Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, 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("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −1.09618 | −0.632878 | −0.316439 | − | 0.948613i | \(-0.602487\pi\) | ||||
−0.316439 | + | 0.948613i | \(0.602487\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.358556 | −0.160351 | −0.0801755 | − | 0.996781i | \(-0.525548\pi\) | ||||
−0.0801755 | + | 0.996781i | \(0.525548\pi\) | |||||||
\(6\) | 1.09618 | 0.447512 | ||||||||
\(7\) | −2.93033 | −1.10756 | −0.553781 | − | 0.832663i | \(-0.686815\pi\) | ||||
−0.553781 | + | 0.832663i | \(0.686815\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.79840 | −0.599465 | ||||||||
\(10\) | 0.358556 | 0.113385 | ||||||||
\(11\) | −2.70254 | −0.814847 | −0.407423 | − | 0.913239i | \(-0.633573\pi\) | ||||
−0.407423 | + | 0.913239i | \(0.633573\pi\) | |||||||
\(12\) | −1.09618 | −0.316439 | ||||||||
\(13\) | 0.734401 | 0.203686 | 0.101843 | − | 0.994800i | \(-0.467526\pi\) | ||||
0.101843 | + | 0.994800i | \(0.467526\pi\) | |||||||
\(14\) | 2.93033 | 0.783164 | ||||||||
\(15\) | 0.393040 | 0.101483 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.422719 | 0.102524 | 0.0512622 | − | 0.998685i | \(-0.483676\pi\) | ||||
0.0512622 | + | 0.998685i | \(0.483676\pi\) | |||||||
\(18\) | 1.79840 | 0.423886 | ||||||||
\(19\) | 8.46145 | 1.94119 | 0.970595 | − | 0.240717i | \(-0.0773826\pi\) | ||||
0.970595 | + | 0.240717i | \(0.0773826\pi\) | |||||||
\(20\) | −0.358556 | −0.0801755 | ||||||||
\(21\) | 3.21216 | 0.700951 | ||||||||
\(22\) | 2.70254 | 0.576184 | ||||||||
\(23\) | −8.04082 | −1.67663 | −0.838314 | − | 0.545188i | \(-0.816458\pi\) | ||||
−0.838314 | + | 0.545188i | \(0.816458\pi\) | |||||||
\(24\) | 1.09618 | 0.223756 | ||||||||
\(25\) | −4.87144 | −0.974288 | ||||||||
\(26\) | −0.734401 | −0.144028 | ||||||||
\(27\) | 5.25989 | 1.01227 | ||||||||
\(28\) | −2.93033 | −0.553781 | ||||||||
\(29\) | −6.64530 | −1.23400 | −0.617001 | − | 0.786962i | \(-0.711653\pi\) | ||||
−0.617001 | + | 0.786962i | \(0.711653\pi\) | |||||||
\(30\) | −0.393040 | −0.0717590 | ||||||||
\(31\) | 3.26346 | 0.586134 | 0.293067 | − | 0.956092i | \(-0.405324\pi\) | ||||
0.293067 | + | 0.956092i | \(0.405324\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.96246 | 0.515699 | ||||||||
\(34\) | −0.422719 | −0.0724957 | ||||||||
\(35\) | 1.05069 | 0.177598 | ||||||||
\(36\) | −1.79840 | −0.299733 | ||||||||
\(37\) | −3.52408 | −0.579356 | −0.289678 | − | 0.957124i | \(-0.593548\pi\) | ||||
−0.289678 | + | 0.957124i | \(0.593548\pi\) | |||||||
\(38\) | −8.46145 | −1.37263 | ||||||||
\(39\) | −0.805034 | −0.128909 | ||||||||
\(40\) | 0.358556 | 0.0566926 | ||||||||
\(41\) | −4.23707 | −0.661719 | −0.330860 | − | 0.943680i | \(-0.607339\pi\) | ||||
−0.330860 | + | 0.943680i | \(0.607339\pi\) | |||||||
\(42\) | −3.21216 | −0.495647 | ||||||||
\(43\) | −0.269063 | −0.0410316 | −0.0205158 | − | 0.999790i | \(-0.506531\pi\) | ||||
−0.0205158 | + | 0.999790i | \(0.506531\pi\) | |||||||
\(44\) | −2.70254 | −0.407423 | ||||||||
\(45\) | 0.644825 | 0.0961248 | ||||||||
\(46\) | 8.04082 | 1.18555 | ||||||||
\(47\) | −13.2554 | −1.93350 | −0.966751 | − | 0.255721i | \(-0.917687\pi\) | ||||
−0.966751 | + | 0.255721i | \(0.917687\pi\) | |||||||
\(48\) | −1.09618 | −0.158220 | ||||||||
\(49\) | 1.58684 | 0.226691 | ||||||||
\(50\) | 4.87144 | 0.688925 | ||||||||
\(51\) | −0.463375 | −0.0648855 | ||||||||
\(52\) | 0.734401 | 0.101843 | ||||||||
\(53\) | 2.29767 | 0.315610 | 0.157805 | − | 0.987470i | \(-0.449558\pi\) | ||||
0.157805 | + | 0.987470i | \(0.449558\pi\) | |||||||
\(54\) | −5.25989 | −0.715781 | ||||||||
\(55\) | 0.969011 | 0.130661 | ||||||||
\(56\) | 2.93033 | 0.391582 | ||||||||
\(57\) | −9.27525 | −1.22854 | ||||||||
\(58\) | 6.64530 | 0.872571 | ||||||||
\(59\) | −12.3501 | −1.60784 | −0.803921 | − | 0.594736i | \(-0.797256\pi\) | ||||
−0.803921 | + | 0.594736i | \(0.797256\pi\) | |||||||
\(60\) | 0.393040 | 0.0507413 | ||||||||
\(61\) | 5.42653 | 0.694796 | 0.347398 | − | 0.937718i | \(-0.387065\pi\) | ||||
0.347398 | + | 0.937718i | \(0.387065\pi\) | |||||||
\(62\) | −3.26346 | −0.414459 | ||||||||
\(63\) | 5.26990 | 0.663945 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.263324 | −0.0326613 | ||||||||
\(66\) | −2.96246 | −0.364654 | ||||||||
\(67\) | −2.25327 | −0.275281 | −0.137640 | − | 0.990482i | \(-0.543952\pi\) | ||||
−0.137640 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(68\) | 0.422719 | 0.0512622 | ||||||||
\(69\) | 8.81417 | 1.06110 | ||||||||
\(70\) | −1.05069 | −0.125581 | ||||||||
\(71\) | −6.19112 | −0.734751 | −0.367375 | − | 0.930073i | \(-0.619744\pi\) | ||||
−0.367375 | + | 0.930073i | \(0.619744\pi\) | |||||||
\(72\) | 1.79840 | 0.211943 | ||||||||
\(73\) | −14.6030 | −1.70916 | −0.854579 | − | 0.519322i | \(-0.826185\pi\) | ||||
−0.854579 | + | 0.519322i | \(0.826185\pi\) | |||||||
\(74\) | 3.52408 | 0.409666 | ||||||||
\(75\) | 5.33996 | 0.616605 | ||||||||
\(76\) | 8.46145 | 0.970595 | ||||||||
\(77\) | 7.91934 | 0.902493 | ||||||||
\(78\) | 0.805034 | 0.0911521 | ||||||||
\(79\) | 7.19226 | 0.809192 | 0.404596 | − | 0.914496i | \(-0.367412\pi\) | ||||
0.404596 | + | 0.914496i | \(0.367412\pi\) | |||||||
\(80\) | −0.358556 | −0.0400877 | ||||||||
\(81\) | −0.370583 | −0.0411759 | ||||||||
\(82\) | 4.23707 | 0.467906 | ||||||||
\(83\) | −2.45871 | −0.269879 | −0.134939 | − | 0.990854i | \(-0.543084\pi\) | ||||
−0.134939 | + | 0.990854i | \(0.543084\pi\) | |||||||
\(84\) | 3.21216 | 0.350476 | ||||||||
\(85\) | −0.151568 | −0.0164399 | ||||||||
\(86\) | 0.269063 | 0.0290138 | ||||||||
\(87\) | 7.28443 | 0.780973 | ||||||||
\(88\) | 2.70254 | 0.288092 | ||||||||
\(89\) | 5.76865 | 0.611476 | 0.305738 | − | 0.952116i | \(-0.401097\pi\) | ||||
0.305738 | + | 0.952116i | \(0.401097\pi\) | |||||||
\(90\) | −0.644825 | −0.0679705 | ||||||||
\(91\) | −2.15204 | −0.225595 | ||||||||
\(92\) | −8.04082 | −0.838314 | ||||||||
\(93\) | −3.57733 | −0.370951 | ||||||||
\(94\) | 13.2554 | 1.36719 | ||||||||
\(95\) | −3.03390 | −0.311272 | ||||||||
\(96\) | 1.09618 | 0.111878 | ||||||||
\(97\) | −7.90103 | −0.802228 | −0.401114 | − | 0.916028i | \(-0.631377\pi\) | ||||
−0.401114 | + | 0.916028i | \(0.631377\pi\) | |||||||
\(98\) | −1.58684 | −0.160295 | ||||||||
\(99\) | 4.86024 | 0.488472 | ||||||||
\(100\) | −4.87144 | −0.487144 | ||||||||
\(101\) | 4.10390 | 0.408353 | 0.204177 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204177 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(102\) | 0.463375 | 0.0458809 | ||||||||
\(103\) | 6.15301 | 0.606274 | 0.303137 | − | 0.952947i | \(-0.401966\pi\) | ||||
0.303137 | + | 0.952947i | \(0.401966\pi\) | |||||||
\(104\) | −0.734401 | −0.0720140 | ||||||||
\(105\) | −1.15174 | −0.112398 | ||||||||
\(106\) | −2.29767 | −0.223170 | ||||||||
\(107\) | 18.7240 | 1.81011 | 0.905057 | − | 0.425290i | \(-0.139828\pi\) | ||||
0.905057 | + | 0.425290i | \(0.139828\pi\) | |||||||
\(108\) | 5.25989 | 0.506133 | ||||||||
\(109\) | 14.3555 | 1.37501 | 0.687505 | − | 0.726180i | \(-0.258706\pi\) | ||||
0.687505 | + | 0.726180i | \(0.258706\pi\) | |||||||
\(110\) | −0.969011 | −0.0923916 | ||||||||
