Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.39621\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(5\) | 1.39621 | 0.624406 | 0.312203 | − | 0.950015i | \(-0.398933\pi\) | ||||
0.312203 | + | 0.950015i | \(0.398933\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.23174 | −0.465556 | −0.232778 | − | 0.972530i | \(-0.574781\pi\) | ||||
−0.232778 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.39621 | −0.441521 | ||||||||
\(11\) | 1.33294 | 0.401897 | 0.200948 | − | 0.979602i | \(-0.435598\pi\) | ||||
0.200948 | + | 0.979602i | \(0.435598\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.02185 | 0.838111 | 0.419056 | − | 0.907961i | \(-0.362361\pi\) | ||||
0.419056 | + | 0.907961i | \(0.362361\pi\) | |||||||
\(14\) | 1.23174 | 0.329197 | ||||||||
\(15\) | −1.39621 | −0.360501 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.38520 | 0.547201 | 0.273601 | − | 0.961843i | \(-0.411785\pi\) | ||||
0.273601 | + | 0.961843i | \(0.411785\pi\) | |||||||
\(20\) | 1.39621 | 0.312203 | ||||||||
\(21\) | 1.23174 | 0.268789 | ||||||||
\(22\) | −1.33294 | −0.284184 | ||||||||
\(23\) | 5.24380 | 1.09341 | 0.546704 | − | 0.837326i | \(-0.315882\pi\) | ||||
0.546704 | + | 0.837326i | \(0.315882\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.05059 | −0.610118 | ||||||||
\(26\) | −3.02185 | −0.592634 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.23174 | −0.232778 | ||||||||
\(29\) | 5.12161 | 0.951059 | 0.475530 | − | 0.879700i | \(-0.342256\pi\) | ||||
0.475530 | + | 0.879700i | \(0.342256\pi\) | |||||||
\(30\) | 1.39621 | 0.254913 | ||||||||
\(31\) | 0.238960 | 0.0429186 | 0.0214593 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214593 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.33294 | −0.232035 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −1.71978 | −0.290696 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.99937 | 0.986291 | 0.493145 | − | 0.869947i | \(-0.335847\pi\) | ||||
0.493145 | + | 0.869947i | \(0.335847\pi\) | |||||||
\(38\) | −2.38520 | −0.386930 | ||||||||
\(39\) | −3.02185 | −0.483884 | ||||||||
\(40\) | −1.39621 | −0.220761 | ||||||||
\(41\) | 6.44784 | 1.00698 | 0.503492 | − | 0.864000i | \(-0.332048\pi\) | ||||
0.503492 | + | 0.864000i | \(0.332048\pi\) | |||||||
\(42\) | −1.23174 | −0.190062 | ||||||||
\(43\) | 5.24123 | 0.799280 | 0.399640 | − | 0.916672i | \(-0.369135\pi\) | ||||
0.399640 | + | 0.916672i | \(0.369135\pi\) | |||||||
\(44\) | 1.33294 | 0.200948 | ||||||||
\(45\) | 1.39621 | 0.208135 | ||||||||
\(46\) | −5.24380 | −0.773156 | ||||||||
\(47\) | −5.48284 | −0.799755 | −0.399877 | − | 0.916569i | \(-0.630947\pi\) | ||||
−0.399877 | + | 0.916569i | \(0.630947\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.48281 | −0.783258 | ||||||||
\(50\) | 3.05059 | 0.431418 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 3.02185 | 0.419056 | ||||||||
\(53\) | −6.85752 | −0.941952 | −0.470976 | − | 0.882146i | \(-0.656098\pi\) | ||||
−0.470976 | + | 0.882146i | \(0.656098\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.86107 | 0.250947 | ||||||||
\(56\) | 1.23174 | 0.164599 | ||||||||
\(57\) | −2.38520 | −0.315927 | ||||||||
\(58\) | −5.12161 | −0.672500 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −1.39621 | −0.180250 | ||||||||
\(61\) | −4.09141 | −0.523851 | −0.261925 | − | 0.965088i | \(-0.584357\pi\) | ||||
−0.261925 | + | 0.965088i | \(0.584357\pi\) | |||||||
\(62\) | −0.238960 | −0.0303480 | ||||||||
\(63\) | −1.23174 | −0.155185 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.21915 | 0.523321 | ||||||||
\(66\) | 1.33294 | 0.164074 | ||||||||
\(67\) | 14.4176 | 1.76139 | 0.880693 | − | 0.473687i | \(-0.157077\pi\) | ||||
0.880693 | + | 0.473687i | \(0.157077\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −5.24380 | −0.631280 | ||||||||
\(70\) | 1.71978 | 0.205553 | ||||||||
\(71\) | 2.45847 | 0.291766 | 0.145883 | − | 0.989302i | \(-0.453398\pi\) | ||||
0.145883 | + | 0.989302i | \(0.453398\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −9.84343 | −1.15209 | −0.576043 | − | 0.817419i | \(-0.695404\pi\) | ||||
−0.576043 | + | 0.817419i | \(0.695404\pi\) | |||||||
\(74\) | −5.99937 | −0.697413 | ||||||||
\(75\) | 3.05059 | 0.352252 | ||||||||
\(76\) | 2.38520 | 0.273601 | ||||||||
\(77\) | −1.64184 | −0.187105 | ||||||||
\(78\) | 3.02185 | 0.342157 | ||||||||
\(79\) | 1.35868 | 0.152863 | 0.0764316 | − | 0.997075i | \(-0.475647\pi\) | ||||
0.0764316 | + | 0.997075i | \(0.475647\pi\) | |||||||
\(80\) | 1.39621 | 0.156101 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.44784 | −0.712045 | ||||||||
\(83\) | 0.183267 | 0.0201162 | 0.0100581 | − | 0.999949i | \(-0.496798\pi\) | ||||
0.0100581 | + | 0.999949i | \(0.496798\pi\) | |||||||
\(84\) | 1.23174 | 0.134394 | ||||||||
\(85\) | 1.39621 | 0.151441 | ||||||||
\(86\) | −5.24123 | −0.565176 | ||||||||
\(87\) | −5.12161 | −0.549094 | ||||||||
\(88\) | −1.33294 | −0.142092 | ||||||||
\(89\) | −9.50534 | −1.00756 | −0.503782 | − | 0.863831i | \(-0.668058\pi\) | ||||
−0.503782 | + | 0.863831i | \(0.668058\pi\) | |||||||
\(90\) | −1.39621 | −0.147174 | ||||||||
\(91\) | −3.72215 | −0.390187 | ||||||||
\(92\) | 5.24380 | 0.546704 | ||||||||
\(93\) | −0.238960 | −0.0247790 | ||||||||
\(94\) | 5.48284 | 0.565512 | ||||||||
\(95\) | 3.33024 | 0.341676 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.31659 | 0.133679 | 0.0668395 | − | 0.997764i | \(-0.478708\pi\) | ||||
0.0668395 | + | 0.997764i | \(0.478708\pi\) | |||||||
\(98\) | 5.48281 | 0.553847 | ||||||||
\(99\) | 1.33294 | 0.133966 | ||||||||
\(100\) | −3.05059 | −0.305059 | ||||||||
\(101\) | −3.12325 | −0.310775 | −0.155387 | − | 0.987854i | \(-0.549663\pi\) | ||||
−0.155387 | + | 0.987854i | \(0.549663\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 15.3042 | 1.50796 | 0.753982 | − | 0.656895i | \(-0.228130\pi\) | ||||
0.753982 | + | 0.656895i | \(0.228130\pi\) | |||||||
\(104\) | −3.02185 | −0.296317 | ||||||||
\(105\) | 1.71978 | 0.167833 | ||||||||
\(106\) | 6.85752 | 0.666061 | ||||||||
\(107\) | 19.5560 | 1.89055 | 0.945277 | − | 0.326270i | \(-0.105792\pi\) | ||||
0.945277 | + | 0.326270i | \(0.105792\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 10.3763 | 0.993870 | 0.496935 | − | 0.867788i | \(-0.334459\pi\) | ||||
0.496935 | + | 0.867788i | \(0.334459\pi\) | |||||||
\(110\) | −1.86107 | −0.177446 | ||||||||
\(111\) | −5.99937 | −0.569435 | ||||||||
\(112\) | −1.23174 | −0.116389 | ||||||||
\(113\) | −9.34541 | −0.879142 | −0.439571 | − | 0.898208i | \(-0.644869\pi\) | ||||
−0.439571 | + | 0.898208i | \(0.644869\pi\) | |||||||
\(114\) | 2.38520 | 0.223394 | ||||||||
\(115\) | 7.32147 | 0.682730 | ||||||||
\(116\) | 5.12161 | 0.475530 | ||||||||
\(117\) | 3.02185 | 0.279370 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −1.23174 | −0.112914 | ||||||||
\(120\) | 1.39621 | 0.127456 | ||||||||
\(121\) | −9.22327 | −0.838479 | ||||||||
\(122\) | 4.09141 | 0.370419 | ||||||||
\(123\) | −6.44784 | −0.581382 | ||||||||
