Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [154,2,Mod(1,154)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(154, 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("154.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 154 = 2 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 154.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: | \(1.22969619113\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 154.1 |
$q$-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 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | −3.23607 | −1.32112 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 3.23607 | 1.02333 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.23607 | −0.934172 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −10.4721 | −2.70389 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.47214 | −1.56972 | −0.784862 | − | 0.619671i | \(-0.787266\pi\) | ||||
−0.784862 | + | 0.619671i | \(0.787266\pi\) | |||||||
\(18\) | 7.47214 | 1.76120 | ||||||||
\(19\) | −2.76393 | −0.634089 | −0.317045 | − | 0.948411i | \(-0.602691\pi\) | ||||
−0.317045 | + | 0.948411i | \(0.602691\pi\) | |||||||
\(20\) | 3.23607 | 0.723607 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −3.23607 | −0.660560 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 1.23607 | 0.242413 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | −10.4721 | −1.91194 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.23607 | −0.563327 | ||||||||
\(34\) | −6.47214 | −1.10996 | ||||||||
\(35\) | 3.23607 | 0.546995 | ||||||||
\(36\) | 7.47214 | 1.24536 | ||||||||
\(37\) | −10.9443 | −1.79923 | −0.899614 | − | 0.436687i | \(-0.856152\pi\) | ||||
−0.899614 | + | 0.436687i | \(0.856152\pi\) | |||||||
\(38\) | −2.76393 | −0.448369 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 3.23607 | 0.511667 | ||||||||
\(41\) | 6.47214 | 1.01078 | 0.505389 | − | 0.862892i | \(-0.331349\pi\) | ||||
0.505389 | + | 0.862892i | \(0.331349\pi\) | |||||||
\(42\) | −3.23607 | −0.499336 | ||||||||
\(43\) | −1.52786 | −0.232997 | −0.116499 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116499 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 24.1803 | 3.60459 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | −3.23607 | −0.467086 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.47214 | 0.773877 | ||||||||
\(51\) | 20.9443 | 2.93278 | ||||||||
\(52\) | 1.23607 | 0.171412 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | −14.4721 | −1.96941 | ||||||||
\(55\) | 3.23607 | 0.436351 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 8.94427 | 1.18470 | ||||||||
\(58\) | −4.47214 | −0.587220 | ||||||||
\(59\) | 7.23607 | 0.942056 | 0.471028 | − | 0.882118i | \(-0.343883\pi\) | ||||
0.471028 | + | 0.882118i | \(0.343883\pi\) | |||||||
\(60\) | −10.4721 | −1.35195 | ||||||||
\(61\) | −5.23607 | −0.670410 | −0.335205 | − | 0.942145i | \(-0.608806\pi\) | ||||
−0.335205 | + | 0.942145i | \(0.608806\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 7.47214 | 0.941401 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | −3.23607 | −0.398332 | ||||||||
\(67\) | −15.4164 | −1.88341 | −0.941707 | − | 0.336434i | \(-0.890779\pi\) | ||||
−0.941707 | + | 0.336434i | \(0.890779\pi\) | |||||||
\(68\) | −6.47214 | −0.784862 | ||||||||
\(69\) | −12.9443 | −1.55831 | ||||||||
\(70\) | 3.23607 | 0.386784 | ||||||||
\(71\) | −2.47214 | −0.293389 | −0.146694 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146694 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(72\) | 7.47214 | 0.880600 | ||||||||
\(73\) | −4.94427 | −0.578683 | −0.289342 | − | 0.957226i | \(-0.593436\pi\) | ||||
−0.289342 | + | 0.957226i | \(0.593436\pi\) | |||||||
\(74\) | −10.9443 | −1.27225 | ||||||||
\(75\) | −17.7082 | −2.04477 | ||||||||
\(76\) | −2.76393 | −0.317045 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 3.23607 | 0.361803 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 6.47214 | 0.714728 | ||||||||
\(83\) | 10.1803 | 1.11744 | 0.558719 | − | 0.829357i | \(-0.311293\pi\) | ||||
0.558719 | + | 0.829357i | \(0.311293\pi\) | |||||||
\(84\) | −3.23607 | −0.353084 | ||||||||
\(85\) | −20.9443 | −2.27173 | ||||||||
\(86\) | −1.52786 | −0.164754 | ||||||||
\(87\) | 14.4721 | 1.55158 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 24.1803 | 2.54883 | ||||||||
\(91\) | 1.23607 | 0.129575 | ||||||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | −6.47214 | −0.671129 | ||||||||
\(94\) | −2.00000 | −0.206284 | ||||||||
\(95\) | −8.94427 | −0.917663 | ||||||||
\(96\) | −3.23607 | −0.330280 | ||||||||
\(97\) | 3.52786 | 0.358200 | 0.179100 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179100 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 7.47214 | 0.750978 | ||||||||
\(100\) | 5.47214 | 0.547214 | ||||||||
\(101\) | −14.1803 | −1.41100 | −0.705498 | − | 0.708712i | \(-0.749277\pi\) | ||||
−0.705498 | + | 0.708712i | \(0.749277\pi\) | |||||||
\(102\) | 20.9443 | 2.07379 | ||||||||
\(103\) | 2.94427 | 0.290108 | 0.145054 | − | 0.989424i | \(-0.453664\pi\) | ||||
0.145054 | + | 0.989424i | \(0.453664\pi\) | |||||||
\(104\) | 1.23607 | 0.121206 | ||||||||
\(105\) | −10.4721 | −1.02198 | ||||||||
\(106\) | −0.472136 | −0.0458579 | ||||||||
\(107\) | −6.47214 | −0.625685 | −0.312842 | − | 0.949805i | \(-0.601281\pi\) | ||||
−0.312842 | + | 0.949805i | \(0.601281\pi\) | |||||||
\(108\) | −14.4721 | −1.39258 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 3.23607 | 0.308547 | ||||||||
\(111\) | 35.4164 | 3.36158 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 8.47214 | 0.796992 | 0.398496 | − | 0.917170i | \(-0.369532\pi\) | ||||
0.398496 | + | 0.917170i | \(0.369532\pi\) | |||||||
\(114\) | 8.94427 | 0.837708 | ||||||||
\(115\) | 12.9443 | 1.20706 | ||||||||
\(116\) | −4.47214 | −0.415227 | ||||||||
\(117\) | 9.23607 | 0.853875 | ||||||||
\(118\) | 7.23607 | 0.666134 | ||||||||
\(119\) | −6.47214 | −0.593300 | ||||||||
\(120\) | −10.4721 | −0.955971 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.23607 | −0.474051 | ||||||||
\(123\) | −20.9443 | −1.88848 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | 7.47214 | 0.665671 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.94427 | 0.435319 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | 9.23607 | 0.806959 | 0.403480 | − | 0.914989i | \(-0.367801\pi\) | ||||
0.403480 | + | 0.914989i | \(0.367801\pi\) | |||||||
\(132\) | −3.23607 | −0.281664 | ||||||||
\(133\) | −2.76393 | −0.239663 | ||||||||
\(134\) | −15.4164 | −1.33177 | ||||||||
\(135\) | −46.8328 | −4.03073 | ||||||||
\(136\) | −6.47214 | −0.554981 | ||||||||
\(137\) | 15.8885 | 1.35745 | 0.678725 | − | 0.734393i | \(-0.262533\pi\) | ||||
0.678725 | + | 0.734393i | \(0.262533\pi\) | |||||||
\(138\) | −12.9443 | −1.10189 | ||||||||
