Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 12x^{6} + 7x^{5} + 41x^{4} - 6x^{3} - 28x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.70201\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | ||||||||
\(3\) | 1.70201 | 0.982655 | 0.491328 | − | 0.870975i | \(-0.336512\pi\) | ||||
0.491328 | + | 0.870975i | \(0.336512\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.70201 | −0.694842 | ||||||||
\(7\) | 0.961819 | 0.363533 | 0.181767 | − | 0.983342i | \(-0.441818\pi\) | ||||
0.181767 | + | 0.983342i | \(0.441818\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.103166 | −0.0343885 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.70201 | 0.491328 | ||||||||
\(13\) | −2.37582 | −0.658935 | −0.329468 | − | 0.944167i | \(-0.606869\pi\) | ||||
−0.329468 | + | 0.944167i | \(0.606869\pi\) | |||||||
\(14\) | −0.961819 | −0.257057 | ||||||||
\(15\) | 1.70201 | 0.439457 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.206466 | 0.0500755 | 0.0250377 | − | 0.999687i | \(-0.492029\pi\) | ||||
0.0250377 | + | 0.999687i | \(0.492029\pi\) | |||||||
\(18\) | 0.103166 | 0.0243163 | ||||||||
\(19\) | −0.413677 | −0.0949041 | −0.0474520 | − | 0.998874i | \(-0.515110\pi\) | ||||
−0.0474520 | + | 0.998874i | \(0.515110\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.63702 | 0.357228 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −4.37582 | −0.912422 | −0.456211 | − | 0.889872i | \(-0.650794\pi\) | ||||
−0.456211 | + | 0.889872i | \(0.650794\pi\) | |||||||
\(24\) | −1.70201 | −0.347421 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.37582 | 0.465937 | ||||||||
\(27\) | −5.28162 | −1.01645 | ||||||||
\(28\) | 0.961819 | 0.181767 | ||||||||
\(29\) | −5.05157 | −0.938053 | −0.469026 | − | 0.883184i | \(-0.655395\pi\) | ||||
−0.469026 | + | 0.883184i | \(0.655395\pi\) | |||||||
\(30\) | −1.70201 | −0.310743 | ||||||||
\(31\) | −6.59571 | −1.18462 | −0.592312 | − | 0.805709i | \(-0.701785\pi\) | ||||
−0.592312 | + | 0.805709i | \(0.701785\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.70201 | 0.296282 | ||||||||
\(34\) | −0.206466 | −0.0354087 | ||||||||
\(35\) | 0.961819 | 0.162577 | ||||||||
\(36\) | −0.103166 | −0.0171943 | ||||||||
\(37\) | −9.05446 | −1.48854 | −0.744272 | − | 0.667877i | \(-0.767203\pi\) | ||||
−0.744272 | + | 0.667877i | \(0.767203\pi\) | |||||||
\(38\) | 0.413677 | 0.0671073 | ||||||||
\(39\) | −4.04367 | −0.647506 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −7.15062 | −1.11674 | −0.558370 | − | 0.829592i | \(-0.688573\pi\) | ||||
−0.558370 | + | 0.829592i | \(0.688573\pi\) | |||||||
\(42\) | −1.63702 | −0.252598 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −0.103166 | −0.0153790 | ||||||||
\(46\) | 4.37582 | 0.645180 | ||||||||
\(47\) | −10.4220 | −1.52020 | −0.760102 | − | 0.649804i | \(-0.774851\pi\) | ||||
−0.760102 | + | 0.649804i | \(0.774851\pi\) | |||||||
\(48\) | 1.70201 | 0.245664 | ||||||||
\(49\) | −6.07490 | −0.867843 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0.351408 | 0.0492069 | ||||||||
\(52\) | −2.37582 | −0.329468 | ||||||||
\(53\) | 9.81295 | 1.34791 | 0.673956 | − | 0.738771i | \(-0.264594\pi\) | ||||
0.673956 | + | 0.738771i | \(0.264594\pi\) | |||||||
\(54\) | 5.28162 | 0.718737 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −0.961819 | −0.128528 | ||||||||
\(57\) | −0.704082 | −0.0932580 | ||||||||
\(58\) | 5.05157 | 0.663303 | ||||||||
\(59\) | 5.21881 | 0.679431 | 0.339716 | − | 0.940528i | \(-0.389669\pi\) | ||||
0.339716 | + | 0.940528i | \(0.389669\pi\) | |||||||
\(60\) | 1.70201 | 0.219728 | ||||||||
\(61\) | 7.54665 | 0.966249 | 0.483124 | − | 0.875552i | \(-0.339502\pi\) | ||||
0.483124 | + | 0.875552i | \(0.339502\pi\) | |||||||
\(62\) | 6.59571 | 0.837656 | ||||||||
\(63\) | −0.0992265 | −0.0125014 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.37582 | −0.294685 | ||||||||
\(66\) | −1.70201 | −0.209503 | ||||||||
\(67\) | 7.11705 | 0.869486 | 0.434743 | − | 0.900555i | \(-0.356839\pi\) | ||||
0.434743 | + | 0.900555i | \(0.356839\pi\) | |||||||
\(68\) | 0.206466 | 0.0250377 | ||||||||
\(69\) | −7.44769 | −0.896597 | ||||||||
\(70\) | −0.961819 | −0.114959 | ||||||||
\(71\) | 1.63446 | 0.193974 | 0.0969872 | − | 0.995286i | \(-0.469079\pi\) | ||||
0.0969872 | + | 0.995286i | \(0.469079\pi\) | |||||||
\(72\) | 0.103166 | 0.0121582 | ||||||||
\(73\) | −9.11062 | −1.06632 | −0.533159 | − | 0.846015i | \(-0.678995\pi\) | ||||
−0.533159 | + | 0.846015i | \(0.678995\pi\) | |||||||
\(74\) | 9.05446 | 1.05256 | ||||||||
\(75\) | 1.70201 | 0.196531 | ||||||||
\(76\) | −0.413677 | −0.0474520 | ||||||||
\(77\) | 0.961819 | 0.109609 | ||||||||
\(78\) | 4.04367 | 0.457856 | ||||||||
\(79\) | 2.19376 | 0.246818 | 0.123409 | − | 0.992356i | \(-0.460617\pi\) | ||||
0.123409 | + | 0.992356i | \(0.460617\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −8.67986 | −0.964429 | ||||||||
\(82\) | 7.15062 | 0.789654 | ||||||||
\(83\) | −5.54961 | −0.609148 | −0.304574 | − | 0.952489i | \(-0.598514\pi\) | ||||
−0.304574 | + | 0.952489i | \(0.598514\pi\) | |||||||
\(84\) | 1.63702 | 0.178614 | ||||||||
\(85\) | 0.206466 | 0.0223944 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | −8.59782 | −0.921783 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −16.7071 | −1.77095 | −0.885474 | − | 0.464689i | \(-0.846166\pi\) | ||||
−0.885474 | + | 0.464689i | \(0.846166\pi\) | |||||||
\(90\) | 0.103166 | 0.0108746 | ||||||||
\(91\) | −2.28511 | −0.239545 | ||||||||
\(92\) | −4.37582 | −0.456211 | ||||||||
\(93\) | −11.2260 | −1.16408 | ||||||||
\(94\) | 10.4220 | 1.07495 | ||||||||
\(95\) | −0.413677 | −0.0424424 | ||||||||
\(96\) | −1.70201 | −0.173711 | ||||||||
\(97\) | 2.79975 | 0.284271 | 0.142136 | − | 0.989847i | \(-0.454603\pi\) | ||||
0.142136 | + | 0.989847i | \(0.454603\pi\) | |||||||
\(98\) | 6.07490 | 0.613658 | ||||||||
\(99\) | −0.103166 | −0.0103685 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.4724 | 1.83807 | 0.919036 | − | 0.394174i | \(-0.128969\pi\) | ||||
0.919036 | + | 0.394174i | \(0.128969\pi\) | |||||||
\(102\) | −0.351408 | −0.0347945 | ||||||||
\(103\) | −14.9220 | −1.47031 | −0.735153 | − | 0.677901i | \(-0.762890\pi\) | ||||
−0.735153 | + | 0.677901i | \(0.762890\pi\) | |||||||
\(104\) | 2.37582 | 0.232969 | ||||||||
\(105\) | 1.63702 | 0.159757 | ||||||||
\(106\) | −9.81295 | −0.953118 | ||||||||
\(107\) | 17.2230 | 1.66501 | 0.832503 | − | 0.554020i | \(-0.186907\pi\) | ||||
0.832503 | + | 0.554020i | \(0.186907\pi\) | |||||||
\(108\) | −5.28162 | −0.508224 | ||||||||
\(109\) | 4.94258 | 0.473413 | 0.236706 | − | 0.971581i | \(-0.423932\pi\) | ||||
0.236706 | + | 0.971581i | \(0.423932\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −15.4108 | −1.46273 | ||||||||
\(112\) | 0.961819 | 0.0908833 | ||||||||
\(113\) | −1.33914 | −0.125976 | −0.0629880 | − | 0.998014i | \(-0.520063\pi\) | ||||
−0.0629880 | + | 0.998014i | \(0.520063\pi\) | |||||||
\(114\) | 0.704082 | 0.0659434 | ||||||||
\(115\) | −4.37582 | −0.408048 | ||||||||
\(116\) | −5.05157 | −0.469026 | ||||||||
\(117\) | 0.245103 | 0.0226598 | ||||||||
