Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8038,2,Mod(1,8038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8038 = 2 \cdot 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8038.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: | \(64.1837531447\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8038.1 |
$q$-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 | ||||||||
\(3\) | −2.93359 | −1.69371 | −0.846855 | − | 0.531824i | \(-0.821507\pi\) | ||||
−0.846855 | + | 0.531824i | \(0.821507\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.13721 | 0.955788 | 0.477894 | − | 0.878418i | \(-0.341400\pi\) | ||||
0.477894 | + | 0.878418i | \(0.341400\pi\) | |||||||
\(6\) | −2.93359 | −1.19763 | ||||||||
\(7\) | 0.512181 | 0.193586 | 0.0967930 | − | 0.995305i | \(-0.469142\pi\) | ||||
0.0967930 | + | 0.995305i | \(0.469142\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.60596 | 1.86865 | ||||||||
\(10\) | 2.13721 | 0.675844 | ||||||||
\(11\) | −3.75894 | −1.13336 | −0.566681 | − | 0.823937i | \(-0.691773\pi\) | ||||
−0.566681 | + | 0.823937i | \(0.691773\pi\) | |||||||
\(12\) | −2.93359 | −0.846855 | ||||||||
\(13\) | 0.496248 | 0.137634 | 0.0688171 | − | 0.997629i | \(-0.478077\pi\) | ||||
0.0688171 | + | 0.997629i | \(0.478077\pi\) | |||||||
\(14\) | 0.512181 | 0.136886 | ||||||||
\(15\) | −6.26969 | −1.61883 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.791674 | 0.192009 | 0.0960046 | − | 0.995381i | \(-0.469394\pi\) | ||||
0.0960046 | + | 0.995381i | \(0.469394\pi\) | |||||||
\(18\) | 5.60596 | 1.32134 | ||||||||
\(19\) | −7.88651 | −1.80929 | −0.904644 | − | 0.426168i | \(-0.859863\pi\) | ||||
−0.904644 | + | 0.426168i | \(0.859863\pi\) | |||||||
\(20\) | 2.13721 | 0.477894 | ||||||||
\(21\) | −1.50253 | −0.327879 | ||||||||
\(22\) | −3.75894 | −0.801408 | ||||||||
\(23\) | 3.47552 | 0.724697 | 0.362348 | − | 0.932043i | \(-0.381975\pi\) | ||||
0.362348 | + | 0.932043i | \(0.381975\pi\) | |||||||
\(24\) | −2.93359 | −0.598817 | ||||||||
\(25\) | −0.432347 | −0.0864694 | ||||||||
\(26\) | 0.496248 | 0.0973221 | ||||||||
\(27\) | −7.64481 | −1.47124 | ||||||||
\(28\) | 0.512181 | 0.0967930 | ||||||||
\(29\) | 10.6545 | 1.97849 | 0.989245 | − | 0.146270i | \(-0.0467267\pi\) | ||||
0.989245 | + | 0.146270i | \(0.0467267\pi\) | |||||||
\(30\) | −6.26969 | −1.14468 | ||||||||
\(31\) | −4.77695 | −0.857965 | −0.428982 | − | 0.903313i | \(-0.641128\pi\) | ||||
−0.428982 | + | 0.903313i | \(0.641128\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.0272 | 1.91959 | ||||||||
\(34\) | 0.791674 | 0.135771 | ||||||||
\(35\) | 1.09464 | 0.185027 | ||||||||
\(36\) | 5.60596 | 0.934326 | ||||||||
\(37\) | 8.16170 | 1.34178 | 0.670888 | − | 0.741559i | \(-0.265913\pi\) | ||||
0.670888 | + | 0.741559i | \(0.265913\pi\) | |||||||
\(38\) | −7.88651 | −1.27936 | ||||||||
\(39\) | −1.45579 | −0.233113 | ||||||||
\(40\) | 2.13721 | 0.337922 | ||||||||
\(41\) | −9.76999 | −1.52582 | −0.762908 | − | 0.646507i | \(-0.776229\pi\) | ||||
−0.762908 | + | 0.646507i | \(0.776229\pi\) | |||||||
\(42\) | −1.50253 | −0.231845 | ||||||||
\(43\) | 3.17097 | 0.483568 | 0.241784 | − | 0.970330i | \(-0.422268\pi\) | ||||
0.241784 | + | 0.970330i | \(0.422268\pi\) | |||||||
\(44\) | −3.75894 | −0.566681 | ||||||||
\(45\) | 11.9811 | 1.78603 | ||||||||
\(46\) | 3.47552 | 0.512438 | ||||||||
\(47\) | 6.28598 | 0.916905 | 0.458453 | − | 0.888719i | \(-0.348404\pi\) | ||||
0.458453 | + | 0.888719i | \(0.348404\pi\) | |||||||
\(48\) | −2.93359 | −0.423427 | ||||||||
\(49\) | −6.73767 | −0.962524 | ||||||||
\(50\) | −0.432347 | −0.0611431 | ||||||||
\(51\) | −2.32245 | −0.325208 | ||||||||
\(52\) | 0.496248 | 0.0688171 | ||||||||
\(53\) | −4.96994 | −0.682673 | −0.341337 | − | 0.939941i | \(-0.610880\pi\) | ||||
−0.341337 | + | 0.939941i | \(0.610880\pi\) | |||||||
\(54\) | −7.64481 | −1.04033 | ||||||||
\(55\) | −8.03362 | −1.08325 | ||||||||
\(56\) | 0.512181 | 0.0684430 | ||||||||
\(57\) | 23.1358 | 3.06441 | ||||||||
\(58\) | 10.6545 | 1.39900 | ||||||||
\(59\) | −11.5166 | −1.49933 | −0.749665 | − | 0.661817i | \(-0.769786\pi\) | ||||
−0.749665 | + | 0.661817i | \(0.769786\pi\) | |||||||
\(60\) | −6.26969 | −0.809414 | ||||||||
\(61\) | −0.835492 | −0.106974 | −0.0534869 | − | 0.998569i | \(-0.517034\pi\) | ||||
−0.0534869 | + | 0.998569i | \(0.517034\pi\) | |||||||
\(62\) | −4.77695 | −0.606673 | ||||||||
\(63\) | 2.87126 | 0.361745 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.06058 | 0.131549 | ||||||||
\(66\) | 11.0272 | 1.35735 | ||||||||
\(67\) | 9.34626 | 1.14183 | 0.570914 | − | 0.821010i | \(-0.306589\pi\) | ||||
0.570914 | + | 0.821010i | \(0.306589\pi\) | |||||||
\(68\) | 0.791674 | 0.0960046 | ||||||||
\(69\) | −10.1958 | −1.22743 | ||||||||
\(70\) | 1.09464 | 0.130834 | ||||||||
\(71\) | −12.0889 | −1.43469 | −0.717345 | − | 0.696718i | \(-0.754643\pi\) | ||||
−0.717345 | + | 0.696718i | \(0.754643\pi\) | |||||||
\(72\) | 5.60596 | 0.660668 | ||||||||
\(73\) | −9.29368 | −1.08774 | −0.543871 | − | 0.839169i | \(-0.683042\pi\) | ||||
−0.543871 | + | 0.839169i | \(0.683042\pi\) | |||||||
\(74\) | 8.16170 | 0.948779 | ||||||||
\(75\) | 1.26833 | 0.146454 | ||||||||
\(76\) | −7.88651 | −0.904644 | ||||||||
\(77\) | −1.92525 | −0.219403 | ||||||||
\(78\) | −1.45579 | −0.164835 | ||||||||
\(79\) | −6.52746 | −0.734396 | −0.367198 | − | 0.930143i | \(-0.619683\pi\) | ||||
−0.367198 | + | 0.930143i | \(0.619683\pi\) | |||||||
\(80\) | 2.13721 | 0.238947 | ||||||||
\(81\) | 5.60887 | 0.623208 | ||||||||
\(82\) | −9.76999 | −1.07892 | ||||||||
\(83\) | −10.9223 | −1.19887 | −0.599437 | − | 0.800422i | \(-0.704609\pi\) | ||||
−0.599437 | + | 0.800422i | \(0.704609\pi\) | |||||||
\(84\) | −1.50253 | −0.163939 | ||||||||
\(85\) | 1.69197 | 0.183520 | ||||||||
\(86\) | 3.17097 | 0.341934 | ||||||||
\(87\) | −31.2559 | −3.35099 | ||||||||
\(88\) | −3.75894 | −0.400704 | ||||||||
\(89\) | −3.10941 | −0.329596 | −0.164798 | − | 0.986327i | \(-0.552697\pi\) | ||||
−0.164798 | + | 0.986327i | \(0.552697\pi\) | |||||||
\(90\) | 11.9811 | 1.26292 | ||||||||
\(91\) | 0.254168 | 0.0266441 | ||||||||
\(92\) | 3.47552 | 0.362348 | ||||||||
\(93\) | 14.0136 | 1.45314 | ||||||||
\(94\) | 6.28598 | 0.648350 | ||||||||
\(95\) | −16.8551 | −1.72930 | ||||||||
\(96\) | −2.93359 | −0.299408 | ||||||||
\(97\) | −8.79117 | −0.892608 | −0.446304 | − | 0.894881i | \(-0.647260\pi\) | ||||
−0.446304 | + | 0.894881i | \(0.647260\pi\) | |||||||
\(98\) | −6.73767 | −0.680608 | ||||||||
\(99\) | −21.0724 | −2.11786 | ||||||||
\(100\) | −0.432347 | −0.0432347 | ||||||||
\(101\) | 15.3006 | 1.52247 | 0.761233 | − | 0.648478i | \(-0.224594\pi\) | ||||
0.761233 | + | 0.648478i | \(0.224594\pi\) | |||||||
\(102\) | −2.32245 | −0.229957 | ||||||||
\(103\) | 7.60134 | 0.748982 | 0.374491 | − | 0.927230i | \(-0.377817\pi\) | ||||
0.374491 | + | 0.927230i | \(0.377817\pi\) | |||||||
\(104\) | 0.496248 | 0.0486611 | ||||||||
\(105\) | −3.21121 | −0.313382 | ||||||||
\(106\) | −4.96994 | −0.482723 | ||||||||
\(107\) | −9.87990 | −0.955126 | −0.477563 | − | 0.878597i | \(-0.658480\pi\) | ||||
−0.477563 | + | 0.878597i | \(0.658480\pi\) | |||||||
