\) | −11.5310 | −0.380789 | ||||||||
\(918\) | −23.0471 | −0.760667 | ||||||||
\(919\) | −0.209240 | −0.00690220 | −0.00345110 | − | 0.999994i | \(-0.501099\pi\) | ||||
−0.00345110 | + | 0.999994i | \(0.501099\pi\) | |||||||
\(920\) | 1.53555 | 0.0506257 | ||||||||
\(921\) | −20.5148 | −0.675987 | ||||||||
\(922\) | −30.4549 | −1.00298 | ||||||||
\(923\) | 8.54611 | 0.281299 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.9993 | −0.558935 | ||||||||
\(926\) | 16.4686 | 0.541190 | ||||||||
\(927\) | 0.598971 | 0.0196728 | ||||||||
\(928\) | 5.64462 | 0.185294 | ||||||||
\(929\) | 12.5178 | 0.410695 | 0.205348 | − | 0.978689i | \(-0.434168\pi\) | ||||
0.205348 | + | 0.978689i | \(0.434168\pi\) | |||||||
\(930\) | −9.12433 | −0.299199 | ||||||||
\(931\) | −4.56226 | −0.149522 | ||||||||
\(932\) | −12.5120 | −0.409843 | ||||||||
\(933\) | −9.17233 | −0.300288 | ||||||||
\(934\) | −36.8201 | −1.20479 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.269969 | −0.00882422 | ||||||||
\(937\) | 38.2958 | 1.25107 | 0.625534 | − | 0.780197i | \(-0.284881\pi\) | ||||
0.625534 | + | 0.780197i | \(0.284881\pi\) | |||||||
\(938\) | 3.43443 | 0.112138 | ||||||||
\(939\) | 14.6516 | 0.478135 | ||||||||
\(940\) | −7.65422 | −0.249653 | ||||||||
\(941\) | 58.5062 | 1.90725 | 0.953623 | − | 0.301002i | \(-0.0973212\pi\) | ||||
0.953623 | + | 0.301002i | \(0.0973212\pi\) | |||||||
\(942\) | 20.2289 | 0.659094 | ||||||||
\(943\) | 9.88797 | 0.321997 | ||||||||
\(944\) | 7.97498 | 0.259563 | ||||||||
\(945\) | 10.3134 | 0.335496 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.2392 | −1.11262 | −0.556312 | − | 0.830974i | \(-0.687784\pi\) | ||||
−0.556312 | + | 0.830974i | \(0.687784\pi\) | |||||||
\(948\) | −11.9018 | −0.386553 | ||||||||
\(949\) | −19.0130 | −0.617187 | ||||||||
\(950\) | 4.67909 | 0.151810 | ||||||||
\(951\) | −30.8587 | −1.00066 | ||||||||
\(952\) | 14.6369 | 0.474383 | ||||||||
\(953\) | −24.3715 | −0.789471 | −0.394736 | − | 0.918795i | \(-0.629164\pi\) | ||||
−0.394736 | + | 0.918795i | \(0.629164\pi\) | |||||||
\(954\) | −0.848706 | −0.0274779 | ||||||||
\(955\) | 11.7394 | 0.379877 | ||||||||
\(956\) | 11.2492 | 0.363826 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.1691 | −1.00703 | ||||||||
\(959\) | 0.208142 | 0.00672126 | ||||||||
\(960\) | −0.948032 | −0.0305976 | ||||||||
\(961\) | 61.6309 | 1.98809 | ||||||||
\(962\) | 4.92065 | 0.158648 | ||||||||
\(963\) | 1.46172 | 0.0471033 | ||||||||
\(964\) | 23.4105 | 0.754003 | ||||||||
\(965\) | −6.87355 | −0.221268 | ||||||||
\(966\) | −15.4250 | −0.496293 | ||||||||
\(967\) | 44.3499 | 1.42620 | 0.713099 | − | 0.701063i | \(-0.247291\pi\) | ||||
0.713099 | + | 0.701063i | \(0.247291\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.20373 | −0.231417 | ||||||||
\(970\) | −3.98875 | −0.128071 | ||||||||
\(971\) | −19.7687 | −0.634408 | −0.317204 | − | 0.948357i | \(-0.602744\pi\) | ||||
−0.317204 | + | 0.948357i | \(0.602744\pi\) | |||||||
\(972\) | 2.06794 | 0.0663292 | ||||||||
\(973\) | −57.0426 | −1.82870 | ||||||||
\(974\) | 40.4109 | 1.29485 | ||||||||
\(975\) | −10.6058 | −0.339658 | ||||||||
\(976\) | 9.37992 | 0.300244 | ||||||||
\(977\) | 18.2277 | 0.583155 | 0.291577 | − | 0.956547i | \(-0.405820\pi\) | ||||
0.291577 | + | 0.956547i | \(0.405820\pi\) | |||||||
\(978\) | 22.8134 | 0.729494 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.58447 | −0.0825579 | ||||||||
\(981\) | −0.778296 | −0.0248491 | ||||||||
\(982\) | −9.86715 | −0.314873 | ||||||||
\(983\) | 56.2431 | 1.79388 | 0.896939 | − | 0.442155i | \(-0.145786\pi\) | ||||
0.896939 | + | 0.442155i | \(0.145786\pi\) | |||||||
\(984\) | −6.10471 | −0.194611 | ||||||||
\(985\) | 8.04964 | 0.256483 | ||||||||
\(986\) | 24.2974 | 0.773788 | ||||||||
\(987\) | 76.8886 | 2.44739 | ||||||||
\(988\) | −1.35442 | −0.0430897 | ||||||||
\(989\) | 21.5358 | 0.684798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.6909 | 1.54672 | 0.773358 | − | 0.633970i | \(-0.218576\pi\) | ||||
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(992\) | 9.62449 | 0.305578 | ||||||||
\(993\) | 10.9966 | 0.348968 | ||||||||
\(994\) | 21.4555 | 0.680527 | ||||||||
\(995\) | 0.553435 | 0.0175451 | ||||||||
\(996\) | −1.71456 | −0.0543279 | ||||||||
\(997\) | −50.2387 | −1.59107 | −0.795537 | − | 0.605905i | \(-0.792811\pi\) | ||||
−0.795537 | + | 0.605905i | \(0.792811\pi\) | |||||||
\(998\) | −13.4498 | −0.425745 | ||||||||
\(999\) | −19.4518 | −0.615429 |
(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 | 4598.2.a.cb.1.5 | yes | 8 | |
11.10 | odd | 2 | 4598.2.a.by.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.by.1.5 | ✓ | 8 | 11.10 | odd | 2 | ||
4598.2.a.cb.1.5 | yes | 8 | 1.1 | even | 1 | trivial |