\(124\) | 0.238960 | 0.0214593 | ||||||||
\(125\) | −11.2403 | −1.00537 | ||||||||
\(126\) | 1.23174 | 0.109732 | ||||||||
\(127\) | −9.30279 | −0.825489 | −0.412744 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.24123 | −0.461464 | ||||||||
\(130\) | −4.21915 | −0.370044 | ||||||||
\(131\) | 0.579803 | 0.0506577 | 0.0253288 | − | 0.999679i | \(-0.491937\pi\) | ||||
0.0253288 | + | 0.999679i | \(0.491937\pi\) | |||||||
\(132\) | −1.33294 | −0.116018 | ||||||||
\(133\) | −2.93795 | −0.254753 | ||||||||
\(134\) | −14.4176 | −1.24549 | ||||||||
\(135\) | −1.39621 | −0.120167 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −9.81475 | −0.838530 | −0.419265 | − | 0.907864i | \(-0.637712\pi\) | ||||
−0.419265 | + | 0.907864i | \(0.637712\pi\) | |||||||
\(138\) | 5.24380 | 0.446382 | ||||||||
\(139\) | −1.30210 | −0.110443 | −0.0552213 | − | 0.998474i | \(-0.517586\pi\) | ||||
−0.0552213 | + | 0.998474i | \(0.517586\pi\) | |||||||
\(140\) | −1.71978 | −0.145348 | ||||||||
\(141\) | 5.48284 | 0.461739 | ||||||||
\(142\) | −2.45847 | −0.206310 | ||||||||
\(143\) | 4.02795 | 0.336834 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.15086 | 0.593847 | ||||||||
\(146\) | 9.84343 | 0.814648 | ||||||||
\(147\) | 5.48281 | 0.452214 | ||||||||
\(148\) | 5.99937 | 0.493145 | ||||||||
\(149\) | −7.26871 | −0.595476 | −0.297738 | − | 0.954648i | \(-0.596232\pi\) | ||||
−0.297738 | + | 0.954648i | \(0.596232\pi\) | |||||||
\(150\) | −3.05059 | −0.249079 | ||||||||
\(151\) | −4.46621 | −0.363455 | −0.181727 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181727 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(152\) | −2.38520 | −0.193465 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 1.64184 | 0.132303 | ||||||||
\(155\) | 0.333640 | 0.0267986 | ||||||||
\(156\) | −3.02185 | −0.241942 | ||||||||
\(157\) | 14.8615 | 1.18608 | 0.593039 | − | 0.805174i | \(-0.297928\pi\) | ||||
0.593039 | + | 0.805174i | \(0.297928\pi\) | |||||||
\(158\) | −1.35868 | −0.108091 | ||||||||
\(159\) | 6.85752 | 0.543836 | ||||||||
\(160\) | −1.39621 | −0.110380 | ||||||||
\(161\) | −6.45902 | −0.509042 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 7.24912 | 0.567795 | 0.283897 | − | 0.958855i | \(-0.408372\pi\) | ||||
0.283897 | + | 0.958855i | \(0.408372\pi\) | |||||||
\(164\) | 6.44784 | 0.503492 | ||||||||
\(165\) | −1.86107 | −0.144884 | ||||||||
\(166\) | −0.183267 | −0.0142243 | ||||||||
\(167\) | 16.8368 | 1.30287 | 0.651437 | − | 0.758703i | \(-0.274167\pi\) | ||||
0.651437 | + | 0.758703i | \(0.274167\pi\) | |||||||
\(168\) | −1.23174 | −0.0950311 | ||||||||
\(169\) | −3.86841 | −0.297570 | ||||||||
\(170\) | −1.39621 | −0.107085 | ||||||||
\(171\) | 2.38520 | 0.182400 | ||||||||
\(172\) | 5.24123 | 0.399640 | ||||||||
\(173\) | −12.5264 | −0.952366 | −0.476183 | − | 0.879346i | \(-0.657980\pi\) | ||||
−0.476183 | + | 0.879346i | \(0.657980\pi\) | |||||||
\(174\) | 5.12161 | 0.388268 | ||||||||
\(175\) | 3.75754 | 0.284044 | ||||||||
\(176\) | 1.33294 | 0.100474 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 9.50534 | 0.712455 | ||||||||
\(179\) | 17.6585 | 1.31986 | 0.659931 | − | 0.751326i | \(-0.270586\pi\) | ||||
0.659931 | + | 0.751326i | \(0.270586\pi\) | |||||||
\(180\) | 1.39621 | 0.104068 | ||||||||
\(181\) | 1.52082 | 0.113041 | 0.0565207 | − | 0.998401i | \(-0.481999\pi\) | ||||
0.0565207 | + | 0.998401i | \(0.481999\pi\) | |||||||
\(182\) | 3.72215 | 0.275904 | ||||||||
\(183\) | 4.09141 | 0.302445 | ||||||||
\(184\) | −5.24380 | −0.386578 | ||||||||
\(185\) | 8.37641 | 0.615846 | ||||||||
\(186\) | 0.238960 | 0.0175214 | ||||||||
\(187\) | 1.33294 | 0.0974743 | ||||||||
\(188\) | −5.48284 | −0.399877 | ||||||||
\(189\) | 1.23174 | 0.0895962 | ||||||||
\(190\) | −3.33024 | −0.241601 | ||||||||
\(191\) | 2.16514 | 0.156664 | 0.0783319 | − | 0.996927i | \(-0.475041\pi\) | ||||
0.0783319 | + | 0.996927i | \(0.475041\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 25.9722 | 1.86952 | 0.934758 | − | 0.355284i | \(-0.115616\pi\) | ||||
0.934758 | + | 0.355284i | \(0.115616\pi\) | |||||||
\(194\) | −1.31659 | −0.0945253 | ||||||||
\(195\) | −4.21915 | −0.302140 | ||||||||
\(196\) | −5.48281 | −0.391629 | ||||||||
\(197\) | −19.9099 | −1.41852 | −0.709261 | − | 0.704946i | \(-0.750971\pi\) | ||||
−0.709261 | + | 0.704946i | \(0.750971\pi\) | |||||||
\(198\) | −1.33294 | −0.0947280 | ||||||||
\(199\) | −10.8532 | −0.769362 | −0.384681 | − | 0.923050i | \(-0.625689\pi\) | ||||
−0.384681 | + | 0.923050i | \(0.625689\pi\) | |||||||
\(200\) | 3.05059 | 0.215709 | ||||||||
\(201\) | −14.4176 | −1.01694 | ||||||||
\(202\) | 3.12325 | 0.219751 | ||||||||
\(203\) | −6.30851 | −0.442771 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 9.00256 | 0.628766 | ||||||||
\(206\) | −15.3042 | −1.06629 | ||||||||
\(207\) | 5.24380 | 0.364469 | ||||||||
\(208\) | 3.02185 | 0.209528 | ||||||||
\(209\) | 3.17932 | 0.219918 | ||||||||
\(210\) | −1.71978 | −0.118676 | ||||||||
\(211\) | −6.02741 | −0.414944 | −0.207472 | − | 0.978241i | \(-0.566524\pi\) | ||||
−0.207472 | + | 0.978241i | \(0.566524\pi\) | |||||||
\(212\) | −6.85752 | −0.470976 | ||||||||
\(213\) | −2.45847 | −0.168451 | ||||||||
\(214\) | −19.5560 | −1.33682 | ||||||||
\(215\) | 7.31787 | 0.499075 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.294338 | −0.0199810 | ||||||||
\(218\) | −10.3763 | −0.702772 | ||||||||
\(219\) | 9.84343 | 0.665157 | ||||||||
\(220\) | 1.86107 | 0.125473 | ||||||||
\(221\) | 3.02185 | 0.203272 | ||||||||
\(222\) | 5.99937 | 0.402652 | ||||||||
\(223\) | −6.10343 | −0.408716 | −0.204358 | − | 0.978896i | \(-0.565511\pi\) | ||||
−0.204358 | + | 0.978896i | \(0.565511\pi\) | |||||||
\(224\) | 1.23174 | 0.0822994 | ||||||||
\(225\) | −3.05059 | −0.203373 | ||||||||
\(226\) | 9.34541 | 0.621647 | ||||||||
\(227\) | −22.7438 | −1.50956 | −0.754780 | − | 0.655978i | \(-0.772256\pi\) | ||||
−0.754780 | + | 0.655978i | \(0.772256\pi\) | |||||||
\(228\) | −2.38520 | −0.157963 | ||||||||
\(229\) | 29.1330 | 1.92516 | 0.962582 | − | 0.270989i | \(-0.0873508\pi\) | ||||
0.962582 | + | 0.270989i | \(0.0873508\pi\) | |||||||
\(230\) | −7.32147 | −0.482763 | ||||||||
\(231\) | 1.64184 | 0.108025 | ||||||||
\(232\) | −5.12161 | −0.336250 | ||||||||
\(233\) | 19.7915 | 1.29658 | 0.648291 | − | 0.761392i | \(-0.275484\pi\) | ||||
0.648291 | + | 0.761392i | \(0.275484\pi\) | |||||||
\(234\) | −3.02185 | −0.197545 | ||||||||
\(235\) | −7.65522 | −0.499371 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | −1.35868 | −0.0882556 | ||||||||
\(238\) | 1.23174 | 0.0798421 | ||||||||
\(239\) | −20.7500 | −1.34221 | −0.671104 | − | 0.741363i | \(-0.734180\pi\) | ||||
−0.671104 | + | 0.741363i | \(0.734180\pi\) | |||||||
\(240\) | −1.39621 | −0.0901252 | ||||||||
\(241\) | −14.6805 | −0.945655 | −0.472827 | − | 0.881155i | \(-0.656767\pi\) | ||||
−0.472827 | + | 0.881155i | \(0.656767\pi\) | |||||||
\(242\) | 9.22327 | 0.592894 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.09141 | −0.261925 | ||||||||