\(108\) | −7.64481 | −0.735622 | ||||||||
\(109\) | 0.372892 | 0.0357166 | 0.0178583 | − | 0.999841i | \(-0.494315\pi\) | ||||
0.0178583 | + | 0.999841i | \(0.494315\pi\) | |||||||
\(110\) | −8.03362 | −0.765976 | ||||||||
\(111\) | −23.9431 | −2.27258 | ||||||||
\(112\) | 0.512181 | 0.0483965 | ||||||||
\(113\) | 14.0372 | 1.32051 | 0.660256 | − | 0.751041i | \(-0.270448\pi\) | ||||
0.660256 | + | 0.751041i | \(0.270448\pi\) | |||||||
\(114\) | 23.1358 | 2.16686 | ||||||||
\(115\) | 7.42791 | 0.692656 | ||||||||
\(116\) | 10.6545 | 0.989245 | ||||||||
\(117\) | 2.78194 | 0.257191 | ||||||||
\(118\) | −11.5166 | −1.06019 | ||||||||
\(119\) | 0.405480 | 0.0371703 | ||||||||
\(120\) | −6.26969 | −0.572342 | ||||||||
\(121\) | 3.12960 | 0.284509 | ||||||||
\(122\) | −0.835492 | −0.0756419 | ||||||||
\(123\) | 28.6612 | 2.58429 | ||||||||
\(124\) | −4.77695 | −0.428982 | ||||||||
\(125\) | −11.6100 | −1.03843 | ||||||||
\(126\) | 2.87126 | 0.255792 | ||||||||
\(127\) | 17.0192 | 1.51021 | 0.755103 | − | 0.655606i | \(-0.227587\pi\) | ||||
0.755103 | + | 0.655606i | \(0.227587\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.30232 | −0.819023 | ||||||||
\(130\) | 1.06058 | 0.0930193 | ||||||||
\(131\) | 0.145300 | 0.0126949 | 0.00634745 | − | 0.999980i | \(-0.497980\pi\) | ||||
0.00634745 | + | 0.999980i | \(0.497980\pi\) | |||||||
\(132\) | 11.0272 | 0.959793 | ||||||||
\(133\) | −4.03932 | −0.350253 | ||||||||
\(134\) | 9.34626 | 0.807394 | ||||||||
\(135\) | −16.3385 | −1.40620 | ||||||||
\(136\) | 0.791674 | 0.0678855 | ||||||||
\(137\) | 16.7232 | 1.42876 | 0.714381 | − | 0.699757i | \(-0.246708\pi\) | ||||
0.714381 | + | 0.699757i | \(0.246708\pi\) | |||||||
\(138\) | −10.1958 | −0.867921 | ||||||||
\(139\) | −11.3603 | −0.963570 | −0.481785 | − | 0.876290i | \(-0.660011\pi\) | ||||
−0.481785 | + | 0.876290i | \(0.660011\pi\) | |||||||
\(140\) | 1.09464 | 0.0925136 | ||||||||
\(141\) | −18.4405 | −1.55297 | ||||||||
\(142\) | −12.0889 | −1.01448 | ||||||||
\(143\) | −1.86536 | −0.155989 | ||||||||
\(144\) | 5.60596 | 0.467163 | ||||||||
\(145\) | 22.7709 | 1.89102 | ||||||||
\(146\) | −9.29368 | −0.769150 | ||||||||
\(147\) | 19.7656 | 1.63024 | ||||||||
\(148\) | 8.16170 | 0.670888 | ||||||||
\(149\) | 10.3572 | 0.848492 | 0.424246 | − | 0.905547i | \(-0.360539\pi\) | ||||
0.424246 | + | 0.905547i | \(0.360539\pi\) | |||||||
\(150\) | 1.26833 | 0.103559 | ||||||||
\(151\) | 14.6775 | 1.19443 | 0.597217 | − | 0.802079i | \(-0.296273\pi\) | ||||
0.597217 | + | 0.802079i | \(0.296273\pi\) | |||||||
\(152\) | −7.88651 | −0.639680 | ||||||||
\(153\) | 4.43809 | 0.358798 | ||||||||
\(154\) | −1.92525 | −0.155141 | ||||||||
\(155\) | −10.2093 | −0.820033 | ||||||||
\(156\) | −1.45579 | −0.116556 | ||||||||
\(157\) | −16.7771 | −1.33895 | −0.669477 | − | 0.742833i | \(-0.733482\pi\) | ||||
−0.669477 | + | 0.742833i | \(0.733482\pi\) | |||||||
\(158\) | −6.52746 | −0.519296 | ||||||||
\(159\) | 14.5798 | 1.15625 | ||||||||
\(160\) | 2.13721 | 0.168961 | ||||||||
\(161\) | 1.78010 | 0.140291 | ||||||||
\(162\) | 5.60887 | 0.440675 | ||||||||
\(163\) | −14.4114 | −1.12879 | −0.564395 | − | 0.825505i | \(-0.690890\pi\) | ||||
−0.564395 | + | 0.825505i | \(0.690890\pi\) | |||||||
\(164\) | −9.76999 | −0.762908 | ||||||||
\(165\) | 23.5674 | 1.83472 | ||||||||
\(166\) | −10.9223 | −0.847732 | ||||||||
\(167\) | 24.2361 | 1.87545 | 0.937724 | − | 0.347381i | \(-0.112929\pi\) | ||||
0.937724 | + | 0.347381i | \(0.112929\pi\) | |||||||
\(168\) | −1.50253 | −0.115923 | ||||||||
\(169\) | −12.7537 | −0.981057 | ||||||||
\(170\) | 1.69197 | 0.129768 | ||||||||
\(171\) | −44.2114 | −3.38093 | ||||||||
\(172\) | 3.17097 | 0.241784 | ||||||||
\(173\) | 15.7039 | 1.19394 | 0.596972 | − | 0.802262i | \(-0.296370\pi\) | ||||
0.596972 | + | 0.802262i | \(0.296370\pi\) | |||||||
\(174\) | −31.2559 | −2.36951 | ||||||||
\(175\) | −0.221440 | −0.0167393 | ||||||||
\(176\) | −3.75894 | −0.283340 | ||||||||
\(177\) | 33.7849 | 2.53943 | ||||||||
\(178\) | −3.10941 | −0.233060 | ||||||||
\(179\) | −17.5159 | −1.30920 | −0.654600 | − | 0.755975i | \(-0.727163\pi\) | ||||
−0.654600 | + | 0.755975i | \(0.727163\pi\) | |||||||
\(180\) | 11.9811 | 0.893017 | ||||||||
\(181\) | −10.6523 | −0.791779 | −0.395890 | − | 0.918298i | \(-0.629564\pi\) | ||||
−0.395890 | + | 0.918298i | \(0.629564\pi\) | |||||||
\(182\) | 0.254168 | 0.0188402 | ||||||||
\(183\) | 2.45099 | 0.181183 | ||||||||
\(184\) | 3.47552 | 0.256219 | ||||||||
\(185\) | 17.4432 | 1.28245 | ||||||||
\(186\) | 14.0136 | 1.02753 | ||||||||
\(187\) | −2.97585 | −0.217616 | ||||||||
\(188\) | 6.28598 | 0.458453 | ||||||||
\(189\) | −3.91552 | −0.284812 | ||||||||
\(190\) | −16.8551 | −1.22280 | ||||||||
\(191\) | −0.526669 | −0.0381085 | −0.0190542 | − | 0.999818i | \(-0.506066\pi\) | ||||
−0.0190542 | + | 0.999818i | \(0.506066\pi\) | |||||||
\(192\) | −2.93359 | −0.211714 | ||||||||
\(193\) | −4.91514 | −0.353800 | −0.176900 | − | 0.984229i | \(-0.556607\pi\) | ||||
−0.176900 | + | 0.984229i | \(0.556607\pi\) | |||||||
\(194\) | −8.79117 | −0.631169 | ||||||||
\(195\) | −3.11132 | −0.222806 | ||||||||
\(196\) | −6.73767 | −0.481262 | ||||||||
\(197\) | 13.1721 | 0.938476 | 0.469238 | − | 0.883072i | \(-0.344529\pi\) | ||||
0.469238 | + | 0.883072i | \(0.344529\pi\) | |||||||
\(198\) | −21.0724 | −1.49755 | ||||||||
\(199\) | −2.33670 | −0.165644 | −0.0828220 | − | 0.996564i | \(-0.526393\pi\) | ||||
−0.0828220 | + | 0.996564i | \(0.526393\pi\) | |||||||
\(200\) | −0.432347 | −0.0305716 | ||||||||
\(201\) | −27.4181 | −1.93392 | ||||||||
\(202\) | 15.3006 | 1.07655 | ||||||||
\(203\) | 5.45702 | 0.383008 | ||||||||
\(204\) | −2.32245 | −0.162604 | ||||||||
\(205\) | −20.8805 | −1.45836 | ||||||||
\(206\) | 7.60134 | 0.529610 | ||||||||
\(207\) | 19.4836 | 1.35421 | ||||||||
\(208\) | 0.496248 | 0.0344086 | ||||||||
\(209\) | 29.6449 | 2.05058 | ||||||||
\(210\) | −3.21121 | −0.221595 | ||||||||
\(211\) | 10.6670 | 0.734349 | 0.367174 | − | 0.930152i | \(-0.380325\pi\) | ||||
0.367174 | + | 0.930152i | \(0.380325\pi\) | |||||||
\(212\) | −4.96994 | −0.341337 | ||||||||
\(213\) | 35.4639 | 2.42995 | ||||||||
\(214\) | −9.87990 | −0.675376 | ||||||||
\(215\) | 6.77701 | 0.462188 | ||||||||
\(216\) | −7.64481 | −0.520163 | ||||||||
\(217\) | −2.44666 | −0.166090 | ||||||||
\(218\) | 0.372892 | 0.0252554 | ||||||||
\(219\) | 27.2638 | 1.84232 | ||||||||
\(220\) | −8.03362 | −0.541627 | ||||||||
\(221\) | 0.392866 | 0.0264270 | ||||||||
\(222\) | −23.9431 | −1.60696 | ||||||||
\(223\) | −6.24952 | −0.418499 | −0.209250 | − | 0.977862i | \(-0.567102\pi\) | ||||
−0.209250 | + | 0.977862i | \(0.567102\pi\) | |||||||
\(224\) | 0.512181 | 0.0342215 | ||||||||
\(225\) | −2.42372 | −0.161581 | ||||||||
\(226\) | 14.0372 | 0.933743 | ||||||||
\(227\) | −2.71972 | −0.180514 | −0.0902571 | − | 0.995918i | \(-0.528769\pi\) | ||||
−0.0902571 | + | 0.995918i | \(0.528769\pi\) | |||||||
\(228\) | 23.1358 | 1.53220 | ||||||||
\(229\) | −15.5315 | −1.02635 | −0.513177 | − | 0.858283i | \(-0.671531\pi\) | ||||
−0.513177 | + | 0.858283i | \(0.671531\pi\) | |||||||
\(230\) | 7.42791 | 0.489782 | ||||||||
\(231\) | 5.64791 | 0.371605 | ||||||||
