Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.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: | \(31.9800860095\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.10407557.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 2x^{3} + 18x^{2} + 7x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1335) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.763968\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.652386 | −0.461306 | −0.230653 | − | 0.973036i | \(-0.574086\pi\) | ||||
−0.230653 | + | 0.973036i | \(0.574086\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.57439 | −0.787196 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.82035 | 0.688029 | 0.344015 | − | 0.938964i | \(-0.388213\pi\) | ||||
0.344015 | + | 0.938964i | \(0.388213\pi\) | |||||||
\(8\) | 2.33188 | 0.824445 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.652386 | −0.206302 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.79030 | 0.773891 | 0.386946 | − | 0.922103i | \(-0.373530\pi\) | ||||
0.386946 | + | 0.922103i | \(0.373530\pi\) | |||||||
\(14\) | −1.18757 | −0.317392 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.62750 | 0.406875 | ||||||||
\(17\) | 1.78238 | 0.432290 | 0.216145 | − | 0.976361i | \(-0.430652\pi\) | ||||
0.216145 | + | 0.976361i | \(0.430652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.57439 | −0.352045 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.55073 | 0.948893 | 0.474447 | − | 0.880284i | \(-0.342648\pi\) | ||||
0.474447 | + | 0.880284i | \(0.342648\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.82035 | −0.357001 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.86595 | −0.541614 | ||||||||
\(29\) | 8.34897 | 1.55036 | 0.775182 | − | 0.631738i | \(-0.217658\pi\) | ||||
0.775182 | + | 0.631738i | \(0.217658\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.64071 | −0.294680 | −0.147340 | − | 0.989086i | \(-0.547071\pi\) | ||||
−0.147340 | + | 0.989086i | \(0.547071\pi\) | |||||||
\(32\) | −5.72552 | −1.01214 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.16280 | −0.199418 | ||||||||
\(35\) | 1.82035 | 0.307696 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.217624 | 0.0357771 | 0.0178885 | − | 0.999840i | \(-0.494306\pi\) | ||||
0.0178885 | + | 0.999840i | \(0.494306\pi\) | |||||||
\(38\) | −1.30477 | −0.211662 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.33188 | 0.368703 | ||||||||
\(41\) | 1.16563 | 0.182040 | 0.0910201 | − | 0.995849i | \(-0.470987\pi\) | ||||
0.0910201 | + | 0.995849i | \(0.470987\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8997 | −1.66219 | −0.831094 | − | 0.556132i | \(-0.812285\pi\) | ||||
−0.831094 | + | 0.556132i | \(0.812285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.96883 | −0.437731 | ||||||||
\(47\) | 4.02366 | 0.586911 | 0.293456 | − | 0.955973i | \(-0.405195\pi\) | ||||
0.293456 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.68631 | −0.526615 | ||||||||
\(50\) | −0.652386 | −0.0922613 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.39304 | −0.609204 | ||||||||
\(53\) | 1.85182 | 0.254367 | 0.127183 | − | 0.991879i | \(-0.459406\pi\) | ||||
0.127183 | + | 0.991879i | \(0.459406\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.24485 | 0.567242 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.44675 | −0.715193 | ||||||||
\(59\) | 5.34104 | 0.695344 | 0.347672 | − | 0.937616i | \(-0.386972\pi\) | ||||
0.347672 | + | 0.937616i | \(0.386972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.47661 | −0.701208 | −0.350604 | − | 0.936524i | \(-0.614024\pi\) | ||||
−0.350604 | + | 0.936524i | \(0.614024\pi\) | |||||||
\(62\) | 1.07038 | 0.135938 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.480251 | 0.0600314 | ||||||||
\(65\) | 2.79030 | 0.346095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3032 | 1.25873 | 0.629367 | − | 0.777108i | \(-0.283314\pi\) | ||||
0.629367 | + | 0.777108i | \(0.283314\pi\) | |||||||
\(68\) | −2.80616 | −0.340297 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.18757 | −0.141942 | ||||||||
\(71\) | 1.67217 | 0.198450 | 0.0992252 | − | 0.995065i | \(-0.468364\pi\) | ||||
0.0992252 | + | 0.995065i | \(0.468364\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9234 | −1.62961 | −0.814803 | − | 0.579737i | \(-0.803155\pi\) | ||||
−0.814803 | + | 0.579737i | \(0.803155\pi\) | |||||||
\(74\) | −0.141974 | −0.0165042 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.14879 | −0.361191 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.85023 | 0.770711 | 0.385356 | − | 0.922768i | \(-0.374079\pi\) | ||||
0.385356 | + | 0.922768i | \(0.374079\pi\) | |||||||
\(80\) | 1.62750 | 0.181960 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.760437 | −0.0839763 | ||||||||
\(83\) | 0.910024 | 0.0998881 | 0.0499440 | − | 0.998752i | \(-0.484096\pi\) | ||||
0.0499440 | + | 0.998752i | \(0.484096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.78238 | 0.193326 | ||||||||
\(86\) | 7.11081 | 0.766778 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | 0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.07934 | 0.532460 | ||||||||
\(92\) | −7.16464 | −0.746966 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.62498 | −0.270746 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.63942 | 0.572596 | 0.286298 | − | 0.958141i | \(-0.407575\pi\) | ||||
0.286298 | + | 0.958141i | \(0.407575\pi\) | |||||||
\(98\) | 2.40489 | 0.242931 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.57439 | −0.157439 | ||||||||
\(101\) | 7.32955 | 0.729317 | 0.364659 | − | 0.931141i | \(-0.381186\pi\) | ||||
0.364659 | + | 0.931141i | \(0.381186\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8036 | −1.55718 | −0.778589 | − | 0.627534i | \(-0.784064\pi\) | ||||
−0.778589 | + | 0.627534i | \(0.784064\pi\) | |||||||
\(104\) | 6.50666 | 0.638031 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.20810 | −0.117341 | ||||||||
\(107\) | −2.29261 | −0.221635 | −0.110818 | − | 0.993841i | \(-0.535347\pi\) | ||||
−0.110818 | + | 0.993841i | \(0.535347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.65392 | 0.637330 | 0.318665 | − | 0.947867i | \(-0.396766\pi\) | ||||
0.318665 | + | 0.947867i | \(0.396766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.96263 | 0.279942 | ||||||||