\(245\) | −7.65517 | −0.489071 | ||||||||
\(246\) | 6.44784 | 0.411099 | ||||||||
\(247\) | 7.20771 | 0.458616 | ||||||||
\(248\) | −0.238960 | −0.0151740 | ||||||||
\(249\) | −0.183267 | −0.0116141 | ||||||||
\(250\) | 11.2403 | 0.710901 | ||||||||
\(251\) | 15.2730 | 0.964024 | 0.482012 | − | 0.876165i | \(-0.339906\pi\) | ||||
0.482012 | + | 0.876165i | \(0.339906\pi\) | |||||||
\(252\) | −1.23174 | −0.0775926 | ||||||||
\(253\) | 6.98968 | 0.439437 | ||||||||
\(254\) | 9.30279 | 0.583709 | ||||||||
\(255\) | −1.39621 | −0.0874343 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.63132 | 0.538407 | 0.269204 | − | 0.963083i | \(-0.413240\pi\) | ||||
0.269204 | + | 0.963083i | \(0.413240\pi\) | |||||||
\(258\) | 5.24123 | 0.326305 | ||||||||
\(259\) | −7.38969 | −0.459173 | ||||||||
\(260\) | 4.21915 | 0.261661 | ||||||||
\(261\) | 5.12161 | 0.317020 | ||||||||
\(262\) | −0.579803 | −0.0358204 | ||||||||
\(263\) | 15.4180 | 0.950713 | 0.475357 | − | 0.879793i | \(-0.342319\pi\) | ||||
0.475357 | + | 0.879793i | \(0.342319\pi\) | |||||||
\(264\) | 1.33294 | 0.0820368 | ||||||||
\(265\) | −9.57456 | −0.588160 | ||||||||
\(266\) | 2.93795 | 0.180137 | ||||||||
\(267\) | 9.50534 | 0.581717 | ||||||||
\(268\) | 14.4176 | 0.880693 | ||||||||
\(269\) | −0.513904 | −0.0313333 | −0.0156666 | − | 0.999877i | \(-0.504987\pi\) | ||||
−0.0156666 | + | 0.999877i | \(0.504987\pi\) | |||||||
\(270\) | 1.39621 | 0.0849709 | ||||||||
\(271\) | 0.211744 | 0.0128625 | 0.00643127 | − | 0.999979i | \(-0.497953\pi\) | ||||
0.00643127 | + | 0.999979i | \(0.497953\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 3.72215 | 0.225275 | ||||||||
\(274\) | 9.81475 | 0.592931 | ||||||||
\(275\) | −4.06625 | −0.245204 | ||||||||
\(276\) | −5.24380 | −0.315640 | ||||||||
\(277\) | 25.6652 | 1.54207 | 0.771037 | − | 0.636790i | \(-0.219738\pi\) | ||||
0.771037 | + | 0.636790i | \(0.219738\pi\) | |||||||
\(278\) | 1.30210 | 0.0780947 | ||||||||
\(279\) | 0.238960 | 0.0143062 | ||||||||
\(280\) | 1.71978 | 0.102776 | ||||||||
\(281\) | −20.1926 | −1.20459 | −0.602295 | − | 0.798274i | \(-0.705747\pi\) | ||||
−0.602295 | + | 0.798274i | \(0.705747\pi\) | |||||||
\(282\) | −5.48284 | −0.326499 | ||||||||
\(283\) | 23.5657 | 1.40083 | 0.700417 | − | 0.713734i | \(-0.252998\pi\) | ||||
0.700417 | + | 0.713734i | \(0.252998\pi\) | |||||||
\(284\) | 2.45847 | 0.145883 | ||||||||
\(285\) | −3.33024 | −0.197267 | ||||||||
\(286\) | −4.02795 | −0.238178 | ||||||||
\(287\) | −7.94209 | −0.468807 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −7.15086 | −0.419913 | ||||||||
\(291\) | −1.31659 | −0.0771796 | ||||||||
\(292\) | −9.84343 | −0.576043 | ||||||||
\(293\) | −8.18650 | −0.478261 | −0.239130 | − | 0.970987i | \(-0.576862\pi\) | ||||
−0.239130 | + | 0.970987i | \(0.576862\pi\) | |||||||
\(294\) | −5.48281 | −0.319764 | ||||||||
\(295\) | −1.39621 | −0.0812907 | ||||||||
\(296\) | −5.99937 | −0.348706 | ||||||||
\(297\) | −1.33294 | −0.0773451 | ||||||||
\(298\) | 7.26871 | 0.421065 | ||||||||
\(299\) | 15.8460 | 0.916398 | ||||||||
\(300\) | 3.05059 | 0.176126 | ||||||||
\(301\) | −6.45585 | −0.372109 | ||||||||
\(302\) | 4.46621 | 0.257001 | ||||||||
\(303\) | 3.12325 | 0.179426 | ||||||||
\(304\) | 2.38520 | 0.136800 | ||||||||
\(305\) | −5.71248 | −0.327095 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −0.820077 | −0.0468043 | −0.0234021 | − | 0.999726i | \(-0.507450\pi\) | ||||
−0.0234021 | + | 0.999726i | \(0.507450\pi\) | |||||||
\(308\) | −1.64184 | −0.0935526 | ||||||||
\(309\) | −15.3042 | −0.870624 | ||||||||
\(310\) | −0.333640 | −0.0189495 | ||||||||
\(311\) | −0.565621 | −0.0320734 | −0.0160367 | − | 0.999871i | \(-0.505105\pi\) | ||||
−0.0160367 | + | 0.999871i | \(0.505105\pi\) | |||||||
\(312\) | 3.02185 | 0.171079 | ||||||||
\(313\) | 3.77250 | 0.213234 | 0.106617 | − | 0.994300i | \(-0.465998\pi\) | ||||
0.106617 | + | 0.994300i | \(0.465998\pi\) | |||||||
\(314\) | −14.8615 | −0.838683 | ||||||||
\(315\) | −1.71978 | −0.0968985 | ||||||||
\(316\) | 1.35868 | 0.0764316 | ||||||||
\(317\) | 13.8954 | 0.780443 | 0.390221 | − | 0.920721i | \(-0.372398\pi\) | ||||
0.390221 | + | 0.920721i | \(0.372398\pi\) | |||||||
\(318\) | −6.85752 | −0.384550 | ||||||||
\(319\) | 6.82680 | 0.382227 | ||||||||
\(320\) | 1.39621 | 0.0780507 | ||||||||
\(321\) | −19.5560 | −1.09151 | ||||||||
\(322\) | 6.45902 | 0.359947 | ||||||||
\(323\) | 2.38520 | 0.132716 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −9.21843 | −0.511346 | ||||||||
\(326\) | −7.24912 | −0.401492 | ||||||||
\(327\) | −10.3763 | −0.573811 | ||||||||
\(328\) | −6.44784 | −0.356022 | ||||||||
\(329\) | 6.75346 | 0.372330 | ||||||||
\(330\) | 1.86107 | 0.102449 | ||||||||
\(331\) | 26.2630 | 1.44355 | 0.721774 | − | 0.692129i | \(-0.243327\pi\) | ||||
0.721774 | + | 0.692129i | \(0.243327\pi\) | |||||||
\(332\) | 0.183267 | 0.0100581 | ||||||||
\(333\) | 5.99937 | 0.328764 | ||||||||
\(334\) | −16.8368 | −0.921271 | ||||||||
\(335\) | 20.1300 | 1.09982 | ||||||||
\(336\) | 1.23174 | 0.0671972 | ||||||||
\(337\) | −26.4216 | −1.43927 | −0.719637 | − | 0.694350i | \(-0.755692\pi\) | ||||
−0.719637 | + | 0.694350i | \(0.755692\pi\) | |||||||
\(338\) | 3.86841 | 0.210414 | ||||||||
\(339\) | 9.34541 | 0.507573 | ||||||||
\(340\) | 1.39621 | 0.0757203 | ||||||||
\(341\) | 0.318520 | 0.0172488 | ||||||||
\(342\) | −2.38520 | −0.128977 | ||||||||
\(343\) | 15.3756 | 0.830206 | ||||||||
\(344\) | −5.24123 | −0.282588 | ||||||||
\(345\) | −7.32147 | −0.394175 | ||||||||
\(346\) | 12.5264 | 0.673425 | ||||||||
\(347\) | −33.1388 | −1.77898 | −0.889492 | − | 0.456952i | \(-0.848941\pi\) | ||||
−0.889492 | + | 0.456952i | \(0.848941\pi\) | |||||||
\(348\) | −5.12161 | −0.274547 | ||||||||
\(349\) | −28.3322 | −1.51659 | −0.758294 | − | 0.651912i | \(-0.773967\pi\) | ||||
−0.758294 | + | 0.651912i | \(0.773967\pi\) | |||||||
\(350\) | −3.75754 | −0.200849 | ||||||||
\(351\) | −3.02185 | −0.161295 | ||||||||
\(352\) | −1.33294 | −0.0710460 | ||||||||
\(353\) | 11.7666 | 0.626271 | 0.313136 | − | 0.949708i | \(-0.398621\pi\) | ||||
0.313136 | + | 0.949708i | \(0.398621\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 3.43254 | 0.182181 | ||||||||
\(356\) | −9.50534 | −0.503782 | ||||||||
\(357\) | 1.23174 | 0.0651908 | ||||||||
\(358\) | −17.6585 | −0.933283 | ||||||||
\(359\) | −26.2799 | −1.38700 | −0.693500 | − | 0.720457i | \(-0.743932\pi\) | ||||
−0.693500 | + | 0.720457i | \(0.743932\pi\) | |||||||
\(360\) | −1.39621 | −0.0735869 | ||||||||
\(361\) | −13.3108 | −0.700571 | ||||||||
\(362\) | −1.52082 | −0.0799323 | ||||||||
\(363\) | 9.22327 | 0.484096 | ||||||||
\(364\) | −3.72215 | −0.195094 | ||||||||
\(365\) | −13.7435 | −0.719369 | ||||||||
\(366\) | −4.09141 | −0.213861 | ||||||||
\(367\) | 1.49221 | 0.0778927 | 0.0389464 | − | 0.999241i | \(-0.487600\pi\) | ||||
0.0389464 | + | 0.999241i | \(0.487600\pi\) | |||||||
\(368\) | 5.24380 | 0.273352 | ||||||||
\(369\) | 6.44784 | 0.335661 | ||||||||
