Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −2.35470 | −1.35949 | −0.679743 | − | 0.733450i | \(-0.737909\pi\) | ||||
−0.679743 | + | 0.733450i | \(0.737909\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.425735 | 0.190394 | 0.0951971 | − | 0.995458i | \(-0.469652\pi\) | ||||
0.0951971 | + | 0.995458i | \(0.469652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.578482 | −0.218646 | −0.109323 | − | 0.994006i | \(-0.534868\pi\) | ||||
−0.109323 | + | 0.994006i | \(0.534868\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.54461 | 0.848203 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.03768 | −1.21741 | −0.608703 | − | 0.793398i | \(-0.708310\pi\) | ||||
−0.608703 | + | 0.793398i | \(0.708310\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.33254 | −0.924281 | −0.462141 | − | 0.886807i | \(-0.652918\pi\) | ||||
−0.462141 | + | 0.886807i | \(0.652918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00248 | −0.258838 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.84439 | −1.90254 | −0.951271 | − | 0.308355i | \(-0.900222\pi\) | ||||
−0.951271 | + | 0.308355i | \(0.900222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.14927 | −0.493076 | −0.246538 | − | 0.969133i | \(-0.579293\pi\) | ||||
−0.246538 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.36215 | 0.297246 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.686334 | −0.143111 | −0.0715553 | − | 0.997437i | \(-0.522796\pi\) | ||||
−0.0715553 | + | 0.997437i | \(0.522796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.81875 | −0.963750 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.07231 | 0.206365 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.07780 | −0.571533 | −0.285766 | − | 0.958299i | \(-0.592248\pi\) | ||||
−0.285766 | + | 0.958299i | \(0.592248\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.74521 | −0.672660 | −0.336330 | − | 0.941744i | \(-0.609186\pi\) | ||||
−0.336330 | + | 0.941744i | \(0.609186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.50752 | 1.65505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.246280 | −0.0416289 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.44935 | −0.895867 | −0.447934 | − | 0.894067i | \(-0.647840\pi\) | ||||
−0.447934 | + | 0.894067i | \(0.647840\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.84714 | 1.25655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.94114 | −0.459328 | −0.229664 | − | 0.973270i | \(-0.573763\pi\) | ||||
−0.229664 | + | 0.973270i | \(0.573763\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8673 | 1.65725 | 0.828627 | − | 0.559801i | \(-0.189122\pi\) | ||||
0.828627 | + | 0.559801i | \(0.189122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.08333 | 0.161493 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.16598 | −0.607671 | −0.303836 | − | 0.952724i | \(-0.598267\pi\) | ||||
−0.303836 | + | 0.952724i | \(0.598267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66536 | −0.952194 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.4712 | 2.58648 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0788 | −1.38443 | −0.692217 | − | 0.721689i | \(-0.743366\pi\) | ||||
−0.692217 | + | 0.721689i | \(0.743366\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.71898 | −0.231787 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.06088 | 0.670330 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.27982 | 1.07794 | 0.538971 | − | 0.842325i | \(-0.318813\pi\) | ||||
0.538971 | + | 0.842325i | \(0.318813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2143 | −1.56388 | −0.781939 | − | 0.623355i | \(-0.785769\pi\) | ||||
−0.781939 | + | 0.623355i | \(0.785769\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.47201 | −0.185456 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.41878 | −0.175978 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.40169 | −0.904261 | −0.452130 | − | 0.891952i | \(-0.649336\pi\) | ||||
−0.452130 | + | 0.891952i | \(0.649336\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.61611 | 0.194557 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.81940 | −0.215923 | −0.107962 | − | 0.994155i | \(-0.534432\pi\) | ||||
−0.107962 | + | 0.994155i | \(0.534432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6016 | 1.35787 | 0.678934 | − | 0.734199i | \(-0.262442\pi\) | ||||
0.678934 | + | 0.734199i | \(0.262442\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.3467 | 1.31021 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.33573 | 0.266181 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.2276 | 1.71324 | 0.856620 | − | 0.515947i | \(-0.172560\pi\) | ||||
0.856620 | + | 0.515947i | \(0.172560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1588 | −1.12875 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.49183 | 0.822335 | 0.411167 | − | 0.911560i | \(-0.365121\pi\) | ||||
0.411167 | + | 0.911560i | \(0.365121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.33963 | −0.362233 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.24729 | 0.776991 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.487590 | −0.0516844 | −0.0258422 | − | 0.999666i | \(-0.508227\pi\) | ||||
−0.0258422 | + | 0.999666i | \(0.508227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.92782 | 0.202090 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.81886 | 0.914473 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.915018 | −0.0938789 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00611 | 0.508293 | 0.254147 | − | 0.967166i | \(-0.418205\pi\) | ||||
0.254147 | + | 0.967166i | \(0.418205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.2743 | −1.03261 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.389675 | 0.0387741 | 0.0193871 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193871 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.42326 | 0.238771 | 0.119386 | − | 0.992848i | \(-0.461908\pi\) | ||||
0.119386 | + | 0.992848i | \(0.461908\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.579915 | 0.0565939 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.95974 | −0.672823 | −0.336412 | − | 0.941715i | \(-0.609213\pi\) | ||||
−0.336412 | + | 0.941715i | \(0.609213\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.29549 | 0.698781 | 0.349390 | − | 0.936977i | \(-0.386389\pi\) | ||||
0.349390 | + | 0.936977i | \(0.386389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8316 | 1.21792 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.84270 | 0.925924 | 0.462962 | − | 0.886378i | \(-0.346787\pi\) | ||||
0.462962 | + | 0.886378i | \(0.346787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.292196 | −0.0272474 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.48002 | −0.783978 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.53784 | 0.415983 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.30284 | 0.482077 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.92549 | 0.624450 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.18018 | −0.373887 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.2346 | −1.52932 | −0.764661 | − | 0.644433i | \(-0.777094\pi\) | ||||
−0.764661 | + | 0.644433i | \(0.777094\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.5893 | −2.25302 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3091 | −1.16282 | −0.581411 | − | 0.813610i | \(-0.697499\pi\) | ||||
−0.581411 | + | 0.813610i | \(0.697499\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.24331 | 0.107809 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.456518 | 0.0392908 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.83442 | −0.327596 | −0.163798 | − | 0.986494i | \(-0.552375\pi\) | ||||
−0.163798 | + | 0.986494i | \(0.552375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7402 | −1.33507 | −0.667534 | − | 0.744579i | \(-0.732650\pi\) | ||||
−0.667534 | + | 0.744579i | \(0.732650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.80964 | 0.826121 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.4557 | 1.12523 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.31032 | −0.108817 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.6949 | 1.29449 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.24421 | −0.511546 | −0.255773 | − | 0.966737i | \(-0.582330\pi\) | ||||
−0.255773 | + | 0.966737i | \(0.582330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.44920 | 0.443450 | 0.221725 | − | 0.975109i | \(-0.428831\pi\) | ||||
0.221725 | + | 0.975109i | \(0.428831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.9609 | −1.61374 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.59447 | −0.128071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.764245 | 0.0609934 | 0.0304967 | − | 0.999535i | \(-0.490291\pi\) | ||||
0.0304967 | + | 0.999535i | \(0.490291\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.7326 | 1.88212 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.397032 | 0.0312905 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.1108 | −1.34022 | −0.670111 | − | 0.742261i | \(-0.733754\pi\) | ||||
−0.670111 | + | 0.742261i | \(0.733754\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.04768 | 0.315111 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.81723 | 0.450151 | 0.225075 | − | 0.974341i | \(-0.427737\pi\) | ||||
0.225075 | + | 0.974341i | \(0.427737\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.89416 | −0.145704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.46905 | −0.418229 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.4925 | −1.86213 | −0.931064 | − | 0.364857i | \(-0.881118\pi\) | ||||
−0.931064 | + | 0.364857i | \(0.881118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.78756 | 0.210720 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.4965 | −1.46545 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.9428 | −1.86431 | −0.932155 | − | 0.362059i | \(-0.882074\pi\) | ||||
−0.932155 | + | 0.362059i | \(0.882074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.82699 | −0.433117 | −0.216559 | − | 0.976270i | \(-0.569483\pi\) | ||||
−0.216559 | + | 0.976270i | \(0.569483\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.7610 | 2.12607 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.31997 | −0.170568 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.6731 | 2.31617 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.620310 | −0.0451209 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8190 | −0.999907 | −0.499953 | − | 0.866052i | \(-0.666650\pi\) | ||||
−0.499953 | + | 0.866052i | \(0.666650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.49356 | −0.395435 | −0.197718 | − | 0.980259i | \(-0.563353\pi\) | ||||
−0.197718 | + | 0.980259i | \(0.563353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.34080 | 0.239239 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.80083 | 0.413292 | 0.206646 | − | 0.978416i | \(-0.433745\pi\) | ||||
0.206646 | + | 0.978416i | \(0.433745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5121 | 0.957845 | 0.478923 | − | 0.877857i | \(-0.341027\pi\) | ||||
0.478923 | + | 0.877857i | \(0.341027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.4288 | 1.22933 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.78045 | 0.124963 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.25214 | −0.0874535 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.74645 | −0.121387 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.67806 | 0.600274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.955150 | 0.0657552 | 0.0328776 | − | 0.999459i | \(-0.489533\pi\) | ||||
0.0328776 | + | 0.999459i | \(0.489533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.28414 | 0.293545 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.62660 | 0.315532 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.16654 | 0.147074 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.3183 | −1.84600 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.1418 | 1.75848 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9958 | 1.40598 | 0.702992 | − | 0.711197i | \(-0.251847\pi\) | ||||
0.702992 | + | 0.711197i | \(0.251847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.2618 | −0.817456 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.92570 | −0.326930 | −0.163465 | − | 0.986549i | \(-0.552267\pi\) | ||||
−0.163465 | + | 0.986549i | \(0.552267\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.7148 | 1.43495 | 0.717477 | − | 0.696583i | \(-0.245297\pi\) | ||||
0.717477 | + | 0.696583i | \(0.245297\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.49993 | −0.361869 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.5291 | 1.14837 | 0.574184 | − | 0.818727i | \(-0.305320\pi\) | ||||
0.574184 | + | 0.818727i | \(0.305320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.77360 | −0.115697 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35.8565 | −2.32913 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.69333 | 0.174217 | 0.0871086 | − | 0.996199i | \(-0.472237\pi\) | ||||
0.0871086 | + | 0.996199i | \(0.472237\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4270 | −1.83115 | −0.915573 | − | 0.402152i | \(-0.868262\pi\) | ||||
−0.915573 | + | 0.402152i | \(0.868262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.7040 | 1.32816 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.83767 | −0.181292 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.16253 | 0.455741 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.6410 | −1.11795 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.30627 | −0.587407 | −0.293703 | − | 0.955897i | \(-0.594888\pi\) | ||||
−0.293703 | + | 0.955897i | \(0.594888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.77120 | 0.174224 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.86382 | 0.492451 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.6483 | 1.59990 | 0.799950 | − | 0.600067i | \(-0.204859\pi\) | ||||
0.799950 | + | 0.600067i | \(0.204859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.15235 | 0.195878 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.83179 | −0.484776 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.3920 | 1.25743 | 0.628713 | − | 0.777637i | \(-0.283582\pi\) | ||||
0.628713 | + | 0.777637i | \(0.283582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.29091 | −0.263588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.14813 | 0.0702642 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.377432 | −0.0230124 | −0.0115062 | − | 0.999934i | \(-0.503663\pi\) | ||||
−0.0115062 | + | 0.999934i | \(0.503663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4554 | 0.756609 | 0.378304 | − | 0.925681i | \(-0.376507\pi\) | ||||
0.378304 | + | 0.925681i | \(0.376507\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.53943 | −0.274739 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.4566 | 1.17327 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.69975 | −0.342465 | −0.171233 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171233 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.53011 | −0.570553 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.53871 | 0.151447 | 0.0757233 | − | 0.997129i | \(-0.475873\pi\) | ||||
0.0757233 | + | 0.997129i | \(0.475873\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5674 | −0.806496 | −0.403248 | − | 0.915091i | \(-0.632119\pi\) | ||||
−0.403248 | + | 0.915091i | \(0.632119\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.15459 | 0.127627 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.70139 | 0.100430 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.5344 | 2.61967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.7879 | −0.691018 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.7111 | −0.625747 | −0.312874 | − | 0.949795i | \(-0.601292\pi\) | ||||
−0.312874 | + | 0.949795i | \(0.601292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.52501 | 0.205234 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.32963 | −0.251230 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.28724 | 0.132274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.28657 | −0.362352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.917568 | −0.0527129 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.20004 | −0.297753 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.2690 | 0.643154 | 0.321577 | − | 0.946883i | \(-0.395787\pi\) | ||||
0.321577 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.70606 | −0.324606 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.1837 | 0.974396 | 0.487198 | − | 0.873292i | \(-0.338019\pi\) | ||||
0.487198 | + | 0.873292i | \(0.338019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7705 | 0.891403 | 0.445702 | − | 0.895182i | \(-0.352954\pi\) | ||||
0.445702 | + | 0.895182i | \(0.352954\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.626686 | −0.0353098 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.5078 | −0.702506 | −0.351253 | − | 0.936281i | \(-0.614244\pi\) | ||||
−0.351253 | + | 0.936281i | \(0.614244\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4272 | 0.695787 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.3881 | 0.914694 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.8597 | 0.938099 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.0587 | 0.890776 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.1787 | −0.949983 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.40995 | 0.132865 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.56009 | 0.195680 | 0.0978401 | − | 0.995202i | \(-0.468807\pi\) | ||||
0.0978401 | + | 0.995202i | \(0.468807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.8665 | −0.759877 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.15116 | −0.172166 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.9049 | 0.811922 | 0.405961 | − | 0.913890i | \(-0.366937\pi\) | ||||
0.405961 | + | 0.913890i | \(0.366937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.1766 | −1.25878 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1220 | 0.818901 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.90517 | 0.426839 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.688034 | 0.0370425 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.75308 | 0.201476 | 0.100738 | − | 0.994913i | \(-0.467880\pi\) | ||||
0.100738 | + | 0.994913i | \(0.467880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0028 | 0.910138 | 0.455069 | − | 0.890456i | \(-0.349615\pi\) | ||||
0.455069 | + | 0.890456i | \(0.349615\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.57351 | −0.190740 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.57205 | 0.349795 | 0.174897 | − | 0.984587i | \(-0.444041\pi\) | ||||
0.174897 | + | 0.984587i | \(0.444041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.774582 | −0.0411105 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.6852 | −0.565523 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.3117 | −1.12479 | −0.562394 | − | 0.826870i | \(-0.690119\pi\) | ||||
−0.562394 | + | 0.826870i | \(0.690119\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3806 | −0.756876 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.4866 | −0.655377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.93921 | 0.258530 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.23696 | 0.482165 | 0.241083 | − | 0.970505i | \(-0.422498\pi\) | ||||
0.241083 | + | 0.970505i | \(0.422498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.48404 | −0.389604 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.83043 | 0.302701 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7862 | 1.28338 | 0.641689 | − | 0.766965i | \(-0.278234\pi\) | ||||
0.641689 | + | 0.766965i | \(0.278234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.84307 | 0.508294 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2569 | 0.528257 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.9546 | −0.870898 | −0.435449 | − | 0.900213i | \(-0.643410\pi\) | ||||
−0.435449 | + | 0.900213i | \(0.643410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 40.5823 | 2.07909 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.2009 | 0.725631 | 0.362816 | − | 0.931861i | \(-0.381816\pi\) | ||||
0.362816 | + | 0.931861i | \(0.381816\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.994399 | 0.0506793 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.6532 | 1.40569 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.27384 | 0.267394 | 0.133697 | − | 0.991022i | \(-0.457315\pi\) | ||||
0.133697 | + | 0.991022i | \(0.457315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.38387 | 0.272274 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.3389 | 1.58084 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.48292 | 0.326191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4577 | 1.17731 | 0.588655 | − | 0.808384i | \(-0.299658\pi\) | ||||
0.588655 | + | 0.808384i | \(0.299658\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.92763 | −0.146565 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.2981 | 0.564199 | 0.282100 | − | 0.959385i | \(-0.408969\pi\) | ||||
0.282100 | + | 0.959385i | \(0.408969\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.4811 | 0.621727 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.32495 | −0.214908 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.0027 | 1.09063 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1786 | −0.552748 | −0.276374 | − | 0.961050i | \(-0.589133\pi\) | ||||
−0.276374 | + | 0.961050i | \(0.589133\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.02890 | 0.445363 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.78973 | −0.235687 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.18953 | 0.156568 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.0635 | 1.81501 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0526 | 0.881925 | 0.440963 | − | 0.897525i | \(-0.354637\pi\) | ||||
0.440963 | + | 0.897525i | \(0.354637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.48272 | −0.267211 | −0.133606 | − | 0.991035i | \(-0.542656\pi\) | ||||
−0.133606 | + | 0.991035i | \(0.542656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.6008 | −0.515429 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37.8001 | 1.83358 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.06574 | 0.341935 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.6842 | −1.52973 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.95184 | −0.334858 | −0.167429 | − | 0.985884i | \(-0.553547\pi\) | ||||
−0.167429 | + | 0.985884i | \(0.553547\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1796 | −0.585316 | −0.292658 | − | 0.956217i | \(-0.594540\pi\) | ||||
−0.292658 | + | 0.956217i | \(0.594540\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.08542 | 0.147935 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.47512 | 0.0705645 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.1095 | 1.43705 | 0.718523 | − | 0.695503i | \(-0.244818\pi\) | ||||
0.718523 | + | 0.695503i | \(0.244818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.9607 | −0.807654 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.472461 | −0.0224473 | −0.0112236 | − | 0.999937i | \(-0.503573\pi\) | ||||
−0.0112236 | + | 0.999937i | \(0.503573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.207584 | −0.00984041 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.7032 | 0.695440 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.38542 | 0.206961 | 0.103480 | − | 0.994631i | \(-0.467002\pi\) | ||||
0.103480 | + | 0.994631i | \(0.467002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8754 | 0.559189 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.8312 | −0.602864 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.820738 | 0.0384768 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8117 | 1.11387 | 0.556933 | − | 0.830558i | \(-0.311978\pi\) | ||||
0.556933 | + | 0.830558i | \(0.311978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.41158 | −0.392619 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.3553 | −1.36721 | −0.683607 | − | 0.729850i | \(-0.739590\pi\) | ||||
−0.683607 | + | 0.729850i | \(0.739590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.1192 | −1.39976 | −0.699880 | − | 0.714261i | \(-0.746763\pi\) | ||||
−0.699880 | + | 0.714261i | \(0.746763\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.75449 | 0.174110 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.7073 | −1.14332 | −0.571659 | − | 0.820491i | \(-0.693700\pi\) | ||||
−0.571659 | + | 0.820491i | \(0.693700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.28175 | 0.197713 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.79957 | −0.0829197 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −43.8788 | −2.01755 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3568 | 0.475202 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.6467 | −1.17428 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.5561 | −1.25907 | −0.629536 | − | 0.776971i | \(-0.716755\pi\) | ||||
−0.629536 | + | 0.776971i | \(0.716755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1602 | 0.828033 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.934892 | −0.0425391 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.13127 | 0.0967761 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.6362 | −1.16169 | −0.580844 | − | 0.814015i | \(-0.697277\pi\) | ||||
−0.580844 | + | 0.814015i | \(0.697277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.2908 | 1.82201 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.23326 | 0.0556562 | 0.0278281 | − | 0.999613i | \(-0.491141\pi\) | ||||
0.0278281 | + | 0.999613i | \(0.491141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.1434 | 1.08737 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.37413 | −0.196603 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.05249 | 0.0472107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0051 | 0.626955 | 0.313478 | − | 0.949596i | \(-0.398506\pi\) | ||||
0.313478 | + | 0.949596i | \(0.398506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6978 | −0.611974 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.1129 | 0.896791 | 0.448395 | − | 0.893835i | \(-0.351996\pi\) | ||||
0.448395 | + | 0.893835i | \(0.351996\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.165898 | 0.00738237 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.46017 | 0.198083 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.4957 | −1.79494 | −0.897469 | − | 0.441077i | \(-0.854597\pi\) | ||||
−0.897469 | + | 0.441077i | \(0.854597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.71134 | −0.296892 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.30468 | −0.101754 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.03167 | 0.0454607 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.8209 | 0.739782 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.6724 | 2.53154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.5074 | 0.504146 | 0.252073 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252073 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5286 | −0.679018 | −0.339509 | − | 0.940603i | \(-0.610261\pi\) | ||||
−0.339509 | + | 0.940603i | \(0.610261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.56387 | −0.286471 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.3789 | 1.27977 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5289 | −0.979519 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.0689 | 0.914313 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.80146 | 0.424548 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.96300 | −0.128102 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 58.7327 | 2.53451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.9126 | 1.15921 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8592 | −0.552859 | −0.276430 | − | 0.961034i | \(-0.589151\pi\) | ||||
−0.276430 | + | 0.961034i | \(0.589151\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.7208 | 0.588817 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.10594 | 0.133044 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.01903 | 0.129085 | 0.0645423 | − | 0.997915i | \(-0.479441\pi\) | ||||
0.0645423 | + | 0.997915i | \(0.479441\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.0806 | −1.32649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.61502 | 0.281809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.80891 | −0.374593 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.46284 | 0.231885 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.7793 | −1.60076 | −0.800379 | − | 0.599494i | \(-0.795369\pi\) | ||||
−0.800379 | + | 0.599494i | \(0.795369\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.2159 | −1.53177 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −74.5806 | −3.14880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.09824 | 0.299155 | 0.149578 | − | 0.988750i | \(-0.452209\pi\) | ||||
0.149578 | + | 0.988750i | \(0.452209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.19038 | 0.176291 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.87668 | 0.246797 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.2532 | 1.22636 | 0.613180 | − | 0.789943i | \(-0.289890\pi\) | ||||
0.613180 | + | 0.789943i | \(0.289890\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.5640 | 1.15352 | 0.576760 | − | 0.816914i | \(-0.304317\pi\) | ||||
0.576760 | + | 0.816914i | \(0.304317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.5396 | 1.35936 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.30727 | 0.137923 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.0184 | 0.875008 | 0.437504 | − | 0.899216i | \(-0.355863\pi\) | ||||
0.437504 | + | 0.899216i | \(0.355863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9357 | 0.537589 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.33389 | −0.179800 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.6951 | 1.68542 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.61024 | −0.149265 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.0366 | 1.69376 | 0.846881 | − | 0.531782i | \(-0.178477\pi\) | ||||
0.846881 | + | 0.531782i | \(0.178477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.04948 | 0.331673 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.6592 | −0.561865 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.9158 | −1.63915 | −0.819573 | − | 0.572975i | \(-0.805789\pi\) | ||||
−0.819573 | + | 0.572975i | \(0.805789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.93191 | 0.0792008 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.8169 | −1.30218 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.4693 | 0.632060 | 0.316030 | − | 0.948749i | \(-0.397650\pi\) | ||||
0.316030 | + | 0.948749i | \(0.397650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.2013 | −1.31352 | −0.656759 | − | 0.754100i | \(-0.728073\pi\) | ||||
−0.656759 | + | 0.754100i | \(0.728073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.8344 | −0.766997 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.25760 | 0.0917846 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.7254 | −0.475918 | −0.237959 | − | 0.971275i | \(-0.576478\pi\) | ||||
−0.237959 | + | 0.971275i | \(0.576478\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.19243 | −0.169886 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.8833 | 0.561659 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.9557 | −1.49263 | −0.746313 | − | 0.665596i | \(-0.768178\pi\) | ||||
−0.746313 | + | 0.665596i | \(0.768178\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.94842 | 0.118892 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.2797 | −0.494360 | −0.247180 | − | 0.968970i | \(-0.579504\pi\) | ||||
−0.247180 | + | 0.968970i | \(0.579504\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0383 | −0.403475 | −0.201738 | − | 0.979440i | \(-0.564659\pi\) | ||||
−0.201738 | + | 0.979440i | \(0.564659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.735961 | −0.0295331 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.282062 | 0.0113006 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.3141 | 0.892564 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.4342 | −0.816064 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.7468 | 1.70443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4380 | 1.01267 | 0.506335 | − | 0.862337i | \(-0.331000\pi\) | ||||
0.506335 | + | 0.862337i | \(0.331000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.24909 | −0.0893934 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.33736 | −0.291174 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.2126 | 0.880095 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.62967 | −0.183147 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.7497 | −1.76751 | −0.883753 | − | 0.467955i | \(-0.844991\pi\) | ||||
−0.883753 | + | 0.467955i | \(0.844991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.8475 | −1.57143 | −0.785717 | − | 0.618587i | \(-0.787706\pi\) | ||||
−0.785717 | + | 0.618587i | \(0.787706\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.8943 | −0.428961 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.2531 | −1.70045 | −0.850226 | − | 0.526417i | \(-0.823535\pi\) | ||||
−0.850226 | + | 0.526417i | \(0.823535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.4313 | −1.31229 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.10155 | −0.199946 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.39120 | 0.0544420 | 0.0272210 | − | 0.999629i | \(-0.491334\pi\) | ||||
0.0272210 | + | 0.999629i | \(0.491334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.66615 | −0.221395 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.5216 | 1.15175 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.5780 | −0.723694 | −0.361847 | − | 0.932237i | \(-0.617854\pi\) | ||||
−0.361847 | + | 0.932237i | \(0.617854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.6574 | −1.19243 | −0.596217 | − | 0.802823i | \(-0.703330\pi\) | ||||
−0.596217 | + | 0.802823i | \(0.703330\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −61.5560 | −2.39064 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.529322 | 0.0205262 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.11240 | 0.0817924 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −49.4389 | −1.91142 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.3173 | 1.90387 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.17390 | 0.276533 | 0.138267 | − | 0.990395i | \(-0.455847\pi\) | ||||
0.138267 | + | 0.990395i | \(0.455847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.16718 | −0.198885 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.7193 | 1.52654 | 0.763269 | − | 0.646081i | \(-0.223593\pi\) | ||||
0.763269 | + | 0.646081i | \(0.223593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.89595 | −0.111136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.5985 | 0.444457 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.0188 | −0.383359 | −0.191680 | − | 0.981458i | \(-0.561393\pi\) | ||||
−0.191680 | + | 0.981458i | \(0.561393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.63244 | −0.0623724 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −51.1318 | −1.95080 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.5882 | 1.27961 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0164 | 0.647333 | 0.323667 | − | 0.946171i | \(-0.395084\pi\) | ||||
0.323667 | + | 0.946171i | \(0.395084\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.94351 | 0.225775 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.70115 | −0.254189 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.0714 | 0.873892 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −41.2757 | −1.56119 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0982 | 0.608019 | 0.304010 | − | 0.952669i | \(-0.401675\pi\) | ||||
0.304010 | + | 0.952669i | \(0.401675\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.7121 | 0.441731 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.17630 | 0.157289 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.225420 | −0.00847780 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.6319 | −1.63863 | −0.819316 | − | 0.573343i | \(-0.805646\pi\) | ||||
−0.819316 | + | 0.573343i | \(0.805646\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 38.7484 | 1.45318 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.57047 | 0.0962649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.72857 | 0.214236 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.34199 | −0.236846 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.5782 | 1.51331 | 0.756656 | − | 0.653813i | \(-0.226832\pi\) | ||||
0.756656 | + | 0.653813i | \(0.226832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.40181 | −0.0522063 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 66.9371 | 2.48942 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.8311 | 0.550815 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.0836 | 0.448155 | 0.224078 | − | 0.974571i | \(-0.428063\pi\) | ||||
0.224078 | + | 0.974571i | \(0.428063\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.2753 | −0.676862 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −85.2476 | −3.15300 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.78346 | 0.139745 | 0.0698726 | − | 0.997556i | \(-0.477741\pi\) | ||||
0.0698726 | + | 0.997556i | \(0.477741\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.68187 | 0.246464 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.8857 | 1.10085 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.6879 | −0.687444 | −0.343722 | − | 0.939072i | \(-0.611688\pi\) | ||||
−0.343722 | + | 0.939072i | \(0.611688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.8656 | −0.619574 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.4136 | −1.26251 | −0.631256 | − | 0.775574i | \(-0.717460\pi\) | ||||
−0.631256 | + | 0.775574i | \(0.717460\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.65838 | −0.0973954 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.0638 | 0.697507 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.02609 | 0.147110 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.9135 | 0.798571 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.31991 | 0.0844303 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.83996 | −0.139566 | −0.0697829 | − | 0.997562i | \(-0.522231\pi\) | ||||
−0.0697829 | + | 0.997562i | \(0.522231\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.52534 | −0.236855 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.05432 | 0.328219 | 0.164109 | − | 0.986442i | \(-0.447525\pi\) | ||||
0.164109 | + | 0.986442i | \(0.447525\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.22031 | −0.152785 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.49805 | −0.307247 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.5929 | −0.996321 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.7040 | −0.422057 | −0.211028 | − | 0.977480i | \(-0.567681\pi\) | ||||
−0.211028 | + | 0.977480i | \(0.567681\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −60.3941 | −2.17504 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.1490 | 0.544871 | 0.272435 | − | 0.962174i | \(-0.412171\pi\) | ||||
0.272435 | + | 0.962174i | \(0.412171\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0473 | 0.648276 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.42284 | −0.266293 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.32129 | 0.226484 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.34615 | 0.262866 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.30034 | −0.117945 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.325365 | 0.0116128 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.4277 | 1.61932 | 0.809661 | − | 0.586898i | \(-0.199651\pi\) | ||||
0.809661 | + | 0.586898i | \(0.199651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.0171 | −1.70945 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.69383 | −0.202449 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.7046 | 1.44546 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.1038 | 0.358345 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.95885 | 0.317339 | 0.158669 | − | 0.987332i | \(-0.449280\pi\) | ||||
0.158669 | + | 0.987332i | \(0.449280\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.6796 | 1.15612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.24073 | −0.0438389 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.8436 | −1.65308 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.169030 | 0.00595754 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.888738 | 0.0312851 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.2722 | −1.13463 | −0.567314 | − | 0.823501i | \(-0.692017\pi\) | ||||
−0.567314 | + | 0.823501i | \(0.692017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4792 | 0.824466 | 0.412233 | − | 0.911078i | \(-0.364749\pi\) | ||||
0.412233 | + | 0.911078i | \(0.364749\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.3286 | −1.02860 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.28466 | −0.255171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.3569 | −0.817153 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.90554 | 0.171414 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.7928 | −1.24918 | −0.624589 | − | 0.780954i | \(-0.714733\pi\) | ||||
−0.624589 | + | 0.780954i | \(0.714733\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0590 | 0.524922 | 0.262461 | − | 0.964943i | \(-0.415466\pi\) | ||||
0.262461 | + | 0.964943i | \(0.415466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −45.8144 | −1.59505 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.12303 | −0.282465 | −0.141233 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141233 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.7777 | 1.03422 | 0.517112 | − | 0.855918i | \(-0.327007\pi\) | ||||
0.517112 | + | 0.855918i | \(0.327007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.4212 | 0.465577 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 52.2856 | 1.81159 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.47659 | 0.0857061 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.01602 | −0.138814 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1416 | −0.764412 | −0.382206 | − | 0.924077i | \(-0.624836\pi\) | ||||
−0.382206 | + | 0.924077i | \(0.624836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.5272 | −0.673351 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.97790 | −0.205890 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.806408 | −0.0277413 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.06760 | −0.105404 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.9471 | 1.09642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.74007 | 0.128208 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.6944 | 1.63302 | 0.816512 | − | 0.577328i | \(-0.195905\pi\) | ||||
0.816512 | + | 0.577328i | \(0.195905\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.32836 | −0.0796284 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.64474 | −0.0561831 | −0.0280916 | − | 0.999605i | \(-0.508943\pi\) | ||||
−0.0280916 | + | 0.999605i | \(0.508943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.7961 | −0.982510 | −0.491255 | − | 0.871016i | \(-0.663462\pi\) | ||||
−0.491255 | + | 0.871016i | \(0.663462\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00627 | −0.136533 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.0031 | 1.60000 | 0.800002 | − | 0.599998i | \(-0.204832\pi\) | ||||
0.800002 | + | 0.599998i | \(0.204832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.4273 | −0.354538 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −104.865 | −3.56141 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −61.4842 | −2.08571 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.6665 | 0.835791 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.7386 | 0.431136 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.41816 | 0.0817488 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.87569 | −0.0633375 | −0.0316688 | − | 0.999498i | \(-0.510082\pi\) | ||||
−0.0316688 | + | 0.999498i | \(0.510082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.2213 | 0.850695 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8497 | 0.668754 | 0.334377 | − | 0.942439i | \(-0.391474\pi\) | ||||
0.334377 | + | 0.942439i | \(0.391474\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.442016 | −0.0148750 | −0.00743751 | − | 0.999972i | \(-0.502367\pi\) | ||||
−0.00743751 | + | 0.999972i | \(0.502367\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.30033 | −0.279013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.8829 | −1.13768 | −0.568839 | − | 0.822449i | \(-0.692607\pi\) | ||||
−0.568839 | + | 0.822449i | \(0.692607\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.96990 | 0.334380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.0179 | 1.37415 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.95382 | 0.299628 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.6190 | −0.354954 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.38576 | −0.179825 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.5270 | 0.384447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 79.0623 | 2.63395 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.8030 | 0.492612 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.48075 | −0.0824630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.9331 | −0.794687 | −0.397343 | − | 0.917670i | \(-0.630068\pi\) | ||||
−0.397343 | + | 0.917670i | \(0.630068\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.991571 | 0.0328883 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.6188 | −1.04758 | −0.523789 | − | 0.851848i | \(-0.675482\pi\) | ||||
−0.523789 | + | 0.851848i | \(0.675482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.2496 | −1.00112 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.2445 | 0.404792 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.69908 | 0.254246 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.83120 | 0.0933926 | 0.0466963 | − | 0.998909i | \(-0.485131\pi\) | ||||
0.0466963 | + | 0.998909i | \(0.485131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.5350 | −0.874359 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.06323 | 0.199574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.2590 | 0.863392 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.16626 | 0.202527 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.1741 | −1.81021 | −0.905103 | − | 0.425193i | \(-0.860206\pi\) | ||||
−0.905103 | + | 0.425193i | \(0.860206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.3257 | 0.469504 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.4624 | −1.32468 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.4843 | 0.440985 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.60307 | 0.281050 | 0.140525 | − | 0.990077i | \(-0.455121\pi\) | ||||
0.140525 | + | 0.990077i | \(0.455121\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.1349 | −1.21185 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.5099 | −0.864197 | −0.432098 | − | 0.901826i | \(-0.642227\pi\) | ||||
−0.432098 | + | 0.901826i | \(0.642227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.01860 | 0.0657347 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.264087 | −0.00859077 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.8199 | 0.741549 | 0.370774 | − | 0.928723i | \(-0.379092\pi\) | ||||
0.370774 | + | 0.928723i | \(0.379092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.6629 | −1.25505 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.4520 | 0.955047 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.5763 | −0.990463 | −0.495232 | − | 0.868761i | \(-0.664917\pi\) | ||||
−0.495232 | + | 0.868761i | \(0.664917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.88322 | −0.190376 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.2622 | −0.945913 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.21814 | 0.0716275 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.9734 | −0.547528 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.7098 | −0.570691 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.33880 | −0.0752886 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.9697 | −1.12455 | −0.562275 | − | 0.826950i | \(-0.690074\pi\) | ||||
−0.562275 | + | 0.826950i | \(0.690074\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.6995 | −1.27533 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.89375 | 0.285414 | 0.142707 | − | 0.989765i | \(-0.454419\pi\) | ||||
0.142707 | + | 0.989765i | \(0.454419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.10544 | 0.291907 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −37.8134 | −1.21100 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.0338 | 0.896881 | 0.448440 | − | 0.893813i | \(-0.351980\pi\) | ||||
0.448440 | + | 0.893813i | \(0.351980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.96873 | 0.0629209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.5642 | 0.592708 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.7595 | 0.534546 | 0.267273 | − | 0.963621i | \(-0.413878\pi\) | ||||
0.267273 | + | 0.963621i | \(0.413878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.46961 | 0.0786885 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.67470 | −0.180628 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.45863 | −0.237171 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9457 | 0.919491 | 0.459745 | − | 0.888051i | \(-0.347941\pi\) | ||||
0.459745 | + | 0.888051i | \(0.347941\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.38294 | −0.266025 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.75255 | 0.182368 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.2081 | 1.36841 | 0.684207 | − | 0.729288i | \(-0.260148\pi\) | ||||
0.684207 | + | 0.729288i | \(0.260148\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.84337 | −0.184876 |
(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 | 6008.2.a.d.1.7 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.d.1.7 | ✓ | 49 | 1.1 | even | 1 | trivial |