\(113\) | −0.623266 | −0.0586320 | −0.0293160 | − | 0.999570i | \(-0.509333\pi\) | ||||
−0.0293160 | + | 0.999570i | \(0.509333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.55073 | 0.424358 | ||||||||
\(116\) | −13.1446 | −1.22044 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.48442 | −0.320767 | ||||||||
\(119\) | 3.24456 | 0.297428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 3.57286 | 0.323472 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.58312 | 0.231971 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.31939 | 0.205812 | 0.102906 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102906 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(128\) | 11.1377 | 0.984446 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.82035 | −0.159656 | ||||||||
\(131\) | 5.35678 | 0.468024 | 0.234012 | − | 0.972234i | \(-0.424815\pi\) | ||||
0.234012 | + | 0.972234i | \(0.424815\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.64071 | 0.315690 | ||||||||
\(134\) | −6.72165 | −0.580662 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.15629 | 0.356399 | ||||||||
\(137\) | −2.72940 | −0.233188 | −0.116594 | − | 0.993180i | \(-0.537198\pi\) | ||||
−0.116594 | + | 0.993180i | \(0.537198\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.95281 | −0.504911 | −0.252456 | − | 0.967608i | \(-0.581238\pi\) | ||||
−0.252456 | + | 0.967608i | \(0.581238\pi\) | |||||||
\(140\) | −2.86595 | −0.242217 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.09090 | −0.0915464 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.34897 | 0.693344 | ||||||||
\(146\) | 9.08341 | 0.751748 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.342625 | −0.0281636 | ||||||||
\(149\) | −15.8194 | −1.29597 | −0.647987 | − | 0.761652i | \(-0.724389\pi\) | ||||
−0.647987 | + | 0.761652i | \(0.724389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7583 | 1.11964 | 0.559818 | − | 0.828615i | \(-0.310871\pi\) | ||||
0.559818 | + | 0.828615i | \(0.310871\pi\) | |||||||
\(152\) | 4.66377 | 0.378281 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.64071 | −0.131785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.49287 | −0.358570 | −0.179285 | − | 0.983797i | \(-0.557378\pi\) | ||||
−0.179285 | + | 0.983797i | \(0.557378\pi\) | |||||||
\(158\) | −4.46899 | −0.355534 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.72552 | −0.452642 | ||||||||
\(161\) | 8.28395 | 0.652867 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.9391 | −0.935142 | −0.467571 | − | 0.883956i | \(-0.654871\pi\) | ||||
−0.467571 | + | 0.883956i | \(0.654871\pi\) | |||||||
\(164\) | −1.83515 | −0.143301 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.593686 | −0.0460790 | ||||||||
\(167\) | 21.4963 | 1.66344 | 0.831719 | − | 0.555197i | \(-0.187357\pi\) | ||||
0.831719 | + | 0.555197i | \(0.187357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.21420 | −0.401092 | ||||||||
\(170\) | −1.16280 | −0.0891825 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.1604 | 1.30847 | ||||||||
\(173\) | −10.0116 | −0.761170 | −0.380585 | − | 0.924746i | \(-0.624277\pi\) | ||||
−0.380585 | + | 0.924746i | \(0.624277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.82035 | 0.137606 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.652386 | −0.0488984 | ||||||||
\(179\) | −15.6251 | −1.16788 | −0.583938 | − | 0.811799i | \(-0.698489\pi\) | ||||
−0.583938 | + | 0.811799i | \(0.698489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8343 | 1.02829 | 0.514147 | − | 0.857702i | \(-0.328109\pi\) | ||||
0.514147 | + | 0.857702i | \(0.328109\pi\) | |||||||
\(182\) | −3.31369 | −0.245627 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.6118 | 0.782311 | ||||||||
\(185\) | 0.217624 | 0.0160000 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.33482 | −0.462014 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.30477 | −0.0946581 | ||||||||
\(191\) | 1.49457 | 0.108143 | 0.0540716 | − | 0.998537i | \(-0.482780\pi\) | ||||
0.0540716 | + | 0.998537i | \(0.482780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.86514 | −0.638127 | −0.319064 | − | 0.947733i | \(-0.603368\pi\) | ||||
−0.319064 | + | 0.947733i | \(0.603368\pi\) | |||||||
\(194\) | −3.67908 | −0.264142 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.80370 | 0.414550 | ||||||||
\(197\) | 12.3256 | 0.878163 | 0.439082 | − | 0.898447i | \(-0.355304\pi\) | ||||
0.439082 | + | 0.898447i | \(0.355304\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.4663 | 1.52170 | 0.760852 | − | 0.648925i | \(-0.224781\pi\) | ||||
0.760852 | + | 0.648925i | \(0.224781\pi\) | |||||||
\(200\) | 2.33188 | 0.164889 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.78169 | −0.336439 | ||||||||
\(203\) | 15.1981 | 1.06670 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.16563 | 0.0814108 | ||||||||
\(206\) | 10.3101 | 0.718336 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.54122 | 0.314877 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.76086 | 0.465437 | 0.232718 | − | 0.972544i | \(-0.425238\pi\) | ||||
0.232718 | + | 0.972544i | \(0.425238\pi\) | |||||||
\(212\) | −2.91549 | −0.200237 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.49567 | 0.102242 | ||||||||
\(215\) | −10.8997 | −0.743353 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.98667 | −0.202749 | ||||||||
\(218\) | −4.34092 | −0.294004 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.97337 | 0.334545 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.9311 | 1.33469 | 0.667343 | − | 0.744750i | \(-0.267432\pi\) | ||||
0.667343 | + | 0.744750i | \(0.267432\pi\) | |||||||
\(224\) | −10.4225 | −0.696381 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.406610 | 0.0270473 | ||||||||
\(227\) | −2.84119 | −0.188577 | −0.0942884 | − | 0.995545i | \(-0.530058\pi\) | ||||
−0.0942884 | + | 0.995545i | \(0.530058\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.10370 | 0.205098 | 0.102549 | − | 0.994728i | \(-0.467300\pi\) | ||||
0.102549 | + | 0.994728i | \(0.467300\pi\) | |||||||
\(230\) | −2.96883 | −0.195759 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.4688 | 1.27819 | ||||||||
\(233\) | −4.83762 | −0.316923 | −0.158462 | − | 0.987365i | \(-0.550653\pi\) | ||||
−0.158462 | + | 0.987365i | \(0.550653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.02366 | 0.262475 | ||||||||