\(370\) | −8.37641 | −0.435469 | ||||||||
\(371\) | 8.44670 | 0.438531 | ||||||||
\(372\) | −0.238960 | −0.0123895 | ||||||||
\(373\) | 17.2112 | 0.891161 | 0.445581 | − | 0.895242i | \(-0.352997\pi\) | ||||
0.445581 | + | 0.895242i | \(0.352997\pi\) | |||||||
\(374\) | −1.33294 | −0.0689247 | ||||||||
\(375\) | 11.2403 | 0.580449 | ||||||||
\(376\) | 5.48284 | 0.282756 | ||||||||
\(377\) | 15.4767 | 0.797093 | ||||||||
\(378\) | −1.23174 | −0.0633541 | ||||||||
\(379\) | 18.4947 | 0.950011 | 0.475006 | − | 0.879983i | \(-0.342446\pi\) | ||||
0.475006 | + | 0.879983i | \(0.342446\pi\) | |||||||
\(380\) | 3.33024 | 0.170838 | ||||||||
\(381\) | 9.30279 | 0.476596 | ||||||||
\(382\) | −2.16514 | −0.110778 | ||||||||
\(383\) | −29.8949 | −1.52756 | −0.763780 | − | 0.645477i | \(-0.776659\pi\) | ||||
−0.763780 | + | 0.645477i | \(0.776659\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −2.29236 | −0.116830 | ||||||||
\(386\) | −25.9722 | −1.32195 | ||||||||
\(387\) | 5.24123 | 0.266427 | ||||||||
\(388\) | 1.31659 | 0.0668395 | ||||||||
\(389\) | 9.84584 | 0.499204 | 0.249602 | − | 0.968348i | \(-0.419700\pi\) | ||||
0.249602 | + | 0.968348i | \(0.419700\pi\) | |||||||
\(390\) | 4.21915 | 0.213645 | ||||||||
\(391\) | 5.24380 | 0.265190 | ||||||||
\(392\) | 5.48281 | 0.276924 | ||||||||
\(393\) | −0.579803 | −0.0292472 | ||||||||
\(394\) | 19.9099 | 1.00305 | ||||||||
\(395\) | 1.89700 | 0.0954487 | ||||||||
\(396\) | 1.33294 | 0.0669828 | ||||||||
\(397\) | −27.0890 | −1.35956 | −0.679780 | − | 0.733416i | \(-0.737925\pi\) | ||||
−0.679780 | + | 0.733416i | \(0.737925\pi\) | |||||||
\(398\) | 10.8532 | 0.544021 | ||||||||
\(399\) | 2.93795 | 0.147081 | ||||||||
\(400\) | −3.05059 | −0.152529 | ||||||||
\(401\) | 38.2155 | 1.90839 | 0.954195 | − | 0.299186i | \(-0.0967152\pi\) | ||||
0.954195 | + | 0.299186i | \(0.0967152\pi\) | |||||||
\(402\) | 14.4176 | 0.719083 | ||||||||
\(403\) | 0.722103 | 0.0359705 | ||||||||
\(404\) | −3.12325 | −0.155387 | ||||||||
\(405\) | 1.39621 | 0.0693784 | ||||||||
\(406\) | 6.30851 | 0.313086 | ||||||||
\(407\) | 7.99681 | 0.396387 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 11.5634 | 0.571772 | 0.285886 | − | 0.958264i | \(-0.407712\pi\) | ||||
0.285886 | + | 0.958264i | \(0.407712\pi\) | |||||||
\(410\) | −9.00256 | −0.444605 | ||||||||
\(411\) | 9.81475 | 0.484126 | ||||||||
\(412\) | 15.3042 | 0.753982 | ||||||||
\(413\) | 1.23174 | 0.0606102 | ||||||||
\(414\) | −5.24380 | −0.257719 | ||||||||
\(415\) | 0.255880 | 0.0125607 | ||||||||
\(416\) | −3.02185 | −0.148159 | ||||||||
\(417\) | 1.30210 | 0.0637641 | ||||||||
\(418\) | −3.17932 | −0.155506 | ||||||||
\(419\) | −19.3900 | −0.947263 | −0.473632 | − | 0.880723i | \(-0.657057\pi\) | ||||
−0.473632 | + | 0.880723i | \(0.657057\pi\) | |||||||
\(420\) | 1.71978 | 0.0839166 | ||||||||
\(421\) | 38.4482 | 1.87385 | 0.936924 | − | 0.349532i | \(-0.113659\pi\) | ||||
0.936924 | + | 0.349532i | \(0.113659\pi\) | |||||||
\(422\) | 6.02741 | 0.293410 | ||||||||
\(423\) | −5.48284 | −0.266585 | ||||||||
\(424\) | 6.85752 | 0.333030 | ||||||||
\(425\) | −3.05059 | −0.147975 | ||||||||
\(426\) | 2.45847 | 0.119113 | ||||||||
\(427\) | 5.03957 | 0.243882 | ||||||||
\(428\) | 19.5560 | 0.945277 | ||||||||
\(429\) | −4.02795 | −0.194471 | ||||||||
\(430\) | −7.31787 | −0.352899 | ||||||||
\(431\) | 19.4651 | 0.937599 | 0.468800 | − | 0.883304i | \(-0.344687\pi\) | ||||
0.468800 | + | 0.883304i | \(0.344687\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 21.4455 | 1.03060 | 0.515302 | − | 0.857008i | \(-0.327680\pi\) | ||||
0.515302 | + | 0.857008i | \(0.327680\pi\) | |||||||
\(434\) | 0.294338 | 0.0141287 | ||||||||
\(435\) | −7.15086 | −0.342858 | ||||||||
\(436\) | 10.3763 | 0.496935 | ||||||||
\(437\) | 12.5075 | 0.598315 | ||||||||
\(438\) | −9.84343 | −0.470337 | ||||||||
\(439\) | −12.0458 | −0.574913 | −0.287457 | − | 0.957794i | \(-0.592810\pi\) | ||||
−0.287457 | + | 0.957794i | \(0.592810\pi\) | |||||||
\(440\) | −1.86107 | −0.0887230 | ||||||||
\(441\) | −5.48281 | −0.261086 | ||||||||
\(442\) | −3.02185 | −0.143735 | ||||||||
\(443\) | 35.4527 | 1.68441 | 0.842204 | − | 0.539159i | \(-0.181258\pi\) | ||||
0.842204 | + | 0.539159i | \(0.181258\pi\) | |||||||
\(444\) | −5.99937 | −0.284718 | ||||||||
\(445\) | −13.2715 | −0.629128 | ||||||||
\(446\) | 6.10343 | 0.289006 | ||||||||
\(447\) | 7.26871 | 0.343798 | ||||||||
\(448\) | −1.23174 | −0.0581944 | ||||||||
\(449\) | 10.4628 | 0.493769 | 0.246885 | − | 0.969045i | \(-0.420593\pi\) | ||||
0.246885 | + | 0.969045i | \(0.420593\pi\) | |||||||
\(450\) | 3.05059 | 0.143806 | ||||||||
\(451\) | 8.59459 | 0.404703 | ||||||||
\(452\) | −9.34541 | −0.439571 | ||||||||
\(453\) | 4.46621 | 0.209841 | ||||||||
\(454\) | 22.7438 | 1.06742 | ||||||||
\(455\) | −5.19692 | −0.243635 | ||||||||
\(456\) | 2.38520 | 0.111697 | ||||||||
\(457\) | 25.8809 | 1.21066 | 0.605330 | − | 0.795975i | \(-0.293041\pi\) | ||||
0.605330 | + | 0.795975i | \(0.293041\pi\) | |||||||
\(458\) | −29.1330 | −1.36130 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 7.32147 | 0.341365 | ||||||||
\(461\) | −13.0148 | −0.606158 | −0.303079 | − | 0.952965i | \(-0.598015\pi\) | ||||
−0.303079 | + | 0.952965i | \(0.598015\pi\) | |||||||
\(462\) | −1.64184 | −0.0763854 | ||||||||
\(463\) | 35.2018 | 1.63596 | 0.817982 | − | 0.575243i | \(-0.195093\pi\) | ||||
0.817982 | + | 0.575243i | \(0.195093\pi\) | |||||||
\(464\) | 5.12161 | 0.237765 | ||||||||
\(465\) | −0.333640 | −0.0154722 | ||||||||
\(466\) | −19.7915 | −0.916822 | ||||||||
\(467\) | −25.3681 | −1.17390 | −0.586949 | − | 0.809624i | \(-0.699671\pi\) | ||||
−0.586949 | + | 0.809624i | \(0.699671\pi\) | |||||||
\(468\) | 3.02185 | 0.139685 | ||||||||
\(469\) | −17.7588 | −0.820023 | ||||||||
\(470\) | 7.65522 | 0.353109 | ||||||||
\(471\) | −14.8615 | −0.684782 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 6.98624 | 0.321228 | ||||||||
\(474\) | 1.35868 | 0.0624061 | ||||||||
\(475\) | −7.27625 | −0.333857 | ||||||||
\(476\) | −1.23174 | −0.0564569 | ||||||||
\(477\) | −6.85752 | −0.313984 | ||||||||
\(478\) | 20.7500 | 0.949085 | ||||||||
\(479\) | −6.29957 | −0.287835 | −0.143917 | − | 0.989590i | \(-0.545970\pi\) | ||||
−0.143917 | + | 0.989590i | \(0.545970\pi\) | |||||||
\(480\) | 1.39621 | 0.0637281 | ||||||||
\(481\) | 18.1292 | 0.826621 | ||||||||
\(482\) | 14.6805 | 0.668679 | ||||||||
\(483\) | 6.45902 | 0.293896 | ||||||||
\(484\) | −9.22327 | −0.419240 | ||||||||
\(485\) | 1.83823 | 0.0834699 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −1.07461 | −0.0486953 | −0.0243476 | − | 0.999704i | \(-0.507751\pi\) | ||||
−0.0243476 | + | 0.999704i | \(0.507751\pi\) | |||||||
\(488\) | 4.09141 | 0.185209 | ||||||||
\(489\) | −7.24912 | −0.327816 | ||||||||
\(490\) | 7.65517 | 0.345825 | ||||||||
\(491\) | −15.9517 | −0.719891 | −0.359945 | − | 0.932973i | \(-0.617205\pi\) | ||||
−0.359945 | + | 0.932973i | \(0.617205\pi\) | |||||||
\(492\) | −6.44784 | −0.290691 | ||||||||
\(493\) | 5.12161 | 0.230666 | ||||||||
\(494\) | −7.20771 | −0.324290 | ||||||||
\(495\) | 1.86107 | 0.0836489 | ||||||||
\(496\) | 0.238960 | 0.0107296 | ||||||||
\(497\) | −3.02820 | −0.135833 | ||||||||
\(498\) | 0.183267 | 0.00821241 | ||||||||
\(499\) | 32.3491 | 1.44815 | 0.724073 | − | 0.689723i | \(-0.242268\pi\) | ||||
0.724073 | + | 0.689723i | \(0.242268\pi\) | |||||||
\(500\) | −11.2403 | −0.502683 | ||||||||
\(501\) | −16.8368 | −0.752215 | ||||||||
\(502\) | −15.2730 | −0.681668 | ||||||||
\(503\) | 11.5567 | 0.515286 | 0.257643 | − | 0.966240i | \(-0.417054\pi\) | ||||
0.257643 | + | 0.966240i | \(0.417054\pi\) | |||||||
\(504\) | 1.23174 | 0.0548662 | ||||||||
\(505\) | −4.36072 | −0.194050 | ||||||||
\(506\) | −6.98968 | −0.310729 | ||||||||
\(507\) | 3.86841 | 0.171802 | ||||||||
\(508\) | −9.30279 | −0.412744 | ||||||||
\(509\) | 31.6757 | 1.40400 | 0.702000 | − | 0.712177i | \(-0.252290\pi\) | ||||
0.702000 | + | 0.712177i | \(0.252290\pi\) | |||||||
\(510\) | 1.39621 | 0.0618254 | ||||||||
\(511\) | 12.1246 | 0.536360 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.38520 | −0.105309 | ||||||||
\(514\) | −8.63132 | −0.380711 | ||||||||
\(515\) | 21.3679 | 0.941582 | ||||||||
\(516\) | −5.24123 | −0.230732 | ||||||||
\(517\) | −7.30830 | −0.321419 | ||||||||
\(518\) | 7.38969 | 0.324684 | ||||||||
\(519\) | 12.5264 | 0.549849 | ||||||||
\(520\) | −4.21915 | −0.185022 | ||||||||
\(521\) | −31.9605 | −1.40022 | −0.700108 | − | 0.714037i | \(-0.746865\pi\) | ||||
−0.700108 | + | 0.714037i | \(0.746865\pi\) | |||||||
\(522\) | −5.12161 | −0.224167 | ||||||||
\(523\) | 17.3949 | 0.760625 | 0.380313 | − | 0.924858i | \(-0.375816\pi\) | ||||
0.380313 | + | 0.924858i | \(0.375816\pi\) | |||||||
\(524\) | 0.579803 | 0.0253288 | ||||||||
\(525\) | −3.75754 | −0.163993 | ||||||||
\(526\) | −15.4180 | −0.672256 | ||||||||
\(527\) | 0.238960 | 0.0104093 | ||||||||
\(528\) | −1.33294 | −0.0580088 | ||||||||
\(529\) | 4.49746 | 0.195542 | ||||||||
\(530\) | 9.57456 | 0.415892 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | −2.93795 | −0.127376 | ||||||||
\(533\) | 19.4844 | 0.843964 | ||||||||
\(534\) | −9.50534 | −0.411336 | ||||||||
\(535\) | 27.3044 | 1.18047 | ||||||||
\(536\) | −14.4176 | −0.622744 | ||||||||
\(537\) | −17.6585 | −0.762022 | ||||||||
\(538\) | 0.513904 | 0.0221560 | ||||||||
\(539\) | −7.30825 | −0.314789 | ||||||||
\(540\) | −1.39621 | −0.0600835 | ||||||||
\(541\) | −27.1614 | −1.16776 | −0.583880 | − | 0.811840i | \(-0.698466\pi\) | ||||
−0.583880 | + | 0.811840i | \(0.698466\pi\) | |||||||
\(542\) | −0.211744 | −0.00909519 | ||||||||
\(543\) | −1.52082 | −0.0652645 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 14.4875 | 0.620578 | ||||||||
\(546\) | −3.72215 | −0.159293 | ||||||||
\(547\) | 28.7298 | 1.22840 | 0.614198 | − | 0.789152i | \(-0.289480\pi\) | ||||
0.614198 | + | 0.789152i | \(0.289480\pi\) | |||||||
\(548\) | −9.81475 | −0.419265 | ||||||||
\(549\) | −4.09141 | −0.174617 | ||||||||
\(550\) | 4.06625 | 0.173386 | ||||||||
\(551\) | 12.2160 | 0.520421 | ||||||||
\(552\) | 5.24380 | 0.223191 | ||||||||
\(553\) | −1.67354 | −0.0711663 | ||||||||
\(554\) | −25.6652 | −1.09041 | ||||||||
\(555\) | −8.37641 | −0.355559 | ||||||||
\(556\) | −1.30210 | −0.0552213 | ||||||||
\(557\) | 24.7181 | 1.04734 | 0.523670 | − | 0.851921i | \(-0.324562\pi\) | ||||
0.523670 | + | 0.851921i | \(0.324562\pi\) | |||||||
\(558\) | −0.238960 | −0.0101160 | ||||||||
\(559\) | 15.8382 | 0.669885 | ||||||||
\(560\) | −1.71978 | −0.0726739 | ||||||||
\(561\) | −1.33294 | −0.0562768 | ||||||||
\(562\) | 20.1926 | 0.851773 | ||||||||
\(563\) | −6.51171 | −0.274436 | −0.137218 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137218 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(564\) | 5.48284 | 0.230869 | ||||||||
\(565\) | −13.0482 | −0.548941 | ||||||||
\(566\) | −23.5657 | −0.990539 | ||||||||
\(567\) | −1.23174 | −0.0517284 | ||||||||
\(568\) | −2.45847 | −0.103155 | ||||||||
\(569\) | −24.9423 | −1.04564 | −0.522818 | − | 0.852445i | \(-0.675119\pi\) | ||||
−0.522818 | + | 0.852445i | \(0.675119\pi\) | |||||||
\(570\) | 3.33024 | 0.139488 | ||||||||
\(571\) | 27.8848 | 1.16694 | 0.583472 | − | 0.812133i | \(-0.301694\pi\) | ||||
0.583472 | + | 0.812133i | \(0.301694\pi\) | |||||||
\(572\) | 4.02795 | 0.168417 | ||||||||
\(573\) | −2.16514 | −0.0904498 | ||||||||
\(574\) | 7.94209 | 0.331496 | ||||||||
\(575\) | −15.9967 | −0.667108 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 12.4115 | 0.516698 | 0.258349 | − | 0.966052i | \(-0.416822\pi\) | ||||
0.258349 | + | 0.966052i | \(0.416822\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −25.9722 | −1.07937 | ||||||||
\(580\) | 7.15086 | 0.296923 | ||||||||
\(581\) | −0.225739 | −0.00936521 | ||||||||
\(582\) | 1.31659 | 0.0545742 | ||||||||
\(583\) | −9.14066 | −0.378567 | ||||||||
\(584\) | 9.84343 | 0.407324 | ||||||||
\(585\) | 4.21915 | 0.174440 | ||||||||
\(586\) | 8.18650 | 0.338181 | ||||||||
\(587\) | 44.3772 | 1.83164 | 0.915821 | − | 0.401587i | \(-0.131541\pi\) | ||||
0.915821 | + | 0.401587i | \(0.131541\pi\) | |||||||
\(588\) | 5.48281 | 0.226107 | ||||||||
\(589\) | 0.569967 | 0.0234851 | ||||||||
\(590\) | 1.39621 | 0.0574812 | ||||||||
\(591\) | 19.9099 | 0.818984 | ||||||||
\(592\) | 5.99937 | 0.246573 | ||||||||
\(593\) | 26.2219 | 1.07681 | 0.538403 | − | 0.842688i | \(-0.319028\pi\) | ||||
0.538403 | + | 0.842688i | \(0.319028\pi\) | |||||||
\(594\) | 1.33294 | 0.0546912 | ||||||||
\(595\) | −1.71978 | −0.0705040 | ||||||||
\(596\) | −7.26871 | −0.297738 | ||||||||
\(597\) | 10.8532 | 0.444192 | ||||||||
\(598\) | −15.8460 | −0.647991 | ||||||||
\(599\) | 34.0986 | 1.39323 | 0.696616 | − | 0.717444i | \(-0.254688\pi\) | ||||
0.696616 | + | 0.717444i | \(0.254688\pi\) | |||||||
\(600\) | −3.05059 | −0.124540 | ||||||||
\(601\) | 20.7898 | 0.848033 | 0.424017 | − | 0.905654i | \(-0.360620\pi\) | ||||
0.424017 | + | 0.905654i | \(0.360620\pi\) | |||||||
\(602\) | 6.45585 | 0.263121 | ||||||||
\(603\) | 14.4176 | 0.587129 | ||||||||
\(604\) | −4.46621 | −0.181727 | ||||||||
\(605\) | −12.8777 | −0.523551 | ||||||||
\(606\) | −3.12325 | −0.126873 | ||||||||
\(607\) | 41.4237 | 1.68134 | 0.840668 | − | 0.541550i | \(-0.182162\pi\) | ||||
0.840668 | + | 0.541550i | \(0.182162\pi\) | |||||||
\(608\) | −2.38520 | −0.0967325 | ||||||||
\(609\) | 6.30851 | 0.255634 | ||||||||
\(610\) | 5.71248 | 0.231291 | ||||||||
\(611\) | −16.5683 | −0.670283 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −3.82735 | −0.154585 | −0.0772926 | − | 0.997008i | \(-0.524628\pi\) | ||||
−0.0772926 | + | 0.997008i | \(0.524628\pi\) | |||||||
\(614\) | 0.820077 | 0.0330956 | ||||||||
\(615\) | −9.00256 | −0.363018 | ||||||||
\(616\) | 1.64184 | 0.0661517 | ||||||||
\(617\) | −27.9532 | −1.12535 | −0.562677 | − | 0.826677i | \(-0.690229\pi\) | ||||
−0.562677 | + | 0.826677i | \(0.690229\pi\) | |||||||
\(618\) | 15.3042 | 0.615624 | ||||||||
\(619\) | 9.63003 | 0.387064 | 0.193532 | − | 0.981094i | \(-0.438006\pi\) | ||||
0.193532 | + | 0.981094i | \(0.438006\pi\) | |||||||
\(620\) | 0.333640 | 0.0133993 | ||||||||
\(621\) | −5.24380 | −0.210427 | ||||||||
\(622\) | 0.565621 | 0.0226793 | ||||||||
\(623\) | 11.7081 | 0.469077 | ||||||||
\(624\) | −3.02185 | −0.120971 | ||||||||
\(625\) | −0.440976 | −0.0176390 | ||||||||
\(626\) | −3.77250 | −0.150779 | ||||||||
\(627\) | −3.17932 | −0.126970 | ||||||||
\(628\) | 14.8615 | 0.593039 | ||||||||
\(629\) | 5.99937 | 0.239211 | ||||||||
\(630\) | 1.71978 | 0.0685176 | ||||||||
\(631\) | 29.6927 | 1.18205 | 0.591025 | − | 0.806653i | \(-0.298724\pi\) | ||||
0.591025 | + | 0.806653i | \(0.298724\pi\) | |||||||
\(632\) | −1.35868 | −0.0540453 | ||||||||
\(633\) | 6.02741 | 0.239568 | ||||||||
\(634\) | −13.8954 | −0.551856 | ||||||||
\(635\) | −12.9887 | −0.515440 | ||||||||
\(636\) | 6.85752 | 0.271918 | ||||||||
\(637\) | −16.5682 | −0.656457 | ||||||||
\(638\) | −6.82680 | −0.270276 | ||||||||
\(639\) | 2.45847 | 0.0972554 | ||||||||
\(640\) | −1.39621 | −0.0551902 | ||||||||
\(641\) | −42.4598 | −1.67706 | −0.838531 | − | 0.544854i | \(-0.816585\pi\) | ||||
−0.838531 | + | 0.544854i | \(0.816585\pi\) | |||||||
\(642\) | 19.5560 | 0.771815 | ||||||||
\(643\) | 21.5021 | 0.847960 | 0.423980 | − | 0.905672i | \(-0.360633\pi\) | ||||
0.423980 | + | 0.905672i | \(0.360633\pi\) | |||||||
\(644\) | −6.45902 | −0.254521 | ||||||||
\(645\) | −7.31787 | −0.288141 | ||||||||
\(646\) | −2.38520 | −0.0938443 | ||||||||
\(647\) | −1.56383 | −0.0614806 | −0.0307403 | − | 0.999527i | \(-0.509786\pi\) | ||||
−0.0307403 | + | 0.999527i | \(0.509786\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −1.33294 | −0.0523225 | ||||||||
\(650\) | 9.21843 | 0.361576 | ||||||||
\(651\) | 0.294338 | 0.0115360 | ||||||||
\(652\) | 7.24912 | 0.283897 | ||||||||
\(653\) | −33.6465 | −1.31669 | −0.658344 | − | 0.752717i | \(-0.728743\pi\) | ||||
−0.658344 | + | 0.752717i | \(0.728743\pi\) | |||||||
\(654\) | 10.3763 | 0.405746 | ||||||||
\(655\) | 0.809529 | 0.0316309 | ||||||||
\(656\) | 6.44784 | 0.251746 | ||||||||
\(657\) | −9.84343 | −0.384029 | ||||||||
\(658\) | −6.75346 | −0.263277 | ||||||||
\(659\) | 40.8857 | 1.59268 | 0.796340 | − | 0.604850i | \(-0.206767\pi\) | ||||
0.796340 | + | 0.604850i | \(0.206767\pi\) | |||||||
\(660\) | −1.86107 | −0.0724420 | ||||||||
\(661\) | −26.0265 | −1.01231 | −0.506157 | − | 0.862442i | \(-0.668934\pi\) | ||||
−0.506157 | + | 0.862442i | \(0.668934\pi\) | |||||||
\(662\) | −26.2630 | −1.02074 | ||||||||
\(663\) | −3.02185 | −0.117359 | ||||||||
\(664\) | −0.183267 | −0.00711215 | ||||||||
\(665\) | −4.10201 | −0.159069 | ||||||||
\(666\) | −5.99937 | −0.232471 | ||||||||
\(667\) | 26.8567 | 1.03990 | ||||||||
\(668\) | 16.8368 | 0.651437 | ||||||||
\(669\) | 6.10343 | 0.235972 | ||||||||
\(670\) | −20.1300 | −0.777690 | ||||||||
\(671\) | −5.45360 | −0.210534 | ||||||||
\(672\) | −1.23174 | −0.0475156 | ||||||||
\(673\) | 22.1661 | 0.854439 | 0.427220 | − | 0.904148i | \(-0.359493\pi\) | ||||
0.427220 | + | 0.904148i | \(0.359493\pi\) | |||||||
\(674\) | 26.4216 | 1.01772 | ||||||||
\(675\) | 3.05059 | 0.117417 | ||||||||
\(676\) | −3.86841 | −0.148785 | ||||||||
\(677\) | −42.7753 | −1.64399 | −0.821994 | − | 0.569497i | \(-0.807138\pi\) | ||||
−0.821994 | + | 0.569497i | \(0.807138\pi\) | |||||||
\(678\) | −9.34541 | −0.358908 | ||||||||
\(679\) | −1.62170 | −0.0622350 | ||||||||
\(680\) | −1.39621 | −0.0535423 | ||||||||
\(681\) | 22.7438 | 0.871544 | ||||||||
\(682\) | −0.318520 | −0.0121968 | ||||||||
\(683\) | −40.0387 | −1.53204 | −0.766020 | − | 0.642817i | \(-0.777765\pi\) | ||||
−0.766020 | + | 0.642817i | \(0.777765\pi\) | |||||||
\(684\) | 2.38520 | 0.0912002 | ||||||||
\(685\) | −13.7035 | −0.523583 | ||||||||
\(686\) | −15.3756 | −0.587044 | ||||||||
\(687\) | −29.1330 | −1.11149 | ||||||||
\(688\) | 5.24123 | 0.199820 | ||||||||
\(689\) | −20.7224 | −0.789461 | ||||||||
\(690\) | 7.32147 | 0.278723 | ||||||||
\(691\) | −0.691794 | −0.0263171 | −0.0131585 | − | 0.999913i | \(-0.504189\pi\) | ||||
−0.0131585 | + | 0.999913i | \(0.504189\pi\) | |||||||
\(692\) | −12.5264 | −0.476183 | ||||||||
\(693\) | −1.64184 | −0.0623684 | ||||||||
\(694\) | 33.1388 | 1.25793 | ||||||||
\(695\) | −1.81801 | −0.0689610 | ||||||||
\(696\) | 5.12161 | 0.194134 | ||||||||
\(697\) | 6.44784 | 0.244229 | ||||||||
\(698\) | 28.3322 | 1.07239 | ||||||||
\(699\) | −19.7915 | −0.748582 | ||||||||
\(700\) | 3.75754 | 0.142022 | ||||||||
\(701\) | 37.5727 | 1.41910 | 0.709550 | − | 0.704655i | \(-0.248898\pi\) | ||||
0.709550 | + | 0.704655i | \(0.248898\pi\) | |||||||
\(702\) | 3.02185 | 0.114052 | ||||||||
\(703\) | 14.3097 | 0.539700 | ||||||||
\(704\) | 1.33294 | 0.0502371 | ||||||||
\(705\) | 7.65522 | 0.288312 | ||||||||
\(706\) | −11.7666 | −0.442841 | ||||||||
\(707\) | 3.84704 | 0.144683 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | 14.0912 | 0.529205 | 0.264603 | − | 0.964358i | \(-0.414759\pi\) | ||||
0.264603 | + | 0.964358i | \(0.414759\pi\) | |||||||
\(710\) | −3.43254 | −0.128821 | ||||||||
\(711\) | 1.35868 | 0.0509544 | ||||||||
\(712\) | 9.50534 | 0.356228 | ||||||||
\(713\) | 1.25306 | 0.0469275 | ||||||||
\(714\) | −1.23174 | −0.0460969 | ||||||||
\(715\) | 5.62388 | 0.210321 | ||||||||
\(716\) | 17.6585 | 0.659931 | ||||||||
\(717\) | 20.7500 | 0.774924 | ||||||||
\(718\) | 26.2799 | 0.980757 | ||||||||
\(719\) | −8.23341 | −0.307055 | −0.153527 | − | 0.988144i | \(-0.549063\pi\) | ||||
−0.153527 | + | 0.988144i | \(0.549063\pi\) | |||||||
\(720\) | 1.39621 | 0.0520338 | ||||||||
\(721\) | −18.8508 | −0.702041 | ||||||||
\(722\) | 13.3108 | 0.495378 | ||||||||
\(723\) | 14.6805 | 0.545974 | ||||||||
\(724\) | 1.52082 | 0.0565207 | ||||||||
\(725\) | −15.6239 | −0.580258 | ||||||||
\(726\) | −9.22327 | −0.342308 | ||||||||
\(727\) | −19.1597 | −0.710592 | −0.355296 | − | 0.934754i | \(-0.615620\pi\) | ||||
−0.355296 | + | 0.934754i | \(0.615620\pi\) | |||||||
\(728\) | 3.72215 | 0.137952 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.7435 | 0.508671 | ||||||||
\(731\) | 5.24123 | 0.193854 | ||||||||
\(732\) | 4.09141 | 0.151223 | ||||||||
\(733\) | 40.9223 | 1.51150 | 0.755750 | − | 0.654860i | \(-0.227272\pi\) | ||||
0.755750 | + | 0.654860i | \(0.227272\pi\) | |||||||
\(734\) | −1.49221 | −0.0550785 | ||||||||
\(735\) | 7.65517 | 0.282365 | ||||||||
\(736\) | −5.24380 | −0.193289 | ||||||||
\(737\) | 19.2178 | 0.707895 | ||||||||
\(738\) | −6.44784 | −0.237348 | ||||||||
\(739\) | 15.9018 | 0.584955 | 0.292478 | − | 0.956272i | \(-0.405520\pi\) | ||||
0.292478 | + | 0.956272i | \(0.405520\pi\) | |||||||
\(740\) | 8.37641 | 0.307923 | ||||||||
\(741\) | −7.20771 | −0.264782 | ||||||||
\(742\) | −8.44670 | −0.310088 | ||||||||
\(743\) | 29.0634 | 1.06623 | 0.533116 | − | 0.846042i | \(-0.321021\pi\) | ||||
0.533116 | + | 0.846042i | \(0.321021\pi\) | |||||||
\(744\) | 0.238960 | 0.00876072 | ||||||||
\(745\) | −10.1487 | −0.371819 | ||||||||
\(746\) | −17.2112 | −0.630146 | ||||||||
\(747\) | 0.183267 | 0.00670540 | ||||||||
\(748\) | 1.33294 | 0.0487371 | ||||||||
\(749\) | −24.0880 | −0.880157 | ||||||||
\(750\) | −11.2403 | −0.410439 | ||||||||
\(751\) | 10.3721 | 0.378484 | 0.189242 | − | 0.981930i | \(-0.439397\pi\) | ||||
0.189242 | + | 0.981930i | \(0.439397\pi\) | |||||||
\(752\) | −5.48284 | −0.199939 | ||||||||
\(753\) | −15.2730 | −0.556579 | ||||||||
\(754\) | −15.4767 | −0.563630 | ||||||||
\(755\) | −6.23578 | −0.226943 | ||||||||
\(756\) | 1.23174 | 0.0447981 | ||||||||
\(757\) | 41.6545 | 1.51396 | 0.756979 | − | 0.653439i | \(-0.226674\pi\) | ||||
0.756979 | + | 0.653439i | \(0.226674\pi\) | |||||||
\(758\) | −18.4947 | −0.671759 | ||||||||
\(759\) | −6.98968 | −0.253709 | ||||||||
\(760\) | −3.33024 | −0.120801 | ||||||||
\(761\) | 42.9826 | 1.55812 | 0.779059 | − | 0.626951i | \(-0.215697\pi\) | ||||
0.779059 | + | 0.626951i | \(0.215697\pi\) | |||||||
\(762\) | −9.30279 | −0.337004 | ||||||||
\(763\) | −12.7810 | −0.462702 | ||||||||
\(764\) | 2.16514 | 0.0783319 | ||||||||
\(765\) | 1.39621 | 0.0504802 | ||||||||
\(766\) | 29.8949 | 1.08015 | ||||||||
\(767\) | −3.02185 | −0.109113 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −46.8981 | −1.69119 | −0.845595 | − | 0.533825i | \(-0.820754\pi\) | ||||
−0.845595 | + | 0.533825i | \(0.820754\pi\) | |||||||
\(770\) | 2.29236 | 0.0826110 | ||||||||
\(771\) | −8.63132 | −0.310850 | ||||||||
\(772\) | 25.9722 | 0.934758 | ||||||||
\(773\) | 34.8556 | 1.25367 | 0.626834 | − | 0.779153i | \(-0.284350\pi\) | ||||
0.626834 | + | 0.779153i | \(0.284350\pi\) | |||||||
\(774\) | −5.24123 | −0.188392 | ||||||||
\(775\) | −0.728970 | −0.0261854 | ||||||||
\(776\) | −1.31659 | −0.0472627 | ||||||||
\(777\) | 7.38969 | 0.265104 | ||||||||
\(778\) | −9.84584 | −0.352991 | ||||||||
\(779\) | 15.3794 | 0.551023 | ||||||||
\(780\) | −4.21915 | −0.151070 | ||||||||
\(781\) | 3.27699 | 0.117260 | ||||||||
\(782\) | −5.24380 | −0.187518 | ||||||||
\(783\) | −5.12161 | −0.183031 | ||||||||
\(784\) | −5.48281 | −0.195815 | ||||||||
\(785\) | 20.7498 | 0.740594 | ||||||||
\(786\) | 0.579803 | 0.0206809 | ||||||||
\(787\) | 9.81117 | 0.349730 | 0.174865 | − | 0.984592i | \(-0.444051\pi\) | ||||
0.174865 | + | 0.984592i | \(0.444051\pi\) | |||||||
\(788\) | −19.9099 | −0.709261 | ||||||||
\(789\) | −15.4180 | −0.548895 | ||||||||
\(790\) | −1.89700 | −0.0674924 | ||||||||
\(791\) | 11.5111 | 0.409289 | ||||||||
\(792\) | −1.33294 | −0.0473640 | ||||||||
\(793\) | −12.3636 | −0.439045 | ||||||||
\(794\) | 27.0890 | 0.961354 | ||||||||
\(795\) | 9.57456 | 0.339575 | ||||||||
\(796\) | −10.8532 | −0.384681 | ||||||||
\(797\) | 4.43107 | 0.156956 | 0.0784782 | − | 0.996916i | \(-0.474994\pi\) | ||||
0.0784782 | + | 0.996916i | \(0.474994\pi\) | |||||||
\(798\) | −2.93795 | −0.104002 | ||||||||
\(799\) | −5.48284 | −0.193969 | ||||||||
\(800\) | 3.05059 | 0.107855 | ||||||||
\(801\) | −9.50534 | −0.335855 | ||||||||
\(802\) | −38.2155 | −1.34944 | ||||||||
\(803\) | −13.1207 | −0.463020 | ||||||||
\(804\) | −14.4176 | −0.508469 | ||||||||
\(805\) | −9.01817 | −0.317849 | ||||||||
\(806\) | −0.722103 | −0.0254350 | ||||||||
\(807\) | 0.513904 | 0.0180903 | ||||||||
\(808\) | 3.12325 | 0.109875 | ||||||||
\(809\) | −0.121244 | −0.00426270 | −0.00213135 | − | 0.999998i | \(-0.500678\pi\) | ||||
−0.00213135 | + | 0.999998i | \(0.500678\pi\) | |||||||
\(810\) | −1.39621 | −0.0490579 | ||||||||
\(811\) | 39.1636 | 1.37522 | 0.687609 | − | 0.726081i | \(-0.258660\pi\) | ||||
0.687609 | + | 0.726081i | \(0.258660\pi\) | |||||||
\(812\) | −6.30851 | −0.221385 | ||||||||
\(813\) | −0.211744 | −0.00742619 | ||||||||
\(814\) | −7.99681 | −0.280288 | ||||||||
\(815\) | 10.1213 | 0.354534 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 12.5013 | 0.437367 | ||||||||
\(818\) | −11.5634 | −0.404304 | ||||||||
\(819\) | −3.72215 | −0.130062 | ||||||||
\(820\) | 9.00256 | 0.314383 | ||||||||
\(821\) | −22.4498 | −0.783505 | −0.391752 | − | 0.920071i | \(-0.628131\pi\) | ||||
−0.391752 | + | 0.920071i | \(0.628131\pi\) | |||||||
\(822\) | −9.81475 | −0.342329 | ||||||||
\(823\) | −17.1175 | −0.596678 | −0.298339 | − | 0.954460i | \(-0.596433\pi\) | ||||
−0.298339 | + | 0.954460i | \(0.596433\pi\) | |||||||
\(824\) | −15.3042 | −0.533146 | ||||||||
\(825\) | 4.06625 | 0.141569 | ||||||||
\(826\) | −1.23174 | −0.0428579 | ||||||||
\(827\) | −44.2346 | −1.53819 | −0.769094 | − | 0.639136i | \(-0.779292\pi\) | ||||
−0.769094 | + | 0.639136i | \(0.779292\pi\) | |||||||
\(828\) | 5.24380 | 0.182235 | ||||||||
\(829\) | 55.3045 | 1.92081 | 0.960403 | − | 0.278614i | \(-0.0898752\pi\) | ||||
0.960403 | + | 0.278614i | \(0.0898752\pi\) | |||||||
\(830\) | −0.255880 | −0.00888174 | ||||||||
\(831\) | −25.6652 | −0.890317 | ||||||||
\(832\) | 3.02185 | 0.104764 | ||||||||
\(833\) | −5.48281 | −0.189968 | ||||||||
\(834\) | −1.30210 | −0.0450880 | ||||||||
\(835\) | 23.5078 | 0.813522 | ||||||||
\(836\) | 3.17932 | 0.109959 | ||||||||
\(837\) | −0.238960 | −0.00825968 | ||||||||
\(838\) | 19.3900 | 0.669816 | ||||||||
\(839\) | −43.0150 | −1.48504 | −0.742521 | − | 0.669823i | \(-0.766370\pi\) | ||||
−0.742521 | + | 0.669823i | \(0.766370\pi\) | |||||||
\(840\) | −1.71978 | −0.0593380 | ||||||||
\(841\) | −2.76911 | −0.0954866 | ||||||||
\(842\) | −38.4482 | −1.32501 | ||||||||
\(843\) | 20.1926 | 0.695470 | ||||||||
\(844\) | −6.02741 | −0.207472 | ||||||||
\(845\) | −5.40112 | −0.185804 | ||||||||
\(846\) | 5.48284 | 0.188504 | ||||||||
\(847\) | 11.3607 | 0.390359 | ||||||||
\(848\) | −6.85752 | −0.235488 | ||||||||
\(849\) | −23.5657 | −0.808771 | ||||||||
\(850\) | 3.05059 | 0.104634 | ||||||||
\(851\) | 31.4595 | 1.07842 | ||||||||
\(852\) | −2.45847 | −0.0842257 | ||||||||
\(853\) | 5.97823 | 0.204691 | 0.102345 | − | 0.994749i | \(-0.467365\pi\) | ||||
0.102345 | + | 0.994749i | \(0.467365\pi\) | |||||||
\(854\) | −5.03957 | −0.172450 | ||||||||
\(855\) | 3.33024 | 0.113892 | ||||||||
\(856\) | −19.5560 | −0.668411 | ||||||||
\(857\) | −8.12750 | −0.277630 | −0.138815 | − | 0.990318i | \(-0.544329\pi\) | ||||
−0.138815 | + | 0.990318i | \(0.544329\pi\) | |||||||
\(858\) | 4.02795 | 0.137512 | ||||||||
\(859\) | 23.2508 | 0.793307 | 0.396653 | − | 0.917968i | \(-0.370171\pi\) | ||||
0.396653 | + | 0.917968i | \(0.370171\pi\) | |||||||
\(860\) | 7.31787 | 0.249537 | ||||||||
\(861\) | 7.94209 | 0.270666 | ||||||||
\(862\) | −19.4651 | −0.662983 | ||||||||
\(863\) | −28.3579 | −0.965312 | −0.482656 | − | 0.875810i | \(-0.660328\pi\) | ||||
−0.482656 | + | 0.875810i | \(0.660328\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −17.4896 | −0.594663 | ||||||||
\(866\) | −21.4455 | −0.728747 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −0.294338 | −0.00999049 | ||||||||
\(869\) | 1.81104 | 0.0614352 | ||||||||
\(870\) | 7.15086 | 0.242437 | ||||||||
\(871\) | 43.5678 | 1.47624 | ||||||||
\(872\) | −10.3763 | −0.351386 | ||||||||
\(873\) | 1.31659 | 0.0445597 | ||||||||
\(874\) | −12.5075 | −0.423072 | ||||||||
\(875\) | 13.8452 | 0.468054 | ||||||||
