Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58389 | −1.82709 | −0.913543 | − | 0.406741i | \(-0.866665\pi\) | ||||
−0.913543 | + | 0.406741i | \(0.866665\pi\) | |||||||
\(3\) | 1.40748 | 0.812611 | 0.406305 | − | 0.913737i | \(-0.366817\pi\) | ||||
0.406305 | + | 0.913737i | \(0.366817\pi\) | |||||||
\(4\) | 4.67649 | 2.33825 | ||||||||
\(5\) | −2.16822 | −0.969659 | −0.484830 | − | 0.874609i | \(-0.661118\pi\) | ||||
−0.484830 | + | 0.874609i | \(0.661118\pi\) | |||||||
\(6\) | −3.63678 | −1.48471 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −6.91577 | −2.44509 | ||||||||
\(9\) | −1.01899 | −0.339663 | ||||||||
\(10\) | 5.60245 | 1.77165 | ||||||||
\(11\) | −3.16802 | −0.955195 | −0.477597 | − | 0.878579i | \(-0.658492\pi\) | ||||
−0.477597 | + | 0.878579i | \(0.658492\pi\) | |||||||
\(12\) | 6.58209 | 1.90008 | ||||||||
\(13\) | 1.21704 | 0.337547 | 0.168773 | − | 0.985655i | \(-0.446019\pi\) | ||||
0.168773 | + | 0.985655i | \(0.446019\pi\) | |||||||
\(14\) | −2.58389 | −0.690574 | ||||||||
\(15\) | −3.05174 | −0.787956 | ||||||||
\(16\) | 8.51660 | 2.12915 | ||||||||
\(17\) | 4.73910 | 1.14940 | 0.574701 | − | 0.818364i | \(-0.305118\pi\) | ||||
0.574701 | + | 0.818364i | \(0.305118\pi\) | |||||||
\(18\) | 2.63296 | 0.620595 | ||||||||
\(19\) | −4.76821 | −1.09390 | −0.546951 | − | 0.837165i | \(-0.684212\pi\) | ||||
−0.546951 | + | 0.837165i | \(0.684212\pi\) | |||||||
\(20\) | −10.1397 | −2.26730 | ||||||||
\(21\) | 1.40748 | 0.307138 | ||||||||
\(22\) | 8.18583 | 1.74522 | ||||||||
\(23\) | −5.72257 | −1.19324 | −0.596619 | − | 0.802525i | \(-0.703490\pi\) | ||||
−0.596619 | + | 0.802525i | \(0.703490\pi\) | |||||||
\(24\) | −9.73383 | −1.98691 | ||||||||
\(25\) | −0.298806 | −0.0597612 | ||||||||
\(26\) | −3.14471 | −0.616727 | ||||||||
\(27\) | −5.65666 | −1.08863 | ||||||||
\(28\) | 4.67649 | 0.883774 | ||||||||
\(29\) | −8.90251 | −1.65315 | −0.826577 | − | 0.562824i | \(-0.809715\pi\) | ||||
−0.826577 | + | 0.562824i | \(0.809715\pi\) | |||||||
\(30\) | 7.88536 | 1.43966 | ||||||||
\(31\) | −3.13011 | −0.562184 | −0.281092 | − | 0.959681i | \(-0.590697\pi\) | ||||
−0.281092 | + | 0.959681i | \(0.590697\pi\) | |||||||
\(32\) | −8.17444 | −1.44505 | ||||||||
\(33\) | −4.45894 | −0.776202 | ||||||||
\(34\) | −12.2453 | −2.10006 | ||||||||
\(35\) | −2.16822 | −0.366497 | ||||||||
\(36\) | −4.76530 | −0.794217 | ||||||||
\(37\) | −1.91415 | −0.314684 | −0.157342 | − | 0.987544i | \(-0.550292\pi\) | ||||
−0.157342 | + | 0.987544i | \(0.550292\pi\) | |||||||
\(38\) | 12.3205 | 1.99865 | ||||||||
\(39\) | 1.71297 | 0.274294 | ||||||||
\(40\) | 14.9949 | 2.37091 | ||||||||
\(41\) | 5.76268 | 0.899979 | 0.449990 | − | 0.893034i | \(-0.351428\pi\) | ||||
0.449990 | + | 0.893034i | \(0.351428\pi\) | |||||||
\(42\) | −3.63678 | −0.561168 | ||||||||
\(43\) | 4.63071 | 0.706177 | 0.353089 | − | 0.935590i | \(-0.385131\pi\) | ||||
0.353089 | + | 0.935590i | \(0.385131\pi\) | |||||||
\(44\) | −14.8152 | −2.23348 | ||||||||
\(45\) | 2.20940 | 0.329358 | ||||||||
\(46\) | 14.7865 | 2.18015 | ||||||||
\(47\) | 2.89486 | 0.422258 | 0.211129 | − | 0.977458i | \(-0.432286\pi\) | ||||
0.211129 | + | 0.977458i | \(0.432286\pi\) | |||||||
\(48\) | 11.9870 | 1.73017 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.772083 | 0.109189 | ||||||||
\(51\) | 6.67021 | 0.934016 | ||||||||
\(52\) | 5.69149 | 0.789268 | ||||||||
\(53\) | −0.623615 | −0.0856601 | −0.0428301 | − | 0.999082i | \(-0.513637\pi\) | ||||
−0.0428301 | + | 0.999082i | \(0.513637\pi\) | |||||||
\(54\) | 14.6162 | 1.98901 | ||||||||
\(55\) | 6.86898 | 0.926213 | ||||||||
\(56\) | −6.91577 | −0.924158 | ||||||||
\(57\) | −6.71117 | −0.888917 | ||||||||
\(58\) | 23.0031 | 3.02046 | ||||||||
\(59\) | −12.4131 | −1.61605 | −0.808027 | − | 0.589145i | \(-0.799465\pi\) | ||||
−0.808027 | + | 0.589145i | \(0.799465\pi\) | |||||||
\(60\) | −14.2714 | −1.84243 | ||||||||
\(61\) | 13.0829 | 1.67509 | 0.837544 | − | 0.546369i | \(-0.183991\pi\) | ||||
0.837544 | + | 0.546369i | \(0.183991\pi\) | |||||||
\(62\) | 8.08786 | 1.02716 | ||||||||
\(63\) | −1.01899 | −0.128381 | ||||||||
\(64\) | 4.08866 | 0.511083 | ||||||||
\(65\) | −2.63882 | −0.327305 | ||||||||
\(66\) | 11.5214 | 1.41819 | ||||||||
\(67\) | 11.9649 | 1.46174 | 0.730870 | − | 0.682517i | \(-0.239115\pi\) | ||||
0.730870 | + | 0.682517i | \(0.239115\pi\) | |||||||
\(68\) | 22.1624 | 2.68758 | ||||||||
\(69\) | −8.05442 | −0.969638 | ||||||||
\(70\) | 5.60245 | 0.669621 | ||||||||
\(71\) | −7.16977 | −0.850896 | −0.425448 | − | 0.904983i | \(-0.639883\pi\) | ||||
−0.425448 | + | 0.904983i | \(0.639883\pi\) | |||||||
\(72\) | 7.04710 | 0.830509 | ||||||||
\(73\) | 6.07721 | 0.711283 | 0.355642 | − | 0.934622i | \(-0.384262\pi\) | ||||
0.355642 | + | 0.934622i | \(0.384262\pi\) | |||||||
\(74\) | 4.94595 | 0.574955 | ||||||||
\(75\) | −0.420565 | −0.0485626 | ||||||||
\(76\) | −22.2985 | −2.55781 | ||||||||
\(77\) | −3.16802 | −0.361030 | ||||||||
\(78\) | −4.42612 | −0.501159 | ||||||||
\(79\) | −11.1885 | −1.25880 | −0.629400 | − | 0.777081i | \(-0.716699\pi\) | ||||
−0.629400 | + | 0.777081i | \(0.716699\pi\) | |||||||
\(80\) | −18.4659 | −2.06455 | ||||||||
\(81\) | −4.90469 | −0.544965 | ||||||||
\(82\) | −14.8901 | −1.64434 | ||||||||
\(83\) | 2.54325 | 0.279158 | 0.139579 | − | 0.990211i | \(-0.455425\pi\) | ||||
0.139579 | + | 0.990211i | \(0.455425\pi\) | |||||||
\(84\) | 6.58209 | 0.718165 | ||||||||
\(85\) | −10.2754 | −1.11453 | ||||||||
\(86\) | −11.9653 | −1.29025 | ||||||||
\(87\) | −12.5301 | −1.34337 | ||||||||
\(88\) | 21.9093 | 2.33554 | ||||||||
\(89\) | −8.94330 | −0.947988 | −0.473994 | − | 0.880528i | \(-0.657188\pi\) | ||||
−0.473994 | + | 0.880528i | \(0.657188\pi\) | |||||||
\(90\) | −5.70885 | −0.601765 | ||||||||
\(91\) | 1.21704 | 0.127581 | ||||||||
\(92\) | −26.7616 | −2.79008 | ||||||||
\(93\) | −4.40558 | −0.456837 | ||||||||
\(94\) | −7.47999 | −0.771502 | ||||||||
\(95\) | 10.3385 | 1.06071 | ||||||||
\(96\) | −11.5054 | −1.17426 | ||||||||
\(97\) | 9.11453 | 0.925441 | 0.462720 | − | 0.886504i | \(-0.346873\pi\) | ||||
0.462720 | + | 0.886504i | \(0.346873\pi\) | |||||||
\(98\) | −2.58389 | −0.261012 | ||||||||
\(99\) | 3.22819 | 0.324445 | ||||||||
\(100\) | −1.39737 | −0.139737 | ||||||||
\(101\) | 15.3894 | 1.53130 | 0.765650 | − | 0.643258i | \(-0.222418\pi\) | ||||
0.765650 | + | 0.643258i | \(0.222418\pi\) | |||||||
\(102\) | −17.2351 | −1.70653 | ||||||||
\(103\) | 9.62828 | 0.948703 | 0.474351 | − | 0.880336i | \(-0.342683\pi\) | ||||
0.474351 | + | 0.880336i | \(0.342683\pi\) | |||||||
\(104\) | −8.41678 | −0.825333 | ||||||||
\(105\) | −3.05174 | −0.297819 | ||||||||
\(106\) | 1.61135 | 0.156509 | ||||||||
\(107\) | 4.81884 | 0.465855 | 0.232927 | − | 0.972494i | \(-0.425170\pi\) | ||||
0.232927 | + | 0.972494i | \(0.425170\pi\) | |||||||
\(108\) | −26.4533 | −2.54547 | ||||||||
\(109\) | −4.66377 | −0.446708 | −0.223354 | − | 0.974737i | \(-0.571701\pi\) | ||||
−0.223354 | + | 0.974737i | \(0.571701\pi\) | |||||||
\(110\) | −17.7487 | −1.69227 | ||||||||
