Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,2,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(17.2955970778\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.87939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.22668 | −0.995802 | −0.497901 | − | 0.867234i | \(-0.665896\pi\) | ||||
−0.497901 | + | 0.867234i | \(0.665896\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.65270 | −1.00263 | −0.501314 | − | 0.865266i | \(-0.667150\pi\) | ||||
−0.501314 | + | 0.865266i | \(0.667150\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.22668 | 0.704139 | ||||||||
\(11\) | 2.22668 | 0.671370 | 0.335685 | − | 0.941974i | \(-0.391032\pi\) | ||||
0.335685 | + | 0.941974i | \(0.391032\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.29086 | −1.46742 | −0.733710 | − | 0.679463i | \(-0.762213\pi\) | ||||
−0.733710 | + | 0.679463i | \(0.762213\pi\) | |||||||
\(14\) | 2.65270 | 0.708965 | ||||||||
\(15\) | −2.22668 | −0.574927 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.41147 | −0.827404 | −0.413702 | − | 0.910412i | \(-0.635764\pi\) | ||||
−0.413702 | + | 0.910412i | \(0.635764\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.22668 | −0.497901 | ||||||||
\(21\) | −2.65270 | −0.578867 | ||||||||
\(22\) | −2.22668 | −0.474730 | ||||||||
\(23\) | 2.22668 | 0.464295 | 0.232148 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232148 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −0.0418891 | −0.00837781 | ||||||||
\(26\) | 5.29086 | 1.03762 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.65270 | −0.501314 | ||||||||
\(29\) | 4.81521 | 0.894162 | 0.447081 | − | 0.894494i | \(-0.352464\pi\) | ||||
0.447081 | + | 0.894494i | \(0.352464\pi\) | |||||||
\(30\) | 2.22668 | 0.406535 | ||||||||
\(31\) | 10.3131 | 1.85230 | 0.926148 | − | 0.377160i | \(-0.123099\pi\) | ||||
0.926148 | + | 0.377160i | \(0.123099\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.22668 | 0.387616 | ||||||||
\(34\) | 3.41147 | 0.585063 | ||||||||
\(35\) | 5.90673 | 0.998419 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.30541 | 0.379007 | 0.189503 | − | 0.981880i | \(-0.439312\pi\) | ||||
0.189503 | + | 0.981880i | \(0.439312\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.29086 | −0.847216 | ||||||||
\(40\) | 2.22668 | 0.352069 | ||||||||
\(41\) | −7.23442 | −1.12983 | −0.564913 | − | 0.825150i | \(-0.691090\pi\) | ||||
−0.564913 | + | 0.825150i | \(0.691090\pi\) | |||||||
\(42\) | 2.65270 | 0.409321 | ||||||||
\(43\) | −5.92127 | −0.902986 | −0.451493 | − | 0.892275i | \(-0.649108\pi\) | ||||
−0.451493 | + | 0.892275i | \(0.649108\pi\) | |||||||
\(44\) | 2.22668 | 0.335685 | ||||||||
\(45\) | −2.22668 | −0.331934 | ||||||||
\(46\) | −2.22668 | −0.328306 | ||||||||
\(47\) | 11.0077 | 1.60564 | 0.802822 | − | 0.596219i | \(-0.203331\pi\) | ||||
0.802822 | + | 0.596219i | \(0.203331\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0.0368366 | 0.00526238 | ||||||||
\(50\) | 0.0418891 | 0.00592401 | ||||||||
\(51\) | −3.41147 | −0.477702 | ||||||||
\(52\) | −5.29086 | −0.733710 | ||||||||
\(53\) | 9.82295 | 1.34929 | 0.674643 | − | 0.738144i | \(-0.264298\pi\) | ||||
0.674643 | + | 0.738144i | \(0.264298\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.95811 | −0.668552 | ||||||||
\(56\) | 2.65270 | 0.354482 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.81521 | −0.632268 | ||||||||
\(59\) | 4.95811 | 0.645491 | 0.322746 | − | 0.946486i | \(-0.395394\pi\) | ||||
0.322746 | + | 0.946486i | \(0.395394\pi\) | |||||||
\(60\) | −2.22668 | −0.287463 | ||||||||
\(61\) | −5.70233 | −0.730109 | −0.365054 | − | 0.930986i | \(-0.618950\pi\) | ||||
−0.365054 | + | 0.930986i | \(0.618950\pi\) | |||||||
\(62\) | −10.3131 | −1.30977 | ||||||||
\(63\) | −2.65270 | −0.334209 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.7811 | 1.46126 | ||||||||
\(66\) | −2.22668 | −0.274086 | ||||||||
\(67\) | 8.57398 | 1.04748 | 0.523739 | − | 0.851879i | \(-0.324537\pi\) | ||||
0.523739 | + | 0.851879i | \(0.324537\pi\) | |||||||
\(68\) | −3.41147 | −0.413702 | ||||||||
\(69\) | 2.22668 | 0.268061 | ||||||||
\(70\) | −5.90673 | −0.705989 | ||||||||
\(71\) | 4.40373 | 0.522627 | 0.261313 | − | 0.965254i | \(-0.415844\pi\) | ||||
0.261313 | + | 0.965254i | \(0.415844\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.79561 | −0.327201 | −0.163601 | − | 0.986527i | \(-0.552311\pi\) | ||||
−0.163601 | + | 0.986527i | \(0.552311\pi\) | |||||||
\(74\) | −2.30541 | −0.267998 | ||||||||
\(75\) | −0.0418891 | −0.00483693 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.90673 | −0.673134 | ||||||||
\(78\) | 5.29086 | 0.599072 | ||||||||
\(79\) | 13.8007 | 1.55270 | 0.776348 | − | 0.630305i | \(-0.217070\pi\) | ||||
0.776348 | + | 0.630305i | \(0.217070\pi\) | |||||||
\(80\) | −2.22668 | −0.248951 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.23442 | 0.798908 | ||||||||
\(83\) | −10.5030 | −1.15285 | −0.576427 | − | 0.817149i | \(-0.695553\pi\) | ||||
−0.576427 | + | 0.817149i | \(0.695553\pi\) | |||||||
\(84\) | −2.65270 | −0.289434 | ||||||||
\(85\) | 7.59627 | 0.823931 | ||||||||
\(86\) | 5.92127 | 0.638507 | ||||||||
\(87\) | 4.81521 | 0.516244 | ||||||||
\(88\) | −2.22668 | −0.237365 | ||||||||
\(89\) | 7.81521 | 0.828410 | 0.414205 | − | 0.910184i | \(-0.364060\pi\) | ||||
0.414205 | + | 0.910184i | \(0.364060\pi\) | |||||||
\(90\) | 2.22668 | 0.234713 | ||||||||
\(91\) | 14.0351 | 1.47128 | ||||||||
\(92\) | 2.22668 | 0.232148 | ||||||||
\(93\) | 10.3131 | 1.06942 | ||||||||
\(94\) | −11.0077 | −1.13536 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −17.7888 | −1.80618 | −0.903089 | − | 0.429452i | \(-0.858707\pi\) | ||||
−0.903089 | + | 0.429452i | \(0.858707\pi\) | |||||||
\(98\) | −0.0368366 | −0.00372106 | ||||||||
\(99\) | 2.22668 | 0.223790 | ||||||||
\(100\) | −0.0418891 | −0.00418891 | ||||||||
\(101\) | 17.9067 | 1.78179 | 0.890893 | − | 0.454213i | \(-0.150080\pi\) | ||||
0.890893 | + | 0.454213i | \(0.150080\pi\) | |||||||
\(102\) | 3.41147 | 0.337786 | ||||||||
\(103\) | 4.24628 | 0.418399 | 0.209199 | − | 0.977873i | \(-0.432914\pi\) | ||||
0.209199 | + | 0.977873i | \(0.432914\pi\) | |||||||
\(104\) | 5.29086 | 0.518811 | ||||||||
\(105\) | 5.90673 | 0.576437 | ||||||||
\(106\) | −9.82295 | −0.954089 | ||||||||
\(107\) | 15.6040 | 1.50850 | 0.754248 | − | 0.656589i | \(-0.228002\pi\) | ||||
0.754248 | + | 0.656589i | \(0.228002\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −1.36184 | −0.130441 | −0.0652205 | − | 0.997871i | \(-0.520775\pi\) | ||||
−0.0652205 | + | 0.997871i | \(0.520775\pi\) | |||||||
\(110\) | 4.95811 | 0.472737 | ||||||||
\(111\) | 2.30541 | 0.218820 | ||||||||
\(112\) | −2.65270 | −0.250657 | ||||||||
\(113\) | 17.2003 | 1.61807 | 0.809033 | − | 0.587763i | \(-0.199991\pi\) | ||||
0.809033 | + | 0.587763i | \(0.199991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.95811 | −0.462346 | ||||||||
\(116\) | 4.81521 | 0.447081 | ||||||||
\(117\) | −5.29086 | −0.489140 | ||||||||
\(118\) | −4.95811 | −0.456431 | ||||||||
\(119\) | 9.04963 | 0.829578 | ||||||||
