Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.316645497.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 12x^{4} + 24x^{3} + 13x^{2} - 24x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.260281\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 | ||||||||
\(3\) | 0.260281 | 0.150273 | 0.0751366 | − | 0.997173i | \(-0.476061\pi\) | ||||
0.0751366 | + | 0.997173i | \(0.476061\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.36375 | 1.95153 | 0.975764 | − | 0.218824i | \(-0.0702221\pi\) | ||||
0.975764 | + | 0.218824i | \(0.0702221\pi\) | |||||||
\(6\) | −0.260281 | −0.106259 | ||||||||
\(7\) | −0.775135 | −0.292973 | −0.146487 | − | 0.989213i | \(-0.546797\pi\) | ||||
−0.146487 | + | 0.989213i | \(0.546797\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.93225 | −0.977418 | ||||||||
\(10\) | −4.36375 | −1.37994 | ||||||||
\(11\) | 4.36375 | 1.31572 | 0.657860 | − | 0.753140i | \(-0.271462\pi\) | ||||
0.657860 | + | 0.753140i | \(0.271462\pi\) | |||||||
\(12\) | 0.260281 | 0.0751366 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.775135 | 0.207163 | ||||||||
\(15\) | 1.13580 | 0.293262 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.93885 | −1.68292 | −0.841459 | − | 0.540321i | \(-0.818303\pi\) | ||||
−0.841459 | + | 0.540321i | \(0.818303\pi\) | |||||||
\(18\) | 2.93225 | 0.691139 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 4.36375 | 0.975764 | ||||||||
\(21\) | −0.201753 | −0.0440260 | ||||||||
\(22\) | −4.36375 | −0.930355 | ||||||||
\(23\) | −4.08036 | −0.850813 | −0.425407 | − | 0.905002i | \(-0.639869\pi\) | ||||
−0.425407 | + | 0.905002i | \(0.639869\pi\) | |||||||
\(24\) | −0.260281 | −0.0531296 | ||||||||
\(25\) | 14.0423 | 2.80846 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.54405 | −0.297153 | ||||||||
\(28\) | −0.775135 | −0.146487 | ||||||||
\(29\) | 2.54367 | 0.472348 | 0.236174 | − | 0.971711i | \(-0.424106\pi\) | ||||
0.236174 | + | 0.971711i | \(0.424106\pi\) | |||||||
\(30\) | −1.13580 | −0.207368 | ||||||||
\(31\) | −6.41220 | −1.15167 | −0.575833 | − | 0.817567i | \(-0.695322\pi\) | ||||
−0.575833 | + | 0.817567i | \(0.695322\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.13580 | 0.197717 | ||||||||
\(34\) | 6.93885 | 1.19000 | ||||||||
\(35\) | −3.38249 | −0.571746 | ||||||||
\(36\) | −2.93225 | −0.488709 | ||||||||
\(37\) | 6.64765 | 1.09287 | 0.546434 | − | 0.837502i | \(-0.315985\pi\) | ||||
0.546434 | + | 0.837502i | \(0.315985\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.36375 | −0.689970 | ||||||||
\(41\) | −1.20663 | −0.188444 | −0.0942221 | − | 0.995551i | \(-0.530036\pi\) | ||||
−0.0942221 | + | 0.995551i | \(0.530036\pi\) | |||||||
\(42\) | 0.201753 | 0.0311311 | ||||||||
\(43\) | 8.33493 | 1.27106 | 0.635532 | − | 0.772074i | \(-0.280781\pi\) | ||||
0.635532 | + | 0.772074i | \(0.280781\pi\) | |||||||
\(44\) | 4.36375 | 0.657860 | ||||||||
\(45\) | −12.7956 | −1.90746 | ||||||||
\(46\) | 4.08036 | 0.601616 | ||||||||
\(47\) | 1.36375 | 0.198923 | 0.0994617 | − | 0.995041i | \(-0.468288\pi\) | ||||
0.0994617 | + | 0.995041i | \(0.468288\pi\) | |||||||
\(48\) | 0.260281 | 0.0375683 | ||||||||
\(49\) | −6.39917 | −0.914167 | ||||||||
\(50\) | −14.0423 | −1.98588 | ||||||||
\(51\) | −1.80605 | −0.252897 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.52493 | 0.484186 | 0.242093 | − | 0.970253i | \(-0.422166\pi\) | ||||
0.242093 | + | 0.970253i | \(0.422166\pi\) | |||||||
\(54\) | 1.54405 | 0.210119 | ||||||||
\(55\) | 19.0423 | 2.56767 | ||||||||
\(56\) | 0.775135 | 0.103582 | ||||||||
\(57\) | 0.260281 | 0.0344750 | ||||||||
\(58\) | −2.54367 | −0.334001 | ||||||||
\(59\) | 12.4214 | 1.61712 | 0.808562 | − | 0.588410i | \(-0.200246\pi\) | ||||
0.808562 | + | 0.588410i | \(0.200246\pi\) | |||||||
\(60\) | 1.13580 | 0.146631 | ||||||||
\(61\) | 2.03105 | 0.260049 | 0.130024 | − | 0.991511i | \(-0.458494\pi\) | ||||
0.130024 | + | 0.991511i | \(0.458494\pi\) | |||||||
\(62\) | 6.41220 | 0.814351 | ||||||||
\(63\) | 2.27289 | 0.286357 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.13580 | −0.139807 | ||||||||
\(67\) | 11.5249 | 1.40799 | 0.703995 | − | 0.710205i | \(-0.251398\pi\) | ||||
0.703995 | + | 0.710205i | \(0.251398\pi\) | |||||||
\(68\) | −6.93885 | −0.841459 | ||||||||
\(69\) | −1.06204 | −0.127854 | ||||||||
\(70\) | 3.38249 | 0.404285 | ||||||||
\(71\) | −12.1096 | −1.43714 | −0.718570 | − | 0.695455i | \(-0.755203\pi\) | ||||
−0.718570 | + | 0.695455i | \(0.755203\pi\) | |||||||
\(72\) | 2.93225 | 0.345569 | ||||||||
\(73\) | 2.30351 | 0.269605 | 0.134802 | − | 0.990872i | \(-0.456960\pi\) | ||||
0.134802 | + | 0.990872i | \(0.456960\pi\) | |||||||
\(74\) | −6.64765 | −0.772774 | ||||||||
\(75\) | 3.65495 | 0.422037 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −3.38249 | −0.385471 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.16942 | 0.919132 | 0.459566 | − | 0.888144i | \(-0.348005\pi\) | ||||
0.459566 | + | 0.888144i | \(0.348005\pi\) | |||||||
\(80\) | 4.36375 | 0.487882 | ||||||||
\(81\) | 8.39487 | 0.932764 | ||||||||
\(82\) | 1.20663 | 0.133250 | ||||||||
\(83\) | −2.75361 | −0.302248 | −0.151124 | − | 0.988515i | \(-0.548289\pi\) | ||||
−0.151124 | + | 0.988515i | \(0.548289\pi\) | |||||||
\(84\) | −0.201753 | −0.0220130 | ||||||||
\(85\) | −30.2794 | −3.28426 | ||||||||
\(86\) | −8.33493 | −0.898779 | ||||||||
\(87\) | 0.662069 | 0.0709813 | ||||||||
\(88\) | −4.36375 | −0.465177 | ||||||||
\(89\) | 3.34501 | 0.354570 | 0.177285 | − | 0.984160i | \(-0.443269\pi\) | ||||
0.177285 | + | 0.984160i | \(0.443269\pi\) | |||||||
\(90\) | 12.7956 | 1.34878 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.08036 | −0.425407 | ||||||||
\(93\) | −1.66897 | −0.173064 | ||||||||
\(94\) | −1.36375 | −0.140660 | ||||||||
\(95\) | 4.36375 | 0.447711 | ||||||||
\(96\) | −0.260281 | −0.0265648 | ||||||||
\(97\) | 2.12923 | 0.216190 | 0.108095 | − | 0.994141i | \(-0.465525\pi\) | ||||
0.108095 | + | 0.994141i | \(0.465525\pi\) | |||||||
\(98\) | 6.39917 | 0.646413 | ||||||||
\(99\) | −12.7956 | −1.28601 | ||||||||
\(100\) | 14.0423 | 1.40423 | ||||||||
\(101\) | 11.5122 | 1.14550 | 0.572751 | − | 0.819729i | \(-0.305876\pi\) | ||||
0.572751 | + | 0.819729i | \(0.305876\pi\) | |||||||
\(102\) | 1.80605 | 0.178826 | ||||||||
\(103\) | 8.59033 | 0.846431 | 0.423215 | − | 0.906029i | \(-0.360901\pi\) | ||||
0.423215 | + | 0.906029i | \(0.360901\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.880398 | −0.0859181 | ||||||||
\(106\) | −3.52493 | −0.342371 | ||||||||
\(107\) | 12.2990 | 1.18899 | 0.594495 | − | 0.804099i | \(-0.297352\pi\) | ||||
0.594495 | + | 0.804099i | \(0.297352\pi\) | |||||||
\(108\) | −1.54405 | −0.148576 | ||||||||
\(109\) | 8.17344 | 0.782874 | 0.391437 | − | 0.920205i | \(-0.371978\pi\) | ||||
0.391437 | + | 0.920205i | \(0.371978\pi\) | |||||||
\(110\) | −19.0423 | −1.81561 | ||||||||
\(111\) | 1.73026 | 0.164229 | ||||||||
\(112\) | −0.775135 | −0.0732433 | ||||||||
\(113\) | 4.05116 | 0.381101 | 0.190551 | − | 0.981677i | \(-0.438973\pi\) | ||||
