Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, 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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0060616952\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.539189 | −0.241133 | −0.120566 | − | 0.992705i | \(-0.538471\pi\) | ||||
−0.120566 | + | 0.992705i | \(0.538471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.07838 | 0.407588 | 0.203794 | − | 0.979014i | \(-0.434673\pi\) | ||||
0.203794 | + | 0.979014i | \(0.434673\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.70928 | −1.11839 | −0.559194 | − | 0.829037i | \(-0.688889\pi\) | ||||
−0.559194 | + | 0.829037i | \(0.688889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.34017 | 1.20375 | 0.601874 | − | 0.798591i | \(-0.294421\pi\) | ||||
0.601874 | + | 0.798591i | \(0.294421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.46081 | 0.354299 | 0.177149 | − | 0.984184i | \(-0.443312\pi\) | ||||
0.177149 | + | 0.984184i | \(0.443312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.41855 | 0.784269 | 0.392135 | − | 0.919908i | \(-0.371737\pi\) | ||||
0.392135 | + | 0.919908i | \(0.371737\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.68035 | −1.80998 | −0.904989 | − | 0.425436i | \(-0.860121\pi\) | ||||
−0.904989 | + | 0.425436i | \(0.860121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.70928 | −0.941855 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.15676 | −0.400499 | −0.200250 | − | 0.979745i | \(-0.564175\pi\) | ||||
−0.200250 | + | 0.979745i | \(0.564175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.26180 | −0.226625 | −0.113313 | − | 0.993559i | \(-0.536146\pi\) | ||||
−0.113313 | + | 0.993559i | \(0.536146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.581449 | −0.0982829 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.7587 | 1.93312 | 0.966561 | − | 0.256436i | \(-0.0825484\pi\) | ||||
0.966561 | + | 0.256436i | \(0.0825484\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.95774 | −1.55514 | −0.777569 | − | 0.628798i | \(-0.783547\pi\) | ||||
−0.777569 | + | 0.628798i | \(0.783547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.80098 | −1.49464 | −0.747318 | − | 0.664467i | \(-0.768659\pi\) | ||||
−0.747318 | + | 0.664467i | \(0.768659\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.70928 | 1.12451 | 0.562257 | − | 0.826963i | \(-0.309933\pi\) | ||||
0.562257 | + | 0.826963i | \(0.309933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.83710 | −0.833872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.55971 | 1.31313 | 0.656563 | − | 0.754271i | \(-0.272009\pi\) | ||||
0.656563 | + | 0.754271i | \(0.272009\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.92162 | −0.901118 | −0.450559 | − | 0.892747i | \(-0.648775\pi\) | ||||
−0.450559 | + | 0.892747i | \(0.648775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70928 | 0.218850 | 0.109425 | − | 0.993995i | \(-0.465099\pi\) | ||||
0.109425 | + | 0.993995i | \(0.465099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.34017 | −0.290263 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.879362 | −0.107431 | −0.0537156 | − | 0.998556i | \(-0.517106\pi\) | ||||
−0.0537156 | + | 0.998556i | \(0.517106\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41855 | 0.166029 | 0.0830144 | − | 0.996548i | \(-0.473545\pi\) | ||||
0.0830144 | + | 0.996548i | \(0.473545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.8999 | −1.78888 | −0.894438 | − | 0.447192i | \(-0.852424\pi\) | ||||
−0.894438 | + | 0.447192i | \(0.852424\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.183417 | 0.0201327 | 0.0100663 | − | 0.999949i | \(-0.496796\pi\) | ||||
0.0100663 | + | 0.999949i | \(0.496796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.787653 | −0.0854330 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.15676 | −0.652615 | −0.326307 | − | 0.945264i | \(-0.605804\pi\) | ||||
−0.326307 | + | 0.945264i | \(0.605804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.68035 | 0.490634 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84324 | −0.189113 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.23513 | 0.937686 | 0.468843 | − | 0.883282i | \(-0.344671\pi\) | ||||
0.468843 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.72261 | 0.867932 | 0.433966 | − | 0.900929i | \(-0.357114\pi\) | ||||
0.433966 | + | 0.900929i | \(0.357114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.61757 | 0.356449 | 0.178225 | − | 0.983990i | \(-0.442965\pi\) | ||||
0.178225 | + | 0.983990i | \(0.442965\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.8082 | 1.14154 | 0.570770 | − | 0.821110i | \(-0.306645\pi\) | ||||
0.570770 | + | 0.821110i | \(0.306645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.921622 | −0.0882754 | −0.0441377 | − | 0.999025i | \(-0.514054\pi\) | ||||
−0.0441377 | + | 0.999025i | \(0.514054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0361 | −1.22633 | −0.613167 | − | 0.789953i | \(-0.710105\pi\) | ||||
−0.613167 | + | 0.789953i | \(0.710105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.68035 | 0.436445 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.57531 | 0.144408 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.75872 | 0.250793 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.23513 | 0.468245 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.34017 | 0.562599 | 0.281300 | − | 0.959620i | \(-0.409235\pi\) | ||||
0.281300 | + | 0.959620i | \(0.409235\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.60197 | −0.664187 | −0.332094 | − | 0.943246i | \(-0.607755\pi\) | ||||
−0.332094 | + | 0.943246i | \(0.607755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.68649 | 0.319659 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.92162 | −0.591354 | −0.295677 | − | 0.955288i | \(-0.595545\pi\) | ||||
−0.295677 | + | 0.955288i | \(0.595545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5392 | −1.40284 | −0.701418 | − | 0.712750i | \(-0.747449\pi\) | ||||
−0.701418 | + | 0.712750i | \(0.747449\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.0989 | −1.34626 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.16290 | 0.0965735 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0566 | 1.47926 | 0.739629 | − | 0.673015i | \(-0.235001\pi\) | ||||
0.739629 | + | 0.673015i | \(0.235001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.64423 | 0.296563 | 0.148282 | − | 0.988945i | \(-0.452626\pi\) | ||||
0.148282 | + | 0.988945i | \(0.452626\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.680346 | 0.0546467 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.2351 | −1.05628 | −0.528139 | − | 0.849158i | \(-0.677110\pi\) | ||||
−0.528139 | + | 0.849158i | \(0.677110\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.36069 | −0.737726 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.98440 | −0.155430 | −0.0777152 | − | 0.996976i | \(-0.524762\pi\) | ||||
−0.0777152 | + | 0.996976i | \(0.524762\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.83710 | 0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.5814 | −0.956550 | −0.478275 | − | 0.878210i | \(-0.658738\pi\) | ||||
−0.478275 | + | 0.878210i | \(0.658738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.07838 | −0.383889 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.3545 | −1.37188 | −0.685942 | − | 0.727657i | \(-0.740610\pi\) | ||||
−0.685942 | + | 0.727657i | \(0.740610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.2329 | −1.50390 | −0.751949 | − | 0.659222i | \(-0.770886\pi\) | ||||
−0.751949 | + | 0.659222i | \(0.770886\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.34017 | −0.466139 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.41855 | −0.396244 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.55252 | −0.401766 | −0.200883 | − | 0.979615i | \(-0.564381\pi\) | ||||
−0.200883 | + | 0.979615i | \(0.564381\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.424694 | −0.0305701 | −0.0152851 | − | 0.999883i | \(-0.504866\pi\) | ||||
−0.0152851 | + | 0.999883i | \(0.504866\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.27125 | 0.589302 | 0.294651 | − | 0.955605i | \(-0.404797\pi\) | ||||
0.294651 | + | 0.955605i | \(0.404797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.97334 | −0.139886 | −0.0699431 | − | 0.997551i | \(-0.522282\pi\) | ||||
−0.0699431 | + | 0.997551i | \(0.522282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.32580 | −0.163239 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.36910 | 0.374994 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.6803 | −0.877118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.10504 | 0.489131 | 0.244566 | − | 0.969633i | \(-0.421355\pi\) | ||||
0.244566 | + | 0.969633i | \(0.421355\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.28458 | 0.360405 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.36069 | −0.0923698 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.34017 | 0.426486 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.39803 | 0.294514 | 0.147257 | − | 0.989098i | \(-0.452956\pi\) | ||||
0.147257 | + | 0.989098i | \(0.452956\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3402 | −0.686301 | −0.343151 | − | 0.939280i | \(-0.611494\pi\) | ||||
−0.343151 | + | 0.939280i | \(0.611494\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.2907 | −0.944358 | −0.472179 | − | 0.881503i | \(-0.656532\pi\) | ||||
−0.472179 | + | 0.881503i | \(0.656532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.65368 | −0.435897 | −0.217949 | − | 0.975960i | \(-0.569937\pi\) | ||||
−0.217949 | + | 0.975960i | \(0.569937\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.15676 | −0.271157 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.5936 | −1.52614 | −0.763070 | − | 0.646316i | \(-0.776309\pi\) | ||||
−0.763070 | + | 0.646316i | \(0.776309\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.78539 | 0.372669 | 0.186335 | − | 0.982486i | \(-0.440339\pi\) | ||||
0.186335 | + | 0.982486i | \(0.440339\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.14730 | 0.201074 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.8371 | 0.944062 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0205 | −1.70552 | −0.852760 | − | 0.522303i | \(-0.825073\pi\) | ||||
−0.852760 | + | 0.522303i | \(0.825073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.1978 | 2.02426 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.48133 | −0.404294 | −0.202147 | − | 0.979355i | \(-0.564792\pi\) | ||||
−0.202147 | + | 0.979355i | \(0.564792\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.6803 | 0.787918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.97948 | −0.307048 | −0.153524 | − | 0.988145i | \(-0.549062\pi\) | ||||
−0.153524 | + | 0.988145i | \(0.549062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.15449 | −0.316638 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.8732 | −1.82140 | −0.910701 | − | 0.413066i | \(-0.864458\pi\) | ||||
−0.910701 | + | 0.413066i | \(0.864458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.48133 | −0.272221 | −0.136111 | − | 0.990694i | \(-0.543460\pi\) | ||||
−0.136111 | + | 0.990694i | \(0.543460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.4680 | 1.05336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7526 | −1.00657 | −0.503283 | − | 0.864122i | \(-0.667874\pi\) | ||||
−0.503283 | + | 0.864122i | \(0.667874\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.8576 | 1.06530 | 0.532648 | − | 0.846337i | \(-0.321197\pi\) | ||||
0.532648 | + | 0.846337i | \(0.321197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.94214 | −0.353224 | −0.176612 | − | 0.984281i | \(-0.556514\pi\) | ||||
−0.176612 | + | 0.984281i | \(0.556514\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7382 | −0.633856 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8660 | −0.874472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.68035 | −0.507111 | −0.253556 | − | 0.967321i | \(-0.581600\pi\) | ||||
−0.253556 | + | 0.967321i | \(0.581600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.73206 | 0.217289 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.6742 | −2.17876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5692 | −0.609196 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.921622 | −0.0527719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.8154 | 1.47336 | 0.736680 | − | 0.676241i | \(-0.236392\pi\) | ||||
0.736680 | + | 0.676241i | \(0.236392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.97948 | −0.282360 | −0.141180 | − | 0.989984i | \(-0.545090\pi\) | ||||
−0.141180 | + | 0.989984i | \(0.545090\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6742 | −0.659865 | −0.329932 | − | 0.944005i | \(-0.607026\pi\) | ||||
−0.329932 | + | 0.944005i | \(0.607026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.2557 | 0.576015 | 0.288007 | − | 0.957628i | \(-0.407007\pi\) | ||||
0.288007 | + | 0.957628i | \(0.407007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.99386 | 0.277866 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.4391 | −1.13376 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.31351 | 0.458339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5597 | 1.18503 | 0.592514 | − | 0.805560i | \(-0.298135\pi\) | ||||
0.592514 | + | 0.805560i | \(0.298135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.474142 | 0.0259052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.1194 | 1.58624 | 0.793118 | − | 0.609068i | \(-0.208456\pi\) | ||||
0.793118 | + | 0.609068i | \(0.208456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.68035 | 0.253455 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8432 | −0.747465 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.6020 | −0.622826 | −0.311413 | − | 0.950275i | \(-0.600802\pi\) | ||||
−0.311413 | + | 0.950275i | \(0.600802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.24128 | −0.227030 | −0.113515 | − | 0.993536i | \(-0.536211\pi\) | ||||
−0.113515 | + | 0.993536i | \(0.536211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.8638 | 1.11047 | 0.555233 | − | 0.831695i | \(-0.312629\pi\) | ||||
0.555233 | + | 0.831695i | \(0.312629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.15676 | 0.114469 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.2039 | 1.22466 | 0.612328 | − | 0.790603i | \(-0.290233\pi\) | ||||
0.612328 | + | 0.790603i | \(0.290233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.31351 | −0.384922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.764867 | −0.0400350 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.2967 | 1.89467 | 0.947336 | − | 0.320242i | \(-0.103764\pi\) | ||||
0.947336 | + | 0.320242i | \(0.103764\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3090 | 0.535215 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.1834 | −0.527277 | −0.263639 | − | 0.964622i | \(-0.584923\pi\) | ||||
−0.263639 | + | 0.964622i | \(0.584923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.36069 | −0.482100 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.638086 | −0.0327763 | −0.0163881 | − | 0.999866i | \(-0.505217\pi\) | ||||
−0.0163881 | + | 0.999866i | \(0.505217\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.7031 | 0.649100 | 0.324550 | − | 0.945869i | \(-0.394787\pi\) | ||||
0.324550 | + | 0.945869i | \(0.394787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.15676 | 0.109918 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.5597 | 1.19452 | 0.597262 | − | 0.802046i | \(-0.296255\pi\) | ||||
0.597262 | + | 0.802046i | \(0.296255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.6803 | −0.641273 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.57304 | 0.431356 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.546377 | −0.0274219 | −0.0137109 | − | 0.999906i | \(-0.504364\pi\) | ||||
−0.0137109 | + | 0.999906i | \(0.504364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4173 | 0.670029 | 0.335015 | − | 0.942213i | \(-0.391259\pi\) | ||||
0.335015 | + | 0.942213i | \(0.391259\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.47641 | −0.272799 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −43.6163 | −2.16198 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.6514 | −1.36727 | −0.683637 | − | 0.729822i | \(-0.739603\pi\) | ||||
−0.683637 | + | 0.729822i | \(0.739603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.46412 | −0.367286 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0988967 | −0.00485465 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.5525 | 0.662084 | 0.331042 | − | 0.943616i | \(-0.392600\pi\) | ||||
0.331042 | + | 0.943616i | \(0.392600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8059 | 1.01402 | 0.507009 | − | 0.861941i | \(-0.330751\pi\) | ||||
0.507009 | + | 0.861941i | \(0.330751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.87936 | −0.333698 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.84324 | 0.0892009 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.70701 | −0.323065 | −0.161533 | − | 0.986867i | \(-0.551644\pi\) | ||||
−0.161533 | + | 0.986867i | \(0.551644\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.4885 | 0.888501 | 0.444251 | − | 0.895902i | \(-0.353470\pi\) | ||||
0.444251 | + | 0.895902i | \(0.353470\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.6742 | −1.41951 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.48133 | 0.118427 | 0.0592137 | − | 0.998245i | \(-0.481141\pi\) | ||||
0.0592137 | + | 0.998245i | \(0.481141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.02505 | −0.238748 | −0.119374 | − | 0.992849i | \(-0.538089\pi\) | ||||
−0.119374 | + | 0.992849i | \(0.538089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.31965 | 0.157367 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.43907 | −0.303878 | −0.151939 | − | 0.988390i | \(-0.548552\pi\) | ||||
−0.151939 | + | 0.988390i | \(0.548552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.9360 | 1.73925 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.52359 | −0.118308 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.9939 | −1.26272 | −0.631360 | − | 0.775490i | \(-0.717503\pi\) | ||||
−0.631360 | + | 0.775490i | \(0.717503\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.3340 | −0.527878 | −0.263939 | − | 0.964539i | \(-0.585022\pi\) | ||||
−0.263939 | + | 0.964539i | \(0.585022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.89374 | 0.413327 | 0.206664 | − | 0.978412i | \(-0.433739\pi\) | ||||
0.206664 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.5174 | −0.903160 | −0.451580 | − | 0.892231i | \(-0.649139\pi\) | ||||
−0.451580 | + | 0.892231i | \(0.649139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.948284 | −0.0437877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.3545 | 1.67158 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0989 | −0.738668 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3074 | −0.790794 | −0.395397 | − | 0.918510i | \(-0.629393\pi\) | ||||
−0.395397 | + | 0.918510i | \(0.629393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.0349 | 2.32699 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.97948 | −0.226107 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.0833 | −1.27258 | −0.636288 | − | 0.771452i | \(-0.719531\pi\) | ||||
−0.636288 | + | 0.771452i | \(0.719531\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.9649 | −1.35230 | −0.676149 | − | 0.736765i | \(-0.736352\pi\) | ||||
−0.676149 | + | 0.736765i | \(0.736352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.15061 | −0.141896 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.31351 | −0.193487 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.9143 | −1.42868 | −0.714339 | − | 0.699800i | \(-0.753273\pi\) | ||||
−0.714339 | + | 0.699800i | \(0.753273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.2267 | −1.21398 | −0.606990 | − | 0.794710i | \(-0.707623\pi\) | ||||
−0.606990 | + | 0.794710i | \(0.707623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.70313 | −0.209287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.6537 | −1.00411 | −0.502053 | − | 0.864837i | \(-0.667422\pi\) | ||||
−0.502053 | + | 0.864837i | \(0.667422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.52973 | 0.0676714 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.95055 | −0.0859516 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.5958 | −1.25764 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.6647 | −0.730096 | −0.365048 | − | 0.930989i | \(-0.618947\pi\) | ||||
−0.365048 | + | 0.930989i | \(0.618947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.1399 | −1.49284 | −0.746418 | − | 0.665478i | \(-0.768228\pi\) | ||||
−0.746418 | + | 0.665478i | \(0.768228\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.84324 | −0.0802930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.3484 | 2.27602 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.2183 | −1.87199 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.36683 | −0.275262 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.6514 | 0.932593 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.5503 | −0.453591 | −0.226795 | − | 0.973942i | \(-0.572825\pi\) | ||||
−0.226795 | + | 0.973942i | \(0.572825\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.496928 | 0.0212861 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2979 | −0.525821 | −0.262910 | − | 0.964820i | \(-0.584682\pi\) | ||||
−0.262910 | + | 0.964820i | \(0.584682\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.37298 | −0.314099 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.1461 | −0.729125 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5609 | 0.744080 | 0.372040 | − | 0.928217i | \(-0.378658\pi\) | ||||
0.372040 | + | 0.928217i | \(0.378658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.5380 | −1.79916 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2245 | 0.768069 | 0.384035 | − | 0.923319i | \(-0.374534\pi\) | ||||
0.384035 | + | 0.923319i | \(0.374534\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.02893 | 0.295709 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.89988 | −0.0796471 | −0.0398236 | − | 0.999207i | \(-0.512680\pi\) | ||||
−0.0398236 | + | 0.999207i | \(0.512680\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.3701 | 0.685069 | 0.342535 | − | 0.939505i | \(-0.388715\pi\) | ||||
0.342535 | + | 0.939505i | \(0.388715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.8781 | 1.70474 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.5525 | −0.980504 | −0.490252 | − | 0.871581i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871581i | \(0.663095\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.197793 | 0.00820585 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.4596 | −1.46859 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.3874 | 0.965299 | 0.482650 | − | 0.875813i | \(-0.339674\pi\) | ||||
0.482650 | + | 0.875813i | \(0.339674\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.31351 | −0.177735 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 46.5802 | 1.91282 | 0.956410 | − | 0.292026i | \(-0.0943294\pi\) | ||||
0.956410 | + | 0.292026i | \(0.0943294\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.849388 | −0.0348215 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.3135 | −0.829988 | −0.414994 | − | 0.909824i | \(-0.636216\pi\) | ||||
−0.414994 | + | 0.909824i | \(0.636216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3607 | −0.626576 | −0.313288 | − | 0.949658i | \(-0.601430\pi\) | ||||
−0.313288 | + | 0.949658i | \(0.601430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.48747 | −0.0604744 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.7682 | 0.680599 | 0.340300 | − | 0.940317i | \(-0.389471\pi\) | ||||
0.340300 | + | 0.940317i | \(0.389471\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.4596 | 1.35363 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0761 | −0.568529 | −0.284264 | − | 0.958746i | \(-0.591749\pi\) | ||||
−0.284264 | + | 0.958746i | \(0.591749\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.7854 | −1.60170 | −0.800850 | − | 0.598865i | \(-0.795618\pi\) | ||||
−0.800850 | + | 0.598865i | \(0.795618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.7887 | −1.19731 | −0.598654 | − | 0.801007i | \(-0.704298\pi\) | ||||
−0.598654 | + | 0.801007i | \(0.704298\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.63931 | −0.265998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.7237 | 0.828946 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.1773 | 0.684903 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.2122 | 1.60082 | 0.800411 | − | 0.599452i | \(-0.204615\pi\) | ||||
0.800411 | + | 0.599452i | \(0.204615\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.41855 | −0.135661 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.3340 | −1.00377 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.08944 | −0.0430303 | −0.0215152 | − | 0.999769i | \(-0.506849\pi\) | ||||
−0.0215152 | + | 0.999769i | \(0.506849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.7308 | −0.778108 | −0.389054 | − | 0.921215i | \(-0.627198\pi\) | ||||
−0.389054 | + | 0.921215i | \(0.627198\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6270 | 0.653676 | 0.326838 | − | 0.945080i | \(-0.394017\pi\) | ||||
0.326838 | + | 0.945080i | \(0.394017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.6742 | 1.00780 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.6225 | −0.572222 | −0.286111 | − | 0.958196i | \(-0.592363\pi\) | ||||
−0.286111 | + | 0.958196i | \(0.592363\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.09890 | 0.160157 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.9504 | −1.82893 | −0.914463 | − | 0.404669i | \(-0.867387\pi\) | ||||
−0.914463 | + | 0.404669i | \(0.867387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.4801 | 1.18554 | 0.592769 | − | 0.805372i | \(-0.298035\pi\) | ||||
0.592769 | + | 0.805372i | \(0.298035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.98771 | −0.0770802 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.7214 | 0.724895 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.34017 | −0.244760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.51745 | 0.366871 | 0.183435 | − | 0.983032i | \(-0.441278\pi\) | ||||
0.183435 | + | 0.983032i | \(0.441278\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.1445 | 1.08168 | 0.540840 | − | 0.841126i | \(-0.318106\pi\) | ||||
0.540840 | + | 0.841126i | \(0.318106\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.95896 | 0.382190 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0267 | 0.995883 | 0.497941 | − | 0.867211i | \(-0.334090\pi\) | ||||
0.497941 | + | 0.867211i | \(0.334090\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.73206 | 0.142595 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.4908 | 1.58067 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.1412 | −0.994456 | −0.497228 | − | 0.867620i | \(-0.665649\pi\) | ||||
−0.497228 | + | 0.867620i | \(0.665649\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.91775 | 0.338269 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.5464 | −0.550983 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0616 | −0.946562 | −0.473281 | − | 0.880912i | \(-0.656930\pi\) | ||||
−0.473281 | + | 0.880912i | \(0.656930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.1978 | 1.51609 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.40626 | 0.353759 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.3812 | 0.840544 | 0.420272 | − | 0.907398i | \(-0.361935\pi\) | ||||
0.420272 | + | 0.907398i | \(0.361935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.9528 | 0.410186 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.68035 | 0.324627 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.3607 | 0.647445 | 0.323722 | − | 0.946152i | \(-0.395066\pi\) | ||||
0.323722 | + | 0.946152i | \(0.395066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.90110 | 0.145285 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.1568 | 0.377212 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.2401 | 1.19572 | 0.597859 | − | 0.801602i | \(-0.296018\pi\) | ||||
0.597859 | + | 0.801602i | \(0.296018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.3174 | −0.529548 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.7093 | 0.654107 | 0.327054 | − | 0.945006i | \(-0.393944\pi\) | ||||
0.327054 | + | 0.945006i | \(0.393944\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.26180 | 0.120150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.3701 | 1.26433 | 0.632163 | − | 0.774835i | \(-0.282167\pi\) | ||||
0.632163 | + | 0.774835i | \(0.282167\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.5174 | 0.422534 | 0.211267 | − | 0.977428i | \(-0.432241\pi\) | ||||
0.211267 | + | 0.977428i | \(0.432241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.73594 | −0.356697 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.7337 | 0.465278 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.6647 | −0.389162 | −0.194581 | − | 0.980886i | \(-0.562335\pi\) | ||||
−0.194581 | + | 0.980886i | \(0.562335\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.96493 | −0.0715110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.5113 | 1.69048 | 0.845241 | − | 0.534385i | \(-0.179457\pi\) | ||||
0.845241 | + | 0.534385i | \(0.179457\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.7259 | 1.76631 | 0.883157 | − | 0.469078i | \(-0.155414\pi\) | ||||
0.883157 | + | 0.469078i | \(0.155414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.993857 | −0.0359800 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.0410 | −1.08472 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.3607 | 1.41938 | 0.709691 | − | 0.704513i | \(-0.248834\pi\) | ||||
0.709691 | + | 0.704513i | \(0.248834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.9204 | −0.896324 | −0.448162 | − | 0.893952i | \(-0.647921\pi\) | ||||
−0.448162 | + | 0.893952i | \(0.647921\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.94214 | 0.213448 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.0410 | −1.21965 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.8371 | 0.530913 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.13624 | 0.254703 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.6237 | 0.592571 | 0.296286 | − | 0.955099i | \(-0.404252\pi\) | ||||
0.296286 | + | 0.955099i | \(0.404252\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0579 | −0.499840 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.41855 | 0.263440 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.7698 | −0.558595 | −0.279297 | − | 0.960205i | \(-0.590101\pi\) | ||||
−0.279297 | + | 0.960205i | \(0.590101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2618 | 0.398414 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.26180 | −0.185685 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.04718 | 0.177890 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.1256 | 1.62169 | 0.810844 | − | 0.585262i | \(-0.199008\pi\) | ||||
0.810844 | + | 0.585262i | \(0.199008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.2401 | −0.991642 | −0.495821 | − | 0.868425i | \(-0.665133\pi\) | ||||
−0.495821 | + | 0.868425i | \(0.665133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.06997 | 0.0374793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.5052 | −1.17220 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.27739 | 0.184182 | 0.0920912 | − | 0.995751i | \(-0.470645\pi\) | ||||
0.0920912 | + | 0.995751i | \(0.470645\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.2089 | 1.33188 | 0.665939 | − | 0.746007i | \(-0.268031\pi\) | ||||
0.665939 | + | 0.746007i | \(0.268031\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.8043 | 0.758210 | 0.379105 | − | 0.925354i | \(-0.376232\pi\) | ||||
0.379105 | + | 0.925354i | \(0.376232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0784 | −0.662619 | −0.331310 | − | 0.943522i | \(-0.607490\pi\) | ||||
−0.331310 | + | 0.943522i | \(0.607490\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.52690 | −0.295440 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.539189 | −0.0186594 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0289 | −0.518856 | −0.259428 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259428 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3484 | −0.839600 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.14730 | −0.108270 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.97495 | 0.102220 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −102.070 | −3.49891 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.9542 | −1.60768 | −0.803841 | − | 0.594844i | \(-0.797214\pi\) | ||||
−0.803841 | + | 0.594844i | \(0.797214\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.1050 | 1.33580 | 0.667901 | − | 0.744250i | \(-0.267193\pi\) | ||||
0.667901 | + | 0.744250i | \(0.267193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.1711 | −1.57534 | −0.787669 | − | 0.616098i | \(-0.788712\pi\) | ||||
−0.787669 | + | 0.616098i | \(0.788712\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.5380 | 0.494878 | 0.247439 | − | 0.968903i | \(-0.420411\pi\) | ||||
0.247439 | + | 0.968903i | \(0.420411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.78378 | 0.230655 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.9770 | 2.00066 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.81658 | −0.129320 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.64545 | 0.190851 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.9504 | 1.24773 | 0.623863 | − | 0.781534i | \(-0.285562\pi\) | ||||
0.623863 | + | 0.781534i | \(0.285562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.6959 | 0.360356 | 0.180178 | − | 0.983634i | \(-0.442333\pi\) | ||||
0.180178 | + | 0.983634i | \(0.442333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.7731 | −1.13656 | −0.568278 | − | 0.822837i | \(-0.692390\pi\) | ||||
−0.568278 | + | 0.822837i | \(0.692390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.1748 | −1.91974 | −0.959871 | − | 0.280440i | \(-0.909519\pi\) | ||||
−0.959871 | + | 0.280440i | \(0.909519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.83710 | 0.229309 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.3545 | 0.881921 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.89657 | 0.330806 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.72138 | 0.0907632 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.9649 | 0.465239 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9093 | 0.362639 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.0205 | 1.03002 | 0.515010 | − | 0.857184i | \(-0.327788\pi\) | ||||
0.515010 | + | 0.857184i | \(0.327788\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7214 | 0.620267 | 0.310134 | − | 0.950693i | \(-0.399626\pi\) | ||||
0.310134 | + | 0.950693i | \(0.399626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.680346 | −0.0225162 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.19779 | −0.270715 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.5958 | −0.547446 | −0.273723 | − | 0.961809i | \(-0.588255\pi\) | ||||
−0.273723 | + | 0.961809i | \(0.588255\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.3607 | −0.571434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −55.3751 | −1.82072 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.2557 | 1.91131 | 0.955653 | − | 0.294495i | \(-0.0951515\pi\) | ||||
0.955653 | + | 0.294495i | \(0.0951515\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.9544 | −0.653980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.92162 | 0.0955473 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.8326 | −0.615233 | −0.307617 | − | 0.951510i | \(-0.599531\pi\) | ||||
−0.307617 | + | 0.951510i | \(0.599531\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.3123 | −0.988152 | −0.494076 | − | 0.869419i | \(-0.664494\pi\) | ||||
−0.494076 | + | 0.869419i | \(0.664494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 86.4366 | 2.81476 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.1750 | −1.30551 | −0.652756 | − | 0.757568i | \(-0.726387\pi\) | ||||
−0.652756 | + | 0.757568i | \(0.726387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.15676 | 0.199857 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4440 | 1.40729 | 0.703644 | − | 0.710552i | \(-0.251555\pi\) | ||||
0.703644 | + | 0.710552i | \(0.251555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.99386 | 0.0968789 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.46412 | −0.241029 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4079 | −0.948641 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.228990 | 0.00737145 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.60650 | −0.0516617 | −0.0258308 | − | 0.999666i | \(-0.508223\pi\) | ||||
−0.0258308 | + | 0.999666i | \(0.508223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5609 | 0.691923 | 0.345962 | − | 0.938249i | \(-0.387553\pi\) | ||||
0.345962 | + | 0.938249i | \(0.387553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.8355 | −0.571780 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.1966 | 1.79789 | 0.898944 | − | 0.438064i | \(-0.144336\pi\) | ||||
0.898944 | + | 0.438064i | \(0.144336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.8371 | 0.729877 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.7259 | 1.04379 | 0.521897 | − | 0.853008i | \(-0.325224\pi\) | ||||
0.521897 | + | 0.853008i | \(0.325224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.45977 | −0.142100 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 85.0759 | 2.70526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.7370 | −0.976392 | −0.488196 | − | 0.872734i | \(-0.662345\pi\) | ||||
−0.488196 | + | 0.872734i | \(0.662345\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.06400 | 0.0337311 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.3789 | −0.930440 | −0.465220 | − | 0.885195i | \(-0.654025\pi\) | ||||
−0.465220 | + | 0.885195i | \(0.654025\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 6012.2.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 6012.2.a.c.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
6012.2.a.c.1.2 | yes | 3 | 3.2 | odd | 2 |