Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.38 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.856487 | 0.605627 | 0.302814 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302814 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(3\) | −2.63249 | −1.51987 | −0.759934 | − | 0.650001i | \(-0.774769\pi\) | ||||
−0.759934 | + | 0.650001i | \(0.774769\pi\) | |||||||
\(4\) | −1.26643 | −0.633215 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.25469 | −0.920473 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.79765 | −0.989120 | ||||||||
\(9\) | 3.92999 | 1.31000 | ||||||||
\(10\) | −0.856487 | −0.270845 | ||||||||
\(11\) | 3.55049 | 1.07051 | 0.535257 | − | 0.844689i | \(-0.320215\pi\) | ||||
0.535257 | + | 0.844689i | \(0.320215\pi\) | |||||||
\(12\) | 3.33386 | 0.962403 | ||||||||
\(13\) | 3.64418 | 1.01071 | 0.505357 | − | 0.862910i | \(-0.331361\pi\) | ||||
0.505357 | + | 0.862910i | \(0.331361\pi\) | |||||||
\(14\) | −0.856487 | −0.228906 | ||||||||
\(15\) | 2.63249 | 0.679705 | ||||||||
\(16\) | 0.136708 | 0.0341770 | ||||||||
\(17\) | 1.73278 | 0.420261 | 0.210130 | − | 0.977673i | \(-0.432611\pi\) | ||||
0.210130 | + | 0.977673i | \(0.432611\pi\) | |||||||
\(18\) | 3.36598 | 0.793369 | ||||||||
\(19\) | −5.55244 | −1.27382 | −0.636909 | − | 0.770939i | \(-0.719787\pi\) | ||||
−0.636909 | + | 0.770939i | \(0.719787\pi\) | |||||||
\(20\) | 1.26643 | 0.283183 | ||||||||
\(21\) | 2.63249 | 0.574456 | ||||||||
\(22\) | 3.04095 | 0.648333 | ||||||||
\(23\) | −4.03981 | −0.842360 | −0.421180 | − | 0.906977i | \(-0.638384\pi\) | ||||
−0.421180 | + | 0.906977i | \(0.638384\pi\) | |||||||
\(24\) | 7.36479 | 1.50333 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.12119 | 0.612116 | ||||||||
\(27\) | −2.44818 | −0.471152 | ||||||||
\(28\) | 1.26643 | 0.239333 | ||||||||
\(29\) | 0.860600 | 0.159809 | 0.0799047 | − | 0.996803i | \(-0.474538\pi\) | ||||
0.0799047 | + | 0.996803i | \(0.474538\pi\) | |||||||
\(30\) | 2.25469 | 0.411648 | ||||||||
\(31\) | 10.7794 | 1.93605 | 0.968023 | − | 0.250861i | \(-0.0807137\pi\) | ||||
0.968023 | + | 0.250861i | \(0.0807137\pi\) | |||||||
\(32\) | 5.71240 | 1.00982 | ||||||||
\(33\) | −9.34663 | −1.62704 | ||||||||
\(34\) | 1.48410 | 0.254522 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −4.97706 | −0.829509 | ||||||||
\(37\) | 5.89164 | 0.968580 | 0.484290 | − | 0.874907i | \(-0.339078\pi\) | ||||
0.484290 | + | 0.874907i | \(0.339078\pi\) | |||||||
\(38\) | −4.75559 | −0.771459 | ||||||||
\(39\) | −9.59326 | −1.53615 | ||||||||
\(40\) | 2.79765 | 0.442348 | ||||||||
\(41\) | −6.58941 | −1.02909 | −0.514546 | − | 0.857463i | \(-0.672040\pi\) | ||||
−0.514546 | + | 0.857463i | \(0.672040\pi\) | |||||||
\(42\) | 2.25469 | 0.347906 | ||||||||
\(43\) | −0.110729 | −0.0168860 | −0.00844301 | − | 0.999964i | \(-0.502688\pi\) | ||||
−0.00844301 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(44\) | −4.49646 | −0.677866 | ||||||||
\(45\) | −3.92999 | −0.585848 | ||||||||
\(46\) | −3.46005 | −0.510156 | ||||||||
\(47\) | −3.16720 | −0.461984 | −0.230992 | − | 0.972956i | \(-0.574197\pi\) | ||||
−0.230992 | + | 0.972956i | \(0.574197\pi\) | |||||||
\(48\) | −0.359882 | −0.0519445 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.856487 | 0.121125 | ||||||||
\(51\) | −4.56152 | −0.638741 | ||||||||
\(52\) | −4.61510 | −0.639999 | ||||||||
\(53\) | −7.84850 | −1.07807 | −0.539037 | − | 0.842282i | \(-0.681212\pi\) | ||||
−0.539037 | + | 0.842282i | \(0.681212\pi\) | |||||||
\(54\) | −2.09683 | −0.285343 | ||||||||
\(55\) | −3.55049 | −0.478749 | ||||||||
\(56\) | 2.79765 | 0.373852 | ||||||||
\(57\) | 14.6167 | 1.93603 | ||||||||
\(58\) | 0.737093 | 0.0967850 | ||||||||
\(59\) | −13.2508 | −1.72510 | −0.862550 | − | 0.505971i | \(-0.831134\pi\) | ||||
−0.862550 | + | 0.505971i | \(0.831134\pi\) | |||||||
\(60\) | −3.33386 | −0.430400 | ||||||||
\(61\) | 9.20667 | 1.17879 | 0.589397 | − | 0.807844i | \(-0.299365\pi\) | ||||
0.589397 | + | 0.807844i | \(0.299365\pi\) | |||||||
\(62\) | 9.23245 | 1.17252 | ||||||||
\(63\) | −3.92999 | −0.495132 | ||||||||
\(64\) | 4.61918 | 0.577397 | ||||||||
\(65\) | −3.64418 | −0.452005 | ||||||||
\(66\) | −8.00526 | −0.985380 | ||||||||
\(67\) | −7.27971 | −0.889358 | −0.444679 | − | 0.895690i | \(-0.646682\pi\) | ||||
−0.444679 | + | 0.895690i | \(0.646682\pi\) | |||||||
\(68\) | −2.19445 | −0.266116 | ||||||||
\(69\) | 10.6348 | 1.28027 | ||||||||
\(70\) | 0.856487 | 0.102370 | ||||||||
\(71\) | −15.2682 | −1.81200 | −0.905998 | − | 0.423281i | \(-0.860878\pi\) | ||||
−0.905998 | + | 0.423281i | \(0.860878\pi\) | |||||||
\(72\) | −10.9947 | −1.29574 | ||||||||
\(73\) | 7.88613 | 0.923002 | 0.461501 | − | 0.887140i | \(-0.347311\pi\) | ||||
0.461501 | + | 0.887140i | \(0.347311\pi\) | |||||||
\(74\) | 5.04611 | 0.586599 | ||||||||
\(75\) | −2.63249 | −0.303973 | ||||||||
\(76\) | 7.03178 | 0.806601 | ||||||||
\(77\) | −3.55049 | −0.404616 | ||||||||
\(78\) | −8.21649 | −0.930335 | ||||||||
\(79\) | −4.82787 | −0.543178 | −0.271589 | − | 0.962413i | \(-0.587549\pi\) | ||||
−0.271589 | + | 0.962413i | \(0.587549\pi\) | |||||||
\(80\) | −0.136708 | −0.0152844 | ||||||||
\(81\) | −5.34516 | −0.593907 | ||||||||
\(82\) | −5.64374 | −0.623247 | ||||||||
\(83\) | 3.46176 | 0.379978 | 0.189989 | − | 0.981786i | \(-0.439155\pi\) | ||||
0.189989 | + | 0.981786i | \(0.439155\pi\) | |||||||
\(84\) | −3.33386 | −0.363754 | ||||||||
\(85\) | −1.73278 | −0.187946 | ||||||||
\(86\) | −0.0948379 | −0.0102266 | ||||||||
\(87\) | −2.26552 | −0.242889 | ||||||||
\(88\) | −9.93306 | −1.05887 | ||||||||
\(89\) | −14.6181 | −1.54952 | −0.774760 | − | 0.632255i | \(-0.782129\pi\) | ||||
−0.774760 | + | 0.632255i | \(0.782129\pi\) | |||||||
\(90\) | −3.36598 | −0.354806 | ||||||||
\(91\) | −3.64418 | −0.382014 | ||||||||
\(92\) | 5.11615 | 0.533395 | ||||||||
\(93\) | −28.3768 | −2.94253 | ||||||||
\(94\) | −2.71266 | −0.279790 | ||||||||
\(95\) | 5.55244 | 0.569668 | ||||||||
\(96\) | −15.0378 | −1.53479 | ||||||||
\(97\) | 12.2918 | 1.24805 | 0.624023 | − | 0.781406i | \(-0.285497\pi\) | ||||
0.624023 | + | 0.781406i | \(0.285497\pi\) | |||||||
\(98\) | 0.856487 | 0.0865182 | ||||||||
\(99\) | 13.9534 | 1.40237 | ||||||||
\(100\) | −1.26643 | −0.126643 | ||||||||
\(101\) | 13.3332 | 1.32671 | 0.663354 | − | 0.748306i | \(-0.269132\pi\) | ||||
0.663354 | + | 0.748306i | \(0.269132\pi\) | |||||||
\(102\) | −3.90688 | −0.386839 | ||||||||
\(103\) | 18.2028 | 1.79357 | 0.896787 | − | 0.442462i | \(-0.145895\pi\) | ||||
0.896787 | + | 0.442462i | \(0.145895\pi\) | |||||||
\(104\) | −10.1952 | −0.999717 | ||||||||
\(105\) | −2.63249 | −0.256904 | ||||||||
\(106\) | −6.72214 | −0.652912 | ||||||||
\(107\) | 9.09035 | 0.878797 | 0.439399 | − | 0.898292i | \(-0.355192\pi\) | ||||
0.439399 | + | 0.898292i | \(0.355192\pi\) | |||||||
\(108\) | 3.10045 | 0.298341 | ||||||||
\(109\) | 5.06523 | 0.485161 | 0.242581 | − | 0.970131i | \(-0.422006\pi\) | ||||
0.242581 | + | 0.970131i | \(0.422006\pi\) | |||||||
\(110\) | −3.04095 | −0.289943 | ||||||||
\(111\) | −15.5097 | −1.47211 | ||||||||
\(112\) | −0.136708 | −0.0129177 | ||||||||
\(113\) | −9.84021 | −0.925690 | −0.462845 | − | 0.886439i | \(-0.653171\pi\) | ||||
−0.462845 | + | 0.886439i | \(0.653171\pi\) | |||||||
\(114\) | 12.5190 | 1.17251 | ||||||||
\(115\) | 4.03981 | 0.376715 | ||||||||
\(116\) | −1.08989 | −0.101194 | ||||||||
\(117\) | 14.3216 | 1.32403 | ||||||||
\(118\) | −11.3491 | −1.04477 | ||||||||
\(119\) | −1.73278 | −0.158844 | ||||||||
\(120\) | −7.36479 | −0.672310 | ||||||||
\(121\) | 1.60601 | 0.146001 | ||||||||
\(122\) | 7.88539 | 0.713910 | ||||||||
\(123\) | 17.3465 | 1.56408 | ||||||||
\(124\) | −13.6514 | −1.22593 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.36598 | −0.299865 | ||||||||
\(127\) | −15.4698 | −1.37272 | −0.686361 | − | 0.727261i | \(-0.740793\pi\) | ||||
−0.686361 | + | 0.727261i | \(0.740793\pi\) | |||||||
\(128\) | −7.46853 | −0.660131 | ||||||||
\(129\) | 0.291493 | 0.0256645 | ||||||||
\(130\) | −3.12119 | −0.273747 | ||||||||
\(131\) | −11.7321 | −1.02504 | −0.512521 | − | 0.858675i | \(-0.671288\pi\) | ||||
−0.512521 | + | 0.858675i | \(0.671288\pi\) | |||||||
\(132\) | 11.8369 | 1.03027 | ||||||||
\(133\) | 5.55244 | 0.481458 | ||||||||
\(134\) | −6.23498 | −0.538620 | ||||||||
\(135\) | 2.44818 | 0.210706 | ||||||||
\(136\) | −4.84772 | −0.415689 | ||||||||
\(137\) | −20.3100 | −1.73520 | −0.867601 | − | 0.497261i | \(-0.834339\pi\) | ||||
−0.867601 | + | 0.497261i | \(0.834339\pi\) | |||||||
\(138\) | 9.10853 | 0.775369 | ||||||||
\(139\) | −12.8852 | −1.09290 | −0.546452 | − | 0.837490i | \(-0.684022\pi\) | ||||
−0.546452 | + | 0.837490i | \(0.684022\pi\) | |||||||
\(140\) | −1.26643 | −0.107033 | ||||||||
\(141\) | 8.33761 | 0.702154 | ||||||||
\(142\) | −13.0770 | −1.09740 | ||||||||
\(143\) | 12.9386 | 1.08198 | ||||||||
\(144\) | 0.537261 | 0.0447718 | ||||||||
\(145\) | −0.860600 | −0.0714690 | ||||||||
\(146\) | 6.75436 | 0.558995 | ||||||||
\(147\) | −2.63249 | −0.217124 | ||||||||
\(148\) | −7.46136 | −0.613320 | ||||||||
\(149\) | 5.99189 | 0.490875 | 0.245437 | − | 0.969412i | \(-0.421068\pi\) | ||||
0.245437 | + | 0.969412i | \(0.421068\pi\) | |||||||
\(150\) | −2.25469 | −0.184095 | ||||||||
\(151\) | 15.9970 | 1.30181 | 0.650907 | − | 0.759157i | \(-0.274389\pi\) | ||||
0.650907 | + | 0.759157i | \(0.274389\pi\) | |||||||
\(152\) | 15.5338 | 1.25996 | ||||||||
\(153\) | 6.80980 | 0.550540 | ||||||||
\(154\) | −3.04095 | −0.245047 | ||||||||
\(155\) | −10.7794 | −0.865826 | ||||||||
\(156\) | 12.1492 | 0.972714 | ||||||||
\(157\) | 6.60969 | 0.527511 | 0.263755 | − | 0.964590i | \(-0.415039\pi\) | ||||
0.263755 | + | 0.964590i | \(0.415039\pi\) | |||||||
\(158\) | −4.13501 | −0.328964 | ||||||||
\(159\) | 20.6611 | 1.63853 | ||||||||
\(160\) | −5.71240 | −0.451605 | ||||||||
\(161\) | 4.03981 | 0.318382 | ||||||||
\(162\) | −4.57806 | −0.359686 | ||||||||
\(163\) | 12.5705 | 0.984596 | 0.492298 | − | 0.870427i | \(-0.336157\pi\) | ||||
0.492298 | + | 0.870427i | \(0.336157\pi\) | |||||||
\(164\) | 8.34503 | 0.651637 | ||||||||
\(165\) | 9.34663 | 0.727634 | ||||||||
\(166\) | 2.96495 | 0.230125 | ||||||||
\(167\) | −7.77580 | −0.601710 | −0.300855 | − | 0.953670i | \(-0.597272\pi\) | ||||
−0.300855 | + | 0.953670i | \(0.597272\pi\) | |||||||
\(168\) | −7.36479 | −0.568206 | ||||||||
\(169\) | 0.280046 | 0.0215420 | ||||||||
\(170\) | −1.48410 | −0.113826 | ||||||||
\(171\) | −21.8210 | −1.66870 | ||||||||
\(172\) | 0.140231 | 0.0106925 | ||||||||
\(173\) | 13.1364 | 0.998743 | 0.499372 | − | 0.866388i | \(-0.333564\pi\) | ||||
0.499372 | + | 0.866388i | \(0.333564\pi\) | |||||||
\(174\) | −1.94039 | −0.147100 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0.485381 | 0.0365870 | ||||||||
\(177\) | 34.8824 | 2.62192 | ||||||||
\(178\) | −12.5202 | −0.938432 | ||||||||
\(179\) | −24.4689 | −1.82889 | −0.914446 | − | 0.404709i | \(-0.867373\pi\) | ||||
−0.914446 | + | 0.404709i | \(0.867373\pi\) | |||||||
\(180\) | 4.97706 | 0.370968 | ||||||||
\(181\) | −4.33981 | −0.322576 | −0.161288 | − | 0.986907i | \(-0.551565\pi\) | ||||
−0.161288 | + | 0.986907i | \(0.551565\pi\) | |||||||
\(182\) | −3.12119 | −0.231358 | ||||||||
\(183\) | −24.2364 | −1.79161 | ||||||||
\(184\) | 11.3020 | 0.833195 | ||||||||
\(185\) | −5.89164 | −0.433162 | ||||||||
\(186\) | −24.3043 | −1.78208 | ||||||||
\(187\) | 6.15223 | 0.449895 | ||||||||
\(188\) | 4.01104 | 0.292535 | ||||||||
\(189\) | 2.44818 | 0.178079 | ||||||||
\(190\) | 4.75559 | 0.345007 | ||||||||
\(191\) | 20.2980 | 1.46871 | 0.734354 | − | 0.678767i | \(-0.237485\pi\) | ||||
0.734354 | + | 0.678767i | \(0.237485\pi\) | |||||||
\(192\) | −12.1599 | −0.877567 | ||||||||
\(193\) | −0.292300 | −0.0210402 | −0.0105201 | − | 0.999945i | \(-0.503349\pi\) | ||||
−0.0105201 | + | 0.999945i | \(0.503349\pi\) | |||||||
\(194\) | 10.5278 | 0.755851 | ||||||||
\(195\) | 9.59326 | 0.686987 | ||||||||
\(196\) | −1.26643 | −0.0904593 | ||||||||
\(197\) | 9.92841 | 0.707370 | 0.353685 | − | 0.935365i | \(-0.384929\pi\) | ||||
0.353685 | + | 0.935365i | \(0.384929\pi\) | |||||||
\(198\) | 11.9509 | 0.849313 | ||||||||
\(199\) | 22.1854 | 1.57268 | 0.786342 | − | 0.617792i | \(-0.211973\pi\) | ||||
0.786342 | + | 0.617792i | \(0.211973\pi\) | |||||||
\(200\) | −2.79765 | −0.197824 | ||||||||
\(201\) | 19.1637 | 1.35171 | ||||||||
\(202\) | 11.4197 | 0.803491 | ||||||||
\(203\) | −0.860600 | −0.0604023 | ||||||||
\(204\) | 5.77685 | 0.404460 | ||||||||
\(205\) | 6.58941 | 0.460224 | ||||||||
\(206\) | 15.5904 | 1.08624 | ||||||||
\(207\) | −15.8764 | −1.10349 | ||||||||
\(208\) | 0.498189 | 0.0345432 | ||||||||
\(209\) | −19.7139 | −1.36364 | ||||||||
\(210\) | −2.25469 | −0.155588 | ||||||||
\(211\) | 23.0559 | 1.58723 | 0.793616 | − | 0.608420i | \(-0.208196\pi\) | ||||
0.793616 | + | 0.608420i | \(0.208196\pi\) | |||||||
\(212\) | 9.93959 | 0.682654 | ||||||||
\(213\) | 40.1932 | 2.75399 | ||||||||
\(214\) | 7.78576 | 0.532224 | ||||||||
\(215\) | 0.110729 | 0.00755166 | ||||||||
\(216\) | 6.84916 | 0.466026 | ||||||||
\(217\) | −10.7794 | −0.731757 | ||||||||
\(218\) | 4.33830 | 0.293827 | ||||||||
\(219\) | −20.7601 | −1.40284 | ||||||||
\(220\) | 4.49646 | 0.303151 | ||||||||
\(221\) | 6.31456 | 0.424763 | ||||||||
\(222\) | −13.2838 | −0.891552 | ||||||||
\(223\) | 0.903309 | 0.0604901 | 0.0302450 | − | 0.999543i | \(-0.490371\pi\) | ||||
0.0302450 | + | 0.999543i | \(0.490371\pi\) | |||||||
\(224\) | −5.71240 | −0.381676 | ||||||||
\(225\) | 3.92999 | 0.261999 | ||||||||
\(226\) | −8.42801 | −0.560623 | ||||||||
\(227\) | 2.24378 | 0.148925 | 0.0744625 | − | 0.997224i | \(-0.476276\pi\) | ||||
0.0744625 | + | 0.997224i | \(0.476276\pi\) | |||||||
\(228\) | −18.5111 | −1.22593 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 3.46005 | 0.228149 | ||||||||
\(231\) | 9.34663 | 0.614963 | ||||||||
\(232\) | −2.40766 | −0.158071 | ||||||||
\(233\) | −2.56766 | −0.168213 | −0.0841065 | − | 0.996457i | \(-0.526804\pi\) | ||||
−0.0841065 | + | 0.996457i | \(0.526804\pi\) | |||||||
\(234\) | 12.2662 | 0.801869 | ||||||||
\(235\) | 3.16720 | 0.206605 | ||||||||
\(236\) | 16.7812 | 1.09236 | ||||||||
\(237\) | 12.7093 | 0.825559 | ||||||||
\(238\) | −1.48410 | −0.0962001 | ||||||||
\(239\) | −13.5580 | −0.876997 | −0.438498 | − | 0.898732i | \(-0.644489\pi\) | ||||
−0.438498 | + | 0.898732i | \(0.644489\pi\) | |||||||
\(240\) | 0.359882 | 0.0232303 | ||||||||
\(241\) | −11.4220 | −0.735759 | −0.367879 | − | 0.929874i | \(-0.619916\pi\) | ||||
−0.367879 | + | 0.929874i | \(0.619916\pi\) | |||||||
\(242\) | 1.37553 | 0.0884223 | ||||||||
\(243\) | 21.4156 | 1.37381 | ||||||||
\(244\) | −11.6596 | −0.746430 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 14.8571 | 0.947252 | ||||||||
\(247\) | −20.2341 | −1.28746 | ||||||||
\(248\) | −30.1572 | −1.91498 | ||||||||
\(249\) | −9.11305 | −0.577516 | ||||||||
\(250\) | −0.856487 | −0.0541690 | ||||||||
\(251\) | −13.9311 | −0.879325 | −0.439662 | − | 0.898163i | \(-0.644902\pi\) | ||||
−0.439662 | + | 0.898163i | \(0.644902\pi\) | |||||||
\(252\) | 4.97706 | 0.313525 | ||||||||
\(253\) | −14.3433 | −0.901758 | ||||||||
\(254\) | −13.2497 | −0.831358 | ||||||||
\(255\) | 4.56152 | 0.285654 | ||||||||
\(256\) | −15.6350 | −0.977191 | ||||||||
\(257\) | 21.8309 | 1.36178 | 0.680888 | − | 0.732387i | \(-0.261594\pi\) | ||||
0.680888 | + | 0.732387i | \(0.261594\pi\) | |||||||
\(258\) | 0.249660 | 0.0155431 | ||||||||
\(259\) | −5.89164 | −0.366089 | ||||||||
\(260\) | 4.61510 | 0.286216 | ||||||||
\(261\) | 3.38215 | 0.209350 | ||||||||
\(262\) | −10.0484 | −0.620794 | ||||||||
\(263\) | 25.8202 | 1.59214 | 0.796070 | − | 0.605205i | \(-0.206909\pi\) | ||||
0.796070 | + | 0.605205i | \(0.206909\pi\) | |||||||
\(264\) | 26.1486 | 1.60934 | ||||||||
\(265\) | 7.84850 | 0.482130 | ||||||||
\(266\) | 4.75559 | 0.291584 | ||||||||
\(267\) | 38.4821 | 2.35506 | ||||||||
\(268\) | 9.21925 | 0.563155 | ||||||||
\(269\) | 5.58452 | 0.340494 | 0.170247 | − | 0.985401i | \(-0.445543\pi\) | ||||
0.170247 | + | 0.985401i | \(0.445543\pi\) | |||||||
\(270\) | 2.09683 | 0.127609 | ||||||||
\(271\) | −16.9554 | −1.02996 | −0.514982 | − | 0.857201i | \(-0.672202\pi\) | ||||
−0.514982 | + | 0.857201i | \(0.672202\pi\) | |||||||
\(272\) | 0.236885 | 0.0143633 | ||||||||
\(273\) | 9.59326 | 0.580610 | ||||||||
\(274\) | −17.3953 | −1.05089 | ||||||||
\(275\) | 3.55049 | 0.214103 | ||||||||
\(276\) | −13.4682 | −0.810690 | ||||||||
\(277\) | 4.18846 | 0.251660 | 0.125830 | − | 0.992052i | \(-0.459841\pi\) | ||||
0.125830 | + | 0.992052i | \(0.459841\pi\) | |||||||
\(278\) | −11.0360 | −0.661893 | ||||||||
\(279\) | 42.3631 | 2.53621 | ||||||||
\(280\) | −2.79765 | −0.167192 | ||||||||
\(281\) | 16.4708 | 0.982563 | 0.491282 | − | 0.871001i | \(-0.336529\pi\) | ||||
0.491282 | + | 0.871001i | \(0.336529\pi\) | |||||||
\(282\) | 7.14105 | 0.425244 | ||||||||
\(283\) | −14.2253 | −0.845603 | −0.422802 | − | 0.906222i | \(-0.638953\pi\) | ||||
−0.422802 | + | 0.906222i | \(0.638953\pi\) | |||||||
\(284\) | 19.3361 | 1.14738 | ||||||||
\(285\) | −14.6167 | −0.865820 | ||||||||
\(286\) | 11.0818 | 0.655279 | ||||||||
\(287\) | 6.58941 | 0.388960 | ||||||||
\(288\) | 22.4496 | 1.32286 | ||||||||
\(289\) | −13.9975 | −0.823381 | ||||||||
\(290\) | −0.737093 | −0.0432836 | ||||||||
\(291\) | −32.3581 | −1.89686 | ||||||||
\(292\) | −9.98724 | −0.584459 | ||||||||
\(293\) | −15.5453 | −0.908168 | −0.454084 | − | 0.890959i | \(-0.650033\pi\) | ||||
−0.454084 | + | 0.890959i | \(0.650033\pi\) | |||||||
\(294\) | −2.25469 | −0.131496 | ||||||||
\(295\) | 13.2508 | 0.771489 | ||||||||
\(296\) | −16.4828 | −0.958042 | ||||||||
\(297\) | −8.69225 | −0.504375 | ||||||||
\(298\) | 5.13197 | 0.297287 | ||||||||
\(299\) | −14.7218 | −0.851384 | ||||||||
\(300\) | 3.33386 | 0.192481 | ||||||||
\(301\) | 0.110729 | 0.00638231 | ||||||||
\(302\) | 13.7012 | 0.788415 | ||||||||
\(303\) | −35.0996 | −2.01642 | ||||||||
\(304\) | −0.759064 | −0.0435353 | ||||||||
\(305\) | −9.20667 | −0.527173 | ||||||||
\(306\) | 5.83251 | 0.333422 | ||||||||
\(307\) | 8.51363 | 0.485899 | 0.242949 | − | 0.970039i | \(-0.421885\pi\) | ||||
0.242949 | + | 0.970039i | \(0.421885\pi\) | |||||||
\(308\) | 4.49646 | 0.256209 | ||||||||
\(309\) | −47.9186 | −2.72599 | ||||||||
\(310\) | −9.23245 | −0.524368 | ||||||||
\(311\) | 33.5618 | 1.90312 | 0.951559 | − | 0.307467i | \(-0.0994815\pi\) | ||||
0.951559 | + | 0.307467i | \(0.0994815\pi\) | |||||||
\(312\) | 26.8386 | 1.51944 | ||||||||
\(313\) | 21.6056 | 1.22122 | 0.610609 | − | 0.791932i | \(-0.290925\pi\) | ||||
0.610609 | + | 0.791932i | \(0.290925\pi\) | |||||||
\(314\) | 5.66111 | 0.319475 | ||||||||
\(315\) | 3.92999 | 0.221430 | ||||||||
\(316\) | 6.11417 | 0.343949 | ||||||||
\(317\) | 18.7062 | 1.05065 | 0.525323 | − | 0.850903i | \(-0.323944\pi\) | ||||
0.525323 | + | 0.850903i | \(0.323944\pi\) | |||||||
\(318\) | 17.6959 | 0.992339 | ||||||||
\(319\) | 3.05556 | 0.171078 | ||||||||
\(320\) | −4.61918 | −0.258220 | ||||||||
\(321\) | −23.9302 | −1.33565 | ||||||||
\(322\) | 3.46005 | 0.192821 | ||||||||
\(323\) | −9.62116 | −0.535336 | ||||||||
\(324\) | 6.76928 | 0.376071 | ||||||||
\(325\) | 3.64418 | 0.202143 | ||||||||
\(326\) | 10.7664 | 0.596298 | ||||||||
\(327\) | −13.3342 | −0.737380 | ||||||||
\(328\) | 18.4349 | 1.01790 | ||||||||
\(329\) | 3.16720 | 0.174613 | ||||||||
\(330\) | 8.00526 | 0.440675 | ||||||||
\(331\) | −12.3498 | −0.678806 | −0.339403 | − | 0.940641i | \(-0.610225\pi\) | ||||
−0.339403 | + | 0.940641i | \(0.610225\pi\) | |||||||
\(332\) | −4.38408 | −0.240608 | ||||||||
\(333\) | 23.1541 | 1.26884 | ||||||||
\(334\) | −6.65987 | −0.364412 | ||||||||
\(335\) | 7.27971 | 0.397733 | ||||||||
\(336\) | 0.359882 | 0.0196332 | ||||||||
\(337\) | 24.4158 | 1.33001 | 0.665007 | − | 0.746837i | \(-0.268428\pi\) | ||||
0.665007 | + | 0.746837i | \(0.268428\pi\) | |||||||
\(338\) | 0.239855 | 0.0130464 | ||||||||
\(339\) | 25.9042 | 1.40693 | ||||||||
\(340\) | 2.19445 | 0.119011 | ||||||||
\(341\) | 38.2724 | 2.07257 | ||||||||
\(342\) | −18.6894 | −1.01061 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.309782 | 0.0167023 | ||||||||
\(345\) | −10.6348 | −0.572556 | ||||||||
\(346\) | 11.2512 | 0.604866 | ||||||||
\(347\) | −28.4587 | −1.52774 | −0.763870 | − | 0.645370i | \(-0.776703\pi\) | ||||
−0.763870 | + | 0.645370i | \(0.776703\pi\) | |||||||
\(348\) | 2.86912 | 0.153801 | ||||||||
\(349\) | −7.48265 | −0.400537 | −0.200269 | − | 0.979741i | \(-0.564181\pi\) | ||||
−0.200269 | + | 0.979741i | \(0.564181\pi\) | |||||||
\(350\) | −0.856487 | −0.0457811 | ||||||||
\(351\) | −8.92161 | −0.476200 | ||||||||
\(352\) | 20.2818 | 1.08103 | ||||||||
\(353\) | 34.5266 | 1.83767 | 0.918833 | − | 0.394645i | \(-0.129133\pi\) | ||||
0.918833 | + | 0.394645i | \(0.129133\pi\) | |||||||
\(354\) | 29.8763 | 1.58791 | ||||||||
\(355\) | 15.2682 | 0.810350 | ||||||||
\(356\) | 18.5129 | 0.981180 | ||||||||
\(357\) | 4.56152 | 0.241421 | ||||||||
\(358\) | −20.9573 | −1.10763 | ||||||||
\(359\) | 27.0624 | 1.42830 | 0.714149 | − | 0.699994i | \(-0.246814\pi\) | ||||
0.714149 | + | 0.699994i | \(0.246814\pi\) | |||||||
\(360\) | 10.9947 | 0.579474 | ||||||||
\(361\) | 11.8296 | 0.622610 | ||||||||
\(362\) | −3.71699 | −0.195361 | ||||||||
\(363\) | −4.22781 | −0.221902 | ||||||||
\(364\) | 4.61510 | 0.241897 | ||||||||
\(365\) | −7.88613 | −0.412779 | ||||||||
\(366\) | −20.7582 | −1.08505 | ||||||||
\(367\) | −30.2584 | −1.57948 | −0.789738 | − | 0.613444i | \(-0.789783\pi\) | ||||
−0.789738 | + | 0.613444i | \(0.789783\pi\) | |||||||
\(368\) | −0.552275 | −0.0287893 | ||||||||
\(369\) | −25.8963 | −1.34811 | ||||||||
\(370\) | −5.04611 | −0.262335 | ||||||||
\(371\) | 7.84850 | 0.407474 | ||||||||
\(372\) | 35.9372 | 1.86326 | ||||||||
\(373\) | 17.8223 | 0.922804 | 0.461402 | − | 0.887191i | \(-0.347347\pi\) | ||||
0.461402 | + | 0.887191i | \(0.347347\pi\) | |||||||
\(374\) | 5.26930 | 0.272469 | ||||||||
\(375\) | 2.63249 | 0.135941 | ||||||||
\(376\) | 8.86073 | 0.456957 | ||||||||
\(377\) | 3.13618 | 0.161522 | ||||||||
\(378\) | 2.09683 | 0.107849 | ||||||||
\(379\) | 19.4051 | 0.996772 | 0.498386 | − | 0.866955i | \(-0.333926\pi\) | ||||
0.498386 | + | 0.866955i | \(0.333926\pi\) | |||||||
\(380\) | −7.03178 | −0.360723 | ||||||||
\(381\) | 40.7240 | 2.08635 | ||||||||
\(382\) | 17.3849 | 0.889490 | ||||||||
\(383\) | 2.54839 | 0.130217 | 0.0651084 | − | 0.997878i | \(-0.479261\pi\) | ||||
0.0651084 | + | 0.997878i | \(0.479261\pi\) | |||||||
\(384\) | 19.6608 | 1.00331 | ||||||||
\(385\) | 3.55049 | 0.180950 | ||||||||
\(386\) | −0.250351 | −0.0127425 | ||||||||
\(387\) | −0.435164 | −0.0221206 | ||||||||
\(388\) | −15.5667 | −0.790282 | ||||||||
\(389\) | 25.9129 | 1.31384 | 0.656918 | − | 0.753962i | \(-0.271860\pi\) | ||||
0.656918 | + | 0.753962i | \(0.271860\pi\) | |||||||
\(390\) | 8.21649 | 0.416058 | ||||||||
\(391\) | −7.00011 | −0.354011 | ||||||||
\(392\) | −2.79765 | −0.141303 | ||||||||
\(393\) | 30.8847 | 1.55793 | ||||||||
\(394\) | 8.50355 | 0.428402 | ||||||||
\(395\) | 4.82787 | 0.242917 | ||||||||
\(396\) | −17.6710 | −0.888002 | ||||||||
\(397\) | 21.3591 | 1.07198 | 0.535992 | − | 0.844223i | \(-0.319938\pi\) | ||||
0.535992 | + | 0.844223i | \(0.319938\pi\) | |||||||
\(398\) | 19.0015 | 0.952460 | ||||||||
\(399\) | −14.6167 | −0.731752 | ||||||||
\(400\) | 0.136708 | 0.00683541 | ||||||||
\(401\) | −0.353510 | −0.0176535 | −0.00882673 | − | 0.999961i | \(-0.502810\pi\) | ||||
−0.00882673 | + | 0.999961i | \(0.502810\pi\) | |||||||
\(402\) | 16.4135 | 0.818631 | ||||||||
\(403\) | 39.2823 | 1.95679 | ||||||||
\(404\) | −16.8856 | −0.840092 | ||||||||
\(405\) | 5.34516 | 0.265603 | ||||||||
\(406\) | −0.737093 | −0.0365813 | ||||||||
\(407\) | 20.9182 | 1.03688 | ||||||||
\(408\) | 12.7616 | 0.631791 | ||||||||
\(409\) | 16.1106 | 0.796619 | 0.398310 | − | 0.917251i | \(-0.369597\pi\) | ||||
0.398310 | + | 0.917251i | \(0.369597\pi\) | |||||||
\(410\) | 5.64374 | 0.278724 | ||||||||
\(411\) | 53.4659 | 2.63728 | ||||||||
\(412\) | −23.0526 | −1.13572 | ||||||||
\(413\) | 13.2508 | 0.652027 | ||||||||
\(414\) | −13.5979 | −0.668302 | ||||||||
\(415\) | −3.46176 | −0.169931 | ||||||||
\(416\) | 20.8170 | 1.02064 | ||||||||
\(417\) | 33.9200 | 1.66107 | ||||||||
\(418\) | −16.8847 | −0.825858 | ||||||||
\(419\) | −8.54075 | −0.417243 | −0.208621 | − | 0.977996i | \(-0.566898\pi\) | ||||
−0.208621 | + | 0.977996i | \(0.566898\pi\) | |||||||
\(420\) | 3.33386 | 0.162676 | ||||||||
\(421\) | 2.00275 | 0.0976079 | 0.0488039 | − | 0.998808i | \(-0.484459\pi\) | ||||
0.0488039 | + | 0.998808i | \(0.484459\pi\) | |||||||
\(422\) | 19.7470 | 0.961271 | ||||||||
\(423\) | −12.4471 | −0.605197 | ||||||||
\(424\) | 21.9574 | 1.06635 | ||||||||
\(425\) | 1.73278 | 0.0840522 | ||||||||
\(426\) | 34.4250 | 1.66789 | ||||||||
\(427\) | −9.20667 | −0.445542 | ||||||||
\(428\) | −11.5123 | −0.556468 | ||||||||
\(429\) | −34.0608 | −1.64447 | ||||||||
\(430\) | 0.0948379 | 0.00457349 | ||||||||
\(431\) | 16.0059 | 0.770975 | 0.385488 | − | 0.922713i | \(-0.374033\pi\) | ||||
0.385488 | + | 0.922713i | \(0.374033\pi\) | |||||||
\(432\) | −0.334686 | −0.0161026 | ||||||||
\(433\) | −32.3465 | −1.55447 | −0.777237 | − | 0.629207i | \(-0.783380\pi\) | ||||
−0.777237 | + | 0.629207i | \(0.783380\pi\) | |||||||
\(434\) | −9.23245 | −0.443172 | ||||||||
\(435\) | 2.26552 | 0.108623 | ||||||||
\(436\) | −6.41476 | −0.307211 | ||||||||
\(437\) | 22.4308 | 1.07301 | ||||||||
\(438\) | −17.7808 | −0.849598 | ||||||||
\(439\) | 4.83225 | 0.230631 | 0.115315 | − | 0.993329i | \(-0.463212\pi\) | ||||
0.115315 | + | 0.993329i | \(0.463212\pi\) | |||||||
\(440\) | 9.93306 | 0.473540 | ||||||||
\(441\) | 3.92999 | 0.187142 | ||||||||
\(442\) | 5.40834 | 0.257248 | ||||||||
\(443\) | −19.0604 | −0.905586 | −0.452793 | − | 0.891616i | \(-0.649572\pi\) | ||||
−0.452793 | + | 0.891616i | \(0.649572\pi\) | |||||||
\(444\) | 19.6419 | 0.932165 | ||||||||
\(445\) | 14.6181 | 0.692967 | ||||||||
\(446\) | 0.773672 | 0.0366345 | ||||||||
\(447\) | −15.7736 | −0.746064 | ||||||||
\(448\) | −4.61918 | −0.218236 | ||||||||
\(449\) | −30.4444 | −1.43676 | −0.718380 | − | 0.695651i | \(-0.755116\pi\) | ||||
−0.718380 | + | 0.695651i | \(0.755116\pi\) | |||||||
\(450\) | 3.36598 | 0.158674 | ||||||||
\(451\) | −23.3957 | −1.10166 | ||||||||
\(452\) | 12.4620 | 0.586161 | ||||||||
\(453\) | −42.1118 | −1.97859 | ||||||||
\(454\) | 1.92177 | 0.0901930 | ||||||||
\(455\) | 3.64418 | 0.170842 | ||||||||
\(456\) | −40.8925 | −1.91497 | ||||||||
\(457\) | −17.3648 | −0.812292 | −0.406146 | − | 0.913808i | \(-0.633128\pi\) | ||||
−0.406146 | + | 0.913808i | \(0.633128\pi\) | |||||||
\(458\) | 0.856487 | 0.0400210 | ||||||||
\(459\) | −4.24216 | −0.198007 | ||||||||
\(460\) | −5.11615 | −0.238542 | ||||||||
\(461\) | −31.9156 | −1.48646 | −0.743230 | − | 0.669036i | \(-0.766707\pi\) | ||||
−0.743230 | + | 0.669036i | \(0.766707\pi\) | |||||||
\(462\) | 8.00526 | 0.372439 | ||||||||
\(463\) | −29.7968 | −1.38477 | −0.692386 | − | 0.721527i | \(-0.743441\pi\) | ||||
−0.692386 | + | 0.721527i | \(0.743441\pi\) | |||||||
\(464\) | 0.117651 | 0.00546181 | ||||||||
\(465\) | 28.3768 | 1.31594 | ||||||||
\(466\) | −2.19917 | −0.101874 | ||||||||
\(467\) | 18.5892 | 0.860207 | 0.430103 | − | 0.902780i | \(-0.358477\pi\) | ||||
0.430103 | + | 0.902780i | \(0.358477\pi\) | |||||||
\(468\) | −18.1373 | −0.838396 | ||||||||
\(469\) | 7.27971 | 0.336146 | ||||||||
\(470\) | 2.71266 | 0.125126 | ||||||||
\(471\) | −17.3999 | −0.801746 | ||||||||
\(472\) | 37.0710 | 1.70633 | ||||||||
\(473\) | −0.393143 | −0.0180767 | ||||||||
\(474\) | 10.8854 | 0.499981 | ||||||||
\(475\) | −5.55244 | −0.254763 | ||||||||
\(476\) | 2.19445 | 0.100582 | ||||||||
\(477\) | −30.8445 | −1.41227 | ||||||||
\(478\) | −11.6123 | −0.531133 | ||||||||
\(479\) | 35.0047 | 1.59941 | 0.799703 | − | 0.600396i | \(-0.204990\pi\) | ||||
0.799703 | + | 0.600396i | \(0.204990\pi\) | |||||||
\(480\) | 15.0378 | 0.686379 | ||||||||
\(481\) | 21.4702 | 0.978957 | ||||||||
\(482\) | −9.78283 | −0.445596 | ||||||||
\(483\) | −10.6348 | −0.483898 | ||||||||
\(484\) | −2.03390 | −0.0924502 | ||||||||
\(485\) | −12.2918 | −0.558143 | ||||||||
\(486\) | 18.3422 | 0.832018 | ||||||||
\(487\) | −3.71353 | −0.168276 | −0.0841380 | − | 0.996454i | \(-0.526814\pi\) | ||||
−0.0841380 | + | 0.996454i | \(0.526814\pi\) | |||||||
\(488\) | −25.7571 | −1.16597 | ||||||||
\(489\) | −33.0916 | −1.49646 | ||||||||
\(490\) | −0.856487 | −0.0386921 | ||||||||
\(491\) | −12.8128 | −0.578233 | −0.289116 | − | 0.957294i | \(-0.593361\pi\) | ||||
−0.289116 | + | 0.957294i | \(0.593361\pi\) | |||||||
\(492\) | −21.9682 | −0.990402 | ||||||||
\(493\) | 1.49123 | 0.0671617 | ||||||||
\(494\) | −17.3302 | −0.779724 | ||||||||
\(495\) | −13.9534 | −0.627159 | ||||||||
\(496\) | 1.47364 | 0.0661683 | ||||||||
\(497\) | 15.2682 | 0.684870 | ||||||||
\(498\) | −7.80520 | −0.349759 | ||||||||
\(499\) | 9.59370 | 0.429473 | 0.214736 | − | 0.976672i | \(-0.431111\pi\) | ||||
0.214736 | + | 0.976672i | \(0.431111\pi\) | |||||||
\(500\) | 1.26643 | 0.0566365 | ||||||||
\(501\) | 20.4697 | 0.914519 | ||||||||
\(502\) | −11.9318 | −0.532543 | ||||||||
\(503\) | 27.6814 | 1.23425 | 0.617127 | − | 0.786864i | \(-0.288296\pi\) | ||||
0.617127 | + | 0.786864i | \(0.288296\pi\) | |||||||
\(504\) | 10.9947 | 0.489745 | ||||||||
\(505\) | −13.3332 | −0.593322 | ||||||||
\(506\) | −12.2849 | −0.546130 | ||||||||
\(507\) | −0.737217 | −0.0327409 | ||||||||
\(508\) | 19.5914 | 0.869228 | ||||||||
\(509\) | −22.5672 | −1.00028 | −0.500138 | − | 0.865946i | \(-0.666717\pi\) | ||||
−0.500138 | + | 0.865946i | \(0.666717\pi\) | |||||||
\(510\) | 3.90688 | 0.173000 | ||||||||
\(511\) | −7.88613 | −0.348862 | ||||||||
\(512\) | 1.54585 | 0.0683178 | ||||||||
\(513\) | 13.5934 | 0.600162 | ||||||||
\(514\) | 18.6979 | 0.824729 | ||||||||
\(515\) | −18.2028 | −0.802111 | ||||||||
\(516\) | −0.369155 | −0.0162512 | ||||||||
\(517\) | −11.2451 | −0.494560 | ||||||||
\(518\) | −5.04611 | −0.221714 | ||||||||
\(519\) | −34.5814 | −1.51796 | ||||||||
\(520\) | 10.1952 | 0.447087 | ||||||||
\(521\) | 37.2192 | 1.63060 | 0.815301 | − | 0.579038i | \(-0.196572\pi\) | ||||
0.815301 | + | 0.579038i | \(0.196572\pi\) | |||||||
\(522\) | 2.89676 | 0.126788 | ||||||||
\(523\) | 30.7280 | 1.34364 | 0.671821 | − | 0.740714i | \(-0.265513\pi\) | ||||
0.671821 | + | 0.740714i | \(0.265513\pi\) | |||||||
\(524\) | 14.8579 | 0.649073 | ||||||||
\(525\) | 2.63249 | 0.114891 | ||||||||
\(526\) | 22.1146 | 0.964244 | ||||||||
\(527\) | 18.6784 | 0.813645 | ||||||||
\(528\) | −1.27776 | −0.0556074 | ||||||||
\(529\) | −6.67990 | −0.290430 | ||||||||
\(530\) | 6.72214 | 0.291991 | ||||||||
\(531\) | −52.0753 | −2.25987 | ||||||||
\(532\) | −7.03178 | −0.304866 | ||||||||
\(533\) | −24.0130 | −1.04012 | ||||||||
\(534\) | 32.9594 | 1.42629 | ||||||||
\(535\) | −9.09035 | −0.393010 | ||||||||
\(536\) | 20.3661 | 0.879682 | ||||||||
\(537\) | 64.4140 | 2.77967 | ||||||||
\(538\) | 4.78307 | 0.206213 | ||||||||
\(539\) | 3.55049 | 0.152931 | ||||||||
\(540\) | −3.10045 | −0.133422 | ||||||||
\(541\) | −32.4936 | −1.39701 | −0.698506 | − | 0.715605i | \(-0.746151\pi\) | ||||
−0.698506 | + | 0.715605i | \(0.746151\pi\) | |||||||
\(542\) | −14.5220 | −0.623775 | ||||||||
\(543\) | 11.4245 | 0.490272 | ||||||||
\(544\) | 9.89833 | 0.424387 | ||||||||
\(545\) | −5.06523 | −0.216971 | ||||||||
\(546\) | 8.21649 | 0.351634 | ||||||||
\(547\) | 31.4853 | 1.34621 | 0.673107 | − | 0.739545i | \(-0.264959\pi\) | ||||
0.673107 | + | 0.739545i | \(0.264959\pi\) | |||||||
\(548\) | 25.7212 | 1.09876 | ||||||||
\(549\) | 36.1821 | 1.54421 | ||||||||
\(550\) | 3.04095 | 0.129667 | ||||||||
\(551\) | −4.77843 | −0.203568 | ||||||||
\(552\) | −29.7524 | −1.26635 | ||||||||
\(553\) | 4.82787 | 0.205302 | ||||||||
\(554\) | 3.58736 | 0.152412 | ||||||||
\(555\) | 15.5097 | 0.658349 | ||||||||
\(556\) | 16.3182 | 0.692044 | ||||||||
\(557\) | 21.6638 | 0.917923 | 0.458961 | − | 0.888456i | \(-0.348222\pi\) | ||||
0.458961 | + | 0.888456i | \(0.348222\pi\) | |||||||
\(558\) | 36.2834 | 1.53600 | ||||||||
\(559\) | −0.403516 | −0.0170669 | ||||||||
\(560\) | 0.136708 | 0.00577697 | ||||||||
\(561\) | −16.1957 | −0.683781 | ||||||||
\(562\) | 14.1070 | 0.595067 | ||||||||
\(563\) | −18.1117 | −0.763318 | −0.381659 | − | 0.924303i | \(-0.624647\pi\) | ||||
−0.381659 | + | 0.924303i | \(0.624647\pi\) | |||||||
\(564\) | −10.5590 | −0.444614 | ||||||||
\(565\) | 9.84021 | 0.413981 | ||||||||
\(566\) | −12.1837 | −0.512121 | ||||||||
\(567\) | 5.34516 | 0.224476 | ||||||||
\(568\) | 42.7150 | 1.79228 | ||||||||
\(569\) | 4.56776 | 0.191491 | 0.0957453 | − | 0.995406i | \(-0.469477\pi\) | ||||
0.0957453 | + | 0.995406i | \(0.469477\pi\) | |||||||
\(570\) | −12.5190 | −0.524364 | ||||||||
\(571\) | −3.16213 | −0.132331 | −0.0661656 | − | 0.997809i | \(-0.521077\pi\) | ||||
−0.0661656 | + | 0.997809i | \(0.521077\pi\) | |||||||
\(572\) | −16.3859 | −0.685129 | ||||||||
\(573\) | −53.4341 | −2.23224 | ||||||||
\(574\) | 5.64374 | 0.235565 | ||||||||
\(575\) | −4.03981 | −0.168472 | ||||||||
\(576\) | 18.1533 | 0.756388 | ||||||||
\(577\) | 37.6863 | 1.56890 | 0.784450 | − | 0.620192i | \(-0.212945\pi\) | ||||
0.784450 | + | 0.620192i | \(0.212945\pi\) | |||||||
\(578\) | −11.9886 | −0.498662 | ||||||||
\(579\) | 0.769475 | 0.0319783 | ||||||||
\(580\) | 1.08989 | 0.0452552 | ||||||||
\(581\) | −3.46176 | −0.143618 | ||||||||
\(582\) | −27.7142 | −1.14879 | ||||||||
\(583\) | −27.8661 | −1.15409 | ||||||||
\(584\) | −22.0627 | −0.912959 | ||||||||
\(585\) | −14.3216 | −0.592124 | ||||||||
\(586\) | −13.3144 | −0.550012 | ||||||||
\(587\) | 14.6206 | 0.603455 | 0.301727 | − | 0.953394i | \(-0.402437\pi\) | ||||
0.301727 | + | 0.953394i | \(0.402437\pi\) | |||||||
\(588\) | 3.33386 | 0.137486 | ||||||||
\(589\) | −59.8522 | −2.46617 | ||||||||
\(590\) | 11.3491 | 0.467235 | ||||||||
\(591\) | −26.1364 | −1.07511 | ||||||||
\(592\) | 0.805435 | 0.0331032 | ||||||||
\(593\) | −22.8867 | −0.939843 | −0.469922 | − | 0.882708i | \(-0.655718\pi\) | ||||
−0.469922 | + | 0.882708i | \(0.655718\pi\) | |||||||
\(594\) | −7.44479 | −0.305464 | ||||||||
\(595\) | 1.73278 | 0.0710371 | ||||||||
\(596\) | −7.58831 | −0.310829 | ||||||||
\(597\) | −58.4028 | −2.39027 | ||||||||
\(598\) | −12.6090 | −0.515622 | ||||||||
\(599\) | −33.3985 | −1.36463 | −0.682313 | − | 0.731061i | \(-0.739026\pi\) | ||||
−0.682313 | + | 0.731061i | \(0.739026\pi\) | |||||||
\(600\) | 7.36479 | 0.300666 | ||||||||
\(601\) | 22.8200 | 0.930847 | 0.465424 | − | 0.885088i | \(-0.345902\pi\) | ||||
0.465424 | + | 0.885088i | \(0.345902\pi\) | |||||||
\(602\) | 0.0948379 | 0.00386531 | ||||||||
\(603\) | −28.6092 | −1.16506 | ||||||||
\(604\) | −20.2591 | −0.824329 | ||||||||
\(605\) | −1.60601 | −0.0652937 | ||||||||
\(606\) | −30.0623 | −1.22120 | ||||||||
\(607\) | 9.56943 | 0.388411 | 0.194206 | − | 0.980961i | \(-0.437787\pi\) | ||||
0.194206 | + | 0.980961i | \(0.437787\pi\) | |||||||
\(608\) | −31.7177 | −1.28632 | ||||||||
\(609\) | 2.26552 | 0.0918035 | ||||||||
\(610\) | −7.88539 | −0.319270 | ||||||||
\(611\) | −11.5418 | −0.466933 | ||||||||
\(612\) | −8.62415 | −0.348610 | ||||||||
\(613\) | 20.6257 | 0.833066 | 0.416533 | − | 0.909121i | \(-0.363245\pi\) | ||||
0.416533 | + | 0.909121i | \(0.363245\pi\) | |||||||
\(614\) | 7.29181 | 0.294274 | ||||||||
\(615\) | −17.3465 | −0.699480 | ||||||||
\(616\) | 9.93306 | 0.400214 | ||||||||
\(617\) | −17.5933 | −0.708281 | −0.354141 | − | 0.935192i | \(-0.615227\pi\) | ||||
−0.354141 | + | 0.935192i | \(0.615227\pi\) | |||||||
\(618\) | −41.0416 | −1.65094 | ||||||||
\(619\) | −6.00625 | −0.241412 | −0.120706 | − | 0.992688i | \(-0.538516\pi\) | ||||
−0.120706 | + | 0.992688i | \(0.538516\pi\) | |||||||
\(620\) | 13.6514 | 0.548254 | ||||||||
\(621\) | 9.89019 | 0.396880 | ||||||||
\(622\) | 28.7453 | 1.15258 | ||||||||
\(623\) | 14.6181 | 0.585664 | ||||||||
\(624\) | −1.31148 | −0.0525011 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.5049 | 0.739603 | ||||||||
\(627\) | 51.8966 | 2.07255 | ||||||||
\(628\) | −8.37072 | −0.334028 | ||||||||
\(629\) | 10.2089 | 0.407056 | ||||||||
\(630\) | 3.36598 | 0.134104 | ||||||||
\(631\) | 6.01438 | 0.239429 | 0.119714 | − | 0.992808i | \(-0.461802\pi\) | ||||
0.119714 | + | 0.992808i | \(0.461802\pi\) | |||||||
\(632\) | 13.5067 | 0.537269 | ||||||||
\(633\) | −60.6943 | −2.41238 | ||||||||
\(634\) | 16.0216 | 0.636301 | ||||||||
\(635\) | 15.4698 | 0.613899 | ||||||||
\(636\) | −26.1658 | −1.03754 | ||||||||
\(637\) | 3.64418 | 0.144388 | ||||||||
\(638\) | 2.61704 | 0.103610 | ||||||||
\(639\) | −60.0037 | −2.37371 | ||||||||
\(640\) | 7.46853 | 0.295220 | ||||||||
\(641\) | −46.0811 | −1.82009 | −0.910046 | − | 0.414506i | \(-0.863954\pi\) | ||||
−0.910046 | + | 0.414506i | \(0.863954\pi\) | |||||||
\(642\) | −20.4959 | −0.808909 | ||||||||
\(643\) | 17.8923 | 0.705602 | 0.352801 | − | 0.935698i | \(-0.385229\pi\) | ||||
0.352801 | + | 0.935698i | \(0.385229\pi\) | |||||||
\(644\) | −5.11615 | −0.201604 | ||||||||
\(645\) | −0.291493 | −0.0114775 | ||||||||
\(646\) | −8.24039 | −0.324214 | ||||||||
\(647\) | 34.0425 | 1.33835 | 0.669174 | − | 0.743106i | \(-0.266648\pi\) | ||||
0.669174 | + | 0.743106i | \(0.266648\pi\) | |||||||
\(648\) | 14.9539 | 0.587445 | ||||||||
\(649\) | −47.0467 | −1.84675 | ||||||||
\(650\) | 3.12119 | 0.122423 | ||||||||
\(651\) | 28.3768 | 1.11217 | ||||||||
\(652\) | −15.9196 | −0.623461 | ||||||||
\(653\) | −26.9418 | −1.05431 | −0.527157 | − | 0.849768i | \(-0.676742\pi\) | ||||
−0.527157 | + | 0.849768i | \(0.676742\pi\) | |||||||
\(654\) | −11.4205 | −0.446578 | ||||||||
\(655\) | 11.7321 | 0.458413 | ||||||||
\(656\) | −0.900825 | −0.0351713 | ||||||||
\(657\) | 30.9924 | 1.20913 | ||||||||
\(658\) | 2.71266 | 0.105751 | ||||||||
\(659\) | 8.55450 | 0.333236 | 0.166618 | − | 0.986022i | \(-0.446715\pi\) | ||||
0.166618 | + | 0.986022i | \(0.446715\pi\) | |||||||
\(660\) | −11.8369 | −0.460749 | ||||||||
\(661\) | 11.8917 | 0.462533 | 0.231267 | − | 0.972890i | \(-0.425713\pi\) | ||||
0.231267 | + | 0.972890i | \(0.425713\pi\) | |||||||
\(662\) | −10.5774 | −0.411103 | ||||||||
\(663\) | −16.6230 | −0.645584 | ||||||||
\(664\) | −9.68481 | −0.375844 | ||||||||
\(665\) | −5.55244 | −0.215314 | ||||||||
\(666\) | 19.8312 | 0.768442 | ||||||||
\(667\) | −3.47667 | −0.134617 | ||||||||
\(668\) | 9.84751 | 0.381012 | ||||||||
\(669\) | −2.37795 | −0.0919369 | ||||||||
\(670\) | 6.23498 | 0.240878 | ||||||||
\(671\) | 32.6882 | 1.26192 | ||||||||
\(672\) | 15.0378 | 0.580096 | ||||||||
\(673\) | 41.9195 | 1.61588 | 0.807939 | − | 0.589266i | \(-0.200583\pi\) | ||||
0.807939 | + | 0.589266i | \(0.200583\pi\) | |||||||
\(674\) | 20.9118 | 0.805493 | ||||||||
\(675\) | −2.44818 | −0.0942305 | ||||||||
\(676\) | −0.354659 | −0.0136407 | ||||||||
\(677\) | 28.3631 | 1.09008 | 0.545041 | − | 0.838409i | \(-0.316514\pi\) | ||||
0.545041 | + | 0.838409i | \(0.316514\pi\) | |||||||
\(678\) | 22.1866 | 0.852072 | ||||||||
\(679\) | −12.2918 | −0.471717 | ||||||||
\(680\) | 4.84772 | 0.185902 | ||||||||
\(681\) | −5.90672 | −0.226346 | ||||||||
\(682\) | 32.7798 | 1.25520 | ||||||||
\(683\) | −24.8857 | −0.952225 | −0.476112 | − | 0.879384i | \(-0.657954\pi\) | ||||
−0.476112 | + | 0.879384i | \(0.657954\pi\) | |||||||
\(684\) | 27.6348 | 1.05664 | ||||||||
\(685\) | 20.3100 | 0.776006 | ||||||||
\(686\) | −0.856487 | −0.0327008 | ||||||||
\(687\) | −2.63249 | −0.100436 | ||||||||
\(688\) | −0.0151376 | −0.000577114 0 | ||||||||
\(689\) | −28.6014 | −1.08962 | ||||||||
\(690\) | −9.10853 | −0.346756 | ||||||||
\(691\) | −42.4390 | −1.61445 | −0.807227 | − | 0.590240i | \(-0.799033\pi\) | ||||
−0.807227 | + | 0.590240i | \(0.799033\pi\) | |||||||
\(692\) | −16.6364 | −0.632419 | ||||||||
\(693\) | −13.9534 | −0.530046 | ||||||||
\(694\) | −24.3745 | −0.925242 | ||||||||
\(695\) | 12.8852 | 0.488762 | ||||||||
\(696\) | 6.33814 | 0.240247 | ||||||||
\(697\) | −11.4180 | −0.432487 | ||||||||
\(698\) | −6.40879 | −0.242576 | ||||||||
\(699\) | 6.75933 | 0.255662 | ||||||||
\(700\) | 1.26643 | 0.0478666 | ||||||||
\(701\) | −46.0102 | −1.73778 | −0.868891 | − | 0.495003i | \(-0.835167\pi\) | ||||
−0.868891 | + | 0.495003i | \(0.835167\pi\) | |||||||
\(702\) | −7.64124 | −0.288400 | ||||||||
\(703\) | −32.7130 | −1.23379 | ||||||||
\(704\) | 16.4004 | 0.618112 | ||||||||
\(705\) | −8.33761 | −0.314013 | ||||||||
\(706\) | 29.5716 | 1.11294 | ||||||||
\(707\) | −13.3332 | −0.501448 | ||||||||
\(708\) | −44.1762 | −1.66024 | ||||||||
\(709\) | −16.9925 | −0.638167 | −0.319083 | − | 0.947727i | \(-0.603375\pi\) | ||||
−0.319083 | + | 0.947727i | \(0.603375\pi\) | |||||||
\(710\) | 13.0770 | 0.490770 | ||||||||
\(711\) | −18.9735 | −0.711561 | ||||||||
\(712\) | 40.8965 | 1.53266 | ||||||||
\(713\) | −43.5470 | −1.63085 | ||||||||
\(714\) | 3.90688 | 0.146211 | ||||||||
\(715\) | −12.9386 | −0.483878 | ||||||||
\(716\) | 30.9882 | 1.15808 | ||||||||
\(717\) | 35.6914 | 1.33292 | ||||||||
\(718\) | 23.1786 | 0.865017 | ||||||||
\(719\) | −10.0471 | −0.374695 | −0.187348 | − | 0.982294i | \(-0.559989\pi\) | ||||
−0.187348 | + | 0.982294i | \(0.559989\pi\) | |||||||
\(720\) | −0.537261 | −0.0200225 | ||||||||
\(721\) | −18.2028 | −0.677907 | ||||||||
\(722\) | 10.1319 | 0.377070 | ||||||||
\(723\) | 30.0684 | 1.11826 | ||||||||
\(724\) | 5.49607 | 0.204260 | ||||||||
\(725\) | 0.860600 | 0.0319619 | ||||||||
\(726\) | −3.62106 | −0.134390 | ||||||||
\(727\) | −12.4464 | −0.461613 | −0.230806 | − | 0.973000i | \(-0.574136\pi\) | ||||
−0.230806 | + | 0.973000i | \(0.574136\pi\) | |||||||
\(728\) | 10.1952 | 0.377858 | ||||||||
\(729\) | −40.3408 | −1.49410 | ||||||||
\(730\) | −6.75436 | −0.249990 | ||||||||
\(731\) | −0.191869 | −0.00709653 | ||||||||
\(732\) | 30.6938 | 1.13447 | ||||||||
\(733\) | 11.6226 | 0.429290 | 0.214645 | − | 0.976692i | \(-0.431141\pi\) | ||||
0.214645 | + | 0.976692i | \(0.431141\pi\) | |||||||
\(734\) | −25.9159 | −0.956574 | ||||||||
\(735\) | 2.63249 | 0.0971007 | ||||||||
\(736\) | −23.0770 | −0.850630 | ||||||||
\(737\) | −25.8466 | −0.952071 | ||||||||
\(738\) | −22.1798 | −0.816451 | ||||||||
\(739\) | −23.1131 | −0.850228 | −0.425114 | − | 0.905140i | \(-0.639766\pi\) | ||||
−0.425114 | + | 0.905140i | \(0.639766\pi\) | |||||||
\(740\) | 7.46136 | 0.274285 | ||||||||
\(741\) | 53.2660 | 1.95677 | ||||||||
\(742\) | 6.72214 | 0.246777 | ||||||||
\(743\) | −21.3039 | −0.781563 | −0.390781 | − | 0.920484i | \(-0.627795\pi\) | ||||
−0.390781 | + | 0.920484i | \(0.627795\pi\) | |||||||
\(744\) | 79.3884 | 2.91052 | ||||||||
\(745\) | −5.99189 | −0.219526 | ||||||||
\(746\) | 15.2646 | 0.558875 | ||||||||
\(747\) | 13.6047 | 0.497769 | ||||||||
\(748\) | −7.79137 | −0.284881 | ||||||||
\(749\) | −9.09035 | −0.332154 | ||||||||
\(750\) | 2.25469 | 0.0823296 | ||||||||
\(751\) | −4.55756 | −0.166308 | −0.0831539 | − | 0.996537i | \(-0.526499\pi\) | ||||
−0.0831539 | + | 0.996537i | \(0.526499\pi\) | |||||||
\(752\) | −0.432982 | −0.0157892 | ||||||||
\(753\) | 36.6735 | 1.33646 | ||||||||
\(754\) | 2.68610 | 0.0978219 | ||||||||
\(755\) | −15.9970 | −0.582189 | ||||||||
\(756\) | −3.10045 | −0.112762 | ||||||||
\(757\) | −20.7668 | −0.754781 | −0.377390 | − | 0.926054i | \(-0.623178\pi\) | ||||
−0.377390 | + | 0.926054i | \(0.623178\pi\) | |||||||
\(758\) | 16.6202 | 0.603672 | ||||||||
\(759\) | 37.7587 | 1.37055 | ||||||||
\(760\) | −15.5338 | −0.563470 | ||||||||
\(761\) | 29.2905 | 1.06178 | 0.530889 | − | 0.847441i | \(-0.321858\pi\) | ||||
0.530889 | + | 0.847441i | \(0.321858\pi\) | |||||||
\(762\) | 34.8796 | 1.26355 | ||||||||
\(763\) | −5.06523 | −0.183374 | ||||||||
\(764\) | −25.7059 | −0.930009 | ||||||||
\(765\) | −6.80980 | −0.246209 | ||||||||
\(766\) | 2.18267 | 0.0788629 | ||||||||
\(767\) | −48.2881 | −1.74358 | ||||||||
\(768\) | 41.1591 | 1.48520 | ||||||||
\(769\) | 27.8095 | 1.00284 | 0.501419 | − | 0.865205i | \(-0.332812\pi\) | ||||
0.501419 | + | 0.865205i | \(0.332812\pi\) | |||||||
\(770\) | 3.04095 | 0.109588 | ||||||||
\(771\) | −57.4697 | −2.06972 | ||||||||
\(772\) | 0.370177 | 0.0133230 | ||||||||
\(773\) | 19.0304 | 0.684475 | 0.342237 | − | 0.939614i | \(-0.388815\pi\) | ||||
0.342237 | + | 0.939614i | \(0.388815\pi\) | |||||||
\(774\) | −0.372712 | −0.0133969 | ||||||||
\(775\) | 10.7794 | 0.387209 | ||||||||
\(776\) | −34.3883 | −1.23447 | ||||||||
\(777\) | 15.5097 | 0.556406 | ||||||||
\(778\) | 22.1941 | 0.795696 | ||||||||
\(779\) | 36.5873 | 1.31088 | ||||||||
\(780\) | −12.1492 | −0.435011 | ||||||||
\(781\) | −54.2095 | −1.93977 | ||||||||
\(782\) | −5.99550 | −0.214399 | ||||||||
\(783\) | −2.10690 | −0.0752946 | ||||||||
\(784\) | 0.136708 | 0.00488243 | ||||||||
\(785\) | −6.60969 | −0.235910 | ||||||||
\(786\) | 26.4523 | 0.943524 | ||||||||
\(787\) | 6.21902 | 0.221684 | 0.110842 | − | 0.993838i | \(-0.464645\pi\) | ||||
0.110842 | + | 0.993838i | \(0.464645\pi\) | |||||||
\(788\) | −12.5736 | −0.447917 | ||||||||
\(789\) | −67.9712 | −2.41984 | ||||||||
\(790\) | 4.13501 | 0.147117 | ||||||||
\(791\) | 9.84021 | 0.349878 | ||||||||
\(792\) | −39.0368 | −1.38711 | ||||||||
\(793\) | 33.5508 | 1.19142 | ||||||||
\(794\) | 18.2938 | 0.649223 | ||||||||
\(795\) | −20.6611 | −0.732773 | ||||||||
\(796\) | −28.0963 | −0.995847 | ||||||||
\(797\) | 31.0263 | 1.09901 | 0.549504 | − | 0.835491i | \(-0.314817\pi\) | ||||
0.549504 | + | 0.835491i | \(0.314817\pi\) | |||||||
\(798\) | −12.5190 | −0.443169 | ||||||||
\(799\) | −5.48806 | −0.194154 | ||||||||
\(800\) | 5.71240 | 0.201964 | ||||||||
\(801\) | −57.4491 | −2.02987 | ||||||||
\(802\) | −0.302777 | −0.0106914 | ||||||||
\(803\) | 27.9997 | 0.988087 | ||||||||
\(804\) | −24.2696 | −0.855921 | ||||||||
\(805\) | −4.03981 | −0.142385 | ||||||||
\(806\) | 33.6447 | 1.18508 | ||||||||
\(807\) | −14.7012 | −0.517506 | ||||||||
\(808\) | −37.3018 | −1.31227 | ||||||||
\(809\) | 30.8294 | 1.08390 | 0.541952 | − | 0.840410i | \(-0.317686\pi\) | ||||
0.541952 | + | 0.840410i | \(0.317686\pi\) | |||||||
\(810\) | 4.57806 | 0.160857 | ||||||||
\(811\) | −5.90206 | −0.207249 | −0.103625 | − | 0.994616i | \(-0.533044\pi\) | ||||
−0.103625 | + | 0.994616i | \(0.533044\pi\) | |||||||
\(812\) | 1.08989 | 0.0382477 | ||||||||
\(813\) | 44.6348 | 1.56541 | ||||||||
\(814\) | 17.9162 | 0.627962 | ||||||||
\(815\) | −12.5705 | −0.440325 | ||||||||
\(816\) | −0.623597 | −0.0218303 | ||||||||
\(817\) | 0.614816 | 0.0215097 | ||||||||
\(818\) | 13.7985 | 0.482455 | ||||||||
\(819\) | −14.3216 | −0.500437 | ||||||||
\(820\) | −8.34503 | −0.291421 | ||||||||
\(821\) | 12.5323 | 0.437381 | 0.218690 | − | 0.975794i | \(-0.429821\pi\) | ||||
0.218690 | + | 0.975794i | \(0.429821\pi\) | |||||||
\(822\) | 45.7928 | 1.59721 | ||||||||
\(823\) | 24.7168 | 0.861573 | 0.430787 | − | 0.902454i | \(-0.358236\pi\) | ||||
0.430787 | + | 0.902454i | \(0.358236\pi\) | |||||||
\(824\) | −50.9251 | −1.77406 | ||||||||
\(825\) | −9.34663 | −0.325408 | ||||||||
\(826\) | 11.3491 | 0.394885 | ||||||||
\(827\) | −40.7361 | −1.41653 | −0.708267 | − | 0.705944i | \(-0.750523\pi\) | ||||
−0.708267 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(828\) | 20.1064 | 0.698745 | ||||||||
\(829\) | 19.2353 | 0.668071 | 0.334036 | − | 0.942560i | \(-0.391589\pi\) | ||||
0.334036 | + | 0.942560i | \(0.391589\pi\) | |||||||
\(830\) | −2.96495 | −0.102915 | ||||||||
\(831\) | −11.0261 | −0.382490 | ||||||||
\(832\) | 16.8331 | 0.583583 | ||||||||
\(833\) | 1.73278 | 0.0600373 | ||||||||
\(834\) | 29.0520 | 1.00599 | ||||||||
\(835\) | 7.77580 | 0.269093 | ||||||||
\(836\) | 24.9663 | 0.863478 | ||||||||
\(837\) | −26.3900 | −0.912173 | ||||||||
\(838\) | −7.31503 | −0.252694 | ||||||||
\(839\) | 37.9958 | 1.31176 | 0.655881 | − | 0.754864i | \(-0.272297\pi\) | ||||
0.655881 | + | 0.754864i | \(0.272297\pi\) | |||||||
\(840\) | 7.36479 | 0.254109 | ||||||||
\(841\) | −28.2594 | −0.974461 | ||||||||
\(842\) | 1.71532 | 0.0591140 | ||||||||
\(843\) | −43.3591 | −1.49337 | ||||||||
\(844\) | −29.1987 | −1.00506 | ||||||||
\(845\) | −0.280046 | −0.00963387 | ||||||||
\(846\) | −10.6607 | −0.366524 | ||||||||
\(847\) | −1.60601 | −0.0551833 | ||||||||
\(848\) | −1.07295 | −0.0368454 | ||||||||
\(849\) | 37.4478 | 1.28520 | ||||||||
\(850\) | 1.48410 | 0.0509043 | ||||||||
\(851\) | −23.8011 | −0.815893 | ||||||||
\(852\) | −50.9019 | −1.74387 | ||||||||
\(853\) | 28.9980 | 0.992874 | 0.496437 | − | 0.868073i | \(-0.334641\pi\) | ||||
0.496437 | + | 0.868073i | \(0.334641\pi\) | |||||||
\(854\) | −7.88539 | −0.269833 | ||||||||
\(855\) | 21.8210 | 0.746263 | ||||||||
\(856\) | −25.4317 | −0.869236 | ||||||||
\(857\) | 44.4439 | 1.51817 | 0.759087 | − | 0.650990i | \(-0.225646\pi\) | ||||
0.759087 | + | 0.650990i | \(0.225646\pi\) | |||||||
\(858\) | −29.1726 | −0.995937 | ||||||||
\(859\) | −25.3916 | −0.866352 | −0.433176 | − | 0.901309i | \(-0.642607\pi\) | ||||
−0.433176 | + | 0.901309i | \(0.642607\pi\) | |||||||
\(860\) | −0.140231 | −0.00478182 | ||||||||
\(861\) | −17.3465 | −0.591168 | ||||||||
\(862\) | 13.7088 | 0.466924 | ||||||||
\(863\) | 10.9023 | 0.371119 | 0.185559 | − | 0.982633i | \(-0.440590\pi\) | ||||
0.185559 | + | 0.982633i | \(0.440590\pi\) | |||||||
\(864\) | −13.9850 | −0.475778 | ||||||||
\(865\) | −13.1364 | −0.446651 | ||||||||
\(866\) | −27.7044 | −0.941433 | ||||||||
\(867\) | 36.8482 | 1.25143 | ||||||||
\(868\) | 13.6514 | 0.463360 | ||||||||
\(869\) | −17.1413 | −0.581480 | ||||||||
\(870\) | 1.94039 | 0.0657853 | ||||||||
\(871\) | −26.5286 | −0.898887 | ||||||||
\(872\) | −14.1708 | −0.479883 | ||||||||
\(873\) | 48.3067 | 1.63493 | ||||||||
\(874\) | 19.2117 | 0.649846 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 26.2913 | 0.888300 | ||||||||
\(877\) | 5.88907 | 0.198860 | 0.0994299 | − | 0.995045i | \(-0.468298\pi\) | ||||
0.0994299 | + | 0.995045i | \(0.468298\pi\) | |||||||
\(878\) | 4.13876 | 0.139676 | ||||||||
\(879\) | 40.9229 | 1.38029 | ||||||||
\(880\) | −0.485381 | −0.0163622 | ||||||||
\(881\) | −50.5002 | −1.70139 | −0.850697 | − | 0.525656i | \(-0.823820\pi\) | ||||
−0.850697 | + | 0.525656i | \(0.823820\pi\) | |||||||
\(882\) | 3.36598 | 0.113338 | ||||||||
\(883\) | −53.2629 | −1.79244 | −0.896220 | − | 0.443610i | \(-0.853698\pi\) | ||||
−0.896220 | + | 0.443610i | \(0.853698\pi\) | |||||||
\(884\) | −7.99696 | −0.268967 | ||||||||
\(885\) | −34.8824 | −1.17256 | ||||||||
\(886\) | −16.3250 | −0.548448 | ||||||||
\(887\) | −6.12696 | −0.205723 | −0.102862 | − | 0.994696i | \(-0.532800\pi\) | ||||
−0.102862 | + | 0.994696i | \(0.532800\pi\) | |||||||
\(888\) | 43.3907 | 1.45610 | ||||||||
\(889\) | 15.4698 | 0.518840 | ||||||||
\(890\) | 12.5202 | 0.419680 | ||||||||
\(891\) | −18.9780 | −0.635786 | ||||||||
\(892\) | −1.14398 | −0.0383032 | ||||||||
\(893\) | 17.5857 | 0.588483 | ||||||||
\(894\) | −13.5098 | −0.451837 | ||||||||
\(895\) | 24.4689 | 0.817905 | ||||||||
\(896\) | 7.46853 | 0.249506 | ||||||||
\(897\) | 38.7550 | 1.29399 | ||||||||
\(898\) | −26.0752 | −0.870141 | ||||||||
\(899\) | 9.27680 | 0.309399 | ||||||||
\(900\) | −4.97706 | −0.165902 | ||||||||
\(901\) | −13.5997 | −0.453073 | ||||||||
\(902\) | −20.0381 | −0.667195 | ||||||||
\(903\) | −0.291493 | −0.00970027 | ||||||||
\(904\) | 27.5295 | 0.915618 | ||||||||
\(905\) | 4.33981 | 0.144260 | ||||||||
\(906\) | −36.0682 | −1.19829 | ||||||||
\(907\) | −0.680992 | −0.0226120 | −0.0113060 | − | 0.999936i | \(-0.503599\pi\) | ||||
−0.0113060 | + | 0.999936i | \(0.503599\pi\) | |||||||
\(908\) | −2.84159 | −0.0943016 | ||||||||
\(909\) | 52.3995 | 1.73798 | ||||||||
\(910\) | 3.12119 | 0.103466 | ||||||||
\(911\) | 27.1975 | 0.901095 | 0.450547 | − | 0.892752i | \(-0.351229\pi\) | ||||
0.450547 | + | 0.892752i | \(0.351229\pi\) | |||||||
\(912\) | 1.99823 | 0.0661678 | ||||||||
\(913\) | 12.2910 | 0.406772 | ||||||||
\(914\) | −14.8727 | −0.491947 | ||||||||
\(915\) | 24.2364 | 0.801232 | ||||||||
\(916\) | −1.26643 | −0.0418440 | ||||||||
\(917\) | 11.7321 | 0.387430 | ||||||||
\(918\) | −3.63335 | −0.119918 | ||||||||
\(919\) | 52.4848 | 1.73132 | 0.865658 | − | 0.500636i | \(-0.166901\pi\) | ||||
0.865658 | + | 0.500636i | \(0.166901\pi\) | |||||||
\(920\) | −11.3020 | −0.372616 | ||||||||
\(921\) | −22.4120 | −0.738501 | ||||||||
\(922\) | −27.3353 | −0.900241 | ||||||||
\(923\) | −55.6399 | −1.83141 | ||||||||
\(924\) | −11.8369 | −0.389404 | ||||||||
\(925\) | 5.89164 | 0.193716 | ||||||||
\(926\) | −25.5205 | −0.838657 | ||||||||
\(927\) | 71.5367 | 2.34957 | ||||||||
\(928\) | 4.91609 | 0.161379 | ||||||||
\(929\) | 24.4566 | 0.802396 | 0.401198 | − | 0.915991i | \(-0.368594\pi\) | ||||
0.401198 | + | 0.915991i | \(0.368594\pi\) | |||||||
\(930\) | 24.3043 | 0.796970 | ||||||||
\(931\) | −5.55244 | −0.181974 | ||||||||
\(932\) | 3.25176 | 0.106515 | ||||||||
\(933\) | −88.3511 | −2.89249 | ||||||||
\(934\) | 15.9214 | 0.520965 | ||||||||
\(935\) | −6.15223 | −0.201199 | ||||||||
\(936\) | −40.0668 | −1.30963 | ||||||||
\(937\) | −22.7369 | −0.742782 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(938\) | 6.23498 | 0.203579 | ||||||||
\(939\) | −56.8763 | −1.85609 | ||||||||
\(940\) | −4.01104 | −0.130826 | ||||||||
\(941\) | 55.5343 | 1.81037 | 0.905183 | − | 0.425022i | \(-0.139734\pi\) | ||||
0.905183 | + | 0.425022i | \(0.139734\pi\) | |||||||
\(942\) | −14.9028 | −0.485560 | ||||||||
\(943\) | 26.6200 | 0.866866 | ||||||||
\(944\) | −1.81149 | −0.0589588 | ||||||||
\(945\) | −2.44818 | −0.0796393 | ||||||||
\(946\) | −0.336722 | −0.0109478 | ||||||||
\(947\) | −28.2234 | −0.917138 | −0.458569 | − | 0.888659i | \(-0.651638\pi\) | ||||
−0.458569 | + | 0.888659i | \(0.651638\pi\) | |||||||
\(948\) | −16.0955 | −0.522757 | ||||||||
\(949\) | 28.7385 | 0.932890 | ||||||||
\(950\) | −4.75559 | −0.154292 | ||||||||
\(951\) | −49.2439 | −1.59684 | ||||||||
\(952\) | 4.84772 | 0.157116 | ||||||||
\(953\) | 0.665028 | 0.0215424 | 0.0107712 | − | 0.999942i | \(-0.496571\pi\) | ||||
0.0107712 | + | 0.999942i | \(0.496571\pi\) | |||||||
\(954\) | −26.4179 | −0.855312 | ||||||||
\(955\) | −20.2980 | −0.656826 | ||||||||
\(956\) | 17.1703 | 0.555328 | ||||||||
\(957\) | −8.04371 | −0.260016 | ||||||||
\(958\) | 29.9811 | 0.968644 | ||||||||
\(959\) | 20.3100 | 0.655845 | ||||||||
\(960\) | 12.1599 | 0.392460 | ||||||||
\(961\) | 85.1965 | 2.74828 | ||||||||
\(962\) | 18.3889 | 0.592883 | ||||||||
\(963\) | 35.7250 | 1.15122 | ||||||||
\(964\) | 14.4652 | 0.465894 | ||||||||
\(965\) | 0.292300 | 0.00940946 | ||||||||
\(966\) | −9.10853 | −0.293062 | ||||||||
\(967\) | −30.8715 | −0.992760 | −0.496380 | − | 0.868105i | \(-0.665338\pi\) | ||||
−0.496380 | + | 0.868105i | \(0.665338\pi\) | |||||||
\(968\) | −4.49307 | −0.144413 | ||||||||
\(969\) | 25.3276 | 0.813639 | ||||||||
\(970\) | −10.5278 | −0.338027 | ||||||||
\(971\) | −33.4091 | −1.07215 | −0.536075 | − | 0.844170i | \(-0.680094\pi\) | ||||
−0.536075 | + | 0.844170i | \(0.680094\pi\) | |||||||
\(972\) | −27.1214 | −0.869919 | ||||||||
\(973\) | 12.8852 | 0.413079 | ||||||||
\(974\) | −3.18059 | −0.101913 | ||||||||
\(975\) | −9.59326 | −0.307230 | ||||||||
\(976\) | 1.25863 | 0.0402877 | ||||||||
\(977\) | −25.2855 | −0.808954 | −0.404477 | − | 0.914548i | \(-0.632546\pi\) | ||||
−0.404477 | + | 0.914548i | \(0.632546\pi\) | |||||||
\(978\) | −28.3425 | −0.906294 | ||||||||
\(979\) | −51.9016 | −1.65878 | ||||||||
\(980\) | 1.26643 | 0.0404546 | ||||||||
\(981\) | 19.9063 | 0.635559 | ||||||||
\(982\) | −10.9740 | −0.350194 | ||||||||
\(983\) | 13.0141 | 0.415085 | 0.207543 | − | 0.978226i | \(-0.433453\pi\) | ||||
0.207543 | + | 0.978226i | \(0.433453\pi\) | |||||||
\(984\) | −48.5296 | −1.54707 | ||||||||
\(985\) | −9.92841 | −0.316345 | ||||||||
\(986\) | 1.27722 | 0.0406750 | ||||||||
\(987\) | −8.33761 | −0.265389 | ||||||||
\(988\) | 25.6251 | 0.815242 | ||||||||
\(989\) | 0.447325 | 0.0142241 | ||||||||
\(990\) | −11.9509 | −0.379825 | ||||||||
\(991\) | −3.00882 | −0.0955783 | −0.0477891 | − | 0.998857i | \(-0.515218\pi\) | ||||
−0.0477891 | + | 0.998857i | \(0.515218\pi\) | |||||||
\(992\) | 61.5765 | 1.95506 | ||||||||
\(993\) | 32.5106 | 1.03169 | ||||||||
\(994\) | 13.0770 | 0.414776 | ||||||||
\(995\) | −22.1854 | −0.703325 | ||||||||
\(996\) | 11.5410 | 0.365692 | ||||||||
\(997\) | 13.0191 | 0.412319 | 0.206160 | − | 0.978518i | \(-0.433903\pi\) | ||||
0.206160 | + | 0.978518i | \(0.433903\pi\) | |||||||
\(998\) | 8.21687 | 0.260101 | ||||||||
\(999\) | −14.4238 | −0.456349 |
(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 | 8015.2.a.l.1.38 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.38 | ✓ | 62 | 1.1 | even | 1 | trivial |