\(232\) | 10.6545 | 0.699502 | ||||||||
\(233\) | −26.5727 | −1.74084 | −0.870419 | − | 0.492312i | \(-0.836152\pi\) | ||||
−0.870419 | + | 0.492312i | \(0.836152\pi\) | |||||||
\(234\) | 2.78194 | 0.181861 | ||||||||
\(235\) | 13.4344 | 0.876367 | ||||||||
\(236\) | −11.5166 | −0.749665 | ||||||||
\(237\) | 19.1489 | 1.24385 | ||||||||
\(238\) | 0.405480 | 0.0262834 | ||||||||
\(239\) | −13.8726 | −0.897343 | −0.448672 | − | 0.893697i | \(-0.648103\pi\) | ||||
−0.448672 | + | 0.893697i | \(0.648103\pi\) | |||||||
\(240\) | −6.26969 | −0.404707 | ||||||||
\(241\) | −1.51488 | −0.0975818 | −0.0487909 | − | 0.998809i | \(-0.515537\pi\) | ||||
−0.0487909 | + | 0.998809i | \(0.515537\pi\) | |||||||
\(242\) | 3.12960 | 0.201178 | ||||||||
\(243\) | 6.48029 | 0.415711 | ||||||||
\(244\) | −0.835492 | −0.0534869 | ||||||||
\(245\) | −14.3998 | −0.919969 | ||||||||
\(246\) | 28.6612 | 1.82737 | ||||||||
\(247\) | −3.91366 | −0.249020 | ||||||||
\(248\) | −4.77695 | −0.303336 | ||||||||
\(249\) | 32.0414 | 2.03054 | ||||||||
\(250\) | −11.6100 | −0.734284 | ||||||||
\(251\) | −14.9268 | −0.942169 | −0.471084 | − | 0.882088i | \(-0.656137\pi\) | ||||
−0.471084 | + | 0.882088i | \(0.656137\pi\) | |||||||
\(252\) | 2.87126 | 0.180872 | ||||||||
\(253\) | −13.0643 | −0.821344 | ||||||||
\(254\) | 17.0192 | 1.06788 | ||||||||
\(255\) | −4.96355 | −0.310830 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.1086 | −1.75337 | −0.876683 | − | 0.481069i | \(-0.840249\pi\) | ||||
−0.876683 | + | 0.481069i | \(0.840249\pi\) | |||||||
\(258\) | −9.30232 | −0.579137 | ||||||||
\(259\) | 4.18027 | 0.259749 | ||||||||
\(260\) | 1.06058 | 0.0657746 | ||||||||
\(261\) | 59.7286 | 3.69711 | ||||||||
\(262\) | 0.145300 | 0.00897665 | ||||||||
\(263\) | −13.2633 | −0.817848 | −0.408924 | − | 0.912568i | \(-0.634096\pi\) | ||||
−0.408924 | + | 0.912568i | \(0.634096\pi\) | |||||||
\(264\) | 11.0272 | 0.678676 | ||||||||
\(265\) | −10.6218 | −0.652491 | ||||||||
\(266\) | −4.03932 | −0.247666 | ||||||||
\(267\) | 9.12173 | 0.558241 | ||||||||
\(268\) | 9.34626 | 0.570914 | ||||||||
\(269\) | 24.8275 | 1.51376 | 0.756881 | − | 0.653553i | \(-0.226722\pi\) | ||||
0.756881 | + | 0.653553i | \(0.226722\pi\) | |||||||
\(270\) | −16.3385 | −0.994332 | ||||||||
\(271\) | −11.7641 | −0.714618 | −0.357309 | − | 0.933986i | \(-0.616306\pi\) | ||||
−0.357309 | + | 0.933986i | \(0.616306\pi\) | |||||||
\(272\) | 0.791674 | 0.0480023 | ||||||||
\(273\) | −0.745626 | −0.0451273 | ||||||||
\(274\) | 16.7232 | 1.01029 | ||||||||
\(275\) | 1.62516 | 0.0980011 | ||||||||
\(276\) | −10.1958 | −0.613713 | ||||||||
\(277\) | −24.8395 | −1.49246 | −0.746229 | − | 0.665689i | \(-0.768138\pi\) | ||||
−0.746229 | + | 0.665689i | \(0.768138\pi\) | |||||||
\(278\) | −11.3603 | −0.681347 | ||||||||
\(279\) | −26.7793 | −1.60324 | ||||||||
\(280\) | 1.09464 | 0.0654170 | ||||||||
\(281\) | 18.8372 | 1.12373 | 0.561865 | − | 0.827229i | \(-0.310084\pi\) | ||||
0.561865 | + | 0.827229i | \(0.310084\pi\) | |||||||
\(282\) | −18.4405 | −1.09812 | ||||||||
\(283\) | −12.0030 | −0.713505 | −0.356752 | − | 0.934199i | \(-0.616116\pi\) | ||||
−0.356752 | + | 0.934199i | \(0.616116\pi\) | |||||||
\(284\) | −12.0889 | −0.717345 | ||||||||
\(285\) | 49.4460 | 2.92893 | ||||||||
\(286\) | −1.86536 | −0.110301 | ||||||||
\(287\) | −5.00400 | −0.295377 | ||||||||
\(288\) | 5.60596 | 0.330334 | ||||||||
\(289\) | −16.3733 | −0.963132 | ||||||||
\(290\) | 22.7709 | 1.33715 | ||||||||
\(291\) | 25.7897 | 1.51182 | ||||||||
\(292\) | −9.29368 | −0.543871 | ||||||||
\(293\) | −26.5703 | −1.55226 | −0.776128 | − | 0.630575i | \(-0.782819\pi\) | ||||
−0.776128 | + | 0.630575i | \(0.782819\pi\) | |||||||
\(294\) | 19.7656 | 1.15275 | ||||||||
\(295\) | −24.6133 | −1.43304 | ||||||||
\(296\) | 8.16170 | 0.474389 | ||||||||
\(297\) | 28.7363 | 1.66745 | ||||||||
\(298\) | 10.3572 | 0.599975 | ||||||||
\(299\) | 1.72472 | 0.0997431 | ||||||||
\(300\) | 1.26833 | 0.0732270 | ||||||||
\(301\) | 1.62411 | 0.0936120 | ||||||||
\(302\) | 14.6775 | 0.844593 | ||||||||
\(303\) | −44.8857 | −2.57862 | ||||||||
\(304\) | −7.88651 | −0.452322 | ||||||||
\(305\) | −1.78562 | −0.102244 | ||||||||
\(306\) | 4.43809 | 0.253709 | ||||||||
\(307\) | −3.01042 | −0.171814 | −0.0859070 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859070 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(308\) | −1.92525 | −0.109702 | ||||||||
\(309\) | −22.2992 | −1.26856 | ||||||||
\(310\) | −10.2093 | −0.579851 | ||||||||
\(311\) | −32.6484 | −1.85132 | −0.925659 | − | 0.378358i | \(-0.876489\pi\) | ||||
−0.925659 | + | 0.378358i | \(0.876489\pi\) | |||||||
\(312\) | −1.45579 | −0.0824177 | ||||||||
\(313\) | 14.7984 | 0.836457 | 0.418228 | − | 0.908342i | \(-0.362651\pi\) | ||||
0.418228 | + | 0.908342i | \(0.362651\pi\) | |||||||
\(314\) | −16.7771 | −0.946784 | ||||||||
\(315\) | 6.13648 | 0.345751 | ||||||||
\(316\) | −6.52746 | −0.367198 | ||||||||
\(317\) | −20.5053 | −1.15169 | −0.575845 | − | 0.817559i | \(-0.695327\pi\) | ||||
−0.575845 | + | 0.817559i | \(0.695327\pi\) | |||||||
\(318\) | 14.5798 | 0.817592 | ||||||||
\(319\) | −40.0496 | −2.24234 | ||||||||
\(320\) | 2.13721 | 0.119473 | ||||||||
\(321\) | 28.9836 | 1.61771 | ||||||||
\(322\) | 1.78010 | 0.0992009 | ||||||||
\(323\) | −6.24354 | −0.347400 | ||||||||
\(324\) | 5.60887 | 0.311604 | ||||||||
\(325\) | −0.214551 | −0.0119012 | ||||||||
\(326\) | −14.4114 | −0.798174 | ||||||||
\(327\) | −1.09391 | −0.0604935 | ||||||||
\(328\) | −9.76999 | −0.539458 | ||||||||
\(329\) | 3.21956 | 0.177500 | ||||||||
\(330\) | 23.5674 | 1.29734 | ||||||||
\(331\) | 4.60693 | 0.253220 | 0.126610 | − | 0.991953i | \(-0.459590\pi\) | ||||
0.126610 | + | 0.991953i | \(0.459590\pi\) | |||||||
\(332\) | −10.9223 | −0.599437 | ||||||||
\(333\) | 45.7541 | 2.50731 | ||||||||
\(334\) | 24.2361 | 1.32614 | ||||||||
\(335\) | 19.9749 | 1.09135 | ||||||||
\(336\) | −1.50253 | −0.0819696 | ||||||||
\(337\) | −26.8660 | −1.46348 | −0.731741 | − | 0.681582i | \(-0.761292\pi\) | ||||
−0.731741 | + | 0.681582i | \(0.761292\pi\) | |||||||
\(338\) | −12.7537 | −0.693712 | ||||||||
\(339\) | −41.1795 | −2.23656 | ||||||||
\(340\) | 1.69197 | 0.0917600 | ||||||||
\(341\) | 17.9562 | 0.972385 | ||||||||
\(342\) | −44.2114 | −2.39068 | ||||||||
\(343\) | −7.03617 | −0.379917 | ||||||||
\(344\) | 3.17097 | 0.170967 | ||||||||
\(345\) | −21.7905 | −1.17316 | ||||||||
\(346\) | 15.7039 | 0.844246 | ||||||||
\(347\) | 7.82858 | 0.420260 | 0.210130 | − | 0.977673i | \(-0.432611\pi\) | ||||
0.210130 | + | 0.977673i | \(0.432611\pi\) | |||||||
\(348\) | −31.2559 | −1.67549 | ||||||||
\(349\) | 7.56079 | 0.404720 | 0.202360 | − | 0.979311i | \(-0.435139\pi\) | ||||
0.202360 | + | 0.979311i | \(0.435139\pi\) | |||||||
\(350\) | −0.221440 | −0.0118365 | ||||||||
\(351\) | −3.79372 | −0.202494 | ||||||||
\(352\) | −3.75894 | −0.200352 | ||||||||
\(353\) | 8.62179 | 0.458892 | 0.229446 | − | 0.973321i | \(-0.426309\pi\) | ||||
0.229446 | + | 0.973321i | \(0.426309\pi\) | |||||||
\(354\) | 33.7849 | 1.79565 | ||||||||
\(355\) | −25.8365 | −1.37126 | ||||||||
\(356\) | −3.10941 | −0.164798 | ||||||||
\(357\) | −1.18951 | −0.0629557 | ||||||||