0.190551 | + | 0.981677i | \(0.438973\pi\) | |||||||
\(114\) | −0.260281 | −0.0243775 | ||||||||
\(115\) | −17.8057 | −1.66039 | ||||||||
\(116\) | 2.54367 | 0.236174 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.4214 | −1.14348 | ||||||||
\(119\) | 5.37854 | 0.493050 | ||||||||
\(120\) | −1.13580 | −0.103684 | ||||||||
\(121\) | 8.04232 | 0.731120 | ||||||||
\(122\) | −2.03105 | −0.183882 | ||||||||
\(123\) | −0.314063 | −0.0283181 | ||||||||
\(124\) | −6.41220 | −0.575833 | ||||||||
\(125\) | 39.4584 | 3.52927 | ||||||||
\(126\) | −2.27289 | −0.202485 | ||||||||
\(127\) | 6.03228 | 0.535279 | 0.267639 | − | 0.963519i | \(-0.413756\pi\) | ||||
0.267639 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.16942 | 0.191007 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.8272 | 1.12071 | 0.560357 | − | 0.828251i | \(-0.310664\pi\) | ||||
0.560357 | + | 0.828251i | \(0.310664\pi\) | |||||||
\(132\) | 1.13580 | 0.0988587 | ||||||||
\(133\) | −0.775135 | −0.0672127 | ||||||||
\(134\) | −11.5249 | −0.995599 | ||||||||
\(135\) | −6.73786 | −0.579902 | ||||||||
\(136\) | 6.93885 | 0.595001 | ||||||||
\(137\) | −13.5152 | −1.15468 | −0.577339 | − | 0.816504i | \(-0.695909\pi\) | ||||
−0.577339 | + | 0.816504i | \(0.695909\pi\) | |||||||
\(138\) | 1.06204 | 0.0904067 | ||||||||
\(139\) | 2.17364 | 0.184365 | 0.0921827 | − | 0.995742i | \(-0.470616\pi\) | ||||
0.0921827 | + | 0.995742i | \(0.470616\pi\) | |||||||
\(140\) | −3.38249 | −0.285873 | ||||||||
\(141\) | 0.354958 | 0.0298929 | ||||||||
\(142\) | 12.1096 | 1.01621 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.93225 | −0.244354 | ||||||||
\(145\) | 11.1000 | 0.921801 | ||||||||
\(146\) | −2.30351 | −0.190639 | ||||||||
\(147\) | −1.66558 | −0.137375 | ||||||||
\(148\) | 6.64765 | 0.546434 | ||||||||
\(149\) | 10.4236 | 0.853935 | 0.426968 | − | 0.904267i | \(-0.359582\pi\) | ||||
0.426968 | + | 0.904267i | \(0.359582\pi\) | |||||||
\(150\) | −3.65495 | −0.298425 | ||||||||
\(151\) | −7.19913 | −0.585857 | −0.292928 | − | 0.956134i | \(-0.594630\pi\) | ||||
−0.292928 | + | 0.956134i | \(0.594630\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 20.3465 | 1.64491 | ||||||||
\(154\) | 3.38249 | 0.272569 | ||||||||
\(155\) | −27.9813 | −2.24751 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.5120 | 1.63704 | 0.818519 | − | 0.574479i | \(-0.194795\pi\) | ||||
0.818519 | + | 0.574479i | \(0.194795\pi\) | |||||||
\(158\) | −8.16942 | −0.649924 | ||||||||
\(159\) | 0.917471 | 0.0727602 | ||||||||
\(160\) | −4.36375 | −0.344985 | ||||||||
\(161\) | 3.16283 | 0.249266 | ||||||||
\(162\) | −8.39487 | −0.659564 | ||||||||
\(163\) | 2.11182 | 0.165411 | 0.0827053 | − | 0.996574i | \(-0.473644\pi\) | ||||
0.0827053 | + | 0.996574i | \(0.473644\pi\) | |||||||
\(164\) | −1.20663 | −0.0942221 | ||||||||
\(165\) | 4.95635 | 0.385851 | ||||||||
\(166\) | 2.75361 | 0.213722 | ||||||||
\(167\) | 20.3048 | 1.57123 | 0.785615 | − | 0.618715i | \(-0.212346\pi\) | ||||
0.785615 | + | 0.618715i | \(0.212346\pi\) | |||||||
\(168\) | 0.201753 | 0.0155656 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 30.2794 | 2.32232 | ||||||||
\(171\) | −2.93225 | −0.224235 | ||||||||
\(172\) | 8.33493 | 0.635532 | ||||||||
\(173\) | 23.1299 | 1.75854 | 0.879268 | − | 0.476327i | \(-0.158032\pi\) | ||||
0.879268 | + | 0.476327i | \(0.158032\pi\) | |||||||
\(174\) | −0.662069 | −0.0501914 | ||||||||
\(175\) | −10.8847 | −0.822805 | ||||||||
\(176\) | 4.36375 | 0.328930 | ||||||||
\(177\) | 3.23304 | 0.243011 | ||||||||
\(178\) | −3.34501 | −0.250719 | ||||||||
\(179\) | −13.1550 | −0.983253 | −0.491626 | − | 0.870806i | \(-0.663597\pi\) | ||||
−0.491626 | + | 0.870806i | \(0.663597\pi\) | |||||||
\(180\) | −12.7956 | −0.953730 | ||||||||
\(181\) | −0.551157 | −0.0409672 | −0.0204836 | − | 0.999790i | \(-0.506521\pi\) | ||||
−0.0204836 | + | 0.999790i | \(0.506521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.528643 | 0.0390784 | ||||||||
\(184\) | 4.08036 | 0.300808 | ||||||||
\(185\) | 29.0087 | 2.13276 | ||||||||
\(186\) | 1.66897 | 0.122375 | ||||||||
\(187\) | −30.2794 | −2.21425 | ||||||||
\(188\) | 1.36375 | 0.0994617 | ||||||||
\(189\) | 1.19685 | 0.0870579 | ||||||||
\(190\) | −4.36375 | −0.316580 | ||||||||
\(191\) | −5.61275 | −0.406124 | −0.203062 | − | 0.979166i | \(-0.565089\pi\) | ||||
−0.203062 | + | 0.979166i | \(0.565089\pi\) | |||||||
\(192\) | 0.260281 | 0.0187841 | ||||||||
\(193\) | −7.88071 | −0.567266 | −0.283633 | − | 0.958933i | \(-0.591540\pi\) | ||||
−0.283633 | + | 0.958933i | \(0.591540\pi\) | |||||||
\(194\) | −2.12923 | −0.152870 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.39917 | −0.457083 | ||||||||
\(197\) | 6.81454 | 0.485516 | 0.242758 | − | 0.970087i | \(-0.421948\pi\) | ||||
0.242758 | + | 0.970087i | \(0.421948\pi\) | |||||||
\(198\) | 12.7956 | 0.909345 | ||||||||
\(199\) | −24.2470 | −1.71882 | −0.859411 | − | 0.511286i | \(-0.829169\pi\) | ||||
−0.859411 | + | 0.511286i | \(0.829169\pi\) | |||||||
\(200\) | −14.0423 | −0.992942 | ||||||||
\(201\) | 2.99971 | 0.211583 | ||||||||
\(202\) | −11.5122 | −0.809993 | ||||||||
\(203\) | −1.97169 | −0.138386 | ||||||||
\(204\) | −1.80605 | −0.126449 | ||||||||
\(205\) | −5.26544 | −0.367754 | ||||||||
\(206\) | −8.59033 | −0.598517 | ||||||||
\(207\) | 11.9646 | 0.831600 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.36375 | 0.301847 | ||||||||
\(210\) | 0.880398 | 0.0607533 | ||||||||
\(211\) | −5.05776 | −0.348190 | −0.174095 | − | 0.984729i | \(-0.555700\pi\) | ||||
−0.174095 | + | 0.984729i | \(0.555700\pi\) | |||||||
\(212\) | 3.52493 | 0.242093 | ||||||||
\(213\) | −3.15188 | −0.215964 | ||||||||
\(214\) | −12.2990 | −0.840743 | ||||||||
\(215\) | 36.3716 | 2.48052 | ||||||||
\(216\) | 1.54405 | 0.105059 | ||||||||
\(217\) | 4.97032 | 0.337407 | ||||||||
\(218\) | −8.17344 | −0.553575 | ||||||||
\(219\) | 0.599558 | 0.0405144 | ||||||||
\(220\) | 19.0423 | 1.28383 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.73026 | −0.116127 | ||||||||
\(223\) | −14.0800 | −0.942864 | −0.471432 | − | 0.881902i | \(-0.656263\pi\) | ||||
−0.471432 | + | 0.881902i | \(0.656263\pi\) | |||||||
\(224\) | 0.775135 | 0.0517909 | ||||||||
\(225\) | −41.1756 | −2.74504 | ||||||||
\(226\) | −4.05116 | −0.269479 | ||||||||
\(227\) | 18.6540 | 1.23811 | 0.619056 | − | 0.785347i | \(-0.287515\pi\) | ||||
0.619056 | + | 0.785347i | \(0.287515\pi\) | |||||||
\(228\) | 0.260281 | 0.0172375 | ||||||||
\(229\) | 5.65636 | 0.373783 | 0.186891 | − | 0.982381i | \(-0.440159\pi\) | ||||
0.186891 | + | 0.982381i | \(0.440159\pi\) | |||||||
\(230\) | 17.8057 | 1.17407 | ||||||||
\(231\) | −0.880398 | −0.0579260 | ||||||||
\(232\) | −2.54367 | −0.167000 | ||||||||
\(233\) | −19.9409 | −1.30637 | −0.653185 | − | 0.757198i | \(-0.726568\pi\) | ||||
−0.653185 | + | 0.757198i | \(0.726568\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.95107 | 0.388205 | ||||||||
\(236\) | 12.4214 | 0.808562 | ||||||||
\(237\) | 2.12634 | 0.138121 | ||||||||
\(238\) | −5.37854 | −0.348639 | ||||||||
