Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(1,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.53113 | 1.33464 | 0.667321 | − | 0.744771i | \(-0.267441\pi\) | ||||
0.667321 | + | 0.744771i | \(0.267441\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.53113 | −0.461653 | −0.230826 | − | 0.972995i | \(-0.574143\pi\) | ||||
−0.230826 | + | 0.972995i | \(0.574143\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 3.53113 | 0.943734 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.53113 | −0.810097 | −0.405048 | − | 0.914295i | \(-0.632745\pi\) | ||||
−0.405048 | + | 0.914295i | \(0.632745\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 3.53113 | 0.770555 | ||||||||
\(22\) | −1.53113 | −0.326438 | ||||||||
\(23\) | −1.53113 | −0.319262 | −0.159631 | − | 0.987177i | \(-0.551031\pi\) | ||||
−0.159631 | + | 0.987177i | \(0.551031\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.53113 | 0.667321 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.53113 | −0.266535 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −3.53113 | −0.596870 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.06226 | 1.48983 | 0.744913 | − | 0.667162i | \(-0.232491\pi\) | ||||
0.744913 | + | 0.667162i | \(0.232491\pi\) | |||||||
\(38\) | −3.53113 | −0.572825 | ||||||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.06226 | −1.41529 | −0.707643 | − | 0.706570i | \(-0.750242\pi\) | ||||
−0.707643 | + | 0.706570i | \(0.750242\pi\) | |||||||
\(42\) | 3.53113 | 0.544865 | ||||||||
\(43\) | −0.468871 | −0.0715022 | −0.0357511 | − | 0.999361i | \(-0.511382\pi\) | ||||
−0.0357511 | + | 0.999361i | \(0.511382\pi\) | |||||||
\(44\) | −1.53113 | −0.230826 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.53113 | −0.225753 | ||||||||
\(47\) | 11.0623 | 1.61360 | 0.806798 | − | 0.590827i | \(-0.201199\pi\) | ||||
0.806798 | + | 0.590827i | \(0.201199\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.46887 | 0.781267 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 6.00000 | 0.832050 | ||||||||
\(53\) | 5.53113 | 0.759759 | 0.379879 | − | 0.925036i | \(-0.375965\pi\) | ||||
0.379879 | + | 0.925036i | \(0.375965\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.53113 | 0.206457 | ||||||||
\(56\) | 3.53113 | 0.471867 | ||||||||
\(57\) | −3.53113 | −0.467709 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.06226 | 0.919428 | 0.459714 | − | 0.888067i | \(-0.347952\pi\) | ||||
0.459714 | + | 0.888067i | \(0.347952\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −11.0623 | −1.41638 | −0.708188 | − | 0.706023i | \(-0.750487\pi\) | ||||
−0.708188 | + | 0.706023i | \(0.750487\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 3.53113 | 0.444880 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.00000 | −0.744208 | ||||||||
\(66\) | −1.53113 | −0.188469 | ||||||||
\(67\) | −11.0623 | −1.35147 | −0.675735 | − | 0.737145i | \(-0.736174\pi\) | ||||
−0.675735 | + | 0.737145i | \(0.736174\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | −1.53113 | −0.184326 | ||||||||
\(70\) | −3.53113 | −0.422051 | ||||||||
\(71\) | −4.46887 | −0.530357 | −0.265179 | − | 0.964199i | \(-0.585431\pi\) | ||||
−0.265179 | + | 0.964199i | \(0.585431\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −0.468871 | −0.0548772 | −0.0274386 | − | 0.999623i | \(-0.508735\pi\) | ||||
−0.0274386 | + | 0.999623i | \(0.508735\pi\) | |||||||
\(74\) | 9.06226 | 1.05347 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −3.53113 | −0.405048 | ||||||||
\(77\) | −5.40661 | −0.616141 | ||||||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | −0.468871 | −0.0527521 | −0.0263761 | − | 0.999652i | \(-0.508397\pi\) | ||||
−0.0263761 | + | 0.999652i | \(0.508397\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.06226 | −1.00076 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 3.53113 | 0.385278 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | −0.468871 | −0.0505597 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.53113 | −0.163219 | ||||||||
\(89\) | 1.53113 | 0.162299 | 0.0811497 | − | 0.996702i | \(-0.474141\pi\) | ||||
0.0811497 | + | 0.996702i | \(0.474141\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 21.1868 | 2.22098 | ||||||||
\(92\) | −1.53113 | −0.159631 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 11.0623 | 1.14098 | ||||||||
\(95\) | 3.53113 | 0.362286 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −16.1245 | −1.63720 | −0.818598 | − | 0.574367i | \(-0.805248\pi\) | ||||
−0.818598 | + | 0.574367i | \(0.805248\pi\) | |||||||
\(98\) | 5.46887 | 0.552439 | ||||||||
\(99\) | −1.53113 | −0.153884 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −17.5311 | −1.74441 | −0.872206 | − | 0.489138i | \(-0.837311\pi\) | ||||
−0.872206 | + | 0.489138i | \(0.837311\pi\) | |||||||
\(102\) | −4.00000 | −0.396059 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | −3.53113 | −0.344603 | ||||||||
\(106\) | 5.53113 | 0.537231 | ||||||||
\(107\) | −14.5934 | −1.41080 | −0.705398 | − | 0.708811i | \(-0.749232\pi\) | ||||
−0.705398 | + | 0.708811i | \(0.749232\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −1.06226 | −0.101746 | −0.0508729 | − | 0.998705i | \(-0.516200\pi\) | ||||
−0.0508729 | + | 0.998705i | \(0.516200\pi\) | |||||||
\(110\) | 1.53113 | 0.145987 | ||||||||
\(111\) | 9.06226 | 0.860151 | ||||||||
\(112\) | 3.53113 | 0.333660 | ||||||||
\(113\) | 16.5934 | 1.56097 | 0.780487 | − | 0.625172i | \(-0.214971\pi\) | ||||
0.780487 | + | 0.625172i | \(0.214971\pi\) | |||||||
\(114\) | −3.53113 | −0.330721 | ||||||||
\(115\) | 1.53113 | 0.142779 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | 0.554700 | ||||||||
\(118\) | 7.06226 | 0.650134 | ||||||||
\(119\) | −14.1245 | −1.29479 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −8.65564 | −0.786877 | ||||||||
\(122\) | −11.0623 | −1.00153 | ||||||||
\(123\) | −9.06226 | −0.817116 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.53113 | 0.314578 | ||||||||
\(127\) | −9.06226 | −0.804145 | −0.402073 | − | 0.915608i | \(-0.631710\pi\) | ||||
−0.402073 | + | 0.915608i | \(0.631710\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.468871 | −0.0412818 | ||||||||
\(130\) | −6.00000 | −0.526235 | ||||||||
\(131\) | 7.06226 | 0.617032 | 0.308516 | − | 0.951219i | \(-0.400168\pi\) | ||||
0.308516 | + | 0.951219i | \(0.400168\pi\) | |||||||
\(132\) | −1.53113 | −0.133268 | ||||||||
\(133\) | −12.4689 | −1.08119 | ||||||||
