Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7537.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.37933\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 | ||||||||
\(5\) | 1.09744 | 0.490789 | 0.245395 | − | 0.969423i | \(-0.421082\pi\) | ||||
0.245395 | + | 0.969423i | \(0.421082\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.89307 | 0.715512 | 0.357756 | − | 0.933815i | \(-0.383542\pi\) | ||||
0.357756 | + | 0.933815i | \(0.383542\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.09744 | −0.347040 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.23184 | −0.619001 | −0.309500 | − | 0.950899i | \(-0.600162\pi\) | ||||
−0.309500 | + | 0.950899i | \(0.600162\pi\) | |||||||
\(14\) | −1.89307 | −0.505944 | ||||||||
\(15\) | 1.09744 | 0.283357 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.681143 | −0.165201 | −0.0826007 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826007 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.28190 | −0.294087 | −0.147044 | − | 0.989130i | \(-0.546976\pi\) | ||||
−0.147044 | + | 0.989130i | \(0.546976\pi\) | |||||||
\(20\) | 1.09744 | 0.245395 | ||||||||
\(21\) | 1.89307 | 0.413101 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.26291 | −1.09739 | −0.548696 | − | 0.836022i | \(-0.684876\pi\) | ||||
−0.548696 | + | 0.836022i | \(0.684876\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.79563 | −0.759126 | ||||||||
\(26\) | 2.23184 | 0.437699 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.89307 | 0.357756 | ||||||||
\(29\) | −3.13440 | −0.582043 | −0.291022 | − | 0.956716i | \(-0.593995\pi\) | ||||
−0.291022 | + | 0.956716i | \(0.593995\pi\) | |||||||
\(30\) | −1.09744 | −0.200364 | ||||||||
\(31\) | −7.33288 | −1.31702 | −0.658512 | − | 0.752570i | \(-0.728814\pi\) | ||||
−0.658512 | + | 0.752570i | \(0.728814\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.681143 | 0.116815 | ||||||||
\(35\) | 2.07752 | 0.351166 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.82670 | −1.61550 | −0.807750 | − | 0.589526i | \(-0.799315\pi\) | ||||
−0.807750 | + | 0.589526i | \(0.799315\pi\) | |||||||
\(38\) | 1.28190 | 0.207951 | ||||||||
\(39\) | −2.23184 | −0.357380 | ||||||||
\(40\) | −1.09744 | −0.173520 | ||||||||
\(41\) | 1.24493 | 0.194426 | 0.0972130 | − | 0.995264i | \(-0.469007\pi\) | ||||
0.0972130 | + | 0.995264i | \(0.469007\pi\) | |||||||
\(42\) | −1.89307 | −0.292107 | ||||||||
\(43\) | −9.93363 | −1.51486 | −0.757432 | − | 0.652914i | \(-0.773546\pi\) | ||||
−0.757432 | + | 0.652914i | \(0.773546\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.09744 | 0.163596 | ||||||||
\(46\) | 5.26291 | 0.775973 | ||||||||
\(47\) | 7.93003 | 1.15671 | 0.578357 | − | 0.815784i | \(-0.303694\pi\) | ||||
0.578357 | + | 0.815784i | \(0.303694\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.41630 | −0.488042 | ||||||||
\(50\) | 3.79563 | 0.536783 | ||||||||
\(51\) | −0.681143 | −0.0953791 | ||||||||
\(52\) | −2.23184 | −0.309500 | ||||||||
\(53\) | 1.56472 | 0.214930 | 0.107465 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107465 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.09744 | −0.147979 | ||||||||
\(56\) | −1.89307 | −0.252972 | ||||||||
\(57\) | −1.28190 | −0.169791 | ||||||||
\(58\) | 3.13440 | 0.411567 | ||||||||
\(59\) | −4.96396 | −0.646253 | −0.323126 | − | 0.946356i | \(-0.604734\pi\) | ||||
−0.323126 | + | 0.946356i | \(0.604734\pi\) | |||||||
\(60\) | 1.09744 | 0.141679 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 7.33288 | 0.931276 | ||||||||
\(63\) | 1.89307 | 0.238504 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.44930 | −0.303799 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 0.379334 | 0.0463430 | 0.0231715 | − | 0.999732i | \(-0.492624\pi\) | ||||
0.0231715 | + | 0.999732i | \(0.492624\pi\) | |||||||
\(68\) | −0.681143 | −0.0826007 | ||||||||
\(69\) | −5.26291 | −0.633580 | ||||||||
\(70\) | −2.07752 | −0.248312 | ||||||||
\(71\) | −4.64813 | −0.551632 | −0.275816 | − | 0.961210i | \(-0.588948\pi\) | ||||
−0.275816 | + | 0.961210i | \(0.588948\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −9.94800 | −1.16433 | −0.582163 | − | 0.813072i | \(-0.697793\pi\) | ||||
−0.582163 | + | 0.813072i | \(0.697793\pi\) | |||||||
\(74\) | 9.82670 | 1.14233 | ||||||||
\(75\) | −3.79563 | −0.438282 | ||||||||
\(76\) | −1.28190 | −0.147044 | ||||||||
\(77\) | −1.89307 | −0.215735 | ||||||||
\(78\) | 2.23184 | 0.252706 | ||||||||
\(79\) | −2.17690 | −0.244921 | −0.122460 | − | 0.992473i | \(-0.539078\pi\) | ||||
−0.122460 | + | 0.992473i | \(0.539078\pi\) | |||||||
\(80\) | 1.09744 | 0.122697 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.24493 | −0.137480 | ||||||||
\(83\) | −0.375732 | −0.0412420 | −0.0206210 | − | 0.999787i | \(-0.506564\pi\) | ||||
−0.0206210 | + | 0.999787i | \(0.506564\pi\) | |||||||
\(84\) | 1.89307 | 0.206551 | ||||||||
\(85\) | −0.747512 | −0.0810791 | ||||||||
\(86\) | 9.93363 | 1.07117 | ||||||||
\(87\) | −3.13440 | −0.336043 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 12.4009 | 1.31449 | 0.657247 | − | 0.753675i | \(-0.271721\pi\) | ||||
0.657247 | + | 0.753675i | \(0.271721\pi\) | |||||||
\(90\) | −1.09744 | −0.115680 | ||||||||
\(91\) | −4.22502 | −0.442902 | ||||||||
\(92\) | −5.26291 | −0.548696 | ||||||||
\(93\) | −7.33288 | −0.760384 | ||||||||
\(94\) | −7.93003 | −0.817920 | ||||||||
\(95\) | −1.40680 | −0.144335 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.48793 | 0.354145 | 0.177073 | − | 0.984198i | \(-0.443337\pi\) | ||||
0.177073 | + | 0.984198i | \(0.443337\pi\) | |||||||
\(98\) | 3.41630 | 0.345098 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −3.79563 | −0.379563 | ||||||||
\(101\) | −11.0045 | −1.09499 | −0.547496 | − | 0.836809i | \(-0.684419\pi\) | ||||
−0.547496 | + | 0.836809i | \(0.684419\pi\) | |||||||
\(102\) | 0.681143 | 0.0674432 | ||||||||
\(103\) | 16.9457 | 1.66971 | 0.834855 | − | 0.550470i | \(-0.185551\pi\) | ||||
0.834855 | + | 0.550470i | \(0.185551\pi\) | |||||||
\(104\) | 2.23184 | 0.218850 | ||||||||
\(105\) | 2.07752 | 0.202746 | ||||||||
\(106\) | −1.56472 | −0.151979 | ||||||||
\(107\) | −3.69424 | −0.357136 | −0.178568 | − | 0.983928i | \(-0.557146\pi\) | ||||
−0.178568 | + | 0.983928i | \(0.557146\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −0.250827 | −0.0240248 | −0.0120124 | − | 0.999928i | \(-0.503824\pi\) | ||||
−0.0120124 | + | 0.999928i | \(0.503824\pi\) | |||||||
\(110\) | 1.09744 | 0.104637 | ||||||||
\(111\) | −9.82670 | −0.932709 | ||||||||
\(112\) | 1.89307 | 0.178878 | ||||||||
\(113\) | 3.17496 | 0.298675 | 0.149338 | − | 0.988786i | \(-0.452286\pi\) | ||||
0.149338 | + | 0.988786i | \(0.452286\pi\) | |||||||
\(114\) | 1.28190 | 0.120061 | ||||||||
\(115\) | −5.77572 | −0.538588 | ||||||||
\(116\) | −3.13440 | −0.291022 | ||||||||
\(117\) | −2.23184 | −0.206334 | ||||||||
\(118\) | 4.96396 | 0.456970 | ||||||||
\(119\) | −1.28945 | −0.118204 | ||||||||
\(120\) | −1.09744 | −0.100182 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 1.24493 | 0.112252 | ||||||||