\(139\) | −8.29180 | −0.703301 | −0.351650 | − | 0.936131i | \(-0.614379\pi\) | ||||
−0.351650 | + | 0.936131i | \(0.614379\pi\) | |||||||
\(140\) | 3.23607 | 0.273498 | ||||||||
\(141\) | 6.47214 | 0.545052 | ||||||||
\(142\) | −2.47214 | −0.207457 | ||||||||
\(143\) | 1.23607 | 0.103365 | ||||||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | −14.4721 | −1.20185 | ||||||||
\(146\) | −4.94427 | −0.409191 | ||||||||
\(147\) | −3.23607 | −0.266906 | ||||||||
\(148\) | −10.9443 | −0.899614 | ||||||||
\(149\) | 22.3607 | 1.83186 | 0.915929 | − | 0.401340i | \(-0.131455\pi\) | ||||
0.915929 | + | 0.401340i | \(0.131455\pi\) | |||||||
\(150\) | −17.7082 | −1.44587 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | −2.76393 | −0.224184 | ||||||||
\(153\) | −48.3607 | −3.90973 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 6.47214 | 0.519854 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | 18.6525 | 1.48863 | 0.744315 | − | 0.667829i | \(-0.232776\pi\) | ||||
0.744315 | + | 0.667829i | \(0.232776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.52786 | 0.121168 | ||||||||
\(160\) | 3.23607 | 0.255834 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 24.4164 | 1.91833 | ||||||||
\(163\) | 7.41641 | 0.580898 | 0.290449 | − | 0.956890i | \(-0.406195\pi\) | ||||
0.290449 | + | 0.956890i | \(0.406195\pi\) | |||||||
\(164\) | 6.47214 | 0.505389 | ||||||||
\(165\) | −10.4721 | −0.815255 | ||||||||
\(166\) | 10.1803 | 0.790148 | ||||||||
\(167\) | −15.4164 | −1.19296 | −0.596479 | − | 0.802629i | \(-0.703434\pi\) | ||||
−0.596479 | + | 0.802629i | \(0.703434\pi\) | |||||||
\(168\) | −3.23607 | −0.249668 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | −20.9443 | −1.60635 | ||||||||
\(171\) | −20.6525 | −1.57933 | ||||||||
\(172\) | −1.52786 | −0.116499 | ||||||||
\(173\) | 1.23607 | 0.0939765 | 0.0469883 | − | 0.998895i | \(-0.485038\pi\) | ||||
0.0469883 | + | 0.998895i | \(0.485038\pi\) | |||||||
\(174\) | 14.4721 | 1.09713 | ||||||||
\(175\) | 5.47214 | 0.413655 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −23.4164 | −1.76008 | ||||||||
\(178\) | 10.0000 | 0.749532 | ||||||||
\(179\) | 8.94427 | 0.668526 | 0.334263 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334263 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(180\) | 24.1803 | 1.80230 | ||||||||
\(181\) | 4.76393 | 0.354100 | 0.177050 | − | 0.984202i | \(-0.443345\pi\) | ||||
0.177050 | + | 0.984202i | \(0.443345\pi\) | |||||||
\(182\) | 1.23607 | 0.0916235 | ||||||||
\(183\) | 16.9443 | 1.25256 | ||||||||
\(184\) | 4.00000 | 0.294884 | ||||||||
\(185\) | −35.4164 | −2.60387 | ||||||||
\(186\) | −6.47214 | −0.474560 | ||||||||
\(187\) | −6.47214 | −0.473289 | ||||||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | −14.4721 | −1.05269 | ||||||||
\(190\) | −8.94427 | −0.648886 | ||||||||
\(191\) | 6.47214 | 0.468307 | 0.234154 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234154 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(192\) | −3.23607 | −0.233543 | ||||||||
\(193\) | 2.94427 | 0.211933 | 0.105967 | − | 0.994370i | \(-0.466206\pi\) | ||||
0.105967 | + | 0.994370i | \(0.466206\pi\) | |||||||
\(194\) | 3.52786 | 0.253286 | ||||||||
\(195\) | −12.9443 | −0.926959 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 7.47214 | 0.531022 | ||||||||
\(199\) | 1.05573 | 0.0748386 | 0.0374193 | − | 0.999300i | \(-0.488086\pi\) | ||||
0.0374193 | + | 0.999300i | \(0.488086\pi\) | |||||||
\(200\) | 5.47214 | 0.386938 | ||||||||
\(201\) | 49.8885 | 3.51887 | ||||||||
\(202\) | −14.1803 | −0.997725 | ||||||||
\(203\) | −4.47214 | −0.313882 | ||||||||
\(204\) | 20.9443 | 1.46639 | ||||||||
\(205\) | 20.9443 | 1.46281 | ||||||||
\(206\) | 2.94427 | 0.205137 | ||||||||
\(207\) | 29.8885 | 2.07740 | ||||||||
\(208\) | 1.23607 | 0.0857059 | ||||||||
\(209\) | −2.76393 | −0.191185 | ||||||||
\(210\) | −10.4721 | −0.722646 | ||||||||
\(211\) | −22.4721 | −1.54705 | −0.773523 | − | 0.633768i | \(-0.781507\pi\) | ||||
−0.773523 | + | 0.633768i | \(0.781507\pi\) | |||||||
\(212\) | −0.472136 | −0.0324264 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | −6.47214 | −0.442426 | ||||||||
\(215\) | −4.94427 | −0.337197 | ||||||||
\(216\) | −14.4721 | −0.984704 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | 16.0000 | 1.08118 | ||||||||
\(220\) | 3.23607 | 0.218176 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 35.4164 | 2.37699 | ||||||||
\(223\) | 8.47214 | 0.567336 | 0.283668 | − | 0.958923i | \(-0.408449\pi\) | ||||
0.283668 | + | 0.958923i | \(0.408449\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 40.8885 | 2.72590 | ||||||||
\(226\) | 8.47214 | 0.563558 | ||||||||
\(227\) | −14.7639 | −0.979917 | −0.489958 | − | 0.871746i | \(-0.662988\pi\) | ||||
−0.489958 | + | 0.871746i | \(0.662988\pi\) | |||||||
\(228\) | 8.94427 | 0.592349 | ||||||||
\(229\) | 12.7639 | 0.843464 | 0.421732 | − | 0.906720i | \(-0.361422\pi\) | ||||
0.421732 | + | 0.906720i | \(0.361422\pi\) | |||||||
\(230\) | 12.9443 | 0.853520 | ||||||||
\(231\) | −3.23607 | −0.212918 | ||||||||
\(232\) | −4.47214 | −0.293610 | ||||||||
\(233\) | 2.94427 | 0.192886 | 0.0964428 | − | 0.995339i | \(-0.469254\pi\) | ||||
0.0964428 | + | 0.995339i | \(0.469254\pi\) | |||||||
\(234\) | 9.23607 | 0.603781 | ||||||||
\(235\) | −6.47214 | −0.422196 | ||||||||
\(236\) | 7.23607 | 0.471028 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.47214 | −0.419526 | ||||||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | −10.4721 | −0.675973 | ||||||||
\(241\) | −11.4164 | −0.735395 | −0.367698 | − | 0.929945i | \(-0.619854\pi\) | ||||
−0.367698 | + | 0.929945i | \(0.619854\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | −5.23607 | −0.335205 | ||||||||
\(245\) | 3.23607 | 0.206745 | ||||||||
\(246\) | −20.9443 | −1.33536 | ||||||||
\(247\) | −3.41641 | −0.217381 | ||||||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | −32.9443 | −2.08776 | ||||||||
\(250\) | 1.52786 | 0.0966306 | ||||||||
\(251\) | 24.7639 | 1.56309 | 0.781543 | − | 0.623852i | \(-0.214433\pi\) | ||||
0.781543 | + | 0.623852i | \(0.214433\pi\) | |||||||
\(252\) | 7.47214 | 0.470700 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | 67.7771 | 4.24437 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.9443 | −0.682685 | −0.341342 | − | 0.939939i | \(-0.610882\pi\) | ||||
−0.341342 | + | 0.939939i | \(0.610882\pi\) | |||||||
\(258\) | 4.94427 | 0.307817 | ||||||||
\(259\) | −10.9443 | −0.680044 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | −33.4164 | −2.06842 | ||||||||
\(262\) | 9.23607 | 0.570606 | ||||||||
\(263\) | 12.9443 | 0.798178 | 0.399089 | − | 0.916912i | \(-0.369326\pi\) | ||||
0.399089 | + | 0.916912i | \(0.369326\pi\) | |||||||
\(264\) | −3.23607 | −0.199166 | ||||||||
\(265\) | −1.52786 | −0.0938559 | ||||||||
\(266\) | −2.76393 | −0.169468 | ||||||||
