Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 2x^{8} - 11x^{7} + 11x^{6} + 34x^{5} - 20x^{4} - 36x^{3} + 13x^{2} + 10x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.65050\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31671 | −0.931054 | −0.465527 | − | 0.885034i | \(-0.654135\pi\) | ||||
−0.465527 | + | 0.885034i | \(0.654135\pi\) | |||||||
\(3\) | 2.24751 | 1.29760 | 0.648801 | − | 0.760958i | \(-0.275271\pi\) | ||||
0.648801 | + | 0.760958i | \(0.275271\pi\) | |||||||
\(4\) | −0.266275 | −0.133138 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.95932 | −1.20814 | ||||||||
\(7\) | 2.74324 | 1.03685 | 0.518424 | − | 0.855124i | \(-0.326519\pi\) | ||||
0.518424 | + | 0.855124i | \(0.326519\pi\) | |||||||
\(8\) | 2.98403 | 1.05501 | ||||||||
\(9\) | 2.05132 | 0.683773 | ||||||||
\(10\) | 1.31671 | 0.416380 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.598458 | −0.172760 | ||||||||
\(13\) | −0.823772 | −0.228473 | −0.114237 | − | 0.993454i | \(-0.536442\pi\) | ||||
−0.114237 | + | 0.993454i | \(0.536442\pi\) | |||||||
\(14\) | −3.61205 | −0.965361 | ||||||||
\(15\) | −2.24751 | −0.580306 | ||||||||
\(16\) | −3.39655 | −0.849137 | ||||||||
\(17\) | 4.43351 | 1.07528 | 0.537642 | − | 0.843173i | \(-0.319315\pi\) | ||||
0.537642 | + | 0.843173i | \(0.319315\pi\) | |||||||
\(18\) | −2.70099 | −0.636629 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0.266275 | 0.0595410 | ||||||||
\(21\) | 6.16547 | 1.34542 | ||||||||
\(22\) | 1.31671 | 0.280723 | ||||||||
\(23\) | 5.39996 | 1.12597 | 0.562985 | − | 0.826467i | \(-0.309653\pi\) | ||||
0.562985 | + | 0.826467i | \(0.309653\pi\) | |||||||
\(24\) | 6.70664 | 1.36899 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.08467 | 0.212721 | ||||||||
\(27\) | −2.13218 | −0.410338 | ||||||||
\(28\) | −0.730457 | −0.138043 | ||||||||
\(29\) | 2.90610 | 0.539649 | 0.269825 | − | 0.962909i | \(-0.413034\pi\) | ||||
0.269825 | + | 0.962909i | \(0.413034\pi\) | |||||||
\(30\) | 2.95932 | 0.540296 | ||||||||
\(31\) | −7.05785 | −1.26763 | −0.633813 | − | 0.773486i | \(-0.718511\pi\) | ||||
−0.633813 | + | 0.773486i | \(0.718511\pi\) | |||||||
\(32\) | −1.49579 | −0.264420 | ||||||||
\(33\) | −2.24751 | −0.391242 | ||||||||
\(34\) | −5.83765 | −1.00115 | ||||||||
\(35\) | −2.74324 | −0.463692 | ||||||||
\(36\) | −0.546215 | −0.0910359 | ||||||||
\(37\) | 8.40534 | 1.38183 | 0.690915 | − | 0.722936i | \(-0.257208\pi\) | ||||
0.690915 | + | 0.722936i | \(0.257208\pi\) | |||||||
\(38\) | −1.31671 | −0.213599 | ||||||||
\(39\) | −1.85144 | −0.296467 | ||||||||
\(40\) | −2.98403 | −0.471816 | ||||||||
\(41\) | −10.6533 | −1.66377 | −0.831885 | − | 0.554947i | \(-0.812738\pi\) | ||||
−0.831885 | + | 0.554947i | \(0.812738\pi\) | |||||||
\(42\) | −8.11813 | −1.25266 | ||||||||
\(43\) | 10.3406 | 1.57693 | 0.788463 | − | 0.615082i | \(-0.210877\pi\) | ||||
0.788463 | + | 0.615082i | \(0.210877\pi\) | |||||||
\(44\) | 0.266275 | 0.0401425 | ||||||||
\(45\) | −2.05132 | −0.305792 | ||||||||
\(46\) | −7.11019 | −1.04834 | ||||||||
\(47\) | 12.7551 | 1.86052 | 0.930259 | − | 0.366904i | \(-0.119582\pi\) | ||||
0.930259 | + | 0.366904i | \(0.119582\pi\) | |||||||
\(48\) | −7.63378 | −1.10184 | ||||||||
\(49\) | 0.525367 | 0.0750524 | ||||||||
\(50\) | −1.31671 | −0.186211 | ||||||||
\(51\) | 9.96438 | 1.39529 | ||||||||
\(52\) | 0.219350 | 0.0304184 | ||||||||
\(53\) | 2.37381 | 0.326068 | 0.163034 | − | 0.986620i | \(-0.447872\pi\) | ||||
0.163034 | + | 0.986620i | \(0.447872\pi\) | |||||||
\(54\) | 2.80746 | 0.382047 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 8.18590 | 1.09389 | ||||||||
\(57\) | 2.24751 | 0.297690 | ||||||||
\(58\) | −3.82649 | −0.502443 | ||||||||
\(59\) | 14.8451 | 1.93266 | 0.966331 | − | 0.257303i | \(-0.0828340\pi\) | ||||
0.966331 | + | 0.257303i | \(0.0828340\pi\) | |||||||
\(60\) | 0.598458 | 0.0772605 | ||||||||
\(61\) | −8.71368 | −1.11567 | −0.557836 | − | 0.829951i | \(-0.688368\pi\) | ||||
−0.557836 | + | 0.829951i | \(0.688368\pi\) | |||||||
\(62\) | 9.29313 | 1.18023 | ||||||||
\(63\) | 5.62726 | 0.708968 | ||||||||
\(64\) | 8.76261 | 1.09533 | ||||||||
\(65\) | 0.823772 | 0.102176 | ||||||||
\(66\) | 2.95932 | 0.364267 | ||||||||
\(67\) | −10.1782 | −1.24346 | −0.621730 | − | 0.783231i | \(-0.713570\pi\) | ||||
−0.621730 | + | 0.783231i | \(0.713570\pi\) | |||||||
\(68\) | −1.18054 | −0.143161 | ||||||||
\(69\) | 12.1365 | 1.46106 | ||||||||
\(70\) | 3.61205 | 0.431723 | ||||||||
\(71\) | 7.46427 | 0.885845 | 0.442923 | − | 0.896560i | \(-0.353942\pi\) | ||||
0.442923 | + | 0.896560i | \(0.353942\pi\) | |||||||
\(72\) | 6.12119 | 0.721389 | ||||||||
\(73\) | −0.797840 | −0.0933801 | −0.0466900 | − | 0.998909i | \(-0.514867\pi\) | ||||
−0.0466900 | + | 0.998909i | \(0.514867\pi\) | |||||||
\(74\) | −11.0674 | −1.28656 | ||||||||
\(75\) | 2.24751 | 0.259521 | ||||||||
\(76\) | −0.266275 | −0.0305439 | ||||||||
\(77\) | −2.74324 | −0.312621 | ||||||||
\(78\) | 2.43781 | 0.276027 | ||||||||
\(79\) | −0.962752 | −0.108318 | −0.0541590 | − | 0.998532i | \(-0.517248\pi\) | ||||
−0.0541590 | + | 0.998532i | \(0.517248\pi\) | |||||||
\(80\) | 3.39655 | 0.379745 | ||||||||
\(81\) | −10.9460 | −1.21623 | ||||||||
\(82\) | 14.0273 | 1.54906 | ||||||||
\(83\) | 0.110739 | 0.0121552 | 0.00607762 | − | 0.999982i | \(-0.498065\pi\) | ||||
0.00607762 | + | 0.999982i | \(0.498065\pi\) | |||||||
\(84\) | −1.64171 | −0.179126 | ||||||||
\(85\) | −4.43351 | −0.480882 | ||||||||
\(86\) | −13.6156 | −1.46820 | ||||||||
\(87\) | 6.53150 | 0.700250 | ||||||||
\(88\) | −2.98403 | −0.318098 | ||||||||
\(89\) | 11.1632 | 1.18330 | 0.591648 | − | 0.806197i | \(-0.298478\pi\) | ||||
0.591648 | + | 0.806197i | \(0.298478\pi\) | |||||||
\(90\) | 2.70099 | 0.284709 | ||||||||
\(91\) | −2.25980 | −0.236892 | ||||||||
\(92\) | −1.43788 | −0.149909 | ||||||||
\(93\) | −15.8626 | −1.64488 | ||||||||
\(94\) | −16.7947 | −1.73224 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | −3.36180 | −0.343113 | ||||||||
\(97\) | 15.0623 | 1.52935 | 0.764675 | − | 0.644416i | \(-0.222900\pi\) | ||||
0.764675 | + | 0.644416i | \(0.222900\pi\) | |||||||
\(98\) | −0.691755 | −0.0698778 | ||||||||
\(99\) | −2.05132 | −0.206165 | ||||||||
\(100\) | −0.266275 | −0.0266275 | ||||||||
\(101\) | 1.64259 | 0.163444 | 0.0817219 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817219 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(102\) | −13.1202 | −1.29909 | ||||||||
\(103\) | −18.7841 | −1.85085 | −0.925426 | − | 0.378928i | \(-0.876293\pi\) | ||||
−0.925426 | + | 0.378928i | \(0.876293\pi\) | |||||||
\(104\) | −2.45816 | −0.241042 | ||||||||
\(105\) | −6.16547 | −0.601688 | ||||||||
\(106\) | −3.12562 | −0.303587 | ||||||||
\(107\) | −19.0393 | −1.84060 | −0.920299 | − | 0.391215i | \(-0.872055\pi\) | ||||
−0.920299 | + | 0.391215i | \(0.872055\pi\) | |||||||
\(108\) | 0.567746 | 0.0546314 | ||||||||
\(109\) | 16.7693 | 1.60621 | 0.803104 | − | 0.595839i | \(-0.203180\pi\) | ||||
0.803104 | + | 0.595839i | \(0.203180\pi\) | |||||||
\(110\) | −1.31671 | −0.125543 | ||||||||
\(111\) | 18.8911 | 1.79307 | ||||||||
\(112\) | −9.31754 | −0.880425 | ||||||||