\(236\) | −8.40889 | −0.547372 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.11670 | −0.137205 | ||||||||
\(239\) | 21.9339 | 1.41878 | 0.709392 | − | 0.704815i | \(-0.248970\pi\) | ||||
0.709392 | + | 0.704815i | \(0.248970\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7742 | 0.758442 | 0.379221 | − | 0.925306i | \(-0.376192\pi\) | ||||
0.379221 | + | 0.925306i | \(0.376192\pi\) | |||||||
\(242\) | 7.17624 | 0.461306 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.62234 | 0.551989 | ||||||||
\(245\) | −3.68631 | −0.235510 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.58061 | 0.355086 | ||||||||
\(248\) | −3.82594 | −0.242948 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.652386 | −0.0412605 | ||||||||
\(251\) | −23.5628 | −1.48727 | −0.743635 | − | 0.668586i | \(-0.766900\pi\) | ||||
−0.743635 | + | 0.668586i | \(0.766900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.51313 | −0.0949425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.22660 | −0.514163 | ||||||||
\(257\) | 21.5945 | 1.34703 | 0.673515 | − | 0.739173i | \(-0.264784\pi\) | ||||
0.673515 | + | 0.739173i | \(0.264784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.396152 | 0.0246157 | ||||||||
\(260\) | −4.39304 | −0.272445 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.49469 | −0.215902 | ||||||||
\(263\) | 21.4320 | 1.32156 | 0.660778 | − | 0.750581i | \(-0.270226\pi\) | ||||
0.660778 | + | 0.750581i | \(0.270226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.85182 | 0.113756 | ||||||||
\(266\) | −2.37515 | −0.145630 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.2213 | −0.990871 | ||||||||
\(269\) | −10.5968 | −0.646096 | −0.323048 | − | 0.946383i | \(-0.604708\pi\) | ||||
−0.323048 | + | 0.946383i | \(0.604708\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.325304 | −0.0197608 | −0.00988040 | − | 0.999951i | \(-0.503145\pi\) | ||||
−0.00988040 | + | 0.999951i | \(0.503145\pi\) | |||||||
\(272\) | 2.90082 | 0.175888 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.78062 | 0.107571 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1310 | −0.668800 | −0.334400 | − | 0.942431i | \(-0.608534\pi\) | ||||
−0.334400 | + | 0.942431i | \(0.608534\pi\) | |||||||
\(278\) | 3.88353 | 0.232919 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.24485 | 0.253679 | ||||||||
\(281\) | 30.5089 | 1.82001 | 0.910006 | − | 0.414596i | \(-0.136077\pi\) | ||||
0.910006 | + | 0.414596i | \(0.136077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.74938 | 0.341765 | 0.170882 | − | 0.985291i | \(-0.445338\pi\) | ||||
0.170882 | + | 0.985291i | \(0.445338\pi\) | |||||||
\(284\) | −2.63266 | −0.156219 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.12185 | 0.125249 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.8231 | −0.813126 | ||||||||
\(290\) | −5.44675 | −0.319844 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.9209 | 1.28282 | ||||||||
\(293\) | 23.8582 | 1.39381 | 0.696906 | − | 0.717163i | \(-0.254560\pi\) | ||||
0.696906 | + | 0.717163i | \(0.254560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.34104 | 0.310967 | ||||||||
\(296\) | 0.507472 | 0.0294962 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.3203 | 0.597841 | ||||||||
\(299\) | 12.6979 | 0.734340 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8413 | −1.14363 | ||||||||
\(302\) | −8.97574 | −0.516496 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.25500 | 0.186687 | ||||||||
\(305\) | −5.47661 | −0.313590 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0644 | 0.859770 | 0.429885 | − | 0.902884i | \(-0.358554\pi\) | ||||
0.429885 | + | 0.902884i | \(0.358554\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.07038 | 0.0607932 | ||||||||
\(311\) | −18.3987 | −1.04330 | −0.521648 | − | 0.853161i | \(-0.674683\pi\) | ||||
−0.521648 | + | 0.853161i | \(0.674683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5426 | 0.821999 | 0.410999 | − | 0.911636i | \(-0.365180\pi\) | ||||
0.410999 | + | 0.911636i | \(0.365180\pi\) | |||||||
\(314\) | 2.93108 | 0.165411 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7850 | −0.606701 | ||||||||
\(317\) | 18.5719 | 1.04310 | 0.521550 | − | 0.853221i | \(-0.325354\pi\) | ||||
0.521550 | + | 0.853221i | \(0.325354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.480251 | 0.0268468 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.40433 | −0.301172 | ||||||||
\(323\) | 3.56475 | 0.198348 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.79030 | 0.154778 | ||||||||
\(326\) | 7.78889 | 0.431387 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.71810 | 0.150082 | ||||||||
\(329\) | 7.32449 | 0.403812 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5503 | 0.799754 | 0.399877 | − | 0.916569i | \(-0.369053\pi\) | ||||
0.399877 | + | 0.916569i | \(0.369053\pi\) | |||||||
\(332\) | −1.43273 | −0.0786315 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.0239 | −0.767354 | ||||||||
\(335\) | 10.3032 | 0.562923 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.8283 | 1.67932 | 0.839662 | − | 0.543109i | \(-0.182753\pi\) | ||||
0.839662 | + | 0.543109i | \(0.182753\pi\) | |||||||
\(338\) | 3.40167 | 0.185026 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.80616 | −0.152185 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4529 | −1.05036 | ||||||||
\(344\) | −25.4168 | −1.37038 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.53144 | 0.351132 | ||||||||
\(347\) | 17.8228 | 0.956775 | 0.478388 | − | 0.878149i | \(-0.341221\pi\) | ||||
0.478388 | + | 0.878149i | \(0.341221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.69024 | 0.197534 | 0.0987671 | − | 0.995111i | \(-0.468510\pi\) | ||||
0.0987671 | + | 0.995111i | \(0.468510\pi\) | |||||||
\(350\) | −1.18757 | −0.0634785 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.79637 | 0.414959 | 0.207480 | − | 0.978239i | \(-0.433474\pi\) | ||||
0.207480 | + | 0.978239i | \(0.433474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.67217 | 0.0887497 | ||||||||
\(356\) | −1.57439 | −0.0834427 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.1936 | 0.538748 | ||||||||
\(359\) | 7.06971 | 0.373125 | 0.186563 | − | 0.982443i | \(-0.440265\pi\) | ||||