\(124\) | −7.33288 | −0.658512 | ||||||||
\(125\) | −9.65266 | −0.863360 | ||||||||
\(126\) | −1.89307 | −0.168648 | ||||||||
\(127\) | −15.3189 | −1.35933 | −0.679664 | − | 0.733523i | \(-0.737875\pi\) | ||||
−0.679664 | + | 0.733523i | \(0.737875\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.93363 | −0.874607 | ||||||||
\(130\) | 2.44930 | 0.214818 | ||||||||
\(131\) | 3.97346 | 0.347163 | 0.173581 | − | 0.984820i | \(-0.444466\pi\) | ||||
0.173581 | + | 0.984820i | \(0.444466\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −2.42671 | −0.210423 | ||||||||
\(134\) | −0.379334 | −0.0327694 | ||||||||
\(135\) | 1.09744 | 0.0944524 | ||||||||
\(136\) | 0.681143 | 0.0584075 | ||||||||
\(137\) | 20.7171 | 1.76998 | 0.884990 | − | 0.465610i | \(-0.154165\pi\) | ||||
0.884990 | + | 0.465610i | \(0.154165\pi\) | |||||||
\(138\) | 5.26291 | 0.448008 | ||||||||
\(139\) | −8.52683 | −0.723236 | −0.361618 | − | 0.932326i | \(-0.617776\pi\) | ||||
−0.361618 | + | 0.932326i | \(0.617776\pi\) | |||||||
\(140\) | 2.07752 | 0.175583 | ||||||||
\(141\) | 7.93003 | 0.667829 | ||||||||
\(142\) | 4.64813 | 0.390063 | ||||||||
\(143\) | 2.23184 | 0.186636 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.43981 | −0.285661 | ||||||||
\(146\) | 9.94800 | 0.823303 | ||||||||
\(147\) | −3.41630 | −0.281771 | ||||||||
\(148\) | −9.82670 | −0.807750 | ||||||||
\(149\) | −9.78974 | −0.802006 | −0.401003 | − | 0.916077i | \(-0.631338\pi\) | ||||
−0.401003 | + | 0.916077i | \(0.631338\pi\) | |||||||
\(150\) | 3.79563 | 0.309912 | ||||||||
\(151\) | 22.1720 | 1.80433 | 0.902166 | − | 0.431389i | \(-0.141976\pi\) | ||||
0.902166 | + | 0.431389i | \(0.141976\pi\) | |||||||
\(152\) | 1.28190 | 0.103975 | ||||||||
\(153\) | −0.681143 | −0.0550671 | ||||||||
\(154\) | 1.89307 | 0.152548 | ||||||||
\(155\) | −8.04738 | −0.646381 | ||||||||
\(156\) | −2.23184 | −0.178690 | ||||||||
\(157\) | 15.6053 | 1.24544 | 0.622718 | − | 0.782446i | \(-0.286028\pi\) | ||||
0.622718 | + | 0.782446i | \(0.286028\pi\) | |||||||
\(158\) | 2.17690 | 0.173185 | ||||||||
\(159\) | 1.56472 | 0.124090 | ||||||||
\(160\) | −1.09744 | −0.0867601 | ||||||||
\(161\) | −9.96304 | −0.785197 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 11.8002 | 0.924260 | 0.462130 | − | 0.886812i | \(-0.347085\pi\) | ||||
0.462130 | + | 0.886812i | \(0.347085\pi\) | |||||||
\(164\) | 1.24493 | 0.0972130 | ||||||||
\(165\) | −1.09744 | −0.0854355 | ||||||||
\(166\) | 0.375732 | 0.0291625 | ||||||||
\(167\) | 4.59218 | 0.355354 | 0.177677 | − | 0.984089i | \(-0.443142\pi\) | ||||
0.177677 | + | 0.984089i | \(0.443142\pi\) | |||||||
\(168\) | −1.89307 | −0.146053 | ||||||||
\(169\) | −8.01890 | −0.616838 | ||||||||
\(170\) | 0.747512 | 0.0573316 | ||||||||
\(171\) | −1.28190 | −0.0980290 | ||||||||
\(172\) | −9.93363 | −0.757432 | ||||||||
\(173\) | 8.67257 | 0.659364 | 0.329682 | − | 0.944092i | \(-0.393059\pi\) | ||||
0.329682 | + | 0.944092i | \(0.393059\pi\) | |||||||
\(174\) | 3.13440 | 0.237618 | ||||||||
\(175\) | −7.18538 | −0.543164 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −4.96396 | −0.373114 | ||||||||
\(178\) | −12.4009 | −0.929487 | ||||||||
\(179\) | 4.70954 | 0.352007 | 0.176004 | − | 0.984390i | \(-0.443683\pi\) | ||||
0.176004 | + | 0.984390i | \(0.443683\pi\) | |||||||
\(180\) | 1.09744 | 0.0817982 | ||||||||
\(181\) | 25.0480 | 1.86181 | 0.930903 | − | 0.365268i | \(-0.119022\pi\) | ||||
0.930903 | + | 0.365268i | \(0.119022\pi\) | |||||||
\(182\) | 4.22502 | 0.313179 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 5.26291 | 0.387987 | ||||||||
\(185\) | −10.7842 | −0.792870 | ||||||||
\(186\) | 7.33288 | 0.537673 | ||||||||
\(187\) | 0.681143 | 0.0498101 | ||||||||
\(188\) | 7.93003 | 0.578357 | ||||||||
\(189\) | 1.89307 | 0.137700 | ||||||||
\(190\) | 1.40680 | 0.102060 | ||||||||
\(191\) | 11.1194 | 0.804569 | 0.402284 | − | 0.915515i | \(-0.368216\pi\) | ||||
0.402284 | + | 0.915515i | \(0.368216\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −22.9582 | −1.65257 | −0.826285 | − | 0.563252i | \(-0.809550\pi\) | ||||
−0.826285 | + | 0.563252i | \(0.809550\pi\) | |||||||
\(194\) | −3.48793 | −0.250419 | ||||||||
\(195\) | −2.44930 | −0.175398 | ||||||||
\(196\) | −3.41630 | −0.244021 | ||||||||
\(197\) | 22.7688 | 1.62221 | 0.811105 | − | 0.584900i | \(-0.198866\pi\) | ||||
0.811105 | + | 0.584900i | \(0.198866\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 23.2106 | 1.64535 | 0.822676 | − | 0.568510i | \(-0.192480\pi\) | ||||
0.822676 | + | 0.568510i | \(0.192480\pi\) | |||||||
\(200\) | 3.79563 | 0.268392 | ||||||||
\(201\) | 0.379334 | 0.0267561 | ||||||||
\(202\) | 11.0045 | 0.774276 | ||||||||
\(203\) | −5.93363 | −0.416459 | ||||||||
\(204\) | −0.681143 | −0.0476895 | ||||||||
\(205\) | 1.36624 | 0.0954222 | ||||||||
\(206\) | −16.9457 | −1.18066 | ||||||||
\(207\) | −5.26291 | −0.365797 | ||||||||
\(208\) | −2.23184 | −0.154750 | ||||||||
\(209\) | 1.28190 | 0.0886706 | ||||||||
\(210\) | −2.07752 | −0.143363 | ||||||||
\(211\) | −20.7135 | −1.42598 | −0.712988 | − | 0.701177i | \(-0.752658\pi\) | ||||
−0.712988 | + | 0.701177i | \(0.752658\pi\) | |||||||
\(212\) | 1.56472 | 0.107465 | ||||||||
\(213\) | −4.64813 | −0.318485 | ||||||||
\(214\) | 3.69424 | 0.252533 | ||||||||
\(215\) | −10.9015 | −0.743479 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −13.8816 | −0.942347 | ||||||||
\(218\) | 0.250827 | 0.0169881 | ||||||||
\(219\) | −9.94800 | −0.672224 | ||||||||
\(220\) | −1.09744 | −0.0739893 | ||||||||
\(221\) | 1.52020 | 0.102260 | ||||||||
\(222\) | 9.82670 | 0.659525 | ||||||||
\(223\) | −18.7681 | −1.25680 | −0.628402 | − | 0.777889i | \(-0.716290\pi\) | ||||
−0.628402 | + | 0.777889i | \(0.716290\pi\) | |||||||
\(224\) | −1.89307 | −0.126486 | ||||||||
\(225\) | −3.79563 | −0.253042 | ||||||||
\(226\) | −3.17496 | −0.211195 | ||||||||
\(227\) | −9.21553 | −0.611656 | −0.305828 | − | 0.952087i | \(-0.598933\pi\) | ||||
−0.305828 | + | 0.952087i | \(0.598933\pi\) | |||||||
\(228\) | −1.28190 | −0.0848956 | ||||||||
\(229\) | −20.5664 | −1.35906 | −0.679532 | − | 0.733646i | \(-0.737817\pi\) | ||||
−0.679532 | + | 0.733646i | \(0.737817\pi\) | |||||||
\(230\) | 5.77572 | 0.380839 | ||||||||
\(231\) | −1.89307 | −0.124555 | ||||||||
\(232\) | 3.13440 | 0.205783 | ||||||||
\(233\) | 22.7946 | 1.49332 | 0.746662 | − | 0.665203i | \(-0.231655\pi\) | ||||
0.746662 | + | 0.665203i | \(0.231655\pi\) | |||||||
\(234\) | 2.23184 | 0.145900 | ||||||||
\(235\) | 8.70272 | 0.567703 | ||||||||
\(236\) | −4.96396 | −0.323126 | ||||||||
\(237\) | −2.17690 | −0.141405 | ||||||||
\(238\) | 1.28945 | 0.0835826 | ||||||||
\(239\) | −16.3629 | −1.05843 | −0.529215 | − | 0.848488i | \(-0.677514\pi\) | ||||
−0.529215 | + | 0.848488i | \(0.677514\pi\) | |||||||
\(240\) | 1.09744 | 0.0708393 | ||||||||
\(241\) | 19.8816 | 1.28069 | 0.640344 | − | 0.768088i | \(-0.278792\pi\) | ||||
0.640344 | + | 0.768088i | \(0.278792\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −3.74917 | −0.239526 | ||||||||
\(246\) | −1.24493 | −0.0793741 | ||||||||
\(247\) | 2.86098 | 0.182040 | ||||||||
\(248\) | 7.33288 | 0.465638 | ||||||||
\(249\) | −0.375732 | −0.0238111 | ||||||||
\(250\) | 9.65266 | 0.610488 | ||||||||
\(251\) | 27.2397 | 1.71935 | 0.859677 | − | 0.510838i | \(-0.170665\pi\) | ||||
0.859677 | + | 0.510838i | \(0.170665\pi\) | |||||||
\(252\) | 1.89307 | 0.119252 | ||||||||
\(253\) | 5.26291 | 0.330876 | ||||||||
\(254\) | 15.3189 | 0.961191 | ||||||||
\(255\) | −0.747512 | −0.0468110 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.4500 | −0.714228 | −0.357114 | − | 0.934061i | \(-0.616239\pi\) | ||||
−0.357114 | + | 0.934061i | \(0.616239\pi\) | |||||||
\(258\) | 9.93363 | 0.618441 | ||||||||
\(259\) | −18.6026 | −1.15591 | ||||||||
\(260\) | −2.44930 | −0.151899 | ||||||||
\(261\) | −3.13440 | −0.194014 | ||||||||
\(262\) | −3.97346 | −0.245481 | ||||||||
\(263\) | −3.56545 | −0.219855 | −0.109928 | − | 0.993940i | \(-0.535062\pi\) | ||||
−0.109928 | + | 0.993940i | \(0.535062\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 1.71718 | 0.105485 | ||||||||
\(266\) | 2.42671 | 0.148791 | ||||||||
\(267\) | 12.4009 | 0.758923 | ||||||||
\(268\) | 0.379334 | 0.0231715 | ||||||||
\(269\) | −1.21874 | −0.0743080 | −0.0371540 | − | 0.999310i | \(-0.511829\pi\) | ||||
−0.0371540 | + | 0.999310i | \(0.511829\pi\) | |||||||
\(270\) | −1.09744 | −0.0667880 | ||||||||
\(271\) | −12.5513 | −0.762435 | −0.381218 | − | 0.924485i | \(-0.624495\pi\) | ||||
−0.381218 | + | 0.924485i | \(0.624495\pi\) | |||||||
\(272\) | −0.681143 | −0.0413004 | ||||||||
\(273\) | −4.22502 | −0.255710 | ||||||||
\(274\) | −20.7171 | −1.25157 | ||||||||
\(275\) | 3.79563 | 0.228885 | ||||||||
\(276\) | −5.26291 | −0.316790 | ||||||||
\(277\) | −15.9781 | −0.960034 | −0.480017 | − | 0.877259i | \(-0.659369\pi\) | ||||
−0.480017 | + | 0.877259i | \(0.659369\pi\) | |||||||
\(278\) | 8.52683 | 0.511405 | ||||||||
\(279\) | −7.33288 | −0.439008 | ||||||||
\(280\) | −2.07752 | −0.124156 | ||||||||
\(281\) | −21.3516 | −1.27373 | −0.636864 | − | 0.770976i | \(-0.719769\pi\) | ||||
−0.636864 | + | 0.770976i | \(0.719769\pi\) | |||||||
\(282\) | −7.93003 | −0.472226 | ||||||||
\(283\) | 10.1285 | 0.602077 | 0.301039 | − | 0.953612i | \(-0.402667\pi\) | ||||
0.301039 | + | 0.953612i | \(0.402667\pi\) | |||||||
\(284\) | −4.64813 | −0.275816 | ||||||||
\(285\) | −1.40680 | −0.0833317 | ||||||||
\(286\) | −2.23184 | −0.131971 | ||||||||
\(287\) | 2.35674 | 0.139114 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.5360 | −0.972708 | ||||||||
\(290\) | 3.43981 | 0.201993 | ||||||||
\(291\) | 3.48793 | 0.204466 | ||||||||
\(292\) | −9.94800 | −0.582163 | ||||||||
\(293\) | 14.3894 | 0.840638 | 0.420319 | − | 0.907376i | \(-0.361918\pi\) | ||||
0.420319 | + | 0.907376i | \(0.361918\pi\) | |||||||
\(294\) | 3.41630 | 0.199242 | ||||||||
\(295\) | −5.44764 | −0.317174 | ||||||||
\(296\) | 9.82670 | 0.571165 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 9.78974 | 0.567104 | ||||||||
\(299\) | 11.7460 | 0.679286 | ||||||||
\(300\) | −3.79563 | −0.219141 | ||||||||
\(301\) | −18.8050 | −1.08390 | ||||||||
\(302\) | −22.1720 | −1.27586 | ||||||||
\(303\) | −11.0045 | −0.632194 | ||||||||
\(304\) | −1.28190 | −0.0735218 | ||||||||
\(305\) | 1.09744 | 0.0628391 | ||||||||
\(306\) | 0.681143 | 0.0389383 | ||||||||
\(307\) | −6.97900 | −0.398313 | −0.199156 | − | 0.979968i | \(-0.563820\pi\) | ||||
−0.199156 | + | 0.979968i | \(0.563820\pi\) | |||||||
\(308\) | −1.89307 | −0.107868 | ||||||||
\(309\) | 16.9457 | 0.964008 | ||||||||
\(310\) | 8.04738 | 0.457061 | ||||||||
\(311\) | 32.4526 | 1.84022 | 0.920110 | − | 0.391660i | \(-0.128099\pi\) | ||||
0.920110 | + | 0.391660i | \(0.128099\pi\) | |||||||
\(312\) | 2.23184 | 0.126353 | ||||||||
\(313\) | −1.57689 | −0.0891309 | −0.0445655 | − | 0.999006i | \(-0.514190\pi\) | ||||
−0.0445655 | + | 0.999006i | \(0.514190\pi\) | |||||||
\(314\) | −15.6053 | −0.880657 | ||||||||
\(315\) | 2.07752 | 0.117055 | ||||||||
\(316\) | −2.17690 | −0.122460 | ||||||||
\(317\) | −0.766221 | −0.0430353 | −0.0215176 | − | 0.999768i | \(-0.506850\pi\) | ||||
−0.0215176 | + | 0.999768i | \(0.506850\pi\) | |||||||
\(318\) | −1.56472 | −0.0877449 | ||||||||
\(319\) | 3.13440 | 0.175493 | ||||||||
\(320\) | 1.09744 | 0.0613487 | ||||||||
\(321\) | −3.69424 | −0.206192 | ||||||||
\(322\) | 9.96304 | 0.555218 | ||||||||
\(323\) | 0.873154 | 0.0485836 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 8.47123 | 0.469899 | ||||||||
\(326\) | −11.8002 | −0.653550 | ||||||||
\(327\) | −0.250827 | −0.0138707 | ||||||||
\(328\) | −1.24493 | −0.0687400 | ||||||||
\(329\) | 15.0121 | 0.827643 | ||||||||
\(330\) | 1.09744 | 0.0604120 | ||||||||
\(331\) | −5.64686 | −0.310379 | −0.155190 | − | 0.987885i | \(-0.549599\pi\) | ||||
−0.155190 | + | 0.987885i | \(0.549599\pi\) | |||||||
\(332\) | −0.375732 | −0.0206210 | ||||||||
\(333\) | −9.82670 | −0.538500 | ||||||||
\(334\) | −4.59218 | −0.251273 | ||||||||
\(335\) | 0.416295 | 0.0227446 | ||||||||
\(336\) | 1.89307 | 0.103275 | ||||||||
\(337\) | 17.9620 | 0.978454 | 0.489227 | − | 0.872157i | \(-0.337279\pi\) | ||||
0.489227 | + | 0.872157i | \(0.337279\pi\) | |||||||
\(338\) | 8.01890 | 0.436171 | ||||||||
\(339\) | 3.17496 | 0.172440 | ||||||||
\(340\) | −0.747512 | −0.0405395 | ||||||||
\(341\) | 7.33288 | 0.397098 | ||||||||
\(342\) | 1.28190 | 0.0693170 | ||||||||
\(343\) | −19.7188 | −1.06471 | ||||||||
\(344\) | 9.93363 | 0.535585 | ||||||||
\(345\) | −5.77572 | −0.310954 | ||||||||
\(346\) | −8.67257 | −0.466240 | ||||||||
\(347\) | 12.4217 | 0.666834 | 0.333417 | − | 0.942779i | \(-0.391798\pi\) | ||||
0.333417 | + | 0.942779i | \(0.391798\pi\) | |||||||
\(348\) | −3.13440 | −0.168021 | ||||||||
\(349\) | −13.9412 | −0.746254 | −0.373127 | − | 0.927780i | \(-0.621715\pi\) | ||||
−0.373127 | + | 0.927780i | \(0.621715\pi\) | |||||||
\(350\) | 7.18538 | 0.384075 | ||||||||
\(351\) | −2.23184 | −0.119127 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 22.6367 | 1.20483 | 0.602415 | − | 0.798183i | \(-0.294205\pi\) | ||||
0.602415 | + | 0.798183i | \(0.294205\pi\) | |||||||
\(354\) | 4.96396 | 0.263832 | ||||||||
\(355\) | −5.10104 | −0.270735 | ||||||||
\(356\) | 12.4009 | 0.657247 | ||||||||
\(357\) | −1.28945 | −0.0682449 | ||||||||
\(358\) | −4.70954 | −0.248907 | ||||||||
\(359\) | −30.6791 | −1.61918 | −0.809591 | − | 0.586995i | \(-0.800311\pi\) | ||||
−0.809591 | + | 0.586995i | \(0.800311\pi\) | |||||||
\(360\) | −1.09744 | −0.0578401 | ||||||||
\(361\) | −17.3567 | −0.913513 | ||||||||
\(362\) | −25.0480 | −1.31650 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −4.22502 | −0.221451 | ||||||||
\(365\) | −10.9173 | −0.571439 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | 3.41177 | 0.178093 | 0.0890464 | − | 0.996027i | \(-0.471618\pi\) | ||||
0.0890464 | + | 0.996027i | \(0.471618\pi\) | |||||||
\(368\) | −5.26291 | −0.274348 | ||||||||
\(369\) | 1.24493 | 0.0648087 | ||||||||
\(370\) | 10.7842 | 0.560644 | ||||||||
\(371\) | 2.96211 | 0.153785 | ||||||||
\(372\) | −7.33288 | −0.380192 | ||||||||
\(373\) | −36.5324 | −1.89157 | −0.945787 | − | 0.324788i | \(-0.894707\pi\) | ||||
−0.945787 | + | 0.324788i | \(0.894707\pi\) | |||||||
\(374\) | −0.681143 | −0.0352211 | ||||||||
\(375\) | −9.65266 | −0.498461 | ||||||||
\(376\) | −7.93003 | −0.408960 | ||||||||
\(377\) | 6.99547 | 0.360285 | ||||||||
\(378\) | −1.89307 | −0.0973689 | ||||||||
\(379\) | 12.3952 | 0.636699 | 0.318349 | − | 0.947973i | \(-0.396871\pi\) | ||||
0.318349 | + | 0.947973i | \(0.396871\pi\) | |||||||
\(380\) | −1.40680 | −0.0721674 | ||||||||
\(381\) | −15.3189 | −0.784809 | ||||||||
\(382\) | −11.1194 | −0.568916 | ||||||||
\(383\) | −26.4615 | −1.35212 | −0.676061 | − | 0.736846i | \(-0.736314\pi\) | ||||
−0.676061 | + | 0.736846i | \(0.736314\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.07752 | −0.105880 | ||||||||
\(386\) | 22.9582 | 1.16854 | ||||||||
\(387\) | −9.93363 | −0.504955 | ||||||||
\(388\) | 3.48793 | 0.177073 | ||||||||
\(389\) | 14.4379 | 0.732029 | 0.366015 | − | 0.930609i | \(-0.380722\pi\) | ||||
0.366015 | + | 0.930609i | \(0.380722\pi\) | |||||||
\(390\) | 2.44930 | 0.124025 | ||||||||
\(391\) | 3.58479 | 0.181291 | ||||||||
\(392\) | 3.41630 | 0.172549 | ||||||||
\(393\) | 3.97346 | 0.200434 | ||||||||
\(394\) | −22.7688 | −1.14708 | ||||||||
\(395\) | −2.38902 | −0.120204 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 23.9308 | 1.20105 | 0.600525 | − | 0.799606i | \(-0.294958\pi\) | ||||
0.600525 | + | 0.799606i | \(0.294958\pi\) | |||||||
\(398\) | −23.2106 | −1.16344 | ||||||||
\(399\) | −2.42671 | −0.121488 | ||||||||
\(400\) | −3.79563 | −0.189781 | ||||||||
\(401\) | 16.3381 | 0.815888 | 0.407944 | − | 0.913007i | \(-0.366246\pi\) | ||||
0.407944 | + | 0.913007i | \(0.366246\pi\) | |||||||
\(402\) | −0.379334 | −0.0189195 | ||||||||
\(403\) | 16.3658 | 0.815238 | ||||||||
\(404\) | −11.0045 | −0.547496 | ||||||||
\(405\) | 1.09744 | 0.0545321 | ||||||||
\(406\) | 5.93363 | 0.294481 | ||||||||
\(407\) | 9.82670 | 0.487091 | ||||||||
\(408\) | 0.681143 | 0.0337216 | ||||||||
\(409\) | 7.87768 | 0.389526 | 0.194763 | − | 0.980850i | \(-0.437606\pi\) | ||||
0.194763 | + | 0.980850i | \(0.437606\pi\) | |||||||
\(410\) | −1.36624 | −0.0674737 | ||||||||
\(411\) | 20.7171 | 1.02190 | ||||||||
\(412\) | 16.9457 | 0.834855 | ||||||||
\(413\) | −9.39712 | −0.462402 | ||||||||
\(414\) | 5.26291 | 0.258658 | ||||||||
\(415\) | −0.412343 | −0.0202411 | ||||||||
\(416\) | 2.23184 | 0.109425 | ||||||||
\(417\) | −8.52683 | −0.417561 | ||||||||
\(418\) | −1.28190 | −0.0626996 | ||||||||
\(419\) | −28.4228 | −1.38855 | −0.694273 | − | 0.719712i | \(-0.744274\pi\) | ||||
−0.694273 | + | 0.719712i | \(0.744274\pi\) | |||||||
\(420\) | 2.07752 | 0.101373 | ||||||||
\(421\) | −11.7474 | −0.572534 | −0.286267 | − | 0.958150i | \(-0.592414\pi\) | ||||
−0.286267 | + | 0.958150i | \(0.592414\pi\) | |||||||
\(422\) | 20.7135 | 1.00832 | ||||||||
\(423\) | 7.93003 | 0.385571 | ||||||||
\(424\) | −1.56472 | −0.0759893 | ||||||||
\(425\) | 2.58537 | 0.125409 | ||||||||
\(426\) | 4.64813 | 0.225203 | ||||||||
\(427\) | 1.89307 | 0.0916120 | ||||||||
\(428\) | −3.69424 | −0.178568 | ||||||||
\(429\) | 2.23184 | 0.107754 | ||||||||
\(430\) | 10.9015 | 0.525719 | ||||||||
\(431\) | −12.9291 | −0.622773 | −0.311387 | − | 0.950283i | \(-0.600793\pi\) | ||||
−0.311387 | + | 0.950283i | \(0.600793\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 3.25284 | 0.156321 | 0.0781607 | − | 0.996941i | \(-0.475095\pi\) | ||||
0.0781607 | + | 0.996941i | \(0.475095\pi\) | |||||||
\(434\) | 13.8816 | 0.666340 | ||||||||
\(435\) | −3.43981 | −0.164926 | ||||||||
\(436\) | −0.250827 | −0.0120124 | ||||||||
\(437\) | 6.74650 | 0.322729 | ||||||||
\(438\) | 9.94800 | 0.475334 | ||||||||
\(439\) | −7.77001 | −0.370842 | −0.185421 | − | 0.982659i | \(-0.559365\pi\) | ||||
−0.185421 | + | 0.982659i | \(0.559365\pi\) | |||||||
\(440\) | 1.09744 | 0.0523183 | ||||||||
\(441\) | −3.41630 | −0.162681 | ||||||||
\(442\) | −1.52020 | −0.0723086 | ||||||||
\(443\) | −39.2243 | −1.86360 | −0.931801 | − | 0.362969i | \(-0.881763\pi\) | ||||
−0.931801 | + | 0.362969i | \(0.881763\pi\) | |||||||
\(444\) | −9.82670 | −0.466354 | ||||||||
\(445\) | 13.6092 | 0.645139 | ||||||||
\(446\) | 18.7681 | 0.888694 | ||||||||
\(447\) | −9.78974 | −0.463039 | ||||||||
\(448\) | 1.89307 | 0.0894390 | ||||||||
\(449\) | −40.2154 | −1.89788 | −0.948942 | − | 0.315451i | \(-0.897844\pi\) | ||||
−0.948942 | + | 0.315451i | \(0.897844\pi\) | |||||||
\(450\) | 3.79563 | 0.178928 | ||||||||
\(451\) | −1.24493 | −0.0586216 | ||||||||
\(452\) | 3.17496 | 0.149338 | ||||||||
\(453\) | 22.1720 | 1.04173 | ||||||||
\(454\) | 9.21553 | 0.432506 | ||||||||
\(455\) | −4.63670 | −0.217372 | ||||||||
\(456\) | 1.28190 | 0.0600303 | ||||||||
\(457\) | 10.3675 | 0.484973 | 0.242487 | − | 0.970155i | \(-0.422037\pi\) | ||||
0.242487 | + | 0.970155i | \(0.422037\pi\) | |||||||
\(458\) | 20.5664 | 0.961004 | ||||||||
\(459\) | −0.681143 | −0.0317930 | ||||||||
\(460\) | −5.77572 | −0.269294 | ||||||||
\(461\) | −27.0570 | −1.26017 | −0.630085 | − | 0.776526i | \(-0.716980\pi\) | ||||
−0.630085 | + | 0.776526i | \(0.716980\pi\) | |||||||
\(462\) | 1.89307 | 0.0880735 | ||||||||
\(463\) | 9.07954 | 0.421962 | 0.210981 | − | 0.977490i | \(-0.432334\pi\) | ||||
0.210981 | + | 0.977490i | \(0.432334\pi\) | |||||||
\(464\) | −3.13440 | −0.145511 | ||||||||
\(465\) | −8.04738 | −0.373188 | ||||||||
\(466\) | −22.7946 | −1.05594 | ||||||||
\(467\) | −36.2732 | −1.67853 | −0.839263 | − | 0.543726i | \(-0.817013\pi\) | ||||
−0.839263 | + | 0.543726i | \(0.817013\pi\) | |||||||
\(468\) | −2.23184 | −0.103167 | ||||||||
\(469\) | 0.718104 | 0.0331590 | ||||||||
\(470\) | −8.70272 | −0.401426 | ||||||||
\(471\) | 15.6053 | 0.719053 | ||||||||
\(472\) | 4.96396 | 0.228485 | ||||||||
\(473\) | 9.93363 | 0.456749 | ||||||||
\(474\) | 2.17690 | 0.0999885 | ||||||||
\(475\) | 4.86560 | 0.223249 | ||||||||
\(476\) | −1.28945 | −0.0591018 | ||||||||
\(477\) | 1.56472 | 0.0716434 | ||||||||
\(478\) | 16.3629 | 0.748423 | ||||||||
\(479\) | 31.2522 | 1.42795 | 0.713975 | − | 0.700171i | \(-0.246893\pi\) | ||||
0.713975 | + | 0.700171i | \(0.246893\pi\) | |||||||
\(480\) | −1.09744 | −0.0500910 | ||||||||
\(481\) | 21.9316 | 0.999995 | ||||||||
\(482\) | −19.8816 | −0.905584 | ||||||||
\(483\) | −9.96304 | −0.453334 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 3.82779 | 0.173811 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −39.5203 | −1.79083 | −0.895417 | − | 0.445228i | \(-0.853123\pi\) | ||||
−0.895417 | + | 0.445228i | \(0.853123\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 11.8002 | 0.533621 | ||||||||
\(490\) | 3.74917 | 0.169370 | ||||||||
\(491\) | 16.6941 | 0.753396 | 0.376698 | − | 0.926336i | \(-0.377059\pi\) | ||||
0.376698 | + | 0.926336i | \(0.377059\pi\) | |||||||