\(113\) | 10.8292 | 1.01873 | 0.509364 | − | 0.860551i | \(-0.329881\pi\) | ||||
0.509364 | + | 0.860551i | \(0.329881\pi\) | |||||||
\(114\) | −2.95932 | −0.277166 | ||||||||
\(115\) | −5.39996 | −0.503549 | ||||||||
\(116\) | −0.773823 | −0.0718477 | ||||||||
\(117\) | −1.68982 | −0.156224 | ||||||||
\(118\) | −19.5466 | −1.79941 | ||||||||
\(119\) | 12.1622 | 1.11491 | ||||||||
\(120\) | −6.70664 | −0.612230 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.4734 | 1.03875 | ||||||||
\(123\) | −23.9435 | −2.15891 | ||||||||
\(124\) | 1.87933 | 0.168769 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.40946 | −0.660088 | ||||||||
\(127\) | −8.47608 | −0.752130 | −0.376065 | − | 0.926593i | \(-0.622723\pi\) | ||||
−0.376065 | + | 0.926593i | \(0.622723\pi\) | |||||||
\(128\) | −8.54624 | −0.755388 | ||||||||
\(129\) | 23.2406 | 2.04622 | ||||||||
\(130\) | −1.08467 | −0.0951317 | ||||||||
\(131\) | 10.7024 | 0.935071 | 0.467536 | − | 0.883974i | \(-0.345142\pi\) | ||||
0.467536 | + | 0.883974i | \(0.345142\pi\) | |||||||
\(132\) | 0.598458 | 0.0520890 | ||||||||
\(133\) | 2.74324 | 0.237869 | ||||||||
\(134\) | 13.4017 | 1.15773 | ||||||||
\(135\) | 2.13218 | 0.183509 | ||||||||
\(136\) | 13.2297 | 1.13444 | ||||||||
\(137\) | 19.2944 | 1.64843 | 0.824215 | − | 0.566277i | \(-0.191617\pi\) | ||||
0.824215 | + | 0.566277i | \(0.191617\pi\) | |||||||
\(138\) | −15.9802 | −1.36033 | ||||||||
\(139\) | 5.32362 | 0.451544 | 0.225772 | − | 0.974180i | \(-0.427510\pi\) | ||||
0.225772 | + | 0.974180i | \(0.427510\pi\) | |||||||
\(140\) | 0.730457 | 0.0617349 | ||||||||
\(141\) | 28.6672 | 2.41421 | ||||||||
\(142\) | −9.82827 | −0.824770 | ||||||||
\(143\) | 0.823772 | 0.0688873 | ||||||||
\(144\) | −6.96740 | −0.580616 | ||||||||
\(145\) | −2.90610 | −0.241338 | ||||||||
\(146\) | 1.05052 | 0.0869419 | ||||||||
\(147\) | 1.18077 | 0.0973882 | ||||||||
\(148\) | −2.23814 | −0.183974 | ||||||||
\(149\) | −17.7842 | −1.45694 | −0.728470 | − | 0.685078i | \(-0.759768\pi\) | ||||
−0.728470 | + | 0.685078i | \(0.759768\pi\) | |||||||
\(150\) | −2.95932 | −0.241628 | ||||||||
\(151\) | −9.70582 | −0.789849 | −0.394924 | − | 0.918714i | \(-0.629229\pi\) | ||||
−0.394924 | + | 0.918714i | \(0.629229\pi\) | |||||||
\(152\) | 2.98403 | 0.242037 | ||||||||
\(153\) | 9.09454 | 0.735250 | ||||||||
\(154\) | 3.61205 | 0.291067 | ||||||||
\(155\) | 7.05785 | 0.566900 | ||||||||
\(156\) | 0.492993 | 0.0394710 | ||||||||
\(157\) | 6.78280 | 0.541327 | 0.270663 | − | 0.962674i | \(-0.412757\pi\) | ||||
0.270663 | + | 0.962674i | \(0.412757\pi\) | |||||||
\(158\) | 1.26766 | 0.100850 | ||||||||
\(159\) | 5.33517 | 0.423106 | ||||||||
\(160\) | 1.49579 | 0.118252 | ||||||||
\(161\) | 14.8134 | 1.16746 | ||||||||
\(162\) | 14.4128 | 1.13237 | ||||||||
\(163\) | −16.7229 | −1.30984 | −0.654918 | − | 0.755700i | \(-0.727297\pi\) | ||||
−0.654918 | + | 0.755700i | \(0.727297\pi\) | |||||||
\(164\) | 2.83672 | 0.221511 | ||||||||
\(165\) | 2.24751 | 0.174969 | ||||||||
\(166\) | −0.145812 | −0.0113172 | ||||||||
\(167\) | −9.05766 | −0.700903 | −0.350452 | − | 0.936581i | \(-0.613972\pi\) | ||||
−0.350452 | + | 0.936581i | \(0.613972\pi\) | |||||||
\(168\) | 18.3979 | 1.41943 | ||||||||
\(169\) | −12.3214 | −0.947800 | ||||||||
\(170\) | 5.83765 | 0.447727 | ||||||||
\(171\) | 2.05132 | 0.156868 | ||||||||
\(172\) | −2.75345 | −0.209948 | ||||||||
\(173\) | 8.57947 | 0.652285 | 0.326142 | − | 0.945321i | \(-0.394251\pi\) | ||||
0.326142 | + | 0.945321i | \(0.394251\pi\) | |||||||
\(174\) | −8.60009 | −0.651971 | ||||||||
\(175\) | 2.74324 | 0.207369 | ||||||||
\(176\) | 3.39655 | 0.256024 | ||||||||
\(177\) | 33.3645 | 2.50783 | ||||||||
\(178\) | −14.6987 | −1.10171 | ||||||||
\(179\) | −9.13708 | −0.682937 | −0.341469 | − | 0.939893i | \(-0.610924\pi\) | ||||
−0.341469 | + | 0.939893i | \(0.610924\pi\) | |||||||
\(180\) | 0.546215 | 0.0407125 | ||||||||
\(181\) | −18.3843 | −1.36650 | −0.683248 | − | 0.730187i | \(-0.739433\pi\) | ||||
−0.683248 | + | 0.730187i | \(0.739433\pi\) | |||||||
\(182\) | 2.97551 | 0.220559 | ||||||||
\(183\) | −19.5841 | −1.44770 | ||||||||
\(184\) | 16.1136 | 1.18791 | ||||||||
\(185\) | −8.40534 | −0.617973 | ||||||||
\(186\) | 20.8864 | 1.53147 | ||||||||
\(187\) | −4.43351 | −0.324211 | ||||||||
\(188\) | −3.39636 | −0.247705 | ||||||||
\(189\) | −5.84907 | −0.425457 | ||||||||
\(190\) | 1.31671 | 0.0955242 | ||||||||
\(191\) | −4.72197 | −0.341670 | −0.170835 | − | 0.985300i | \(-0.554647\pi\) | ||||
−0.170835 | + | 0.985300i | \(0.554647\pi\) | |||||||
\(192\) | 19.6941 | 1.42130 | ||||||||
\(193\) | 3.20004 | 0.230344 | 0.115172 | − | 0.993346i | \(-0.463258\pi\) | ||||
0.115172 | + | 0.993346i | \(0.463258\pi\) | |||||||
\(194\) | −19.8327 | −1.42391 | ||||||||
\(195\) | 1.85144 | 0.132584 | ||||||||
\(196\) | −0.139892 | −0.00999230 | ||||||||
\(197\) | −16.7733 | −1.19505 | −0.597525 | − | 0.801850i | \(-0.703849\pi\) | ||||
−0.597525 | + | 0.801850i | \(0.703849\pi\) | |||||||
\(198\) | 2.70099 | 0.191951 | ||||||||
\(199\) | −1.76433 | −0.125070 | −0.0625351 | − | 0.998043i | \(-0.519919\pi\) | ||||
−0.0625351 | + | 0.998043i | \(0.519919\pi\) | |||||||
\(200\) | 2.98403 | 0.211003 | ||||||||
\(201\) | −22.8756 | −1.61352 | ||||||||
\(202\) | −2.16281 | −0.152175 | ||||||||
\(203\) | 7.97213 | 0.559534 | ||||||||
\(204\) | −2.65327 | −0.185766 | ||||||||
\(205\) | 10.6533 | 0.744061 | ||||||||
\(206\) | 24.7332 | 1.72324 | ||||||||
\(207\) | 11.0770 | 0.769908 | ||||||||
\(208\) | 2.79798 | 0.194005 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 8.11813 | 0.560204 | ||||||||
\(211\) | 23.8350 | 1.64087 | 0.820434 | − | 0.571741i | \(-0.193732\pi\) | ||||
0.820434 | + | 0.571741i | \(0.193732\pi\) | |||||||
\(212\) | −0.632087 | −0.0434119 | ||||||||
\(213\) | 16.7760 | 1.14948 | ||||||||
\(214\) | 25.0692 | 1.71370 | ||||||||
\(215\) | −10.3406 | −0.705223 | ||||||||
\(216\) | −6.36247 | −0.432911 | ||||||||
\(217\) | −19.3614 | −1.31434 | ||||||||
\(218\) | −22.0803 | −1.49547 | ||||||||
\(219\) | −1.79316 | −0.121170 | ||||||||
\(220\) | −0.266275 | −0.0179523 | ||||||||
\(221\) | −3.65220 | −0.245674 | ||||||||
\(222\) | −24.8741 | −1.66944 | ||||||||
\(223\) | −13.4106 | −0.898037 | −0.449019 | − | 0.893522i | \(-0.648226\pi\) | ||||
−0.449019 | + | 0.893522i | \(0.648226\pi\) | |||||||
\(224\) | −4.10331 | −0.274164 | ||||||||
\(225\) | 2.05132 | 0.136755 | ||||||||
\(226\) | −14.2590 | −0.948492 | ||||||||
\(227\) | 4.43325 | 0.294245 | 0.147123 | − | 0.989118i | \(-0.452999\pi\) | ||||
0.147123 | + | 0.989118i | \(0.452999\pi\) | |||||||
\(228\) | −0.598458 | −0.0396338 | ||||||||
\(229\) | 14.0125 | 0.925970 | 0.462985 | − | 0.886366i | \(-0.346778\pi\) | ||||
0.462985 | + | 0.886366i | \(0.346778\pi\) | |||||||
\(230\) | 7.11019 | 0.468832 | ||||||||
\(231\) | −6.16547 | −0.405658 | ||||||||
\(232\) | 8.67188 | 0.569337 | ||||||||
\(233\) | −2.70680 | −0.177329 | −0.0886643 | − | 0.996062i | \(-0.528260\pi\) | ||||
−0.0886643 | + | 0.996062i | \(0.528260\pi\) | |||||||
\(234\) | 2.22500 | 0.145453 | ||||||||
\(235\) | −12.7551 | −0.832049 | ||||||||
\(236\) | −3.95287 | −0.257310 | ||||||||