\(111\) | −2.69413 | −0.255716 | ||||||||
\(112\) | 8.51660 | 0.804743 | ||||||||
\(113\) | −9.47571 | −0.891400 | −0.445700 | − | 0.895182i | \(-0.647045\pi\) | ||||
−0.445700 | + | 0.895182i | \(0.647045\pi\) | |||||||
\(114\) | 17.3409 | 1.62413 | ||||||||
\(115\) | 12.4078 | 1.15703 | ||||||||
\(116\) | −41.6325 | −3.86548 | ||||||||
\(117\) | −1.24015 | −0.114652 | ||||||||
\(118\) | 32.0742 | 2.95267 | ||||||||
\(119\) | 4.73910 | 0.434433 | ||||||||
\(120\) | 21.1051 | 1.92662 | ||||||||
\(121\) | −0.963631 | −0.0876028 | ||||||||
\(122\) | −33.8047 | −3.06053 | ||||||||
\(123\) | 8.11088 | 0.731333 | ||||||||
\(124\) | −14.6379 | −1.31453 | ||||||||
\(125\) | 11.4890 | 1.02761 | ||||||||
\(126\) | 2.63296 | 0.234563 | ||||||||
\(127\) | 8.40274 | 0.745622 | 0.372811 | − | 0.927907i | \(-0.378394\pi\) | ||||
0.372811 | + | 0.927907i | \(0.378394\pi\) | |||||||
\(128\) | 5.78423 | 0.511258 | ||||||||
\(129\) | 6.51765 | 0.573847 | ||||||||
\(130\) | 6.81842 | 0.598015 | ||||||||
\(131\) | 16.9422 | 1.48025 | 0.740123 | − | 0.672472i | \(-0.234767\pi\) | ||||
0.740123 | + | 0.672472i | \(0.234767\pi\) | |||||||
\(132\) | −20.8522 | −1.81495 | ||||||||
\(133\) | −4.76821 | −0.413456 | ||||||||
\(134\) | −30.9159 | −2.67073 | ||||||||
\(135\) | 12.2649 | 1.05560 | ||||||||
\(136\) | −32.7745 | −2.81039 | ||||||||
\(137\) | −3.15859 | −0.269857 | −0.134928 | − | 0.990855i | \(-0.543080\pi\) | ||||
−0.134928 | + | 0.990855i | \(0.543080\pi\) | |||||||
\(138\) | 20.8117 | 1.77161 | ||||||||
\(139\) | −22.6268 | −1.91918 | −0.959591 | − | 0.281398i | \(-0.909202\pi\) | ||||
−0.959591 | + | 0.281398i | \(0.909202\pi\) | |||||||
\(140\) | −10.1397 | −0.856960 | ||||||||
\(141\) | 4.07446 | 0.343132 | ||||||||
\(142\) | 18.5259 | 1.55466 | ||||||||
\(143\) | −3.85562 | −0.322423 | ||||||||
\(144\) | −8.67834 | −0.723195 | ||||||||
\(145\) | 19.3026 | 1.60300 | ||||||||
\(146\) | −15.7028 | −1.29958 | ||||||||
\(147\) | 1.40748 | 0.116087 | ||||||||
\(148\) | −8.95150 | −0.735809 | ||||||||
\(149\) | −6.38916 | −0.523420 | −0.261710 | − | 0.965147i | \(-0.584286\pi\) | ||||
−0.261710 | + | 0.965147i | \(0.584286\pi\) | |||||||
\(150\) | 1.08669 | 0.0887282 | ||||||||
\(151\) | 20.3502 | 1.65607 | 0.828036 | − | 0.560675i | \(-0.189458\pi\) | ||||
0.828036 | + | 0.560675i | \(0.189458\pi\) | |||||||
\(152\) | 32.9758 | 2.67469 | ||||||||
\(153\) | −4.82910 | −0.390410 | ||||||||
\(154\) | 8.18583 | 0.659633 | ||||||||
\(155\) | 6.78678 | 0.545127 | ||||||||
\(156\) | 8.01068 | 0.641368 | ||||||||
\(157\) | 6.88006 | 0.549089 | 0.274544 | − | 0.961574i | \(-0.411473\pi\) | ||||
0.274544 | + | 0.961574i | \(0.411473\pi\) | |||||||
\(158\) | 28.9098 | 2.29994 | ||||||||
\(159\) | −0.877728 | −0.0696084 | ||||||||
\(160\) | 17.7240 | 1.40121 | ||||||||
\(161\) | −5.72257 | −0.451002 | ||||||||
\(162\) | 12.6732 | 0.995699 | ||||||||
\(163\) | 15.5669 | 1.21929 | 0.609647 | − | 0.792673i | \(-0.291311\pi\) | ||||
0.609647 | + | 0.792673i | \(0.291311\pi\) | |||||||
\(164\) | 26.9491 | 2.10437 | ||||||||
\(165\) | 9.66798 | 0.752651 | ||||||||
\(166\) | −6.57149 | −0.510046 | ||||||||
\(167\) | −6.65907 | −0.515294 | −0.257647 | − | 0.966239i | \(-0.582947\pi\) | ||||
−0.257647 | + | 0.966239i | \(0.582947\pi\) | |||||||
\(168\) | −9.73383 | −0.750981 | ||||||||
\(169\) | −11.5188 | −0.886062 | ||||||||
\(170\) | 26.5506 | 2.03634 | ||||||||
\(171\) | 4.85876 | 0.371558 | ||||||||
\(172\) | 21.6555 | 1.65122 | ||||||||
\(173\) | 10.6468 | 0.809461 | 0.404731 | − | 0.914436i | \(-0.367365\pi\) | ||||
0.404731 | + | 0.914436i | \(0.367365\pi\) | |||||||
\(174\) | 32.3765 | 2.45446 | ||||||||
\(175\) | −0.298806 | −0.0225876 | ||||||||
\(176\) | −26.9808 | −2.03375 | ||||||||
\(177\) | −17.4713 | −1.31322 | ||||||||
\(178\) | 23.1085 | 1.73206 | ||||||||
\(179\) | −14.5977 | −1.09108 | −0.545542 | − | 0.838083i | \(-0.683676\pi\) | ||||
−0.545542 | + | 0.838083i | \(0.683676\pi\) | |||||||
\(180\) | 10.3322 | 0.770120 | ||||||||
\(181\) | −24.7977 | −1.84320 | −0.921599 | − | 0.388142i | \(-0.873117\pi\) | ||||
−0.921599 | + | 0.388142i | \(0.873117\pi\) | |||||||
\(182\) | −3.14471 | −0.233101 | ||||||||
\(183\) | 18.4139 | 1.36120 | ||||||||
\(184\) | 39.5760 | 2.91758 | ||||||||
\(185\) | 4.15030 | 0.305136 | ||||||||
\(186\) | 11.3835 | 0.834681 | ||||||||
\(187\) | −15.0136 | −1.09790 | ||||||||
\(188\) | 13.5378 | 0.987344 | ||||||||
\(189\) | −5.65666 | −0.411462 | ||||||||
\(190\) | −26.7137 | −1.93801 | ||||||||
\(191\) | 16.5849 | 1.20004 | 0.600022 | − | 0.799984i | \(-0.295159\pi\) | ||||
0.600022 | + | 0.799984i | \(0.295159\pi\) | |||||||
\(192\) | 5.75472 | 0.415311 | ||||||||
\(193\) | −9.06703 | −0.652659 | −0.326329 | − | 0.945256i | \(-0.605812\pi\) | ||||
−0.326329 | + | 0.945256i | \(0.605812\pi\) | |||||||
\(194\) | −23.5510 | −1.69086 | ||||||||
\(195\) | −3.71410 | −0.265972 | ||||||||
\(196\) | 4.67649 | 0.334035 | ||||||||
\(197\) | −2.64107 | −0.188169 | −0.0940843 | − | 0.995564i | \(-0.529992\pi\) | ||||
−0.0940843 | + | 0.995564i | \(0.529992\pi\) | |||||||
\(198\) | −8.34128 | −0.592789 | ||||||||
\(199\) | 18.4052 | 1.30471 | 0.652355 | − | 0.757913i | \(-0.273781\pi\) | ||||
0.652355 | + | 0.757913i | \(0.273781\pi\) | |||||||
\(200\) | 2.06647 | 0.146122 | ||||||||
\(201\) | 16.8403 | 1.18783 | ||||||||
\(202\) | −39.7645 | −2.79782 | ||||||||
\(203\) | −8.90251 | −0.624834 | ||||||||
\(204\) | 31.1932 | 2.18396 | ||||||||
\(205\) | −12.4948 | −0.872673 | ||||||||
\(206\) | −24.8784 | −1.73336 | ||||||||
\(207\) | 5.83124 | 0.405299 | ||||||||
\(208\) | 10.3651 | 0.718688 | ||||||||
\(209\) | 15.1058 | 1.04489 | ||||||||
\(210\) | 7.88536 | 0.544142 | ||||||||
\(211\) | 18.9919 | 1.30745 | 0.653727 | − | 0.756731i | \(-0.273205\pi\) | ||||
0.653727 | + | 0.756731i | \(0.273205\pi\) | |||||||
\(212\) | −2.91633 | −0.200295 | ||||||||
\(213\) | −10.0913 | −0.691447 | ||||||||
\(214\) | −12.4514 | −0.851157 | ||||||||
\(215\) | −10.0404 | −0.684751 | ||||||||
\(216\) | 39.1202 | 2.66179 | ||||||||
\(217\) | −3.13011 | −0.212486 | ||||||||
\(218\) | 12.0507 | 0.816175 | ||||||||
\(219\) | 8.55357 | 0.577996 | ||||||||
\(220\) | 32.1228 | 2.16572 | ||||||||
\(221\) | 5.76769 | 0.387977 | ||||||||
\(222\) | 6.96134 | 0.467215 | ||||||||
\(223\) | −22.9562 | −1.53726 | −0.768629 | − | 0.639694i | \(-0.779061\pi\) | ||||
−0.768629 | + | 0.639694i | \(0.779061\pi\) | |||||||
\(224\) | −8.17444 | −0.546178 | ||||||||
\(225\) | 0.304481 | 0.0202987 | ||||||||
\(226\) | 24.4842 | 1.62866 | ||||||||
\(227\) | 10.5094 | 0.697532 | 0.348766 | − | 0.937210i | \(-0.386601\pi\) | ||||
0.348766 | + | 0.937210i | \(0.386601\pi\) | |||||||
\(228\) | −31.3848 | −2.07851 | ||||||||
\(229\) | 21.1762 | 1.39936 | 0.699680 | − | 0.714456i | \(-0.253326\pi\) | ||||
0.699680 | + | 0.714456i | \(0.253326\pi\) | |||||||
\(230\) | −32.0604 | −2.11400 | ||||||||
\(231\) | −4.45894 | −0.293377 | ||||||||
\(232\) | 61.5677 | 4.04212 | ||||||||
\(233\) | −20.1853 | −1.32238 | −0.661191 | − | 0.750217i | \(-0.729949\pi\) | ||||