\(118\) | −5.21881 | −0.480431 | ||||||||
\(119\) | 0.198583 | 0.0182041 | ||||||||
\(120\) | −1.70201 | −0.155371 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.54665 | −0.683241 | ||||||||
\(123\) | −12.1704 | −1.09737 | ||||||||
\(124\) | −6.59571 | −0.592312 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.0992265 | 0.00883980 | ||||||||
\(127\) | −2.61565 | −0.232101 | −0.116051 | − | 0.993243i | \(-0.537024\pi\) | ||||
−0.116051 | + | 0.993243i | \(0.537024\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.70201 | −0.149854 | ||||||||
\(130\) | 2.37582 | 0.208374 | ||||||||
\(131\) | −9.98567 | −0.872452 | −0.436226 | − | 0.899837i | \(-0.643685\pi\) | ||||
−0.436226 | + | 0.899837i | \(0.643685\pi\) | |||||||
\(132\) | 1.70201 | 0.148141 | ||||||||
\(133\) | −0.397883 | −0.0345008 | ||||||||
\(134\) | −7.11705 | −0.614820 | ||||||||
\(135\) | −5.28162 | −0.454569 | ||||||||
\(136\) | −0.206466 | −0.0177043 | ||||||||
\(137\) | −15.5593 | −1.32932 | −0.664661 | − | 0.747145i | \(-0.731424\pi\) | ||||
−0.664661 | + | 0.747145i | \(0.731424\pi\) | |||||||
\(138\) | 7.44769 | 0.633990 | ||||||||
\(139\) | 9.87107 | 0.837253 | 0.418627 | − | 0.908158i | \(-0.362512\pi\) | ||||
0.418627 | + | 0.908158i | \(0.362512\pi\) | |||||||
\(140\) | 0.961819 | 0.0812885 | ||||||||
\(141\) | −17.7383 | −1.49384 | ||||||||
\(142\) | −1.63446 | −0.137161 | ||||||||
\(143\) | −2.37582 | −0.198676 | ||||||||
\(144\) | −0.103166 | −0.00859713 | ||||||||
\(145\) | −5.05157 | −0.419510 | ||||||||
\(146\) | 9.11062 | 0.754000 | ||||||||
\(147\) | −10.3395 | −0.852791 | ||||||||
\(148\) | −9.05446 | −0.744272 | ||||||||
\(149\) | 19.6052 | 1.60612 | 0.803060 | − | 0.595898i | \(-0.203204\pi\) | ||||
0.803060 | + | 0.595898i | \(0.203204\pi\) | |||||||
\(150\) | −1.70201 | −0.138968 | ||||||||
\(151\) | −8.91621 | −0.725591 | −0.362795 | − | 0.931869i | \(-0.618178\pi\) | ||||
−0.362795 | + | 0.931869i | \(0.618178\pi\) | |||||||
\(152\) | 0.413677 | 0.0335537 | ||||||||
\(153\) | −0.0213002 | −0.00172202 | ||||||||
\(154\) | −0.961819 | −0.0775056 | ||||||||
\(155\) | −6.59571 | −0.529780 | ||||||||
\(156\) | −4.04367 | −0.323753 | ||||||||
\(157\) | 13.1048 | 1.04588 | 0.522940 | − | 0.852369i | \(-0.324835\pi\) | ||||
0.522940 | + | 0.852369i | \(0.324835\pi\) | |||||||
\(158\) | −2.19376 | −0.174527 | ||||||||
\(159\) | 16.7017 | 1.32453 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −4.20875 | −0.331696 | ||||||||
\(162\) | 8.67986 | 0.681954 | ||||||||
\(163\) | 9.93240 | 0.777965 | 0.388983 | − | 0.921245i | \(-0.372827\pi\) | ||||
0.388983 | + | 0.921245i | \(0.372827\pi\) | |||||||
\(164\) | −7.15062 | −0.558370 | ||||||||
\(165\) | 1.70201 | 0.132501 | ||||||||
\(166\) | 5.54961 | 0.430733 | ||||||||
\(167\) | 5.82283 | 0.450584 | 0.225292 | − | 0.974291i | \(-0.427666\pi\) | ||||
0.225292 | + | 0.974291i | \(0.427666\pi\) | |||||||
\(168\) | −1.63702 | −0.126299 | ||||||||
\(169\) | −7.35546 | −0.565805 | ||||||||
\(170\) | −0.206466 | −0.0158353 | ||||||||
\(171\) | 0.0426772 | 0.00326361 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | 21.4892 | 1.63379 | 0.816897 | − | 0.576784i | \(-0.195693\pi\) | ||||
0.816897 | + | 0.576784i | \(0.195693\pi\) | |||||||
\(174\) | 8.59782 | 0.651799 | ||||||||
\(175\) | 0.961819 | 0.0727067 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 8.88246 | 0.667647 | ||||||||
\(178\) | 16.7071 | 1.25225 | ||||||||
\(179\) | −5.87243 | −0.438926 | −0.219463 | − | 0.975621i | \(-0.570431\pi\) | ||||
−0.219463 | + | 0.975621i | \(0.570431\pi\) | |||||||
\(180\) | −0.103166 | −0.00768950 | ||||||||
\(181\) | 2.70569 | 0.201113 | 0.100556 | − | 0.994931i | \(-0.467938\pi\) | ||||
0.100556 | + | 0.994931i | \(0.467938\pi\) | |||||||
\(182\) | 2.28511 | 0.169384 | ||||||||
\(183\) | 12.8445 | 0.949490 | ||||||||
\(184\) | 4.37582 | 0.322590 | ||||||||
\(185\) | −9.05446 | −0.665697 | ||||||||
\(186\) | 11.2260 | 0.823127 | ||||||||
\(187\) | 0.206466 | 0.0150983 | ||||||||
\(188\) | −10.4220 | −0.760102 | ||||||||
\(189\) | −5.07996 | −0.369513 | ||||||||
\(190\) | 0.413677 | 0.0300113 | ||||||||
\(191\) | 17.2199 | 1.24599 | 0.622994 | − | 0.782227i | \(-0.285916\pi\) | ||||
0.622994 | + | 0.782227i | \(0.285916\pi\) | |||||||
\(192\) | 1.70201 | 0.122832 | ||||||||
\(193\) | −9.74778 | −0.701660 | −0.350830 | − | 0.936439i | \(-0.614101\pi\) | ||||
−0.350830 | + | 0.936439i | \(0.614101\pi\) | |||||||
\(194\) | −2.79975 | −0.201010 | ||||||||
\(195\) | −4.04367 | −0.289574 | ||||||||
\(196\) | −6.07490 | −0.433922 | ||||||||
\(197\) | −20.1939 | −1.43875 | −0.719377 | − | 0.694619i | \(-0.755573\pi\) | ||||
−0.719377 | + | 0.694619i | \(0.755573\pi\) | |||||||
\(198\) | 0.103166 | 0.00733165 | ||||||||
\(199\) | −11.4718 | −0.813216 | −0.406608 | − | 0.913603i | \(-0.633289\pi\) | ||||
−0.406608 | + | 0.913603i | \(0.633289\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 12.1133 | 0.854405 | ||||||||
\(202\) | −18.4724 | −1.29971 | ||||||||
\(203\) | −4.85869 | −0.341013 | ||||||||
\(204\) | 0.351408 | 0.0246035 | ||||||||
\(205\) | −7.15062 | −0.499421 | ||||||||
\(206\) | 14.9220 | 1.03966 | ||||||||
\(207\) | 0.451434 | 0.0313768 | ||||||||
\(208\) | −2.37582 | −0.164734 | ||||||||
\(209\) | −0.413677 | −0.0286147 | ||||||||
\(210\) | −1.63702 | −0.112965 | ||||||||
\(211\) | −4.90180 | −0.337454 | −0.168727 | − | 0.985663i | \(-0.553966\pi\) | ||||
−0.168727 | + | 0.985663i | \(0.553966\pi\) | |||||||
\(212\) | 9.81295 | 0.673956 | ||||||||
\(213\) | 2.78186 | 0.190610 | ||||||||
\(214\) | −17.2230 | −1.17734 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 5.28162 | 0.359368 | ||||||||
\(217\) | −6.34388 | −0.430650 | ||||||||
\(218\) | −4.94258 | −0.334753 | ||||||||
\(219\) | −15.5064 | −1.04782 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −0.490528 | −0.0329965 | ||||||||
\(222\) | 15.4108 | 1.03430 | ||||||||
\(223\) | 23.1695 | 1.55155 | 0.775773 | − | 0.631012i | \(-0.217360\pi\) | ||||
0.775773 | + | 0.631012i | \(0.217360\pi\) | |||||||
\(224\) | −0.961819 | −0.0642642 | ||||||||
\(225\) | −0.103166 | −0.00687770 | ||||||||
\(226\) | 1.33914 | 0.0890785 | ||||||||
\(227\) | 1.95283 | 0.129614 | 0.0648068 | − | 0.997898i | \(-0.479357\pi\) | ||||
0.0648068 | + | 0.997898i | \(0.479357\pi\) | |||||||
\(228\) | −0.704082 | −0.0466290 | ||||||||
\(229\) | −27.9257 | −1.84538 | −0.922692 | − | 0.385537i | \(-0.874016\pi\) | ||||
−0.922692 | + | 0.385537i | \(0.874016\pi\) | |||||||
\(230\) | 4.37582 | 0.288533 | ||||||||
\(231\) | 1.63702 | 0.107708 | ||||||||
\(232\) | 5.05157 | 0.331652 | ||||||||
\(233\) | −17.6982 | −1.15945 | −0.579724 | − | 0.814813i | \(-0.696840\pi\) | ||||
−0.579724 | + | 0.814813i | \(0.696840\pi\) | |||||||
\(234\) | −0.245103 | −0.0160229 | ||||||||
\(235\) | −10.4220 | −0.679856 | ||||||||
\(236\) | 5.21881 | 0.339716 | ||||||||
\(237\) | 3.73381 | 0.242537 | ||||||||
\(238\) | −0.198583 | −0.0128722 | ||||||||
\(239\) | 1.11014 | 0.0718088 | 0.0359044 | − | 0.999355i | \(-0.488569\pi\) | ||||
0.0359044 | + | 0.999355i | \(0.488569\pi\) | |||||||