0.186563 | + | 0.982443i | \(0.440265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −9.02529 | −0.474359 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.99688 | −0.419151 | ||||||||
\(365\) | −13.9234 | −0.728782 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.84431 | 0.357270 | 0.178635 | − | 0.983915i | \(-0.442832\pi\) | ||||
0.178635 | + | 0.983915i | \(0.442832\pi\) | |||||||
\(368\) | 7.40631 | 0.386081 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.141974 | −0.00738090 | ||||||||
\(371\) | 3.37097 | 0.175012 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.8978 | −0.771381 | −0.385690 | − | 0.922628i | \(-0.626037\pi\) | ||||
−0.385690 | + | 0.922628i | \(0.626037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.38270 | 0.483876 | ||||||||
\(377\) | 23.2962 | 1.19981 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7085 | 0.755525 | 0.377762 | − | 0.925903i | \(-0.376694\pi\) | ||||
0.377762 | + | 0.925903i | \(0.376694\pi\) | |||||||
\(380\) | −3.14879 | −0.161529 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.975036 | −0.0498872 | ||||||||
\(383\) | 2.12921 | 0.108798 | 0.0543988 | − | 0.998519i | \(-0.482676\pi\) | ||||
0.0543988 | + | 0.998519i | \(0.482676\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.78349 | 0.294372 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.87866 | −0.450746 | ||||||||
\(389\) | −10.3879 | −0.526687 | −0.263343 | − | 0.964702i | \(-0.584825\pi\) | ||||
−0.263343 | + | 0.964702i | \(0.584825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.11112 | 0.410197 | ||||||||
\(392\) | −8.59604 | −0.434166 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.04105 | −0.405102 | ||||||||
\(395\) | 6.85023 | 0.344673 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.20577 | −0.361647 | −0.180824 | − | 0.983516i | \(-0.557876\pi\) | ||||
−0.180824 | + | 0.983516i | \(0.557876\pi\) | |||||||
\(398\) | −14.0043 | −0.701972 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.62750 | 0.0813749 | ||||||||
\(401\) | −14.0547 | −0.701858 | −0.350929 | − | 0.936402i | \(-0.614134\pi\) | ||||
−0.350929 | + | 0.936402i | \(0.614134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.57808 | −0.228050 | ||||||||
\(404\) | −11.5396 | −0.574116 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.91501 | −0.492074 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.6725 | −0.725509 | −0.362755 | − | 0.931885i | \(-0.618164\pi\) | ||||
−0.362755 | + | 0.931885i | \(0.618164\pi\) | |||||||
\(410\) | −0.760437 | −0.0375553 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24.8811 | 1.22581 | ||||||||
\(413\) | 9.72258 | 0.478417 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.910024 | 0.0446713 | ||||||||
\(416\) | −15.9760 | −0.783285 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.6612 | −1.20478 | −0.602389 | − | 0.798202i | \(-0.705785\pi\) | ||||
−0.602389 | + | 0.798202i | \(0.705785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.4721 | 1.58259 | 0.791297 | − | 0.611432i | \(-0.209406\pi\) | ||||
0.791297 | + | 0.611432i | \(0.209406\pi\) | |||||||
\(422\) | −4.41069 | −0.214709 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.31822 | 0.209711 | ||||||||
\(425\) | 1.78238 | 0.0864580 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.96938 | −0.482452 | ||||||||
\(428\) | 3.60947 | 0.174470 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.11081 | 0.342914 | ||||||||
\(431\) | −30.9369 | −1.49018 | −0.745089 | − | 0.666965i | \(-0.767593\pi\) | ||||
−0.745089 | + | 0.666965i | \(0.767593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.659905 | 0.0317130 | 0.0158565 | − | 0.999874i | \(-0.494953\pi\) | ||||
0.0158565 | + | 0.999874i | \(0.494953\pi\) | |||||||
\(434\) | 1.94846 | 0.0935292 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.4759 | −0.501704 | ||||||||
\(437\) | 9.10147 | 0.435382 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3644 | 0.781032 | 0.390516 | − | 0.920596i | \(-0.372297\pi\) | ||||
0.390516 | + | 0.920596i | \(0.372297\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.24456 | −0.154328 | ||||||||
\(443\) | 25.3266 | 1.20330 | 0.601651 | − | 0.798759i | \(-0.294510\pi\) | ||||
0.601651 | + | 0.798759i | \(0.294510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | −13.0028 | −0.615699 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.874227 | 0.0413033 | ||||||||
\(449\) | 16.9890 | 0.801761 | 0.400880 | − | 0.916130i | \(-0.368704\pi\) | ||||
0.400880 | + | 0.916130i | \(0.368704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.981266 | 0.0461549 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.85355 | 0.0869916 | ||||||||
\(455\) | 5.07934 | 0.238123 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.2823 | −1.65043 | −0.825217 | − | 0.564815i | \(-0.808947\pi\) | ||||
−0.825217 | + | 0.564815i | \(0.808947\pi\) | |||||||
\(458\) | −2.02481 | −0.0946131 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.16464 | −0.334053 | ||||||||
\(461\) | −9.07343 | −0.422592 | −0.211296 | − | 0.977422i | \(-0.567768\pi\) | ||||
−0.211296 | + | 0.977422i | \(0.567768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.3436 | −0.991923 | −0.495962 | − | 0.868344i | \(-0.665184\pi\) | ||||
−0.495962 | + | 0.868344i | \(0.665184\pi\) | |||||||
\(464\) | 13.5879 | 0.630804 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.15600 | 0.146199 | ||||||||
\(467\) | 6.70744 | 0.310384 | 0.155192 | − | 0.987884i | \(-0.450400\pi\) | ||||
0.155192 | + | 0.987884i | \(0.450400\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7555 | 0.866046 | ||||||||
\(470\) | −2.62498 | −0.121081 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.4547 | 0.573273 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | −5.10821 | −0.234134 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.3093 | −0.654494 | ||||||||
\(479\) | −20.9346 | −0.956525 | −0.478262 | − | 0.878217i | \(-0.658733\pi\) | ||||
−0.478262 | + | 0.878217i | \(0.658733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.607236 | 0.0276876 | ||||||||
\(482\) | −7.68131 | −0.349874 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.3183 | 0.787196 | ||||||||
\(485\) | 5.63942 | 0.256073 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.75495 | 0.351410 | 0.175705 | − | 0.984443i | \(-0.443779\pi\) | ||||
0.175705 | + | 0.984443i | \(0.443779\pi\) | |||||||