\(267\) | −32.3607 | −1.98044 | ||||||||
\(268\) | −15.4164 | −0.941707 | ||||||||
\(269\) | −27.2361 | −1.66061 | −0.830306 | − | 0.557307i | \(-0.811834\pi\) | ||||
−0.830306 | + | 0.557307i | \(0.811834\pi\) | |||||||
\(270\) | −46.8328 | −2.85015 | ||||||||
\(271\) | −16.9443 | −1.02929 | −0.514646 | − | 0.857403i | \(-0.672076\pi\) | ||||
−0.514646 | + | 0.857403i | \(0.672076\pi\) | |||||||
\(272\) | −6.47214 | −0.392431 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 15.8885 | 0.959862 | ||||||||
\(275\) | 5.47214 | 0.329982 | ||||||||
\(276\) | −12.9443 | −0.779154 | ||||||||
\(277\) | 12.4721 | 0.749378 | 0.374689 | − | 0.927151i | \(-0.377749\pi\) | ||||
0.374689 | + | 0.927151i | \(0.377749\pi\) | |||||||
\(278\) | −8.29180 | −0.497309 | ||||||||
\(279\) | 14.9443 | 0.894690 | ||||||||
\(280\) | 3.23607 | 0.193392 | ||||||||
\(281\) | −24.8328 | −1.48140 | −0.740701 | − | 0.671835i | \(-0.765506\pi\) | ||||
−0.740701 | + | 0.671835i | \(0.765506\pi\) | |||||||
\(282\) | 6.47214 | 0.385410 | ||||||||
\(283\) | −16.6525 | −0.989887 | −0.494943 | − | 0.868925i | \(-0.664811\pi\) | ||||
−0.494943 | + | 0.868925i | \(0.664811\pi\) | |||||||
\(284\) | −2.47214 | −0.146694 | ||||||||
\(285\) | 28.9443 | 1.71451 | ||||||||
\(286\) | 1.23607 | 0.0730902 | ||||||||
\(287\) | 6.47214 | 0.382038 | ||||||||
\(288\) | 7.47214 | 0.440300 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | −14.4721 | −0.849833 | ||||||||
\(291\) | −11.4164 | −0.669242 | ||||||||
\(292\) | −4.94427 | −0.289342 | ||||||||
\(293\) | 4.65248 | 0.271801 | 0.135900 | − | 0.990723i | \(-0.456607\pi\) | ||||
0.135900 | + | 0.990723i | \(0.456607\pi\) | |||||||
\(294\) | −3.23607 | −0.188731 | ||||||||
\(295\) | 23.4164 | 1.36336 | ||||||||
\(296\) | −10.9443 | −0.636123 | ||||||||
\(297\) | −14.4721 | −0.839759 | ||||||||
\(298\) | 22.3607 | 1.29532 | ||||||||
\(299\) | 4.94427 | 0.285935 | ||||||||
\(300\) | −17.7082 | −1.02238 | ||||||||
\(301\) | −1.52786 | −0.0880646 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | 45.8885 | 2.63623 | ||||||||
\(304\) | −2.76393 | −0.158522 | ||||||||
\(305\) | −16.9443 | −0.970226 | ||||||||
\(306\) | −48.3607 | −2.76460 | ||||||||
\(307\) | 32.0689 | 1.83027 | 0.915134 | − | 0.403150i | \(-0.132085\pi\) | ||||
0.915134 | + | 0.403150i | \(0.132085\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | −9.52786 | −0.542021 | ||||||||
\(310\) | 6.47214 | 0.367593 | ||||||||
\(311\) | 5.41641 | 0.307136 | 0.153568 | − | 0.988138i | \(-0.450924\pi\) | ||||
0.153568 | + | 0.988138i | \(0.450924\pi\) | |||||||
\(312\) | −4.00000 | −0.226455 | ||||||||
\(313\) | 28.4721 | 1.60934 | 0.804670 | − | 0.593722i | \(-0.202342\pi\) | ||||
0.804670 | + | 0.593722i | \(0.202342\pi\) | |||||||
\(314\) | 18.6525 | 1.05262 | ||||||||
\(315\) | 24.1803 | 1.36241 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0557 | −0.733283 | −0.366641 | − | 0.930362i | \(-0.619492\pi\) | ||||
−0.366641 | + | 0.930362i | \(0.619492\pi\) | |||||||
\(318\) | 1.52786 | 0.0856784 | ||||||||
\(319\) | −4.47214 | −0.250392 | ||||||||
\(320\) | 3.23607 | 0.180902 | ||||||||
\(321\) | 20.9443 | 1.16900 | ||||||||
\(322\) | 4.00000 | 0.222911 | ||||||||
\(323\) | 17.8885 | 0.995345 | ||||||||
\(324\) | 24.4164 | 1.35647 | ||||||||
\(325\) | 6.76393 | 0.375195 | ||||||||
\(326\) | 7.41641 | 0.410757 | ||||||||
\(327\) | 32.3607 | 1.78955 | ||||||||
\(328\) | 6.47214 | 0.357364 | ||||||||
\(329\) | −2.00000 | −0.110264 | ||||||||
\(330\) | −10.4721 | −0.576472 | ||||||||
\(331\) | 0.944272 | 0.0519019 | 0.0259509 | − | 0.999663i | \(-0.491739\pi\) | ||||
0.0259509 | + | 0.999663i | \(0.491739\pi\) | |||||||
\(332\) | 10.1803 | 0.558719 | ||||||||
\(333\) | −81.7771 | −4.48136 | ||||||||
\(334\) | −15.4164 | −0.843548 | ||||||||
\(335\) | −49.8885 | −2.72570 | ||||||||
\(336\) | −3.23607 | −0.176542 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | −11.4721 | −0.624002 | ||||||||
\(339\) | −27.4164 | −1.48905 | ||||||||
\(340\) | −20.9443 | −1.13586 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | −20.6525 | −1.11676 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −1.52786 | −0.0823769 | ||||||||
\(345\) | −41.8885 | −2.25520 | ||||||||
\(346\) | 1.23607 | 0.0664514 | ||||||||
\(347\) | −6.47214 | −0.347442 | −0.173721 | − | 0.984795i | \(-0.555579\pi\) | ||||
−0.173721 | + | 0.984795i | \(0.555579\pi\) | |||||||
\(348\) | 14.4721 | 0.775788 | ||||||||
\(349\) | 8.29180 | 0.443850 | 0.221925 | − | 0.975064i | \(-0.428766\pi\) | ||||
0.221925 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(350\) | 5.47214 | 0.292498 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −34.9443 | −1.85990 | −0.929948 | − | 0.367691i | \(-0.880148\pi\) | ||||
−0.929948 | + | 0.367691i | \(0.880148\pi\) | |||||||
\(354\) | −23.4164 | −1.24457 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 20.9443 | 1.10849 | ||||||||
\(358\) | 8.94427 | 0.472719 | ||||||||
\(359\) | −26.8328 | −1.41618 | −0.708091 | − | 0.706121i | \(-0.750443\pi\) | ||||
−0.708091 | + | 0.706121i | \(0.750443\pi\) | |||||||
\(360\) | 24.1803 | 1.27442 | ||||||||
\(361\) | −11.3607 | −0.597931 | ||||||||
\(362\) | 4.76393 | 0.250387 | ||||||||
\(363\) | −3.23607 | −0.169850 | ||||||||
\(364\) | 1.23607 | 0.0647876 | ||||||||
\(365\) | −16.0000 | −0.837478 | ||||||||
\(366\) | 16.9443 | 0.885691 | ||||||||
\(367\) | 21.4164 | 1.11793 | 0.558964 | − | 0.829192i | \(-0.311199\pi\) | ||||
0.558964 | + | 0.829192i | \(0.311199\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 48.3607 | 2.51756 | ||||||||
\(370\) | −35.4164 | −1.84121 | ||||||||
\(371\) | −0.472136 | −0.0245121 | ||||||||
\(372\) | −6.47214 | −0.335565 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | −6.47214 | −0.334666 | ||||||||
\(375\) | −4.94427 | −0.255321 | ||||||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | −5.52786 | −0.284699 | ||||||||
\(378\) | −14.4721 | −0.744366 | ||||||||
\(379\) | 5.52786 | 0.283947 | 0.141974 | − | 0.989870i | \(-0.454655\pi\) | ||||
0.141974 | + | 0.989870i | \(0.454655\pi\) | |||||||
\(380\) | −8.94427 | −0.458831 | ||||||||
\(381\) | 38.8328 | 1.98947 | ||||||||
\(382\) | 6.47214 | 0.331143 | ||||||||
\(383\) | 11.8885 | 0.607476 | 0.303738 | − | 0.952756i | \(-0.401765\pi\) | ||||
0.303738 | + | 0.952756i | \(0.401765\pi\) | |||||||
\(384\) | −3.23607 | −0.165140 | ||||||||
\(385\) | 3.23607 | 0.164925 | ||||||||
\(386\) | 2.94427 | 0.149859 | ||||||||
\(387\) | −11.4164 | −0.580329 | ||||||||
\(388\) | 3.52786 | 0.179100 | ||||||||
\(389\) | 6.58359 | 0.333801 | 0.166901 | − | 0.985974i | \(-0.446624\pi\) | ||||
0.166901 | + | 0.985974i | \(0.446624\pi\) | |||||||
\(390\) | −12.9443 | −0.655459 | ||||||||
\(391\) | −25.8885 | −1.30924 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −29.8885 | −1.50768 | ||||||||
\(394\) | 18.0000 | 0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.47214 | 0.375489 | ||||||||
\(397\) | −10.2918 | −0.516530 | −0.258265 | − | 0.966074i | \(-0.583151\pi\) | ||||
−0.258265 | + | 0.966074i | \(0.583151\pi\) | |||||||
\(398\) | 1.05573 | 0.0529189 | ||||||||
\(399\) | 8.94427 | 0.447774 | ||||||||
\(400\) | 5.47214 | 0.273607 | ||||||||
\(401\) | −30.3607 | −1.51614 | −0.758070 | − | 0.652173i | \(-0.773857\pi\) | ||||
−0.758070 | + | 0.652173i | \(0.773857\pi\) | |||||||
\(402\) | 49.8885 | 2.48821 | ||||||||
\(403\) | 2.47214 | 0.123146 | ||||||||
\(404\) | −14.1803 | −0.705498 | ||||||||
\(405\) | 79.0132 | 3.92620 | ||||||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | −10.9443 | −0.542487 | ||||||||
\(408\) | 20.9443 | 1.03690 | ||||||||
\(409\) | −23.4164 | −1.15787 | −0.578933 | − | 0.815375i | \(-0.696531\pi\) | ||||
−0.578933 | + | 0.815375i | \(0.696531\pi\) | |||||||
\(410\) | 20.9443 | 1.03436 | ||||||||
\(411\) | −51.4164 | −2.53618 | ||||||||
\(412\) | 2.94427 | 0.145054 | ||||||||
\(413\) | 7.23607 | 0.356064 | ||||||||
\(414\) | 29.8885 | 1.46894 | ||||||||
\(415\) | 32.9443 | 1.61717 | ||||||||
\(416\) | 1.23607 | 0.0606032 | ||||||||
\(417\) | 26.8328 | 1.31401 | ||||||||
\(418\) | −2.76393 | −0.135188 | ||||||||
\(419\) | 12.7639 | 0.623559 | 0.311779 | − | 0.950155i | \(-0.399075\pi\) | ||||
0.311779 | + | 0.950155i | \(0.399075\pi\) | |||||||
\(420\) | −10.4721 | −0.510988 | ||||||||
\(421\) | 7.52786 | 0.366886 | 0.183443 | − | 0.983030i | \(-0.441276\pi\) | ||||
0.183443 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(422\) | −22.4721 | −1.09393 | ||||||||
\(423\) | −14.9443 | −0.726615 | ||||||||
\(424\) | −0.472136 | −0.0229289 | ||||||||
\(425\) | −35.4164 | −1.71795 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | −5.23607 | −0.253391 | ||||||||
\(428\) | −6.47214 | −0.312842 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | −4.94427 | −0.238434 | ||||||||
\(431\) | 40.9443 | 1.97222 | 0.986108 | − | 0.166105i | \(-0.0531190\pi\) | ||||
0.986108 | + | 0.166105i | \(0.0531190\pi\) | |||||||
\(432\) | −14.4721 | −0.696291 | ||||||||
\(433\) | 19.5279 | 0.938449 | 0.469225 | − | 0.883079i | \(-0.344533\pi\) | ||||
0.469225 | + | 0.883079i | \(0.344533\pi\) | |||||||
\(434\) | 2.00000 | 0.0960031 | ||||||||
\(435\) | 46.8328 | 2.24546 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | −11.0557 | −0.528867 | ||||||||
\(438\) | 16.0000 | 0.764510 | ||||||||
\(439\) | −8.94427 | −0.426887 | −0.213443 | − | 0.976955i | \(-0.568468\pi\) | ||||
−0.213443 | + | 0.976955i | \(0.568468\pi\) | |||||||
\(440\) | 3.23607 | 0.154273 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | −8.00000 | −0.380521 | ||||||||
\(443\) | −7.05573 | −0.335228 | −0.167614 | − | 0.985853i | \(-0.553606\pi\) | ||||
−0.167614 | + | 0.985853i | \(0.553606\pi\) | |||||||
\(444\) | 35.4164 | 1.68079 | ||||||||
\(445\) | 32.3607 | 1.53404 | ||||||||
\(446\) | 8.47214 | 0.401167 | ||||||||
\(447\) | −72.3607 | −3.42254 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 1.05573 | 0.0498229 | 0.0249114 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249114 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(450\) | 40.8885 | 1.92750 | ||||||||
\(451\) | 6.47214 | 0.304761 | ||||||||
\(452\) | 8.47214 | 0.398496 | ||||||||
\(453\) | −38.8328 | −1.82452 | ||||||||
\(454\) | −14.7639 | −0.692906 | ||||||||
\(455\) | 4.00000 | 0.187523 | ||||||||
\(456\) | 8.94427 | 0.418854 | ||||||||
\(457\) | 9.05573 | 0.423609 | 0.211805 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211805 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(458\) | 12.7639 | 0.596419 | ||||||||
\(459\) | 93.6656 | 4.37194 | ||||||||
\(460\) | 12.9443 | 0.603530 | ||||||||
\(461\) | 29.2361 | 1.36166 | 0.680830 | − | 0.732442i | \(-0.261619\pi\) | ||||
0.680830 | + | 0.732442i | \(0.261619\pi\) | |||||||
\(462\) | −3.23607 | −0.150556 | ||||||||
\(463\) | −21.5279 | −1.00048 | −0.500242 | − | 0.865885i | \(-0.666756\pi\) | ||||
−0.500242 | + | 0.865885i | \(0.666756\pi\) | |||||||
\(464\) | −4.47214 | −0.207614 | ||||||||
\(465\) | −20.9443 | −0.971267 | ||||||||
\(466\) | 2.94427 | 0.136391 | ||||||||
\(467\) | 13.1246 | 0.607335 | 0.303667 | − | 0.952778i | \(-0.401789\pi\) | ||||
0.303667 | + | 0.952778i | \(0.401789\pi\) | |||||||
\(468\) | 9.23607 | 0.426937 | ||||||||
\(469\) | −15.4164 | −0.711864 | ||||||||
\(470\) | −6.47214 | −0.298537 | ||||||||
\(471\) | −60.3607 | −2.78127 | ||||||||
\(472\) | 7.23607 | 0.333067 | ||||||||
\(473\) | −1.52786 | −0.0702513 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.1246 | −0.693965 | ||||||||
\(476\) | −6.47214 | −0.296650 | ||||||||
\(477\) | −3.52786 | −0.161530 | ||||||||
\(478\) | 20.0000 | 0.914779 | ||||||||
\(479\) | −32.3607 | −1.47860 | −0.739299 | − | 0.673378i | \(-0.764843\pi\) | ||||
−0.739299 | + | 0.673378i | \(0.764843\pi\) | |||||||
\(480\) | −10.4721 | −0.477985 | ||||||||
\(481\) | −13.5279 | −0.616818 | ||||||||
\(482\) | −11.4164 | −0.520003 | ||||||||
\(483\) | −12.9443 | −0.588985 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 11.4164 | 0.518392 | ||||||||
\(486\) | −35.5967 | −1.61470 | ||||||||
\(487\) | −0.944272 | −0.0427890 | −0.0213945 | − | 0.999771i | \(-0.506811\pi\) | ||||
−0.0213945 | + | 0.999771i | \(0.506811\pi\) | |||||||
\(488\) | −5.23607 | −0.237026 | ||||||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 3.23607 | 0.146191 | ||||||||
\(491\) | 0.944272 | 0.0426144 | 0.0213072 | − | 0.999773i | \(-0.493217\pi\) | ||||
0.0213072 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(492\) | −20.9443 | −0.944241 | ||||||||
\(493\) | 28.9443 | 1.30358 | ||||||||
\(494\) | −3.41641 | −0.153711 | ||||||||
\(495\) | 24.1803 | 1.08683 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −2.47214 | −0.110890 | ||||||||
\(498\) | −32.9443 | −1.47627 | ||||||||
\(499\) | 12.3607 | 0.553340 | 0.276670 | − | 0.960965i | \(-0.410769\pi\) | ||||
0.276670 | + | 0.960965i | \(0.410769\pi\) | |||||||
\(500\) | 1.52786 | 0.0683282 | ||||||||
\(501\) | 49.8885 | 2.22886 | ||||||||
\(502\) | 24.7639 | 1.10527 | ||||||||
\(503\) | 4.00000 | 0.178351 | 0.0891756 | − | 0.996016i | \(-0.471577\pi\) | ||||
0.0891756 | + | 0.996016i | \(0.471577\pi\) | |||||||
\(504\) | 7.47214 | 0.332835 | ||||||||
\(505\) | −45.8885 | −2.04201 | ||||||||
\(506\) | 4.00000 | 0.177822 | ||||||||
\(507\) | 37.1246 | 1.64876 | ||||||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | −34.0689 | −1.51008 | −0.755038 | − | 0.655681i | \(-0.772382\pi\) | ||||
−0.755038 | + | 0.655681i | \(0.772382\pi\) | |||||||
\(510\) | 67.7771 | 3.00122 | ||||||||
\(511\) | −4.94427 | −0.218722 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 40.0000 | 1.76604 | ||||||||
\(514\) | −10.9443 | −0.482731 | ||||||||
\(515\) | 9.52786 | 0.419848 | ||||||||
\(516\) | 4.94427 | 0.217659 | ||||||||
\(517\) | −2.00000 | −0.0879599 | ||||||||
\(518\) | −10.9443 | −0.480864 | ||||||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | 34.3607 | 1.50537 | 0.752684 | − | 0.658382i | \(-0.228759\pi\) | ||||
0.752684 | + | 0.658382i | \(0.228759\pi\) | |||||||
\(522\) | −33.4164 | −1.46260 | ||||||||
\(523\) | −27.7082 | −1.21160 | −0.605798 | − | 0.795619i | \(-0.707146\pi\) | ||||
−0.605798 | + | 0.795619i | \(0.707146\pi\) | |||||||
\(524\) | 9.23607 | 0.403480 | ||||||||
\(525\) | −17.7082 | −0.772849 | ||||||||
\(526\) | 12.9443 | 0.564397 | ||||||||
\(527\) | −12.9443 | −0.563861 | ||||||||
\(528\) | −3.23607 | −0.140832 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −1.52786 | −0.0663662 | ||||||||
\(531\) | 54.0689 | 2.34639 | ||||||||
\(532\) | −2.76393 | −0.119832 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | −32.3607 | −1.40038 | ||||||||
\(535\) | −20.9443 | −0.905500 | ||||||||
\(536\) | −15.4164 | −0.665887 | ||||||||
\(537\) | −28.9443 | −1.24904 | ||||||||
\(538\) | −27.2361 | −1.17423 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −46.8328 | −2.01536 | ||||||||
\(541\) | −9.05573 | −0.389336 | −0.194668 | − | 0.980869i | \(-0.562363\pi\) | ||||
−0.194668 | + | 0.980869i | \(0.562363\pi\) | |||||||
\(542\) | −16.9443 | −0.727819 | ||||||||
\(543\) | −15.4164 | −0.661581 | ||||||||
\(544\) | −6.47214 | −0.277491 | ||||||||
\(545\) | −32.3607 | −1.38618 | ||||||||
\(546\) | −4.00000 | −0.171184 | ||||||||
\(547\) | 16.9443 | 0.724485 | 0.362242 | − | 0.932084i | \(-0.382011\pi\) | ||||
0.362242 | + | 0.932084i | \(0.382011\pi\) | |||||||
\(548\) | 15.8885 | 0.678725 | ||||||||
\(549\) | −39.1246 | −1.66980 | ||||||||
\(550\) | 5.47214 | 0.233333 | ||||||||
\(551\) | 12.3607 | 0.526583 | ||||||||
\(552\) | −12.9443 | −0.550945 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.4721 | 0.529890 | ||||||||
\(555\) | 114.610 | 4.86492 | ||||||||
\(556\) | −8.29180 | −0.351650 | ||||||||
\(557\) | −28.8328 | −1.22169 | −0.610843 | − | 0.791752i | \(-0.709169\pi\) | ||||
−0.610843 | + | 0.791752i | \(0.709169\pi\) | |||||||
\(558\) | 14.9443 | 0.632641 | ||||||||
\(559\) | −1.88854 | −0.0798769 | ||||||||
\(560\) | 3.23607 | 0.136749 | ||||||||
\(561\) | 20.9443 | 0.884268 | ||||||||
\(562\) | −24.8328 | −1.04751 | ||||||||
\(563\) | 26.7639 | 1.12797 | 0.563983 | − | 0.825787i | \(-0.309268\pi\) | ||||
0.563983 | + | 0.825787i | \(0.309268\pi\) | |||||||
\(564\) | 6.47214 | 0.272526 | ||||||||
\(565\) | 27.4164 | 1.15342 | ||||||||
\(566\) | −16.6525 | −0.699956 | ||||||||
\(567\) | 24.4164 | 1.02539 | ||||||||
\(568\) | −2.47214 | −0.103729 | ||||||||
\(569\) | 16.8328 | 0.705668 | 0.352834 | − | 0.935686i | \(-0.385218\pi\) | ||||
0.352834 | + | 0.935686i | \(0.385218\pi\) | |||||||
\(570\) | 28.9443 | 1.21234 | ||||||||
\(571\) | −45.8885 | −1.92038 | −0.960188 | − | 0.279355i | \(-0.909879\pi\) | ||||
−0.960188 | + | 0.279355i | \(0.909879\pi\) | |||||||
\(572\) | 1.23607 | 0.0516826 | ||||||||
\(573\) | −20.9443 | −0.874960 | ||||||||
\(574\) | 6.47214 | 0.270142 | ||||||||
\(575\) | 21.8885 | 0.912815 | ||||||||
\(576\) | 7.47214 | 0.311339 | ||||||||
\(577\) | 9.05573 | 0.376995 | 0.188497 | − | 0.982074i | \(-0.439638\pi\) | ||||
0.188497 | + | 0.982074i | \(0.439638\pi\) | |||||||
\(578\) | 24.8885 | 1.03523 | ||||||||
\(579\) | −9.52786 | −0.395965 | ||||||||
\(580\) | −14.4721 | −0.600923 | ||||||||
\(581\) | 10.1803 | 0.422352 | ||||||||
\(582\) | −11.4164 | −0.473225 | ||||||||
\(583\) | −0.472136 | −0.0195539 | ||||||||
\(584\) | −4.94427 | −0.204595 | ||||||||
\(585\) | 29.8885 | 1.23574 | ||||||||
\(586\) | 4.65248 | 0.192192 | ||||||||
\(587\) | −28.1803 | −1.16313 | −0.581564 | − | 0.813501i | \(-0.697559\pi\) | ||||
−0.581564 | + | 0.813501i | \(0.697559\pi\) | |||||||
\(588\) | −3.23607 | −0.133453 | ||||||||
\(589\) | −5.52786 | −0.227772 | ||||||||
\(590\) | 23.4164 | 0.964038 | ||||||||
\(591\) | −58.2492 | −2.39605 | ||||||||
\(592\) | −10.9443 | −0.449807 | ||||||||
\(593\) | 24.0000 | 0.985562 | 0.492781 | − | 0.870153i | \(-0.335980\pi\) | ||||
0.492781 | + | 0.870153i | \(0.335980\pi\) | |||||||
\(594\) | −14.4721 | −0.593799 | ||||||||
\(595\) | −20.9443 | −0.858631 | ||||||||
\(596\) | 22.3607 | 0.915929 | ||||||||
\(597\) | −3.41641 | −0.139824 | ||||||||
\(598\) | 4.94427 | 0.202186 | ||||||||
\(599\) | 12.3607 | 0.505044 | 0.252522 | − | 0.967591i | \(-0.418740\pi\) | ||||
0.252522 | + | 0.967591i | \(0.418740\pi\) | |||||||
\(600\) | −17.7082 | −0.722934 | ||||||||
\(601\) | 18.8328 | 0.768207 | 0.384103 | − | 0.923290i | \(-0.374511\pi\) | ||||
0.384103 | + | 0.923290i | \(0.374511\pi\) | |||||||
\(602\) | −1.52786 | −0.0622711 | ||||||||
\(603\) | −115.193 | −4.69104 | ||||||||
\(604\) | 12.0000 | 0.488273 | ||||||||
\(605\) | 3.23607 | 0.131565 | ||||||||
\(606\) | 45.8885 | 1.86409 | ||||||||
\(607\) | −32.0000 | −1.29884 | −0.649420 | − | 0.760430i | \(-0.724988\pi\) | ||||
−0.649420 | + | 0.760430i | \(0.724988\pi\) | |||||||
\(608\) | −2.76393 | −0.112092 | ||||||||
\(609\) | 14.4721 | 0.586441 | ||||||||
\(610\) | −16.9443 | −0.686054 | ||||||||
\(611\) | −2.47214 | −0.100012 | ||||||||
\(612\) | −48.3607 | −1.95486 | ||||||||
\(613\) | 19.5279 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(614\) | 32.0689 | 1.29419 | ||||||||
\(615\) | −67.7771 | −2.73304 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −5.41641 | −0.218056 | −0.109028 | − | 0.994039i | \(-0.534774\pi\) | ||||
−0.109028 | + | 0.994039i | \(0.534774\pi\) | |||||||
\(618\) | −9.52786 | −0.383267 | ||||||||
\(619\) | −48.5410 | −1.95103 | −0.975514 | − | 0.219937i | \(-0.929415\pi\) | ||||
−0.975514 | + | 0.219937i | \(0.929415\pi\) | |||||||
\(620\) | 6.47214 | 0.259927 | ||||||||
\(621\) | −57.8885 | −2.32299 | ||||||||
\(622\) | 5.41641 | 0.217178 | ||||||||
\(623\) | 10.0000 | 0.400642 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 28.4721 | 1.13798 | ||||||||
\(627\) | 8.94427 | 0.357200 | ||||||||
\(628\) | 18.6525 | 0.744315 | ||||||||
\(629\) | 70.8328 | 2.82429 | ||||||||
\(630\) | 24.1803 | 0.963368 | ||||||||
\(631\) | −4.58359 | −0.182470 | −0.0912350 | − | 0.995829i | \(-0.529081\pi\) | ||||
−0.0912350 | + | 0.995829i | \(0.529081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 72.7214 | 2.89041 | ||||||||
\(634\) | −13.0557 | −0.518509 | ||||||||
\(635\) | −38.8328 | −1.54103 | ||||||||
\(636\) | 1.52786 | 0.0605838 | ||||||||
\(637\) | 1.23607 | 0.0489748 | ||||||||
\(638\) | −4.47214 | −0.177054 | ||||||||
\(639\) | −18.4721 | −0.730746 | ||||||||
\(640\) | 3.23607 | 0.127917 | ||||||||
\(641\) | 36.4721 | 1.44056 | 0.720281 | − | 0.693682i | \(-0.244013\pi\) | ||||
0.720281 | + | 0.693682i | \(0.244013\pi\) | |||||||
\(642\) | 20.9443 | 0.826604 | ||||||||
\(643\) | −23.2361 | −0.916341 | −0.458171 | − | 0.888864i | \(-0.651495\pi\) | ||||
−0.458171 | + | 0.888864i | \(0.651495\pi\) | |||||||
\(644\) | 4.00000 | 0.157622 | ||||||||
\(645\) | 16.0000 | 0.629999 | ||||||||
\(646\) | 17.8885 | 0.703815 | ||||||||
\(647\) | 24.8328 | 0.976279 | 0.488139 | − | 0.872766i | \(-0.337676\pi\) | ||||
0.488139 | + | 0.872766i | \(0.337676\pi\) | |||||||
\(648\) | 24.4164 | 0.959167 | ||||||||
\(649\) | 7.23607 | 0.284041 | ||||||||
\(650\) | 6.76393 | 0.265303 | ||||||||
\(651\) | −6.47214 | −0.253663 | ||||||||
\(652\) | 7.41641 | 0.290449 | ||||||||
\(653\) | 1.63932 | 0.0641516 | 0.0320758 | − | 0.999485i | \(-0.489788\pi\) | ||||
0.0320758 | + | 0.999485i | \(0.489788\pi\) | |||||||
\(654\) | 32.3607 | 1.26540 | ||||||||
\(655\) | 29.8885 | 1.16784 | ||||||||
\(656\) | 6.47214 | 0.252694 | ||||||||
\(657\) | −36.9443 | −1.44133 | ||||||||
\(658\) | −2.00000 | −0.0779681 | ||||||||
\(659\) | 43.4164 | 1.69126 | 0.845632 | − | 0.533767i | \(-0.179224\pi\) | ||||
0.845632 | + | 0.533767i | \(0.179224\pi\) | |||||||
\(660\) | −10.4721 | −0.407627 | ||||||||
\(661\) | 37.1246 | 1.44398 | 0.721990 | − | 0.691903i | \(-0.243228\pi\) | ||||
0.721990 | + | 0.691903i | \(0.243228\pi\) | |||||||
\(662\) | 0.944272 | 0.0367002 | ||||||||
\(663\) | 25.8885 | 1.00543 | ||||||||
\(664\) | 10.1803 | 0.395074 | ||||||||
\(665\) | −8.94427 | −0.346844 | ||||||||
\(666\) | −81.7771 | −3.16880 | ||||||||
\(667\) | −17.8885 | −0.692647 | ||||||||
\(668\) | −15.4164 | −0.596479 | ||||||||
\(669\) | −27.4164 | −1.05998 | ||||||||
\(670\) | −49.8885 | −1.92736 | ||||||||
\(671\) | −5.23607 | −0.202136 | ||||||||
\(672\) | −3.23607 | −0.124834 | ||||||||
\(673\) | 31.8885 | 1.22921 | 0.614607 | − | 0.788834i | \(-0.289315\pi\) | ||||
0.614607 | + | 0.788834i | \(0.289315\pi\) | |||||||
\(674\) | 18.0000 | 0.693334 | ||||||||
\(675\) | −79.1935 | −3.04816 | ||||||||
\(676\) | −11.4721 | −0.441236 | ||||||||
\(677\) | 32.0689 | 1.23251 | 0.616254 | − | 0.787548i | \(-0.288650\pi\) | ||||
0.616254 | + | 0.787548i | \(0.288650\pi\) | |||||||
\(678\) | −27.4164 | −1.05292 | ||||||||
\(679\) | 3.52786 | 0.135387 | ||||||||
\(680\) | −20.9443 | −0.803176 | ||||||||
\(681\) | 47.7771 | 1.83082 | ||||||||
\(682\) | 2.00000 | 0.0765840 | ||||||||
\(683\) | 15.0557 | 0.576091 | 0.288046 | − | 0.957617i | \(-0.406994\pi\) | ||||
0.288046 | + | 0.957617i | \(0.406994\pi\) | |||||||
\(684\) | −20.6525 | −0.789667 | ||||||||
\(685\) | 51.4164 | 1.96452 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −41.3050 | −1.57588 | ||||||||
\(688\) | −1.52786 | −0.0582493 | ||||||||
\(689\) | −0.583592 | −0.0222331 | ||||||||
\(690\) | −41.8885 | −1.59467 | ||||||||
\(691\) | −18.6525 | −0.709574 | −0.354787 | − | 0.934947i | \(-0.615447\pi\) | ||||
−0.354787 | + | 0.934947i | \(0.615447\pi\) | |||||||
\(692\) | 1.23607 | 0.0469883 | ||||||||
\(693\) | 7.47214 | 0.283843 | ||||||||
\(694\) | −6.47214 | −0.245679 | ||||||||
\(695\) | −26.8328 | −1.01783 | ||||||||
\(696\) | 14.4721 | 0.548565 | ||||||||
\(697\) | −41.8885 | −1.58664 | ||||||||
\(698\) | 8.29180 | 0.313849 | ||||||||
\(699\) | −9.52786 | −0.360377 | ||||||||
\(700\) | 5.47214 | 0.206827 | ||||||||
\(701\) | 46.7214 | 1.76464 | 0.882321 | − | 0.470649i | \(-0.155980\pi\) | ||||
0.882321 | + | 0.470649i | \(0.155980\pi\) | |||||||
\(702\) | −17.8885 | −0.675160 | ||||||||
\(703\) | 30.2492 | 1.14087 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 20.9443 | 0.788807 | ||||||||
\(706\) | −34.9443 | −1.31515 | ||||||||
\(707\) | −14.1803 | −0.533307 | ||||||||
\(708\) | −23.4164 | −0.880042 | ||||||||
\(709\) | −4.47214 | −0.167955 | −0.0839773 | − | 0.996468i | \(-0.526762\pi\) | ||||
−0.0839773 | + | 0.996468i | \(0.526762\pi\) | |||||||
\(710\) | −8.00000 | −0.300235 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0000 | 0.374766 | ||||||||
\(713\) | 8.00000 | 0.299602 | ||||||||
\(714\) | 20.9443 | 0.783820 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 8.94427 | 0.334263 | ||||||||
\(717\) | −64.7214 | −2.41706 | ||||||||
\(718\) | −26.8328 | −1.00139 | ||||||||
\(719\) | −36.8328 | −1.37363 | −0.686816 | − | 0.726831i | \(-0.740992\pi\) | ||||
−0.686816 | + | 0.726831i | \(0.740992\pi\) | |||||||
\(720\) | 24.1803 | 0.901148 | ||||||||
\(721\) | 2.94427 | 0.109650 | ||||||||
\(722\) | −11.3607 | −0.422801 | ||||||||
\(723\) | 36.9443 | 1.37397 | ||||||||
\(724\) | 4.76393 | 0.177050 | ||||||||
\(725\) | −24.4721 | −0.908872 | ||||||||
\(726\) | −3.23607 | −0.120102 | ||||||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 1.23607 | 0.0458117 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | −16.0000 | −0.592187 | ||||||||
\(731\) | 9.88854 | 0.365741 | ||||||||
\(732\) | 16.9443 | 0.626278 | ||||||||
\(733\) | 8.87539 | 0.327820 | 0.163910 | − | 0.986475i | \(-0.447589\pi\) | ||||
0.163910 | + | 0.986475i | \(0.447589\pi\) | |||||||
\(734\) | 21.4164 | 0.790494 | ||||||||
\(735\) | −10.4721 | −0.386271 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | −15.4164 | −0.567871 | ||||||||
\(738\) | 48.3607 | 1.78018 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | −35.4164 | −1.30193 | ||||||||
\(741\) | 11.0557 | 0.406142 | ||||||||
\(742\) | −0.472136 | −0.0173327 | ||||||||
\(743\) | −13.8885 | −0.509521 | −0.254761 | − | 0.967004i | \(-0.581997\pi\) | ||||
−0.254761 | + | 0.967004i | \(0.581997\pi\) | |||||||
\(744\) | −6.47214 | −0.237280 | ||||||||
\(745\) | 72.3607 | 2.65109 | ||||||||
\(746\) | −6.00000 | −0.219676 | ||||||||
\(747\) | 76.0689 | 2.78321 | ||||||||
\(748\) | −6.47214 | −0.236645 | ||||||||
\(749\) | −6.47214 | −0.236487 | ||||||||
\(750\) | −4.94427 | −0.180539 | ||||||||
\(751\) | 0.944272 | 0.0344570 | 0.0172285 | − | 0.999852i | \(-0.494516\pi\) | ||||
0.0172285 | + | 0.999852i | \(0.494516\pi\) | |||||||
\(752\) | −2.00000 | −0.0729325 | ||||||||
\(753\) | −80.1378 | −2.92038 | ||||||||
\(754\) | −5.52786 | −0.201313 | ||||||||
\(755\) | 38.8328 | 1.41327 | ||||||||
\(756\) | −14.4721 | −0.526346 | ||||||||
\(757\) | 39.3050 | 1.42856 | 0.714281 | − | 0.699859i | \(-0.246754\pi\) | ||||
0.714281 | + | 0.699859i | \(0.246754\pi\) | |||||||
\(758\) | 5.52786 | 0.200781 | ||||||||
\(759\) | −12.9443 | −0.469847 | ||||||||
\(760\) | −8.94427 | −0.324443 | ||||||||
\(761\) | 15.4164 | 0.558844 | 0.279422 | − | 0.960168i | \(-0.409857\pi\) | ||||
0.279422 | + | 0.960168i | \(0.409857\pi\) | |||||||
\(762\) | 38.8328 | 1.40676 | ||||||||
\(763\) | −10.0000 | −0.362024 | ||||||||
\(764\) | 6.47214 | 0.234154 | ||||||||
\(765\) | −156.498 | −5.65821 | ||||||||
\(766\) | 11.8885 | 0.429551 | ||||||||
\(767\) | 8.94427 | 0.322959 | ||||||||
\(768\) | −3.23607 | −0.116772 | ||||||||
\(769\) | −16.5836 | −0.598020 | −0.299010 | − | 0.954250i | \(-0.596656\pi\) | ||||
−0.299010 | + | 0.954250i | \(0.596656\pi\) | |||||||
\(770\) | 3.23607 | 0.116620 | ||||||||
\(771\) | 35.4164 | 1.27549 | ||||||||
\(772\) | 2.94427 | 0.105967 | ||||||||
\(773\) | 2.29180 | 0.0824302 | 0.0412151 | − | 0.999150i | \(-0.486877\pi\) | ||||
0.0412151 | + | 0.999150i | \(0.486877\pi\) | |||||||
\(774\) | −11.4164 | −0.410354 | ||||||||
\(775\) | 10.9443 | 0.393130 | ||||||||
\(776\) | 3.52786 | 0.126643 | ||||||||
\(777\) | 35.4164 | 1.27056 | ||||||||
\(778\) | 6.58359 | 0.236033 | ||||||||
\(779\) | −17.8885 | −0.640924 | ||||||||
\(780\) | −12.9443 | −0.463479 | ||||||||
\(781\) | −2.47214 | −0.0884600 | ||||||||
\(782\) | −25.8885 | −0.925772 | ||||||||
\(783\) | 64.7214 | 2.31295 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 60.3607 | 2.15437 | ||||||||
\(786\) | −29.8885 | −1.06609 | ||||||||
\(787\) | −5.81966 | −0.207448 | −0.103724 | − | 0.994606i | \(-0.533076\pi\) | ||||
−0.103724 | + | 0.994606i | \(0.533076\pi\) | |||||||
\(788\) | 18.0000 | 0.641223 | ||||||||
\(789\) | −41.8885 | −1.49127 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.47214 | 0.301234 | ||||||||
\(792\) | 7.47214 | 0.265511 | ||||||||
\(793\) | −6.47214 | −0.229832 | ||||||||
\(794\) | −10.2918 | −0.365242 | ||||||||
\(795\) | 4.94427 | 0.175355 | ||||||||
\(796\) | 1.05573 | 0.0374193 | ||||||||
\(797\) | 7.59675 | 0.269091 | 0.134545 | − | 0.990907i | \(-0.457043\pi\) | ||||
0.134545 | + | 0.990907i | \(0.457043\pi\) | |||||||
\(798\) | 8.94427 | 0.316624 | ||||||||
\(799\) | 12.9443 | 0.457935 | ||||||||
\(800\) | 5.47214 | 0.193469 | ||||||||
\(801\) | 74.7214 | 2.64015 | ||||||||
\(802\) | −30.3607 | −1.07207 | ||||||||
\(803\) | −4.94427 | −0.174480 | ||||||||
\(804\) | 49.8885 | 1.75943 | ||||||||
\(805\) | 12.9443 | 0.456226 | ||||||||
\(806\) | 2.47214 | 0.0870773 | ||||||||
\(807\) | 88.1378 | 3.10260 | ||||||||
\(808\) | −14.1803 | −0.498863 | ||||||||
\(809\) | −38.9443 | −1.36921 | −0.684604 | − | 0.728915i | \(-0.740025\pi\) | ||||
−0.684604 | + | 0.728915i | \(0.740025\pi\) | |||||||
\(810\) | 79.0132 | 2.77624 | ||||||||
\(811\) | 9.23607 | 0.324322 | 0.162161 | − | 0.986764i | \(-0.448154\pi\) | ||||
0.162161 | + | 0.986764i | \(0.448154\pi\) | |||||||
\(812\) | −4.47214 | −0.156941 | ||||||||
\(813\) | 54.8328 | 1.92307 | ||||||||
\(814\) | −10.9443 | −0.383597 | ||||||||
\(815\) | 24.0000 | 0.840683 | ||||||||
\(816\) | 20.9443 | 0.733196 | ||||||||
\(817\) | 4.22291 | 0.147741 | ||||||||
\(818\) | −23.4164 | −0.818736 | ||||||||
\(819\) | 9.23607 | 0.322734 | ||||||||
\(820\) | 20.9443 | 0.731406 | ||||||||
\(821\) | 25.4164 | 0.887039 | 0.443519 | − | 0.896265i | \(-0.353730\pi\) | ||||
0.443519 | + | 0.896265i | \(0.353730\pi\) | |||||||
\(822\) | −51.4164 | −1.79335 | ||||||||
\(823\) | 34.2492 | 1.19385 | 0.596926 | − | 0.802296i | \(-0.296388\pi\) | ||||
0.596926 | + | 0.802296i | \(0.296388\pi\) | |||||||
\(824\) | 2.94427 | 0.102569 | ||||||||
\(825\) | −17.7082 | −0.616521 | ||||||||
\(826\) | 7.23607 | 0.251775 | ||||||||
\(827\) | −0.944272 | −0.0328356 | −0.0164178 | − | 0.999865i | \(-0.505226\pi\) | ||||
−0.0164178 | + | 0.999865i | \(0.505226\pi\) | |||||||
\(828\) | 29.8885 | 1.03870 | ||||||||
\(829\) | −1.70820 | −0.0593284 | −0.0296642 | − | 0.999560i | \(-0.509444\pi\) | ||||
−0.0296642 | + | 0.999560i | \(0.509444\pi\) | |||||||
\(830\) | 32.9443 | 1.14351 | ||||||||
\(831\) | −40.3607 | −1.40010 | ||||||||
\(832\) | 1.23607 | 0.0428529 | ||||||||
\(833\) | −6.47214 | −0.224246 | ||||||||
\(834\) | 26.8328 | 0.929144 | ||||||||
\(835\) | −49.8885 | −1.72646 | ||||||||
\(836\) | −2.76393 | −0.0955926 | ||||||||
\(837\) | −28.9443 | −1.00046 | ||||||||
\(838\) | 12.7639 | 0.440923 | ||||||||
\(839\) | −36.8328 | −1.27161 | −0.635805 | − | 0.771850i | \(-0.719332\pi\) | ||||
−0.635805 | + | 0.771850i | \(0.719332\pi\) | |||||||
\(840\) | −10.4721 | −0.361323 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 7.52786 | 0.259427 | ||||||||
\(843\) | 80.3607 | 2.76777 | ||||||||
\(844\) | −22.4721 | −0.773523 | ||||||||
\(845\) | −37.1246 | −1.27713 | ||||||||
\(846\) | −14.9443 | −0.513795 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | 53.8885 | 1.84945 | ||||||||
\(850\) | −35.4164 | −1.21477 | ||||||||
\(851\) | −43.7771 | −1.50066 | ||||||||
\(852\) | 8.00000 | 0.274075 | ||||||||
\(853\) | −34.5410 | −1.18266 | −0.591331 | − | 0.806429i | \(-0.701397\pi\) | ||||
−0.591331 | + | 0.806429i | \(0.701397\pi\) | |||||||
\(854\) | −5.23607 | −0.179175 | ||||||||
\(855\) | −66.8328 | −2.28563 | ||||||||
\(856\) | −6.47214 | −0.221213 | ||||||||
\(857\) | −37.5279 | −1.28193 | −0.640964 | − | 0.767571i | \(-0.721465\pi\) | ||||
−0.640964 | + | 0.767571i | \(0.721465\pi\) | |||||||
\(858\) | −4.00000 | −0.136558 | ||||||||
\(859\) | −25.1246 | −0.857241 | −0.428620 | − | 0.903485i | \(-0.641000\pi\) | ||||
−0.428620 | + | 0.903485i | \(0.641000\pi\) | |||||||
\(860\) | −4.94427 | −0.168598 | ||||||||
\(861\) | −20.9443 | −0.713779 | ||||||||
\(862\) | 40.9443 | 1.39457 | ||||||||
\(863\) | 27.4164 | 0.933265 | 0.466633 | − | 0.884451i | \(-0.345467\pi\) | ||||
0.466633 | + | 0.884451i | \(0.345467\pi\) | |||||||
\(864\) | −14.4721 | −0.492352 | ||||||||
\(865\) | 4.00000 | 0.136004 | ||||||||
\(866\) | 19.5279 | 0.663584 | ||||||||
\(867\) | −80.5410 | −2.73532 | ||||||||
\(868\) | 2.00000 | 0.0678844 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 46.8328 | 1.58778 | ||||||||
\(871\) | −19.0557 | −0.645679 | ||||||||
\(872\) | −10.0000 | −0.338643 | ||||||||
\(873\) | 26.3607 | 0.892174 | ||||||||
\(874\) | −11.0557 | −0.373966 | ||||||||
\(875\) | 1.52786 | 0.0516512 | ||||||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | 26.9443 | 0.909843 | 0.454922 | − | 0.890531i | \(-0.349667\pi\) | ||||
0.454922 | + | 0.890531i | \(0.349667\pi\) | |||||||
\(878\) | −8.94427 | −0.301855 | ||||||||
\(879\) | −15.0557 | −0.507817 | ||||||||
\(880\) | 3.23607 | 0.109088 | ||||||||
\(881\) | −24.8328 | −0.836639 | −0.418319 | − | 0.908300i | \(-0.637381\pi\) | ||||
−0.418319 | + | 0.908300i | \(0.637381\pi\) | |||||||
\(882\) | 7.47214 | 0.251600 | ||||||||
\(883\) | 50.8328 | 1.71066 | 0.855330 | − | 0.518083i | \(-0.173354\pi\) | ||||
0.855330 | + | 0.518083i | \(0.173354\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | −75.7771 | −2.54722 | ||||||||
\(886\) | −7.05573 | −0.237042 | ||||||||
\(887\) | 0.360680 | 0.0121104 | 0.00605522 | − | 0.999982i | \(-0.498073\pi\) | ||||
0.00605522 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(888\) | 35.4164 | 1.18850 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 32.3607 | 1.08473 | ||||||||
\(891\) | 24.4164 | 0.817980 | ||||||||
\(892\) | 8.47214 | 0.283668 | ||||||||
\(893\) | 5.52786 | 0.184983 | ||||||||
\(894\) | −72.3607 | −2.42010 | ||||||||
\(895\) | 28.9443 | 0.967500 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | 1.05573 | 0.0352301 | ||||||||
\(899\) | −8.94427 | −0.298308 | ||||||||
\(900\) | 40.8885 | 1.36295 | ||||||||
\(901\) | 3.05573 | 0.101801 | ||||||||
\(902\) | 6.47214 | 0.215499 | ||||||||
\(903\) | 4.94427 | 0.164535 | ||||||||
\(904\) | 8.47214 | 0.281779 | ||||||||
\(905\) | 15.4164 | 0.512459 | ||||||||
\(906\) | −38.8328 | −1.29013 | ||||||||
\(907\) | 20.3607 | 0.676065 | 0.338033 | − | 0.941134i | \(-0.390239\pi\) | ||||
0.338033 | + | 0.941134i | \(0.390239\pi\) | |||||||
\(908\) | −14.7639 | −0.489958 | ||||||||
\(909\) | −105.957 | −3.51439 | ||||||||
\(910\) | 4.00000 | 0.132599 | ||||||||
\(911\) | −28.0000 | −0.927681 | −0.463841 | − | 0.885919i | \(-0.653529\pi\) | ||||
−0.463841 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(912\) | 8.94427 | 0.296174 | ||||||||
\(913\) | 10.1803 | 0.336920 | ||||||||
\(914\) | 9.05573 | 0.299537 | ||||||||
\(915\) | 54.8328 | 1.81272 | ||||||||
\(916\) | 12.7639 | 0.421732 | ||||||||
\(917\) | 9.23607 | 0.305002 | ||||||||
\(918\) | 93.6656 | 3.09143 | ||||||||
\(919\) | −57.8885 | −1.90957 | −0.954783 | − | 0.297302i | \(-0.903913\pi\) | ||||
−0.954783 | + | 0.297302i | \(0.903913\pi\) | |||||||
\(920\) | 12.9443 | 0.426760 | ||||||||
\(921\) | −103.777 | −3.41957 | ||||||||
\(922\) | 29.2361 | 0.962839 | ||||||||
\(923\) | −3.05573 | −0.100581 | ||||||||
\(924\) | −3.23607 | −0.106459 | ||||||||
\(925\) | −59.8885 | −1.96912 | ||||||||
\(926\) | −21.5279 | −0.707450 | ||||||||
\(927\) | 22.0000 | 0.722575 | ||||||||
\(928\) | −4.47214 | −0.146805 | ||||||||
\(929\) | −40.2492 | −1.32053 | −0.660267 | − | 0.751031i | \(-0.729557\pi\) | ||||
−0.660267 | + | 0.751031i | \(0.729557\pi\) | |||||||
\(930\) | −20.9443 | −0.686790 | ||||||||
\(931\) | −2.76393 | −0.0905842 | ||||||||
\(932\) | 2.94427 | 0.0964428 | ||||||||
\(933\) | −17.5279 | −0.573837 | ||||||||
\(934\) | 13.1246 | 0.429450 | ||||||||
\(935\) | −20.9443 | −0.684951 | ||||||||
\(936\) | 9.23607 | 0.301890 | ||||||||
\(937\) | −20.9443 | −0.684220 | −0.342110 | − | 0.939660i | \(-0.611141\pi\) | ||||
−0.342110 | + | 0.939660i | \(0.611141\pi\) | |||||||
\(938\) | −15.4164 | −0.503364 | ||||||||
\(939\) | −92.1378 | −3.00680 | ||||||||
\(940\) | −6.47214 | −0.211098 | ||||||||
\(941\) | −34.1803 | −1.11425 | −0.557124 | − | 0.830430i | \(-0.688095\pi\) | ||||
−0.557124 | + | 0.830430i | \(0.688095\pi\) | |||||||
\(942\) | −60.3607 | −1.96666 | ||||||||
\(943\) | 25.8885 | 0.843047 | ||||||||
\(944\) | 7.23607 | 0.235514 | ||||||||
\(945\) | −46.8328 | −1.52347 | ||||||||
\(946\) | −1.52786 | −0.0496751 | ||||||||
\(947\) | −0.944272 | −0.0306847 | −0.0153424 | − | 0.999882i | \(-0.504884\pi\) | ||||
−0.0153424 | + | 0.999882i | \(0.504884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.11146 | −0.198386 | ||||||||
\(950\) | −15.1246 | −0.490707 | ||||||||
\(951\) | 42.2492 | 1.37002 | ||||||||
\(952\) | −6.47214 | −0.209763 | ||||||||
\(953\) | 5.05573 | 0.163771 | 0.0818855 | − | 0.996642i | \(-0.473906\pi\) | ||||
0.0818855 | + | 0.996642i | \(0.473906\pi\) | |||||||
\(954\) | −3.52786 | −0.114219 | ||||||||
\(955\) | 20.9443 | 0.677741 | ||||||||
\(956\) | 20.0000 | 0.646846 | ||||||||
\(957\) | 14.4721 | 0.467818 | ||||||||
\(958\) | −32.3607 | −1.04553 | ||||||||
\(959\) | 15.8885 | 0.513068 | ||||||||
\(960\) | −10.4721 | −0.337987 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −13.5279 | −0.436156 | ||||||||
\(963\) | −48.3607 | −1.55840 | ||||||||
\(964\) | −11.4164 | −0.367698 | ||||||||
\(965\) | 9.52786 | 0.306713 | ||||||||
\(966\) | −12.9443 | −0.416475 | ||||||||
\(967\) | 10.1115 | 0.325163 | 0.162581 | − | 0.986695i | \(-0.448018\pi\) | ||||
0.162581 | + | 0.986695i | \(0.448018\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −57.8885 | −1.85965 | ||||||||
\(970\) | 11.4164 | 0.366559 | ||||||||
\(971\) | −16.5410 | −0.530827 | −0.265413 | − | 0.964135i | \(-0.585508\pi\) | ||||
−0.265413 | + | 0.964135i | \(0.585508\pi\) | |||||||
\(972\) | −35.5967 | −1.14177 | ||||||||
\(973\) | −8.29180 | −0.265823 | ||||||||
\(974\) | −0.944272 | −0.0302564 | ||||||||
\(975\) | −21.8885 | −0.700994 | ||||||||
\(976\) | −5.23607 | −0.167602 | ||||||||
\(977\) | 24.8328 | 0.794472 | 0.397236 | − | 0.917716i | \(-0.369969\pi\) | ||||
0.397236 | + | 0.917716i | \(0.369969\pi\) | |||||||
\(978\) | −24.0000 | −0.767435 | ||||||||
\(979\) | 10.0000 | 0.319601 | ||||||||
\(980\) | 3.23607 | 0.103372 | ||||||||
\(981\) | −74.7214 | −2.38567 | ||||||||
\(982\) | 0.944272 | 0.0301329 | ||||||||
\(983\) | 14.0000 | 0.446531 | 0.223265 | − | 0.974758i | \(-0.428328\pi\) | ||||
0.223265 | + | 0.974758i | \(0.428328\pi\) | |||||||
\(984\) | −20.9443 | −0.667679 | ||||||||
\(985\) | 58.2492 | 1.85597 | ||||||||
\(986\) | 28.9443 | 0.921773 | ||||||||
\(987\) | 6.47214 | 0.206010 | ||||||||
\(988\) | −3.41641 | −0.108690 | ||||||||
\(989\) | −6.11146 | −0.194333 | ||||||||
\(990\) | 24.1803 | 0.768502 | ||||||||
\(991\) | 44.3607 | 1.40916 | 0.704582 | − | 0.709623i | \(-0.251135\pi\) | ||||
0.704582 | + | 0.709623i | \(0.251135\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | −3.05573 | −0.0969706 | ||||||||
\(994\) | −2.47214 | −0.0784114 | ||||||||
\(995\) | 3.41641 | 0.108307 | ||||||||
\(996\) | −32.9443 | −1.04388 | ||||||||
\(997\) | 1.81966 | 0.0576292 | 0.0288146 | − | 0.999585i | \(-0.490827\pi\) | ||||
0.0288146 | + | 0.999585i | \(0.490827\pi\) | |||||||
\(998\) | 12.3607 | 0.391270 | ||||||||
\(999\) | 158.387 | 5.01114 |
(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 | 154.2.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1386.2.a.m.1.1 | 2 | |||
4.3 | odd | 2 | 1232.2.a.p.1.2 | 2 | |||
5.2 | odd | 4 | 3850.2.c.q.1849.4 | 4 | |||
5.3 | odd | 4 | 3850.2.c.q.1849.1 | 4 | |||
5.4 | even | 2 | 3850.2.a.bj.1.2 | 2 | |||
7.2 | even | 3 | 1078.2.e.q.67.2 | 4 | |||
7.3 | odd | 6 | 1078.2.e.n.177.1 | 4 | |||
7.4 | even | 3 | 1078.2.e.q.177.2 | 4 | |||
7.5 | odd | 6 | 1078.2.e.n.67.1 | 4 | |||
7.6 | odd | 2 | 1078.2.a.w.1.2 | 2 | |||
8.3 | odd | 2 | 4928.2.a.bk.1.1 | 2 | |||
8.5 | even | 2 | 4928.2.a.bt.1.2 | 2 | |||
11.10 | odd | 2 | 1694.2.a.l.1.1 | 2 | |||
21.20 | even | 2 | 9702.2.a.cu.1.2 | 2 | |||
28.27 | even | 2 | 8624.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1078.2.a.w.1.2 | 2 | 7.6 | odd | 2 | |||
1078.2.e.n.67.1 | 4 | 7.5 | odd | 6 | |||
1078.2.e.n.177.1 | 4 | 7.3 | odd | 6 | |||
1078.2.e.q.67.2 | 4 | 7.2 | even | 3 | |||
1078.2.e.q.177.2 | 4 | 7.4 | even | 3 | |||
1232.2.a.p.1.2 | 2 | 4.3 | odd | 2 | |||
1386.2.a.m.1.1 | 2 | 3.2 | odd | 2 | |||
1694.2.a.l.1.1 | 2 | 11.10 | odd | 2 | |||
3850.2.a.bj.1.2 | 2 | 5.4 | even | 2 | |||
3850.2.c.q.1849.1 | 4 | 5.3 | odd | 4 | |||
3850.2.c.q.1849.4 | 4 | 5.2 | odd | 4 | |||
4928.2.a.bk.1.1 | 2 | 8.3 | odd | 2 | |||
4928.2.a.bt.1.2 | 2 | 8.5 | even | 2 | |||
8624.2.a.bf.1.1 | 2 | 28.27 | even | 2 | |||
9702.2.a.cu.1.2 | 2 | 21.20 | even | 2 |