\(111\) | 3.86302 | 0.366662 | ||||||||
\(112\) | −2.93033 | −0.276890 | ||||||||
\(113\) | 9.25940 | 0.871051 | 0.435525 | − | 0.900176i | \(-0.356563\pi\) | ||||
0.435525 | + | 0.900176i | \(0.356563\pi\) | |||||||
\(114\) | 9.27525 | 0.868707 | ||||||||
\(115\) | 2.88308 | 0.268849 | ||||||||
\(116\) | −6.64530 | −0.617001 | ||||||||
\(117\) | −1.32074 | −0.122103 | ||||||||
\(118\) | 12.3501 | 1.13692 | ||||||||
\(119\) | −1.23871 | −0.113552 | ||||||||
\(120\) | −0.393040 | −0.0358795 | ||||||||
\(121\) | −3.69627 | −0.336025 | ||||||||
\(122\) | −5.42653 | −0.491295 | ||||||||
\(123\) | 4.64458 | 0.418788 | ||||||||
\(124\) | 3.26346 | 0.293067 | ||||||||
\(125\) | 3.53946 | 0.316579 | ||||||||
\(126\) | −5.26990 | −0.469480 | ||||||||
\(127\) | −4.51743 | −0.400857 | −0.200428 | − | 0.979708i | \(-0.564233\pi\) | ||||
−0.200428 | + | 0.979708i | \(0.564233\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.294940 | 0.0259680 | ||||||||
\(130\) | 0.263324 | 0.0230950 | ||||||||
\(131\) | 11.9861 | 1.04723 | 0.523616 | − | 0.851954i | \(-0.324583\pi\) | ||||
0.523616 | + | 0.851954i | \(0.324583\pi\) | |||||||
\(132\) | 2.96246 | 0.257849 | ||||||||
\(133\) | −24.7949 | −2.14999 | ||||||||
\(134\) | 2.25327 | 0.194653 | ||||||||
\(135\) | −1.88596 | −0.162318 | ||||||||
\(136\) | −0.422719 | −0.0362479 | ||||||||
\(137\) | 1.25766 | 0.107449 | 0.0537246 | − | 0.998556i | \(-0.482891\pi\) | ||||
0.0537246 | + | 0.998556i | \(0.482891\pi\) | |||||||
\(138\) | −8.81417 | −0.750312 | ||||||||
\(139\) | 8.62203 | 0.731311 | 0.365655 | − | 0.930750i | \(-0.380845\pi\) | ||||
0.365655 | + | 0.930750i | \(0.380845\pi\) | |||||||
\(140\) | 1.05069 | 0.0887992 | ||||||||
\(141\) | 14.5303 | 1.22367 | ||||||||
\(142\) | 6.19112 | 0.519547 | ||||||||
\(143\) | −1.98475 | −0.165973 | ||||||||
\(144\) | −1.79840 | −0.149866 | ||||||||
\(145\) | 2.38271 | 0.197873 | ||||||||
\(146\) | 14.6030 | 1.20856 | ||||||||
\(147\) | −1.73946 | −0.143468 | ||||||||
\(148\) | −3.52408 | −0.289678 | ||||||||
\(149\) | 20.3125 | 1.66407 | 0.832033 | − | 0.554727i | \(-0.187177\pi\) | ||||
0.832033 | + | 0.554727i | \(0.187177\pi\) | |||||||
\(150\) | −5.33996 | −0.436006 | ||||||||
\(151\) | 7.78097 | 0.633206 | 0.316603 | − | 0.948558i | \(-0.397458\pi\) | ||||
0.316603 | + | 0.948558i | \(0.397458\pi\) | |||||||
\(152\) | −8.46145 | −0.686315 | ||||||||
\(153\) | −0.760216 | −0.0614598 | ||||||||
\(154\) | −7.91934 | −0.638159 | ||||||||
\(155\) | −1.17013 | −0.0939871 | ||||||||
\(156\) | −0.805034 | −0.0644543 | ||||||||
\(157\) | −7.94526 | −0.634101 | −0.317051 | − | 0.948409i | \(-0.602692\pi\) | ||||
−0.317051 | + | 0.948409i | \(0.602692\pi\) | |||||||
\(158\) | −7.19226 | −0.572185 | ||||||||
\(159\) | −2.51866 | −0.199742 | ||||||||
\(160\) | 0.358556 | 0.0283463 | ||||||||
\(161\) | 23.5623 | 1.85697 | ||||||||
\(162\) | 0.370583 | 0.0291157 | ||||||||
\(163\) | 5.48851 | 0.429893 | 0.214947 | − | 0.976626i | \(-0.431042\pi\) | ||||
0.214947 | + | 0.976626i | \(0.431042\pi\) | |||||||
\(164\) | −4.23707 | −0.330860 | ||||||||
\(165\) | −1.06221 | −0.0826928 | ||||||||
\(166\) | 2.45871 | 0.190833 | ||||||||
\(167\) | 6.87509 | 0.532010 | 0.266005 | − | 0.963972i | \(-0.414296\pi\) | ||||
0.266005 | + | 0.963972i | \(0.414296\pi\) | |||||||
\(168\) | −3.21216 | −0.247824 | ||||||||
\(169\) | −12.4607 | −0.958512 | ||||||||
\(170\) | 0.151568 | 0.0116248 | ||||||||
\(171\) | −15.2170 | −1.16368 | ||||||||
\(172\) | −0.269063 | −0.0205158 | ||||||||
\(173\) | −1.08625 | −0.0825858 | −0.0412929 | − | 0.999147i | \(-0.513148\pi\) | ||||
−0.0412929 | + | 0.999147i | \(0.513148\pi\) | |||||||
\(174\) | −7.28443 | −0.552231 | ||||||||
\(175\) | 14.2749 | 1.07908 | ||||||||
\(176\) | −2.70254 | −0.203712 | ||||||||
\(177\) | 13.5379 | 1.01757 | ||||||||
\(178\) | −5.76865 | −0.432379 | ||||||||
\(179\) | −4.58642 | −0.342805 | −0.171402 | − | 0.985201i | \(-0.554830\pi\) | ||||
−0.171402 | + | 0.985201i | \(0.554830\pi\) | |||||||
\(180\) | 0.644825 | 0.0480624 | ||||||||
\(181\) | −16.6934 | −1.24081 | −0.620405 | − | 0.784281i | \(-0.713032\pi\) | ||||
−0.620405 | + | 0.784281i | \(0.713032\pi\) | |||||||
\(182\) | 2.15204 | 0.159520 | ||||||||
\(183\) | −5.94844 | −0.439721 | ||||||||
\(184\) | 8.04082 | 0.592777 | ||||||||
\(185\) | 1.26358 | 0.0929002 | ||||||||
\(186\) | 3.57733 | 0.262302 | ||||||||
\(187\) | −1.14242 | −0.0835417 | ||||||||
\(188\) | −13.2554 | −0.966751 | ||||||||
\(189\) | −15.4132 | −1.12115 | ||||||||
\(190\) | 3.03390 | 0.220102 | ||||||||
\(191\) | −12.8395 | −0.929037 | −0.464518 | − | 0.885563i | \(-0.653773\pi\) | ||||
−0.464518 | + | 0.885563i | \(0.653773\pi\) | |||||||
\(192\) | −1.09618 | −0.0791098 | ||||||||
\(193\) | 9.93167 | 0.714897 | 0.357448 | − | 0.933933i | \(-0.383647\pi\) | ||||
0.357448 | + | 0.933933i | \(0.383647\pi\) | |||||||
\(194\) | 7.90103 | 0.567261 | ||||||||
\(195\) | 0.288649 | 0.0206706 | ||||||||
\(196\) | 1.58684 | 0.113346 | ||||||||
\(197\) | 4.63936 | 0.330541 | 0.165270 | − | 0.986248i | \(-0.447150\pi\) | ||||
0.165270 | + | 0.986248i | \(0.447150\pi\) | |||||||
\(198\) | −4.86024 | −0.345402 | ||||||||
\(199\) | −11.9552 | −0.847483 | −0.423741 | − | 0.905783i | \(-0.639283\pi\) | ||||
−0.423741 | + | 0.905783i | \(0.639283\pi\) | |||||||
\(200\) | 4.87144 | 0.344463 | ||||||||
\(201\) | 2.46998 | 0.174219 | ||||||||
\(202\) | −4.10390 | −0.288749 | ||||||||
\(203\) | 19.4729 | 1.36673 | ||||||||
\(204\) | −0.463375 | −0.0324427 | ||||||||
\(205\) | 1.51923 | 0.106107 | ||||||||
\(206\) | −6.15301 | −0.428701 | ||||||||
\(207\) | 14.4606 | 1.00508 | ||||||||
\(208\) | 0.734401 | 0.0509216 | ||||||||
\(209\) | −22.8674 | −1.58177 | ||||||||
\(210\) | 1.15174 | 0.0794775 | ||||||||
\(211\) | 21.8957 | 1.50736 | 0.753681 | − | 0.657241i | \(-0.228276\pi\) | ||||
0.753681 | + | 0.657241i | \(0.228276\pi\) | |||||||
\(212\) | 2.29767 | 0.157805 | ||||||||
\(213\) | 6.78656 | 0.465008 | ||||||||
\(214\) | −18.7240 | −1.27994 | ||||||||
\(215\) | 0.0964739 | 0.00657946 | ||||||||
\(216\) | −5.25989 | −0.357890 | ||||||||
\(217\) | −9.56301 | −0.649179 | ||||||||
\(218\) | −14.3555 | −0.972278 | ||||||||
\(219\) | 16.0075 | 1.08169 | ||||||||
\(220\) | 0.969011 | 0.0653307 | ||||||||
\(221\) | 0.310445 | 0.0208828 | ||||||||
\(222\) | −3.86302 | −0.259269 | ||||||||
\(223\) | 14.9834 | 1.00336 | 0.501681 | − | 0.865053i | \(-0.332715\pi\) | ||||
0.501681 | + | 0.865053i | \(0.332715\pi\) | |||||||
\(224\) | 2.93033 | 0.195791 | ||||||||
\(225\) | 8.76078 | 0.584052 | ||||||||
\(226\) | −9.25940 | −0.615926 | ||||||||
\(227\) | −4.60248 | −0.305477 | −0.152739 | − | 0.988267i | \(-0.548809\pi\) | ||||
−0.152739 | + | 0.988267i | \(0.548809\pi\) | |||||||
\(228\) | −9.27525 | −0.614268 | ||||||||
\(229\) | −13.7986 | −0.911838 | −0.455919 | − | 0.890021i | \(-0.650689\pi\) | ||||
−0.455919 | + | 0.890021i | \(0.650689\pi\) | |||||||
\(230\) | −2.88308 | −0.190105 | ||||||||
\(231\) | −8.68100 | −0.571168 | ||||||||
\(232\) | 6.64530 | 0.436286 | ||||||||
\(233\) | −16.4695 | −1.07895 | −0.539477 | − | 0.842000i | \(-0.681378\pi\) | ||||
−0.539477 | + | 0.842000i | \(0.681378\pi\) | |||||||