\(240\) | 1.70201 | 0.109864 | ||||||||
\(241\) | 7.88619 | 0.507994 | 0.253997 | − | 0.967205i | \(-0.418255\pi\) | ||||
0.253997 | + | 0.967205i | \(0.418255\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 1.07165 | 0.0687461 | ||||||||
\(244\) | 7.54665 | 0.483124 | ||||||||
\(245\) | −6.07490 | −0.388111 | ||||||||
\(246\) | 12.1704 | 0.775958 | ||||||||
\(247\) | 0.982824 | 0.0625356 | ||||||||
\(248\) | 6.59571 | 0.418828 | ||||||||
\(249\) | −9.44548 | −0.598583 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 15.9387 | 1.00604 | 0.503020 | − | 0.864275i | \(-0.332222\pi\) | ||||
0.503020 | + | 0.864275i | \(0.332222\pi\) | |||||||
\(252\) | −0.0992265 | −0.00625068 | ||||||||
\(253\) | −4.37582 | −0.275106 | ||||||||
\(254\) | 2.61565 | 0.164121 | ||||||||
\(255\) | 0.351408 | 0.0220060 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.73607 | 0.108293 | 0.0541465 | − | 0.998533i | \(-0.482756\pi\) | ||||
0.0541465 | + | 0.998533i | \(0.482756\pi\) | |||||||
\(258\) | 1.70201 | 0.105962 | ||||||||
\(259\) | −8.70875 | −0.541135 | ||||||||
\(260\) | −2.37582 | −0.147342 | ||||||||
\(261\) | 0.521148 | 0.0322582 | ||||||||
\(262\) | 9.98567 | 0.616917 | ||||||||
\(263\) | 3.85858 | 0.237931 | 0.118965 | − | 0.992898i | \(-0.462042\pi\) | ||||
0.118965 | + | 0.992898i | \(0.462042\pi\) | |||||||
\(264\) | −1.70201 | −0.104751 | ||||||||
\(265\) | 9.81295 | 0.602805 | ||||||||
\(266\) | 0.397883 | 0.0243957 | ||||||||
\(267\) | −28.4356 | −1.74023 | ||||||||
\(268\) | 7.11705 | 0.434743 | ||||||||
\(269\) | −0.849440 | −0.0517913 | −0.0258957 | − | 0.999665i | \(-0.508244\pi\) | ||||
−0.0258957 | + | 0.999665i | \(0.508244\pi\) | |||||||
\(270\) | 5.28162 | 0.321429 | ||||||||
\(271\) | 8.59360 | 0.522024 | 0.261012 | − | 0.965336i | \(-0.415944\pi\) | ||||
0.261012 | + | 0.965336i | \(0.415944\pi\) | |||||||
\(272\) | 0.206466 | 0.0125189 | ||||||||
\(273\) | −3.88928 | −0.235390 | ||||||||
\(274\) | 15.5593 | 0.939972 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −7.44769 | −0.448298 | ||||||||
\(277\) | 9.73658 | 0.585015 | 0.292507 | − | 0.956263i | \(-0.405510\pi\) | ||||
0.292507 | + | 0.956263i | \(0.405510\pi\) | |||||||
\(278\) | −9.87107 | −0.592028 | ||||||||
\(279\) | 0.680450 | 0.0407374 | ||||||||
\(280\) | −0.961819 | −0.0574797 | ||||||||
\(281\) | −8.69294 | −0.518578 | −0.259289 | − | 0.965800i | \(-0.583488\pi\) | ||||
−0.259289 | + | 0.965800i | \(0.583488\pi\) | |||||||
\(282\) | 17.7383 | 1.05630 | ||||||||
\(283\) | −8.80745 | −0.523548 | −0.261774 | − | 0.965129i | \(-0.584308\pi\) | ||||
−0.261774 | + | 0.965129i | \(0.584308\pi\) | |||||||
\(284\) | 1.63446 | 0.0969872 | ||||||||
\(285\) | −0.704082 | −0.0417062 | ||||||||
\(286\) | 2.37582 | 0.140485 | ||||||||
\(287\) | −6.87760 | −0.405972 | ||||||||
\(288\) | 0.103166 | 0.00607909 | ||||||||
\(289\) | −16.9574 | −0.997492 | ||||||||
\(290\) | 5.05157 | 0.296638 | ||||||||
\(291\) | 4.76520 | 0.279341 | ||||||||
\(292\) | −9.11062 | −0.533159 | ||||||||
\(293\) | 9.46882 | 0.553174 | 0.276587 | − | 0.960989i | \(-0.410797\pi\) | ||||
0.276587 | + | 0.960989i | \(0.410797\pi\) | |||||||
\(294\) | 10.3395 | 0.603014 | ||||||||
\(295\) | 5.21881 | 0.303851 | ||||||||
\(296\) | 9.05446 | 0.526280 | ||||||||
\(297\) | −5.28162 | −0.306470 | ||||||||
\(298\) | −19.6052 | −1.13570 | ||||||||
\(299\) | 10.3962 | 0.601227 | ||||||||
\(300\) | 1.70201 | 0.0982655 | ||||||||
\(301\) | −0.961819 | −0.0554383 | ||||||||
\(302\) | 8.91621 | 0.513070 | ||||||||
\(303\) | 31.4402 | 1.80619 | ||||||||
\(304\) | −0.413677 | −0.0237260 | ||||||||
\(305\) | 7.54665 | 0.432120 | ||||||||
\(306\) | 0.0213002 | 0.00121765 | ||||||||
\(307\) | −8.96899 | −0.511887 | −0.255944 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255944 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(308\) | 0.961819 | 0.0548047 | ||||||||
\(309\) | −25.3973 | −1.44480 | ||||||||
\(310\) | 6.59571 | 0.374611 | ||||||||
\(311\) | 18.6547 | 1.05781 | 0.528905 | − | 0.848681i | \(-0.322603\pi\) | ||||
0.528905 | + | 0.848681i | \(0.322603\pi\) | |||||||
\(312\) | 4.04367 | 0.228928 | ||||||||
\(313\) | 25.3697 | 1.43398 | 0.716990 | − | 0.697084i | \(-0.245519\pi\) | ||||
0.716990 | + | 0.697084i | \(0.245519\pi\) | |||||||
\(314\) | −13.1048 | −0.739549 | ||||||||
\(315\) | −0.0992265 | −0.00559078 | ||||||||
\(316\) | 2.19376 | 0.123409 | ||||||||
\(317\) | −28.8646 | −1.62120 | −0.810600 | − | 0.585600i | \(-0.800859\pi\) | ||||
−0.810600 | + | 0.585600i | \(0.800859\pi\) | |||||||
\(318\) | −16.7017 | −0.936586 | ||||||||
\(319\) | −5.05157 | −0.282834 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 29.3136 | 1.63613 | ||||||||
\(322\) | 4.20875 | 0.234545 | ||||||||
\(323\) | −0.0854105 | −0.00475236 | ||||||||
\(324\) | −8.67986 | −0.482214 | ||||||||
\(325\) | −2.37582 | −0.131787 | ||||||||
\(326\) | −9.93240 | −0.550105 | ||||||||
\(327\) | 8.41231 | 0.465202 | ||||||||
\(328\) | 7.15062 | 0.394827 | ||||||||
\(329\) | −10.0241 | −0.552645 | ||||||||
\(330\) | −1.70201 | −0.0936925 | ||||||||
\(331\) | 32.7920 | 1.80241 | 0.901205 | − | 0.433394i | \(-0.142684\pi\) | ||||
0.901205 | + | 0.433394i | \(0.142684\pi\) | |||||||
\(332\) | −5.54961 | −0.304574 | ||||||||
\(333\) | 0.934108 | 0.0511888 | ||||||||
\(334\) | −5.82283 | −0.318611 | ||||||||
\(335\) | 7.11705 | 0.388846 | ||||||||
\(336\) | 1.63702 | 0.0893070 | ||||||||
\(337\) | −26.1589 | −1.42497 | −0.712483 | − | 0.701689i | \(-0.752430\pi\) | ||||
−0.712483 | + | 0.701689i | \(0.752430\pi\) | |||||||
\(338\) | 7.35546 | 0.400084 | ||||||||
\(339\) | −2.27923 | −0.123791 | ||||||||
\(340\) | 0.206466 | 0.0111972 | ||||||||
\(341\) | −6.59571 | −0.357178 | ||||||||
\(342\) | −0.0426772 | −0.00230772 | ||||||||
\(343\) | −12.5757 | −0.679023 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | −7.44769 | −0.400970 | ||||||||
\(346\) | −21.4892 | −1.15527 | ||||||||
\(347\) | 17.0650 | 0.916099 | 0.458049 | − | 0.888927i | \(-0.348548\pi\) | ||||
0.458049 | + | 0.888927i | \(0.348548\pi\) | |||||||
\(348\) | −8.59782 | −0.460891 | ||||||||
\(349\) | 22.3693 | 1.19740 | 0.598701 | − | 0.800973i | \(-0.295684\pi\) | ||||
0.598701 | + | 0.800973i | \(0.295684\pi\) | |||||||
\(350\) | −0.961819 | −0.0514114 | ||||||||
\(351\) | 12.5482 | 0.669773 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 31.2738 | 1.66454 | 0.832269 | − | 0.554372i | \(-0.187042\pi\) | ||||
0.832269 | + | 0.554372i | \(0.187042\pi\) | |||||||
\(354\) | −8.88246 | −0.472098 | ||||||||
\(355\) | 1.63446 | 0.0867480 | ||||||||
\(356\) | −16.7071 | −0.885474 | ||||||||
\(357\) | 0.337991 | 0.0178884 | ||||||||
\(358\) | 5.87243 | 0.310368 | ||||||||
\(359\) | 24.3617 | 1.28576 | 0.642881 | − | 0.765966i | \(-0.277739\pi\) | ||||
0.642881 | + | 0.765966i | \(0.277739\pi\) | |||||||
\(360\) | 0.103166 | 0.00543730 | ||||||||
\(361\) | −18.8289 | −0.990993 | ||||||||
\(362\) | −2.70569 | −0.142208 | ||||||||
\(363\) | 1.70201 | 0.0893323 | ||||||||
\(364\) | −2.28511 | −0.119772 | ||||||||
\(365\) | −9.11062 | −0.476872 | ||||||||
\(366\) | −12.8445 | −0.671391 | ||||||||