\(120\) | 2.22668 | 0.203267 | ||||||||
\(121\) | −6.04189 | −0.549263 | ||||||||
\(122\) | 5.70233 | 0.516265 | ||||||||
\(123\) | −7.23442 | −0.652306 | ||||||||
\(124\) | 10.3131 | 0.926148 | ||||||||
\(125\) | 11.2267 | 1.00414 | ||||||||
\(126\) | 2.65270 | 0.236322 | ||||||||
\(127\) | −13.1925 | −1.17065 | −0.585324 | − | 0.810799i | \(-0.699033\pi\) | ||||
−0.585324 | + | 0.810799i | \(0.699033\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.92127 | −0.521339 | ||||||||
\(130\) | −11.7811 | −1.03327 | ||||||||
\(131\) | 7.50299 | 0.655540 | 0.327770 | − | 0.944758i | \(-0.393703\pi\) | ||||
0.327770 | + | 0.944758i | \(0.393703\pi\) | |||||||
\(132\) | 2.22668 | 0.193808 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.57398 | −0.740679 | ||||||||
\(135\) | −2.22668 | −0.191642 | ||||||||
\(136\) | 3.41147 | 0.292531 | ||||||||
\(137\) | 6.63041 | 0.566475 | 0.283237 | − | 0.959050i | \(-0.408592\pi\) | ||||
0.283237 | + | 0.959050i | \(0.408592\pi\) | |||||||
\(138\) | −2.22668 | −0.189548 | ||||||||
\(139\) | −8.50980 | −0.721792 | −0.360896 | − | 0.932606i | \(-0.617529\pi\) | ||||
−0.360896 | + | 0.932606i | \(0.617529\pi\) | |||||||
\(140\) | 5.90673 | 0.499209 | ||||||||
\(141\) | 11.0077 | 0.927019 | ||||||||
\(142\) | −4.40373 | −0.369553 | ||||||||
\(143\) | −11.7811 | −0.985182 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.7219 | −0.890408 | ||||||||
\(146\) | 2.79561 | 0.231366 | ||||||||
\(147\) | 0.0368366 | 0.00303823 | ||||||||
\(148\) | 2.30541 | 0.189503 | ||||||||
\(149\) | −3.41147 | −0.279479 | −0.139739 | − | 0.990188i | \(-0.544626\pi\) | ||||
−0.139739 | + | 0.990188i | \(0.544626\pi\) | |||||||
\(150\) | 0.0418891 | 0.00342023 | ||||||||
\(151\) | 3.04189 | 0.247545 | 0.123773 | − | 0.992311i | \(-0.460501\pi\) | ||||
0.123773 | + | 0.992311i | \(0.460501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.41147 | −0.275801 | ||||||||
\(154\) | 5.90673 | 0.475978 | ||||||||
\(155\) | −22.9641 | −1.84452 | ||||||||
\(156\) | −5.29086 | −0.423608 | ||||||||
\(157\) | −15.5253 | −1.23905 | −0.619526 | − | 0.784976i | \(-0.712675\pi\) | ||||
−0.619526 | + | 0.784976i | \(0.712675\pi\) | |||||||
\(158\) | −13.8007 | −1.09792 | ||||||||
\(159\) | 9.82295 | 0.779010 | ||||||||
\(160\) | 2.22668 | 0.176035 | ||||||||
\(161\) | −5.90673 | −0.465515 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.43882 | 0.347675 | 0.173837 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173837 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(164\) | −7.23442 | −0.564913 | ||||||||
\(165\) | −4.95811 | −0.385988 | ||||||||
\(166\) | 10.5030 | 0.815190 | ||||||||
\(167\) | −8.15064 | −0.630716 | −0.315358 | − | 0.948973i | \(-0.602125\pi\) | ||||
−0.315358 | + | 0.948973i | \(0.602125\pi\) | |||||||
\(168\) | 2.65270 | 0.204661 | ||||||||
\(169\) | 14.9932 | 1.15332 | ||||||||
\(170\) | −7.59627 | −0.582607 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.92127 | −0.451493 | ||||||||
\(173\) | −15.9659 | −1.21386 | −0.606931 | − | 0.794755i | \(-0.707599\pi\) | ||||
−0.606931 | + | 0.794755i | \(0.707599\pi\) | |||||||
\(174\) | −4.81521 | −0.365040 | ||||||||
\(175\) | 0.111119 | 0.00839983 | ||||||||
\(176\) | 2.22668 | 0.167842 | ||||||||
\(177\) | 4.95811 | 0.372674 | ||||||||
\(178\) | −7.81521 | −0.585775 | ||||||||
\(179\) | 1.45336 | 0.108629 | 0.0543147 | − | 0.998524i | \(-0.482703\pi\) | ||||
0.0543147 | + | 0.998524i | \(0.482703\pi\) | |||||||
\(180\) | −2.22668 | −0.165967 | ||||||||
\(181\) | −1.12567 | −0.0836702 | −0.0418351 | − | 0.999125i | \(-0.513320\pi\) | ||||
−0.0418351 | + | 0.999125i | \(0.513320\pi\) | |||||||
\(182\) | −14.0351 | −1.04035 | ||||||||
\(183\) | −5.70233 | −0.421529 | ||||||||
\(184\) | −2.22668 | −0.164153 | ||||||||
\(185\) | −5.13341 | −0.377416 | ||||||||
\(186\) | −10.3131 | −0.756197 | ||||||||
\(187\) | −7.59627 | −0.555494 | ||||||||
\(188\) | 11.0077 | 0.802822 | ||||||||
\(189\) | −2.65270 | −0.192956 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.32770 | −0.0960687 | −0.0480344 | − | 0.998846i | \(-0.515296\pi\) | ||||
−0.0480344 | + | 0.998846i | \(0.515296\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.9855 | 1.07868 | 0.539338 | − | 0.842089i | \(-0.318674\pi\) | ||||
0.539338 | + | 0.842089i | \(0.318674\pi\) | |||||||
\(194\) | 17.7888 | 1.27716 | ||||||||
\(195\) | 11.7811 | 0.843659 | ||||||||
\(196\) | 0.0368366 | 0.00263119 | ||||||||
\(197\) | 23.0077 | 1.63923 | 0.819617 | − | 0.572912i | \(-0.194186\pi\) | ||||
0.819617 | + | 0.572912i | \(0.194186\pi\) | |||||||
\(198\) | −2.22668 | −0.158243 | ||||||||
\(199\) | 9.68273 | 0.686391 | 0.343195 | − | 0.939264i | \(-0.388491\pi\) | ||||
0.343195 | + | 0.939264i | \(0.388491\pi\) | |||||||
\(200\) | 0.0418891 | 0.00296200 | ||||||||
\(201\) | 8.57398 | 0.604762 | ||||||||
\(202\) | −17.9067 | −1.25991 | ||||||||
\(203\) | −12.7733 | −0.896511 | ||||||||
\(204\) | −3.41147 | −0.238851 | ||||||||
\(205\) | 16.1088 | 1.12508 | ||||||||
\(206\) | −4.24628 | −0.295852 | ||||||||
\(207\) | 2.22668 | 0.154765 | ||||||||
\(208\) | −5.29086 | −0.366855 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −5.90673 | −0.407603 | ||||||||
\(211\) | −1.10607 | −0.0761448 | −0.0380724 | − | 0.999275i | \(-0.512122\pi\) | ||||
−0.0380724 | + | 0.999275i | \(0.512122\pi\) | |||||||
\(212\) | 9.82295 | 0.674643 | ||||||||
\(213\) | 4.40373 | 0.301739 | ||||||||
\(214\) | −15.6040 | −1.06667 | ||||||||
\(215\) | 13.1848 | 0.899195 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −27.3577 | −1.85716 | ||||||||
\(218\) | 1.36184 | 0.0922357 | ||||||||
\(219\) | −2.79561 | −0.188910 | ||||||||
\(220\) | −4.95811 | −0.334276 | ||||||||
\(221\) | 18.0496 | 1.21415 | ||||||||
\(222\) | −2.30541 | −0.154729 | ||||||||
\(223\) | 25.2867 | 1.69333 | 0.846663 | − | 0.532130i | \(-0.178608\pi\) | ||||
0.846663 | + | 0.532130i | \(0.178608\pi\) | |||||||
\(224\) | 2.65270 | 0.177241 | ||||||||
\(225\) | −0.0418891 | −0.00279260 | ||||||||
\(226\) | −17.2003 | −1.14415 | ||||||||
\(227\) | 3.42871 | 0.227572 | 0.113786 | − | 0.993505i | \(-0.463702\pi\) | ||||
0.113786 | + | 0.993505i | \(0.463702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.9418 | 1.97861 | 0.989305 | − | 0.145860i | \(-0.0465950\pi\) | ||||
0.989305 | + | 0.145860i | \(0.0465950\pi\) | |||||||
\(230\) | 4.95811 | 0.326928 | ||||||||
\(231\) | −5.90673 | −0.388634 | ||||||||
\(232\) | −4.81521 | −0.316134 | ||||||||
\(233\) | −10.3773 | −0.679841 | −0.339921 | − | 0.940454i | \(-0.610400\pi\) | ||||
−0.339921 | + | 0.940454i | \(0.610400\pi\) | |||||||
\(234\) | 5.29086 | 0.345874 | ||||||||
\(235\) | −24.5107 | −1.59890 | ||||||||
\(236\) | 4.95811 | 0.322746 | ||||||||
\(237\) | 13.8007 | 0.896449 | ||||||||
\(238\) | −9.04963 | −0.586600 | ||||||||
\(239\) | −16.0155 | −1.03596 | −0.517978 | − | 0.855394i | \(-0.673315\pi\) | ||||
−0.517978 | + | 0.855394i | \(0.673315\pi\) | |||||||
\(240\) | −2.22668 | −0.143732 | ||||||||
\(241\) | 25.5817 | 1.64786 | 0.823932 | − | 0.566689i | \(-0.191776\pi\) | ||||
0.823932 | + | 0.566689i | \(0.191776\pi\) | |||||||
\(242\) | 6.04189 | 0.388387 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.70233 | −0.365054 | ||||||||
\(245\) | −0.0820234 | −0.00524029 | ||||||||
\(246\) | 7.23442 | 0.461250 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.3131 | −0.654886 | ||||||||
\(249\) | −10.5030 | −0.665600 | ||||||||
\(250\) | −11.2267 | −0.710038 | ||||||||
\(251\) | 10.6895 | 0.674718 | 0.337359 | − | 0.941376i | \(-0.390466\pi\) | ||||
0.337359 | + | 0.941376i | \(0.390466\pi\) | |||||||
\(252\) | −2.65270 | −0.167105 | ||||||||
\(253\) | 4.95811 | 0.311714 | ||||||||
\(254\) | 13.1925 | 0.827773 | ||||||||
\(255\) | 7.59627 | 0.475697 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.7793 | −1.91996 | −0.959980 | − | 0.280068i | \(-0.909643\pi\) | ||||
−0.959980 | + | 0.280068i | \(0.909643\pi\) | |||||||
\(258\) | 5.92127 | 0.368642 | ||||||||
\(259\) | −6.11556 | −0.380003 | ||||||||
\(260\) | 11.7811 | 0.730630 | ||||||||
\(261\) | 4.81521 | 0.298054 | ||||||||
\(262\) | −7.50299 | −0.463536 | ||||||||
\(263\) | 3.14290 | 0.193800 | 0.0968999 | − | 0.995294i | \(-0.469107\pi\) | ||||
0.0968999 | + | 0.995294i | \(0.469107\pi\) | |||||||
\(264\) | −2.22668 | −0.137043 | ||||||||
\(265\) | −21.8726 | −1.34362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.81521 | 0.478283 | ||||||||
\(268\) | 8.57398 | 0.523739 | ||||||||
\(269\) | 14.8803 | 0.907269 | 0.453635 | − | 0.891188i | \(-0.350127\pi\) | ||||
0.453635 | + | 0.891188i | \(0.350127\pi\) | |||||||
\(270\) | 2.22668 | 0.135512 | ||||||||
\(271\) | 15.2344 | 0.925425 | 0.462713 | − | 0.886508i | \(-0.346876\pi\) | ||||
0.462713 | + | 0.886508i | \(0.346876\pi\) | |||||||
\(272\) | −3.41147 | −0.206851 | ||||||||
\(273\) | 14.0351 | 0.849442 | ||||||||
\(274\) | −6.63041 | −0.400558 | ||||||||
\(275\) | −0.0932736 | −0.00562461 | ||||||||
\(276\) | 2.22668 | 0.134030 | ||||||||
\(277\) | −12.2094 | −0.733594 | −0.366797 | − | 0.930301i | \(-0.619546\pi\) | ||||
−0.366797 | + | 0.930301i | \(0.619546\pi\) | |||||||
\(278\) | 8.50980 | 0.510384 | ||||||||
\(279\) | 10.3131 | 0.617432 | ||||||||
\(280\) | −5.90673 | −0.352994 | ||||||||
\(281\) | −2.24392 | −0.133861 | −0.0669305 | − | 0.997758i | \(-0.521321\pi\) | ||||
−0.0669305 | + | 0.997758i | \(0.521321\pi\) | |||||||
\(282\) | −11.0077 | −0.655501 | ||||||||
\(283\) | −14.7888 | −0.879103 | −0.439551 | − | 0.898217i | \(-0.644863\pi\) | ||||
−0.439551 | + | 0.898217i | \(0.644863\pi\) | |||||||
\(284\) | 4.40373 | 0.261313 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7811 | 0.696629 | ||||||||
\(287\) | 19.1908 | 1.13280 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −5.36184 | −0.315403 | ||||||||
\(290\) | 10.7219 | 0.629614 | ||||||||
\(291\) | −17.7888 | −1.04280 | ||||||||
\(292\) | −2.79561 | −0.163601 | ||||||||
\(293\) | −12.0496 | −0.703947 | −0.351973 | − | 0.936010i | \(-0.614489\pi\) | ||||
−0.351973 | + | 0.936010i | \(0.614489\pi\) | |||||||
\(294\) | −0.0368366 | −0.00214836 | ||||||||
\(295\) | −11.0401 | −0.642781 | ||||||||
\(296\) | −2.30541 | −0.133999 | ||||||||
\(297\) | 2.22668 | 0.129205 | ||||||||
\(298\) | 3.41147 | 0.197621 | ||||||||
\(299\) | −11.7811 | −0.681316 | ||||||||
\(300\) | −0.0418891 | −0.00241847 | ||||||||
\(301\) | 15.7074 | 0.905359 | ||||||||
\(302\) | −3.04189 | −0.175041 | ||||||||
\(303\) | 17.9067 | 1.02871 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.6973 | 0.727044 | ||||||||
\(306\) | 3.41147 | 0.195021 | ||||||||
\(307\) | 22.5945 | 1.28954 | 0.644768 | − | 0.764378i | \(-0.276954\pi\) | ||||
0.644768 | + | 0.764378i | \(0.276954\pi\) | |||||||
\(308\) | −5.90673 | −0.336567 | ||||||||
\(309\) | 4.24628 | 0.241563 | ||||||||
\(310\) | 22.9641 | 1.30427 | ||||||||
\(311\) | −11.3259 | −0.642235 | −0.321118 | − | 0.947039i | \(-0.604058\pi\) | ||||
−0.321118 | + | 0.947039i | \(0.604058\pi\) | |||||||
\(312\) | 5.29086 | 0.299536 | ||||||||
\(313\) | −5.95811 | −0.336772 | −0.168386 | − | 0.985721i | \(-0.553856\pi\) | ||||
−0.168386 | + | 0.985721i | \(0.553856\pi\) | |||||||
\(314\) | 15.5253 | 0.876142 | ||||||||
\(315\) | 5.90673 | 0.332806 | ||||||||
\(316\) | 13.8007 | 0.776348 | ||||||||
\(317\) | −8.92396 | −0.501220 | −0.250610 | − | 0.968088i | \(-0.580631\pi\) | ||||
−0.250610 | + | 0.968088i | \(0.580631\pi\) | |||||||
\(318\) | −9.82295 | −0.550844 | ||||||||
\(319\) | 10.7219 | 0.600313 | ||||||||
\(320\) | −2.22668 | −0.124475 | ||||||||
\(321\) | 15.6040 | 0.870931 | ||||||||
\(322\) | 5.90673 | 0.329169 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.221629 | 0.0122938 | ||||||||
\(326\) | −4.43882 | −0.245843 | ||||||||
\(327\) | −1.36184 | −0.0753102 | ||||||||
\(328\) | 7.23442 | 0.399454 | ||||||||
\(329\) | −29.2003 | −1.60986 | ||||||||
\(330\) | 4.95811 | 0.272935 | ||||||||
\(331\) | 6.65951 | 0.366040 | 0.183020 | − | 0.983109i | \(-0.441413\pi\) | ||||
0.183020 | + | 0.983109i | \(0.441413\pi\) | |||||||
\(332\) | −10.5030 | −0.576427 | ||||||||
\(333\) | 2.30541 | 0.126336 | ||||||||
\(334\) | 8.15064 | 0.445983 | ||||||||
\(335\) | −19.0915 | −1.04308 | ||||||||
\(336\) | −2.65270 | −0.144717 | ||||||||
\(337\) | −10.8298 | −0.589934 | −0.294967 | − | 0.955507i | \(-0.595309\pi\) | ||||
−0.294967 | + | 0.955507i | \(0.595309\pi\) | |||||||
\(338\) | −14.9932 | −0.815522 | ||||||||
\(339\) | 17.2003 | 0.934191 | ||||||||
\(340\) | 7.59627 | 0.411965 | ||||||||
\(341\) | 22.9641 | 1.24358 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4712 | 0.997352 | ||||||||
\(344\) | 5.92127 | 0.319254 | ||||||||
\(345\) | −4.95811 | −0.266936 | ||||||||
\(346\) | 15.9659 | 0.858330 | ||||||||
\(347\) | 20.6614 | 1.10916 | 0.554580 | − | 0.832130i | \(-0.312879\pi\) | ||||
0.554580 | + | 0.832130i | \(0.312879\pi\) | |||||||
\(348\) | 4.81521 | 0.258122 | ||||||||
\(349\) | −2.03952 | −0.109173 | −0.0545866 | − | 0.998509i | \(-0.517384\pi\) | ||||
−0.0545866 | + | 0.998509i | \(0.517384\pi\) | |||||||
\(350\) | −0.111119 | −0.00593958 | ||||||||
\(351\) | −5.29086 | −0.282405 | ||||||||
\(352\) | −2.22668 | −0.118683 | ||||||||
\(353\) | 31.3013 | 1.66600 | 0.833000 | − | 0.553273i | \(-0.186622\pi\) | ||||
0.833000 | + | 0.553273i | \(0.186622\pi\) | |||||||
\(354\) | −4.95811 | −0.263521 | ||||||||
\(355\) | −9.80571 | −0.520433 | ||||||||
\(356\) | 7.81521 | 0.414205 | ||||||||
\(357\) | 9.04963 | 0.478957 | ||||||||
\(358\) | −1.45336 | −0.0768126 | ||||||||
\(359\) | −8.90673 | −0.470079 | −0.235040 | − | 0.971986i | \(-0.575522\pi\) | ||||
−0.235040 | + | 0.971986i | \(0.575522\pi\) | |||||||
\(360\) | 2.22668 | 0.117356 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 1.12567 | 0.0591638 | ||||||||
\(363\) | −6.04189 | −0.317117 | ||||||||
\(364\) | 14.0351 | 0.735638 | ||||||||
\(365\) | 6.22493 | 0.325828 | ||||||||
\(366\) | 5.70233 | 0.298066 | ||||||||
\(367\) | 3.44057 | 0.179596 | 0.0897981 | − | 0.995960i | \(-0.471378\pi\) | ||||
0.0897981 | + | 0.995960i | \(0.471378\pi\) | |||||||
\(368\) | 2.22668 | 0.116074 | ||||||||
\(369\) | −7.23442 | −0.376609 | ||||||||
\(370\) | 5.13341 | 0.266873 | ||||||||
\(371\) | −26.0574 | −1.35283 | ||||||||