−0.661191 | + | 0.750217i | \(0.729949\pi\) | |||||||
\(234\) | 3.20442 | 0.209480 | ||||||||
\(235\) | −6.27670 | −0.409446 | ||||||||
\(236\) | −58.0500 | −3.77873 | ||||||||
\(237\) | −15.7476 | −1.02291 | ||||||||
\(238\) | −12.2453 | −0.793747 | ||||||||
\(239\) | 7.99700 | 0.517283 | 0.258642 | − | 0.965973i | \(-0.416725\pi\) | ||||
0.258642 | + | 0.965973i | \(0.416725\pi\) | |||||||
\(240\) | −25.9905 | −1.67768 | ||||||||
\(241\) | 0.668492 | 0.0430614 | 0.0215307 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215307 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(242\) | 2.48992 | 0.160058 | ||||||||
\(243\) | 10.0667 | 0.645781 | ||||||||
\(244\) | 61.1819 | 3.91677 | ||||||||
\(245\) | −2.16822 | −0.138523 | ||||||||
\(246\) | −20.9576 | −1.33621 | ||||||||
\(247\) | −5.80311 | −0.369243 | ||||||||
\(248\) | 21.6471 | 1.37459 | ||||||||
\(249\) | 3.57959 | 0.226847 | ||||||||
\(250\) | −29.6863 | −1.87753 | ||||||||
\(251\) | 17.7432 | 1.11994 | 0.559969 | − | 0.828513i | \(-0.310813\pi\) | ||||
0.559969 | + | 0.828513i | \(0.310813\pi\) | |||||||
\(252\) | −4.76530 | −0.300186 | ||||||||
\(253\) | 18.1292 | 1.13977 | ||||||||
\(254\) | −21.7118 | −1.36232 | ||||||||
\(255\) | −14.4625 | −0.905677 | ||||||||
\(256\) | −23.1231 | −1.44520 | ||||||||
\(257\) | 7.89004 | 0.492167 | 0.246083 | − | 0.969249i | \(-0.420856\pi\) | ||||
0.246083 | + | 0.969249i | \(0.420856\pi\) | |||||||
\(258\) | −16.8409 | −1.04847 | ||||||||
\(259\) | −1.91415 | −0.118939 | ||||||||
\(260\) | −12.3404 | −0.765321 | ||||||||
\(261\) | 9.07157 | 0.561516 | ||||||||
\(262\) | −43.7768 | −2.70454 | ||||||||
\(263\) | −11.5866 | −0.714461 | −0.357230 | − | 0.934016i | \(-0.616279\pi\) | ||||
−0.357230 | + | 0.934016i | \(0.616279\pi\) | |||||||
\(264\) | 30.8370 | 1.89789 | ||||||||
\(265\) | 1.35214 | 0.0830611 | ||||||||
\(266\) | 12.3205 | 0.755420 | ||||||||
\(267\) | −12.5875 | −0.770345 | ||||||||
\(268\) | 55.9536 | 3.41791 | ||||||||
\(269\) | 11.8549 | 0.722808 | 0.361404 | − | 0.932409i | \(-0.382298\pi\) | ||||
0.361404 | + | 0.932409i | \(0.382298\pi\) | |||||||
\(270\) | −31.6912 | −1.92866 | ||||||||
\(271\) | 30.5579 | 1.85626 | 0.928130 | − | 0.372256i | \(-0.121416\pi\) | ||||
0.928130 | + | 0.372256i | \(0.121416\pi\) | |||||||
\(272\) | 40.3611 | 2.44725 | ||||||||
\(273\) | 1.71297 | 0.103673 | ||||||||
\(274\) | 8.16146 | 0.493052 | ||||||||
\(275\) | 0.946625 | 0.0570836 | ||||||||
\(276\) | −37.6664 | −2.26725 | ||||||||
\(277\) | 19.8591 | 1.19322 | 0.596609 | − | 0.802532i | \(-0.296514\pi\) | ||||
0.596609 | + | 0.802532i | \(0.296514\pi\) | |||||||
\(278\) | 58.4652 | 3.50651 | ||||||||
\(279\) | 3.18955 | 0.190953 | ||||||||
\(280\) | 14.9949 | 0.896119 | ||||||||
\(281\) | −11.1487 | −0.665075 | −0.332538 | − | 0.943090i | \(-0.607905\pi\) | ||||
−0.332538 | + | 0.943090i | \(0.607905\pi\) | |||||||
\(282\) | −10.5280 | −0.626931 | ||||||||
\(283\) | 2.27771 | 0.135396 | 0.0676980 | − | 0.997706i | \(-0.478435\pi\) | ||||
0.0676980 | + | 0.997706i | \(0.478435\pi\) | |||||||
\(284\) | −33.5294 | −1.98960 | ||||||||
\(285\) | 14.5513 | 0.861946 | ||||||||
\(286\) | 9.96250 | 0.589095 | ||||||||
\(287\) | 5.76268 | 0.340160 | ||||||||
\(288\) | 8.32968 | 0.490831 | ||||||||
\(289\) | 5.45911 | 0.321124 | ||||||||
\(290\) | −49.8759 | −2.92881 | ||||||||
\(291\) | 12.8286 | 0.752023 | ||||||||
\(292\) | 28.4200 | 1.66316 | ||||||||
\(293\) | −12.3883 | −0.723735 | −0.361867 | − | 0.932230i | \(-0.617861\pi\) | ||||
−0.361867 | + | 0.932230i | \(0.617861\pi\) | |||||||
\(294\) | −3.63678 | −0.212102 | ||||||||
\(295\) | 26.9145 | 1.56702 | ||||||||
\(296\) | 13.2378 | 0.769431 | ||||||||
\(297\) | 17.9204 | 1.03985 | ||||||||
\(298\) | 16.5089 | 0.956334 | ||||||||
\(299\) | −6.96461 | −0.402774 | ||||||||
\(300\) | −1.96677 | −0.113551 | ||||||||
\(301\) | 4.63071 | 0.266910 | ||||||||
\(302\) | −52.5826 | −3.02579 | ||||||||
\(303\) | 21.6603 | 1.24435 | ||||||||
\(304\) | −40.6089 | −2.32908 | ||||||||
\(305\) | −28.3666 | −1.62426 | ||||||||
\(306\) | 12.4779 | 0.713313 | ||||||||
\(307\) | 12.2605 | 0.699744 | 0.349872 | − | 0.936797i | \(-0.386225\pi\) | ||||
0.349872 | + | 0.936797i | \(0.386225\pi\) | |||||||
\(308\) | −14.8152 | −0.844177 | ||||||||
\(309\) | 13.5516 | 0.770926 | ||||||||
\(310\) | −17.5363 | −0.995995 | ||||||||
\(311\) | 10.3731 | 0.588204 | 0.294102 | − | 0.955774i | \(-0.404979\pi\) | ||||
0.294102 | + | 0.955774i | \(0.404979\pi\) | |||||||
\(312\) | −11.8465 | −0.670675 | ||||||||
\(313\) | 10.3129 | 0.582918 | 0.291459 | − | 0.956583i | \(-0.405859\pi\) | ||||
0.291459 | + | 0.956583i | \(0.405859\pi\) | |||||||
\(314\) | −17.7773 | −1.00323 | ||||||||
\(315\) | 2.20940 | 0.124486 | ||||||||
\(316\) | −52.3228 | −2.94339 | ||||||||
\(317\) | −29.3545 | −1.64871 | −0.824355 | − | 0.566073i | \(-0.808462\pi\) | ||||
−0.824355 | + | 0.566073i | \(0.808462\pi\) | |||||||
\(318\) | 2.26795 | 0.127181 | ||||||||
\(319\) | 28.2033 | 1.57908 | ||||||||
\(320\) | −8.86514 | −0.495576 | ||||||||
\(321\) | 6.78244 | 0.378559 | ||||||||
\(322\) | 14.7865 | 0.824019 | ||||||||
\(323\) | −22.5970 | −1.25733 | ||||||||
\(324\) | −22.9367 | −1.27426 | ||||||||
\(325\) | −0.363660 | −0.0201722 | ||||||||
\(326\) | −40.2232 | −2.22775 | ||||||||
\(327\) | −6.56418 | −0.363000 | ||||||||
\(328\) | −39.8534 | −2.20053 | ||||||||
\(329\) | 2.89486 | 0.159599 | ||||||||
\(330\) | −24.9810 | −1.37516 | ||||||||
\(331\) | −24.2184 | −1.33117 | −0.665583 | − | 0.746324i | \(-0.731817\pi\) | ||||
−0.665583 | + | 0.746324i | \(0.731817\pi\) | |||||||
\(332\) | 11.8935 | 0.652741 | ||||||||
\(333\) | 1.95050 | 0.106887 | ||||||||
\(334\) | 17.2063 | 0.941487 | ||||||||
\(335\) | −25.9425 | −1.41739 | ||||||||
\(336\) | 11.9870 | 0.653943 | ||||||||
\(337\) | 17.6280 | 0.960256 | 0.480128 | − | 0.877198i | \(-0.340590\pi\) | ||||
0.480128 | + | 0.877198i | \(0.340590\pi\) | |||||||
\(338\) | 29.7633 | 1.61891 | ||||||||
\(339\) | −13.3369 | −0.724361 | ||||||||
\(340\) | −48.0530 | −2.60604 | ||||||||
\(341\) | 9.91626 | 0.536996 | ||||||||
\(342\) | −12.5545 | −0.678870 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −32.0249 | −1.72667 | ||||||||
\(345\) | 17.4638 | 0.940218 | ||||||||
\(346\) | −27.5102 | −1.47896 | ||||||||
\(347\) | −14.4860 | −0.777650 | −0.388825 | − | 0.921312i | \(-0.627119\pi\) | ||||
−0.388825 | + | 0.921312i | \(0.627119\pi\) | |||||||
\(348\) | −58.5971 | −3.14113 | ||||||||
\(349\) | −29.0156 | −1.55317 | −0.776584 | − | 0.630013i | \(-0.783049\pi\) | ||||
−0.776584 | + | 0.630013i | \(0.783049\pi\) | |||||||
\(350\) | 0.772083 | 0.0412696 | ||||||||
\(351\) | −6.88440 | −0.367462 | ||||||||
\(352\) | 25.8968 | 1.38031 | ||||||||
\(353\) | −19.6237 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(354\) | 45.1439 | 2.39937 | ||||||||
\(355\) | 15.5457 | 0.825079 | ||||||||
\(356\) | −41.8233 | −2.21663 | ||||||||
\(357\) | 6.67021 | 0.353025 | ||||||||
\(358\) | 37.7189 | 1.99351 | ||||||||
\(359\) | 35.2330 | 1.85953 | 0.929763 | − | 0.368160i | \(-0.120012\pi\) | ||||