\(134\) | −11.0623 | −0.955634 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | 0.937742 | 0.0801167 | 0.0400584 | − | 0.999197i | \(-0.487246\pi\) | ||||
0.0400584 | + | 0.999197i | \(0.487246\pi\) | |||||||
\(138\) | −1.53113 | −0.130338 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | −3.53113 | −0.298435 | ||||||||
\(141\) | 11.0623 | 0.931610 | ||||||||
\(142\) | −4.46887 | −0.375019 | ||||||||
\(143\) | −9.18677 | −0.768237 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.468871 | −0.0388041 | ||||||||
\(147\) | 5.46887 | 0.451065 | ||||||||
\(148\) | 9.06226 | 0.744913 | ||||||||
\(149\) | −10.4689 | −0.857643 | −0.428822 | − | 0.903389i | \(-0.641071\pi\) | ||||
−0.428822 | + | 0.903389i | \(0.641071\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −18.1245 | −1.47495 | −0.737476 | − | 0.675373i | \(-0.763983\pi\) | ||||
−0.737476 | + | 0.675373i | \(0.763983\pi\) | |||||||
\(152\) | −3.53113 | −0.286412 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | −5.40661 | −0.435677 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | −14.4689 | −1.15474 | −0.577371 | − | 0.816482i | \(-0.695921\pi\) | ||||
−0.577371 | + | 0.816482i | \(0.695921\pi\) | |||||||
\(158\) | −0.468871 | −0.0373014 | ||||||||
\(159\) | 5.53113 | 0.438647 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −5.40661 | −0.426101 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −11.0623 | −0.866463 | −0.433231 | − | 0.901283i | \(-0.642627\pi\) | ||||
−0.433231 | + | 0.901283i | \(0.642627\pi\) | |||||||
\(164\) | −9.06226 | −0.707643 | ||||||||
\(165\) | 1.53113 | 0.119198 | ||||||||
\(166\) | −8.00000 | −0.620920 | ||||||||
\(167\) | 0.593387 | 0.0459176 | 0.0229588 | − | 0.999736i | \(-0.492691\pi\) | ||||
0.0229588 | + | 0.999736i | \(0.492691\pi\) | |||||||
\(168\) | 3.53113 | 0.272433 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | −3.53113 | −0.270032 | ||||||||
\(172\) | −0.468871 | −0.0357511 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.53113 | 0.266928 | ||||||||
\(176\) | −1.53113 | −0.115413 | ||||||||
\(177\) | 7.06226 | 0.530832 | ||||||||
\(178\) | 1.53113 | 0.114763 | ||||||||
\(179\) | 13.0623 | 0.976319 | 0.488159 | − | 0.872754i | \(-0.337668\pi\) | ||||
0.488159 | + | 0.872754i | \(0.337668\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 26.5934 | 1.97667 | 0.988335 | − | 0.152293i | \(-0.0486657\pi\) | ||||
0.988335 | + | 0.152293i | \(0.0486657\pi\) | |||||||
\(182\) | 21.1868 | 1.57047 | ||||||||
\(183\) | −11.0623 | −0.817746 | ||||||||
\(184\) | −1.53113 | −0.112876 | ||||||||
\(185\) | −9.06226 | −0.666270 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | 6.12452 | 0.447869 | ||||||||
\(188\) | 11.0623 | 0.806798 | ||||||||
\(189\) | 3.53113 | 0.256852 | ||||||||
\(190\) | 3.53113 | 0.256175 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | −16.1245 | −1.15767 | ||||||||
\(195\) | −6.00000 | −0.429669 | ||||||||
\(196\) | 5.46887 | 0.390634 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | −1.53113 | −0.108813 | ||||||||
\(199\) | −0.468871 | −0.0332374 | −0.0166187 | − | 0.999862i | \(-0.505290\pi\) | ||||
−0.0166187 | + | 0.999862i | \(0.505290\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −11.0623 | −0.780272 | ||||||||
\(202\) | −17.5311 | −1.23349 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 9.06226 | 0.632936 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.53113 | −0.106421 | ||||||||
\(208\) | 6.00000 | 0.416025 | ||||||||
\(209\) | 5.40661 | 0.373983 | ||||||||
\(210\) | −3.53113 | −0.243671 | ||||||||
\(211\) | 22.5934 | 1.55539 | 0.777696 | − | 0.628640i | \(-0.216388\pi\) | ||||
0.777696 | + | 0.628640i | \(0.216388\pi\) | |||||||
\(212\) | 5.53113 | 0.379879 | ||||||||
\(213\) | −4.46887 | −0.306202 | ||||||||
\(214\) | −14.5934 | −0.997583 | ||||||||
\(215\) | 0.468871 | 0.0319767 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.53113 | 0.239709 | ||||||||
\(218\) | −1.06226 | −0.0719452 | ||||||||
\(219\) | −0.468871 | −0.0316834 | ||||||||
\(220\) | 1.53113 | 0.103229 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | 9.06226 | 0.608219 | ||||||||
\(223\) | 2.00000 | 0.133930 | 0.0669650 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669650 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(224\) | 3.53113 | 0.235933 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 16.5934 | 1.10378 | ||||||||
\(227\) | −16.4689 | −1.09308 | −0.546539 | − | 0.837434i | \(-0.684055\pi\) | ||||
−0.546539 | + | 0.837434i | \(0.684055\pi\) | |||||||
\(228\) | −3.53113 | −0.233855 | ||||||||
\(229\) | 18.5934 | 1.22869 | 0.614343 | − | 0.789039i | \(-0.289421\pi\) | ||||
0.614343 | + | 0.789039i | \(0.289421\pi\) | |||||||
\(230\) | 1.53113 | 0.100960 | ||||||||
\(231\) | −5.40661 | −0.355729 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.53113 | 0.624405 | 0.312203 | − | 0.950016i | \(-0.398933\pi\) | ||||
0.312203 | + | 0.950016i | \(0.398933\pi\) | |||||||
\(234\) | 6.00000 | 0.392232 | ||||||||
\(235\) | −11.0623 | −0.721622 | ||||||||
\(236\) | 7.06226 | 0.459714 | ||||||||
\(237\) | −0.468871 | −0.0304565 | ||||||||
\(238\) | −14.1245 | −0.915556 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | −8.65564 | −0.556406 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.0623 | −0.708188 | ||||||||
\(245\) | −5.46887 | −0.349393 | ||||||||
\(246\) | −9.06226 | −0.577788 | ||||||||
\(247\) | −21.1868 | −1.34808 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −8.00000 | −0.506979 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −13.0623 | −0.824482 | −0.412241 | − | 0.911075i | \(-0.635254\pi\) | ||||
−0.412241 | + | 0.911075i | \(0.635254\pi\) | |||||||
\(252\) | 3.53113 | 0.222440 | ||||||||
\(253\) | 2.34436 | 0.147388 | ||||||||
\(254\) | −9.06226 | −0.568617 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.6556 | −1.72511 | −0.862556 | − | 0.505962i | \(-0.831138\pi\) | ||||
−0.862556 | + | 0.505962i | \(0.831138\pi\) | |||||||
\(258\) | −0.468871 | −0.0291906 | ||||||||
\(259\) | 32.0000 | 1.98838 | ||||||||
\(260\) | −6.00000 | −0.372104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.06226 | 0.436308 | ||||||||
\(263\) | −6.93774 | −0.427800 | −0.213900 | − | 0.976856i | \(-0.568617\pi\) | ||||
−0.213900 | + | 0.976856i | \(0.568617\pi\) | |||||||
\(264\) | −1.53113 | −0.0942345 | ||||||||
\(265\) | −5.53113 | −0.339775 | ||||||||
\(266\) | −12.4689 | −0.764516 | ||||||||
\(267\) | 1.53113 | 0.0937036 | ||||||||
\(268\) | −11.0623 | −0.675735 | ||||||||
\(269\) | 29.1868 | 1.77955 | 0.889774 | − | 0.456400i | \(-0.150862\pi\) | ||||
0.889774 | + | 0.456400i | \(0.150862\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −19.5311 | −1.18643 | −0.593216 | − | 0.805043i | \(-0.702142\pi\) | ||||
−0.593216 | + | 0.805043i | \(0.702142\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 21.1868 | 1.28228 | ||||||||
\(274\) | 0.937742 | 0.0566511 | ||||||||
\(275\) | −1.53113 | −0.0923305 | ||||||||
\(276\) | −1.53113 | −0.0921631 | ||||||||
\(277\) | 1.06226 | 0.0638249 | 0.0319124 | − | 0.999491i | \(-0.489840\pi\) | ||||
0.0319124 | + | 0.999491i | \(0.489840\pi\) | |||||||
\(278\) | 6.00000 | 0.359856 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | −3.53113 | −0.211025 | ||||||||
\(281\) | −1.06226 | −0.0633690 | −0.0316845 | − | 0.999498i | \(-0.510087\pi\) | ||||
−0.0316845 | + | 0.999498i | \(0.510087\pi\) | |||||||
\(282\) | 11.0623 | 0.658748 | ||||||||
\(283\) | −12.0000 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(284\) | −4.46887 | −0.265179 | ||||||||
\(285\) | 3.53113 | 0.209166 | ||||||||
\(286\) | −9.18677 | −0.543225 | ||||||||
\(287\) | −32.0000 | −1.88890 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.1245 | −0.945236 | ||||||||
\(292\) | −0.468871 | −0.0274386 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 5.46887 | 0.318951 | ||||||||
\(295\) | −7.06226 | −0.411181 | ||||||||
\(296\) | 9.06226 | 0.526733 | ||||||||
\(297\) | −1.53113 | −0.0888451 | ||||||||
\(298\) | −10.4689 | −0.606445 | ||||||||
\(299\) | −9.18677 | −0.531285 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −1.65564 | −0.0954298 | ||||||||
\(302\) | −18.1245 | −1.04295 | ||||||||
\(303\) | −17.5311 | −1.00714 | ||||||||
\(304\) | −3.53113 | −0.202524 | ||||||||
\(305\) | 11.0623 | 0.633423 | ||||||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | 2.12452 | 0.121253 | 0.0606263 | − | 0.998161i | \(-0.480690\pi\) | ||||
0.0606263 | + | 0.998161i | \(0.480690\pi\) | |||||||
\(308\) | −5.40661 | −0.308070 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.00000 | −0.0567962 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | 27.0623 | 1.52965 | 0.764825 | − | 0.644239i | \(-0.222826\pi\) | ||||
0.764825 | + | 0.644239i | \(0.222826\pi\) | |||||||
\(314\) | −14.4689 | −0.816526 | ||||||||
\(315\) | −3.53113 | −0.198957 | ||||||||
\(316\) | −0.468871 | −0.0263761 | ||||||||
\(317\) | 29.0623 | 1.63230 | 0.816150 | − | 0.577841i | \(-0.196105\pi\) | ||||
0.816150 | + | 0.577841i | \(0.196105\pi\) | |||||||
\(318\) | 5.53113 | 0.310170 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −14.5934 | −0.814523 | ||||||||
\(322\) | −5.40661 | −0.301299 | ||||||||
\(323\) | 14.1245 | 0.785909 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | −11.0623 | −0.612682 | ||||||||
\(327\) | −1.06226 | −0.0587430 | ||||||||
\(328\) | −9.06226 | −0.500379 | ||||||||
\(329\) | 39.0623 | 2.15357 | ||||||||
\(330\) | 1.53113 | 0.0842859 | ||||||||
\(331\) | 29.0623 | 1.59741 | 0.798703 | − | 0.601725i | \(-0.205520\pi\) | ||||
0.798703 | + | 0.601725i | \(0.205520\pi\) | |||||||
\(332\) | −8.00000 | −0.439057 | ||||||||
\(333\) | 9.06226 | 0.496609 | ||||||||
\(334\) | 0.593387 | 0.0324687 | ||||||||
\(335\) | 11.0623 | 0.604396 | ||||||||
\(336\) | 3.53113 | 0.192639 | ||||||||
\(337\) | 29.1868 | 1.58990 | 0.794952 | − | 0.606672i | \(-0.207496\pi\) | ||||
0.794952 | + | 0.606672i | \(0.207496\pi\) | |||||||
\(338\) | 23.0000 | 1.25104 | ||||||||
\(339\) | 16.5934 | 0.901229 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | −1.53113 | −0.0829153 | ||||||||
\(342\) | −3.53113 | −0.190942 | ||||||||
\(343\) | −5.40661 | −0.291930 | ||||||||
\(344\) | −0.468871 | −0.0252798 | ||||||||
\(345\) | 1.53113 | 0.0824332 | ||||||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | −22.1245 | −1.18771 | −0.593853 | − | 0.804573i | \(-0.702394\pi\) | ||||
−0.593853 | + | 0.804573i | \(0.702394\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0623 | 1.34155 | 0.670776 | − | 0.741660i | \(-0.265961\pi\) | ||||
0.670776 | + | 0.741660i | \(0.265961\pi\) | |||||||
\(350\) | 3.53113 | 0.188747 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | −1.53113 | −0.0816094 | ||||||||
\(353\) | −23.0623 | −1.22748 | −0.613740 | − | 0.789508i | \(-0.710336\pi\) | ||||
−0.613740 | + | 0.789508i | \(0.710336\pi\) | |||||||
\(354\) | 7.06226 | 0.375355 | ||||||||
\(355\) | 4.46887 | 0.237183 | ||||||||
\(356\) | 1.53113 | 0.0811497 | ||||||||
\(357\) | −14.1245 | −0.747549 | ||||||||
\(358\) | 13.0623 | 0.690362 | ||||||||
\(359\) | 11.5311 | 0.608590 | 0.304295 | − | 0.952578i | \(-0.401579\pi\) | ||||
0.304295 | + | 0.952578i | \(0.401579\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −6.53113 | −0.343744 | ||||||||
\(362\) | 26.5934 | 1.39772 | ||||||||
\(363\) | −8.65564 | −0.454304 | ||||||||
\(364\) | 21.1868 | 1.11049 | ||||||||
\(365\) | 0.468871 | 0.0245418 | ||||||||
\(366\) | −11.0623 | −0.578233 | ||||||||
\(367\) | −10.0000 | −0.521996 | −0.260998 | − | 0.965339i | \(-0.584052\pi\) | ||||
−0.260998 | + | 0.965339i | \(0.584052\pi\) | |||||||
\(368\) | −1.53113 | −0.0798156 | ||||||||
\(369\) | −9.06226 | −0.471762 | ||||||||
\(370\) | −9.06226 | −0.471124 | ||||||||
\(371\) | 19.5311 | 1.01401 | ||||||||
\(372\) | 1.00000 | 0.0518476 | ||||||||
\(373\) | −10.4689 | −0.542058 | −0.271029 | − | 0.962571i | \(-0.587364\pi\) | ||||
−0.271029 | + | 0.962571i | \(0.587364\pi\) | |||||||
\(374\) | 6.12452 | 0.316691 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 11.0623 | 0.570492 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.53113 | 0.181622 | ||||||||
\(379\) | −2.59339 | −0.133213 | −0.0666067 | − | 0.997779i | \(-0.521217\pi\) | ||||
−0.0666067 | + | 0.997779i | \(0.521217\pi\) | |||||||
\(380\) | 3.53113 | 0.181143 | ||||||||
\(381\) | −9.06226 | −0.464274 | ||||||||
\(382\) | −8.00000 | −0.409316 | ||||||||
\(383\) | 13.0623 | 0.667450 | 0.333725 | − | 0.942670i | \(-0.391694\pi\) | ||||
0.333725 | + | 0.942670i | \(0.391694\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 5.40661 | 0.275547 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | −0.468871 | −0.0238341 | ||||||||
\(388\) | −16.1245 | −0.818598 | ||||||||
\(389\) | 27.0623 | 1.37211 | 0.686055 | − | 0.727549i | \(-0.259341\pi\) | ||||
0.686055 | + | 0.727549i | \(0.259341\pi\) | |||||||
\(390\) | −6.00000 | −0.303822 | ||||||||
\(391\) | 6.12452 | 0.309730 | ||||||||
\(392\) | 5.46887 | 0.276220 | ||||||||
\(393\) | 7.06226 | 0.356244 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 0.468871 | 0.0235915 | ||||||||
\(396\) | −1.53113 | −0.0769421 | ||||||||
\(397\) | −18.7179 | −0.939425 | −0.469712 | − | 0.882820i | \(-0.655642\pi\) | ||||
−0.469712 | + | 0.882820i | \(0.655642\pi\) | |||||||
\(398\) | −0.468871 | −0.0235024 | ||||||||
\(399\) | −12.4689 | −0.624224 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −34.7179 | −1.73373 | −0.866865 | − | 0.498544i | \(-0.833868\pi\) | ||||
−0.866865 | + | 0.498544i | \(0.833868\pi\) | |||||||
\(402\) | −11.0623 | −0.551735 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | −17.5311 | −0.872206 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8755 | −0.687782 | ||||||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | −9.06226 | −0.448100 | −0.224050 | − | 0.974578i | \(-0.571928\pi\) | ||||
−0.224050 | + | 0.974578i | \(0.571928\pi\) | |||||||
\(410\) | 9.06226 | 0.447553 | ||||||||
\(411\) | 0.937742 | 0.0462554 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.9377 | 1.22711 | ||||||||
\(414\) | −1.53113 | −0.0752509 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 6.00000 | 0.294174 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 5.40661 | 0.264446 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −3.53113 | −0.172301 | ||||||||
\(421\) | 38.2490 | 1.86414 | 0.932072 | − | 0.362273i | \(-0.117999\pi\) | ||||
0.932072 | + | 0.362273i | \(0.117999\pi\) | |||||||
\(422\) | 22.5934 | 1.09983 | ||||||||
\(423\) | 11.0623 | 0.537865 | ||||||||
\(424\) | 5.53113 | 0.268615 | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | −4.46887 | −0.216518 | ||||||||
\(427\) | −39.0623 | −1.89036 | ||||||||
\(428\) | −14.5934 | −0.705398 | ||||||||
\(429\) | −9.18677 | −0.443542 | ||||||||
\(430\) | 0.468871 | 0.0226110 | ||||||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −1.40661 | −0.0675975 | −0.0337988 | − | 0.999429i | \(-0.510761\pi\) | ||||
−0.0337988 | + | 0.999429i | \(0.510761\pi\) | |||||||
\(434\) | 3.53113 | 0.169500 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.06226 | −0.0508729 | ||||||||
\(437\) | 5.40661 | 0.258633 | ||||||||
\(438\) | −0.468871 | −0.0224035 | ||||||||
\(439\) | −8.93774 | −0.426575 | −0.213288 | − | 0.976989i | \(-0.568417\pi\) | ||||
−0.213288 | + | 0.976989i | \(0.568417\pi\) | |||||||
\(440\) | 1.53113 | 0.0729937 | ||||||||
\(441\) | 5.46887 | 0.260422 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | 38.5934 | 1.83363 | 0.916814 | − | 0.399316i | \(-0.130752\pi\) | ||||
0.916814 | + | 0.399316i | \(0.130752\pi\) | |||||||
\(444\) | 9.06226 | 0.430076 | ||||||||
\(445\) | −1.53113 | −0.0725825 | ||||||||
\(446\) | 2.00000 | 0.0947027 | ||||||||
\(447\) | −10.4689 | −0.495161 | ||||||||
\(448\) | 3.53113 | 0.166830 | ||||||||
\(449\) | 28.1245 | 1.32728 | 0.663639 | − | 0.748053i | \(-0.269011\pi\) | ||||
0.663639 | + | 0.748053i | \(0.269011\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 13.8755 | 0.653371 | ||||||||
\(452\) | 16.5934 | 0.780487 | ||||||||
\(453\) | −18.1245 | −0.851564 | ||||||||
\(454\) | −16.4689 | −0.772922 | ||||||||
\(455\) | −21.1868 | −0.993251 | ||||||||
\(456\) | −3.53113 | −0.165360 | ||||||||
\(457\) | 31.0623 | 1.45303 | 0.726516 | − | 0.687150i | \(-0.241138\pi\) | ||||
0.726516 | + | 0.687150i | \(0.241138\pi\) | |||||||
\(458\) | 18.5934 | 0.868812 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 1.53113 | 0.0713893 | ||||||||
\(461\) | 24.0000 | 1.11779 | 0.558896 | − | 0.829238i | \(-0.311225\pi\) | ||||
0.558896 | + | 0.829238i | \(0.311225\pi\) | |||||||
\(462\) | −5.40661 | −0.251538 | ||||||||
\(463\) | −35.1868 | −1.63527 | −0.817634 | − | 0.575738i | \(-0.804715\pi\) | ||||
−0.817634 | + | 0.575738i | \(0.804715\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 9.53113 | 0.441521 | ||||||||
\(467\) | 10.1245 | 0.468507 | 0.234253 | − | 0.972176i | \(-0.424735\pi\) | ||||
0.234253 | + | 0.972176i | \(0.424735\pi\) | |||||||
\(468\) | 6.00000 | 0.277350 | ||||||||
\(469\) | −39.0623 | −1.80373 | ||||||||
\(470\) | −11.0623 | −0.510264 | ||||||||
\(471\) | −14.4689 | −0.666690 | ||||||||
\(472\) | 7.06226 | 0.325067 | ||||||||
\(473\) | 0.717902 | 0.0330092 | ||||||||
\(474\) | −0.468871 | −0.0215360 | ||||||||
\(475\) | −3.53113 | −0.162019 | ||||||||
\(476\) | −14.1245 | −0.647396 | ||||||||
\(477\) | 5.53113 | 0.253253 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | 41.6556 | 1.90329 | 0.951647 | − | 0.307192i | \(-0.0993895\pi\) | ||||
0.951647 | + | 0.307192i | \(0.0993895\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 54.3735 | 2.47922 | ||||||||
\(482\) | 2.00000 | 0.0910975 | ||||||||
\(483\) | −5.40661 | −0.246009 | ||||||||
\(484\) | −8.65564 | −0.393438 | ||||||||
\(485\) | 16.1245 | 0.732177 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 6.93774 | 0.314379 | 0.157190 | − | 0.987568i | \(-0.449757\pi\) | ||||
0.157190 | + | 0.987568i | \(0.449757\pi\) | |||||||
\(488\) | −11.0623 | −0.500765 | ||||||||
\(489\) | −11.0623 | −0.500253 | ||||||||
\(490\) | −5.46887 | −0.247058 | ||||||||
\(491\) | 16.5934 | 0.748849 | 0.374425 | − | 0.927257i | \(-0.377840\pi\) | ||||
0.374425 | + | 0.927257i | \(0.377840\pi\) | |||||||
\(492\) | −9.06226 | −0.408558 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −21.1868 | −0.953238 | ||||||||
\(495\) | 1.53113 | 0.0688191 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −15.7802 | −0.707837 | ||||||||
\(498\) | −8.00000 | −0.358489 | ||||||||
\(499\) | 9.06226 | 0.405682 | 0.202841 | − | 0.979212i | \(-0.434982\pi\) | ||||
0.202841 | + | 0.979212i | \(0.434982\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0.593387 | 0.0265106 | ||||||||
\(502\) | −13.0623 | −0.582997 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 3.53113 | 0.157289 | ||||||||
\(505\) | 17.5311 | 0.780125 | ||||||||
\(506\) | 2.34436 | 0.104219 | ||||||||
\(507\) | 23.0000 | 1.02147 | ||||||||
\(508\) | −9.06226 | −0.402073 | ||||||||
\(509\) | 5.87548 | 0.260426 | 0.130213 | − | 0.991486i | \(-0.458434\pi\) | ||||
0.130213 | + | 0.991486i | \(0.458434\pi\) | |||||||
\(510\) | 4.00000 | 0.177123 | ||||||||
\(511\) | −1.65564 | −0.0732414 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.53113 | −0.155903 | ||||||||
\(514\) | −27.6556 | −1.21984 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.468871 | −0.0206409 | ||||||||
\(517\) | −16.9377 | −0.744921 | ||||||||
\(518\) | 32.0000 | 1.40600 | ||||||||
\(519\) | 14.0000 | 0.614532 | ||||||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | 20.1245 | 0.881671 | 0.440836 | − | 0.897588i | \(-0.354682\pi\) | ||||
0.440836 | + | 0.897588i | \(0.354682\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.5934 | −0.638124 | −0.319062 | − | 0.947734i | \(-0.603368\pi\) | ||||
−0.319062 | + | 0.947734i | \(0.603368\pi\) | |||||||
\(524\) | 7.06226 | 0.308516 | ||||||||
\(525\) | 3.53113 | 0.154111 | ||||||||
\(526\) | −6.93774 | −0.302500 | ||||||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | −1.53113 | −0.0666338 | ||||||||
\(529\) | −20.6556 | −0.898071 | ||||||||
\(530\) | −5.53113 | −0.240257 | ||||||||
\(531\) | 7.06226 | 0.306476 | ||||||||
\(532\) | −12.4689 | −0.540594 | ||||||||
\(533\) | −54.3735 | −2.35518 | ||||||||
\(534\) | 1.53113 | 0.0662584 | ||||||||
\(535\) | 14.5934 | 0.630927 | ||||||||
\(536\) | −11.0623 | −0.477817 | ||||||||
\(537\) | 13.0623 | 0.563678 | ||||||||
\(538\) | 29.1868 | 1.25833 | ||||||||
\(539\) | −8.37355 | −0.360674 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 28.1245 | 1.20917 | 0.604584 | − | 0.796542i | \(-0.293340\pi\) | ||||
0.604584 | + | 0.796542i | \(0.293340\pi\) | |||||||
\(542\) | −19.5311 | −0.838934 | ||||||||
\(543\) | 26.5934 | 1.14123 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 1.06226 | 0.0455021 | ||||||||
\(546\) | 21.1868 | 0.906710 | ||||||||
\(547\) | 41.1868 | 1.76102 | 0.880510 | − | 0.474028i | \(-0.157201\pi\) | ||||
0.880510 | + | 0.474028i | \(0.157201\pi\) | |||||||
\(548\) | 0.937742 | 0.0400584 | ||||||||
\(549\) | −11.0623 | −0.472126 | ||||||||
\(550\) | −1.53113 | −0.0652876 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.53113 | −0.0651692 | ||||||||
\(553\) | −1.65564 | −0.0704052 | ||||||||
\(554\) | 1.06226 | 0.0451310 | ||||||||
\(555\) | −9.06226 | −0.384671 | ||||||||
\(556\) | 6.00000 | 0.254457 | ||||||||
\(557\) | 45.7802 | 1.93977 | 0.969884 | − | 0.243568i | \(-0.0783179\pi\) | ||||
0.969884 | + | 0.243568i | \(0.0783179\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | −2.81323 | −0.118987 | ||||||||
\(560\) | −3.53113 | −0.149217 | ||||||||
\(561\) | 6.12452 | 0.258577 | ||||||||
\(562\) | −1.06226 | −0.0448086 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 11.0623 | 0.465805 | ||||||||
\(565\) | −16.5934 | −0.698089 | ||||||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | 3.53113 | 0.148293 | ||||||||
\(568\) | −4.46887 | −0.187510 | ||||||||
\(569\) | 17.5311 | 0.734943 | 0.367472 | − | 0.930035i | \(-0.380224\pi\) | ||||
0.367472 | + | 0.930035i | \(0.380224\pi\) | |||||||
\(570\) | 3.53113 | 0.147903 | ||||||||
\(571\) | 3.87548 | 0.162184 | 0.0810920 | − | 0.996707i | \(-0.474159\pi\) | ||||
0.0810920 | + | 0.996707i | \(0.474159\pi\) | |||||||
\(572\) | −9.18677 | −0.384118 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | −32.0000 | −1.33565 | ||||||||
\(575\) | −1.53113 | −0.0638525 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −11.1868 | −0.465711 | −0.232856 | − | 0.972511i | \(-0.574807\pi\) | ||||
−0.232856 | + | 0.972511i | \(0.574807\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.2490 | −1.17197 | ||||||||
\(582\) | −16.1245 | −0.668383 | ||||||||
\(583\) | −8.46887 | −0.350745 | ||||||||
\(584\) | −0.468871 | −0.0194020 | ||||||||
\(585\) | −6.00000 | −0.248069 | ||||||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | 20.2490 | 0.835767 | 0.417883 | − | 0.908501i | \(-0.362772\pi\) | ||||
0.417883 | + | 0.908501i | \(0.362772\pi\) | |||||||
\(588\) | 5.46887 | 0.225532 | ||||||||
\(589\) | −3.53113 | −0.145498 | ||||||||
\(590\) | −7.06226 | −0.290749 | ||||||||
\(591\) | 6.00000 | 0.246807 | ||||||||
\(592\) | 9.06226 | 0.372456 | ||||||||
\(593\) | −14.0000 | −0.574911 | −0.287456 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287456 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(594\) | −1.53113 | −0.0628230 | ||||||||
\(595\) | 14.1245 | 0.579049 | ||||||||
\(596\) | −10.4689 | −0.428822 | ||||||||
\(597\) | −0.468871 | −0.0191896 | ||||||||
\(598\) | −9.18677 | −0.375675 | ||||||||
\(599\) | 10.5934 | 0.432834 | 0.216417 | − | 0.976301i | \(-0.430563\pi\) | ||||
0.216417 | + | 0.976301i | \(0.430563\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 30.0000 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(602\) | −1.65564 | −0.0674790 | ||||||||
\(603\) | −11.0623 | −0.450490 | ||||||||
\(604\) | −18.1245 | −0.737476 | ||||||||
\(605\) | 8.65564 | 0.351902 | ||||||||
\(606\) | −17.5311 | −0.712153 | ||||||||
\(607\) | −38.5934 | −1.56646 | −0.783229 | − | 0.621734i | \(-0.786429\pi\) | ||||
−0.783229 | + | 0.621734i | \(0.786429\pi\) | |||||||
\(608\) | −3.53113 | −0.143206 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.0623 | 0.447898 | ||||||||
\(611\) | 66.3735 | 2.68519 | ||||||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | −30.0000 | −1.21169 | −0.605844 | − | 0.795583i | \(-0.707165\pi\) | ||||
−0.605844 | + | 0.795583i | \(0.707165\pi\) | |||||||
\(614\) | 2.12452 | 0.0857385 | ||||||||
\(615\) | 9.06226 | 0.365426 | ||||||||
\(616\) | −5.40661 | −0.217839 | ||||||||
\(617\) | 20.5934 | 0.829059 | 0.414529 | − | 0.910036i | \(-0.363946\pi\) | ||||
0.414529 | + | 0.910036i | \(0.363946\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.0000 | −1.36658 | −0.683288 | − | 0.730149i | \(-0.739451\pi\) | ||||
−0.683288 | + | 0.730149i | \(0.739451\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | −1.53113 | −0.0614421 | ||||||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | 5.40661 | 0.216611 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 27.0623 | 1.08163 | ||||||||
\(627\) | 5.40661 | 0.215919 | ||||||||
\(628\) | −14.4689 | −0.577371 | ||||||||
\(629\) | −36.2490 | −1.44534 | ||||||||
\(630\) | −3.53113 | −0.140684 | ||||||||
\(631\) | −9.65564 | −0.384385 | −0.192193 | − | 0.981357i | \(-0.561560\pi\) | ||||
−0.192193 | + | 0.981357i | \(0.561560\pi\) | |||||||
\(632\) | −0.468871 | −0.0186507 | ||||||||
\(633\) | 22.5934 | 0.898006 | ||||||||
\(634\) | 29.0623 | 1.15421 | ||||||||
\(635\) | 9.06226 | 0.359625 | ||||||||
\(636\) | 5.53113 | 0.219324 | ||||||||
\(637\) | 32.8132 | 1.30011 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.46887 | −0.176786 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −22.0000 | −0.868948 | −0.434474 | − | 0.900684i | \(-0.643066\pi\) | ||||
−0.434474 | + | 0.900684i | \(0.643066\pi\) | |||||||
\(642\) | −14.5934 | −0.575955 | ||||||||
\(643\) | 6.59339 | 0.260018 | 0.130009 | − | 0.991513i | \(-0.458499\pi\) | ||||
0.130009 | + | 0.991513i | \(0.458499\pi\) | |||||||
\(644\) | −5.40661 | −0.213050 | ||||||||
\(645\) | 0.468871 | 0.0184618 | ||||||||
\(646\) | 14.1245 | 0.555722 | ||||||||
\(647\) | 1.53113 | 0.0601949 | 0.0300974 | − | 0.999547i | \(-0.490418\pi\) | ||||
0.0300974 | + | 0.999547i | \(0.490418\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −10.8132 | −0.424456 | ||||||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 3.53113 | 0.138396 | ||||||||
\(652\) | −11.0623 | −0.433231 | ||||||||
\(653\) | −26.2490 | −1.02720 | −0.513602 | − | 0.858029i | \(-0.671689\pi\) | ||||
−0.513602 | + | 0.858029i | \(0.671689\pi\) | |||||||
\(654\) | −1.06226 | −0.0415376 | ||||||||
\(655\) | −7.06226 | −0.275945 | ||||||||
\(656\) | −9.06226 | −0.353822 | ||||||||
\(657\) | −0.468871 | −0.0182924 | ||||||||
\(658\) | 39.0623 | 1.52281 | ||||||||
\(659\) | 16.0000 | 0.623272 | 0.311636 | − | 0.950202i | \(-0.399123\pi\) | ||||
0.311636 | + | 0.950202i | \(0.399123\pi\) | |||||||
\(660\) | 1.53113 | 0.0595991 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | 29.0623 | 1.12954 | ||||||||
\(663\) | −24.0000 | −0.932083 | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 12.4689 | 0.483522 | ||||||||
\(666\) | 9.06226 | 0.351155 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.593387 | 0.0229588 | ||||||||
\(669\) | 2.00000 | 0.0773245 | ||||||||
\(670\) | 11.0623 | 0.427372 | ||||||||
\(671\) | 16.9377 | 0.653874 | ||||||||
\(672\) | 3.53113 | 0.136216 | ||||||||
\(673\) | 7.06226 | 0.272230 | 0.136115 | − | 0.990693i | \(-0.456538\pi\) | ||||
0.136115 | + | 0.990693i | \(0.456538\pi\) | |||||||
\(674\) | 29.1868 | 1.12423 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 3.40661 | 0.130927 | 0.0654634 | − | 0.997855i | \(-0.479147\pi\) | ||||
0.0654634 | + | 0.997855i | \(0.479147\pi\) | |||||||
\(678\) | 16.5934 | 0.637265 | ||||||||
\(679\) | −56.9377 | −2.18507 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | −16.4689 | −0.631089 | ||||||||
\(682\) | −1.53113 | −0.0586300 | ||||||||
\(683\) | 15.5311 | 0.594282 | 0.297141 | − | 0.954834i | \(-0.403967\pi\) | ||||
0.297141 | + | 0.954834i | \(0.403967\pi\) | |||||||
\(684\) | −3.53113 | −0.135016 | ||||||||
\(685\) | −0.937742 | −0.0358293 | ||||||||
\(686\) | −5.40661 | −0.206425 | ||||||||
\(687\) | 18.5934 | 0.709382 | ||||||||
\(688\) | −0.468871 | −0.0178755 | ||||||||
\(689\) | 33.1868 | 1.26432 | ||||||||
\(690\) | 1.53113 | 0.0582891 | ||||||||
\(691\) | −7.53113 | −0.286498 | −0.143249 | − | 0.989687i | \(-0.545755\pi\) | ||||
−0.143249 | + | 0.989687i | \(0.545755\pi\) | |||||||
\(692\) | 14.0000 | 0.532200 | ||||||||
\(693\) | −5.40661 | −0.205380 | ||||||||
\(694\) | −22.1245 | −0.839835 | ||||||||
\(695\) | −6.00000 | −0.227593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.2490 | 1.37303 | ||||||||
\(698\) | 25.0623 | 0.948620 | ||||||||
\(699\) | 9.53113 | 0.360500 | ||||||||
\(700\) | 3.53113 | 0.133464 | ||||||||
\(701\) | −21.5311 | −0.813220 | −0.406610 | − | 0.913602i | \(-0.633289\pi\) | ||||
−0.406610 | + | 0.913602i | \(0.633289\pi\) | |||||||
\(702\) | 6.00000 | 0.226455 | ||||||||
\(703\) | −32.0000 | −1.20690 | ||||||||
\(704\) | −1.53113 | −0.0577066 | ||||||||
\(705\) | −11.0623 | −0.416629 | ||||||||
\(706\) | −23.0623 | −0.867960 | ||||||||
\(707\) | −61.9047 | −2.32816 | ||||||||
\(708\) | 7.06226 | 0.265416 | ||||||||
\(709\) | 25.4066 | 0.954165 | 0.477083 | − | 0.878858i | \(-0.341694\pi\) | ||||
0.477083 | + | 0.878858i | \(0.341694\pi\) | |||||||
\(710\) | 4.46887 | 0.167714 | ||||||||
\(711\) | −0.468871 | −0.0175840 | ||||||||
\(712\) | 1.53113 | 0.0573815 | ||||||||
\(713\) | −1.53113 | −0.0573412 | ||||||||
\(714\) | −14.1245 | −0.528597 | ||||||||
\(715\) | 9.18677 | 0.343566 | ||||||||
\(716\) | 13.0623 | 0.488159 | ||||||||
\(717\) | −8.00000 | −0.298765 | ||||||||
\(718\) | 11.5311 | 0.430338 | ||||||||
\(719\) | −33.1868 | −1.23766 | −0.618829 | − | 0.785526i | \(-0.712393\pi\) | ||||
−0.618829 | + | 0.785526i | \(0.712393\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.53113 | −0.243063 | ||||||||
\(723\) | 2.00000 | 0.0743808 | ||||||||
\(724\) | 26.5934 | 0.988335 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.65564 | −0.321241 | ||||||||
\(727\) | −50.8424 | −1.88564 | −0.942820 | − | 0.333301i | \(-0.891837\pi\) | ||||
−0.942820 | + | 0.333301i | \(0.891837\pi\) | |||||||
\(728\) | 21.1868 | 0.785234 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.468871 | 0.0173537 | ||||||||
\(731\) | 1.87548 | 0.0693673 | ||||||||
\(732\) | −11.0623 | −0.408873 | ||||||||
\(733\) | 4.12452 | 0.152342 | 0.0761712 | − | 0.997095i | \(-0.475730\pi\) | ||||
0.0761712 | + | 0.997095i | \(0.475730\pi\) | |||||||
\(734\) | −10.0000 | −0.369107 | ||||||||
\(735\) | −5.46887 | −0.201722 | ||||||||
\(736\) | −1.53113 | −0.0564382 | ||||||||
\(737\) | 16.9377 | 0.623910 | ||||||||
\(738\) | −9.06226 | −0.333586 | ||||||||
\(739\) | 27.1868 | 1.00008 | 0.500041 | − | 0.866002i | \(-0.333318\pi\) | ||||
0.500041 | + | 0.866002i | \(0.333318\pi\) | |||||||
\(740\) | −9.06226 | −0.333135 | ||||||||
\(741\) | −21.1868 | −0.778316 | ||||||||
\(742\) | 19.5311 | 0.717010 | ||||||||
\(743\) | 11.6556 | 0.427604 | 0.213802 | − | 0.976877i | \(-0.431415\pi\) | ||||
0.213802 | + | 0.976877i | \(0.431415\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 10.4689 | 0.383550 | ||||||||
\(746\) | −10.4689 | −0.383293 | ||||||||
\(747\) | −8.00000 | −0.292705 | ||||||||
\(748\) | 6.12452 | 0.223934 | ||||||||
\(749\) | −51.5311 | −1.88291 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 47.0623 | 1.71733 | 0.858663 | − | 0.512540i | \(-0.171296\pi\) | ||||
0.858663 | + | 0.512540i | \(0.171296\pi\) | |||||||
\(752\) | 11.0623 | 0.403399 | ||||||||
\(753\) | −13.0623 | −0.476015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1245 | 0.659619 | ||||||||
\(756\) | 3.53113 | 0.128426 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | −2.59339 | −0.0941960 | ||||||||
\(759\) | 2.34436 | 0.0850947 | ||||||||
\(760\) | 3.53113 | 0.128088 | ||||||||
\(761\) | −12.5934 | −0.456510 | −0.228255 | − | 0.973601i | \(-0.573302\pi\) | ||||
−0.228255 | + | 0.973601i | \(0.573302\pi\) | |||||||
\(762\) | −9.06226 | −0.328291 | ||||||||
\(763\) | −3.75097 | −0.135794 | ||||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | 13.0623 | 0.471959 | ||||||||
\(767\) | 42.3735 | 1.53002 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −28.5934 | −1.03110 | −0.515552 | − | 0.856858i | \(-0.672413\pi\) | ||||
−0.515552 | + | 0.856858i | \(0.672413\pi\) | |||||||
\(770\) | 5.40661 | 0.194841 | ||||||||
\(771\) | −27.6556 | −0.995994 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 14.4689 | 0.520409 | 0.260205 | − | 0.965554i | \(-0.416210\pi\) | ||||
0.260205 | + | 0.965554i | \(0.416210\pi\) | |||||||
\(774\) | −0.468871 | −0.0168532 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | −16.1245 | −0.578836 | ||||||||
\(777\) | 32.0000 | 1.14799 | ||||||||
\(778\) | 27.0623 | 0.970229 | ||||||||
\(779\) | 32.0000 | 1.14652 | ||||||||
\(780\) | −6.00000 | −0.214834 | ||||||||
\(781\) | 6.84242 | 0.244841 | ||||||||
\(782\) | 6.12452 | 0.219012 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.46887 | 0.195317 | ||||||||
\(785\) | 14.4689 | 0.516416 | ||||||||
\(786\) | 7.06226 | 0.251902 | ||||||||
\(787\) | −28.4689 | −1.01481 | −0.507403 | − | 0.861709i | \(-0.669394\pi\) | ||||
−0.507403 | + | 0.861709i | \(0.669394\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | −6.93774 | −0.246990 | ||||||||
\(790\) | 0.468871 | 0.0166817 | ||||||||
\(791\) | 58.5934 | 2.08334 | ||||||||
\(792\) | −1.53113 | −0.0544063 | ||||||||
\(793\) | −66.3735 | −2.35699 | ||||||||
\(794\) | −18.7179 | −0.664273 | ||||||||
\(795\) | −5.53113 | −0.196169 | ||||||||
\(796\) | −0.468871 | −0.0166187 | ||||||||
\(797\) | −20.1245 | −0.712847 | −0.356423 | − | 0.934325i | \(-0.616004\pi\) | ||||
−0.356423 | + | 0.934325i | \(0.616004\pi\) | |||||||
\(798\) | −12.4689 | −0.441393 | ||||||||
\(799\) | −44.2490 | −1.56542 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 1.53113 | 0.0540998 | ||||||||
\(802\) | −34.7179 | −1.22593 | ||||||||
\(803\) | 0.717902 | 0.0253342 | ||||||||
\(804\) | −11.0623 | −0.390136 | ||||||||
\(805\) | 5.40661 | 0.190558 | ||||||||
\(806\) | 6.00000 | 0.211341 | ||||||||
\(807\) | 29.1868 | 1.02742 | ||||||||
\(808\) | −17.5311 | −0.616743 | ||||||||
\(809\) | −8.59339 | −0.302127 | −0.151064 | − | 0.988524i | \(-0.548270\pi\) | ||||
−0.151064 | + | 0.988524i | \(0.548270\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −39.7802 | −1.39687 | −0.698435 | − | 0.715673i | \(-0.746120\pi\) | ||||
−0.698435 | + | 0.715673i | \(0.746120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.5311 | −0.684987 | ||||||||
\(814\) | −13.8755 | −0.486335 | ||||||||
\(815\) | 11.0623 | 0.387494 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 1.65564 | 0.0579237 | ||||||||
\(818\) | −9.06226 | −0.316854 | ||||||||
\(819\) | 21.1868 | 0.740326 | ||||||||
\(820\) | 9.06226 | 0.316468 | ||||||||
\(821\) | 9.87548 | 0.344657 | 0.172328 | − | 0.985040i | \(-0.444871\pi\) | ||||
0.172328 | + | 0.985040i | \(0.444871\pi\) | |||||||
\(822\) | 0.937742 | 0.0327075 | ||||||||
\(823\) | 7.87548 | 0.274522 | 0.137261 | − | 0.990535i | \(-0.456170\pi\) | ||||
0.137261 | + | 0.990535i | \(0.456170\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.53113 | −0.0533071 | ||||||||
\(826\) | 24.9377 | 0.867695 | ||||||||
\(827\) | 8.00000 | 0.278187 | 0.139094 | − | 0.990279i | \(-0.455581\pi\) | ||||
0.139094 | + | 0.990279i | \(0.455581\pi\) | |||||||
\(828\) | −1.53113 | −0.0532104 | ||||||||
\(829\) | −9.65564 | −0.335354 | −0.167677 | − | 0.985842i | \(-0.553627\pi\) | ||||
−0.167677 | + | 0.985842i | \(0.553627\pi\) | |||||||
\(830\) | 8.00000 | 0.277684 | ||||||||
\(831\) | 1.06226 | 0.0368493 | ||||||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | −21.8755 | −0.757941 | ||||||||
\(834\) | 6.00000 | 0.207763 | ||||||||
\(835\) | −0.593387 | −0.0205350 | ||||||||
\(836\) | 5.40661 | 0.186992 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.8424 | −1.89337 | −0.946685 | − | 0.322160i | \(-0.895591\pi\) | ||||
−0.946685 | + | 0.322160i | \(0.895591\pi\) | |||||||
\(840\) | −3.53113 | −0.121836 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 38.2490 | 1.31815 | ||||||||
\(843\) | −1.06226 | −0.0365861 | ||||||||
\(844\) | 22.5934 | 0.777696 | ||||||||
\(845\) | −23.0000 | −0.791224 | ||||||||
\(846\) | 11.0623 | 0.380328 | ||||||||
\(847\) | −30.5642 | −1.05020 | ||||||||
\(848\) | 5.53113 | 0.189940 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | −4.00000 | −0.137199 | ||||||||
\(851\) | −13.8755 | −0.475645 | ||||||||
\(852\) | −4.46887 | −0.153101 | ||||||||
\(853\) | 1.28210 | 0.0438982 | 0.0219491 | − | 0.999759i | \(-0.493013\pi\) | ||||
0.0219491 | + | 0.999759i | \(0.493013\pi\) | |||||||
\(854\) | −39.0623 | −1.33668 | ||||||||
\(855\) | 3.53113 | 0.120762 | ||||||||
\(856\) | −14.5934 | −0.498792 | ||||||||
\(857\) | 14.0000 | 0.478231 | 0.239115 | − | 0.970991i | \(-0.423143\pi\) | ||||
0.239115 | + | 0.970991i | \(0.423143\pi\) | |||||||
\(858\) | −9.18677 | −0.313631 | ||||||||
\(859\) | −6.93774 | −0.236713 | −0.118356 | − | 0.992971i | \(-0.537763\pi\) | ||||
−0.118356 | + | 0.992971i | \(0.537763\pi\) | |||||||
\(860\) | 0.468871 | 0.0159884 | ||||||||
\(861\) | −32.0000 | −1.09056 | ||||||||
\(862\) | −24.0000 | −0.817443 | ||||||||
\(863\) | 41.5311 | 1.41374 | 0.706868 | − | 0.707345i | \(-0.250107\pi\) | ||||
0.706868 | + | 0.707345i | \(0.250107\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | −1.40661 | −0.0477987 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 3.53113 | 0.119854 | ||||||||
\(869\) | 0.717902 | 0.0243532 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −66.3735 | −2.24898 | ||||||||
\(872\) | −1.06226 | −0.0359726 | ||||||||
\(873\) | −16.1245 | −0.545732 | ||||||||
\(874\) | 5.40661 | 0.182881 | ||||||||
\(875\) | −3.53113 | −0.119374 | ||||||||
\(876\) | −0.468871 | −0.0158417 | ||||||||
\(877\) | 44.1245 | 1.48998 | 0.744990 | − | 0.667076i | \(-0.232454\pi\) | ||||
0.744990 | + | 0.667076i | \(0.232454\pi\) | |||||||
\(878\) | −8.93774 | −0.301634 | ||||||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | 1.53113 | 0.0516143 | ||||||||
\(881\) | 36.1245 | 1.21707 | 0.608533 | − | 0.793529i | \(-0.291758\pi\) | ||||
0.608533 | + | 0.793529i | \(0.291758\pi\) | |||||||
\(882\) | 5.46887 | 0.184146 | ||||||||
\(883\) | −53.6556 | −1.80566 | −0.902828 | − | 0.430002i | \(-0.858513\pi\) | ||||
−0.902828 | + | 0.430002i | \(0.858513\pi\) | |||||||
\(884\) | −24.0000 | −0.807207 | ||||||||
\(885\) | −7.06226 | −0.237395 | ||||||||
\(886\) | 38.5934 | 1.29657 | ||||||||
\(887\) | −25.1868 | −0.845689 | −0.422845 | − | 0.906202i | \(-0.638968\pi\) | ||||
−0.422845 | + | 0.906202i | \(0.638968\pi\) | |||||||
\(888\) | 9.06226 | 0.304109 | ||||||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | −1.53113 | −0.0513236 | ||||||||
\(891\) | −1.53113 | −0.0512947 | ||||||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | −39.0623 | −1.30717 | ||||||||
\(894\) | −10.4689 | −0.350131 | ||||||||
\(895\) | −13.0623 | −0.436623 | ||||||||
\(896\) | 3.53113 | 0.117967 | ||||||||
\(897\) | −9.18677 | −0.306737 | ||||||||
\(898\) | 28.1245 | 0.938527 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −22.1245 | −0.737074 | ||||||||
\(902\) | 13.8755 | 0.462003 | ||||||||
\(903\) | −1.65564 | −0.0550964 | ||||||||
\(904\) | 16.5934 | 0.551888 | ||||||||
\(905\) | −26.5934 | −0.883994 | ||||||||
\(906\) | −18.1245 | −0.602147 | ||||||||
\(907\) | −32.2490 | −1.07081 | −0.535406 | − | 0.844595i | \(-0.679841\pi\) | ||||
−0.535406 | + | 0.844595i | \(0.679841\pi\) | |||||||
\(908\) | −16.4689 | −0.546539 | ||||||||
\(909\) | −17.5311 | −0.581471 | ||||||||
\(910\) | −21.1868 | −0.702335 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | −3.53113 | −0.116927 | ||||||||
\(913\) | 12.2490 | 0.405384 | ||||||||
\(914\) | 31.0623 | 1.02745 | ||||||||
\(915\) | 11.0623 | 0.365707 | ||||||||
\(916\) | 18.5934 | 0.614343 | ||||||||
\(917\) | 24.9377 | 0.823517 | ||||||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | −8.93774 | −0.294829 | −0.147414 | − | 0.989075i | \(-0.547095\pi\) | ||||
−0.147414 | + | 0.989075i | \(0.547095\pi\) | |||||||
\(920\) | 1.53113 | 0.0504798 | ||||||||
\(921\) | 2.12452 | 0.0700052 | ||||||||
\(922\) | 24.0000 | 0.790398 | ||||||||
\(923\) | −26.8132 | −0.882568 | ||||||||
\(924\) | −5.40661 | −0.177865 | ||||||||
\(925\) | 9.06226 | 0.297965 | ||||||||
\(926\) | −35.1868 | −1.15631 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.8424 | 1.20876 | 0.604380 | − | 0.796696i | \(-0.293421\pi\) | ||||
0.604380 | + | 0.796696i | \(0.293421\pi\) | |||||||
\(930\) | −1.00000 | −0.0327913 | ||||||||
\(931\) | −19.3113 | −0.632902 | ||||||||
\(932\) | 9.53113 | 0.312203 | ||||||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | 10.1245 | 0.331284 | ||||||||
\(935\) | −6.12452 | −0.200293 | ||||||||
\(936\) | 6.00000 | 0.196116 | ||||||||
\(937\) | −25.0623 | −0.818748 | −0.409374 | − | 0.912367i | \(-0.634253\pi\) | ||||
−0.409374 | + | 0.912367i | \(0.634253\pi\) | |||||||
\(938\) | −39.0623 | −1.27543 | ||||||||
\(939\) | 27.0623 | 0.883143 | ||||||||
\(940\) | −11.0623 | −0.360811 | ||||||||
\(941\) | −21.8755 | −0.713120 | −0.356560 | − | 0.934272i | \(-0.616051\pi\) | ||||
−0.356560 | + | 0.934272i | \(0.616051\pi\) | |||||||
\(942\) | −14.4689 | −0.471421 | ||||||||
\(943\) | 13.8755 | 0.451848 | ||||||||
\(944\) | 7.06226 | 0.229857 | ||||||||
\(945\) | −3.53113 | −0.114868 | ||||||||
\(946\) | 0.717902 | 0.0233410 | ||||||||
\(947\) | 35.0623 | 1.13937 | 0.569685 | − | 0.821863i | \(-0.307065\pi\) | ||||
0.569685 | + | 0.821863i | \(0.307065\pi\) | |||||||
\(948\) | −0.468871 | −0.0152282 | ||||||||
\(949\) | −2.81323 | −0.0913212 | ||||||||
\(950\) | −3.53113 | −0.114565 | ||||||||
\(951\) | 29.0623 | 0.942408 | ||||||||
\(952\) | −14.1245 | −0.457778 | ||||||||
\(953\) | 54.1245 | 1.75327 | 0.876633 | − | 0.481161i | \(-0.159785\pi\) | ||||
0.876633 | + | 0.481161i | \(0.159785\pi\) | |||||||
\(954\) | 5.53113 | 0.179077 | ||||||||
\(955\) | 8.00000 | 0.258874 | ||||||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.6556 | 1.34583 | ||||||||
\(959\) | 3.31129 | 0.106927 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 54.3735 | 1.75307 | ||||||||
\(963\) | −14.5934 | −0.470265 | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | −5.40661 | −0.173955 | ||||||||
\(967\) | −17.0623 | −0.548685 | −0.274343 | − | 0.961632i | \(-0.588460\pi\) | ||||
−0.274343 | + | 0.961632i | \(0.588460\pi\) | |||||||
\(968\) | −8.65564 | −0.278203 | ||||||||
\(969\) | 14.1245 | 0.453745 | ||||||||
\(970\) | 16.1245 | 0.517727 | ||||||||
\(971\) | −33.1868 | −1.06501 | −0.532507 | − | 0.846426i | \(-0.678750\pi\) | ||||
−0.532507 | + | 0.846426i | \(0.678750\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 21.1868 | 0.679217 | ||||||||
\(974\) | 6.93774 | 0.222300 | ||||||||
\(975\) | 6.00000 | 0.192154 | ||||||||
\(976\) | −11.0623 | −0.354094 | ||||||||
\(977\) | −38.0000 | −1.21573 | −0.607864 | − | 0.794041i | \(-0.707973\pi\) | ||||
−0.607864 | + | 0.794041i | \(0.707973\pi\) | |||||||
\(978\) | −11.0623 | −0.353732 | ||||||||
\(979\) | −2.34436 | −0.0749259 | ||||||||
\(980\) | −5.46887 | −0.174697 | ||||||||
\(981\) | −1.06226 | −0.0339153 | ||||||||
\(982\) | 16.5934 | 0.529516 | ||||||||
\(983\) | 17.0623 | 0.544202 | 0.272101 | − | 0.962269i | \(-0.412282\pi\) | ||||
0.272101 | + | 0.962269i | \(0.412282\pi\) | |||||||
\(984\) | −9.06226 | −0.288894 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.0623 | 1.24337 | ||||||||
\(988\) | −21.1868 | −0.674041 | ||||||||
\(989\) | 0.717902 | 0.0228280 | ||||||||
\(990\) | 1.53113 | 0.0486625 | ||||||||
\(991\) | −24.4689 | −0.777279 | −0.388640 | − | 0.921390i | \(-0.627055\pi\) | ||||
−0.388640 | + | 0.921390i | \(0.627055\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | 29.0623 | 0.922263 | ||||||||
\(994\) | −15.7802 | −0.500516 | ||||||||
\(995\) | 0.468871 | 0.0148642 | ||||||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | 62.2490 | 1.97145 | 0.985723 | − | 0.168373i | \(-0.0538514\pi\) | ||||
0.985723 | + | 0.168373i | \(0.0538514\pi\) | |||||||
\(998\) | 9.06226 | 0.286861 | ||||||||
\(999\) | 9.06226 | 0.286717 |
(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 | 930.2.a.q.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2790.2.a.bf.1.2 | 2 | |||
4.3 | odd | 2 | 7440.2.a.bd.1.1 | 2 | |||
5.2 | odd | 4 | 4650.2.d.bg.3349.4 | 4 | |||
5.3 | odd | 4 | 4650.2.d.bg.3349.1 | 4 | |||
5.4 | even | 2 | 4650.2.a.bz.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.q.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2790.2.a.bf.1.2 | 2 | 3.2 | odd | 2 | |||
4650.2.a.bz.1.1 | 2 | 5.4 | even | 2 | |||
4650.2.d.bg.3349.1 | 4 | 5.3 | odd | 4 | |||
4650.2.d.bg.3349.4 | 4 | 5.2 | odd | 4 | |||
7440.2.a.bd.1.1 | 2 | 4.3 | odd | 2 |