\(358\) | −17.5159 | −0.925745 | ||||||||
\(359\) | −8.31771 | −0.438992 | −0.219496 | − | 0.975613i | \(-0.570441\pi\) | ||||
−0.219496 | + | 0.975613i | \(0.570441\pi\) | |||||||
\(360\) | 11.9811 | 0.631459 | ||||||||
\(361\) | 43.1970 | 2.27352 | ||||||||
\(362\) | −10.6523 | −0.559872 | ||||||||
\(363\) | −9.18096 | −0.481876 | ||||||||
\(364\) | 0.254168 | 0.0133220 | ||||||||
\(365\) | −19.8625 | −1.03965 | ||||||||
\(366\) | 2.45099 | 0.128115 | ||||||||
\(367\) | −3.19579 | −0.166819 | −0.0834095 | − | 0.996515i | \(-0.526581\pi\) | ||||
−0.0834095 | + | 0.996515i | \(0.526581\pi\) | |||||||
\(368\) | 3.47552 | 0.181174 | ||||||||
\(369\) | −54.7702 | −2.85122 | ||||||||
\(370\) | 17.4432 | 0.906831 | ||||||||
\(371\) | −2.54550 | −0.132156 | ||||||||
\(372\) | 14.0136 | 0.726572 | ||||||||
\(373\) | −34.9203 | −1.80810 | −0.904051 | − | 0.427424i | \(-0.859421\pi\) | ||||
−0.904051 | + | 0.427424i | \(0.859421\pi\) | |||||||
\(374\) | −2.97585 | −0.153878 | ||||||||
\(375\) | 34.0591 | 1.75881 | ||||||||
\(376\) | 6.28598 | 0.324175 | ||||||||
\(377\) | 5.28727 | 0.272308 | ||||||||
\(378\) | −3.91552 | −0.201393 | ||||||||
\(379\) | −24.9331 | −1.28072 | −0.640362 | − | 0.768073i | \(-0.721216\pi\) | ||||
−0.640362 | + | 0.768073i | \(0.721216\pi\) | |||||||
\(380\) | −16.8551 | −0.864648 | ||||||||
\(381\) | −49.9273 | −2.55785 | ||||||||
\(382\) | −0.526669 | −0.0269468 | ||||||||
\(383\) | −3.63985 | −0.185988 | −0.0929939 | − | 0.995667i | \(-0.529644\pi\) | ||||
−0.0929939 | + | 0.995667i | \(0.529644\pi\) | |||||||
\(384\) | −2.93359 | −0.149704 | ||||||||
\(385\) | −4.11467 | −0.209703 | ||||||||
\(386\) | −4.91514 | −0.250174 | ||||||||
\(387\) | 17.7763 | 0.903620 | ||||||||
\(388\) | −8.79117 | −0.446304 | ||||||||
\(389\) | 29.1880 | 1.47989 | 0.739945 | − | 0.672668i | \(-0.234852\pi\) | ||||
0.739945 | + | 0.672668i | \(0.234852\pi\) | |||||||
\(390\) | −3.11132 | −0.157548 | ||||||||
\(391\) | 2.75148 | 0.139148 | ||||||||
\(392\) | −6.73767 | −0.340304 | ||||||||
\(393\) | −0.426250 | −0.0215015 | ||||||||
\(394\) | 13.1721 | 0.663603 | ||||||||
\(395\) | −13.9505 | −0.701927 | ||||||||
\(396\) | −21.0724 | −1.05893 | ||||||||
\(397\) | 32.9156 | 1.65199 | 0.825993 | − | 0.563681i | \(-0.190615\pi\) | ||||
0.825993 | + | 0.563681i | \(0.190615\pi\) | |||||||
\(398\) | −2.33670 | −0.117128 | ||||||||
\(399\) | 11.8497 | 0.593227 | ||||||||
\(400\) | −0.432347 | −0.0216174 | ||||||||
\(401\) | 3.99011 | 0.199257 | 0.0996284 | − | 0.995025i | \(-0.468235\pi\) | ||||
0.0996284 | + | 0.995025i | \(0.468235\pi\) | |||||||
\(402\) | −27.4181 | −1.36749 | ||||||||
\(403\) | −2.37055 | −0.118085 | ||||||||
\(404\) | 15.3006 | 0.761233 | ||||||||
\(405\) | 11.9873 | 0.595655 | ||||||||
\(406\) | 5.45702 | 0.270828 | ||||||||
\(407\) | −30.6793 | −1.52072 | ||||||||
\(408\) | −2.32245 | −0.114978 | ||||||||
\(409\) | −16.0808 | −0.795145 | −0.397573 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397573 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(410\) | −20.8805 | −1.03121 | ||||||||
\(411\) | −49.0591 | −2.41991 | ||||||||
\(412\) | 7.60134 | 0.374491 | ||||||||
\(413\) | −5.89857 | −0.290250 | ||||||||
\(414\) | 19.4836 | 0.957568 | ||||||||
\(415\) | −23.3431 | −1.14587 | ||||||||
\(416\) | 0.496248 | 0.0243305 | ||||||||
\(417\) | 33.3265 | 1.63201 | ||||||||
\(418\) | 29.6449 | 1.44998 | ||||||||
\(419\) | 4.85887 | 0.237371 | 0.118686 | − | 0.992932i | \(-0.462132\pi\) | ||||
0.118686 | + | 0.992932i | \(0.462132\pi\) | |||||||
\(420\) | −3.21121 | −0.156691 | ||||||||
\(421\) | 20.6219 | 1.00505 | 0.502524 | − | 0.864563i | \(-0.332405\pi\) | ||||
0.502524 | + | 0.864563i | \(0.332405\pi\) | |||||||
\(422\) | 10.6670 | 0.519263 | ||||||||
\(423\) | 35.2389 | 1.71338 | ||||||||
\(424\) | −4.96994 | −0.241361 | ||||||||
\(425\) | −0.342278 | −0.0166029 | ||||||||
\(426\) | 35.4639 | 1.71823 | ||||||||
\(427\) | −0.427923 | −0.0207086 | ||||||||
\(428\) | −9.87990 | −0.477563 | ||||||||
\(429\) | 5.47221 | 0.264201 | ||||||||
\(430\) | 6.77701 | 0.326816 | ||||||||
\(431\) | 3.55708 | 0.171338 | 0.0856692 | − | 0.996324i | \(-0.472697\pi\) | ||||
0.0856692 | + | 0.996324i | \(0.472697\pi\) | |||||||
\(432\) | −7.64481 | −0.367811 | ||||||||
\(433\) | −37.0515 | −1.78058 | −0.890291 | − | 0.455392i | \(-0.849499\pi\) | ||||
−0.890291 | + | 0.455392i | \(0.849499\pi\) | |||||||
\(434\) | −2.44666 | −0.117443 | ||||||||
\(435\) | −66.8004 | −3.20283 | ||||||||
\(436\) | 0.372892 | 0.0178583 | ||||||||
\(437\) | −27.4097 | −1.31119 | ||||||||
\(438\) | 27.2638 | 1.30272 | ||||||||
\(439\) | 39.8988 | 1.90427 | 0.952133 | − | 0.305685i | \(-0.0988855\pi\) | ||||
0.952133 | + | 0.305685i | \(0.0988855\pi\) | |||||||
\(440\) | −8.03362 | −0.382988 | ||||||||
\(441\) | −37.7711 | −1.79862 | ||||||||
\(442\) | 0.392866 | 0.0186867 | ||||||||
\(443\) | 20.2233 | 0.960839 | 0.480420 | − | 0.877039i | \(-0.340484\pi\) | ||||
0.480420 | + | 0.877039i | \(0.340484\pi\) | |||||||
\(444\) | −23.9431 | −1.13629 | ||||||||
\(445\) | −6.64544 | −0.315024 | ||||||||
\(446\) | −6.24952 | −0.295924 | ||||||||
\(447\) | −30.3837 | −1.43710 | ||||||||
\(448\) | 0.512181 | 0.0241983 | ||||||||
\(449\) | 15.6372 | 0.737967 | 0.368984 | − | 0.929436i | \(-0.379706\pi\) | ||||
0.368984 | + | 0.929436i | \(0.379706\pi\) | |||||||
\(450\) | −2.42372 | −0.114255 | ||||||||
\(451\) | 36.7248 | 1.72930 | ||||||||
\(452\) | 14.0372 | 0.660256 | ||||||||
\(453\) | −43.0577 | −2.02303 | ||||||||
\(454\) | −2.71972 | −0.127643 | ||||||||
\(455\) | 0.543210 | 0.0254661 | ||||||||
\(456\) | 23.1358 | 1.08343 | ||||||||
\(457\) | −6.84392 | −0.320145 | −0.160073 | − | 0.987105i | \(-0.551173\pi\) | ||||
−0.160073 | + | 0.987105i | \(0.551173\pi\) | |||||||
\(458\) | −15.5315 | −0.725741 | ||||||||
\(459\) | −6.05220 | −0.282492 | ||||||||
\(460\) | 7.42791 | 0.346328 | ||||||||
\(461\) | −23.9589 | −1.11588 | −0.557938 | − | 0.829883i | \(-0.688407\pi\) | ||||
−0.557938 | + | 0.829883i | \(0.688407\pi\) | |||||||
\(462\) | 5.64791 | 0.262764 | ||||||||
\(463\) | −23.6330 | −1.09832 | −0.549160 | − | 0.835717i | \(-0.685052\pi\) | ||||
−0.549160 | + | 0.835717i | \(0.685052\pi\) | |||||||
\(464\) | 10.6545 | 0.494622 | ||||||||
\(465\) | 29.9500 | 1.38890 | ||||||||
\(466\) | −26.5727 | −1.23096 | ||||||||
\(467\) | 35.4564 | 1.64073 | 0.820364 | − | 0.571842i | \(-0.193771\pi\) | ||||
0.820364 | + | 0.571842i | \(0.193771\pi\) | |||||||
\(468\) | 2.78194 | 0.128595 | ||||||||
\(469\) | 4.78697 | 0.221042 | ||||||||
\(470\) | 13.4344 | 0.619685 | ||||||||
\(471\) | 49.2170 | 2.26780 | ||||||||
\(472\) | −11.5166 | −0.530094 | ||||||||
\(473\) | −11.9195 | −0.548057 | ||||||||
\(474\) | 19.1489 | 0.879537 | ||||||||
\(475\) | 3.40971 | 0.156448 | ||||||||
\(476\) | 0.405480 | 0.0185852 | ||||||||
\(477\) | −27.8612 | −1.27568 | ||||||||
\(478\) | −13.8726 | −0.634517 | ||||||||
\(479\) | 13.4062 | 0.612545 | 0.306272 | − | 0.951944i | \(-0.400918\pi\) | ||||
0.306272 | + | 0.951944i | \(0.400918\pi\) | |||||||
\(480\) | −6.26969 | −0.286171 | ||||||||
\(481\) | 4.05022 | 0.184674 | ||||||||
\(482\) | −1.51488 | −0.0690008 | ||||||||