\(367\) | −30.0924 | −1.57081 | −0.785404 | − | 0.618983i | \(-0.787545\pi\) | ||||
−0.785404 | + | 0.618983i | \(0.787545\pi\) | |||||||
\(368\) | −4.37582 | −0.228106 | ||||||||
\(369\) | 0.737698 | 0.0384030 | ||||||||
\(370\) | 9.05446 | 0.470719 | ||||||||
\(371\) | 9.43828 | 0.490011 | ||||||||
\(372\) | −11.2260 | −0.582039 | ||||||||
\(373\) | 7.87615 | 0.407811 | 0.203906 | − | 0.978991i | \(-0.434636\pi\) | ||||
0.203906 | + | 0.978991i | \(0.434636\pi\) | |||||||
\(374\) | −0.206466 | −0.0106761 | ||||||||
\(375\) | 1.70201 | 0.0878914 | ||||||||
\(376\) | 10.4220 | 0.537473 | ||||||||
\(377\) | 12.0016 | 0.618116 | ||||||||
\(378\) | 5.07996 | 0.261285 | ||||||||
\(379\) | −33.5862 | −1.72521 | −0.862603 | − | 0.505882i | \(-0.831167\pi\) | ||||
−0.862603 | + | 0.505882i | \(0.831167\pi\) | |||||||
\(380\) | −0.413677 | −0.0212212 | ||||||||
\(381\) | −4.45186 | −0.228076 | ||||||||
\(382\) | −17.2199 | −0.881046 | ||||||||
\(383\) | −35.5745 | −1.81777 | −0.908886 | − | 0.417044i | \(-0.863066\pi\) | ||||
−0.908886 | + | 0.417044i | \(0.863066\pi\) | |||||||
\(384\) | −1.70201 | −0.0868553 | ||||||||
\(385\) | 0.961819 | 0.0490188 | ||||||||
\(386\) | 9.74778 | 0.496149 | ||||||||
\(387\) | 0.103166 | 0.00524420 | ||||||||
\(388\) | 2.79975 | 0.142136 | ||||||||
\(389\) | −9.06568 | −0.459648 | −0.229824 | − | 0.973232i | \(-0.573815\pi\) | ||||
−0.229824 | + | 0.973232i | \(0.573815\pi\) | |||||||
\(390\) | 4.04367 | 0.204759 | ||||||||
\(391\) | −0.903461 | −0.0456900 | ||||||||
\(392\) | 6.07490 | 0.306829 | ||||||||
\(393\) | −16.9957 | −0.857319 | ||||||||
\(394\) | 20.1939 | 1.01735 | ||||||||
\(395\) | 2.19376 | 0.110380 | ||||||||
\(396\) | −0.103166 | −0.00518426 | ||||||||
\(397\) | −13.6754 | −0.686350 | −0.343175 | − | 0.939272i | \(-0.611502\pi\) | ||||
−0.343175 | + | 0.939272i | \(0.611502\pi\) | |||||||
\(398\) | 11.4718 | 0.575031 | ||||||||
\(399\) | −0.677200 | −0.0339024 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 21.7514 | 1.08622 | 0.543108 | − | 0.839663i | \(-0.317247\pi\) | ||||
0.543108 | + | 0.839663i | \(0.317247\pi\) | |||||||
\(402\) | −12.1133 | −0.604156 | ||||||||
\(403\) | 15.6702 | 0.780590 | ||||||||
\(404\) | 18.4724 | 0.919036 | ||||||||
\(405\) | −8.67986 | −0.431306 | ||||||||
\(406\) | 4.85869 | 0.241133 | ||||||||
\(407\) | −9.05446 | −0.448813 | ||||||||
\(408\) | −0.351408 | −0.0173973 | ||||||||
\(409\) | 19.7331 | 0.975737 | 0.487869 | − | 0.872917i | \(-0.337775\pi\) | ||||
0.487869 | + | 0.872917i | \(0.337775\pi\) | |||||||
\(410\) | 7.15062 | 0.353144 | ||||||||
\(411\) | −26.4821 | −1.30626 | ||||||||
\(412\) | −14.9220 | −0.735153 | ||||||||
\(413\) | 5.01955 | 0.246996 | ||||||||
\(414\) | −0.451434 | −0.0221868 | ||||||||
\(415\) | −5.54961 | −0.272419 | ||||||||
\(416\) | 2.37582 | 0.116484 | ||||||||
\(417\) | 16.8007 | 0.822731 | ||||||||
\(418\) | 0.413677 | 0.0202336 | ||||||||
\(419\) | −33.4352 | −1.63342 | −0.816708 | − | 0.577052i | \(-0.804203\pi\) | ||||
−0.816708 | + | 0.577052i | \(0.804203\pi\) | |||||||
\(420\) | 1.63702 | 0.0798786 | ||||||||
\(421\) | 16.1852 | 0.788820 | 0.394410 | − | 0.918935i | \(-0.370949\pi\) | ||||
0.394410 | + | 0.918935i | \(0.370949\pi\) | |||||||
\(422\) | 4.90180 | 0.238616 | ||||||||
\(423\) | 1.07519 | 0.0522775 | ||||||||
\(424\) | −9.81295 | −0.476559 | ||||||||
\(425\) | 0.206466 | 0.0100151 | ||||||||
\(426\) | −2.78186 | −0.134782 | ||||||||
\(427\) | 7.25851 | 0.351264 | ||||||||
\(428\) | 17.2230 | 0.832503 | ||||||||
\(429\) | −4.04367 | −0.195230 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | 23.9093 | 1.15167 | 0.575834 | − | 0.817566i | \(-0.304677\pi\) | ||||
0.575834 | + | 0.817566i | \(0.304677\pi\) | |||||||
\(432\) | −5.28162 | −0.254112 | ||||||||
\(433\) | −26.9709 | −1.29614 | −0.648069 | − | 0.761581i | \(-0.724423\pi\) | ||||
−0.648069 | + | 0.761581i | \(0.724423\pi\) | |||||||
\(434\) | 6.34388 | 0.304516 | ||||||||
\(435\) | −8.59782 | −0.412234 | ||||||||
\(436\) | 4.94258 | 0.236706 | ||||||||
\(437\) | 1.81018 | 0.0865926 | ||||||||
\(438\) | 15.5064 | 0.740923 | ||||||||
\(439\) | −34.1093 | −1.62795 | −0.813974 | − | 0.580901i | \(-0.802700\pi\) | ||||
−0.813974 | + | 0.580901i | \(0.802700\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 0.626721 | 0.0298438 | ||||||||
\(442\) | 0.490528 | 0.0233320 | ||||||||
\(443\) | −16.1902 | −0.769220 | −0.384610 | − | 0.923079i | \(-0.625664\pi\) | ||||
−0.384610 | + | 0.923079i | \(0.625664\pi\) | |||||||
\(444\) | −15.4108 | −0.731363 | ||||||||
\(445\) | −16.7071 | −0.791992 | ||||||||
\(446\) | −23.1695 | −1.09711 | ||||||||
\(447\) | 33.3682 | 1.57826 | ||||||||
\(448\) | 0.961819 | 0.0454417 | ||||||||
\(449\) | 15.2420 | 0.719315 | 0.359657 | − | 0.933084i | \(-0.382894\pi\) | ||||
0.359657 | + | 0.933084i | \(0.382894\pi\) | |||||||
\(450\) | 0.103166 | 0.00486327 | ||||||||
\(451\) | −7.15062 | −0.336710 | ||||||||
\(452\) | −1.33914 | −0.0629880 | ||||||||
\(453\) | −15.1755 | −0.713006 | ||||||||
\(454\) | −1.95283 | −0.0916507 | ||||||||
\(455\) | −2.28511 | −0.107128 | ||||||||
\(456\) | 0.704082 | 0.0329717 | ||||||||
\(457\) | −12.3146 | −0.576054 | −0.288027 | − | 0.957622i | \(-0.592999\pi\) | ||||
−0.288027 | + | 0.957622i | \(0.592999\pi\) | |||||||
\(458\) | 27.9257 | 1.30488 | ||||||||
\(459\) | −1.09048 | −0.0508991 | ||||||||
\(460\) | −4.37582 | −0.204024 | ||||||||
\(461\) | −7.78904 | −0.362772 | −0.181386 | − | 0.983412i | \(-0.558058\pi\) | ||||
−0.181386 | + | 0.983412i | \(0.558058\pi\) | |||||||
\(462\) | −1.63702 | −0.0761613 | ||||||||
\(463\) | −32.6817 | −1.51885 | −0.759424 | − | 0.650596i | \(-0.774519\pi\) | ||||
−0.759424 | + | 0.650596i | \(0.774519\pi\) | |||||||
\(464\) | −5.05157 | −0.234513 | ||||||||
\(465\) | −11.2260 | −0.520591 | ||||||||
\(466\) | 17.6982 | 0.819853 | ||||||||
\(467\) | 4.73048 | 0.218900 | 0.109450 | − | 0.993992i | \(-0.465091\pi\) | ||||
0.109450 | + | 0.993992i | \(0.465091\pi\) | |||||||
\(468\) | 0.245103 | 0.0113299 | ||||||||
\(469\) | 6.84531 | 0.316087 | ||||||||
\(470\) | 10.4220 | 0.480731 | ||||||||
\(471\) | 22.3046 | 1.02774 | ||||||||
\(472\) | −5.21881 | −0.240215 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −3.73381 | −0.171499 | ||||||||
\(475\) | −0.413677 | −0.0189808 | ||||||||
\(476\) | 0.198583 | 0.00910205 | ||||||||
\(477\) | −1.01236 | −0.0463527 | ||||||||
\(478\) | −1.11014 | −0.0507765 | ||||||||
\(479\) | 4.04389 | 0.184770 | 0.0923851 | − | 0.995723i | \(-0.470551\pi\) | ||||
0.0923851 | + | 0.995723i | \(0.470551\pi\) | |||||||
\(480\) | −1.70201 | −0.0776857 | ||||||||
\(481\) | 21.5118 | 0.980854 | ||||||||
\(482\) | −7.88619 | −0.359206 | ||||||||
\(483\) | −7.16333 | −0.325943 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 2.79975 | 0.127130 | ||||||||
\(486\) | −1.07165 | −0.0486109 | ||||||||
\(487\) | −3.81325 | −0.172795 | −0.0863975 | − | 0.996261i | \(-0.527536\pi\) | ||||
−0.0863975 | + | 0.996261i | \(0.527536\pi\) | |||||||
\(488\) | −7.54665 | −0.341621 | ||||||||
\(489\) | 16.9050 | 0.764472 | ||||||||
\(490\) | 6.07490 | 0.274436 | ||||||||
\(491\) | −34.9008 | −1.57505 | −0.787526 | − | 0.616281i | \(-0.788639\pi\) | ||||
−0.787526 | + | 0.616281i | \(0.788639\pi\) | |||||||
\(492\) | −12.1704 | −0.548685 | ||||||||
\(493\) | −1.04298 | −0.0469734 | ||||||||
\(494\) | −0.982824 | −0.0442194 | ||||||||
\(495\) | −0.103166 | −0.00463694 | ||||||||
\(496\) | −6.59571 | −0.296156 | ||||||||
\(497\) | 1.57205 | 0.0705162 | ||||||||
\(498\) | 9.44548 | 0.423262 | ||||||||
\(499\) | −14.5870 | −0.653005 | −0.326502 | − | 0.945196i | \(-0.605870\pi\) | ||||
−0.326502 | + | 0.945196i | \(0.605870\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 9.91050 | 0.442769 | ||||||||
\(502\) | −15.9387 | −0.711378 | ||||||||
\(503\) | −12.2195 | −0.544840 | −0.272420 | − | 0.962179i | \(-0.587824\pi\) | ||||
−0.272420 | + | 0.962179i | \(0.587824\pi\) | |||||||
\(504\) | 0.0992265 | 0.00441990 | ||||||||
\(505\) | 18.4724 | 0.822011 | ||||||||
\(506\) | 4.37582 | 0.194529 | ||||||||
\(507\) | −12.5191 | −0.555991 | ||||||||
\(508\) | −2.61565 | −0.116051 | ||||||||
\(509\) | 11.9850 | 0.531226 | 0.265613 | − | 0.964080i | \(-0.414426\pi\) | ||||
0.265613 | + | 0.964080i | \(0.414426\pi\) | |||||||
\(510\) | −0.351408 | −0.0155606 | ||||||||
\(511\) | −8.76277 | −0.387642 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.18488 | 0.0964650 | ||||||||
\(514\) | −1.73607 | −0.0765747 | ||||||||
\(515\) | −14.9220 | −0.657541 | ||||||||
\(516\) | −1.70201 | −0.0749268 | ||||||||
\(517\) | −10.4220 | −0.458359 | ||||||||
\(518\) | 8.70875 | 0.382641 | ||||||||
\(519\) | 36.5748 | 1.60546 | ||||||||
\(520\) | 2.37582 | 0.104187 | ||||||||
\(521\) | 12.3064 | 0.539151 | 0.269576 | − | 0.962979i | \(-0.413117\pi\) | ||||
0.269576 | + | 0.962979i | \(0.413117\pi\) | |||||||
\(522\) | −0.521148 | −0.0228100 | ||||||||
\(523\) | 24.2620 | 1.06090 | 0.530451 | − | 0.847715i | \(-0.322022\pi\) | ||||
0.530451 | + | 0.847715i | \(0.322022\pi\) | |||||||
\(524\) | −9.98567 | −0.436226 | ||||||||
\(525\) | 1.63702 | 0.0714456 | ||||||||
\(526\) | −3.85858 | −0.168242 | ||||||||
\(527\) | −1.36179 | −0.0593206 | ||||||||
\(528\) | 1.70201 | 0.0740704 | ||||||||
\(529\) | −3.85216 | −0.167485 | ||||||||
\(530\) | −9.81295 | −0.426247 | ||||||||
\(531\) | −0.538401 | −0.0233646 | ||||||||
\(532\) | −0.397883 | −0.0172504 | ||||||||
\(533\) | 16.9886 | 0.735859 | ||||||||
\(534\) | 28.4356 | 1.23053 | ||||||||
\(535\) | 17.2230 | 0.744614 | ||||||||
\(536\) | −7.11705 | −0.307410 | ||||||||
\(537\) | −9.99493 | −0.431313 | ||||||||
\(538\) | 0.849440 | 0.0366220 | ||||||||
\(539\) | −6.07490 | −0.261665 | ||||||||
\(540\) | −5.28162 | −0.227285 | ||||||||
\(541\) | 3.56831 | 0.153414 | 0.0767068 | − | 0.997054i | \(-0.475559\pi\) | ||||
0.0767068 | + | 0.997054i | \(0.475559\pi\) | |||||||
\(542\) | −8.59360 | −0.369127 | ||||||||
\(543\) | 4.60511 | 0.197624 | ||||||||
\(544\) | −0.206466 | −0.00885217 | ||||||||
\(545\) | 4.94258 | 0.211717 | ||||||||
\(546\) | 3.88928 | 0.166446 | ||||||||
\(547\) | 15.1247 | 0.646684 | 0.323342 | − | 0.946282i | \(-0.395194\pi\) | ||||
0.323342 | + | 0.946282i | \(0.395194\pi\) | |||||||
\(548\) | −15.5593 | −0.664661 | ||||||||
\(549\) | −0.778553 | −0.0332279 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 2.08972 | 0.0890250 | ||||||||
\(552\) | 7.44769 | 0.316995 | ||||||||
\(553\) | 2.11000 | 0.0897265 | ||||||||
\(554\) | −9.73658 | −0.413668 | ||||||||
\(555\) | −15.4108 | −0.654151 | ||||||||
\(556\) | 9.87107 | 0.418627 | ||||||||
\(557\) | −0.572118 | −0.0242414 | −0.0121207 | − | 0.999927i | \(-0.503858\pi\) | ||||
−0.0121207 | + | 0.999927i | \(0.503858\pi\) | |||||||
\(558\) | −0.680450 | −0.0288057 | ||||||||
\(559\) | 2.37582 | 0.100487 | ||||||||
\(560\) | 0.961819 | 0.0406443 | ||||||||
\(561\) | 0.351408 | 0.0148364 | ||||||||
\(562\) | 8.69294 | 0.366690 | ||||||||
\(563\) | 37.1756 | 1.56676 | 0.783382 | − | 0.621540i | \(-0.213493\pi\) | ||||
0.783382 | + | 0.621540i | \(0.213493\pi\) | |||||||
\(564\) | −17.7383 | −0.746918 | ||||||||
\(565\) | −1.33914 | −0.0563382 | ||||||||
\(566\) | 8.80745 | 0.370205 | ||||||||
\(567\) | −8.34845 | −0.350602 | ||||||||
\(568\) | −1.63446 | −0.0685803 | ||||||||
\(569\) | 14.7054 | 0.616482 | 0.308241 | − | 0.951308i | \(-0.400260\pi\) | ||||
0.308241 | + | 0.951308i | \(0.400260\pi\) | |||||||
\(570\) | 0.704082 | 0.0294908 | ||||||||
\(571\) | 22.3192 | 0.934029 | 0.467014 | − | 0.884250i | \(-0.345330\pi\) | ||||
0.467014 | + | 0.884250i | \(0.345330\pi\) | |||||||
\(572\) | −2.37582 | −0.0993382 | ||||||||
\(573\) | 29.3084 | 1.22438 | ||||||||
\(574\) | 6.87760 | 0.287066 | ||||||||
\(575\) | −4.37582 | −0.182484 | ||||||||
\(576\) | −0.103166 | −0.00429856 | ||||||||
\(577\) | −29.7288 | −1.23763 | −0.618814 | − | 0.785538i | \(-0.712387\pi\) | ||||
−0.618814 | + | 0.785538i | \(0.712387\pi\) | |||||||
\(578\) | 16.9574 | 0.705334 | ||||||||
\(579\) | −16.5908 | −0.689490 | ||||||||
\(580\) | −5.05157 | −0.209755 | ||||||||
\(581\) | −5.33772 | −0.221446 | ||||||||
\(582\) | −4.76520 | −0.197524 | ||||||||
\(583\) | 9.81295 | 0.406411 | ||||||||
\(584\) | 9.11062 | 0.377000 | ||||||||
\(585\) | 0.245103 | 0.0101338 | ||||||||
\(586\) | −9.46882 | −0.391153 | ||||||||
\(587\) | −27.2434 | −1.12445 | −0.562227 | − | 0.826983i | \(-0.690055\pi\) | ||||
−0.562227 | + | 0.826983i | \(0.690055\pi\) | |||||||
\(588\) | −10.3395 | −0.426396 | ||||||||
\(589\) | 2.72849 | 0.112426 | ||||||||
\(590\) | −5.21881 | −0.214855 | ||||||||
\(591\) | −34.3702 | −1.41380 | ||||||||
\(592\) | −9.05446 | −0.372136 | ||||||||
\(593\) | −10.1627 | −0.417333 | −0.208666 | − | 0.977987i | \(-0.566912\pi\) | ||||
−0.208666 | + | 0.977987i | \(0.566912\pi\) | |||||||
\(594\) | 5.28162 | 0.216707 | ||||||||
\(595\) | 0.198583 | 0.00814112 | ||||||||
\(596\) | 19.6052 | 0.803060 | ||||||||
\(597\) | −19.5251 | −0.799111 | ||||||||
\(598\) | −10.3962 | −0.425132 | ||||||||
\(599\) | 8.32534 | 0.340164 | 0.170082 | − | 0.985430i | \(-0.445597\pi\) | ||||
0.170082 | + | 0.985430i | \(0.445597\pi\) | |||||||
\(600\) | −1.70201 | −0.0694842 | ||||||||
\(601\) | −15.7094 | −0.640799 | −0.320400 | − | 0.947282i | \(-0.603817\pi\) | ||||
−0.320400 | + | 0.947282i | \(0.603817\pi\) | |||||||
\(602\) | 0.961819 | 0.0392008 | ||||||||
\(603\) | −0.734234 | −0.0299003 | ||||||||
\(604\) | −8.91621 | −0.362795 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −31.4402 | −1.27717 | ||||||||
\(607\) | −32.9503 | −1.33741 | −0.668706 | − | 0.743527i | \(-0.733151\pi\) | ||||
−0.668706 | + | 0.743527i | \(0.733151\pi\) | |||||||
\(608\) | 0.413677 | 0.0167768 | ||||||||
\(609\) | −8.26954 | −0.335099 | ||||||||
\(610\) | −7.54665 | −0.305555 | ||||||||
\(611\) | 24.7608 | 1.00172 | ||||||||
\(612\) | −0.0213002 | −0.000861010 0 | ||||||||
\(613\) | −28.9790 | −1.17045 | −0.585226 | − | 0.810870i | \(-0.698994\pi\) | ||||
−0.585226 | + | 0.810870i | \(0.698994\pi\) | |||||||
\(614\) | 8.96899 | 0.361959 | ||||||||
\(615\) | −12.1704 | −0.490759 | ||||||||
\(616\) | −0.961819 | −0.0387528 | ||||||||