\(237\) | −2.16380 | −0.140554 | ||||||||
\(238\) | −16.0141 | −1.03804 | ||||||||
\(239\) | −28.1731 | −1.82237 | −0.911183 | − | 0.412002i | \(-0.864830\pi\) | ||||
−0.911183 | + | 0.412002i | \(0.864830\pi\) | |||||||
\(240\) | 7.63378 | 0.492759 | ||||||||
\(241\) | −18.4455 | −1.18818 | −0.594091 | − | 0.804398i | \(-0.702488\pi\) | ||||
−0.594091 | + | 0.804398i | \(0.702488\pi\) | |||||||
\(242\) | −1.31671 | −0.0846413 | ||||||||
\(243\) | −18.2049 | −1.16784 | ||||||||
\(244\) | 2.32024 | 0.148538 | ||||||||
\(245\) | −0.525367 | −0.0335644 | ||||||||
\(246\) | 31.5266 | 2.01007 | ||||||||
\(247\) | −0.823772 | −0.0524154 | ||||||||
\(248\) | −21.0608 | −1.33736 | ||||||||
\(249\) | 0.248888 | 0.0157727 | ||||||||
\(250\) | 1.31671 | 0.0832760 | ||||||||
\(251\) | −0.411540 | −0.0259761 | −0.0129881 | − | 0.999916i | \(-0.504134\pi\) | ||||
−0.0129881 | + | 0.999916i | \(0.504134\pi\) | |||||||
\(252\) | −1.49840 | −0.0943903 | ||||||||
\(253\) | −5.39996 | −0.339493 | ||||||||
\(254\) | 11.1605 | 0.700274 | ||||||||
\(255\) | −9.96438 | −0.623994 | ||||||||
\(256\) | −6.27230 | −0.392019 | ||||||||
\(257\) | −14.4753 | −0.902944 | −0.451472 | − | 0.892285i | \(-0.649101\pi\) | ||||
−0.451472 | + | 0.892285i | \(0.649101\pi\) | |||||||
\(258\) | −30.6012 | −1.90515 | ||||||||
\(259\) | 23.0579 | 1.43275 | ||||||||
\(260\) | −0.219350 | −0.0136035 | ||||||||
\(261\) | 5.96133 | 0.368997 | ||||||||
\(262\) | −14.0919 | −0.870602 | ||||||||
\(263\) | 4.91687 | 0.303187 | 0.151594 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151594 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(264\) | −6.70664 | −0.412765 | ||||||||
\(265\) | −2.37381 | −0.145822 | ||||||||
\(266\) | −3.61205 | −0.221469 | ||||||||
\(267\) | 25.0894 | 1.53545 | ||||||||
\(268\) | 2.71020 | 0.165552 | ||||||||
\(269\) | 11.4936 | 0.700778 | 0.350389 | − | 0.936604i | \(-0.386049\pi\) | ||||
0.350389 | + | 0.936604i | \(0.386049\pi\) | |||||||
\(270\) | −2.80746 | −0.170856 | ||||||||
\(271\) | −18.6741 | −1.13437 | −0.567185 | − | 0.823591i | \(-0.691967\pi\) | ||||
−0.567185 | + | 0.823591i | \(0.691967\pi\) | |||||||
\(272\) | −15.0586 | −0.913064 | ||||||||
\(273\) | −5.07894 | −0.307391 | ||||||||
\(274\) | −25.4051 | −1.53478 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −3.23165 | −0.194522 | ||||||||
\(277\) | −10.3277 | −0.620529 | −0.310265 | − | 0.950650i | \(-0.600418\pi\) | ||||
−0.310265 | + | 0.950650i | \(0.600418\pi\) | |||||||
\(278\) | −7.00967 | −0.420412 | ||||||||
\(279\) | −14.4779 | −0.866768 | ||||||||
\(280\) | −8.18590 | −0.489201 | ||||||||
\(281\) | −19.5032 | −1.16346 | −0.581732 | − | 0.813380i | \(-0.697625\pi\) | ||||
−0.581732 | + | 0.813380i | \(0.697625\pi\) | |||||||
\(282\) | −37.7464 | −2.24776 | ||||||||
\(283\) | 6.51668 | 0.387376 | 0.193688 | − | 0.981063i | \(-0.437955\pi\) | ||||
0.193688 | + | 0.981063i | \(0.437955\pi\) | |||||||
\(284\) | −1.98755 | −0.117939 | ||||||||
\(285\) | −2.24751 | −0.133131 | ||||||||
\(286\) | −1.08467 | −0.0641378 | ||||||||
\(287\) | −29.2246 | −1.72508 | ||||||||
\(288\) | −3.06834 | −0.180803 | ||||||||
\(289\) | 2.65604 | 0.156237 | ||||||||
\(290\) | 3.82649 | 0.224699 | ||||||||
\(291\) | 33.8528 | 1.98449 | ||||||||
\(292\) | 0.212445 | 0.0124324 | ||||||||
\(293\) | −2.06584 | −0.120687 | −0.0603437 | − | 0.998178i | \(-0.519220\pi\) | ||||
−0.0603437 | + | 0.998178i | \(0.519220\pi\) | |||||||
\(294\) | −1.55473 | −0.0906737 | ||||||||
\(295\) | −14.8451 | −0.864312 | ||||||||
\(296\) | 25.0818 | 1.45785 | ||||||||
\(297\) | 2.13218 | 0.123721 | ||||||||
\(298\) | 23.4166 | 1.35649 | ||||||||
\(299\) | −4.44834 | −0.257254 | ||||||||
\(300\) | −0.598458 | −0.0345520 | ||||||||
\(301\) | 28.3668 | 1.63503 | ||||||||
\(302\) | 12.7798 | 0.735392 | ||||||||
\(303\) | 3.69174 | 0.212085 | ||||||||
\(304\) | −3.39655 | −0.194805 | ||||||||
\(305\) | 8.71368 | 0.498944 | ||||||||
\(306\) | −11.9749 | −0.684558 | ||||||||
\(307\) | 6.49853 | 0.370890 | 0.185445 | − | 0.982655i | \(-0.440627\pi\) | ||||
0.185445 | + | 0.982655i | \(0.440627\pi\) | |||||||
\(308\) | 0.730457 | 0.0416217 | ||||||||
\(309\) | −42.2175 | −2.40167 | ||||||||
\(310\) | −9.29313 | −0.527815 | ||||||||
\(311\) | 17.2796 | 0.979834 | 0.489917 | − | 0.871769i | \(-0.337027\pi\) | ||||
0.489917 | + | 0.871769i | \(0.337027\pi\) | |||||||
\(312\) | −5.52474 | −0.312777 | ||||||||
\(313\) | −22.9407 | −1.29669 | −0.648343 | − | 0.761348i | \(-0.724538\pi\) | ||||
−0.648343 | + | 0.761348i | \(0.724538\pi\) | |||||||
\(314\) | −8.93098 | −0.504004 | ||||||||
\(315\) | −5.62726 | −0.317060 | ||||||||
\(316\) | 0.256357 | 0.0144212 | ||||||||
\(317\) | −16.4474 | −0.923778 | −0.461889 | − | 0.886938i | \(-0.652828\pi\) | ||||
−0.461889 | + | 0.886938i | \(0.652828\pi\) | |||||||
\(318\) | −7.02487 | −0.393935 | ||||||||
\(319\) | −2.90610 | −0.162710 | ||||||||
\(320\) | −8.76261 | −0.489845 | ||||||||
\(321\) | −42.7911 | −2.38837 | ||||||||
\(322\) | −19.5049 | −1.08697 | ||||||||
\(323\) | 4.43351 | 0.246687 | ||||||||
\(324\) | 2.91466 | 0.161926 | ||||||||
\(325\) | −0.823772 | −0.0456946 | ||||||||
\(326\) | 22.0192 | 1.21953 | ||||||||
\(327\) | 37.6892 | 2.08422 | ||||||||
\(328\) | −31.7898 | −1.75530 | ||||||||
\(329\) | 34.9902 | 1.92907 | ||||||||
\(330\) | −2.95932 | −0.162905 | ||||||||
\(331\) | −30.8271 | −1.69441 | −0.847206 | − | 0.531265i | \(-0.821717\pi\) | ||||
−0.847206 | + | 0.531265i | \(0.821717\pi\) | |||||||
\(332\) | −0.0294872 | −0.00161832 | ||||||||
\(333\) | 17.2420 | 0.944857 | ||||||||
\(334\) | 11.9263 | 0.652579 | ||||||||
\(335\) | 10.1782 | 0.556093 | ||||||||
\(336\) | −20.9413 | −1.14244 | ||||||||
\(337\) | −18.9430 | −1.03189 | −0.515946 | − | 0.856621i | \(-0.672559\pi\) | ||||
−0.515946 | + | 0.856621i | \(0.672559\pi\) | |||||||
\(338\) | 16.2237 | 0.882453 | ||||||||
\(339\) | 24.3389 | 1.32191 | ||||||||
\(340\) | 1.18054 | 0.0640235 | ||||||||
\(341\) | 7.05785 | 0.382204 | ||||||||
\(342\) | −2.70099 | −0.146053 | ||||||||
\(343\) | −17.7615 | −0.959029 | ||||||||
\(344\) | 30.8566 | 1.66368 | ||||||||
\(345\) | −12.1365 | −0.653407 | ||||||||
\(346\) | −11.2967 | −0.607313 | ||||||||
\(347\) | −2.14728 | −0.115272 | −0.0576361 | − | 0.998338i | \(-0.518356\pi\) | ||||
−0.0576361 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(348\) | −1.73918 | −0.0932297 | ||||||||
\(349\) | 4.95553 | 0.265264 | 0.132632 | − | 0.991165i | \(-0.457657\pi\) | ||||
0.132632 | + | 0.991165i | \(0.457657\pi\) | |||||||
\(350\) | −3.61205 | −0.193072 | ||||||||
\(351\) | 1.75643 | 0.0937512 | ||||||||
\(352\) | 1.49579 | 0.0797258 | ||||||||
\(353\) | 27.1851 | 1.44692 | 0.723459 | − | 0.690367i | \(-0.242551\pi\) | ||||
0.723459 | + | 0.690367i | \(0.242551\pi\) | |||||||
\(354\) | −43.9313 | −2.33492 | ||||||||
\(355\) | −7.46427 | −0.396162 | ||||||||
\(356\) | −2.97248 | −0.157541 | ||||||||
\(357\) | 27.3347 | 1.44671 | ||||||||
\(358\) | 12.0309 | 0.635852 | ||||||||
\(359\) | −4.00177 | −0.211205 | −0.105603 | − | 0.994408i | \(-0.533677\pi\) | ||||
−0.105603 | + | 0.994408i | \(0.533677\pi\) | |||||||
\(360\) | −6.12119 | −0.322615 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 24.2068 | 1.27228 | ||||||||
\(363\) | 2.24751 | 0.117964 | ||||||||
\(364\) | 0.601730 | 0.0315392 | ||||||||
\(365\) | 0.797840 | 0.0417608 | ||||||||
\(366\) | 25.7866 | 1.34789 | ||||||||
\(367\) | −21.6919 | −1.13231 | −0.566153 | − | 0.824300i | \(-0.691569\pi\) | ||||
−0.566153 | + | 0.824300i | \(0.691569\pi\) | |||||||
\(368\) | −18.3412 | −0.956103 | ||||||||
\(369\) | −21.8534 | −1.13764 | ||||||||
\(370\) | 11.0674 | 0.575367 | ||||||||
\(371\) | 6.51193 | 0.338083 | ||||||||
\(372\) | 4.22382 | 0.218995 | ||||||||
\(373\) | −25.8940 | −1.34074 | −0.670371 | − | 0.742026i | \(-0.733865\pi\) | ||||
−0.670371 | + | 0.742026i | \(0.733865\pi\) | |||||||
\(374\) | 5.83765 | 0.301858 | ||||||||
\(375\) | −2.24751 | −0.116061 | ||||||||
\(376\) | 38.0615 | 1.96287 | ||||||||
\(377\) | −2.39396 | −0.123295 | ||||||||
\(378\) | 7.70153 | 0.396124 | ||||||||
\(379\) | 21.6754 | 1.11339 | 0.556694 | − | 0.830718i | \(-0.312070\pi\) | ||||
0.556694 | + | 0.830718i | \(0.312070\pi\) | |||||||
\(380\) | 0.266275 | 0.0136596 | ||||||||
\(381\) | −19.0501 | −0.975966 | ||||||||
\(382\) | 6.21747 | 0.318113 | ||||||||
\(383\) | −7.45213 | −0.380786 | −0.190393 | − | 0.981708i | \(-0.560976\pi\) | ||||
−0.190393 | + | 0.981708i | \(0.560976\pi\) | |||||||
\(384\) | −19.2078 | −0.980194 | ||||||||
\(385\) | 2.74324 | 0.139808 | ||||||||
\(386\) | −4.21352 | −0.214463 | ||||||||
\(387\) | 21.2119 | 1.07826 | ||||||||
\(388\) | −4.01073 | −0.203614 | ||||||||
\(389\) | −15.9821 | −0.810323 | −0.405162 | − | 0.914245i | \(-0.632785\pi\) | ||||
−0.405162 | + | 0.914245i | \(0.632785\pi\) | |||||||
\(390\) | −2.43781 | −0.123443 | ||||||||
\(391\) | 23.9408 | 1.21074 | ||||||||
\(392\) | 1.56771 | 0.0791812 | ||||||||
\(393\) | 24.0537 | 1.21335 | ||||||||
\(394\) | 22.0856 | 1.11266 | ||||||||
\(395\) | 0.962752 | 0.0484413 | ||||||||
\(396\) | 0.546215 | 0.0274484 | ||||||||
\(397\) | −29.8765 | −1.49946 | −0.749729 | − | 0.661746i | \(-0.769816\pi\) | ||||
−0.749729 | + | 0.661746i | \(0.769816\pi\) | |||||||
\(398\) | 2.32311 | 0.116447 | ||||||||
\(399\) | 6.16547 | 0.308660 | ||||||||
\(400\) | −3.39655 | −0.169827 | ||||||||
\(401\) | 7.73230 | 0.386133 | 0.193066 | − | 0.981186i | \(-0.438157\pi\) | ||||
0.193066 | + | 0.981186i | \(0.438157\pi\) | |||||||
\(402\) | 30.1205 | 1.50227 | ||||||||
\(403\) | 5.81406 | 0.289619 | ||||||||
\(404\) | −0.437381 | −0.0217605 | ||||||||
\(405\) | 10.9460 | 0.543914 | ||||||||
\(406\) | −10.4970 | −0.520956 | ||||||||
\(407\) | −8.40534 | −0.416637 | ||||||||
\(408\) | 29.7340 | 1.47205 | ||||||||
\(409\) | −25.9708 | −1.28417 | −0.642087 | − | 0.766632i | \(-0.721931\pi\) | ||||
−0.642087 | + | 0.766632i | \(0.721931\pi\) | |||||||
\(410\) | −14.0273 | −0.692761 | ||||||||
\(411\) | 43.3644 | 2.13901 | ||||||||
\(412\) | 5.00174 | 0.246418 | ||||||||
\(413\) | 40.7235 | 2.00387 | ||||||||
\(414\) | −14.5852 | −0.716826 | ||||||||
\(415\) | −0.110739 | −0.00543599 | ||||||||
\(416\) | 1.23219 | 0.0604130 | ||||||||
\(417\) | 11.9649 | 0.585925 | ||||||||
\(418\) | 1.31671 | 0.0644024 | ||||||||
\(419\) | −7.42032 | −0.362507 | −0.181253 | − | 0.983436i | \(-0.558015\pi\) | ||||
−0.181253 | + | 0.983436i | \(0.558015\pi\) | |||||||
\(420\) | 1.64171 | 0.0801074 | ||||||||
\(421\) | 16.8440 | 0.820928 | 0.410464 | − | 0.911877i | \(-0.365367\pi\) | ||||
0.410464 | + | 0.911877i | \(0.365367\pi\) | |||||||
\(422\) | −31.3838 | −1.52774 | ||||||||
\(423\) | 26.1647 | 1.27217 | ||||||||
\(424\) | 7.08351 | 0.344006 | ||||||||
\(425\) | 4.43351 | 0.215057 | ||||||||
\(426\) | −22.0892 | −1.07022 | ||||||||
\(427\) | −23.9037 | −1.15678 | ||||||||
\(428\) | 5.06970 | 0.245053 | ||||||||
\(429\) | 1.85144 | 0.0893883 | ||||||||
\(430\) | 13.6156 | 0.656601 | ||||||||
\(431\) | 1.56149 | 0.0752144 | 0.0376072 | − | 0.999293i | \(-0.488026\pi\) | ||||
0.0376072 | + | 0.999293i | \(0.488026\pi\) | |||||||
\(432\) | 7.24204 | 0.348433 | ||||||||
\(433\) | 30.7097 | 1.47581 | 0.737907 | − | 0.674902i | \(-0.235814\pi\) | ||||
0.737907 | + | 0.674902i | \(0.235814\pi\) | |||||||
\(434\) | 25.4933 | 1.22372 | ||||||||
\(435\) | −6.53150 | −0.313161 | ||||||||
\(436\) | −4.46525 | −0.213847 | ||||||||
\(437\) | 5.39996 | 0.258315 | ||||||||
\(438\) | 2.36106 | 0.112816 | ||||||||
\(439\) | −38.5063 | −1.83781 | −0.918903 | − | 0.394484i | \(-0.870923\pi\) | ||||
−0.918903 | + | 0.394484i | \(0.870923\pi\) | |||||||
\(440\) | 2.98403 | 0.142258 | ||||||||
\(441\) | 1.07769 | 0.0513188 | ||||||||
\(442\) | 4.80889 | 0.228736 | ||||||||
\(443\) | 21.8516 | 1.03820 | 0.519101 | − | 0.854713i | \(-0.326267\pi\) | ||||
0.519101 | + | 0.854713i | \(0.326267\pi\) | |||||||
\(444\) | −5.03024 | −0.238725 | ||||||||
\(445\) | −11.1632 | −0.529186 | ||||||||
\(446\) | 17.6578 | 0.836122 | ||||||||
\(447\) | −39.9703 | −1.89053 | ||||||||
\(448\) | 24.0379 | 1.13569 | ||||||||
\(449\) | −6.60543 | −0.311730 | −0.155865 | − | 0.987778i | \(-0.549816\pi\) | ||||
−0.155865 | + | 0.987778i | \(0.549816\pi\) | |||||||
\(450\) | −2.70099 | −0.127326 | ||||||||
\(451\) | 10.6533 | 0.501646 | ||||||||
\(452\) | −2.88356 | −0.135631 | ||||||||
\(453\) | −21.8140 | −1.02491 | ||||||||
\(454\) | −5.83730 | −0.273958 | ||||||||
\(455\) | 2.25980 | 0.105941 | ||||||||
\(456\) | 6.70664 | 0.314067 | ||||||||
\(457\) | 6.48912 | 0.303548 | 0.151774 | − | 0.988415i | \(-0.451501\pi\) | ||||
0.151774 | + | 0.988415i | \(0.451501\pi\) | |||||||
\(458\) | −18.4504 | −0.862129 | ||||||||
\(459\) | −9.45303 | −0.441230 | ||||||||
\(460\) | 1.43788 | 0.0670414 | ||||||||
\(461\) | 33.7065 | 1.56987 | 0.784933 | − | 0.619580i | \(-0.212697\pi\) | ||||
0.784933 | + | 0.619580i | \(0.212697\pi\) | |||||||
\(462\) | 8.11813 | 0.377690 | ||||||||
\(463\) | 12.0591 | 0.560436 | 0.280218 | − | 0.959936i | \(-0.409593\pi\) | ||||
0.280218 | + | 0.959936i | \(0.409593\pi\) | |||||||
\(464\) | −9.87070 | −0.458236 | ||||||||
\(465\) | 15.8626 | 0.735611 | ||||||||
\(466\) | 3.56408 | 0.165103 | ||||||||
\(467\) | 7.68943 | 0.355824 | 0.177912 | − | 0.984046i | \(-0.443066\pi\) | ||||
0.177912 | + | 0.984046i | \(0.443066\pi\) | |||||||
\(468\) | 0.449957 | 0.0207993 | ||||||||
\(469\) | −27.9212 | −1.28928 | ||||||||
\(470\) | 16.7947 | 0.774683 | ||||||||
\(471\) | 15.2444 | 0.702427 | ||||||||
\(472\) | 44.2980 | 2.03898 | ||||||||
\(473\) | −10.3406 | −0.475461 | ||||||||
\(474\) | 2.84909 | 0.130863 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | −3.23849 | −0.148436 | ||||||||
\(477\) | 4.86944 | 0.222956 | ||||||||
\(478\) | 37.0958 | 1.69672 | ||||||||
\(479\) | 11.8771 | 0.542680 | 0.271340 | − | 0.962484i | \(-0.412533\pi\) | ||||
0.271340 | + | 0.962484i | \(0.412533\pi\) | |||||||
\(480\) | 3.36180 | 0.153445 | ||||||||
\(481\) | −6.92409 | −0.315711 | ||||||||
\(482\) | 24.2874 | 1.10626 | ||||||||
\(483\) | 33.2933 | 1.51490 | ||||||||
\(484\) | −0.266275 | −0.0121034 | ||||||||
\(485\) | −15.0623 | −0.683946 | ||||||||
\(486\) | 23.9705 | 1.08732 | ||||||||
\(487\) | 20.8445 | 0.944556 | 0.472278 | − | 0.881450i | \(-0.343432\pi\) | ||||
0.472278 | + | 0.881450i | \(0.343432\pi\) | |||||||
\(488\) | −26.0019 | −1.17705 | ||||||||
\(489\) | −37.5849 | −1.69965 | ||||||||
\(490\) | 0.691755 | 0.0312503 | ||||||||
\(491\) | −16.4510 | −0.742425 | −0.371212 | − | 0.928548i | \(-0.621058\pi\) | ||||
−0.371212 | + | 0.928548i | \(0.621058\pi\) | |||||||
\(492\) | 6.37557 | 0.287433 | ||||||||
\(493\) | 12.8842 | 0.580277 | ||||||||
\(494\) | 1.08467 | 0.0488015 | ||||||||
\(495\) | 2.05132 | 0.0921999 | ||||||||
\(496\) | 23.9723 | 1.07639 | ||||||||
\(497\) | 20.4763 | 0.918486 | ||||||||
\(498\) | −0.327714 | −0.0146852 | ||||||||
\(499\) | −5.40939 | −0.242158 | −0.121079 | − | 0.992643i | \(-0.538635\pi\) | ||||
−0.121079 | + | 0.992643i | \(0.538635\pi\) | |||||||
\(500\) | 0.266275 | 0.0119082 | ||||||||
\(501\) | −20.3572 | −0.909494 | ||||||||
\(502\) | 0.541878 | 0.0241852 | ||||||||
\(503\) | −2.39558 | −0.106814 | −0.0534068 | − | 0.998573i | \(-0.517008\pi\) | ||||
−0.0534068 | + | 0.998573i | \(0.517008\pi\) | |||||||
\(504\) | 16.7919 | 0.747970 | ||||||||
\(505\) | −1.64259 | −0.0730943 | ||||||||
\(506\) | 7.11019 | 0.316086 | ||||||||
\(507\) | −27.6925 | −1.22987 | ||||||||
\(508\) | 2.25697 | 0.100137 | ||||||||
\(509\) | −10.7037 | −0.474435 | −0.237217 | − | 0.971457i | \(-0.576235\pi\) | ||||
−0.237217 | + | 0.971457i | \(0.576235\pi\) | |||||||
\(510\) | 13.1202 | 0.580972 | ||||||||
\(511\) | −2.18867 | −0.0968209 | ||||||||
\(512\) | 25.3513 | 1.12038 | ||||||||
\(513\) | −2.13218 | −0.0941379 | ||||||||
\(514\) | 19.0598 | 0.840690 | ||||||||
\(515\) | 18.7841 | 0.827726 | ||||||||
\(516\) | −6.18841 | −0.272430 | ||||||||
\(517\) | −12.7551 | −0.560967 | ||||||||
\(518\) | −30.3605 | −1.33397 | ||||||||
\(519\) | 19.2825 | 0.846407 | ||||||||
\(520\) | 2.45816 | 0.107797 | ||||||||
\(521\) | 41.3484 | 1.81151 | 0.905754 | − | 0.423805i | \(-0.139306\pi\) | ||||
0.905754 | + | 0.423805i | \(0.139306\pi\) | |||||||
\(522\) | −7.84935 | −0.343557 | ||||||||
\(523\) | 26.7932 | 1.17158 | 0.585792 | − | 0.810461i | \(-0.300783\pi\) | ||||
0.585792 | + | 0.810461i | \(0.300783\pi\) | |||||||
\(524\) | −2.84978 | −0.124493 | ||||||||
\(525\) | 6.16547 | 0.269083 | ||||||||
\(526\) | −6.47409 | −0.282284 | ||||||||
\(527\) | −31.2910 | −1.36306 | ||||||||
\(528\) | 7.63378 | 0.332218 | ||||||||
\(529\) | 6.15961 | 0.267809 | ||||||||
\(530\) | 3.12562 | 0.135768 | ||||||||
\(531\) | 30.4519 | 1.32150 | ||||||||
\(532\) | −0.730457 | −0.0316693 | ||||||||
\(533\) | 8.77591 | 0.380127 | ||||||||
\(534\) | −33.0355 | −1.42959 | ||||||||
\(535\) | 19.0393 | 0.823141 | ||||||||
\(536\) | −30.3719 | −1.31187 | ||||||||
\(537\) | −20.5357 | −0.886181 | ||||||||
\(538\) | −15.1337 | −0.652462 | ||||||||
\(539\) | −0.525367 | −0.0226291 | ||||||||
\(540\) | −0.567746 | −0.0244319 | ||||||||
\(541\) | 4.24816 | 0.182643 | 0.0913214 | − | 0.995821i | \(-0.470891\pi\) | ||||
0.0913214 | + | 0.995821i | \(0.470891\pi\) | |||||||
\(542\) | 24.5883 | 1.05616 | ||||||||
\(543\) | −41.3190 | −1.77317 | ||||||||
\(544\) | −6.63159 | −0.284327 | ||||||||
\(545\) | −16.7693 | −0.718318 | ||||||||
\(546\) | 6.68749 | 0.286198 | ||||||||
\(547\) | −34.9167 | −1.49293 | −0.746466 | − | 0.665424i | \(-0.768251\pi\) | ||||
−0.746466 | + | 0.665424i | \(0.768251\pi\) | |||||||
\(548\) | −5.13762 | −0.219468 | ||||||||
\(549\) | −17.8745 | −0.762866 | ||||||||
\(550\) | 1.31671 | 0.0561447 | ||||||||
\(551\) | 2.90610 | 0.123804 | ||||||||
\(552\) | 36.2156 | 1.54144 | ||||||||
\(553\) | −2.64106 | −0.112309 | ||||||||
\(554\) | 13.5985 | 0.577746 | ||||||||
\(555\) | −18.8911 | −0.801884 | ||||||||
\(556\) | −1.41755 | −0.0601175 | ||||||||
\(557\) | 15.7363 | 0.666768 | 0.333384 | − | 0.942791i | \(-0.391809\pi\) | ||||
0.333384 | + | 0.942791i | \(0.391809\pi\) | |||||||
\(558\) | 19.0632 | 0.807008 | ||||||||
\(559\) | −8.51830 | −0.360286 | ||||||||
\(560\) | 9.31754 | 0.393738 | ||||||||
\(561\) | −9.96438 | −0.420696 | ||||||||
\(562\) | 25.6801 | 1.08325 | ||||||||
\(563\) | 25.6865 | 1.08256 | 0.541278 | − | 0.840844i | \(-0.317941\pi\) | ||||
0.541278 | + | 0.840844i | \(0.317941\pi\) | |||||||
\(564\) | −7.63337 | −0.321423 | ||||||||
\(565\) | −10.8292 | −0.455589 | ||||||||
\(566\) | −8.58058 | −0.360669 | ||||||||
\(567\) | −30.0276 | −1.26104 | ||||||||
\(568\) | 22.2736 | 0.934578 | ||||||||
\(569\) | −7.78096 | −0.326195 | −0.163097 | − | 0.986610i | \(-0.552149\pi\) | ||||
−0.163097 | + | 0.986610i | \(0.552149\pi\) | |||||||
\(570\) | 2.95932 | 0.123952 | ||||||||
\(571\) | −3.39607 | −0.142121 | −0.0710605 | − | 0.997472i | \(-0.522638\pi\) | ||||
−0.0710605 | + | 0.997472i | \(0.522638\pi\) | |||||||
\(572\) | −0.219350 | −0.00917149 | ||||||||
\(573\) | −10.6127 | −0.443352 | ||||||||
\(574\) | 38.4804 | 1.60614 | ||||||||
\(575\) | 5.39996 | 0.225194 | ||||||||
\(576\) | 17.9749 | 0.748954 | ||||||||
\(577\) | 26.6095 | 1.10777 | 0.553885 | − | 0.832593i | \(-0.313145\pi\) | ||||
0.553885 | + | 0.832593i | \(0.313145\pi\) | |||||||
\(578\) | −3.49723 | −0.145466 | ||||||||
\(579\) | 7.19213 | 0.298895 | ||||||||
\(580\) | 0.773823 | 0.0321312 | ||||||||
\(581\) | 0.303785 | 0.0126031 | ||||||||
\(582\) | −44.5744 | −1.84767 | ||||||||
\(583\) | −2.37381 | −0.0983132 | ||||||||
\(584\) | −2.38077 | −0.0985172 | ||||||||
\(585\) | 1.68982 | 0.0698654 | ||||||||
\(586\) | 2.72011 | 0.112367 | ||||||||
\(587\) | 40.0612 | 1.65350 | 0.826751 | − | 0.562568i | \(-0.190186\pi\) | ||||
0.826751 | + | 0.562568i | \(0.190186\pi\) | |||||||
\(588\) | −0.314410 | −0.0129660 | ||||||||
\(589\) | −7.05785 | −0.290813 | ||||||||
\(590\) | 19.5466 | 0.804722 | ||||||||
\(591\) | −37.6983 | −1.55070 | ||||||||
\(592\) | −28.5491 | −1.17336 | ||||||||
\(593\) | 13.6756 | 0.561590 | 0.280795 | − | 0.959768i | \(-0.409402\pi\) | ||||
0.280795 | + | 0.959768i | \(0.409402\pi\) | |||||||
\(594\) | −2.80746 | −0.115191 | ||||||||
\(595\) | −12.1622 | −0.498601 | ||||||||
\(596\) | 4.73550 | 0.193974 | ||||||||
\(597\) | −3.96536 | −0.162291 | ||||||||
\(598\) | 5.85717 | 0.239518 | ||||||||
\(599\) | −19.1403 | −0.782051 | −0.391026 | − | 0.920380i | \(-0.627880\pi\) | ||||
−0.391026 | + | 0.920380i | \(0.627880\pi\) | |||||||
\(600\) | 6.70664 | 0.273797 | ||||||||
\(601\) | −28.2509 | −1.15238 | −0.576189 | − | 0.817316i | \(-0.695461\pi\) | ||||
−0.576189 | + | 0.817316i | \(0.695461\pi\) | |||||||
\(602\) | −37.3508 | −1.52230 | ||||||||
\(603\) | −20.8787 | −0.850244 | ||||||||
\(604\) | 2.58442 | 0.105159 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −4.86095 | −0.197463 | ||||||||
\(607\) | 11.6697 | 0.473660 | 0.236830 | − | 0.971551i | \(-0.423892\pi\) | ||||
0.236830 | + | 0.971551i | \(0.423892\pi\) | |||||||
\(608\) | −1.49579 | −0.0606622 | ||||||||
\(609\) | 17.9175 | 0.726053 | ||||||||
\(610\) | −11.4734 | −0.464544 | ||||||||
\(611\) | −10.5073 | −0.425078 | ||||||||
\(612\) | −2.42165 | −0.0978895 | ||||||||
\(613\) | 28.0921 | 1.13463 | 0.567314 | − | 0.823502i | \(-0.307983\pi\) | ||||
0.567314 | + | 0.823502i | \(0.307983\pi\) | |||||||
\(614\) | −8.55667 | −0.345319 | ||||||||
\(615\) | 23.9435 | 0.965495 | ||||||||
\(616\) | −8.18590 | −0.329819 | ||||||||
