Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.16553\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16553 | −0.824155 | −0.412077 | − | 0.911149i | \(-0.635197\pi\) | ||||
−0.412077 | + | 0.911149i | \(0.635197\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.641537 | −0.320769 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.16553 | 0.475826 | ||||||||
\(7\) | −4.15990 | −1.57230 | −0.786148 | − | 0.618038i | \(-0.787928\pi\) | ||||
−0.786148 | + | 0.618038i | \(0.787928\pi\) | |||||||
\(8\) | 3.07879 | 1.08852 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.81209 | −1.14939 | −0.574694 | − | 0.818369i | \(-0.694879\pi\) | ||||
−0.574694 | + | 0.818369i | \(0.694879\pi\) | |||||||
\(12\) | 0.641537 | 0.185196 | ||||||||
\(13\) | 4.61360 | 1.27958 | 0.639791 | − | 0.768549i | \(-0.279021\pi\) | ||||
0.639791 | + | 0.768549i | \(0.279021\pi\) | |||||||
\(14\) | 4.84850 | 1.29582 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.30535 | −0.576339 | ||||||||
\(17\) | 1.23057 | 0.298457 | 0.149229 | − | 0.988803i | \(-0.452321\pi\) | ||||
0.149229 | + | 0.988803i | \(0.452321\pi\) | |||||||
\(18\) | −1.16553 | −0.274718 | ||||||||
\(19\) | −2.53013 | −0.580452 | −0.290226 | − | 0.956958i | \(-0.593730\pi\) | ||||
−0.290226 | + | 0.956958i | \(0.593730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.15990 | 0.907766 | ||||||||
\(22\) | 4.44310 | 0.947273 | ||||||||
\(23\) | 2.58264 | 0.538517 | 0.269259 | − | 0.963068i | \(-0.413221\pi\) | ||||
0.269259 | + | 0.963068i | \(0.413221\pi\) | |||||||
\(24\) | −3.07879 | −0.628456 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.37729 | −1.05457 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.66873 | 0.504343 | ||||||||
\(29\) | −5.43386 | −1.00904 | −0.504521 | − | 0.863399i | \(-0.668331\pi\) | ||||
−0.504521 | + | 0.863399i | \(0.668331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.09333 | −1.09439 | −0.547197 | − | 0.837004i | \(-0.684305\pi\) | ||||
−0.547197 | + | 0.837004i | \(0.684305\pi\) | |||||||
\(32\) | −3.47062 | −0.613526 | ||||||||
\(33\) | 3.81209 | 0.663599 | ||||||||
\(34\) | −1.43427 | −0.245975 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.641537 | −0.106923 | ||||||||
\(37\) | 1.49075 | 0.245078 | 0.122539 | − | 0.992464i | \(-0.460896\pi\) | ||||
0.122539 | + | 0.992464i | \(0.460896\pi\) | |||||||
\(38\) | 2.94894 | 0.478382 | ||||||||
\(39\) | −4.61360 | −0.738767 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.04423 | 0.787777 | 0.393888 | − | 0.919158i | \(-0.371130\pi\) | ||||
0.393888 | + | 0.919158i | \(0.371130\pi\) | |||||||
\(42\) | −4.84850 | −0.748139 | ||||||||
\(43\) | 12.3022 | 1.87607 | 0.938037 | − | 0.346534i | \(-0.112641\pi\) | ||||
0.938037 | + | 0.346534i | \(0.112641\pi\) | |||||||
\(44\) | 2.44560 | 0.368687 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.01015 | −0.443822 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 2.30535 | 0.332749 | ||||||||
\(49\) | 10.3048 | 1.47212 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23057 | −0.172314 | ||||||||
\(52\) | −2.95979 | −0.410450 | ||||||||
\(53\) | 6.27544 | 0.861998 | 0.430999 | − | 0.902352i | \(-0.358161\pi\) | ||||
0.430999 | + | 0.902352i | \(0.358161\pi\) | |||||||
\(54\) | 1.16553 | 0.158609 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.8075 | −1.71147 | ||||||||
\(57\) | 2.53013 | 0.335124 | ||||||||
\(58\) | 6.33333 | 0.831607 | ||||||||
\(59\) | 2.67129 | 0.347772 | 0.173886 | − | 0.984766i | \(-0.444368\pi\) | ||||
0.173886 | + | 0.984766i | \(0.444368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7902 | 1.63762 | 0.818811 | − | 0.574064i | \(-0.194634\pi\) | ||||
0.818811 | + | 0.574064i | \(0.194634\pi\) | |||||||
\(62\) | 7.10197 | 0.901951 | ||||||||
\(63\) | −4.15990 | −0.524099 | ||||||||
\(64\) | 8.65583 | 1.08198 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.44310 | −0.546908 | ||||||||
\(67\) | 11.3306 | 1.38425 | 0.692127 | − | 0.721776i | \(-0.256674\pi\) | ||||
0.692127 | + | 0.721776i | \(0.256674\pi\) | |||||||
\(68\) | −0.789458 | −0.0957358 | ||||||||
\(69\) | −2.58264 | −0.310913 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.49400 | −0.414661 | −0.207331 | − | 0.978271i | \(-0.566478\pi\) | ||||
−0.207331 | + | 0.978271i | \(0.566478\pi\) | |||||||
\(72\) | 3.07879 | 0.362839 | ||||||||
\(73\) | −14.2798 | −1.67132 | −0.835662 | − | 0.549244i | \(-0.814916\pi\) | ||||
−0.835662 | + | 0.549244i | \(0.814916\pi\) | |||||||
\(74\) | −1.73752 | −0.201982 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.62317 | 0.186191 | ||||||||
\(77\) | 15.8579 | 1.80718 | ||||||||
\(78\) | 5.37729 | 0.608858 | ||||||||
\(79\) | 5.30405 | 0.596752 | 0.298376 | − | 0.954448i | \(-0.403555\pi\) | ||||
0.298376 | + | 0.954448i | \(0.403555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.87921 | −0.649250 | ||||||||
\(83\) | −5.94379 | −0.652415 | −0.326208 | − | 0.945298i | \(-0.605771\pi\) | ||||
−0.326208 | + | 0.945298i | \(0.605771\pi\) | |||||||
\(84\) | −2.66873 | −0.291183 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.3386 | −1.54618 | ||||||||
\(87\) | 5.43386 | 0.582571 | ||||||||
\(88\) | −11.7366 | −1.25113 | ||||||||
\(89\) | −1.23460 | −0.130868 | −0.0654338 | − | 0.997857i | \(-0.520843\pi\) | ||||
−0.0654338 | + | 0.997857i | \(0.520843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.1921 | −2.01188 | ||||||||
\(92\) | −1.65686 | −0.172740 | ||||||||
\(93\) | 6.09333 | 0.631849 | ||||||||
\(94\) | −1.16553 | −0.120215 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.47062 | 0.354219 | ||||||||
\(97\) | −14.5416 | −1.47647 | −0.738236 | − | 0.674542i | \(-0.764341\pi\) | ||||
−0.738236 | + | 0.674542i | \(0.764341\pi\) | |||||||
\(98\) | −12.0106 | −1.21325 | ||||||||
\(99\) | −3.81209 | −0.383129 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.91317 | −0.588382 | −0.294191 | − | 0.955747i | \(-0.595050\pi\) | ||||
−0.294191 | + | 0.955747i | \(0.595050\pi\) | |||||||
\(102\) | 1.43427 | 0.142014 | ||||||||
\(103\) | −3.70244 | −0.364813 | −0.182406 | − | 0.983223i | \(-0.558389\pi\) | ||||
−0.182406 | + | 0.983223i | \(0.558389\pi\) | |||||||
\(104\) | 14.2043 | 1.39285 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.31422 | −0.710420 | ||||||||
\(107\) | 18.6364 | 1.80165 | 0.900826 | − | 0.434181i | \(-0.142962\pi\) | ||||
0.900826 | + | 0.434181i | \(0.142962\pi\) | |||||||
\(108\) | 0.641537 | 0.0617320 | ||||||||
\(109\) | −11.8589 | −1.13588 | −0.567940 | − | 0.823070i | \(-0.692259\pi\) | ||||
−0.567940 | + | 0.823070i | \(0.692259\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.49075 | −0.141496 | ||||||||
\(112\) | 9.59006 | 0.906175 | ||||||||
\(113\) | 12.2064 | 1.14828 | 0.574142 | − | 0.818755i | \(-0.305336\pi\) | ||||
0.574142 | + | 0.818755i | \(0.305336\pi\) | |||||||