\(617\) | −17.1103 | −0.688833 | −0.344416 | − | 0.938817i | \(-0.611923\pi\) | ||||
−0.344416 | + | 0.938817i | \(0.611923\pi\) | |||||||
\(618\) | 25.3973 | 1.02163 | ||||||||
\(619\) | 7.74766 | 0.311405 | 0.155702 | − | 0.987804i | \(-0.450236\pi\) | ||||
0.155702 | + | 0.987804i | \(0.450236\pi\) | |||||||
\(620\) | −6.59571 | −0.264890 | ||||||||
\(621\) | 23.1114 | 0.927429 | ||||||||
\(622\) | −18.6547 | −0.747985 | ||||||||
\(623\) | −16.0692 | −0.643799 | ||||||||
\(624\) | −4.04367 | −0.161877 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −25.3697 | −1.01398 | ||||||||
\(627\) | −0.704082 | −0.0281183 | ||||||||
\(628\) | 13.1048 | 0.522940 | ||||||||
\(629\) | −1.86944 | −0.0745395 | ||||||||
\(630\) | 0.0992265 | 0.00395328 | ||||||||
\(631\) | −11.5964 | −0.461646 | −0.230823 | − | 0.972996i | \(-0.574142\pi\) | ||||
−0.230823 | + | 0.972996i | \(0.574142\pi\) | |||||||
\(632\) | −2.19376 | −0.0872633 | ||||||||
\(633\) | −8.34291 | −0.331601 | ||||||||
\(634\) | 28.8646 | 1.14636 | ||||||||
\(635\) | −2.61565 | −0.103799 | ||||||||
\(636\) | 16.7017 | 0.662267 | ||||||||
\(637\) | 14.4329 | 0.571853 | ||||||||
\(638\) | 5.05157 | 0.199994 | ||||||||
\(639\) | −0.168620 | −0.00667049 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 3.15569 | 0.124642 | 0.0623211 | − | 0.998056i | \(-0.480150\pi\) | ||||
0.0623211 | + | 0.998056i | \(0.480150\pi\) | |||||||
\(642\) | −29.3136 | −1.15692 | ||||||||
\(643\) | −23.6766 | −0.933715 | −0.466858 | − | 0.884332i | \(-0.654614\pi\) | ||||
−0.466858 | + | 0.884332i | \(0.654614\pi\) | |||||||
\(644\) | −4.20875 | −0.165848 | ||||||||
\(645\) | −1.70201 | −0.0670165 | ||||||||
\(646\) | 0.0854105 | 0.00336043 | ||||||||
\(647\) | 33.0208 | 1.29818 | 0.649091 | − | 0.760710i | \(-0.275149\pi\) | ||||
0.649091 | + | 0.760710i | \(0.275149\pi\) | |||||||
\(648\) | 8.67986 | 0.340977 | ||||||||
\(649\) | 5.21881 | 0.204856 | ||||||||
\(650\) | 2.37582 | 0.0931875 | ||||||||
\(651\) | −10.7973 | −0.423181 | ||||||||
\(652\) | 9.93240 | 0.388983 | ||||||||
\(653\) | −39.1416 | −1.53173 | −0.765865 | − | 0.643001i | \(-0.777689\pi\) | ||||
−0.765865 | + | 0.643001i | \(0.777689\pi\) | |||||||
\(654\) | −8.41231 | −0.328947 | ||||||||
\(655\) | −9.98567 | −0.390172 | ||||||||
\(656\) | −7.15062 | −0.279185 | ||||||||
\(657\) | 0.939902 | 0.0366691 | ||||||||
\(658\) | 10.0241 | 0.390779 | ||||||||
\(659\) | −33.6319 | −1.31011 | −0.655056 | − | 0.755580i | \(-0.727355\pi\) | ||||
−0.655056 | + | 0.755580i | \(0.727355\pi\) | |||||||
\(660\) | 1.70201 | 0.0662506 | ||||||||
\(661\) | 43.8811 | 1.70678 | 0.853389 | − | 0.521275i | \(-0.174543\pi\) | ||||
0.853389 | + | 0.521275i | \(0.174543\pi\) | |||||||
\(662\) | −32.7920 | −1.27450 | ||||||||
\(663\) | −0.834883 | −0.0324242 | ||||||||
\(664\) | 5.54961 | 0.215366 | ||||||||
\(665\) | −0.397883 | −0.0154292 | ||||||||
\(666\) | −0.934108 | −0.0361959 | ||||||||
\(667\) | 22.1048 | 0.855900 | ||||||||
\(668\) | 5.82283 | 0.225292 | ||||||||
\(669\) | 39.4347 | 1.52463 | ||||||||
\(670\) | −7.11705 | −0.274956 | ||||||||
\(671\) | 7.54665 | 0.291335 | ||||||||
\(672\) | −1.63702 | −0.0631496 | ||||||||
\(673\) | −14.1334 | −0.544802 | −0.272401 | − | 0.962184i | \(-0.587818\pi\) | ||||
−0.272401 | + | 0.962184i | \(0.587818\pi\) | |||||||
\(674\) | 26.1589 | 1.00760 | ||||||||
\(675\) | −5.28162 | −0.203289 | ||||||||
\(676\) | −7.35546 | −0.282902 | ||||||||
\(677\) | −20.3729 | −0.782995 | −0.391498 | − | 0.920179i | \(-0.628043\pi\) | ||||
−0.391498 | + | 0.920179i | \(0.628043\pi\) | |||||||
\(678\) | 2.27923 | 0.0875334 | ||||||||
\(679\) | 2.69285 | 0.103342 | ||||||||
\(680\) | −0.206466 | −0.00791763 | ||||||||
\(681\) | 3.32373 | 0.127366 | ||||||||
\(682\) | 6.59571 | 0.252563 | ||||||||
\(683\) | 16.1894 | 0.619471 | 0.309736 | − | 0.950823i | \(-0.399759\pi\) | ||||
0.309736 | + | 0.950823i | \(0.399759\pi\) | |||||||
\(684\) | 0.0426772 | 0.00163180 | ||||||||
\(685\) | −15.5593 | −0.594491 | ||||||||
\(686\) | 12.5757 | 0.480142 | ||||||||
\(687\) | −47.5299 | −1.81338 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | −23.3138 | −0.888187 | ||||||||
\(690\) | 7.44769 | 0.283529 | ||||||||
\(691\) | 10.5271 | 0.400470 | 0.200235 | − | 0.979748i | \(-0.435829\pi\) | ||||
0.200235 | + | 0.979748i | \(0.435829\pi\) | |||||||
\(692\) | 21.4892 | 0.816897 | ||||||||
\(693\) | −0.0992265 | −0.00376930 | ||||||||
\(694\) | −17.0650 | −0.647779 | ||||||||
\(695\) | 9.87107 | 0.374431 | ||||||||
\(696\) | 8.59782 | 0.325899 | ||||||||
\(697\) | −1.47636 | −0.0559212 | ||||||||
\(698\) | −22.3693 | −0.846690 | ||||||||
\(699\) | −30.1225 | −1.13934 | ||||||||
\(700\) | 0.961819 | 0.0363533 | ||||||||
\(701\) | 37.6120 | 1.42059 | 0.710293 | − | 0.703906i | \(-0.248562\pi\) | ||||
0.710293 | + | 0.703906i | \(0.248562\pi\) | |||||||
\(702\) | −12.5482 | −0.473601 | ||||||||
\(703\) | 3.74562 | 0.141269 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −17.7383 | −0.668064 | ||||||||
\(706\) | −31.2738 | −1.17701 | ||||||||
\(707\) | 17.7671 | 0.668200 | ||||||||
\(708\) | 8.88246 | 0.333823 | ||||||||
\(709\) | −5.33959 | −0.200532 | −0.100266 | − | 0.994961i | \(-0.531969\pi\) | ||||
−0.100266 | + | 0.994961i | \(0.531969\pi\) | |||||||
\(710\) | −1.63446 | −0.0613401 | ||||||||
\(711\) | −0.226321 | −0.00848769 | ||||||||
\(712\) | 16.7071 | 0.626125 | ||||||||
\(713\) | 28.8617 | 1.08088 | ||||||||
\(714\) | −0.337991 | −0.0126490 | ||||||||
\(715\) | −2.37582 | −0.0888508 | ||||||||
\(716\) | −5.87243 | −0.219463 | ||||||||
\(717\) | 1.88946 | 0.0705633 | ||||||||
\(718\) | −24.3617 | −0.909171 | ||||||||
\(719\) | 28.7331 | 1.07156 | 0.535782 | − | 0.844356i | \(-0.320017\pi\) | ||||
0.535782 | + | 0.844356i | \(0.320017\pi\) | |||||||
\(720\) | −0.103166 | −0.00384475 | ||||||||
\(721\) | −14.3522 | −0.534505 | ||||||||
\(722\) | 18.8289 | 0.700738 | ||||||||
\(723\) | 13.4224 | 0.499183 | ||||||||
\(724\) | 2.70569 | 0.100556 | ||||||||
\(725\) | −5.05157 | −0.187611 | ||||||||
\(726\) | −1.70201 | −0.0631675 | ||||||||
\(727\) | −40.7811 | −1.51249 | −0.756244 | − | 0.654289i | \(-0.772968\pi\) | ||||
−0.756244 | + | 0.654289i | \(0.772968\pi\) | |||||||
\(728\) | 2.28511 | 0.0846919 | ||||||||
\(729\) | 27.8635 | 1.03198 | ||||||||
\(730\) | 9.11062 | 0.337199 | ||||||||
\(731\) | −0.206466 | −0.00763644 | ||||||||
\(732\) | 12.8445 | 0.474745 | ||||||||
\(733\) | −0.227142 | −0.00838967 | −0.00419484 | − | 0.999991i | \(-0.501335\pi\) | ||||
−0.00419484 | + | 0.999991i | \(0.501335\pi\) | |||||||
\(734\) | 30.0924 | 1.11073 | ||||||||
\(735\) | −10.3395 | −0.381380 | ||||||||
\(736\) | 4.37582 | 0.161295 | ||||||||
\(737\) | 7.11705 | 0.262160 | ||||||||
\(738\) | −0.737698 | −0.0271550 | ||||||||
\(739\) | −20.3171 | −0.747375 | −0.373688 | − | 0.927555i | \(-0.621907\pi\) | ||||
−0.373688 | + | 0.927555i | \(0.621907\pi\) | |||||||
\(740\) | −9.05446 | −0.332849 | ||||||||
\(741\) | 1.67278 | 0.0614510 | ||||||||
\(742\) | −9.43828 | −0.346490 | ||||||||
\(743\) | 34.4385 | 1.26343 | 0.631713 | − | 0.775202i | \(-0.282352\pi\) | ||||
0.631713 | + | 0.775202i | \(0.282352\pi\) | |||||||