\(617\) | 20.7862 | 0.836822 | 0.418411 | − | 0.908258i | \(-0.362587\pi\) | ||||
0.418411 | + | 0.908258i | \(0.362587\pi\) | |||||||
\(618\) | 55.5882 | 2.23609 | ||||||||
\(619\) | 44.7320 | 1.79793 | 0.898965 | − | 0.438021i | \(-0.144321\pi\) | ||||
0.898965 | + | 0.438021i | \(0.144321\pi\) | |||||||
\(620\) | −1.87933 | −0.0754757 | ||||||||
\(621\) | −11.5137 | −0.462028 | ||||||||
\(622\) | −22.7522 | −0.912279 | ||||||||
\(623\) | 30.6233 | 1.22690 | ||||||||
\(624\) | 6.28850 | 0.251741 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 30.2063 | 1.20729 | ||||||||
\(627\) | −2.24751 | −0.0897570 | ||||||||
\(628\) | −1.80609 | −0.0720710 | ||||||||
\(629\) | 37.2652 | 1.48586 | ||||||||
\(630\) | 7.40946 | 0.295200 | ||||||||
\(631\) | −5.71483 | −0.227504 | −0.113752 | − | 0.993509i | \(-0.536287\pi\) | ||||
−0.113752 | + | 0.993509i | \(0.536287\pi\) | |||||||
\(632\) | −2.87288 | −0.114277 | ||||||||
\(633\) | 53.5695 | 2.12920 | ||||||||
\(634\) | 21.6565 | 0.860088 | ||||||||
\(635\) | 8.47608 | 0.336363 | ||||||||
\(636\) | −1.42062 | −0.0563314 | ||||||||
\(637\) | −0.432782 | −0.0171475 | ||||||||
\(638\) | 3.82649 | 0.151492 | ||||||||
\(639\) | 15.3116 | 0.605717 | ||||||||
\(640\) | 8.54624 | 0.337820 | ||||||||
\(641\) | 9.13627 | 0.360861 | 0.180431 | − | 0.983588i | \(-0.442251\pi\) | ||||
0.180431 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(642\) | 56.3434 | 2.22370 | ||||||||
\(643\) | 38.5090 | 1.51865 | 0.759324 | − | 0.650712i | \(-0.225530\pi\) | ||||
0.759324 | + | 0.650712i | \(0.225530\pi\) | |||||||
\(644\) | −3.94444 | −0.155433 | ||||||||
\(645\) | −23.2406 | −0.915099 | ||||||||
\(646\) | −5.83765 | −0.229679 | ||||||||
\(647\) | 5.06693 | 0.199202 | 0.0996009 | − | 0.995027i | \(-0.468243\pi\) | ||||
0.0996009 | + | 0.995027i | \(0.468243\pi\) | |||||||
\(648\) | −32.6633 | −1.28314 | ||||||||
\(649\) | −14.8451 | −0.582719 | ||||||||
\(650\) | 1.08467 | 0.0425442 | ||||||||
\(651\) | −43.5149 | −1.70548 | ||||||||
\(652\) | 4.45289 | 0.174389 | ||||||||
\(653\) | −43.3175 | −1.69515 | −0.847573 | − | 0.530678i | \(-0.821937\pi\) | ||||
−0.847573 | + | 0.530678i | \(0.821937\pi\) | |||||||
\(654\) | −49.6258 | −1.94052 | ||||||||
\(655\) | −10.7024 | −0.418177 | ||||||||
\(656\) | 36.1845 | 1.41277 | ||||||||
\(657\) | −1.63662 | −0.0638507 | ||||||||
\(658\) | −46.0720 | −1.79607 | ||||||||
\(659\) | 48.8179 | 1.90168 | 0.950838 | − | 0.309689i | \(-0.100225\pi\) | ||||
0.950838 | + | 0.309689i | \(0.100225\pi\) | |||||||
\(660\) | −0.598458 | −0.0232949 | ||||||||
\(661\) | 3.07287 | 0.119521 | 0.0597605 | − | 0.998213i | \(-0.480966\pi\) | ||||
0.0597605 | + | 0.998213i | \(0.480966\pi\) | |||||||
\(662\) | 40.5904 | 1.57759 | ||||||||
\(663\) | −8.20838 | −0.318787 | ||||||||
\(664\) | 0.330449 | 0.0128239 | ||||||||
\(665\) | −2.74324 | −0.106378 | ||||||||
\(666\) | −22.7027 | −0.879714 | ||||||||
\(667\) | 15.6928 | 0.607629 | ||||||||
\(668\) | 2.41183 | 0.0933166 | ||||||||
\(669\) | −30.1404 | −1.16530 | ||||||||
\(670\) | −13.4017 | −0.517752 | ||||||||
\(671\) | 8.71368 | 0.336388 | ||||||||
\(672\) | −9.22223 | −0.355755 | ||||||||
\(673\) | −21.3366 | −0.822465 | −0.411233 | − | 0.911530i | \(-0.634902\pi\) | ||||
−0.411233 | + | 0.911530i | \(0.634902\pi\) | |||||||
\(674\) | 24.9424 | 0.960747 | ||||||||
\(675\) | −2.13218 | −0.0820675 | ||||||||
\(676\) | 3.28089 | 0.126188 | ||||||||
\(677\) | −16.2317 | −0.623836 | −0.311918 | − | 0.950109i | \(-0.600971\pi\) | ||||
−0.311918 | + | 0.950109i | \(0.600971\pi\) | |||||||
\(678\) | −32.0472 | −1.23077 | ||||||||
\(679\) | 41.3196 | 1.58570 | ||||||||
\(680\) | −13.2297 | −0.507337 | ||||||||
\(681\) | 9.96379 | 0.381813 | ||||||||
\(682\) | −9.29313 | −0.355853 | ||||||||
\(683\) | 13.0211 | 0.498238 | 0.249119 | − | 0.968473i | \(-0.419859\pi\) | ||||
0.249119 | + | 0.968473i | \(0.419859\pi\) | |||||||
\(684\) | −0.546215 | −0.0208851 | ||||||||
\(685\) | −19.2944 | −0.737201 | ||||||||
\(686\) | 23.3867 | 0.892909 | ||||||||
\(687\) | 31.4932 | 1.20154 | ||||||||
\(688\) | −35.1223 | −1.33903 | ||||||||
\(689\) | −1.95548 | −0.0744978 | ||||||||
\(690\) | 15.9802 | 0.608357 | ||||||||
\(691\) | −12.8934 | −0.490489 | −0.245245 | − | 0.969461i | \(-0.578868\pi\) | ||||
−0.245245 | + | 0.969461i | \(0.578868\pi\) | |||||||
\(692\) | −2.28450 | −0.0868437 | ||||||||
\(693\) | −5.62726 | −0.213762 | ||||||||
\(694\) | 2.82735 | 0.107325 | ||||||||
\(695\) | −5.32362 | −0.201937 | ||||||||
\(696\) | 19.4902 | 0.738773 | ||||||||
\(697\) | −47.2317 | −1.78903 | ||||||||
\(698\) | −6.52500 | −0.246975 | ||||||||
\(699\) | −6.08358 | −0.230102 | ||||||||
\(700\) | −0.730457 | −0.0276087 | ||||||||
\(701\) | −18.4505 | −0.696865 | −0.348433 | − | 0.937334i | \(-0.613286\pi\) | ||||
−0.348433 | + | 0.937334i | \(0.613286\pi\) | |||||||
\(702\) | −2.31271 | −0.0872874 | ||||||||
\(703\) | 8.40534 | 0.317014 | ||||||||
\(704\) | −8.76261 | −0.330253 | ||||||||
\(705\) | −28.6672 | −1.07967 | ||||||||
\(706\) | −35.7949 | −1.34716 | ||||||||
\(707\) | 4.50602 | 0.169466 | ||||||||
\(708\) | −8.88413 | −0.333886 | ||||||||
\(709\) | 40.8332 | 1.53352 | 0.766762 | − | 0.641932i | \(-0.221867\pi\) | ||||
0.766762 | + | 0.641932i | \(0.221867\pi\) | |||||||
\(710\) | 9.82827 | 0.368848 | ||||||||
\(711\) | −1.97491 | −0.0740649 | ||||||||
\(712\) | 33.3113 | 1.24839 | ||||||||
\(713\) | −38.1121 | −1.42731 | ||||||||
\(714\) | −35.9919 | −1.34696 | ||||||||
\(715\) | −0.823772 | −0.0308073 | ||||||||
\(716\) | 2.43298 | 0.0909247 | ||||||||
\(717\) | −63.3194 | −2.36471 | ||||||||
\(718\) | 5.26916 | 0.196643 | ||||||||
\(719\) | −45.9049 | −1.71196 | −0.855982 | − | 0.517005i | \(-0.827047\pi\) | ||||
−0.855982 | + | 0.517005i | \(0.827047\pi\) | |||||||
\(720\) | 6.96740 | 0.259660 | ||||||||
\(721\) | −51.5293 | −1.91905 | ||||||||
\(722\) | −1.31671 | −0.0490029 | ||||||||
\(723\) | −41.4566 | −1.54179 | ||||||||
\(724\) | 4.89529 | 0.181932 | ||||||||
\(725\) | 2.90610 | 0.107930 | ||||||||
\(726\) | −2.95932 | −0.109831 | ||||||||
\(727\) | 46.7486 | 1.73381 | 0.866905 | − | 0.498473i | \(-0.166106\pi\) | ||||
0.866905 | + | 0.498473i | \(0.166106\pi\) | |||||||
\(728\) | −6.74332 | −0.249924 | ||||||||
\(729\) | −8.07753 | −0.299168 | ||||||||
\(730\) | −1.05052 | −0.0388816 | ||||||||
\(731\) | 45.8452 | 1.69565 | ||||||||
\(732\) | 5.21477 | 0.192743 | ||||||||
\(733\) | 7.20742 | 0.266212 | 0.133106 | − | 0.991102i | \(-0.457505\pi\) | ||||
0.133106 | + | 0.991102i | \(0.457505\pi\) | |||||||
\(734\) | 28.5619 | 1.05424 | ||||||||
\(735\) | −1.18077 | −0.0435533 | ||||||||
\(736\) | −8.07720 | −0.297730 | ||||||||
\(737\) | 10.1782 | 0.374918 | ||||||||
\(738\) | 28.7745 | 1.05921 | ||||||||
\(739\) | −15.8711 | −0.583828 | −0.291914 | − | 0.956445i | \(-0.594292\pi\) | ||||
−0.291914 | + | 0.956445i | \(0.594292\pi\) | |||||||
\(740\) | 2.23814 | 0.0822755 | ||||||||
\(741\) | −1.85144 | −0.0680143 | ||||||||
\(742\) | −8.57432 | −0.314773 | ||||||||
\(743\) | −18.8696 | −0.692258 | −0.346129 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346129 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(744\) | −47.3344 | −1.73536 | ||||||||
\(745\) | 17.7842 | 0.651563 | ||||||||
\(746\) | 34.0949 | 1.24830 | ||||||||
\(747\) | 0.227162 | 0.00831141 | ||||||||
\(748\) | 1.18054 | 0.0431646 | ||||||||
\(749\) | −52.2294 | −1.90842 | ||||||||
\(750\) | 2.95932 | 0.108059 | ||||||||
\(751\) | 20.6044 | 0.751866 | 0.375933 | − | 0.926647i | \(-0.377322\pi\) | ||||
0.375933 | + | 0.926647i | \(0.377322\pi\) | |||||||
\(752\) | −43.3232 | −1.57983 | ||||||||
\(753\) | −0.924941 | −0.0337067 | ||||||||
\(754\) | 3.15216 | 0.114795 | ||||||||
\(755\) | 9.70582 | 0.353231 | ||||||||
\(756\) | 1.55746 | 0.0566444 | ||||||||
\(757\) | 2.85131 | 0.103633 | 0.0518164 | − | 0.998657i | \(-0.483499\pi\) | ||||
0.0518164 | + | 0.998657i | \(0.483499\pi\) | |||||||
\(758\) | −28.5402 | −1.03663 | ||||||||
\(759\) | −12.1365 | −0.440527 | ||||||||
\(760\) | −2.98403 | −0.108242 | ||||||||
\(761\) | −8.39479 | −0.304311 | −0.152155 | − | 0.988357i | \(-0.548621\pi\) | ||||
−0.152155 | + | 0.988357i | \(0.548621\pi\) | |||||||
\(762\) | 25.0835 | 0.908678 | ||||||||
\(763\) | 46.0022 | 1.66539 | ||||||||
\(764\) | 1.25735 | 0.0454892 | ||||||||
\(765\) | −9.09454 | −0.328814 | ||||||||
\(766\) | 9.81230 | 0.354533 | ||||||||
\(767\) | −12.2289 | −0.441561 | ||||||||
\(768\) | −14.0971 | −0.508685 | ||||||||
\(769\) | 2.19228 | 0.0790557 | 0.0395278 | − | 0.999218i | \(-0.487415\pi\) | ||||
0.0395278 | + | 0.999218i | \(0.487415\pi\) | |||||||
\(770\) | −3.61205 | −0.130169 | ||||||||
\(771\) | −32.5334 | −1.17166 | ||||||||
\(772\) | −0.852091 | −0.0306674 | ||||||||
\(773\) | −43.6273 | −1.56916 | −0.784582 | − | 0.620025i | \(-0.787123\pi\) | ||||
−0.784582 | + | 0.620025i | \(0.787123\pi\) | |||||||
\(774\) | −27.9299 | −1.00392 | ||||||||
\(775\) | −7.05785 | −0.253525 | ||||||||
\(776\) | 44.9465 | 1.61348 | ||||||||
\(777\) | 51.8229 | 1.85914 | ||||||||
\(778\) | 21.0437 | 0.754455 | ||||||||
\(779\) | −10.6533 | −0.381695 | ||||||||
\(780\) | −0.492993 | −0.0176520 | ||||||||
\(781\) | −7.46427 | −0.267092 | ||||||||
\(782\) | −31.5231 | −1.12726 | ||||||||
\(783\) | −6.19632 | −0.221438 | ||||||||
\(784\) | −1.78443 | −0.0637297 | ||||||||
\(785\) | −6.78280 | −0.242089 | ||||||||
\(786\) | −31.6718 | −1.12970 | ||||||||
\(787\) | 12.4440 | 0.443582 | 0.221791 | − | 0.975094i | \(-0.428810\pi\) | ||||
0.221791 | + | 0.975094i | \(0.428810\pi\) | |||||||
\(788\) | 4.46632 | 0.159106 | ||||||||
\(789\) | 11.0507 | 0.393416 | ||||||||
\(790\) | −1.26766 | −0.0451015 | ||||||||
\(791\) | 29.7072 | 1.05627 | ||||||||
\(792\) | −6.12119 | −0.217507 | ||||||||
\(793\) | 7.17808 | 0.254901 | ||||||||
\(794\) | 39.3386 | 1.39608 | ||||||||
\(795\) | −5.33517 | −0.189219 | ||||||||
\(796\) | 0.469798 | 0.0166516 | ||||||||
\(797\) | −32.4735 | −1.15027 | −0.575134 | − | 0.818059i | \(-0.695050\pi\) | ||||
−0.575134 | + | 0.818059i | \(0.695050\pi\) | |||||||
\(798\) | −8.11813 | −0.287379 | ||||||||
\(799\) | 56.5497 | 2.00059 | ||||||||
\(800\) | −1.49579 | −0.0528841 | ||||||||
\(801\) | 22.8992 | 0.809105 | ||||||||
\(802\) | −10.1812 | −0.359510 | ||||||||
\(803\) | 0.797840 | 0.0281551 | ||||||||
\(804\) | 6.09120 | 0.214820 | ||||||||
\(805\) | −14.8134 | −0.522104 | ||||||||
\(806\) | −7.65542 | −0.269651 | ||||||||
\(807\) | 25.8320 | 0.909331 | ||||||||
\(808\) | 4.90153 | 0.172435 | ||||||||
\(809\) | −6.49725 | −0.228431 | −0.114215 | − | 0.993456i | \(-0.536435\pi\) | ||||
−0.114215 | + | 0.993456i | \(0.536435\pi\) | |||||||
\(810\) | −14.4128 | −0.506413 | ||||||||
\(811\) | 19.0752 | 0.669820 | 0.334910 | − | 0.942250i | \(-0.391294\pi\) | ||||
0.334910 | + | 0.942250i | \(0.391294\pi\) | |||||||
\(812\) | −2.12278 | −0.0744951 | ||||||||
\(813\) | −41.9702 | −1.47196 | ||||||||
\(814\) | 11.0674 | 0.387912 | ||||||||
\(815\) | 16.7229 | 0.585777 | ||||||||
\(816\) | −33.8445 | −1.18479 | ||||||||
\(817\) | 10.3406 | 0.361772 | ||||||||
\(818\) | 34.1960 | 1.19563 | ||||||||
\(819\) | −4.63558 | −0.161980 | ||||||||
\(820\) | −2.83672 | −0.0990626 | ||||||||
\(821\) | −3.43435 | −0.119860 | −0.0599299 | − | 0.998203i | \(-0.519088\pi\) | ||||
−0.0599299 | + | 0.998203i | \(0.519088\pi\) | |||||||
\(822\) | −57.0983 | −1.99153 | ||||||||
\(823\) | 9.46472 | 0.329919 | 0.164960 | − | 0.986300i | \(-0.447251\pi\) | ||||
0.164960 | + | 0.986300i | \(0.447251\pi\) | |||||||
\(824\) | −56.0523 | −1.95267 | ||||||||
\(825\) | −2.24751 | −0.0782484 | ||||||||
\(826\) | −53.6211 | −1.86572 | ||||||||
\(827\) | −7.05327 | −0.245266 | −0.122633 | − | 0.992452i | \(-0.539134\pi\) | ||||
−0.122633 | + | 0.992452i | \(0.539134\pi\) | |||||||
\(828\) | −2.94954 | −0.102504 | ||||||||
\(829\) | −7.70745 | −0.267691 | −0.133845 | − | 0.991002i | \(-0.542733\pi\) | ||||
−0.133845 | + | 0.991002i | \(0.542733\pi\) | |||||||
\(830\) | 0.145812 | 0.00506120 | ||||||||
\(831\) | −23.2116 | −0.805200 | ||||||||
\(832\) | −7.21839 | −0.250253 | ||||||||
\(833\) | 2.32922 | 0.0807027 | ||||||||
\(834\) | −15.7543 | −0.545528 | ||||||||
\(835\) | 9.05766 | 0.313453 | ||||||||
\(836\) | 0.266275 | 0.00920933 | ||||||||
\(837\) | 15.0486 | 0.520155 | ||||||||
\(838\) | 9.77041 | 0.337513 | ||||||||
\(839\) | −3.64475 | −0.125831 | −0.0629154 | − | 0.998019i | \(-0.520040\pi\) | ||||
−0.0629154 | + | 0.998019i | \(0.520040\pi\) | |||||||
\(840\) | −18.3979 | −0.634789 | ||||||||
\(841\) | −20.5546 | −0.708779 | ||||||||
\(842\) | −22.1787 | −0.764329 | ||||||||
\(843\) | −43.8338 | −1.50971 | ||||||||
\(844\) | −6.34667 | −0.218462 | ||||||||
\(845\) | 12.3214 | 0.423869 | ||||||||
\(846\) | −34.4513 | −1.18446 | ||||||||
\(847\) | 2.74324 | 0.0942588 | ||||||||
\(848\) | −8.06276 | −0.276876 | ||||||||
\(849\) | 14.6463 | 0.502661 | ||||||||
\(850\) | −5.83765 | −0.200230 | ||||||||
\(851\) | 45.3886 | 1.55590 | ||||||||
\(852\) | −4.46705 | −0.153038 | ||||||||
\(853\) | 37.9565 | 1.29960 | 0.649802 | − | 0.760103i | \(-0.274852\pi\) | ||||
0.649802 | + | 0.760103i | \(0.274852\pi\) | |||||||
\(854\) | 31.4743 | 1.07703 | ||||||||
\(855\) | −2.05132 | −0.0701536 | ||||||||
\(856\) | −56.8138 | −1.94186 | ||||||||
\(857\) | −45.6479 | −1.55930 | −0.779652 | − | 0.626214i | \(-0.784604\pi\) | ||||
−0.779652 | + | 0.626214i | \(0.784604\pi\) | |||||||
\(858\) | −2.43781 | −0.0832254 | ||||||||
\(859\) | 6.68610 | 0.228127 | 0.114063 | − | 0.993473i | \(-0.463613\pi\) | ||||
0.114063 | + | 0.993473i | \(0.463613\pi\) | |||||||
\(860\) | 2.75345 | 0.0938918 | ||||||||
\(861\) | −65.6828 | −2.23846 | ||||||||
\(862\) | −2.05603 | −0.0700287 | ||||||||
\(863\) | −57.8059 | −1.96774 | −0.983868 | − | 0.178898i | \(-0.942747\pi\) | ||||
−0.983868 | + | 0.178898i | \(0.942747\pi\) | |||||||
\(864\) | 3.18928 | 0.108502 | ||||||||
\(865\) | −8.57947 | −0.291711 | ||||||||
\(866\) | −40.4358 | −1.37406 | ||||||||
\(867\) | 5.96948 | 0.202734 | ||||||||
\(868\) | 5.15546 | 0.174988 | ||||||||
\(869\) | 0.962752 | 0.0326591 | ||||||||
\(870\) | 8.60009 | 0.291570 | ||||||||
\(871\) | 8.38449 | 0.284098 | ||||||||
\(872\) | 50.0400 | 1.69457 | ||||||||
\(873\) | 30.8977 | 1.04573 | ||||||||
\(874\) | −7.11019 | −0.240506 | ||||||||
\(875\) | −2.74324 | −0.0927384 | ||||||||
\(876\) | 0.477473 | 0.0161323 | ||||||||