\(876\) | 9.84343 | 0.332579 | ||||||||
\(877\) | 31.9525 | 1.07896 | 0.539480 | − | 0.841999i | \(-0.318621\pi\) | ||||
0.539480 | + | 0.841999i | \(0.318621\pi\) | |||||||
\(878\) | 12.0458 | 0.406525 | ||||||||
\(879\) | 8.18650 | 0.276124 | ||||||||
\(880\) | 1.86107 | 0.0627366 | ||||||||
\(881\) | −8.29509 | −0.279469 | −0.139734 | − | 0.990189i | \(-0.544625\pi\) | ||||
−0.139734 | + | 0.990189i | \(0.544625\pi\) | |||||||
\(882\) | 5.48281 | 0.184616 | ||||||||
\(883\) | −47.1516 | −1.58678 | −0.793389 | − | 0.608715i | \(-0.791685\pi\) | ||||
−0.793389 | + | 0.608715i | \(0.791685\pi\) | |||||||
\(884\) | 3.02185 | 0.101636 | ||||||||
\(885\) | 1.39621 | 0.0469332 | ||||||||
\(886\) | −35.4527 | −1.19106 | ||||||||
\(887\) | 42.5563 | 1.42890 | 0.714450 | − | 0.699686i | \(-0.246677\pi\) | ||||
0.714450 | + | 0.699686i | \(0.246677\pi\) | |||||||
\(888\) | 5.99937 | 0.201326 | ||||||||
\(889\) | 11.4587 | 0.384311 | ||||||||
\(890\) | 13.2715 | 0.444861 | ||||||||
\(891\) | 1.33294 | 0.0446552 | ||||||||
\(892\) | −6.10343 | −0.204358 | ||||||||
\(893\) | −13.0777 | −0.437627 | ||||||||
\(894\) | −7.26871 | −0.243102 | ||||||||
\(895\) | 24.6551 | 0.824129 | ||||||||
\(896\) | 1.23174 | 0.0411497 | ||||||||
\(897\) | −15.8460 | −0.529082 | ||||||||
\(898\) | −10.4628 | −0.349148 | ||||||||
\(899\) | 1.22386 | 0.0408181 | ||||||||
\(900\) | −3.05059 | −0.101686 | ||||||||
\(901\) | −6.85752 | −0.228457 | ||||||||
\(902\) | −8.59459 | −0.286168 | ||||||||
\(903\) | 6.45585 | 0.214837 | ||||||||
\(904\) | 9.34541 | 0.310824 | ||||||||
\(905\) | 2.12338 | 0.0705837 | ||||||||
\(906\) | −4.46621 | −0.148380 | ||||||||
\(907\) | −17.5953 | −0.584242 | −0.292121 | − | 0.956381i | \(-0.594361\pi\) | ||||
−0.292121 | + | 0.956381i | \(0.594361\pi\) | |||||||
\(908\) | −22.7438 | −0.754780 | ||||||||
\(909\) | −3.12325 | −0.103592 | ||||||||
\(910\) | 5.19692 | 0.172276 | ||||||||
\(911\) | −7.12161 | −0.235949 | −0.117975 | − | 0.993017i | \(-0.537640\pi\) | ||||
−0.117975 | + | 0.993017i | \(0.537640\pi\) | |||||||
\(912\) | −2.38520 | −0.0789817 | ||||||||
\(913\) | 0.244285 | 0.00808464 | ||||||||
\(914\) | −25.8809 | −0.856065 | ||||||||
\(915\) | 5.71248 | 0.188849 | ||||||||
\(916\) | 29.1330 | 0.962582 | ||||||||
\(917\) | −0.714169 | −0.0235839 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −44.8470 | −1.47936 | −0.739682 | − | 0.672956i | \(-0.765024\pi\) | ||||
−0.739682 | + | 0.672956i | \(0.765024\pi\) | |||||||
\(920\) | −7.32147 | −0.241382 | ||||||||
\(921\) | 0.820077 | 0.0270225 | ||||||||
\(922\) | 13.0148 | 0.428619 | ||||||||
\(923\) | 7.42912 | 0.244533 | ||||||||
\(924\) | 1.64184 | 0.0540126 | ||||||||
\(925\) | −18.3016 | −0.601753 | ||||||||
\(926\) | −35.2018 | −1.15680 | ||||||||
\(927\) | 15.3042 | 0.502655 | ||||||||
\(928\) | −5.12161 | −0.168125 | ||||||||
\(929\) | 43.1047 | 1.41422 | 0.707110 | − | 0.707104i | \(-0.249999\pi\) | ||||
0.707110 | + | 0.707104i | \(0.249999\pi\) | |||||||
\(930\) | 0.333640 | 0.0109405 | ||||||||
\(931\) | −13.0776 | −0.428600 | ||||||||
\(932\) | 19.7915 | 0.648291 | ||||||||
\(933\) | 0.565621 | 0.0185176 | ||||||||
\(934\) | 25.3681 | 0.830071 | ||||||||
\(935\) | 1.86107 | 0.0608635 | ||||||||
\(936\) | −3.02185 | −0.0987723 | ||||||||
\(937\) | 5.56059 | 0.181657 | 0.0908283 | − | 0.995867i | \(-0.471049\pi\) | ||||
0.0908283 | + | 0.995867i | \(0.471049\pi\) | |||||||
\(938\) | 17.7588 | 0.579844 | ||||||||
\(939\) | −3.77250 | −0.123111 | ||||||||
\(940\) | −7.65522 | −0.249686 | ||||||||
\(941\) | −27.1729 | −0.885810 | −0.442905 | − | 0.896569i | \(-0.646052\pi\) | ||||
−0.442905 | + | 0.896569i | \(0.646052\pi\) | |||||||
\(942\) | 14.8615 | 0.484214 | ||||||||
\(943\) | 33.8112 | 1.10104 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 1.71978 | 0.0559444 | ||||||||
\(946\) | −6.98624 | −0.227142 | ||||||||
\(947\) | −13.2653 | −0.431065 | −0.215532 | − | 0.976497i | \(-0.569149\pi\) | ||||
−0.215532 | + | 0.976497i | \(0.569149\pi\) | |||||||
\(948\) | −1.35868 | −0.0441278 | ||||||||
\(949\) | −29.7454 | −0.965576 | ||||||||
\(950\) | 7.27625 | 0.236073 | ||||||||
\(951\) | −13.8954 | −0.450589 | ||||||||
\(952\) | 1.23174 | 0.0399211 | ||||||||
\(953\) | −13.2911 | −0.430541 | −0.215270 | − | 0.976555i | \(-0.569063\pi\) | ||||
−0.215270 | + | 0.976555i | \(0.569063\pi\) | |||||||
\(954\) | 6.85752 | 0.222020 | ||||||||
\(955\) | 3.02299 | 0.0978217 | ||||||||
\(956\) | −20.7500 | −0.671104 | ||||||||
\(957\) | −6.82680 | −0.220679 | ||||||||
\(958\) | 6.29957 | 0.203530 | ||||||||
\(959\) | 12.0893 | 0.390382 | ||||||||
\(960\) | −1.39621 | −0.0450626 | ||||||||
\(961\) | −30.9429 | −0.998158 | ||||||||
\(962\) | −18.1292 | −0.584509 | ||||||||
\(963\) | 19.5560 | 0.630184 | ||||||||
\(964\) | −14.6805 | −0.472827 | ||||||||
\(965\) | 36.2627 | 1.16734 | ||||||||
\(966\) | −6.45902 | −0.207816 | ||||||||
\(967\) | −31.8430 | −1.02400 | −0.512002 | − | 0.858984i | \(-0.671096\pi\) | ||||
−0.512002 | + | 0.858984i | \(0.671096\pi\) | |||||||
\(968\) | 9.22327 | 0.296447 | ||||||||
\(969\) | −2.38520 | −0.0766235 | ||||||||
\(970\) | −1.83823 | −0.0590222 | ||||||||
\(971\) | −19.2626 | −0.618167 | −0.309084 | − | 0.951035i | \(-0.600022\pi\) | ||||
−0.309084 | + | 0.951035i | \(0.600022\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 1.60385 | 0.0514172 | ||||||||
\(974\) | 1.07461 | 0.0344328 | ||||||||
\(975\) | 9.21843 | 0.295226 | ||||||||
\(976\) | −4.09141 | −0.130963 | ||||||||
\(977\) | 24.4202 | 0.781271 | 0.390635 | − | 0.920545i | \(-0.372255\pi\) | ||||
0.390635 | + | 0.920545i | \(0.372255\pi\) | |||||||
\(978\) | 7.24912 | 0.231801 | ||||||||
\(979\) | −12.6700 | −0.404936 | ||||||||
\(980\) | −7.65517 | −0.244535 | ||||||||
\(981\) | 10.3763 | 0.331290 | ||||||||
\(982\) | 15.9517 | 0.509040 | ||||||||
\(983\) | −14.7485 | −0.470404 | −0.235202 | − | 0.971947i | \(-0.575575\pi\) | ||||
−0.235202 | + | 0.971947i | \(0.575575\pi\) | |||||||
\(984\) | 6.44784 | 0.205550 | ||||||||
\(985\) | −27.7985 | −0.885733 | ||||||||
\(986\) | −5.12161 | −0.163105 | ||||||||
\(987\) | −6.75346 | −0.214965 | ||||||||
\(988\) | 7.20771 | 0.229308 | ||||||||
\(989\) | 27.4840 | 0.873939 | ||||||||
\(990\) | −1.86107 | −0.0591487 | ||||||||
\(991\) | −56.4977 | −1.79471 | −0.897355 | − | 0.441310i | \(-0.854514\pi\) | ||||
−0.897355 | + | 0.441310i | \(0.854514\pi\) | |||||||
\(992\) | −0.238960 | −0.00758700 | ||||||||
\(993\) | −26.2630 | −0.833433 | ||||||||
\(994\) | 3.02820 | 0.0960487 | ||||||||
\(995\) | −15.1534 | −0.480394 | ||||||||
\(996\) | −0.183267 | −0.00580705 | ||||||||
\(997\) | −41.1781 | −1.30412 | −0.652061 | − | 0.758166i | \(-0.726095\pi\) | ||||
−0.652061 | + | 0.758166i | \(0.726095\pi\) | |||||||
\(998\) | −32.3491 | −1.02399 | ||||||||
\(999\) | −5.99937 | −0.189812 |
(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 | 6018.2.a.x.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.x.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial |