Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0838915322\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.65544\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.05137 | −1.76171 | −0.880856 | − | 0.473385i | \(-0.843032\pi\) | ||||
−0.880856 | + | 0.473385i | \(0.843032\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.65544 | −1.18755 | −0.593775 | − | 0.804631i | \(-0.702363\pi\) | ||||
−0.593775 | + | 0.804631i | \(0.702363\pi\) | |||||||
\(6\) | 3.05137 | 1.24572 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.31088 | 2.10363 | ||||||||
\(10\) | 2.65544 | 0.839725 | ||||||||
\(11\) | −0.395932 | −0.119378 | −0.0596890 | − | 0.998217i | \(-0.519011\pi\) | ||||
−0.0596890 | + | 0.998217i | \(0.519011\pi\) | |||||||
\(12\) | −3.05137 | −0.880856 | ||||||||
\(13\) | −0.259511 | −0.0719753 | −0.0359876 | − | 0.999352i | \(-0.511458\pi\) | ||||
−0.0359876 | + | 0.999352i | \(0.511458\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.10275 | 2.09212 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.948626 | −0.230076 | −0.115038 | − | 0.993361i | \(-0.536699\pi\) | ||||
−0.115038 | + | 0.993361i | \(0.536699\pi\) | |||||||
\(18\) | −6.31088 | −1.48749 | ||||||||
\(19\) | −2.25951 | −0.518367 | −0.259184 | − | 0.965828i | \(-0.583453\pi\) | ||||
−0.259184 | + | 0.965828i | \(0.583453\pi\) | |||||||
\(20\) | −2.65544 | −0.593775 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.395932 | 0.0844130 | ||||||||
\(23\) | −7.84324 | −1.63543 | −0.817714 | − | 0.575625i | \(-0.804759\pi\) | ||||
−0.817714 | + | 0.575625i | \(0.804759\pi\) | |||||||
\(24\) | 3.05137 | 0.622859 | ||||||||
\(25\) | 2.05137 | 0.410275 | ||||||||
\(26\) | 0.259511 | 0.0508942 | ||||||||
\(27\) | −10.1027 | −1.94427 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.01770 | 1.67455 | 0.837273 | − | 0.546786i | \(-0.184149\pi\) | ||||
0.837273 | + | 0.546786i | \(0.184149\pi\) | |||||||
\(30\) | −8.10275 | −1.47935 | ||||||||
\(31\) | −1.20814 | −0.216988 | −0.108494 | − | 0.994097i | \(-0.534603\pi\) | ||||
−0.108494 | + | 0.994097i | \(0.534603\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.20814 | 0.210310 | ||||||||
\(34\) | 0.948626 | 0.162688 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.31088 | 1.05181 | ||||||||
\(37\) | −0.102748 | −0.0168917 | −0.00844587 | − | 0.999964i | \(-0.502688\pi\) | ||||
−0.00844587 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(38\) | 2.25951 | 0.366541 | ||||||||
\(39\) | 0.791864 | 0.126800 | ||||||||
\(40\) | 2.65544 | 0.419862 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.10275 | 0.320666 | 0.160333 | − | 0.987063i | \(-0.448743\pi\) | ||||
0.160333 | + | 0.987063i | \(0.448743\pi\) | |||||||
\(44\) | −0.395932 | −0.0596890 | ||||||||
\(45\) | −16.7582 | −2.49816 | ||||||||
\(46\) | 7.84324 | 1.15642 | ||||||||
\(47\) | −8.25951 | −1.20477 | −0.602387 | − | 0.798204i | \(-0.705783\pi\) | ||||
−0.602387 | + | 0.798204i | \(0.705783\pi\) | |||||||
\(48\) | −3.05137 | −0.440428 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.05137 | −0.290108 | ||||||||
\(51\) | 2.89461 | 0.405327 | ||||||||
\(52\) | −0.259511 | −0.0359876 | ||||||||
\(53\) | 1.70682 | 0.234449 | 0.117225 | − | 0.993105i | \(-0.462600\pi\) | ||||
0.117225 | + | 0.993105i | \(0.462600\pi\) | |||||||
\(54\) | 10.1027 | 1.37481 | ||||||||
\(55\) | 1.05137 | 0.141767 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.89461 | 0.913214 | ||||||||
\(58\) | −9.01770 | −1.18408 | ||||||||
\(59\) | 1.96633 | 0.255994 | 0.127997 | − | 0.991775i | \(-0.459145\pi\) | ||||
0.127997 | + | 0.991775i | \(0.459145\pi\) | |||||||
\(60\) | 8.10275 | 1.04606 | ||||||||
\(61\) | 14.2392 | 1.82314 | 0.911569 | − | 0.411146i | \(-0.134871\pi\) | ||||
0.911569 | + | 0.411146i | \(0.134871\pi\) | |||||||
\(62\) | 1.20814 | 0.153433 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.689115 | 0.0854742 | ||||||||
\(66\) | −1.20814 | −0.148711 | ||||||||
\(67\) | 2.12309 | 0.259377 | 0.129688 | − | 0.991555i | \(-0.458602\pi\) | ||||
0.129688 | + | 0.991555i | \(0.458602\pi\) | |||||||
\(68\) | −0.948626 | −0.115038 | ||||||||
\(69\) | 23.9327 | 2.88115 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.89461 | 0.818240 | 0.409120 | − | 0.912481i | \(-0.365836\pi\) | ||||
0.409120 | + | 0.912481i | \(0.365836\pi\) | |||||||
\(72\) | −6.31088 | −0.743745 | ||||||||
\(73\) | −10.1027 | −1.18244 | −0.591219 | − | 0.806511i | \(-0.701353\pi\) | ||||
−0.591219 | + | 0.806511i | \(0.701353\pi\) | |||||||
\(74\) | 0.102748 | 0.0119443 | ||||||||
\(75\) | −6.25951 | −0.722786 | ||||||||
\(76\) | −2.25951 | −0.259184 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.791864 | −0.0896609 | ||||||||
\(79\) | 10.6218 | 1.19504 | 0.597521 | − | 0.801853i | \(-0.296152\pi\) | ||||
0.597521 | + | 0.801853i | \(0.296152\pi\) | |||||||
\(80\) | −2.65544 | −0.296887 | ||||||||
\(81\) | 11.8946 | 1.32162 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | 8.13642 | 0.893088 | 0.446544 | − | 0.894762i | \(-0.352655\pi\) | ||||
0.446544 | + | 0.894762i | \(0.352655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.51902 | 0.273226 | ||||||||
\(86\) | −2.10275 | −0.226745 | ||||||||
\(87\) | −27.5164 | −2.95007 | ||||||||
\(88\) | 0.395932 | 0.0422065 | ||||||||
\(89\) | −2.27284 | −0.240921 | −0.120460 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120460 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(90\) | 16.7582 | 1.76647 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.84324 | −0.817714 | ||||||||
\(93\) | 3.68648 | 0.382270 | ||||||||
\(94\) | 8.25951 | 0.851903 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 3.05137 | 0.311430 | ||||||||
\(97\) | 18.2055 | 1.84849 | 0.924244 | − | 0.381802i | \(-0.124696\pi\) | ||||
0.924244 | + | 0.381802i | \(0.124696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.49868 | −0.251127 | ||||||||
\(100\) | 2.05137 | 0.205137 | ||||||||
\(101\) | −1.63774 | −0.162961 | −0.0814807 | − | 0.996675i | \(-0.525965\pi\) | ||||
−0.0814807 | + | 0.996675i | \(0.525965\pi\) | |||||||
\(102\) | −2.89461 | −0.286609 | ||||||||
\(103\) | 9.82991 | 0.968569 | 0.484285 | − | 0.874910i | \(-0.339080\pi\) | ||||
0.484285 | + | 0.874910i | \(0.339080\pi\) | |||||||
\(104\) | 0.259511 | 0.0254471 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.70682 | −0.165781 | ||||||||
\(107\) | 3.20814 | 0.310142 | 0.155071 | − | 0.987903i | \(-0.450439\pi\) | ||||
0.155071 | + | 0.987903i | \(0.450439\pi\) | |||||||
\(108\) | −10.1027 | −0.972137 | ||||||||
\(109\) | 12.0824 | 1.15728 | 0.578642 | − | 0.815581i | \(-0.303583\pi\) | ||||
0.578642 | + | 0.815581i | \(0.303583\pi\) | |||||||
\(110\) | −1.05137 | −0.100245 | ||||||||
\(111\) | 0.313524 | 0.0297584 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0514 | −1.22777 | −0.613885 | − | 0.789395i | \(-0.710394\pi\) | ||||
−0.613885 | + | 0.789395i | \(0.710394\pi\) | |||||||
\(114\) | −6.89461 | −0.645740 | ||||||||
\(115\) | 20.8273 | 1.94215 | ||||||||
\(116\) | 9.01770 | 0.837273 | ||||||||
\(117\) | −1.63774 | −0.151409 | ||||||||
\(118\) | −1.96633 | −0.181015 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −8.10275 | −0.739676 | ||||||||
\(121\) | −10.8432 | −0.985749 | ||||||||
\(122\) | −14.2392 | −1.28915 | ||||||||
\(123\) | −3.05137 | −0.275133 | ||||||||
\(124\) | −1.20814 | −0.108494 | ||||||||
\(125\) | 7.82991 | 0.700328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8432 | 1.76080 | 0.880401 | − | 0.474229i | \(-0.157273\pi\) | ||||
0.880401 | + | 0.474229i | \(0.157273\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.41627 | −0.564921 | ||||||||
\(130\) | −0.689115 | −0.0604394 | ||||||||
\(131\) | −10.8609 | −0.948925 | −0.474462 | − | 0.880276i | \(-0.657357\pi\) | ||||
−0.474462 | + | 0.880276i | \(0.657357\pi\) | |||||||
\(132\) | 1.20814 | 0.105155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.12309 | −0.183407 | ||||||||
\(135\) | 26.8273 | 2.30892 | ||||||||
\(136\) | 0.948626 | 0.0813440 | ||||||||
\(137\) | 17.9327 | 1.53209 | 0.766045 | − | 0.642787i | \(-0.222222\pi\) | ||||
0.766045 | + | 0.642787i | \(0.222222\pi\) | |||||||
\(138\) | −23.9327 | −2.03728 | ||||||||
\(139\) | −3.44731 | −0.292397 | −0.146198 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146198 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.2029 | 2.12246 | ||||||||
\(142\) | −6.89461 | −0.578583 | ||||||||
\(143\) | 0.102748 | 0.00859226 | ||||||||
\(144\) | 6.31088 | 0.525907 | ||||||||
\(145\) | −23.9460 | −1.98861 | ||||||||
\(146\) | 10.1027 | 0.836109 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.102748 | −0.00844587 | ||||||||
\(149\) | −10.1231 | −0.829316 | −0.414658 | − | 0.909977i | \(-0.636099\pi\) | ||||
−0.414658 | + | 0.909977i | \(0.636099\pi\) | |||||||
\(150\) | 6.25951 | 0.511087 | ||||||||
\(151\) | −18.2055 | −1.48154 | −0.740771 | − | 0.671757i | \(-0.765540\pi\) | ||||
−0.740771 | + | 0.671757i | \(0.765540\pi\) | |||||||
\(152\) | 2.25951 | 0.183271 | ||||||||
\(153\) | −5.98667 | −0.483993 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.20814 | 0.257684 | ||||||||
\(156\) | 0.791864 | 0.0633998 | ||||||||
\(157\) | −13.2569 | −1.05801 | −0.529007 | − | 0.848618i | \(-0.677435\pi\) | ||||
−0.529007 | + | 0.848618i | \(0.677435\pi\) | |||||||
\(158\) | −10.6218 | −0.845023 | ||||||||
\(159\) | −5.20814 | −0.413032 | ||||||||
\(160\) | 2.65544 | 0.209931 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.8946 | −0.934529 | ||||||||
\(163\) | 10.0354 | 0.786033 | 0.393017 | − | 0.919531i | \(-0.371431\pi\) | ||||
0.393017 | + | 0.919531i | \(0.371431\pi\) | |||||||
\(164\) | 1.00000 | 0.0780869 | ||||||||
\(165\) | −3.20814 | −0.249753 | ||||||||
\(166\) | −8.13642 | −0.631509 | ||||||||
\(167\) | −19.4136 | −1.50227 | −0.751136 | − | 0.660147i | \(-0.770494\pi\) | ||||
−0.751136 | + | 0.660147i | \(0.770494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9327 | −0.994820 | ||||||||
\(170\) | −2.51902 | −0.193200 | ||||||||
\(171\) | −14.2595 | −1.09045 | ||||||||
\(172\) | 2.10275 | 0.160333 | ||||||||
\(173\) | 13.6528 | 1.03800 | 0.519002 | − | 0.854773i | \(-0.326304\pi\) | ||||
0.519002 | + | 0.854773i | \(0.326304\pi\) | |||||||
\(174\) | 27.5164 | 2.08601 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.395932 | −0.0298445 | ||||||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | 2.27284 | 0.170357 | ||||||||
\(179\) | −3.70682 | −0.277060 | −0.138530 | − | 0.990358i | \(-0.544238\pi\) | ||||
−0.138530 | + | 0.990358i | \(0.544238\pi\) | |||||||
\(180\) | −16.7582 | −1.24908 | ||||||||
\(181\) | 5.84324 | 0.434324 | 0.217162 | − | 0.976136i | \(-0.430320\pi\) | ||||
0.217162 | + | 0.976136i | \(0.430320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −43.4490 | −3.21185 | ||||||||
\(184\) | 7.84324 | 0.578211 | ||||||||
\(185\) | 0.272843 | 0.0200598 | ||||||||
\(186\) | −3.68648 | −0.270306 | ||||||||
\(187\) | 0.375591 | 0.0274659 | ||||||||
\(188\) | −8.25951 | −0.602387 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | −10.3489 | −0.748822 | −0.374411 | − | 0.927263i | \(-0.622155\pi\) | ||||
−0.374411 | + | 0.927263i | \(0.622155\pi\) | |||||||
\(192\) | −3.05137 | −0.220214 | ||||||||
\(193\) | 11.4136 | 0.821571 | 0.410786 | − | 0.911732i | \(-0.365254\pi\) | ||||
0.410786 | + | 0.911732i | \(0.365254\pi\) | |||||||
\(194\) | −18.2055 | −1.30708 | ||||||||
\(195\) | −2.10275 | −0.150581 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.9707 | −1.63659 | −0.818297 | − | 0.574795i | \(-0.805082\pi\) | ||||
−0.818297 | + | 0.574795i | \(0.805082\pi\) | |||||||
\(198\) | 2.49868 | 0.177573 | ||||||||
\(199\) | 20.9840 | 1.48752 | 0.743759 | − | 0.668448i | \(-0.233041\pi\) | ||||
0.743759 | + | 0.668448i | \(0.233041\pi\) | |||||||
\(200\) | −2.05137 | −0.145054 | ||||||||
\(201\) | −6.47834 | −0.456947 | ||||||||
\(202\) | 1.63774 | 0.115231 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.89461 | 0.202663 | ||||||||
\(205\) | −2.65544 | −0.185464 | ||||||||
\(206\) | −9.82991 | −0.684882 | ||||||||
\(207\) | −49.4978 | −3.44033 | ||||||||
\(208\) | −0.259511 | −0.0179938 | ||||||||
\(209\) | 0.894612 | 0.0618816 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.66877 | −0.596783 | −0.298392 | − | 0.954444i | \(-0.596450\pi\) | ||||
−0.298392 | + | 0.954444i | \(0.596450\pi\) | |||||||
\(212\) | 1.70682 | 0.117225 | ||||||||
\(213\) | −21.0380 | −1.44150 | ||||||||
\(214\) | −3.20814 | −0.219304 | ||||||||
\(215\) | −5.58373 | −0.380807 | ||||||||
\(216\) | 10.1027 | 0.687405 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.0824 | −0.818324 | ||||||||
\(219\) | 30.8273 | 2.08311 | ||||||||
\(220\) | 1.05137 | 0.0708836 | ||||||||
\(221\) | 0.246178 | 0.0165597 | ||||||||
\(222\) | −0.313524 | −0.0210424 | ||||||||
\(223\) | −14.8273 | −0.992907 | −0.496454 | − | 0.868063i | \(-0.665365\pi\) | ||||
−0.496454 | + | 0.868063i | \(0.665365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.9460 | 0.863066 | ||||||||
\(226\) | 13.0514 | 0.868165 | ||||||||
\(227\) | −4.42960 | −0.294003 | −0.147002 | − | 0.989136i | \(-0.546962\pi\) | ||||
−0.147002 | + | 0.989136i | \(0.546962\pi\) | |||||||
\(228\) | 6.89461 | 0.456607 | ||||||||
\(229\) | 22.3623 | 1.47774 | 0.738870 | − | 0.673848i | \(-0.235360\pi\) | ||||
0.738870 | + | 0.673848i | \(0.235360\pi\) | |||||||
\(230\) | −20.8273 | −1.37331 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.01770 | −0.592041 | ||||||||
\(233\) | −22.9300 | −1.50220 | −0.751098 | − | 0.660191i | \(-0.770475\pi\) | ||||
−0.751098 | + | 0.660191i | \(0.770475\pi\) | |||||||
\(234\) | 1.63774 | 0.107062 | ||||||||
\(235\) | 21.9327 | 1.43073 | ||||||||
\(236\) | 1.96633 | 0.127997 | ||||||||
\(237\) | −32.4110 | −2.10532 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.2055 | −0.660139 | −0.330069 | − | 0.943957i | \(-0.607072\pi\) | ||||
−0.330069 | + | 0.943957i | \(0.607072\pi\) | |||||||
\(240\) | 8.10275 | 0.523030 | ||||||||
\(241\) | 25.1408 | 1.61946 | 0.809730 | − | 0.586802i | \(-0.199613\pi\) | ||||
0.809730 | + | 0.586802i | \(0.199613\pi\) | |||||||
\(242\) | 10.8432 | 0.697030 | ||||||||
\(243\) | −5.98667 | −0.384045 | ||||||||
\(244\) | 14.2392 | 0.911569 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.05137 | 0.194549 | ||||||||
\(247\) | 0.586367 | 0.0373096 | ||||||||
\(248\) | 1.20814 | 0.0767167 | ||||||||
\(249\) | −24.8273 | −1.57336 | ||||||||
\(250\) | −7.82991 | −0.495207 | ||||||||
\(251\) | −0.901621 | −0.0569098 | −0.0284549 | − | 0.999595i | \(-0.509059\pi\) | ||||
−0.0284549 | + | 0.999595i | \(0.509059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.10539 | 0.195234 | ||||||||
\(254\) | −19.8432 | −1.24508 | ||||||||
\(255\) | −7.68648 | −0.481346 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.8566 | 0.739593 | 0.369796 | − | 0.929113i | \(-0.379427\pi\) | ||||
0.369796 | + | 0.929113i | \(0.379427\pi\) | |||||||
\(258\) | 6.41627 | 0.399460 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.689115 | 0.0427371 | ||||||||
\(261\) | 56.9097 | 3.52262 | ||||||||
\(262\) | 10.8609 | 0.670991 | ||||||||
\(263\) | 0.519021 | 0.0320042 | 0.0160021 | − | 0.999872i | \(-0.494906\pi\) | ||||
0.0160021 | + | 0.999872i | \(0.494906\pi\) | |||||||
\(264\) | −1.20814 | −0.0743556 | ||||||||
\(265\) | −4.53235 | −0.278420 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.93529 | 0.424433 | ||||||||
\(268\) | 2.12309 | 0.129688 | ||||||||
\(269\) | 4.65544 | 0.283847 | 0.141924 | − | 0.989878i | \(-0.454671\pi\) | ||||
0.141924 | + | 0.989878i | \(0.454671\pi\) | |||||||
\(270\) | −26.8273 | −1.63266 | ||||||||
\(271\) | 7.24354 | 0.440014 | 0.220007 | − | 0.975498i | \(-0.429392\pi\) | ||||
0.220007 | + | 0.975498i | \(0.429392\pi\) | |||||||
\(272\) | −0.948626 | −0.0575189 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.9327 | −1.08335 | ||||||||
\(275\) | −0.812204 | −0.0489778 | ||||||||
\(276\) | 23.9327 | 1.44058 | ||||||||
\(277\) | 6.27284 | 0.376899 | 0.188449 | − | 0.982083i | \(-0.439654\pi\) | ||||
0.188449 | + | 0.982083i | \(0.439654\pi\) | |||||||
\(278\) | 3.44731 | 0.206756 | ||||||||
\(279\) | −7.62441 | −0.456461 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7245 | 1.11701 | 0.558506 | − | 0.829501i | \(-0.311375\pi\) | ||||
0.558506 | + | 0.829501i | \(0.311375\pi\) | |||||||
\(282\) | −25.2029 | −1.50081 | ||||||||
\(283\) | −13.6174 | −0.809470 | −0.404735 | − | 0.914434i | \(-0.632636\pi\) | ||||
−0.404735 | + | 0.914434i | \(0.632636\pi\) | |||||||
\(284\) | 6.89461 | 0.409120 | ||||||||
\(285\) | −18.3082 | −1.08449 | ||||||||
\(286\) | −0.102748 | −0.00607565 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.31088 | −0.371872 | ||||||||
\(289\) | −16.1001 | −0.947065 | ||||||||
\(290\) | 23.9460 | 1.40616 | ||||||||
\(291\) | −55.5518 | −3.25650 | ||||||||
\(292\) | −10.1027 | −0.591219 | ||||||||
\(293\) | −13.0514 | −0.762469 | −0.381235 | − | 0.924478i | \(-0.624501\pi\) | ||||
−0.381235 | + | 0.924478i | \(0.624501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.22147 | −0.304006 | ||||||||
\(296\) | 0.102748 | 0.00597213 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 10.1231 | 0.586415 | ||||||||
\(299\) | 2.03540 | 0.117710 | ||||||||
\(300\) | −6.25951 | −0.361393 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.2055 | 1.04761 | ||||||||
\(303\) | 4.99736 | 0.287091 | ||||||||
\(304\) | −2.25951 | −0.129592 | ||||||||
\(305\) | −37.8113 | −2.16507 | ||||||||
\(306\) | 5.98667 | 0.342235 | ||||||||
\(307\) | 14.7936 | 0.844315 | 0.422157 | − | 0.906523i | \(-0.361273\pi\) | ||||
0.422157 | + | 0.906523i | \(0.361273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.9947 | −1.70634 | ||||||||
\(310\) | −3.20814 | −0.182210 | ||||||||
\(311\) | −34.5678 | −1.96016 | −0.980079 | − | 0.198609i | \(-0.936358\pi\) | ||||
−0.980079 | + | 0.198609i | \(0.936358\pi\) | |||||||
\(312\) | −0.791864 | −0.0448305 | ||||||||
\(313\) | −6.01333 | −0.339894 | −0.169947 | − | 0.985453i | \(-0.554360\pi\) | ||||
−0.169947 | + | 0.985453i | \(0.554360\pi\) | |||||||
\(314\) | 13.2569 | 0.748129 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6218 | 0.597521 | ||||||||
\(317\) | −24.4313 | −1.37220 | −0.686100 | − | 0.727507i | \(-0.740679\pi\) | ||||
−0.686100 | + | 0.727507i | \(0.740679\pi\) | |||||||
\(318\) | 5.20814 | 0.292058 | ||||||||
\(319\) | −3.57040 | −0.199904 | ||||||||
\(320\) | −2.65544 | −0.148444 | ||||||||
\(321\) | −9.78922 | −0.546381 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.14343 | 0.119264 | ||||||||
\(324\) | 11.8946 | 0.660812 | ||||||||
\(325\) | −0.532353 | −0.0295296 | ||||||||
\(326\) | −10.0354 | −0.555810 | ||||||||
\(327\) | −36.8679 | −2.03880 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.20814 | 0.176602 | ||||||||
\(331\) | −23.1471 | −1.27228 | −0.636140 | − | 0.771573i | \(-0.719470\pi\) | ||||
−0.636140 | + | 0.771573i | \(0.719470\pi\) | |||||||
\(332\) | 8.13642 | 0.446544 | ||||||||
\(333\) | −0.648434 | −0.0355340 | ||||||||
\(334\) | 19.4136 | 1.06227 | ||||||||
\(335\) | −5.63774 | −0.308023 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.6598 | −1.39778 | −0.698890 | − | 0.715230i | \(-0.746322\pi\) | ||||
−0.698890 | + | 0.715230i | \(0.746322\pi\) | |||||||
\(338\) | 12.9327 | 0.703444 | ||||||||
\(339\) | 39.8246 | 2.16298 | ||||||||
\(340\) | 2.51902 | 0.136613 | ||||||||
\(341\) | 0.478340 | 0.0259035 | ||||||||
\(342\) | 14.2595 | 0.771066 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.10275 | −0.113373 | ||||||||
\(345\) | −63.5518 | −3.42151 | ||||||||
\(346\) | −13.6528 | −0.733979 | ||||||||
\(347\) | 10.7715 | 0.578246 | 0.289123 | − | 0.957292i | \(-0.406636\pi\) | ||||
0.289123 | + | 0.957292i | \(0.406636\pi\) | |||||||
\(348\) | −27.5164 | −1.47503 | ||||||||
\(349\) | 13.6935 | 0.732995 | 0.366498 | − | 0.930419i | \(-0.380557\pi\) | ||||
0.366498 | + | 0.930419i | \(0.380557\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.62177 | 0.139940 | ||||||||
\(352\) | 0.395932 | 0.0211032 | ||||||||
\(353\) | 5.10011 | 0.271451 | 0.135726 | − | 0.990746i | \(-0.456663\pi\) | ||||
0.135726 | + | 0.990746i | \(0.456663\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | −18.3082 | −0.971701 | ||||||||
\(356\) | −2.27284 | −0.120460 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.70682 | 0.195911 | ||||||||
\(359\) | 7.20814 | 0.380431 | 0.190215 | − | 0.981742i | \(-0.439081\pi\) | ||||
0.190215 | + | 0.981742i | \(0.439081\pi\) | |||||||
\(360\) | 16.7582 | 0.883234 | ||||||||
\(361\) | −13.8946 | −0.731295 | ||||||||
\(362\) | −5.84324 | −0.307114 | ||||||||
\(363\) | 33.0868 | 1.73661 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.8273 | 1.40420 | ||||||||
\(366\) | 43.4490 | 2.27112 | ||||||||
\(367\) | −33.0328 | −1.72430 | −0.862148 | − | 0.506656i | \(-0.830881\pi\) | ||||
−0.862148 | + | 0.506656i | \(0.830881\pi\) | |||||||
\(368\) | −7.84324 | −0.408857 | ||||||||
\(369\) | 6.31088 | 0.328532 | ||||||||
\(370\) | −0.272843 | −0.0141844 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.68648 | 0.191135 | ||||||||
\(373\) | 28.2409 | 1.46226 | 0.731129 | − | 0.682239i | \(-0.238994\pi\) | ||||
0.731129 | + | 0.682239i | \(0.238994\pi\) | |||||||
\(374\) | −0.375591 | −0.0194214 | ||||||||
\(375\) | −23.8920 | −1.23378 | ||||||||
\(376\) | 8.25951 | 0.425952 | ||||||||
\(377\) | −2.34019 | −0.120526 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.8920 | −1.22725 | −0.613624 | − | 0.789598i | \(-0.710289\pi\) | ||||
−0.613624 | + | 0.789598i | \(0.710289\pi\) | |||||||
\(380\) | 6.00000 | 0.307794 | ||||||||
\(381\) | −60.5491 | −3.10203 | ||||||||
\(382\) | 10.3489 | 0.529497 | ||||||||
\(383\) | 30.2409 | 1.54524 | 0.772619 | − | 0.634870i | \(-0.218946\pi\) | ||||
0.772619 | + | 0.634870i | \(0.218946\pi\) | |||||||
\(384\) | 3.05137 | 0.155715 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.4136 | −0.580939 | ||||||||
\(387\) | 13.2702 | 0.674562 | ||||||||
\(388\) | 18.2055 | 0.924244 | ||||||||
\(389\) | 11.7892 | 0.597737 | 0.298869 | − | 0.954294i | \(-0.403391\pi\) | ||||
0.298869 | + | 0.954294i | \(0.403391\pi\) | |||||||
\(390\) | 2.10275 | 0.106477 | ||||||||
\(391\) | 7.44030 | 0.376272 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.1408 | 1.67173 | ||||||||
\(394\) | 22.9707 | 1.15725 | ||||||||
\(395\) | −28.2055 | −1.41917 | ||||||||
\(396\) | −2.49868 | −0.125563 | ||||||||
\(397\) | −18.5678 | −0.931889 | −0.465944 | − | 0.884814i | \(-0.654285\pi\) | ||||
−0.465944 | + | 0.884814i | \(0.654285\pi\) | |||||||
\(398\) | −20.9840 | −1.05183 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.05137 | 0.102569 | ||||||||
\(401\) | −29.9814 | −1.49720 | −0.748600 | − | 0.663022i | \(-0.769273\pi\) | ||||
−0.748600 | + | 0.663022i | \(0.769273\pi\) | |||||||
\(402\) | 6.47834 | 0.323110 | ||||||||
\(403\) | 0.313524 | 0.0156177 | ||||||||
\(404\) | −1.63774 | −0.0814807 | ||||||||
\(405\) | −31.5855 | −1.56949 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0406814 | 0.00201650 | ||||||||
\(408\) | −2.89461 | −0.143305 | ||||||||
\(409\) | 30.2055 | 1.49357 | 0.746783 | − | 0.665068i | \(-0.231597\pi\) | ||||
0.746783 | + | 0.665068i | \(0.231597\pi\) | |||||||
\(410\) | 2.65544 | 0.131143 | ||||||||
\(411\) | −54.7192 | −2.69910 | ||||||||
\(412\) | 9.82991 | 0.484285 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 49.4978 | 2.43268 | ||||||||
\(415\) | −21.6058 | −1.06059 | ||||||||
\(416\) | 0.259511 | 0.0127236 | ||||||||
\(417\) | 10.5190 | 0.515119 | ||||||||
\(418\) | −0.894612 | −0.0437569 | ||||||||
\(419\) | −5.82290 | −0.284467 | −0.142234 | − | 0.989833i | \(-0.545428\pi\) | ||||
−0.142234 | + | 0.989833i | \(0.545428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.91495 | −0.142066 | −0.0710331 | − | 0.997474i | \(-0.522630\pi\) | ||||
−0.0710331 | + | 0.997474i | \(0.522630\pi\) | |||||||
\(422\) | 8.66877 | 0.421989 | ||||||||
\(423\) | −52.1248 | −2.53440 | ||||||||
\(424\) | −1.70682 | −0.0828903 | ||||||||
\(425\) | −1.94599 | −0.0943942 | ||||||||
\(426\) | 21.0380 | 1.01930 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.20814 | 0.155071 | ||||||||
\(429\) | −0.313524 | −0.0151371 | ||||||||
\(430\) | 5.58373 | 0.269271 | ||||||||
\(431\) | 15.8432 | 0.763142 | 0.381571 | − | 0.924340i | \(-0.375383\pi\) | ||||
0.381571 | + | 0.924340i | \(0.375383\pi\) | |||||||
\(432\) | −10.1027 | −0.486069 | ||||||||
\(433\) | −7.89725 | −0.379518 | −0.189759 | − | 0.981831i | \(-0.560771\pi\) | ||||
−0.189759 | + | 0.981831i | \(0.560771\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 73.0682 | 3.50335 | ||||||||
\(436\) | 12.0824 | 0.578642 | ||||||||
\(437\) | 17.7219 | 0.847752 | ||||||||
\(438\) | −30.8273 | −1.47298 | ||||||||
\(439\) | −15.0868 | −0.720053 | −0.360026 | − | 0.932942i | \(-0.617232\pi\) | ||||
−0.360026 | + | 0.932942i | \(0.617232\pi\) | |||||||
\(440\) | −1.05137 | −0.0501223 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.246178 | −0.0117095 | ||||||||
\(443\) | −9.58373 | −0.455337 | −0.227668 | − | 0.973739i | \(-0.573110\pi\) | ||||
−0.227668 | + | 0.973739i | \(0.573110\pi\) | |||||||
\(444\) | 0.313524 | 0.0148792 | ||||||||
\(445\) | 6.03540 | 0.286106 | ||||||||
\(446\) | 14.8273 | 0.702091 | ||||||||
\(447\) | 30.8893 | 1.46102 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.8946 | −1.36362 | −0.681811 | − | 0.731529i | \(-0.738807\pi\) | ||||
−0.681811 | + | 0.731529i | \(0.738807\pi\) | |||||||
\(450\) | −12.9460 | −0.610280 | ||||||||
\(451\) | −0.395932 | −0.0186437 | ||||||||
\(452\) | −13.0514 | −0.613885 | ||||||||
\(453\) | 55.5518 | 2.61005 | ||||||||
\(454\) | 4.42960 | 0.207892 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.89461 | −0.322870 | ||||||||
\(457\) | 18.3489 | 0.858327 | 0.429163 | − | 0.903227i | \(-0.358808\pi\) | ||||
0.429163 | + | 0.903227i | \(0.358808\pi\) | |||||||
\(458\) | −22.3623 | −1.04492 | ||||||||
\(459\) | 9.58373 | 0.447330 | ||||||||
\(460\) | 20.8273 | 0.971076 | ||||||||
\(461\) | 10.7936 | 0.502708 | 0.251354 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251354 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.97334 | −0.184657 | −0.0923283 | − | 0.995729i | \(-0.529431\pi\) | ||||
−0.0923283 | + | 0.995729i | \(0.529431\pi\) | |||||||
\(464\) | 9.01770 | 0.418636 | ||||||||
\(465\) | −9.78922 | −0.453964 | ||||||||
\(466\) | 22.9300 | 1.06221 | ||||||||
\(467\) | 12.9016 | 0.597016 | 0.298508 | − | 0.954407i | \(-0.403511\pi\) | ||||
0.298508 | + | 0.954407i | \(0.403511\pi\) | |||||||
\(468\) | −1.63774 | −0.0757046 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −21.9327 | −1.01168 | ||||||||
\(471\) | 40.4517 | 1.86391 | ||||||||
\(472\) | −1.96633 | −0.0905075 | ||||||||
\(473\) | −0.832545 | −0.0382805 | ||||||||
\(474\) | 32.4110 | 1.48869 | ||||||||
\(475\) | −4.63510 | −0.212673 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7715 | 0.493194 | ||||||||
\(478\) | 10.2055 | 0.466789 | ||||||||
\(479\) | −40.6438 | −1.85706 | −0.928532 | − | 0.371252i | \(-0.878929\pi\) | ||||
−0.928532 | + | 0.371252i | \(0.878929\pi\) | |||||||
\(480\) | −8.10275 | −0.369838 | ||||||||
\(481\) | 0.0266643 | 0.00121579 | ||||||||
\(482\) | −25.1408 | −1.14513 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8432 | −0.492874 | ||||||||
\(485\) | −48.3436 | −2.19517 | ||||||||
\(486\) | 5.98667 | 0.271561 | ||||||||
\(487\) | −23.6191 | −1.07028 | −0.535142 | − | 0.844762i | \(-0.679742\pi\) | ||||
−0.535142 | + | 0.844762i | \(0.679742\pi\) | |||||||
\(488\) | −14.2392 | −0.644577 | ||||||||
\(489\) | −30.6218 | −1.38476 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.519021 | −0.0234231 | −0.0117115 | − | 0.999931i | \(-0.503728\pi\) | ||||
−0.0117115 | + | 0.999931i | \(0.503728\pi\) | |||||||
\(492\) | −3.05137 | −0.137567 | ||||||||
\(493\) | −8.55442 | −0.385272 | ||||||||
\(494\) | −0.586367 | −0.0263819 | ||||||||
\(495\) | 6.63510 | 0.298226 | ||||||||
\(496\) | −1.20814 | −0.0542469 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 24.8273 | 1.11254 | ||||||||
\(499\) | 14.8069 | 0.662849 | 0.331425 | − | 0.943482i | \(-0.392471\pi\) | ||||
0.331425 | + | 0.943482i | \(0.392471\pi\) | |||||||
\(500\) | 7.82991 | 0.350164 | ||||||||
\(501\) | 59.2383 | 2.64657 | ||||||||
\(502\) | 0.901621 | 0.0402413 | ||||||||
\(503\) | −29.5837 | −1.31907 | −0.659537 | − | 0.751672i | \(-0.729247\pi\) | ||||
−0.659537 | + | 0.751672i | \(0.729247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.34893 | 0.193525 | ||||||||
\(506\) | −3.10539 | −0.138051 | ||||||||
\(507\) | 39.4624 | 1.75259 | ||||||||
\(508\) | 19.8432 | 0.880401 | ||||||||
\(509\) | −2.88128 | −0.127710 | −0.0638552 | − | 0.997959i | \(-0.520340\pi\) | ||||
−0.0638552 | + | 0.997959i | \(0.520340\pi\) | |||||||
\(510\) | 7.68648 | 0.340363 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 22.8273 | 1.00785 | ||||||||
\(514\) | −11.8566 | −0.522971 | ||||||||
\(515\) | −26.1027 | −1.15022 | ||||||||
\(516\) | −6.41627 | −0.282461 | ||||||||
\(517\) | 3.27020 | 0.143823 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −41.6598 | −1.82866 | ||||||||
\(520\) | −0.689115 | −0.0302197 | ||||||||
\(521\) | −12.3216 | −0.539818 | −0.269909 | − | 0.962886i | \(-0.586994\pi\) | ||||
−0.269909 | + | 0.962886i | \(0.586994\pi\) | |||||||
\(522\) | −56.9097 | −2.49087 | ||||||||
\(523\) | 18.4447 | 0.806529 | 0.403264 | − | 0.915083i | \(-0.367875\pi\) | ||||
0.403264 | + | 0.915083i | \(0.367875\pi\) | |||||||
\(524\) | −10.8609 | −0.474462 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.519021 | −0.0226304 | ||||||||
\(527\) | 1.14607 | 0.0499236 | ||||||||
\(528\) | 1.20814 | 0.0525774 | ||||||||
\(529\) | 38.5164 | 1.67463 | ||||||||
\(530\) | 4.53235 | 0.196873 | ||||||||
\(531\) | 12.4093 | 0.538516 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.259511 | −0.0112406 | ||||||||
\(534\) | −6.93529 | −0.300120 | ||||||||
\(535\) | −8.51902 | −0.368309 | ||||||||
\(536\) | −2.12309 | −0.0917035 | ||||||||
\(537\) | 11.3109 | 0.488101 | ||||||||
\(538\) | −4.65544 | −0.200710 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 26.8273 | 1.15446 | ||||||||
\(541\) | 20.0761 | 0.863138 | 0.431569 | − | 0.902080i | \(-0.357960\pi\) | ||||
0.431569 | + | 0.902080i | \(0.357960\pi\) | |||||||
\(542\) | −7.24354 | −0.311137 | ||||||||
\(543\) | −17.8299 | −0.765154 | ||||||||
\(544\) | 0.948626 | 0.0406720 | ||||||||
\(545\) | −32.0841 | −1.37433 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.7068 | −1.61223 | −0.806114 | − | 0.591761i | \(-0.798433\pi\) | ||||
−0.806114 | + | 0.591761i | \(0.798433\pi\) | |||||||
\(548\) | 17.9327 | 0.766045 | ||||||||
\(549\) | 89.8618 | 3.83521 | ||||||||
\(550\) | 0.812204 | 0.0346325 | ||||||||
\(551\) | −20.3756 | −0.868029 | ||||||||
\(552\) | −23.9327 | −1.01864 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.27284 | −0.266508 | ||||||||
\(555\) | −0.832545 | −0.0353396 | ||||||||
\(556\) | −3.44731 | −0.146198 | ||||||||
\(557\) | 28.2879 | 1.19860 | 0.599298 | − | 0.800526i | \(-0.295446\pi\) | ||||
0.599298 | + | 0.800526i | \(0.295446\pi\) | |||||||
\(558\) | 7.62441 | 0.322767 | ||||||||
\(559\) | −0.545685 | −0.0230800 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14607 | −0.0483871 | ||||||||
\(562\) | −18.7245 | −0.789846 | ||||||||
\(563\) | −30.5324 | −1.28679 | −0.643393 | − | 0.765536i | \(-0.722474\pi\) | ||||
−0.643393 | + | 0.765536i | \(0.722474\pi\) | |||||||
\(564\) | 25.2029 | 1.06123 | ||||||||
\(565\) | 34.6572 | 1.45804 | ||||||||
\(566\) | 13.6174 | 0.572382 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.89461 | −0.289292 | ||||||||
\(569\) | 17.0514 | 0.714831 | 0.357415 | − | 0.933946i | \(-0.383658\pi\) | ||||
0.357415 | + | 0.933946i | \(0.383658\pi\) | |||||||
\(570\) | 18.3082 | 0.766848 | ||||||||
\(571\) | −21.3312 | −0.892684 | −0.446342 | − | 0.894862i | \(-0.647274\pi\) | ||||
−0.446342 | + | 0.894862i | \(0.647274\pi\) | |||||||
\(572\) | 0.102748 | 0.00429613 | ||||||||
\(573\) | 31.5784 | 1.31921 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0894 | −0.670975 | ||||||||
\(576\) | 6.31088 | 0.262954 | ||||||||
\(577\) | 11.0780 | 0.461185 | 0.230592 | − | 0.973050i | \(-0.425934\pi\) | ||||
0.230592 | + | 0.973050i | \(0.425934\pi\) | |||||||
\(578\) | 16.1001 | 0.669676 | ||||||||
\(579\) | −34.8273 | −1.44737 | ||||||||
\(580\) | −23.9460 | −0.994303 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 55.5518 | 2.30270 | ||||||||
\(583\) | −0.675783 | −0.0279881 | ||||||||
\(584\) | 10.1027 | 0.418055 | ||||||||
\(585\) | 4.34893 | 0.179806 | ||||||||
\(586\) | 13.0514 | 0.539147 | ||||||||
\(587\) | −14.4917 | −0.598135 | −0.299068 | − | 0.954232i | \(-0.596676\pi\) | ||||
−0.299068 | + | 0.954232i | \(0.596676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.72980 | 0.112479 | ||||||||
\(590\) | 5.22147 | 0.214964 | ||||||||
\(591\) | 70.0922 | 2.88321 | ||||||||
\(592\) | −0.102748 | −0.00422294 | ||||||||
\(593\) | 9.48098 | 0.389337 | 0.194669 | − | 0.980869i | \(-0.437637\pi\) | ||||
0.194669 | + | 0.980869i | \(0.437637\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.1231 | −0.414658 | ||||||||
\(597\) | −64.0301 | −2.62058 | ||||||||
\(598\) | −2.03540 | −0.0832338 | ||||||||
\(599\) | −42.2409 | −1.72592 | −0.862958 | − | 0.505275i | \(-0.831391\pi\) | ||||
−0.862958 | + | 0.505275i | \(0.831391\pi\) | |||||||
\(600\) | 6.25951 | 0.255543 | ||||||||
\(601\) | −43.3277 | −1.76737 | −0.883686 | − | 0.468079i | \(-0.844946\pi\) | ||||
−0.883686 | + | 0.468079i | \(0.844946\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3986 | 0.545632 | ||||||||
\(604\) | −18.2055 | −0.740771 | ||||||||
\(605\) | 28.7936 | 1.17063 | ||||||||
\(606\) | −4.99736 | −0.203004 | ||||||||
\(607\) | 10.0000 | 0.405887 | 0.202944 | − | 0.979190i | \(-0.434949\pi\) | ||||
0.202944 | + | 0.979190i | \(0.434949\pi\) | |||||||
\(608\) | 2.25951 | 0.0916353 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.8113 | 1.53093 | ||||||||
\(611\) | 2.14343 | 0.0867139 | ||||||||
\(612\) | −5.98667 | −0.241997 | ||||||||
\(613\) | 31.6545 | 1.27851 | 0.639257 | − | 0.768993i | \(-0.279242\pi\) | ||||
0.639257 | + | 0.768993i | \(0.279242\pi\) | |||||||
\(614\) | −14.7936 | −0.597021 | ||||||||
\(615\) | 8.10275 | 0.326734 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.8459 | 0.839223 | 0.419612 | − | 0.907704i | \(-0.362166\pi\) | ||||
0.419612 | + | 0.907704i | \(0.362166\pi\) | |||||||
\(618\) | 29.9947 | 1.20656 | ||||||||
\(619\) | 0.177103 | 0.00711836 | 0.00355918 | − | 0.999994i | \(-0.498867\pi\) | ||||
0.00355918 | + | 0.999994i | \(0.498867\pi\) | |||||||
\(620\) | 3.20814 | 0.128842 | ||||||||
\(621\) | 79.2383 | 3.17972 | ||||||||
\(622\) | 34.5678 | 1.38604 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.791864 | 0.0316999 | ||||||||
\(625\) | −31.0487 | −1.24195 | ||||||||
\(626\) | 6.01333 | 0.240341 | ||||||||
\(627\) | −2.72980 | −0.109018 | ||||||||
\(628\) | −13.2569 | −0.529007 | ||||||||
\(629\) | 0.0974699 | 0.00388638 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.63510 | −0.343758 | −0.171879 | − | 0.985118i | \(-0.554984\pi\) | ||||
−0.171879 | + | 0.985118i | \(0.554984\pi\) | |||||||
\(632\) | −10.6218 | −0.422511 | ||||||||
\(633\) | 26.4517 | 1.05136 | ||||||||
\(634\) | 24.4313 | 0.970292 | ||||||||
\(635\) | −52.6926 | −2.09104 | ||||||||
\(636\) | −5.20814 | −0.206516 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.57040 | 0.141353 | ||||||||
\(639\) | 43.5111 | 1.72127 | ||||||||
\(640\) | 2.65544 | 0.104966 | ||||||||
\(641\) | 49.4084 | 1.95151 | 0.975756 | − | 0.218860i | \(-0.0702337\pi\) | ||||
0.975756 | + | 0.218860i | \(0.0702337\pi\) | |||||||
\(642\) | 9.78922 | 0.386350 | ||||||||
\(643\) | −19.9106 | −0.785197 | −0.392598 | − | 0.919710i | \(-0.628424\pi\) | ||||
−0.392598 | + | 0.919710i | \(0.628424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0380 | 0.670872 | ||||||||
\(646\) | −2.14343 | −0.0843321 | ||||||||
\(647\) | −31.1001 | −1.22267 | −0.611336 | − | 0.791371i | \(-0.709367\pi\) | ||||
−0.611336 | + | 0.791371i | \(0.709367\pi\) | |||||||
\(648\) | −11.8946 | −0.467264 | ||||||||
\(649\) | −0.778532 | −0.0305600 | ||||||||
\(650\) | 0.532353 | 0.0208806 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0354 | 0.393017 | ||||||||
\(653\) | 28.9097 | 1.13132 | 0.565661 | − | 0.824638i | \(-0.308621\pi\) | ||||
0.565661 | + | 0.824638i | \(0.308621\pi\) | |||||||
\(654\) | 36.8679 | 1.44165 | ||||||||
\(655\) | 28.8406 | 1.12690 | ||||||||
\(656\) | 1.00000 | 0.0390434 | ||||||||
\(657\) | −63.7573 | −2.48741 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.2258 | 1.25534 | 0.627670 | − | 0.778479i | \(-0.284009\pi\) | ||||
0.627670 | + | 0.778479i | \(0.284009\pi\) | |||||||
\(660\) | −3.20814 | −0.124877 | ||||||||
\(661\) | 15.6581 | 0.609029 | 0.304514 | − | 0.952508i | \(-0.401506\pi\) | ||||
0.304514 | + | 0.952508i | \(0.401506\pi\) | |||||||
\(662\) | 23.1471 | 0.899638 | ||||||||
\(663\) | −0.751182 | −0.0291735 | ||||||||
\(664\) | −8.13642 | −0.315754 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.648434 | 0.0251263 | ||||||||
\(667\) | −70.7280 | −2.73860 | ||||||||
\(668\) | −19.4136 | −0.751136 | ||||||||
\(669\) | 45.2435 | 1.74922 | ||||||||
\(670\) | 5.63774 | 0.217805 | ||||||||
\(671\) | −5.63774 | −0.217643 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.3870 | −0.824407 | −0.412204 | − | 0.911092i | \(-0.635241\pi\) | ||||
−0.412204 | + | 0.911092i | \(0.635241\pi\) | |||||||
\(674\) | 25.6598 | 0.988379 | ||||||||
\(675\) | −20.7245 | −0.797687 | ||||||||
\(676\) | −12.9327 | −0.497410 | ||||||||
\(677\) | −22.5614 | −0.867106 | −0.433553 | − | 0.901128i | \(-0.642740\pi\) | ||||
−0.433553 | + | 0.901128i | \(0.642740\pi\) | |||||||
\(678\) | −39.8246 | −1.52946 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.51902 | −0.0966000 | ||||||||
\(681\) | 13.5164 | 0.517949 | ||||||||
\(682\) | −0.478340 | −0.0183166 | ||||||||
\(683\) | 42.8069 | 1.63796 | 0.818981 | − | 0.573821i | \(-0.194539\pi\) | ||||
0.818981 | + | 0.573821i | \(0.194539\pi\) | |||||||
\(684\) | −14.2595 | −0.545226 | ||||||||
\(685\) | −47.6191 | −1.81943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −68.2356 | −2.60335 | ||||||||
\(688\) | 2.10275 | 0.0801665 | ||||||||
\(689\) | −0.442937 | −0.0168746 | ||||||||
\(690\) | 63.5518 | 2.41938 | ||||||||
\(691\) | 41.6058 | 1.58276 | 0.791380 | − | 0.611325i | \(-0.209363\pi\) | ||||
0.791380 | + | 0.611325i | \(0.209363\pi\) | |||||||
\(692\) | 13.6528 | 0.519002 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.7715 | −0.408881 | ||||||||
\(695\) | 9.15412 | 0.347236 | ||||||||
\(696\) | 27.5164 | 1.04301 | ||||||||
\(697\) | −0.948626 | −0.0359318 | ||||||||
\(698\) | −13.6935 | −0.518306 | ||||||||
\(699\) | 69.9681 | 2.64643 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.34893 | 0.164257 | 0.0821284 | − | 0.996622i | \(-0.473828\pi\) | ||||
0.0821284 | + | 0.996622i | \(0.473828\pi\) | |||||||
\(702\) | −2.62177 | −0.0989523 | ||||||||
\(703\) | 0.232161 | 0.00875613 | ||||||||
\(704\) | −0.395932 | −0.0149222 | ||||||||
\(705\) | −66.9247 | −2.52053 | ||||||||
\(706\) | −5.10011 | −0.191945 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.00000 | −0.225494 | ||||||||
\(709\) | 16.6421 | 0.625008 | 0.312504 | − | 0.949917i | \(-0.398832\pi\) | ||||
0.312504 | + | 0.949917i | \(0.398832\pi\) | |||||||
\(710\) | 18.3082 | 0.687096 | ||||||||
\(711\) | 67.0328 | 2.51393 | ||||||||
\(712\) | 2.27284 | 0.0851784 | ||||||||
\(713\) | 9.47570 | 0.354868 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.272843 | −0.0102037 | ||||||||
\(716\) | −3.70682 | −0.138530 | ||||||||
\(717\) | 31.1408 | 1.16297 | ||||||||
\(718\) | −7.20814 | −0.269005 | ||||||||
\(719\) | 19.2081 | 0.716343 | 0.358171 | − | 0.933656i | \(-0.383400\pi\) | ||||
0.358171 | + | 0.933656i | \(0.383400\pi\) | |||||||
\(720\) | −16.7582 | −0.624541 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.8946 | 0.517104 | ||||||||
\(723\) | −76.7140 | −2.85302 | ||||||||
\(724\) | 5.84324 | 0.217162 | ||||||||
\(725\) | 18.4987 | 0.687024 | ||||||||
\(726\) | −33.0868 | −1.22797 | ||||||||
\(727\) | −29.2029 | −1.08307 | −0.541537 | − | 0.840677i | \(-0.682157\pi\) | ||||
−0.541537 | + | 0.840677i | \(0.682157\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.4163 | −0.645047 | ||||||||
\(730\) | −26.8273 | −0.992922 | ||||||||
\(731\) | −1.99472 | −0.0737774 | ||||||||
\(732\) | −43.4490 | −1.60592 | ||||||||
\(733\) | −4.17182 | −0.154090 | −0.0770449 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770449 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(734\) | 33.0328 | 1.21926 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.84324 | 0.289106 | ||||||||
\(737\) | −0.840599 | −0.0309638 | ||||||||
\(738\) | −6.31088 | −0.232307 | ||||||||
\(739\) | 15.1408 | 0.556963 | 0.278481 | − | 0.960442i | \(-0.410169\pi\) | ||||
0.278481 | + | 0.960442i | \(0.410169\pi\) | |||||||
\(740\) | 0.272843 | 0.0100299 | ||||||||
\(741\) | −1.78922 | −0.0657288 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.4871 | −1.11846 | −0.559231 | − | 0.829012i | \(-0.688904\pi\) | ||||
−0.559231 | + | 0.829012i | \(0.688904\pi\) | |||||||
\(744\) | −3.68648 | −0.135153 | ||||||||
\(745\) | 26.8813 | 0.984854 | ||||||||
\(746\) | −28.2409 | −1.03397 | ||||||||
\(747\) | 51.3480 | 1.87873 | ||||||||
\(748\) | 0.375591 | 0.0137330 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 23.8920 | 0.872411 | ||||||||
\(751\) | −10.4924 | −0.382872 | −0.191436 | − | 0.981505i | \(-0.561314\pi\) | ||||
−0.191436 | + | 0.981505i | \(0.561314\pi\) | |||||||
\(752\) | −8.25951 | −0.301193 | ||||||||
\(753\) | 2.75118 | 0.100259 | ||||||||
\(754\) | 2.34019 | 0.0852246 | ||||||||
\(755\) | 48.3436 | 1.75941 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.5721 | −1.43827 | −0.719137 | − | 0.694869i | \(-0.755462\pi\) | ||||
−0.719137 | + | 0.694869i | \(0.755462\pi\) | |||||||
\(758\) | 23.8920 | 0.867796 | ||||||||
\(759\) | −9.47570 | −0.343946 | ||||||||
\(760\) | −6.00000 | −0.217643 | ||||||||
\(761\) | 22.6891 | 0.822480 | 0.411240 | − | 0.911527i | \(-0.365096\pi\) | ||||
0.411240 | + | 0.911527i | \(0.365096\pi\) | |||||||
\(762\) | 60.5491 | 2.19346 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.3489 | −0.374411 | ||||||||
\(765\) | 15.8973 | 0.574766 | ||||||||
\(766\) | −30.2409 | −1.09265 | ||||||||
\(767\) | −0.510283 | −0.0184252 | ||||||||
\(768\) | −3.05137 | −0.110107 | ||||||||
\(769\) | 4.55970 | 0.164427 | 0.0822135 | − | 0.996615i | \(-0.473801\pi\) | ||||
0.0822135 | + | 0.996615i | \(0.473801\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.1788 | −1.30295 | ||||||||
\(772\) | 11.4136 | 0.410786 | ||||||||
\(773\) | −55.2923 | −1.98872 | −0.994362 | − | 0.106035i | \(-0.966185\pi\) | ||||
−0.994362 | + | 0.106035i | \(0.966185\pi\) | |||||||
\(774\) | −13.2702 | −0.476988 | ||||||||
\(775\) | −2.47834 | −0.0890246 | ||||||||
\(776\) | −18.2055 | −0.653539 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.7892 | −0.422664 | ||||||||
\(779\) | −2.25951 | −0.0809554 | ||||||||
\(780\) | −2.10275 | −0.0752905 | ||||||||
\(781\) | −2.72980 | −0.0976798 | ||||||||
\(782\) | −7.44030 | −0.266064 | ||||||||
\(783\) | −91.1036 | −3.25578 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.2029 | 1.25644 | ||||||||
\(786\) | −33.1408 | −1.18209 | ||||||||
\(787\) | 45.9663 | 1.63852 | 0.819261 | − | 0.573420i | \(-0.194384\pi\) | ||||
0.819261 | + | 0.573420i | \(0.194384\pi\) | |||||||
\(788\) | −22.9707 | −0.818297 | ||||||||
\(789\) | −1.58373 | −0.0563822 | ||||||||
\(790\) | 28.2055 | 1.00351 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.49868 | 0.0887867 | ||||||||
\(793\) | −3.69521 | −0.131221 | ||||||||
\(794\) | 18.5678 | 0.658945 | ||||||||
\(795\) | 13.8299 | 0.490496 | ||||||||
\(796\) | 20.9840 | 0.743759 | ||||||||
\(797\) | −27.4154 | −0.971102 | −0.485551 | − | 0.874208i | \(-0.661381\pi\) | ||||
−0.485551 | + | 0.874208i | \(0.661381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.83518 | 0.277189 | ||||||||
\(800\) | −2.05137 | −0.0725270 | ||||||||
\(801\) | −14.3436 | −0.506808 | ||||||||
\(802\) | 29.9814 | 1.05868 | ||||||||
\(803\) | 4.00000 | 0.141157 | ||||||||
\(804\) | −6.47834 | −0.228473 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.313524 | −0.0110434 | ||||||||
\(807\) | −14.2055 | −0.500057 | ||||||||
\(808\) | 1.63774 | 0.0576155 | ||||||||
\(809\) | 20.8627 | 0.733492 | 0.366746 | − | 0.930321i | \(-0.380472\pi\) | ||||
0.366746 | + | 0.930321i | \(0.380472\pi\) | |||||||
\(810\) | 31.5855 | 1.10980 | ||||||||
\(811\) | −9.79623 | −0.343992 | −0.171996 | − | 0.985098i | \(-0.555022\pi\) | ||||
−0.171996 | + | 0.985098i | \(0.555022\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.1027 | −0.775177 | ||||||||
\(814\) | −0.0406814 | −0.00142588 | ||||||||
\(815\) | −26.6484 | −0.933454 | ||||||||
\(816\) | 2.89461 | 0.101332 | ||||||||
\(817\) | −4.75118 | −0.166223 | ||||||||
\(818\) | −30.2055 | −1.05611 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.65544 | −0.0927321 | ||||||||
\(821\) | −46.5190 | −1.62353 | −0.811763 | − | 0.583988i | \(-0.801492\pi\) | ||||
−0.811763 | + | 0.583988i | \(0.801492\pi\) | |||||||
\(822\) | 54.7192 | 1.90855 | ||||||||
\(823\) | −28.9707 | −1.00985 | −0.504927 | − | 0.863162i | \(-0.668481\pi\) | ||||
−0.504927 | + | 0.863162i | \(0.668481\pi\) | |||||||
\(824\) | −9.82991 | −0.342441 | ||||||||
\(825\) | 2.47834 | 0.0862847 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.6722 | 1.20567 | 0.602836 | − | 0.797865i | \(-0.294037\pi\) | ||||
0.602836 | + | 0.797865i | \(0.294037\pi\) | |||||||
\(828\) | −49.4978 | −1.72017 | ||||||||
\(829\) | 22.2038 | 0.771169 | 0.385584 | − | 0.922673i | \(-0.374000\pi\) | ||||
0.385584 | + | 0.922673i | \(0.374000\pi\) | |||||||
\(830\) | 21.6058 | 0.749948 | ||||||||
\(831\) | −19.1408 | −0.663987 | ||||||||
\(832\) | −0.259511 | −0.00899691 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.5190 | −0.364244 | ||||||||
\(835\) | 51.5518 | 1.78402 | ||||||||
\(836\) | 0.894612 | 0.0309408 | ||||||||
\(837\) | 12.2055 | 0.421884 | ||||||||
\(838\) | 5.82290 | 0.201149 | ||||||||
\(839\) | −34.5411 | −1.19249 | −0.596245 | − | 0.802802i | \(-0.703341\pi\) | ||||
−0.596245 | + | 0.802802i | \(0.703341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.3189 | 1.80410 | ||||||||
\(842\) | 2.91495 | 0.100456 | ||||||||
\(843\) | −57.1355 | −1.96785 | ||||||||
\(844\) | −8.66877 | −0.298392 | ||||||||
\(845\) | 34.3419 | 1.18140 | ||||||||
\(846\) | 52.1248 | 1.79209 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.70682 | 0.0586123 | ||||||||
\(849\) | 41.5518 | 1.42605 | ||||||||
\(850\) | 1.94599 | 0.0667468 | ||||||||
\(851\) | 0.805881 | 0.0276252 | ||||||||
\(852\) | −21.0380 | −0.720751 | ||||||||
\(853\) | 56.3454 | 1.92923 | 0.964615 | − | 0.263664i | \(-0.0849311\pi\) | ||||
0.964615 | + | 0.263664i | \(0.0849311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37.8653 | 1.29497 | ||||||||
\(856\) | −3.20814 | −0.109652 | ||||||||
\(857\) | 11.2702 | 0.384983 | 0.192491 | − | 0.981299i | \(-0.438343\pi\) | ||||
0.192491 | + | 0.981299i | \(0.438343\pi\) | |||||||
\(858\) | 0.313524 | 0.0107035 | ||||||||
\(859\) | 1.30388 | 0.0444877 | 0.0222438 | − | 0.999753i | \(-0.492919\pi\) | ||||
0.0222438 | + | 0.999753i | \(0.492919\pi\) | |||||||
\(860\) | −5.58373 | −0.190404 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.8432 | −0.539623 | ||||||||
\(863\) | −33.2029 | −1.13024 | −0.565119 | − | 0.825009i | \(-0.691170\pi\) | ||||
−0.565119 | + | 0.825009i | \(0.691170\pi\) | |||||||
\(864\) | 10.1027 | 0.343702 | ||||||||
\(865\) | −36.2542 | −1.23268 | ||||||||
\(866\) | 7.89725 | 0.268360 | ||||||||
\(867\) | 49.1275 | 1.66846 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.20550 | −0.142662 | ||||||||
\(870\) | −73.0682 | −2.47724 | ||||||||
\(871\) | −0.550964 | −0.0186687 | ||||||||
\(872\) | −12.0824 | −0.409162 | ||||||||
\(873\) | 114.893 | 3.88853 | ||||||||
\(874\) | −17.7219 | −0.599451 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30.8273 | 1.04156 | ||||||||
\(877\) | −41.3056 | −1.39479 | −0.697396 | − | 0.716686i | \(-0.745658\pi\) | ||||
−0.697396 | + | 0.716686i | \(0.745658\pi\) | |||||||
\(878\) | 15.0868 | 0.509154 | ||||||||
\(879\) | 39.8246 | 1.34325 | ||||||||
\(880\) | 1.05137 | 0.0354418 | ||||||||
\(881\) | 21.1001 | 0.710881 | 0.355440 | − | 0.934699i | \(-0.384331\pi\) | ||||
0.355440 | + | 0.934699i | \(0.384331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.70946 | −0.158486 | −0.0792429 | − | 0.996855i | \(-0.525250\pi\) | ||||
−0.0792429 | + | 0.996855i | \(0.525250\pi\) | |||||||
\(884\) | 0.246178 | 0.00827987 | ||||||||
\(885\) | 15.9327 | 0.535570 | ||||||||
\(886\) | 9.58373 | 0.321972 | ||||||||
\(887\) | 26.5411 | 0.891163 | 0.445581 | − | 0.895241i | \(-0.352997\pi\) | ||||
0.445581 | + | 0.895241i | \(0.352997\pi\) | |||||||
\(888\) | −0.313524 | −0.0105212 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.03540 | −0.202307 | ||||||||
\(891\) | −4.70946 | −0.157773 | ||||||||
\(892\) | −14.8273 | −0.496454 | ||||||||
\(893\) | 18.6625 | 0.624515 | ||||||||
\(894\) | −30.8893 | −1.03309 | ||||||||
\(895\) | 9.84324 | 0.329023 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.21078 | −0.207372 | ||||||||
\(898\) | 28.8946 | 0.964226 | ||||||||
\(899\) | −10.8946 | −0.363356 | ||||||||
\(900\) | 12.9460 | 0.431533 | ||||||||
\(901\) | −1.61913 | −0.0539410 | ||||||||
\(902\) | 0.395932 | 0.0131831 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.0514 | 0.434082 | ||||||||
\(905\) | −15.5164 | −0.515782 | ||||||||
\(906\) | −55.5518 | −1.84558 | ||||||||
\(907\) | 4.83255 | 0.160462 | 0.0802310 | − | 0.996776i | \(-0.474434\pi\) | ||||
0.0802310 | + | 0.996776i | \(0.474434\pi\) | |||||||
\(908\) | −4.42960 | −0.147002 | ||||||||
\(909\) | −10.3356 | −0.342810 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.8113 | −0.722640 | −0.361320 | − | 0.932442i | \(-0.617674\pi\) | ||||
−0.361320 | + | 0.932442i | \(0.617674\pi\) | |||||||
\(912\) | 6.89461 | 0.228303 | ||||||||
\(913\) | −3.22147 | −0.106615 | ||||||||
\(914\) | −18.3489 | −0.606929 | ||||||||
\(915\) | 115.376 | 3.81423 | ||||||||
\(916\) | 22.3623 | 0.738870 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −9.58373 | −0.316310 | ||||||||
\(919\) | −22.6891 | −0.748445 | −0.374222 | − | 0.927339i | \(-0.622090\pi\) | ||||
−0.374222 | + | 0.927339i | \(0.622090\pi\) | |||||||
\(920\) | −20.8273 | −0.686655 | ||||||||
\(921\) | −45.1408 | −1.48744 | ||||||||
\(922\) | −10.7936 | −0.355468 | ||||||||
\(923\) | −1.78922 | −0.0588930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.210776 | −0.00693026 | ||||||||
\(926\) | 3.97334 | 0.130572 | ||||||||
\(927\) | 62.0354 | 2.03751 | ||||||||
\(928\) | −9.01770 | −0.296021 | ||||||||
\(929\) | 37.2081 | 1.22076 | 0.610380 | − | 0.792109i | \(-0.291017\pi\) | ||||
0.610380 | + | 0.792109i | \(0.291017\pi\) | |||||||
\(930\) | 9.78922 | 0.321001 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −22.9300 | −0.751098 | ||||||||
\(933\) | 105.479 | 3.45323 | ||||||||
\(934\) | −12.9016 | −0.422154 | ||||||||
\(935\) | −0.997361 | −0.0326172 | ||||||||
\(936\) | 1.63774 | 0.0535312 | ||||||||
\(937\) | −39.9681 | −1.30570 | −0.652850 | − | 0.757487i | \(-0.726427\pi\) | ||||
−0.652850 | + | 0.757487i | \(0.726427\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.3489 | 0.598795 | ||||||||
\(940\) | 21.9327 | 0.715364 | ||||||||
\(941\) | −29.8316 | −0.972484 | −0.486242 | − | 0.873824i | \(-0.661633\pi\) | ||||
−0.486242 | + | 0.873824i | \(0.661633\pi\) | |||||||
\(942\) | −40.4517 | −1.31799 | ||||||||
\(943\) | −7.84324 | −0.255411 | ||||||||
\(944\) | 1.96633 | 0.0639985 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.832545 | 0.0270684 | ||||||||
\(947\) | 1.01138 | 0.0328654 | 0.0164327 | − | 0.999865i | \(-0.494769\pi\) | ||||
0.0164327 | + | 0.999865i | \(0.494769\pi\) | |||||||
\(948\) | −32.4110 | −1.05266 | ||||||||
\(949\) | 2.62177 | 0.0851062 | ||||||||
\(950\) | 4.63510 | 0.150383 | ||||||||
\(951\) | 74.5491 | 2.41742 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.2656 | 1.14237 | 0.571183 | − | 0.820823i | \(-0.306485\pi\) | ||||
0.571183 | + | 0.820823i | \(0.306485\pi\) | |||||||
\(954\) | −10.7715 | −0.348741 | ||||||||
\(955\) | 27.4810 | 0.889264 | ||||||||
\(956\) | −10.2055 | −0.330069 | ||||||||
\(957\) | 10.8946 | 0.352173 | ||||||||
\(958\) | 40.6438 | 1.31314 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.10275 | 0.261515 | ||||||||
\(961\) | −29.5404 | −0.952916 | ||||||||
\(962\) | −0.0266643 | −0.000859692 0 | ||||||||
\(963\) | 20.2462 | 0.652424 | ||||||||
\(964\) | 25.1408 | 0.809730 | ||||||||
\(965\) | −30.3082 | −0.975657 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.6838 | 1.24399 | 0.621994 | − | 0.783022i | \(-0.286323\pi\) | ||||
0.621994 | + | 0.783022i | \(0.286323\pi\) | |||||||
\(968\) | 10.8432 | 0.348515 | ||||||||
\(969\) | −6.54041 | −0.210108 | ||||||||
\(970\) | 48.3436 | 1.55222 | ||||||||
\(971\) | 12.4703 | 0.400191 | 0.200095 | − | 0.979776i | \(-0.435875\pi\) | ||||
0.200095 | + | 0.979776i | \(0.435875\pi\) | |||||||
\(972\) | −5.98667 | −0.192022 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.6191 | 0.756806 | ||||||||
\(975\) | 1.62441 | 0.0520227 | ||||||||
\(976\) | 14.2392 | 0.455785 | ||||||||
\(977\) | −53.5111 | −1.71197 | −0.855986 | − | 0.516999i | \(-0.827049\pi\) | ||||
−0.855986 | + | 0.516999i | \(0.827049\pi\) | |||||||
\(978\) | 30.6218 | 0.979176 | ||||||||
\(979\) | 0.899891 | 0.0287606 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 76.2507 | 2.43450 | ||||||||
\(982\) | 0.519021 | 0.0165626 | ||||||||
\(983\) | 28.7866 | 0.918149 | 0.459075 | − | 0.888398i | \(-0.348181\pi\) | ||||
0.459075 | + | 0.888398i | \(0.348181\pi\) | |||||||
\(984\) | 3.05137 | 0.0972743 | ||||||||
\(985\) | 60.9974 | 1.94354 | ||||||||
\(986\) | 8.55442 | 0.272428 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.586367 | 0.0186548 | ||||||||
\(989\) | −16.4924 | −0.524426 | ||||||||
\(990\) | −6.63510 | −0.210877 | ||||||||
\(991\) | −26.2409 | −0.833570 | −0.416785 | − | 0.909005i | \(-0.636843\pi\) | ||||
−0.416785 | + | 0.909005i | \(0.636843\pi\) | |||||||
\(992\) | 1.20814 | 0.0383584 | ||||||||
\(993\) | 70.6305 | 2.24139 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −55.7219 | −1.76650 | ||||||||
\(996\) | −24.8273 | −0.786682 | ||||||||
\(997\) | 11.8078 | 0.373958 | 0.186979 | − | 0.982364i | \(-0.440130\pi\) | ||||
0.186979 | + | 0.982364i | \(0.440130\pi\) | |||||||
\(998\) | −14.8069 | −0.468705 | ||||||||
\(999\) | 1.03804 | 0.0328422 |
(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 | 4018.2.a.bd.1.1 | ✓ | 3 | |
7.6 | odd | 2 | 4018.2.a.be.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4018.2.a.bd.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
4018.2.a.be.1.3 | yes | 3 | 7.6 | odd | 2 |