\(234\) | 1.32074 | 0.0863398 | ||||||||
\(235\) | 4.75280 | 0.310039 | ||||||||
\(236\) | −12.3501 | −0.803921 | ||||||||
\(237\) | −7.88398 | −0.512120 | ||||||||
\(238\) | 1.23871 | 0.0802934 | ||||||||
\(239\) | −11.9731 | −0.774474 | −0.387237 | − | 0.921980i | \(-0.626570\pi\) | ||||
−0.387237 | + | 0.921980i | \(0.626570\pi\) | |||||||
\(240\) | 0.393040 | 0.0253706 | ||||||||
\(241\) | −9.79923 | −0.631224 | −0.315612 | − | 0.948888i | \(-0.602210\pi\) | ||||
−0.315612 | + | 0.948888i | \(0.602210\pi\) | |||||||
\(242\) | 3.69627 | 0.237605 | ||||||||
\(243\) | −15.3734 | −0.986207 | ||||||||
\(244\) | 5.42653 | 0.347398 | ||||||||
\(245\) | −0.568971 | −0.0363502 | ||||||||
\(246\) | −4.64458 | −0.296128 | ||||||||
\(247\) | 6.21410 | 0.395394 | ||||||||
\(248\) | −3.26346 | −0.207230 | ||||||||
\(249\) | 2.69518 | 0.170800 | ||||||||
\(250\) | −3.53946 | −0.223855 | ||||||||
\(251\) | 7.68150 | 0.484852 | 0.242426 | − | 0.970170i | \(-0.422057\pi\) | ||||
0.242426 | + | 0.970170i | \(0.422057\pi\) | |||||||
\(252\) | 5.26990 | 0.331972 | ||||||||
\(253\) | 21.7307 | 1.36619 | ||||||||
\(254\) | 4.51743 | 0.283449 | ||||||||
\(255\) | 0.166146 | 0.0104044 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.4175 | −1.52312 | −0.761560 | − | 0.648094i | \(-0.775566\pi\) | ||||
−0.761560 | + | 0.648094i | \(0.775566\pi\) | |||||||
\(258\) | −0.294940 | −0.0183622 | ||||||||
\(259\) | 10.3267 | 0.641672 | ||||||||
\(260\) | −0.263324 | −0.0163306 | ||||||||
\(261\) | 11.9509 | 0.739741 | ||||||||
\(262\) | −11.9861 | −0.740505 | ||||||||
\(263\) | 24.5723 | 1.51519 | 0.757597 | − | 0.652723i | \(-0.226373\pi\) | ||||
0.757597 | + | 0.652723i | \(0.226373\pi\) | |||||||
\(264\) | −2.96246 | −0.182327 | ||||||||
\(265\) | −0.823843 | −0.0506083 | ||||||||
\(266\) | 24.7949 | 1.52027 | ||||||||
\(267\) | −6.32346 | −0.386990 | ||||||||
\(268\) | −2.25327 | −0.137640 | ||||||||
\(269\) | 26.3214 | 1.60485 | 0.802423 | − | 0.596756i | \(-0.203544\pi\) | ||||
0.802423 | + | 0.596756i | \(0.203544\pi\) | |||||||
\(270\) | 1.88596 | 0.114776 | ||||||||
\(271\) | 14.7005 | 0.892994 | 0.446497 | − | 0.894785i | \(-0.352671\pi\) | ||||
0.446497 | + | 0.894785i | \(0.352671\pi\) | |||||||
\(272\) | 0.422719 | 0.0256311 | ||||||||
\(273\) | 2.35902 | 0.142774 | ||||||||
\(274\) | −1.25766 | −0.0759780 | ||||||||
\(275\) | 13.1653 | 0.793895 | ||||||||
\(276\) | 8.81417 | 0.530550 | ||||||||
\(277\) | 31.7443 | 1.90733 | 0.953665 | − | 0.300872i | \(-0.0972777\pi\) | ||||
0.953665 | + | 0.300872i | \(0.0972777\pi\) | |||||||
\(278\) | −8.62203 | −0.517115 | ||||||||
\(279\) | −5.86899 | −0.351367 | ||||||||
\(280\) | −1.05069 | −0.0627905 | ||||||||
\(281\) | −21.4480 | −1.27948 | −0.639740 | − | 0.768591i | \(-0.720958\pi\) | ||||
−0.639740 | + | 0.768591i | \(0.720958\pi\) | |||||||
\(282\) | −14.5303 | −0.865266 | ||||||||
\(283\) | 25.4345 | 1.51193 | 0.755963 | − | 0.654614i | \(-0.227169\pi\) | ||||
0.755963 | + | 0.654614i | \(0.227169\pi\) | |||||||
\(284\) | −6.19112 | −0.367375 | ||||||||
\(285\) | 3.32569 | 0.196997 | ||||||||
\(286\) | 1.98475 | 0.117361 | ||||||||
\(287\) | 12.4160 | 0.732894 | ||||||||
\(288\) | 1.79840 | 0.105972 | ||||||||
\(289\) | −16.8213 | −0.989489 | ||||||||
\(290\) | −2.38271 | −0.139918 | ||||||||
\(291\) | 8.66093 | 0.507713 | ||||||||
\(292\) | −14.6030 | −0.854579 | ||||||||
\(293\) | −31.1876 | −1.82200 | −0.910998 | − | 0.412411i | \(-0.864687\pi\) | ||||
−0.910998 | + | 0.412411i | \(0.864687\pi\) | |||||||
\(294\) | 1.73946 | 0.101447 | ||||||||
\(295\) | 4.42818 | 0.257819 | ||||||||
\(296\) | 3.52408 | 0.204833 | ||||||||
\(297\) | −14.2151 | −0.824842 | ||||||||
\(298\) | −20.3125 | −1.17667 | ||||||||
\(299\) | −5.90519 | −0.341506 | ||||||||
\(300\) | 5.33996 | 0.308303 | ||||||||
\(301\) | 0.788442 | 0.0454451 | ||||||||
\(302\) | −7.78097 | −0.447744 | ||||||||
\(303\) | −4.49860 | −0.258438 | ||||||||
\(304\) | 8.46145 | 0.485298 | ||||||||
\(305\) | −1.94571 | −0.111411 | ||||||||
\(306\) | 0.760216 | 0.0434587 | ||||||||
\(307\) | 15.3678 | 0.877085 | 0.438542 | − | 0.898711i | \(-0.355495\pi\) | ||||
0.438542 | + | 0.898711i | \(0.355495\pi\) | |||||||
\(308\) | 7.91934 | 0.451246 | ||||||||
\(309\) | −6.74479 | −0.383698 | ||||||||
\(310\) | 1.17013 | 0.0664589 | ||||||||
\(311\) | 31.9496 | 1.81169 | 0.905847 | − | 0.423605i | \(-0.139235\pi\) | ||||
0.905847 | + | 0.423605i | \(0.139235\pi\) | |||||||
\(312\) | 0.805034 | 0.0455761 | ||||||||
\(313\) | −29.7455 | −1.68132 | −0.840658 | − | 0.541566i | \(-0.817832\pi\) | ||||
−0.840658 | + | 0.541566i | \(0.817832\pi\) | |||||||
\(314\) | 7.94526 | 0.448377 | ||||||||
\(315\) | −1.88955 | −0.106464 | ||||||||
\(316\) | 7.19226 | 0.404596 | ||||||||
\(317\) | 16.4561 | 0.924269 | 0.462134 | − | 0.886810i | \(-0.347084\pi\) | ||||
0.462134 | + | 0.886810i | \(0.347084\pi\) | |||||||
\(318\) | 2.51866 | 0.141239 | ||||||||
\(319\) | 17.9592 | 1.00552 | ||||||||
\(320\) | −0.358556 | −0.0200439 | ||||||||
\(321\) | −20.5248 | −1.14558 | ||||||||
\(322\) | −23.5623 | −1.31307 | ||||||||
\(323\) | 3.57682 | 0.199019 | ||||||||
\(324\) | −0.370583 | −0.0205879 | ||||||||
\(325\) | −3.57759 | −0.198449 | ||||||||
\(326\) | −5.48851 | −0.303980 | ||||||||
\(327\) | −15.7362 | −0.870213 | ||||||||
\(328\) | 4.23707 | 0.233953 | ||||||||
\(329\) | 38.8428 | 2.14147 | ||||||||
\(330\) | 1.06221 | 0.0584726 | ||||||||
\(331\) | 8.39583 | 0.461476 | 0.230738 | − | 0.973016i | \(-0.425886\pi\) | ||||
0.230738 | + | 0.973016i | \(0.425886\pi\) | |||||||
\(332\) | −2.45871 | −0.134939 | ||||||||
\(333\) | 6.33770 | 0.347304 | ||||||||
\(334\) | −6.87509 | −0.376188 | ||||||||
\(335\) | 0.807922 | 0.0441415 | ||||||||
\(336\) | 3.21216 | 0.175238 | ||||||||
\(337\) | −1.46106 | −0.0795890 | −0.0397945 | − | 0.999208i | \(-0.512670\pi\) | ||||
−0.0397945 | + | 0.999208i | \(0.512670\pi\) | |||||||
\(338\) | 12.4607 | 0.677770 | ||||||||
\(339\) | −10.1499 | −0.551269 | ||||||||
\(340\) | −0.151568 | −0.00821994 | ||||||||
\(341\) | −8.81962 | −0.477609 | ||||||||
\(342\) | 15.2170 | 0.822844 | ||||||||
\(343\) | 15.8623 | 0.856486 | ||||||||
\(344\) | 0.269063 | 0.0145069 | ||||||||
\(345\) | −3.16037 | −0.170149 | ||||||||
\(346\) | 1.08625 | 0.0583970 | ||||||||
\(347\) | −1.47347 | −0.0791002 | −0.0395501 | − | 0.999218i | \(-0.512592\pi\) | ||||
−0.0395501 | + | 0.999218i | \(0.512592\pi\) | |||||||
\(348\) | 7.28443 | 0.390486 | ||||||||
\(349\) | 20.6350 | 1.10457 | 0.552284 | − | 0.833656i | \(-0.313756\pi\) | ||||
0.552284 | + | 0.833656i | \(0.313756\pi\) | |||||||
\(350\) | −14.2749 | −0.763027 | ||||||||
\(351\) | 3.86287 | 0.206185 | ||||||||
\(352\) | 2.70254 | 0.144046 | ||||||||
\(353\) | 12.8922 | 0.686183 | 0.343092 | − | 0.939302i | \(-0.388526\pi\) | ||||
0.343092 | + | 0.939302i | \(0.388526\pi\) | |||||||
\(354\) | −13.5379 | −0.719529 | ||||||||
\(355\) | 2.21986 | 0.117818 | ||||||||
\(356\) | 5.76865 | 0.305738 | ||||||||
\(357\) | 1.35784 | 0.0718646 | ||||||||
\(358\) | 4.58642 | 0.242400 | ||||||||
\(359\) | 24.5565 | 1.29604 | 0.648022 | − | 0.761621i | \(-0.275596\pi\) | ||||
0.648022 | + | 0.761621i | \(0.275596\pi\) | |||||||
\(360\) | −0.644825 | −0.0339853 | ||||||||
\(361\) | 52.5962 | 2.76822 | ||||||||
\(362\) | 16.6934 | 0.877385 | ||||||||
\(363\) | 4.05177 | 0.212663 | ||||||||
\(364\) | −2.15204 | −0.112798 | ||||||||
\(365\) | 5.23600 | 0.274065 | ||||||||
\(366\) | 5.94844 | 0.310930 | ||||||||
\(367\) | 30.9871 | 1.61751 | 0.808757 | − | 0.588143i | \(-0.200141\pi\) | ||||
0.808757 | + | 0.588143i | \(0.200141\pi\) | |||||||
\(368\) | −8.04082 | −0.419157 | ||||||||
\(369\) | 7.61993 | 0.396678 | ||||||||
\(370\) | −1.26358 | −0.0656904 | ||||||||
\(371\) | −6.73294 | −0.349557 | ||||||||
\(372\) | −3.57733 | −0.185476 | ||||||||
\(373\) | −8.80764 | −0.456042 | −0.228021 | − | 0.973656i | \(-0.573226\pi\) | ||||
−0.228021 | + | 0.973656i | \(0.573226\pi\) | |||||||
\(374\) | 1.14242 | 0.0590729 | ||||||||
\(375\) | −3.87987 | −0.200356 | ||||||||
\(376\) | 13.2554 | 0.683596 | ||||||||
\(377\) | −4.88032 | −0.251349 | ||||||||
\(378\) | 15.4132 | 0.792771 | ||||||||
\(379\) | −10.3435 | −0.531312 | −0.265656 | − | 0.964068i | \(-0.585589\pi\) | ||||
−0.265656 | + | 0.964068i | \(0.585589\pi\) | |||||||
\(380\) | −3.03390 | −0.155636 | ||||||||
\(381\) | 4.95190 | 0.253694 | ||||||||
\(382\) | 12.8395 | 0.656928 | ||||||||
\(383\) | 12.6260 | 0.645156 | 0.322578 | − | 0.946543i | \(-0.395451\pi\) | ||||
0.322578 | + | 0.946543i | \(0.395451\pi\) | |||||||
\(384\) | 1.09618 | 0.0559390 | ||||||||
\(385\) | −2.83952 | −0.144716 | ||||||||
\(386\) | −9.93167 | −0.505509 | ||||||||
\(387\) | 0.483881 | 0.0245971 | ||||||||
\(388\) | −7.90103 | −0.401114 | ||||||||
\(389\) | 1.18354 | 0.0600080 | 0.0300040 | − | 0.999550i | \(-0.490448\pi\) | ||||
0.0300040 | + | 0.999550i | \(0.490448\pi\) | |||||||
\(390\) | −0.288649 | −0.0146163 | ||||||||
\(391\) | −3.39901 | −0.171895 | ||||||||
\(392\) | −1.58684 | −0.0801475 | ||||||||
\(393\) | −13.1389 | −0.662770 | ||||||||
\(394\) | −4.63936 | −0.233728 | ||||||||
\(395\) | −2.57882 | −0.129755 | ||||||||
\(396\) | 4.86024 | 0.244236 | ||||||||
\(397\) | 14.4391 | 0.724679 | 0.362339 | − | 0.932046i | \(-0.381978\pi\) | ||||
0.362339 | + | 0.932046i | \(0.381978\pi\) | |||||||
\(398\) | 11.9552 | 0.599261 | ||||||||
\(399\) | 27.1796 | 1.36068 | ||||||||
\(400\) | −4.87144 | −0.243572 | ||||||||
\(401\) | 7.71569 | 0.385303 | 0.192652 | − | 0.981267i | \(-0.438291\pi\) | ||||
0.192652 | + | 0.981267i | \(0.438291\pi\) | |||||||
\(402\) | −2.46998 | −0.123191 | ||||||||
\(403\) | 2.39669 | 0.119387 | ||||||||
\(404\) | 4.10390 | 0.204177 | ||||||||
\(405\) | 0.132875 | 0.00660259 | ||||||||
\(406\) | −19.4729 | −0.966426 | ||||||||
\(407\) | 9.52398 | 0.472086 | ||||||||
\(408\) | 0.463375 | 0.0229405 | ||||||||
\(409\) | 2.51025 | 0.124124 | 0.0620619 | − | 0.998072i | \(-0.480232\pi\) | ||||
0.0620619 | + | 0.998072i | \(0.480232\pi\) | |||||||
\(410\) | −1.51923 | −0.0750292 | ||||||||
\(411\) | −1.37862 | −0.0680022 | ||||||||
\(412\) | 6.15301 | 0.303137 | ||||||||
\(413\) | 36.1898 | 1.78078 | ||||||||
\(414\) | −14.4606 | −0.710699 | ||||||||
\(415\) | 0.881585 | 0.0432753 | ||||||||
\(416\) | −0.734401 | −0.0360070 | ||||||||
\(417\) | −9.45127 | −0.462831 | ||||||||
\(418\) | 22.8674 | 1.11848 | ||||||||
\(419\) | 11.5020 | 0.561912 | 0.280956 | − | 0.959721i | \(-0.409349\pi\) | ||||
0.280956 | + | 0.959721i | \(0.409349\pi\) | |||||||
\(420\) | −1.15174 | −0.0561991 | ||||||||
\(421\) | 23.1953 | 1.13047 | 0.565234 | − | 0.824931i | \(-0.308786\pi\) | ||||
0.565234 | + | 0.824931i | \(0.308786\pi\) | |||||||
\(422\) | −21.8957 | −1.06587 | ||||||||
\(423\) | 23.8385 | 1.15907 | ||||||||
\(424\) | −2.29767 | −0.111585 | ||||||||
\(425\) | −2.05925 | −0.0998883 | ||||||||
\(426\) | −6.78656 | −0.328810 | ||||||||
\(427\) | −15.9015 | −0.769529 | ||||||||
\(428\) | 18.7240 | 0.905057 | ||||||||
\(429\) | 2.17564 | 0.105041 | ||||||||
\(430\) | −0.0964739 | −0.00465238 | ||||||||
\(431\) | −8.18662 | −0.394336 | −0.197168 | − | 0.980370i | \(-0.563174\pi\) | ||||
−0.197168 | + | 0.980370i | \(0.563174\pi\) | |||||||
\(432\) | 5.25989 | 0.253067 | ||||||||
\(433\) | −14.8621 | −0.714229 | −0.357114 | − | 0.934061i | \(-0.616239\pi\) | ||||
−0.357114 | + | 0.934061i | \(0.616239\pi\) | |||||||
\(434\) | 9.56301 | 0.459039 | ||||||||
\(435\) | −2.61187 | −0.125230 | ||||||||
\(436\) | 14.3555 | 0.687505 | ||||||||
\(437\) | −68.0371 | −3.25465 | ||||||||
\(438\) | −16.0075 | −0.764869 | ||||||||
\(439\) | 8.67971 | 0.414260 | 0.207130 | − | 0.978313i | \(-0.433588\pi\) | ||||
0.207130 | + | 0.978313i | \(0.433588\pi\) | |||||||
\(440\) | −0.969011 | −0.0461958 | ||||||||
\(441\) | −2.85377 | −0.135894 | ||||||||
\(442\) | −0.310445 | −0.0147664 | ||||||||
\(443\) | −28.4688 | −1.35259 | −0.676296 | − | 0.736630i | \(-0.736416\pi\) | ||||
−0.676296 | + | 0.736630i | \(0.736416\pi\) | |||||||
\(444\) | 3.86302 | 0.183331 | ||||||||
\(445\) | −2.06838 | −0.0980507 | ||||||||
\(446\) | −14.9834 | −0.709484 | ||||||||
\(447\) | −22.2661 | −1.05315 | ||||||||
\(448\) | −2.93033 | −0.138445 | ||||||||
\(449\) | −12.7608 | −0.602218 | −0.301109 | − | 0.953590i | \(-0.597357\pi\) | ||||
−0.301109 | + | 0.953590i | \(0.597357\pi\) | |||||||
\(450\) | −8.76078 | −0.412987 | ||||||||
\(451\) | 11.4509 | 0.539200 | ||||||||
\(452\) | 9.25940 | 0.435525 | ||||||||
\(453\) | −8.52932 | −0.400742 | ||||||||
\(454\) | 4.60248 | 0.216005 | ||||||||
\(455\) | 0.771626 | 0.0361744 | ||||||||
\(456\) | 9.27525 | 0.434353 | ||||||||
\(457\) | −16.2696 | −0.761058 | −0.380529 | − | 0.924769i | \(-0.624258\pi\) | ||||
−0.380529 | + | 0.924769i | \(0.624258\pi\) | |||||||
\(458\) | 13.7986 | 0.644767 | ||||||||
\(459\) | 2.22346 | 0.103782 | ||||||||
\(460\) | 2.88308 | 0.134424 | ||||||||
\(461\) | −7.67436 | −0.357431 | −0.178715 | − | 0.983901i | \(-0.557194\pi\) | ||||
−0.178715 | + | 0.983901i | \(0.557194\pi\) | |||||||
\(462\) | 8.68100 | 0.403877 | ||||||||
\(463\) | −8.10682 | −0.376756 | −0.188378 | − | 0.982097i | \(-0.560323\pi\) | ||||
−0.188378 | + | 0.982097i | \(0.560323\pi\) | |||||||
\(464\) | −6.64530 | −0.308500 | ||||||||
\(465\) | 1.28267 | 0.0594824 | ||||||||
\(466\) | 16.4695 | 0.762936 | ||||||||
\(467\) | −34.5921 | −1.60073 | −0.800367 | − | 0.599511i | \(-0.795362\pi\) | ||||
−0.800367 | + | 0.599511i | \(0.795362\pi\) | |||||||
\(468\) | −1.32074 | −0.0610514 | ||||||||
\(469\) | 6.60282 | 0.304890 | ||||||||
\(470\) | −4.75280 | −0.219231 | ||||||||
\(471\) | 8.70942 | 0.401309 | ||||||||
\(472\) | 12.3501 | 0.568458 | ||||||||
\(473\) | 0.727152 | 0.0334345 | ||||||||
\(474\) | 7.88398 | 0.362123 | ||||||||
\(475\) | −41.2194 | −1.89128 | ||||||||
\(476\) | −1.23871 | −0.0567760 | ||||||||
\(477\) | −4.13213 | −0.189197 | ||||||||
\(478\) | 11.9731 | 0.547636 | ||||||||
\(479\) | 27.7791 | 1.26926 | 0.634630 | − | 0.772816i | \(-0.281153\pi\) | ||||
0.634630 | + | 0.772816i | \(0.281153\pi\) | |||||||
\(480\) | −0.393040 | −0.0179398 | ||||||||
\(481\) | −2.58809 | −0.118007 | ||||||||
\(482\) | 9.79923 | 0.446343 | ||||||||
\(483\) | −25.8284 | −1.17523 | ||||||||
\(484\) | −3.69627 | −0.168012 | ||||||||
\(485\) | 2.83296 | 0.128638 | ||||||||
\(486\) | 15.3734 | 0.697354 | ||||||||
\(487\) | −34.7919 | −1.57657 | −0.788287 | − | 0.615308i | \(-0.789032\pi\) | ||||
−0.788287 | + | 0.615308i | \(0.789032\pi\) | |||||||
\(488\) | −5.42653 | −0.245648 | ||||||||
\(489\) | −6.01637 | −0.272070 | ||||||||
\(490\) | 0.568971 | 0.0257035 | ||||||||
\(491\) | 3.24788 | 0.146575 | 0.0732874 | − | 0.997311i | \(-0.476651\pi\) | ||||
0.0732874 | + | 0.997311i | \(0.476651\pi\) | |||||||
\(492\) | 4.64458 | 0.209394 | ||||||||
\(493\) | −2.80910 | −0.126515 | ||||||||
\(494\) | −6.21410 | −0.279586 | ||||||||
\(495\) | −1.74267 | −0.0783270 | ||||||||
\(496\) | 3.26346 | 0.146534 | ||||||||
\(497\) | 18.1420 | 0.813781 | ||||||||
\(498\) | −2.69518 | −0.120774 | ||||||||
\(499\) | 1.21762 | 0.0545081 | 0.0272541 | − | 0.999629i | \(-0.491324\pi\) | ||||
0.0272541 | + | 0.999629i | \(0.491324\pi\) | |||||||
\(500\) | 3.53946 | 0.158289 | ||||||||
\(501\) | −7.53631 | −0.336698 | ||||||||
\(502\) | −7.68150 | −0.342842 | ||||||||
\(503\) | −27.0511 | −1.20615 | −0.603074 | − | 0.797685i | \(-0.706058\pi\) | ||||
−0.603074 | + | 0.797685i | \(0.706058\pi\) | |||||||
\(504\) | −5.26990 | −0.234740 | ||||||||
\(505\) | −1.47148 | −0.0654798 | ||||||||
\(506\) | −21.7307 | −0.966046 | ||||||||
\(507\) | 13.6591 | 0.606621 | ||||||||
\(508\) | −4.51743 | −0.200428 | ||||||||
\(509\) | 36.7216 | 1.62766 | 0.813828 | − | 0.581106i | \(-0.197380\pi\) | ||||
0.813828 | + | 0.581106i | \(0.197380\pi\) | |||||||
\(510\) | −0.166146 | −0.00735705 | ||||||||
\(511\) | 42.7918 | 1.89300 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 44.5063 | 1.96500 | ||||||||
\(514\) | 24.4175 | 1.07701 | ||||||||
\(515\) | −2.20620 | −0.0972166 | ||||||||
\(516\) | 0.294940 | 0.0129840 | ||||||||
\(517\) | 35.8233 | 1.57551 | ||||||||
\(518\) | −10.3267 | −0.453731 | ||||||||
\(519\) | 1.19072 | 0.0522667 | ||||||||
\(520\) | 0.263324 | 0.0115475 | ||||||||
\(521\) | −38.4714 | −1.68546 | −0.842732 | − | 0.538334i | \(-0.819054\pi\) | ||||
−0.842732 | + | 0.538334i | \(0.819054\pi\) | |||||||
\(522\) | −11.9509 | −0.523076 | ||||||||
\(523\) | 9.02479 | 0.394627 | 0.197313 | − | 0.980340i | \(-0.436778\pi\) | ||||
0.197313 | + | 0.980340i | \(0.436778\pi\) | |||||||
\(524\) | 11.9861 | 0.523616 | ||||||||
\(525\) | −15.6478 | −0.682928 | ||||||||
\(526\) | −24.5723 | −1.07140 | ||||||||
\(527\) | 1.37952 | 0.0600930 | ||||||||
\(528\) | 2.96246 | 0.128925 | ||||||||
\(529\) | 41.6549 | 1.81108 | ||||||||
\(530\) | 0.823843 | 0.0357855 | ||||||||
\(531\) | 22.2103 | 0.963845 | ||||||||
\(532\) | −24.7949 | −1.07499 | ||||||||
\(533\) | −3.11171 | −0.134783 | ||||||||
\(534\) | 6.32346 | 0.273643 | ||||||||
\(535\) | −6.71358 | −0.290254 | ||||||||
\(536\) | 2.25327 | 0.0973264 | ||||||||
\(537\) | 5.02752 | 0.216954 | ||||||||
\(538\) | −26.3214 | −1.13480 | ||||||||
\(539\) | −4.28850 | −0.184719 | ||||||||
\(540\) | −1.88596 | −0.0811589 | ||||||||
\(541\) | 0.258241 | 0.0111027 | 0.00555133 | − | 0.999985i | \(-0.498233\pi\) | ||||
0.00555133 | + | 0.999985i | \(0.498233\pi\) | |||||||
\(542\) | −14.7005 | −0.631442 | ||||||||
\(543\) | 18.2989 | 0.785282 | ||||||||
\(544\) | −0.422719 | −0.0181239 | ||||||||
\(545\) | −5.14725 | −0.220484 | ||||||||
\(546\) | −2.35902 | −0.100957 | ||||||||
\(547\) | −13.3586 | −0.571173 | −0.285587 | − | 0.958353i | \(-0.592188\pi\) | ||||
−0.285587 | + | 0.958353i | \(0.592188\pi\) | |||||||
\(548\) | 1.25766 | 0.0537246 | ||||||||
\(549\) | −9.75906 | −0.416506 | ||||||||
\(550\) | −13.1653 | −0.561369 | ||||||||
\(551\) | −56.2289 | −2.39543 | ||||||||
\(552\) | −8.81417 | −0.375156 | ||||||||
\(553\) | −21.0757 | −0.896229 | ||||||||
\(554\) | −31.7443 | −1.34869 | ||||||||
\(555\) | −1.38511 | −0.0587945 | ||||||||
\(556\) | 8.62203 | 0.365655 | ||||||||
\(557\) | −37.8202 | −1.60249 | −0.801247 | − | 0.598334i | \(-0.795830\pi\) | ||||
−0.801247 | + | 0.598334i | \(0.795830\pi\) | |||||||
\(558\) | 5.86899 | 0.248454 | ||||||||
\(559\) | −0.197600 | −0.00835758 | ||||||||
\(560\) | 1.05069 | 0.0443996 | ||||||||
\(561\) | 1.25229 | 0.0528717 | ||||||||
\(562\) | 21.4480 | 0.904729 | ||||||||
\(563\) | −0.802330 | −0.0338142 | −0.0169071 | − | 0.999857i | \(-0.505382\pi\) | ||||
−0.0169071 | + | 0.999857i | \(0.505382\pi\) | |||||||
\(564\) | 14.5303 | 0.611835 | ||||||||
\(565\) | −3.32001 | −0.139674 | ||||||||
\(566\) | −25.4345 | −1.06909 | ||||||||
\(567\) | 1.08593 | 0.0456048 | ||||||||
\(568\) | 6.19112 | 0.259774 | ||||||||
\(569\) | 7.01152 | 0.293938 | 0.146969 | − | 0.989141i | \(-0.453048\pi\) | ||||
0.146969 | + | 0.989141i | \(0.453048\pi\) | |||||||
\(570\) | −3.32569 | −0.139298 | ||||||||
\(571\) | 19.1422 | 0.801078 | 0.400539 | − | 0.916280i | \(-0.368823\pi\) | ||||
0.400539 | + | 0.916280i | \(0.368823\pi\) | |||||||
\(572\) | −1.98475 | −0.0829866 | ||||||||
\(573\) | 14.0744 | 0.587967 | ||||||||
\(574\) | −12.4160 | −0.518235 | ||||||||
\(575\) | 39.1704 | 1.63352 | ||||||||
\(576\) | −1.79840 | −0.0749332 | ||||||||
\(577\) | −30.6062 | −1.27415 | −0.637077 | − | 0.770800i | \(-0.719857\pi\) | ||||
−0.637077 | + | 0.770800i | \(0.719857\pi\) | |||||||
\(578\) | 16.8213 | 0.699674 | ||||||||
\(579\) | −10.8869 | −0.452443 | ||||||||
\(580\) | 2.38271 | 0.0989367 | ||||||||
\(581\) | 7.20484 | 0.298907 | ||||||||
\(582\) | −8.66093 | −0.359007 | ||||||||
\(583\) | −6.20955 | −0.257173 | ||||||||
\(584\) | 14.6030 | 0.604278 | ||||||||
\(585\) | 0.473560 | 0.0195793 | ||||||||
\(586\) | 31.1876 | 1.28835 | ||||||||
\(587\) | 16.1249 | 0.665547 | 0.332773 | − | 0.943007i | \(-0.392016\pi\) | ||||
0.332773 | + | 0.943007i | \(0.392016\pi\) | |||||||
\(588\) | −1.73946 | −0.0717340 | ||||||||
\(589\) | 27.6136 | 1.13780 | ||||||||
\(590\) | −4.42818 | −0.182305 | ||||||||
\(591\) | −5.08556 | −0.209192 | ||||||||
\(592\) | −3.52408 | −0.144839 | ||||||||
\(593\) | 46.1521 | 1.89524 | 0.947619 | − | 0.319403i | \(-0.103482\pi\) | ||||
0.947619 | + | 0.319403i | \(0.103482\pi\) | |||||||
\(594\) | 14.2151 | 0.583251 | ||||||||
\(595\) | 0.444145 | 0.0182082 | ||||||||
\(596\) | 20.3125 | 0.832033 | ||||||||
\(597\) | 13.1050 | 0.536353 | ||||||||
\(598\) | 5.90519 | 0.241481 | ||||||||
\(599\) | −21.7115 | −0.887107 | −0.443553 | − | 0.896248i | \(-0.646282\pi\) | ||||
−0.443553 | + | 0.896248i | \(0.646282\pi\) | |||||||
\(600\) | −5.33996 | −0.218003 | ||||||||
\(601\) | −17.7558 | −0.724273 | −0.362136 | − | 0.932125i | \(-0.617953\pi\) | ||||
−0.362136 | + | 0.932125i | \(0.617953\pi\) | |||||||
\(602\) | −0.788442 | −0.0321345 | ||||||||
\(603\) | 4.05227 | 0.165021 | ||||||||
\(604\) | 7.78097 | 0.316603 | ||||||||
\(605\) | 1.32532 | 0.0538819 | ||||||||
\(606\) | 4.49860 | 0.182743 | ||||||||
\(607\) | −25.2321 | −1.02414 | −0.512071 | − | 0.858943i | \(-0.671121\pi\) | ||||
−0.512071 | + | 0.858943i | \(0.671121\pi\) | |||||||
\(608\) | −8.46145 | −0.343157 | ||||||||
\(609\) | −21.3458 | −0.864975 | ||||||||
\(610\) | 1.94571 | 0.0787796 | ||||||||
\(611\) | −9.73480 | −0.393828 | ||||||||
\(612\) | −0.760216 | −0.0307299 | ||||||||
\(613\) | −11.4350 | −0.461856 | −0.230928 | − | 0.972971i | \(-0.574176\pi\) | ||||
−0.230928 | + | 0.972971i | \(0.574176\pi\) | |||||||
\(614\) | −15.3678 | −0.620192 | ||||||||
\(615\) | −1.66534 | −0.0671530 | ||||||||
\(616\) | −7.91934 | −0.319079 | ||||||||
\(617\) | −2.43581 | −0.0980618 | −0.0490309 | − | 0.998797i | \(-0.515613\pi\) | ||||
−0.0490309 | + | 0.998797i | \(0.515613\pi\) | |||||||
\(618\) | 6.74479 | 0.271315 | ||||||||
\(619\) | −10.3162 | −0.414643 | −0.207322 | − | 0.978273i | \(-0.566475\pi\) | ||||
−0.207322 | + | 0.978273i | \(0.566475\pi\) | |||||||
\(620\) | −1.17013 | −0.0469936 | ||||||||
\(621\) | −42.2939 | −1.69719 | ||||||||
\(622\) | −31.9496 | −1.28106 | ||||||||
\(623\) | −16.9041 | −0.677247 | ||||||||
\(624\) | −0.805034 | −0.0322271 | ||||||||
\(625\) | 23.0881 | 0.923524 | ||||||||
\(626\) | 29.7455 | 1.18887 | ||||||||
\(627\) | 25.0667 | 1.00107 | ||||||||
\(628\) | −7.94526 | −0.317051 | ||||||||
\(629\) | −1.48970 | −0.0593981 | ||||||||
\(630\) | 1.88955 | 0.0752815 | ||||||||
\(631\) | 5.94009 | 0.236471 | 0.118236 | − | 0.992986i | \(-0.462276\pi\) | ||||
0.118236 | + | 0.992986i | \(0.462276\pi\) | |||||||
\(632\) | −7.19226 | −0.286093 | ||||||||
\(633\) | −24.0016 | −0.953976 | ||||||||
\(634\) | −16.4561 | −0.653557 | ||||||||
\(635\) | 1.61975 | 0.0642778 | ||||||||
\(636\) | −2.51866 | −0.0998712 | ||||||||
\(637\) | 1.16538 | 0.0461740 | ||||||||
\(638\) | −17.9592 | −0.711012 | ||||||||
\(639\) | 11.1341 | 0.440458 | ||||||||
\(640\) | 0.358556 | 0.0141732 | ||||||||
\(641\) | −13.0381 | −0.514976 | −0.257488 | − | 0.966282i | \(-0.582895\pi\) | ||||
−0.257488 | + | 0.966282i | \(0.582895\pi\) | |||||||
\(642\) | 20.5248 | 0.810049 | ||||||||
\(643\) | 36.9822 | 1.45844 | 0.729219 | − | 0.684281i | \(-0.239884\pi\) | ||||
0.729219 | + | 0.684281i | \(0.239884\pi\) | |||||||
\(644\) | 23.5623 | 0.928484 | ||||||||
\(645\) | −0.105752 | −0.00416400 | ||||||||
\(646\) | −3.57682 | −0.140728 | ||||||||
\(647\) | 33.1192 | 1.30205 | 0.651025 | − | 0.759056i | \(-0.274339\pi\) | ||||
0.651025 | + | 0.759056i | \(0.274339\pi\) | |||||||
\(648\) | 0.370583 | 0.0145579 | ||||||||
\(649\) | 33.3766 | 1.31014 | ||||||||
\(650\) | 3.57759 | 0.140325 | ||||||||
\(651\) | 10.4827 | 0.410851 | ||||||||
\(652\) | 5.48851 | 0.214947 | ||||||||
\(653\) | 42.6703 | 1.66982 | 0.834908 | − | 0.550389i | \(-0.185521\pi\) | ||||
0.834908 | + | 0.550389i | \(0.185521\pi\) | |||||||
\(654\) | 15.7362 | 0.615334 | ||||||||
\(655\) | −4.29769 | −0.167925 | ||||||||
\(656\) | −4.23707 | −0.165430 | ||||||||
\(657\) | 26.2621 | 1.02458 | ||||||||
\(658\) | −38.8428 | −1.51425 | ||||||||
\(659\) | 6.23098 | 0.242725 | 0.121362 | − | 0.992608i | \(-0.461274\pi\) | ||||
0.121362 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(660\) | −1.06221 | −0.0413464 | ||||||||
\(661\) | 7.65082 | 0.297583 | 0.148791 | − | 0.988869i | \(-0.452462\pi\) | ||||
0.148791 | + | 0.988869i | \(0.452462\pi\) | |||||||
\(662\) | −8.39583 | −0.326313 | ||||||||
\(663\) | −0.340303 | −0.0132163 | ||||||||
\(664\) | 2.45871 | 0.0954165 | ||||||||
\(665\) | 8.89034 | 0.344752 | ||||||||
\(666\) | −6.33770 | −0.245581 | ||||||||
\(667\) | 53.4337 | 2.06896 | ||||||||
\(668\) | 6.87509 | 0.266005 | ||||||||
\(669\) | −16.4244 | −0.635005 | ||||||||
\(670\) | −0.807922 | −0.0312127 | ||||||||
\(671\) | −14.6654 | −0.566153 | ||||||||
\(672\) | −3.21216 | −0.123912 | ||||||||
\(673\) | −27.1191 | −1.04536 | −0.522682 | − | 0.852528i | \(-0.675068\pi\) | ||||
−0.522682 | + | 0.852528i | \(0.675068\pi\) | |||||||
\(674\) | 1.46106 | 0.0562779 | ||||||||
\(675\) | −25.6232 | −0.986239 | ||||||||
\(676\) | −12.4607 | −0.479256 | ||||||||
\(677\) | −39.7777 | −1.52878 | −0.764390 | − | 0.644754i | \(-0.776960\pi\) | ||||
−0.764390 | + | 0.644754i | \(0.776960\pi\) | |||||||
\(678\) | 10.1499 | 0.389806 | ||||||||
\(679\) | 23.1526 | 0.888517 | ||||||||
\(680\) | 0.151568 | 0.00581238 | ||||||||
\(681\) | 5.04513 | 0.193330 | ||||||||
\(682\) | 8.81962 | 0.337721 | ||||||||
\(683\) | −13.7287 | −0.525314 | −0.262657 | − | 0.964889i | \(-0.584599\pi\) | ||||
−0.262657 | + | 0.964889i | \(0.584599\pi\) | |||||||
\(684\) | −15.2170 | −0.581838 | ||||||||
\(685\) | −0.450941 | −0.0172296 | ||||||||
\(686\) | −15.8623 | −0.605627 | ||||||||
\(687\) | 15.1257 | 0.577082 | ||||||||
\(688\) | −0.269063 | −0.0102579 | ||||||||
\(689\) | 1.68741 | 0.0642853 | ||||||||
\(690\) | 3.16037 | 0.120313 | ||||||||
\(691\) | −26.7142 | −1.01626 | −0.508128 | − | 0.861282i | \(-0.669662\pi\) | ||||
−0.508128 | + | 0.861282i | \(0.669662\pi\) | |||||||
\(692\) | −1.08625 | −0.0412929 | ||||||||
\(693\) | −14.2421 | −0.541013 | ||||||||
\(694\) | 1.47347 | 0.0559323 | ||||||||
\(695\) | −3.09148 | −0.117266 | ||||||||
\(696\) | −7.28443 | −0.276116 | ||||||||
\(697\) | −1.79109 | −0.0678424 | ||||||||
\(698\) | −20.6350 | −0.781048 | ||||||||
\(699\) | 18.0535 | 0.682846 | ||||||||
\(700\) | 14.2749 | 0.539541 | ||||||||
\(701\) | −40.8236 | −1.54188 | −0.770942 | − | 0.636905i | \(-0.780214\pi\) | ||||
−0.770942 | + | 0.636905i | \(0.780214\pi\) | |||||||
\(702\) | −3.86287 | −0.145795 | ||||||||
\(703\) | −29.8189 | −1.12464 | ||||||||
\(704\) | −2.70254 | −0.101856 | ||||||||
\(705\) | −5.20991 | −0.196217 | ||||||||
\(706\) | −12.8922 | −0.485205 | ||||||||
\(707\) | −12.0258 | −0.452276 | ||||||||
\(708\) | 13.5379 | 0.508784 | ||||||||
\(709\) | 29.0677 | 1.09166 | 0.545830 | − | 0.837896i | \(-0.316215\pi\) | ||||
0.545830 | + | 0.837896i | \(0.316215\pi\) | |||||||
\(710\) | −2.21986 | −0.0833099 | ||||||||
\(711\) | −12.9345 | −0.485083 | ||||||||
\(712\) | −5.76865 | −0.216189 | ||||||||
\(713\) | −26.2409 | −0.982729 | ||||||||
\(714\) | −1.35784 | −0.0508159 | ||||||||
\(715\) | 0.711643 | 0.0266139 | ||||||||
\(716\) | −4.58642 | −0.171402 | ||||||||
\(717\) | 13.1246 | 0.490147 | ||||||||
\(718\) | −24.5565 | −0.916442 | ||||||||
\(719\) | −6.42812 | −0.239728 | −0.119864 | − | 0.992790i | \(-0.538246\pi\) | ||||
−0.119864 | + | 0.992790i | \(0.538246\pi\) | |||||||
\(720\) | 0.644825 | 0.0240312 | ||||||||
\(721\) | −18.0304 | −0.671486 | ||||||||
\(722\) | −52.5962 | −1.95743 | ||||||||
\(723\) | 10.7417 | 0.399488 | ||||||||
\(724\) | −16.6934 | −0.620405 | ||||||||
\(725\) | 32.3722 | 1.20227 | ||||||||
\(726\) | −4.05177 | −0.150375 | ||||||||
\(727\) | −29.4922 | −1.09380 | −0.546902 | − | 0.837197i | \(-0.684193\pi\) | ||||
−0.546902 | + | 0.837197i | \(0.684193\pi\) | |||||||
\(728\) | 2.15204 | 0.0797599 | ||||||||
\(729\) | 17.9638 | 0.665325 | ||||||||
\(730\) | −5.23600 | −0.193793 | ||||||||
\(731\) | −0.113738 | −0.00420675 | ||||||||
\(732\) | −5.94844 | −0.219861 | ||||||||
\(733\) | 24.1213 | 0.890942 | 0.445471 | − | 0.895296i | \(-0.353036\pi\) | ||||
0.445471 | + | 0.895296i | \(0.353036\pi\) | |||||||
\(734\) | −30.9871 | −1.14376 | ||||||||
\(735\) | 0.623692 | 0.0230052 | ||||||||
\(736\) | 8.04082 | 0.296389 | ||||||||
\(737\) | 6.08955 | 0.224311 | ||||||||
\(738\) | −7.61993 | −0.280494 | ||||||||
\(739\) | 13.4016 | 0.492986 | 0.246493 | − | 0.969145i | \(-0.420722\pi\) | ||||
0.246493 | + | 0.969145i | \(0.420722\pi\) | |||||||
\(740\) | 1.26358 | 0.0464501 | ||||||||
\(741\) | −6.81176 | −0.250236 | ||||||||
\(742\) | 6.73294 | 0.247174 | ||||||||
\(743\) | −20.4592 | −0.750574 | −0.375287 | − | 0.926909i | \(-0.622456\pi\) | ||||
−0.375287 | + | 0.926909i | \(0.622456\pi\) | |||||||
\(744\) | 3.57733 | 0.131151 | ||||||||
\(745\) | −7.28316 | −0.266834 | ||||||||
\(746\) | 8.80764 | 0.322471 | ||||||||
\(747\) | 4.42174 | 0.161783 | ||||||||
\(748\) | −1.14242 | −0.0417708 | ||||||||
\(749\) | −54.8674 | −2.00481 | ||||||||
\(750\) | 3.87987 | 0.141673 | ||||||||
\(751\) | 36.2381 | 1.32235 | 0.661173 | − | 0.750233i | \(-0.270059\pi\) | ||||
0.661173 | + | 0.750233i | \(0.270059\pi\) | |||||||
\(752\) | −13.2554 | −0.483375 | ||||||||
\(753\) | −8.42029 | −0.306852 | ||||||||
\(754\) | 4.88032 | 0.177731 | ||||||||
\(755\) | −2.78991 | −0.101535 | ||||||||
\(756\) | −15.4132 | −0.560573 | ||||||||
\(757\) | −8.11863 | −0.295076 | −0.147538 | − | 0.989056i | \(-0.547135\pi\) | ||||
−0.147538 | + | 0.989056i | \(0.547135\pi\) | |||||||
\(758\) | 10.3435 | 0.375694 | ||||||||
\(759\) | −23.8206 | −0.864635 | ||||||||
\(760\) | 3.03390 | 0.110051 | ||||||||
\(761\) | 11.1274 | 0.403367 | 0.201683 | − | 0.979451i | \(-0.435359\pi\) | ||||
0.201683 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(762\) | −4.95190 | −0.179388 | ||||||||
\(763\) | −42.0664 | −1.52291 | ||||||||
\(764\) | −12.8395 | −0.464518 | ||||||||
\(765\) | 0.272580 | 0.00985514 | ||||||||
\(766\) | −12.6260 | −0.456194 | ||||||||
\(767\) | −9.06990 | −0.327495 | ||||||||
\(768\) | −1.09618 | −0.0395549 | ||||||||
\(769\) | −12.7554 | −0.459972 | −0.229986 | − | 0.973194i | \(-0.573868\pi\) | ||||
−0.229986 | + | 0.973194i | \(0.573868\pi\) | |||||||
\(770\) | 2.83952 | 0.102329 | ||||||||
\(771\) | 26.7659 | 0.963949 | ||||||||
\(772\) | 9.93167 | 0.357448 | ||||||||
\(773\) | −4.78832 | −0.172224 | −0.0861120 | − | 0.996285i | \(-0.527444\pi\) | ||||
−0.0861120 | + | 0.996285i | \(0.527444\pi\) | |||||||
\(774\) | −0.483881 | −0.0173927 | ||||||||
\(775\) | −15.8977 | −0.571063 | ||||||||
\(776\) | 7.90103 | 0.283630 | ||||||||
\(777\) | −11.3199 | −0.406100 | ||||||||
\(778\) | −1.18354 | −0.0424321 | ||||||||
\(779\) | −35.8518 | −1.28452 | ||||||||
\(780\) | 0.288649 | 0.0103353 | ||||||||
\(781\) | 16.7318 | 0.598709 | ||||||||
\(782\) | 3.39901 | 0.121548 | ||||||||
\(783\) | −34.9536 | −1.24914 | ||||||||
\(784\) | 1.58684 | 0.0566729 | ||||||||
\(785\) | 2.84882 | 0.101679 | ||||||||
\(786\) | 13.1389 | 0.468649 | ||||||||
\(787\) | 6.76875 | 0.241280 | 0.120640 | − | 0.992696i | \(-0.461505\pi\) | ||||
0.120640 | + | 0.992696i | \(0.461505\pi\) | |||||||
\(788\) | 4.63936 | 0.165270 | ||||||||
\(789\) | −26.9356 | −0.958933 | ||||||||
\(790\) | 2.57882 | 0.0917504 | ||||||||
\(791\) | −27.1331 | −0.964742 | ||||||||
\(792\) | −4.86024 | −0.172701 | ||||||||
\(793\) | 3.98525 | 0.141520 | ||||||||
\(794\) | −14.4391 | −0.512425 | ||||||||
\(795\) | 0.903078 | 0.0320289 | ||||||||
\(796\) | −11.9552 | −0.423741 | ||||||||
\(797\) | 50.8398 | 1.80084 | 0.900418 | − | 0.435025i | \(-0.143260\pi\) | ||||
0.900418 | + | 0.435025i | \(0.143260\pi\) | |||||||
\(798\) | −27.1796 | −0.962146 | ||||||||
\(799\) | −5.60332 | −0.198231 | ||||||||
\(800\) | 4.87144 | 0.172231 | ||||||||
\(801\) | −10.3743 | −0.366559 | ||||||||
\(802\) | −7.71569 | −0.272451 | ||||||||
\(803\) | 39.4653 | 1.39270 | ||||||||
\(804\) | 2.46998 | 0.0871095 | ||||||||
\(805\) | −8.44839 | −0.297766 | ||||||||
\(806\) | −2.39669 | −0.0844197 | ||||||||
\(807\) | −28.8529 | −1.01567 | ||||||||
\(808\) | −4.10390 | −0.144375 | ||||||||
\(809\) | 14.5923 | 0.513039 | 0.256520 | − | 0.966539i | \(-0.417424\pi\) | ||||
0.256520 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(810\) | −0.132875 | −0.00466873 | ||||||||
\(811\) | −13.1291 | −0.461026 | −0.230513 | − | 0.973069i | \(-0.574040\pi\) | ||||
−0.230513 | + | 0.973069i | \(0.574040\pi\) | |||||||
\(812\) | 19.4729 | 0.683366 | ||||||||
\(813\) | −16.1144 | −0.565156 | ||||||||
\(814\) | −9.52398 | −0.333815 | ||||||||
\(815\) | −1.96793 | −0.0689338 | ||||||||
\(816\) | −0.463375 | −0.0162214 | ||||||||
\(817\) | −2.27666 | −0.0796503 | ||||||||
\(818\) | −2.51025 | −0.0877688 | ||||||||
\(819\) | 3.87022 | 0.135236 | ||||||||
\(820\) | 1.51923 | 0.0530537 | ||||||||
\(821\) | −8.57345 | −0.299215 | −0.149608 | − | 0.988745i | \(-0.547801\pi\) | ||||
−0.149608 | + | 0.988745i | \(0.547801\pi\) | |||||||
\(822\) | 1.37862 | 0.0480848 | ||||||||
\(823\) | 17.0908 | 0.595747 | 0.297874 | − | 0.954605i | \(-0.403723\pi\) | ||||
0.297874 | + | 0.954605i | \(0.403723\pi\) | |||||||
\(824\) | −6.15301 | −0.214350 | ||||||||
\(825\) | −14.4315 | −0.502439 | ||||||||
\(826\) | −36.1898 | −1.25920 | ||||||||
\(827\) | 22.1162 | 0.769057 | 0.384528 | − | 0.923113i | \(-0.374364\pi\) | ||||
0.384528 | + | 0.923113i | \(0.374364\pi\) | |||||||
\(828\) | 14.4606 | 0.502540 | ||||||||
\(829\) | −37.9819 | −1.31917 | −0.659583 | − | 0.751632i | \(-0.729267\pi\) | ||||
−0.659583 | + | 0.751632i | \(0.729267\pi\) | |||||||
\(830\) | −0.881585 | −0.0306003 | ||||||||
\(831\) | −34.7973 | −1.20711 | ||||||||
\(832\) | 0.734401 | 0.0254608 | ||||||||
\(833\) | 0.670788 | 0.0232414 | ||||||||
\(834\) | 9.45127 | 0.327271 | ||||||||
\(835\) | −2.46510 | −0.0853083 | ||||||||
\(836\) | −22.8674 | −0.790887 | ||||||||
\(837\) | 17.1654 | 0.593324 | ||||||||
\(838\) | −11.5020 | −0.397332 | ||||||||
\(839\) | −47.7541 | −1.64866 | −0.824328 | − | 0.566113i | \(-0.808447\pi\) | ||||
−0.824328 | + | 0.566113i | \(0.808447\pi\) | |||||||
\(840\) | 1.15174 | 0.0397388 | ||||||||
\(841\) | 15.1601 | 0.522761 | ||||||||
\(842\) | −23.1953 | −0.799362 | ||||||||
\(843\) | 23.5108 | 0.809755 | ||||||||
\(844\) | 21.8957 | 0.753681 | ||||||||
\(845\) | 4.46784 | 0.153698 | ||||||||
\(846\) | −23.8385 | −0.819584 | ||||||||
\(847\) | 10.8313 | 0.372168 | ||||||||
\(848\) | 2.29767 | 0.0789024 | ||||||||
\(849\) | −27.8808 | −0.956865 | ||||||||
\(850\) | 2.05925 | 0.0706317 | ||||||||
\(851\) | 28.3365 | 0.971364 | ||||||||
\(852\) | 6.78656 | 0.232504 | ||||||||
\(853\) | −4.93563 | −0.168993 | −0.0844963 | − | 0.996424i | \(-0.526928\pi\) | ||||
−0.0844963 | + | 0.996424i | \(0.526928\pi\) | |||||||
\(854\) | 15.9015 | 0.544139 | ||||||||
\(855\) | 5.45616 | 0.186597 | ||||||||
\(856\) | −18.7240 | −0.639972 | ||||||||
\(857\) | 26.6849 | 0.911539 | 0.455770 | − | 0.890098i | \(-0.349364\pi\) | ||||
0.455770 | + | 0.890098i | \(0.349364\pi\) | |||||||
\(858\) | −2.17564 | −0.0742750 | ||||||||
\(859\) | −10.0307 | −0.342245 | −0.171122 | − | 0.985250i | \(-0.554739\pi\) | ||||
−0.171122 | + | 0.985250i | \(0.554739\pi\) | |||||||
\(860\) | 0.0964739 | 0.00328973 | ||||||||
\(861\) | −13.6102 | −0.463833 | ||||||||
\(862\) | 8.18662 | 0.278837 | ||||||||
\(863\) | −49.9245 | −1.69945 | −0.849724 | − | 0.527228i | \(-0.823231\pi\) | ||||
−0.849724 | + | 0.527228i | \(0.823231\pi\) | |||||||
\(864\) | −5.25989 | −0.178945 | ||||||||
\(865\) | 0.389480 | 0.0132427 | ||||||||
\(866\) | 14.8621 | 0.505036 | ||||||||
\(867\) | 18.4391 | 0.626226 | ||||||||
\(868\) | −9.56301 | −0.324590 | ||||||||
\(869\) | −19.4374 | −0.659367 | ||||||||
\(870\) | 2.61187 | 0.0885508 | ||||||||
\(871\) | −1.65480 | −0.0560709 | ||||||||
\(872\) | −14.3555 | −0.486139 | ||||||||
\(873\) | 14.2092 | 0.480908 | ||||||||
\(874\) | 68.0371 | 2.30139 | ||||||||
\(875\) | −10.3718 | −0.350630 | ||||||||
\(876\) | 16.0075 | 0.540844 | ||||||||
\(877\) | −24.7868 | −0.836990 | −0.418495 | − | 0.908219i | \(-0.637442\pi\) | ||||
−0.418495 | + | 0.908219i | \(0.637442\pi\) | |||||||
\(878\) | −8.67971 | −0.292926 | ||||||||
\(879\) | 34.1871 | 1.15310 | ||||||||
\(880\) | 0.969011 | 0.0326654 | ||||||||
\(881\) | −36.4293 | −1.22734 | −0.613668 | − | 0.789564i | \(-0.710306\pi\) | ||||
−0.613668 | + | 0.789564i | \(0.710306\pi\) | |||||||
\(882\) | 2.85377 | 0.0960914 | ||||||||
\(883\) | −28.6990 | −0.965797 | −0.482899 | − | 0.875676i | \(-0.660416\pi\) | ||||
−0.482899 | + | 0.875676i | \(0.660416\pi\) | |||||||
\(884\) | 0.310445 | 0.0104414 | ||||||||
\(885\) | −4.85407 | −0.163168 | ||||||||
\(886\) | 28.4688 | 0.956428 | ||||||||
\(887\) | 34.3180 | 1.15229 | 0.576144 | − | 0.817348i | \(-0.304557\pi\) | ||||
0.576144 | + | 0.817348i | \(0.304557\pi\) | |||||||
\(888\) | −3.86302 | −0.129634 | ||||||||
\(889\) | 13.2376 | 0.443974 | ||||||||
\(890\) | 2.06838 | 0.0693323 | ||||||||
\(891\) | 1.00152 | 0.0335520 | ||||||||
\(892\) | 14.9834 | 0.501681 | ||||||||
\(893\) | −112.160 | −3.75330 | ||||||||
\(894\) | 22.2661 | 0.744690 | ||||||||
\(895\) | 1.64449 | 0.0549691 | ||||||||
\(896\) | 2.93033 | 0.0978955 | ||||||||
\(897\) | 6.47314 | 0.216132 | ||||||||
\(898\) | 12.7608 | 0.425833 | ||||||||
\(899\) | −21.6867 | −0.723290 | ||||||||
\(900\) | 8.76078 | 0.292026 | ||||||||
\(901\) | 0.971270 | 0.0323577 | ||||||||
\(902\) | −11.4509 | −0.381272 | ||||||||
\(903\) | −0.864272 | −0.0287612 | ||||||||
\(904\) | −9.25940 | −0.307963 | ||||||||
\(905\) | 5.98551 | 0.198965 | ||||||||
\(906\) | 8.52932 | 0.283368 | ||||||||
\(907\) | 11.6428 | 0.386593 | 0.193297 | − | 0.981140i | \(-0.438082\pi\) | ||||
0.193297 | + | 0.981140i | \(0.438082\pi\) | |||||||
\(908\) | −4.60248 | −0.152739 | ||||||||
\(909\) | −7.38043 | −0.244794 | ||||||||
\(910\) | −0.771626 | −0.0255791 | ||||||||
\(911\) | 22.5346 | 0.746606 | 0.373303 | − | 0.927709i | \(-0.378225\pi\) | ||||
0.373303 | + | 0.927709i | \(0.378225\pi\) | |||||||
\(912\) | −9.27525 | −0.307134 | ||||||||
\(913\) | 6.64477 | 0.219910 | ||||||||
\(914\) | 16.2696 | 0.538149 | ||||||||
\(915\) | 2.13285 | 0.0705097 | ||||||||
\(916\) | −13.7986 | −0.455919 | ||||||||
\(917\) | −35.1233 | −1.15987 | ||||||||
\(918\) | −2.22346 | −0.0733850 | ||||||||
\(919\) | 31.4988 | 1.03905 | 0.519525 | − | 0.854455i | \(-0.326109\pi\) | ||||
0.519525 | + | 0.854455i | \(0.326109\pi\) | |||||||
\(920\) | −2.88308 | −0.0950524 | ||||||||
\(921\) | −16.8458 | −0.555088 | ||||||||
\(922\) | 7.67436 | 0.252742 | ||||||||
\(923\) | −4.54677 | −0.149659 | ||||||||
\(924\) | −8.68100 | −0.285584 | ||||||||
\(925\) | 17.1674 | 0.564459 | ||||||||
\(926\) | 8.10682 | 0.266407 | ||||||||
\(927\) | −11.0656 | −0.363440 | ||||||||
\(928\) | 6.64530 | 0.218143 | ||||||||
\(929\) | −50.6852 | −1.66293 | −0.831464 | − | 0.555579i | \(-0.812497\pi\) | ||||
−0.831464 | + | 0.555579i | \(0.812497\pi\) | |||||||
\(930\) | −1.28267 | −0.0420604 | ||||||||
\(931\) | 13.4270 | 0.440051 | ||||||||
\(932\) | −16.4695 | −0.539477 | ||||||||
\(933\) | −35.0224 | −1.14658 | ||||||||
\(934\) | 34.5921 | 1.13189 | ||||||||
\(935\) | 0.409619 | 0.0133960 | ||||||||
\(936\) | 1.32074 | 0.0431699 | ||||||||
\(937\) | 22.9403 | 0.749426 | 0.374713 | − | 0.927141i | \(-0.377741\pi\) | ||||
0.374713 | + | 0.927141i | \(0.377741\pi\) | |||||||
\(938\) | −6.60282 | −0.215590 | ||||||||
\(939\) | 32.6064 | 1.06407 | ||||||||
\(940\) | 4.75280 | 0.155019 | ||||||||
\(941\) | 7.43703 | 0.242440 | 0.121220 | − | 0.992626i | \(-0.461319\pi\) | ||||
0.121220 | + | 0.992626i | \(0.461319\pi\) | |||||||
\(942\) | −8.70942 | −0.283768 | ||||||||
\(943\) | 34.0695 | 1.10946 | ||||||||
\(944\) | −12.3501 | −0.401960 | ||||||||
\(945\) | 5.52650 | 0.179777 | ||||||||
\(946\) | −0.727152 | −0.0236418 | ||||||||
\(947\) | 10.4075 | 0.338199 | 0.169099 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169099 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(948\) | −7.88398 | −0.256060 | ||||||||
\(949\) | −10.7245 | −0.348132 | ||||||||
\(950\) | 41.2194 | 1.33734 | ||||||||
\(951\) | −18.0388 | −0.584949 | ||||||||
\(952\) | 1.23871 | 0.0401467 | ||||||||
\(953\) | −27.4734 | −0.889952 | −0.444976 | − | 0.895543i | \(-0.646788\pi\) | ||||
−0.444976 | + | 0.895543i | \(0.646788\pi\) | |||||||
\(954\) | 4.13213 | 0.133782 | ||||||||
\(955\) | 4.60369 | 0.148972 | ||||||||
\(956\) | −11.9731 | −0.387237 | ||||||||
\(957\) | −19.6865 | −0.636373 | ||||||||
\(958\) | −27.7791 | −0.897502 | ||||||||
\(959\) | −3.68536 | −0.119006 | ||||||||
\(960\) | 0.393040 | 0.0126853 | ||||||||
\(961\) | −20.3499 | −0.656447 | ||||||||
\(962\) | 2.58809 | 0.0834434 | ||||||||
\(963\) | −33.6731 | −1.08510 | ||||||||
\(964\) | −9.79923 | −0.315612 | ||||||||
\(965\) | −3.56105 | −0.114634 | ||||||||
\(966\) | 25.8284 | 0.831016 | ||||||||
\(967\) | 16.0041 | 0.514656 | 0.257328 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257328 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(968\) | 3.69627 | 0.118803 | ||||||||
\(969\) | −3.92082 | −0.125955 | ||||||||
\(970\) | −2.83296 | −0.0909608 | ||||||||
\(971\) | −4.02698 | −0.129232 | −0.0646160 | − | 0.997910i | \(-0.520582\pi\) | ||||
−0.0646160 | + | 0.997910i | \(0.520582\pi\) | |||||||
\(972\) | −15.3734 | −0.493104 | ||||||||
\(973\) | −25.2654 | −0.809971 | ||||||||
\(974\) | 34.7919 | 1.11481 | ||||||||
\(975\) | 3.92167 | 0.125594 | ||||||||
\(976\) | 5.42653 | 0.173699 | ||||||||
\(977\) | 60.5704 | 1.93782 | 0.968910 | − | 0.247414i | \(-0.0795809\pi\) | ||||
0.968910 | + | 0.247414i | \(0.0795809\pi\) | |||||||
\(978\) | 6.01637 | 0.192382 | ||||||||
\(979\) | −15.5900 | −0.498259 | ||||||||
\(980\) | −0.568971 | −0.0181751 | ||||||||
\(981\) | −25.8169 | −0.824270 | ||||||||
\(982\) | −3.24788 | −0.103644 | ||||||||
\(983\) | −28.9909 | −0.924667 | −0.462334 | − | 0.886706i | \(-0.652988\pi\) | ||||
−0.462334 | + | 0.886706i | \(0.652988\pi\) | |||||||
\(984\) | −4.64458 | −0.148064 | ||||||||
\(985\) | −1.66347 | −0.0530025 | ||||||||
\(986\) | 2.80910 | 0.0894598 | ||||||||
\(987\) | −42.5785 | −1.35529 | ||||||||
\(988\) | 6.21410 | 0.197697 | ||||||||
\(989\) | 2.16348 | 0.0687948 | ||||||||
\(990\) | 1.74267 | 0.0553856 | ||||||||
\(991\) | 54.5881 | 1.73405 | 0.867023 | − | 0.498267i | \(-0.166030\pi\) | ||||
0.867023 | + | 0.498267i | \(0.166030\pi\) | |||||||
\(992\) | −3.26346 | −0.103615 | ||||||||
\(993\) | −9.20331 | −0.292058 | ||||||||
\(994\) | −18.1420 | −0.575430 | ||||||||
\(995\) | 4.28661 | 0.135895 | ||||||||
\(996\) | 2.69518 | 0.0854001 | ||||||||
\(997\) | −25.0683 | −0.793920 | −0.396960 | − | 0.917836i | \(-0.629935\pi\) | ||||
−0.396960 | + | 0.917836i | \(0.629935\pi\) | |||||||
\(998\) | −1.21762 | −0.0385431 | ||||||||
\(999\) | −18.5363 | −0.586462 |
(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 | 4034.2.a.c.1.16 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.c.1.16 | ✓ | 49 | 1.1 | even | 1 | trivial |