\(488\) | −12.7708 | −0.578108 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.40489 | 0.108642 | ||||||||
\(491\) | −2.44614 | −0.110393 | −0.0551965 | − | 0.998476i | \(-0.517579\pi\) | ||||
−0.0551965 | + | 0.998476i | \(0.517579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.8810 | 0.670207 | ||||||||
\(494\) | −3.64071 | −0.163803 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.67025 | −0.119898 | ||||||||
\(497\) | 3.04395 | 0.136540 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.5082 | −1.67910 | −0.839549 | − | 0.543285i | \(-0.817180\pi\) | ||||
−0.839549 | + | 0.543285i | \(0.817180\pi\) | |||||||
\(500\) | −1.57439 | −0.0704090 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.3720 | 0.686087 | ||||||||
\(503\) | −11.3670 | −0.506828 | −0.253414 | − | 0.967358i | \(-0.581554\pi\) | ||||
−0.253414 | + | 0.967358i | \(0.581554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.32955 | 0.326161 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.65163 | −0.162015 | ||||||||
\(509\) | 28.9326 | 1.28241 | 0.641207 | − | 0.767368i | \(-0.278434\pi\) | ||||
0.641207 | + | 0.767368i | \(0.278434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.3455 | −1.12122 | ||||||||
\(512\) | −16.9086 | −0.747260 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.0880 | −0.621394 | ||||||||
\(515\) | −15.8036 | −0.696391 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.258444 | −0.0113554 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.50666 | 0.285336 | ||||||||
\(521\) | −16.7110 | −0.732123 | −0.366062 | − | 0.930591i | \(-0.619294\pi\) | ||||
−0.366062 | + | 0.930591i | \(0.619294\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.158812 | 0.00694435 | 0.00347217 | − | 0.999994i | \(-0.498895\pi\) | ||||
0.00347217 | + | 0.999994i | \(0.498895\pi\) | |||||||
\(524\) | −8.43367 | −0.368427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.9820 | −0.609642 | ||||||||
\(527\) | −2.92436 | −0.127387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.29083 | −0.0996012 | ||||||||
\(530\) | −1.20810 | −0.0524765 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.73191 | −0.248510 | ||||||||
\(533\) | 3.25245 | 0.140879 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.29261 | −0.0991182 | ||||||||
\(536\) | 24.0258 | 1.03776 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.91318 | 0.298048 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.777063 | −0.0334085 | −0.0167043 | − | 0.999860i | \(-0.505317\pi\) | ||||
−0.0167043 | + | 0.999860i | \(0.505317\pi\) | |||||||
\(542\) | 0.212224 | 0.00911578 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.2050 | −0.437537 | ||||||||
\(545\) | 6.65392 | 0.285023 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.4549 | 0.746317 | 0.373159 | − | 0.927768i | \(-0.378275\pi\) | ||||
0.373159 | + | 0.927768i | \(0.378275\pi\) | |||||||
\(548\) | 4.29714 | 0.183565 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.6979 | 0.711356 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.4699 | 0.530272 | ||||||||
\(554\) | 7.26174 | 0.308522 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.37207 | 0.397464 | ||||||||
\(557\) | 30.0347 | 1.27261 | 0.636306 | − | 0.771436i | \(-0.280461\pi\) | ||||
0.636306 | + | 0.771436i | \(0.280461\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.4135 | −1.28635 | ||||||||
\(560\) | 2.96263 | 0.125194 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.9036 | −0.839583 | ||||||||
\(563\) | −32.3323 | −1.36264 | −0.681322 | − | 0.731984i | \(-0.738595\pi\) | ||||
−0.681322 | + | 0.731984i | \(0.738595\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.623266 | −0.0262210 | ||||||||
\(566\) | −3.75081 | −0.157658 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.89931 | 0.163611 | ||||||||
\(569\) | −35.5875 | −1.49191 | −0.745953 | − | 0.665998i | \(-0.768006\pi\) | ||||
−0.745953 | + | 0.665998i | \(0.768006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.60420 | −0.318226 | −0.159113 | − | 0.987260i | \(-0.550863\pi\) | ||||
−0.159113 | + | 0.987260i | \(0.550863\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.38427 | −0.0577781 | ||||||||
\(575\) | 4.55073 | 0.189779 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.9193 | −0.912512 | −0.456256 | − | 0.889849i | \(-0.650810\pi\) | ||||
−0.456256 | + | 0.889849i | \(0.650810\pi\) | |||||||
\(578\) | 9.01801 | 0.375100 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.1446 | −0.545798 | ||||||||
\(581\) | 1.65657 | 0.0687259 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −32.4677 | −1.34352 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.5648 | −0.642974 | ||||||||
\(587\) | −25.1988 | −1.04007 | −0.520033 | − | 0.854146i | \(-0.674080\pi\) | ||||
−0.520033 | + | 0.854146i | \(0.674080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.28142 | −0.135209 | ||||||||
\(590\) | −3.48442 | −0.143451 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.354182 | 0.0145568 | ||||||||
\(593\) | −25.9594 | −1.06602 | −0.533012 | − | 0.846107i | \(-0.678940\pi\) | ||||
−0.533012 | + | 0.846107i | \(0.678940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.24456 | 0.133014 | ||||||||
\(596\) | 24.9059 | 1.02019 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.28395 | −0.338756 | ||||||||
\(599\) | −12.6905 | −0.518520 | −0.259260 | − | 0.965808i | \(-0.583479\pi\) | ||||
−0.259260 | + | 0.965808i | \(0.583479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.3306 | −1.03326 | −0.516628 | − | 0.856210i | \(-0.672813\pi\) | ||||
−0.516628 | + | 0.856210i | \(0.672813\pi\) | |||||||
\(602\) | 12.9442 | 0.527566 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.6610 | −0.881374 | ||||||||
\(605\) | −11.0000 | −0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.5251 | 1.52310 | 0.761548 | − | 0.648108i | \(-0.224439\pi\) | ||||
0.761548 | + | 0.648108i | \(0.224439\pi\) | |||||||
\(608\) | −11.4510 | −0.464401 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.57286 | 0.144661 | ||||||||
\(611\) | 11.2272 | 0.454205 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.8508 | −0.720988 | −0.360494 | − | 0.932761i | \(-0.617392\pi\) | ||||
−0.360494 | + | 0.932761i | \(0.617392\pi\) | |||||||
\(614\) | −9.82779 | −0.396617 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.45701 | −0.219691 | −0.109845 | − | 0.993949i | \(-0.535036\pi\) | ||||
−0.109845 | + | 0.993949i | \(0.535036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.7454 | 1.03480 | 0.517398 | − | 0.855745i | \(-0.326901\pi\) | ||||
0.517398 | + | 0.855745i | \(0.326901\pi\) | |||||||
\(620\) | 2.58312 | 0.103741 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0031 | 0.481279 | ||||||||
\(623\) | 1.82035 | 0.0729310 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.48741 | −0.379193 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.07354 | 0.282265 | ||||||||
\(629\) | 0.387887 | 0.0154661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.01663 | −0.358947 | −0.179473 | − | 0.983763i | \(-0.557439\pi\) | ||||
−0.179473 | + | 0.983763i | \(0.557439\pi\) | |||||||
\(632\) | 15.9739 | 0.635409 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.1160 | −0.481189 | ||||||||
\(635\) | 2.31939 | 0.0920420 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.2859 | −0.407543 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.1377 | 0.440258 | ||||||||
\(641\) | 3.27591 | 0.129391 | 0.0646954 | − | 0.997905i | \(-0.479392\pi\) | ||||
0.0646954 | + | 0.997905i | \(0.479392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.97703 | 0.117402 | 0.0587012 | − | 0.998276i | \(-0.481304\pi\) | ||||
0.0587012 | + | 0.998276i | \(0.481304\pi\) | |||||||
\(644\) | −13.0422 | −0.513934 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.32559 | −0.0914993 | ||||||||
\(647\) | 13.1367 | 0.516457 | 0.258229 | − | 0.966084i | \(-0.416861\pi\) | ||||
0.258229 | + | 0.966084i | \(0.416861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.82035 | −0.0714002 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.7968 | 0.736140 | ||||||||
\(653\) | 11.4476 | 0.447981 | 0.223991 | − | 0.974591i | \(-0.428092\pi\) | ||||
0.223991 | + | 0.974591i | \(0.428092\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.35678 | 0.209307 | ||||||||
\(656\) | 1.89705 | 0.0740675 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.77839 | −0.186281 | ||||||||
\(659\) | −9.21943 | −0.359138 | −0.179569 | − | 0.983745i | \(-0.557470\pi\) | ||||
−0.179569 | + | 0.983745i | \(0.557470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.4746 | −1.14643 | −0.573215 | − | 0.819405i | \(-0.694304\pi\) | ||||
−0.573215 | + | 0.819405i | \(0.694304\pi\) | |||||||
\(662\) | −9.49238 | −0.368932 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.12207 | 0.0823522 | ||||||||
\(665\) | 3.64071 | 0.141181 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.9939 | 1.47113 | ||||||||
\(668\) | −33.8437 | −1.30945 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.72165 | −0.259680 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.3371 | −0.938127 | −0.469063 | − | 0.883165i | \(-0.655408\pi\) | ||||
−0.469063 | + | 0.883165i | \(0.655408\pi\) | |||||||
\(674\) | −20.1119 | −0.774683 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.20920 | 0.315738 | ||||||||
\(677\) | 20.8965 | 0.803120 | 0.401560 | − | 0.915833i | \(-0.368468\pi\) | ||||
0.401560 | + | 0.915833i | \(0.368468\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.2657 | 0.393963 | ||||||||
\(680\) | 4.15629 | 0.159387 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.9543 | −1.64360 | −0.821800 | − | 0.569777i | \(-0.807030\pi\) | ||||
−0.821800 | + | 0.569777i | \(0.807030\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.72940 | −0.104285 | ||||||||
\(686\) | 12.6908 | 0.484536 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.7392 | −0.676303 | ||||||||
\(689\) | 5.16714 | 0.196852 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.65865 | 0.215265 | 0.107633 | − | 0.994191i | \(-0.465673\pi\) | ||||
0.107633 | + | 0.994191i | \(0.465673\pi\) | |||||||
\(692\) | 15.7622 | 0.599190 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.6273 | −0.441367 | ||||||||
\(695\) | −5.95281 | −0.225803 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.07758 | 0.0786941 | ||||||||
\(698\) | −2.40746 | −0.0911238 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.86595 | −0.108323 | ||||||||
\(701\) | −21.1882 | −0.800268 | −0.400134 | − | 0.916457i | \(-0.631037\pi\) | ||||
−0.400134 | + | 0.916457i | \(0.631037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.435247 | 0.0164157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.08624 | −0.191423 | ||||||||
\(707\) | 13.3424 | 0.501792 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.4198 | 1.21755 | 0.608775 | − | 0.793343i | \(-0.291661\pi\) | ||||
0.608775 | + | 0.793343i | \(0.291661\pi\) | |||||||
\(710\) | −1.09090 | −0.0409408 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.33188 | 0.0873910 | ||||||||
\(713\) | −7.46643 | −0.279620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.6001 | 0.919347 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.61218 | −0.172125 | ||||||||
\(719\) | 5.94389 | 0.221670 | 0.110835 | − | 0.993839i | \(-0.464648\pi\) | ||||
0.110835 | + | 0.993839i | \(0.464648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.7682 | −1.07138 | ||||||||
\(722\) | 9.78579 | 0.364189 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.7806 | −0.809470 | ||||||||
\(725\) | 8.34897 | 0.310073 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.02688 | 0.0751728 | 0.0375864 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375864 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(728\) | 11.8444 | 0.438984 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.08341 | 0.336192 | ||||||||
\(731\) | −19.4274 | −0.718547 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.253776 | 0.00937345 | 0.00468672 | − | 0.999989i | \(-0.498508\pi\) | ||||
0.00468672 | + | 0.999989i | \(0.498508\pi\) | |||||||
\(734\) | −4.46513 | −0.164811 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.0553 | −0.960412 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.3564 | −0.638466 | −0.319233 | − | 0.947676i | \(-0.603425\pi\) | ||||
−0.319233 | + | 0.947676i | \(0.603425\pi\) | |||||||
\(740\) | −0.342625 | −0.0125951 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.19917 | −0.0807341 | ||||||||
\(743\) | 13.1549 | 0.482605 | 0.241303 | − | 0.970450i | \(-0.422425\pi\) | ||||
0.241303 | + | 0.970450i | \(0.422425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8194 | −0.579577 | ||||||||
\(746\) | 9.71914 | 0.355843 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.17336 | −0.152491 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.6949 | −0.718675 | −0.359338 | − | 0.933208i | \(-0.616997\pi\) | ||||
−0.359338 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(752\) | 6.54850 | 0.238799 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.1981 | −0.553481 | ||||||||
\(755\) | 13.7583 | 0.500717 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.5117 | 0.709165 | 0.354582 | − | 0.935025i | \(-0.384623\pi\) | ||||
0.354582 | + | 0.935025i | \(0.384623\pi\) | |||||||
\(758\) | −9.59561 | −0.348528 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.66377 | 0.169173 | ||||||||
\(761\) | 9.91619 | 0.359462 | 0.179731 | − | 0.983716i | \(-0.442477\pi\) | ||||
0.179731 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1125 | 0.438502 | ||||||||
\(764\) | −2.35304 | −0.0851300 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.38907 | −0.0501890 | ||||||||
\(767\) | 14.9031 | 0.538121 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.392247 | −0.0141448 | −0.00707239 | − | 0.999975i | \(-0.502251\pi\) | ||||
−0.00707239 | + | 0.999975i | \(0.502251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.9572 | 0.502331 | ||||||||
\(773\) | 12.7537 | 0.458718 | 0.229359 | − | 0.973342i | \(-0.426337\pi\) | ||||
0.229359 | + | 0.973342i | \(0.426337\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.64071 | −0.0589360 | ||||||||
\(776\) | 13.1505 | 0.472074 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.77691 | 0.242964 | ||||||||
\(779\) | 2.33125 | 0.0835257 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.29158 | −0.189226 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.99946 | −0.214267 | ||||||||
\(785\) | −4.49287 | −0.160357 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.9336 | −0.639264 | −0.319632 | − | 0.947542i | \(-0.603559\pi\) | ||||
−0.319632 | + | 0.947542i | \(0.603559\pi\) | |||||||
\(788\) | −19.4054 | −0.691287 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.46899 | −0.159000 | ||||||||
\(791\) | −1.13457 | −0.0403405 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2814 | −0.542659 | ||||||||
\(794\) | 4.70094 | 0.166830 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.7964 | −1.19788 | ||||||||
\(797\) | 24.7798 | 0.877747 | 0.438873 | − | 0.898549i | \(-0.355378\pi\) | ||||
0.438873 | + | 0.898549i | \(0.355378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.17168 | 0.253716 | ||||||||
\(800\) | −5.72552 | −0.202428 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.16908 | 0.323771 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.28395 | 0.291971 | ||||||||
\(806\) | 2.98667 | 0.105201 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.0916 | 0.601282 | ||||||||
\(809\) | 7.10308 | 0.249731 | 0.124866 | − | 0.992174i | \(-0.460150\pi\) | ||||
0.124866 | + | 0.992174i | \(0.460150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.8724 | 0.873387 | 0.436694 | − | 0.899610i | \(-0.356149\pi\) | ||||
0.436694 | + | 0.899610i | \(0.356149\pi\) | |||||||
\(812\) | −23.9278 | −0.839699 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.9391 | −0.418208 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.7994 | −0.762664 | ||||||||
\(818\) | 9.57214 | 0.334682 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.83515 | −0.0640863 | ||||||||
\(821\) | 4.62542 | 0.161428 | 0.0807141 | − | 0.996737i | \(-0.474280\pi\) | ||||
0.0807141 | + | 0.996737i | \(0.474280\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.1088 | 1.50268 | 0.751339 | − | 0.659917i | \(-0.229408\pi\) | ||||
0.751339 | + | 0.659917i | \(0.229408\pi\) | |||||||
\(824\) | −36.8522 | −1.28381 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.34287 | −0.220697 | ||||||||
\(827\) | −14.0115 | −0.487228 | −0.243614 | − | 0.969872i | \(-0.578333\pi\) | ||||
−0.243614 | + | 0.969872i | \(0.578333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.980406 | 0.0340509 | 0.0170255 | − | 0.999855i | \(-0.494580\pi\) | ||||
0.0170255 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(830\) | −0.593686 | −0.0206072 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.34005 | 0.0464577 | ||||||||
\(833\) | −6.57039 | −0.227651 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.4963 | 0.743912 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.0886 | 0.555772 | ||||||||
\(839\) | 26.5036 | 0.915006 | 0.457503 | − | 0.889208i | \(-0.348744\pi\) | ||||
0.457503 | + | 0.889208i | \(0.348744\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.7052 | 1.40363 | ||||||||
\(842\) | −21.1843 | −0.730061 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.6442 | −0.366390 | ||||||||
\(845\) | −5.21420 | −0.179374 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0239 | −0.688029 | ||||||||
\(848\) | 3.01383 | 0.103495 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.16280 | −0.0398836 | ||||||||
\(851\) | 0.990346 | 0.0339486 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.72438 | −0.230238 | −0.115119 | − | 0.993352i | \(-0.536725\pi\) | ||||
−0.115119 | + | 0.993352i | \(0.536725\pi\) | |||||||
\(854\) | 6.50388 | 0.222558 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.34610 | −0.182726 | ||||||||
\(857\) | −38.5694 | −1.31751 | −0.658753 | − | 0.752359i | \(-0.728916\pi\) | ||||
−0.658753 | + | 0.752359i | \(0.728916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2437 | −0.485989 | −0.242994 | − | 0.970028i | \(-0.578130\pi\) | ||||
−0.242994 | + | 0.970028i | \(0.578130\pi\) | |||||||
\(860\) | 17.1604 | 0.585165 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.1828 | 0.687429 | ||||||||
\(863\) | 52.7921 | 1.79706 | 0.898532 | − | 0.438908i | \(-0.144635\pi\) | ||||
0.898532 | + | 0.438908i | \(0.144635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0116 | −0.340405 | ||||||||
\(866\) | −0.430512 | −0.0146294 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.70220 | 0.159603 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.7490 | 0.974123 | ||||||||
\(872\) | 15.5162 | 0.525444 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.93767 | −0.200845 | ||||||||
\(875\) | 1.82035 | 0.0615392 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.6756 | −1.84627 | −0.923133 | − | 0.384481i | \(-0.874380\pi\) | ||||
−0.923133 | + | 0.384481i | \(0.874380\pi\) | |||||||
\(878\) | −10.6759 | −0.360295 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.3990 | −0.855715 | −0.427858 | − | 0.903846i | \(-0.640732\pi\) | ||||
−0.427858 | + | 0.903846i | \(0.640732\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5793 | 0.726201 | 0.363101 | − | 0.931750i | \(-0.381718\pi\) | ||||
0.363101 | + | 0.931750i | \(0.381718\pi\) | |||||||
\(884\) | −7.83004 | −0.263353 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.5227 | −0.555091 | ||||||||
\(887\) | 25.5398 | 0.857541 | 0.428771 | − | 0.903413i | \(-0.358947\pi\) | ||||
0.428771 | + | 0.903413i | \(0.358947\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.22211 | 0.141605 | ||||||||
\(890\) | −0.652386 | −0.0218680 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −31.3794 | −1.05066 | ||||||||
\(893\) | 8.04732 | 0.269293 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.6251 | −0.522290 | ||||||||
\(896\) | 20.2746 | 0.677328 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.0834 | −0.369857 | ||||||||
\(899\) | −13.6982 | −0.456861 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.30064 | 0.109960 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.45338 | −0.0483388 | ||||||||
\(905\) | 13.8343 | 0.459867 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.0122 | 1.85985 | 0.929927 | − | 0.367743i | \(-0.119869\pi\) | ||||
0.929927 | + | 0.367743i | \(0.119869\pi\) | |||||||
\(908\) | 4.47316 | 0.148447 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.31369 | −0.109848 | ||||||||
\(911\) | −25.8303 | −0.855795 | −0.427897 | − | 0.903827i | \(-0.640746\pi\) | ||||
−0.427897 | + | 0.903827i | \(0.640746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 23.0176 | 0.761356 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.88644 | −0.161453 | ||||||||
\(917\) | 9.75124 | 0.322014 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.1130 | −0.564507 | −0.282253 | − | 0.959340i | \(-0.591082\pi\) | ||||
−0.282253 | + | 0.959340i | \(0.591082\pi\) | |||||||
\(920\) | 10.6118 | 0.349860 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.91937 | 0.194944 | ||||||||
\(923\) | 4.66587 | 0.153579 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.217624 | 0.00715542 | ||||||||
\(926\) | 13.9243 | 0.457580 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −47.8022 | −1.56918 | ||||||||
\(929\) | −5.83985 | −0.191599 | −0.0957997 | − | 0.995401i | \(-0.530541\pi\) | ||||
−0.0957997 | + | 0.995401i | \(0.530541\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.37262 | −0.241628 | ||||||||
\(932\) | 7.61632 | 0.249481 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.37584 | −0.143182 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −60.5365 | −1.97764 | −0.988821 | − | 0.149108i | \(-0.952360\pi\) | ||||
−0.988821 | + | 0.149108i | \(0.952360\pi\) | |||||||
\(938\) | −12.2358 | −0.399513 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.33482 | −0.206619 | ||||||||
\(941\) | −35.6006 | −1.16055 | −0.580273 | − | 0.814422i | \(-0.697054\pi\) | ||||
−0.580273 | + | 0.814422i | \(0.697054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.30445 | 0.172737 | ||||||||
\(944\) | 8.69253 | 0.282918 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.71771 | 0.185801 | 0.0929004 | − | 0.995675i | \(-0.470386\pi\) | ||||
0.0929004 | + | 0.995675i | \(0.470386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.8504 | −1.26114 | ||||||||
\(950\) | −1.30477 | −0.0423324 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.56593 | 0.245213 | ||||||||
\(953\) | 5.96701 | 0.193291 | 0.0966453 | − | 0.995319i | \(-0.469189\pi\) | ||||
0.0966453 | + | 0.995319i | \(0.469189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.49457 | 0.0483631 | ||||||||
\(956\) | −34.5325 | −1.11686 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.6574 | 0.441251 | ||||||||
\(959\) | −4.96847 | −0.160440 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3081 | −0.913164 | ||||||||
\(962\) | −0.396152 | −0.0127725 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.5372 | −0.597043 | ||||||||
\(965\) | −8.86514 | −0.285379 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.9553 | 0.384457 | 0.192228 | − | 0.981350i | \(-0.438429\pi\) | ||||
0.192228 | + | 0.981350i | \(0.438429\pi\) | |||||||
\(968\) | −25.6507 | −0.824445 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.67908 | −0.118128 | ||||||||
\(971\) | −21.2451 | −0.681789 | −0.340895 | − | 0.940102i | \(-0.610730\pi\) | ||||
−0.340895 | + | 0.940102i | \(0.610730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8362 | −0.347394 | ||||||||
\(974\) | −5.05922 | −0.162108 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.91318 | −0.285304 | ||||||||
\(977\) | 16.9619 | 0.542658 | 0.271329 | − | 0.962487i | \(-0.412537\pi\) | ||||
0.271329 | + | 0.962487i | \(0.412537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.80370 | 0.185392 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.59583 | 0.0509250 | ||||||||
\(983\) | 10.3405 | 0.329811 | 0.164906 | − | 0.986309i | \(-0.447268\pi\) | ||||
0.164906 | + | 0.986309i | \(0.447268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.3256 | 0.392727 | ||||||||
\(986\) | −9.70815 | −0.309171 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.78607 | −0.279522 | ||||||||
\(989\) | −49.6016 | −1.57724 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.6759 | −1.54624 | −0.773121 | − | 0.634259i | \(-0.781305\pi\) | ||||
−0.773121 | + | 0.634259i | \(0.781305\pi\) | |||||||
\(992\) | 9.39392 | 0.298257 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.98583 | −0.0629866 | ||||||||
\(995\) | 21.4663 | 0.680527 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.7687 | 1.57619 | 0.788096 | − | 0.615552i | \(-0.211067\pi\) | ||||
0.788096 | + | 0.615552i | \(0.211067\pi\) | |||||||
\(998\) | 24.4698 | 0.774578 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4005.2.a.n.1.2 | 6 | ||
3.2 | odd | 2 | 1335.2.a.g.1.5 | ✓ | 6 | ||
15.14 | odd | 2 | 6675.2.a.u.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1335.2.a.g.1.5 | ✓ | 6 | 3.2 | odd | 2 | ||
4005.2.a.n.1.2 | 6 | 1.1 | even | 1 | trivial | ||
6675.2.a.u.1.2 | 6 | 15.14 | odd | 2 |