\(492\) | 1.24493 | 0.0561260 | ||||||||
\(493\) | 2.13497 | 0.0961544 | ||||||||
\(494\) | −2.86098 | −0.128722 | ||||||||
\(495\) | −1.09744 | −0.0493262 | ||||||||
\(496\) | −7.33288 | −0.329256 | ||||||||
\(497\) | −8.79923 | −0.394699 | ||||||||
\(498\) | 0.375732 | 0.0168370 | ||||||||
\(499\) | 27.9042 | 1.24916 | 0.624582 | − | 0.780959i | \(-0.285269\pi\) | ||||
0.624582 | + | 0.780959i | \(0.285269\pi\) | |||||||
\(500\) | −9.65266 | −0.431680 | ||||||||
\(501\) | 4.59218 | 0.205164 | ||||||||
\(502\) | −27.2397 | −1.21577 | ||||||||
\(503\) | 5.58269 | 0.248920 | 0.124460 | − | 0.992225i | \(-0.460280\pi\) | ||||
0.124460 | + | 0.992225i | \(0.460280\pi\) | |||||||
\(504\) | −1.89307 | −0.0843239 | ||||||||
\(505\) | −12.0768 | −0.537410 | ||||||||
\(506\) | −5.26291 | −0.233965 | ||||||||
\(507\) | −8.01890 | −0.356132 | ||||||||
\(508\) | −15.3189 | −0.679664 | ||||||||
\(509\) | 37.1870 | 1.64828 | 0.824141 | − | 0.566384i | \(-0.191658\pi\) | ||||
0.824141 | + | 0.566384i | \(0.191658\pi\) | |||||||
\(510\) | 0.747512 | 0.0331004 | ||||||||
\(511\) | −18.8322 | −0.833089 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.28190 | −0.0565971 | ||||||||
\(514\) | 11.4500 | 0.505036 | ||||||||
\(515\) | 18.5969 | 0.819476 | ||||||||
\(516\) | −9.93363 | −0.437304 | ||||||||
\(517\) | −7.93003 | −0.348762 | ||||||||
\(518\) | 18.6026 | 0.817351 | ||||||||
\(519\) | 8.67257 | 0.380684 | ||||||||
\(520\) | 2.44930 | 0.107409 | ||||||||
\(521\) | −42.4810 | −1.86113 | −0.930564 | − | 0.366130i | \(-0.880682\pi\) | ||||
−0.930564 | + | 0.366130i | \(0.880682\pi\) | |||||||
\(522\) | 3.13440 | 0.137189 | ||||||||
\(523\) | 4.96900 | 0.217279 | 0.108640 | − | 0.994081i | \(-0.465351\pi\) | ||||
0.108640 | + | 0.994081i | \(0.465351\pi\) | |||||||
\(524\) | 3.97346 | 0.173581 | ||||||||
\(525\) | −7.18538 | −0.313596 | ||||||||
\(526\) | 3.56545 | 0.155461 | ||||||||
\(527\) | 4.99474 | 0.217574 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 4.69819 | 0.204269 | ||||||||
\(530\) | −1.71718 | −0.0745895 | ||||||||
\(531\) | −4.96396 | −0.215418 | ||||||||
\(532\) | −2.42671 | −0.105211 | ||||||||
\(533\) | −2.77849 | −0.120350 | ||||||||
\(534\) | −12.4009 | −0.536640 | ||||||||
\(535\) | −4.05420 | −0.175278 | ||||||||
\(536\) | −0.379334 | −0.0163847 | ||||||||
\(537\) | 4.70954 | 0.203231 | ||||||||
\(538\) | 1.21874 | 0.0525437 | ||||||||
\(539\) | 3.41630 | 0.147150 | ||||||||
\(540\) | 1.09744 | 0.0472262 | ||||||||
\(541\) | −24.3973 | −1.04892 | −0.524461 | − | 0.851434i | \(-0.675733\pi\) | ||||
−0.524461 | + | 0.851434i | \(0.675733\pi\) | |||||||
\(542\) | 12.5513 | 0.539123 | ||||||||
\(543\) | 25.0480 | 1.07491 | ||||||||
\(544\) | 0.681143 | 0.0292038 | ||||||||
\(545\) | −0.275267 | −0.0117911 | ||||||||
\(546\) | 4.22502 | 0.180814 | ||||||||
\(547\) | −42.1161 | −1.80075 | −0.900376 | − | 0.435112i | \(-0.856709\pi\) | ||||
−0.900376 | + | 0.435112i | \(0.856709\pi\) | |||||||
\(548\) | 20.7171 | 0.884990 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −3.79563 | −0.161846 | ||||||||
\(551\) | 4.01797 | 0.171171 | ||||||||
\(552\) | 5.26291 | 0.224004 | ||||||||
\(553\) | −4.12103 | −0.175244 | ||||||||
\(554\) | 15.9781 | 0.678846 | ||||||||
\(555\) | −10.7842 | −0.457764 | ||||||||
\(556\) | −8.52683 | −0.361618 | ||||||||
\(557\) | −5.40292 | −0.228929 | −0.114465 | − | 0.993427i | \(-0.536515\pi\) | ||||
−0.114465 | + | 0.993427i | \(0.536515\pi\) | |||||||
\(558\) | 7.33288 | 0.310425 | ||||||||
\(559\) | 22.1703 | 0.937702 | ||||||||
\(560\) | 2.07752 | 0.0877914 | ||||||||
\(561\) | 0.681143 | 0.0287579 | ||||||||
\(562\) | 21.3516 | 0.900662 | ||||||||
\(563\) | −9.19975 | −0.387723 | −0.193862 | − | 0.981029i | \(-0.562101\pi\) | ||||
−0.193862 | + | 0.981029i | \(0.562101\pi\) | |||||||
\(564\) | 7.93003 | 0.333914 | ||||||||
\(565\) | 3.48433 | 0.146587 | ||||||||
\(566\) | −10.1285 | −0.425733 | ||||||||
\(567\) | 1.89307 | 0.0795014 | ||||||||
\(568\) | 4.64813 | 0.195031 | ||||||||
\(569\) | 38.5036 | 1.61416 | 0.807078 | − | 0.590445i | \(-0.201048\pi\) | ||||
0.807078 | + | 0.590445i | \(0.201048\pi\) | |||||||
\(570\) | 1.40680 | 0.0589244 | ||||||||
\(571\) | −15.8679 | −0.664051 | −0.332025 | − | 0.943270i | \(-0.607732\pi\) | ||||
−0.332025 | + | 0.943270i | \(0.607732\pi\) | |||||||
\(572\) | 2.23184 | 0.0933178 | ||||||||
\(573\) | 11.1194 | 0.464518 | ||||||||
\(574\) | −2.35674 | −0.0983686 | ||||||||
\(575\) | 19.9760 | 0.833059 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.64546 | 0.151762 | 0.0758812 | − | 0.997117i | \(-0.475823\pi\) | ||||
0.0758812 | + | 0.997117i | \(0.475823\pi\) | |||||||
\(578\) | 16.5360 | 0.687809 | ||||||||
\(579\) | −22.9582 | −0.954112 | ||||||||
\(580\) | −3.43981 | −0.142830 | ||||||||
\(581\) | −0.711287 | −0.0295091 | ||||||||
\(582\) | −3.48793 | −0.144579 | ||||||||
\(583\) | −1.56472 | −0.0648039 | ||||||||
\(584\) | 9.94800 | 0.411651 | ||||||||
\(585\) | −2.44930 | −0.101266 | ||||||||
\(586\) | −14.3894 | −0.594421 | ||||||||
\(587\) | 10.5624 | 0.435958 | 0.217979 | − | 0.975953i | \(-0.430054\pi\) | ||||
0.217979 | + | 0.975953i | \(0.430054\pi\) | |||||||
\(588\) | −3.41630 | −0.140886 | ||||||||
\(589\) | 9.39998 | 0.387320 | ||||||||
\(590\) | 5.44764 | 0.224276 | ||||||||
\(591\) | 22.7688 | 0.936584 | ||||||||
\(592\) | −9.82670 | −0.403875 | ||||||||
\(593\) | −24.8969 | −1.02239 | −0.511197 | − | 0.859463i | \(-0.670798\pi\) | ||||
−0.511197 | + | 0.859463i | \(0.670798\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −1.41509 | −0.0580131 | ||||||||
\(596\) | −9.78974 | −0.401003 | ||||||||
\(597\) | 23.2106 | 0.949945 | ||||||||
\(598\) | −11.7460 | −0.480328 | ||||||||
\(599\) | −11.6412 | −0.475645 | −0.237822 | − | 0.971309i | \(-0.576434\pi\) | ||||
−0.237822 | + | 0.971309i | \(0.576434\pi\) | |||||||
\(600\) | 3.79563 | 0.154956 | ||||||||
\(601\) | −25.3150 | −1.03262 | −0.516310 | − | 0.856402i | \(-0.672695\pi\) | ||||
−0.516310 | + | 0.856402i | \(0.672695\pi\) | |||||||
\(602\) | 18.8050 | 0.766436 | ||||||||
\(603\) | 0.379334 | 0.0154477 | ||||||||
\(604\) | 22.1720 | 0.902166 | ||||||||
\(605\) | 1.09744 | 0.0446172 | ||||||||
\(606\) | 11.0045 | 0.447028 | ||||||||
\(607\) | 21.8181 | 0.885571 | 0.442785 | − | 0.896628i | \(-0.353990\pi\) | ||||
0.442785 | + | 0.896628i | \(0.353990\pi\) | |||||||
\(608\) | 1.28190 | 0.0519877 | ||||||||
\(609\) | −5.93363 | −0.240443 | ||||||||
\(610\) | −1.09744 | −0.0444340 | ||||||||
\(611\) | −17.6985 | −0.716006 | ||||||||
\(612\) | −0.681143 | −0.0275336 | ||||||||
\(613\) | −44.2177 | −1.78594 | −0.892969 | − | 0.450118i | \(-0.851382\pi\) | ||||
−0.892969 | + | 0.450118i | \(0.851382\pi\) | |||||||
\(614\) | 6.97900 | 0.281649 | ||||||||
\(615\) | 1.36624 | 0.0550920 | ||||||||
\(616\) | 1.89307 | 0.0762739 | ||||||||
\(617\) | 11.2273 | 0.451995 | 0.225997 | − | 0.974128i | \(-0.427436\pi\) | ||||
0.225997 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(618\) | −16.9457 | −0.681656 | ||||||||
\(619\) | 5.37344 | 0.215977 | 0.107988 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107988 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(620\) | −8.04738 | −0.323191 | ||||||||
\(621\) | −5.26291 | −0.211193 | ||||||||
\(622\) | −32.4526 | −1.30123 | ||||||||
\(623\) | 23.4758 | 0.940536 | ||||||||
\(624\) | −2.23184 | −0.0893450 | ||||||||
\(625\) | 8.38495 | 0.335398 | ||||||||
\(626\) | 1.57689 | 0.0630251 | ||||||||
\(627\) | 1.28190 | 0.0511940 | ||||||||
\(628\) | 15.6053 | 0.622718 | ||||||||
\(629\) | 6.69339 | 0.266883 | ||||||||
\(630\) | −2.07752 | −0.0827706 | ||||||||
\(631\) | 12.9902 | 0.517130 | 0.258565 | − | 0.965994i | \(-0.416750\pi\) | ||||
0.258565 | + | 0.965994i | \(0.416750\pi\) | |||||||
\(632\) | 2.17690 | 0.0865926 | ||||||||
\(633\) | −20.7135 | −0.823287 | ||||||||
\(634\) | 0.766221 | 0.0304305 | ||||||||
\(635\) | −16.8115 | −0.667144 | ||||||||
\(636\) | 1.56472 | 0.0620450 | ||||||||
\(637\) | 7.62462 | 0.302098 | ||||||||
\(638\) | −3.13440 | −0.124092 | ||||||||
\(639\) | −4.64813 | −0.183877 | ||||||||
\(640\) | −1.09744 | −0.0433801 | ||||||||
\(641\) | 11.2773 | 0.445426 | 0.222713 | − | 0.974884i | \(-0.428509\pi\) | ||||
0.222713 | + | 0.974884i | \(0.428509\pi\) | |||||||
\(642\) | 3.69424 | 0.145800 | ||||||||
\(643\) | −34.5108 | −1.36097 | −0.680486 | − | 0.732761i | \(-0.738231\pi\) | ||||
−0.680486 | + | 0.732761i | \(0.738231\pi\) | |||||||
\(644\) | −9.96304 | −0.392599 | ||||||||
\(645\) | −10.9015 | −0.429248 | ||||||||
\(646\) | −0.873154 | −0.0343538 | ||||||||
\(647\) | −33.8046 | −1.32900 | −0.664498 | − | 0.747290i | \(-0.731355\pi\) | ||||
−0.664498 | + | 0.747290i | \(0.731355\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 4.96396 | 0.194853 | ||||||||
\(650\) | −8.47123 | −0.332269 | ||||||||
\(651\) | −13.8816 | −0.544064 | ||||||||
\(652\) | 11.8002 | 0.462130 | ||||||||
\(653\) | 21.5888 | 0.844835 | 0.422418 | − | 0.906401i | \(-0.361182\pi\) | ||||
0.422418 | + | 0.906401i | \(0.361182\pi\) | |||||||
\(654\) | 0.250827 | 0.00980810 | ||||||||
\(655\) | 4.36062 | 0.170384 | ||||||||
\(656\) | 1.24493 | 0.0486065 | ||||||||
\(657\) | −9.94800 | −0.388109 | ||||||||
\(658\) | −15.0121 | −0.585232 | ||||||||
\(659\) | −17.0164 | −0.662864 | −0.331432 | − | 0.943479i | \(-0.607532\pi\) | ||||
−0.331432 | + | 0.943479i | \(0.607532\pi\) | |||||||
\(660\) | −1.09744 | −0.0427177 | ||||||||
\(661\) | 2.27527 | 0.0884976 | 0.0442488 | − | 0.999021i | \(-0.485911\pi\) | ||||
0.0442488 | + | 0.999021i | \(0.485911\pi\) | |||||||
\(662\) | 5.64686 | 0.219471 | ||||||||
\(663\) | 1.52020 | 0.0590397 | ||||||||
\(664\) | 0.375732 | 0.0145812 | ||||||||
\(665\) | −2.66317 | −0.103273 | ||||||||
\(666\) | 9.82670 | 0.380777 | ||||||||
\(667\) | 16.4961 | 0.638730 | ||||||||
\(668\) | 4.59218 | 0.177677 | ||||||||
\(669\) | −18.7681 | −0.725616 | ||||||||
\(670\) | −0.416295 | −0.0160829 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −1.89307 | −0.0730267 | ||||||||
\(673\) | 32.1321 | 1.23860 | 0.619301 | − | 0.785154i | \(-0.287416\pi\) | ||||
0.619301 | + | 0.785154i | \(0.287416\pi\) | |||||||
\(674\) | −17.9620 | −0.691871 | ||||||||
\(675\) | −3.79563 | −0.146094 | ||||||||
\(676\) | −8.01890 | −0.308419 | ||||||||
\(677\) | 14.6716 | 0.563874 | 0.281937 | − | 0.959433i | \(-0.409023\pi\) | ||||
0.281937 | + | 0.959433i | \(0.409023\pi\) | |||||||
\(678\) | −3.17496 | −0.121934 | ||||||||
\(679\) | 6.60288 | 0.253395 | ||||||||
\(680\) | 0.747512 | 0.0286658 | ||||||||
\(681\) | −9.21553 | −0.353140 | ||||||||
\(682\) | −7.33288 | −0.280790 | ||||||||
\(683\) | −16.8678 | −0.645430 | −0.322715 | − | 0.946496i | \(-0.604595\pi\) | ||||
−0.322715 | + | 0.946496i | \(0.604595\pi\) | |||||||
\(684\) | −1.28190 | −0.0490145 | ||||||||
\(685\) | 22.7357 | 0.868687 | ||||||||
\(686\) | 19.7188 | 0.752865 | ||||||||
\(687\) | −20.5664 | −0.784656 | ||||||||
\(688\) | −9.93363 | −0.378716 | ||||||||
\(689\) | −3.49219 | −0.133042 | ||||||||
\(690\) | 5.77572 | 0.219878 | ||||||||
\(691\) | −30.4512 | −1.15842 | −0.579210 | − | 0.815179i | \(-0.696639\pi\) | ||||
−0.579210 | + | 0.815179i | \(0.696639\pi\) | |||||||
\(692\) | 8.67257 | 0.329682 | ||||||||
\(693\) | −1.89307 | −0.0719117 | ||||||||
\(694\) | −12.4217 | −0.471523 | ||||||||
\(695\) | −9.35767 | −0.354957 | ||||||||
\(696\) | 3.13440 | 0.118809 | ||||||||
\(697\) | −0.847978 | −0.0321195 | ||||||||
\(698\) | 13.9412 | 0.527682 | ||||||||
\(699\) | 22.7946 | 0.862171 | ||||||||
\(700\) | −7.18538 | −0.271582 | ||||||||
\(701\) | 21.2720 | 0.803431 | 0.401715 | − | 0.915765i | \(-0.368414\pi\) | ||||
0.401715 | + | 0.915765i | \(0.368414\pi\) | |||||||
\(702\) | 2.23184 | 0.0842353 | ||||||||
\(703\) | 12.5968 | 0.475097 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 8.70272 | 0.327763 | ||||||||
\(706\) | −22.6367 | −0.851943 | ||||||||
\(707\) | −20.8323 | −0.783480 | ||||||||
\(708\) | −4.96396 | −0.186557 | ||||||||
\(709\) | −27.9123 | −1.04827 | −0.524133 | − | 0.851636i | \(-0.675611\pi\) | ||||
−0.524133 | + | 0.851636i | \(0.675611\pi\) | |||||||
\(710\) | 5.10104 | 0.191439 | ||||||||
\(711\) | −2.17690 | −0.0816403 | ||||||||
\(712\) | −12.4009 | −0.464744 | ||||||||
\(713\) | 38.5923 | 1.44529 | ||||||||
\(714\) | 1.28945 | 0.0482564 | ||||||||
\(715\) | 2.44930 | 0.0915988 | ||||||||
\(716\) | 4.70954 | 0.176004 | ||||||||
\(717\) | −16.3629 | −0.611085 | ||||||||
\(718\) | 30.6791 | 1.14493 | ||||||||
\(719\) | −43.7145 | −1.63028 | −0.815138 | − | 0.579266i | \(-0.803339\pi\) | ||||
−0.815138 | + | 0.579266i | \(0.803339\pi\) | |||||||
\(720\) | 1.09744 | 0.0408991 | ||||||||
\(721\) | 32.0794 | 1.19470 | ||||||||
\(722\) | 17.3567 | 0.645951 | ||||||||
\(723\) | 19.8816 | 0.739406 | ||||||||
\(724\) | 25.0480 | 0.930903 | ||||||||
\(725\) | 11.8970 | 0.441844 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 51.3419 | 1.90417 | 0.952083 | − | 0.305838i | \(-0.0989368\pi\) | ||||
0.952083 | + | 0.305838i | \(0.0989368\pi\) | |||||||
\(728\) | 4.22502 | 0.156590 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.9173 | 0.404068 | ||||||||
\(731\) | 6.76622 | 0.250258 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | 33.2479 | 1.22804 | 0.614019 | − | 0.789291i | \(-0.289552\pi\) | ||||
0.614019 | + | 0.789291i | \(0.289552\pi\) | |||||||
\(734\) | −3.41177 | −0.125931 | ||||||||
\(735\) | −3.74917 | −0.138290 | ||||||||
\(736\) | 5.26291 | 0.193993 | ||||||||
\(737\) | −0.379334 | −0.0139729 | ||||||||
\(738\) | −1.24493 | −0.0458266 | ||||||||
\(739\) | 2.02185 | 0.0743751 | 0.0371875 | − | 0.999308i | \(-0.488160\pi\) | ||||
0.0371875 | + | 0.999308i | \(0.488160\pi\) | |||||||
\(740\) | −10.7842 | −0.396435 | ||||||||
\(741\) | 2.86098 | 0.105101 | ||||||||
\(742\) | −2.96211 | −0.108743 | ||||||||
\(743\) | −32.6676 | −1.19846 | −0.599229 | − | 0.800578i | \(-0.704526\pi\) | ||||
−0.599229 | + | 0.800578i | \(0.704526\pi\) | |||||||
\(744\) | 7.33288 | 0.268836 | ||||||||
\(745\) | −10.7436 | −0.393616 | ||||||||
\(746\) | 36.5324 | 1.33754 | ||||||||
\(747\) | −0.375732 | −0.0137473 | ||||||||
\(748\) | 0.681143 | 0.0249050 | ||||||||
\(749\) | −6.99344 | −0.255535 | ||||||||
\(750\) | 9.65266 | 0.352465 | ||||||||
\(751\) | −0.527916 | −0.0192639 | −0.00963197 | − | 0.999954i | \(-0.503066\pi\) | ||||
−0.00963197 | + | 0.999954i | \(0.503066\pi\) | |||||||
\(752\) | 7.93003 | 0.289178 | ||||||||
\(753\) | 27.2397 | 0.992669 | ||||||||
\(754\) | −6.99547 | −0.254760 | ||||||||
\(755\) | 24.3324 | 0.885547 | ||||||||
\(756\) | 1.89307 | 0.0688502 | ||||||||
\(757\) | −43.3383 | −1.57516 | −0.787579 | − | 0.616213i | \(-0.788666\pi\) | ||||
−0.787579 | + | 0.616213i | \(0.788666\pi\) | |||||||
\(758\) | −12.3952 | −0.450214 | ||||||||
\(759\) | 5.26291 | 0.191031 | ||||||||
\(760\) | 1.40680 | 0.0510300 | ||||||||
\(761\) | −28.2789 | −1.02511 | −0.512554 | − | 0.858655i | \(-0.671301\pi\) | ||||
−0.512554 | + | 0.858655i | \(0.671301\pi\) | |||||||
\(762\) | 15.3189 | 0.554944 | ||||||||
\(763\) | −0.474832 | −0.0171901 | ||||||||
\(764\) | 11.1194 | 0.402284 | ||||||||
\(765\) | −0.747512 | −0.0270264 | ||||||||
\(766\) | 26.4615 | 0.956095 | ||||||||
\(767\) | 11.0788 | 0.400031 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 40.2542 | 1.45161 | 0.725803 | − | 0.687903i | \(-0.241469\pi\) | ||||
0.725803 | + | 0.687903i | \(0.241469\pi\) | |||||||
\(770\) | 2.07752 | 0.0748688 | ||||||||
\(771\) | −11.4500 | −0.412360 | ||||||||
\(772\) | −22.9582 | −0.826285 | ||||||||
\(773\) | 45.5694 | 1.63902 | 0.819509 | − | 0.573067i | \(-0.194246\pi\) | ||||
0.819509 | + | 0.573067i | \(0.194246\pi\) | |||||||
\(774\) | 9.93363 | 0.357057 | ||||||||
\(775\) | 27.8329 | 0.999787 | ||||||||
\(776\) | −3.48793 | −0.125209 | ||||||||
\(777\) | −18.6026 | −0.667365 | ||||||||
\(778\) | −14.4379 | −0.517623 | ||||||||
\(779\) | −1.59588 | −0.0571782 | ||||||||
\(780\) | −2.44930 | −0.0876992 | ||||||||
\(781\) | 4.64813 | 0.166323 | ||||||||
\(782\) | −3.58479 | −0.128192 | ||||||||
\(783\) | −3.13440 | −0.112014 | ||||||||
\(784\) | −3.41630 | −0.122011 | ||||||||
\(785\) | 17.1258 | 0.611247 | ||||||||
\(786\) | −3.97346 | −0.141729 | ||||||||
\(787\) | −34.3460 | −1.22430 | −0.612151 | − | 0.790741i | \(-0.709695\pi\) | ||||
−0.612151 | + | 0.790741i | \(0.709695\pi\) | |||||||
\(788\) | 22.7688 | 0.811105 | ||||||||
\(789\) | −3.56545 | −0.126933 | ||||||||
\(790\) | 2.38902 | 0.0849974 | ||||||||
\(791\) | 6.01042 | 0.213706 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −2.23184 | −0.0792549 | ||||||||
\(794\) | −23.9308 | −0.849271 | ||||||||
\(795\) | 1.71718 | 0.0609021 | ||||||||
\(796\) | 23.2106 | 0.822676 | ||||||||
\(797\) | 42.2162 | 1.49537 | 0.747687 | − | 0.664052i | \(-0.231164\pi\) | ||||
0.747687 | + | 0.664052i | \(0.231164\pi\) | |||||||
\(798\) | 2.42671 | 0.0859048 | ||||||||
\(799\) | −5.40148 | −0.191091 | ||||||||
\(800\) | 3.79563 | 0.134196 | ||||||||
\(801\) | 12.4009 | 0.438165 | ||||||||
\(802\) | −16.3381 | −0.576920 | ||||||||
\(803\) | 9.94800 | 0.351057 | ||||||||
\(804\) | 0.379334 | 0.0133781 | ||||||||
\(805\) | −10.9338 | −0.385367 | ||||||||
\(806\) | −16.3658 | −0.576461 | ||||||||
\(807\) | −1.21874 | −0.0429018 | ||||||||
\(808\) | 11.0045 | 0.387138 | ||||||||
\(809\) | −48.6770 | −1.71139 | −0.855696 | − | 0.517479i | \(-0.826870\pi\) | ||||
−0.855696 | + | 0.517479i | \(0.826870\pi\) | |||||||
\(810\) | −1.09744 | −0.0385601 | ||||||||
\(811\) | 36.5079 | 1.28197 | 0.640983 | − | 0.767555i | \(-0.278527\pi\) | ||||
0.640983 | + | 0.767555i | \(0.278527\pi\) | |||||||
\(812\) | −5.93363 | −0.208230 | ||||||||
\(813\) | −12.5513 | −0.440192 | ||||||||
\(814\) | −9.82670 | −0.344426 | ||||||||
\(815\) | 12.9499 | 0.453617 | ||||||||
\(816\) | −0.681143 | −0.0238448 | ||||||||
\(817\) | 12.7339 | 0.445502 | ||||||||
\(818\) | −7.87768 | −0.275437 | ||||||||
\(819\) | −4.22502 | −0.147634 | ||||||||
\(820\) | 1.36624 | 0.0477111 | ||||||||
\(821\) | 29.7837 | 1.03946 | 0.519729 | − | 0.854331i | \(-0.326033\pi\) | ||||
0.519729 | + | 0.854331i | \(0.326033\pi\) | |||||||
\(822\) | −20.7171 | −0.722591 | ||||||||
\(823\) | −25.2877 | −0.881475 | −0.440737 | − | 0.897636i | \(-0.645283\pi\) | ||||
−0.440737 | + | 0.897636i | \(0.645283\pi\) | |||||||
\(824\) | −16.9457 | −0.590332 | ||||||||
\(825\) | 3.79563 | 0.132147 | ||||||||
\(826\) | 9.39712 | 0.326968 | ||||||||
\(827\) | 25.4033 | 0.883358 | 0.441679 | − | 0.897173i | \(-0.354383\pi\) | ||||
0.441679 | + | 0.897173i | \(0.354383\pi\) | |||||||
\(828\) | −5.26291 | −0.182899 | ||||||||
\(829\) | −12.9522 | −0.449848 | −0.224924 | − | 0.974376i | \(-0.572213\pi\) | ||||
−0.224924 | + | 0.974376i | \(0.572213\pi\) | |||||||
\(830\) | 0.412343 | 0.0143126 | ||||||||
\(831\) | −15.9781 | −0.554276 | ||||||||
\(832\) | −2.23184 | −0.0773751 | ||||||||
\(833\) | 2.32699 | 0.0806253 | ||||||||
\(834\) | 8.52683 | 0.295260 | ||||||||
\(835\) | 5.03964 | 0.174404 | ||||||||
\(836\) | 1.28190 | 0.0443353 | ||||||||
\(837\) | −7.33288 | −0.253461 | ||||||||
\(838\) | 28.4228 | 0.981851 | ||||||||
\(839\) | 21.0013 | 0.725045 | 0.362522 | − | 0.931975i | \(-0.381916\pi\) | ||||
0.362522 | + | 0.931975i | \(0.381916\pi\) | |||||||
\(840\) | −2.07752 | −0.0716814 | ||||||||
\(841\) | −19.1755 | −0.661225 | ||||||||
\(842\) | 11.7474 | 0.404843 | ||||||||
\(843\) | −21.3516 | −0.735388 | ||||||||
\(844\) | −20.7135 | −0.712988 | ||||||||
\(845\) | −8.80025 | −0.302738 | ||||||||
\(846\) | −7.93003 | −0.272640 | ||||||||
\(847\) | 1.89307 | 0.0650466 | ||||||||
\(848\) | 1.56472 | 0.0537326 | ||||||||
\(849\) | 10.1285 | 0.347609 | ||||||||
\(850\) | −2.58537 | −0.0886773 | ||||||||
\(851\) | 51.7170 | 1.77284 | ||||||||
\(852\) | −4.64813 | −0.159242 | ||||||||
\(853\) | 28.6195 | 0.979912 | 0.489956 | − | 0.871747i | \(-0.337013\pi\) | ||||
0.489956 | + | 0.871747i | \(0.337013\pi\) | |||||||
\(854\) | −1.89307 | −0.0647794 | ||||||||
\(855\) | −1.40680 | −0.0481116 | ||||||||
\(856\) | 3.69424 | 0.126266 | ||||||||
\(857\) | 31.4924 | 1.07576 | 0.537879 | − | 0.843022i | \(-0.319226\pi\) | ||||
0.537879 | + | 0.843022i | \(0.319226\pi\) | |||||||
\(858\) | −2.23184 | −0.0761937 | ||||||||
\(859\) | −50.7420 | −1.73129 | −0.865647 | − | 0.500655i | \(-0.833093\pi\) | ||||
−0.865647 | + | 0.500655i | \(0.833093\pi\) | |||||||
\(860\) | −10.9015 | −0.371740 | ||||||||
\(861\) | 2.35674 | 0.0803176 | ||||||||
\(862\) | 12.9291 | 0.440367 | ||||||||
\(863\) | 33.5565 | 1.14228 | 0.571139 | − | 0.820853i | \(-0.306502\pi\) | ||||
0.571139 | + | 0.820853i | \(0.306502\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 9.51761 | 0.323609 | ||||||||
\(866\) | −3.25284 | −0.110536 | ||||||||
\(867\) | −16.5360 | −0.561594 | ||||||||
\(868\) | −13.8816 | −0.471173 | ||||||||
\(869\) | 2.17690 | 0.0738464 | ||||||||
\(870\) | 3.43981 | 0.116620 | ||||||||
\(871\) | −0.846612 | −0.0286863 | ||||||||
\(872\) | 0.250827 | 0.00849406 | ||||||||
\(873\) | 3.48793 | 0.118048 | ||||||||
\(874\) | −6.74650 | −0.228204 | ||||||||
\(875\) | −18.2731 | −0.617745 | ||||||||
\(876\) | −9.94800 | −0.336112 | ||||||||
\(877\) | −22.3493 | −0.754682 | −0.377341 | − | 0.926074i | \(-0.623162\pi\) | ||||
−0.377341 | + | 0.926074i | \(0.623162\pi\) | |||||||
\(878\) | 7.77001 | 0.262225 | ||||||||
\(879\) | 14.3894 | 0.485342 | ||||||||
\(880\) | −1.09744 | −0.0369946 | ||||||||
\(881\) | 1.50433 | 0.0506822 | 0.0253411 | − | 0.999679i | \(-0.491933\pi\) | ||||
0.0253411 | + | 0.999679i | \(0.491933\pi\) | |||||||
\(882\) | 3.41630 | 0.115033 | ||||||||
\(883\) | 13.6853 | 0.460546 | 0.230273 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230273 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(884\) | 1.52020 | 0.0511299 | ||||||||
\(885\) | −5.44764 | −0.183121 | ||||||||
\(886\) | 39.2243 | 1.31777 | ||||||||
\(887\) | 2.02403 | 0.0679602 | 0.0339801 | − | 0.999423i | \(-0.489182\pi\) | ||||
0.0339801 | + | 0.999423i | \(0.489182\pi\) | |||||||
\(888\) | 9.82670 | 0.329762 | ||||||||
\(889\) | −28.9996 | −0.972616 | ||||||||
\(890\) | −13.6092 | −0.456182 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −18.7681 | −0.628402 | ||||||||
\(893\) | −10.1655 | −0.340174 | ||||||||
\(894\) | 9.78974 | 0.327418 | ||||||||
\(895\) | 5.16842 | 0.172761 | ||||||||
\(896\) | −1.89307 | −0.0632429 | ||||||||
\(897\) | 11.7460 | 0.392186 | ||||||||
\(898\) | 40.2154 | 1.34201 | ||||||||
\(899\) | 22.9842 | 0.766565 | ||||||||
\(900\) | −3.79563 | −0.126521 | ||||||||
\(901\) | −1.06580 | −0.0355068 | ||||||||
\(902\) | 1.24493 | 0.0414518 | ||||||||
\(903\) | −18.8050 | −0.625792 | ||||||||
\(904\) | −3.17496 | −0.105598 | ||||||||
\(905\) | 27.4887 | 0.913754 | ||||||||
\(906\) | −22.1720 | −0.736616 | ||||||||
\(907\) | 8.19201 | 0.272011 | 0.136006 | − | 0.990708i | \(-0.456573\pi\) | ||||
0.136006 | + | 0.990708i | \(0.456573\pi\) | |||||||
\(908\) | −9.21553 | −0.305828 | ||||||||
\(909\) | −11.0045 | −0.364997 | ||||||||
\(910\) | 4.63670 | 0.153705 | ||||||||
\(911\) | −20.9303 | −0.693453 | −0.346726 | − | 0.937966i | \(-0.612707\pi\) | ||||
−0.346726 | + | 0.937966i | \(0.612707\pi\) | |||||||
\(912\) | −1.28190 | −0.0424478 | ||||||||
\(913\) | 0.375732 | 0.0124349 | ||||||||
\(914\) | −10.3675 | −0.342928 | ||||||||
\(915\) | 1.09744 | 0.0362802 | ||||||||
\(916\) | −20.5664 | −0.679532 | ||||||||
\(917\) | 7.52202 | 0.248399 | ||||||||
\(918\) | 0.681143 | 0.0224811 | ||||||||
\(919\) | 16.6805 | 0.550238 | 0.275119 | − | 0.961410i | \(-0.411283\pi\) | ||||
0.275119 | + | 0.961410i | \(0.411283\pi\) | |||||||
\(920\) | 5.77572 | 0.190420 | ||||||||
\(921\) | −6.97900 | −0.229966 | ||||||||
\(922\) | 27.0570 | 0.891074 | ||||||||
\(923\) | 10.3739 | 0.341460 | ||||||||
\(924\) | −1.89307 | −0.0622773 | ||||||||
\(925\) | 37.2985 | 1.22637 | ||||||||
\(926\) | −9.07954 | −0.298372 | ||||||||
\(927\) | 16.9457 | 0.556570 | ||||||||
\(928\) | 3.13440 | 0.102892 | ||||||||
\(929\) | −43.0814 | −1.41346 | −0.706728 | − | 0.707486i | \(-0.749829\pi\) | ||||
−0.706728 | + | 0.707486i | \(0.749829\pi\) | |||||||
\(930\) | 8.04738 | 0.263884 | ||||||||
\(931\) | 4.37933 | 0.143527 | ||||||||
\(932\) | 22.7946 | 0.746662 | ||||||||
\(933\) | 32.4526 | 1.06245 | ||||||||
\(934\) | 36.2732 | 1.18690 | ||||||||
\(935\) | 0.747512 | 0.0244463 | ||||||||
\(936\) | 2.23184 | 0.0729499 | ||||||||
\(937\) | 46.8708 | 1.53120 | 0.765602 | − | 0.643315i | \(-0.222441\pi\) | ||||
0.765602 | + | 0.643315i | \(0.222441\pi\) | |||||||
\(938\) | −0.718104 | −0.0234469 | ||||||||
\(939\) | −1.57689 | −0.0514598 | ||||||||
\(940\) | 8.70272 | 0.283851 | ||||||||
\(941\) | −54.6845 | −1.78266 | −0.891331 | − | 0.453353i | \(-0.850228\pi\) | ||||
−0.891331 | + | 0.453353i | \(0.850228\pi\) | |||||||
\(942\) | −15.6053 | −0.508447 | ||||||||
\(943\) | −6.55197 | −0.213362 | ||||||||
\(944\) | −4.96396 | −0.161563 | ||||||||
\(945\) | 2.07752 | 0.0675819 | ||||||||
\(946\) | −9.93363 | −0.322970 | ||||||||
\(947\) | 18.9356 | 0.615323 | 0.307662 | − | 0.951496i | \(-0.400454\pi\) | ||||
0.307662 | + | 0.951496i | \(0.400454\pi\) | |||||||
\(948\) | −2.17690 | −0.0707025 | ||||||||
\(949\) | 22.2023 | 0.720718 | ||||||||
\(950\) | −4.86560 | −0.157861 | ||||||||
\(951\) | −0.766221 | −0.0248464 | ||||||||
\(952\) | 1.28945 | 0.0417913 | ||||||||
\(953\) | 24.6894 | 0.799769 | 0.399885 | − | 0.916566i | \(-0.369050\pi\) | ||||
0.399885 | + | 0.916566i | \(0.369050\pi\) | |||||||
\(954\) | −1.56472 | −0.0506596 | ||||||||
\(955\) | 12.2028 | 0.394874 | ||||||||
\(956\) | −16.3629 | −0.529215 | ||||||||
\(957\) | 3.13440 | 0.101321 | ||||||||
\(958\) | −31.2522 | −1.00971 | ||||||||
\(959\) | 39.2188 | 1.26644 | ||||||||
\(960\) | 1.09744 | 0.0354197 | ||||||||
\(961\) | 22.7711 | 0.734552 | ||||||||
\(962\) | −21.9316 | −0.707103 | ||||||||
\(963\) | −3.69424 | −0.119045 | ||||||||
\(964\) | 19.8816 | 0.640344 | ||||||||
\(965\) | −25.1952 | −0.811064 | ||||||||
\(966\) | 9.96304 | 0.320556 | ||||||||
\(967\) | −5.76421 | −0.185364 | −0.0926822 | − | 0.995696i | \(-0.529544\pi\) | ||||
−0.0926822 | + | 0.995696i | \(0.529544\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0.873154 | 0.0280497 | ||||||||
\(970\) | −3.82779 | −0.122903 | ||||||||
\(971\) | 7.17968 | 0.230407 | 0.115203 | − | 0.993342i | \(-0.463248\pi\) | ||||
0.115203 | + | 0.993342i | \(0.463248\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −16.1419 | −0.517484 | ||||||||
\(974\) | 39.5203 | 1.26631 | ||||||||
\(975\) | 8.47123 | 0.271296 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | 6.46043 | 0.206687 | 0.103344 | − | 0.994646i | \(-0.467046\pi\) | ||||
0.103344 | + | 0.994646i | \(0.467046\pi\) | |||||||
\(978\) | −11.8002 | −0.377327 | ||||||||
\(979\) | −12.4009 | −0.396335 | ||||||||
\(980\) | −3.74917 | −0.119763 | ||||||||
\(981\) | −0.250827 | −0.00800828 | ||||||||
\(982\) | −16.6941 | −0.532732 | ||||||||
\(983\) | −4.86350 | −0.155121 | −0.0775607 | − | 0.996988i | \(-0.524713\pi\) | ||||
−0.0775607 | + | 0.996988i | \(0.524713\pi\) | |||||||
\(984\) | −1.24493 | −0.0396870 | ||||||||
\(985\) | 24.9874 | 0.796164 | ||||||||
\(986\) | −2.13497 | −0.0679914 | ||||||||
\(987\) | 15.0121 | 0.477840 | ||||||||
\(988\) | 2.86098 | 0.0910200 | ||||||||
\(989\) | 52.2798 | 1.66240 | ||||||||
\(990\) | 1.09744 | 0.0348789 | ||||||||
\(991\) | −7.85572 | −0.249545 | −0.124773 | − | 0.992185i | \(-0.539820\pi\) | ||||
−0.124773 | + | 0.992185i | \(0.539820\pi\) | |||||||
\(992\) | 7.33288 | 0.232819 | ||||||||
\(993\) | −5.64686 | −0.179198 | ||||||||
\(994\) | 8.79923 | 0.279095 | ||||||||
\(995\) | 25.4722 | 0.807522 | ||||||||
\(996\) | −0.375732 | −0.0119055 | ||||||||
\(997\) | 19.6343 | 0.621825 | 0.310912 | − | 0.950439i | \(-0.399365\pi\) | ||||
0.310912 | + | 0.950439i | \(0.399365\pi\) | |||||||
\(998\) | −27.9042 | −0.883293 | ||||||||
\(999\) | −9.82670 | −0.310903 |
(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 | 4026.2.a.r.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.r.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |