Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (of order \(2\), degree \(1\), 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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.10 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.b.2157.9 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.49114 | −0.860912 | −0.430456 | − | 0.902612i | \(-0.641647\pi\) | ||||
−0.430456 | + | 0.902612i | \(0.641647\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.37882i | 0.616626i | 0.951285 | + | 0.308313i | \(0.0997643\pi\) | ||||
−0.951285 | + | 0.308313i | \(0.900236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.776492 | −0.258831 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93568 | − | 2.09327i | −0.814212 | − | 0.580568i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.05601i | − | 0.530860i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.801929 | 0.194496 | 0.0972482 | − | 0.995260i | \(-0.468996\pi\) | ||||
0.0972482 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0452303i | 0.0103765i | 0.999987 | + | 0.00518827i | \(0.00165149\pi\) | ||||
−0.999987 | + | 0.00518827i | \(0.998349\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.49114i | 0.325394i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.18836 | 1.29036 | 0.645181 | − | 0.764030i | \(-0.276782\pi\) | ||||
0.645181 | + | 0.764030i | \(0.276782\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.09886 | 0.619773 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63129 | 1.08374 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.84316 | −1.45644 | −0.728219 | − | 0.685344i | \(-0.759652\pi\) | ||||
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.31339i | − | 0.415497i | −0.978182 | − | 0.207749i | \(-0.933386\pi\) | ||
0.978182 | − | 0.207749i | \(-0.0666136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.49114i | 0.259575i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.37882 | 0.233063 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.74996i | − | 0.616489i | −0.951307 | − | 0.308245i | \(-0.900258\pi\) | ||
0.951307 | − | 0.308245i | \(-0.0997415\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.37752 | + | 3.12136i | 0.700964 | + | 0.499818i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.15820i | 0.337054i | 0.985697 | + | 0.168527i | \(0.0539010\pi\) | ||||
−0.985697 | + | 0.168527i | \(0.946099\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.55492 | −0.694618 | −0.347309 | − | 0.937751i | \(-0.612905\pi\) | ||||
−0.347309 | + | 0.937751i | \(0.612905\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.07064i | − | 0.159602i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.91517i | 0.279357i | 0.990197 | + | 0.139678i | \(0.0446069\pi\) | ||||
−0.990197 | + | 0.139678i | \(0.955393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.19579 | −0.167444 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.32588 | 0.182123 | 0.0910615 | − | 0.995845i | \(-0.470974\pi\) | ||||
0.0910615 | + | 0.995845i | \(0.470974\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.37882 | 0.185920 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.0674448i | − | 0.00893329i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.56985i | 1.11570i | 0.829942 | + | 0.557850i | \(0.188374\pi\) | ||||
−0.829942 | + | 0.557850i | \(0.811626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.82926 | 1.00243 | 0.501217 | − | 0.865321i | \(-0.332886\pi\) | ||||
0.501217 | + | 0.865321i | \(0.332886\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.776492i | 0.0978288i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.88623 | − | 4.04777i | 0.357993 | − | 0.502064i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0545i | 1.59487i | 0.603407 | + | 0.797433i | \(0.293809\pi\) | ||||
−0.603407 | + | 0.797433i | \(0.706191\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.22773 | −1.11089 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.36987i | − | 0.162573i | −0.996691 | − | 0.0812867i | \(-0.974097\pi\) | ||
0.996691 | − | 0.0812867i | \(-0.0259029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.13718i | − | 0.718303i | −0.933279 | − | 0.359151i | \(-0.883066\pi\) | ||
0.933279 | − | 0.359151i | \(-0.116934\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.62085 | −0.533570 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.88057 | −0.999142 | −0.499571 | − | 0.866273i | \(-0.666509\pi\) | ||||
−0.499571 | + | 0.866273i | \(0.666509\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.06758 | −0.674176 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.20617i | 0.461687i | 0.972991 | + | 0.230844i | \(0.0741486\pi\) | ||||
−0.972991 | + | 0.230844i | \(0.925851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.10571i | 0.119931i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.6953 | 1.25387 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.55584i | 1.01292i | 0.862264 | + | 0.506458i | \(0.169046\pi\) | ||||
−0.862264 | + | 0.506458i | \(0.830954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.09327 | + | 2.93568i | −0.219434 | + | 0.307743i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.44960i | 0.357707i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0623643 | −0.00639844 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.59559i | 0.568146i | 0.958803 | + | 0.284073i | \(0.0916858\pi\) | ||||
−0.958803 | + | 0.284073i | \(0.908314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.776492i | 0.0780404i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.25485 | −0.522877 | −0.261439 | − | 0.965220i | \(-0.584197\pi\) | ||||
−0.261439 | + | 0.965220i | \(0.584197\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0374 | −1.28461 | −0.642306 | − | 0.766448i | \(-0.722022\pi\) | ||||
−0.642306 | + | 0.766448i | \(0.722022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.05601 | −0.200646 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.92739 | −0.959717 | −0.479859 | − | 0.877346i | \(-0.659312\pi\) | ||||
−0.479859 | + | 0.877346i | \(0.659312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.4848i | − | 1.29161i | −0.763503 | − | 0.645805i | \(-0.776522\pi\) | ||
0.763503 | − | 0.645805i | \(-0.223478\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.59172i | 0.530743i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0357 | 1.22629 | 0.613147 | − | 0.789969i | \(-0.289903\pi\) | ||||
0.613147 | + | 0.789969i | \(0.289903\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.53261i | 0.795670i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.27953 | + | 1.62541i | 0.210743 | + | 0.150269i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.801929i | − | 0.0735128i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.21818i | − | 0.290173i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1668i | 0.998793i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0769 | −0.894181 | −0.447091 | − | 0.894489i | \(-0.647540\pi\) | ||||
−0.447091 | + | 0.894489i | \(0.647540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.79203 | 0.598005 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.92342 | −0.779643 | −0.389821 | − | 0.920890i | \(-0.627463\pi\) | ||||
−0.389821 | + | 0.920890i | \(0.627463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0452303 | 0.00392196 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.76452i | 0.668263i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 20.2513i | − | 1.73018i | −0.501615 | − | 0.865091i | \(-0.667260\pi\) | ||
0.501615 | − | 0.865091i | \(-0.332740\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.85480 | −0.581416 | −0.290708 | − | 0.956812i | \(-0.593891\pi\) | ||||
−0.290708 | + | 0.956812i | \(0.593891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.85580i | − | 0.240502i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.09327 | + | 2.93568i | −0.175048 | + | 0.245494i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.8143i | − | 0.898077i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.49114 | 0.122987 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.974168i | 0.0798070i | 0.999204 | + | 0.0399035i | \(0.0127050\pi\) | ||||
−0.999204 | + | 0.0399035i | \(0.987295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.9920i | − | 1.05728i | −0.848847 | − | 0.528638i | \(-0.822703\pi\) | ||
0.848847 | − | 0.528638i | \(-0.177297\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.622692 | −0.0503417 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.18974 | 0.256206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3467 | 0.905563 | 0.452782 | − | 0.891621i | \(-0.350432\pi\) | ||||
0.452782 | + | 0.891621i | \(0.350432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.97707 | −0.156792 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.18836i | − | 0.487711i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.04804i | − | 0.317067i | −0.987354 | − | 0.158533i | \(-0.949323\pi\) | ||
0.987354 | − | 0.158533i | \(-0.0506765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.05601 | −0.160060 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.22415i | 0.559022i | 0.960143 | + | 0.279511i | \(0.0901723\pi\) | ||||
−0.960143 | + | 0.279511i | \(0.909828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.23645 | + | 12.2903i | 0.325881 | + | 0.945411i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 0.0351210i | − | 0.00268577i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.2479 | −1.23530 | −0.617651 | − | 0.786453i | \(-0.711915\pi\) | ||||
−0.617651 | + | 0.786453i | \(0.711915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.09886i | − | 0.234252i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.7789i | − | 0.960519i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.9732 | −1.79184 | −0.895920 | − | 0.444216i | \(-0.853482\pi\) | ||||
−0.895920 | + | 0.444216i | \(0.853482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.32148 | 0.544201 | 0.272101 | − | 0.962269i | \(-0.412282\pi\) | ||||
0.272101 | + | 0.962269i | \(0.412282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6746 | −0.863008 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.17050 | 0.380143 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.801929i | − | 0.0586429i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 5.63129i | − | 0.409616i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4656 | 1.11905 | 0.559527 | − | 0.828812i | \(-0.310983\pi\) | ||||
0.559527 | + | 0.828812i | \(0.310983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.4032i | 1.18073i | 0.807137 | + | 0.590364i | \(0.201016\pi\) | ||||
−0.807137 | + | 0.590364i | \(0.798984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.30379 | + | 6.03580i | −0.308201 | + | 0.432233i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.53639i | 0.323204i | 0.986856 | + | 0.161602i | \(0.0516661\pi\) | ||||
−0.986856 | + | 0.161602i | \(0.948334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.56527 | −0.678064 | −0.339032 | − | 0.940775i | \(-0.610099\pi\) | ||||
−0.339032 | + | 0.940775i | \(0.610099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 19.4662i | − | 1.37304i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.84316i | 0.550482i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.97576 | −0.207836 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.80521 | −0.333985 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0452303 | 0.00312864 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.5121 | −1.68748 | −0.843742 | − | 0.536748i | \(-0.819652\pi\) | ||||
−0.843742 | + | 0.536748i | \(0.819652\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.04267i | 0.139961i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6.28040i | − | 0.428319i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.31339 | −0.157043 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.15141i | 0.618395i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.35421 | − | 1.67865i | −0.158361 | − | 0.112918i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.87329i | 0.326340i | 0.986598 | + | 0.163170i | \(0.0521719\pi\) | ||||
−0.986598 | + | 0.163170i | \(0.947828\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.40624 | −0.160416 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.4033i | 1.81882i | 0.415897 | + | 0.909412i | \(0.363468\pi\) | ||||
−0.415897 | + | 0.909412i | \(0.636532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.18332i | − | 0.408606i | −0.978908 | − | 0.204303i | \(-0.934507\pi\) | ||
0.978908 | − | 0.204303i | \(-0.0654927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.49114 | 0.0981100 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1947 | −0.864411 | −0.432205 | − | 0.901775i | \(-0.642264\pi\) | ||||
−0.432205 | + | 0.901775i | \(0.642264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.64067 | −0.172259 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.2422 | 0.860173 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.9098i | 1.15849i | 0.815154 | + | 0.579244i | \(0.196652\pi\) | ||||
−0.815154 | + | 0.579244i | \(0.803348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4891i | 1.25540i | 0.778454 | + | 0.627701i | \(0.216004\pi\) | ||||
−0.778454 | + | 0.627701i | \(0.783996\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.84623 | −0.503336 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.37882i | − | 0.0880894i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0946792 | − | 0.132782i | 0.00602429 | − | 0.00844870i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.27200i | − | 0.397472i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.04285 | −0.255183 | −0.127591 | − | 0.991827i | \(-0.540725\pi\) | ||||
−0.127591 | + | 0.991827i | \(0.540725\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.18836i | − | 0.389059i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 1.64878i | − | 0.103250i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.2244 | −1.13681 | −0.568405 | − | 0.822749i | \(-0.692439\pi\) | ||||
−0.568405 | + | 0.822749i | \(0.692439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.74996 | −0.233011 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.09015 | 0.376971 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2306 | 0.692508 | 0.346254 | − | 0.938141i | \(-0.387454\pi\) | ||||
0.346254 | + | 0.938141i | \(0.387454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82814i | 0.112302i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.2491i | − | 0.872032i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.6499 | −0.771281 | −0.385640 | − | 0.922649i | \(-0.626019\pi\) | ||||
−0.385640 | + | 0.922649i | \(0.626019\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.5896i | 1.43297i | 0.697603 | + | 0.716484i | \(0.254250\pi\) | ||||
−0.697603 | + | 0.716484i | \(0.745750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.12136 | − | 4.37752i | 0.188914 | − | 0.264940i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.09886i | − | 0.186869i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.3386 | −1.76279 | −0.881394 | − | 0.472383i | \(-0.843394\pi\) | ||||
−0.881394 | + | 0.472383i | \(0.843394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.79633i | 0.107543i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5026i | 0.865153i | 0.901597 | + | 0.432577i | \(0.142396\pi\) | ||||
−0.901597 | + | 0.432577i | \(0.857604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.2156 | 0.607254 | 0.303627 | − | 0.952791i | \(-0.401802\pi\) | ||||
0.303627 | + | 0.952791i | \(0.401802\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0929941 | 0.00550849 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.15820 | 0.127394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3569 | −0.962171 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 8.34382i | − | 0.489123i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.6529i | 1.03129i | 0.856801 | + | 0.515647i | \(0.172448\pi\) | ||||
−0.856801 | + | 0.515647i | \(0.827552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.8163 | −0.687969 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.63129i | − | 0.326761i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.1670 | − | 12.9539i | −1.05063 | − | 0.749143i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.55492i | 0.262541i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.83574 | 0.450151 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.7951i | 0.618127i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.9238i | 1.70784i | 0.520405 | + | 0.853920i | \(0.325781\pi\) | ||||
−0.520405 | + | 0.853920i | \(0.674219\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.4406 | 1.10594 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.7093 | 1.28772 | 0.643862 | − | 0.765142i | \(-0.277331\pi\) | ||||
0.643862 | + | 0.765142i | \(0.277331\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2929 | −0.581791 | −0.290896 | − | 0.956755i | \(-0.593953\pi\) | ||||
−0.290896 | + | 0.956755i | \(0.593953\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.07064 | −0.0603237 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.55697i | 0.143614i | 0.997419 | + | 0.0718068i | \(0.0228765\pi\) | ||||
−0.997419 | + | 0.0718068i | \(0.977124\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.84316i | 0.439133i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.8032 | 0.826232 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0362715i | 0.00201820i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.09728 | − | 6.48676i | −0.504626 | − | 0.359821i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.1078i | 1.11196i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.91517 | 0.105587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.4274i | 1.12279i | 0.827547 | + | 0.561396i | \(0.189736\pi\) | ||||
−0.827547 | + | 0.561396i | \(0.810264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.91181i | 0.159566i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.9998 | −0.983436 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.41864 | 0.295172 | 0.147586 | − | 0.989049i | \(-0.452850\pi\) | ||||
0.147586 | + | 0.989049i | \(0.452850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.4381 | −1.05573 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.31339 | −0.125277 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 12.7233i | − | 0.685002i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.01725 | −0.269340 | −0.134670 | − | 0.990890i | \(-0.542997\pi\) | ||||
−0.134670 | + | 0.990890i | \(0.542997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.9128i | 1.44061i | 0.693657 | + | 0.720306i | \(0.255998\pi\) | ||||
−0.693657 | + | 0.720306i | \(0.744002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.5317 | − | 11.7878i | −0.882395 | − | 0.629186i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.73979i | 0.358723i | 0.983783 | + | 0.179361i | \(0.0574031\pi\) | ||||
−0.983783 | + | 0.179361i | \(0.942597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.88880 | 0.100247 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.19579i | 0.0632880i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 0.933367i | − | 0.0492612i | −0.999697 | − | 0.0246306i | \(-0.992159\pi\) | ||
0.999697 | − | 0.0246306i | \(-0.00784096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9980 | 0.999892 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.49114 | 0.0782647 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.46204 | 0.442924 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.6499 | −1.54771 | −0.773856 | − | 0.633362i | \(-0.781675\pi\) | ||||
−0.773856 | + | 0.633362i | \(0.781675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.67582i | − | 0.0872398i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.32588i | − | 0.0688360i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.5132 | −1.06214 | −0.531068 | − | 0.847329i | \(-0.678209\pi\) | ||||
−0.531068 | + | 0.847329i | \(0.678209\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 16.6514i | − | 0.859873i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.0250 | + | 16.4178i | 1.18585 | + | 0.845562i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.0229i | − | 1.38807i | −0.719940 | − | 0.694037i | \(-0.755830\pi\) | ||
0.719940 | − | 0.694037i | \(-0.244170\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.0261 | 0.769811 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.2421i | − | 1.08542i | −0.839921 | − | 0.542709i | \(-0.817399\pi\) | ||
0.839921 | − | 0.542709i | \(-0.182601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.37882i | − | 0.0702710i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.53686 | 0.179789 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2249 | 0.771931 | 0.385966 | − | 0.922513i | \(-0.373868\pi\) | ||||
0.385966 | + | 0.922513i | \(0.373868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.96263 | 0.250971 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.3061 | 0.671204 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 12.2447i | − | 0.616097i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 25.7143i | − | 1.29057i | −0.763944 | − | 0.645283i | \(-0.776739\pi\) | ||
0.763944 | − | 0.645283i | \(-0.223261\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0674448 | −0.00337647 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 32.1744i | − | 1.60671i | −0.595497 | − | 0.803357i | \(-0.703045\pi\) | ||
0.595497 | − | 0.803357i | \(-0.296955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.84255 | + | 6.79138i | −0.241225 | + | 0.338303i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 8.36609i | − | 0.415714i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.74996 | −0.185879 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.2195i | − | 1.09868i | −0.835599 | − | 0.549341i | \(-0.814879\pi\) | ||
0.835599 | − | 0.549341i | \(-0.185121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.1975i | 1.48953i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.56985 | 0.421695 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.79954 | −0.284688 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.2215 | 0.500548 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.7205 | 1.20768 | 0.603839 | − | 0.797107i | \(-0.293637\pi\) | ||||
0.603839 | + | 0.797107i | \(0.293637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.5645i | − | 0.758569i | −0.925280 | − | 0.379285i | \(-0.876170\pi\) | ||
0.925280 | − | 0.379285i | \(-0.123830\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.48712i | − | 0.0723062i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.48507 | 0.120544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.82926i | − | 0.378885i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.12136 | − | 4.37752i | 0.150701 | − | 0.211349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.08765i | 0.245063i | 0.992465 | + | 0.122532i | \(0.0391013\pi\) | ||||
−0.992465 | + | 0.122532i | \(0.960899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.6678 | 1.08934 | 0.544672 | − | 0.838649i | \(-0.316654\pi\) | ||||
0.544672 | + | 0.838649i | \(0.316654\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.1256i | 0.773165i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.279901i | 0.0133895i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2165 | −0.583061 | −0.291531 | − | 0.956561i | \(-0.594165\pi\) | ||||
−0.291531 | + | 0.956561i | \(0.594165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.776492 | 0.0369758 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.07771 | −0.0987150 | −0.0493575 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493575 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.1757 | −0.624590 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.45262i | − | 0.0687068i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.9045i | 1.69444i | 0.531244 | + | 0.847219i | \(0.321725\pi\) | ||||
−0.531244 | + | 0.847219i | \(0.678275\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.15820 | 0.101625 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.3730i | 0.910222i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.04777 | − | 2.88623i | −0.189762 | − | 0.135309i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.11925i | − | 0.0523561i | −0.999657 | − | 0.0261781i | \(-0.991666\pi\) | ||
0.999657 | − | 0.0261781i | \(-0.00833369\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.51590 | 0.210784 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 26.2572i | − | 1.22292i | −0.791276 | − | 0.611459i | \(-0.790583\pi\) | ||
0.791276 | − | 0.611459i | \(-0.209417\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.1914i | 1.72843i | 0.503121 | + | 0.864216i | \(0.332185\pi\) | ||||
−0.503121 | + | 0.864216i | \(0.667815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.75636 | −0.220571 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.96476 | −0.414840 | −0.207420 | − | 0.978252i | \(-0.566507\pi\) | ||||
−0.207420 | + | 0.978252i | \(0.566507\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.0545 | 0.602803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9195 | −0.779610 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.55492i | 0.209435i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.140163i | 0.00643110i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.02953 | −0.0471390 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.2673i | 1.83986i | 0.392081 | + | 0.919931i | \(0.371755\pi\) | ||||
−0.392081 | + | 0.919931i | \(0.628245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.84967 | + | 11.0087i | −0.357914 | + | 0.501953i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.22773i | 0.419876i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.71529 | −0.350333 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.97904i | 0.316250i | 0.987419 | + | 0.158125i | \(0.0505450\pi\) | ||||
−0.987419 | + | 0.158125i | \(0.949455\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.03620i | 0.272966i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.3699 | −0.829023 | −0.414512 | − | 0.910044i | \(-0.636048\pi\) | ||||
−0.414512 | + | 0.910044i | \(0.636048\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.28966 | −0.283272 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.07064 | −0.0481217 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.36987 | −0.0614469 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.3859i | − | 0.823065i | −0.911395 | − | 0.411533i | \(-0.864994\pi\) | ||
0.911395 | − | 0.411533i | \(-0.135006\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 10.7722i | − | 0.481268i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.5148 | 1.09306 | 0.546531 | − | 0.837439i | \(-0.315948\pi\) | ||||
0.546531 | + | 0.837439i | \(0.315948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.24548i | − | 0.322419i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.31715 | − | 18.3267i | −0.280555 | − | 0.813915i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5.95666i | − | 0.264024i | −0.991248 | − | 0.132012i | \(-0.957856\pi\) | ||
0.991248 | − | 0.132012i | \(-0.0421438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.13718 | −0.271493 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.254705i | 0.0112455i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 17.9762i | − | 0.792125i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.91517 | 0.0842293 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.2279 | 1.06349 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.6556 | 0.817315 | 0.408658 | − | 0.912688i | \(-0.365997\pi\) | ||||
0.408658 | + | 0.912688i | \(0.365997\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.6725 | −0.947674 | −0.473837 | − | 0.880612i | \(-0.657131\pi\) | ||||
−0.473837 | + | 0.880612i | \(0.657131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.62085i | 0.201670i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.85518i | − | 0.0808128i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.2958 | 0.665033 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.65442i | − | 0.288777i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.51769 | − | 6.33578i | 0.195683 | − | 0.274433i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 13.6881i | − | 0.591786i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.7474 | 1.54262 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 23.6938i | − | 1.01867i | −0.860567 | − | 0.509337i | \(-0.829891\pi\) | ||
0.860567 | − | 0.509337i | \(-0.170109\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.9174 | −0.468509 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.5931 | 0.796439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.1652 | −0.776688 | −0.388344 | − | 0.921514i | \(-0.626953\pi\) | ||||
−0.388344 | + | 0.921514i | \(0.626953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.07936 | −0.259461 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.354749i | − | 0.0151128i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.88057i | 0.377640i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.70996 | −0.327270 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.84539i | − | 0.332420i | −0.986090 | − | 0.166210i | \(-0.946847\pi\) | ||
0.986090 | − | 0.166210i | \(-0.0531529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.3718 | + | 9.53467i | 0.565566 | + | 0.403273i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.19579i | 0.0504864i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3111 | 0.982446 | 0.491223 | − | 0.871034i | \(-0.336550\pi\) | ||||
0.491223 | + | 0.871034i | \(0.336550\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.9738i | 0.756164i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.06758i | 0.254815i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.92117 | 0.206306 | 0.103153 | − | 0.994666i | \(-0.467107\pi\) | ||||
0.103153 | + | 0.994666i | \(0.467107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.9300 | 1.00144 | 0.500719 | − | 0.865610i | \(-0.333069\pi\) | ||||
0.500719 | + | 0.865610i | \(0.333069\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.0615 | −0.963407 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.1769 | 0.799731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.2779i | 0.511134i | 0.966791 | + | 0.255567i | \(0.0822621\pi\) | ||||
−0.966791 | + | 0.255567i | \(0.917738\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 24.4595i | − | 1.01650i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.20617 | 0.174501 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.32588i | − | 0.0549122i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.24114 | + | 3.14306i | −0.0926596 | + | 0.129949i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.8757i | 1.56330i | 0.623720 | + | 0.781648i | \(0.285621\pi\) | ||||
−0.623720 | + | 0.781648i | \(0.714379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.104635 | 0.00431142 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 6.76441i | − | 0.278251i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 41.0910i | − | 1.68740i | −0.536811 | − | 0.843702i | \(-0.680371\pi\) | ||
0.536811 | − | 0.843702i | \(-0.319629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.10571 | 0.0453298 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2632 | 0.583753 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.4676 | −0.631990 | −0.315995 | − | 0.948761i | \(-0.602338\pi\) | ||||
−0.315995 | + | 0.948761i | \(0.602338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.93017 | −0.364269 | −0.182135 | − | 0.983274i | \(-0.558301\pi\) | ||||
−0.182135 | + | 0.983274i | \(0.558301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 10.1368i | − | 0.412800i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1.37882i | − | 0.0560569i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.19652 | 0.170331 | 0.0851657 | − | 0.996367i | \(-0.472858\pi\) | ||||
0.0851657 | + | 0.996367i | \(0.472858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 11.6953i | − | 0.473917i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.00898 | − | 5.62234i | 0.162186 | − | 0.227456i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.2786i | 0.536316i | 0.963375 | + | 0.268158i | \(0.0864149\pi\) | ||||
−0.963375 | + | 0.268158i | \(0.913585\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.43728 | 0.178928 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 44.6391i | − | 1.79710i | −0.438870 | − | 0.898550i | \(-0.644621\pi\) | ||
0.438870 | − | 0.898550i | \(-0.355379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.48610i | 0.381279i | 0.981660 | + | 0.190639i | \(0.0610561\pi\) | ||||
−0.981660 | + | 0.190639i | \(0.938944\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.8484 | 1.39842 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.55584 | 0.382846 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.0972860 | 0.00389144 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0674448 | −0.00269349 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.00720i | − | 0.119905i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.8053i | − | 0.430151i | −0.976597 | − | 0.215075i | \(-0.931000\pi\) | ||
0.976597 | − | 0.215075i | \(-0.0689997\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.5511 | 1.45278 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 13.8942i | − | 0.551375i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.93568 | + | 2.09327i | 0.116316 | + | 0.0829383i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.06369i | 0.0420790i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.5052 | 0.454427 | 0.227213 | − | 0.973845i | \(-0.427039\pi\) | ||||
0.227213 | + | 0.973845i | \(0.427039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.2080i | − | 0.481438i | −0.970595 | − | 0.240719i | \(-0.922617\pi\) | ||
0.970595 | − | 0.240719i | \(-0.0773833\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.36497i | 0.368745i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.38289 | 0.172309 | 0.0861547 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861547 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.56985 | 0.336396 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.44960 | 0.135200 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.6643 | 0.495592 | 0.247796 | − | 0.968812i | \(-0.420294\pi\) | ||||
0.247796 | + | 0.968812i | \(0.420294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.3038i | − | 0.480748i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.76547i | 0.185919i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.1021 | 0.666203 | 0.333101 | − | 0.942891i | \(-0.391905\pi\) | ||||
0.333101 | + | 0.942891i | \(0.391905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.0572i | 1.90810i | 0.299643 | + | 0.954051i | \(0.403132\pi\) | ||||
−0.299643 | + | 0.954051i | \(0.596868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.51046 | + | 2.50311i | 0.136335 | + | 0.0972129i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0623643i | 0.00241838i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.5363 | −1.87933 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 7.26678i | − | 0.280950i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.82926i | − | 0.302245i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.6787 | −1.10548 | −0.552742 | − | 0.833353i | \(-0.686418\pi\) | ||||
−0.552742 | + | 0.833353i | \(0.686418\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.4506 | 0.671674 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0793 | 1.57881 | 0.789403 | − | 0.613876i | \(-0.210390\pi\) | ||||
0.789403 | + | 0.613876i | \(0.210390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.59559 | 0.214739 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 40.8623i | − | 1.56585i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.10104i | 0.0803940i | 0.999192 | + | 0.0401970i | \(0.0127986\pi\) | ||||
−0.999192 | + | 0.0401970i | \(0.987201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.9228 | 1.06687 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.22022i | 0.351773i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.89235 | − | 2.77541i | −0.148287 | − | 0.105735i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 48.7134i | − | 1.85315i | −0.376115 | − | 0.926573i | \(-0.622740\pi\) | ||
0.376115 | − | 0.926573i | \(-0.377260\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.776492 | 0.0294965 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 9.45151i | − | 0.358516i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.73072i | 0.0655557i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.6751 | 0.744182 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1876 | 1.36679 | 0.683393 | − | 0.730051i | \(-0.260504\pi\) | ||||
0.683393 | + | 0.730051i | \(0.260504\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.169612 | 0.00639703 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.93762 | 0.148300 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.25485i | 0.197629i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.460582i | 0.0172975i | 0.999963 | + | 0.00864876i | \(0.00275302\pi\) | ||||
−0.999963 | + | 0.00864876i | \(0.997247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.89569 | 0.258609 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 14.3161i | − | 0.536142i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.04777 | − | 2.88623i | −0.151378 | − | 0.107939i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 26.7061i | − | 0.997357i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.0938 | −1.53254 | −0.766271 | − | 0.642518i | \(-0.777890\pi\) | ||||
−0.766271 | + | 0.642518i | \(0.777890\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0374i | 0.485538i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 29.0610i | − | 1.08079i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.3049 | −0.902661 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5980 | 0.652675 | 0.326337 | − | 0.945253i | \(-0.394185\pi\) | ||||
0.326337 | + | 0.945253i | \(0.394185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9026 | 1.10750 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.65272 | −0.135101 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.72639i | 0.359252i | 0.983735 | + | 0.179626i | \(0.0574888\pi\) | ||||
−0.983735 | + | 0.179626i | \(0.942511\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.05601i | 0.0758372i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.0545 | 0.480870 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 39.8300i | − | 1.46517i | −0.680676 | − | 0.732585i | \(-0.738314\pi\) | ||
0.680676 | − | 0.732585i | \(-0.261686\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.141180 | + | 0.197997i | −0.00518638 | + | 0.00727359i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.40607i | − | 0.124957i | −0.998046 | − | 0.0624784i | \(-0.980100\pi\) | ||
0.998046 | − | 0.0624784i | \(-0.0199004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.34320 | −0.0492110 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.26606i | − | 0.119499i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.92739i | 0.362739i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0147 | 0.474912 | 0.237456 | − | 0.971398i | \(-0.423686\pi\) | ||||
0.237456 | + | 0.971398i | \(0.423686\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.02848 | 0.219690 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.9136 | 0.651944 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.8498 | −1.63009 | −0.815047 | − | 0.579395i | \(-0.803289\pi\) | ||||
−0.815047 | + | 0.579395i | \(0.803289\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.22773i | 0.334945i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 34.7548i | − | 1.25986i | −0.776652 | − | 0.629930i | \(-0.783084\pi\) | ||
0.776652 | − | 0.629930i | \(-0.216916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.4848 | −0.488182 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 0.858578i | − | 0.0310419i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9390 | − | 25.1584i | 0.647740 | − | 0.908416i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.7642i | 1.36181i | 0.732372 | + | 0.680905i | \(0.238413\pi\) | ||||
−0.732372 | + | 0.680905i | \(0.761587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.1753 | 0.978693 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.9080i | 0.680074i | 0.940412 | + | 0.340037i | \(0.110440\pi\) | ||||
−0.940412 | + | 0.340037i | \(0.889560\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.16889i | − | 0.257514i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.59172 | 0.200602 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0976158 | −0.00349745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.36987 | −0.0490177 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −44.1671 | −1.57840 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6450i | 0.558393i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.7701i | 1.91670i | 0.285601 | + | 0.958349i | \(0.407807\pi\) | ||||
−0.285601 | + | 0.958349i | \(0.592193\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.7464 | −0.596188 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 13.0357i | − | 0.463495i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.9842 | − | 16.3888i | −0.816194 | − | 0.581982i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 2.72602i | − | 0.0966819i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.1715 | −0.466559 | −0.233279 | − | 0.972410i | \(-0.574946\pi\) | ||||
−0.233279 | + | 0.972410i | \(0.574946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.53584i | 0.0543339i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.42003i | − | 0.262174i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.13718 | −0.216576 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.53261 | 0.300735 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.8629 | 0.664005 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.3683 | −1.52475 | −0.762374 | − | 0.647137i | \(-0.775966\pi\) | ||||
−0.762374 | + | 0.647137i | \(0.775966\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.4125i | 1.34884i | 0.738346 | + | 0.674422i | \(0.235607\pi\) | ||||
−0.738346 | + | 0.674422i | \(0.764393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 35.1755i | − | 1.23366i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.58150 | 0.195511 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.206020i | − | 0.00720774i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.62541 | − | 2.27953i | 0.0567963 | − | 0.0796533i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 34.5301i | − | 1.20511i | −0.798078 | − | 0.602554i | \(-0.794150\pi\) | ||
0.798078 | − | 0.602554i | \(-0.205850\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.8457 | −1.38893 | −0.694466 | − | 0.719525i | \(-0.744359\pi\) | ||||
−0.694466 | + | 0.719525i | \(0.744359\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.62085i | 0.160877i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.90160i | − | 0.135672i | −0.997696 | − | 0.0678359i | \(-0.978391\pi\) | ||
0.997696 | − | 0.0678359i | \(-0.0216094\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1801 | 1.29132 | 0.645658 | − | 0.763626i | \(-0.276583\pi\) | ||||
0.645658 | + | 0.763626i | \(0.276583\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.7481 | 1.51760 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.801929 | −0.0277852 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.96078 | −0.344707 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 13.0274i | − | 0.450292i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 10.4262i | − | 0.359952i | −0.983671 | − | 0.179976i | \(-0.942398\pi\) | ||
0.983671 | − | 0.179976i | \(-0.0576020\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.5152 | 1.12121 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 21.6255i | − | 0.744821i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.9461 | + | 5.84129i | −0.582964 | + | 0.200946i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.2329 | −0.522792 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 23.2061i | − | 0.795494i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.4123i | 1.17826i | 0.808040 | + | 0.589128i | \(0.200529\pi\) | ||||
−0.808040 | + | 0.589128i | \(0.799471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0484254 | 0.00165611 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.6969 | −0.365401 | −0.182700 | − | 0.983169i | \(-0.558484\pi\) | ||||
−0.182700 | + | 0.983169i | \(0.558484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.8625 | −0.438862 | −0.219431 | − | 0.975628i | \(-0.570420\pi\) | ||||
−0.219431 | + | 0.975628i | \(0.570420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.21818 | −0.109675 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.29654i | − | 0.0441348i | −0.999756 | − | 0.0220674i | \(-0.992975\pi\) | ||
0.999756 | − | 0.0220674i | \(-0.00702484\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 22.4028i | − | 0.761718i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.3905 | 0.828345 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.88057i | 0.301253i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.3267 | − | 38.3240i | 0.925929 | − | 1.29856i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.34493i | − | 0.147054i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1668 | 0.377508 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 4.67717i | − | 0.157937i | −0.996877 | − | 0.0789685i | \(-0.974837\pi\) | ||
0.996877 | − | 0.0789685i | \(-0.0251626\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 26.3230i | − | 0.887854i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.8608 | 0.534364 | 0.267182 | − | 0.963646i | \(-0.413907\pi\) | ||||
0.267182 | + | 0.963646i | \(0.413907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7381 | −0.630586 | −0.315293 | − | 0.948994i | \(-0.602103\pi\) | ||||
−0.315293 | + | 0.948994i | \(0.602103\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.6197 | 0.592281 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.74195 | −0.293526 | −0.146763 | − | 0.989172i | \(-0.546885\pi\) | ||||
−0.146763 | + | 0.989172i | \(0.546885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0769i | 0.337969i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.06758i | 0.203272i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0866239 | −0.00289876 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 33.0546i | − | 1.10489i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.0897 | + | 19.3161i | 0.904497 | + | 0.644946i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.1443i | 0.605146i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.06326 | 0.0354223 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6.79203i | − | 0.226025i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0950i | 0.335568i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.9691 | −0.497040 | −0.248520 | − | 0.968627i | \(-0.579944\pi\) | ||||
−0.248520 | + | 0.968627i | \(0.579944\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.08035 | 0.135337 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.6555 | 0.651214 | 0.325607 | − | 0.945505i | \(-0.394431\pi\) | ||||
0.325607 | + | 0.945505i | \(0.394431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.20617 | 0.139204 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 16.0971i | − | 0.532153i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.92342i | 0.294677i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.1037 | 1.94965 | 0.974826 | − | 0.222966i | \(-0.0715740\pi\) | ||||
0.974826 | + | 0.222966i | \(0.0715740\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 44.6206i | − | 1.47030i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.86750 | + | 4.02149i | −0.0943849 | + | 0.132369i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 11.6206i | − | 0.382083i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.1234 | 0.332497 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 34.1152i | − | 1.11928i | −0.828735 | − | 0.559642i | \(-0.810939\pi\) | ||
0.828735 | − | 0.559642i | \(-0.189061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.0452303i | − | 0.00148236i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.8627 | −1.10862 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.10571 | 0.0361607 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.66720 | −0.152471 | −0.0762353 | − | 0.997090i | \(-0.524290\pi\) | ||||
−0.0762353 | + | 0.997090i | \(0.524290\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.3482 | 0.500871 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 29.0694i | − | 0.947634i | −0.880623 | − | 0.473817i | \(-0.842876\pi\) | ||
0.880623 | − | 0.473817i | \(-0.157124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3557i | 0.434921i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.76452 | 0.252580 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 60.3612i | 1.96148i | 0.195329 | + | 0.980738i | \(0.437423\pi\) | ||||
−0.195329 | + | 0.980738i | \(0.562577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.8468 | + | 18.0168i | −0.417024 | + | 0.584850i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.81280i | − | 0.123639i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.49297 | −0.145542 | −0.0727709 | − | 0.997349i | \(-0.523184\pi\) | ||||
−0.0727709 | + | 0.997349i | \(0.523184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.3243i | 0.690037i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 11.6953i | − | 0.378055i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.2513 | −0.653947 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.6482 | 0.827362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.70854 | 0.248404 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.6170 | −0.728067 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.07203i | − | 0.0666321i | −0.999445 | − | 0.0333160i | \(-0.989393\pi\) | ||
0.999445 | − | 0.0333160i | \(-0.0106068\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.0540860i | − | 0.00173749i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.2443 | 1.13104 | 0.565522 | − | 0.824733i | \(-0.308675\pi\) | ||||
0.565522 | + | 0.824733i | \(0.308675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.85480i | 0.219755i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.5653 | + | 9.67268i | 0.434439 | + | 0.309774i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 47.2830i | − | 1.51272i | −0.654157 | − | 0.756359i | \(-0.726976\pi\) | ||
0.654157 | − | 0.756359i | \(-0.273024\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.55584 | 0.305406 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4708i | 0.334308i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1778i | 0.962521i | 0.876578 | + | 0.481261i | \(0.159821\pi\) | ||||
−0.876578 | + | 0.481261i | \(0.840179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.25485 | −0.199296 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.85580 | −0.0909011 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.1874 | −0.896309 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.35538 | −0.170119 | −0.0850596 | − | 0.996376i | \(-0.527108\pi\) | ||||
−0.0850596 | + | 0.996376i | \(0.527108\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 30.4602i | − | 0.966625i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 13.1888i | − | 0.418112i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.1781 | 0.322343 | 0.161171 | − | 0.986926i | \(-0.448473\pi\) | ||||
0.161171 | + | 0.986926i | \(0.448473\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 21.1171i | − | 0.668116i |
(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 | 4004.2.m.b.2157.10 | yes | 30 | |
13.12 | even | 2 | inner | 4004.2.m.b.2157.9 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.b.2157.9 | ✓ | 30 | 13.12 | even | 2 | inner | |
4004.2.m.b.2157.10 | yes | 30 | 1.1 | even | 1 | trivial |