Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-1.97610\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.97610 | 0.883738 | 0.441869 | − | 0.897080i | \(-0.354316\pi\) | ||||
0.441869 | + | 0.897080i | \(0.354316\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.65524 | 1.75952 | 0.879758 | − | 0.475422i | \(-0.157705\pi\) | ||||
0.879758 | + | 0.475422i | \(0.157705\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.97610 | 0.624897 | ||||||||
\(11\) | 2.35768 | 0.710867 | 0.355433 | − | 0.934702i | \(-0.384333\pi\) | ||||
0.355433 | + | 0.934702i | \(0.384333\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 4.65524 | 1.24417 | ||||||||
\(15\) | −1.97610 | −0.510226 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.40007 | −0.339566 | −0.169783 | − | 0.985481i | \(-0.554307\pi\) | ||||
−0.169783 | + | 0.985481i | \(0.554307\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.22562 | −0.969423 | −0.484712 | − | 0.874674i | \(-0.661075\pi\) | ||||
−0.484712 | + | 0.874674i | \(0.661075\pi\) | |||||||
\(20\) | 1.97610 | 0.441869 | ||||||||
\(21\) | −4.65524 | −1.01586 | ||||||||
\(22\) | 2.35768 | 0.502659 | ||||||||
\(23\) | −1.68831 | −0.352036 | −0.176018 | − | 0.984387i | \(-0.556322\pi\) | ||||
−0.176018 | + | 0.984387i | \(0.556322\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.09504 | −0.219008 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.65524 | 0.879758 | ||||||||
\(29\) | 0.920725 | 0.170974 | 0.0854872 | − | 0.996339i | \(-0.472755\pi\) | ||||
0.0854872 | + | 0.996339i | \(0.472755\pi\) | |||||||
\(30\) | −1.97610 | −0.360784 | ||||||||
\(31\) | −4.23306 | −0.760280 | −0.380140 | − | 0.924929i | \(-0.624124\pi\) | ||||
−0.380140 | + | 0.924929i | \(0.624124\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.35768 | −0.410419 | ||||||||
\(34\) | −1.40007 | −0.240110 | ||||||||
\(35\) | 9.19921 | 1.55495 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.22354 | 0.201149 | 0.100575 | − | 0.994930i | \(-0.467932\pi\) | ||||
0.100575 | + | 0.994930i | \(0.467932\pi\) | |||||||
\(38\) | −4.22562 | −0.685486 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 1.97610 | 0.312448 | ||||||||
\(41\) | −8.28255 | −1.29352 | −0.646759 | − | 0.762695i | \(-0.723876\pi\) | ||||
−0.646759 | + | 0.762695i | \(0.723876\pi\) | |||||||
\(42\) | −4.65524 | −0.718319 | ||||||||
\(43\) | 9.40003 | 1.43349 | 0.716746 | − | 0.697335i | \(-0.245631\pi\) | ||||
0.716746 | + | 0.697335i | \(0.245631\pi\) | |||||||
\(44\) | 2.35768 | 0.355433 | ||||||||
\(45\) | 1.97610 | 0.294579 | ||||||||
\(46\) | −1.68831 | −0.248927 | ||||||||
\(47\) | 13.2833 | 1.93757 | 0.968783 | − | 0.247909i | \(-0.0797434\pi\) | ||||
0.968783 | + | 0.247909i | \(0.0797434\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 14.6713 | 2.09590 | ||||||||
\(50\) | −1.09504 | −0.154862 | ||||||||
\(51\) | 1.40007 | 0.196049 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 11.7500 | 1.61399 | 0.806996 | − | 0.590556i | \(-0.201092\pi\) | ||||
0.806996 | + | 0.590556i | \(0.201092\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.65900 | 0.628220 | ||||||||
\(56\) | 4.65524 | 0.622083 | ||||||||
\(57\) | 4.22562 | 0.559697 | ||||||||
\(58\) | 0.920725 | 0.120897 | ||||||||
\(59\) | 4.69835 | 0.611673 | 0.305837 | − | 0.952084i | \(-0.401064\pi\) | ||||
0.305837 | + | 0.952084i | \(0.401064\pi\) | |||||||
\(60\) | −1.97610 | −0.255113 | ||||||||
\(61\) | −1.74167 | −0.222998 | −0.111499 | − | 0.993765i | \(-0.535565\pi\) | ||||
−0.111499 | + | 0.993765i | \(0.535565\pi\) | |||||||
\(62\) | −4.23306 | −0.537599 | ||||||||
\(63\) | 4.65524 | 0.586505 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.97610 | −0.245105 | ||||||||
\(66\) | −2.35768 | −0.290210 | ||||||||
\(67\) | 10.0174 | 1.22383 | 0.611913 | − | 0.790925i | \(-0.290400\pi\) | ||||
0.611913 | + | 0.790925i | \(0.290400\pi\) | |||||||
\(68\) | −1.40007 | −0.169783 | ||||||||
\(69\) | 1.68831 | 0.203248 | ||||||||
\(70\) | 9.19921 | 1.09952 | ||||||||
\(71\) | 6.96979 | 0.827162 | 0.413581 | − | 0.910467i | \(-0.364278\pi\) | ||||
0.413581 | + | 0.910467i | \(0.364278\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.5943 | 1.35701 | 0.678505 | − | 0.734595i | \(-0.262628\pi\) | ||||
0.678505 | + | 0.734595i | \(0.262628\pi\) | |||||||
\(74\) | 1.22354 | 0.142234 | ||||||||
\(75\) | 1.09504 | 0.126444 | ||||||||
\(76\) | −4.22562 | −0.484712 | ||||||||
\(77\) | 10.9756 | 1.25078 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −4.59328 | −0.516785 | −0.258392 | − | 0.966040i | \(-0.583193\pi\) | ||||
−0.258392 | + | 0.966040i | \(0.583193\pi\) | |||||||
\(80\) | 1.97610 | 0.220934 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.28255 | −0.914655 | ||||||||
\(83\) | −2.82344 | −0.309913 | −0.154956 | − | 0.987921i | \(-0.549524\pi\) | ||||
−0.154956 | + | 0.987921i | \(0.549524\pi\) | |||||||
\(84\) | −4.65524 | −0.507928 | ||||||||
\(85\) | −2.76667 | −0.300087 | ||||||||
\(86\) | 9.40003 | 1.01363 | ||||||||
\(87\) | −0.920725 | −0.0987121 | ||||||||
\(88\) | 2.35768 | 0.251329 | ||||||||
\(89\) | 3.99760 | 0.423745 | 0.211873 | − | 0.977297i | \(-0.432044\pi\) | ||||
0.211873 | + | 0.977297i | \(0.432044\pi\) | |||||||
\(90\) | 1.97610 | 0.208299 | ||||||||
\(91\) | −4.65524 | −0.488002 | ||||||||
\(92\) | −1.68831 | −0.176018 | ||||||||
\(93\) | 4.23306 | 0.438948 | ||||||||
\(94\) | 13.2833 | 1.37007 | ||||||||
\(95\) | −8.35023 | −0.856716 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.8358 | −1.20174 | −0.600872 | − | 0.799345i | \(-0.705180\pi\) | ||||
−0.600872 | + | 0.799345i | \(0.705180\pi\) | |||||||
\(98\) | 14.6713 | 1.48202 | ||||||||
\(99\) | 2.35768 | 0.236956 | ||||||||
\(100\) | −1.09504 | −0.109504 | ||||||||
\(101\) | −7.65739 | −0.761939 | −0.380969 | − | 0.924588i | \(-0.624410\pi\) | ||||
−0.380969 | + | 0.924588i | \(0.624410\pi\) | |||||||
\(102\) | 1.40007 | 0.138627 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −9.19921 | −0.897751 | ||||||||
\(106\) | 11.7500 | 1.14127 | ||||||||
\(107\) | −2.19049 | −0.211763 | −0.105882 | − | 0.994379i | \(-0.533766\pi\) | ||||
−0.105882 | + | 0.994379i | \(0.533766\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 15.4443 | 1.47930 | 0.739649 | − | 0.672993i | \(-0.234991\pi\) | ||||
0.739649 | + | 0.672993i | \(0.234991\pi\) | |||||||
\(110\) | 4.65900 | 0.444218 | ||||||||
\(111\) | −1.22354 | −0.116134 | ||||||||
\(112\) | 4.65524 | 0.439879 | ||||||||
\(113\) | 16.2250 | 1.52632 | 0.763159 | − | 0.646211i | \(-0.223647\pi\) | ||||
0.763159 | + | 0.646211i | \(0.223647\pi\) | |||||||
\(114\) | 4.22562 | 0.395765 | ||||||||
\(115\) | −3.33626 | −0.311108 | ||||||||
\(116\) | 0.920725 | 0.0854872 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 4.69835 | 0.432518 | ||||||||
\(119\) | −6.51765 | −0.597472 | ||||||||
\(120\) | −1.97610 | −0.180392 | ||||||||
\(121\) | −5.44135 | −0.494668 | ||||||||
\(122\) | −1.74167 | −0.157684 | ||||||||
\(123\) | 8.28255 | 0.746813 | ||||||||
\(124\) | −4.23306 | −0.380140 | ||||||||
\(125\) | −12.0444 | −1.07728 | ||||||||
\(126\) | 4.65524 | 0.414722 | ||||||||
\(127\) | 12.1773 | 1.08056 | 0.540279 | − | 0.841486i | \(-0.318319\pi\) | ||||
0.540279 | + | 0.841486i | \(0.318319\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.40003 | −0.827627 | ||||||||
\(130\) | −1.97610 | −0.173315 | ||||||||
\(131\) | −11.5772 | −1.01151 | −0.505754 | − | 0.862678i | \(-0.668786\pi\) | ||||
−0.505754 | + | 0.862678i | \(0.668786\pi\) | |||||||
\(132\) | −2.35768 | −0.205210 | ||||||||
\(133\) | −19.6713 | −1.70572 | ||||||||
\(134\) | 10.0174 | 0.865375 | ||||||||
\(135\) | −1.97610 | −0.170075 | ||||||||
\(136\) | −1.40007 | −0.120055 | ||||||||
\(137\) | 5.67371 | 0.484738 | 0.242369 | − | 0.970184i | \(-0.422076\pi\) | ||||
0.242369 | + | 0.970184i | \(0.422076\pi\) | |||||||
\(138\) | 1.68831 | 0.143718 | ||||||||
\(139\) | −19.7870 | −1.67831 | −0.839154 | − | 0.543894i | \(-0.816949\pi\) | ||||
−0.839154 | + | 0.543894i | \(0.816949\pi\) | |||||||
\(140\) | 9.19921 | 0.777475 | ||||||||
\(141\) | −13.2833 | −1.11865 | ||||||||
\(142\) | 6.96979 | 0.584892 | ||||||||
\(143\) | −2.35768 | −0.197159 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.81944 | 0.151096 | ||||||||
\(146\) | 11.5943 | 0.959552 | ||||||||
\(147\) | −14.6713 | −1.21007 | ||||||||
\(148\) | 1.22354 | 0.100575 | ||||||||
\(149\) | −19.8323 | −1.62473 | −0.812364 | − | 0.583151i | \(-0.801820\pi\) | ||||
−0.812364 | + | 0.583151i | \(0.801820\pi\) | |||||||
\(150\) | 1.09504 | 0.0894096 | ||||||||
\(151\) | −16.6789 | −1.35731 | −0.678656 | − | 0.734456i | \(-0.737437\pi\) | ||||
−0.678656 | + | 0.734456i | \(0.737437\pi\) | |||||||
\(152\) | −4.22562 | −0.342743 | ||||||||
\(153\) | −1.40007 | −0.113189 | ||||||||
\(154\) | 10.9756 | 0.884436 | ||||||||
\(155\) | −8.36493 | −0.671888 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 7.72650 | 0.616641 | 0.308321 | − | 0.951282i | \(-0.400233\pi\) | ||||
0.308321 | + | 0.951282i | \(0.400233\pi\) | |||||||
\(158\) | −4.59328 | −0.365422 | ||||||||
\(159\) | −11.7500 | −0.931839 | ||||||||
\(160\) | 1.97610 | 0.156224 | ||||||||
\(161\) | −7.85948 | −0.619414 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 19.9507 | 1.56266 | 0.781330 | − | 0.624118i | \(-0.214542\pi\) | ||||
0.781330 | + | 0.624118i | \(0.214542\pi\) | |||||||
\(164\) | −8.28255 | −0.646759 | ||||||||
\(165\) | −4.65900 | −0.362703 | ||||||||
\(166\) | −2.82344 | −0.219141 | ||||||||
\(167\) | 15.6969 | 1.21466 | 0.607330 | − | 0.794449i | \(-0.292240\pi\) | ||||
0.607330 | + | 0.794449i | \(0.292240\pi\) | |||||||
\(168\) | −4.65524 | −0.359160 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.76667 | −0.212194 | ||||||||
\(171\) | −4.22562 | −0.323141 | ||||||||
\(172\) | 9.40003 | 0.716746 | ||||||||
\(173\) | −8.94426 | −0.680019 | −0.340010 | − | 0.940422i | \(-0.610430\pi\) | ||||
−0.340010 | + | 0.940422i | \(0.610430\pi\) | |||||||
\(174\) | −0.920725 | −0.0698000 | ||||||||
\(175\) | −5.09767 | −0.385348 | ||||||||
\(176\) | 2.35768 | 0.177717 | ||||||||
\(177\) | −4.69835 | −0.353150 | ||||||||
\(178\) | 3.99760 | 0.299633 | ||||||||
\(179\) | 22.5180 | 1.68307 | 0.841535 | − | 0.540202i | \(-0.181652\pi\) | ||||
0.841535 | + | 0.540202i | \(0.181652\pi\) | |||||||
\(180\) | 1.97610 | 0.147290 | ||||||||
\(181\) | −4.81147 | −0.357634 | −0.178817 | − | 0.983882i | \(-0.557227\pi\) | ||||
−0.178817 | + | 0.983882i | \(0.557227\pi\) | |||||||
\(182\) | −4.65524 | −0.345069 | ||||||||
\(183\) | 1.74167 | 0.128748 | ||||||||
\(184\) | −1.68831 | −0.124464 | ||||||||
\(185\) | 2.41784 | 0.177763 | ||||||||
\(186\) | 4.23306 | 0.310383 | ||||||||
\(187\) | −3.30091 | −0.241386 | ||||||||
\(188\) | 13.2833 | 0.968783 | ||||||||
\(189\) | −4.65524 | −0.338619 | ||||||||
\(190\) | −8.35023 | −0.605790 | ||||||||
\(191\) | 7.01017 | 0.507238 | 0.253619 | − | 0.967304i | \(-0.418379\pi\) | ||||
0.253619 | + | 0.967304i | \(0.418379\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.1251 | 0.872781 | 0.436391 | − | 0.899757i | \(-0.356257\pi\) | ||||
0.436391 | + | 0.899757i | \(0.356257\pi\) | |||||||
\(194\) | −11.8358 | −0.849761 | ||||||||
\(195\) | 1.97610 | 0.141511 | ||||||||
\(196\) | 14.6713 | 1.04795 | ||||||||
\(197\) | −17.9383 | −1.27805 | −0.639026 | − | 0.769185i | \(-0.720662\pi\) | ||||
−0.639026 | + | 0.769185i | \(0.720662\pi\) | |||||||
\(198\) | 2.35768 | 0.167553 | ||||||||
\(199\) | −11.7186 | −0.830710 | −0.415355 | − | 0.909659i | \(-0.636343\pi\) | ||||
−0.415355 | + | 0.909659i | \(0.636343\pi\) | |||||||
\(200\) | −1.09504 | −0.0774310 | ||||||||
\(201\) | −10.0174 | −0.706576 | ||||||||
\(202\) | −7.65739 | −0.538772 | ||||||||
\(203\) | 4.28620 | 0.300832 | ||||||||
\(204\) | 1.40007 | 0.0980243 | ||||||||
\(205\) | −16.3671 | −1.14313 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −1.68831 | −0.117345 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −9.96265 | −0.689131 | ||||||||
\(210\) | −9.19921 | −0.634806 | ||||||||
\(211\) | 15.2946 | 1.05293 | 0.526463 | − | 0.850198i | \(-0.323518\pi\) | ||||
0.526463 | + | 0.850198i | \(0.323518\pi\) | |||||||
\(212\) | 11.7500 | 0.806996 | ||||||||
\(213\) | −6.96979 | −0.477562 | ||||||||
\(214\) | −2.19049 | −0.149739 | ||||||||
\(215\) | 18.5754 | 1.26683 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −19.7059 | −1.33772 | ||||||||
\(218\) | 15.4443 | 1.04602 | ||||||||
\(219\) | −11.5943 | −0.783471 | ||||||||
\(220\) | 4.65900 | 0.314110 | ||||||||
\(221\) | 1.40007 | 0.0941787 | ||||||||
\(222\) | −1.22354 | −0.0821189 | ||||||||
\(223\) | 14.1192 | 0.945489 | 0.472744 | − | 0.881200i | \(-0.343263\pi\) | ||||
0.472744 | + | 0.881200i | \(0.343263\pi\) | |||||||
\(224\) | 4.65524 | 0.311041 | ||||||||
\(225\) | −1.09504 | −0.0730026 | ||||||||
\(226\) | 16.2250 | 1.07927 | ||||||||
\(227\) | −1.43072 | −0.0949605 | −0.0474803 | − | 0.998872i | \(-0.515119\pi\) | ||||
−0.0474803 | + | 0.998872i | \(0.515119\pi\) | |||||||
\(228\) | 4.22562 | 0.279848 | ||||||||
\(229\) | 25.0949 | 1.65832 | 0.829158 | − | 0.559015i | \(-0.188820\pi\) | ||||
0.829158 | + | 0.559015i | \(0.188820\pi\) | |||||||
\(230\) | −3.33626 | −0.219986 | ||||||||
\(231\) | −10.9756 | −0.722139 | ||||||||
\(232\) | 0.920725 | 0.0604486 | ||||||||
\(233\) | −0.642463 | −0.0420892 | −0.0210446 | − | 0.999779i | \(-0.506699\pi\) | ||||
−0.0210446 | + | 0.999779i | \(0.506699\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 26.2491 | 1.71230 | ||||||||
\(236\) | 4.69835 | 0.305837 | ||||||||
\(237\) | 4.59328 | 0.298366 | ||||||||
\(238\) | −6.51765 | −0.422477 | ||||||||
\(239\) | −8.20641 | −0.530829 | −0.265414 | − | 0.964134i | \(-0.585509\pi\) | ||||
−0.265414 | + | 0.964134i | \(0.585509\pi\) | |||||||
\(240\) | −1.97610 | −0.127557 | ||||||||
\(241\) | 6.48254 | 0.417577 | 0.208789 | − | 0.977961i | \(-0.433048\pi\) | ||||
0.208789 | + | 0.977961i | \(0.433048\pi\) | |||||||
\(242\) | −5.44135 | −0.349783 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.74167 | −0.111499 | ||||||||
\(245\) | 28.9919 | 1.85222 | ||||||||
\(246\) | 8.28255 | 0.528076 | ||||||||
\(247\) | 4.22562 | 0.268870 | ||||||||
\(248\) | −4.23306 | −0.268799 | ||||||||
\(249\) | 2.82344 | 0.178928 | ||||||||
\(250\) | −12.0444 | −0.761754 | ||||||||
\(251\) | −29.4254 | −1.85732 | −0.928658 | − | 0.370936i | \(-0.879037\pi\) | ||||
−0.928658 | + | 0.370936i | \(0.879037\pi\) | |||||||
\(252\) | 4.65524 | 0.293253 | ||||||||
\(253\) | −3.98049 | −0.250251 | ||||||||
\(254\) | 12.1773 | 0.764070 | ||||||||
\(255\) | 2.76667 | 0.173256 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.86093 | 0.178460 | 0.0892300 | − | 0.996011i | \(-0.471559\pi\) | ||||
0.0892300 | + | 0.996011i | \(0.471559\pi\) | |||||||
\(258\) | −9.40003 | −0.585221 | ||||||||
\(259\) | 5.69589 | 0.353925 | ||||||||
\(260\) | −1.97610 | −0.122552 | ||||||||
\(261\) | 0.920725 | 0.0569915 | ||||||||
\(262\) | −11.5772 | −0.715244 | ||||||||
\(263\) | −3.22757 | −0.199021 | −0.0995103 | − | 0.995037i | \(-0.531728\pi\) | ||||
−0.0995103 | + | 0.995037i | \(0.531728\pi\) | |||||||
\(264\) | −2.35768 | −0.145105 | ||||||||
\(265\) | 23.2192 | 1.42635 | ||||||||
\(266\) | −19.6713 | −1.20612 | ||||||||
\(267\) | −3.99760 | −0.244649 | ||||||||
\(268\) | 10.0174 | 0.611913 | ||||||||
\(269\) | −2.39878 | −0.146256 | −0.0731281 | − | 0.997323i | \(-0.523298\pi\) | ||||
−0.0731281 | + | 0.997323i | \(0.523298\pi\) | |||||||
\(270\) | −1.97610 | −0.120261 | ||||||||
\(271\) | 0.749348 | 0.0455197 | 0.0227598 | − | 0.999741i | \(-0.492755\pi\) | ||||
0.0227598 | + | 0.999741i | \(0.492755\pi\) | |||||||
\(272\) | −1.40007 | −0.0848916 | ||||||||
\(273\) | 4.65524 | 0.281748 | ||||||||
\(274\) | 5.67371 | 0.342761 | ||||||||
\(275\) | −2.58175 | −0.155685 | ||||||||
\(276\) | 1.68831 | 0.101624 | ||||||||
\(277\) | 21.0829 | 1.26675 | 0.633374 | − | 0.773846i | \(-0.281669\pi\) | ||||
0.633374 | + | 0.773846i | \(0.281669\pi\) | |||||||
\(278\) | −19.7870 | −1.18674 | ||||||||
\(279\) | −4.23306 | −0.253427 | ||||||||
\(280\) | 9.19921 | 0.549758 | ||||||||
\(281\) | −22.8003 | −1.36015 | −0.680077 | − | 0.733141i | \(-0.738054\pi\) | ||||
−0.680077 | + | 0.733141i | \(0.738054\pi\) | |||||||
\(282\) | −13.2833 | −0.791008 | ||||||||
\(283\) | −31.8124 | −1.89105 | −0.945525 | − | 0.325550i | \(-0.894451\pi\) | ||||
−0.945525 | + | 0.325550i | \(0.894451\pi\) | |||||||
\(284\) | 6.96979 | 0.413581 | ||||||||
\(285\) | 8.35023 | 0.494625 | ||||||||
\(286\) | −2.35768 | −0.139412 | ||||||||
\(287\) | −38.5573 | −2.27596 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.0398 | −0.884695 | ||||||||
\(290\) | 1.81944 | 0.106841 | ||||||||
\(291\) | 11.8358 | 0.693827 | ||||||||
\(292\) | 11.5943 | 0.678505 | ||||||||
\(293\) | 23.9481 | 1.39906 | 0.699530 | − | 0.714603i | \(-0.253393\pi\) | ||||
0.699530 | + | 0.714603i | \(0.253393\pi\) | |||||||
\(294\) | −14.6713 | −0.855646 | ||||||||
\(295\) | 9.28440 | 0.540559 | ||||||||
\(296\) | 1.22354 | 0.0711170 | ||||||||
\(297\) | −2.35768 | −0.136806 | ||||||||
\(298\) | −19.8323 | −1.14886 | ||||||||
\(299\) | 1.68831 | 0.0976373 | ||||||||
\(300\) | 1.09504 | 0.0632221 | ||||||||
\(301\) | 43.7594 | 2.52225 | ||||||||
\(302\) | −16.6789 | −0.959765 | ||||||||
\(303\) | 7.65739 | 0.439906 | ||||||||
\(304\) | −4.22562 | −0.242356 | ||||||||
\(305\) | −3.44172 | −0.197072 | ||||||||
\(306\) | −1.40007 | −0.0800365 | ||||||||
\(307\) | −19.9043 | −1.13600 | −0.567999 | − | 0.823029i | \(-0.692282\pi\) | ||||
−0.567999 | + | 0.823029i | \(0.692282\pi\) | |||||||
\(308\) | 10.9756 | 0.625391 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −8.36493 | −0.475096 | ||||||||
\(311\) | −3.07394 | −0.174307 | −0.0871536 | − | 0.996195i | \(-0.527777\pi\) | ||||
−0.0871536 | + | 0.996195i | \(0.527777\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 17.0139 | 0.961681 | 0.480841 | − | 0.876808i | \(-0.340332\pi\) | ||||
0.480841 | + | 0.876808i | \(0.340332\pi\) | |||||||
\(314\) | 7.72650 | 0.436031 | ||||||||
\(315\) | 9.19921 | 0.518317 | ||||||||
\(316\) | −4.59328 | −0.258392 | ||||||||
\(317\) | −15.5410 | −0.872867 | −0.436434 | − | 0.899736i | \(-0.643759\pi\) | ||||
−0.436434 | + | 0.899736i | \(0.643759\pi\) | |||||||
\(318\) | −11.7500 | −0.658910 | ||||||||
\(319\) | 2.17077 | 0.121540 | ||||||||
\(320\) | 1.97610 | 0.110467 | ||||||||
\(321\) | 2.19049 | 0.122261 | ||||||||
\(322\) | −7.85948 | −0.437991 | ||||||||
\(323\) | 5.91615 | 0.329183 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.09504 | 0.0607419 | ||||||||
\(326\) | 19.9507 | 1.10497 | ||||||||
\(327\) | −15.4443 | −0.854073 | ||||||||
\(328\) | −8.28255 | −0.457327 | ||||||||
\(329\) | 61.8369 | 3.40918 | ||||||||
\(330\) | −4.65900 | −0.256470 | ||||||||
\(331\) | −15.1150 | −0.830794 | −0.415397 | − | 0.909640i | \(-0.636357\pi\) | ||||
−0.415397 | + | 0.909640i | \(0.636357\pi\) | |||||||
\(332\) | −2.82344 | −0.154956 | ||||||||
\(333\) | 1.22354 | 0.0670498 | ||||||||
\(334\) | 15.6969 | 0.858895 | ||||||||
\(335\) | 19.7954 | 1.08154 | ||||||||
\(336\) | −4.65524 | −0.253964 | ||||||||
\(337\) | −3.85788 | −0.210152 | −0.105076 | − | 0.994464i | \(-0.533509\pi\) | ||||
−0.105076 | + | 0.994464i | \(0.533509\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −16.2250 | −0.881220 | ||||||||
\(340\) | −2.76667 | −0.150044 | ||||||||
\(341\) | −9.98019 | −0.540458 | ||||||||
\(342\) | −4.22562 | −0.228495 | ||||||||
\(343\) | 35.7116 | 1.92825 | ||||||||
\(344\) | 9.40003 | 0.506816 | ||||||||
\(345\) | 3.33626 | 0.179618 | ||||||||
\(346\) | −8.94426 | −0.480846 | ||||||||
\(347\) | −0.410196 | −0.0220205 | −0.0110102 | − | 0.999939i | \(-0.503505\pi\) | ||||
−0.0110102 | + | 0.999939i | \(0.503505\pi\) | |||||||
\(348\) | −0.920725 | −0.0493560 | ||||||||
\(349\) | 24.9299 | 1.33447 | 0.667233 | − | 0.744849i | \(-0.267478\pi\) | ||||
0.667233 | + | 0.744849i | \(0.267478\pi\) | |||||||
\(350\) | −5.09767 | −0.272482 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 2.35768 | 0.125665 | ||||||||
\(353\) | −1.62571 | −0.0865279 | −0.0432639 | − | 0.999064i | \(-0.513776\pi\) | ||||
−0.0432639 | + | 0.999064i | \(0.513776\pi\) | |||||||
\(354\) | −4.69835 | −0.249715 | ||||||||
\(355\) | 13.7730 | 0.730994 | ||||||||
\(356\) | 3.99760 | 0.211873 | ||||||||
\(357\) | 6.51765 | 0.344951 | ||||||||
\(358\) | 22.5180 | 1.19011 | ||||||||
\(359\) | −3.25356 | −0.171716 | −0.0858582 | − | 0.996307i | \(-0.527363\pi\) | ||||
−0.0858582 | + | 0.996307i | \(0.527363\pi\) | |||||||
\(360\) | 1.97610 | 0.104149 | ||||||||
\(361\) | −1.14415 | −0.0602184 | ||||||||
\(362\) | −4.81147 | −0.252885 | ||||||||
\(363\) | 5.44135 | 0.285597 | ||||||||
\(364\) | −4.65524 | −0.244001 | ||||||||
\(365\) | 22.9115 | 1.19924 | ||||||||
\(366\) | 1.74167 | 0.0910387 | ||||||||
\(367\) | −15.5365 | −0.810998 | −0.405499 | − | 0.914095i | \(-0.632902\pi\) | ||||
−0.405499 | + | 0.914095i | \(0.632902\pi\) | |||||||
\(368\) | −1.68831 | −0.0880091 | ||||||||
\(369\) | −8.28255 | −0.431172 | ||||||||
\(370\) | 2.41784 | 0.125698 | ||||||||
\(371\) | 54.6993 | 2.83985 | ||||||||
\(372\) | 4.23306 | 0.219474 | ||||||||
\(373\) | −12.8180 | −0.663692 | −0.331846 | − | 0.943334i | \(-0.607671\pi\) | ||||
−0.331846 | + | 0.943334i | \(0.607671\pi\) | |||||||
\(374\) | −3.30091 | −0.170686 | ||||||||
\(375\) | 12.0444 | 0.621970 | ||||||||
\(376\) | 13.2833 | 0.685033 | ||||||||
\(377\) | −0.920725 | −0.0474198 | ||||||||
\(378\) | −4.65524 | −0.239440 | ||||||||
\(379\) | −26.0379 | −1.33748 | −0.668739 | − | 0.743497i | \(-0.733166\pi\) | ||||
−0.668739 | + | 0.743497i | \(0.733166\pi\) | |||||||
\(380\) | −8.35023 | −0.428358 | ||||||||
\(381\) | −12.1773 | −0.623860 | ||||||||
\(382\) | 7.01017 | 0.358672 | ||||||||
\(383\) | −37.9053 | −1.93687 | −0.968436 | − | 0.249262i | \(-0.919812\pi\) | ||||
−0.968436 | + | 0.249262i | \(0.919812\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 21.6888 | 1.10536 | ||||||||
\(386\) | 12.1251 | 0.617150 | ||||||||
\(387\) | 9.40003 | 0.477831 | ||||||||
\(388\) | −11.8358 | −0.600872 | ||||||||
\(389\) | −25.9319 | −1.31480 | −0.657399 | − | 0.753542i | \(-0.728344\pi\) | ||||
−0.657399 | + | 0.753542i | \(0.728344\pi\) | |||||||
\(390\) | 1.97610 | 0.100064 | ||||||||
\(391\) | 2.36374 | 0.119540 | ||||||||
\(392\) | 14.6713 | 0.741011 | ||||||||
\(393\) | 11.5772 | 0.583995 | ||||||||
\(394\) | −17.9383 | −0.903719 | ||||||||
\(395\) | −9.07677 | −0.456702 | ||||||||
\(396\) | 2.35768 | 0.118478 | ||||||||
\(397\) | 13.6737 | 0.686264 | 0.343132 | − | 0.939287i | \(-0.388512\pi\) | ||||
0.343132 | + | 0.939287i | \(0.388512\pi\) | |||||||
\(398\) | −11.7186 | −0.587401 | ||||||||
\(399\) | 19.6713 | 0.984795 | ||||||||
\(400\) | −1.09504 | −0.0547520 | ||||||||
\(401\) | −1.62541 | −0.0811692 | −0.0405846 | − | 0.999176i | \(-0.512922\pi\) | ||||
−0.0405846 | + | 0.999176i | \(0.512922\pi\) | |||||||
\(402\) | −10.0174 | −0.499624 | ||||||||
\(403\) | 4.23306 | 0.210864 | ||||||||
\(404\) | −7.65739 | −0.380969 | ||||||||
\(405\) | 1.97610 | 0.0981931 | ||||||||
\(406\) | 4.28620 | 0.212720 | ||||||||
\(407\) | 2.88472 | 0.142990 | ||||||||
\(408\) | 1.40007 | 0.0693137 | ||||||||
\(409\) | 12.6629 | 0.626142 | 0.313071 | − | 0.949730i | \(-0.398642\pi\) | ||||
0.313071 | + | 0.949730i | \(0.398642\pi\) | |||||||
\(410\) | −16.3671 | −0.808315 | ||||||||
\(411\) | −5.67371 | −0.279863 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 21.8720 | 1.07625 | ||||||||
\(414\) | −1.68831 | −0.0829758 | ||||||||
\(415\) | −5.57939 | −0.273882 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 19.7870 | 0.968971 | ||||||||
\(418\) | −9.96265 | −0.487289 | ||||||||
\(419\) | −26.5504 | −1.29707 | −0.648535 | − | 0.761185i | \(-0.724618\pi\) | ||||
−0.648535 | + | 0.761185i | \(0.724618\pi\) | |||||||
\(420\) | −9.19921 | −0.448875 | ||||||||
\(421\) | −31.5279 | −1.53658 | −0.768288 | − | 0.640104i | \(-0.778891\pi\) | ||||
−0.768288 | + | 0.640104i | \(0.778891\pi\) | |||||||
\(422\) | 15.2946 | 0.744531 | ||||||||
\(423\) | 13.2833 | 0.645856 | ||||||||
\(424\) | 11.7500 | 0.570633 | ||||||||
\(425\) | 1.53313 | 0.0743677 | ||||||||
\(426\) | −6.96979 | −0.337688 | ||||||||
\(427\) | −8.10791 | −0.392369 | ||||||||
\(428\) | −2.19049 | −0.105882 | ||||||||
\(429\) | 2.35768 | 0.113830 | ||||||||
\(430\) | 18.5754 | 0.895784 | ||||||||
\(431\) | −0.0732573 | −0.00352868 | −0.00176434 | − | 0.999998i | \(-0.500562\pi\) | ||||
−0.00176434 | + | 0.999998i | \(0.500562\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −28.0122 | −1.34618 | −0.673091 | − | 0.739560i | \(-0.735034\pi\) | ||||
−0.673091 | + | 0.739560i | \(0.735034\pi\) | |||||||
\(434\) | −19.7059 | −0.945914 | ||||||||
\(435\) | −1.81944 | −0.0872356 | ||||||||
\(436\) | 15.4443 | 0.739649 | ||||||||
\(437\) | 7.13414 | 0.341272 | ||||||||
\(438\) | −11.5943 | −0.553997 | ||||||||
\(439\) | 35.9419 | 1.71542 | 0.857708 | − | 0.514137i | \(-0.171888\pi\) | ||||
0.857708 | + | 0.514137i | \(0.171888\pi\) | |||||||
\(440\) | 4.65900 | 0.222109 | ||||||||
\(441\) | 14.6713 | 0.698632 | ||||||||
\(442\) | 1.40007 | 0.0665944 | ||||||||
\(443\) | 7.72845 | 0.367190 | 0.183595 | − | 0.983002i | \(-0.441227\pi\) | ||||
0.183595 | + | 0.983002i | \(0.441227\pi\) | |||||||
\(444\) | −1.22354 | −0.0580668 | ||||||||
\(445\) | 7.89965 | 0.374480 | ||||||||
\(446\) | 14.1192 | 0.668562 | ||||||||
\(447\) | 19.8323 | 0.938037 | ||||||||
\(448\) | 4.65524 | 0.219939 | ||||||||
\(449\) | −40.5691 | −1.91458 | −0.957288 | − | 0.289135i | \(-0.906632\pi\) | ||||
−0.957288 | + | 0.289135i | \(0.906632\pi\) | |||||||
\(450\) | −1.09504 | −0.0516207 | ||||||||
\(451\) | −19.5276 | −0.919519 | ||||||||
\(452\) | 16.2250 | 0.763159 | ||||||||
\(453\) | 16.6789 | 0.783645 | ||||||||
\(454\) | −1.43072 | −0.0671472 | ||||||||
\(455\) | −9.19921 | −0.431266 | ||||||||
\(456\) | 4.22562 | 0.197883 | ||||||||
\(457\) | 13.7808 | 0.644638 | 0.322319 | − | 0.946631i | \(-0.395538\pi\) | ||||
0.322319 | + | 0.946631i | \(0.395538\pi\) | |||||||
\(458\) | 25.0949 | 1.17261 | ||||||||
\(459\) | 1.40007 | 0.0653495 | ||||||||
\(460\) | −3.33626 | −0.155554 | ||||||||
\(461\) | −15.1040 | −0.703465 | −0.351732 | − | 0.936101i | \(-0.614407\pi\) | ||||
−0.351732 | + | 0.936101i | \(0.614407\pi\) | |||||||
\(462\) | −10.9756 | −0.510629 | ||||||||
\(463\) | −19.0640 | −0.885980 | −0.442990 | − | 0.896527i | \(-0.646082\pi\) | ||||
−0.442990 | + | 0.896527i | \(0.646082\pi\) | |||||||
\(464\) | 0.920725 | 0.0427436 | ||||||||
\(465\) | 8.36493 | 0.387914 | ||||||||
\(466\) | −0.642463 | −0.0297615 | ||||||||
\(467\) | −30.1782 | −1.39648 | −0.698240 | − | 0.715864i | \(-0.746033\pi\) | ||||
−0.698240 | + | 0.715864i | \(0.746033\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 46.6336 | 2.15334 | ||||||||
\(470\) | 26.2491 | 1.21078 | ||||||||
\(471\) | −7.72650 | −0.356018 | ||||||||
\(472\) | 4.69835 | 0.216259 | ||||||||
\(473\) | 22.1623 | 1.01902 | ||||||||
\(474\) | 4.59328 | 0.210976 | ||||||||
\(475\) | 4.62722 | 0.212311 | ||||||||
\(476\) | −6.51765 | −0.298736 | ||||||||
\(477\) | 11.7500 | 0.537998 | ||||||||
\(478\) | −8.20641 | −0.375353 | ||||||||
\(479\) | 16.5702 | 0.757111 | 0.378556 | − | 0.925578i | \(-0.376421\pi\) | ||||
0.378556 | + | 0.925578i | \(0.376421\pi\) | |||||||
\(480\) | −1.97610 | −0.0901961 | ||||||||
\(481\) | −1.22354 | −0.0557888 | ||||||||
\(482\) | 6.48254 | 0.295272 | ||||||||
\(483\) | 7.85948 | 0.357619 | ||||||||
\(484\) | −5.44135 | −0.247334 | ||||||||
\(485\) | −23.3887 | −1.06203 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 2.30340 | 0.104377 | 0.0521884 | − | 0.998637i | \(-0.483380\pi\) | ||||
0.0521884 | + | 0.998637i | \(0.483380\pi\) | |||||||
\(488\) | −1.74167 | −0.0788418 | ||||||||
\(489\) | −19.9507 | −0.902202 | ||||||||
\(490\) | 28.9919 | 1.30972 | ||||||||
\(491\) | 33.2881 | 1.50227 | 0.751134 | − | 0.660149i | \(-0.229507\pi\) | ||||
0.751134 | + | 0.660149i | \(0.229507\pi\) | |||||||
\(492\) | 8.28255 | 0.373406 | ||||||||
\(493\) | −1.28908 | −0.0580571 | ||||||||
\(494\) | 4.22562 | 0.190120 | ||||||||
\(495\) | 4.65900 | 0.209407 | ||||||||
\(496\) | −4.23306 | −0.190070 | ||||||||
\(497\) | 32.4461 | 1.45541 | ||||||||
\(498\) | 2.82344 | 0.126521 | ||||||||
\(499\) | 16.7316 | 0.749009 | 0.374504 | − | 0.927225i | \(-0.377813\pi\) | ||||
0.374504 | + | 0.927225i | \(0.377813\pi\) | |||||||
\(500\) | −12.0444 | −0.538642 | ||||||||
\(501\) | −15.6969 | −0.701285 | ||||||||
\(502\) | −29.4254 | −1.31332 | ||||||||
\(503\) | 5.43676 | 0.242413 | 0.121206 | − | 0.992627i | \(-0.461324\pi\) | ||||
0.121206 | + | 0.992627i | \(0.461324\pi\) | |||||||
\(504\) | 4.65524 | 0.207361 | ||||||||
\(505\) | −15.1317 | −0.673354 | ||||||||
\(506\) | −3.98049 | −0.176954 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 12.1773 | 0.540279 | ||||||||
\(509\) | −34.1782 | −1.51492 | −0.757461 | − | 0.652880i | \(-0.773561\pi\) | ||||
−0.757461 | + | 0.652880i | \(0.773561\pi\) | |||||||
\(510\) | 2.76667 | 0.122510 | ||||||||
\(511\) | 53.9743 | 2.38768 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.22562 | 0.186566 | ||||||||
\(514\) | 2.86093 | 0.126190 | ||||||||
\(515\) | −1.97610 | −0.0870773 | ||||||||
\(516\) | −9.40003 | −0.413813 | ||||||||
\(517\) | 31.3177 | 1.37735 | ||||||||
\(518\) | 5.69589 | 0.250263 | ||||||||
\(519\) | 8.94426 | 0.392609 | ||||||||
\(520\) | −1.97610 | −0.0866576 | ||||||||
\(521\) | 25.9293 | 1.13599 | 0.567993 | − | 0.823034i | \(-0.307720\pi\) | ||||
0.567993 | + | 0.823034i | \(0.307720\pi\) | |||||||
\(522\) | 0.920725 | 0.0402990 | ||||||||
\(523\) | 6.35658 | 0.277954 | 0.138977 | − | 0.990296i | \(-0.455619\pi\) | ||||
0.138977 | + | 0.990296i | \(0.455619\pi\) | |||||||
\(524\) | −11.5772 | −0.505754 | ||||||||
\(525\) | 5.09767 | 0.222481 | ||||||||
\(526\) | −3.22757 | −0.140729 | ||||||||
\(527\) | 5.92657 | 0.258165 | ||||||||
\(528\) | −2.35768 | −0.102605 | ||||||||
\(529\) | −20.1496 | −0.876070 | ||||||||
\(530\) | 23.2192 | 1.00858 | ||||||||
\(531\) | 4.69835 | 0.203891 | ||||||||
\(532\) | −19.6713 | −0.852858 | ||||||||
\(533\) | 8.28255 | 0.358757 | ||||||||
\(534\) | −3.99760 | −0.172993 | ||||||||
\(535\) | −4.32863 | −0.187143 | ||||||||
\(536\) | 10.0174 | 0.432688 | ||||||||
\(537\) | −22.5180 | −0.971721 | ||||||||
\(538\) | −2.39878 | −0.103419 | ||||||||
\(539\) | 34.5901 | 1.48990 | ||||||||
\(540\) | −1.97610 | −0.0850377 | ||||||||
\(541\) | −17.6478 | −0.758737 | −0.379369 | − | 0.925246i | \(-0.623859\pi\) | ||||
−0.379369 | + | 0.925246i | \(0.623859\pi\) | |||||||
\(542\) | 0.749348 | 0.0321873 | ||||||||
\(543\) | 4.81147 | 0.206480 | ||||||||
\(544\) | −1.40007 | −0.0600274 | ||||||||
\(545\) | 30.5195 | 1.30731 | ||||||||
\(546\) | 4.65524 | 0.199226 | ||||||||
\(547\) | −14.6376 | −0.625859 | −0.312929 | − | 0.949776i | \(-0.601310\pi\) | ||||
−0.312929 | + | 0.949776i | \(0.601310\pi\) | |||||||
\(548\) | 5.67371 | 0.242369 | ||||||||
\(549\) | −1.74167 | −0.0743328 | ||||||||
\(550\) | −2.58175 | −0.110086 | ||||||||
\(551\) | −3.89063 | −0.165747 | ||||||||
\(552\) | 1.68831 | 0.0718591 | ||||||||
\(553\) | −21.3828 | −0.909291 | ||||||||
\(554\) | 21.0829 | 0.895727 | ||||||||
\(555\) | −2.41784 | −0.102632 | ||||||||
\(556\) | −19.7870 | −0.839154 | ||||||||
\(557\) | −30.4552 | −1.29043 | −0.645213 | − | 0.764002i | \(-0.723232\pi\) | ||||
−0.645213 | + | 0.764002i | \(0.723232\pi\) | |||||||
\(558\) | −4.23306 | −0.179200 | ||||||||
\(559\) | −9.40003 | −0.397579 | ||||||||
\(560\) | 9.19921 | 0.388738 | ||||||||
\(561\) | 3.30091 | 0.139364 | ||||||||
\(562\) | −22.8003 | −0.961774 | ||||||||
\(563\) | −6.82548 | −0.287660 | −0.143830 | − | 0.989602i | \(-0.545942\pi\) | ||||
−0.143830 | + | 0.989602i | \(0.545942\pi\) | |||||||
\(564\) | −13.2833 | −0.559327 | ||||||||
\(565\) | 32.0622 | 1.34886 | ||||||||
\(566\) | −31.8124 | −1.33717 | ||||||||
\(567\) | 4.65524 | 0.195502 | ||||||||
\(568\) | 6.96979 | 0.292446 | ||||||||
\(569\) | 2.03472 | 0.0853001 | 0.0426501 | − | 0.999090i | \(-0.486420\pi\) | ||||
0.0426501 | + | 0.999090i | \(0.486420\pi\) | |||||||
\(570\) | 8.35023 | 0.349753 | ||||||||
\(571\) | 9.03720 | 0.378195 | 0.189098 | − | 0.981958i | \(-0.439444\pi\) | ||||
0.189098 | + | 0.981958i | \(0.439444\pi\) | |||||||
\(572\) | −2.35768 | −0.0985795 | ||||||||
\(573\) | −7.01017 | −0.292854 | ||||||||
\(574\) | −38.5573 | −1.60935 | ||||||||
\(575\) | 1.84876 | 0.0770987 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.3567 | 0.556046 | 0.278023 | − | 0.960574i | \(-0.410321\pi\) | ||||
0.278023 | + | 0.960574i | \(0.410321\pi\) | |||||||
\(578\) | −15.0398 | −0.625574 | ||||||||
\(579\) | −12.1251 | −0.503901 | ||||||||
\(580\) | 1.81944 | 0.0755482 | ||||||||
\(581\) | −13.1438 | −0.545296 | ||||||||
\(582\) | 11.8358 | 0.490610 | ||||||||
\(583\) | 27.7028 | 1.14733 | ||||||||
\(584\) | 11.5943 | 0.479776 | ||||||||
\(585\) | −1.97610 | −0.0817016 | ||||||||
\(586\) | 23.9481 | 0.989285 | ||||||||
\(587\) | −41.3212 | −1.70551 | −0.852755 | − | 0.522311i | \(-0.825070\pi\) | ||||
−0.852755 | + | 0.522311i | \(0.825070\pi\) | |||||||
\(588\) | −14.6713 | −0.605033 | ||||||||
\(589\) | 17.8873 | 0.737033 | ||||||||
\(590\) | 9.28440 | 0.382233 | ||||||||
\(591\) | 17.9383 | 0.737883 | ||||||||
\(592\) | 1.22354 | 0.0502873 | ||||||||
\(593\) | 9.26916 | 0.380639 | 0.190319 | − | 0.981722i | \(-0.439048\pi\) | ||||
0.190319 | + | 0.981722i | \(0.439048\pi\) | |||||||
\(594\) | −2.35768 | −0.0967367 | ||||||||
\(595\) | −12.8795 | −0.528009 | ||||||||
\(596\) | −19.8323 | −0.812364 | ||||||||
\(597\) | 11.7186 | 0.479611 | ||||||||
\(598\) | 1.68831 | 0.0690400 | ||||||||
\(599\) | 2.06596 | 0.0844128 | 0.0422064 | − | 0.999109i | \(-0.486561\pi\) | ||||
0.0422064 | + | 0.999109i | \(0.486561\pi\) | |||||||
\(600\) | 1.09504 | 0.0447048 | ||||||||
\(601\) | 41.7134 | 1.70152 | 0.850762 | − | 0.525552i | \(-0.176141\pi\) | ||||
0.850762 | + | 0.525552i | \(0.176141\pi\) | |||||||
\(602\) | 43.7594 | 1.78350 | ||||||||
\(603\) | 10.0174 | 0.407942 | ||||||||
\(604\) | −16.6789 | −0.678656 | ||||||||
\(605\) | −10.7526 | −0.437157 | ||||||||
\(606\) | 7.65739 | 0.311060 | ||||||||
\(607\) | 4.01768 | 0.163073 | 0.0815364 | − | 0.996670i | \(-0.474017\pi\) | ||||
0.0815364 | + | 0.996670i | \(0.474017\pi\) | |||||||
\(608\) | −4.22562 | −0.171371 | ||||||||
\(609\) | −4.28620 | −0.173685 | ||||||||
\(610\) | −3.44172 | −0.139351 | ||||||||
\(611\) | −13.2833 | −0.537384 | ||||||||
\(612\) | −1.40007 | −0.0565944 | ||||||||
\(613\) | −33.7009 | −1.36117 | −0.680583 | − | 0.732671i | \(-0.738274\pi\) | ||||
−0.680583 | + | 0.732671i | \(0.738274\pi\) | |||||||
\(614\) | −19.9043 | −0.803272 | ||||||||
\(615\) | 16.3671 | 0.659986 | ||||||||
\(616\) | 10.9756 | 0.442218 | ||||||||
\(617\) | 20.1016 | 0.809259 | 0.404630 | − | 0.914481i | \(-0.367400\pi\) | ||||
0.404630 | + | 0.914481i | \(0.367400\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 9.78828 | 0.393424 | 0.196712 | − | 0.980461i | \(-0.436974\pi\) | ||||
0.196712 | + | 0.980461i | \(0.436974\pi\) | |||||||
\(620\) | −8.36493 | −0.335944 | ||||||||
\(621\) | 1.68831 | 0.0677494 | ||||||||
\(622\) | −3.07394 | −0.123254 | ||||||||
\(623\) | 18.6098 | 0.745586 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −18.3257 | −0.733028 | ||||||||
\(626\) | 17.0139 | 0.680011 | ||||||||
\(627\) | 9.96265 | 0.397870 | ||||||||
\(628\) | 7.72650 | 0.308321 | ||||||||
\(629\) | −1.71304 | −0.0683035 | ||||||||
\(630\) | 9.19921 | 0.366505 | ||||||||
\(631\) | −26.1972 | −1.04289 | −0.521447 | − | 0.853284i | \(-0.674608\pi\) | ||||
−0.521447 | + | 0.853284i | \(0.674608\pi\) | |||||||
\(632\) | −4.59328 | −0.182711 | ||||||||
\(633\) | −15.2946 | −0.607907 | ||||||||
\(634\) | −15.5410 | −0.617210 | ||||||||
\(635\) | 24.0635 | 0.954929 | ||||||||
\(636\) | −11.7500 | −0.465920 | ||||||||
\(637\) | −14.6713 | −0.581297 | ||||||||
\(638\) | 2.17077 | 0.0859418 | ||||||||
\(639\) | 6.96979 | 0.275721 | ||||||||
\(640\) | 1.97610 | 0.0781121 | ||||||||
\(641\) | −17.6597 | −0.697516 | −0.348758 | − | 0.937213i | \(-0.613397\pi\) | ||||
−0.348758 | + | 0.937213i | \(0.613397\pi\) | |||||||
\(642\) | 2.19049 | 0.0864519 | ||||||||
\(643\) | −41.3631 | −1.63120 | −0.815601 | − | 0.578615i | \(-0.803593\pi\) | ||||
−0.815601 | + | 0.578615i | \(0.803593\pi\) | |||||||
\(644\) | −7.85948 | −0.309707 | ||||||||
\(645\) | −18.5754 | −0.731405 | ||||||||
\(646\) | 5.91615 | 0.232768 | ||||||||
\(647\) | −48.1061 | −1.89124 | −0.945622 | − | 0.325267i | \(-0.894546\pi\) | ||||
−0.945622 | + | 0.325267i | \(0.894546\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 11.0772 | 0.434818 | ||||||||
\(650\) | 1.09504 | 0.0429510 | ||||||||
\(651\) | 19.7059 | 0.772335 | ||||||||
\(652\) | 19.9507 | 0.781330 | ||||||||
\(653\) | −20.4563 | −0.800517 | −0.400259 | − | 0.916402i | \(-0.631080\pi\) | ||||
−0.400259 | + | 0.916402i | \(0.631080\pi\) | |||||||
\(654\) | −15.4443 | −0.603921 | ||||||||
\(655\) | −22.8778 | −0.893908 | ||||||||
\(656\) | −8.28255 | −0.323379 | ||||||||
\(657\) | 11.5943 | 0.452337 | ||||||||
\(658\) | 61.8369 | 2.41065 | ||||||||
\(659\) | −12.7352 | −0.496092 | −0.248046 | − | 0.968748i | \(-0.579788\pi\) | ||||
−0.248046 | + | 0.968748i | \(0.579788\pi\) | |||||||
\(660\) | −4.65900 | −0.181351 | ||||||||
\(661\) | −0.422485 | −0.0164328 | −0.00821639 | − | 0.999966i | \(-0.502615\pi\) | ||||
−0.00821639 | + | 0.999966i | \(0.502615\pi\) | |||||||
\(662\) | −15.1150 | −0.587460 | ||||||||
\(663\) | −1.40007 | −0.0543741 | ||||||||
\(664\) | −2.82344 | −0.109571 | ||||||||
\(665\) | −38.8723 | −1.50740 | ||||||||
\(666\) | 1.22354 | 0.0474113 | ||||||||
\(667\) | −1.55447 | −0.0601892 | ||||||||
\(668\) | 15.6969 | 0.607330 | ||||||||
\(669\) | −14.1192 | −0.545878 | ||||||||
\(670\) | 19.7954 | 0.764764 | ||||||||
\(671\) | −4.10631 | −0.158522 | ||||||||
\(672\) | −4.65524 | −0.179580 | ||||||||
\(673\) | 13.2581 | 0.511064 | 0.255532 | − | 0.966801i | \(-0.417749\pi\) | ||||
0.255532 | + | 0.966801i | \(0.417749\pi\) | |||||||
\(674\) | −3.85788 | −0.148600 | ||||||||
\(675\) | 1.09504 | 0.0421481 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 44.2611 | 1.70109 | 0.850545 | − | 0.525902i | \(-0.176272\pi\) | ||||
0.850545 | + | 0.525902i | \(0.176272\pi\) | |||||||
\(678\) | −16.2250 | −0.623117 | ||||||||
\(679\) | −55.0985 | −2.11449 | ||||||||
\(680\) | −2.76667 | −0.106097 | ||||||||
\(681\) | 1.43072 | 0.0548255 | ||||||||
\(682\) | −9.98019 | −0.382161 | ||||||||
\(683\) | 11.9060 | 0.455571 | 0.227786 | − | 0.973711i | \(-0.426851\pi\) | ||||
0.227786 | + | 0.973711i | \(0.426851\pi\) | |||||||
\(684\) | −4.22562 | −0.161571 | ||||||||
\(685\) | 11.2118 | 0.428381 | ||||||||
\(686\) | 35.7116 | 1.36348 | ||||||||
\(687\) | −25.0949 | −0.957429 | ||||||||
\(688\) | 9.40003 | 0.358373 | ||||||||
\(689\) | −11.7500 | −0.447641 | ||||||||
\(690\) | 3.33626 | 0.127009 | ||||||||
\(691\) | 17.3712 | 0.660831 | 0.330415 | − | 0.943836i | \(-0.392811\pi\) | ||||
0.330415 | + | 0.943836i | \(0.392811\pi\) | |||||||
\(692\) | −8.94426 | −0.340010 | ||||||||
\(693\) | 10.9756 | 0.416927 | ||||||||
\(694\) | −0.410196 | −0.0155708 | ||||||||
\(695\) | −39.1009 | −1.48318 | ||||||||
\(696\) | −0.920725 | −0.0349000 | ||||||||
\(697\) | 11.5961 | 0.439235 | ||||||||
\(698\) | 24.9299 | 0.943610 | ||||||||
\(699\) | 0.642463 | 0.0243002 | ||||||||
\(700\) | −5.09767 | −0.192674 | ||||||||
\(701\) | 49.4216 | 1.86663 | 0.933315 | − | 0.359059i | \(-0.116902\pi\) | ||||
0.933315 | + | 0.359059i | \(0.116902\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −5.17023 | −0.194999 | ||||||||
\(704\) | 2.35768 | 0.0888584 | ||||||||
\(705\) | −26.2491 | −0.988597 | ||||||||
\(706\) | −1.62571 | −0.0611844 | ||||||||
\(707\) | −35.6470 | −1.34064 | ||||||||
\(708\) | −4.69835 | −0.176575 | ||||||||
\(709\) | 2.66753 | 0.100181 | 0.0500907 | − | 0.998745i | \(-0.484049\pi\) | ||||
0.0500907 | + | 0.998745i | \(0.484049\pi\) | |||||||
\(710\) | 13.7730 | 0.516891 | ||||||||
\(711\) | −4.59328 | −0.172262 | ||||||||
\(712\) | 3.99760 | 0.149817 | ||||||||
\(713\) | 7.14670 | 0.267646 | ||||||||
\(714\) | 6.51765 | 0.243917 | ||||||||
\(715\) | −4.65900 | −0.174237 | ||||||||
\(716\) | 22.5180 | 0.841535 | ||||||||
\(717\) | 8.20641 | 0.306474 | ||||||||
\(718\) | −3.25356 | −0.121422 | ||||||||
\(719\) | −32.1454 | −1.19882 | −0.599410 | − | 0.800442i | \(-0.704598\pi\) | ||||
−0.599410 | + | 0.800442i | \(0.704598\pi\) | |||||||
\(720\) | 1.97610 | 0.0736448 | ||||||||
\(721\) | −4.65524 | −0.173370 | ||||||||
\(722\) | −1.14415 | −0.0425808 | ||||||||
\(723\) | −6.48254 | −0.241088 | ||||||||
\(724\) | −4.81147 | −0.178817 | ||||||||
\(725\) | −1.00823 | −0.0374447 | ||||||||
\(726\) | 5.44135 | 0.201947 | ||||||||
\(727\) | −12.3347 | −0.457469 | −0.228735 | − | 0.973489i | \(-0.573459\pi\) | ||||
−0.228735 | + | 0.973489i | \(0.573459\pi\) | |||||||
\(728\) | −4.65524 | −0.172535 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 22.9115 | 0.847992 | ||||||||
\(731\) | −13.1607 | −0.486765 | ||||||||
\(732\) | 1.74167 | 0.0643741 | ||||||||
\(733\) | 9.97138 | 0.368301 | 0.184151 | − | 0.982898i | \(-0.441047\pi\) | ||||
0.184151 | + | 0.982898i | \(0.441047\pi\) | |||||||
\(734\) | −15.5365 | −0.573462 | ||||||||
\(735\) | −28.9919 | −1.06938 | ||||||||
\(736\) | −1.68831 | −0.0622318 | ||||||||
\(737\) | 23.6179 | 0.869977 | ||||||||
\(738\) | −8.28255 | −0.304885 | ||||||||
\(739\) | 21.2278 | 0.780877 | 0.390439 | − | 0.920629i | \(-0.372323\pi\) | ||||
0.390439 | + | 0.920629i | \(0.372323\pi\) | |||||||
\(740\) | 2.41784 | 0.0888816 | ||||||||
\(741\) | −4.22562 | −0.155232 | ||||||||
\(742\) | 54.6993 | 2.00807 | ||||||||
\(743\) | 16.2868 | 0.597505 | 0.298752 | − | 0.954331i | \(-0.403430\pi\) | ||||
0.298752 | + | 0.954331i | \(0.403430\pi\) | |||||||
\(744\) | 4.23306 | 0.155191 | ||||||||
\(745\) | −39.1906 | −1.43583 | ||||||||
\(746\) | −12.8180 | −0.469301 | ||||||||
\(747\) | −2.82344 | −0.103304 | ||||||||
\(748\) | −3.30091 | −0.120693 | ||||||||
\(749\) | −10.1973 | −0.372600 | ||||||||
\(750\) | 12.0444 | 0.439799 | ||||||||
\(751\) | 28.2516 | 1.03092 | 0.515458 | − | 0.856915i | \(-0.327622\pi\) | ||||
0.515458 | + | 0.856915i | \(0.327622\pi\) | |||||||
\(752\) | 13.2833 | 0.484392 | ||||||||
\(753\) | 29.4254 | 1.07232 | ||||||||
\(754\) | −0.920725 | −0.0335308 | ||||||||
\(755\) | −32.9592 | −1.19951 | ||||||||
\(756\) | −4.65524 | −0.169309 | ||||||||
\(757\) | 42.2881 | 1.53699 | 0.768494 | − | 0.639857i | \(-0.221006\pi\) | ||||
0.768494 | + | 0.639857i | \(0.221006\pi\) | |||||||
\(758\) | −26.0379 | −0.945740 | ||||||||
\(759\) | 3.98049 | 0.144482 | ||||||||
\(760\) | −8.35023 | −0.302895 | ||||||||
\(761\) | −31.0413 | −1.12525 | −0.562623 | − | 0.826714i | \(-0.690208\pi\) | ||||
−0.562623 | + | 0.826714i | \(0.690208\pi\) | |||||||
\(762\) | −12.1773 | −0.441136 | ||||||||
\(763\) | 71.8971 | 2.60285 | ||||||||
\(764\) | 7.01017 | 0.253619 | ||||||||
\(765\) | −2.76667 | −0.100029 | ||||||||
\(766\) | −37.9053 | −1.36958 | ||||||||
\(767\) | −4.69835 | −0.169648 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −52.1811 | −1.88170 | −0.940850 | − | 0.338824i | \(-0.889971\pi\) | ||||
−0.940850 | + | 0.338824i | \(0.889971\pi\) | |||||||
\(770\) | 21.6888 | 0.781609 | ||||||||
\(771\) | −2.86093 | −0.103034 | ||||||||
\(772\) | 12.1251 | 0.436391 | ||||||||
\(773\) | 29.9114 | 1.07584 | 0.537918 | − | 0.842997i | \(-0.319211\pi\) | ||||
0.537918 | + | 0.842997i | \(0.319211\pi\) | |||||||
\(774\) | 9.40003 | 0.337877 | ||||||||
\(775\) | 4.63536 | 0.166507 | ||||||||
\(776\) | −11.8358 | −0.424881 | ||||||||
\(777\) | −5.69589 | −0.204339 | ||||||||
\(778\) | −25.9319 | −0.929703 | ||||||||
\(779\) | 34.9989 | 1.25397 | ||||||||
\(780\) | 1.97610 | 0.0707556 | ||||||||
\(781\) | 16.4325 | 0.588002 | ||||||||
\(782\) | 2.36374 | 0.0845273 | ||||||||
\(783\) | −0.920725 | −0.0329040 | ||||||||
\(784\) | 14.6713 | 0.523974 | ||||||||
\(785\) | 15.2683 | 0.544949 | ||||||||
\(786\) | 11.5772 | 0.412946 | ||||||||
\(787\) | 21.5388 | 0.767776 | 0.383888 | − | 0.923380i | \(-0.374585\pi\) | ||||
0.383888 | + | 0.923380i | \(0.374585\pi\) | |||||||
\(788\) | −17.9383 | −0.639026 | ||||||||
\(789\) | 3.22757 | 0.114905 | ||||||||
\(790\) | −9.07677 | −0.322937 | ||||||||
\(791\) | 75.5312 | 2.68558 | ||||||||
\(792\) | 2.35768 | 0.0837765 | ||||||||
\(793\) | 1.74167 | 0.0618486 | ||||||||
\(794\) | 13.6737 | 0.485262 | ||||||||
\(795\) | −23.2192 | −0.823501 | ||||||||
\(796\) | −11.7186 | −0.415355 | ||||||||
\(797\) | 39.2712 | 1.39106 | 0.695528 | − | 0.718499i | \(-0.255170\pi\) | ||||
0.695528 | + | 0.718499i | \(0.255170\pi\) | |||||||
\(798\) | 19.6713 | 0.696355 | ||||||||
\(799\) | −18.5975 | −0.657932 | ||||||||
\(800\) | −1.09504 | −0.0387155 | ||||||||
\(801\) | 3.99760 | 0.141248 | ||||||||
\(802\) | −1.62541 | −0.0573953 | ||||||||
\(803\) | 27.3356 | 0.964654 | ||||||||
\(804\) | −10.0174 | −0.353288 | ||||||||
\(805\) | −15.5311 | −0.547399 | ||||||||
\(806\) | 4.23306 | 0.149103 | ||||||||
\(807\) | 2.39878 | 0.0844410 | ||||||||
\(808\) | −7.65739 | −0.269386 | ||||||||
\(809\) | 44.9800 | 1.58141 | 0.790706 | − | 0.612196i | \(-0.209714\pi\) | ||||
0.790706 | + | 0.612196i | \(0.209714\pi\) | |||||||
\(810\) | 1.97610 | 0.0694330 | ||||||||
\(811\) | 16.1384 | 0.566696 | 0.283348 | − | 0.959017i | \(-0.408555\pi\) | ||||
0.283348 | + | 0.959017i | \(0.408555\pi\) | |||||||
\(812\) | 4.28620 | 0.150416 | ||||||||
\(813\) | −0.749348 | −0.0262808 | ||||||||
\(814\) | 2.88472 | 0.101109 | ||||||||
\(815\) | 39.4245 | 1.38098 | ||||||||
\(816\) | 1.40007 | 0.0490122 | ||||||||
\(817\) | −39.7210 | −1.38966 | ||||||||
\(818\) | 12.6629 | 0.442749 | ||||||||
\(819\) | −4.65524 | −0.162667 | ||||||||
\(820\) | −16.3671 | −0.571565 | ||||||||
\(821\) | 1.55416 | 0.0542404 | 0.0271202 | − | 0.999632i | \(-0.491366\pi\) | ||||
0.0271202 | + | 0.999632i | \(0.491366\pi\) | |||||||
\(822\) | −5.67371 | −0.197893 | ||||||||
\(823\) | −51.6454 | −1.80025 | −0.900123 | − | 0.435636i | \(-0.856523\pi\) | ||||
−0.900123 | + | 0.435636i | \(0.856523\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 2.58175 | 0.0898850 | ||||||||
\(826\) | 21.8720 | 0.761023 | ||||||||
\(827\) | 19.0442 | 0.662233 | 0.331117 | − | 0.943590i | \(-0.392575\pi\) | ||||
0.331117 | + | 0.943590i | \(0.392575\pi\) | |||||||
\(828\) | −1.68831 | −0.0586727 | ||||||||
\(829\) | −26.9045 | −0.934431 | −0.467215 | − | 0.884144i | \(-0.654743\pi\) | ||||
−0.467215 | + | 0.884144i | \(0.654743\pi\) | |||||||
\(830\) | −5.57939 | −0.193664 | ||||||||
\(831\) | −21.0829 | −0.731358 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −20.5408 | −0.711695 | ||||||||
\(834\) | 19.7870 | 0.685166 | ||||||||
\(835\) | 31.0185 | 1.07344 | ||||||||
\(836\) | −9.96265 | −0.344565 | ||||||||
\(837\) | 4.23306 | 0.146316 | ||||||||
\(838\) | −26.5504 | −0.917167 | ||||||||
\(839\) | −41.9742 | −1.44911 | −0.724555 | − | 0.689217i | \(-0.757955\pi\) | ||||
−0.724555 | + | 0.689217i | \(0.757955\pi\) | |||||||
\(840\) | −9.19921 | −0.317403 | ||||||||
\(841\) | −28.1523 | −0.970768 | ||||||||
\(842\) | −31.5279 | −1.08652 | ||||||||
\(843\) | 22.8003 | 0.785285 | ||||||||
\(844\) | 15.2946 | 0.526463 | ||||||||
\(845\) | 1.97610 | 0.0679798 | ||||||||
\(846\) | 13.2833 | 0.456689 | ||||||||
\(847\) | −25.3308 | −0.870377 | ||||||||
\(848\) | 11.7500 | 0.403498 | ||||||||
\(849\) | 31.8124 | 1.09180 | ||||||||
\(850\) | 1.53313 | 0.0525859 | ||||||||
\(851\) | −2.06572 | −0.0708119 | ||||||||
\(852\) | −6.96979 | −0.238781 | ||||||||
\(853\) | −2.02827 | −0.0694467 | −0.0347234 | − | 0.999397i | \(-0.511055\pi\) | ||||
−0.0347234 | + | 0.999397i | \(0.511055\pi\) | |||||||
\(854\) | −8.10791 | −0.277447 | ||||||||
\(855\) | −8.35023 | −0.285572 | ||||||||
\(856\) | −2.19049 | −0.0748695 | ||||||||
\(857\) | −10.4055 | −0.355446 | −0.177723 | − | 0.984081i | \(-0.556873\pi\) | ||||
−0.177723 | + | 0.984081i | \(0.556873\pi\) | |||||||
\(858\) | 2.35768 | 0.0804898 | ||||||||
\(859\) | 29.9199 | 1.02085 | 0.510427 | − | 0.859921i | \(-0.329487\pi\) | ||||
0.510427 | + | 0.859921i | \(0.329487\pi\) | |||||||
\(860\) | 18.5754 | 0.633415 | ||||||||
\(861\) | 38.5573 | 1.31403 | ||||||||
\(862\) | −0.0732573 | −0.00249515 | ||||||||
\(863\) | 1.86961 | 0.0636422 | 0.0318211 | − | 0.999494i | \(-0.489869\pi\) | ||||
0.0318211 | + | 0.999494i | \(0.489869\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −17.6747 | −0.600959 | ||||||||
\(866\) | −28.0122 | −0.951894 | ||||||||
\(867\) | 15.0398 | 0.510779 | ||||||||
\(868\) | −19.7059 | −0.668862 | ||||||||
\(869\) | −10.8295 | −0.367365 | ||||||||
\(870\) | −1.81944 | −0.0616849 | ||||||||
\(871\) | −10.0174 | −0.339428 | ||||||||
\(872\) | 15.4443 | 0.523011 | ||||||||
\(873\) | −11.8358 | −0.400581 | ||||||||
\(874\) | 7.13414 | 0.241316 | ||||||||
\(875\) | −56.0695 | −1.89550 | ||||||||
\(876\) | −11.5943 | −0.391735 | ||||||||
\(877\) | −9.92590 | −0.335174 | −0.167587 | − | 0.985857i | \(-0.553597\pi\) | ||||
−0.167587 | + | 0.985857i | \(0.553597\pi\) | |||||||
\(878\) | 35.9419 | 1.21298 | ||||||||
\(879\) | −23.9481 | −0.807748 | ||||||||
\(880\) | 4.65900 | 0.157055 | ||||||||
\(881\) | −24.5217 | −0.826158 | −0.413079 | − | 0.910695i | \(-0.635547\pi\) | ||||
−0.413079 | + | 0.910695i | \(0.635547\pi\) | |||||||
\(882\) | 14.6713 | 0.494007 | ||||||||
\(883\) | 27.9675 | 0.941180 | 0.470590 | − | 0.882352i | \(-0.344041\pi\) | ||||
0.470590 | + | 0.882352i | \(0.344041\pi\) | |||||||
\(884\) | 1.40007 | 0.0470894 | ||||||||
\(885\) | −9.28440 | −0.312092 | ||||||||
\(886\) | 7.72845 | 0.259642 | ||||||||
\(887\) | 34.0164 | 1.14216 | 0.571080 | − | 0.820895i | \(-0.306525\pi\) | ||||
0.571080 | + | 0.820895i | \(0.306525\pi\) | |||||||
\(888\) | −1.22354 | −0.0410594 | ||||||||
\(889\) | 56.6881 | 1.90126 | ||||||||
\(890\) | 7.89965 | 0.264797 | ||||||||
\(891\) | 2.35768 | 0.0789852 | ||||||||
\(892\) | 14.1192 | 0.472744 | ||||||||
\(893\) | −56.1301 | −1.87832 | ||||||||
\(894\) | 19.8323 | 0.663292 | ||||||||
\(895\) | 44.4977 | 1.48739 | ||||||||
\(896\) | 4.65524 | 0.155521 | ||||||||
\(897\) | −1.68831 | −0.0563709 | ||||||||
\(898\) | −40.5691 | −1.35381 | ||||||||
\(899\) | −3.89748 | −0.129988 | ||||||||
\(900\) | −1.09504 | −0.0365013 | ||||||||
\(901\) | −16.4509 | −0.548057 | ||||||||
\(902\) | −19.5276 | −0.650198 | ||||||||
\(903\) | −43.7594 | −1.45622 | ||||||||
\(904\) | 16.2250 | 0.539635 | ||||||||
\(905\) | −9.50794 | −0.316054 | ||||||||
\(906\) | 16.6789 | 0.554121 | ||||||||
\(907\) | −15.4638 | −0.513466 | −0.256733 | − | 0.966482i | \(-0.582646\pi\) | ||||
−0.256733 | + | 0.966482i | \(0.582646\pi\) | |||||||
\(908\) | −1.43072 | −0.0474803 | ||||||||
\(909\) | −7.65739 | −0.253980 | ||||||||
\(910\) | −9.19921 | −0.304951 | ||||||||
\(911\) | −5.47641 | −0.181442 | −0.0907208 | − | 0.995876i | \(-0.528917\pi\) | ||||
−0.0907208 | + | 0.995876i | \(0.528917\pi\) | |||||||
\(912\) | 4.22562 | 0.139924 | ||||||||
\(913\) | −6.65676 | −0.220307 | ||||||||
\(914\) | 13.7808 | 0.455828 | ||||||||
\(915\) | 3.44172 | 0.113780 | ||||||||
\(916\) | 25.0949 | 0.829158 | ||||||||
\(917\) | −53.8948 | −1.77976 | ||||||||
\(918\) | 1.40007 | 0.0462091 | ||||||||
\(919\) | −24.7430 | −0.816195 | −0.408098 | − | 0.912938i | \(-0.633808\pi\) | ||||
−0.408098 | + | 0.912938i | \(0.633808\pi\) | |||||||
\(920\) | −3.33626 | −0.109993 | ||||||||
\(921\) | 19.9043 | 0.655869 | ||||||||
\(922\) | −15.1040 | −0.497425 | ||||||||
\(923\) | −6.96979 | −0.229414 | ||||||||
\(924\) | −10.9756 | −0.361070 | ||||||||
\(925\) | −1.33983 | −0.0440533 | ||||||||
\(926\) | −19.0640 | −0.626482 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 0.920725 | 0.0302243 | ||||||||
\(929\) | −51.9988 | −1.70602 | −0.853012 | − | 0.521891i | \(-0.825227\pi\) | ||||
−0.853012 | + | 0.521891i | \(0.825227\pi\) | |||||||
\(930\) | 8.36493 | 0.274297 | ||||||||
\(931\) | −61.9952 | −2.03181 | ||||||||
\(932\) | −0.642463 | −0.0210446 | ||||||||
\(933\) | 3.07394 | 0.100636 | ||||||||
\(934\) | −30.1782 | −0.987460 | ||||||||
\(935\) | −6.52292 | −0.213322 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −47.7692 | −1.56055 | −0.780276 | − | 0.625435i | \(-0.784921\pi\) | ||||
−0.780276 | + | 0.625435i | \(0.784921\pi\) | |||||||
\(938\) | 46.6336 | 1.52264 | ||||||||
\(939\) | −17.0139 | −0.555227 | ||||||||
\(940\) | 26.2491 | 0.856150 | ||||||||
\(941\) | 49.4890 | 1.61330 | 0.806648 | − | 0.591032i | \(-0.201279\pi\) | ||||
0.806648 | + | 0.591032i | \(0.201279\pi\) | |||||||
\(942\) | −7.72650 | −0.251743 | ||||||||
\(943\) | 13.9835 | 0.455365 | ||||||||
\(944\) | 4.69835 | 0.152918 | ||||||||
\(945\) | −9.19921 | −0.299250 | ||||||||
\(946\) | 22.1623 | 0.720557 | ||||||||
\(947\) | 9.12725 | 0.296596 | 0.148298 | − | 0.988943i | \(-0.452621\pi\) | ||||
0.148298 | + | 0.988943i | \(0.452621\pi\) | |||||||
\(948\) | 4.59328 | 0.149183 | ||||||||
\(949\) | −11.5943 | −0.376367 | ||||||||
\(950\) | 4.62722 | 0.150127 | ||||||||
\(951\) | 15.5410 | 0.503950 | ||||||||
\(952\) | −6.51765 | −0.211238 | ||||||||
\(953\) | 29.1733 | 0.945016 | 0.472508 | − | 0.881326i | \(-0.343349\pi\) | ||||
0.472508 | + | 0.881326i | \(0.343349\pi\) | |||||||
\(954\) | 11.7500 | 0.380422 | ||||||||
\(955\) | 13.8528 | 0.448265 | ||||||||
\(956\) | −8.20641 | −0.265414 | ||||||||
\(957\) | −2.17077 | −0.0701712 | ||||||||
\(958\) | 16.5702 | 0.535359 | ||||||||
\(959\) | 26.4125 | 0.852903 | ||||||||
\(960\) | −1.97610 | −0.0637783 | ||||||||
\(961\) | −13.0812 | −0.421975 | ||||||||
\(962\) | −1.22354 | −0.0394486 | ||||||||
\(963\) | −2.19049 | −0.0705877 | ||||||||
\(964\) | 6.48254 | 0.208789 | ||||||||
\(965\) | 23.9603 | 0.771310 | ||||||||
\(966\) | 7.85948 | 0.252875 | ||||||||
\(967\) | −30.1231 | −0.968693 | −0.484346 | − | 0.874876i | \(-0.660943\pi\) | ||||
−0.484346 | + | 0.874876i | \(0.660943\pi\) | |||||||
\(968\) | −5.44135 | −0.174892 | ||||||||
\(969\) | −5.91615 | −0.190054 | ||||||||
\(970\) | −23.3887 | −0.750966 | ||||||||
\(971\) | −21.9567 | −0.704622 | −0.352311 | − | 0.935883i | \(-0.614604\pi\) | ||||
−0.352311 | + | 0.935883i | \(0.614604\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −92.1130 | −2.95301 | ||||||||
\(974\) | 2.30340 | 0.0738056 | ||||||||
\(975\) | −1.09504 | −0.0350693 | ||||||||
\(976\) | −1.74167 | −0.0557496 | ||||||||
\(977\) | 36.3325 | 1.16238 | 0.581190 | − | 0.813768i | \(-0.302587\pi\) | ||||
0.581190 | + | 0.813768i | \(0.302587\pi\) | |||||||
\(978\) | −19.9507 | −0.637953 | ||||||||
\(979\) | 9.42507 | 0.301226 | ||||||||
\(980\) | 28.9919 | 0.926111 | ||||||||
\(981\) | 15.4443 | 0.493100 | ||||||||
\(982\) | 33.2881 | 1.06226 | ||||||||
\(983\) | −60.1263 | −1.91773 | −0.958866 | − | 0.283858i | \(-0.908385\pi\) | ||||
−0.958866 | + | 0.283858i | \(0.908385\pi\) | |||||||
\(984\) | 8.28255 | 0.264038 | ||||||||
\(985\) | −35.4478 | −1.12946 | ||||||||
\(986\) | −1.28908 | −0.0410526 | ||||||||
\(987\) | −61.8369 | −1.96829 | ||||||||
\(988\) | 4.22562 | 0.134435 | ||||||||
\(989\) | −15.8701 | −0.504641 | ||||||||
\(990\) | 4.65900 | 0.148073 | ||||||||
\(991\) | 43.3331 | 1.37652 | 0.688261 | − | 0.725463i | \(-0.258374\pi\) | ||||
0.688261 | + | 0.725463i | \(0.258374\pi\) | |||||||
\(992\) | −4.23306 | −0.134400 | ||||||||
\(993\) | 15.1150 | 0.479659 | ||||||||
\(994\) | 32.4461 | 1.02913 | ||||||||
\(995\) | −23.1571 | −0.734130 | ||||||||
\(996\) | 2.82344 | 0.0894641 | ||||||||
\(997\) | 4.68320 | 0.148318 | 0.0741592 | − | 0.997246i | \(-0.476373\pi\) | ||||
0.0741592 | + | 0.997246i | \(0.476373\pi\) | |||||||
\(998\) | 16.7316 | 0.529629 | ||||||||
\(999\) | −1.22354 | −0.0387112 |
(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 | 8034.2.a.bc.1.12 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.12 | ✓ | 15 | 1.1 | even | 1 | trivial |