0.929763 | + | 0.368160i | \(0.120012\pi\) | |||||||
\(360\) | −15.2797 | −0.805311 | ||||||||
\(361\) | 3.73580 | 0.196621 | ||||||||
\(362\) | 64.0746 | 3.36768 | ||||||||
\(363\) | −1.35629 | −0.0711870 | ||||||||
\(364\) | 5.69149 | 0.298315 | ||||||||
\(365\) | −13.1767 | −0.689702 | ||||||||
\(366\) | −47.5795 | −2.48702 | ||||||||
\(367\) | 32.1168 | 1.67648 | 0.838241 | − | 0.545300i | \(-0.183584\pi\) | ||||
0.838241 | + | 0.545300i | \(0.183584\pi\) | |||||||
\(368\) | −48.7368 | −2.54058 | ||||||||
\(369\) | −5.87212 | −0.305690 | ||||||||
\(370\) | −10.7239 | −0.557510 | ||||||||
\(371\) | −0.623615 | −0.0323765 | ||||||||
\(372\) | −20.6027 | −1.06820 | ||||||||
\(373\) | 14.6269 | 0.757352 | 0.378676 | − | 0.925529i | \(-0.376380\pi\) | ||||
0.378676 | + | 0.925529i | \(0.376380\pi\) | |||||||
\(374\) | 38.7935 | 2.00596 | ||||||||
\(375\) | 16.1706 | 0.835045 | ||||||||
\(376\) | −20.0202 | −1.03246 | ||||||||
\(377\) | −10.8347 | −0.558017 | ||||||||
\(378\) | 14.6162 | 0.751776 | ||||||||
\(379\) | −30.3842 | −1.56073 | −0.780366 | − | 0.625323i | \(-0.784967\pi\) | ||||
−0.780366 | + | 0.625323i | \(0.784967\pi\) | |||||||
\(380\) | 48.3481 | 2.48021 | ||||||||
\(381\) | 11.8267 | 0.605901 | ||||||||
\(382\) | −42.8537 | −2.19258 | ||||||||
\(383\) | −31.9295 | −1.63152 | −0.815760 | − | 0.578390i | \(-0.803681\pi\) | ||||
−0.815760 | + | 0.578390i | \(0.803681\pi\) | |||||||
\(384\) | 8.14120 | 0.415454 | ||||||||
\(385\) | 6.86898 | 0.350076 | ||||||||
\(386\) | 23.4282 | 1.19246 | ||||||||
\(387\) | −4.71865 | −0.239863 | ||||||||
\(388\) | 42.6241 | 2.16391 | ||||||||
\(389\) | 9.15773 | 0.464315 | 0.232158 | − | 0.972678i | \(-0.425421\pi\) | ||||
0.232158 | + | 0.972678i | \(0.425421\pi\) | |||||||
\(390\) | 9.59682 | 0.485954 | ||||||||
\(391\) | −27.1198 | −1.37151 | ||||||||
\(392\) | −6.91577 | −0.349299 | ||||||||
\(393\) | 23.8458 | 1.20286 | ||||||||
\(394\) | 6.82424 | 0.343800 | ||||||||
\(395\) | 24.2591 | 1.22061 | ||||||||
\(396\) | 15.0966 | 0.758632 | ||||||||
\(397\) | 30.1762 | 1.51450 | 0.757249 | − | 0.653126i | \(-0.226543\pi\) | ||||
0.757249 | + | 0.653126i | \(0.226543\pi\) | |||||||
\(398\) | −47.5571 | −2.38382 | ||||||||
\(399\) | −6.71117 | −0.335979 | ||||||||
\(400\) | −2.54481 | −0.127241 | ||||||||
\(401\) | −17.5757 | −0.877689 | −0.438845 | − | 0.898563i | \(-0.644612\pi\) | ||||
−0.438845 | + | 0.898563i | \(0.644612\pi\) | |||||||
\(402\) | −43.5136 | −2.17026 | ||||||||
\(403\) | −3.80948 | −0.189764 | ||||||||
\(404\) | 71.9683 | 3.58056 | ||||||||
\(405\) | 10.6345 | 0.528430 | ||||||||
\(406\) | 23.0031 | 1.14163 | ||||||||
\(407\) | 6.06406 | 0.300584 | ||||||||
\(408\) | −46.1296 | −2.28376 | ||||||||
\(409\) | 9.08657 | 0.449302 | 0.224651 | − | 0.974439i | \(-0.427876\pi\) | ||||
0.224651 | + | 0.974439i | \(0.427876\pi\) | |||||||
\(410\) | 32.2851 | 1.59445 | ||||||||
\(411\) | −4.44567 | −0.219289 | ||||||||
\(412\) | 45.0266 | 2.21830 | ||||||||
\(413\) | −12.4131 | −0.610811 | ||||||||
\(414\) | −15.0673 | −0.740517 | ||||||||
\(415\) | −5.51434 | −0.270688 | ||||||||
\(416\) | −9.94864 | −0.487772 | ||||||||
\(417\) | −31.8469 | −1.55955 | ||||||||
\(418\) | −39.0317 | −1.90910 | ||||||||
\(419\) | 28.0626 | 1.37095 | 0.685474 | − | 0.728097i | \(-0.259595\pi\) | ||||
0.685474 | + | 0.728097i | \(0.259595\pi\) | |||||||
\(420\) | −14.2714 | −0.696375 | ||||||||
\(421\) | −30.2588 | −1.47473 | −0.737363 | − | 0.675497i | \(-0.763929\pi\) | ||||
−0.737363 | + | 0.675497i | \(0.763929\pi\) | |||||||
\(422\) | −49.0729 | −2.38883 | ||||||||
\(423\) | −2.94983 | −0.143426 | ||||||||
\(424\) | 4.31278 | 0.209447 | ||||||||
\(425\) | −1.41607 | −0.0686897 | ||||||||
\(426\) | 26.0749 | 1.26333 | ||||||||
\(427\) | 13.0829 | 0.633124 | ||||||||
\(428\) | 22.5353 | 1.08928 | ||||||||
\(429\) | −5.42672 | −0.262004 | ||||||||
\(430\) | 25.9434 | 1.25110 | ||||||||
\(431\) | −29.1887 | −1.40597 | −0.702986 | − | 0.711204i | \(-0.748150\pi\) | ||||
−0.702986 | + | 0.711204i | \(0.748150\pi\) | |||||||
\(432\) | −48.1756 | −2.31785 | ||||||||
\(433\) | 20.7721 | 0.998244 | 0.499122 | − | 0.866532i | \(-0.333656\pi\) | ||||
0.499122 | + | 0.866532i | \(0.333656\pi\) | |||||||
\(434\) | 8.08786 | 0.388230 | ||||||||
\(435\) | 27.1681 | 1.30261 | ||||||||
\(436\) | −21.8101 | −1.04451 | ||||||||
\(437\) | 27.2864 | 1.30529 | ||||||||
\(438\) | −22.1015 | −1.05605 | ||||||||
\(439\) | 0.684286 | 0.0326592 | 0.0163296 | − | 0.999867i | \(-0.494802\pi\) | ||||
0.0163296 | + | 0.999867i | \(0.494802\pi\) | |||||||
\(440\) | −47.5043 | −2.26468 | ||||||||
\(441\) | −1.01899 | −0.0485234 | ||||||||
\(442\) | −14.9031 | −0.708867 | ||||||||
\(443\) | 4.10502 | 0.195035 | 0.0975176 | − | 0.995234i | \(-0.468910\pi\) | ||||
0.0975176 | + | 0.995234i | \(0.468910\pi\) | |||||||
\(444\) | −12.5991 | −0.597926 | ||||||||
\(445\) | 19.3911 | 0.919225 | ||||||||
\(446\) | 59.3162 | 2.80871 | ||||||||
\(447\) | −8.99263 | −0.425337 | ||||||||
\(448\) | 4.08866 | 0.193171 | ||||||||
\(449\) | −28.5382 | −1.34680 | −0.673401 | − | 0.739277i | \(-0.735167\pi\) | ||||
−0.673401 | + | 0.739277i | \(0.735167\pi\) | |||||||
\(450\) | −0.786745 | −0.0370875 | ||||||||
\(451\) | −18.2563 | −0.859656 | ||||||||
\(452\) | −44.3131 | −2.08431 | ||||||||
\(453\) | 28.6425 | 1.34574 | ||||||||
\(454\) | −27.1551 | −1.27445 | ||||||||
\(455\) | −2.63882 | −0.123710 | ||||||||
\(456\) | 46.4129 | 2.17348 | ||||||||
\(457\) | −38.9381 | −1.82145 | −0.910724 | − | 0.413016i | \(-0.864475\pi\) | ||||
−0.910724 | + | 0.413016i | \(0.864475\pi\) | |||||||
\(458\) | −54.7169 | −2.55675 | ||||||||
\(459\) | −26.8075 | −1.25127 | ||||||||
\(460\) | 58.0250 | 2.70543 | ||||||||
\(461\) | −26.6744 | −1.24235 | −0.621175 | − | 0.783672i | \(-0.713345\pi\) | ||||
−0.621175 | + | 0.783672i | \(0.713345\pi\) | |||||||
\(462\) | 11.5214 | 0.536025 | ||||||||
\(463\) | −1.71039 | −0.0794884 | −0.0397442 | − | 0.999210i | \(-0.512654\pi\) | ||||
−0.0397442 | + | 0.999210i | \(0.512654\pi\) | |||||||
\(464\) | −75.8191 | −3.51982 | ||||||||
\(465\) | 9.55228 | 0.442976 | ||||||||
\(466\) | 52.1566 | 2.41611 | ||||||||
\(467\) | 38.5151 | 1.78227 | 0.891134 | − | 0.453740i | \(-0.149911\pi\) | ||||
0.891134 | + | 0.453740i | \(0.149911\pi\) | |||||||
\(468\) | −5.79958 | −0.268085 | ||||||||
\(469\) | 11.9649 | 0.552486 | ||||||||
\(470\) | 16.2183 | 0.748094 | ||||||||
\(471\) | 9.68358 | 0.446196 | ||||||||
\(472\) | 85.8465 | 3.95140 | ||||||||
\(473\) | −14.6702 | −0.674537 | ||||||||
\(474\) | 40.6900 | 1.86895 | ||||||||
\(475\) | 1.42477 | 0.0653729 | ||||||||
\(476\) | 22.1624 | 1.01581 | ||||||||
\(477\) | 0.635458 | 0.0290956 | ||||||||
\(478\) | −20.6634 | −0.945121 | ||||||||
\(479\) | 27.0967 | 1.23808 | 0.619039 | − | 0.785360i | \(-0.287522\pi\) | ||||
0.619039 | + | 0.785360i | \(0.287522\pi\) | |||||||
\(480\) | 24.9463 | 1.13864 | ||||||||
\(481\) | −2.32960 | −0.106221 | ||||||||
\(482\) | −1.72731 | −0.0786768 | ||||||||
\(483\) | −8.05442 | −0.366489 | ||||||||
\(484\) | −4.50641 | −0.204837 | ||||||||
\(485\) | −19.7623 | −0.897362 | ||||||||
\(486\) | −26.0113 | −1.17990 | ||||||||
\(487\) | −18.3006 | −0.829278 | −0.414639 | − | 0.909986i | \(-0.636092\pi\) | ||||
−0.414639 | + | 0.909986i | \(0.636092\pi\) | |||||||
\(488\) | −90.4780 | −4.09575 | ||||||||
\(489\) | 21.9101 | 0.990811 | ||||||||
\(490\) | 5.60245 | 0.253093 | ||||||||
\(491\) | 29.4340 | 1.32834 | 0.664169 | − | 0.747583i | \(-0.268786\pi\) | ||||
0.664169 | + | 0.747583i | \(0.268786\pi\) | |||||||
\(492\) | 37.9305 | 1.71004 | ||||||||
\(493\) | −42.1899 | −1.90014 | ||||||||
\(494\) | 14.9946 | 0.674639 | ||||||||
\(495\) | −6.99943 | −0.314601 | ||||||||
\(496\) | −26.6579 | −1.19698 | ||||||||
\(497\) | −7.16977 | −0.321608 | ||||||||
\(498\) | −9.24926 | −0.414469 | ||||||||
\(499\) | 5.64540 | 0.252723 | 0.126361 | − | 0.991984i | \(-0.459670\pi\) | ||||
0.126361 | + | 0.991984i | \(0.459670\pi\) | |||||||
\(500\) | 53.7282 | 2.40280 | ||||||||
\(501\) | −9.37253 | −0.418734 | ||||||||
\(502\) | −45.8464 | −2.04623 | ||||||||
\(503\) | 11.9336 | 0.532091 | 0.266046 | − | 0.963960i | \(-0.414283\pi\) | ||||
0.266046 | + | 0.963960i | \(0.414283\pi\) | |||||||
\(504\) | 7.04710 | 0.313903 | ||||||||
\(505\) | −33.3676 | −1.48484 | ||||||||
\(506\) | −46.8439 | −2.08247 | ||||||||
\(507\) | −16.2125 | −0.720024 | ||||||||
\(508\) | 39.2953 | 1.74345 | ||||||||
\(509\) | 9.50300 | 0.421213 | 0.210607 | − | 0.977571i | \(-0.432456\pi\) | ||||
0.210607 | + | 0.977571i | \(0.432456\pi\) | |||||||
\(510\) | 37.3695 | 1.65475 | ||||||||
\(511\) | 6.07721 | 0.268840 | ||||||||
\(512\) | 48.1792 | 2.12924 | ||||||||
\(513\) | 26.9721 | 1.19085 | ||||||||
\(514\) | −20.3870 | −0.899232 | ||||||||
\(515\) | −20.8763 | −0.919918 | ||||||||
\(516\) | 30.4798 | 1.34180 | ||||||||
\(517\) | −9.17097 | −0.403339 | ||||||||
\(518\) | 4.94595 | 0.217312 | ||||||||
\(519\) | 14.9852 | 0.657777 | ||||||||
\(520\) | 18.2495 | 0.800292 | ||||||||
\(521\) | 14.5153 | 0.635929 | 0.317965 | − | 0.948103i | \(-0.397001\pi\) | ||||
0.317965 | + | 0.948103i | \(0.397001\pi\) | |||||||
\(522\) | −23.4400 | −1.02594 | ||||||||
\(523\) | −27.1413 | −1.18680 | −0.593402 | − | 0.804906i | \(-0.702216\pi\) | ||||
−0.593402 | + | 0.804906i | \(0.702216\pi\) | |||||||
\(524\) | 79.2300 | 3.46118 | ||||||||
\(525\) | −0.420565 | −0.0183550 | ||||||||
\(526\) | 29.9385 | 1.30538 | ||||||||
\(527\) | −14.8339 | −0.646175 | ||||||||
\(528\) | −37.9750 | −1.65265 | ||||||||
\(529\) | 9.74778 | 0.423817 | ||||||||
\(530\) | −3.49378 | −0.151760 | ||||||||
\(531\) | 12.6489 | 0.548915 | ||||||||
\(532\) | −22.2985 | −0.966762 | ||||||||
\(533\) | 7.01342 | 0.303785 | ||||||||
\(534\) | 32.5249 | 1.40749 | ||||||||
\(535\) | −10.4483 | −0.451720 | ||||||||
\(536\) | −82.7462 | −3.57409 | ||||||||
\(537\) | −20.5460 | −0.886627 | ||||||||
\(538\) | −30.6318 | −1.32063 | ||||||||
\(539\) | −3.16802 | −0.136456 | ||||||||
\(540\) | 57.3568 | 2.46824 | ||||||||
\(541\) | −11.9558 | −0.514019 | −0.257010 | − | 0.966409i | \(-0.582737\pi\) | ||||
−0.257010 | + | 0.966409i | \(0.582737\pi\) | |||||||
\(542\) | −78.9583 | −3.39155 | ||||||||
\(543\) | −34.9024 | −1.49780 | ||||||||
\(544\) | −38.7395 | −1.66094 | ||||||||
\(545\) | 10.1121 | 0.433155 | ||||||||
\(546\) | −4.42612 | −0.189420 | ||||||||
\(547\) | 21.6130 | 0.924106 | 0.462053 | − | 0.886852i | \(-0.347113\pi\) | ||||
0.462053 | + | 0.886852i | \(0.347113\pi\) | |||||||
\(548\) | −14.7711 | −0.630992 | ||||||||
\(549\) | −13.3313 | −0.568966 | ||||||||
\(550\) | −2.44598 | −0.104297 | ||||||||
\(551\) | 42.4490 | 1.80839 | ||||||||
\(552\) | 55.7025 | 2.37086 | ||||||||
\(553\) | −11.1885 | −0.475782 | ||||||||
\(554\) | −51.3138 | −2.18011 | ||||||||
\(555\) | 5.84148 | 0.247957 | ||||||||
\(556\) | −105.814 | −4.48752 | ||||||||
\(557\) | 34.7922 | 1.47419 | 0.737096 | − | 0.675788i | \(-0.236197\pi\) | ||||
0.737096 | + | 0.675788i | \(0.236197\pi\) | |||||||
\(558\) | −8.24145 | −0.348889 | ||||||||
\(559\) | 5.63578 | 0.238368 | ||||||||
\(560\) | −18.4659 | −0.780327 | ||||||||
\(561\) | −21.1314 | −0.892168 | ||||||||
\(562\) | 28.8070 | 1.21515 | ||||||||
\(563\) | 30.9153 | 1.30292 | 0.651462 | − | 0.758681i | \(-0.274156\pi\) | ||||
0.651462 | + | 0.758681i | \(0.274156\pi\) | |||||||
\(564\) | 19.0542 | 0.802326 | ||||||||
\(565\) | 20.5455 | 0.864354 | ||||||||
\(566\) | −5.88537 | −0.247380 | ||||||||
\(567\) | −4.90469 | −0.205977 | ||||||||
\(568\) | 49.5845 | 2.08052 | ||||||||
\(569\) | 16.4744 | 0.690644 | 0.345322 | − | 0.938484i | \(-0.387770\pi\) | ||||
0.345322 | + | 0.938484i | \(0.387770\pi\) | |||||||
\(570\) | −37.5990 | −1.57485 | ||||||||
\(571\) | −30.5979 | −1.28048 | −0.640241 | − | 0.768174i | \(-0.721166\pi\) | ||||
−0.640241 | + | 0.768174i | \(0.721166\pi\) | |||||||
\(572\) | −18.0308 | −0.753905 | ||||||||
\(573\) | 23.3430 | 0.975168 | ||||||||
\(574\) | −14.8901 | −0.621502 | ||||||||
\(575\) | 1.70994 | 0.0713094 | ||||||||
\(576\) | −4.16631 | −0.173596 | ||||||||
\(577\) | 29.5228 | 1.22905 | 0.614526 | − | 0.788897i | \(-0.289347\pi\) | ||||
0.614526 | + | 0.788897i | \(0.289347\pi\) | |||||||
\(578\) | −14.1057 | −0.586721 | ||||||||
\(579\) | −12.7617 | −0.530358 | ||||||||
\(580\) | 90.2686 | 3.74820 | ||||||||
\(581\) | 2.54325 | 0.105512 | ||||||||
\(582\) | −33.1476 | −1.37401 | ||||||||
\(583\) | 1.97563 | 0.0818221 | ||||||||
\(584\) | −42.0285 | −1.73915 | ||||||||
\(585\) | 2.68893 | 0.111174 | ||||||||
\(586\) | 32.0101 | 1.32233 | ||||||||
\(587\) | 18.6398 | 0.769348 | 0.384674 | − | 0.923053i | \(-0.374314\pi\) | ||||
0.384674 | + | 0.923053i | \(0.374314\pi\) | |||||||
\(588\) | 6.58209 | 0.271441 | ||||||||
\(589\) | 14.9250 | 0.614974 | ||||||||
\(590\) | −69.5441 | −2.86308 | ||||||||
\(591\) | −3.71726 | −0.152908 | ||||||||
\(592\) | −16.3020 | −0.670010 | ||||||||
\(593\) | 4.46977 | 0.183551 | 0.0917757 | − | 0.995780i | \(-0.470746\pi\) | ||||
0.0917757 | + | 0.995780i | \(0.470746\pi\) | |||||||
\(594\) | −46.3045 | −1.89989 | ||||||||
\(595\) | −10.2754 | −0.421252 | ||||||||
\(596\) | −29.8788 | −1.22389 | ||||||||
\(597\) | 25.9050 | 1.06022 | ||||||||
\(598\) | 17.9958 | 0.735903 | ||||||||
\(599\) | 23.2416 | 0.949627 | 0.474814 | − | 0.880086i | \(-0.342516\pi\) | ||||
0.474814 | + | 0.880086i | \(0.342516\pi\) | |||||||
\(600\) | 2.90853 | 0.118740 | ||||||||
\(601\) | 20.2537 | 0.826166 | 0.413083 | − | 0.910693i | \(-0.364452\pi\) | ||||
0.413083 | + | 0.910693i | \(0.364452\pi\) | |||||||
\(602\) | −11.9653 | −0.487668 | ||||||||
\(603\) | −12.1921 | −0.496500 | ||||||||
\(604\) | 95.1674 | 3.87230 | ||||||||
\(605\) | 2.08937 | 0.0849448 | ||||||||
\(606\) | −55.9678 | −2.27354 | ||||||||
\(607\) | 15.8435 | 0.643067 | 0.321534 | − | 0.946898i | \(-0.395802\pi\) | ||||
0.321534 | + | 0.946898i | \(0.395802\pi\) | |||||||
\(608\) | 38.9774 | 1.58074 | ||||||||
\(609\) | −12.5301 | −0.507747 | ||||||||
\(610\) | 73.2961 | 2.96767 | ||||||||
\(611\) | 3.52316 | 0.142532 | ||||||||
\(612\) | −22.5833 | −0.912874 | ||||||||
\(613\) | −1.88452 | −0.0761150 | −0.0380575 | − | 0.999276i | \(-0.512117\pi\) | ||||