\(744\) | 11.2260 | 0.411563 | ||||||||
\(745\) | 19.6052 | 0.718279 | ||||||||
\(746\) | −7.87615 | −0.288366 | ||||||||
\(747\) | 0.572528 | 0.0209477 | ||||||||
\(748\) | 0.206466 | 0.00754916 | ||||||||
\(749\) | 16.5654 | 0.605286 | ||||||||
\(750\) | −1.70201 | −0.0621486 | ||||||||
\(751\) | 17.0082 | 0.620638 | 0.310319 | − | 0.950632i | \(-0.399564\pi\) | ||||
0.310319 | + | 0.950632i | \(0.399564\pi\) | |||||||
\(752\) | −10.4220 | −0.380051 | ||||||||
\(753\) | 27.1278 | 0.988591 | ||||||||
\(754\) | −12.0016 | −0.437074 | ||||||||
\(755\) | −8.91621 | −0.324494 | ||||||||
\(756\) | −5.07996 | −0.184756 | ||||||||
\(757\) | −14.1239 | −0.513342 | −0.256671 | − | 0.966499i | \(-0.582626\pi\) | ||||
−0.256671 | + | 0.966499i | \(0.582626\pi\) | |||||||
\(758\) | 33.5862 | 1.21990 | ||||||||
\(759\) | −7.44769 | −0.270334 | ||||||||
\(760\) | 0.413677 | 0.0150057 | ||||||||
\(761\) | −44.1831 | −1.60163 | −0.800817 | − | 0.598909i | \(-0.795601\pi\) | ||||
−0.800817 | + | 0.598909i | \(0.795601\pi\) | |||||||
\(762\) | 4.45186 | 0.161274 | ||||||||
\(763\) | 4.75386 | 0.172101 | ||||||||
\(764\) | 17.2199 | 0.622994 | ||||||||
\(765\) | −0.0213002 | −0.000770111 0 | ||||||||
\(766\) | 35.5745 | 1.28536 | ||||||||
\(767\) | −12.3990 | −0.447701 | ||||||||
\(768\) | 1.70201 | 0.0614160 | ||||||||
\(769\) | −4.06495 | −0.146586 | −0.0732929 | − | 0.997310i | \(-0.523351\pi\) | ||||
−0.0732929 | + | 0.997310i | \(0.523351\pi\) | |||||||
\(770\) | −0.961819 | −0.0346615 | ||||||||
\(771\) | 2.95480 | 0.106415 | ||||||||
\(772\) | −9.74778 | −0.350830 | ||||||||
\(773\) | 13.8922 | 0.499669 | 0.249834 | − | 0.968289i | \(-0.419624\pi\) | ||||
0.249834 | + | 0.968289i | \(0.419624\pi\) | |||||||
\(774\) | −0.103166 | −0.00370821 | ||||||||
\(775\) | −6.59571 | −0.236925 | ||||||||
\(776\) | −2.79975 | −0.100505 | ||||||||
\(777\) | −14.8224 | −0.531750 | ||||||||
\(778\) | 9.06568 | 0.325020 | ||||||||
\(779\) | 2.95805 | 0.105983 | ||||||||
\(780\) | −4.04367 | −0.144787 | ||||||||
\(781\) | 1.63446 | 0.0584855 | ||||||||
\(782\) | 0.903461 | 0.0323077 | ||||||||
\(783\) | 26.6804 | 0.953481 | ||||||||
\(784\) | −6.07490 | −0.216961 | ||||||||
\(785\) | 13.1048 | 0.467732 | ||||||||
\(786\) | 16.9957 | 0.606216 | ||||||||
\(787\) | −16.0702 | −0.572840 | −0.286420 | − | 0.958104i | \(-0.592465\pi\) | ||||
−0.286420 | + | 0.958104i | \(0.592465\pi\) | |||||||
\(788\) | −20.1939 | −0.719377 | ||||||||
\(789\) | 6.56735 | 0.233804 | ||||||||
\(790\) | −2.19376 | −0.0780506 | ||||||||
\(791\) | −1.28801 | −0.0457965 | ||||||||
\(792\) | 0.103166 | 0.00366583 | ||||||||
\(793\) | −17.9295 | −0.636695 | ||||||||
\(794\) | 13.6754 | 0.485323 | ||||||||
\(795\) | 16.7017 | 0.592349 | ||||||||
\(796\) | −11.4718 | −0.406608 | ||||||||
\(797\) | −24.5095 | −0.868172 | −0.434086 | − | 0.900872i | \(-0.642929\pi\) | ||||
−0.434086 | + | 0.900872i | \(0.642929\pi\) | |||||||
\(798\) | 0.677200 | 0.0239726 | ||||||||
\(799\) | −2.15179 | −0.0761249 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 1.72360 | 0.0609002 | ||||||||
\(802\) | −21.7514 | −0.768070 | ||||||||
\(803\) | −9.11062 | −0.321507 | ||||||||
\(804\) | 12.1133 | 0.427203 | ||||||||
\(805\) | −4.20875 | −0.148339 | ||||||||
\(806\) | −15.6702 | −0.551961 | ||||||||
\(807\) | −1.44576 | −0.0508930 | ||||||||
\(808\) | −18.4724 | −0.649856 | ||||||||
\(809\) | −22.7326 | −0.799237 | −0.399618 | − | 0.916682i | \(-0.630857\pi\) | ||||
−0.399618 | + | 0.916682i | \(0.630857\pi\) | |||||||
\(810\) | 8.67986 | 0.304979 | ||||||||
\(811\) | 8.81751 | 0.309625 | 0.154812 | − | 0.987944i | \(-0.450523\pi\) | ||||
0.154812 | + | 0.987944i | \(0.450523\pi\) | |||||||
\(812\) | −4.85869 | −0.170507 | ||||||||
\(813\) | 14.6264 | 0.512970 | ||||||||
\(814\) | 9.05446 | 0.317359 | ||||||||
\(815\) | 9.93240 | 0.347917 | ||||||||
\(816\) | 0.351408 | 0.0123017 | ||||||||
\(817\) | 0.413677 | 0.0144727 | ||||||||
\(818\) | −19.7331 | −0.689950 | ||||||||
\(819\) | 0.235745 | 0.00823759 | ||||||||
\(820\) | −7.15062 | −0.249711 | ||||||||
\(821\) | 39.0023 | 1.36119 | 0.680595 | − | 0.732660i | \(-0.261721\pi\) | ||||
0.680595 | + | 0.732660i | \(0.261721\pi\) | |||||||
\(822\) | 26.4821 | 0.923669 | ||||||||
\(823\) | −31.2002 | −1.08757 | −0.543786 | − | 0.839224i | \(-0.683010\pi\) | ||||
−0.543786 | + | 0.839224i | \(0.683010\pi\) | |||||||
\(824\) | 14.9220 | 0.519832 | ||||||||
\(825\) | 1.70201 | 0.0592563 | ||||||||
\(826\) | −5.01955 | −0.174653 | ||||||||
\(827\) | −55.4006 | −1.92647 | −0.963234 | − | 0.268664i | \(-0.913418\pi\) | ||||
−0.963234 | + | 0.268664i | \(0.913418\pi\) | |||||||
\(828\) | 0.451434 | 0.0156884 | ||||||||
\(829\) | 1.43127 | 0.0497101 | 0.0248551 | − | 0.999691i | \(-0.492088\pi\) | ||||
0.0248551 | + | 0.999691i | \(0.492088\pi\) | |||||||
\(830\) | 5.54961 | 0.192630 | ||||||||
\(831\) | 16.5718 | 0.574868 | ||||||||
\(832\) | −2.37582 | −0.0823669 | ||||||||
\(833\) | −1.25426 | −0.0434577 | ||||||||
\(834\) | −16.8007 | −0.581759 | ||||||||
\(835\) | 5.82283 | 0.201507 | ||||||||
\(836\) | −0.413677 | −0.0143073 | ||||||||
\(837\) | 34.8360 | 1.20411 | ||||||||
\(838\) | 33.4352 | 1.15500 | ||||||||
\(839\) | 2.47077 | 0.0853005 | 0.0426503 | − | 0.999090i | \(-0.486420\pi\) | ||||
0.0426503 | + | 0.999090i | \(0.486420\pi\) | |||||||
\(840\) | −1.63702 | −0.0564827 | ||||||||
\(841\) | −3.48165 | −0.120057 | ||||||||
\(842\) | −16.1852 | −0.557780 | ||||||||
\(843\) | −14.7955 | −0.509583 | ||||||||
\(844\) | −4.90180 | −0.168727 | ||||||||
\(845\) | −7.35546 | −0.253035 | ||||||||
\(846\) | −1.07519 | −0.0369658 | ||||||||
\(847\) | 0.961819 | 0.0330485 | ||||||||
\(848\) | 9.81295 | 0.336978 | ||||||||
\(849\) | −14.9904 | −0.514468 | ||||||||
\(850\) | −0.206466 | −0.00708174 | ||||||||
\(851\) | 39.6207 | 1.35818 | ||||||||
\(852\) | 2.78186 | 0.0953050 | ||||||||
\(853\) | −49.5735 | −1.69736 | −0.848682 | − | 0.528903i | \(-0.822604\pi\) | ||||
−0.848682 | + | 0.528903i | \(0.822604\pi\) | |||||||
\(854\) | −7.25851 | −0.248381 | ||||||||
\(855\) | 0.0426772 | 0.00145953 | ||||||||
\(856\) | −17.2230 | −0.588669 | ||||||||
\(857\) | −32.4395 | −1.10811 | −0.554056 | − | 0.832479i | \(-0.686921\pi\) | ||||
−0.554056 | + | 0.832479i | \(0.686921\pi\) | |||||||
\(858\) | 4.04367 | 0.138049 | ||||||||
\(859\) | −2.78379 | −0.0949816 | −0.0474908 | − | 0.998872i | \(-0.515122\pi\) | ||||
−0.0474908 | + | 0.998872i | \(0.515122\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | −11.7057 | −0.398931 | ||||||||
\(862\) | −23.9093 | −0.814353 | ||||||||
\(863\) | −37.1206 | −1.26360 | −0.631801 | − | 0.775131i | \(-0.717684\pi\) | ||||
−0.631801 | + | 0.775131i | \(0.717684\pi\) | |||||||
\(864\) | 5.28162 | 0.179684 | ||||||||
\(865\) | 21.4892 | 0.730655 | ||||||||
\(866\) | 26.9709 | 0.916508 | ||||||||
\(867\) | −28.8616 | −0.980191 | ||||||||
\(868\) | −6.34388 | −0.215325 | ||||||||
\(869\) | 2.19376 | 0.0744184 | ||||||||
\(870\) | 8.59782 | 0.291493 | ||||||||
\(871\) | −16.9089 | −0.572935 | ||||||||
\(872\) | −4.94258 | −0.167377 | ||||||||
\(873\) | −0.288838 | −0.00977567 | ||||||||
\(874\) | −1.81018 | −0.0612302 | ||||||||
\(875\) | 0.961819 | 0.0325154 | ||||||||
\(876\) | −15.5064 | −0.523911 | ||||||||
\(877\) | −41.3812 | −1.39734 | −0.698672 | − | 0.715442i | \(-0.746225\pi\) | ||||
−0.698672 | + | 0.715442i | \(0.746225\pi\) | |||||||
\(878\) | 34.1093 | 1.15113 | ||||||||
\(879\) | 16.1160 | 0.543580 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 50.3228 | 1.69542 | 0.847709 | − | 0.530462i | \(-0.177982\pi\) | ||||
0.847709 | + | 0.530462i | \(0.177982\pi\) | |||||||
\(882\) | −0.626721 | −0.0211028 | ||||||||
\(883\) | 9.51376 | 0.320163 | 0.160082 | − | 0.987104i | \(-0.448824\pi\) | ||||
0.160082 | + | 0.987104i | \(0.448824\pi\) | |||||||
\(884\) | −0.490528 | −0.0164982 | ||||||||
\(885\) | 8.88246 | 0.298581 | ||||||||
\(886\) | 16.1902 | 0.543920 | ||||||||
\(887\) | 49.4737 | 1.66116 | 0.830582 | − | 0.556896i | \(-0.188008\pi\) | ||||
0.830582 | + | 0.556896i | \(0.188008\pi\) | |||||||
\(888\) | 15.4108 | 0.517152 | ||||||||
\(889\) | −2.51578 | −0.0843766 | ||||||||
\(890\) | 16.7071 | 0.560023 | ||||||||
\(891\) | −8.67986 | −0.290786 | ||||||||
\(892\) | 23.1695 | 0.775773 | ||||||||
\(893\) | 4.31134 | 0.144273 | ||||||||
\(894\) | −33.3682 | −1.11600 | ||||||||
\(895\) | −5.87243 | −0.196294 | ||||||||
\(896\) | −0.961819 | −0.0321321 | ||||||||
\(897\) | 17.6944 | 0.590799 | ||||||||
\(898\) | −15.2420 | −0.508632 | ||||||||
\(899\) | 33.3187 | 1.11124 | ||||||||
\(900\) | −0.103166 | −0.00343885 | ||||||||
\(901\) | 2.02604 | 0.0674973 | ||||||||
\(902\) | 7.15062 | 0.238090 | ||||||||
\(903\) | −1.63702 | −0.0544768 | ||||||||
\(904\) | 1.33914 | 0.0445392 | ||||||||
\(905\) | 2.70569 | 0.0899403 | ||||||||
\(906\) | 15.1755 | 0.504171 | ||||||||
\(907\) | 36.9144 | 1.22572 | 0.612862 | − | 0.790190i | \(-0.290018\pi\) | ||||
0.612862 | + | 0.790190i | \(0.290018\pi\) | |||||||
\(908\) | 1.95283 | 0.0648068 | ||||||||
\(909\) | −1.90571 | −0.0632085 | ||||||||
\(910\) | 2.28511 | 0.0757508 | ||||||||
\(911\) | −20.1105 | −0.666291 | −0.333146 | − | 0.942875i | \(-0.608110\pi\) | ||||
−0.333146 | + | 0.942875i | \(0.608110\pi\) | |||||||
\(912\) | −0.704082 | −0.0233145 | ||||||||
\(913\) | −5.54961 | −0.183665 | ||||||||
\(914\) | 12.3146 | 0.407331 | ||||||||
\(915\) | 12.8445 | 0.424625 | ||||||||
\(916\) | −27.9257 | −0.922692 | ||||||||
\(917\) | −9.60440 | −0.317165 | ||||||||
\(918\) | 1.09048 | 0.0359911 | ||||||||
\(919\) | −3.83727 | −0.126580 | −0.0632899 | − | 0.997995i | \(-0.520159\pi\) | ||||
−0.0632899 | + | 0.997995i | \(0.520159\pi\) | |||||||
\(920\) | 4.37582 | 0.144267 | ||||||||
\(921\) | −15.2653 | −0.503009 | ||||||||
\(922\) | 7.78904 | 0.256518 | ||||||||
\(923\) | −3.88318 | −0.127817 | ||||||||
\(924\) | 1.63702 | 0.0538542 | ||||||||
\(925\) | −9.05446 | −0.297709 | ||||||||
\(926\) | 32.6817 | 1.07399 | ||||||||
\(927\) | 1.53943 | 0.0505616 | ||||||||
\(928\) | 5.05157 | 0.165826 | ||||||||
\(929\) | 57.2835 | 1.87941 | 0.939705 | − | 0.341985i | \(-0.111099\pi\) | ||||
0.939705 | + | 0.341985i | \(0.111099\pi\) | |||||||
\(930\) | 11.2260 | 0.368114 | ||||||||
\(931\) | 2.51305 | 0.0823619 | ||||||||
\(932\) | −17.6982 | −0.579724 | ||||||||
\(933\) | 31.7505 | 1.03946 | ||||||||
\(934\) | −4.73048 | −0.154786 | ||||||||
\(935\) | 0.206466 | 0.00675217 | ||||||||
\(936\) | −0.245103 | −0.00801145 | ||||||||
\(937\) | 17.9301 | 0.585751 | 0.292876 | − | 0.956151i | \(-0.405388\pi\) | ||||
0.292876 | + | 0.956151i | \(0.405388\pi\) | |||||||
\(938\) | −6.84531 | −0.223507 | ||||||||
\(939\) | 43.1794 | 1.40911 | ||||||||
\(940\) | −10.4220 | −0.339928 | ||||||||
\(941\) | 42.8854 | 1.39802 | 0.699012 | − | 0.715110i | \(-0.253623\pi\) | ||||
0.699012 | + | 0.715110i | \(0.253623\pi\) | |||||||
\(942\) | −22.3046 | −0.726722 | ||||||||
\(943\) | 31.2899 | 1.01894 | ||||||||
\(944\) | 5.21881 | 0.169858 | ||||||||
\(945\) | −5.07996 | −0.165251 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −16.2404 | −0.527742 | −0.263871 | − | 0.964558i | \(-0.584999\pi\) | ||||
−0.263871 | + | 0.964558i | \(0.584999\pi\) | |||||||
\(948\) | 3.73381 | 0.121268 | ||||||||
\(949\) | 21.6452 | 0.702634 | ||||||||
\(950\) | 0.413677 | 0.0134215 | ||||||||
\(951\) | −49.1279 | −1.59308 | ||||||||
\(952\) | −0.198583 | −0.00643612 | ||||||||
\(953\) | 42.8358 | 1.38759 | 0.693794 | − | 0.720173i | \(-0.255938\pi\) | ||||
0.693794 | + | 0.720173i | \(0.255938\pi\) | |||||||
\(954\) | 1.01236 | 0.0327763 | ||||||||
\(955\) | 17.2199 | 0.557223 | ||||||||
\(956\) | 1.11014 | 0.0359044 | ||||||||
\(957\) | −8.59782 | −0.277928 | ||||||||
\(958\) | −4.04389 | −0.130652 | ||||||||
\(959\) | −14.9652 | −0.483253 | ||||||||
\(960\) | 1.70201 | 0.0549321 | ||||||||
\(961\) | 12.5034 | 0.403334 | ||||||||
\(962\) | −21.5118 | −0.693568 | ||||||||
\(963\) | −1.77682 | −0.0572571 | ||||||||
\(964\) | 7.88619 | 0.253997 | ||||||||
\(965\) | −9.74778 | −0.313792 | ||||||||
\(966\) | 7.16333 | 0.230476 | ||||||||
\(967\) | 47.4970 | 1.52740 | 0.763700 | − | 0.645572i | \(-0.223381\pi\) | ||||
0.763700 | + | 0.645572i | \(0.223381\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −0.145369 | −0.00466994 | ||||||||
\(970\) | −2.79975 | −0.0898945 | ||||||||
\(971\) | 1.33889 | 0.0429669 | 0.0214835 | − | 0.999769i | \(-0.493161\pi\) | ||||
0.0214835 | + | 0.999769i | \(0.493161\pi\) | |||||||
\(972\) | 1.07165 | 0.0343731 | ||||||||
\(973\) | 9.49418 | 0.304370 | ||||||||
\(974\) | 3.81325 | 0.122185 | ||||||||
\(975\) | −4.04367 | −0.129501 | ||||||||
\(976\) | 7.54665 | 0.241562 | ||||||||
\(977\) | 21.7838 | 0.696926 | 0.348463 | − | 0.937323i | \(-0.386704\pi\) | ||||
0.348463 | + | 0.937323i | \(0.386704\pi\) | |||||||
\(978\) | −16.9050 | −0.540563 | ||||||||
\(979\) | −16.7071 | −0.533961 | ||||||||
\(980\) | −6.07490 | −0.194056 | ||||||||
\(981\) | −0.509903 | −0.0162800 | ||||||||
\(982\) | 34.9008 | 1.11373 | ||||||||
\(983\) | 12.9448 | 0.412873 | 0.206437 | − | 0.978460i | \(-0.433813\pi\) | ||||
0.206437 | + | 0.978460i | \(0.433813\pi\) | |||||||
\(984\) | 12.1704 | 0.387979 | ||||||||
\(985\) | −20.1939 | −0.643431 | ||||||||
\(986\) | 1.04298 | 0.0332152 | ||||||||
\(987\) | −17.0611 | −0.543059 | ||||||||
\(988\) | 0.982824 | 0.0312678 | ||||||||
\(989\) | 4.37582 | 0.139143 | ||||||||
\(990\) | 0.103166 | 0.00327881 | ||||||||
\(991\) | −47.3675 | −1.50468 | −0.752340 | − | 0.658775i | \(-0.771075\pi\) | ||||
−0.752340 | + | 0.658775i | \(0.771075\pi\) | |||||||
\(992\) | 6.59571 | 0.209414 | ||||||||
\(993\) | 55.8122 | 1.77115 | ||||||||
\(994\) | −1.57205 | −0.0498625 | ||||||||
\(995\) | −11.4718 | −0.363681 | ||||||||
\(996\) | −9.44548 | −0.299291 | ||||||||
\(997\) | 13.6998 | 0.433877 | 0.216939 | − | 0.976185i | \(-0.430393\pi\) | ||||
0.216939 | + | 0.976185i | \(0.430393\pi\) | |||||||
\(998\) | 14.5870 | 0.461744 | ||||||||
\(999\) | 47.8222 | 1.51303 |
(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 | 4730.2.a.w.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.w.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial |