Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} - 1007 x^{5} - 384 x^{4} + 579 x^{3} + 44 x^{2} - 112 x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.181424\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.181424 | −0.128286 | −0.0641431 | − | 0.997941i | \(-0.520431\pi\) | ||||
−0.0641431 | + | 0.997941i | \(0.520431\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.96709 | −0.983543 | ||||||||
\(5\) | 3.75467 | 1.67914 | 0.839570 | − | 0.543252i | \(-0.182807\pi\) | ||||
0.839570 | + | 0.543252i | \(0.182807\pi\) | |||||||
\(6\) | −0.181424 | −0.0740660 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.719724 | 0.254461 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.681187 | −0.215410 | ||||||||
\(11\) | 0.260903 | 0.0786653 | 0.0393327 | − | 0.999226i | \(-0.487477\pi\) | ||||
0.0393327 | + | 0.999226i | \(0.487477\pi\) | |||||||
\(12\) | −1.96709 | −0.567849 | ||||||||
\(13\) | −5.44669 | −1.51064 | −0.755319 | − | 0.655357i | \(-0.772518\pi\) | ||||
−0.755319 | + | 0.655357i | \(0.772518\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.75467 | 0.969452 | ||||||||
\(16\) | 3.80360 | 0.950899 | ||||||||
\(17\) | 0.644297 | 0.156265 | 0.0781325 | − | 0.996943i | \(-0.475104\pi\) | ||||
0.0781325 | + | 0.996943i | \(0.475104\pi\) | |||||||
\(18\) | −0.181424 | −0.0427620 | ||||||||
\(19\) | −4.44030 | −1.01867 | −0.509337 | − | 0.860567i | \(-0.670109\pi\) | ||||
−0.509337 | + | 0.860567i | \(0.670109\pi\) | |||||||
\(20\) | −7.38576 | −1.65151 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0473341 | −0.0100917 | ||||||||
\(23\) | −9.20056 | −1.91845 | −0.959225 | − | 0.282644i | \(-0.908788\pi\) | ||||
−0.959225 | + | 0.282644i | \(0.908788\pi\) | |||||||
\(24\) | 0.719724 | 0.146913 | ||||||||
\(25\) | 9.09756 | 1.81951 | ||||||||
\(26\) | 0.988159 | 0.193794 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.61039 | 0.856128 | 0.428064 | − | 0.903748i | \(-0.359196\pi\) | ||||
0.428064 | + | 0.903748i | \(0.359196\pi\) | |||||||
\(30\) | −0.681187 | −0.124367 | ||||||||
\(31\) | −1.77314 | −0.318465 | −0.159233 | − | 0.987241i | \(-0.550902\pi\) | ||||
−0.159233 | + | 0.987241i | \(0.550902\pi\) | |||||||
\(32\) | −2.12951 | −0.376448 | ||||||||
\(33\) | 0.260903 | 0.0454174 | ||||||||
\(34\) | −0.116891 | −0.0200466 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96709 | −0.327848 | ||||||||
\(37\) | −5.73974 | −0.943608 | −0.471804 | − | 0.881704i | \(-0.656397\pi\) | ||||
−0.471804 | + | 0.881704i | \(0.656397\pi\) | |||||||
\(38\) | 0.805577 | 0.130682 | ||||||||
\(39\) | −5.44669 | −0.872168 | ||||||||
\(40\) | 2.70233 | 0.427276 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.73846 | −0.265113 | −0.132556 | − | 0.991175i | \(-0.542319\pi\) | ||||
−0.132556 | + | 0.991175i | \(0.542319\pi\) | |||||||
\(44\) | −0.513219 | −0.0773707 | ||||||||
\(45\) | 3.75467 | 0.559713 | ||||||||
\(46\) | 1.66920 | 0.246110 | ||||||||
\(47\) | −0.476598 | −0.0695190 | −0.0347595 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347595 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(48\) | 3.80360 | 0.549002 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.65051 | −0.233418 | ||||||||
\(51\) | 0.644297 | 0.0902197 | ||||||||
\(52\) | 10.7141 | 1.48578 | ||||||||
\(53\) | −2.26468 | −0.311078 | −0.155539 | − | 0.987830i | \(-0.549711\pi\) | ||||
−0.155539 | + | 0.987830i | \(0.549711\pi\) | |||||||
\(54\) | −0.181424 | −0.0246887 | ||||||||
\(55\) | 0.979606 | 0.132090 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.44030 | −0.588132 | ||||||||
\(58\) | −0.836435 | −0.109829 | ||||||||
\(59\) | 10.3925 | 1.35299 | 0.676495 | − | 0.736448i | \(-0.263498\pi\) | ||||
0.676495 | + | 0.736448i | \(0.263498\pi\) | |||||||
\(60\) | −7.38576 | −0.953497 | ||||||||
\(61\) | −12.3888 | −1.58622 | −0.793109 | − | 0.609079i | \(-0.791539\pi\) | ||||
−0.793109 | + | 0.609079i | \(0.791539\pi\) | |||||||
\(62\) | 0.321690 | 0.0408546 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.22085 | −0.902606 | ||||||||
\(65\) | −20.4505 | −2.53657 | ||||||||
\(66\) | −0.0473341 | −0.00582643 | ||||||||
\(67\) | −7.53205 | −0.920187 | −0.460093 | − | 0.887871i | \(-0.652184\pi\) | ||||
−0.460093 | + | 0.887871i | \(0.652184\pi\) | |||||||
\(68\) | −1.26739 | −0.153693 | ||||||||
\(69\) | −9.20056 | −1.10762 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.69685 | −0.794770 | −0.397385 | − | 0.917652i | \(-0.630082\pi\) | ||||
−0.397385 | + | 0.917652i | \(0.630082\pi\) | |||||||
\(72\) | 0.719724 | 0.0848203 | ||||||||
\(73\) | −14.7968 | −1.73183 | −0.865915 | − | 0.500191i | \(-0.833263\pi\) | ||||
−0.865915 | + | 0.500191i | \(0.833263\pi\) | |||||||
\(74\) | 1.04133 | 0.121052 | ||||||||
\(75\) | 9.09756 | 1.05050 | ||||||||
\(76\) | 8.73445 | 1.00191 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.988159 | 0.111887 | ||||||||
\(79\) | −6.26859 | −0.705272 | −0.352636 | − | 0.935761i | \(-0.614715\pi\) | ||||
−0.352636 | + | 0.935761i | \(0.614715\pi\) | |||||||
\(80\) | 14.2812 | 1.59669 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.181424 | 0.0200349 | ||||||||
\(83\) | 8.81328 | 0.967384 | 0.483692 | − | 0.875238i | \(-0.339296\pi\) | ||||
0.483692 | + | 0.875238i | \(0.339296\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.41912 | 0.262391 | ||||||||
\(86\) | 0.315399 | 0.0340103 | ||||||||
\(87\) | 4.61039 | 0.494286 | ||||||||
\(88\) | 0.187778 | 0.0200173 | ||||||||
\(89\) | −5.73591 | −0.608005 | −0.304002 | − | 0.952671i | \(-0.598323\pi\) | ||||
−0.304002 | + | 0.952671i | \(0.598323\pi\) | |||||||
\(90\) | −0.681187 | −0.0718035 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.0983 | 1.88688 | ||||||||
\(93\) | −1.77314 | −0.183866 | ||||||||
\(94\) | 0.0864664 | 0.00891833 | ||||||||
\(95\) | −16.6719 | −1.71050 | ||||||||
\(96\) | −2.12951 | −0.217342 | ||||||||
\(97\) | −2.67661 | −0.271768 | −0.135884 | − | 0.990725i | \(-0.543387\pi\) | ||||
−0.135884 | + | 0.990725i | \(0.543387\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.260903 | 0.0262218 | ||||||||
\(100\) | −17.8957 | −1.78957 | ||||||||
\(101\) | 10.8832 | 1.08292 | 0.541460 | − | 0.840727i | \(-0.317872\pi\) | ||||
0.541460 | + | 0.840727i | \(0.317872\pi\) | |||||||
\(102\) | −0.116891 | −0.0115739 | ||||||||
\(103\) | −6.46670 | −0.637182 | −0.318591 | − | 0.947892i | \(-0.603210\pi\) | ||||
−0.318591 | + | 0.947892i | \(0.603210\pi\) | |||||||
\(104\) | −3.92011 | −0.384399 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.410868 | 0.0399070 | ||||||||
\(107\) | 13.7274 | 1.32708 | 0.663539 | − | 0.748141i | \(-0.269054\pi\) | ||||
0.663539 | + | 0.748141i | \(0.269054\pi\) | |||||||
\(108\) | −1.96709 | −0.189283 | ||||||||
\(109\) | −4.61957 | −0.442474 | −0.221237 | − | 0.975220i | \(-0.571009\pi\) | ||||
−0.221237 | + | 0.975220i | \(0.571009\pi\) | |||||||
\(110\) | −0.177724 | −0.0169453 | ||||||||
\(111\) | −5.73974 | −0.544792 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.96683 | −0.749456 | −0.374728 | − | 0.927135i | \(-0.622264\pi\) | ||||
−0.374728 | + | 0.927135i | \(0.622264\pi\) | |||||||
\(114\) | 0.805577 | 0.0754492 | ||||||||
\(115\) | −34.5451 | −3.22135 | ||||||||
\(116\) | −9.06903 | −0.842038 | ||||||||
\(117\) | −5.44669 | −0.503546 | ||||||||
\(118\) | −1.88545 | −0.173570 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.70233 | 0.246688 | ||||||||
\(121\) | −10.9319 | −0.993812 | ||||||||
\(122\) | 2.24762 | 0.203490 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 3.48791 | 0.313224 | ||||||||
\(125\) | 15.3850 | 1.37607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.53266 | −0.845886 | −0.422943 | − | 0.906156i | \(-0.639003\pi\) | ||||
−0.422943 | + | 0.906156i | \(0.639003\pi\) | |||||||
\(128\) | 5.56906 | 0.492240 | ||||||||
\(129\) | −1.73846 | −0.153063 | ||||||||
\(130\) | 3.71021 | 0.325407 | ||||||||
\(131\) | 7.89826 | 0.690074 | 0.345037 | − | 0.938589i | \(-0.387866\pi\) | ||||
0.345037 | + | 0.938589i | \(0.387866\pi\) | |||||||
\(132\) | −0.513219 | −0.0446700 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.36649 | 0.118047 | ||||||||
\(135\) | 3.75467 | 0.323151 | ||||||||
\(136\) | 0.463716 | 0.0397634 | ||||||||
\(137\) | 12.1886 | 1.04134 | 0.520671 | − | 0.853757i | \(-0.325682\pi\) | ||||
0.520671 | + | 0.853757i | \(0.325682\pi\) | |||||||
\(138\) | 1.66920 | 0.142092 | ||||||||
\(139\) | 23.4534 | 1.98929 | 0.994647 | − | 0.103335i | \(-0.0329515\pi\) | ||||
0.994647 | + | 0.103335i | \(0.0329515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.476598 | −0.0401368 | ||||||||
\(142\) | 1.21497 | 0.101958 | ||||||||
\(143\) | −1.42106 | −0.118835 | ||||||||
\(144\) | 3.80360 | 0.316966 | ||||||||
\(145\) | 17.3105 | 1.43756 | ||||||||
\(146\) | 2.68449 | 0.222170 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.2906 | 0.928078 | ||||||||
\(149\) | 1.91828 | 0.157152 | 0.0785759 | − | 0.996908i | \(-0.474963\pi\) | ||||
0.0785759 | + | 0.996908i | \(0.474963\pi\) | |||||||
\(150\) | −1.65051 | −0.134764 | ||||||||
\(151\) | −0.875982 | −0.0712864 | −0.0356432 | − | 0.999365i | \(-0.511348\pi\) | ||||
−0.0356432 | + | 0.999365i | \(0.511348\pi\) | |||||||
\(152\) | −3.19579 | −0.259213 | ||||||||
\(153\) | 0.644297 | 0.0520883 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.65755 | −0.534747 | ||||||||
\(156\) | 10.7141 | 0.857814 | ||||||||
\(157\) | −21.4256 | −1.70995 | −0.854975 | − | 0.518669i | \(-0.826428\pi\) | ||||
−0.854975 | + | 0.518669i | \(0.826428\pi\) | |||||||
\(158\) | 1.13727 | 0.0904766 | ||||||||
\(159\) | −2.26468 | −0.179601 | ||||||||
\(160\) | −7.99562 | −0.632109 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.181424 | −0.0142540 | ||||||||
\(163\) | 20.4306 | 1.60025 | 0.800123 | − | 0.599836i | \(-0.204768\pi\) | ||||
0.800123 | + | 0.599836i | \(0.204768\pi\) | |||||||
\(164\) | 1.96709 | 0.153604 | ||||||||
\(165\) | 0.979606 | 0.0762622 | ||||||||
\(166\) | −1.59894 | −0.124102 | ||||||||
\(167\) | −8.65888 | −0.670044 | −0.335022 | − | 0.942210i | \(-0.608744\pi\) | ||||
−0.335022 | + | 0.942210i | \(0.608744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.6664 | 1.28203 | ||||||||
\(170\) | −0.438887 | −0.0336611 | ||||||||
\(171\) | −4.44030 | −0.339558 | ||||||||
\(172\) | 3.41970 | 0.260750 | ||||||||
\(173\) | −7.01283 | −0.533176 | −0.266588 | − | 0.963811i | \(-0.585896\pi\) | ||||
−0.266588 | + | 0.963811i | \(0.585896\pi\) | |||||||
\(174\) | −0.836435 | −0.0634100 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.992371 | 0.0748027 | ||||||||
\(177\) | 10.3925 | 0.781149 | ||||||||
\(178\) | 1.04063 | 0.0779986 | ||||||||
\(179\) | 7.18201 | 0.536808 | 0.268404 | − | 0.963306i | \(-0.413504\pi\) | ||||
0.268404 | + | 0.963306i | \(0.413504\pi\) | |||||||
\(180\) | −7.38576 | −0.550502 | ||||||||
\(181\) | 7.76715 | 0.577328 | 0.288664 | − | 0.957431i | \(-0.406789\pi\) | ||||
0.288664 | + | 0.957431i | \(0.406789\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.3888 | −0.915804 | ||||||||
\(184\) | −6.62187 | −0.488171 | ||||||||
\(185\) | −21.5508 | −1.58445 | ||||||||
\(186\) | 0.321690 | 0.0235874 | ||||||||
\(187\) | 0.168099 | 0.0122926 | ||||||||
\(188\) | 0.937510 | 0.0683749 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.02467 | 0.219433 | ||||||||
\(191\) | 4.77261 | 0.345334 | 0.172667 | − | 0.984980i | \(-0.444762\pi\) | ||||
0.172667 | + | 0.984980i | \(0.444762\pi\) | |||||||
\(192\) | −7.22085 | −0.521120 | ||||||||
\(193\) | −24.8481 | −1.78861 | −0.894303 | − | 0.447461i | \(-0.852328\pi\) | ||||
−0.894303 | + | 0.447461i | \(0.852328\pi\) | |||||||
\(194\) | 0.485601 | 0.0348641 | ||||||||
\(195\) | −20.4505 | −1.46449 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.9653 | 1.56497 | 0.782483 | − | 0.622672i | \(-0.213953\pi\) | ||||
0.782483 | + | 0.622672i | \(0.213953\pi\) | |||||||
\(198\) | −0.0473341 | −0.00336389 | ||||||||
\(199\) | 3.47751 | 0.246514 | 0.123257 | − | 0.992375i | \(-0.460666\pi\) | ||||
0.123257 | + | 0.992375i | \(0.460666\pi\) | |||||||
\(200\) | 6.54773 | 0.462995 | ||||||||
\(201\) | −7.53205 | −0.531270 | ||||||||
\(202\) | −1.97447 | −0.138923 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.26739 | −0.0887349 | ||||||||
\(205\) | −3.75467 | −0.262238 | ||||||||
\(206\) | 1.17321 | 0.0817417 | ||||||||
\(207\) | −9.20056 | −0.639483 | ||||||||
\(208\) | −20.7170 | −1.43646 | ||||||||
\(209\) | −1.15849 | −0.0801343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.73884 | −0.601606 | −0.300803 | − | 0.953686i | \(-0.597255\pi\) | ||||
−0.300803 | + | 0.953686i | \(0.597255\pi\) | |||||||
\(212\) | 4.45482 | 0.305959 | ||||||||
\(213\) | −6.69685 | −0.458861 | ||||||||
\(214\) | −2.49048 | −0.170246 | ||||||||
\(215\) | −6.52735 | −0.445162 | ||||||||
\(216\) | 0.719724 | 0.0489710 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.838100 | 0.0567633 | ||||||||
\(219\) | −14.7968 | −0.999873 | ||||||||
\(220\) | −1.92697 | −0.129916 | ||||||||
\(221\) | −3.50928 | −0.236060 | ||||||||
\(222\) | 1.04133 | 0.0698893 | ||||||||
\(223\) | −11.8901 | −0.796223 | −0.398111 | − | 0.917337i | \(-0.630334\pi\) | ||||
−0.398111 | + | 0.917337i | \(0.630334\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.09756 | 0.606504 | ||||||||
\(226\) | 1.44537 | 0.0961448 | ||||||||
\(227\) | 17.4021 | 1.15502 | 0.577508 | − | 0.816385i | \(-0.304025\pi\) | ||||
0.577508 | + | 0.816385i | \(0.304025\pi\) | |||||||
\(228\) | 8.73445 | 0.578453 | ||||||||
\(229\) | 4.00125 | 0.264410 | 0.132205 | − | 0.991222i | \(-0.457794\pi\) | ||||
0.132205 | + | 0.991222i | \(0.457794\pi\) | |||||||
\(230\) | 6.26731 | 0.413254 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.31821 | 0.217851 | ||||||||
\(233\) | −4.04892 | −0.265253 | −0.132627 | − | 0.991166i | \(-0.542341\pi\) | ||||
−0.132627 | + | 0.991166i | \(0.542341\pi\) | |||||||
\(234\) | 0.988159 | 0.0645980 | ||||||||
\(235\) | −1.78947 | −0.116732 | ||||||||
\(236\) | −20.4430 | −1.33072 | ||||||||
\(237\) | −6.26859 | −0.407189 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.86710 | −0.250142 | −0.125071 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125071 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(240\) | 14.2812 | 0.921851 | ||||||||
\(241\) | −21.9664 | −1.41498 | −0.707490 | − | 0.706724i | \(-0.750172\pi\) | ||||
−0.707490 | + | 0.706724i | \(0.750172\pi\) | |||||||
\(242\) | 1.98331 | 0.127492 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 24.3698 | 1.56011 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.181424 | 0.0115672 | ||||||||
\(247\) | 24.1849 | 1.53885 | ||||||||
\(248\) | −1.27617 | −0.0810369 | ||||||||
\(249\) | 8.81328 | 0.558519 | ||||||||
\(250\) | −2.79120 | −0.176531 | ||||||||
\(251\) | 18.8607 | 1.19048 | 0.595238 | − | 0.803549i | \(-0.297058\pi\) | ||||
0.595238 | + | 0.803549i | \(0.297058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.40046 | −0.150915 | ||||||||
\(254\) | 1.72945 | 0.108515 | ||||||||
\(255\) | 2.41912 | 0.151491 | ||||||||
\(256\) | 13.4313 | 0.839458 | ||||||||
\(257\) | −26.3411 | −1.64311 | −0.821556 | − | 0.570127i | \(-0.806894\pi\) | ||||
−0.821556 | + | 0.570127i | \(0.806894\pi\) | |||||||
\(258\) | 0.315399 | 0.0196359 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 40.2279 | 2.49483 | ||||||||
\(261\) | 4.61039 | 0.285376 | ||||||||
\(262\) | −1.43293 | −0.0885269 | ||||||||
\(263\) | 29.7738 | 1.83593 | 0.917964 | − | 0.396663i | \(-0.129832\pi\) | ||||
0.917964 | + | 0.396663i | \(0.129832\pi\) | |||||||
\(264\) | 0.187778 | 0.0115570 | ||||||||
\(265\) | −8.50314 | −0.522344 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.73591 | −0.351032 | ||||||||
\(268\) | 14.8162 | 0.905043 | ||||||||
\(269\) | −0.162754 | −0.00992327 | −0.00496164 | − | 0.999988i | \(-0.501579\pi\) | ||||
−0.00496164 | + | 0.999988i | \(0.501579\pi\) | |||||||
\(270\) | −0.681187 | −0.0414557 | ||||||||
\(271\) | −7.55601 | −0.458995 | −0.229498 | − | 0.973309i | \(-0.573708\pi\) | ||||
−0.229498 | + | 0.973309i | \(0.573708\pi\) | |||||||
\(272\) | 2.45065 | 0.148592 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.21130 | −0.133590 | ||||||||
\(275\) | 2.37358 | 0.143132 | ||||||||
\(276\) | 18.0983 | 1.08939 | ||||||||
\(277\) | −19.1220 | −1.14893 | −0.574466 | − | 0.818529i | \(-0.694790\pi\) | ||||
−0.574466 | + | 0.818529i | \(0.694790\pi\) | |||||||
\(278\) | −4.25501 | −0.255199 | ||||||||
\(279\) | −1.77314 | −0.106155 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.1709 | 1.50157 | 0.750786 | − | 0.660546i | \(-0.229675\pi\) | ||||
0.750786 | + | 0.660546i | \(0.229675\pi\) | |||||||
\(282\) | 0.0864664 | 0.00514900 | ||||||||
\(283\) | 11.8362 | 0.703587 | 0.351793 | − | 0.936078i | \(-0.385572\pi\) | ||||
0.351793 | + | 0.936078i | \(0.385572\pi\) | |||||||
\(284\) | 13.1733 | 0.781690 | ||||||||
\(285\) | −16.6719 | −0.987556 | ||||||||
\(286\) | 0.257814 | 0.0152449 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.12951 | −0.125483 | ||||||||
\(289\) | −16.5849 | −0.975581 | ||||||||
\(290\) | −3.14054 | −0.184419 | ||||||||
\(291\) | −2.67661 | −0.156905 | ||||||||
\(292\) | 29.1065 | 1.70333 | ||||||||
\(293\) | −28.0330 | −1.63770 | −0.818852 | − | 0.574005i | \(-0.805389\pi\) | ||||
−0.818852 | + | 0.574005i | \(0.805389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.0205 | 2.27186 | ||||||||
\(296\) | −4.13103 | −0.240111 | ||||||||
\(297\) | 0.260903 | 0.0151391 | ||||||||
\(298\) | −0.348022 | −0.0201604 | ||||||||
\(299\) | 50.1126 | 2.89808 | ||||||||
\(300\) | −17.8957 | −1.03321 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.158924 | 0.00914506 | ||||||||
\(303\) | 10.8832 | 0.625224 | ||||||||
\(304\) | −16.8891 | −0.968656 | ||||||||
\(305\) | −46.5157 | −2.66348 | ||||||||
\(306\) | −0.116891 | −0.00668221 | ||||||||
\(307\) | 9.82237 | 0.560592 | 0.280296 | − | 0.959914i | \(-0.409567\pi\) | ||||
0.280296 | + | 0.959914i | \(0.409567\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.46670 | −0.367877 | ||||||||
\(310\) | 1.20784 | 0.0686007 | ||||||||
\(311\) | −32.7287 | −1.85588 | −0.927938 | − | 0.372734i | \(-0.878420\pi\) | ||||
−0.927938 | + | 0.372734i | \(0.878420\pi\) | |||||||
\(312\) | −3.92011 | −0.221933 | ||||||||
\(313\) | −7.01115 | −0.396293 | −0.198147 | − | 0.980172i | \(-0.563492\pi\) | ||||
−0.198147 | + | 0.980172i | \(0.563492\pi\) | |||||||
\(314\) | 3.88712 | 0.219363 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.3309 | 0.693665 | ||||||||
\(317\) | −24.3997 | −1.37043 | −0.685213 | − | 0.728343i | \(-0.740291\pi\) | ||||
−0.685213 | + | 0.728343i | \(0.740291\pi\) | |||||||
\(318\) | 0.410868 | 0.0230403 | ||||||||
\(319\) | 1.20287 | 0.0673476 | ||||||||
\(320\) | −27.1119 | −1.51560 | ||||||||
\(321\) | 13.7274 | 0.766189 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.86087 | −0.159183 | ||||||||
\(324\) | −1.96709 | −0.109283 | ||||||||
\(325\) | −49.5515 | −2.74862 | ||||||||
\(326\) | −3.70660 | −0.205289 | ||||||||
\(327\) | −4.61957 | −0.255463 | ||||||||
\(328\) | −0.719724 | −0.0397401 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.177724 | −0.00978339 | ||||||||
\(331\) | 19.1012 | 1.04990 | 0.524949 | − | 0.851134i | \(-0.324084\pi\) | ||||
0.524949 | + | 0.851134i | \(0.324084\pi\) | |||||||
\(332\) | −17.3365 | −0.951463 | ||||||||
\(333\) | −5.73974 | −0.314536 | ||||||||
\(334\) | 1.57093 | 0.0859574 | ||||||||
\(335\) | −28.2804 | −1.54512 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.03171 | −0.110674 | −0.0553372 | − | 0.998468i | \(-0.517623\pi\) | ||||
−0.0553372 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(338\) | −3.02368 | −0.164467 | ||||||||
\(339\) | −7.96683 | −0.432699 | ||||||||
\(340\) | −4.75862 | −0.258073 | ||||||||
\(341\) | −0.462618 | −0.0250521 | ||||||||
\(342\) | 0.805577 | 0.0435606 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.25121 | −0.0674609 | ||||||||
\(345\) | −34.5451 | −1.85984 | ||||||||
\(346\) | 1.27230 | 0.0683990 | ||||||||
\(347\) | 11.7438 | 0.630438 | 0.315219 | − | 0.949019i | \(-0.397922\pi\) | ||||
0.315219 | + | 0.949019i | \(0.397922\pi\) | |||||||
\(348\) | −9.06903 | −0.486151 | ||||||||
\(349\) | 27.2116 | 1.45660 | 0.728302 | − | 0.685257i | \(-0.240310\pi\) | ||||
0.728302 | + | 0.685257i | \(0.240310\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.44669 | −0.290723 | ||||||||
\(352\) | −0.555597 | −0.0296134 | ||||||||
\(353\) | −0.380286 | −0.0202406 | −0.0101203 | − | 0.999949i | \(-0.503221\pi\) | ||||
−0.0101203 | + | 0.999949i | \(0.503221\pi\) | |||||||
\(354\) | −1.88545 | −0.100211 | ||||||||
\(355\) | −25.1445 | −1.33453 | ||||||||
\(356\) | 11.2830 | 0.597999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.30299 | −0.0688651 | ||||||||
\(359\) | −9.44080 | −0.498267 | −0.249133 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249133 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(360\) | 2.70233 | 0.142425 | ||||||||
\(361\) | 0.716247 | 0.0376972 | ||||||||
\(362\) | −1.40915 | −0.0740631 | ||||||||
\(363\) | −10.9319 | −0.573777 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −55.5570 | −2.90799 | ||||||||
\(366\) | 2.24762 | 0.117485 | ||||||||
\(367\) | −15.8328 | −0.826466 | −0.413233 | − | 0.910625i | \(-0.635600\pi\) | ||||
−0.413233 | + | 0.910625i | \(0.635600\pi\) | |||||||
\(368\) | −34.9952 | −1.82425 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 3.90984 | 0.203263 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.48791 | 0.180840 | ||||||||
\(373\) | 20.7543 | 1.07462 | 0.537309 | − | 0.843386i | \(-0.319441\pi\) | ||||
0.537309 | + | 0.843386i | \(0.319441\pi\) | |||||||
\(374\) | −0.0304972 | −0.00157697 | ||||||||
\(375\) | 15.3850 | 0.794477 | ||||||||
\(376\) | −0.343020 | −0.0176899 | ||||||||
\(377\) | −25.1113 | −1.29330 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.409160 | 0.0210171 | 0.0105086 | − | 0.999945i | \(-0.496655\pi\) | ||||
0.0105086 | + | 0.999945i | \(0.496655\pi\) | |||||||
\(380\) | 32.7950 | 1.68235 | ||||||||
\(381\) | −9.53266 | −0.488373 | ||||||||
\(382\) | −0.865865 | −0.0443015 | ||||||||
\(383\) | 38.9703 | 1.99129 | 0.995646 | − | 0.0932202i | \(-0.0297161\pi\) | ||||
0.995646 | + | 0.0932202i | \(0.0297161\pi\) | |||||||
\(384\) | 5.56906 | 0.284195 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.50804 | 0.229453 | ||||||||
\(387\) | −1.73846 | −0.0883709 | ||||||||
\(388\) | 5.26511 | 0.267296 | ||||||||
\(389\) | 22.8774 | 1.15993 | 0.579965 | − | 0.814642i | \(-0.303066\pi\) | ||||
0.579965 | + | 0.814642i | \(0.303066\pi\) | |||||||
\(390\) | 3.71021 | 0.187874 | ||||||||
\(391\) | −5.92790 | −0.299787 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.89826 | 0.398414 | ||||||||
\(394\) | −3.98504 | −0.200763 | ||||||||
\(395\) | −23.5365 | −1.18425 | ||||||||
\(396\) | −0.513219 | −0.0257902 | ||||||||
\(397\) | −24.1253 | −1.21081 | −0.605406 | − | 0.795917i | \(-0.706989\pi\) | ||||
−0.605406 | + | 0.795917i | \(0.706989\pi\) | |||||||
\(398\) | −0.630904 | −0.0316244 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 34.6034 | 1.73017 | ||||||||
\(401\) | −28.1838 | −1.40743 | −0.703716 | − | 0.710481i | \(-0.748477\pi\) | ||||
−0.703716 | + | 0.710481i | \(0.748477\pi\) | |||||||
\(402\) | 1.36649 | 0.0681546 | ||||||||
\(403\) | 9.65773 | 0.481086 | ||||||||
\(404\) | −21.4082 | −1.06510 | ||||||||
\(405\) | 3.75467 | 0.186571 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.49752 | −0.0742292 | ||||||||
\(408\) | 0.463716 | 0.0229574 | ||||||||
\(409\) | 22.9535 | 1.13498 | 0.567489 | − | 0.823381i | \(-0.307915\pi\) | ||||
0.567489 | + | 0.823381i | \(0.307915\pi\) | |||||||
\(410\) | 0.681187 | 0.0336414 | ||||||||
\(411\) | 12.1886 | 0.601219 | ||||||||
\(412\) | 12.7205 | 0.626696 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.66920 | 0.0820368 | ||||||||
\(415\) | 33.0910 | 1.62437 | ||||||||
\(416\) | 11.5988 | 0.568677 | ||||||||
\(417\) | 23.4534 | 1.14852 | ||||||||
\(418\) | 0.210178 | 0.0102801 | ||||||||
\(419\) | −7.20087 | −0.351785 | −0.175893 | − | 0.984409i | \(-0.556281\pi\) | ||||
−0.175893 | + | 0.984409i | \(0.556281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3097 | 0.941096 | 0.470548 | − | 0.882374i | \(-0.344056\pi\) | ||||
0.470548 | + | 0.882374i | \(0.344056\pi\) | |||||||
\(422\) | 1.58543 | 0.0771778 | ||||||||
\(423\) | −0.476598 | −0.0231730 | ||||||||
\(424\) | −1.62995 | −0.0791572 | ||||||||
\(425\) | 5.86153 | 0.284326 | ||||||||
\(426\) | 1.21497 | 0.0588655 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −27.0030 | −1.30524 | ||||||||
\(429\) | −1.42106 | −0.0686093 | ||||||||
\(430\) | 1.18422 | 0.0571080 | ||||||||
\(431\) | −18.8713 | −0.909000 | −0.454500 | − | 0.890747i | \(-0.650182\pi\) | ||||
−0.454500 | + | 0.890747i | \(0.650182\pi\) | |||||||
\(432\) | 3.80360 | 0.183001 | ||||||||
\(433\) | −14.0523 | −0.675311 | −0.337655 | − | 0.941270i | \(-0.609634\pi\) | ||||
−0.337655 | + | 0.941270i | \(0.609634\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.3105 | 0.829975 | ||||||||
\(436\) | 9.08708 | 0.435192 | ||||||||
\(437\) | 40.8532 | 1.95428 | ||||||||
\(438\) | 2.68449 | 0.128270 | ||||||||
\(439\) | −31.8321 | −1.51926 | −0.759631 | − | 0.650355i | \(-0.774620\pi\) | ||||
−0.759631 | + | 0.650355i | \(0.774620\pi\) | |||||||
\(440\) | 0.705046 | 0.0336118 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.636668 | 0.0302832 | ||||||||
\(443\) | −27.6185 | −1.31220 | −0.656098 | − | 0.754676i | \(-0.727794\pi\) | ||||
−0.656098 | + | 0.754676i | \(0.727794\pi\) | |||||||
\(444\) | 11.2906 | 0.535826 | ||||||||
\(445\) | −21.5364 | −1.02093 | ||||||||
\(446\) | 2.15716 | 0.102144 | ||||||||
\(447\) | 1.91828 | 0.0907316 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.46660 | 0.257985 | 0.128992 | − | 0.991646i | \(-0.458826\pi\) | ||||
0.128992 | + | 0.991646i | \(0.458826\pi\) | |||||||
\(450\) | −1.65051 | −0.0778060 | ||||||||
\(451\) | −0.260903 | −0.0122855 | ||||||||
\(452\) | 15.6714 | 0.737122 | ||||||||
\(453\) | −0.875982 | −0.0411572 | ||||||||
\(454\) | −3.15716 | −0.148173 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.19579 | −0.149657 | ||||||||
\(457\) | −14.8767 | −0.695905 | −0.347952 | − | 0.937512i | \(-0.613123\pi\) | ||||
−0.347952 | + | 0.937512i | \(0.613123\pi\) | |||||||
\(458\) | −0.725923 | −0.0339202 | ||||||||
\(459\) | 0.644297 | 0.0300732 | ||||||||
\(460\) | 67.9531 | 3.16833 | ||||||||
\(461\) | 26.0239 | 1.21205 | 0.606026 | − | 0.795445i | \(-0.292763\pi\) | ||||
0.606026 | + | 0.795445i | \(0.292763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.72466 | 0.173099 | 0.0865497 | − | 0.996248i | \(-0.472416\pi\) | ||||
0.0865497 | + | 0.996248i | \(0.472416\pi\) | |||||||
\(464\) | 17.5361 | 0.814091 | ||||||||
\(465\) | −6.65755 | −0.308737 | ||||||||
\(466\) | 0.734571 | 0.0340283 | ||||||||
\(467\) | −6.65419 | −0.307919 | −0.153960 | − | 0.988077i | \(-0.549203\pi\) | ||||
−0.153960 | + | 0.988077i | \(0.549203\pi\) | |||||||
\(468\) | 10.7141 | 0.495259 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.324653 | 0.0149751 | ||||||||
\(471\) | −21.4256 | −0.987240 | ||||||||
\(472\) | 7.47974 | 0.344283 | ||||||||
\(473\) | −0.453570 | −0.0208552 | ||||||||
\(474\) | 1.13727 | 0.0522367 | ||||||||
\(475\) | −40.3959 | −1.85349 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.26468 | −0.103693 | ||||||||
\(478\) | 0.701585 | 0.0320897 | ||||||||
\(479\) | 13.1733 | 0.601903 | 0.300951 | − | 0.953639i | \(-0.402696\pi\) | ||||
0.300951 | + | 0.953639i | \(0.402696\pi\) | |||||||
\(480\) | −7.99562 | −0.364948 | ||||||||
\(481\) | 31.2626 | 1.42545 | ||||||||
\(482\) | 3.98523 | 0.181522 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.5040 | 0.977456 | ||||||||
\(485\) | −10.0498 | −0.456337 | ||||||||
\(486\) | −0.181424 | −0.00822956 | ||||||||
\(487\) | −34.9155 | −1.58217 | −0.791085 | − | 0.611706i | \(-0.790484\pi\) | ||||
−0.791085 | + | 0.611706i | \(0.790484\pi\) | |||||||
\(488\) | −8.91650 | −0.403631 | ||||||||
\(489\) | 20.4306 | 0.923902 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.7111 | 0.979810 | 0.489905 | − | 0.871776i | \(-0.337032\pi\) | ||||
0.489905 | + | 0.871776i | \(0.337032\pi\) | |||||||
\(492\) | 1.96709 | 0.0886831 | ||||||||
\(493\) | 2.97046 | 0.133783 | ||||||||
\(494\) | −4.38772 | −0.197413 | ||||||||
\(495\) | 0.979606 | 0.0440300 | ||||||||
\(496\) | −6.74430 | −0.302828 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.59894 | −0.0716503 | ||||||||
\(499\) | 7.15448 | 0.320278 | 0.160139 | − | 0.987094i | \(-0.448806\pi\) | ||||
0.160139 | + | 0.987094i | \(0.448806\pi\) | |||||||
\(500\) | −30.2636 | −1.35343 | ||||||||
\(501\) | −8.65888 | −0.386850 | ||||||||
\(502\) | −3.42178 | −0.152722 | ||||||||
\(503\) | −40.5245 | −1.80690 | −0.903448 | − | 0.428698i | \(-0.858973\pi\) | ||||
−0.903448 | + | 0.428698i | \(0.858973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.8628 | 1.81837 | ||||||||
\(506\) | 0.435500 | 0.0193604 | ||||||||
\(507\) | 16.6664 | 0.740180 | ||||||||
\(508\) | 18.7515 | 0.831965 | ||||||||
\(509\) | −40.0598 | −1.77562 | −0.887811 | − | 0.460209i | \(-0.847774\pi\) | ||||
−0.887811 | + | 0.460209i | \(0.847774\pi\) | |||||||
\(510\) | −0.438887 | −0.0194342 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.5749 | −0.599931 | ||||||||
\(513\) | −4.44030 | −0.196044 | ||||||||
\(514\) | 4.77891 | 0.210789 | ||||||||
\(515\) | −24.2803 | −1.06992 | ||||||||
\(516\) | 3.41970 | 0.150544 | ||||||||
\(517\) | −0.124346 | −0.00546874 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.01283 | −0.307829 | ||||||||
\(520\) | −14.7187 | −0.645459 | ||||||||
\(521\) | 26.8711 | 1.17724 | 0.588621 | − | 0.808409i | \(-0.299671\pi\) | ||||
0.588621 | + | 0.808409i | \(0.299671\pi\) | |||||||
\(522\) | −0.836435 | −0.0366098 | ||||||||
\(523\) | −32.0580 | −1.40180 | −0.700899 | − | 0.713261i | \(-0.747218\pi\) | ||||
−0.700899 | + | 0.713261i | \(0.747218\pi\) | |||||||
\(524\) | −15.5366 | −0.678717 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.40167 | −0.235524 | ||||||||
\(527\) | −1.14243 | −0.0497649 | ||||||||
\(528\) | 0.992371 | 0.0431874 | ||||||||
\(529\) | 61.6503 | 2.68045 | ||||||||
\(530\) | 1.54267 | 0.0670094 | ||||||||
\(531\) | 10.3925 | 0.450996 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.44669 | 0.235922 | ||||||||
\(534\) | 1.04063 | 0.0450325 | ||||||||
\(535\) | 51.5419 | 2.22835 | ||||||||
\(536\) | −5.42100 | −0.234152 | ||||||||
\(537\) | 7.18201 | 0.309926 | ||||||||
\(538\) | 0.0295274 | 0.00127302 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.38576 | −0.317832 | ||||||||
\(541\) | −25.8202 | −1.11010 | −0.555048 | − | 0.831818i | \(-0.687300\pi\) | ||||
−0.555048 | + | 0.831818i | \(0.687300\pi\) | |||||||
\(542\) | 1.37084 | 0.0588827 | ||||||||
\(543\) | 7.76715 | 0.333320 | ||||||||
\(544\) | −1.37204 | −0.0588257 | ||||||||
\(545\) | −17.3450 | −0.742976 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.89760 | 0.166649 | 0.0833247 | − | 0.996522i | \(-0.473446\pi\) | ||||
0.0833247 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(548\) | −23.9760 | −1.02420 | ||||||||
\(549\) | −12.3888 | −0.528740 | ||||||||
\(550\) | −0.430625 | −0.0183619 | ||||||||
\(551\) | −20.4715 | −0.872115 | ||||||||
\(552\) | −6.62187 | −0.281845 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.46920 | 0.147392 | ||||||||
\(555\) | −21.5508 | −0.914782 | ||||||||
\(556\) | −46.1349 | −1.95655 | ||||||||
\(557\) | 8.54683 | 0.362141 | 0.181070 | − | 0.983470i | \(-0.442044\pi\) | ||||
0.181070 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(558\) | 0.321690 | 0.0136182 | ||||||||
\(559\) | 9.46885 | 0.400490 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.168099 | 0.00709716 | ||||||||
\(562\) | −4.56661 | −0.192631 | ||||||||
\(563\) | 16.7189 | 0.704619 | 0.352309 | − | 0.935884i | \(-0.385396\pi\) | ||||
0.352309 | + | 0.935884i | \(0.385396\pi\) | |||||||
\(564\) | 0.937510 | 0.0394763 | ||||||||
\(565\) | −29.9128 | −1.25844 | ||||||||
\(566\) | −2.14736 | −0.0902604 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.81989 | −0.202238 | ||||||||
\(569\) | −6.95737 | −0.291668 | −0.145834 | − | 0.989309i | \(-0.546587\pi\) | ||||
−0.145834 | + | 0.989309i | \(0.546587\pi\) | |||||||
\(570\) | 3.02467 | 0.126690 | ||||||||
\(571\) | 2.95282 | 0.123572 | 0.0617858 | − | 0.998089i | \(-0.480320\pi\) | ||||
0.0617858 | + | 0.998089i | \(0.480320\pi\) | |||||||
\(572\) | 2.79534 | 0.116879 | ||||||||
\(573\) | 4.77261 | 0.199379 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −83.7026 | −3.49064 | ||||||||
\(576\) | −7.22085 | −0.300869 | ||||||||
\(577\) | 30.0904 | 1.25268 | 0.626341 | − | 0.779550i | \(-0.284552\pi\) | ||||
0.626341 | + | 0.779550i | \(0.284552\pi\) | |||||||
\(578\) | 3.00890 | 0.125154 | ||||||||
\(579\) | −24.8481 | −1.03265 | ||||||||
\(580\) | −34.0512 | −1.41390 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.485601 | 0.0201288 | ||||||||
\(583\) | −0.590863 | −0.0244710 | ||||||||
\(584\) | −10.6496 | −0.440683 | ||||||||
\(585\) | −20.4505 | −0.845525 | ||||||||
\(586\) | 5.08585 | 0.210095 | ||||||||
\(587\) | 1.23855 | 0.0511203 | 0.0255602 | − | 0.999673i | \(-0.491863\pi\) | ||||
0.0255602 | + | 0.999673i | \(0.491863\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.87326 | 0.324412 | ||||||||
\(590\) | −7.07925 | −0.291448 | ||||||||
\(591\) | 21.9653 | 0.903533 | ||||||||
\(592\) | −21.8317 | −0.897276 | ||||||||
\(593\) | −37.3341 | −1.53313 | −0.766564 | − | 0.642167i | \(-0.778035\pi\) | ||||
−0.766564 | + | 0.642167i | \(0.778035\pi\) | |||||||
\(594\) | −0.0473341 | −0.00194214 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.77342 | −0.154565 | ||||||||
\(597\) | 3.47751 | 0.142325 | ||||||||
\(598\) | −9.09162 | −0.371784 | ||||||||
\(599\) | −0.376353 | −0.0153774 | −0.00768868 | − | 0.999970i | \(-0.502447\pi\) | ||||
−0.00768868 | + | 0.999970i | \(0.502447\pi\) | |||||||
\(600\) | 6.54773 | 0.267310 | ||||||||
\(601\) | −22.4269 | −0.914810 | −0.457405 | − | 0.889258i | \(-0.651221\pi\) | ||||
−0.457405 | + | 0.889258i | \(0.651221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.53205 | −0.306729 | ||||||||
\(604\) | 1.72313 | 0.0701132 | ||||||||
\(605\) | −41.0458 | −1.66875 | ||||||||
\(606\) | −1.97447 | −0.0802075 | ||||||||
\(607\) | −11.8223 | −0.479853 | −0.239927 | − | 0.970791i | \(-0.577123\pi\) | ||||
−0.239927 | + | 0.970791i | \(0.577123\pi\) | |||||||
\(608\) | 9.45567 | 0.383478 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.43907 | 0.341688 | ||||||||
\(611\) | 2.59588 | 0.105018 | ||||||||
\(612\) | −1.26739 | −0.0512311 | ||||||||
\(613\) | 6.63056 | 0.267806 | 0.133903 | − | 0.990994i | \(-0.457249\pi\) | ||||
0.133903 | + | 0.990994i | \(0.457249\pi\) | |||||||
\(614\) | −1.78201 | −0.0719162 | ||||||||
\(615\) | −3.75467 | −0.151403 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.0331 | −1.00780 | −0.503898 | − | 0.863763i | \(-0.668101\pi\) | ||||
−0.503898 | + | 0.863763i | \(0.668101\pi\) | |||||||
\(618\) | 1.17321 | 0.0471936 | ||||||||
\(619\) | 28.6287 | 1.15069 | 0.575343 | − | 0.817912i | \(-0.304869\pi\) | ||||
0.575343 | + | 0.817912i | \(0.304869\pi\) | |||||||
\(620\) | 13.0960 | 0.525947 | ||||||||
\(621\) | −9.20056 | −0.369206 | ||||||||
\(622\) | 5.93778 | 0.238083 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −20.7170 | −0.829343 | ||||||||
\(625\) | 12.2777 | 0.491109 | ||||||||
\(626\) | 1.27199 | 0.0508389 | ||||||||
\(627\) | −1.15849 | −0.0462656 | ||||||||
\(628\) | 42.1460 | 1.68181 | ||||||||
\(629\) | −3.69810 | −0.147453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0807 | 0.759591 | 0.379796 | − | 0.925070i | \(-0.375994\pi\) | ||||
0.379796 | + | 0.925070i | \(0.375994\pi\) | |||||||
\(632\) | −4.51166 | −0.179464 | ||||||||
\(633\) | −8.73884 | −0.347338 | ||||||||
\(634\) | 4.42670 | 0.175807 | ||||||||
\(635\) | −35.7920 | −1.42036 | ||||||||
\(636\) | 4.45482 | 0.176645 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.218229 | −0.00863976 | ||||||||
\(639\) | −6.69685 | −0.264923 | ||||||||
\(640\) | 20.9100 | 0.826540 | ||||||||
\(641\) | 9.07184 | 0.358316 | 0.179158 | − | 0.983820i | \(-0.442663\pi\) | ||||
0.179158 | + | 0.983820i | \(0.442663\pi\) | |||||||
\(642\) | −2.49048 | −0.0982914 | ||||||||
\(643\) | 3.54904 | 0.139960 | 0.0699802 | − | 0.997548i | \(-0.477706\pi\) | ||||
0.0699802 | + | 0.997548i | \(0.477706\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.52735 | −0.257014 | ||||||||
\(646\) | 0.519031 | 0.0204210 | ||||||||
\(647\) | −12.4651 | −0.490053 | −0.245027 | − | 0.969516i | \(-0.578797\pi\) | ||||
−0.245027 | + | 0.969516i | \(0.578797\pi\) | |||||||
\(648\) | 0.719724 | 0.0282734 | ||||||||
\(649\) | 2.71144 | 0.106433 | ||||||||
\(650\) | 8.98984 | 0.352610 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −40.1887 | −1.57391 | ||||||||
\(653\) | −3.89910 | −0.152584 | −0.0762918 | − | 0.997086i | \(-0.524308\pi\) | ||||
−0.0762918 | + | 0.997086i | \(0.524308\pi\) | |||||||
\(654\) | 0.838100 | 0.0327723 | ||||||||
\(655\) | 29.6554 | 1.15873 | ||||||||
\(656\) | −3.80360 | −0.148505 | ||||||||
\(657\) | −14.7968 | −0.577277 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.7940 | 1.00479 | 0.502396 | − | 0.864638i | \(-0.332452\pi\) | ||||
0.502396 | + | 0.864638i | \(0.332452\pi\) | |||||||
\(660\) | −1.92697 | −0.0750072 | ||||||||
\(661\) | −22.7358 | −0.884321 | −0.442160 | − | 0.896936i | \(-0.645788\pi\) | ||||
−0.442160 | + | 0.896936i | \(0.645788\pi\) | |||||||
\(662\) | −3.46542 | −0.134687 | ||||||||
\(663\) | −3.50928 | −0.136289 | ||||||||
\(664\) | 6.34314 | 0.246161 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.04133 | 0.0403506 | ||||||||
\(667\) | −42.4182 | −1.64244 | ||||||||
\(668\) | 17.0328 | 0.659017 | ||||||||
\(669\) | −11.8901 | −0.459700 | ||||||||
\(670\) | 5.13074 | 0.198218 | ||||||||
\(671\) | −3.23227 | −0.124780 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.37936 | −0.0917177 | −0.0458589 | − | 0.998948i | \(-0.514602\pi\) | ||||
−0.0458589 | + | 0.998948i | \(0.514602\pi\) | |||||||
\(674\) | 0.368602 | 0.0141980 | ||||||||
\(675\) | 9.09756 | 0.350165 | ||||||||
\(676\) | −32.7842 | −1.26093 | ||||||||
\(677\) | 23.5460 | 0.904945 | 0.452473 | − | 0.891778i | \(-0.350542\pi\) | ||||
0.452473 | + | 0.891778i | \(0.350542\pi\) | |||||||
\(678\) | 1.44537 | 0.0555092 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.74110 | 0.0667682 | ||||||||
\(681\) | 17.4021 | 0.666849 | ||||||||
\(682\) | 0.0839299 | 0.00321384 | ||||||||
\(683\) | 26.6161 | 1.01844 | 0.509218 | − | 0.860638i | \(-0.329935\pi\) | ||||
0.509218 | + | 0.860638i | \(0.329935\pi\) | |||||||
\(684\) | 8.73445 | 0.333970 | ||||||||
\(685\) | 45.7642 | 1.74856 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.00125 | 0.152657 | ||||||||
\(688\) | −6.61240 | −0.252095 | ||||||||
\(689\) | 12.3350 | 0.469927 | ||||||||
\(690\) | 6.26731 | 0.238592 | ||||||||
\(691\) | −34.0673 | −1.29598 | −0.647990 | − | 0.761649i | \(-0.724390\pi\) | ||||
−0.647990 | + | 0.761649i | \(0.724390\pi\) | |||||||
\(692\) | 13.7948 | 0.524401 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.13060 | −0.0808764 | ||||||||
\(695\) | 88.0599 | 3.34030 | ||||||||
\(696\) | 3.31821 | 0.125776 | ||||||||
\(697\) | −0.644297 | −0.0244045 | ||||||||
\(698\) | −4.93684 | −0.186862 | ||||||||
\(699\) | −4.04892 | −0.153144 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6554 | 0.742374 | 0.371187 | − | 0.928558i | \(-0.378951\pi\) | ||||
0.371187 | + | 0.928558i | \(0.378951\pi\) | |||||||
\(702\) | 0.988159 | 0.0372957 | ||||||||
\(703\) | 25.4862 | 0.961229 | ||||||||
\(704\) | −1.88394 | −0.0710038 | ||||||||
\(705\) | −1.78947 | −0.0673954 | ||||||||
\(706\) | 0.0689929 | 0.00259658 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −20.4430 | −0.768293 | ||||||||
\(709\) | 1.60380 | 0.0602318 | 0.0301159 | − | 0.999546i | \(-0.490412\pi\) | ||||
0.0301159 | + | 0.999546i | \(0.490412\pi\) | |||||||
\(710\) | 4.56181 | 0.171202 | ||||||||
\(711\) | −6.26859 | −0.235091 | ||||||||
\(712\) | −4.12827 | −0.154713 | ||||||||
\(713\) | 16.3139 | 0.610959 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.33561 | −0.199540 | ||||||||
\(716\) | −14.1276 | −0.527974 | ||||||||
\(717\) | −3.86710 | −0.144420 | ||||||||
\(718\) | 1.71279 | 0.0639207 | ||||||||
\(719\) | 50.9143 | 1.89878 | 0.949392 | − | 0.314093i | \(-0.101700\pi\) | ||||
0.949392 | + | 0.314093i | \(0.101700\pi\) | |||||||
\(720\) | 14.2812 | 0.532231 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.129944 | −0.00483603 | ||||||||
\(723\) | −21.9664 | −0.816939 | ||||||||
\(724\) | −15.2786 | −0.567826 | ||||||||
\(725\) | 41.9433 | 1.55773 | ||||||||
\(726\) | 1.98331 | 0.0736077 | ||||||||
\(727\) | −13.8327 | −0.513026 | −0.256513 | − | 0.966541i | \(-0.582574\pi\) | ||||
−0.256513 | + | 0.966541i | \(0.582574\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.0794 | 0.373054 | ||||||||
\(731\) | −1.12009 | −0.0414279 | ||||||||
\(732\) | 24.3698 | 0.900732 | ||||||||
\(733\) | 15.8688 | 0.586128 | 0.293064 | − | 0.956093i | \(-0.405325\pi\) | ||||
0.293064 | + | 0.956093i | \(0.405325\pi\) | |||||||
\(734\) | 2.87245 | 0.106024 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.5927 | 0.722197 | ||||||||
\(737\) | −1.96514 | −0.0723868 | ||||||||
\(738\) | 0.181424 | 0.00667831 | ||||||||
\(739\) | −9.23223 | −0.339613 | −0.169806 | − | 0.985477i | \(-0.554314\pi\) | ||||
−0.169806 | + | 0.985477i | \(0.554314\pi\) | |||||||
\(740\) | 42.3923 | 1.55837 | ||||||||
\(741\) | 24.1849 | 0.888455 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.1930 | −1.73134 | −0.865671 | − | 0.500613i | \(-0.833108\pi\) | ||||
−0.865671 | + | 0.500613i | \(0.833108\pi\) | |||||||
\(744\) | −1.27617 | −0.0467867 | ||||||||
\(745\) | 7.20252 | 0.263880 | ||||||||
\(746\) | −3.76533 | −0.137858 | ||||||||
\(747\) | 8.81328 | 0.322461 | ||||||||
\(748\) | −0.330666 | −0.0120903 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.79120 | −0.101920 | ||||||||
\(751\) | −53.5127 | −1.95271 | −0.976354 | − | 0.216178i | \(-0.930641\pi\) | ||||
−0.976354 | + | 0.216178i | \(0.930641\pi\) | |||||||
\(752\) | −1.81279 | −0.0661056 | ||||||||
\(753\) | 18.8607 | 0.687322 | ||||||||
\(754\) | 4.55580 | 0.165912 | ||||||||
\(755\) | −3.28902 | −0.119700 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.7682 | 1.08194 | 0.540972 | − | 0.841040i | \(-0.318056\pi\) | ||||
0.540972 | + | 0.841040i | \(0.318056\pi\) | |||||||
\(758\) | −0.0742315 | −0.00269621 | ||||||||
\(759\) | −2.40046 | −0.0871311 | ||||||||
\(760\) | −11.9991 | −0.435255 | ||||||||
\(761\) | 5.31595 | 0.192703 | 0.0963515 | − | 0.995347i | \(-0.469283\pi\) | ||||
0.0963515 | + | 0.995347i | \(0.469283\pi\) | |||||||
\(762\) | 1.72945 | 0.0626515 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.38813 | −0.339650 | ||||||||
\(765\) | 2.41912 | 0.0874636 | ||||||||
\(766\) | −7.07015 | −0.255455 | ||||||||
\(767\) | −56.6047 | −2.04388 | ||||||||
\(768\) | 13.4313 | 0.484661 | ||||||||
\(769\) | 22.3645 | 0.806484 | 0.403242 | − | 0.915093i | \(-0.367883\pi\) | ||||
0.403242 | + | 0.915093i | \(0.367883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.3411 | −0.948651 | ||||||||
\(772\) | 48.8784 | 1.75917 | ||||||||
\(773\) | −48.1980 | −1.73356 | −0.866780 | − | 0.498690i | \(-0.833815\pi\) | ||||
−0.866780 | + | 0.498690i | \(0.833815\pi\) | |||||||
\(774\) | 0.315399 | 0.0113368 | ||||||||
\(775\) | −16.1312 | −0.579451 | ||||||||
\(776\) | −1.92642 | −0.0691544 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.15051 | −0.148803 | ||||||||
\(779\) | 4.44030 | 0.159090 | ||||||||
\(780\) | 40.2279 | 1.44039 | ||||||||
\(781\) | −1.74723 | −0.0625208 | ||||||||
\(782\) | 1.07546 | 0.0384585 | ||||||||
\(783\) | 4.61039 | 0.164762 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −80.4461 | −2.87125 | ||||||||
\(786\) | −1.43293 | −0.0511111 | ||||||||
\(787\) | 7.84045 | 0.279482 | 0.139741 | − | 0.990188i | \(-0.455373\pi\) | ||||
0.139741 | + | 0.990188i | \(0.455373\pi\) | |||||||
\(788\) | −43.2077 | −1.53921 | ||||||||
\(789\) | 29.7738 | 1.05997 | ||||||||
\(790\) | 4.27009 | 0.151923 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.187778 | 0.00667242 | ||||||||
\(793\) | 67.4777 | 2.39620 | ||||||||
\(794\) | 4.37690 | 0.155330 | ||||||||
\(795\) | −8.50314 | −0.301575 | ||||||||
\(796\) | −6.84057 | −0.242457 | ||||||||
\(797\) | 5.10550 | 0.180846 | 0.0904230 | − | 0.995903i | \(-0.471178\pi\) | ||||
0.0904230 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.307071 | −0.0108634 | ||||||||
\(800\) | −19.3734 | −0.684952 | ||||||||
\(801\) | −5.73591 | −0.202668 | ||||||||
\(802\) | 5.11322 | 0.180554 | ||||||||
\(803\) | −3.86052 | −0.136235 | ||||||||
\(804\) | 14.8162 | 0.522527 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.75214 | −0.0617166 | ||||||||
\(807\) | −0.162754 | −0.00572920 | ||||||||
\(808\) | 7.83291 | 0.275561 | ||||||||
\(809\) | −2.94662 | −0.103598 | −0.0517989 | − | 0.998658i | \(-0.516495\pi\) | ||||
−0.0517989 | + | 0.998658i | \(0.516495\pi\) | |||||||
\(810\) | −0.681187 | −0.0239345 | ||||||||
\(811\) | −54.8372 | −1.92559 | −0.962797 | − | 0.270227i | \(-0.912901\pi\) | ||||
−0.962797 | + | 0.270227i | \(0.912901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.55601 | −0.265001 | ||||||||
\(814\) | 0.271686 | 0.00952258 | ||||||||
\(815\) | 76.7101 | 2.68704 | ||||||||
\(816\) | 2.45065 | 0.0857898 | ||||||||
\(817\) | 7.71929 | 0.270064 | ||||||||
\(818\) | −4.16432 | −0.145602 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.38576 | 0.257922 | ||||||||
\(821\) | 14.2257 | 0.496479 | 0.248240 | − | 0.968699i | \(-0.420148\pi\) | ||||
0.248240 | + | 0.968699i | \(0.420148\pi\) | |||||||
\(822\) | −2.21130 | −0.0771281 | ||||||||
\(823\) | 20.2318 | 0.705235 | 0.352617 | − | 0.935768i | \(-0.385292\pi\) | ||||
0.352617 | + | 0.935768i | \(0.385292\pi\) | |||||||
\(824\) | −4.65424 | −0.162138 | ||||||||
\(825\) | 2.37358 | 0.0826375 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.5932 | 1.27247 | 0.636235 | − | 0.771496i | \(-0.280491\pi\) | ||||
0.636235 | + | 0.771496i | \(0.280491\pi\) | |||||||
\(828\) | 18.0983 | 0.628959 | ||||||||
\(829\) | −26.4761 | −0.919551 | −0.459776 | − | 0.888035i | \(-0.652070\pi\) | ||||
−0.459776 | + | 0.888035i | \(0.652070\pi\) | |||||||
\(830\) | −6.00350 | −0.208384 | ||||||||
\(831\) | −19.1220 | −0.663336 | ||||||||
\(832\) | 39.3297 | 1.36351 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.25501 | −0.147339 | ||||||||
\(835\) | −32.5113 | −1.12510 | ||||||||
\(836\) | 2.27885 | 0.0788155 | ||||||||
\(837\) | −1.77314 | −0.0612886 | ||||||||
\(838\) | 1.30641 | 0.0451292 | ||||||||
\(839\) | −18.2255 | −0.629214 | −0.314607 | − | 0.949222i | \(-0.601873\pi\) | ||||
−0.314607 | + | 0.949222i | \(0.601873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.74431 | −0.267045 | ||||||||
\(842\) | −3.50324 | −0.120730 | ||||||||
\(843\) | 25.1709 | 0.866933 | ||||||||
\(844\) | 17.1900 | 0.591706 | ||||||||
\(845\) | 62.5768 | 2.15271 | ||||||||
\(846\) | 0.0864664 | 0.00297278 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.61394 | −0.295804 | ||||||||
\(849\) | 11.8362 | 0.406216 | ||||||||
\(850\) | −1.06342 | −0.0364751 | ||||||||
\(851\) | 52.8088 | 1.81026 | ||||||||
\(852\) | 13.1733 | 0.451309 | ||||||||
\(853\) | 11.2283 | 0.384450 | 0.192225 | − | 0.981351i | \(-0.438430\pi\) | ||||
0.192225 | + | 0.981351i | \(0.438430\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.6719 | −0.570166 | ||||||||
\(856\) | 9.87995 | 0.337690 | ||||||||
\(857\) | 27.6762 | 0.945399 | 0.472700 | − | 0.881224i | \(-0.343280\pi\) | ||||
0.472700 | + | 0.881224i | \(0.343280\pi\) | |||||||
\(858\) | 0.257814 | 0.00880163 | ||||||||
\(859\) | −2.69466 | −0.0919407 | −0.0459704 | − | 0.998943i | \(-0.514638\pi\) | ||||
−0.0459704 | + | 0.998943i | \(0.514638\pi\) | |||||||
\(860\) | 12.8399 | 0.437835 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.42371 | 0.116612 | ||||||||
\(863\) | −18.8692 | −0.642314 | −0.321157 | − | 0.947026i | \(-0.604072\pi\) | ||||
−0.321157 | + | 0.947026i | \(0.604072\pi\) | |||||||
\(864\) | −2.12951 | −0.0724475 | ||||||||
\(865\) | −26.3309 | −0.895277 | ||||||||
\(866\) | 2.54943 | 0.0866330 | ||||||||
\(867\) | −16.5849 | −0.563252 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.63550 | −0.0554804 | ||||||||
\(870\) | −3.14054 | −0.106474 | ||||||||
\(871\) | 41.0247 | 1.39007 | ||||||||
\(872\) | −3.32482 | −0.112592 | ||||||||
\(873\) | −2.67661 | −0.0905894 | ||||||||
\(874\) | −7.41176 | −0.250706 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 29.1065 | 0.983417 | ||||||||
\(877\) | 48.9667 | 1.65349 | 0.826743 | − | 0.562580i | \(-0.190191\pi\) | ||||
0.826743 | + | 0.562580i | \(0.190191\pi\) | |||||||
\(878\) | 5.77510 | 0.194900 | ||||||||
\(879\) | −28.0330 | −0.945528 | ||||||||
\(880\) | 3.72603 | 0.125604 | ||||||||
\(881\) | 52.3303 | 1.76305 | 0.881526 | − | 0.472136i | \(-0.156517\pi\) | ||||
0.881526 | + | 0.472136i | \(0.156517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0442 | −0.438971 | −0.219486 | − | 0.975616i | \(-0.570438\pi\) | ||||
−0.219486 | + | 0.975616i | \(0.570438\pi\) | |||||||
\(884\) | 6.90306 | 0.232175 | ||||||||
\(885\) | 39.0205 | 1.31166 | ||||||||
\(886\) | 5.01066 | 0.168336 | ||||||||
\(887\) | 21.7131 | 0.729053 | 0.364527 | − | 0.931193i | \(-0.381231\pi\) | ||||
0.364527 | + | 0.931193i | \(0.381231\pi\) | |||||||
\(888\) | −4.13103 | −0.138628 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.90723 | 0.130971 | ||||||||
\(891\) | 0.260903 | 0.00874059 | ||||||||
\(892\) | 23.3889 | 0.783119 | ||||||||
\(893\) | 2.11624 | 0.0708172 | ||||||||
\(894\) | −0.348022 | −0.0116396 | ||||||||
\(895\) | 26.9661 | 0.901376 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50.1126 | 1.67321 | ||||||||
\(898\) | −0.991772 | −0.0330959 | ||||||||
\(899\) | −8.17486 | −0.272647 | ||||||||
\(900\) | −17.8957 | −0.596522 | ||||||||
\(901\) | −1.45913 | −0.0486106 | ||||||||
\(902\) | 0.0473341 | 0.00157605 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.73392 | −0.190707 | ||||||||
\(905\) | 29.1631 | 0.969414 | ||||||||
\(906\) | 0.158924 | 0.00527990 | ||||||||
\(907\) | 39.7891 | 1.32117 | 0.660587 | − | 0.750749i | \(-0.270307\pi\) | ||||
0.660587 | + | 0.750749i | \(0.270307\pi\) | |||||||
\(908\) | −34.2314 | −1.13601 | ||||||||
\(909\) | 10.8832 | 0.360973 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8173 | 0.987890 | 0.493945 | − | 0.869493i | \(-0.335554\pi\) | ||||
0.493945 | + | 0.869493i | \(0.335554\pi\) | |||||||
\(912\) | −16.8891 | −0.559254 | ||||||||
\(913\) | 2.29941 | 0.0760995 | ||||||||
\(914\) | 2.69900 | 0.0892749 | ||||||||
\(915\) | −46.5157 | −1.53776 | ||||||||
\(916\) | −7.87081 | −0.260059 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.116891 | −0.00385798 | ||||||||
\(919\) | 43.1595 | 1.42370 | 0.711850 | − | 0.702331i | \(-0.247857\pi\) | ||||
0.711850 | + | 0.702331i | \(0.247857\pi\) | |||||||
\(920\) | −24.8629 | −0.819707 | ||||||||
\(921\) | 9.82237 | 0.323658 | ||||||||
\(922\) | −4.72135 | −0.155489 | ||||||||
\(923\) | 36.4757 | 1.20061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.2176 | −1.71690 | ||||||||
\(926\) | −0.675742 | −0.0222063 | ||||||||
\(927\) | −6.46670 | −0.212394 | ||||||||
\(928\) | −9.81788 | −0.322288 | ||||||||
\(929\) | −5.59313 | −0.183505 | −0.0917524 | − | 0.995782i | \(-0.529247\pi\) | ||||
−0.0917524 | + | 0.995782i | \(0.529247\pi\) | |||||||
\(930\) | 1.20784 | 0.0396066 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.96457 | 0.260888 | ||||||||
\(933\) | −32.7287 | −1.07149 | ||||||||
\(934\) | 1.20723 | 0.0395018 | ||||||||
\(935\) | 0.631157 | 0.0206411 | ||||||||
\(936\) | −3.92011 | −0.128133 | ||||||||
\(937\) | 29.0922 | 0.950400 | 0.475200 | − | 0.879878i | \(-0.342376\pi\) | ||||
0.475200 | + | 0.879878i | \(0.342376\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.01115 | −0.228800 | ||||||||
\(940\) | 3.52004 | 0.114811 | ||||||||
\(941\) | −38.9512 | −1.26977 | −0.634887 | − | 0.772605i | \(-0.718953\pi\) | ||||
−0.634887 | + | 0.772605i | \(0.718953\pi\) | |||||||
\(942\) | 3.88712 | 0.126649 | ||||||||
\(943\) | 9.20056 | 0.299611 | ||||||||
\(944\) | 39.5289 | 1.28656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0822885 | 0.00267543 | ||||||||
\(947\) | 29.6641 | 0.963954 | 0.481977 | − | 0.876184i | \(-0.339919\pi\) | ||||
0.481977 | + | 0.876184i | \(0.339919\pi\) | |||||||
\(948\) | 12.3309 | 0.400488 | ||||||||
\(949\) | 80.5933 | 2.61617 | ||||||||
\(950\) | 7.32878 | 0.237777 | ||||||||
\(951\) | −24.3997 | −0.791216 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.2806 | 0.721738 | 0.360869 | − | 0.932616i | \(-0.382480\pi\) | ||||
0.360869 | + | 0.932616i | \(0.382480\pi\) | |||||||
\(954\) | 0.410868 | 0.0133023 | ||||||||
\(955\) | 17.9196 | 0.579864 | ||||||||
\(956\) | 7.60692 | 0.246025 | ||||||||
\(957\) | 1.20287 | 0.0388831 | ||||||||
\(958\) | −2.38995 | −0.0772158 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −27.1119 | −0.875033 | ||||||||
\(961\) | −27.8560 | −0.898580 | ||||||||
\(962\) | −5.67178 | −0.182866 | ||||||||
\(963\) | 13.7274 | 0.442360 | ||||||||
\(964\) | 43.2098 | 1.39169 | ||||||||
\(965\) | −93.2965 | −3.00332 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0980 | 1.41810 | 0.709048 | − | 0.705160i | \(-0.249125\pi\) | ||||
0.709048 | + | 0.705160i | \(0.249125\pi\) | |||||||
\(968\) | −7.86798 | −0.252886 | ||||||||
\(969\) | −2.86087 | −0.0919044 | ||||||||
\(970\) | 1.82327 | 0.0585417 | ||||||||
\(971\) | −3.31986 | −0.106539 | −0.0532697 | − | 0.998580i | \(-0.516964\pi\) | ||||
−0.0532697 | + | 0.998580i | \(0.516964\pi\) | |||||||
\(972\) | −1.96709 | −0.0630943 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.33450 | 0.202971 | ||||||||
\(975\) | −49.5515 | −1.58692 | ||||||||
\(976\) | −47.1219 | −1.50833 | ||||||||
\(977\) | −7.33853 | −0.234780 | −0.117390 | − | 0.993086i | \(-0.537453\pi\) | ||||
−0.117390 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(978\) | −3.70660 | −0.118524 | ||||||||
\(979\) | −1.49652 | −0.0478289 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.61957 | −0.147491 | ||||||||
\(982\) | −3.93892 | −0.125696 | ||||||||
\(983\) | −38.0704 | −1.21426 | −0.607128 | − | 0.794604i | \(-0.707679\pi\) | ||||
−0.607128 | + | 0.794604i | \(0.707679\pi\) | |||||||
\(984\) | −0.719724 | −0.0229440 | ||||||||
\(985\) | 82.4726 | 2.62780 | ||||||||
\(986\) | −0.538913 | −0.0171625 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −47.5738 | −1.51352 | ||||||||
\(989\) | 15.9948 | 0.508606 | ||||||||
\(990\) | −0.177724 | −0.00564844 | ||||||||
\(991\) | 38.8149 | 1.23300 | 0.616498 | − | 0.787357i | \(-0.288551\pi\) | ||||
0.616498 | + | 0.787357i | \(0.288551\pi\) | |||||||
\(992\) | 3.77592 | 0.119886 | ||||||||
\(993\) | 19.1012 | 0.606159 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0569 | 0.413932 | ||||||||
\(996\) | −17.3365 | −0.549327 | ||||||||
\(997\) | −18.9298 | −0.599514 | −0.299757 | − | 0.954016i | \(-0.596906\pi\) | ||||
−0.299757 | + | 0.954016i | \(0.596906\pi\) | |||||||
\(998\) | −1.29799 | −0.0410873 | ||||||||
\(999\) | −5.73974 | −0.181597 |
(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 | 6027.2.a.bk.1.8 | 14 | ||
7.3 | odd | 6 | 861.2.i.g.247.7 | ✓ | 28 | ||
7.5 | odd | 6 | 861.2.i.g.739.7 | yes | 28 | ||
7.6 | odd | 2 | 6027.2.a.bj.1.8 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.g.247.7 | ✓ | 28 | 7.3 | odd | 6 | ||
861.2.i.g.739.7 | yes | 28 | 7.5 | odd | 6 | ||
6027.2.a.bj.1.8 | 14 | 7.6 | odd | 2 | |||
6027.2.a.bk.1.8 | 14 | 1.1 | even | 1 | trivial |