\(483\) | −5.22207 | −0.237613 | ||||||||
\(484\) | 3.12960 | 0.142254 | ||||||||
\(485\) | −18.7886 | −0.853144 | ||||||||
\(486\) | 6.48029 | 0.293952 | ||||||||
\(487\) | 12.6732 | 0.574276 | 0.287138 | − | 0.957889i | \(-0.407296\pi\) | ||||
0.287138 | + | 0.957889i | \(0.407296\pi\) | |||||||
\(488\) | −0.835492 | −0.0378209 | ||||||||
\(489\) | 42.2772 | 1.91184 | ||||||||
\(490\) | −14.3998 | −0.650516 | ||||||||
\(491\) | −26.4360 | −1.19304 | −0.596519 | − | 0.802599i | \(-0.703450\pi\) | ||||
−0.596519 | + | 0.802599i | \(0.703450\pi\) | |||||||
\(492\) | 28.6612 | 1.29215 | ||||||||
\(493\) | 8.43489 | 0.379888 | ||||||||
\(494\) | −3.91366 | −0.176084 | ||||||||
\(495\) | −45.0361 | −2.02422 | ||||||||
\(496\) | −4.77695 | −0.214491 | ||||||||
\(497\) | −6.19171 | −0.277736 | ||||||||
\(498\) | 32.0414 | 1.43581 | ||||||||
\(499\) | 29.2330 | 1.30865 | 0.654325 | − | 0.756213i | \(-0.272953\pi\) | ||||
0.654325 | + | 0.756213i | \(0.272953\pi\) | |||||||
\(500\) | −11.6100 | −0.519217 | ||||||||
\(501\) | −71.0989 | −3.17646 | ||||||||
\(502\) | −14.9268 | −0.666214 | ||||||||
\(503\) | −13.0045 | −0.579840 | −0.289920 | − | 0.957051i | \(-0.593629\pi\) | ||||
−0.289920 | + | 0.957051i | \(0.593629\pi\) | |||||||
\(504\) | 2.87126 | 0.127896 | ||||||||
\(505\) | 32.7006 | 1.45516 | ||||||||
\(506\) | −13.0643 | −0.580778 | ||||||||
\(507\) | 37.4143 | 1.66163 | ||||||||
\(508\) | 17.0192 | 0.755103 | ||||||||
\(509\) | −21.6487 | −0.959563 | −0.479781 | − | 0.877388i | \(-0.659284\pi\) | ||||
−0.479781 | + | 0.877388i | \(0.659284\pi\) | |||||||
\(510\) | −4.96355 | −0.219790 | ||||||||
\(511\) | −4.76004 | −0.210572 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 60.2908 | 2.66190 | ||||||||
\(514\) | −28.1086 | −1.23982 | ||||||||
\(515\) | 16.2456 | 0.715868 | ||||||||
\(516\) | −9.30232 | −0.409512 | ||||||||
\(517\) | −23.6286 | −1.03919 | ||||||||
\(518\) | 4.18027 | 0.183670 | ||||||||
\(519\) | −46.0688 | −2.02219 | ||||||||
\(520\) | 1.06058 | 0.0465097 | ||||||||
\(521\) | −26.3267 | −1.15339 | −0.576697 | − | 0.816958i | \(-0.695659\pi\) | ||||
−0.576697 | + | 0.816958i | \(0.695659\pi\) | |||||||
\(522\) | 59.7286 | 2.61425 | ||||||||
\(523\) | −44.4467 | −1.94352 | −0.971759 | − | 0.235976i | \(-0.924171\pi\) | ||||
−0.971759 | + | 0.235976i | \(0.924171\pi\) | |||||||
\(524\) | 0.145300 | 0.00634745 | ||||||||
\(525\) | 0.649614 | 0.0283515 | ||||||||
\(526\) | −13.2633 | −0.578306 | ||||||||
\(527\) | −3.78178 | −0.164737 | ||||||||
\(528\) | 11.0272 | 0.479896 | ||||||||
\(529\) | −10.9207 | −0.474815 | ||||||||
\(530\) | −10.6218 | −0.461381 | ||||||||
\(531\) | −64.5614 | −2.80173 | ||||||||
\(532\) | −4.03932 | −0.175127 | ||||||||
\(533\) | −4.84834 | −0.210005 | ||||||||
\(534\) | 9.12173 | 0.394736 | ||||||||
\(535\) | −21.1154 | −0.912898 | ||||||||
\(536\) | 9.34626 | 0.403697 | ||||||||
\(537\) | 51.3845 | 2.21741 | ||||||||
\(538\) | 24.8275 | 1.07039 | ||||||||
\(539\) | 25.3265 | 1.09089 | ||||||||
\(540\) | −16.3385 | −0.703099 | ||||||||
\(541\) | −5.15523 | −0.221640 | −0.110820 | − | 0.993840i | \(-0.535348\pi\) | ||||
−0.110820 | + | 0.993840i | \(0.535348\pi\) | |||||||
\(542\) | −11.7641 | −0.505311 | ||||||||
\(543\) | 31.2495 | 1.34104 | ||||||||
\(544\) | 0.791674 | 0.0339427 | ||||||||
\(545\) | 0.796948 | 0.0341375 | ||||||||
\(546\) | −0.745626 | −0.0319098 | ||||||||
\(547\) | −22.7363 | −0.972136 | −0.486068 | − | 0.873921i | \(-0.661569\pi\) | ||||
−0.486068 | + | 0.873921i | \(0.661569\pi\) | |||||||
\(548\) | 16.7232 | 0.714381 | ||||||||
\(549\) | −4.68373 | −0.199897 | ||||||||
\(550\) | 1.62516 | 0.0692973 | ||||||||
\(551\) | −84.0267 | −3.57966 | ||||||||
\(552\) | −10.1958 | −0.433961 | ||||||||
\(553\) | −3.34324 | −0.142169 | ||||||||
\(554\) | −24.8395 | −1.05533 | ||||||||
\(555\) | −51.1713 | −2.17210 | ||||||||
\(556\) | −11.3603 | −0.481785 | ||||||||
\(557\) | 37.6512 | 1.59533 | 0.797667 | − | 0.603098i | \(-0.206067\pi\) | ||||
0.797667 | + | 0.603098i | \(0.206067\pi\) | |||||||
\(558\) | −26.7793 | −1.13366 | ||||||||
\(559\) | 1.57358 | 0.0665555 | ||||||||
\(560\) | 1.09464 | 0.0462568 | ||||||||
\(561\) | 8.72993 | 0.368578 | ||||||||
\(562\) | 18.8372 | 0.794598 | ||||||||
\(563\) | 41.6686 | 1.75612 | 0.878062 | − | 0.478548i | \(-0.158837\pi\) | ||||
0.878062 | + | 0.478548i | \(0.158837\pi\) | |||||||
\(564\) | −18.4405 | −0.776485 | ||||||||
\(565\) | 30.0005 | 1.26213 | ||||||||
\(566\) | −12.0030 | −0.504524 | ||||||||
\(567\) | 2.87275 | 0.120644 | ||||||||
\(568\) | −12.0889 | −0.507239 | ||||||||
\(569\) | −27.5309 | −1.15415 | −0.577077 | − | 0.816690i | \(-0.695807\pi\) | ||||
−0.577077 | + | 0.816690i | \(0.695807\pi\) | |||||||
\(570\) | 49.4460 | 2.07106 | ||||||||
\(571\) | −24.4727 | −1.02415 | −0.512075 | − | 0.858941i | \(-0.671123\pi\) | ||||
−0.512075 | + | 0.858941i | \(0.671123\pi\) | |||||||
\(572\) | −1.86536 | −0.0779947 | ||||||||
\(573\) | 1.54503 | 0.0645447 | ||||||||
\(574\) | −5.00400 | −0.208863 | ||||||||
\(575\) | −1.50263 | −0.0626641 | ||||||||
\(576\) | 5.60596 | 0.233581 | ||||||||
\(577\) | 30.4840 | 1.26907 | 0.634533 | − | 0.772896i | \(-0.281192\pi\) | ||||
0.634533 | + | 0.772896i | \(0.281192\pi\) | |||||||
\(578\) | −16.3733 | −0.681038 | ||||||||
\(579\) | 14.4190 | 0.599234 | ||||||||
\(580\) | 22.7709 | 0.945508 | ||||||||
\(581\) | −5.59417 | −0.232085 | ||||||||
\(582\) | 25.7897 | 1.06902 | ||||||||
\(583\) | 18.6817 | 0.773716 | ||||||||
\(584\) | −9.29368 | −0.384575 | ||||||||
\(585\) | 5.94558 | 0.245820 | ||||||||
\(586\) | −26.5703 | −1.09761 | ||||||||
\(587\) | 6.36677 | 0.262785 | 0.131392 | − | 0.991330i | \(-0.458055\pi\) | ||||
0.131392 | + | 0.991330i | \(0.458055\pi\) | |||||||
\(588\) | 19.7656 | 0.815118 | ||||||||
\(589\) | 37.6734 | 1.55231 | ||||||||
\(590\) | −24.6133 | −1.01331 | ||||||||
\(591\) | −38.6417 | −1.58951 | ||||||||
\(592\) | 8.16170 | 0.335444 | ||||||||
\(593\) | −34.2163 | −1.40510 | −0.702548 | − | 0.711636i | \(-0.747955\pi\) | ||||
−0.702548 | + | 0.711636i | \(0.747955\pi\) | |||||||
\(594\) | 28.7363 | 1.17907 | ||||||||
\(595\) | 0.866595 | 0.0355269 | ||||||||
\(596\) | 10.3572 | 0.424246 | ||||||||
\(597\) | 6.85491 | 0.280553 | ||||||||
\(598\) | 1.72472 | 0.0705290 | ||||||||
\(599\) | −10.1414 | −0.414366 | −0.207183 | − | 0.978302i | \(-0.566430\pi\) | ||||
−0.207183 | + | 0.978302i | \(0.566430\pi\) | |||||||
\(600\) | 1.26833 | 0.0517793 | ||||||||
\(601\) | −36.1932 | −1.47635 | −0.738176 | − | 0.674608i | \(-0.764313\pi\) | ||||
−0.738176 | + | 0.674608i | \(0.764313\pi\) | |||||||
\(602\) | 1.62411 | 0.0661937 | ||||||||
\(603\) | 52.3947 | 2.13368 | ||||||||
\(604\) | 14.6775 | 0.597217 | ||||||||
\(605\) | 6.68860 | 0.271930 | ||||||||
\(606\) | −44.8857 | −1.82336 | ||||||||
\(607\) | 32.6689 | 1.32599 | 0.662996 | − | 0.748623i | \(-0.269285\pi\) | ||||
0.662996 | + | 0.748623i | \(0.269285\pi\) | |||||||
\(608\) | −7.88651 | −0.319840 | ||||||||
\(609\) | −16.0087 | −0.648704 | ||||||||
\(610\) | −1.78562 | −0.0722976 | ||||||||
\(611\) | 3.11940 | 0.126198 | ||||||||
\(612\) | 4.43809 | 0.179399 | ||||||||
\(613\) | −3.25737 | −0.131564 | −0.0657819 | − | 0.997834i | \(-0.520954\pi\) | ||||
−0.0657819 | + | 0.997834i | \(0.520954\pi\) | |||||||
\(614\) | −3.01042 | −0.121491 | ||||||||
\(615\) | 61.2548 | 2.47003 | ||||||||
\(616\) | −1.92525 | −0.0775707 | ||||||||
\(617\) | −4.15597 | −0.167313 | −0.0836566 | − | 0.996495i | \(-0.526660\pi\) | ||||
−0.0836566 | + | 0.996495i | \(0.526660\pi\) | |||||||
\(618\) | −22.2992 | −0.897006 | ||||||||
\(619\) | 5.87241 | 0.236032 | 0.118016 | − | 0.993012i | \(-0.462347\pi\) | ||||
0.118016 | + | 0.993012i | \(0.462347\pi\) | |||||||
\(620\) | −10.2093 | −0.410016 | ||||||||
\(621\) | −26.5697 | −1.06621 | ||||||||
\(622\) | −32.6484 | −1.30908 | ||||||||
\(623\) | −1.59258 | −0.0638053 | ||||||||
\(624\) | −1.45579 | −0.0582781 | ||||||||
\(625\) | −22.6513 | −0.906054 | ||||||||
\(626\) | 14.7984 | 0.591464 | ||||||||
\(627\) | −86.9659 | −3.47308 | ||||||||
\(628\) | −16.7771 | −0.669477 | ||||||||
\(629\) | 6.46141 | 0.257633 | ||||||||
\(630\) | 6.13648 | 0.244483 | ||||||||
\(631\) | −14.6696 | −0.583986 | −0.291993 | − | 0.956420i | \(-0.594318\pi\) | ||||
−0.291993 | + | 0.956420i | \(0.594318\pi\) | |||||||
\(632\) | −6.52746 | −0.259648 | ||||||||
\(633\) | −31.2927 | −1.24377 | ||||||||
\(634\) | −20.5053 | −0.814368 | ||||||||
\(635\) | 36.3735 | 1.44344 | ||||||||
\(636\) | 14.5798 | 0.578125 | ||||||||
\(637\) | −3.34355 | −0.132476 | ||||||||
\(638\) | −40.0496 | −1.58558 | ||||||||
\(639\) | −67.7699 | −2.68094 | ||||||||
\(640\) | 2.13721 | 0.0844805 | ||||||||
\(641\) | 50.1773 | 1.98188 | 0.990941 | − | 0.134297i | \(-0.0428775\pi\) | ||||
0.990941 | + | 0.134297i | \(0.0428775\pi\) | |||||||
\(642\) | 28.9836 | 1.14389 | ||||||||
\(643\) | −8.40217 | −0.331349 | −0.165675 | − | 0.986180i | \(-0.552980\pi\) | ||||
−0.165675 | + | 0.986180i | \(0.552980\pi\) | |||||||
\(644\) | 1.78010 | 0.0701456 | ||||||||
\(645\) | −19.8810 | −0.782813 | ||||||||
\(646\) | −6.24354 | −0.245649 | ||||||||
\(647\) | −30.0993 | −1.18332 | −0.591662 | − | 0.806186i | \(-0.701528\pi\) | ||||
−0.591662 | + | 0.806186i | \(0.701528\pi\) | |||||||
\(648\) | 5.60887 | 0.220337 | ||||||||
\(649\) | 43.2901 | 1.69928 | ||||||||
\(650\) | −0.214551 | −0.00841539 | ||||||||
\(651\) | 7.17750 | 0.281308 | ||||||||
\(652\) | −14.4114 | −0.564395 | ||||||||
\(653\) | −16.1370 | −0.631490 | −0.315745 | − | 0.948844i | \(-0.602254\pi\) | ||||
−0.315745 | + | 0.948844i | \(0.602254\pi\) | |||||||
\(654\) | −1.09391 | −0.0427754 | ||||||||
\(655\) | 0.310536 | 0.0121336 | ||||||||
\(656\) | −9.76999 | −0.381454 | ||||||||
\(657\) | −52.0999 | −2.03261 | ||||||||
\(658\) | 3.21956 | 0.125511 | ||||||||
\(659\) | 6.97166 | 0.271577 | 0.135789 | − | 0.990738i | \(-0.456643\pi\) | ||||
0.135789 | + | 0.990738i | \(0.456643\pi\) | |||||||
\(660\) | 23.5674 | 0.917358 | ||||||||
\(661\) | −0.204648 | −0.00795990 | −0.00397995 | − | 0.999992i | \(-0.501267\pi\) | ||||
−0.00397995 | + | 0.999992i | \(0.501267\pi\) | |||||||
\(662\) | 4.60693 | 0.179053 | ||||||||
\(663\) | −1.15251 | −0.0447597 | ||||||||
\(664\) | −10.9223 | −0.423866 | ||||||||
\(665\) | −8.63285 | −0.334768 | ||||||||
\(666\) | 45.7541 | 1.77294 | ||||||||
\(667\) | 37.0299 | 1.43381 | ||||||||
\(668\) | 24.2361 | 0.937724 | ||||||||
\(669\) | 18.3335 | 0.708816 | ||||||||
\(670\) | 19.9749 | 0.771697 | ||||||||
\(671\) | 3.14056 | 0.121240 | ||||||||
\(672\) | −1.50253 | −0.0579613 | ||||||||
\(673\) | −42.2927 | −1.63026 | −0.815131 | − | 0.579276i | \(-0.803335\pi\) | ||||
−0.815131 | + | 0.579276i | \(0.803335\pi\) | |||||||
\(674\) | −26.8660 | −1.03484 | ||||||||
\(675\) | 3.30521 | 0.127218 | ||||||||
\(676\) | −12.7537 | −0.490528 | ||||||||
\(677\) | 43.7485 | 1.68139 | 0.840695 | − | 0.541508i | \(-0.182147\pi\) | ||||
0.840695 | + | 0.541508i | \(0.182147\pi\) | |||||||
\(678\) | −41.1795 | −1.58149 | ||||||||
\(679\) | −4.50267 | −0.172797 | ||||||||
\(680\) | 1.69197 | 0.0648841 | ||||||||
\(681\) | 7.97855 | 0.305739 | ||||||||
\(682\) | 17.9562 | 0.687580 | ||||||||
\(683\) | −4.95345 | −0.189538 | −0.0947692 | − | 0.995499i | \(-0.530211\pi\) | ||||
−0.0947692 | + | 0.995499i | \(0.530211\pi\) | |||||||
\(684\) | −44.2114 | −1.69047 | ||||||||
\(685\) | 35.7410 | 1.36559 | ||||||||
\(686\) | −7.03617 | −0.268642 | ||||||||
\(687\) | 45.5632 | 1.73834 | ||||||||
\(688\) | 3.17097 | 0.120892 | ||||||||
\(689\) | −2.46632 | −0.0939592 | ||||||||
\(690\) | −21.7905 | −0.829549 | ||||||||
\(691\) | 11.0630 | 0.420855 | 0.210428 | − | 0.977609i | \(-0.432514\pi\) | ||||
0.210428 | + | 0.977609i | \(0.432514\pi\) | |||||||
\(692\) | 15.7039 | 0.596972 | ||||||||
\(693\) | −10.7929 | −0.409988 | ||||||||
\(694\) | 7.82858 | 0.297169 | ||||||||
\(695\) | −24.2794 | −0.920968 | ||||||||
\(696\) | −31.2559 | −1.18475 | ||||||||
\(697\) | −7.73465 | −0.292971 | ||||||||
\(698\) | 7.56079 | 0.286180 | ||||||||
\(699\) | 77.9535 | 2.94847 | ||||||||
\(700\) | −0.221440 | −0.00836964 | ||||||||
\(701\) | −32.0270 | −1.20964 | −0.604821 | − | 0.796361i | \(-0.706755\pi\) | ||||
−0.604821 | + | 0.796361i | \(0.706755\pi\) | |||||||
\(702\) | −3.79372 | −0.143185 | ||||||||
\(703\) | −64.3673 | −2.42766 | ||||||||
\(704\) | −3.75894 | −0.141670 | ||||||||
\(705\) | −39.4112 | −1.48431 | ||||||||
\(706\) | 8.62179 | 0.324485 | ||||||||
\(707\) | 7.83667 | 0.294728 | ||||||||
\(708\) | 33.7849 | 1.26972 | ||||||||
\(709\) | 19.8478 | 0.745401 | 0.372701 | − | 0.927952i | \(-0.378432\pi\) | ||||
0.372701 | + | 0.927952i | \(0.378432\pi\) | |||||||
\(710\) | −25.8365 | −0.969627 | ||||||||
\(711\) | −36.5926 | −1.37233 | ||||||||
\(712\) | −3.10941 | −0.116530 | ||||||||
\(713\) | −16.6024 | −0.621764 | ||||||||
\(714\) | −1.18951 | −0.0445164 | ||||||||
\(715\) | −3.98667 | −0.149093 | ||||||||
\(716\) | −17.5159 | −0.654600 | ||||||||
\(717\) | 40.6965 | 1.51984 | ||||||||
\(718\) | −8.31771 | −0.310414 | ||||||||
\(719\) | −22.3077 | −0.831938 | −0.415969 | − | 0.909379i | \(-0.636558\pi\) | ||||
−0.415969 | + | 0.909379i | \(0.636558\pi\) | |||||||
\(720\) | 11.9811 | 0.446509 | ||||||||
\(721\) | 3.89326 | 0.144993 | ||||||||
\(722\) | 43.1970 | 1.60762 | ||||||||
\(723\) | 4.44403 | 0.165275 | ||||||||
\(724\) | −10.6523 | −0.395890 | ||||||||
\(725\) | −4.60644 | −0.171079 | ||||||||
\(726\) | −9.18096 | −0.340737 | ||||||||
\(727\) | 48.1921 | 1.78735 | 0.893674 | − | 0.448718i | \(-0.148119\pi\) | ||||
0.893674 | + | 0.448718i | \(0.148119\pi\) | |||||||
\(728\) | 0.254168 | 0.00942011 | ||||||||
\(729\) | −35.8371 | −1.32730 | ||||||||
\(730\) | −19.8625 | −0.735145 | ||||||||
\(731\) | 2.51037 | 0.0928494 | ||||||||
\(732\) | 2.45099 | 0.0905913 | ||||||||
\(733\) | 34.7110 | 1.28208 | 0.641041 | − | 0.767507i | \(-0.278503\pi\) | ||||
0.641041 | + | 0.767507i | \(0.278503\pi\) | |||||||
\(734\) | −3.19579 | −0.117959 | ||||||||
\(735\) | 42.2431 | 1.55816 | ||||||||
\(736\) | 3.47552 | 0.128110 | ||||||||
\(737\) | −35.1320 | −1.29410 | ||||||||
\(738\) | −54.7702 | −2.01612 | ||||||||
\(739\) | 43.7162 | 1.60813 | 0.804063 | − | 0.594545i | \(-0.202668\pi\) | ||||
0.804063 | + | 0.594545i | \(0.202668\pi\) | |||||||
\(740\) | 17.4432 | 0.641226 | ||||||||
\(741\) | 11.4811 | 0.421768 | ||||||||
\(742\) | −2.54550 | −0.0934484 | ||||||||
\(743\) | −24.6376 | −0.903868 | −0.451934 | − | 0.892051i | \(-0.649266\pi\) | ||||
−0.451934 | + | 0.892051i | \(0.649266\pi\) | |||||||
\(744\) | 14.0136 | 0.513764 | ||||||||
\(745\) | 22.1354 | 0.810979 | ||||||||
\(746\) | −34.9203 | −1.27852 | ||||||||
\(747\) | −61.2297 | −2.24028 | ||||||||
\(748\) | −2.97585 | −0.108808 | ||||||||
\(749\) | −5.06029 | −0.184899 | ||||||||
\(750\) | 34.0591 | 1.24366 | ||||||||
\(751\) | 2.94149 | 0.107337 | 0.0536683 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536683 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(752\) | 6.28598 | 0.229226 | ||||||||
\(753\) | 43.7890 | 1.59576 | ||||||||
\(754\) | 5.28727 | 0.192551 | ||||||||
\(755\) | 31.3688 | 1.14163 | ||||||||
\(756\) | −3.91552 | −0.142406 | ||||||||
\(757\) | −6.24680 | −0.227044 | −0.113522 | − | 0.993535i | \(-0.536213\pi\) | ||||
−0.113522 | + | 0.993535i | \(0.536213\pi\) | |||||||
\(758\) | −24.9331 | −0.905609 | ||||||||
\(759\) | 38.3252 | 1.39112 | ||||||||
\(760\) | −16.8551 | −0.611399 | ||||||||
\(761\) | 9.98552 | 0.361975 | 0.180987 | − | 0.983485i | \(-0.442071\pi\) | ||||
0.180987 | + | 0.983485i | \(0.442071\pi\) | |||||||
\(762\) | −49.9273 | −1.80867 | ||||||||
\(763\) | 0.190988 | 0.00691423 | ||||||||
\(764\) | −0.526669 | −0.0190542 | ||||||||
\(765\) | 9.48512 | 0.342935 | ||||||||
\(766\) | −3.63985 | −0.131513 | ||||||||
\(767\) | −5.71507 | −0.206359 | ||||||||
\(768\) | −2.93359 | −0.105857 | ||||||||
\(769\) | 33.6538 | 1.21359 | 0.606793 | − | 0.794860i | \(-0.292456\pi\) | ||||
0.606793 | + | 0.794860i | \(0.292456\pi\) | |||||||
\(770\) | −4.11467 | −0.148282 | ||||||||
\(771\) | 82.4591 | 2.96969 | ||||||||
\(772\) | −4.91514 | −0.176900 | ||||||||
\(773\) | −23.5186 | −0.845905 | −0.422953 | − | 0.906152i | \(-0.639006\pi\) | ||||
−0.422953 | + | 0.906152i | \(0.639006\pi\) | |||||||
\(774\) | 17.7763 | 0.638956 | ||||||||
\(775\) | 2.06530 | 0.0741877 | ||||||||
\(776\) | −8.79117 | −0.315585 | ||||||||
\(777\) | −12.2632 | −0.439939 | ||||||||
\(778\) | 29.1880 | 1.04644 | ||||||||
\(779\) | 77.0511 | 2.76064 | ||||||||
\(780\) | −3.11132 | −0.111403 | ||||||||
\(781\) | 45.4414 | 1.62602 | ||||||||
\(782\) | 2.75148 | 0.0983928 | ||||||||
\(783\) | −81.4515 | −2.91084 | ||||||||
\(784\) | −6.73767 | −0.240631 | ||||||||
\(785\) | −35.8560 | −1.27976 | ||||||||
\(786\) | −0.426250 | −0.0152038 | ||||||||
\(787\) | 18.8879 | 0.673280 | 0.336640 | − | 0.941634i | \(-0.390710\pi\) | ||||
0.336640 | + | 0.941634i | \(0.390710\pi\) | |||||||
\(788\) | 13.1721 | 0.469238 | ||||||||
\(789\) | 38.9090 | 1.38520 | ||||||||
\(790\) | −13.9505 | −0.496337 | ||||||||
\(791\) | 7.18960 | 0.255633 | ||||||||
\(792\) | −21.0724 | −0.748776 | ||||||||
\(793\) | −0.414611 | −0.0147233 | ||||||||
\(794\) | 32.9156 | 1.16813 | ||||||||
\(795\) | 31.1600 | 1.10513 | ||||||||
\(796\) | −2.33670 | −0.0828220 | ||||||||
\(797\) | −22.3235 | −0.790739 | −0.395369 | − | 0.918522i | \(-0.629383\pi\) | ||||
−0.395369 | + | 0.918522i | \(0.629383\pi\) | |||||||
\(798\) | 11.8497 | 0.419475 | ||||||||
\(799\) | 4.97645 | 0.176054 | ||||||||
\(800\) | −0.432347 | −0.0152858 | ||||||||
\(801\) | −17.4312 | −0.615901 | ||||||||
\(802\) | 3.99011 | 0.140896 | ||||||||
\(803\) | 34.9343 | 1.23281 | ||||||||
\(804\) | −27.4181 | −0.966962 | ||||||||
\(805\) | 3.80443 | 0.134089 | ||||||||
\(806\) | −2.37055 | −0.0834990 | ||||||||
\(807\) | −72.8338 | −2.56387 | ||||||||
\(808\) | 15.3006 | 0.538273 | ||||||||
\(809\) | −4.10546 | −0.144340 | −0.0721702 | − | 0.997392i | \(-0.522992\pi\) | ||||
−0.0721702 | + | 0.997392i | \(0.522992\pi\) | |||||||
\(810\) | 11.9873 | 0.421191 | ||||||||
\(811\) | 38.9482 | 1.36766 | 0.683828 | − | 0.729643i | \(-0.260314\pi\) | ||||
0.683828 | + | 0.729643i | \(0.260314\pi\) | |||||||
\(812\) | 5.45702 | 0.191504 | ||||||||
\(813\) | 34.5111 | 1.21036 | ||||||||
\(814\) | −30.6793 | −1.07531 | ||||||||
\(815\) | −30.8002 | −1.07888 | ||||||||
\(816\) | −2.32245 | −0.0813019 | ||||||||
\(817\) | −25.0078 | −0.874913 | ||||||||
\(818\) | −16.0808 | −0.562253 | ||||||||
\(819\) | 1.42486 | 0.0497885 | ||||||||
\(820\) | −20.8805 | −0.729179 | ||||||||
\(821\) | −22.7832 | −0.795139 | −0.397570 | − | 0.917572i | \(-0.630146\pi\) | ||||
−0.397570 | + | 0.917572i | \(0.630146\pi\) | |||||||
\(822\) | −49.0591 | −1.71113 | ||||||||
\(823\) | −8.16719 | −0.284690 | −0.142345 | − | 0.989817i | \(-0.545464\pi\) | ||||
−0.142345 | + | 0.989817i | \(0.545464\pi\) | |||||||
\(824\) | 7.60134 | 0.264805 | ||||||||
\(825\) | −4.76757 | −0.165985 | ||||||||
\(826\) | −5.89857 | −0.205237 | ||||||||
\(827\) | 34.8373 | 1.21141 | 0.605706 | − | 0.795689i | \(-0.292891\pi\) | ||||
0.605706 | + | 0.795689i | \(0.292891\pi\) | |||||||
\(828\) | 19.4836 | 0.677103 | ||||||||
\(829\) | −31.1862 | −1.08314 | −0.541570 | − | 0.840655i | \(-0.682170\pi\) | ||||
−0.541570 | + | 0.840655i | \(0.682170\pi\) | |||||||
\(830\) | −23.3431 | −0.810252 | ||||||||
\(831\) | 72.8688 | 2.52779 | ||||||||
\(832\) | 0.496248 | 0.0172043 | ||||||||
\(833\) | −5.33404 | −0.184814 | ||||||||
\(834\) | 33.3265 | 1.15400 | ||||||||
\(835\) | 51.7976 | 1.79253 | ||||||||
\(836\) | 29.6449 | 1.02529 | ||||||||
\(837\) | 36.5188 | 1.26228 | ||||||||
\(838\) | 4.85887 | 0.167847 | ||||||||
\(839\) | −23.8689 | −0.824047 | −0.412023 | − | 0.911173i | \(-0.635178\pi\) | ||||
−0.412023 | + | 0.911173i | \(0.635178\pi\) | |||||||
\(840\) | −3.21121 | −0.110797 | ||||||||
\(841\) | 84.5182 | 2.91442 | ||||||||
\(842\) | 20.6219 | 0.710676 | ||||||||
\(843\) | −55.2605 | −1.90327 | ||||||||
\(844\) | 10.6670 | 0.367174 | ||||||||
\(845\) | −27.2574 | −0.937682 | ||||||||
\(846\) | 35.2389 | 1.21154 | ||||||||
\(847\) | 1.60292 | 0.0550770 | ||||||||
\(848\) | −4.96994 | −0.170668 | ||||||||
\(849\) | 35.2119 | 1.20847 | ||||||||
\(850\) | −0.342278 | −0.0117400 | ||||||||
\(851\) | 28.3662 | 0.972380 | ||||||||
\(852\) | 35.4639 | 1.21497 | ||||||||
\(853\) | 23.8896 | 0.817963 | 0.408982 | − | 0.912543i | \(-0.365884\pi\) | ||||
0.408982 | + | 0.912543i | \(0.365884\pi\) | |||||||
\(854\) | −0.427923 | −0.0146432 | ||||||||
\(855\) | −94.4889 | −3.23145 | ||||||||
\(856\) | −9.87990 | −0.337688 | ||||||||
\(857\) | −12.1322 | −0.414428 | −0.207214 | − | 0.978296i | \(-0.566440\pi\) | ||||
−0.207214 | + | 0.978296i | \(0.566440\pi\) | |||||||
\(858\) | 5.47221 | 0.186818 | ||||||||
\(859\) | 46.9899 | 1.60327 | 0.801637 | − | 0.597811i | \(-0.203963\pi\) | ||||
0.801637 | + | 0.597811i | \(0.203963\pi\) | |||||||
\(860\) | 6.77701 | 0.231094 | ||||||||
\(861\) | 14.6797 | 0.500283 | ||||||||
\(862\) | 3.55708 | 0.121154 | ||||||||
\(863\) | 18.7609 | 0.638627 | 0.319313 | − | 0.947649i | \(-0.396548\pi\) | ||||
0.319313 | + | 0.947649i | \(0.396548\pi\) | |||||||
\(864\) | −7.64481 | −0.260082 | ||||||||
\(865\) | 33.5625 | 1.14116 | ||||||||
\(866\) | −37.0515 | −1.25906 | ||||||||
\(867\) | 48.0324 | 1.63127 | ||||||||
\(868\) | −2.44666 | −0.0830450 | ||||||||
\(869\) | 24.5363 | 0.832336 | ||||||||
\(870\) | −66.8004 | −2.26474 | ||||||||
\(871\) | 4.63806 | 0.157155 | ||||||||
\(872\) | 0.372892 | 0.0126277 | ||||||||
\(873\) | −49.2829 | −1.66797 | ||||||||
\(874\) | −27.4097 | −0.927148 | ||||||||
\(875\) | −5.94644 | −0.201026 | ||||||||
\(876\) | 27.2638 | 0.921160 | ||||||||
\(877\) | −38.7335 | −1.30794 | −0.653969 | − | 0.756521i | \(-0.726897\pi\) | ||||
−0.653969 | + | 0.756521i | \(0.726897\pi\) | |||||||
\(878\) | 39.8988 | 1.34652 | ||||||||
\(879\) | 77.9465 | 2.62907 | ||||||||
\(880\) | −8.03362 | −0.270813 | ||||||||
\(881\) | 34.0835 | 1.14830 | 0.574152 | − | 0.818749i | \(-0.305332\pi\) | ||||
0.574152 | + | 0.818749i | \(0.305332\pi\) | |||||||
\(882\) | −37.7711 | −1.27182 | ||||||||
\(883\) | −27.1482 | −0.913608 | −0.456804 | − | 0.889567i | \(-0.651006\pi\) | ||||
−0.456804 | + | 0.889567i | \(0.651006\pi\) | |||||||
\(884\) | 0.392866 | 0.0132135 | ||||||||
\(885\) | 72.2054 | 2.42716 | ||||||||
\(886\) | 20.2233 | 0.679416 | ||||||||
\(887\) | −28.5311 | −0.957980 | −0.478990 | − | 0.877820i | \(-0.658997\pi\) | ||||
−0.478990 | + | 0.877820i | \(0.658997\pi\) | |||||||
\(888\) | −23.9431 | −0.803478 | ||||||||
\(889\) | 8.71688 | 0.292355 | ||||||||
\(890\) | −6.64544 | −0.222756 | ||||||||
\(891\) | −21.0834 | −0.706320 | ||||||||
\(892\) | −6.24952 | −0.209250 | ||||||||
\(893\) | −49.5745 | −1.65895 | ||||||||
\(894\) | −30.3837 | −1.01618 | ||||||||
\(895\) | −37.4351 | −1.25132 | ||||||||
\(896\) | 0.512181 | 0.0171108 | ||||||||
\(897\) | −5.05962 | −0.168936 | ||||||||
\(898\) | 15.6372 | 0.521822 | ||||||||
\(899\) | −50.8959 | −1.69747 | ||||||||
\(900\) | −2.42372 | −0.0807906 | ||||||||
\(901\) | −3.93457 | −0.131080 | ||||||||
\(902\) | 36.7248 | 1.22280 | ||||||||
\(903\) | −4.76447 | −0.158551 | ||||||||
\(904\) | 14.0372 | 0.466871 | ||||||||
\(905\) | −22.7662 | −0.756773 | ||||||||
\(906\) | −43.0577 | −1.43050 | ||||||||
\(907\) | −9.10965 | −0.302481 | −0.151241 | − | 0.988497i | \(-0.548327\pi\) | ||||
−0.151241 | + | 0.988497i | \(0.548327\pi\) | |||||||
\(908\) | −2.71972 | −0.0902571 | ||||||||
\(909\) | 85.7745 | 2.84496 | ||||||||
\(910\) | 0.543210 | 0.0180072 | ||||||||
\(911\) | −50.9909 | −1.68940 | −0.844702 | − | 0.535238i | \(-0.820222\pi\) | ||||
−0.844702 | + | 0.535238i | \(0.820222\pi\) | |||||||
\(912\) | 23.1358 | 0.766102 | ||||||||
\(913\) | 41.0561 | 1.35876 | ||||||||
\(914\) | −6.84392 | −0.226377 | ||||||||
\(915\) | 5.23828 | 0.173172 | ||||||||
\(916\) | −15.5315 | −0.513177 | ||||||||
\(917\) | 0.0744197 | 0.00245755 | ||||||||
\(918\) | −6.05220 | −0.199752 | ||||||||
\(919\) | −32.8564 | −1.08383 | −0.541917 | − | 0.840432i | \(-0.682301\pi\) | ||||
−0.541917 | + | 0.840432i | \(0.682301\pi\) | |||||||
\(920\) | 7.42791 | 0.244891 | ||||||||
\(921\) | 8.83135 | 0.291003 | ||||||||
\(922\) | −23.9589 | −0.789044 | ||||||||
\(923\) | −5.99909 | −0.197463 | ||||||||
\(924\) | 5.64791 | 0.185803 | ||||||||
\(925\) | −3.52869 | −0.116023 | ||||||||
\(926\) | −23.6330 | −0.776630 | ||||||||
\(927\) | 42.6128 | 1.39959 | ||||||||
\(928\) | 10.6545 | 0.349751 | ||||||||
\(929\) | −34.4575 | −1.13051 | −0.565256 | − | 0.824915i | \(-0.691223\pi\) | ||||
−0.565256 | + | 0.824915i | \(0.691223\pi\) | |||||||
\(930\) | 29.9500 | 0.982098 | ||||||||
\(931\) | 53.1367 | 1.74148 | ||||||||
\(932\) | −26.5727 | −0.870419 | ||||||||
\(933\) | 95.7769 | 3.13560 | ||||||||
\(934\) | 35.4564 | 1.16017 | ||||||||
\(935\) | −6.36001 | −0.207995 | ||||||||
\(936\) | 2.78194 | 0.0909306 | ||||||||
\(937\) | −8.79159 | −0.287209 | −0.143604 | − | 0.989635i | \(-0.545869\pi\) | ||||
−0.143604 | + | 0.989635i | \(0.545869\pi\) | |||||||
\(938\) | 4.78697 | 0.156300 | ||||||||
\(939\) | −43.4125 | −1.41671 | ||||||||
\(940\) | 13.4344 | 0.438183 | ||||||||
\(941\) | −29.5580 | −0.963563 | −0.481782 | − | 0.876291i | \(-0.660010\pi\) | ||||
−0.481782 | + | 0.876291i | \(0.660010\pi\) | |||||||
\(942\) | 49.2170 | 1.60358 | ||||||||
\(943\) | −33.9558 | −1.10575 | ||||||||
\(944\) | −11.5166 | −0.374833 | ||||||||
\(945\) | −8.36828 | −0.272220 | ||||||||
\(946\) | −11.9195 | −0.387535 | ||||||||
\(947\) | 26.3146 | 0.855109 | 0.427555 | − | 0.903990i | \(-0.359375\pi\) | ||||
0.427555 | + | 0.903990i | \(0.359375\pi\) | |||||||
\(948\) | 19.1489 | 0.621927 | ||||||||
\(949\) | −4.61196 | −0.149711 | ||||||||
\(950\) | 3.40971 | 0.110626 | ||||||||
\(951\) | 60.1541 | 1.95063 | ||||||||
\(952\) | 0.405480 | 0.0131417 | ||||||||
\(953\) | −21.4241 | −0.693996 | −0.346998 | − | 0.937866i | \(-0.612799\pi\) | ||||
−0.346998 | + | 0.937866i | \(0.612799\pi\) | |||||||
\(954\) | −27.8612 | −0.902041 | ||||||||
\(955\) | −1.12560 | −0.0364236 | ||||||||
\(956\) | −13.8726 | −0.448672 | ||||||||
\(957\) | 117.489 | 3.79788 | ||||||||
\(958\) | 13.4062 | 0.433134 | ||||||||
\(959\) | 8.56532 | 0.276588 | ||||||||
\(960\) | −6.26969 | −0.202353 | ||||||||
\(961\) | −8.18078 | −0.263896 | ||||||||
\(962\) | 4.05022 | 0.130584 | ||||||||
\(963\) | −55.3863 | −1.78480 | ||||||||
\(964\) | −1.51488 | −0.0487909 | ||||||||
\(965\) | −10.5047 | −0.338158 | ||||||||
\(966\) | −5.22207 | −0.168017 | ||||||||
\(967\) | 18.1263 | 0.582902 | 0.291451 | − | 0.956586i | \(-0.405862\pi\) | ||||
0.291451 | + | 0.956586i | \(0.405862\pi\) | |||||||
\(968\) | 3.12960 | 0.100589 | ||||||||
\(969\) | 18.3160 | 0.588395 | ||||||||
\(970\) | −18.7886 | −0.603264 | ||||||||
\(971\) | 14.1363 | 0.453654 | 0.226827 | − | 0.973935i | \(-0.427165\pi\) | ||||
0.226827 | + | 0.973935i | \(0.427165\pi\) | |||||||
\(972\) | 6.48029 | 0.207855 | ||||||||
\(973\) | −5.81854 | −0.186534 | ||||||||
\(974\) | 12.6732 | 0.406075 | ||||||||
\(975\) | 0.629405 | 0.0201571 | ||||||||
\(976\) | −0.835492 | −0.0267434 | ||||||||
\(977\) | −40.4882 | −1.29533 | −0.647666 | − | 0.761924i | \(-0.724255\pi\) | ||||
−0.647666 | + | 0.761924i | \(0.724255\pi\) | |||||||
\(978\) | 42.2772 | 1.35188 | ||||||||
\(979\) | 11.6881 | 0.373552 | ||||||||
\(980\) | −14.3998 | −0.459985 | ||||||||
\(981\) | 2.09042 | 0.0667419 | ||||||||
\(982\) | −26.4360 | −0.843606 | ||||||||
\(983\) | 18.4960 | 0.589932 | 0.294966 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294966 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(984\) | 28.6612 | 0.913685 | ||||||||
\(985\) | 28.1516 | 0.896984 | ||||||||
\(986\) | 8.43489 | 0.268621 | ||||||||
\(987\) | −9.44487 | −0.300634 | ||||||||
\(988\) | −3.91366 | −0.124510 | ||||||||
\(989\) | 11.0208 | 0.350440 | ||||||||
\(990\) | −45.0361 | −1.43134 | ||||||||
\(991\) | −25.3351 | −0.804796 | −0.402398 | − | 0.915465i | \(-0.631823\pi\) | ||||
−0.402398 | + | 0.915465i | \(0.631823\pi\) | |||||||
\(992\) | −4.77695 | −0.151668 | ||||||||
\(993\) | −13.5149 | −0.428881 | ||||||||
\(994\) | −6.19171 | −0.196389 | ||||||||
\(995\) | −4.99400 | −0.158320 | ||||||||
\(996\) | 32.0414 | 1.01527 | ||||||||
\(997\) | 56.5943 | 1.79236 | 0.896180 | − | 0.443692i | \(-0.146331\pi\) | ||||
0.896180 | + | 0.443692i | \(0.146331\pi\) | |||||||
\(998\) | 29.2330 | 0.925356 | ||||||||
\(999\) | −62.3946 | −1.97408 |
(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 | 8038.2.a.a.1.8 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8038.2.a.a.1.8 | ✓ | 75 | 1.1 | even | 1 | trivial |