\(372\) | 10.3131 | 0.534712 | ||||||||
\(373\) | −6.31996 | −0.327235 | −0.163617 | − | 0.986524i | \(-0.552316\pi\) | ||||
−0.163617 | + | 0.986524i | \(0.552316\pi\) | |||||||
\(374\) | 7.59627 | 0.392794 | ||||||||
\(375\) | 11.2267 | 0.579743 | ||||||||
\(376\) | −11.0077 | −0.567681 | ||||||||
\(377\) | −25.4766 | −1.31211 | ||||||||
\(378\) | 2.65270 | 0.136440 | ||||||||
\(379\) | −14.4074 | −0.740056 | −0.370028 | − | 0.929021i | \(-0.620652\pi\) | ||||
−0.370028 | + | 0.929021i | \(0.620652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.1925 | −0.675874 | ||||||||
\(382\) | 1.32770 | 0.0679308 | ||||||||
\(383\) | −1.89124 | −0.0966381 | −0.0483190 | − | 0.998832i | \(-0.515386\pi\) | ||||
−0.0483190 | + | 0.998832i | \(0.515386\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 13.1524 | 0.670308 | ||||||||
\(386\) | −14.9855 | −0.762739 | ||||||||
\(387\) | −5.92127 | −0.300995 | ||||||||
\(388\) | −17.7888 | −0.903089 | ||||||||
\(389\) | −7.37733 | −0.374045 | −0.187023 | − | 0.982356i | \(-0.559884\pi\) | ||||
−0.187023 | + | 0.982356i | \(0.559884\pi\) | |||||||
\(390\) | −11.7811 | −0.596557 | ||||||||
\(391\) | −7.59627 | −0.384160 | ||||||||
\(392\) | −0.0368366 | −0.00186053 | ||||||||
\(393\) | 7.50299 | 0.378476 | ||||||||
\(394\) | −23.0077 | −1.15911 | ||||||||
\(395\) | −30.7297 | −1.54618 | ||||||||
\(396\) | 2.22668 | 0.111895 | ||||||||
\(397\) | −11.5767 | −0.581016 | −0.290508 | − | 0.956873i | \(-0.593824\pi\) | ||||
−0.290508 | + | 0.956873i | \(0.593824\pi\) | |||||||
\(398\) | −9.68273 | −0.485352 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0418891 | −0.00209445 | ||||||||
\(401\) | 15.2098 | 0.759540 | 0.379770 | − | 0.925081i | \(-0.376003\pi\) | ||||
0.379770 | + | 0.925081i | \(0.376003\pi\) | |||||||
\(402\) | −8.57398 | −0.427631 | ||||||||
\(403\) | −54.5654 | −2.71810 | ||||||||
\(404\) | 17.9067 | 0.890893 | ||||||||
\(405\) | −2.22668 | −0.110645 | ||||||||
\(406\) | 12.7733 | 0.633929 | ||||||||
\(407\) | 5.13341 | 0.254454 | ||||||||
\(408\) | 3.41147 | 0.168893 | ||||||||
\(409\) | −1.53116 | −0.0757108 | −0.0378554 | − | 0.999283i | \(-0.512053\pi\) | ||||
−0.0378554 | + | 0.999283i | \(0.512053\pi\) | |||||||
\(410\) | −16.1088 | −0.795555 | ||||||||
\(411\) | 6.63041 | 0.327054 | ||||||||
\(412\) | 4.24628 | 0.209199 | ||||||||
\(413\) | −13.1524 | −0.647187 | ||||||||
\(414\) | −2.22668 | −0.109435 | ||||||||
\(415\) | 23.3868 | 1.14801 | ||||||||
\(416\) | 5.29086 | 0.259406 | ||||||||
\(417\) | −8.50980 | −0.416727 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.7374 | −1.30621 | −0.653104 | − | 0.757268i | \(-0.726534\pi\) | ||||
−0.653104 | + | 0.757268i | \(0.726534\pi\) | |||||||
\(420\) | 5.90673 | 0.288219 | ||||||||
\(421\) | 23.8726 | 1.16348 | 0.581739 | − | 0.813375i | \(-0.302372\pi\) | ||||
0.581739 | + | 0.813375i | \(0.302372\pi\) | |||||||
\(422\) | 1.10607 | 0.0538425 | ||||||||
\(423\) | 11.0077 | 0.535215 | ||||||||
\(424\) | −9.82295 | −0.477045 | ||||||||
\(425\) | 0.142903 | 0.00693184 | ||||||||
\(426\) | −4.40373 | −0.213362 | ||||||||
\(427\) | 15.1266 | 0.732028 | ||||||||
\(428\) | 15.6040 | 0.754248 | ||||||||
\(429\) | −11.7811 | −0.568795 | ||||||||
\(430\) | −13.1848 | −0.635827 | ||||||||
\(431\) | 15.7793 | 0.760062 | 0.380031 | − | 0.924974i | \(-0.375913\pi\) | ||||
0.380031 | + | 0.924974i | \(0.375913\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −13.4183 | −0.644841 | −0.322421 | − | 0.946596i | \(-0.604497\pi\) | ||||
−0.322421 | + | 0.946596i | \(0.604497\pi\) | |||||||
\(434\) | 27.3577 | 1.31321 | ||||||||
\(435\) | −10.7219 | −0.514077 | ||||||||
\(436\) | −1.36184 | −0.0652205 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.79561 | 0.133579 | ||||||||
\(439\) | 18.9017 | 0.902128 | 0.451064 | − | 0.892492i | \(-0.351045\pi\) | ||||
0.451064 | + | 0.892492i | \(0.351045\pi\) | |||||||
\(440\) | 4.95811 | 0.236369 | ||||||||
\(441\) | 0.0368366 | 0.00175413 | ||||||||
\(442\) | −18.0496 | −0.858533 | ||||||||
\(443\) | −11.2935 | −0.536573 | −0.268286 | − | 0.963339i | \(-0.586457\pi\) | ||||
−0.268286 | + | 0.963339i | \(0.586457\pi\) | |||||||
\(444\) | 2.30541 | 0.109410 | ||||||||
\(445\) | −17.4020 | −0.824933 | ||||||||
\(446\) | −25.2867 | −1.19736 | ||||||||
\(447\) | −3.41147 | −0.161357 | ||||||||
\(448\) | −2.65270 | −0.125328 | ||||||||
\(449\) | −8.75465 | −0.413158 | −0.206579 | − | 0.978430i | \(-0.566233\pi\) | ||||
−0.206579 | + | 0.978430i | \(0.566233\pi\) | |||||||
\(450\) | 0.0418891 | 0.00197467 | ||||||||
\(451\) | −16.1088 | −0.758532 | ||||||||
\(452\) | 17.2003 | 0.809033 | ||||||||
\(453\) | 3.04189 | 0.142920 | ||||||||
\(454\) | −3.42871 | −0.160917 | ||||||||
\(455\) | −31.2517 | −1.46510 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8334 | 1.11488 | 0.557439 | − | 0.830218i | \(-0.311784\pi\) | ||||
0.557439 | + | 0.830218i | \(0.311784\pi\) | |||||||
\(458\) | −29.9418 | −1.39909 | ||||||||
\(459\) | −3.41147 | −0.159234 | ||||||||
\(460\) | −4.95811 | −0.231173 | ||||||||
\(461\) | 15.7469 | 0.733407 | 0.366703 | − | 0.930338i | \(-0.380486\pi\) | ||||
0.366703 | + | 0.930338i | \(0.380486\pi\) | |||||||
\(462\) | 5.90673 | 0.274806 | ||||||||
\(463\) | −4.37464 | −0.203307 | −0.101653 | − | 0.994820i | \(-0.532413\pi\) | ||||
−0.101653 | + | 0.994820i | \(0.532413\pi\) | |||||||
\(464\) | 4.81521 | 0.223540 | ||||||||
\(465\) | −22.9641 | −1.06493 | ||||||||
\(466\) | 10.3773 | 0.480720 | ||||||||
\(467\) | 26.1070 | 1.20809 | 0.604044 | − | 0.796951i | \(-0.293555\pi\) | ||||
0.604044 | + | 0.796951i | \(0.293555\pi\) | |||||||
\(468\) | −5.29086 | −0.244570 | ||||||||
\(469\) | −22.7442 | −1.05023 | ||||||||
\(470\) | 24.5107 | 1.13060 | ||||||||
\(471\) | −15.5253 | −0.715367 | ||||||||
\(472\) | −4.95811 | −0.228216 | ||||||||
\(473\) | −13.1848 | −0.606237 | ||||||||
\(474\) | −13.8007 | −0.633885 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.04963 | 0.414789 | ||||||||
\(477\) | 9.82295 | 0.449762 | ||||||||
\(478\) | 16.0155 | 0.732531 | ||||||||
\(479\) | −34.1239 | −1.55916 | −0.779581 | − | 0.626302i | \(-0.784568\pi\) | ||||
−0.779581 | + | 0.626302i | \(0.784568\pi\) | |||||||
\(480\) | 2.22668 | 0.101634 | ||||||||
\(481\) | −12.1976 | −0.556162 | ||||||||
\(482\) | −25.5817 | −1.16522 | ||||||||
\(483\) | −5.90673 | −0.268765 | ||||||||
\(484\) | −6.04189 | −0.274631 | ||||||||
\(485\) | 39.6100 | 1.79860 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −15.7638 | −0.714327 | −0.357164 | − | 0.934042i | \(-0.616256\pi\) | ||||
−0.357164 | + | 0.934042i | \(0.616256\pi\) | |||||||
\(488\) | 5.70233 | 0.258133 | ||||||||
\(489\) | 4.43882 | 0.200730 | ||||||||
\(490\) | 0.0820234 | 0.00370544 | ||||||||
\(491\) | 13.8384 | 0.624520 | 0.312260 | − | 0.949997i | \(-0.398914\pi\) | ||||
0.312260 | + | 0.949997i | \(0.398914\pi\) | |||||||
\(492\) | −7.23442 | −0.326153 | ||||||||
\(493\) | −16.4270 | −0.739833 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.95811 | −0.222851 | ||||||||
\(496\) | 10.3131 | 0.463074 | ||||||||
\(497\) | −11.6818 | −0.524000 | ||||||||
\(498\) | 10.5030 | 0.470650 | ||||||||
\(499\) | −19.9290 | −0.892145 | −0.446073 | − | 0.894997i | \(-0.647178\pi\) | ||||
−0.446073 | + | 0.894997i | \(0.647178\pi\) | |||||||
\(500\) | 11.2267 | 0.502072 | ||||||||
\(501\) | −8.15064 | −0.364144 | ||||||||
\(502\) | −10.6895 | −0.477098 | ||||||||
\(503\) | −14.8803 | −0.663481 | −0.331740 | − | 0.943371i | \(-0.607636\pi\) | ||||
−0.331740 | + | 0.943371i | \(0.607636\pi\) | |||||||
\(504\) | 2.65270 | 0.118161 | ||||||||
\(505\) | −39.8726 | −1.77431 | ||||||||
\(506\) | −4.95811 | −0.220415 | ||||||||
\(507\) | 14.9932 | 0.665871 | ||||||||
\(508\) | −13.1925 | −0.585324 | ||||||||
\(509\) | −36.6860 | −1.62608 | −0.813040 | − | 0.582208i | \(-0.802189\pi\) | ||||
−0.813040 | + | 0.582208i | \(0.802189\pi\) | |||||||
\(510\) | −7.59627 | −0.336368 | ||||||||
\(511\) | 7.41592 | 0.328061 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.7793 | 1.35762 | ||||||||
\(515\) | −9.45512 | −0.416642 | ||||||||
\(516\) | −5.92127 | −0.260670 | ||||||||
\(517\) | 24.5107 | 1.07798 | ||||||||
\(518\) | 6.11556 | 0.268702 | ||||||||
\(519\) | −15.9659 | −0.700823 | ||||||||
\(520\) | −11.7811 | −0.516634 | ||||||||
\(521\) | −37.5354 | −1.64446 | −0.822228 | − | 0.569159i | \(-0.807269\pi\) | ||||
−0.822228 | + | 0.569159i | \(0.807269\pi\) | |||||||
\(522\) | −4.81521 | −0.210756 | ||||||||
\(523\) | 0.396926 | 0.0173564 | 0.00867819 | − | 0.999962i | \(-0.497238\pi\) | ||||
0.00867819 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(524\) | 7.50299 | 0.327770 | ||||||||
\(525\) | 0.111119 | 0.00484964 | ||||||||
\(526\) | −3.14290 | −0.137037 | ||||||||
\(527\) | −35.1830 | −1.53260 | ||||||||
\(528\) | 2.22668 | 0.0969039 | ||||||||
\(529\) | −18.0419 | −0.784430 | ||||||||
\(530\) | 21.8726 | 0.950084 | ||||||||
\(531\) | 4.95811 | 0.215164 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.2763 | 1.65793 | ||||||||
\(534\) | −7.81521 | −0.338197 | ||||||||
\(535\) | −34.7452 | −1.50216 | ||||||||
\(536\) | −8.57398 | −0.370339 | ||||||||
\(537\) | 1.45336 | 0.0627173 | ||||||||
\(538\) | −14.8803 | −0.641536 | ||||||||
\(539\) | 0.0820234 | 0.00353300 | ||||||||
\(540\) | −2.22668 | −0.0958211 | ||||||||
\(541\) | −20.8512 | −0.896464 | −0.448232 | − | 0.893917i | \(-0.647946\pi\) | ||||
−0.448232 | + | 0.893917i | \(0.647946\pi\) | |||||||
\(542\) | −15.2344 | −0.654374 | ||||||||
\(543\) | −1.12567 | −0.0483070 | ||||||||
\(544\) | 3.41147 | 0.146266 | ||||||||
\(545\) | 3.03239 | 0.129893 | ||||||||
\(546\) | −14.0351 | −0.600646 | ||||||||
\(547\) | −5.16519 | −0.220848 | −0.110424 | − | 0.993885i | \(-0.535221\pi\) | ||||
−0.110424 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(548\) | 6.63041 | 0.283237 | ||||||||
\(549\) | −5.70233 | −0.243370 | ||||||||
\(550\) | 0.0932736 | 0.00397720 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.22668 | −0.0947739 | ||||||||
\(553\) | −36.6091 | −1.55678 | ||||||||
\(554\) | 12.2094 | 0.518730 | ||||||||
\(555\) | −5.13341 | −0.217901 | ||||||||
\(556\) | −8.50980 | −0.360896 | ||||||||
\(557\) | 28.9641 | 1.22725 | 0.613624 | − | 0.789598i | \(-0.289711\pi\) | ||||
0.613624 | + | 0.789598i | \(0.289711\pi\) | |||||||
\(558\) | −10.3131 | −0.436590 | ||||||||
\(559\) | 31.3286 | 1.32506 | ||||||||
\(560\) | 5.90673 | 0.249605 | ||||||||
\(561\) | −7.59627 | −0.320715 | ||||||||
\(562\) | 2.24392 | 0.0946540 | ||||||||
\(563\) | −8.75784 | −0.369099 | −0.184549 | − | 0.982823i | \(-0.559083\pi\) | ||||
−0.184549 | + | 0.982823i | \(0.559083\pi\) | |||||||
\(564\) | 11.0077 | 0.463510 | ||||||||
\(565\) | −38.2995 | −1.61127 | ||||||||
\(566\) | 14.7888 | 0.621620 | ||||||||
\(567\) | −2.65270 | −0.111403 | ||||||||
\(568\) | −4.40373 | −0.184777 | ||||||||
\(569\) | 11.3696 | 0.476638 | 0.238319 | − | 0.971187i | \(-0.423404\pi\) | ||||
0.238319 | + | 0.971187i | \(0.423404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.98545 | 0.124937 | 0.0624686 | − | 0.998047i | \(-0.480103\pi\) | ||||
0.0624686 | + | 0.998047i | \(0.480103\pi\) | |||||||
\(572\) | −11.7811 | −0.492591 | ||||||||
\(573\) | −1.32770 | −0.0554653 | ||||||||
\(574\) | −19.1908 | −0.801008 | ||||||||
\(575\) | −0.0932736 | −0.00388978 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.7469 | −0.946966 | −0.473483 | − | 0.880803i | \(-0.657004\pi\) | ||||
−0.473483 | + | 0.880803i | \(0.657004\pi\) | |||||||
\(578\) | 5.36184 | 0.223023 | ||||||||
\(579\) | 14.9855 | 0.622774 | ||||||||
\(580\) | −10.7219 | −0.445204 | ||||||||
\(581\) | 27.8613 | 1.15588 | ||||||||
\(582\) | 17.7888 | 0.737369 | ||||||||
\(583\) | 21.8726 | 0.905870 | ||||||||
\(584\) | 2.79561 | 0.115683 | ||||||||
\(585\) | 11.7811 | 0.487087 | ||||||||
\(586\) | 12.0496 | 0.497766 | ||||||||
\(587\) | −16.5202 | −0.681863 | −0.340931 | − | 0.940088i | \(-0.610742\pi\) | ||||
−0.340931 | + | 0.940088i | \(0.610742\pi\) | |||||||
\(588\) | 0.0368366 | 0.00151912 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 11.0401 | 0.454515 | ||||||||
\(591\) | 23.0077 | 0.946412 | ||||||||
\(592\) | 2.30541 | 0.0947517 | ||||||||
\(593\) | 15.1084 | 0.620429 | 0.310214 | − | 0.950667i | \(-0.399599\pi\) | ||||
0.310214 | + | 0.950667i | \(0.399599\pi\) | |||||||
\(594\) | −2.22668 | −0.0913619 | ||||||||
\(595\) | −20.1506 | −0.826096 | ||||||||
\(596\) | −3.41147 | −0.139739 | ||||||||
\(597\) | 9.68273 | 0.396288 | ||||||||
\(598\) | 11.7811 | 0.481763 | ||||||||
\(599\) | −18.3182 | −0.748461 | −0.374231 | − | 0.927336i | \(-0.622093\pi\) | ||||
−0.374231 | + | 0.927336i | \(0.622093\pi\) | |||||||
\(600\) | 0.0418891 | 0.00171011 | ||||||||
\(601\) | −3.57491 | −0.145824 | −0.0729118 | − | 0.997338i | \(-0.523229\pi\) | ||||
−0.0729118 | + | 0.997338i | \(0.523229\pi\) | |||||||
\(602\) | −15.7074 | −0.640185 | ||||||||
\(603\) | 8.57398 | 0.349159 | ||||||||
\(604\) | 3.04189 | 0.123773 | ||||||||
\(605\) | 13.4534 | 0.546957 | ||||||||
\(606\) | −17.9067 | −0.727411 | ||||||||
\(607\) | 10.9436 | 0.444186 | 0.222093 | − | 0.975026i | \(-0.428711\pi\) | ||||
0.222093 | + | 0.975026i | \(0.428711\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.7733 | −0.517601 | ||||||||
\(610\) | −12.6973 | −0.514098 | ||||||||
\(611\) | −58.2404 | −2.35615 | ||||||||
\(612\) | −3.41147 | −0.137901 | ||||||||
\(613\) | 44.5928 | 1.80108 | 0.900542 | − | 0.434769i | \(-0.143170\pi\) | ||||
0.900542 | + | 0.434769i | \(0.143170\pi\) | |||||||
\(614\) | −22.5945 | −0.911840 | ||||||||
\(615\) | 16.1088 | 0.649568 | ||||||||
\(616\) | 5.90673 | 0.237989 | ||||||||
\(617\) | −1.44738 | −0.0582692 | −0.0291346 | − | 0.999575i | \(-0.509275\pi\) | ||||
−0.0291346 | + | 0.999575i | \(0.509275\pi\) | |||||||
\(618\) | −4.24628 | −0.170811 | ||||||||
\(619\) | −47.2472 | −1.89903 | −0.949513 | − | 0.313728i | \(-0.898422\pi\) | ||||
−0.949513 | + | 0.313728i | \(0.898422\pi\) | |||||||
\(620\) | −22.9641 | −0.922260 | ||||||||
\(621\) | 2.22668 | 0.0893537 | ||||||||
\(622\) | 11.3259 | 0.454129 | ||||||||
\(623\) | −20.7314 | −0.830587 | ||||||||
\(624\) | −5.29086 | −0.211804 | ||||||||
\(625\) | −24.7888 | −0.991552 | ||||||||
\(626\) | 5.95811 | 0.238134 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.5253 | −0.619526 | ||||||||
\(629\) | −7.86484 | −0.313592 | ||||||||
\(630\) | −5.90673 | −0.235330 | ||||||||
\(631\) | 34.8411 | 1.38700 | 0.693502 | − | 0.720455i | \(-0.256067\pi\) | ||||
0.693502 | + | 0.720455i | \(0.256067\pi\) | |||||||
\(632\) | −13.8007 | −0.548961 | ||||||||
\(633\) | −1.10607 | −0.0439622 | ||||||||
\(634\) | 8.92396 | 0.354416 | ||||||||
\(635\) | 29.3756 | 1.16573 | ||||||||
\(636\) | 9.82295 | 0.389505 | ||||||||
\(637\) | −0.194897 | −0.00772212 | ||||||||
\(638\) | −10.7219 | −0.424485 | ||||||||
\(639\) | 4.40373 | 0.174209 | ||||||||
\(640\) | 2.22668 | 0.0880173 | ||||||||
\(641\) | 10.9581 | 0.432819 | 0.216410 | − | 0.976303i | \(-0.430565\pi\) | ||||
0.216410 | + | 0.976303i | \(0.430565\pi\) | |||||||
\(642\) | −15.6040 | −0.615841 | ||||||||
\(643\) | 3.69997 | 0.145913 | 0.0729563 | − | 0.997335i | \(-0.476757\pi\) | ||||
0.0729563 | + | 0.997335i | \(0.476757\pi\) | |||||||
\(644\) | −5.90673 | −0.232758 | ||||||||
\(645\) | 13.1848 | 0.519151 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.2671 | 1.03267 | 0.516334 | − | 0.856387i | \(-0.327296\pi\) | ||||
0.516334 | + | 0.856387i | \(0.327296\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 11.0401 | 0.433363 | ||||||||
\(650\) | −0.221629 | −0.00869301 | ||||||||
\(651\) | −27.3577 | −1.07223 | ||||||||
\(652\) | 4.43882 | 0.173837 | ||||||||
\(653\) | 26.1566 | 1.02359 | 0.511794 | − | 0.859108i | \(-0.328981\pi\) | ||||
0.511794 | + | 0.859108i | \(0.328981\pi\) | |||||||
\(654\) | 1.36184 | 0.0532523 | ||||||||
\(655\) | −16.7068 | −0.652788 | ||||||||
\(656\) | −7.23442 | −0.282457 | ||||||||
\(657\) | −2.79561 | −0.109067 | ||||||||
\(658\) | 29.2003 | 1.13835 | ||||||||
\(659\) | 26.8803 | 1.04711 | 0.523554 | − | 0.851992i | \(-0.324606\pi\) | ||||
0.523554 | + | 0.851992i | \(0.324606\pi\) | |||||||
\(660\) | −4.95811 | −0.192994 | ||||||||
\(661\) | 5.59802 | 0.217738 | 0.108869 | − | 0.994056i | \(-0.465277\pi\) | ||||
0.108869 | + | 0.994056i | \(0.465277\pi\) | |||||||
\(662\) | −6.65951 | −0.258829 | ||||||||
\(663\) | 18.0496 | 0.700990 | ||||||||
\(664\) | 10.5030 | 0.407595 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.30541 | −0.0893327 | ||||||||
\(667\) | 10.7219 | 0.415155 | ||||||||
\(668\) | −8.15064 | −0.315358 | ||||||||
\(669\) | 25.2867 | 0.977642 | ||||||||
\(670\) | 19.0915 | 0.737570 | ||||||||
\(671\) | −12.6973 | −0.490173 | ||||||||
\(672\) | 2.65270 | 0.102330 | ||||||||
\(673\) | 22.9932 | 0.886322 | 0.443161 | − | 0.896442i | \(-0.353857\pi\) | ||||
0.443161 | + | 0.896442i | \(0.353857\pi\) | |||||||
\(674\) | 10.8298 | 0.417147 | ||||||||
\(675\) | −0.0418891 | −0.00161231 | ||||||||
\(676\) | 14.9932 | 0.576661 | ||||||||
\(677\) | 15.3354 | 0.589389 | 0.294694 | − | 0.955592i | \(-0.404782\pi\) | ||||
0.294694 | + | 0.955592i | \(0.404782\pi\) | |||||||
\(678\) | −17.2003 | −0.660573 | ||||||||
\(679\) | 47.1884 | 1.81093 | ||||||||
\(680\) | −7.59627 | −0.291304 | ||||||||
\(681\) | 3.42871 | 0.131388 | ||||||||
\(682\) | −22.9641 | −0.879341 | ||||||||
\(683\) | −19.6459 | −0.751729 | −0.375865 | − | 0.926675i | \(-0.622654\pi\) | ||||
−0.375865 | + | 0.926675i | \(0.622654\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.7638 | −0.564097 | ||||||||
\(686\) | −18.4712 | −0.705234 | ||||||||
\(687\) | 29.9418 | 1.14235 | ||||||||
\(688\) | −5.92127 | −0.225746 | ||||||||
\(689\) | −51.9718 | −1.97997 | ||||||||
\(690\) | 4.95811 | 0.188752 | ||||||||
\(691\) | 19.4688 | 0.740630 | 0.370315 | − | 0.928906i | \(-0.379250\pi\) | ||||
0.370315 | + | 0.928906i | \(0.379250\pi\) | |||||||
\(692\) | −15.9659 | −0.606931 | ||||||||
\(693\) | −5.90673 | −0.224378 | ||||||||
\(694\) | −20.6614 | −0.784295 | ||||||||
\(695\) | 18.9486 | 0.718762 | ||||||||
\(696\) | −4.81521 | −0.182520 | ||||||||
\(697\) | 24.6800 | 0.934823 | ||||||||
\(698\) | 2.03952 | 0.0771972 | ||||||||
\(699\) | −10.3773 | −0.392507 | ||||||||
\(700\) | 0.111119 | 0.00419991 | ||||||||
\(701\) | 22.1179 | 0.835383 | 0.417691 | − | 0.908589i | \(-0.362839\pi\) | ||||
0.417691 | + | 0.908589i | \(0.362839\pi\) | |||||||
\(702\) | 5.29086 | 0.199691 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.22668 | 0.0839212 | ||||||||
\(705\) | −24.5107 | −0.923128 | ||||||||
\(706\) | −31.3013 | −1.17804 | ||||||||
\(707\) | −47.5012 | −1.78647 | ||||||||
\(708\) | 4.95811 | 0.186337 | ||||||||
\(709\) | 9.53983 | 0.358276 | 0.179138 | − | 0.983824i | \(-0.442669\pi\) | ||||
0.179138 | + | 0.983824i | \(0.442669\pi\) | |||||||
\(710\) | 9.80571 | 0.368002 | ||||||||
\(711\) | 13.8007 | 0.517565 | ||||||||
\(712\) | −7.81521 | −0.292887 | ||||||||
\(713\) | 22.9641 | 0.860012 | ||||||||
\(714\) | −9.04963 | −0.338674 | ||||||||
\(715\) | 26.2327 | 0.981046 | ||||||||
\(716\) | 1.45336 | 0.0543147 | ||||||||
\(717\) | −16.0155 | −0.598109 | ||||||||
\(718\) | 8.90673 | 0.332396 | ||||||||
\(719\) | −38.7870 | −1.44651 | −0.723256 | − | 0.690580i | \(-0.757355\pi\) | ||||
−0.723256 | + | 0.690580i | \(0.757355\pi\) | |||||||
\(720\) | −2.22668 | −0.0829835 | ||||||||
\(721\) | −11.2641 | −0.419498 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.5817 | 0.951394 | ||||||||
\(724\) | −1.12567 | −0.0418351 | ||||||||
\(725\) | −0.201705 | −0.00749112 | ||||||||
\(726\) | 6.04189 | 0.224236 | ||||||||
\(727\) | −35.8452 | −1.32943 | −0.664713 | − | 0.747099i | \(-0.731446\pi\) | ||||
−0.664713 | + | 0.747099i | \(0.731446\pi\) | |||||||
\(728\) | −14.0351 | −0.520175 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.22493 | −0.230395 | ||||||||
\(731\) | 20.2003 | 0.747134 | ||||||||
\(732\) | −5.70233 | −0.210764 | ||||||||
\(733\) | 0.403733 | 0.0149122 | 0.00745612 | − | 0.999972i | \(-0.497627\pi\) | ||||
0.00745612 | + | 0.999972i | \(0.497627\pi\) | |||||||
\(734\) | −3.44057 | −0.126994 | ||||||||
\(735\) | −0.0820234 | −0.00302548 | ||||||||
\(736\) | −2.22668 | −0.0820766 | ||||||||
\(737\) | 19.0915 | 0.703245 | ||||||||
\(738\) | 7.23442 | 0.266303 | ||||||||
\(739\) | −0.595333 | −0.0218997 | −0.0109498 | − | 0.999940i | \(-0.503486\pi\) | ||||
−0.0109498 | + | 0.999940i | \(0.503486\pi\) | |||||||
\(740\) | −5.13341 | −0.188708 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.0574 | 0.956596 | ||||||||
\(743\) | 11.8743 | 0.435627 | 0.217814 | − | 0.975990i | \(-0.430108\pi\) | ||||
0.217814 | + | 0.975990i | \(0.430108\pi\) | |||||||
\(744\) | −10.3131 | −0.378098 | ||||||||
\(745\) | 7.59627 | 0.278306 | ||||||||
\(746\) | 6.31996 | 0.231390 | ||||||||
\(747\) | −10.5030 | −0.384284 | ||||||||
\(748\) | −7.59627 | −0.277747 | ||||||||
\(749\) | −41.3928 | −1.51246 | ||||||||
\(750\) | −11.2267 | −0.409940 | ||||||||
\(751\) | 5.45748 | 0.199146 | 0.0995732 | − | 0.995030i | \(-0.468252\pi\) | ||||
0.0995732 | + | 0.995030i | \(0.468252\pi\) | |||||||
\(752\) | 11.0077 | 0.401411 | ||||||||
\(753\) | 10.6895 | 0.389549 | ||||||||
\(754\) | 25.4766 | 0.927803 | ||||||||
\(755\) | −6.77332 | −0.246506 | ||||||||
\(756\) | −2.65270 | −0.0964779 | ||||||||
\(757\) | 12.0939 | 0.439560 | 0.219780 | − | 0.975550i | \(-0.429466\pi\) | ||||
0.219780 | + | 0.975550i | \(0.429466\pi\) | |||||||
\(758\) | 14.4074 | 0.523299 | ||||||||
\(759\) | 4.95811 | 0.179968 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.8726 | −0.684130 | −0.342065 | − | 0.939676i | \(-0.611126\pi\) | ||||
−0.342065 | + | 0.939676i | \(0.611126\pi\) | |||||||
\(762\) | 13.1925 | 0.477915 | ||||||||
\(763\) | 3.61257 | 0.130784 | ||||||||
\(764\) | −1.32770 | −0.0480344 | ||||||||
\(765\) | 7.59627 | 0.274644 | ||||||||
\(766\) | 1.89124 | 0.0683335 | ||||||||
\(767\) | −26.2327 | −0.947207 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −50.2704 | −1.81280 | −0.906399 | − | 0.422422i | \(-0.861180\pi\) | ||||
−0.906399 | + | 0.422422i | \(0.861180\pi\) | |||||||
\(770\) | −13.1524 | −0.473980 | ||||||||
\(771\) | −30.7793 | −1.10849 | ||||||||
\(772\) | 14.9855 | 0.539338 | ||||||||
\(773\) | −21.4843 | −0.772738 | −0.386369 | − | 0.922344i | \(-0.626271\pi\) | ||||
−0.386369 | + | 0.922344i | \(0.626271\pi\) | |||||||
\(774\) | 5.92127 | 0.212836 | ||||||||
\(775\) | −0.432008 | −0.0155182 | ||||||||
\(776\) | 17.7888 | 0.638581 | ||||||||
\(777\) | −6.11556 | −0.219395 | ||||||||
\(778\) | 7.37733 | 0.264490 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 11.7811 | 0.421830 | ||||||||
\(781\) | 9.80571 | 0.350876 | ||||||||
\(782\) | 7.59627 | 0.271642 | ||||||||
\(783\) | 4.81521 | 0.172081 | ||||||||
\(784\) | 0.0368366 | 0.00131559 | ||||||||
\(785\) | 34.5699 | 1.23385 | ||||||||
\(786\) | −7.50299 | −0.267623 | ||||||||
\(787\) | −22.5499 | −0.803818 | −0.401909 | − | 0.915680i | \(-0.631653\pi\) | ||||
−0.401909 | + | 0.915680i | \(0.631653\pi\) | |||||||
\(788\) | 23.0077 | 0.819617 | ||||||||
\(789\) | 3.14290 | 0.111890 | ||||||||
\(790\) | 30.7297 | 1.09331 | ||||||||
\(791\) | −45.6272 | −1.62232 | ||||||||
\(792\) | −2.22668 | −0.0791217 | ||||||||
\(793\) | 30.1702 | 1.07138 | ||||||||
\(794\) | 11.5767 | 0.410841 | ||||||||
\(795\) | −21.8726 | −0.775740 | ||||||||
\(796\) | 9.68273 | 0.343195 | ||||||||
\(797\) | −27.2098 | −0.963819 | −0.481910 | − | 0.876221i | \(-0.660057\pi\) | ||||
−0.481910 | + | 0.876221i | \(0.660057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.5526 | −1.32852 | ||||||||
\(800\) | 0.0418891 | 0.00148100 | ||||||||
\(801\) | 7.81521 | 0.276137 | ||||||||
\(802\) | −15.2098 | −0.537076 | ||||||||
\(803\) | −6.22493 | −0.219673 | ||||||||
\(804\) | 8.57398 | 0.302381 | ||||||||
\(805\) | 13.1524 | 0.463561 | ||||||||
\(806\) | 54.5654 | 1.92198 | ||||||||
\(807\) | 14.8803 | 0.523812 | ||||||||
\(808\) | −17.9067 | −0.629956 | ||||||||
\(809\) | −29.3523 | −1.03197 | −0.515987 | − | 0.856597i | \(-0.672575\pi\) | ||||
−0.515987 | + | 0.856597i | \(0.672575\pi\) | |||||||
\(810\) | 2.22668 | 0.0782376 | ||||||||
\(811\) | 19.1070 | 0.670938 | 0.335469 | − | 0.942051i | \(-0.391105\pi\) | ||||
0.335469 | + | 0.942051i | \(0.391105\pi\) | |||||||
\(812\) | −12.7733 | −0.448256 | ||||||||
\(813\) | 15.2344 | 0.534295 | ||||||||
\(814\) | −5.13341 | −0.179926 | ||||||||
\(815\) | −9.88383 | −0.346215 | ||||||||
\(816\) | −3.41147 | −0.119425 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.53116 | 0.0535356 | ||||||||
\(819\) | 14.0351 | 0.490425 | ||||||||
\(820\) | 16.1088 | 0.562542 | ||||||||
\(821\) | 0.420645 | 0.0146806 | 0.00734031 | − | 0.999973i | \(-0.497663\pi\) | ||||
0.00734031 | + | 0.999973i | \(0.497663\pi\) | |||||||
\(822\) | −6.63041 | −0.231262 | ||||||||
\(823\) | −36.6382 | −1.27713 | −0.638563 | − | 0.769570i | \(-0.720471\pi\) | ||||
−0.638563 | + | 0.769570i | \(0.720471\pi\) | |||||||
\(824\) | −4.24628 | −0.147926 | ||||||||
\(825\) | −0.0932736 | −0.00324737 | ||||||||
\(826\) | 13.1524 | 0.457630 | ||||||||
\(827\) | 29.4861 | 1.02533 | 0.512666 | − | 0.858588i | \(-0.328658\pi\) | ||||
0.512666 | + | 0.858588i | \(0.328658\pi\) | |||||||
\(828\) | 2.22668 | 0.0773825 | ||||||||
\(829\) | −5.62630 | −0.195409 | −0.0977047 | − | 0.995215i | \(-0.531150\pi\) | ||||
−0.0977047 | + | 0.995215i | \(0.531150\pi\) | |||||||
\(830\) | −23.3868 | −0.811768 | ||||||||
\(831\) | −12.2094 | −0.423541 | ||||||||
\(832\) | −5.29086 | −0.183428 | ||||||||
\(833\) | −0.125667 | −0.00435411 | ||||||||
\(834\) | 8.50980 | 0.294670 | ||||||||
\(835\) | 18.1489 | 0.628068 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.3131 | 0.356475 | ||||||||
\(838\) | 26.7374 | 0.923629 | ||||||||
\(839\) | 43.0155 | 1.48506 | 0.742530 | − | 0.669813i | \(-0.233626\pi\) | ||||
0.742530 | + | 0.669813i | \(0.233626\pi\) | |||||||
\(840\) | −5.90673 | −0.203801 | ||||||||
\(841\) | −5.81378 | −0.200475 | ||||||||
\(842\) | −23.8726 | −0.822703 | ||||||||
\(843\) | −2.24392 | −0.0772846 | ||||||||
\(844\) | −1.10607 | −0.0380724 | ||||||||
\(845\) | −33.3851 | −1.14848 | ||||||||
\(846\) | −11.0077 | −0.378454 | ||||||||
\(847\) | 16.0273 | 0.550706 | ||||||||
\(848\) | 9.82295 | 0.337321 | ||||||||
\(849\) | −14.7888 | −0.507550 | ||||||||
\(850\) | −0.142903 | −0.00490155 | ||||||||
\(851\) | 5.13341 | 0.175971 | ||||||||
\(852\) | 4.40373 | 0.150869 | ||||||||
\(853\) | 23.6905 | 0.811146 | 0.405573 | − | 0.914063i | \(-0.367072\pi\) | ||||
0.405573 | + | 0.914063i | \(0.367072\pi\) | |||||||
\(854\) | −15.1266 | −0.517622 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.6040 | −0.533334 | ||||||||
\(857\) | 50.5012 | 1.72509 | 0.862545 | − | 0.505981i | \(-0.168869\pi\) | ||||
0.862545 | + | 0.505981i | \(0.168869\pi\) | |||||||
\(858\) | 11.7811 | 0.402199 | ||||||||
\(859\) | 4.97596 | 0.169777 | 0.0848887 | − | 0.996390i | \(-0.472947\pi\) | ||||
0.0848887 | + | 0.996390i | \(0.472947\pi\) | |||||||
\(860\) | 13.1848 | 0.449598 | ||||||||
\(861\) | 19.1908 | 0.654020 | ||||||||
\(862\) | −15.7793 | −0.537445 | ||||||||
\(863\) | −7.90848 | −0.269208 | −0.134604 | − | 0.990899i | \(-0.542976\pi\) | ||||
−0.134604 | + | 0.990899i | \(0.542976\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 35.5509 | 1.20877 | ||||||||
\(866\) | 13.4183 | 0.455972 | ||||||||
\(867\) | −5.36184 | −0.182098 | ||||||||
\(868\) | −27.3577 | −0.928582 | ||||||||
\(869\) | 30.7297 | 1.04243 | ||||||||
\(870\) | 10.7219 | 0.363508 | ||||||||
\(871\) | −45.3637 | −1.53709 | ||||||||
\(872\) | 1.36184 | 0.0461179 | ||||||||
\(873\) | −17.7888 | −0.602060 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.7811 | −1.00678 | ||||||||
\(876\) | −2.79561 | −0.0944548 | ||||||||
\(877\) | −7.63722 | −0.257891 | −0.128945 | − | 0.991652i | \(-0.541159\pi\) | ||||
−0.128945 | + | 0.991652i | \(0.541159\pi\) | |||||||
\(878\) | −18.9017 | −0.637901 | ||||||||
\(879\) | −12.0496 | −0.406424 | ||||||||
\(880\) | −4.95811 | −0.167138 | ||||||||
\(881\) | 18.8898 | 0.636414 | 0.318207 | − | 0.948021i | \(-0.396919\pi\) | ||||
0.318207 | + | 0.948021i | \(0.396919\pi\) | |||||||
\(882\) | −0.0368366 | −0.00124035 | ||||||||
\(883\) | 53.6965 | 1.80703 | 0.903515 | − | 0.428557i | \(-0.140978\pi\) | ||||
0.903515 | + | 0.428557i | \(0.140978\pi\) | |||||||
\(884\) | 18.0496 | 0.607075 | ||||||||
\(885\) | −11.0401 | −0.371110 | ||||||||
\(886\) | 11.2935 | 0.379414 | ||||||||
\(887\) | −48.8117 | −1.63894 | −0.819468 | − | 0.573125i | \(-0.805731\pi\) | ||||
−0.819468 | + | 0.573125i | \(0.805731\pi\) | |||||||
\(888\) | −2.30541 | −0.0773644 | ||||||||
\(889\) | 34.9959 | 1.17372 | ||||||||
\(890\) | 17.4020 | 0.583316 | ||||||||
\(891\) | 2.22668 | 0.0745966 | ||||||||
\(892\) | 25.2867 | 0.846663 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.41147 | 0.114097 | ||||||||
\(895\) | −3.23618 | −0.108173 | ||||||||
\(896\) | 2.65270 | 0.0886206 | ||||||||
\(897\) | −11.7811 | −0.393358 | ||||||||
\(898\) | 8.75465 | 0.292147 | ||||||||
\(899\) | 49.6599 | 1.65625 | ||||||||
\(900\) | −0.0418891 | −0.00139630 | ||||||||
\(901\) | −33.5107 | −1.11640 | ||||||||
\(902\) | 16.1088 | 0.536363 | ||||||||
\(903\) | 15.7074 | 0.522709 | ||||||||
\(904\) | −17.2003 | −0.572073 | ||||||||
\(905\) | 2.50650 | 0.0833190 | ||||||||
\(906\) | −3.04189 | −0.101060 | ||||||||
\(907\) | −40.5776 | −1.34736 | −0.673679 | − | 0.739025i | \(-0.735287\pi\) | ||||
−0.673679 | + | 0.739025i | \(0.735287\pi\) | |||||||
\(908\) | 3.42871 | 0.113786 | ||||||||
\(909\) | 17.9067 | 0.593929 | ||||||||
\(910\) | 31.2517 | 1.03598 | ||||||||
\(911\) | 36.0384 | 1.19400 | 0.597002 | − | 0.802239i | \(-0.296358\pi\) | ||||
0.597002 | + | 0.802239i | \(0.296358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.3868 | −0.773991 | ||||||||
\(914\) | −23.8334 | −0.788338 | ||||||||
\(915\) | 12.6973 | 0.419759 | ||||||||
\(916\) | 29.9418 | 0.989305 | ||||||||
\(917\) | −19.9032 | −0.657262 | ||||||||
\(918\) | 3.41147 | 0.112595 | ||||||||
\(919\) | 26.1917 | 0.863985 | 0.431992 | − | 0.901877i | \(-0.357811\pi\) | ||||
0.431992 | + | 0.901877i | \(0.357811\pi\) | |||||||
\(920\) | 4.95811 | 0.163464 | ||||||||
\(921\) | 22.5945 | 0.744514 | ||||||||
\(922\) | −15.7469 | −0.518597 | ||||||||
\(923\) | −23.2995 | −0.766913 | ||||||||
\(924\) | −5.90673 | −0.194317 | ||||||||
\(925\) | −0.0965714 | −0.00317525 | ||||||||
\(926\) | 4.37464 | 0.143760 | ||||||||
\(927\) | 4.24628 | 0.139466 | ||||||||
\(928\) | −4.81521 | −0.158067 | ||||||||
\(929\) | 48.3242 | 1.58547 | 0.792733 | − | 0.609570i | \(-0.208658\pi\) | ||||
0.792733 | + | 0.609570i | \(0.208658\pi\) | |||||||
\(930\) | 22.9641 | 0.753022 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.3773 | −0.339921 | ||||||||
\(933\) | −11.3259 | −0.370795 | ||||||||
\(934\) | −26.1070 | −0.854247 | ||||||||
\(935\) | 16.9145 | 0.553162 | ||||||||
\(936\) | 5.29086 | 0.172937 | ||||||||
\(937\) | 59.1917 | 1.93371 | 0.966854 | − | 0.255328i | \(-0.0821835\pi\) | ||||
0.966854 | + | 0.255328i | \(0.0821835\pi\) | |||||||
\(938\) | 22.7442 | 0.742625 | ||||||||
\(939\) | −5.95811 | −0.194436 | ||||||||
\(940\) | −24.5107 | −0.799452 | ||||||||
\(941\) | 5.79023 | 0.188756 | 0.0943781 | − | 0.995536i | \(-0.469914\pi\) | ||||
0.0943781 | + | 0.995536i | \(0.469914\pi\) | |||||||
\(942\) | 15.5253 | 0.505841 | ||||||||
\(943\) | −16.1088 | −0.524573 | ||||||||
\(944\) | 4.95811 | 0.161373 | ||||||||
\(945\) | 5.90673 | 0.192146 | ||||||||
\(946\) | 13.1848 | 0.428675 | ||||||||
\(947\) | −45.9130 | −1.49197 | −0.745987 | − | 0.665961i | \(-0.768022\pi\) | ||||
−0.745987 | + | 0.665961i | \(0.768022\pi\) | |||||||
\(948\) | 13.8007 | 0.448225 | ||||||||
\(949\) | 14.7912 | 0.480142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.92396 | −0.289379 | ||||||||
\(952\) | −9.04963 | −0.293300 | ||||||||
\(953\) | 28.5526 | 0.924910 | 0.462455 | − | 0.886643i | \(-0.346969\pi\) | ||||
0.462455 | + | 0.886643i | \(0.346969\pi\) | |||||||
\(954\) | −9.82295 | −0.318030 | ||||||||
\(955\) | 2.95636 | 0.0956654 | ||||||||
\(956\) | −16.0155 | −0.517978 | ||||||||
\(957\) | 10.7219 | 0.346591 | ||||||||
\(958\) | 34.1239 | 1.10249 | ||||||||
\(959\) | −17.5885 | −0.567963 | ||||||||
\(960\) | −2.22668 | −0.0718658 | ||||||||
\(961\) | 75.3610 | 2.43100 | ||||||||
\(962\) | 12.1976 | 0.393266 | ||||||||
\(963\) | 15.6040 | 0.502832 | ||||||||
\(964\) | 25.5817 | 0.823932 | ||||||||
\(965\) | −33.3678 | −1.07415 | ||||||||
\(966\) | 5.90673 | 0.190046 | ||||||||
\(967\) | −22.0797 | −0.710034 | −0.355017 | − | 0.934860i | \(-0.615525\pi\) | ||||
−0.355017 | + | 0.934860i | \(0.615525\pi\) | |||||||
\(968\) | 6.04189 | 0.194194 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −39.6100 | −1.27180 | ||||||||
\(971\) | −12.6709 | −0.406628 | −0.203314 | − | 0.979114i | \(-0.565171\pi\) | ||||
−0.203314 | + | 0.979114i | \(0.565171\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 22.5740 | 0.723689 | ||||||||
\(974\) | 15.7638 | 0.505105 | ||||||||
\(975\) | 0.221629 | 0.00709781 | ||||||||
\(976\) | −5.70233 | −0.182527 | ||||||||
\(977\) | −17.2499 | −0.551873 | −0.275937 | − | 0.961176i | \(-0.588988\pi\) | ||||
−0.275937 | + | 0.961176i | \(0.588988\pi\) | |||||||
\(978\) | −4.43882 | −0.141938 | ||||||||
\(979\) | 17.4020 | 0.556170 | ||||||||
\(980\) | −0.0820234 | −0.00262014 | ||||||||
\(981\) | −1.36184 | −0.0434803 | ||||||||
\(982\) | −13.8384 | −0.441602 | ||||||||
\(983\) | −6.07604 | −0.193795 | −0.0968977 | − | 0.995294i | \(-0.530892\pi\) | ||||
−0.0968977 | + | 0.995294i | \(0.530892\pi\) | |||||||
\(984\) | 7.23442 | 0.230625 | ||||||||
\(985\) | −51.2309 | −1.63235 | ||||||||
\(986\) | 16.4270 | 0.523141 | ||||||||
\(987\) | −29.2003 | −0.929455 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.1848 | −0.419252 | ||||||||
\(990\) | 4.95811 | 0.157579 | ||||||||
\(991\) | −9.98040 | −0.317038 | −0.158519 | − | 0.987356i | \(-0.550672\pi\) | ||||
−0.158519 | + | 0.987356i | \(0.550672\pi\) | |||||||
\(992\) | −10.3131 | −0.327443 | ||||||||
\(993\) | 6.65951 | 0.211333 | ||||||||
\(994\) | 11.6818 | 0.370524 | ||||||||
\(995\) | −21.5604 | −0.683509 | ||||||||
\(996\) | −10.5030 | −0.332800 | ||||||||
\(997\) | 25.3040 | 0.801385 | 0.400692 | − | 0.916213i | \(-0.368770\pi\) | ||||
0.400692 | + | 0.916213i | \(0.368770\pi\) | |||||||
\(998\) | 19.9290 | 0.630842 | ||||||||
\(999\) | 2.30541 | 0.0729399 |
(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 | 2166.2.a.q.1.1 | 3 | ||
3.2 | odd | 2 | 6498.2.a.br.1.3 | 3 | |||
19.4 | even | 9 | 114.2.i.a.73.1 | yes | 6 | ||
19.5 | even | 9 | 114.2.i.a.25.1 | ✓ | 6 | ||
19.18 | odd | 2 | 2166.2.a.s.1.1 | 3 | |||
57.5 | odd | 18 | 342.2.u.e.253.1 | 6 | |||
57.23 | odd | 18 | 342.2.u.e.73.1 | 6 | |||
57.56 | even | 2 | 6498.2.a.bm.1.3 | 3 | |||
76.23 | odd | 18 | 912.2.bo.a.529.1 | 6 | |||
76.43 | odd | 18 | 912.2.bo.a.481.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.i.a.25.1 | ✓ | 6 | 19.5 | even | 9 | ||
114.2.i.a.73.1 | yes | 6 | 19.4 | even | 9 | ||
342.2.u.e.73.1 | 6 | 57.23 | odd | 18 | |||
342.2.u.e.253.1 | 6 | 57.5 | odd | 18 | |||
912.2.bo.a.481.1 | 6 | 76.43 | odd | 18 | |||
912.2.bo.a.529.1 | 6 | 76.23 | odd | 18 | |||
2166.2.a.q.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2166.2.a.s.1.1 | 3 | 19.18 | odd | 2 | |||
6498.2.a.bm.1.3 | 3 | 57.56 | even | 2 | |||
6498.2.a.br.1.3 | 3 | 3.2 | odd | 2 |