\(114\) | −2.94894 | −0.276194 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.48602 | 0.323669 | ||||||||
\(117\) | 4.61360 | 0.426527 | ||||||||
\(118\) | −3.11347 | −0.286618 | ||||||||
\(119\) | −5.11906 | −0.469263 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.53200 | 0.321091 | ||||||||
\(122\) | −14.9074 | −1.34965 | ||||||||
\(123\) | −5.04423 | −0.454823 | ||||||||
\(124\) | 3.90910 | 0.351048 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.84850 | 0.431939 | ||||||||
\(127\) | −11.6492 | −1.03370 | −0.516850 | − | 0.856076i | \(-0.672895\pi\) | ||||
−0.516850 | + | 0.856076i | \(0.672895\pi\) | |||||||
\(128\) | −3.14739 | −0.278193 | ||||||||
\(129\) | −12.3022 | −1.08315 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.96872 | −0.259378 | −0.129689 | − | 0.991555i | \(-0.541398\pi\) | ||||
−0.129689 | + | 0.991555i | \(0.541398\pi\) | |||||||
\(132\) | −2.44560 | −0.212862 | ||||||||
\(133\) | 10.5251 | 0.912642 | ||||||||
\(134\) | −13.2062 | −1.14084 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.78868 | 0.324876 | ||||||||
\(137\) | 8.98119 | 0.767315 | 0.383658 | − | 0.923475i | \(-0.374664\pi\) | ||||
0.383658 | + | 0.923475i | \(0.374664\pi\) | |||||||
\(138\) | 3.01015 | 0.256241 | ||||||||
\(139\) | −15.3614 | −1.30293 | −0.651467 | − | 0.758677i | \(-0.725846\pi\) | ||||
−0.651467 | + | 0.758677i | \(0.725846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 4.07236 | 0.341745 | ||||||||
\(143\) | −17.5874 | −1.47073 | ||||||||
\(144\) | −2.30535 | −0.192113 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.6435 | 1.37743 | ||||||||
\(147\) | −10.3048 | −0.849926 | ||||||||
\(148\) | −0.956372 | −0.0786133 | ||||||||
\(149\) | 10.6569 | 0.873046 | 0.436523 | − | 0.899693i | \(-0.356210\pi\) | ||||
0.436523 | + | 0.899693i | \(0.356210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.11859 | 0.416545 | 0.208272 | − | 0.978071i | \(-0.433216\pi\) | ||||
0.208272 | + | 0.978071i | \(0.433216\pi\) | |||||||
\(152\) | −7.78975 | −0.631832 | ||||||||
\(153\) | 1.23057 | 0.0994858 | ||||||||
\(154\) | −18.4829 | −1.48939 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.95979 | 0.236973 | ||||||||
\(157\) | 11.5178 | 0.919221 | 0.459611 | − | 0.888121i | \(-0.347989\pi\) | ||||
0.459611 | + | 0.888121i | \(0.347989\pi\) | |||||||
\(158\) | −6.18204 | −0.491816 | ||||||||
\(159\) | −6.27544 | −0.497675 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7435 | −0.846709 | ||||||||
\(162\) | −1.16553 | −0.0915728 | ||||||||
\(163\) | −6.71301 | −0.525804 | −0.262902 | − | 0.964823i | \(-0.584680\pi\) | ||||
−0.262902 | + | 0.964823i | \(0.584680\pi\) | |||||||
\(164\) | −3.23606 | −0.252694 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.92767 | 0.537691 | ||||||||
\(167\) | −16.8981 | −1.30761 | −0.653806 | − | 0.756662i | \(-0.726829\pi\) | ||||
−0.653806 | + | 0.756662i | \(0.726829\pi\) | |||||||
\(168\) | 12.8075 | 0.988119 | ||||||||
\(169\) | 8.28526 | 0.637328 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.53013 | −0.193484 | ||||||||
\(172\) | −7.89235 | −0.601786 | ||||||||
\(173\) | 13.5026 | 1.02658 | 0.513292 | − | 0.858214i | \(-0.328426\pi\) | ||||
0.513292 | + | 0.858214i | \(0.328426\pi\) | |||||||
\(174\) | −6.33333 | −0.480129 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.78821 | 0.662436 | ||||||||
\(177\) | −2.67129 | −0.200787 | ||||||||
\(178\) | 1.43897 | 0.107855 | ||||||||
\(179\) | −5.85657 | −0.437741 | −0.218870 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218870 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2839 | 1.35903 | 0.679515 | − | 0.733662i | \(-0.262190\pi\) | ||||
0.679515 | + | 0.733662i | \(0.262190\pi\) | |||||||
\(182\) | 22.3690 | 1.65810 | ||||||||
\(183\) | −12.7902 | −0.945481 | ||||||||
\(184\) | 7.95141 | 0.586186 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.10197 | −0.520741 | ||||||||
\(187\) | −4.69104 | −0.343043 | ||||||||
\(188\) | −0.641537 | −0.0467889 | ||||||||
\(189\) | 4.15990 | 0.302589 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.42659 | −0.392655 | −0.196327 | − | 0.980538i | \(-0.562902\pi\) | ||||
−0.196327 | + | 0.980538i | \(0.562902\pi\) | |||||||
\(192\) | −8.65583 | −0.624681 | ||||||||
\(193\) | −17.7710 | −1.27918 | −0.639592 | − | 0.768715i | \(-0.720896\pi\) | ||||
−0.639592 | + | 0.768715i | \(0.720896\pi\) | |||||||
\(194\) | 16.9487 | 1.21684 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.61092 | −0.472208 | ||||||||
\(197\) | 2.41574 | 0.172114 | 0.0860571 | − | 0.996290i | \(-0.472573\pi\) | ||||
0.0860571 | + | 0.996290i | \(0.472573\pi\) | |||||||
\(198\) | 4.44310 | 0.315758 | ||||||||
\(199\) | −7.71405 | −0.546834 | −0.273417 | − | 0.961896i | \(-0.588154\pi\) | ||||
−0.273417 | + | 0.961896i | \(0.588154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3306 | −0.799200 | ||||||||
\(202\) | 6.89198 | 0.484918 | ||||||||
\(203\) | 22.6043 | 1.58651 | ||||||||
\(204\) | 0.789458 | 0.0552731 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.31531 | 0.300662 | ||||||||
\(207\) | 2.58264 | 0.179506 | ||||||||
\(208\) | −10.6360 | −0.737472 | ||||||||
\(209\) | 9.64507 | 0.667164 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.21651 | 0.0837481 | 0.0418740 | − | 0.999123i | \(-0.486667\pi\) | ||||
0.0418740 | + | 0.999123i | \(0.486667\pi\) | |||||||
\(212\) | −4.02593 | −0.276502 | ||||||||
\(213\) | 3.49400 | 0.239405 | ||||||||
\(214\) | −21.7213 | −1.48484 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.07879 | −0.209485 | ||||||||
\(217\) | 25.3477 | 1.72071 | ||||||||
\(218\) | 13.8220 | 0.936141 | ||||||||
\(219\) | 14.2798 | 0.964939 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.67736 | 0.381901 | ||||||||
\(222\) | 1.73752 | 0.116614 | ||||||||
\(223\) | −28.0985 | −1.88161 | −0.940806 | − | 0.338945i | \(-0.889930\pi\) | ||||
−0.940806 | + | 0.338945i | \(0.889930\pi\) | |||||||
\(224\) | 14.4375 | 0.964644 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.2270 | −0.946365 | ||||||||
\(227\) | −25.5840 | −1.69807 | −0.849034 | − | 0.528339i | \(-0.822815\pi\) | ||||
−0.849034 | + | 0.528339i | \(0.822815\pi\) | |||||||
\(228\) | −1.62317 | −0.107497 | ||||||||
\(229\) | −28.8181 | −1.90435 | −0.952176 | − | 0.305550i | \(-0.901160\pi\) | ||||
−0.952176 | + | 0.305550i | \(0.901160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.8579 | −1.04337 | ||||||||
\(232\) | −16.7297 | −1.09836 | ||||||||
\(233\) | −7.58573 | −0.496957 | −0.248479 | − | 0.968637i | \(-0.579931\pi\) | ||||
−0.248479 | + | 0.968637i | \(0.579931\pi\) | |||||||
\(234\) | −5.37729 | −0.351524 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.71373 | −0.111555 | ||||||||
\(237\) | −5.30405 | −0.344535 | ||||||||
\(238\) | 5.96642 | 0.386746 | ||||||||
\(239\) | −6.26770 | −0.405424 | −0.202712 | − | 0.979238i | \(-0.564976\pi\) | ||||
−0.202712 | + | 0.979238i | \(0.564976\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.08604 | 0.198790 | 0.0993948 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993948 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(242\) | −4.11665 | −0.264628 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −8.20541 | −0.525298 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.87921 | 0.374845 | ||||||||
\(247\) | −11.6730 | −0.742735 | ||||||||
\(248\) | −18.7601 | −1.19127 | ||||||||
\(249\) | 5.94379 | 0.376672 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.3257 | −1.78790 | −0.893950 | − | 0.448166i | \(-0.852077\pi\) | ||||
−0.893950 | + | 0.448166i | \(0.852077\pi\) | |||||||
\(252\) | 2.66873 | 0.168114 | ||||||||
\(253\) | −9.84524 | −0.618965 | ||||||||
\(254\) | 13.5775 | 0.851928 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.6433 | −0.852705 | ||||||||
\(257\) | 31.1489 | 1.94301 | 0.971506 | − | 0.237015i | \(-0.0761689\pi\) | ||||
0.971506 | + | 0.237015i | \(0.0761689\pi\) | |||||||
\(258\) | 14.3386 | 0.892685 | ||||||||
\(259\) | −6.20138 | −0.385335 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.43386 | −0.336348 | ||||||||
\(262\) | 3.46014 | 0.213768 | ||||||||
\(263\) | 20.2925 | 1.25129 | 0.625643 | − | 0.780109i | \(-0.284836\pi\) | ||||
0.625643 | + | 0.780109i | \(0.284836\pi\) | |||||||
\(264\) | 11.7366 | 0.722339 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.2673 | −0.752158 | ||||||||
\(267\) | 1.23460 | 0.0755565 | ||||||||
\(268\) | −7.26901 | −0.444025 | ||||||||
\(269\) | −12.3091 | −0.750498 | −0.375249 | − | 0.926924i | \(-0.622443\pi\) | ||||
−0.375249 | + | 0.926924i | \(0.622443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.15010 | 0.252101 | 0.126050 | − | 0.992024i | \(-0.459770\pi\) | ||||
0.126050 | + | 0.992024i | \(0.459770\pi\) | |||||||
\(272\) | −2.83690 | −0.172013 | ||||||||
\(273\) | 19.1921 | 1.16156 | ||||||||
\(274\) | −10.4679 | −0.632387 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.65686 | 0.0997312 | ||||||||
\(277\) | −26.8137 | −1.61108 | −0.805541 | − | 0.592540i | \(-0.798125\pi\) | ||||
−0.805541 | + | 0.592540i | \(0.798125\pi\) | |||||||
\(278\) | 17.9042 | 1.07382 | ||||||||
\(279\) | −6.09333 | −0.364798 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.98903 | −0.416930 | −0.208465 | − | 0.978030i | \(-0.566847\pi\) | ||||
−0.208465 | + | 0.978030i | \(0.566847\pi\) | |||||||
\(282\) | 1.16553 | 0.0694064 | ||||||||
\(283\) | 20.1757 | 1.19932 | 0.599660 | − | 0.800255i | \(-0.295303\pi\) | ||||
0.599660 | + | 0.800255i | \(0.295303\pi\) | |||||||
\(284\) | 2.24153 | 0.133010 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.4987 | 1.21211 | ||||||||
\(287\) | −20.9835 | −1.23862 | ||||||||
\(288\) | −3.47062 | −0.204509 | ||||||||
\(289\) | −15.4857 | −0.910923 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.5416 | 0.852442 | ||||||||
\(292\) | 9.16102 | 0.536108 | ||||||||
\(293\) | 2.10609 | 0.123039 | 0.0615196 | − | 0.998106i | \(-0.480405\pi\) | ||||
0.0615196 | + | 0.998106i | \(0.480405\pi\) | |||||||
\(294\) | 12.0106 | 0.700471 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.58971 | 0.266772 | ||||||||
\(297\) | 3.81209 | 0.221200 | ||||||||
\(298\) | −12.4209 | −0.719525 | ||||||||
\(299\) | 11.9153 | 0.689077 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −51.1762 | −2.94975 | ||||||||
\(302\) | −5.96587 | −0.343297 | ||||||||
\(303\) | 5.91317 | 0.339703 | ||||||||
\(304\) | 5.83285 | 0.334537 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.43427 | −0.0819917 | ||||||||
\(307\) | −17.1013 | −0.976020 | −0.488010 | − | 0.872838i | \(-0.662277\pi\) | ||||
−0.488010 | + | 0.872838i | \(0.662277\pi\) | |||||||
\(308\) | −10.1734 | −0.579686 | ||||||||
\(309\) | 3.70244 | 0.210625 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.7032 | 1.74102 | 0.870510 | − | 0.492150i | \(-0.163789\pi\) | ||||
0.870510 | + | 0.492150i | \(0.163789\pi\) | |||||||
\(312\) | −14.2043 | −0.804161 | ||||||||
\(313\) | −1.89191 | −0.106937 | −0.0534686 | − | 0.998570i | \(-0.517028\pi\) | ||||
−0.0534686 | + | 0.998570i | \(0.517028\pi\) | |||||||
\(314\) | −13.4244 | −0.757581 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.40275 | −0.191420 | ||||||||
\(317\) | 18.9576 | 1.06476 | 0.532382 | − | 0.846504i | \(-0.321297\pi\) | ||||
0.532382 | + | 0.846504i | \(0.321297\pi\) | |||||||
\(318\) | 7.31422 | 0.410161 | ||||||||
\(319\) | 20.7143 | 1.15978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.6364 | −1.04018 | ||||||||
\(322\) | 12.5219 | 0.697819 | ||||||||
\(323\) | −3.11351 | −0.173240 | ||||||||
\(324\) | −0.641537 | −0.0356410 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.82422 | 0.433344 | ||||||||
\(327\) | 11.8589 | 0.655801 | ||||||||
\(328\) | 15.5302 | 0.857509 | ||||||||
\(329\) | −4.15990 | −0.229343 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.7036 | −1.90748 | −0.953742 | − | 0.300626i | \(-0.902804\pi\) | ||||
−0.953742 | + | 0.300626i | \(0.902804\pi\) | |||||||
\(332\) | 3.81316 | 0.209274 | ||||||||
\(333\) | 1.49075 | 0.0816926 | ||||||||
\(334\) | 19.6952 | 1.07768 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.59006 | −0.523180 | ||||||||
\(337\) | 0.0144912 | 0.000789386 0 | 0.000394693 | − | 1.00000i | \(-0.499874\pi\) | ||||
0.000394693 | 1.00000i | \(0.499874\pi\) | ||||||||
\(338\) | −9.65673 | −0.525257 | ||||||||
\(339\) | −12.2064 | −0.662963 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.2283 | 1.25788 | ||||||||
\(342\) | 2.94894 | 0.159461 | ||||||||
\(343\) | −13.7477 | −0.742305 | ||||||||
\(344\) | 37.8761 | 2.04214 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.7377 | −0.846064 | ||||||||
\(347\) | −30.3323 | −1.62832 | −0.814162 | − | 0.580638i | \(-0.802803\pi\) | ||||
−0.814162 | + | 0.580638i | \(0.802803\pi\) | |||||||
\(348\) | −3.48602 | −0.186871 | ||||||||
\(349\) | −4.89284 | −0.261908 | −0.130954 | − | 0.991388i | \(-0.541804\pi\) | ||||
−0.130954 | + | 0.991388i | \(0.541804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.61360 | −0.246256 | ||||||||
\(352\) | 13.2303 | 0.705178 | ||||||||
\(353\) | −24.2132 | −1.28874 | −0.644369 | − | 0.764715i | \(-0.722880\pi\) | ||||
−0.644369 | + | 0.764715i | \(0.722880\pi\) | |||||||
\(354\) | 3.11347 | 0.165479 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.792044 | 0.0419783 | ||||||||
\(357\) | 5.11906 | 0.270929 | ||||||||
\(358\) | 6.82602 | 0.360766 | ||||||||
\(359\) | −8.29577 | −0.437834 | −0.218917 | − | 0.975743i | \(-0.570252\pi\) | ||||
−0.218917 | + | 0.975743i | \(0.570252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.5984 | −0.663076 | ||||||||
\(362\) | −21.3104 | −1.12005 | ||||||||
\(363\) | −3.53200 | −0.185382 | ||||||||
\(364\) | 12.3125 | 0.645348 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.9074 | 0.779223 | ||||||||
\(367\) | 11.0837 | 0.578564 | 0.289282 | − | 0.957244i | \(-0.406583\pi\) | ||||
0.289282 | + | 0.957244i | \(0.406583\pi\) | |||||||
\(368\) | −5.95390 | −0.310368 | ||||||||
\(369\) | 5.04423 | 0.262592 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.1052 | −1.35532 | ||||||||
\(372\) | −3.90910 | −0.202677 | ||||||||
\(373\) | −1.43233 | −0.0741634 | −0.0370817 | − | 0.999312i | \(-0.511806\pi\) | ||||
−0.0370817 | + | 0.999312i | \(0.511806\pi\) | |||||||
\(374\) | 5.46756 | 0.282721 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.07879 | 0.158777 | ||||||||
\(377\) | −25.0696 | −1.29115 | ||||||||
\(378\) | −4.84850 | −0.249380 | ||||||||
\(379\) | −12.1820 | −0.625749 | −0.312874 | − | 0.949795i | \(-0.601292\pi\) | ||||
−0.312874 | + | 0.949795i | \(0.601292\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.6492 | 0.596807 | ||||||||
\(382\) | 6.32486 | 0.323608 | ||||||||
\(383\) | 22.4757 | 1.14846 | 0.574228 | − | 0.818696i | \(-0.305302\pi\) | ||||
0.574228 | + | 0.818696i | \(0.305302\pi\) | |||||||
\(384\) | 3.14739 | 0.160615 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.7126 | 1.05425 | ||||||||
\(387\) | 12.3022 | 0.625358 | ||||||||
\(388\) | 9.32896 | 0.473606 | ||||||||
\(389\) | 7.90866 | 0.400985 | 0.200492 | − | 0.979695i | \(-0.435746\pi\) | ||||
0.200492 | + | 0.979695i | \(0.435746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.17812 | 0.160725 | ||||||||
\(392\) | 31.7264 | 1.60242 | ||||||||
\(393\) | 2.96872 | 0.149752 | ||||||||
\(394\) | −2.81562 | −0.141849 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.44560 | 0.122896 | ||||||||
\(397\) | −22.6540 | −1.13697 | −0.568486 | − | 0.822693i | \(-0.692471\pi\) | ||||
−0.568486 | + | 0.822693i | \(0.692471\pi\) | |||||||
\(398\) | 8.99096 | 0.450676 | ||||||||
\(399\) | −10.5251 | −0.526914 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.4361 | 1.66972 | 0.834859 | − | 0.550464i | \(-0.185549\pi\) | ||||
0.834859 | + | 0.550464i | \(0.185549\pi\) | |||||||
\(402\) | 13.2062 | 0.658664 | ||||||||
\(403\) | −28.1122 | −1.40037 | ||||||||
\(404\) | 3.79352 | 0.188735 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −26.3461 | −1.30753 | ||||||||
\(407\) | −5.68287 | −0.281689 | ||||||||
\(408\) | −3.78868 | −0.187567 | ||||||||
\(409\) | 14.3473 | 0.709430 | 0.354715 | − | 0.934974i | \(-0.384578\pi\) | ||||
0.354715 | + | 0.934974i | \(0.384578\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.98119 | −0.443010 | ||||||||
\(412\) | 2.37526 | 0.117020 | ||||||||
\(413\) | −11.1123 | −0.546801 | ||||||||
\(414\) | −3.01015 | −0.147941 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.0121 | −0.785056 | ||||||||
\(417\) | 15.3614 | 0.752250 | ||||||||
\(418\) | −11.2416 | −0.549846 | ||||||||
\(419\) | −8.05906 | −0.393711 | −0.196855 | − | 0.980433i | \(-0.563073\pi\) | ||||
−0.196855 | + | 0.980433i | \(0.563073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.407998 | 0.0198846 | 0.00994231 | − | 0.999951i | \(-0.496835\pi\) | ||||
0.00994231 | + | 0.999951i | \(0.496835\pi\) | |||||||
\(422\) | −1.41788 | −0.0690214 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 19.3208 | 0.938301 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.07236 | −0.197307 | ||||||||
\(427\) | −53.2061 | −2.57483 | ||||||||
\(428\) | −11.9560 | −0.577913 | ||||||||
\(429\) | 17.5874 | 0.849129 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.7588 | −0.566402 | −0.283201 | − | 0.959061i | \(-0.591396\pi\) | ||||
−0.283201 | + | 0.959061i | \(0.591396\pi\) | |||||||
\(432\) | 2.30535 | 0.110916 | ||||||||
\(433\) | −4.25415 | −0.204442 | −0.102221 | − | 0.994762i | \(-0.532595\pi\) | ||||
−0.102221 | + | 0.994762i | \(0.532595\pi\) | |||||||
\(434\) | −29.5435 | −1.41813 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.60795 | 0.364355 | ||||||||
\(437\) | −6.53441 | −0.312583 | ||||||||
\(438\) | −16.6435 | −0.795259 | ||||||||
\(439\) | −4.77103 | −0.227709 | −0.113854 | − | 0.993497i | \(-0.536320\pi\) | ||||
−0.113854 | + | 0.993497i | \(0.536320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.3048 | 0.490705 | ||||||||
\(442\) | −6.61714 | −0.314745 | ||||||||
\(443\) | 6.80236 | 0.323190 | 0.161595 | − | 0.986857i | \(-0.448336\pi\) | ||||
0.161595 | + | 0.986857i | \(0.448336\pi\) | |||||||
\(444\) | 0.956372 | 0.0453874 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 32.7496 | 1.55074 | ||||||||
\(447\) | −10.6569 | −0.504053 | ||||||||
\(448\) | −36.0074 | −1.70119 | ||||||||
\(449\) | −1.56203 | −0.0737165 | −0.0368583 | − | 0.999321i | \(-0.511735\pi\) | ||||
−0.0368583 | + | 0.999321i | \(0.511735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.2291 | −0.905461 | ||||||||
\(452\) | −7.83088 | −0.368334 | ||||||||
\(453\) | −5.11859 | −0.240492 | ||||||||
\(454\) | 29.8189 | 1.39947 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.78975 | 0.364788 | ||||||||
\(457\) | −4.03564 | −0.188779 | −0.0943896 | − | 0.995535i | \(-0.530090\pi\) | ||||
−0.0943896 | + | 0.995535i | \(0.530090\pi\) | |||||||
\(458\) | 33.5884 | 1.56948 | ||||||||
\(459\) | −1.23057 | −0.0574382 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.7992 | 0.875567 | 0.437784 | − | 0.899080i | \(-0.355764\pi\) | ||||
0.437784 | + | 0.899080i | \(0.355764\pi\) | |||||||
\(462\) | 18.4829 | 0.859902 | ||||||||
\(463\) | −35.4554 | −1.64775 | −0.823876 | − | 0.566771i | \(-0.808193\pi\) | ||||
−0.823876 | + | 0.566771i | \(0.808193\pi\) | |||||||
\(464\) | 12.5270 | 0.581550 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.84140 | 0.409570 | ||||||||
\(467\) | −41.6376 | −1.92676 | −0.963379 | − | 0.268143i | \(-0.913590\pi\) | ||||
−0.963379 | + | 0.268143i | \(0.913590\pi\) | |||||||
\(468\) | −2.95979 | −0.136817 | ||||||||
\(469\) | −47.1343 | −2.17646 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5178 | −0.530713 | ||||||||
\(472\) | 8.22435 | 0.378557 | ||||||||
\(473\) | −46.8972 | −2.15634 | ||||||||
\(474\) | 6.18204 | 0.283950 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.28407 | 0.150525 | ||||||||
\(477\) | 6.27544 | 0.287333 | ||||||||
\(478\) | 7.30520 | 0.334132 | ||||||||
\(479\) | −23.2251 | −1.06118 | −0.530591 | − | 0.847628i | \(-0.678030\pi\) | ||||
−0.530591 | + | 0.847628i | \(0.678030\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.87772 | 0.313597 | ||||||||
\(482\) | −3.59688 | −0.163833 | ||||||||
\(483\) | 10.7435 | 0.488848 | ||||||||
\(484\) | −2.26591 | −0.102996 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.16553 | 0.0528696 | ||||||||
\(487\) | 4.25601 | 0.192858 | 0.0964291 | − | 0.995340i | \(-0.469258\pi\) | ||||
0.0964291 | + | 0.995340i | \(0.469258\pi\) | |||||||
\(488\) | 39.3785 | 1.78258 | ||||||||
\(489\) | 6.71301 | 0.303573 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.2980 | 1.32220 | 0.661101 | − | 0.750297i | \(-0.270089\pi\) | ||||
0.661101 | + | 0.750297i | \(0.270089\pi\) | |||||||
\(492\) | 3.23606 | 0.145893 | ||||||||
\(493\) | −6.68675 | −0.301156 | ||||||||
\(494\) | 13.6052 | 0.612129 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.0473 | 0.630742 | ||||||||
\(497\) | 14.5347 | 0.651971 | ||||||||
\(498\) | −6.92767 | −0.310436 | ||||||||
\(499\) | 28.3988 | 1.27130 | 0.635651 | − | 0.771976i | \(-0.280732\pi\) | ||||
0.635651 | + | 0.771976i | \(0.280732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.8981 | 0.754950 | ||||||||
\(502\) | 33.0145 | 1.47351 | ||||||||
\(503\) | 23.0789 | 1.02904 | 0.514518 | − | 0.857480i | \(-0.327971\pi\) | ||||
0.514518 | + | 0.857480i | \(0.327971\pi\) | |||||||
\(504\) | −12.8075 | −0.570491 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.4749 | 0.510123 | ||||||||
\(507\) | −8.28526 | −0.367961 | ||||||||
\(508\) | 7.47340 | 0.331578 | ||||||||
\(509\) | 34.4963 | 1.52902 | 0.764510 | − | 0.644612i | \(-0.222981\pi\) | ||||
0.764510 | + | 0.644612i | \(0.222981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.4026 | 2.62782 | ||||||||
\(512\) | 22.1964 | 0.980954 | ||||||||
\(513\) | 2.53013 | 0.111708 | ||||||||
\(514\) | −36.3050 | −1.60134 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.89235 | 0.347441 | ||||||||
\(517\) | −3.81209 | −0.167655 | ||||||||
\(518\) | 7.22790 | 0.317576 | ||||||||
\(519\) | −13.5026 | −0.592698 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.8601 | −1.26438 | −0.632191 | − | 0.774813i | \(-0.717844\pi\) | ||||
−0.632191 | + | 0.774813i | \(0.717844\pi\) | |||||||
\(522\) | 6.33333 | 0.277202 | ||||||||
\(523\) | 2.81087 | 0.122911 | 0.0614553 | − | 0.998110i | \(-0.480426\pi\) | ||||
0.0614553 | + | 0.998110i | \(0.480426\pi\) | |||||||
\(524\) | 1.90455 | 0.0832005 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.6515 | −1.03125 | ||||||||
\(527\) | −7.49828 | −0.326630 | ||||||||
\(528\) | −8.78821 | −0.382458 | ||||||||
\(529\) | −16.3300 | −0.709999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.67129 | 0.115924 | ||||||||
\(532\) | −6.75224 | −0.292747 | ||||||||
\(533\) | 23.2721 | 1.00802 | ||||||||
\(534\) | −1.43897 | −0.0622702 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 34.8846 | 1.50679 | ||||||||
\(537\) | 5.85657 | 0.252730 | ||||||||
\(538\) | 14.3466 | 0.618526 | ||||||||
\(539\) | −39.2828 | −1.69203 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.59709 | −0.412611 | −0.206305 | − | 0.978488i | \(-0.566144\pi\) | ||||
−0.206305 | + | 0.978488i | \(0.566144\pi\) | |||||||
\(542\) | −4.83707 | −0.207770 | ||||||||
\(543\) | −18.2839 | −0.784636 | ||||||||
\(544\) | −4.27085 | −0.183111 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −22.3690 | −0.957305 | ||||||||
\(547\) | −36.0808 | −1.54270 | −0.771352 | − | 0.636409i | \(-0.780419\pi\) | ||||
−0.771352 | + | 0.636409i | \(0.780419\pi\) | |||||||
\(548\) | −5.76177 | −0.246131 | ||||||||
\(549\) | 12.7902 | 0.545874 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.7484 | 0.585700 | ||||||||
\(552\) | −7.95141 | −0.338435 | ||||||||
\(553\) | −22.0644 | −0.938272 | ||||||||
\(554\) | 31.2523 | 1.32778 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.85489 | 0.417941 | ||||||||
\(557\) | 21.1230 | 0.895008 | 0.447504 | − | 0.894282i | \(-0.352313\pi\) | ||||
0.447504 | + | 0.894282i | \(0.352313\pi\) | |||||||
\(558\) | 7.10197 | 0.300650 | ||||||||
\(559\) | 56.7576 | 2.40059 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.69104 | 0.198056 | ||||||||
\(562\) | 8.14593 | 0.343615 | ||||||||
\(563\) | 11.8546 | 0.499612 | 0.249806 | − | 0.968296i | \(-0.419633\pi\) | ||||
0.249806 | + | 0.968296i | \(0.419633\pi\) | |||||||
\(564\) | 0.641537 | 0.0270136 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.5154 | −0.988425 | ||||||||
\(567\) | −4.15990 | −0.174700 | ||||||||
\(568\) | −10.7573 | −0.451366 | ||||||||
\(569\) | 6.36909 | 0.267006 | 0.133503 | − | 0.991048i | \(-0.457377\pi\) | ||||
0.133503 | + | 0.991048i | \(0.457377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.2702 | 1.68526 | 0.842628 | − | 0.538496i | \(-0.181007\pi\) | ||||
0.842628 | + | 0.538496i | \(0.181007\pi\) | |||||||
\(572\) | 11.2830 | 0.471765 | ||||||||
\(573\) | 5.42659 | 0.226699 | ||||||||
\(574\) | 24.4570 | 1.02081 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.65583 | 0.360660 | ||||||||
\(577\) | −26.1825 | −1.08999 | −0.544996 | − | 0.838438i | \(-0.683469\pi\) | ||||
−0.544996 | + | 0.838438i | \(0.683469\pi\) | |||||||
\(578\) | 18.0491 | 0.750742 | ||||||||
\(579\) | 17.7710 | 0.738537 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.7256 | 1.02579 | ||||||||
\(582\) | −16.9487 | −0.702544 | ||||||||
\(583\) | −23.9225 | −0.990770 | ||||||||
\(584\) | −43.9646 | −1.81927 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.45472 | −0.101403 | ||||||||
\(587\) | −4.54659 | −0.187658 | −0.0938289 | − | 0.995588i | \(-0.529911\pi\) | ||||
−0.0938289 | + | 0.995588i | \(0.529911\pi\) | |||||||
\(588\) | 6.61092 | 0.272630 | ||||||||
\(589\) | 15.4169 | 0.635243 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.41574 | −0.0993702 | ||||||||
\(592\) | −3.43671 | −0.141248 | ||||||||
\(593\) | 23.1314 | 0.949891 | 0.474946 | − | 0.880015i | \(-0.342468\pi\) | ||||
0.474946 | + | 0.880015i | \(0.342468\pi\) | |||||||
\(594\) | −4.44310 | −0.182303 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.83679 | −0.280046 | ||||||||
\(597\) | 7.71405 | 0.315715 | ||||||||
\(598\) | −13.8876 | −0.567906 | ||||||||
\(599\) | −41.6490 | −1.70173 | −0.850866 | − | 0.525383i | \(-0.823922\pi\) | ||||
−0.850866 | + | 0.525383i | \(0.823922\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.66645 | 0.353512 | 0.176756 | − | 0.984255i | \(-0.443440\pi\) | ||||
0.176756 | + | 0.984255i | \(0.443440\pi\) | |||||||
\(602\) | 59.6474 | 2.43105 | ||||||||
\(603\) | 11.3306 | 0.461418 | ||||||||
\(604\) | −3.28376 | −0.133614 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.89198 | −0.279968 | ||||||||
\(607\) | 11.3275 | 0.459771 | 0.229885 | − | 0.973218i | \(-0.426165\pi\) | ||||
0.229885 | + | 0.973218i | \(0.426165\pi\) | |||||||
\(608\) | 8.78113 | 0.356122 | ||||||||
\(609\) | −22.6043 | −0.915974 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.61360 | 0.186646 | ||||||||
\(612\) | −0.789458 | −0.0319119 | ||||||||
\(613\) | −22.4281 | −0.905863 | −0.452931 | − | 0.891545i | \(-0.649622\pi\) | ||||
−0.452931 | + | 0.891545i | \(0.649622\pi\) | |||||||
\(614\) | 19.9320 | 0.804392 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.8232 | 1.96714 | ||||||||
\(617\) | 42.5696 | 1.71379 | 0.856893 | − | 0.515494i | \(-0.172392\pi\) | ||||
0.856893 | + | 0.515494i | \(0.172392\pi\) | |||||||
\(618\) | −4.31531 | −0.173587 | ||||||||
\(619\) | 19.1959 | 0.771549 | 0.385774 | − | 0.922593i | \(-0.373934\pi\) | ||||
0.385774 | + | 0.922593i | \(0.373934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.58264 | −0.103638 | ||||||||
\(622\) | −35.7856 | −1.43487 | ||||||||
\(623\) | 5.13583 | 0.205763 | ||||||||
\(624\) | 10.6360 | 0.425780 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.20508 | 0.0881328 | ||||||||
\(627\) | −9.64507 | −0.385187 | ||||||||
\(628\) | −7.38910 | −0.294857 | ||||||||
\(629\) | 1.83448 | 0.0731453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.0498 | −1.19627 | −0.598133 | − | 0.801397i | \(-0.704090\pi\) | ||||
−0.598133 | + | 0.801397i | \(0.704090\pi\) | |||||||
\(632\) | 16.3301 | 0.649576 | ||||||||
\(633\) | −1.21651 | −0.0483520 | ||||||||
\(634\) | −22.0957 | −0.877531 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.02593 | 0.159639 | ||||||||
\(637\) | 47.5422 | 1.88369 | ||||||||
\(638\) | −24.1432 | −0.955839 | ||||||||
\(639\) | −3.49400 | −0.138220 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.0046 | 0.829631 | 0.414815 | − | 0.909906i | \(-0.363846\pi\) | ||||
0.414815 | + | 0.909906i | \(0.363846\pi\) | |||||||
\(642\) | 21.7213 | 0.857273 | ||||||||
\(643\) | 12.2565 | 0.483351 | 0.241675 | − | 0.970357i | \(-0.422303\pi\) | ||||
0.241675 | + | 0.970357i | \(0.422303\pi\) | |||||||
\(644\) | 6.89238 | 0.271598 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.62889 | 0.142777 | ||||||||
\(647\) | 12.9252 | 0.508143 | 0.254072 | − | 0.967185i | \(-0.418230\pi\) | ||||
0.254072 | + | 0.967185i | \(0.418230\pi\) | |||||||
\(648\) | 3.07879 | 0.120946 | ||||||||
\(649\) | −10.1832 | −0.399725 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.3477 | −0.993454 | ||||||||
\(652\) | 4.30665 | 0.168661 | ||||||||
\(653\) | 2.34399 | 0.0917276 | 0.0458638 | − | 0.998948i | \(-0.485396\pi\) | ||||
0.0458638 | + | 0.998948i | \(0.485396\pi\) | |||||||
\(654\) | −13.8220 | −0.540481 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.6287 | −0.454026 | ||||||||
\(657\) | −14.2798 | −0.557108 | ||||||||
\(658\) | 4.84850 | 0.189014 | ||||||||
\(659\) | −12.3566 | −0.481345 | −0.240672 | − | 0.970606i | \(-0.577368\pi\) | ||||
−0.240672 | + | 0.970606i | \(0.577368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.5750 | 1.34481 | 0.672405 | − | 0.740184i | \(-0.265261\pi\) | ||||
0.672405 | + | 0.740184i | \(0.265261\pi\) | |||||||
\(662\) | 40.4482 | 1.57206 | ||||||||
\(663\) | −5.67736 | −0.220490 | ||||||||
\(664\) | −18.2997 | −0.710166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.73752 | −0.0673274 | ||||||||
\(667\) | −14.0337 | −0.543387 | ||||||||
\(668\) | 10.8407 | 0.419441 | ||||||||
\(669\) | 28.0985 | 1.08635 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.7574 | −1.88226 | ||||||||
\(672\) | −14.4375 | −0.556937 | ||||||||
\(673\) | 21.9687 | 0.846831 | 0.423416 | − | 0.905936i | \(-0.360831\pi\) | ||||
0.423416 | + | 0.905936i | \(0.360831\pi\) | |||||||
\(674\) | −0.0168899 | −0.000650576 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.31531 | −0.204435 | ||||||||
\(677\) | −12.3690 | −0.475379 | −0.237689 | − | 0.971341i | \(-0.576390\pi\) | ||||
−0.237689 | + | 0.971341i | \(0.576390\pi\) | |||||||
\(678\) | 14.2270 | 0.546384 | ||||||||
\(679\) | 60.4915 | 2.32145 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.5840 | 0.980380 | ||||||||
\(682\) | −27.0733 | −1.03669 | ||||||||
\(683\) | −7.40119 | −0.283198 | −0.141599 | − | 0.989924i | \(-0.545224\pi\) | ||||
−0.141599 | + | 0.989924i | \(0.545224\pi\) | |||||||
\(684\) | 1.62317 | 0.0620636 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.0233 | 0.611774 | ||||||||
\(687\) | 28.8181 | 1.09948 | ||||||||
\(688\) | −28.3610 | −1.08125 | ||||||||
\(689\) | 28.9523 | 1.10300 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0653 | 1.14374 | 0.571869 | − | 0.820345i | \(-0.306219\pi\) | ||||
0.571869 | + | 0.820345i | \(0.306219\pi\) | |||||||
\(692\) | −8.66242 | −0.329296 | ||||||||
\(693\) | 15.8579 | 0.602392 | ||||||||
\(694\) | 35.3533 | 1.34199 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16.7297 | 0.634139 | ||||||||
\(697\) | 6.20729 | 0.235118 | ||||||||
\(698\) | 5.70276 | 0.215853 | ||||||||
\(699\) | 7.58573 | 0.286918 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.69687 | −0.139629 | −0.0698144 | − | 0.997560i | \(-0.522241\pi\) | ||||
−0.0698144 | + | 0.997560i | \(0.522241\pi\) | |||||||
\(702\) | 5.37729 | 0.202953 | ||||||||
\(703\) | −3.77179 | −0.142256 | ||||||||
\(704\) | −32.9968 | −1.24361 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.2212 | 1.06212 | ||||||||
\(707\) | 24.5982 | 0.925111 | ||||||||
\(708\) | 1.71373 | 0.0644060 | ||||||||
\(709\) | −27.5176 | −1.03345 | −0.516723 | − | 0.856153i | \(-0.672848\pi\) | ||||
−0.516723 | + | 0.856153i | \(0.672848\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.30405 | 0.198917 | ||||||||
\(712\) | −3.80109 | −0.142452 | ||||||||
\(713\) | −15.7369 | −0.589351 | ||||||||
\(714\) | −5.96642 | −0.223288 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.75721 | 0.140414 | ||||||||
\(717\) | 6.26770 | 0.234072 | ||||||||
\(718\) | 9.66898 | 0.360843 | ||||||||
\(719\) | −25.3414 | −0.945074 | −0.472537 | − | 0.881311i | \(-0.656662\pi\) | ||||
−0.472537 | + | 0.881311i | \(0.656662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4018 | 0.573593 | ||||||||
\(722\) | 14.6839 | 0.546477 | ||||||||
\(723\) | −3.08604 | −0.114771 | ||||||||
\(724\) | −11.7298 | −0.435934 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.11665 | 0.152783 | ||||||||
\(727\) | 35.6248 | 1.32125 | 0.660625 | − | 0.750716i | \(-0.270291\pi\) | ||||
0.660625 | + | 0.750716i | \(0.270291\pi\) | |||||||
\(728\) | −59.0886 | −2.18997 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.1388 | 0.559928 | ||||||||
\(732\) | 8.20541 | 0.303281 | ||||||||
\(733\) | −26.4007 | −0.975131 | −0.487565 | − | 0.873086i | \(-0.662115\pi\) | ||||
−0.487565 | + | 0.873086i | \(0.662115\pi\) | |||||||
\(734\) | −12.9184 | −0.476827 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.96337 | −0.330394 | ||||||||
\(737\) | −43.1933 | −1.59104 | ||||||||
\(738\) | −5.87921 | −0.216417 | ||||||||
\(739\) | −2.48916 | −0.0915652 | −0.0457826 | − | 0.998951i | \(-0.514578\pi\) | ||||
−0.0457826 | + | 0.998951i | \(0.514578\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6730 | 0.428818 | ||||||||
\(742\) | 30.4265 | 1.11699 | ||||||||
\(743\) | −44.8468 | −1.64527 | −0.822634 | − | 0.568571i | \(-0.807496\pi\) | ||||
−0.822634 | + | 0.568571i | \(0.807496\pi\) | |||||||
\(744\) | 18.7601 | 0.687779 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.66943 | 0.0611221 | ||||||||
\(747\) | −5.94379 | −0.217472 | ||||||||
\(748\) | 3.00948 | 0.110037 | ||||||||
\(749\) | −77.5258 | −2.83273 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.4960 | −1.40474 | −0.702370 | − | 0.711812i | \(-0.747875\pi\) | ||||
−0.702370 | + | 0.711812i | \(0.747875\pi\) | |||||||
\(752\) | −2.30535 | −0.0840676 | ||||||||
\(753\) | 28.3257 | 1.03224 | ||||||||
\(754\) | 29.2194 | 1.06411 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.66873 | −0.0970609 | ||||||||
\(757\) | −1.70387 | −0.0619284 | −0.0309642 | − | 0.999520i | \(-0.509858\pi\) | ||||
−0.0309642 | + | 0.999520i | \(0.509858\pi\) | |||||||
\(758\) | 14.1985 | 0.515714 | ||||||||
\(759\) | 9.84524 | 0.357360 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2211 | −0.624263 | −0.312132 | − | 0.950039i | \(-0.601043\pi\) | ||||
−0.312132 | + | 0.950039i | \(0.601043\pi\) | |||||||
\(762\) | −13.5775 | −0.491861 | ||||||||
\(763\) | 49.3320 | 1.78594 | ||||||||
\(764\) | 3.48136 | 0.125951 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.1961 | −0.946505 | ||||||||
\(767\) | 12.3243 | 0.445003 | ||||||||
\(768\) | 13.6433 | 0.492310 | ||||||||
\(769\) | 1.47987 | 0.0533656 | 0.0266828 | − | 0.999644i | \(-0.491506\pi\) | ||||
0.0266828 | + | 0.999644i | \(0.491506\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.1489 | −1.12180 | ||||||||
\(772\) | 11.4007 | 0.410322 | ||||||||
\(773\) | 33.0531 | 1.18884 | 0.594418 | − | 0.804156i | \(-0.297383\pi\) | ||||
0.594418 | + | 0.804156i | \(0.297383\pi\) | |||||||
\(774\) | −14.3386 | −0.515392 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −44.7705 | −1.60717 | ||||||||
\(777\) | 6.20138 | 0.222473 | ||||||||
\(778\) | −9.21779 | −0.330474 | ||||||||
\(779\) | −12.7626 | −0.457266 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.3194 | 0.476606 | ||||||||
\(782\) | −3.70420 | −0.132462 | ||||||||
\(783\) | 5.43386 | 0.194190 | ||||||||
\(784\) | −23.7562 | −0.848437 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.46014 | −0.123419 | ||||||||
\(787\) | −2.79404 | −0.0995968 | −0.0497984 | − | 0.998759i | \(-0.515858\pi\) | ||||
−0.0497984 | + | 0.998759i | \(0.515858\pi\) | |||||||
\(788\) | −1.54979 | −0.0552089 | ||||||||
\(789\) | −20.2925 | −0.722431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50.7776 | −1.80544 | ||||||||
\(792\) | −11.7366 | −0.417043 | ||||||||
\(793\) | 59.0089 | 2.09547 | ||||||||
\(794\) | 26.4039 | 0.937041 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.94885 | 0.175407 | ||||||||
\(797\) | −31.7140 | −1.12337 | −0.561684 | − | 0.827352i | \(-0.689846\pi\) | ||||
−0.561684 | + | 0.827352i | \(0.689846\pi\) | |||||||
\(798\) | 12.2673 | 0.434259 | ||||||||
\(799\) | 1.23057 | 0.0435345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.23460 | −0.0436226 | ||||||||
\(802\) | −38.9708 | −1.37611 | ||||||||
\(803\) | 54.4358 | 1.92100 | ||||||||
\(804\) | 7.26901 | 0.256358 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.7656 | 1.15412 | ||||||||
\(807\) | 12.3091 | 0.433300 | ||||||||
\(808\) | −18.2054 | −0.640465 | ||||||||
\(809\) | 12.9229 | 0.454344 | 0.227172 | − | 0.973855i | \(-0.427052\pi\) | ||||
0.227172 | + | 0.973855i | \(0.427052\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0140 | −0.702786 | −0.351393 | − | 0.936228i | \(-0.614292\pi\) | ||||
−0.351393 | + | 0.936228i | \(0.614292\pi\) | |||||||
\(812\) | −14.5015 | −0.508904 | ||||||||
\(813\) | −4.15010 | −0.145550 | ||||||||
\(814\) | 6.62356 | 0.232156 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.83690 | 0.0993115 | ||||||||
\(817\) | −31.1263 | −1.08897 | ||||||||
\(818\) | −16.7223 | −0.584680 | ||||||||
\(819\) | −19.1921 | −0.670627 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.9297 | −1.25396 | −0.626978 | − | 0.779037i | \(-0.715708\pi\) | ||||
−0.626978 | + | 0.779037i | \(0.715708\pi\) | |||||||
\(822\) | 10.4679 | 0.365109 | ||||||||
\(823\) | −19.8583 | −0.692217 | −0.346108 | − | 0.938195i | \(-0.612497\pi\) | ||||
−0.346108 | + | 0.938195i | \(0.612497\pi\) | |||||||
\(824\) | −11.3991 | −0.397105 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9517 | 0.450649 | ||||||||
\(827\) | 15.4529 | 0.537350 | 0.268675 | − | 0.963231i | \(-0.413414\pi\) | ||||
0.268675 | + | 0.963231i | \(0.413414\pi\) | |||||||
\(828\) | −1.65686 | −0.0575799 | ||||||||
\(829\) | −18.2545 | −0.634004 | −0.317002 | − | 0.948425i | \(-0.602676\pi\) | ||||
−0.317002 | + | 0.948425i | \(0.602676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.8137 | 0.930159 | ||||||||
\(832\) | 39.9345 | 1.38448 | ||||||||
\(833\) | 12.6808 | 0.439364 | ||||||||
\(834\) | −17.9042 | −0.619970 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.18767 | −0.214005 | ||||||||
\(837\) | 6.09333 | 0.210616 | ||||||||
\(838\) | 9.39308 | 0.324479 | ||||||||
\(839\) | 42.3886 | 1.46342 | 0.731709 | − | 0.681617i | \(-0.238723\pi\) | ||||
0.731709 | + | 0.681617i | \(0.238723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.526840 | 0.0181669 | ||||||||
\(842\) | −0.475535 | −0.0163880 | ||||||||
\(843\) | 6.98903 | 0.240715 | ||||||||
\(844\) | −0.780437 | −0.0268638 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.16553 | −0.0400718 | ||||||||
\(847\) | −14.6928 | −0.504850 | ||||||||
\(848\) | −14.4671 | −0.496803 | ||||||||
\(849\) | −20.1757 | −0.692427 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.85007 | 0.131979 | ||||||||
\(852\) | −2.24153 | −0.0767936 | ||||||||
\(853\) | −24.4161 | −0.835993 | −0.417997 | − | 0.908449i | \(-0.637268\pi\) | ||||
−0.417997 | + | 0.908449i | \(0.637268\pi\) | |||||||
\(854\) | 62.0134 | 2.12205 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 57.3777 | 1.96113 | ||||||||
\(857\) | −29.3860 | −1.00381 | −0.501904 | − | 0.864923i | \(-0.667367\pi\) | ||||
−0.501904 | + | 0.864923i | \(0.667367\pi\) | |||||||
\(858\) | −20.4987 | −0.699814 | ||||||||
\(859\) | 15.1898 | 0.518268 | 0.259134 | − | 0.965841i | \(-0.416563\pi\) | ||||
0.259134 | + | 0.965841i | \(0.416563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.9835 | 0.715117 | ||||||||
\(862\) | 13.7053 | 0.466803 | ||||||||
\(863\) | 23.3323 | 0.794240 | 0.397120 | − | 0.917767i | \(-0.370010\pi\) | ||||
0.397120 | + | 0.917767i | \(0.370010\pi\) | |||||||
\(864\) | 3.47062 | 0.118073 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.95835 | 0.168492 | ||||||||
\(867\) | 15.4857 | 0.525922 | ||||||||
\(868\) | −16.2615 | −0.551951 | ||||||||
\(869\) | −20.2195 | −0.685900 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.2749 | 1.77127 | ||||||||
\(872\) | −36.5112 | −1.23643 | ||||||||
\(873\) | −14.5416 | −0.492158 | ||||||||
\(874\) | 7.61606 | 0.257617 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.16102 | −0.309522 | ||||||||
\(877\) | 29.0676 | 0.981543 | 0.490771 | − | 0.871288i | \(-0.336715\pi\) | ||||
0.490771 | + | 0.871288i | \(0.336715\pi\) | |||||||
\(878\) | 5.56078 | 0.187667 | ||||||||
\(879\) | −2.10609 | −0.0710367 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.61823 | −0.0545196 | −0.0272598 | − | 0.999628i | \(-0.508678\pi\) | ||||
−0.0272598 | + | 0.999628i | \(0.508678\pi\) | |||||||
\(882\) | −12.0106 | −0.404417 | ||||||||
\(883\) | 13.6728 | 0.460125 | 0.230063 | − | 0.973176i | \(-0.426107\pi\) | ||||
0.230063 | + | 0.973176i | \(0.426107\pi\) | |||||||
\(884\) | −3.64224 | −0.122502 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.92837 | −0.266359 | ||||||||
\(887\) | −5.09087 | −0.170935 | −0.0854673 | − | 0.996341i | \(-0.527238\pi\) | ||||
−0.0854673 | + | 0.996341i | \(0.527238\pi\) | |||||||
\(888\) | −4.58971 | −0.154021 | ||||||||
\(889\) | 48.4596 | 1.62528 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.81209 | −0.127710 | ||||||||
\(892\) | 18.0262 | 0.603562 | ||||||||
\(893\) | −2.53013 | −0.0846676 | ||||||||
\(894\) | 12.4209 | 0.415418 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.0928 | 0.437401 | ||||||||
\(897\) | −11.9153 | −0.397839 | ||||||||
\(898\) | 1.82059 | 0.0607538 | ||||||||
\(899\) | 33.1103 | 1.10429 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.72238 | 0.257270 | ||||||||
\(902\) | 22.4121 | 0.746240 | ||||||||
\(903\) | 51.1762 | 1.70304 | ||||||||
\(904\) | 37.5811 | 1.24993 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.96587 | 0.198203 | ||||||||
\(907\) | −18.3464 | −0.609181 | −0.304591 | − | 0.952483i | \(-0.598520\pi\) | ||||
−0.304591 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(908\) | 16.4131 | 0.544687 | ||||||||
\(909\) | −5.91317 | −0.196127 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6570 | −0.916316 | −0.458158 | − | 0.888871i | \(-0.651491\pi\) | ||||
−0.458158 | + | 0.888871i | \(0.651491\pi\) | |||||||
\(912\) | −5.83285 | −0.193145 | ||||||||
\(913\) | 22.6582 | 0.749878 | ||||||||
\(914\) | 4.70366 | 0.155583 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4879 | 0.610857 | ||||||||
\(917\) | 12.3496 | 0.407820 | ||||||||
\(918\) | 1.43427 | 0.0473379 | ||||||||
\(919\) | 7.19193 | 0.237240 | 0.118620 | − | 0.992940i | \(-0.462153\pi\) | ||||
0.118620 | + | 0.992940i | \(0.462153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.1013 | 0.563505 | ||||||||
\(922\) | −21.9111 | −0.721603 | ||||||||
\(923\) | −16.1199 | −0.530593 | ||||||||
\(924\) | 10.1734 | 0.334682 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 41.3243 | 1.35800 | ||||||||
\(927\) | −3.70244 | −0.121604 | ||||||||
\(928\) | 18.8589 | 0.619073 | ||||||||
\(929\) | −26.7260 | −0.876852 | −0.438426 | − | 0.898767i | \(-0.644464\pi\) | ||||
−0.438426 | + | 0.898767i | \(0.644464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0725 | −0.854492 | ||||||||
\(932\) | 4.86653 | 0.159408 | ||||||||
\(933\) | −30.7032 | −1.00518 | ||||||||
\(934\) | 48.5299 | 1.58795 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.2043 | 0.464282 | ||||||||
\(937\) | 27.4610 | 0.897112 | 0.448556 | − | 0.893755i | \(-0.351939\pi\) | ||||
0.448556 | + | 0.893755i | \(0.351939\pi\) | |||||||
\(938\) | 54.9364 | 1.79374 | ||||||||
\(939\) | 1.89191 | 0.0617402 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.1964 | −1.44076 | −0.720381 | − | 0.693579i | \(-0.756033\pi\) | ||||
−0.720381 | + | 0.693579i | \(0.756033\pi\) | |||||||
\(942\) | 13.4244 | 0.437389 | ||||||||
\(943\) | 13.0274 | 0.424232 | ||||||||
\(944\) | −6.15827 | −0.200435 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 54.6602 | 1.77715 | ||||||||
\(947\) | 42.5524 | 1.38277 | 0.691384 | − | 0.722487i | \(-0.257001\pi\) | ||||
0.691384 | + | 0.722487i | \(0.257001\pi\) | |||||||
\(948\) | 3.40275 | 0.110516 | ||||||||
\(949\) | −65.8812 | −2.13859 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.9576 | −0.614742 | ||||||||
\(952\) | −15.7605 | −0.510802 | ||||||||
\(953\) | 35.9045 | 1.16306 | 0.581530 | − | 0.813525i | \(-0.302454\pi\) | ||||
0.581530 | + | 0.813525i | \(0.302454\pi\) | |||||||
\(954\) | −7.31422 | −0.236807 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.02097 | 0.130047 | ||||||||
\(957\) | −20.7143 | −0.669600 | ||||||||
\(958\) | 27.0696 | 0.874578 | ||||||||
\(959\) | −37.3609 | −1.20645 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.12868 | 0.197699 | ||||||||
\(962\) | −8.01620 | −0.258453 | ||||||||
\(963\) | 18.6364 | 0.600550 | ||||||||
\(964\) | −1.97981 | −0.0637655 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.5219 | −0.402886 | ||||||||
\(967\) | 38.1824 | 1.22786 | 0.613932 | − | 0.789359i | \(-0.289587\pi\) | ||||
0.613932 | + | 0.789359i | \(0.289587\pi\) | |||||||
\(968\) | 10.8743 | 0.349513 | ||||||||
\(969\) | 3.11351 | 0.100020 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5718 | 0.852731 | 0.426365 | − | 0.904551i | \(-0.359794\pi\) | ||||
0.426365 | + | 0.904551i | \(0.359794\pi\) | |||||||
\(972\) | 0.641537 | 0.0205773 | ||||||||
\(973\) | 63.9018 | 2.04860 | ||||||||
\(974\) | −4.96051 | −0.158945 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.4860 | −0.943824 | ||||||||
\(977\) | −41.8510 | −1.33893 | −0.669466 | − | 0.742843i | \(-0.733477\pi\) | ||||
−0.669466 | + | 0.742843i | \(0.733477\pi\) | |||||||
\(978\) | −7.82422 | −0.250191 | ||||||||
\(979\) | 4.70641 | 0.150418 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8589 | −0.378627 | ||||||||
\(982\) | −34.1478 | −1.08970 | ||||||||
\(983\) | −23.7688 | −0.758108 | −0.379054 | − | 0.925375i | \(-0.623751\pi\) | ||||
−0.379054 | + | 0.925375i | \(0.623751\pi\) | |||||||
\(984\) | −15.5302 | −0.495083 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.79362 | 0.248199 | ||||||||
\(987\) | 4.15990 | 0.132411 | ||||||||
\(988\) | 7.48866 | 0.238246 | ||||||||
\(989\) | 31.7723 | 1.01030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.2351 | 0.928685 | 0.464342 | − | 0.885656i | \(-0.346291\pi\) | ||||
0.464342 | + | 0.885656i | \(0.346291\pi\) | |||||||
\(992\) | 21.1477 | 0.671439 | ||||||||
\(993\) | 34.7036 | 1.10129 | ||||||||
\(994\) | −16.9406 | −0.537325 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.81316 | −0.120825 | ||||||||
\(997\) | 6.57182 | 0.208132 | 0.104066 | − | 0.994570i | \(-0.466815\pi\) | ||||
0.104066 | + | 0.994570i | \(0.466815\pi\) | |||||||
\(998\) | −33.0996 | −1.04775 | ||||||||
\(999\) | −1.49075 | −0.0471653 |
(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 | 3525.2.a.bg.1.3 | 10 | ||
5.2 | odd | 4 | 705.2.c.b.424.7 | ✓ | 20 | ||
5.3 | odd | 4 | 705.2.c.b.424.14 | yes | 20 | ||
5.4 | even | 2 | 3525.2.a.bf.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.b.424.7 | ✓ | 20 | 5.2 | odd | 4 | ||
705.2.c.b.424.14 | yes | 20 | 5.3 | odd | 4 | ||
3525.2.a.bf.1.8 | 10 | 5.4 | even | 2 | |||
3525.2.a.bg.1.3 | 10 | 1.1 | even | 1 | trivial |