\(877\) | −1.92045 | −0.0648490 | −0.0324245 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324245 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(878\) | 50.7016 | 1.71110 | ||||||||
\(879\) | −4.64300 | −0.156604 | ||||||||
\(880\) | −3.39655 | −0.114498 | ||||||||
\(881\) | −46.0047 | −1.54994 | −0.774969 | − | 0.631999i | \(-0.782235\pi\) | ||||
−0.774969 | + | 0.631999i | \(0.782235\pi\) | |||||||
\(882\) | −1.41901 | −0.0477806 | ||||||||
\(883\) | 2.94257 | 0.0990252 | 0.0495126 | − | 0.998773i | \(-0.484233\pi\) | ||||
0.0495126 | + | 0.998773i | \(0.484233\pi\) | |||||||
\(884\) | 0.972492 | 0.0327084 | ||||||||
\(885\) | −33.3645 | −1.12153 | ||||||||
\(886\) | −28.7723 | −0.966623 | ||||||||
\(887\) | 2.48521 | 0.0834453 | 0.0417227 | − | 0.999129i | \(-0.486715\pi\) | ||||
0.0417227 | + | 0.999129i | \(0.486715\pi\) | |||||||
\(888\) | 56.3716 | 1.89171 | ||||||||
\(889\) | −23.2519 | −0.779844 | ||||||||
\(890\) | 14.6987 | 0.492701 | ||||||||
\(891\) | 10.9460 | 0.366706 | ||||||||
\(892\) | 3.57090 | 0.119563 | ||||||||
\(893\) | 12.7551 | 0.426832 | ||||||||
\(894\) | 52.6292 | 1.76019 | ||||||||
\(895\) | 9.13708 | 0.305419 | ||||||||
\(896\) | −23.4444 | −0.783222 | ||||||||
\(897\) | −9.99770 | −0.333814 | ||||||||
\(898\) | 8.69743 | 0.290237 | ||||||||
\(899\) | −20.5108 | −0.684074 | ||||||||
\(900\) | −0.546215 | −0.0182072 | ||||||||
\(901\) | 10.5243 | 0.350616 | ||||||||
\(902\) | −14.0273 | −0.467059 | ||||||||
\(903\) | 63.7547 | 2.12162 | ||||||||
\(904\) | 32.3147 | 1.07477 | ||||||||
\(905\) | 18.3843 | 0.611115 | ||||||||
\(906\) | 28.7227 | 0.954247 | ||||||||
\(907\) | −46.8633 | −1.55607 | −0.778036 | − | 0.628220i | \(-0.783784\pi\) | ||||
−0.778036 | + | 0.628220i | \(0.783784\pi\) | |||||||
\(908\) | −1.18046 | −0.0391751 | ||||||||
\(909\) | 3.36947 | 0.111758 | ||||||||
\(910\) | −2.97551 | −0.0986371 | ||||||||
\(911\) | −32.7237 | −1.08418 | −0.542092 | − | 0.840319i | \(-0.682367\pi\) | ||||
−0.542092 | + | 0.840319i | \(0.682367\pi\) | |||||||
\(912\) | −7.63378 | −0.252780 | ||||||||
\(913\) | −0.110739 | −0.00366494 | ||||||||
\(914\) | −8.54429 | −0.282620 | ||||||||
\(915\) | 19.5841 | 0.647431 | ||||||||
\(916\) | −3.73118 | −0.123282 | ||||||||
\(917\) | 29.3592 | 0.969526 | ||||||||
\(918\) | 12.4469 | 0.410809 | ||||||||
\(919\) | 59.2895 | 1.95578 | 0.977890 | − | 0.209121i | \(-0.0670603\pi\) | ||||
0.977890 | + | 0.209121i | \(0.0670603\pi\) | |||||||
\(920\) | −16.1136 | −0.531251 | ||||||||
\(921\) | 14.6055 | 0.481268 | ||||||||
\(922\) | −44.3816 | −1.46163 | ||||||||
\(923\) | −6.14885 | −0.202392 | ||||||||
\(924\) | 1.64171 | 0.0540084 | ||||||||
\(925\) | 8.40534 | 0.276366 | ||||||||
\(926\) | −15.8784 | −0.521797 | ||||||||
\(927\) | −38.5322 | −1.26556 | ||||||||
\(928\) | −4.34691 | −0.142694 | ||||||||
\(929\) | 24.5262 | 0.804679 | 0.402339 | − | 0.915491i | \(-0.368197\pi\) | ||||
0.402339 | + | 0.915491i | \(0.368197\pi\) | |||||||
\(930\) | −20.8864 | −0.684894 | ||||||||
\(931\) | 0.525367 | 0.0172182 | ||||||||
\(932\) | 0.720756 | 0.0236091 | ||||||||
\(933\) | 38.8361 | 1.27144 | ||||||||
\(934\) | −10.1248 | −0.331292 | ||||||||
\(935\) | 4.43351 | 0.144991 | ||||||||
\(936\) | −5.04246 | −0.164818 | ||||||||
\(937\) | 10.1189 | 0.330571 | 0.165285 | − | 0.986246i | \(-0.447145\pi\) | ||||
0.165285 | + | 0.986246i | \(0.447145\pi\) | |||||||
\(938\) | 36.7641 | 1.20039 | ||||||||
\(939\) | −51.5596 | −1.68258 | ||||||||
\(940\) | 3.39636 | 0.110777 | ||||||||
\(941\) | −50.0082 | −1.63022 | −0.815110 | − | 0.579307i | \(-0.803323\pi\) | ||||
−0.815110 | + | 0.579307i | \(0.803323\pi\) | |||||||
\(942\) | −20.0725 | −0.653997 | ||||||||
\(943\) | −57.5276 | −1.87336 | ||||||||
\(944\) | −50.4219 | −1.64109 | ||||||||
\(945\) | 5.84907 | 0.190270 | ||||||||
\(946\) | 13.6156 | 0.442680 | ||||||||
\(947\) | −8.93511 | −0.290352 | −0.145176 | − | 0.989406i | \(-0.546375\pi\) | ||||
−0.145176 | + | 0.989406i | \(0.546375\pi\) | |||||||
\(948\) | 0.576166 | 0.0187130 | ||||||||
\(949\) | 0.657238 | 0.0213348 | ||||||||
\(950\) | −1.31671 | −0.0427197 | ||||||||
\(951\) | −36.9658 | −1.19870 | ||||||||
\(952\) | 36.2923 | 1.17624 | ||||||||
\(953\) | −23.7421 | −0.769082 | −0.384541 | − | 0.923108i | \(-0.625640\pi\) | ||||
−0.384541 | + | 0.923108i | \(0.625640\pi\) | |||||||
\(954\) | −6.41164 | −0.207584 | ||||||||
\(955\) | 4.72197 | 0.152799 | ||||||||
\(956\) | 7.50180 | 0.242626 | ||||||||
\(957\) | −6.53150 | −0.211133 | ||||||||
\(958\) | −15.6387 | −0.505264 | ||||||||
\(959\) | 52.9291 | 1.70917 | ||||||||
\(960\) | −19.6941 | −0.635624 | ||||||||
\(961\) | 18.8132 | 0.606877 | ||||||||
\(962\) | 9.11701 | 0.293944 | ||||||||
\(963\) | −39.0557 | −1.25855 | ||||||||
\(964\) | 4.91159 | 0.158192 | ||||||||
\(965\) | −3.20004 | −0.103013 | ||||||||
\(966\) | −43.8376 | −1.41045 | ||||||||
\(967\) | 3.55415 | 0.114294 | 0.0571469 | − | 0.998366i | \(-0.481800\pi\) | ||||
0.0571469 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(968\) | 2.98403 | 0.0959103 | ||||||||
\(969\) | 9.96438 | 0.320102 | ||||||||
\(970\) | 19.8327 | 0.636791 | ||||||||
\(971\) | −5.12760 | −0.164553 | −0.0822763 | − | 0.996610i | \(-0.526219\pi\) | ||||
−0.0822763 | + | 0.996610i | \(0.526219\pi\) | |||||||
\(972\) | 4.84751 | 0.155484 | ||||||||
\(973\) | 14.6040 | 0.468182 | ||||||||
\(974\) | −27.4462 | −0.879433 | ||||||||
\(975\) | −1.85144 | −0.0592935 | ||||||||
\(976\) | 29.5964 | 0.947358 | ||||||||
\(977\) | 25.3934 | 0.812407 | 0.406203 | − | 0.913783i | \(-0.366852\pi\) | ||||
0.406203 | + | 0.913783i | \(0.366852\pi\) | |||||||
\(978\) | 49.4884 | 1.58246 | ||||||||
\(979\) | −11.1632 | −0.356777 | ||||||||
\(980\) | 0.139892 | 0.00446869 | ||||||||
\(981\) | 34.3992 | 1.09828 | ||||||||
\(982\) | 21.6612 | 0.691238 | ||||||||
\(983\) | 17.1989 | 0.548560 | 0.274280 | − | 0.961650i | \(-0.411561\pi\) | ||||
0.274280 | + | 0.961650i | \(0.411561\pi\) | |||||||
\(984\) | −71.4481 | −2.27768 | ||||||||
\(985\) | 16.7733 | 0.534443 | ||||||||
\(986\) | −16.9648 | −0.540269 | ||||||||
\(987\) | 78.6410 | 2.50317 | ||||||||
\(988\) | 0.219350 | 0.00697846 | ||||||||
\(989\) | 55.8389 | 1.77557 | ||||||||
\(990\) | −2.70099 | −0.0858431 | ||||||||
\(991\) | 6.07473 | 0.192970 | 0.0964851 | − | 0.995334i | \(-0.469240\pi\) | ||||
0.0964851 | + | 0.995334i | \(0.469240\pi\) | |||||||
\(992\) | 10.5570 | 0.335186 | ||||||||
\(993\) | −69.2844 | −2.19867 | ||||||||
\(994\) | −26.9613 | −0.855161 | ||||||||
\(995\) | 1.76433 | 0.0559331 | ||||||||
\(996\) | −0.0662729 | −0.00209994 | ||||||||
\(997\) | 20.9511 | 0.663527 | 0.331763 | − | 0.943363i | \(-0.392356\pi\) | ||||
0.331763 | + | 0.943363i | \(0.392356\pi\) | |||||||
\(998\) | 7.12260 | 0.225462 | ||||||||
\(999\) | −17.9217 | −0.567017 |
(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 | 1045.2.a.j.1.3 | ✓ | 9 | |
3.2 | odd | 2 | 9405.2.a.bi.1.7 | 9 | |||
5.4 | even | 2 | 5225.2.a.q.1.7 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.a.j.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial | |
5225.2.a.q.1.7 | 9 | 5.4 | even | 2 | |||
9405.2.a.bi.1.7 | 9 | 3.2 | odd | 2 |