\(239\) | −3.43781 | −0.222373 | −0.111187 | − | 0.993800i | \(-0.535465\pi\) | ||||
−0.111187 | + | 0.993800i | \(0.535465\pi\) | |||||||
\(240\) | 1.13580 | 0.0733156 | ||||||||
\(241\) | 5.43845 | 0.350321 | 0.175161 | − | 0.984540i | \(-0.443956\pi\) | ||||
0.175161 | + | 0.984540i | \(0.443956\pi\) | |||||||
\(242\) | −8.04232 | −0.516980 | ||||||||
\(243\) | 6.81718 | 0.437322 | ||||||||
\(244\) | 2.03105 | 0.130024 | ||||||||
\(245\) | −27.9244 | −1.78402 | ||||||||
\(246\) | 0.314063 | 0.0200239 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.41220 | 0.407175 | ||||||||
\(249\) | −0.716713 | −0.0454198 | ||||||||
\(250\) | −39.4584 | −2.49557 | ||||||||
\(251\) | −25.9262 | −1.63644 | −0.818222 | − | 0.574902i | \(-0.805040\pi\) | ||||
−0.818222 | + | 0.574902i | \(0.805040\pi\) | |||||||
\(252\) | 2.27289 | 0.143179 | ||||||||
\(253\) | −17.8057 | −1.11943 | ||||||||
\(254\) | −6.03228 | −0.378499 | ||||||||
\(255\) | −7.88115 | −0.493537 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.88939 | −0.117857 | −0.0589283 | − | 0.998262i | \(-0.518768\pi\) | ||||
−0.0589283 | + | 0.998262i | \(0.518768\pi\) | |||||||
\(258\) | −2.16942 | −0.135062 | ||||||||
\(259\) | −5.15283 | −0.320181 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.45870 | −0.461682 | ||||||||
\(262\) | −12.8272 | −0.792464 | ||||||||
\(263\) | −4.19046 | −0.258395 | −0.129197 | − | 0.991619i | \(-0.541240\pi\) | ||||
−0.129197 | + | 0.991619i | \(0.541240\pi\) | |||||||
\(264\) | −1.13580 | −0.0699037 | ||||||||
\(265\) | 15.3819 | 0.944904 | ||||||||
\(266\) | 0.775135 | 0.0475266 | ||||||||
\(267\) | 0.870641 | 0.0532824 | ||||||||
\(268\) | 11.5249 | 0.703995 | ||||||||
\(269\) | 5.06288 | 0.308689 | 0.154345 | − | 0.988017i | \(-0.450673\pi\) | ||||
0.154345 | + | 0.988017i | \(0.450673\pi\) | |||||||
\(270\) | 6.73786 | 0.410053 | ||||||||
\(271\) | −23.4633 | −1.42529 | −0.712647 | − | 0.701522i | \(-0.752504\pi\) | ||||
−0.712647 | + | 0.701522i | \(0.752504\pi\) | |||||||
\(272\) | −6.93885 | −0.420730 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.5152 | 0.816481 | ||||||||
\(275\) | 61.2772 | 3.69515 | ||||||||
\(276\) | −1.06204 | −0.0639272 | ||||||||
\(277\) | 7.03193 | 0.422508 | 0.211254 | − | 0.977431i | \(-0.432245\pi\) | ||||
0.211254 | + | 0.977431i | \(0.432245\pi\) | |||||||
\(278\) | −2.17364 | −0.130366 | ||||||||
\(279\) | 18.8022 | 1.12566 | ||||||||
\(280\) | 3.38249 | 0.202143 | ||||||||
\(281\) | −20.4814 | −1.22182 | −0.610910 | − | 0.791700i | \(-0.709196\pi\) | ||||
−0.610910 | + | 0.791700i | \(0.709196\pi\) | |||||||
\(282\) | −0.354958 | −0.0211374 | ||||||||
\(283\) | −26.9345 | −1.60109 | −0.800544 | − | 0.599274i | \(-0.795456\pi\) | ||||
−0.800544 | + | 0.599274i | \(0.795456\pi\) | |||||||
\(284\) | −12.1096 | −0.718570 | ||||||||
\(285\) | 1.13580 | 0.0672790 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.935302 | 0.0552091 | ||||||||
\(288\) | 2.93225 | 0.172785 | ||||||||
\(289\) | 31.1476 | 1.83221 | ||||||||
\(290\) | −11.1000 | −0.651812 | ||||||||
\(291\) | 0.554197 | 0.0324876 | ||||||||
\(292\) | 2.30351 | 0.134802 | ||||||||
\(293\) | 9.68946 | 0.566064 | 0.283032 | − | 0.959110i | \(-0.408660\pi\) | ||||
0.283032 | + | 0.959110i | \(0.408660\pi\) | |||||||
\(294\) | 1.66558 | 0.0971386 | ||||||||
\(295\) | 54.2038 | 3.15587 | ||||||||
\(296\) | −6.64765 | −0.386387 | ||||||||
\(297\) | −6.73786 | −0.390970 | ||||||||
\(298\) | −10.4236 | −0.603823 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.65495 | 0.211018 | ||||||||
\(301\) | −6.46069 | −0.372388 | ||||||||
\(302\) | 7.19913 | 0.414263 | ||||||||
\(303\) | 2.99639 | 0.172138 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 8.86298 | 0.507493 | ||||||||
\(306\) | −20.3465 | −1.16313 | ||||||||
\(307\) | 12.5815 | 0.718064 | 0.359032 | − | 0.933325i | \(-0.383107\pi\) | ||||
0.359032 | + | 0.933325i | \(0.383107\pi\) | |||||||
\(308\) | −3.38249 | −0.192736 | ||||||||
\(309\) | 2.23590 | 0.127196 | ||||||||
\(310\) | 27.9813 | 1.58923 | ||||||||
\(311\) | −16.7407 | −0.949280 | −0.474640 | − | 0.880180i | \(-0.657422\pi\) | ||||
−0.474640 | + | 0.880180i | \(0.657422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5101 | −0.650590 | −0.325295 | − | 0.945613i | \(-0.605464\pi\) | ||||
−0.325295 | + | 0.945613i | \(0.605464\pi\) | |||||||
\(314\) | −20.5120 | −1.15756 | ||||||||
\(315\) | 9.91833 | 0.558835 | ||||||||
\(316\) | 8.16942 | 0.459566 | ||||||||
\(317\) | −4.14425 | −0.232764 | −0.116382 | − | 0.993205i | \(-0.537130\pi\) | ||||
−0.116382 | + | 0.993205i | \(0.537130\pi\) | |||||||
\(318\) | −0.917471 | −0.0514492 | ||||||||
\(319\) | 11.1000 | 0.621478 | ||||||||
\(320\) | 4.36375 | 0.243941 | ||||||||
\(321\) | 3.20119 | 0.178673 | ||||||||
\(322\) | −3.16283 | −0.176257 | ||||||||
\(323\) | −6.93885 | −0.386088 | ||||||||
\(324\) | 8.39487 | 0.466382 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.11182 | −0.116963 | ||||||||
\(327\) | 2.12739 | 0.117645 | ||||||||
\(328\) | 1.20663 | 0.0666251 | ||||||||
\(329\) | −1.05709 | −0.0582793 | ||||||||
\(330\) | −4.95635 | −0.272838 | ||||||||
\(331\) | 0.316380 | 0.0173898 | 0.00869492 | − | 0.999962i | \(-0.497232\pi\) | ||||
0.00869492 | + | 0.999962i | \(0.497232\pi\) | |||||||
\(332\) | −2.75361 | −0.151124 | ||||||||
\(333\) | −19.4926 | −1.06819 | ||||||||
\(334\) | −20.3048 | −1.11103 | ||||||||
\(335\) | 50.2917 | 2.74773 | ||||||||
\(336\) | −0.201753 | −0.0110065 | ||||||||
\(337\) | 17.7103 | 0.964739 | 0.482370 | − | 0.875968i | \(-0.339776\pi\) | ||||
0.482370 | + | 0.875968i | \(0.339776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.05444 | 0.0572693 | ||||||||
\(340\) | −30.2794 | −1.64213 | ||||||||
\(341\) | −27.9813 | −1.51527 | ||||||||
\(342\) | 2.93225 | 0.158558 | ||||||||
\(343\) | 10.3862 | 0.560800 | ||||||||
\(344\) | −8.33493 | −0.449389 | ||||||||
\(345\) | −4.63447 | −0.249512 | ||||||||
\(346\) | −23.1299 | −1.24347 | ||||||||
\(347\) | 22.4138 | 1.20324 | 0.601619 | − | 0.798783i | \(-0.294523\pi\) | ||||
0.601619 | + | 0.798783i | \(0.294523\pi\) | |||||||
\(348\) | 0.662069 | 0.0354906 | ||||||||
\(349\) | −20.0965 | −1.07574 | −0.537871 | − | 0.843027i | \(-0.680771\pi\) | ||||
−0.537871 | + | 0.843027i | \(0.680771\pi\) | |||||||
\(350\) | 10.8847 | 0.581811 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.36375 | −0.232589 | ||||||||
\(353\) | −11.7682 | −0.626360 | −0.313180 | − | 0.949694i | \(-0.601394\pi\) | ||||
−0.313180 | + | 0.949694i | \(0.601394\pi\) | |||||||
\(354\) | −3.23304 | −0.171834 | ||||||||
\(355\) | −52.8431 | −2.80462 | ||||||||
\(356\) | 3.34501 | 0.177285 | ||||||||
\(357\) | 1.39993 | 0.0740922 | ||||||||
\(358\) | 13.1550 | 0.695265 | ||||||||
\(359\) | −7.47763 | −0.394654 | −0.197327 | − | 0.980338i | \(-0.563226\pi\) | ||||
−0.197327 | + | 0.980338i | \(0.563226\pi\) | |||||||
\(360\) | 12.7956 | 0.674389 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0.551157 | 0.0289682 | ||||||||
\(363\) | 2.09326 | 0.109868 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0519 | 0.526142 | ||||||||
\(366\) | −0.528643 | −0.0276326 | ||||||||
\(367\) | 16.4233 | 0.857289 | 0.428645 | − | 0.903473i | \(-0.358991\pi\) | ||||
0.428645 | + | 0.903473i | \(0.358991\pi\) | |||||||
\(368\) | −4.08036 | −0.212703 | ||||||||
\(369\) | 3.53815 | 0.184189 | ||||||||
\(370\) | −29.0087 | −1.50809 | ||||||||
\(371\) | −2.73230 | −0.141854 | ||||||||
\(372\) | −1.66897 | −0.0865322 | ||||||||
\(373\) | −12.8349 | −0.664567 | −0.332283 | − | 0.943180i | \(-0.607819\pi\) | ||||
−0.332283 | + | 0.943180i | \(0.607819\pi\) | |||||||
\(374\) | 30.2794 | 1.56571 | ||||||||
\(375\) | 10.2703 | 0.530354 | ||||||||
\(376\) | −1.36375 | −0.0703301 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.19685 | −0.0615592 | ||||||||
\(379\) | −36.0892 | −1.85378 | −0.926889 | − | 0.375334i | \(-0.877528\pi\) | ||||
−0.926889 | + | 0.375334i | \(0.877528\pi\) | |||||||
\(380\) | 4.36375 | 0.223856 | ||||||||
\(381\) | 1.57009 | 0.0804380 | ||||||||
\(382\) | 5.61275 | 0.287173 | ||||||||
\(383\) | −32.8134 | −1.67669 | −0.838344 | − | 0.545142i | \(-0.816476\pi\) | ||||
−0.838344 | + | 0.545142i | \(0.816476\pi\) | |||||||
\(384\) | −0.260281 | −0.0132824 | ||||||||
\(385\) | −14.7604 | −0.752258 | ||||||||
\(386\) | 7.88071 | 0.401117 | ||||||||
\(387\) | −24.4401 | −1.24236 | ||||||||
\(388\) | 2.12923 | 0.108095 | ||||||||
\(389\) | −2.97899 | −0.151041 | −0.0755204 | − | 0.997144i | \(-0.524062\pi\) | ||||
−0.0755204 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.3130 | 1.43185 | ||||||||
\(392\) | 6.39917 | 0.323207 | ||||||||
\(393\) | 3.33866 | 0.168413 | ||||||||
\(394\) | −6.81454 | −0.343312 | ||||||||
\(395\) | 35.6493 | 1.79371 | ||||||||
\(396\) | −12.7956 | −0.643004 | ||||||||
\(397\) | −20.3722 | −1.02245 | −0.511225 | − | 0.859447i | \(-0.670808\pi\) | ||||
−0.511225 | + | 0.859447i | \(0.670808\pi\) | |||||||
\(398\) | 24.2470 | 1.21539 | ||||||||
\(399\) | −0.201753 | −0.0101003 | ||||||||
\(400\) | 14.0423 | 0.702116 | ||||||||
\(401\) | 13.8861 | 0.693438 | 0.346719 | − | 0.937969i | \(-0.387296\pi\) | ||||
0.346719 | + | 0.937969i | \(0.387296\pi\) | |||||||
\(402\) | −2.99971 | −0.149612 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.5122 | 0.572751 | ||||||||
\(405\) | 36.6331 | 1.82032 | ||||||||
\(406\) | 1.97169 | 0.0978533 | ||||||||
\(407\) | 29.0087 | 1.43791 | ||||||||
\(408\) | 1.80605 | 0.0894128 | ||||||||
\(409\) | −31.1280 | −1.53918 | −0.769590 | − | 0.638538i | \(-0.779539\pi\) | ||||
−0.769590 | + | 0.638538i | \(0.779539\pi\) | |||||||
\(410\) | 5.26544 | 0.260041 | ||||||||
\(411\) | −3.51774 | −0.173517 | ||||||||
\(412\) | 8.59033 | 0.423215 | ||||||||
\(413\) | −9.62824 | −0.473775 | ||||||||
\(414\) | −11.9646 | −0.588030 | ||||||||
\(415\) | −12.0161 | −0.589846 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.565756 | 0.0277052 | ||||||||
\(418\) | −4.36375 | −0.213438 | ||||||||
\(419\) | −28.0907 | −1.37232 | −0.686160 | − | 0.727451i | \(-0.740705\pi\) | ||||
−0.686160 | + | 0.727451i | \(0.740705\pi\) | |||||||
\(420\) | −0.880398 | −0.0429590 | ||||||||
\(421\) | −10.8442 | −0.528512 | −0.264256 | − | 0.964453i | \(-0.585126\pi\) | ||||
−0.264256 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(422\) | 5.05776 | 0.246208 | ||||||||
\(423\) | −3.99886 | −0.194431 | ||||||||
\(424\) | −3.52493 | −0.171186 | ||||||||
\(425\) | −97.4375 | −4.72641 | ||||||||
\(426\) | 3.15188 | 0.152709 | ||||||||
\(427\) | −1.57434 | −0.0761874 | ||||||||
\(428\) | 12.2990 | 0.594495 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.3716 | −1.75399 | ||||||||
\(431\) | 6.90864 | 0.332777 | 0.166389 | − | 0.986060i | \(-0.446789\pi\) | ||||
0.166389 | + | 0.986060i | \(0.446789\pi\) | |||||||
\(432\) | −1.54405 | −0.0742882 | ||||||||
\(433\) | 39.3767 | 1.89232 | 0.946161 | − | 0.323697i | \(-0.104926\pi\) | ||||
0.946161 | + | 0.323697i | \(0.104926\pi\) | |||||||
\(434\) | −4.97032 | −0.238583 | ||||||||
\(435\) | 2.88911 | 0.138522 | ||||||||
\(436\) | 8.17344 | 0.391437 | ||||||||
\(437\) | −4.08036 | −0.195190 | ||||||||
\(438\) | −0.599558 | −0.0286480 | ||||||||
\(439\) | −36.9430 | −1.76319 | −0.881597 | − | 0.472003i | \(-0.843531\pi\) | ||||
−0.881597 | + | 0.472003i | \(0.843531\pi\) | |||||||
\(440\) | −19.0423 | −0.907807 | ||||||||
\(441\) | 18.7640 | 0.893523 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0111 | 0.475642 | 0.237821 | − | 0.971309i | \(-0.423567\pi\) | ||||
0.237821 | + | 0.971309i | \(0.423567\pi\) | |||||||
\(444\) | 1.73026 | 0.0821143 | ||||||||
\(445\) | 14.5968 | 0.691953 | ||||||||
\(446\) | 14.0800 | 0.666706 | ||||||||
\(447\) | 2.71306 | 0.128324 | ||||||||
\(448\) | −0.775135 | −0.0366217 | ||||||||
\(449\) | −19.3184 | −0.911694 | −0.455847 | − | 0.890058i | \(-0.650664\pi\) | ||||
−0.455847 | + | 0.890058i | \(0.650664\pi\) | |||||||
\(450\) | 41.1756 | 1.94104 | ||||||||
\(451\) | −5.26544 | −0.247940 | ||||||||
\(452\) | 4.05116 | 0.190551 | ||||||||
\(453\) | −1.87380 | −0.0880386 | ||||||||
\(454\) | −18.6540 | −0.875478 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.260281 | −0.0121888 | ||||||||
\(457\) | 8.71798 | 0.407810 | 0.203905 | − | 0.978991i | \(-0.434637\pi\) | ||||
0.203905 | + | 0.978991i | \(0.434637\pi\) | |||||||
\(458\) | −5.65636 | −0.264304 | ||||||||
\(459\) | 10.7139 | 0.500084 | ||||||||
\(460\) | −17.8057 | −0.830193 | ||||||||
\(461\) | 4.77897 | 0.222579 | 0.111290 | − | 0.993788i | \(-0.464502\pi\) | ||||
0.111290 | + | 0.993788i | \(0.464502\pi\) | |||||||
\(462\) | 0.880398 | 0.0409598 | ||||||||
\(463\) | 24.7123 | 1.14848 | 0.574239 | − | 0.818688i | \(-0.305298\pi\) | ||||
0.574239 | + | 0.818688i | \(0.305298\pi\) | |||||||
\(464\) | 2.54367 | 0.118087 | ||||||||
\(465\) | −7.28298 | −0.337740 | ||||||||
\(466\) | 19.9409 | 0.923744 | ||||||||
\(467\) | −28.5590 | −1.32155 | −0.660776 | − | 0.750583i | \(-0.729773\pi\) | ||||
−0.660776 | + | 0.750583i | \(0.729773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.93334 | −0.412503 | ||||||||
\(470\) | −5.95107 | −0.274502 | ||||||||
\(471\) | 5.33889 | 0.246003 | ||||||||
\(472\) | −12.4214 | −0.571740 | ||||||||
\(473\) | 36.3716 | 1.67237 | ||||||||
\(474\) | −2.12634 | −0.0976662 | ||||||||
\(475\) | 14.0423 | 0.644306 | ||||||||
\(476\) | 5.37854 | 0.246525 | ||||||||
\(477\) | −10.3360 | −0.473252 | ||||||||
\(478\) | 3.43781 | 0.157242 | ||||||||
\(479\) | −33.7512 | −1.54213 | −0.771066 | − | 0.636755i | \(-0.780276\pi\) | ||||
−0.771066 | + | 0.636755i | \(0.780276\pi\) | |||||||
\(480\) | −1.13580 | −0.0518420 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.43845 | −0.247715 | ||||||||
\(483\) | 0.823223 | 0.0374579 | ||||||||
\(484\) | 8.04232 | 0.365560 | ||||||||
\(485\) | 9.29141 | 0.421901 | ||||||||
\(486\) | −6.81718 | −0.309234 | ||||||||
\(487\) | 5.50881 | 0.249628 | 0.124814 | − | 0.992180i | \(-0.460167\pi\) | ||||
0.124814 | + | 0.992180i | \(0.460167\pi\) | |||||||
\(488\) | −2.03105 | −0.0919412 | ||||||||
\(489\) | 0.549666 | 0.0248568 | ||||||||
\(490\) | 27.9244 | 1.26149 | ||||||||
\(491\) | 22.4320 | 1.01234 | 0.506171 | − | 0.862433i | \(-0.331060\pi\) | ||||
0.506171 | + | 0.862433i | \(0.331060\pi\) | |||||||
\(492\) | −0.314063 | −0.0141591 | ||||||||
\(493\) | −17.6502 | −0.794924 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −55.8369 | −2.50968 | ||||||||
\(496\) | −6.41220 | −0.287916 | ||||||||
\(497\) | 9.38654 | 0.421044 | ||||||||
\(498\) | 0.716713 | 0.0321167 | ||||||||
\(499\) | 2.39076 | 0.107025 | 0.0535125 | − | 0.998567i | \(-0.482958\pi\) | ||||
0.0535125 | + | 0.998567i | \(0.482958\pi\) | |||||||
\(500\) | 39.4584 | 1.76463 | ||||||||
\(501\) | 5.28494 | 0.236114 | ||||||||
\(502\) | 25.9262 | 1.15714 | ||||||||
\(503\) | −22.0472 | −0.983035 | −0.491517 | − | 0.870868i | \(-0.663558\pi\) | ||||
−0.491517 | + | 0.870868i | \(0.663558\pi\) | |||||||
\(504\) | −2.27289 | −0.101243 | ||||||||
\(505\) | 50.2362 | 2.23548 | ||||||||
\(506\) | 17.8057 | 0.791558 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.03228 | 0.267639 | ||||||||
\(509\) | 3.86985 | 0.171528 | 0.0857641 | − | 0.996315i | \(-0.472667\pi\) | ||||
0.0857641 | + | 0.996315i | \(0.472667\pi\) | |||||||
\(510\) | 7.88115 | 0.348983 | ||||||||
\(511\) | −1.78553 | −0.0789871 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.54405 | −0.0681715 | ||||||||
\(514\) | 1.88939 | 0.0833372 | ||||||||
\(515\) | 37.4861 | 1.65183 | ||||||||
\(516\) | 2.16942 | 0.0955035 | ||||||||
\(517\) | 5.95107 | 0.261728 | ||||||||
\(518\) | 5.15283 | 0.226402 | ||||||||
\(519\) | 6.02028 | 0.264261 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.7278 | 1.82813 | 0.914064 | − | 0.405570i | \(-0.132927\pi\) | ||||
0.914064 | + | 0.405570i | \(0.132927\pi\) | |||||||
\(522\) | 7.45870 | 0.326458 | ||||||||
\(523\) | −8.08529 | −0.353545 | −0.176773 | − | 0.984252i | \(-0.556566\pi\) | ||||
−0.176773 | + | 0.984252i | \(0.556566\pi\) | |||||||
\(524\) | 12.8272 | 0.560357 | ||||||||
\(525\) | −2.83308 | −0.123646 | ||||||||
\(526\) | 4.19046 | 0.182713 | ||||||||
\(527\) | 44.4933 | 1.93816 | ||||||||
\(528\) | 1.13580 | 0.0494294 | ||||||||
\(529\) | −6.35068 | −0.276117 | ||||||||
\(530\) | −15.3819 | −0.668148 | ||||||||
\(531\) | −36.4226 | −1.58061 | ||||||||
\(532\) | −0.775135 | −0.0336064 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.870641 | −0.0376763 | ||||||||
\(535\) | 53.6698 | 2.32035 | ||||||||
\(536\) | −11.5249 | −0.497799 | ||||||||
\(537\) | −3.42400 | −0.147757 | ||||||||
\(538\) | −5.06288 | −0.218276 | ||||||||
\(539\) | −27.9244 | −1.20279 | ||||||||
\(540\) | −6.73786 | −0.289951 | ||||||||
\(541\) | 33.6272 | 1.44574 | 0.722872 | − | 0.690982i | \(-0.242821\pi\) | ||||
0.722872 | + | 0.690982i | \(0.242821\pi\) | |||||||
\(542\) | 23.4633 | 1.00784 | ||||||||
\(543\) | −0.143456 | −0.00615627 | ||||||||
\(544\) | 6.93885 | 0.297501 | ||||||||
\(545\) | 35.6669 | 1.52780 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.6548 | 1.05417 | 0.527083 | − | 0.849814i | \(-0.323286\pi\) | ||||
0.527083 | + | 0.849814i | \(0.323286\pi\) | |||||||
\(548\) | −13.5152 | −0.577339 | ||||||||
\(549\) | −5.95555 | −0.254177 | ||||||||
\(550\) | −61.2772 | −2.61287 | ||||||||
\(551\) | 2.54367 | 0.108364 | ||||||||
\(552\) | 1.06204 | 0.0452034 | ||||||||
\(553\) | −6.33240 | −0.269281 | ||||||||
\(554\) | −7.03193 | −0.298758 | ||||||||
\(555\) | 7.55041 | 0.320497 | ||||||||
\(556\) | 2.17364 | 0.0921827 | ||||||||
\(557\) | −8.69700 | −0.368504 | −0.184252 | − | 0.982879i | \(-0.558986\pi\) | ||||
−0.184252 | + | 0.982879i | \(0.558986\pi\) | |||||||
\(558\) | −18.8022 | −0.795961 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.38249 | −0.142936 | ||||||||
\(561\) | −7.88115 | −0.332742 | ||||||||
\(562\) | 20.4814 | 0.863957 | ||||||||
\(563\) | 44.6483 | 1.88170 | 0.940851 | − | 0.338821i | \(-0.110028\pi\) | ||||
0.940851 | + | 0.338821i | \(0.110028\pi\) | |||||||
\(564\) | 0.354958 | 0.0149464 | ||||||||
\(565\) | 17.6783 | 0.743730 | ||||||||
\(566\) | 26.9345 | 1.13214 | ||||||||
\(567\) | −6.50716 | −0.273275 | ||||||||
\(568\) | 12.1096 | 0.508106 | ||||||||
\(569\) | −41.8543 | −1.75462 | −0.877312 | − | 0.479920i | \(-0.840666\pi\) | ||||
−0.877312 | + | 0.479920i | \(0.840666\pi\) | |||||||
\(570\) | −1.13580 | −0.0475734 | ||||||||
\(571\) | 1.94613 | 0.0814429 | 0.0407214 | − | 0.999171i | \(-0.487034\pi\) | ||||
0.0407214 | + | 0.999171i | \(0.487034\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.46089 | −0.0610296 | ||||||||
\(574\) | −0.935302 | −0.0390387 | ||||||||
\(575\) | −57.2977 | −2.38948 | ||||||||
\(576\) | −2.93225 | −0.122177 | ||||||||
\(577\) | −17.3159 | −0.720870 | −0.360435 | − | 0.932784i | \(-0.617372\pi\) | ||||
−0.360435 | + | 0.932784i | \(0.617372\pi\) | |||||||
\(578\) | −31.1476 | −1.29557 | ||||||||
\(579\) | −2.05120 | −0.0852448 | ||||||||
\(580\) | 11.1000 | 0.460901 | ||||||||
\(581\) | 2.13442 | 0.0885507 | ||||||||
\(582\) | −0.554197 | −0.0229722 | ||||||||
\(583\) | 15.3819 | 0.637054 | ||||||||
\(584\) | −2.30351 | −0.0953197 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.68946 | −0.400268 | ||||||||
\(587\) | −45.0778 | −1.86056 | −0.930279 | − | 0.366852i | \(-0.880436\pi\) | ||||
−0.930279 | + | 0.366852i | \(0.880436\pi\) | |||||||
\(588\) | −1.66558 | −0.0686874 | ||||||||
\(589\) | −6.41220 | −0.264210 | ||||||||
\(590\) | −54.2038 | −2.23153 | ||||||||
\(591\) | 1.77369 | 0.0729600 | ||||||||
\(592\) | 6.64765 | 0.273217 | ||||||||
\(593\) | 39.5863 | 1.62561 | 0.812807 | − | 0.582533i | \(-0.197938\pi\) | ||||
0.812807 | + | 0.582533i | \(0.197938\pi\) | |||||||
\(594\) | 6.73786 | 0.276458 | ||||||||
\(595\) | 23.4706 | 0.962202 | ||||||||
\(596\) | 10.4236 | 0.426968 | ||||||||
\(597\) | −6.31102 | −0.258293 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.9168 | 0.650341 | 0.325171 | − | 0.945655i | \(-0.394578\pi\) | ||||
0.325171 | + | 0.945655i | \(0.394578\pi\) | |||||||
\(600\) | −3.65495 | −0.149213 | ||||||||
\(601\) | 21.8645 | 0.891870 | 0.445935 | − | 0.895065i | \(-0.352871\pi\) | ||||
0.445935 | + | 0.895065i | \(0.352871\pi\) | |||||||
\(602\) | 6.46069 | 0.263318 | ||||||||
\(603\) | −33.7939 | −1.37619 | ||||||||
\(604\) | −7.19913 | −0.292928 | ||||||||
\(605\) | 35.0947 | 1.42680 | ||||||||
\(606\) | −2.99639 | −0.121720 | ||||||||
\(607\) | −5.59196 | −0.226971 | −0.113485 | − | 0.993540i | \(-0.536201\pi\) | ||||
−0.113485 | + | 0.993540i | \(0.536201\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −0.513193 | −0.0207956 | ||||||||
\(610\) | −8.86298 | −0.358852 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 20.3465 | 0.822457 | ||||||||
\(613\) | −45.9423 | −1.85559 | −0.927796 | − | 0.373088i | \(-0.878299\pi\) | ||||
−0.927796 | + | 0.373088i | \(0.878299\pi\) | |||||||
\(614\) | −12.5815 | −0.507748 | ||||||||
\(615\) | −1.37049 | −0.0552636 | ||||||||
\(616\) | 3.38249 | 0.136285 | ||||||||
\(617\) | 10.6161 | 0.427389 | 0.213695 | − | 0.976900i | \(-0.431450\pi\) | ||||
0.213695 | + | 0.976900i | \(0.431450\pi\) | |||||||
\(618\) | −2.23590 | −0.0899410 | ||||||||
\(619\) | 2.47379 | 0.0994299 | 0.0497149 | − | 0.998763i | \(-0.484169\pi\) | ||||
0.0497149 | + | 0.998763i | \(0.484169\pi\) | |||||||
\(620\) | −27.9813 | −1.12375 | ||||||||
\(621\) | 6.30028 | 0.252822 | ||||||||
\(622\) | 16.7407 | 0.671242 | ||||||||
\(623\) | −2.59283 | −0.103880 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 101.975 | 4.07901 | ||||||||
\(626\) | 11.5101 | 0.460037 | ||||||||
\(627\) | 1.13580 | 0.0453595 | ||||||||
\(628\) | 20.5120 | 0.818519 | ||||||||
\(629\) | −46.1271 | −1.83921 | ||||||||
\(630\) | −9.91833 | −0.395156 | ||||||||
\(631\) | 28.5339 | 1.13592 | 0.567958 | − | 0.823058i | \(-0.307734\pi\) | ||||
0.567958 | + | 0.823058i | \(0.307734\pi\) | |||||||
\(632\) | −8.16942 | −0.324962 | ||||||||
\(633\) | −1.31644 | −0.0523236 | ||||||||
\(634\) | 4.14425 | 0.164589 | ||||||||
\(635\) | 26.3234 | 1.04461 | ||||||||
\(636\) | 0.917471 | 0.0363801 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.1000 | −0.439452 | ||||||||
\(639\) | 35.5083 | 1.40469 | ||||||||
\(640\) | −4.36375 | −0.172492 | ||||||||
\(641\) | 22.3729 | 0.883678 | 0.441839 | − | 0.897094i | \(-0.354326\pi\) | ||||
0.441839 | + | 0.897094i | \(0.354326\pi\) | |||||||
\(642\) | −3.20119 | −0.126341 | ||||||||
\(643\) | 11.1412 | 0.439365 | 0.219682 | − | 0.975571i | \(-0.429498\pi\) | ||||
0.219682 | + | 0.975571i | \(0.429498\pi\) | |||||||
\(644\) | 3.16283 | 0.124633 | ||||||||
\(645\) | 9.46682 | 0.372756 | ||||||||
\(646\) | 6.93885 | 0.273005 | ||||||||
\(647\) | −9.46200 | −0.371990 | −0.185995 | − | 0.982551i | \(-0.559551\pi\) | ||||
−0.185995 | + | 0.982551i | \(0.559551\pi\) | |||||||
\(648\) | −8.39487 | −0.329782 | ||||||||
\(649\) | 54.2038 | 2.12768 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.29368 | 0.0507033 | ||||||||
\(652\) | 2.11182 | 0.0827053 | ||||||||
\(653\) | 9.39067 | 0.367485 | 0.183743 | − | 0.982974i | \(-0.441179\pi\) | ||||
0.183743 | + | 0.982974i | \(0.441179\pi\) | |||||||
\(654\) | −2.12739 | −0.0831875 | ||||||||
\(655\) | 55.9745 | 2.18710 | ||||||||
\(656\) | −1.20663 | −0.0471110 | ||||||||
\(657\) | −6.75446 | −0.263517 | ||||||||
\(658\) | 1.05709 | 0.0412097 | ||||||||
\(659\) | −17.9190 | −0.698027 | −0.349013 | − | 0.937118i | \(-0.613483\pi\) | ||||
−0.349013 | + | 0.937118i | \(0.613483\pi\) | |||||||
\(660\) | 4.95635 | 0.192926 | ||||||||
\(661\) | −0.722654 | −0.0281080 | −0.0140540 | − | 0.999901i | \(-0.504474\pi\) | ||||
−0.0140540 | + | 0.999901i | \(0.504474\pi\) | |||||||
\(662\) | −0.316380 | −0.0122965 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.75361 | 0.106861 | ||||||||
\(665\) | −3.38249 | −0.131168 | ||||||||
\(666\) | 19.4926 | 0.755323 | ||||||||
\(667\) | −10.3791 | −0.401880 | ||||||||
\(668\) | 20.3048 | 0.785615 | ||||||||
\(669\) | −3.66475 | −0.141687 | ||||||||
\(670\) | −50.2917 | −1.94294 | ||||||||
\(671\) | 8.86298 | 0.342152 | ||||||||
\(672\) | 0.201753 | 0.00778278 | ||||||||
\(673\) | 40.2647 | 1.55209 | 0.776045 | − | 0.630677i | \(-0.217223\pi\) | ||||
0.776045 | + | 0.630677i | \(0.217223\pi\) | |||||||
\(674\) | −17.7103 | −0.682174 | ||||||||
\(675\) | −21.6821 | −0.834543 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.1338 | −0.735373 | −0.367686 | − | 0.929950i | \(-0.619850\pi\) | ||||
−0.367686 | + | 0.929950i | \(0.619850\pi\) | |||||||
\(678\) | −1.05444 | −0.0404955 | ||||||||
\(679\) | −1.65044 | −0.0633380 | ||||||||
\(680\) | 30.2794 | 1.16116 | ||||||||
\(681\) | 4.85529 | 0.186055 | ||||||||
\(682\) | 27.9813 | 1.07146 | ||||||||
\(683\) | −34.3981 | −1.31621 | −0.658103 | − | 0.752928i | \(-0.728641\pi\) | ||||
−0.658103 | + | 0.752928i | \(0.728641\pi\) | |||||||
\(684\) | −2.93225 | −0.112118 | ||||||||
\(685\) | −58.9768 | −2.25339 | ||||||||
\(686\) | −10.3862 | −0.396545 | ||||||||
\(687\) | 1.47224 | 0.0561695 | ||||||||
\(688\) | 8.33493 | 0.317766 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.63447 | 0.176431 | ||||||||
\(691\) | 41.8318 | 1.59136 | 0.795678 | − | 0.605719i | \(-0.207115\pi\) | ||||
0.795678 | + | 0.605719i | \(0.207115\pi\) | |||||||
\(692\) | 23.1299 | 0.879268 | ||||||||
\(693\) | 9.91833 | 0.376766 | ||||||||
\(694\) | −22.4138 | −0.850818 | ||||||||
\(695\) | 9.48521 | 0.359794 | ||||||||
\(696\) | −0.662069 | −0.0250957 | ||||||||
\(697\) | 8.37263 | 0.317136 | ||||||||
\(698\) | 20.0965 | 0.760665 | ||||||||
\(699\) | −5.19023 | −0.196312 | ||||||||
\(700\) | −10.8847 | −0.411403 | ||||||||
\(701\) | 9.76756 | 0.368916 | 0.184458 | − | 0.982840i | \(-0.440947\pi\) | ||||
0.184458 | + | 0.982840i | \(0.440947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.64765 | 0.250721 | ||||||||
\(704\) | 4.36375 | 0.164465 | ||||||||
\(705\) | 1.54895 | 0.0583368 | ||||||||
\(706\) | 11.7682 | 0.442903 | ||||||||
\(707\) | −8.92348 | −0.335602 | ||||||||
\(708\) | 3.23304 | 0.121505 | ||||||||
\(709\) | 2.81576 | 0.105748 | 0.0528740 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528740 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(710\) | 52.8431 | 1.98317 | ||||||||
\(711\) | −23.9548 | −0.898376 | ||||||||
\(712\) | −3.34501 | −0.125359 | ||||||||
\(713\) | 26.1641 | 0.979852 | ||||||||
\(714\) | −1.39993 | −0.0523911 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.1550 | −0.491626 | ||||||||
\(717\) | −0.894795 | −0.0334167 | ||||||||
\(718\) | 7.47763 | 0.279063 | ||||||||
\(719\) | 11.0765 | 0.413083 | 0.206542 | − | 0.978438i | \(-0.433779\pi\) | ||||
0.206542 | + | 0.978438i | \(0.433779\pi\) | |||||||
\(720\) | −12.7956 | −0.476865 | ||||||||
\(721\) | −6.65867 | −0.247982 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 1.41552 | 0.0526439 | ||||||||
\(724\) | −0.551157 | −0.0204836 | ||||||||
\(725\) | 35.7191 | 1.32657 | ||||||||
\(726\) | −2.09326 | −0.0776882 | ||||||||
\(727\) | 0.407640 | 0.0151185 | 0.00755927 | − | 0.999971i | \(-0.497594\pi\) | ||||
0.00755927 | + | 0.999971i | \(0.497594\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.4102 | −0.867046 | ||||||||
\(730\) | −10.0519 | −0.372038 | ||||||||
\(731\) | −57.8348 | −2.13910 | ||||||||
\(732\) | 0.528643 | 0.0195392 | ||||||||
\(733\) | 32.2976 | 1.19294 | 0.596470 | − | 0.802636i | \(-0.296570\pi\) | ||||
0.596470 | + | 0.802636i | \(0.296570\pi\) | |||||||
\(734\) | −16.4233 | −0.606195 | ||||||||
\(735\) | −7.26818 | −0.268091 | ||||||||
\(736\) | 4.08036 | 0.150404 | ||||||||
\(737\) | 50.2917 | 1.85252 | ||||||||
\(738\) | −3.53815 | −0.130241 | ||||||||
\(739\) | 3.62754 | 0.133441 | 0.0667206 | − | 0.997772i | \(-0.478746\pi\) | ||||
0.0667206 | + | 0.997772i | \(0.478746\pi\) | |||||||
\(740\) | 29.0087 | 1.06638 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.73230 | 0.100306 | ||||||||
\(743\) | 8.04553 | 0.295162 | 0.147581 | − | 0.989050i | \(-0.452851\pi\) | ||||
0.147581 | + | 0.989050i | \(0.452851\pi\) | |||||||
\(744\) | 1.66897 | 0.0611875 | ||||||||
\(745\) | 45.4860 | 1.66648 | ||||||||
\(746\) | 12.8349 | 0.469920 | ||||||||
\(747\) | 8.07429 | 0.295423 | ||||||||
\(748\) | −30.2794 | −1.10712 | ||||||||
\(749\) | −9.53339 | −0.348342 | ||||||||
\(750\) | −10.2703 | −0.375017 | ||||||||
\(751\) | 18.8879 | 0.689230 | 0.344615 | − | 0.938744i | \(-0.388009\pi\) | ||||
0.344615 | + | 0.938744i | \(0.388009\pi\) | |||||||
\(752\) | 1.36375 | 0.0497309 | ||||||||
\(753\) | −6.74808 | −0.245914 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.4152 | −1.14332 | ||||||||
\(756\) | 1.19685 | 0.0435289 | ||||||||
\(757\) | −21.6822 | −0.788051 | −0.394026 | − | 0.919099i | \(-0.628918\pi\) | ||||
−0.394026 | + | 0.919099i | \(0.628918\pi\) | |||||||
\(758\) | 36.0892 | 1.31082 | ||||||||
\(759\) | −4.63447 | −0.168221 | ||||||||
\(760\) | −4.36375 | −0.158290 | ||||||||
\(761\) | −1.28461 | −0.0465670 | −0.0232835 | − | 0.999729i | \(-0.507412\pi\) | ||||
−0.0232835 | + | 0.999729i | \(0.507412\pi\) | |||||||
\(762\) | −1.57009 | −0.0568783 | ||||||||
\(763\) | −6.33552 | −0.229361 | ||||||||
\(764\) | −5.61275 | −0.203062 | ||||||||
\(765\) | 88.7869 | 3.21010 | ||||||||
\(766\) | 32.8134 | 1.18560 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.260281 | 0.00939207 | ||||||||
\(769\) | 11.4195 | 0.411796 | 0.205898 | − | 0.978573i | \(-0.433988\pi\) | ||||
0.205898 | + | 0.978573i | \(0.433988\pi\) | |||||||
\(770\) | 14.7604 | 0.531927 | ||||||||
\(771\) | −0.491771 | −0.0177107 | ||||||||
\(772\) | −7.88071 | −0.283633 | ||||||||
\(773\) | 35.6963 | 1.28391 | 0.641953 | − | 0.766744i | \(-0.278124\pi\) | ||||
0.641953 | + | 0.766744i | \(0.278124\pi\) | |||||||
\(774\) | 24.4401 | 0.878482 | ||||||||
\(775\) | −90.0422 | −3.23441 | ||||||||
\(776\) | −2.12923 | −0.0764348 | ||||||||
\(777\) | −1.34118 | −0.0481146 | ||||||||
\(778\) | 2.97899 | 0.106802 | ||||||||
\(779\) | −1.20663 | −0.0432321 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.8431 | −1.89087 | ||||||||
\(782\) | −28.3130 | −1.01247 | ||||||||
\(783\) | −3.92756 | −0.140360 | ||||||||
\(784\) | −6.39917 | −0.228542 | ||||||||
\(785\) | 89.5094 | 3.19473 | ||||||||
\(786\) | −3.33866 | −0.119086 | ||||||||
\(787\) | 47.2502 | 1.68429 | 0.842144 | − | 0.539253i | \(-0.181293\pi\) | ||||
0.842144 | + | 0.539253i | \(0.181293\pi\) | |||||||
\(788\) | 6.81454 | 0.242758 | ||||||||
\(789\) | −1.09070 | −0.0388298 | ||||||||
\(790\) | −35.6493 | −1.26835 | ||||||||
\(791\) | −3.14019 | −0.111652 | ||||||||
\(792\) | 12.7956 | 0.454673 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 20.3722 | 0.722981 | ||||||||
\(795\) | 4.00362 | 0.141994 | ||||||||
\(796\) | −24.2470 | −0.859411 | ||||||||
\(797\) | 45.8247 | 1.62319 | 0.811597 | − | 0.584218i | \(-0.198599\pi\) | ||||
0.811597 | + | 0.584218i | \(0.198599\pi\) | |||||||
\(798\) | 0.201753 | 0.00714197 | ||||||||
\(799\) | −9.46286 | −0.334772 | ||||||||
\(800\) | −14.0423 | −0.496471 | ||||||||
\(801\) | −9.80841 | −0.346563 | ||||||||
\(802\) | −13.8861 | −0.490335 | ||||||||
\(803\) | 10.0519 | 0.354725 | ||||||||
\(804\) | 2.99971 | 0.105792 | ||||||||
\(805\) | 13.8018 | 0.486449 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.31777 | 0.0463877 | ||||||||
\(808\) | −11.5122 | −0.404996 | ||||||||
\(809\) | 16.5686 | 0.582522 | 0.291261 | − | 0.956644i | \(-0.405925\pi\) | ||||
0.291261 | + | 0.956644i | \(0.405925\pi\) | |||||||
\(810\) | −36.6331 | −1.28716 | ||||||||
\(811\) | −15.5277 | −0.545252 | −0.272626 | − | 0.962120i | \(-0.587892\pi\) | ||||
−0.272626 | + | 0.962120i | \(0.587892\pi\) | |||||||
\(812\) | −1.97169 | −0.0691928 | ||||||||
\(813\) | −6.10705 | −0.214184 | ||||||||
\(814\) | −29.0087 | −1.01675 | ||||||||
\(815\) | 9.21546 | 0.322804 | ||||||||
\(816\) | −1.80605 | −0.0632244 | ||||||||
\(817\) | 8.33493 | 0.291602 | ||||||||
\(818\) | 31.1280 | 1.08836 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.26544 | −0.183877 | ||||||||
\(821\) | 2.24388 | 0.0783120 | 0.0391560 | − | 0.999233i | \(-0.487533\pi\) | ||||
0.0391560 | + | 0.999233i | \(0.487533\pi\) | |||||||
\(822\) | 3.51774 | 0.122695 | ||||||||
\(823\) | −16.5355 | −0.576391 | −0.288195 | − | 0.957572i | \(-0.593055\pi\) | ||||
−0.288195 | + | 0.957572i | \(0.593055\pi\) | |||||||
\(824\) | −8.59033 | −0.299258 | ||||||||
\(825\) | 15.9493 | 0.555282 | ||||||||
\(826\) | 9.62824 | 0.335009 | ||||||||
\(827\) | 28.8538 | 1.00334 | 0.501672 | − | 0.865058i | \(-0.332718\pi\) | ||||
0.501672 | + | 0.865058i | \(0.332718\pi\) | |||||||
\(828\) | 11.9646 | 0.415800 | ||||||||
\(829\) | −16.8384 | −0.584823 | −0.292411 | − | 0.956293i | \(-0.594458\pi\) | ||||
−0.292411 | + | 0.956293i | \(0.594458\pi\) | |||||||
\(830\) | 12.0161 | 0.417084 | ||||||||
\(831\) | 1.83028 | 0.0634916 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.4028 | 1.53847 | ||||||||
\(834\) | −0.565756 | −0.0195905 | ||||||||
\(835\) | 88.6050 | 3.06630 | ||||||||
\(836\) | 4.36375 | 0.150923 | ||||||||
\(837\) | 9.90077 | 0.342221 | ||||||||
\(838\) | 28.0907 | 0.970376 | ||||||||
\(839\) | −34.0552 | −1.17572 | −0.587859 | − | 0.808964i | \(-0.700029\pi\) | ||||
−0.587859 | + | 0.808964i | \(0.700029\pi\) | |||||||
\(840\) | 0.880398 | 0.0303766 | ||||||||
\(841\) | −22.5297 | −0.776887 | ||||||||
\(842\) | 10.8442 | 0.373714 | ||||||||
\(843\) | −5.33092 | −0.183607 | ||||||||
\(844\) | −5.05776 | −0.174095 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.99886 | 0.137484 | ||||||||
\(847\) | −6.23388 | −0.214199 | ||||||||
\(848\) | 3.52493 | 0.121047 | ||||||||
\(849\) | −7.01052 | −0.240601 | ||||||||
\(850\) | 97.4375 | 3.34208 | ||||||||
\(851\) | −27.1248 | −0.929826 | ||||||||
\(852\) | −3.15188 | −0.107982 | ||||||||
\(853\) | −5.48844 | −0.187921 | −0.0939603 | − | 0.995576i | \(-0.529953\pi\) | ||||
−0.0939603 | + | 0.995576i | \(0.529953\pi\) | |||||||
\(854\) | 1.57434 | 0.0538726 | ||||||||
\(855\) | −12.7956 | −0.437601 | ||||||||
\(856\) | −12.2990 | −0.420371 | ||||||||
\(857\) | −12.5021 | −0.427064 | −0.213532 | − | 0.976936i | \(-0.568497\pi\) | ||||
−0.213532 | + | 0.976936i | \(0.568497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.7834 | −1.28915 | −0.644577 | − | 0.764540i | \(-0.722966\pi\) | ||||
−0.644577 | + | 0.764540i | \(0.722966\pi\) | |||||||
\(860\) | 36.3716 | 1.24026 | ||||||||
\(861\) | 0.243441 | 0.00829645 | ||||||||
\(862\) | −6.90864 | −0.235309 | ||||||||
\(863\) | −35.2458 | −1.19978 | −0.599891 | − | 0.800082i | \(-0.704789\pi\) | ||||
−0.599891 | + | 0.800082i | \(0.704789\pi\) | |||||||
\(864\) | 1.54405 | 0.0525297 | ||||||||
\(865\) | 100.933 | 3.43183 | ||||||||
\(866\) | −39.3767 | −1.33807 | ||||||||
\(867\) | 8.10713 | 0.275333 | ||||||||
\(868\) | 4.97032 | 0.168704 | ||||||||
\(869\) | 35.6493 | 1.20932 | ||||||||
\(870\) | −2.88911 | −0.0979499 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.17344 | −0.276788 | ||||||||
\(873\) | −6.24343 | −0.211308 | ||||||||
\(874\) | 4.08036 | 0.138020 | ||||||||
\(875\) | −30.5856 | −1.03398 | ||||||||
\(876\) | 0.599558 | 0.0202572 | ||||||||
\(877\) | 36.9518 | 1.24777 | 0.623887 | − | 0.781515i | \(-0.285553\pi\) | ||||
0.623887 | + | 0.781515i | \(0.285553\pi\) | |||||||
\(878\) | 36.9430 | 1.24677 | ||||||||
\(879\) | 2.52198 | 0.0850643 | ||||||||
\(880\) | 19.0423 | 0.641916 | ||||||||
\(881\) | 1.25780 | 0.0423764 | 0.0211882 | − | 0.999776i | \(-0.493255\pi\) | ||||
0.0211882 | + | 0.999776i | \(0.493255\pi\) | |||||||
\(882\) | −18.7640 | −0.631816 | ||||||||
\(883\) | 7.95258 | 0.267626 | 0.133813 | − | 0.991007i | \(-0.457278\pi\) | ||||
0.133813 | + | 0.991007i | \(0.457278\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1082 | 0.474242 | ||||||||
\(886\) | −10.0111 | −0.336330 | ||||||||
\(887\) | −6.38803 | −0.214489 | −0.107245 | − | 0.994233i | \(-0.534203\pi\) | ||||
−0.107245 | + | 0.994233i | \(0.534203\pi\) | |||||||
\(888\) | −1.73026 | −0.0580636 | ||||||||
\(889\) | −4.67583 | −0.156822 | ||||||||
\(890\) | −14.5968 | −0.489285 | ||||||||
\(891\) | 36.6331 | 1.22726 | ||||||||
\(892\) | −14.0800 | −0.471432 | ||||||||
\(893\) | 1.36375 | 0.0456362 | ||||||||
\(894\) | −2.71306 | −0.0907385 | ||||||||
\(895\) | −57.4053 | −1.91885 | ||||||||
\(896\) | 0.775135 | 0.0258954 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.3184 | 0.644665 | ||||||||
\(899\) | −16.3106 | −0.543987 | ||||||||
\(900\) | −41.1756 | −1.37252 | ||||||||
\(901\) | −24.4590 | −0.814846 | ||||||||
\(902\) | 5.26544 | 0.175320 | ||||||||
\(903\) | −1.68159 | −0.0559600 | ||||||||
\(904\) | −4.05116 | −0.134740 | ||||||||
\(905\) | −2.40511 | −0.0799487 | ||||||||
\(906\) | 1.87380 | 0.0622527 | ||||||||
\(907\) | −10.0113 | −0.332420 | −0.166210 | − | 0.986090i | \(-0.553153\pi\) | ||||
−0.166210 | + | 0.986090i | \(0.553153\pi\) | |||||||
\(908\) | 18.6540 | 0.619056 | ||||||||
\(909\) | −33.7566 | −1.11964 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.2277 | −1.03462 | −0.517309 | − | 0.855798i | \(-0.673066\pi\) | ||||
−0.517309 | + | 0.855798i | \(0.673066\pi\) | |||||||
\(912\) | 0.260281 | 0.00861876 | ||||||||
\(913\) | −12.0161 | −0.397674 | ||||||||
\(914\) | −8.71798 | −0.288365 | ||||||||
\(915\) | 2.30686 | 0.0762626 | ||||||||
\(916\) | 5.65636 | 0.186891 | ||||||||
\(917\) | −9.94277 | −0.328339 | ||||||||
\(918\) | −10.7139 | −0.353613 | ||||||||
\(919\) | −12.4072 | −0.409277 | −0.204638 | − | 0.978838i | \(-0.565602\pi\) | ||||
−0.204638 | + | 0.978838i | \(0.565602\pi\) | |||||||
\(920\) | 17.8057 | 0.587035 | ||||||||
\(921\) | 3.27472 | 0.107906 | ||||||||
\(922\) | −4.77897 | −0.157387 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.880398 | −0.0289630 | ||||||||
\(925\) | 93.3485 | 3.06928 | ||||||||
\(926\) | −24.7123 | −0.812097 | ||||||||
\(927\) | −25.1890 | −0.827316 | ||||||||
\(928\) | −2.54367 | −0.0835002 | ||||||||
\(929\) | 51.4106 | 1.68673 | 0.843363 | − | 0.537344i | \(-0.180572\pi\) | ||||
0.843363 | + | 0.537344i | \(0.180572\pi\) | |||||||
\(930\) | 7.28298 | 0.238818 | ||||||||
\(931\) | −6.39917 | −0.209724 | ||||||||
\(932\) | −19.9409 | −0.653185 | ||||||||
\(933\) | −4.35729 | −0.142651 | ||||||||
\(934\) | 28.5590 | 0.934479 | ||||||||
\(935\) | −132.132 | −4.32117 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.03140 | −0.0663628 | −0.0331814 | − | 0.999449i | \(-0.510564\pi\) | ||||
−0.0331814 | + | 0.999449i | \(0.510564\pi\) | |||||||
\(938\) | 8.93334 | 0.291684 | ||||||||
\(939\) | −2.99586 | −0.0977663 | ||||||||
\(940\) | 5.95107 | 0.194102 | ||||||||
\(941\) | 42.4246 | 1.38300 | 0.691501 | − | 0.722376i | \(-0.256950\pi\) | ||||
0.691501 | + | 0.722376i | \(0.256950\pi\) | |||||||
\(942\) | −5.33889 | −0.173950 | ||||||||
\(943\) | 4.92349 | 0.160331 | ||||||||
\(944\) | 12.4214 | 0.404281 | ||||||||
\(945\) | 5.22275 | 0.169896 | ||||||||
\(946\) | −36.3716 | −1.18254 | ||||||||
\(947\) | 7.29296 | 0.236989 | 0.118495 | − | 0.992955i | \(-0.462193\pi\) | ||||
0.118495 | + | 0.992955i | \(0.462193\pi\) | |||||||
\(948\) | 2.12634 | 0.0690604 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −14.0423 | −0.455593 | ||||||||
\(951\) | −1.07867 | −0.0349782 | ||||||||
\(952\) | −5.37854 | −0.174320 | ||||||||
\(953\) | −32.7289 | −1.06019 | −0.530096 | − | 0.847938i | \(-0.677844\pi\) | ||||
−0.530096 | + | 0.847938i | \(0.677844\pi\) | |||||||
\(954\) | 10.3360 | 0.334640 | ||||||||
\(955\) | −24.4926 | −0.792563 | ||||||||
\(956\) | −3.43781 | −0.111187 | ||||||||
\(957\) | 2.88911 | 0.0933915 | ||||||||
\(958\) | 33.7512 | 1.09045 | ||||||||
\(959\) | 10.4761 | 0.338290 | ||||||||
\(960\) | 1.13580 | 0.0366578 | ||||||||
\(961\) | 10.1163 | 0.326334 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.0638 | −1.16214 | ||||||||
\(964\) | 5.43845 | 0.175161 | ||||||||
\(965\) | −34.3894 | −1.10704 | ||||||||
\(966\) | −0.823223 | −0.0264868 | ||||||||
\(967\) | 2.05333 | 0.0660307 | 0.0330154 | − | 0.999455i | \(-0.489489\pi\) | ||||
0.0330154 | + | 0.999455i | \(0.489489\pi\) | |||||||
\(968\) | −8.04232 | −0.258490 | ||||||||
\(969\) | −1.80605 | −0.0580187 | ||||||||
\(970\) | −9.29141 | −0.298329 | ||||||||
\(971\) | −41.6592 | −1.33691 | −0.668454 | − | 0.743754i | \(-0.733044\pi\) | ||||
−0.668454 | + | 0.743754i | \(0.733044\pi\) | |||||||
\(972\) | 6.81718 | 0.218661 | ||||||||
\(973\) | −1.68486 | −0.0540142 | ||||||||
\(974\) | −5.50881 | −0.176514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.03105 | 0.0650122 | ||||||||
\(977\) | −56.4520 | −1.80606 | −0.903030 | − | 0.429576i | \(-0.858663\pi\) | ||||
−0.903030 | + | 0.429576i | \(0.858663\pi\) | |||||||
\(978\) | −0.549666 | −0.0175764 | ||||||||
\(979\) | 14.5968 | 0.466515 | ||||||||
\(980\) | −27.9244 | −0.892011 | ||||||||
\(981\) | −23.9666 | −0.765195 | ||||||||
\(982\) | −22.4320 | −0.715835 | ||||||||
\(983\) | −32.1452 | −1.02527 | −0.512636 | − | 0.858606i | \(-0.671331\pi\) | ||||
−0.512636 | + | 0.858606i | \(0.671331\pi\) | |||||||
\(984\) | 0.314063 | 0.0100120 | ||||||||
\(985\) | 29.7370 | 0.947498 | ||||||||
\(986\) | 17.6502 | 0.562096 | ||||||||
\(987\) | −0.275140 | −0.00875781 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.0095 | −1.08144 | ||||||||
\(990\) | 55.8369 | 1.77461 | ||||||||
\(991\) | 35.1925 | 1.11793 | 0.558964 | − | 0.829192i | \(-0.311199\pi\) | ||||
0.558964 | + | 0.829192i | \(0.311199\pi\) | |||||||
\(992\) | 6.41220 | 0.203588 | ||||||||
\(993\) | 0.0823477 | 0.00261323 | ||||||||
\(994\) | −9.38654 | −0.297723 | ||||||||
\(995\) | −105.808 | −3.35433 | ||||||||
\(996\) | −0.716713 | −0.0227099 | ||||||||
\(997\) | −29.2648 | −0.926827 | −0.463413 | − | 0.886142i | \(-0.653375\pi\) | ||||
−0.463413 | + | 0.886142i | \(0.653375\pi\) | |||||||
\(998\) | −2.39076 | −0.0756781 | ||||||||
\(999\) | −10.2643 | −0.324749 |
(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 | 6422.2.a.bc.1.3 | 6 | ||
13.4 | even | 6 | 494.2.g.f.419.4 | yes | 12 | ||
13.10 | even | 6 | 494.2.g.f.191.4 | ✓ | 12 | ||
13.12 | even | 2 | 6422.2.a.bd.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.g.f.191.4 | ✓ | 12 | 13.10 | even | 6 | ||
494.2.g.f.419.4 | yes | 12 | 13.4 | even | 6 | ||
6422.2.a.bc.1.3 | 6 | 1.1 | even | 1 | trivial | ||
6422.2.a.bd.1.3 | 6 | 13.12 | even | 2 |