−0.0380575 | + | 0.999276i | \(0.512117\pi\) | |||||||
\(614\) | −31.6798 | −1.27849 | ||||||||
\(615\) | −17.5862 | −0.709144 | ||||||||
\(616\) | 21.9093 | 0.882751 | ||||||||
\(617\) | 37.1643 | 1.49618 | 0.748089 | − | 0.663599i | \(-0.230972\pi\) | ||||
0.748089 | + | 0.663599i | \(0.230972\pi\) | |||||||
\(618\) | −35.0160 | −1.40855 | ||||||||
\(619\) | 8.30855 | 0.333949 | 0.166974 | − | 0.985961i | \(-0.446600\pi\) | ||||
0.166974 | + | 0.985961i | \(0.446600\pi\) | |||||||
\(620\) | 31.7383 | 1.27464 | ||||||||
\(621\) | 32.3706 | 1.29899 | ||||||||
\(622\) | −26.8030 | −1.07470 | ||||||||
\(623\) | −8.94330 | −0.358306 | ||||||||
\(624\) | 14.5887 | 0.584014 | ||||||||
\(625\) | −23.4167 | −0.936667 | ||||||||
\(626\) | −26.6473 | −1.06504 | ||||||||
\(627\) | 21.2611 | 0.849088 | ||||||||
\(628\) | 32.1746 | 1.28391 | ||||||||
\(629\) | −9.07134 | −0.361698 | ||||||||
\(630\) | −5.70885 | −0.227446 | ||||||||
\(631\) | 31.2650 | 1.24464 | 0.622321 | − | 0.782762i | \(-0.286190\pi\) | ||||
0.622321 | + | 0.782762i | \(0.286190\pi\) | |||||||
\(632\) | 77.3768 | 3.07788 | ||||||||
\(633\) | 26.7307 | 1.06245 | ||||||||
\(634\) | 75.8487 | 3.01234 | ||||||||
\(635\) | −18.2190 | −0.723000 | ||||||||
\(636\) | −4.10469 | −0.162762 | ||||||||
\(637\) | 1.21704 | 0.0482210 | ||||||||
\(638\) | −72.8744 | −2.88512 | ||||||||
\(639\) | 7.30593 | 0.289018 | ||||||||
\(640\) | −12.5415 | −0.495746 | ||||||||
\(641\) | −3.21887 | −0.127138 | −0.0635688 | − | 0.997977i | \(-0.520248\pi\) | ||||
−0.0635688 | + | 0.997977i | \(0.520248\pi\) | |||||||
\(642\) | −17.5251 | −0.691660 | ||||||||
\(643\) | −18.0704 | −0.712628 | −0.356314 | − | 0.934366i | \(-0.615967\pi\) | ||||
−0.356314 | + | 0.934366i | \(0.615967\pi\) | |||||||
\(644\) | −26.7616 | −1.05455 | ||||||||
\(645\) | −14.1317 | −0.556436 | ||||||||
\(646\) | 58.3883 | 2.29726 | ||||||||
\(647\) | −27.3717 | −1.07609 | −0.538047 | − | 0.842915i | \(-0.680838\pi\) | ||||
−0.538047 | + | 0.842915i | \(0.680838\pi\) | |||||||
\(648\) | 33.9197 | 1.33249 | ||||||||
\(649\) | 39.3251 | 1.54365 | ||||||||
\(650\) | 0.939657 | 0.0368564 | ||||||||
\(651\) | −4.40558 | −0.172668 | ||||||||
\(652\) | 72.7985 | 2.85101 | ||||||||
\(653\) | 23.0635 | 0.902543 | 0.451271 | − | 0.892387i | \(-0.350971\pi\) | ||||
0.451271 | + | 0.892387i | \(0.350971\pi\) | |||||||
\(654\) | 16.9611 | 0.663233 | ||||||||
\(655\) | −36.7344 | −1.43533 | ||||||||
\(656\) | 49.0785 | 1.91619 | ||||||||
\(657\) | −6.19262 | −0.241597 | ||||||||
\(658\) | −7.47999 | −0.291600 | ||||||||
\(659\) | 10.5894 | 0.412503 | 0.206252 | − | 0.978499i | \(-0.433873\pi\) | ||||
0.206252 | + | 0.978499i | \(0.433873\pi\) | |||||||
\(660\) | 45.2122 | 1.75988 | ||||||||
\(661\) | −16.6479 | −0.647528 | −0.323764 | − | 0.946138i | \(-0.604948\pi\) | ||||
−0.323764 | + | 0.946138i | \(0.604948\pi\) | |||||||
\(662\) | 62.5778 | 2.43215 | ||||||||
\(663\) | 8.11793 | 0.315274 | ||||||||
\(664\) | −17.5885 | −0.682568 | ||||||||
\(665\) | 10.3385 | 0.400911 | ||||||||
\(666\) | −5.03987 | −0.195291 | ||||||||
\(667\) | 50.9452 | 1.97261 | ||||||||
\(668\) | −31.1411 | −1.20488 | ||||||||
\(669\) | −32.3104 | −1.24919 | ||||||||
\(670\) | 67.0326 | 2.58969 | ||||||||
\(671\) | −41.4468 | −1.60004 | ||||||||
\(672\) | −11.5054 | −0.443830 | ||||||||
\(673\) | 34.7365 | 1.33899 | 0.669496 | − | 0.742815i | \(-0.266510\pi\) | ||||
0.669496 | + | 0.742815i | \(0.266510\pi\) | |||||||
\(674\) | −45.5487 | −1.75447 | ||||||||
\(675\) | 1.69025 | 0.0650576 | ||||||||
\(676\) | −53.8676 | −2.07183 | ||||||||
\(677\) | −26.8774 | −1.03298 | −0.516492 | − | 0.856292i | \(-0.672762\pi\) | ||||
−0.516492 | + | 0.856292i | \(0.672762\pi\) | |||||||
\(678\) | 34.4611 | 1.32347 | ||||||||
\(679\) | 9.11453 | 0.349784 | ||||||||
\(680\) | 71.0625 | 2.72512 | ||||||||
\(681\) | 14.7918 | 0.566822 | ||||||||
\(682\) | −25.6225 | −0.981138 | ||||||||
\(683\) | 23.4514 | 0.897345 | 0.448672 | − | 0.893696i | \(-0.351897\pi\) | ||||
0.448672 | + | 0.893696i | \(0.351897\pi\) | |||||||
\(684\) | 22.7219 | 0.868795 | ||||||||
\(685\) | 6.84854 | 0.261669 | ||||||||
\(686\) | −2.58389 | −0.0986534 | ||||||||
\(687\) | 29.8051 | 1.13714 | ||||||||
\(688\) | 39.4380 | 1.50356 | ||||||||
\(689\) | −0.758966 | −0.0289143 | ||||||||
\(690\) | −45.1245 | −1.71786 | ||||||||
\(691\) | −40.4654 | −1.53938 | −0.769689 | − | 0.638419i | \(-0.779589\pi\) | ||||
−0.769689 | + | 0.638419i | \(0.779589\pi\) | |||||||
\(692\) | 49.7897 | 1.89272 | ||||||||
\(693\) | 3.22819 | 0.122629 | ||||||||
\(694\) | 37.4303 | 1.42083 | ||||||||
\(695\) | 49.0600 | 1.86095 | ||||||||
\(696\) | 86.6555 | 3.28467 | ||||||||
\(697\) | 27.3099 | 1.03444 | ||||||||
\(698\) | 74.9731 | 2.83777 | ||||||||
\(699\) | −28.4105 | −1.07458 | ||||||||
\(700\) | −1.39737 | −0.0528154 | ||||||||
\(701\) | 16.0954 | 0.607915 | 0.303957 | − | 0.952686i | \(-0.401692\pi\) | ||||
0.303957 | + | 0.952686i | \(0.401692\pi\) | |||||||
\(702\) | 17.7885 | 0.671385 | ||||||||
\(703\) | 9.12705 | 0.344233 | ||||||||
\(704\) | −12.9530 | −0.488184 | ||||||||
\(705\) | −8.83434 | −0.332721 | ||||||||
\(706\) | 50.7056 | 1.90833 | ||||||||
\(707\) | 15.3894 | 0.578777 | ||||||||
\(708\) | −81.7044 | −3.07064 | ||||||||
\(709\) | −25.2079 | −0.946703 | −0.473352 | − | 0.880874i | \(-0.656956\pi\) | ||||
−0.473352 | + | 0.880874i | \(0.656956\pi\) | |||||||
\(710\) | −40.1683 | −1.50749 | ||||||||
\(711\) | 11.4009 | 0.427568 | ||||||||
\(712\) | 61.8498 | 2.31792 | ||||||||
\(713\) | 17.9123 | 0.670820 | ||||||||
\(714\) | −17.2351 | −0.645007 | ||||||||
\(715\) | 8.35984 | 0.312640 | ||||||||
\(716\) | −68.2661 | −2.55122 | ||||||||
\(717\) | 11.2556 | 0.420350 | ||||||||
\(718\) | −91.0382 | −3.39751 | ||||||||
\(719\) | 34.6652 | 1.29279 | 0.646397 | − | 0.763001i | \(-0.276275\pi\) | ||||
0.646397 | + | 0.763001i | \(0.276275\pi\) | |||||||
\(720\) | 18.8166 | 0.701253 | ||||||||
\(721\) | 9.62828 | 0.358576 | ||||||||
\(722\) | −9.65290 | −0.359244 | ||||||||
\(723\) | 0.940891 | 0.0349921 | ||||||||
\(724\) | −115.966 | −4.30985 | ||||||||
\(725\) | 2.66012 | 0.0987945 | ||||||||
\(726\) | 3.50452 | 0.130065 | ||||||||
\(727\) | 33.4073 | 1.23901 | 0.619505 | − | 0.784993i | \(-0.287333\pi\) | ||||
0.619505 | + | 0.784993i | \(0.287333\pi\) | |||||||
\(728\) | −8.41678 | −0.311947 | ||||||||
\(729\) | 28.8828 | 1.06973 | ||||||||
\(730\) | 34.0473 | 1.26015 | ||||||||
\(731\) | 21.9454 | 0.811681 | ||||||||
\(732\) | 86.1125 | 3.18281 | ||||||||
\(733\) | −35.1577 | −1.29858 | −0.649289 | − | 0.760542i | \(-0.724933\pi\) | ||||
−0.649289 | + | 0.760542i | \(0.724933\pi\) | |||||||
\(734\) | −82.9863 | −3.06308 | ||||||||
\(735\) | −3.05174 | −0.112565 | ||||||||
\(736\) | 46.7788 | 1.72429 | ||||||||
\(737\) | −37.9050 | −1.39625 | ||||||||
\(738\) | 15.1729 | 0.558522 | ||||||||
\(739\) | −29.9573 | −1.10200 | −0.550998 | − | 0.834506i | \(-0.685753\pi\) | ||||
−0.550998 | + | 0.834506i | \(0.685753\pi\) | |||||||
\(740\) | 19.4088 | 0.713483 | ||||||||
\(741\) | −8.16778 | −0.300051 | ||||||||
\(742\) | 1.61135 | 0.0591547 | ||||||||
\(743\) | 38.5524 | 1.41435 | 0.707175 | − | 0.707039i | \(-0.249969\pi\) | ||||
0.707175 | + | 0.707039i | \(0.249969\pi\) | |||||||
\(744\) | 30.4679 | 1.11701 | ||||||||
\(745\) | 13.8531 | 0.507539 | ||||||||
\(746\) | −37.7943 | −1.38375 | ||||||||
\(747\) | −2.59155 | −0.0948199 | ||||||||
\(748\) | −70.2110 | −2.56717 | ||||||||
\(749\) | 4.81884 | 0.176077 | ||||||||
\(750\) | −41.7830 | −1.52570 | ||||||||
\(751\) | 10.7625 | 0.392729 | 0.196364 | − | 0.980531i | \(-0.437086\pi\) | ||||
0.196364 | + | 0.980531i | \(0.437086\pi\) | |||||||
\(752\) | 24.6543 | 0.899051 | ||||||||
\(753\) | 24.9732 | 0.910074 | ||||||||
\(754\) | 27.9958 | 1.01955 | ||||||||
\(755\) | −44.1237 | −1.60583 | ||||||||
\(756\) | −26.4533 | −0.962099 | ||||||||
\(757\) | 5.24608 | 0.190672 | 0.0953360 | − | 0.995445i | \(-0.469607\pi\) | ||||
0.0953360 | + | 0.995445i | \(0.469607\pi\) | |||||||
\(758\) | 78.5095 | 2.85159 | ||||||||
\(759\) | 25.5166 | 0.926193 | ||||||||
\(760\) | −71.4989 | −2.59354 | ||||||||
\(761\) | 17.7460 | 0.643291 | 0.321646 | − | 0.946860i | \(-0.395764\pi\) | ||||
0.321646 | + | 0.946860i | \(0.395764\pi\) | |||||||
\(762\) | −30.5589 | −1.10703 | ||||||||
\(763\) | −4.66377 | −0.168840 | ||||||||
\(764\) | 77.5593 | 2.80600 | ||||||||
\(765\) | 10.4706 | 0.378564 | ||||||||
\(766\) | 82.5023 | 2.98093 | ||||||||
\(767\) | −15.1073 | −0.545494 | ||||||||
\(768\) | −32.5454 | −1.17438 | ||||||||
\(769\) | 12.5287 | 0.451798 | 0.225899 | − | 0.974151i | \(-0.427468\pi\) | ||||
0.225899 | + | 0.974151i | \(0.427468\pi\) | |||||||
\(770\) | −17.7487 | −0.639619 | ||||||||
\(771\) | 11.1051 | 0.399940 | ||||||||
\(772\) | −42.4019 | −1.52608 | ||||||||
\(773\) | 3.54616 | 0.127547 | 0.0637733 | − | 0.997964i | \(-0.479687\pi\) | ||||
0.0637733 | + | 0.997964i | \(0.479687\pi\) | |||||||
\(774\) | 12.1925 | 0.438250 | ||||||||
\(775\) | 0.935296 | 0.0335968 | ||||||||
\(776\) | −63.0340 | −2.26279 | ||||||||
\(777\) | −2.69413 | −0.0966514 | ||||||||
\(778\) | −23.6626 | −0.848344 | ||||||||
\(779\) | −27.4776 | −0.984489 | ||||||||
\(780\) | −17.3689 | −0.621908 | ||||||||
\(781\) | 22.7140 | 0.812771 | ||||||||
\(782\) | 70.0747 | 2.50587 | ||||||||
\(783\) | 50.3585 | 1.79967 | ||||||||
\(784\) | 8.51660 | 0.304164 | ||||||||
\(785\) | −14.9175 | −0.532429 | ||||||||
\(786\) | −61.6151 | −2.19774 | ||||||||
\(787\) | −16.3250 | −0.581924 | −0.290962 | − | 0.956735i | \(-0.593975\pi\) | ||||
−0.290962 | + | 0.956735i | \(0.593975\pi\) | |||||||
\(788\) | −12.3510 | −0.439984 | ||||||||
\(789\) | −16.3080 | −0.580579 | ||||||||
\(790\) | −62.6828 | −2.23016 | ||||||||
\(791\) | −9.47571 | −0.336917 | ||||||||
\(792\) | −22.3254 | −0.793298 | ||||||||
\(793\) | 15.9224 | 0.565421 | ||||||||
\(794\) | −77.9720 | −2.76712 | ||||||||
\(795\) | 1.90311 | 0.0674964 | ||||||||
\(796\) | 86.0718 | 3.05074 | ||||||||
\(797\) | −23.2658 | −0.824115 | −0.412058 | − | 0.911158i | \(-0.635190\pi\) | ||||
−0.412058 | + | 0.911158i | \(0.635190\pi\) | |||||||
\(798\) | 17.3409 | 0.613863 | ||||||||
\(799\) | 13.7190 | 0.485344 | ||||||||
\(800\) | 2.44257 | 0.0863580 | ||||||||
\(801\) | 9.11314 | 0.321997 | ||||||||
\(802\) | 45.4137 | 1.60361 | ||||||||
\(803\) | −19.2527 | −0.679414 | ||||||||
\(804\) | 78.7537 | 2.77743 | ||||||||
\(805\) | 12.4078 | 0.437318 | ||||||||
\(806\) | 9.84327 | 0.346714 | ||||||||
\(807\) | 16.6856 | 0.587361 | ||||||||
\(808\) | −106.429 | −3.74417 | ||||||||
\(809\) | 52.5787 | 1.84857 | 0.924285 | − | 0.381704i | \(-0.124662\pi\) | ||||
0.924285 | + | 0.381704i | \(0.124662\pi\) | |||||||
\(810\) | −27.4783 | −0.965488 | ||||||||
\(811\) | 13.1212 | 0.460749 | 0.230374 | − | 0.973102i | \(-0.426005\pi\) | ||||
0.230374 | + | 0.973102i | \(0.426005\pi\) | |||||||
\(812\) | −41.6325 | −1.46101 | ||||||||
\(813\) | 43.0097 | 1.50842 | ||||||||
\(814\) | −15.6689 | −0.549194 | ||||||||
\(815\) | −33.7525 | −1.18230 | ||||||||
\(816\) | 56.8075 | 1.98866 | ||||||||
\(817\) | −22.0802 | −0.772489 | ||||||||
\(818\) | −23.4787 | −0.820914 | ||||||||
\(819\) | −1.24015 | −0.0433345 | ||||||||
\(820\) | −58.4317 | −2.04053 | ||||||||
\(821\) | −19.1866 | −0.669617 | −0.334809 | − | 0.942286i | \(-0.608672\pi\) | ||||
−0.334809 | + | 0.942286i | \(0.608672\pi\) | |||||||
\(822\) | 11.4871 | 0.400659 | ||||||||
\(823\) | −52.2064 | −1.81980 | −0.909900 | − | 0.414827i | \(-0.863842\pi\) | ||||
−0.909900 | + | 0.414827i | \(0.863842\pi\) | |||||||
\(824\) | −66.5869 | −2.31967 | ||||||||
\(825\) | 1.33236 | 0.0463868 | ||||||||
\(826\) | 32.0742 | 1.11601 | ||||||||
\(827\) | −17.8820 | −0.621819 | −0.310909 | − | 0.950440i | \(-0.600634\pi\) | ||||
−0.310909 | + | 0.950440i | \(0.600634\pi\) | |||||||
\(828\) | 27.2698 | 0.947690 | ||||||||
\(829\) | −56.3134 | −1.95584 | −0.977922 | − | 0.208968i | \(-0.932989\pi\) | ||||
−0.977922 | + | 0.208968i | \(0.932989\pi\) | |||||||
\(830\) | 14.2485 | 0.494571 | ||||||||
\(831\) | 27.9514 | 0.969622 | ||||||||
\(832\) | 4.97608 | 0.172514 | ||||||||
\(833\) | 4.73910 | 0.164200 | ||||||||
\(834\) | 82.2889 | 2.84943 | ||||||||
\(835\) | 14.4383 | 0.499660 | ||||||||
\(836\) | 70.6421 | 2.44321 | ||||||||
\(837\) | 17.7060 | 0.612008 | ||||||||
\(838\) | −72.5107 | −2.50484 | ||||||||
\(839\) | 20.2365 | 0.698642 | 0.349321 | − | 0.937003i | \(-0.386412\pi\) | ||||
0.349321 | + | 0.937003i | \(0.386412\pi\) | |||||||
\(840\) | 21.1051 | 0.728196 | ||||||||
\(841\) | 50.2546 | 1.73292 | ||||||||
\(842\) | 78.1855 | 2.69445 | ||||||||
\(843\) | −15.6916 | −0.540447 | ||||||||
\(844\) | 88.8153 | 3.05715 | ||||||||
\(845\) | 24.9754 | 0.859178 | ||||||||
\(846\) | 7.62204 | 0.262051 | ||||||||
\(847\) | −0.963631 | −0.0331107 | ||||||||
\(848\) | −5.31108 | −0.182383 | ||||||||
\(849\) | 3.20584 | 0.110024 | ||||||||
\(850\) | 3.65898 | 0.125502 | ||||||||
\(851\) | 10.9538 | 0.375493 | ||||||||
\(852\) | −47.1921 | −1.61677 | ||||||||
\(853\) | 0.939780 | 0.0321775 | 0.0160887 | − | 0.999871i | \(-0.494879\pi\) | ||||
0.0160887 | + | 0.999871i | \(0.494879\pi\) | |||||||
\(854\) | −33.8047 | −1.15677 | ||||||||
\(855\) | −10.5349 | −0.360285 | ||||||||
\(856\) | −33.3260 | −1.13906 | ||||||||
\(857\) | 4.78546 | 0.163468 | 0.0817342 | − | 0.996654i | \(-0.473954\pi\) | ||||
0.0817342 | + | 0.996654i | \(0.473954\pi\) | |||||||
\(858\) | 14.0221 | 0.478705 | ||||||||
\(859\) | 12.6053 | 0.430086 | 0.215043 | − | 0.976605i | \(-0.431011\pi\) | ||||
0.215043 | + | 0.976605i | \(0.431011\pi\) | |||||||
\(860\) | −46.9540 | −1.60112 | ||||||||
\(861\) | 8.11088 | 0.276418 | ||||||||
\(862\) | 75.4205 | 2.56883 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | 46.2401 | 1.57312 | ||||||||
\(865\) | −23.0846 | −0.784901 | ||||||||
\(866\) | −53.6729 | −1.82388 | ||||||||
\(867\) | 7.68360 | 0.260949 | ||||||||
\(868\) | −14.6379 | −0.496844 | ||||||||
\(869\) | 35.4453 | 1.20240 | ||||||||
\(870\) | −70.1995 | −2.37999 | ||||||||
\(871\) | 14.5617 | 0.493406 | ||||||||
\(872\) | 32.2536 | 1.09224 | ||||||||
\(873\) | −9.28762 | −0.314338 | ||||||||
\(874\) | −70.5051 | −2.38487 | ||||||||
\(875\) | 11.4890 | 0.388399 | ||||||||
\(876\) | 40.0007 | 1.35150 | ||||||||
\(877\) | 17.9131 | 0.604881 | 0.302441 | − | 0.953168i | \(-0.402199\pi\) | ||||
0.302441 | + | 0.953168i | \(0.402199\pi\) | |||||||
\(878\) | −1.76812 | −0.0596712 | ||||||||
\(879\) | −17.4364 | −0.588115 | ||||||||
\(880\) | 58.5004 | 1.97205 | ||||||||
\(881\) | 33.5258 | 1.12951 | 0.564757 | − | 0.825258i | \(-0.308970\pi\) | ||||
0.564757 | + | 0.825258i | \(0.308970\pi\) | |||||||
\(882\) | 2.63296 | 0.0886564 | ||||||||
\(883\) | 12.0913 | 0.406904 | 0.203452 | − | 0.979085i | \(-0.434784\pi\) | ||||
0.203452 | + | 0.979085i | \(0.434784\pi\) | |||||||
\(884\) | 26.9726 | 0.907186 | ||||||||
\(885\) | 37.8817 | 1.27338 | ||||||||
\(886\) | −10.6069 | −0.356346 | ||||||||
\(887\) | 24.5908 | 0.825680 | 0.412840 | − | 0.910804i | \(-0.364537\pi\) | ||||
0.412840 | + | 0.910804i | \(0.364537\pi\) | |||||||
\(888\) | 18.6320 | 0.625248 | ||||||||
\(889\) | 8.40274 | 0.281819 | ||||||||
\(890\) | −50.1044 | −1.67950 | ||||||||
\(891\) | 15.5382 | 0.520548 | ||||||||
\(892\) | −107.354 | −3.59449 | ||||||||
\(893\) | −13.8033 | −0.461909 | ||||||||
\(894\) | 23.2360 | 0.777127 | ||||||||
\(895\) | 31.6511 | 1.05798 | ||||||||
\(896\) | 5.78423 | 0.193237 | ||||||||
\(897\) | −9.80257 | −0.327298 | ||||||||
\(898\) | 73.7397 | 2.46072 | ||||||||
\(899\) | 27.8658 | 0.929377 | ||||||||
\(900\) | 1.42390 | 0.0474634 | ||||||||
\(901\) | −2.95538 | −0.0984579 | ||||||||
\(902\) | 47.1723 | 1.57067 | ||||||||
\(903\) | 6.51765 | 0.216894 | ||||||||
\(904\) | 65.5318 | 2.17956 | ||||||||
\(905\) | 53.7670 | 1.78727 | ||||||||
\(906\) | −74.0091 | −2.45879 | ||||||||
\(907\) | 46.2903 | 1.53705 | 0.768523 | − | 0.639822i | \(-0.220992\pi\) | ||||
0.768523 | + | 0.639822i | \(0.220992\pi\) | |||||||
\(908\) | 49.1470 | 1.63100 | ||||||||
\(909\) | −15.6816 | −0.520127 | ||||||||
\(910\) | 6.81842 | 0.226029 | ||||||||
\(911\) | −41.3060 | −1.36853 | −0.684265 | − | 0.729233i | \(-0.739877\pi\) | ||||
−0.684265 | + | 0.729233i | \(0.739877\pi\) | |||||||
\(912\) | −57.1564 | −1.89264 | ||||||||
\(913\) | −8.05708 | −0.266651 | ||||||||
\(914\) | 100.612 | 3.32794 | ||||||||
\(915\) | −39.9255 | −1.31990 | ||||||||
\(916\) | 99.0302 | 3.27205 | ||||||||
\(917\) | 16.9422 | 0.559480 | ||||||||
\(918\) | 69.2677 | 2.28617 | ||||||||
\(919\) | 1.96299 | 0.0647530 | 0.0323765 | − | 0.999476i | \(-0.489692\pi\) | ||||
0.0323765 | + | 0.999476i | \(0.489692\pi\) | |||||||
\(920\) | −85.8095 | −2.82906 | ||||||||
\(921\) | 17.2565 | 0.568620 | ||||||||
\(922\) | 68.9237 | 2.26988 | ||||||||
\(923\) | −8.72592 | −0.287217 | ||||||||
\(924\) | −20.8522 | −0.685987 | ||||||||
\(925\) | 0.571959 | 0.0188059 | ||||||||
\(926\) | 4.41945 | 0.145232 | ||||||||
\(927\) | −9.81113 | −0.322240 | ||||||||
\(928\) | 72.7730 | 2.38889 | ||||||||
\(929\) | 34.1404 | 1.12011 | 0.560054 | − | 0.828456i | \(-0.310780\pi\) | ||||
0.560054 | + | 0.828456i | \(0.310780\pi\) | |||||||
\(930\) | −24.6820 | −0.809356 | ||||||||
\(931\) | −4.76821 | −0.156272 | ||||||||
\(932\) | −94.3964 | −3.09206 | ||||||||
\(933\) | 14.6000 | 0.477981 | ||||||||
\(934\) | −99.5189 | −3.25636 | ||||||||
\(935\) | 32.5528 | 1.06459 | ||||||||
\(936\) | 8.57662 | 0.280336 | ||||||||
\(937\) | −38.4027 | −1.25456 | −0.627280 | − | 0.778794i | \(-0.715832\pi\) | ||||
−0.627280 | + | 0.778794i | \(0.715832\pi\) | |||||||
\(938\) | −30.9159 | −1.00944 | ||||||||
\(939\) | 14.5152 | 0.473685 | ||||||||
\(940\) | −29.3529 | −0.957387 | ||||||||
\(941\) | 26.2195 | 0.854730 | 0.427365 | − | 0.904079i | \(-0.359442\pi\) | ||||
0.427365 | + | 0.904079i | \(0.359442\pi\) | |||||||
\(942\) | −25.0213 | −0.815238 | ||||||||
\(943\) | −32.9773 | −1.07389 | ||||||||
\(944\) | −105.718 | −3.44082 | ||||||||
\(945\) | 12.2649 | 0.398978 | ||||||||
\(946\) | 37.9062 | 1.23244 | ||||||||
\(947\) | −40.1010 | −1.30311 | −0.651554 | − | 0.758603i | \(-0.725882\pi\) | ||||
−0.651554 | + | 0.758603i | \(0.725882\pi\) | |||||||
\(948\) | −73.6434 | −2.39183 | ||||||||
\(949\) | 7.39622 | 0.240091 | ||||||||
\(950\) | −3.68145 | −0.119442 | ||||||||
\(951\) | −41.3159 | −1.33976 | ||||||||
\(952\) | −32.7745 | −1.06223 | ||||||||
\(953\) | 21.1875 | 0.686332 | 0.343166 | − | 0.939275i | \(-0.388501\pi\) | ||||
0.343166 | + | 0.939275i | \(0.388501\pi\) | |||||||
\(954\) | −1.64195 | −0.0531602 | ||||||||
\(955\) | −35.9598 | −1.16363 | ||||||||
\(956\) | 37.3979 | 1.20954 | ||||||||
\(957\) | 39.6957 | 1.28318 | ||||||||
\(958\) | −70.0148 | −2.26208 | ||||||||
\(959\) | −3.15859 | −0.101996 | ||||||||
\(960\) | −12.4775 | −0.402711 | ||||||||
\(961\) | −21.2024 | −0.683949 | ||||||||
\(962\) | 6.01943 | 0.194074 | ||||||||
\(963\) | −4.91035 | −0.158234 | ||||||||
\(964\) | 3.12620 | 0.100688 | ||||||||
\(965\) | 19.6593 | 0.632857 | ||||||||
\(966\) | 20.8117 | 0.669607 | ||||||||
\(967\) | 7.11479 | 0.228796 | 0.114398 | − | 0.993435i | \(-0.463506\pi\) | ||||
0.114398 | + | 0.993435i | \(0.463506\pi\) | |||||||
\(968\) | 6.66425 | 0.214197 | ||||||||
\(969\) | −31.8049 | −1.02172 | ||||||||
\(970\) | 51.0638 | 1.63956 | ||||||||
\(971\) | −1.50885 | −0.0484213 | −0.0242107 | − | 0.999707i | \(-0.507707\pi\) | ||||
−0.0242107 | + | 0.999707i | \(0.507707\pi\) | |||||||
\(972\) | 47.0770 | 1.50999 | ||||||||
\(973\) | −22.6268 | −0.725383 | ||||||||
\(974\) | 47.2867 | 1.51516 | ||||||||
\(975\) | −0.511845 | −0.0163922 | ||||||||
\(976\) | 111.422 | 3.56652 | ||||||||
\(977\) | 24.3726 | 0.779749 | 0.389874 | − | 0.920868i | \(-0.372518\pi\) | ||||
0.389874 | + | 0.920868i | \(0.372518\pi\) | |||||||
\(978\) | −56.6134 | −1.81030 | ||||||||
\(979\) | 28.3326 | 0.905513 | ||||||||
\(980\) | −10.1397 | −0.323900 | ||||||||
\(981\) | 4.75234 | 0.151730 | ||||||||
\(982\) | −76.0542 | −2.42699 | ||||||||
\(983\) | −22.4254 | −0.715261 | −0.357630 | − | 0.933863i | \(-0.616415\pi\) | ||||
−0.357630 | + | 0.933863i | \(0.616415\pi\) | |||||||
\(984\) | −56.0929 | −1.78818 | ||||||||
\(985\) | 5.72643 | 0.182459 | ||||||||
\(986\) | 109.014 | 3.47172 | ||||||||
\(987\) | 4.07446 | 0.129692 | ||||||||
\(988\) | −27.1382 | −0.863381 | ||||||||
\(989\) | −26.4996 | −0.842637 | ||||||||
\(990\) | 18.0858 | 0.574803 | ||||||||
\(991\) | 29.8617 | 0.948588 | 0.474294 | − | 0.880367i | \(-0.342703\pi\) | ||||
0.474294 | + | 0.880367i | \(0.342703\pi\) | |||||||
\(992\) | 25.5869 | 0.812385 | ||||||||
\(993\) | −34.0870 | −1.08172 | ||||||||
\(994\) | 18.5259 | 0.587606 | ||||||||
\(995\) | −39.9066 | −1.26512 | ||||||||
\(996\) | 16.7399 | 0.530424 | ||||||||
\(997\) | −29.8203 | −0.944418 | −0.472209 | − | 0.881487i | \(-0.656543\pi\) | ||||
−0.472209 | + | 0.881487i | \(0.656543\pi\) | |||||||
\(998\) | −14.5871 | −0.461746 | ||||||||
\(999\) | 10.8277 | 0.342573 |
(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 | 6041.2.a.f.1.10 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.10 | ✓ | 132 | 1.1 | even | 1 | trivial |