Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.77580864.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 19x^{4} + 105x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.5 | ||
Root | \(-1.43163i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.2.b.j.599.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 1.43163i | − 0.826550i | −0.910606 | − | 0.413275i | \(-0.864385\pi\) | ||||
0.910606 | − | 0.413275i | \(-0.135615\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.43163 | 0.584459 | ||||||||
\(7\) | 3.08719i | 1.16685i | 0.812168 | + | 0.583424i | \(0.198287\pi\) | ||||
−0.812168 | + | 0.583424i | \(0.801713\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0.950444 | 0.316815 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.46926 | −1.95056 | −0.975278 | − | 0.220983i | \(-0.929074\pi\) | ||||
−0.975278 | + | 0.220983i | \(0.929074\pi\) | |||||||
\(12\) | 1.43163i | 0.413275i | ||||||||
\(13\) | − 3.95044i | − 1.09566i | −0.836591 | − | 0.547828i | \(-0.815455\pi\) | ||||
0.836591 | − | 0.547828i | \(-0.184545\pi\) | |||||||
\(14\) | −3.08719 | −0.825086 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 3.43163i | − 0.832292i | −0.909298 | − | 0.416146i | \(-0.863381\pi\) | ||||
0.909298 | − | 0.416146i | \(-0.136619\pi\) | |||||||
\(18\) | 0.950444i | 0.224022i | ||||||||
\(19\) | −3.08719 | −0.708250 | −0.354125 | − | 0.935198i | \(-0.615221\pi\) | ||||
−0.354125 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.41970 | 0.964459 | ||||||||
\(22\) | − 6.46926i | − 1.37925i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | −1.43163 | −0.292230 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.95044 | 0.774746 | ||||||||
\(27\) | − 5.65556i | − 1.08841i | ||||||||
\(28\) | − 3.08719i | − 0.583424i | ||||||||
\(29\) | −0.863254 | −0.160302 | −0.0801511 | − | 0.996783i | \(-0.525540\pi\) | ||||
−0.0801511 | + | 0.996783i | \(0.525540\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.95044 | −1.06873 | −0.534366 | − | 0.845253i | \(-0.679449\pi\) | ||||
−0.534366 | + | 0.845253i | \(0.679449\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 9.26157i | 1.61223i | ||||||||
\(34\) | 3.43163 | 0.588519 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.950444 | −0.158407 | ||||||||
\(37\) | − 7.03763i | − 1.15698i | −0.815690 | − | 0.578490i | \(-0.803642\pi\) | ||||
0.815690 | − | 0.578490i | \(-0.196358\pi\) | |||||||
\(38\) | − 3.08719i | − 0.500808i | ||||||||
\(39\) | −5.65556 | −0.905615 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.60601 | 0.875511 | 0.437756 | − | 0.899094i | \(-0.355774\pi\) | ||||
0.437756 | + | 0.899094i | \(0.355774\pi\) | |||||||
\(42\) | 4.41970i | 0.681975i | ||||||||
\(43\) | − 8.00000i | − 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | 6.46926 | 0.975278 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 3.90089i | 0.569003i | 0.958676 | + | 0.284501i | \(0.0918281\pi\) | ||||
−0.958676 | + | 0.284501i | \(0.908172\pi\) | |||||||
\(48\) | − 1.43163i | − 0.206638i | ||||||||
\(49\) | −2.53074 | −0.361534 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.91281 | −0.687931 | ||||||||
\(52\) | 3.95044i | 0.547828i | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 5.65556 | 0.769625 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.08719 | 0.412543 | ||||||||
\(57\) | 4.41970i | 0.585404i | ||||||||
\(58\) | − 0.863254i | − 0.113351i | ||||||||
\(59\) | −6.86325 | −0.893520 | −0.446760 | − | 0.894654i | \(-0.647422\pi\) | ||||
−0.446760 | + | 0.894654i | \(0.647422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5069 | −1.72938 | −0.864690 | − | 0.502305i | \(-0.832485\pi\) | ||||
−0.864690 | + | 0.502305i | \(0.832485\pi\) | |||||||
\(62\) | − 5.95044i | − 0.755707i | ||||||||
\(63\) | 2.93420i | 0.369674i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.26157 | −1.14002 | ||||||||
\(67\) | − 10.0753i | − 1.23089i | −0.788180 | − | 0.615445i | \(-0.788976\pi\) | ||||
0.788180 | − | 0.615445i | \(-0.211024\pi\) | |||||||
\(68\) | 3.43163i | 0.416146i | ||||||||
\(69\) | 1.43163 | 0.172348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.56837 | 0.304810 | 0.152405 | − | 0.988318i | \(-0.451298\pi\) | ||||
0.152405 | + | 0.988318i | \(0.451298\pi\) | |||||||
\(72\) | − 0.950444i | − 0.112011i | ||||||||
\(73\) | − 5.90089i | − 0.690647i | −0.938484 | − | 0.345323i | \(-0.887769\pi\) | ||||
0.938484 | − | 0.345323i | \(-0.112231\pi\) | |||||||
\(74\) | 7.03763 | 0.818108 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.08719 | 0.354125 | ||||||||
\(77\) | − 19.9718i | − 2.27600i | ||||||||
\(78\) | − 5.65556i | − 0.640366i | ||||||||
\(79\) | −15.8018 | −1.77784 | −0.888919 | − | 0.458064i | \(-0.848543\pi\) | ||||
−0.888919 | + | 0.458064i | \(0.848543\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.24533 | −0.582814 | ||||||||
\(82\) | 5.60601i | 0.619080i | ||||||||
\(83\) | − 9.03763i | − 0.992009i | −0.868320 | − | 0.496005i | \(-0.834800\pi\) | ||||
0.868320 | − | 0.496005i | \(-0.165200\pi\) | |||||||
\(84\) | −4.41970 | −0.482229 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 1.23586i | 0.132498i | ||||||||
\(88\) | 6.46926i | 0.689625i | ||||||||
\(89\) | −16.7641 | −1.77700 | −0.888498 | − | 0.458881i | \(-0.848250\pi\) | ||||
−0.888498 | + | 0.458881i | \(0.848250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1958 | 1.27846 | ||||||||
\(92\) | − 1.00000i | − 0.104257i | ||||||||
\(93\) | 8.51882i | 0.883360i | ||||||||
\(94\) | −3.90089 | −0.402346 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.43163 | 0.146115 | ||||||||
\(97\) | − 14.2949i | − 1.45143i | −0.687998 | − | 0.725713i | \(-0.741510\pi\) | ||||
0.687998 | − | 0.725713i | \(-0.258490\pi\) | |||||||
\(98\) | − 2.53074i | − 0.255643i | ||||||||
\(99\) | −6.14867 | −0.617964 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.863254 | 0.0858970 | 0.0429485 | − | 0.999077i | \(-0.486325\pi\) | ||||
0.0429485 | + | 0.999077i | \(0.486325\pi\) | |||||||
\(102\) | − 4.91281i | − 0.486441i | ||||||||
\(103\) | − 1.53074i | − 0.150828i | −0.997152 | − | 0.0754141i | \(-0.975972\pi\) | ||||
0.997152 | − | 0.0754141i | \(-0.0240279\pi\) | |||||||
\(104\) | −3.95044 | −0.387373 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 17.6274i | 1.70410i | 0.523457 | + | 0.852052i | \(0.324642\pi\) | ||||
−0.523457 | + | 0.852052i | \(0.675358\pi\) | |||||||
\(108\) | 5.65556i | 0.544207i | ||||||||
\(109\) | 2.91281 | 0.278997 | 0.139498 | − | 0.990222i | \(-0.455451\pi\) | ||||
0.139498 | + | 0.990222i | \(0.455451\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0753 | −0.956302 | ||||||||
\(112\) | 3.08719i | 0.291712i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −4.41970 | −0.413943 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.863254 | 0.0801511 | ||||||||
\(117\) | − 3.75467i | − 0.347120i | ||||||||
\(118\) | − 6.86325i | − 0.631814i | ||||||||
\(119\) | 10.5941 | 0.971158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8513 | 2.80467 | ||||||||
\(122\) | − 13.5069i | − 1.22286i | ||||||||
\(123\) | − 8.02571i | − 0.723654i | ||||||||
\(124\) | 5.95044 | 0.534366 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.93420 | −0.261399 | ||||||||
\(127\) | 20.9385i | 1.85799i | 0.370088 | + | 0.928997i | \(0.379327\pi\) | ||||
−0.370088 | + | 0.928997i | \(0.620673\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −11.4530 | −1.00838 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7641 | 0.940467 | 0.470234 | − | 0.882542i | \(-0.344170\pi\) | ||||
0.470234 | + | 0.882542i | \(0.344170\pi\) | |||||||
\(132\) | − 9.26157i | − 0.806116i | ||||||||
\(133\) | − 9.53074i | − 0.826420i | ||||||||
\(134\) | 10.0753 | 0.870370 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.43163 | −0.294260 | ||||||||
\(137\) | 3.26157i | 0.278655i | 0.990246 | + | 0.139327i | \(0.0444940\pi\) | ||||
−0.990246 | + | 0.139327i | \(0.955506\pi\) | |||||||
\(138\) | 1.43163i | 0.121868i | ||||||||
\(139\) | 16.9385 | 1.43671 | 0.718353 | − | 0.695678i | \(-0.244896\pi\) | ||||
0.718353 | + | 0.695678i | \(0.244896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.58462 | 0.470310 | ||||||||
\(142\) | 2.56837i | 0.215533i | ||||||||
\(143\) | 25.5565i | 2.13714i | ||||||||
\(144\) | 0.950444 | 0.0792037 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.90089 | 0.488361 | ||||||||
\(147\) | 3.62308i | 0.298826i | ||||||||
\(148\) | 7.03763i | 0.578490i | ||||||||
\(149\) | −3.26157 | −0.267198 | −0.133599 | − | 0.991035i | \(-0.542653\pi\) | ||||
−0.133599 | + | 0.991035i | \(0.542653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.294881 | 0.0239971 | 0.0119986 | − | 0.999928i | \(-0.496181\pi\) | ||||
0.0119986 | + | 0.999928i | \(0.496181\pi\) | |||||||
\(152\) | 3.08719i | 0.250404i | ||||||||
\(153\) | − 3.26157i | − 0.263682i | ||||||||
\(154\) | 19.9718 | 1.60938 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.65556 | 0.452807 | ||||||||
\(157\) | 7.13675i | 0.569574i | 0.958591 | + | 0.284787i | \(0.0919229\pi\) | ||||
−0.958591 | + | 0.284787i | \(0.908077\pi\) | |||||||
\(158\) | − 15.8018i | − 1.25712i | ||||||||
\(159\) | 8.58976 | 0.681212 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.08719 | −0.243305 | ||||||||
\(162\) | − 5.24533i | − 0.412112i | ||||||||
\(163\) | 8.12482i | 0.636385i | 0.948026 | + | 0.318193i | \(0.103076\pi\) | ||||
−0.948026 | + | 0.318193i | \(0.896924\pi\) | |||||||
\(164\) | −5.60601 | −0.437756 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.03763 | 0.701456 | ||||||||
\(167\) | − 7.80178i | − 0.603719i | −0.953352 | − | 0.301860i | \(-0.902393\pi\) | ||||
0.953352 | − | 0.301860i | \(-0.0976074\pi\) | |||||||
\(168\) | − 4.41970i | − 0.340988i | ||||||||
\(169\) | −2.60601 | −0.200462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.93420 | −0.224384 | ||||||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | 19.3325i | 1.46982i | 0.678163 | + | 0.734912i | \(0.262777\pi\) | ||||
−0.678163 | + | 0.734912i | \(0.737223\pi\) | |||||||
\(174\) | −1.23586 | −0.0936902 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.46926 | −0.487639 | ||||||||
\(177\) | 9.82562i | 0.738539i | ||||||||
\(178\) | − 16.7641i | − 1.25653i | ||||||||
\(179\) | −2.17438 | −0.162521 | −0.0812604 | − | 0.996693i | \(-0.525895\pi\) | ||||
−0.0812604 | + | 0.996693i | \(0.525895\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.26157 | −0.539748 | −0.269874 | − | 0.962896i | \(-0.586982\pi\) | ||||
−0.269874 | + | 0.962896i | \(0.586982\pi\) | |||||||
\(182\) | 12.1958i | 0.904011i | ||||||||
\(183\) | 19.3368i | 1.42942i | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.51882 | −0.624630 | ||||||||
\(187\) | 22.2001i | 1.62343i | ||||||||
\(188\) | − 3.90089i | − 0.284501i | ||||||||
\(189\) | 17.4598 | 1.27001 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.58976 | 0.621533 | 0.310767 | − | 0.950486i | \(-0.399414\pi\) | ||||
0.310767 | + | 0.950486i | \(0.399414\pi\) | |||||||
\(192\) | 1.43163i | 0.103319i | ||||||||
\(193\) | − 2.44787i | − 0.176202i | −0.996112 | − | 0.0881008i | \(-0.971920\pi\) | ||||
0.996112 | − | 0.0881008i | \(-0.0280798\pi\) | |||||||
\(194\) | 14.2949 | 1.02631 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.53074 | 0.180767 | ||||||||
\(197\) | − 10.7428i | − 0.765389i | −0.923875 | − | 0.382695i | \(-0.874996\pi\) | ||||
0.923875 | − | 0.382695i | \(-0.125004\pi\) | |||||||
\(198\) | − 6.14867i | − 0.436967i | ||||||||
\(199\) | 11.3111 | 0.801824 | 0.400912 | − | 0.916116i | \(-0.368693\pi\) | ||||
0.400912 | + | 0.916116i | \(0.368693\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.4240 | −1.01739 | ||||||||
\(202\) | 0.863254i | 0.0607384i | ||||||||
\(203\) | − 2.66503i | − 0.187048i | ||||||||
\(204\) | 4.91281 | 0.343966 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.53074 | 0.106652 | ||||||||
\(207\) | 0.950444i | 0.0660604i | ||||||||
\(208\) | − 3.95044i | − 0.273914i | ||||||||
\(209\) | 19.9718 | 1.38148 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.1129 | 1.59116 | 0.795579 | − | 0.605850i | \(-0.207167\pi\) | ||||
0.795579 | + | 0.605850i | \(0.207167\pi\) | |||||||
\(212\) | − 6.00000i | − 0.412082i | ||||||||
\(213\) | − 3.67695i | − 0.251941i | ||||||||
\(214\) | −17.6274 | −1.20498 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.65556 | −0.384812 | ||||||||
\(217\) | − 18.3701i | − 1.24705i | ||||||||
\(218\) | 2.91281i | 0.197280i | ||||||||
\(219\) | −8.44787 | −0.570854 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5565 | −0.911906 | ||||||||
\(222\) | − 10.0753i | − 0.676208i | ||||||||
\(223\) | 5.72651i | 0.383475i | 0.981446 | + | 0.191738i | \(0.0614123\pi\) | ||||
−0.981446 | + | 0.191738i | \(0.938588\pi\) | |||||||
\(224\) | −3.08719 | −0.206272 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | − 17.6274i | − 1.16997i | −0.811044 | − | 0.584986i | \(-0.801100\pi\) | ||||
0.811044 | − | 0.584986i | \(-0.198900\pi\) | |||||||
\(228\) | − 4.41970i | − 0.292702i | ||||||||
\(229\) | 16.0753 | 1.06228 | 0.531142 | − | 0.847283i | \(-0.321763\pi\) | ||||
0.531142 | + | 0.847283i | \(0.321763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.5922 | −1.88123 | ||||||||
\(232\) | 0.863254i | 0.0566754i | ||||||||
\(233\) | 6.44787i | 0.422414i | 0.977441 | + | 0.211207i | \(0.0677394\pi\) | ||||
−0.977441 | + | 0.211207i | \(0.932261\pi\) | |||||||
\(234\) | 3.75467 | 0.245451 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.86325 | 0.446760 | ||||||||
\(237\) | 22.6222i | 1.46947i | ||||||||
\(238\) | 10.5941i | 0.686712i | ||||||||
\(239\) | −4.34876 | −0.281298 | −0.140649 | − | 0.990060i | \(-0.544919\pi\) | ||||
−0.140649 | + | 0.990060i | \(0.544919\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.764142 | 0.0492227 | 0.0246114 | − | 0.999697i | \(-0.492165\pi\) | ||||
0.0246114 | + | 0.999697i | \(0.492165\pi\) | |||||||
\(242\) | 30.8513i | 1.98320i | ||||||||
\(243\) | − 9.45734i | − 0.606688i | ||||||||
\(244\) | 13.5069 | 0.864690 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.02571 | 0.511701 | ||||||||
\(247\) | 12.1958i | 0.775998i | ||||||||
\(248\) | 5.95044i | 0.377854i | ||||||||
\(249\) | −12.9385 | −0.819945 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5402 | −1.42273 | −0.711363 | − | 0.702825i | \(-0.751922\pi\) | ||||
−0.711363 | + | 0.702825i | \(0.751922\pi\) | |||||||
\(252\) | − 2.93420i | − 0.184837i | ||||||||
\(253\) | − 6.46926i | − 0.406719i | ||||||||
\(254\) | −20.9385 | −1.31380 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 9.90089i | − 0.617600i | −0.951127 | − | 0.308800i | \(-0.900073\pi\) | ||||
0.951127 | − | 0.308800i | \(-0.0999274\pi\) | |||||||
\(258\) | − 11.4530i | − 0.713034i | ||||||||
\(259\) | 21.7265 | 1.35002 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.820475 | −0.0507861 | ||||||||
\(262\) | 10.7641i | 0.665011i | ||||||||
\(263\) | 7.25725i | 0.447501i | 0.974646 | + | 0.223751i | \(0.0718301\pi\) | ||||
−0.974646 | + | 0.223751i | \(0.928170\pi\) | |||||||
\(264\) | 9.26157 | 0.570010 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.53074 | 0.584367 | ||||||||
\(267\) | 24.0000i | 1.46878i | ||||||||
\(268\) | 10.0753i | 0.615445i | ||||||||
\(269\) | 6.93852 | 0.423049 | 0.211525 | − | 0.977373i | \(-0.432157\pi\) | ||||
0.211525 | + | 0.977373i | \(0.432157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2992 | −0.625632 | −0.312816 | − | 0.949814i | \(-0.601272\pi\) | ||||
−0.312816 | + | 0.949814i | \(0.601272\pi\) | |||||||
\(272\) | − 3.43163i | − 0.208073i | ||||||||
\(273\) | − 17.4598i | − 1.05671i | ||||||||
\(274\) | −3.26157 | −0.197039 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.43163 | −0.0861738 | ||||||||
\(277\) | − 17.8018i | − 1.06961i | −0.844977 | − | 0.534803i | \(-0.820386\pi\) | ||||
0.844977 | − | 0.534803i | \(-0.179614\pi\) | |||||||
\(278\) | 16.9385i | 1.01590i | ||||||||
\(279\) | −5.65556 | −0.338590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.9385 | −1.12978 | −0.564889 | − | 0.825167i | \(-0.691081\pi\) | ||||
−0.564889 | + | 0.825167i | \(0.691081\pi\) | |||||||
\(282\) | 5.58462i | 0.332559i | ||||||||
\(283\) | − 12.6889i | − 0.754275i | −0.926157 | − | 0.377138i | \(-0.876908\pi\) | ||||
0.926157 | − | 0.377138i | \(-0.123092\pi\) | |||||||
\(284\) | −2.56837 | −0.152405 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −25.5565 | −1.51118 | ||||||||
\(287\) | 17.3068i | 1.02159i | ||||||||
\(288\) | 0.950444i | 0.0560054i | ||||||||
\(289\) | 5.22394 | 0.307290 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.4649 | −1.19968 | ||||||||
\(292\) | 5.90089i | 0.345323i | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | −3.62308 | −0.211302 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.03763 | −0.409054 | ||||||||
\(297\) | 36.5873i | 2.12301i | ||||||||
\(298\) | − 3.26157i | − 0.188938i | ||||||||
\(299\) | 3.95044 | 0.228460 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.6975 | 1.42354 | ||||||||
\(302\) | 0.294881i | 0.0169685i | ||||||||
\(303\) | − 1.23586i | − 0.0709982i | ||||||||
\(304\) | −3.08719 | −0.177062 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.26157 | 0.186451 | ||||||||
\(307\) | − 22.9599i | − 1.31039i | −0.755459 | − | 0.655196i | \(-0.772586\pi\) | ||||
0.755459 | − | 0.655196i | \(-0.227414\pi\) | |||||||
\(308\) | 19.9718i | 1.13800i | ||||||||
\(309\) | −2.19145 | −0.124667 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0753 | 1.02495 | 0.512477 | − | 0.858701i | \(-0.328728\pi\) | ||||
0.512477 | + | 0.858701i | \(0.328728\pi\) | |||||||
\(312\) | 5.65556i | 0.320183i | ||||||||
\(313\) | − 15.1625i | − 0.857033i | −0.903534 | − | 0.428516i | \(-0.859036\pi\) | ||||
0.903534 | − | 0.428516i | \(-0.140964\pi\) | |||||||
\(314\) | −7.13675 | −0.402750 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.8018 | 0.888919 | ||||||||
\(317\) | 14.0257i | 0.787762i | 0.919161 | + | 0.393881i | \(0.128868\pi\) | ||||
−0.919161 | + | 0.393881i | \(0.871132\pi\) | |||||||
\(318\) | 8.58976i | 0.481690i | ||||||||
\(319\) | 5.58462 | 0.312678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.2359 | 1.40853 | ||||||||
\(322\) | − 3.08719i | − 0.172042i | ||||||||
\(323\) | 10.5941i | 0.589471i | ||||||||
\(324\) | 5.24533 | 0.291407 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.12482 | −0.449992 | ||||||||
\(327\) | − 4.17006i | − 0.230605i | ||||||||
\(328\) | − 5.60601i | − 0.309540i | ||||||||
\(329\) | −12.0428 | −0.663940 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.7403 | −1.35985 | −0.679925 | − | 0.733282i | \(-0.737988\pi\) | ||||
−0.679925 | + | 0.733282i | \(0.737988\pi\) | |||||||
\(332\) | 9.03763i | 0.496005i | ||||||||
\(333\) | − 6.68888i | − 0.366548i | ||||||||
\(334\) | 7.80178 | 0.426894 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.41970 | 0.241115 | ||||||||
\(337\) | 14.7146i | 0.801555i | 0.916176 | + | 0.400777i | \(0.131260\pi\) | ||||
−0.916176 | + | 0.400777i | \(0.868740\pi\) | |||||||
\(338\) | − 2.60601i | − 0.141748i | ||||||||
\(339\) | 8.58976 | 0.466532 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.4950 | 2.08462 | ||||||||
\(342\) | − 2.93420i | − 0.158663i | ||||||||
\(343\) | 13.7975i | 0.744993i | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.3325 | −1.03932 | ||||||||
\(347\) | 9.43163i | 0.506316i | 0.967425 | + | 0.253158i | \(0.0814693\pi\) | ||||
−0.967425 | + | 0.253158i | \(0.918531\pi\) | |||||||
\(348\) | − 1.23586i | − 0.0662490i | ||||||||
\(349\) | −18.3488 | −0.982187 | −0.491093 | − | 0.871107i | \(-0.663403\pi\) | ||||
−0.491093 | + | 0.871107i | \(0.663403\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.3420 | −1.19253 | ||||||||
\(352\) | − 6.46926i | − 0.344813i | ||||||||
\(353\) | 33.1129i | 1.76242i | 0.472723 | + | 0.881211i | \(0.343271\pi\) | ||||
−0.472723 | + | 0.881211i | \(0.656729\pi\) | |||||||
\(354\) | −9.82562 | −0.522226 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.7641 | 0.888498 | ||||||||
\(357\) | − 15.1668i | − 0.802711i | ||||||||
\(358\) | − 2.17438i | − 0.114920i | ||||||||
\(359\) | −33.0376 | −1.74366 | −0.871830 | − | 0.489809i | \(-0.837067\pi\) | ||||
−0.871830 | + | 0.489809i | \(0.837067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.46926 | −0.498382 | ||||||||
\(362\) | − 7.26157i | − 0.381660i | ||||||||
\(363\) | − 44.1676i | − 2.31820i | ||||||||
\(364\) | −12.1958 | −0.639232 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.3368 | −1.01075 | ||||||||
\(367\) | − 2.27349i | − 0.118675i | −0.998238 | − | 0.0593376i | \(-0.981101\pi\) | ||||
0.998238 | − | 0.0593376i | \(-0.0188989\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 5.32819 | 0.277375 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.5231 | −0.961673 | ||||||||
\(372\) | − 8.51882i | − 0.441680i | ||||||||
\(373\) | − 23.9762i | − 1.24144i | −0.784033 | − | 0.620719i | \(-0.786841\pi\) | ||||
0.784033 | − | 0.620719i | \(-0.213159\pi\) | |||||||
\(374\) | −22.2001 | −1.14794 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.90089 | 0.201173 | ||||||||
\(377\) | 3.41024i | 0.175636i | ||||||||
\(378\) | 17.4598i | 0.898035i | ||||||||
\(379\) | 13.8795 | 0.712942 | 0.356471 | − | 0.934306i | \(-0.383980\pi\) | ||||
0.356471 | + | 0.934306i | \(0.383980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.9762 | 1.53572 | ||||||||
\(382\) | 8.58976i | 0.439490i | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | −1.43163 | −0.0730574 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.44787 | 0.124593 | ||||||||
\(387\) | − 7.60355i | − 0.386510i | ||||||||
\(388\) | 14.2949i | 0.725713i | ||||||||
\(389\) | 26.6436 | 1.35089 | 0.675443 | − | 0.737412i | \(-0.263952\pi\) | ||||
0.675443 | + | 0.737412i | \(0.263952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.43163 | 0.173545 | ||||||||
\(392\) | 2.53074i | 0.127822i | ||||||||
\(393\) | − 15.4102i | − 0.777344i | ||||||||
\(394\) | 10.7428 | 0.541212 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.14867 | 0.308982 | ||||||||
\(397\) | − 8.66749i | − 0.435009i | −0.976059 | − | 0.217504i | \(-0.930208\pi\) | ||||
0.976059 | − | 0.217504i | \(-0.0697916\pi\) | |||||||
\(398\) | 11.3111i | 0.566975i | ||||||||
\(399\) | −13.6445 | −0.683078 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.9762 | 1.99631 | 0.998157 | − | 0.0606854i | \(-0.0193286\pi\) | ||||
0.998157 | + | 0.0606854i | \(0.0193286\pi\) | |||||||
\(402\) | − 14.4240i | − 0.719405i | ||||||||
\(403\) | 23.5069i | 1.17096i | ||||||||
\(404\) | −0.863254 | −0.0429485 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.66503 | 0.132263 | ||||||||
\(407\) | 45.5283i | 2.25675i | ||||||||
\(408\) | 4.91281i | 0.243220i | ||||||||
\(409\) | −30.1248 | −1.48958 | −0.744788 | − | 0.667301i | \(-0.767450\pi\) | ||||
−0.744788 | + | 0.667301i | \(0.767450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.66935 | 0.230322 | ||||||||
\(412\) | 1.53074i | 0.0754141i | ||||||||
\(413\) | − 21.1882i | − 1.04260i | ||||||||
\(414\) | −0.950444 | −0.0467118 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.95044 | 0.193686 | ||||||||
\(417\) | − 24.2496i | − 1.18751i | ||||||||
\(418\) | 19.9718i | 0.976854i | ||||||||
\(419\) | −25.8770 | −1.26418 | −0.632088 | − | 0.774897i | \(-0.717802\pi\) | ||||
−0.632088 | + | 0.774897i | \(0.717802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7146 | −0.522197 | −0.261098 | − | 0.965312i | \(-0.584085\pi\) | ||||
−0.261098 | + | 0.965312i | \(0.584085\pi\) | |||||||
\(422\) | 23.1129i | 1.12512i | ||||||||
\(423\) | 3.70757i | 0.180268i | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.67695 | 0.178149 | ||||||||
\(427\) | − 41.6983i | − 2.01792i | ||||||||
\(428\) | − 17.6274i | − 0.852052i | ||||||||
\(429\) | 36.5873 | 1.76645 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.2496 | 1.55341 | 0.776705 | − | 0.629864i | \(-0.216889\pi\) | ||||
0.776705 | + | 0.629864i | \(0.216889\pi\) | |||||||
\(432\) | − 5.65556i | − 0.272103i | ||||||||
\(433\) | − 20.6393i | − 0.991862i | −0.868362 | − | 0.495931i | \(-0.834827\pi\) | ||||
0.868362 | − | 0.495931i | \(-0.165173\pi\) | |||||||
\(434\) | 18.3701 | 0.881795 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.91281 | −0.139498 | ||||||||
\(437\) | − 3.08719i | − 0.147680i | ||||||||
\(438\) | − 8.44787i | − 0.403655i | ||||||||
\(439\) | 16.2239 | 0.774326 | 0.387163 | − | 0.922011i | \(-0.373455\pi\) | ||||
0.387163 | + | 0.922011i | \(0.373455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.40533 | −0.114539 | ||||||||
\(442\) | − 13.5565i | − 0.644815i | ||||||||
\(443\) | 15.6770i | 0.744834i | 0.928065 | + | 0.372417i | \(0.121471\pi\) | ||||
−0.928065 | + | 0.372417i | \(0.878529\pi\) | |||||||
\(444\) | 10.0753 | 0.478151 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.72651 | −0.271158 | ||||||||
\(447\) | 4.66935i | 0.220853i | ||||||||
\(448\) | − 3.08719i | − 0.145856i | ||||||||
\(449\) | −22.5727 | −1.06527 | −0.532636 | − | 0.846345i | \(-0.678798\pi\) | ||||
−0.532636 | + | 0.846345i | \(0.678798\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.2667 | −1.70773 | ||||||||
\(452\) | − 6.00000i | − 0.282216i | ||||||||
\(453\) | − 0.422160i | − 0.0198348i | ||||||||
\(454\) | 17.6274 | 0.827295 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.41970 | 0.206972 | ||||||||
\(457\) | − 1.45302i | − 0.0679693i | −0.999422 | − | 0.0339846i | \(-0.989180\pi\) | ||||
0.999422 | − | 0.0339846i | \(-0.0108197\pi\) | |||||||
\(458\) | 16.0753i | 0.751148i | ||||||||
\(459\) | −19.4078 | −0.905878 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.7027 | −1.38339 | −0.691695 | − | 0.722189i | \(-0.743136\pi\) | ||||
−0.691695 | + | 0.722189i | \(0.743136\pi\) | |||||||
\(462\) | − 28.5922i | − 1.33023i | ||||||||
\(463\) | − 22.9624i | − 1.06715i | −0.845752 | − | 0.533576i | \(-0.820848\pi\) | ||||
0.845752 | − | 0.533576i | \(-0.179152\pi\) | |||||||
\(464\) | −0.863254 | −0.0400756 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.44787 | −0.298692 | ||||||||
\(467\) | 9.48550i | 0.438937i | 0.975620 | + | 0.219468i | \(0.0704323\pi\) | ||||
−0.975620 | + | 0.219468i | \(0.929568\pi\) | |||||||
\(468\) | 3.75467i | 0.173560i | ||||||||
\(469\) | 31.1043 | 1.43626 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.2172 | 0.470782 | ||||||||
\(472\) | 6.86325i | 0.315907i | ||||||||
\(473\) | 51.7541i | 2.37966i | ||||||||
\(474\) | −22.6222 | −1.03907 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.5941 | −0.485579 | ||||||||
\(477\) | 5.70266i | 0.261107i | ||||||||
\(478\) | − 4.34876i | − 0.198908i | ||||||||
\(479\) | 30.5659 | 1.39659 | 0.698296 | − | 0.715809i | \(-0.253942\pi\) | ||||
0.698296 | + | 0.715809i | \(0.253942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8018 | −1.26765 | ||||||||
\(482\) | 0.764142i | 0.0348057i | ||||||||
\(483\) | 4.41970i | 0.201104i | ||||||||
\(484\) | −30.8513 | −1.40233 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.45734 | 0.428994 | ||||||||
\(487\) | − 21.1367i | − 0.957797i | −0.877870 | − | 0.478899i | \(-0.841036\pi\) | ||||
0.877870 | − | 0.478899i | \(-0.158964\pi\) | |||||||
\(488\) | 13.5069i | 0.611428i | ||||||||
\(489\) | 11.6317 | 0.526004 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.0514 | −1.26594 | −0.632971 | − | 0.774175i | \(-0.718165\pi\) | ||||
−0.632971 | + | 0.774175i | \(0.718165\pi\) | |||||||
\(492\) | 8.02571i | 0.361827i | ||||||||
\(493\) | 2.96237i | 0.133418i | ||||||||
\(494\) | −12.1958 | −0.548714 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.95044 | −0.267183 | ||||||||
\(497\) | 7.92905i | 0.355667i | ||||||||
\(498\) | − 12.9385i | − 0.579789i | ||||||||
\(499\) | −3.80178 | −0.170191 | −0.0850954 | − | 0.996373i | \(-0.527120\pi\) | ||||
−0.0850954 | + | 0.996373i | \(0.527120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.1692 | −0.499005 | ||||||||
\(502\) | − 22.5402i | − 1.00602i | ||||||||
\(503\) | − 19.0872i | − 0.851056i | −0.904945 | − | 0.425528i | \(-0.860088\pi\) | ||||
0.904945 | − | 0.425528i | \(-0.139912\pi\) | |||||||
\(504\) | 2.93420 | 0.130700 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.46926 | 0.287594 | ||||||||
\(507\) | 3.73083i | 0.165692i | ||||||||
\(508\) | − 20.9385i | − 0.928997i | ||||||||
\(509\) | 9.41024 | 0.417101 | 0.208551 | − | 0.978012i | \(-0.433125\pi\) | ||||
0.208551 | + | 0.978012i | \(0.433125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.2172 | 0.805880 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 17.4598i | 0.770869i | ||||||||
\(514\) | 9.90089 | 0.436709 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 11.4530 | 0.504191 | ||||||||
\(517\) | − 25.2359i | − 1.10987i | ||||||||
\(518\) | 21.7265i | 0.954608i | ||||||||
\(519\) | 27.6770 | 1.21488 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.8018 | 1.13040 | 0.565198 | − | 0.824955i | \(-0.308800\pi\) | ||||
0.565198 | + | 0.824955i | \(0.308800\pi\) | |||||||
\(522\) | − 0.820475i | − 0.0359112i | ||||||||
\(523\) | 19.1129i | 0.835749i | 0.908505 | + | 0.417874i | \(0.137225\pi\) | ||||
−0.908505 | + | 0.417874i | \(0.862775\pi\) | |||||||
\(524\) | −10.7641 | −0.470234 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.25725 | −0.316431 | ||||||||
\(527\) | 20.4197i | 0.889496i | ||||||||
\(528\) | 9.26157i | 0.403058i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.52314 | −0.283080 | ||||||||
\(532\) | 9.53074i | 0.413210i | ||||||||
\(533\) | − 22.1462i | − 0.959259i | ||||||||
\(534\) | −24.0000 | −1.03858 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.0753 | −0.435185 | ||||||||
\(537\) | 3.11290i | 0.134332i | ||||||||
\(538\) | 6.93852i | 0.299141i | ||||||||
\(539\) | 16.3720 | 0.705193 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8394 | 1.32589 | 0.662945 | − | 0.748668i | \(-0.269306\pi\) | ||||
0.662945 | + | 0.748668i | \(0.269306\pi\) | |||||||
\(542\) | − 10.2992i | − 0.442389i | ||||||||
\(543\) | 10.3959i | 0.446129i | ||||||||
\(544\) | 3.43163 | 0.147130 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 17.4598 | 0.747210 | ||||||||
\(547\) | 13.8513i | 0.592240i | 0.955151 | + | 0.296120i | \(0.0956929\pi\) | ||||
−0.955151 | + | 0.296120i | \(0.904307\pi\) | |||||||
\(548\) | − 3.26157i | − 0.139327i | ||||||||
\(549\) | −12.8375 | −0.547893 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.66503 | 0.113534 | ||||||||
\(552\) | − 1.43163i | − 0.0609341i | ||||||||
\(553\) | − 48.7831i | − 2.07447i | ||||||||
\(554\) | 17.8018 | 0.756325 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.9385 | −0.718353 | ||||||||
\(557\) | − 28.7641i | − 1.21878i | −0.792872 | − | 0.609388i | \(-0.791415\pi\) | ||||
0.792872 | − | 0.609388i | \(-0.208585\pi\) | |||||||
\(558\) | − 5.65556i | − 0.239419i | ||||||||
\(559\) | −31.6036 | −1.33669 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.7823 | 1.34185 | ||||||||
\(562\) | − 18.9385i | − 0.798873i | ||||||||
\(563\) | − 36.1505i | − 1.52356i | −0.647834 | − | 0.761782i | \(-0.724325\pi\) | ||||
0.647834 | − | 0.761782i | \(-0.275675\pi\) | |||||||
\(564\) | −5.58462 | −0.235155 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.6889 | 0.533353 | ||||||||
\(567\) | − 16.1933i | − 0.680055i | ||||||||
\(568\) | − 2.56837i | − 0.107767i | ||||||||
\(569\) | 10.3488 | 0.433843 | 0.216921 | − | 0.976189i | \(-0.430399\pi\) | ||||
0.216921 | + | 0.976189i | \(0.430399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6060 | 0.820486 | 0.410243 | − | 0.911976i | \(-0.365444\pi\) | ||||
0.410243 | + | 0.911976i | \(0.365444\pi\) | |||||||
\(572\) | − 25.5565i | − 1.06857i | ||||||||
\(573\) | − 12.2973i | − 0.513729i | ||||||||
\(574\) | −17.3068 | −0.722372 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.950444 | −0.0396018 | ||||||||
\(577\) | − 34.1505i | − 1.42171i | −0.703341 | − | 0.710853i | \(-0.748309\pi\) | ||||
0.703341 | − | 0.710853i | \(-0.251691\pi\) | |||||||
\(578\) | 5.22394i | 0.217287i | ||||||||
\(579\) | −3.50444 | −0.145639 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.9009 | 1.15752 | ||||||||
\(582\) | − 20.4649i | − 0.848299i | ||||||||
\(583\) | − 38.8156i | − 1.60758i | ||||||||
\(584\) | −5.90089 | −0.244180 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | − 5.19062i | − 0.214240i | −0.994246 | − | 0.107120i | \(-0.965837\pi\) | ||||
0.994246 | − | 0.107120i | \(-0.0341629\pi\) | |||||||
\(588\) | − 3.62308i | − 0.149413i | ||||||||
\(589\) | 18.3701 | 0.756929 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.3796 | −0.632633 | ||||||||
\(592\) | − 7.03763i | − 0.289245i | ||||||||
\(593\) | 2.09911i | 0.0862002i | 0.999071 | + | 0.0431001i | \(0.0137234\pi\) | ||||
−0.999071 | + | 0.0431001i | \(0.986277\pi\) | |||||||
\(594\) | −36.5873 | −1.50120 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.26157 | 0.133599 | ||||||||
\(597\) | − 16.1933i | − 0.662748i | ||||||||
\(598\) | 3.95044i | 0.161546i | ||||||||
\(599\) | −11.1581 | −0.455909 | −0.227955 | − | 0.973672i | \(-0.573204\pi\) | ||||
−0.227955 | + | 0.973672i | \(0.573204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.57784 | 0.390688 | 0.195344 | − | 0.980735i | \(-0.437418\pi\) | ||||
0.195344 | + | 0.980735i | \(0.437418\pi\) | |||||||
\(602\) | 24.6975i | 1.00660i | ||||||||
\(603\) | − 9.57597i | − 0.389964i | ||||||||
\(604\) | −0.294881 | −0.0119986 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.23586 | 0.0502033 | ||||||||
\(607\) | − 24.6975i | − 1.00244i | −0.865320 | − | 0.501221i | \(-0.832885\pi\) | ||||
0.865320 | − | 0.501221i | \(-0.167115\pi\) | |||||||
\(608\) | − 3.08719i | − 0.125202i | ||||||||
\(609\) | −3.81533 | −0.154605 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.4102 | 0.623431 | ||||||||
\(612\) | 3.26157i | 0.131841i | ||||||||
\(613\) | 26.3488i | 1.06422i | 0.846676 | + | 0.532108i | \(0.178600\pi\) | ||||
−0.846676 | + | 0.532108i | \(0.821400\pi\) | |||||||
\(614\) | 22.9599 | 0.926587 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.9718 | −0.804688 | ||||||||
\(617\) | 5.94612i | 0.239382i | 0.992811 | + | 0.119691i | \(0.0381904\pi\) | ||||
−0.992811 | + | 0.119691i | \(0.961810\pi\) | |||||||
\(618\) | − 2.19145i | − 0.0881530i | ||||||||
\(619\) | −39.6856 | −1.59510 | −0.797549 | − | 0.603254i | \(-0.793871\pi\) | ||||
−0.797549 | + | 0.603254i | \(0.793871\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65556 | 0.226950 | ||||||||
\(622\) | 18.0753i | 0.724752i | ||||||||
\(623\) | − 51.7541i | − 2.07348i | ||||||||
\(624\) | −5.65556 | −0.226404 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.1625 | 0.606014 | ||||||||
\(627\) | − 28.5922i | − 1.14186i | ||||||||
\(628\) | − 7.13675i | − 0.284787i | ||||||||
\(629\) | −24.1505 | −0.962945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0138 | −0.916164 | −0.458082 | − | 0.888910i | \(-0.651463\pi\) | ||||
−0.458082 | + | 0.888910i | \(0.651463\pi\) | |||||||
\(632\) | 15.8018i | 0.628561i | ||||||||
\(633\) | − 33.0891i | − 1.31517i | ||||||||
\(634\) | −14.0257 | −0.557032 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.58976 | −0.340606 | ||||||||
\(637\) | 9.99754i | 0.396117i | ||||||||
\(638\) | 5.58462i | 0.221097i | ||||||||
\(639\) | 2.44109 | 0.0965682 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.4617 | 1.00568 | 0.502838 | − | 0.864381i | \(-0.332289\pi\) | ||||
0.502838 | + | 0.864381i | \(0.332289\pi\) | |||||||
\(642\) | 25.2359i | 0.995980i | ||||||||
\(643\) | 16.4479i | 0.648641i | 0.945947 | + | 0.324320i | \(0.105136\pi\) | ||||
−0.945947 | + | 0.324320i | \(0.894864\pi\) | |||||||
\(644\) | 3.08719 | 0.121652 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5941 | −0.416819 | ||||||||
\(647\) | − 34.9147i | − 1.37264i | −0.727301 | − | 0.686319i | \(-0.759226\pi\) | ||||
0.727301 | − | 0.686319i | \(-0.240774\pi\) | |||||||
\(648\) | 5.24533i | 0.206056i | ||||||||
\(649\) | 44.4002 | 1.74286 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.2992 | −1.03075 | ||||||||
\(652\) | − 8.12482i | − 0.318193i | ||||||||
\(653\) | 34.2754i | 1.34130i | 0.741775 | + | 0.670649i | \(0.233984\pi\) | ||||
−0.741775 | + | 0.670649i | \(0.766016\pi\) | |||||||
\(654\) | 4.17006 | 0.163062 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.60601 | 0.218878 | ||||||||
\(657\) | − 5.60846i | − 0.218807i | ||||||||
\(658\) | − 12.0428i | − 0.469476i | ||||||||
\(659\) | −35.2548 | −1.37333 | −0.686666 | − | 0.726973i | \(-0.740926\pi\) | ||||
−0.686666 | + | 0.726973i | \(0.740926\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.5684 | 1.11118 | 0.555590 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555590 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(662\) | − 24.7403i | − 0.961559i | ||||||||
\(663\) | 19.4078i | 0.753736i | ||||||||
\(664\) | −9.03763 | −0.350728 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.68888 | 0.259189 | ||||||||
\(667\) | − 0.863254i | − 0.0334253i | ||||||||
\(668\) | 7.80178i | 0.301860i | ||||||||
\(669\) | 8.19822 | 0.316962 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 87.3796 | 3.37325 | ||||||||
\(672\) | 4.41970i | 0.170494i | ||||||||
\(673\) | 23.8770i | 0.920392i | 0.887817 | + | 0.460196i | \(0.152221\pi\) | ||||
−0.887817 | + | 0.460196i | \(0.847779\pi\) | |||||||
\(674\) | −14.7146 | −0.566785 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.60601 | 0.100231 | ||||||||
\(677\) | − 6.00000i | − 0.230599i | −0.993331 | − | 0.115299i | \(-0.963217\pi\) | ||||
0.993331 | − | 0.115299i | \(-0.0367827\pi\) | |||||||
\(678\) | 8.58976i | 0.329888i | ||||||||
\(679\) | 44.1310 | 1.69359 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.2359 | −0.967040 | ||||||||
\(682\) | 38.4950i | 1.47405i | ||||||||
\(683\) | − 34.6480i | − 1.32577i | −0.748722 | − | 0.662884i | \(-0.769332\pi\) | ||||
0.748722 | − | 0.662884i | \(-0.230668\pi\) | |||||||
\(684\) | 2.93420 | 0.112192 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.7975 | −0.526789 | ||||||||
\(687\) | − 23.0138i | − 0.878031i | ||||||||
\(688\) | − 8.00000i | − 0.304997i | ||||||||
\(689\) | 23.7027 | 0.903000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.1744 | −0.691386 | −0.345693 | − | 0.938348i | \(-0.612356\pi\) | ||||
−0.345693 | + | 0.938348i | \(0.612356\pi\) | |||||||
\(692\) | − 19.3325i | − 0.734912i | ||||||||
\(693\) | − 18.9821i | − 0.721071i | ||||||||
\(694\) | −9.43163 | −0.358020 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.23586 | 0.0468451 | ||||||||
\(697\) | − 19.2377i | − 0.728681i | ||||||||
\(698\) | − 18.3488i | − 0.694511i | ||||||||
\(699\) | 9.23095 | 0.349146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.6907 | −1.53687 | −0.768434 | − | 0.639929i | \(-0.778964\pi\) | ||||
−0.768434 | + | 0.639929i | \(0.778964\pi\) | |||||||
\(702\) | − 22.3420i | − 0.843244i | ||||||||
\(703\) | 21.7265i | 0.819431i | ||||||||
\(704\) | 6.46926 | 0.243819 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.1129 | −1.24622 | ||||||||
\(707\) | 2.66503i | 0.100229i | ||||||||
\(708\) | − 9.82562i | − 0.369269i | ||||||||
\(709\) | 26.4454 | 0.993178 | 0.496589 | − | 0.867986i | \(-0.334586\pi\) | ||||
0.496589 | + | 0.867986i | \(0.334586\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.0187 | −0.563245 | ||||||||
\(712\) | 16.7641i | 0.628263i | ||||||||
\(713\) | − 5.95044i | − 0.222846i | ||||||||
\(714\) | 15.1668 | 0.567602 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.17438 | 0.0812604 | ||||||||
\(717\) | 6.22580i | 0.232507i | ||||||||
\(718\) | − 33.0376i | − 1.23295i | ||||||||
\(719\) | 2.24778 | 0.0838281 | 0.0419140 | − | 0.999121i | \(-0.486654\pi\) | ||||
0.0419140 | + | 0.999121i | \(0.486654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.72568 | 0.175994 | ||||||||
\(722\) | − 9.46926i | − 0.352409i | ||||||||
\(723\) | − 1.09397i | − 0.0406850i | ||||||||
\(724\) | 7.26157 | 0.269874 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 44.1676 | 1.63921 | ||||||||
\(727\) | 21.4830i | 0.796762i | 0.917220 | + | 0.398381i | \(0.130428\pi\) | ||||
−0.917220 | + | 0.398381i | \(0.869572\pi\) | |||||||
\(728\) | − 12.1958i | − 0.452005i | ||||||||
\(729\) | −29.2754 | −1.08427 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.4530 | −1.01539 | ||||||||
\(732\) | − 19.3368i | − 0.714710i | ||||||||
\(733\) | − 11.3778i | − 0.420247i | −0.977675 | − | 0.210123i | \(-0.932613\pi\) | ||||
0.977675 | − | 0.210123i | \(-0.0673866\pi\) | |||||||
\(734\) | 2.27349 | 0.0839161 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 65.1795i | 2.40092i | ||||||||
\(738\) | 5.32819i | 0.196134i | ||||||||
\(739\) | −21.8770 | −0.804760 | −0.402380 | − | 0.915473i | \(-0.631817\pi\) | ||||
−0.402380 | + | 0.915473i | \(0.631817\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.4598 | 0.641402 | ||||||||
\(742\) | − 18.5231i | − 0.680006i | ||||||||
\(743\) | − 5.36068i | − 0.196664i | −0.995154 | − | 0.0983322i | \(-0.968649\pi\) | ||||
0.995154 | − | 0.0983322i | \(-0.0313508\pi\) | |||||||
\(744\) | 8.51882 | 0.312315 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.9762 | 0.877829 | ||||||||
\(747\) | − 8.58976i | − 0.314283i | ||||||||
\(748\) | − 22.2001i | − 0.811716i | ||||||||
\(749\) | −54.4191 | −1.98843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.3915 | 0.890060 | 0.445030 | − | 0.895516i | \(-0.353193\pi\) | ||||
0.445030 | + | 0.895516i | \(0.353193\pi\) | |||||||
\(752\) | 3.90089i | 0.142251i | ||||||||
\(753\) | 32.2692i | 1.17595i | ||||||||
\(754\) | −3.41024 | −0.124194 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −17.4598 | −0.635007 | ||||||||
\(757\) | 41.9437i | 1.52447i | 0.647301 | + | 0.762234i | \(0.275898\pi\) | ||||
−0.647301 | + | 0.762234i | \(0.724102\pi\) | |||||||
\(758\) | 13.8795i | 0.504126i | ||||||||
\(759\) | −9.26157 | −0.336174 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3745 | −0.666074 | −0.333037 | − | 0.942914i | \(-0.608073\pi\) | ||||
−0.333037 | + | 0.942914i | \(0.608073\pi\) | |||||||
\(762\) | 29.9762i | 1.08592i | ||||||||
\(763\) | 8.99240i | 0.325547i | ||||||||
\(764\) | −8.58976 | −0.310767 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.1129i | 0.978990i | ||||||||
\(768\) | − 1.43163i | − 0.0516594i | ||||||||
\(769\) | −42.4993 | −1.53256 | −0.766282 | − | 0.642505i | \(-0.777895\pi\) | ||||
−0.766282 | + | 0.642505i | \(0.777895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.1744 | −0.510478 | ||||||||
\(772\) | 2.44787i | 0.0881008i | ||||||||
\(773\) | 15.0376i | 0.540866i | 0.962739 | + | 0.270433i | \(0.0871669\pi\) | ||||
−0.962739 | + | 0.270433i | \(0.912833\pi\) | |||||||
\(774\) | 7.60355 | 0.273304 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.2949 | −0.513156 | ||||||||
\(777\) | − 31.1043i | − 1.11586i | ||||||||
\(778\) | 26.6436i | 0.955221i | ||||||||
\(779\) | −17.3068 | −0.620081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.6155 | −0.594548 | ||||||||
\(782\) | 3.43163i | 0.122715i | ||||||||
\(783\) | 4.88219i | 0.174475i | ||||||||
\(784\) | −2.53074 | −0.0903836 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.4102 | 0.549665 | ||||||||
\(787\) | − 8.39154i | − 0.299126i | −0.988752 | − | 0.149563i | \(-0.952213\pi\) | ||||
0.988752 | − | 0.149563i | \(-0.0477867\pi\) | |||||||
\(788\) | 10.7428i | 0.382695i | ||||||||
\(789\) | 10.3897 | 0.369882 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.5231 | −0.658607 | ||||||||
\(792\) | 6.14867i | 0.218483i | ||||||||
\(793\) | 53.3582i | 1.89481i | ||||||||
\(794\) | 8.66749 | 0.307598 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.3111 | −0.400912 | ||||||||
\(797\) | − 22.0514i | − 0.781101i | −0.920581 | − | 0.390551i | \(-0.872285\pi\) | ||||
0.920581 | − | 0.390551i | \(-0.127715\pi\) | |||||||
\(798\) | − 13.6445i | − 0.483009i | ||||||||
\(799\) | 13.3864 | 0.473576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.9334 | −0.562978 | ||||||||
\(802\) | 39.9762i | 1.41161i | ||||||||
\(803\) | 38.1744i | 1.34714i | ||||||||
\(804\) | 14.4240 | 0.508696 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −23.5069 | −0.827995 | ||||||||
\(807\) | − 9.93337i | − 0.349671i | ||||||||
\(808\) | − 0.863254i | − 0.0303692i | ||||||||
\(809\) | −2.04524 | −0.0719066 | −0.0359533 | − | 0.999353i | \(-0.511447\pi\) | ||||
−0.0359533 | + | 0.999353i | \(0.511447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.24965 | 0.149225 | 0.0746126 | − | 0.997213i | \(-0.476228\pi\) | ||||
0.0746126 | + | 0.997213i | \(0.476228\pi\) | |||||||
\(812\) | 2.66503i | 0.0935242i | ||||||||
\(813\) | 14.7446i | 0.517116i | ||||||||
\(814\) | −45.5283 | −1.59577 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.91281 | −0.171983 | ||||||||
\(817\) | 24.6975i | 0.864057i | ||||||||
\(818\) | − 30.1248i | − 1.05329i | ||||||||
\(819\) | 11.5914 | 0.405036 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.2548 | −1.02100 | −0.510500 | − | 0.859878i | \(-0.670540\pi\) | ||||
−0.510500 | + | 0.859878i | \(0.670540\pi\) | |||||||
\(822\) | 4.66935i | 0.162862i | ||||||||
\(823\) | − 13.5846i | − 0.473530i | −0.971567 | − | 0.236765i | \(-0.923913\pi\) | ||||
0.971567 | − | 0.236765i | \(-0.0760871\pi\) | |||||||
\(824\) | −1.53074 | −0.0533258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.1882 | 0.737231 | ||||||||
\(827\) | 24.7880i | 0.861963i | 0.902361 | + | 0.430981i | \(0.141833\pi\) | ||||
−0.902361 | + | 0.430981i | \(0.858167\pi\) | |||||||
\(828\) | − 0.950444i | − 0.0330302i | ||||||||
\(829\) | −26.1505 | −0.908246 | −0.454123 | − | 0.890939i | \(-0.650047\pi\) | ||||
−0.454123 | + | 0.890939i | \(0.650047\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.4855 | −0.884082 | ||||||||
\(832\) | 3.95044i | 0.136957i | ||||||||
\(833\) | 8.68455i | 0.300902i | ||||||||
\(834\) | 24.2496 | 0.839697 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −19.9718 | −0.690740 | ||||||||
\(837\) | 33.6531i | 1.16322i | ||||||||
\(838\) | − 25.8770i | − 0.893908i | ||||||||
\(839\) | −6.37260 | −0.220007 | −0.110003 | − | 0.993931i | \(-0.535086\pi\) | ||||
−0.110003 | + | 0.993931i | \(0.535086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2548 | −0.974303 | ||||||||
\(842\) | − 10.7146i | − 0.369249i | ||||||||
\(843\) | 27.1129i | 0.933818i | ||||||||
\(844\) | −23.1129 | −0.795579 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.70757 | −0.127469 | ||||||||
\(847\) | 95.2439i | 3.27262i | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | −18.1657 | −0.623447 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.03763 | 0.241247 | ||||||||
\(852\) | 3.67695i | 0.125970i | ||||||||
\(853\) | 33.6293i | 1.15144i | 0.817646 | + | 0.575722i | \(0.195279\pi\) | ||||
−0.817646 | + | 0.575722i | \(0.804721\pi\) | |||||||
\(854\) | 41.6983 | 1.42689 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.6274 | 0.602492 | ||||||||
\(857\) | 11.1795i | 0.381885i | 0.981601 | + | 0.190943i | \(0.0611545\pi\) | ||||
−0.981601 | + | 0.190943i | \(0.938846\pi\) | |||||||
\(858\) | 36.5873i | 1.24907i | ||||||||
\(859\) | −47.9009 | −1.63436 | −0.817179 | − | 0.576385i | \(-0.804463\pi\) | ||||
−0.817179 | + | 0.576385i | \(0.804463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.7769 | 0.844394 | ||||||||
\(862\) | 32.2496i | 1.09843i | ||||||||
\(863\) | 30.1180i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(864\) | 5.65556 | 0.192406 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.6393 | 0.701353 | ||||||||
\(867\) | − 7.47873i | − 0.253991i | ||||||||
\(868\) | 18.3701i | 0.623523i | ||||||||
\(869\) | 102.226 | 3.46777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.8018 | −1.34863 | ||||||||
\(872\) | − 2.91281i | − 0.0986402i | ||||||||
\(873\) | − 13.5865i | − 0.459833i | ||||||||
\(874\) | 3.08719 | 0.104426 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.44787 | 0.285427 | ||||||||
\(877\) | − 22.3940i | − 0.756191i | −0.925767 | − | 0.378096i | \(-0.876579\pi\) | ||||
0.925767 | − | 0.378096i | \(-0.123421\pi\) | |||||||
\(878\) | 16.2239i | 0.547531i | ||||||||
\(879\) | 8.58976 | 0.289726 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.1129 | 0.711312 | 0.355656 | − | 0.934617i | \(-0.384258\pi\) | ||||
0.355656 | + | 0.934617i | \(0.384258\pi\) | |||||||
\(882\) | − 2.40533i | − 0.0809915i | ||||||||
\(883\) | − 49.1061i | − 1.65255i | −0.563265 | − | 0.826276i | \(-0.690455\pi\) | ||||
0.563265 | − | 0.826276i | \(-0.309545\pi\) | |||||||
\(884\) | 13.5565 | 0.455953 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.6770 | −0.526678 | ||||||||
\(887\) | − 43.0566i | − 1.44570i | −0.691006 | − | 0.722849i | \(-0.742832\pi\) | ||||
0.691006 | − | 0.722849i | \(-0.257168\pi\) | |||||||
\(888\) | 10.0753i | 0.338104i | ||||||||
\(889\) | −64.6412 | −2.16800 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.9334 | 1.13681 | ||||||||
\(892\) | − 5.72651i | − 0.191738i | ||||||||
\(893\) | − 12.0428i | − 0.402996i | ||||||||
\(894\) | −4.66935 | −0.156166 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.08719 | 0.103136 | ||||||||
\(897\) | − 5.65556i | − 0.188834i | ||||||||
\(898\) | − 22.5727i | − 0.753261i | ||||||||
\(899\) | 5.13675 | 0.171320 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.5898 | 0.685944 | ||||||||
\(902\) | − 36.2667i | − 1.20755i | ||||||||
\(903\) | − 35.3576i | − 1.17663i | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.422160 | 0.0140253 | ||||||||
\(907\) | − 37.9762i | − 1.26098i | −0.776198 | − | 0.630489i | \(-0.782854\pi\) | ||||
0.776198 | − | 0.630489i | \(-0.217146\pi\) | |||||||
\(908\) | 17.6274i | 0.584986i | ||||||||
\(909\) | 0.820475 | 0.0272134 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.7504 | −0.521833 | −0.260916 | − | 0.965361i | \(-0.584025\pi\) | ||||
−0.260916 | + | 0.965361i | \(0.584025\pi\) | |||||||
\(912\) | 4.41970i | 0.146351i | ||||||||
\(913\) | 58.4668i | 1.93497i | ||||||||
\(914\) | 1.45302 | 0.0480615 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0753 | −0.531142 | ||||||||
\(917\) | 33.2309i | 1.09738i | ||||||||
\(918\) | − 19.4078i | − 0.640552i | ||||||||
\(919\) | −30.4240 | −1.00360 | −0.501798 | − | 0.864985i | \(-0.667328\pi\) | ||||
−0.501798 | + | 0.864985i | \(0.667328\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.8700 | −1.08310 | ||||||||
\(922\) | − 29.7027i | − 0.978205i | ||||||||
\(923\) | − 10.1462i | − 0.333967i | ||||||||
\(924\) | 28.5922 | 0.940615 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.9624 | 0.754590 | ||||||||
\(927\) | − 1.45488i | − 0.0477846i | ||||||||
\(928\) | − 0.863254i | − 0.0283377i | ||||||||
\(929\) | 37.8018 | 1.24024 | 0.620118 | − | 0.784509i | \(-0.287085\pi\) | ||||
0.620118 | + | 0.784509i | \(0.287085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.81287 | 0.256057 | ||||||||
\(932\) | − 6.44787i | − 0.211207i | ||||||||
\(933\) | − 25.8770i | − 0.847176i | ||||||||
\(934\) | −9.48550 | −0.310375 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.75467 | −0.122725 | ||||||||
\(937\) | − 32.6907i | − 1.06796i | −0.845497 | − | 0.533980i | \(-0.820696\pi\) | ||||
0.845497 | − | 0.533980i | \(-0.179304\pi\) | |||||||
\(938\) | 31.1043i | 1.01559i | ||||||||
\(939\) | −21.7070 | −0.708381 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.4882 | −1.51547 | −0.757736 | − | 0.652561i | \(-0.773694\pi\) | ||||
−0.757736 | + | 0.652561i | \(0.773694\pi\) | |||||||
\(942\) | 10.2172i | 0.332893i | ||||||||
\(943\) | 5.60601i | 0.182557i | ||||||||
\(944\) | −6.86325 | −0.223380 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.7541 | −1.68267 | ||||||||
\(947\) | − 37.2052i | − 1.20901i | −0.796602 | − | 0.604504i | \(-0.793371\pi\) | ||||
0.796602 | − | 0.604504i | \(-0.206629\pi\) | |||||||
\(948\) | − 22.6222i | − 0.734737i | ||||||||
\(949\) | −23.3111 | −0.756711 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.0796 | 0.651125 | ||||||||
\(952\) | − 10.5941i | − 0.343356i | ||||||||
\(953\) | − 49.1104i | − 1.59084i | −0.606056 | − | 0.795422i | \(-0.707249\pi\) | ||||
0.606056 | − | 0.795422i | \(-0.292751\pi\) | |||||||
\(954\) | −5.70266 | −0.184631 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.34876 | 0.140649 | ||||||||
\(957\) | − 7.99509i | − 0.258445i | ||||||||
\(958\) | 30.5659i | 0.987540i | ||||||||
\(959\) | −10.0691 | −0.325148 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.40778 | 0.142187 | ||||||||
\(962\) | − 27.8018i | − 0.896365i | ||||||||
\(963\) | 16.7538i | 0.539885i | ||||||||
\(964\) | −0.764142 | −0.0246114 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.41970 | −0.142202 | ||||||||
\(967\) | 1.96751i | 0.0632709i | 0.999499 | + | 0.0316355i | \(0.0100716\pi\) | ||||
−0.999499 | + | 0.0316355i | \(0.989928\pi\) | |||||||
\(968\) | − 30.8513i | − 0.991599i | ||||||||
\(969\) | 15.1668 | 0.487227 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.1205 | 0.838247 | 0.419123 | − | 0.907929i | \(-0.362337\pi\) | ||||
0.419123 | + | 0.907929i | \(0.362337\pi\) | |||||||
\(972\) | 9.45734i | 0.303344i | ||||||||
\(973\) | 52.2924i | 1.67642i | ||||||||
\(974\) | 21.1367 | 0.677265 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.5069 | −0.432345 | ||||||||
\(977\) | − 0.639319i | − 0.0204536i | −0.999948 | − | 0.0102268i | \(-0.996745\pi\) | ||||
0.999948 | − | 0.0102268i | \(-0.00325535\pi\) | |||||||
\(978\) | 11.6317i | 0.371941i | ||||||||
\(979\) | 108.452 | 3.46613 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.76846 | 0.0883902 | ||||||||
\(982\) | − 28.0514i | − 0.895157i | ||||||||
\(983\) | 6.46926i | 0.206337i | 0.994664 | + | 0.103169i | \(0.0328981\pi\) | ||||
−0.994664 | + | 0.103169i | \(0.967102\pi\) | |||||||
\(984\) | −8.02571 | −0.255850 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.96237 | −0.0943410 | ||||||||
\(987\) | 17.2408i | 0.548780i | ||||||||
\(988\) | − 12.1958i | − 0.387999i | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.2334 | 1.18276 | 0.591379 | − | 0.806394i | \(-0.298584\pi\) | ||||
0.591379 | + | 0.806394i | \(0.298584\pi\) | |||||||
\(992\) | − 5.95044i | − 0.188927i | ||||||||
\(993\) | 35.4189i | 1.12398i | ||||||||
\(994\) | −7.92905 | −0.251494 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.9385 | 0.409973 | ||||||||
\(997\) | 9.65124i | 0.305658i | 0.988253 | + | 0.152829i | \(0.0488384\pi\) | ||||
−0.988253 | + | 0.152829i | \(0.951162\pi\) | |||||||
\(998\) | − 3.80178i | − 0.120343i | ||||||||
\(999\) | −39.8018 | −1.25927 |
(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 | 1150.2.b.j.599.5 | 6 | ||
5.2 | odd | 4 | 1150.2.a.q.1.2 | 3 | |||
5.3 | odd | 4 | 230.2.a.d.1.2 | ✓ | 3 | ||
5.4 | even | 2 | inner | 1150.2.b.j.599.2 | 6 | ||
15.8 | even | 4 | 2070.2.a.z.1.2 | 3 | |||
20.3 | even | 4 | 1840.2.a.r.1.2 | 3 | |||
20.7 | even | 4 | 9200.2.a.cf.1.2 | 3 | |||
40.3 | even | 4 | 7360.2.a.ce.1.2 | 3 | |||
40.13 | odd | 4 | 7360.2.a.bz.1.2 | 3 | |||
115.68 | even | 4 | 5290.2.a.r.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.d.1.2 | ✓ | 3 | 5.3 | odd | 4 | ||
1150.2.a.q.1.2 | 3 | 5.2 | odd | 4 | |||
1150.2.b.j.599.2 | 6 | 5.4 | even | 2 | inner | ||
1150.2.b.j.599.5 | 6 | 1.1 | even | 1 | trivial | ||
1840.2.a.r.1.2 | 3 | 20.3 | even | 4 | |||
2070.2.a.z.1.2 | 3 | 15.8 | even | 4 | |||
5290.2.a.r.1.2 | 3 | 115.68 | even | 4 | |||
7360.2.a.bz.1.2 | 3 | 40.13 | odd | 4 | |||
7360.2.a.ce.1.2 | 3 | 40.3 | even | 4 | |||
9200.2.a.cf.1.2 | 3 | 20.7 | even | 4 |