Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1569,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("2240.1569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.l (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1569.11 | ||
Character | \(\chi\) | \(=\) | 2240.1569 |
Dual form | 2240.2.l.d.1569.12 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −0.236390 | −0.136480 | −0.0682399 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682399 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.55127 | + | 1.61046i | −0.693747 | + | 0.720219i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.94412 | −0.981373 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.36940i | 1.01591i | 0.861383 | + | 0.507957i | \(0.169599\pi\) | ||||
−0.861383 | + | 0.507957i | \(0.830401\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.01585 | 0.281745 | 0.140872 | − | 0.990028i | \(-0.455009\pi\) | ||||
0.140872 | + | 0.990028i | \(0.455009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.366703 | − | 0.380696i | 0.0946824 | − | 0.0982953i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.988642i | 0.239781i | 0.992787 | + | 0.119890i | \(0.0382543\pi\) | ||||
−0.992787 | + | 0.119890i | \(0.961746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.29607i | 0.526755i | 0.964693 | + | 0.263378i | \(0.0848365\pi\) | ||||
−0.964693 | + | 0.263378i | \(0.915163\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.236390i | 0.0515845i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.806457i | 0.168158i | 0.996459 | + | 0.0840790i | \(0.0267948\pi\) | ||||
−0.996459 | + | 0.0840790i | \(0.973205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.187153 | − | 4.99650i | −0.0374307 | − | 0.999299i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.40513 | 0.270417 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.17517i | − | 0.589613i | −0.955557 | − | 0.294807i | \(-0.904745\pi\) | ||
0.955557 | − | 0.294807i | \(-0.0952553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.77004 | −0.317908 | −0.158954 | − | 0.987286i | \(-0.550812\pi\) | ||||
−0.158954 | + | 0.987286i | \(0.550812\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.796493i | − | 0.138652i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61046 | + | 1.55127i | 0.272217 | + | 0.262212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.11347 | 1.49825 | 0.749123 | − | 0.662431i | \(-0.230475\pi\) | ||||
0.749123 | + | 0.662431i | \(0.230475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.240136 | −0.0384525 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.66890 | −1.35385 | −0.676927 | − | 0.736050i | \(-0.736689\pi\) | ||||
−0.676927 | + | 0.736050i | \(0.736689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0221 | −1.68086 | −0.840430 | − | 0.541921i | \(-0.817697\pi\) | ||||
−0.840430 | + | 0.541921i | \(0.817697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.56711 | − | 4.74138i | 0.680825 | − | 0.706804i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.87647i | − | 1.44063i | −0.693646 | − | 0.720316i | \(-0.743997\pi\) | ||
0.693646 | − | 0.720316i | \(-0.256003\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 0.233705i | − | 0.0327252i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.36450 | 0.599510 | 0.299755 | − | 0.954016i | \(-0.403095\pi\) | ||||
0.299755 | + | 0.954016i | \(0.403095\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.42629 | − | 5.22684i | −0.731680 | − | 0.704787i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.542768i | − | 0.0718914i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.34114i | 0.304790i | 0.988320 | + | 0.152395i | \(0.0486986\pi\) | ||||
−0.988320 | + | 0.152395i | \(0.951301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.2211i | − | 1.30867i | −0.756203 | − | 0.654337i | \(-0.772948\pi\) | ||
0.756203 | − | 0.654337i | \(-0.227052\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.94412i | 0.370924i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.57585 | + | 1.63598i | −0.195460 | + | 0.202918i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.35033 | 0.775816 | 0.387908 | − | 0.921698i | \(-0.373198\pi\) | ||||
0.387908 | + | 0.921698i | \(0.373198\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 0.190638i | − | 0.0229502i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.5115 | −1.48485 | −0.742423 | − | 0.669931i | \(-0.766323\pi\) | ||||
−0.742423 | + | 0.669931i | \(0.766323\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.0894i | − | 1.53200i | −0.642841 | − | 0.766000i | \(-0.722244\pi\) | ||
0.642841 | − | 0.766000i | \(-0.277756\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0442412 | + | 1.18112i | 0.00510853 | + | 0.136384i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.36940 | 0.383979 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.51602 | −0.845619 | −0.422809 | − | 0.906219i | \(-0.638956\pi\) | ||||
−0.422809 | + | 0.906219i | \(0.638956\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.50020 | 0.944467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.5463 | −1.59666 | −0.798330 | − | 0.602220i | \(-0.794283\pi\) | ||||
−0.798330 | + | 0.602220i | \(0.794283\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.59217 | − | 1.53365i | −0.172695 | − | 0.166347i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.750577i | 0.0804703i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.147020 | 0.0155841 | 0.00779204 | − | 0.999970i | \(-0.497520\pi\) | ||||
0.00779204 | + | 0.999970i | \(0.497520\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.01585i | − | 0.106490i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.418419 | 0.0433880 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.69773 | − | 3.56182i | −0.379379 | − | 0.365435i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.75135i | 0.990099i | 0.868865 | + | 0.495050i | \(0.164850\pi\) | ||||
−0.868865 | + | 0.495050i | \(0.835150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9.91993i | − | 0.996990i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.47196i | − | 0.146466i | −0.997315 | − | 0.0732328i | \(-0.976668\pi\) | ||
0.997315 | − | 0.0732328i | \(-0.0233316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.2250i | − | 1.00750i | −0.863850 | − | 0.503749i | \(-0.831954\pi\) | ||
0.863850 | − | 0.503749i | \(-0.168046\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.380696 | − | 0.366703i | −0.0371521 | − | 0.0357866i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.46681 | −0.141802 | −0.0709011 | − | 0.997483i | \(-0.522587\pi\) | ||||
−0.0709011 | + | 0.997483i | \(0.522587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.9914i | − | 1.53170i | −0.643018 | − | 0.765851i | \(-0.722318\pi\) | ||
0.643018 | − | 0.765851i | \(-0.277682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.15433 | −0.204480 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0774799i | 0.00728869i | 0.999993 | + | 0.00364435i | \(0.00116003\pi\) | ||||
−0.999993 | + | 0.00364435i | \(0.998840\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.29877 | − | 1.25103i | −0.121111 | − | 0.116659i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.99077 | −0.276497 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.988642 | 0.0906287 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.352885 | −0.0320805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.04924 | 0.184774 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.33697 | + | 7.44949i | 0.745682 | + | 0.666302i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.7130i | − | 1.12810i | −0.825742 | − | 0.564049i | \(-0.809243\pi\) | ||
0.825742 | − | 0.564049i | \(-0.190757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.60552 | 0.229403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5369i | 1.00799i | 0.863707 | + | 0.503994i | \(0.168136\pi\) | ||||
−0.863707 | + | 0.503994i | \(0.831864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.29607 | 0.199095 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.17973 | + | 2.26290i | −0.187601 | + | 0.194760i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.6090i | − | 1.07726i | −0.842542 | − | 0.538631i | \(-0.818942\pi\) | ||
0.842542 | − | 0.538631i | \(-0.181058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.753066i | − | 0.0638742i | −0.999490 | − | 0.0319371i | \(-0.989832\pi\) | ||
0.999490 | − | 0.0319371i | \(-0.0101676\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.33470i | 0.196617i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.42279i | 0.286228i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.11347 | + | 4.92552i | 0.424651 | + | 0.409042i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.236390 | 0.0194971 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.57940i | − | 0.129389i | −0.997905 | − | 0.0646946i | \(-0.979393\pi\) | ||
0.997905 | − | 0.0646946i | \(-0.0206073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.39158 | 0.764276 | 0.382138 | − | 0.924105i | \(-0.375188\pi\) | ||||
0.382138 | + | 0.924105i | \(0.375188\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.91068i | − | 0.235315i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.74579 | − | 2.85057i | 0.220548 | − | 0.228963i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.04730 | 0.722053 | 0.361027 | − | 0.932555i | \(-0.382426\pi\) | ||||
0.361027 | + | 0.932555i | \(0.382426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.03172 | −0.0818210 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.806457 | 0.0635577 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.118681 | −0.00929585 | −0.00464793 | − | 0.999989i | \(-0.501479\pi\) | ||||
−0.00464793 | + | 0.999989i | \(0.501479\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.28272 | + | 1.23557i | 0.0998596 | + | 0.0961892i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.27336i | 0.175918i | 0.996124 | + | 0.0879590i | \(0.0280345\pi\) | ||||
−0.996124 | + | 0.0879590i | \(0.971966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9681 | −0.920620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6.75991i | − | 0.516943i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2558 | −1.31193 | −0.655967 | − | 0.754789i | \(-0.727739\pi\) | ||||
−0.655967 | + | 0.754789i | \(0.727739\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.99650 | + | 0.187153i | −0.377700 | + | 0.0141475i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.553421i | − | 0.0415977i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.5755i | 1.38839i | 0.719785 | + | 0.694197i | \(0.244241\pi\) | ||||
−0.719785 | + | 0.694197i | \(0.755759\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.04999i | − | 0.672681i | −0.941740 | − | 0.336340i | \(-0.890811\pi\) | ||
0.941740 | − | 0.336340i | \(-0.109189\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.41616i | 0.178608i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.1374 | + | 14.6769i | −1.03940 | + | 1.07906i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.33113 | −0.243597 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.40513i | − | 0.102208i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.08031 | 0.584670 | 0.292335 | − | 0.956316i | \(-0.405568\pi\) | ||||
0.292335 | + | 0.956316i | \(0.405568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 23.5747i | − | 1.69695i | −0.529237 | − | 0.848474i | \(-0.677522\pi\) | ||
0.529237 | − | 0.848474i | \(-0.322478\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.372514 | − | 0.386728i | 0.0266763 | − | 0.0276942i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.47867 | 0.247845 | 0.123923 | − | 0.992292i | \(-0.460453\pi\) | ||||
0.123923 | + | 0.992292i | \(0.460453\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.3657 | −1.37280 | −0.686400 | − | 0.727224i | \(-0.740810\pi\) | ||||
−0.686400 | + | 0.727224i | \(0.740810\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.50115 | −0.105883 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.17517 | −0.222853 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.4478 | − | 13.9609i | 0.939232 | − | 0.975072i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.37431i | − | 0.165026i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.73640 | −0.535138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3617i | 0.851011i | 0.904956 | + | 0.425506i | \(0.139904\pi\) | ||||
−0.904956 | + | 0.425506i | \(0.860096\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.95760 | 0.202651 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.0982 | − | 17.7507i | 1.16609 | − | 1.21059i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.77004i | 0.120158i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.09420i | 0.209087i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00431i | 0.0675570i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.14747i | 0.344700i | 0.985036 | + | 0.172350i | \(0.0551360\pi\) | ||||
−0.985036 | + | 0.172350i | \(0.944864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.551002 | + | 14.7103i | 0.0367335 | + | 0.980686i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.48759 | −0.364224 | −0.182112 | − | 0.983278i | \(-0.558293\pi\) | ||||
−0.182112 | + | 0.983278i | \(0.558293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.128516i | − | 0.00849255i | −0.999991 | − | 0.00424628i | \(-0.998648\pi\) | ||
0.999991 | − | 0.00424628i | \(-0.00135164\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.796493 | −0.0524054 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 22.6055i | − | 1.48094i | −0.672091 | − | 0.740468i | \(-0.734604\pi\) | ||
0.672091 | − | 0.740468i | \(-0.265396\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9056 | + | 15.3210i | 1.03757 | + | 0.999433i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.77671 | 0.115410 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0951 | 0.911737 | 0.455869 | − | 0.890047i | \(-0.349329\pi\) | ||||
0.455869 | + | 0.890047i | \(0.349329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.92029 | −0.510191 | −0.255095 | − | 0.966916i | \(-0.582107\pi\) | ||||
−0.255095 | + | 0.966916i | \(0.582107\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.22475 | −0.399318 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.55127 | − | 1.61046i | 0.0991067 | − | 0.102888i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.33245i | 0.148411i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.43859 | 0.217912 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.1153i | − | 0.701592i | −0.936452 | − | 0.350796i | \(-0.885911\pi\) | ||
0.936452 | − | 0.350796i | \(-0.114089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.71728 | −0.170834 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.376372 | + | 0.362538i | 0.0235693 | + | 0.0227030i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.39563i | 0.336570i | 0.985738 | + | 0.168285i | \(0.0538229\pi\) | ||||
−0.985738 | + | 0.168285i | \(0.946177\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.11347i | − | 0.566284i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.34807i | 0.578631i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.88914i | 0.301478i | 0.988574 | + | 0.150739i | \(0.0481652\pi\) | ||||
−0.988574 | + | 0.150739i | \(0.951835\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.77050 | + | 7.02885i | −0.415908 | + | 0.431779i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0347540 | −0.00212691 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.1206i | 1.71454i | 0.514863 | + | 0.857272i | \(0.327843\pi\) | ||||
−0.514863 | + | 0.857272i | \(0.672157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.2213 | −1.34985 | −0.674924 | − | 0.737887i | \(-0.735824\pi\) | ||||
−0.674924 | + | 0.737887i | \(0.735824\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.240136i | 0.0145337i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.8352 | − | 0.630596i | 1.01520 | − | 0.0380264i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.70300 | 0.282576 | 0.141288 | − | 0.989969i | \(-0.454876\pi\) | ||||
0.141288 | + | 0.989969i | \(0.454876\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.21120 | 0.311986 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.32935 | −0.556542 | −0.278271 | − | 0.960503i | \(-0.589761\pi\) | ||||
−0.278271 | + | 0.960503i | \(0.589761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.1601 | −1.02006 | −0.510031 | − | 0.860156i | \(-0.670366\pi\) | ||||
−0.510031 | + | 0.860156i | \(0.670366\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.874106 | + | 0.841978i | 0.0517776 | + | 0.0498745i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.66890i | 0.511709i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0226 | 0.942505 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2.30512i | − | 0.135129i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1178 | −0.649509 | −0.324754 | − | 0.945798i | \(-0.605282\pi\) | ||||
−0.324754 | + | 0.945798i | \(0.605282\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.77031 | − | 3.63173i | −0.219516 | − | 0.211447i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.73445i | 0.274721i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.819236i | 0.0473776i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0221i | 0.635305i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.347957i | 0.0199896i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.4606 | + | 15.8556i | 0.942532 | + | 0.907889i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2534 | −1.44129 | −0.720643 | − | 0.693307i | \(-0.756153\pi\) | ||||
−0.720643 | + | 0.693307i | \(0.756153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.41708i | 0.137503i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7515 | 1.17671 | 0.588354 | − | 0.808603i | \(-0.299776\pi\) | ||||
0.588354 | + | 0.808603i | \(0.299776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 25.5714i | − | 1.44538i | −0.691170 | − | 0.722692i | \(-0.742905\pi\) | ||
0.691170 | − | 0.722692i | \(-0.257095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.74138 | − | 4.56711i | −0.267147 | − | 0.257328i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.3540 | −1.25552 | −0.627762 | − | 0.778405i | \(-0.716029\pi\) | ||||
−0.627762 | + | 0.778405i | \(0.716029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.6984 | 0.598996 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.346740 | 0.0193531 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.26999 | −0.126306 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.190119 | − | 5.07567i | −0.0105459 | − | 0.281547i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.78021i | 0.209046i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.87647 | −0.544507 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.95850i | 0.437439i | 0.975788 | + | 0.218719i | \(0.0701880\pi\) | ||||
−0.975788 | + | 0.218719i | \(0.929812\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.8312 | −1.47034 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.85105 | + | 10.2269i | −0.538220 | + | 0.558758i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.7896i | 1.13248i | 0.824240 | + | 0.566241i | \(0.191603\pi\) | ||||
−0.824240 | + | 0.566241i | \(0.808397\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 0.0183155i | − | 0.000994759i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.96397i | − | 0.322967i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.307015 | + | 0.295731i | 0.0165291 | + | 0.0159216i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.6336 | 1.48345 | 0.741724 | − | 0.670705i | \(-0.234008\pi\) | ||||
0.741724 | + | 0.670705i | \(0.234008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4381i | 0.826385i | 0.910644 | + | 0.413193i | \(0.135586\pi\) | ||||
−0.910644 | + | 0.413193i | \(0.864414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.42739 | 0.0761887 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.3576i | 1.61577i | 0.589340 | + | 0.807885i | \(0.299388\pi\) | ||||
−0.589340 | + | 0.807885i | \(0.700612\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4087 | − | 20.1493i | 1.03011 | − | 1.06941i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.233705 | −0.0123690 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.44899 | −0.129253 | −0.0646263 | − | 0.997910i | \(-0.520586\pi\) | ||||
−0.0646263 | + | 0.997910i | \(0.520586\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7280 | 0.722529 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0834185 | 0.00437833 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.0799 | + | 20.3051i | 1.10337 | + | 1.06282i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.02179i | 0.314335i | 0.987572 | + | 0.157167i | \(0.0502362\pi\) | ||||
−0.987572 | + | 0.157167i | \(0.949764\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.5223 | 1.32864 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.36450i | − | 0.226594i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5797 | −0.858466 | −0.429233 | − | 0.903194i | \(-0.641216\pi\) | ||||
−0.429233 | + | 0.903194i | \(0.641216\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.97078 | − | 1.76098i | −0.101770 | − | 0.0909368i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.22548i | − | 0.166120i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.55769i | − | 0.182746i | −0.995817 | − | 0.0913731i | \(-0.970874\pi\) | ||
0.995817 | − | 0.0913731i | \(-0.0291256\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00523i | 0.153962i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.0775i | 1.48579i | 0.669407 | + | 0.742896i | \(0.266548\pi\) | ||||
−0.669407 | + | 0.742896i | \(0.733452\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.22684 | + | 5.42629i | −0.266384 | + | 0.276549i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32.4505 | 1.64955 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.98022i | − | 0.506017i | −0.967464 | − | 0.253009i | \(-0.918580\pi\) | ||
0.967464 | − | 0.253009i | \(-0.0814201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.797298 | −0.0403211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.72722i | − | 0.137570i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.6593 | − | 12.1042i | 0.586645 | − | 0.609031i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.52752 | −0.227230 | −0.113615 | − | 0.993525i | \(-0.536243\pi\) | ||||
−0.113615 | + | 0.993525i | \(0.536243\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.542768 | −0.0271724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.6019 | 1.77787 | 0.888937 | − | 0.458029i | \(-0.151444\pi\) | ||||
0.888937 | + | 0.458029i | \(0.151444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.79808 | −0.0895688 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.1861 | + | 13.6892i | −0.655221 | + | 0.680223i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.7070i | 1.52209i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.47440 | −0.369586 | −0.184793 | − | 0.982778i | \(-0.559161\pi\) | ||||
−0.184793 | + | 0.982778i | \(0.559161\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.98064i | 0.147024i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.34114 | 0.115200 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.5651 | − | 23.4262i | 1.10768 | − | 1.14995i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.178017i | 0.00871754i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 29.0445i | − | 1.41892i | −0.704746 | − | 0.709459i | \(-0.748939\pi\) | ||
0.704746 | − | 0.709459i | \(-0.251061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.23277i | − | 0.0600814i | −0.999549 | − | 0.0300407i | \(-0.990436\pi\) | ||
0.999549 | − | 0.0300407i | \(-0.00956369\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.0775i | 1.41380i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.93975 | − | 0.185028i | 0.239613 | − | 0.00897517i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2211 | −0.494633 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 0.809114i | − | 0.0390644i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.4116 | 1.65755 | 0.828775 | − | 0.559582i | \(-0.189038\pi\) | ||||
0.828775 | + | 0.559582i | \(0.189038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.864601i | − | 0.0415501i | −0.999784 | − | 0.0207750i | \(-0.993387\pi\) | ||
0.999784 | − | 0.0207750i | \(-0.00661338\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.20877 | − | 1.16434i | −0.0579562 | − | 0.0558260i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.85168 | −0.0885781 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3822 | 0.734153 | 0.367076 | − | 0.930191i | \(-0.380359\pi\) | ||||
0.367076 | + | 0.930191i | \(0.380359\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.94412 | 0.140196 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5632 | −1.07201 | −0.536006 | − | 0.844214i | \(-0.680067\pi\) | ||||
−0.536006 | + | 0.844214i | \(0.680067\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.228067 | + | 0.236770i | −0.0108114 | + | 0.0112240i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.373354i | 0.0176590i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.45322 | 0.304546 | 0.152273 | − | 0.988338i | \(-0.451341\pi\) | ||||
0.152273 | + | 0.988338i | \(0.451341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 29.2090i | − | 1.37540i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.22008 | −0.104308 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.63598 | + | 1.57585i | 0.0766958 | + | 0.0738768i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.81364i | 0.0848385i | 0.999100 | + | 0.0424192i | \(0.0135065\pi\) | ||||
−0.999100 | + | 0.0424192i | \(0.986493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.38917i | 0.0648409i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.374379i | − | 0.0174366i | −0.999962 | − | 0.00871828i | \(-0.997225\pi\) | ||
0.999962 | − | 0.00871828i | \(-0.00277515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.82245i | 0.224118i | 0.993702 | + | 0.112059i | \(0.0357446\pi\) | ||||
−0.993702 | + | 0.112059i | \(0.964255\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.649078 | + | 0.673846i | −0.0301003 | + | 0.0312488i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.1830 | 1.02651 | 0.513255 | − | 0.858236i | \(-0.328440\pi\) | ||||
0.513255 | + | 0.858236i | \(0.328440\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.35033i | − | 0.293231i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.13869 | −0.0985457 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 37.1380i | − | 1.70761i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.4723 | − | 0.429718i | 0.526386 | − | 0.0197168i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.8496 | −0.588343 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.5177 | −1.02886 | −0.514429 | − | 0.857533i | \(-0.671996\pi\) | ||||
−0.514429 | + | 0.857533i | \(0.671996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.25788 | 0.422123 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.190638 | −0.00867435 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.7041 | − | 15.1269i | −0.713088 | − | 0.686878i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.8362i | − | 1.66921i | −0.550850 | − | 0.834604i | \(-0.685696\pi\) | ||
0.550850 | − | 0.834604i | \(-0.314304\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0280551 | 0.00126870 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.5261i | − | 0.971459i | −0.874109 | − | 0.485729i | \(-0.838554\pi\) | ||
0.874109 | − | 0.485729i | \(-0.161446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.13910 | 0.141378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.9756 | + | 15.3884i | 0.718051 | + | 0.691659i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.5115i | 0.561219i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6995i | 1.15047i | 0.817990 | + | 0.575233i | \(0.195089\pi\) | ||||
−0.817990 | + | 0.575233i | \(0.804911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 0.537400i | − | 0.0240093i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.7371i | 1.28132i | 0.767824 | + | 0.640661i | \(0.221340\pi\) | ||||
−0.767824 | + | 0.640661i | \(0.778660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.37053 | + | 2.28340i | 0.105487 | + | 0.101610i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.82913 | 0.125646 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.89425i | 0.349906i | 0.984577 | + | 0.174953i | \(0.0559774\pi\) | ||||
−0.984577 | + | 0.174953i | \(0.944023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0894 | −0.579041 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.22628i | 0.142444i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.4669 | + | 15.8617i | 0.725619 | + | 0.698948i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.2778 | 1.46356 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.07910 | 0.179053 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.2583 | −1.15040 | −0.575198 | − | 0.818014i | \(-0.695075\pi\) | ||||
−0.575198 | + | 0.818014i | \(0.695075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6053 | −0.551190 | −0.275595 | − | 0.961274i | \(-0.588875\pi\) | ||||
−0.275595 | + | 0.961274i | \(0.588875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.18112 | − | 0.0442412i | 0.0515484 | − | 0.00193084i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.74993i | − | 0.0762282i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3496 | 0.971723 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.89259i | − | 0.299113i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.80626 | −0.381441 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.27542 | − | 2.36224i | 0.0983748 | − | 0.102129i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4.39105i | − | 0.189488i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.36940i | − | 0.145131i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9643i | 0.600371i | 0.953881 | + | 0.300186i | \(0.0970486\pi\) | ||||
−0.953881 | + | 0.300186i | \(0.902951\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.13933i | 0.0918073i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.7535 | + | 24.8069i | 1.10316 | + | 1.06261i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.3936 | 1.12851 | 0.564253 | − | 0.825602i | \(-0.309164\pi\) | ||||
0.564253 | + | 0.825602i | \(0.309164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.0921i | 1.28430i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.29041 | 0.310582 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.51602i | 0.319614i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.34194 | − | 3.46946i | 0.141858 | − | 0.147271i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.7328 | −1.47168 | −0.735839 | − | 0.677157i | \(-0.763212\pi\) | ||||
−0.735839 | + | 0.677157i | \(0.763212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1968 | −0.473573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.787447 | 0.0332460 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −46.3924 | −1.95521 | −0.977604 | − | 0.210452i | \(-0.932507\pi\) | ||||
−0.977604 | + | 0.210452i | \(0.932507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.124778 | − | 0.120192i | −0.00524946 | − | 0.00505651i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 8.50020i | − | 0.356975i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.837791 | −0.0351220 | −0.0175610 | − | 0.999846i | \(-0.505590\pi\) | ||||
−0.0175610 | + | 0.999846i | \(0.505590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.5095i | 1.40233i | 0.712999 | + | 0.701165i | \(0.247336\pi\) | ||||
−0.712999 | + | 0.701165i | \(0.752664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.91010 | −0.0797957 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.02946 | − | 0.150931i | 0.168040 | − | 0.00629427i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.3613i | 1.05580i | 0.849306 | + | 0.527902i | \(0.177021\pi\) | ||||
−0.849306 | + | 0.527902i | \(0.822979\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.57283i | 0.231599i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.5463i | 0.603481i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.7058i | 0.609051i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.63948 | − | 4.81651i | 0.191819 | − | 0.199138i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.2742 | 1.00190 | 0.500951 | − | 0.865476i | \(-0.332984\pi\) | ||||
0.500951 | + | 0.865476i | \(0.332984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.06413i | − | 0.167460i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.822323 | −0.0338259 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.6582i | − | 0.478745i | −0.970928 | − | 0.239373i | \(-0.923058\pi\) | ||
0.970928 | − | 0.239373i | \(-0.0769417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.53365 | + | 1.59217i | −0.0628733 | + | 0.0652725i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.57786 | 0.187360 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5455 | 0.921185 | 0.460593 | − | 0.887612i | \(-0.347637\pi\) | ||||
0.460593 | + | 0.887612i | \(0.347637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.1404 | −1.92290 | −0.961449 | − | 0.274983i | \(-0.911328\pi\) | ||||
−0.961449 | + | 0.274983i | \(0.911328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.6961 | −0.761366 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.547418 | − | 0.568307i | 0.0222557 | − | 0.0231050i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.87557i | 0.197893i | 0.995093 | + | 0.0989466i | \(0.0315473\pi\) | ||||
−0.995093 | + | 0.0989466i | \(0.968453\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.750577 | 0.0304149 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10.0330i | − | 0.405890i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.8086 | −1.85019 | −0.925096 | − | 0.379732i | \(-0.876016\pi\) | ||||
−0.925096 | + | 0.379732i | \(0.876016\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.17892 | + | 3.30022i | −0.128186 | + | 0.133078i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 0.551269i | − | 0.0221932i | −0.999938 | − | 0.0110966i | \(-0.996468\pi\) | ||
0.999938 | − | 0.0110966i | \(-0.00353224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.1227i | − | 0.406866i | −0.979089 | − | 0.203433i | \(-0.934790\pi\) | ||
0.979089 | − | 0.203433i | \(-0.0652099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.13318i | 0.0454728i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.147020i | − | 0.00589023i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9299 | + | 1.87022i | −0.997198 | + | 0.0748089i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.82881 | 0.0730355 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.00996i | 0.359251i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0973 | −1.23796 | −0.618982 | − | 0.785405i | \(-0.712455\pi\) | ||||
−0.618982 | + | 0.785405i | \(0.712455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.92217i | − | 0.116146i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.4738 | + | 19.7213i | 0.812477 | + | 0.782614i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.01585 | −0.0402492 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.8355 | 1.45719 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.2917 | 1.15695 | 0.578476 | − | 0.815699i | \(-0.303648\pi\) | ||||
0.578476 | + | 0.815699i | \(0.303648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.7053 | −1.60526 | −0.802630 | − | 0.596477i | \(-0.796567\pi\) | ||||
−0.802630 | + | 0.596477i | \(0.796567\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.04185 | + | 4.19608i | −0.159148 | + | 0.165221i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.5048i | − | 0.963382i | −0.876341 | − | 0.481691i | \(-0.840023\pi\) | ||
0.876341 | − | 0.481691i | \(-0.159977\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.88824 | −0.309640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 0.418419i | − | 0.0163991i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.4136 | −0.524915 | −0.262457 | − | 0.964944i | \(-0.584533\pi\) | ||||
−0.262457 | + | 0.964944i | \(0.584533\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.5798 | − | 17.8969i | −0.725971 | − | 0.699288i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.5368i | 1.50346i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27.5200i | − | 1.07203i | −0.844210 | − | 0.536013i | \(-0.819930\pi\) | ||
0.844210 | − | 0.536013i | \(-0.180070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.66818i | 0.220466i | 0.993906 | + | 0.110233i | \(0.0351598\pi\) | ||||
−0.993906 | + | 0.110233i | \(0.964840\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.237408i | − | 0.00922017i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.56182 | + | 3.69773i | −0.138121 | + | 0.143392i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.56064 | 0.0991482 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.21681i | − | 0.0470446i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.4389 | 1.32950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 24.8165i | − | 0.956605i | −0.878195 | − | 0.478302i | \(-0.841252\pi\) | ||
0.878195 | − | 0.478302i | \(-0.158748\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.262975 | − | 7.02073i | −0.0101219 | − | 0.270228i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.9321 | 0.804487 | 0.402244 | − | 0.915533i | \(-0.368230\pi\) | ||||
0.402244 | + | 0.915533i | \(0.368230\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.75135 | 0.374222 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.29721 | 0.0497093 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0481 | 0.996702 | 0.498351 | − | 0.866975i | \(-0.333939\pi\) | ||||
0.498351 | + | 0.866975i | \(0.333939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3063 | + | 19.5599i | 0.775864 | + | 0.747346i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0303798i | 0.00115906i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.43366 | 0.168909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.7645i | 1.62684i | 0.581678 | + | 0.813419i | \(0.302396\pi\) | ||||
−0.581678 | + | 0.813419i | \(0.697604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.91993 | −0.376827 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.21278 | + | 1.16820i | 0.0460034 | + | 0.0443125i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.57044i | − | 0.324629i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.34372i | 0.202118i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.0993i | 1.17460i | 0.809368 | + | 0.587302i | \(0.199810\pi\) | ||||
−0.809368 | + | 0.587302i | \(0.800190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.9252i | 0.789209i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.75993 | − | 3.62174i | −0.141607 | − | 0.136402i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.47196 | −0.0553588 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.63578i | − | 0.0614329i | −0.999528 | − | 0.0307164i | \(-0.990221\pi\) | ||
0.999528 | − | 0.0307164i | \(-0.00977888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.1281 | 0.829867 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.42746i | − | 0.0534587i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.51227 | − | 5.30966i | −0.206147 | − | 0.198570i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.33194 | −0.124434 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.5439 | 0.542397 | 0.271198 | − | 0.962523i | \(-0.412580\pi\) | ||||
0.271198 | + | 0.962523i | \(0.412580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2250 | −0.380798 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.87228 | 0.0696307 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.8647 | + | 0.594243i | −0.589200 | + | 0.0220696i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5867i | 0.911870i | 0.890013 | + | 0.455935i | \(0.150695\pi\) | ||||
−0.890013 | + | 0.455935i | \(0.849305\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.0291 | −0.889968 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.8969i | − | 0.403038i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.0758 | 0.926196 | 0.463098 | − | 0.886307i | \(-0.346738\pi\) | ||||
0.463098 | + | 0.886307i | \(0.346738\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.366703 | + | 0.380696i | −0.0135261 | + | 0.0140422i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.3968i | 0.788162i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.1764i | 0.411131i | 0.978643 | + | 0.205566i | \(0.0659034\pi\) | ||||
−0.978643 | + | 0.205566i | \(0.934097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.551369i | − | 0.0202550i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.7436i | 1.82492i | 0.409171 | + | 0.912458i | \(0.365818\pi\) | ||||
−0.409171 | + | 0.912458i | \(0.634182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.54355 | + | 2.45006i | 0.0931886 | + | 0.0897634i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.8260 | 1.56692 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.46681i | 0.0535962i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.24769 | −0.264472 | −0.132236 | − | 0.991218i | \(-0.542216\pi\) | ||||
−0.132236 | + | 0.991218i | \(0.542216\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.62755i | 0.0957531i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.5688 | + | 15.1248i | −0.530214 | + | 0.550446i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.5805 | 1.43858 | 0.719289 | − | 0.694711i | \(-0.244468\pi\) | ||||
0.719289 | + | 0.694711i | \(0.244468\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.642338 | 0.0233154 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9207 | 0.685874 | 0.342937 | − | 0.939358i | \(-0.388578\pi\) | ||||
0.342937 | + | 0.939358i | \(0.388578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.9914 | −0.578929 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.68753 | + | 4.51524i | 0.169478 | + | 0.163249i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.37823i | 0.0858730i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.4149 | −1.60164 | −0.800820 | − | 0.598905i | \(-0.795603\pi\) | ||||
−0.800820 | + | 0.598905i | \(0.795603\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.27547i | − | 0.0459350i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.9670 | −1.32961 | −0.664805 | − | 0.747017i | \(-0.731485\pi\) | ||||
−0.664805 | + | 0.747017i | \(0.731485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.331268 | + | 8.84398i | 0.0118995 | + | 0.317685i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.15433i | 0.0772863i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 19.9044i | − | 0.713150i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 42.1564i | − | 1.50848i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 4.46152i | − | 0.159442i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0348 | + | 14.5703i | −0.500922 | + | 0.520037i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.67376 | −0.166602 | −0.0833008 | − | 0.996524i | \(-0.526546\pi\) | ||||
−0.0833008 | + | 0.996524i | \(0.526546\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.15574i | − | 0.0411456i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0774799 | 0.00275487 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.3830i | − | 0.368712i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.60048 | − | 1.66155i | 0.0567631 | − | 0.0589291i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.2328 | −0.964634 | −0.482317 | − | 0.875997i | \(-0.660205\pi\) | ||||
−0.482317 | + | 0.875997i | \(0.660205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.76429 | 0.345436 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.432844 | −0.0152938 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44.1035 | 1.55638 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.25103 | + | 1.29877i | −0.0440930 | + | 0.0457755i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.64743i | − | 0.234001i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.7755 | 1.11717 | 0.558583 | − | 0.829449i | \(-0.311345\pi\) | ||||
0.558583 | + | 0.829449i | \(0.311345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.8625i | − | 1.82114i | −0.413355 | − | 0.910570i | \(-0.635643\pi\) | ||
0.413355 | − | 0.910570i | \(-0.364357\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.25289 | 0.184227 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.184106 | − | 0.191132i | 0.00644897 | − | 0.00669505i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 25.3076i | − | 0.885401i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.99077i | 0.104506i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1276i | 0.388356i | 0.980966 | + | 0.194178i | \(0.0622039\pi\) | ||||
−0.980966 | + | 0.194178i | \(0.937796\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 44.7666i | − | 1.56047i | −0.625488 | − | 0.780233i | \(-0.715100\pi\) | ||
0.625488 | − | 0.780233i | \(-0.284900\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.97968 | + | 0.149066i | −0.138555 | + | 0.00518983i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.7729 | −1.69600 | −0.848000 | − | 0.529996i | \(-0.822193\pi\) | ||||
−0.848000 | + | 0.529996i | \(0.822193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 40.1625i | − | 1.39490i | −0.716632 | − | 0.697451i | \(-0.754317\pi\) | ||
0.716632 | − | 0.697451i | \(-0.245683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.11174 | −0.0385659 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.988642i | − | 0.0342544i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.66115 | − | 3.52659i | −0.126699 | − | 0.122043i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.48713 | −0.0859678 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.5135 | −1.46773 | −0.733864 | − | 0.679297i | \(-0.762285\pi\) | ||||
−0.733864 | + | 0.679297i | \(0.762285\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9183 | 0.652356 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.20536 | 0.0759568 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.5656 | − | 19.2741i | 0.638677 | − | 0.663048i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.352885i | 0.0121253i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.05647 | 0.139218 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.34963i | 0.251942i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0098 | 0.890560 | 0.445280 | − | 0.895391i | \(-0.353104\pi\) | ||||
0.445280 | + | 0.895391i | \(0.353104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.8866 | + | 10.4864i | 0.372313 | + | 0.358628i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.3029i | 0.454418i | 0.973846 | + | 0.227209i | \(0.0729600\pi\) | ||||
−0.973846 | + | 0.227209i | \(0.927040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.0863i | 0.651217i | 0.945505 | + | 0.325609i | \(0.105569\pi\) | ||||
−0.945505 | + | 0.325609i | \(0.894431\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 2.04924i | − | 0.0698379i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34.5461i | − | 1.17596i | −0.808874 | − | 0.587982i | \(-0.799923\pi\) | ||
0.808874 | − | 0.587982i | \(-0.200077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.7683 | − | 27.7898i | 0.910151 | − | 0.944880i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.78758 | −0.128633 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 25.3245i | − | 0.859075i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.45095 | 0.218582 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 28.7091i | − | 0.971657i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.44949 | − | 8.33697i | 0.251839 | − | 0.281841i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.13633 | −0.240977 | −0.120488 | − | 0.992715i | \(-0.538446\pi\) | ||||
−0.120488 | + | 0.992715i | \(0.538446\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.62814 | 0.0886448 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.5504 | −0.422835 | −0.211418 | − | 0.977396i | \(-0.567808\pi\) | ||||
−0.211418 | + | 0.977396i | \(0.567808\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.7331 | −0.865987 | −0.432993 | − | 0.901397i | \(-0.642543\pi\) | ||||
−0.432993 | + | 0.901397i | \(0.642543\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.891262 | + | 0.858503i | 0.0299595 | + | 0.0288583i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 15.8391i | − | 0.531826i | −0.963997 | − | 0.265913i | \(-0.914327\pi\) | ||
0.963997 | − | 0.265913i | \(-0.0856735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7130 | −0.426381 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.6406i | 0.959497i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.6771 | 0.758860 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.9150 | − | 28.8155i | −0.999948 | − | 0.963194i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 0.193659i | − | 0.00646609i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.62016i | 0.187443i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.31493i | 0.143751i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.60552i | − | 0.0867063i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.5746 | + | 14.0389i | 0.484477 | + | 0.466670i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.5440 | 0.549333 | 0.274667 | − | 0.961540i | \(-0.411433\pi\) | ||||
0.274667 | + | 0.961540i | \(0.411433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.33363i | 0.143738i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.4342 | −1.27338 | −0.636691 | − | 0.771119i | \(-0.719697\pi\) | ||||
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 49.0123i | − | 1.62207i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.89112 | − | 3.74810i | −0.128637 | − | 0.123908i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.5369 | 0.380983 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.8577 | −1.47972 | −0.739860 | − | 0.672761i | \(-0.765108\pi\) | ||||
−0.739860 | + | 0.672761i | \(0.765108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.96964 | 0.196706 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.7098 | −0.418348 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.70562 | − | 45.5354i | −0.0560804 | − | 1.49720i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.1036i | 0.988731i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.4332 | 0.637581 | 0.318791 | − | 0.947825i | \(-0.396723\pi\) | ||||
0.318791 | + | 0.947825i | \(0.396723\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.29607i | − | 0.0752507i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.90544 | −0.160597 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.16747 | − | 5.36465i | 0.168994 | − | 0.175443i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.3664i | 1.18804i | 0.804451 | + | 0.594020i | \(0.202460\pi\) | ||||
−0.804451 | + | 0.594020i | \(0.797540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.04483i | 0.197266i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.6304i | − | 0.411740i | −0.978579 | − | 0.205870i | \(-0.933998\pi\) | ||
0.978579 | − | 0.205870i | \(-0.0660024\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.99110i | − | 0.227661i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.26290 | + | 2.17973i | 0.0736123 | + | 0.0709066i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.6341 | −1.19045 | −0.595224 | − | 0.803560i | \(-0.702937\pi\) | ||||
−0.595224 | + | 0.803560i | \(0.702937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 13.2968i | − | 0.431633i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.28426 | 0.171354 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.97886i | 0.226068i | 0.993591 | + | 0.113034i | \(0.0360568\pi\) | ||||
−0.993591 | + | 0.113034i | \(0.963943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.5347 | + | 13.0130i | −0.405613 | + | 0.421091i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.52900 | −0.0817509 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.6090 | −0.407166 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.8670 | −0.898935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.31848 | 0.139161 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.9662 | + | 36.5707i | 1.22217 | + | 1.17725i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 35.7173i | − | 1.14859i | −0.818648 | − | 0.574296i | \(-0.805276\pi\) | ||
0.818648 | − | 0.574296i | \(-0.194724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.536604 | 0.0172382 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 12.6075i | − | 0.404592i | −0.979324 | − | 0.202296i | \(-0.935160\pi\) | ||
0.979324 | − | 0.202296i | \(-0.0648404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.753066 | −0.0241422 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0449422 | + | 1.19984i | 0.00143930 | + | 0.0384255i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 42.3742i | − | 1.35567i | −0.735213 | − | 0.677836i | \(-0.762918\pi\) | ||
0.735213 | − | 0.677836i | \(-0.237082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.495370i | 0.0158321i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.0807i | 1.50317i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 51.8265i | − | 1.65301i | −0.562930 | − | 0.826505i | \(-0.690326\pi\) | ||
0.562930 | − | 0.826505i | \(-0.309674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.39634 | + | 5.60226i | −0.171942 | + | 0.178503i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.33470 | 0.0743143 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 8.88888i | − | 0.282650i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.2175 | −0.642230 | −0.321115 | − | 0.947040i | \(-0.604058\pi\) | ||||
−0.321115 | + | 0.947040i | \(0.604058\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1.88131i | − | 0.0597016i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.0414 | − | 31.1877i | 0.952376 | − | 0.988717i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.2159 | 1.93873 | 0.969363 | − | 0.245632i | \(-0.0789956\pi\) | ||||
0.969363 | + | 0.245632i | \(0.0789956\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.8056 | 0.405152 |
(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 | 2240.2.l.d.1569.11 | yes | 24 | |
4.3 | odd | 2 | inner | 2240.2.l.d.1569.14 | yes | 24 | |
5.4 | even | 2 | 2240.2.l.c.1569.14 | yes | 24 | ||
8.3 | odd | 2 | 2240.2.l.c.1569.12 | yes | 24 | ||
8.5 | even | 2 | 2240.2.l.c.1569.13 | yes | 24 | ||
20.19 | odd | 2 | 2240.2.l.c.1569.11 | ✓ | 24 | ||
40.19 | odd | 2 | inner | 2240.2.l.d.1569.13 | yes | 24 | |
40.29 | even | 2 | inner | 2240.2.l.d.1569.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.l.c.1569.11 | ✓ | 24 | 20.19 | odd | 2 | ||
2240.2.l.c.1569.12 | yes | 24 | 8.3 | odd | 2 | ||
2240.2.l.c.1569.13 | yes | 24 | 8.5 | even | 2 | ||
2240.2.l.c.1569.14 | yes | 24 | 5.4 | even | 2 | ||
2240.2.l.d.1569.11 | yes | 24 | 1.1 | even | 1 | trivial | |
2240.2.l.d.1569.12 | yes | 24 | 40.29 | even | 2 | inner | |
2240.2.l.d.1569.13 | yes | 24 | 40.19 | odd | 2 | inner | |
2240.2.l.d.1569.14 | yes | 24 | 4.3 | odd | 2 | inner |