Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.23252.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.634868\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(5\) | 3.47747 | 1.55517 | 0.777586 | − | 0.628777i | \(-0.216444\pi\) | ||||
0.777586 | + | 0.628777i | \(0.216444\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.47747 | 1.09967 | ||||||||
\(11\) | −1.26974 | −0.382840 | −0.191420 | − | 0.981508i | \(-0.561309\pi\) | ||||
−0.191420 | + | 0.981508i | \(0.561309\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.47747 | −1.51918 | −0.759588 | − | 0.650404i | \(-0.774600\pi\) | ||||
−0.759588 | + | 0.650404i | \(0.774600\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.47747 | −0.897879 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.03079 | −1.70522 | −0.852608 | − | 0.522551i | \(-0.824981\pi\) | ||||
−0.852608 | + | 0.522551i | \(0.824981\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 3.47747 | 0.777586 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.26974 | −0.270709 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 7.09279 | 1.41856 | ||||||||
\(26\) | −5.47747 | −1.07422 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.40162 | −1.37445 | −0.687223 | − | 0.726446i | \(-0.741171\pi\) | ||||
−0.687223 | + | 0.726446i | \(0.741171\pi\) | |||||||
\(30\) | −3.47747 | −0.634896 | ||||||||
\(31\) | 9.57026 | 1.71887 | 0.859435 | − | 0.511246i | \(-0.170816\pi\) | ||||
0.859435 | + | 0.511246i | \(0.170816\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.26974 | 0.221033 | ||||||||
\(34\) | −7.03079 | −1.20577 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.71642 | 0.282177 | 0.141089 | − | 0.989997i | \(-0.454940\pi\) | ||||
0.141089 | + | 0.989997i | \(0.454940\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 5.47747 | 0.877097 | ||||||||
\(40\) | 3.47747 | 0.549836 | ||||||||
\(41\) | 8.50826 | 1.32877 | 0.664383 | − | 0.747392i | \(-0.268694\pi\) | ||||
0.664383 | + | 0.747392i | \(0.268694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.23852 | −1.10386 | −0.551932 | − | 0.833889i | \(-0.686109\pi\) | ||||
−0.551932 | + | 0.833889i | \(0.686109\pi\) | |||||||
\(44\) | −1.26974 | −0.191420 | ||||||||
\(45\) | 3.47747 | 0.518390 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −12.0169 | −1.75285 | −0.876425 | − | 0.481538i | \(-0.840078\pi\) | ||||
−0.876425 | + | 0.481538i | \(0.840078\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.09279 | 1.00307 | ||||||||
\(51\) | 7.03079 | 0.984507 | ||||||||
\(52\) | −5.47747 | −0.759588 | ||||||||
\(53\) | 7.68520 | 1.05564 | 0.527822 | − | 0.849355i | \(-0.323009\pi\) | ||||
0.527822 | + | 0.849355i | \(0.323009\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.41547 | −0.595381 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −7.40162 | −0.971880 | ||||||||
\(59\) | −7.84830 | −1.02176 | −0.510881 | − | 0.859652i | \(-0.670681\pi\) | ||||
−0.510881 | + | 0.859652i | \(0.670681\pi\) | |||||||
\(60\) | −3.47747 | −0.448939 | ||||||||
\(61\) | −9.92415 | −1.27066 | −0.635329 | − | 0.772242i | \(-0.719135\pi\) | ||||
−0.635329 | + | 0.772242i | \(0.719135\pi\) | |||||||
\(62\) | 9.57026 | 1.21542 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −19.0477 | −2.36258 | ||||||||
\(66\) | 1.26974 | 0.156294 | ||||||||
\(67\) | −4.37637 | −0.534659 | −0.267330 | − | 0.963605i | \(-0.586141\pi\) | ||||
−0.267330 | + | 0.963605i | \(0.586141\pi\) | |||||||
\(68\) | −7.03079 | −0.852608 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0616 | −1.19409 | −0.597045 | − | 0.802208i | \(-0.703659\pi\) | ||||
−0.597045 | + | 0.802208i | \(0.703659\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −13.4944 | −1.57940 | −0.789701 | − | 0.613492i | \(-0.789764\pi\) | ||||
−0.789701 | + | 0.613492i | \(0.789764\pi\) | |||||||
\(74\) | 1.71642 | 0.199529 | ||||||||
\(75\) | −7.09279 | −0.819005 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.47747 | 0.620201 | ||||||||
\(79\) | 13.4944 | 1.51824 | 0.759120 | − | 0.650951i | \(-0.225630\pi\) | ||||
0.759120 | + | 0.650951i | \(0.225630\pi\) | |||||||
\(80\) | 3.47747 | 0.388793 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.50826 | 0.939580 | ||||||||
\(83\) | −5.10664 | −0.560526 | −0.280263 | − | 0.959923i | \(-0.590422\pi\) | ||||
−0.280263 | + | 0.959923i | \(0.590422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.4493 | −2.65190 | ||||||||
\(86\) | −7.23852 | −0.780550 | ||||||||
\(87\) | 7.40162 | 0.793537 | ||||||||
\(88\) | −1.26974 | −0.135354 | ||||||||
\(89\) | −11.0308 | −1.16926 | −0.584631 | − | 0.811300i | \(-0.698761\pi\) | ||||
−0.584631 | + | 0.811300i | \(0.698761\pi\) | |||||||
\(90\) | 3.47747 | 0.366557 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −9.57026 | −0.992390 | ||||||||
\(94\) | −12.0169 | −1.23945 | ||||||||
\(95\) | −6.95494 | −0.713562 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −14.5564 | −1.47798 | −0.738990 | − | 0.673717i | \(-0.764697\pi\) | ||||
−0.738990 | + | 0.673717i | \(0.764697\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.26974 | −0.127613 | ||||||||
\(100\) | 7.09279 | 0.709279 | ||||||||
\(101\) | 0.817512 | 0.0813455 | 0.0406727 | − | 0.999173i | \(-0.487050\pi\) | ||||
0.0406727 | + | 0.999173i | \(0.487050\pi\) | |||||||
\(102\) | 7.03079 | 0.696152 | ||||||||
\(103\) | 4.50826 | 0.444212 | 0.222106 | − | 0.975023i | \(-0.428707\pi\) | ||||
0.222106 | + | 0.975023i | \(0.428707\pi\) | |||||||
\(104\) | −5.47747 | −0.537110 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.68520 | 0.746453 | ||||||||
\(107\) | −3.62363 | −0.350309 | −0.175155 | − | 0.984541i | \(-0.556043\pi\) | ||||
−0.175155 | + | 0.984541i | \(0.556043\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 18.3175 | 1.75449 | 0.877247 | − | 0.480038i | \(-0.159377\pi\) | ||||
0.877247 | + | 0.480038i | \(0.159377\pi\) | |||||||
\(110\) | −4.41547 | −0.420998 | ||||||||
\(111\) | −1.71642 | −0.162915 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5083 | −0.988534 | −0.494267 | − | 0.869310i | \(-0.664563\pi\) | ||||
−0.494267 | + | 0.869310i | \(0.664563\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | −3.47747 | −0.324276 | ||||||||
\(116\) | −7.40162 | −0.687223 | ||||||||
\(117\) | −5.47747 | −0.506392 | ||||||||
\(118\) | −7.84830 | −0.722495 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.47747 | −0.317448 | ||||||||
\(121\) | −9.38777 | −0.853434 | ||||||||
\(122\) | −9.92415 | −0.898490 | ||||||||
\(123\) | −8.50826 | −0.767164 | ||||||||
\(124\) | 9.57026 | 0.859435 | ||||||||
\(125\) | 7.27761 | 0.650930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6149 | 1.03066 | 0.515328 | − | 0.856993i | \(-0.327670\pi\) | ||||
0.515328 | + | 0.856993i | \(0.327670\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.23852 | 0.637316 | ||||||||
\(130\) | −19.0477 | −1.67060 | ||||||||
\(131\) | 19.1405 | 1.67231 | 0.836157 | − | 0.548489i | \(-0.184797\pi\) | ||||
0.836157 | + | 0.548489i | \(0.184797\pi\) | |||||||
\(132\) | 1.26974 | 0.110516 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.37637 | −0.378061 | ||||||||
\(135\) | −3.47747 | −0.299293 | ||||||||
\(136\) | −7.03079 | −0.602885 | ||||||||
\(137\) | 4.86215 | 0.415401 | 0.207701 | − | 0.978192i | \(-0.433402\pi\) | ||||
0.207701 | + | 0.978192i | \(0.433402\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 16.5083 | 1.40021 | 0.700106 | − | 0.714039i | \(-0.253136\pi\) | ||||
0.700106 | + | 0.714039i | \(0.253136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0169 | 1.01201 | ||||||||
\(142\) | −10.0616 | −0.844349 | ||||||||
\(143\) | 6.95494 | 0.581601 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −25.7389 | −2.13750 | ||||||||
\(146\) | −13.4944 | −1.11681 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.71642 | 0.141089 | ||||||||
\(149\) | 18.8257 | 1.54226 | 0.771132 | − | 0.636676i | \(-0.219691\pi\) | ||||
0.771132 | + | 0.636676i | \(0.219691\pi\) | |||||||
\(150\) | −7.09279 | −0.579124 | ||||||||
\(151\) | 15.4632 | 1.25838 | 0.629188 | − | 0.777253i | \(-0.283387\pi\) | ||||
0.629188 | + | 0.777253i | \(0.283387\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | −7.03079 | −0.568406 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.2803 | 2.67314 | ||||||||
\(156\) | 5.47747 | 0.438548 | ||||||||
\(157\) | −12.8791 | −1.02786 | −0.513932 | − | 0.857831i | \(-0.671811\pi\) | ||||
−0.513932 | + | 0.857831i | \(0.671811\pi\) | |||||||
\(158\) | 13.4944 | 1.07356 | ||||||||
\(159\) | −7.68520 | −0.609476 | ||||||||
\(160\) | 3.47747 | 0.274918 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −23.1405 | −1.81251 | −0.906253 | − | 0.422736i | \(-0.861070\pi\) | ||||
−0.906253 | + | 0.422736i | \(0.861070\pi\) | |||||||
\(164\) | 8.50826 | 0.664383 | ||||||||
\(165\) | 4.41547 | 0.343744 | ||||||||
\(166\) | −5.10664 | −0.396352 | ||||||||
\(167\) | 17.4186 | 1.34789 | 0.673944 | − | 0.738782i | \(-0.264599\pi\) | ||||
0.673944 | + | 0.738782i | \(0.264599\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.0027 | 1.30790 | ||||||||
\(170\) | −24.4493 | −1.87518 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | −7.23852 | −0.551932 | ||||||||
\(173\) | −2.84521 | −0.216317 | −0.108159 | − | 0.994134i | \(-0.534495\pi\) | ||||
−0.108159 | + | 0.994134i | \(0.534495\pi\) | |||||||
\(174\) | 7.40162 | 0.561115 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.26974 | −0.0957099 | ||||||||
\(177\) | 7.84830 | 0.589914 | ||||||||
\(178\) | −11.0308 | −0.826793 | ||||||||
\(179\) | 1.13785 | 0.0850471 | 0.0425235 | − | 0.999095i | \(-0.486460\pi\) | ||||
0.0425235 | + | 0.999095i | \(0.486460\pi\) | |||||||
\(180\) | 3.47747 | 0.259195 | ||||||||
\(181\) | −18.9407 | −1.40785 | −0.703924 | − | 0.710275i | \(-0.748571\pi\) | ||||
−0.703924 | + | 0.710275i | \(0.748571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.92415 | 0.733614 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 5.96879 | 0.438834 | ||||||||
\(186\) | −9.57026 | −0.701725 | ||||||||
\(187\) | 8.92724 | 0.652825 | ||||||||
\(188\) | −12.0169 | −0.876425 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.95494 | −0.504564 | ||||||||
\(191\) | −0.151700 | −0.0109766 | −0.00548832 | − | 0.999985i | \(-0.501747\pi\) | ||||
−0.00548832 | + | 0.999985i | \(0.501747\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 10.9237 | 0.786307 | 0.393153 | − | 0.919473i | \(-0.371384\pi\) | ||||
0.393153 | + | 0.919473i | \(0.371384\pi\) | |||||||
\(194\) | −14.5564 | −1.04509 | ||||||||
\(195\) | 19.0477 | 1.36404 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6149 | 0.970021 | 0.485011 | − | 0.874508i | \(-0.338816\pi\) | ||||
0.485011 | + | 0.874508i | \(0.338816\pi\) | |||||||
\(198\) | −1.26974 | −0.0902362 | ||||||||
\(199\) | −22.5698 | −1.59993 | −0.799967 | − | 0.600045i | \(-0.795149\pi\) | ||||
−0.799967 | + | 0.600045i | \(0.795149\pi\) | |||||||
\(200\) | 7.09279 | 0.501536 | ||||||||
\(201\) | 4.37637 | 0.308686 | ||||||||
\(202\) | 0.817512 | 0.0575199 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.03079 | 0.492254 | ||||||||
\(205\) | 29.5872 | 2.06646 | ||||||||
\(206\) | 4.50826 | 0.314105 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −5.47747 | −0.379794 | ||||||||
\(209\) | 2.53947 | 0.175659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.49441 | 0.653622 | 0.326811 | − | 0.945090i | \(-0.394026\pi\) | ||||
0.326811 | + | 0.945090i | \(0.394026\pi\) | |||||||
\(212\) | 7.68520 | 0.527822 | ||||||||
\(213\) | 10.0616 | 0.689408 | ||||||||
\(214\) | −3.62363 | −0.247706 | ||||||||
\(215\) | −25.1717 | −1.71670 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.3175 | 1.24062 | ||||||||
\(219\) | 13.4944 | 0.911868 | ||||||||
\(220\) | −4.41547 | −0.297691 | ||||||||
\(221\) | 38.5109 | 2.59053 | ||||||||
\(222\) | −1.71642 | −0.115198 | ||||||||
\(223\) | −15.2946 | −1.02420 | −0.512100 | − | 0.858926i | \(-0.671132\pi\) | ||||
−0.512100 | + | 0.858926i | \(0.671132\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.09279 | 0.472853 | ||||||||
\(226\) | −10.5083 | −0.698999 | ||||||||
\(227\) | −1.42931 | −0.0948669 | −0.0474335 | − | 0.998874i | \(-0.515104\pi\) | ||||
−0.0474335 | + | 0.998874i | \(0.515104\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | −17.9241 | −1.18446 | −0.592231 | − | 0.805769i | \(-0.701753\pi\) | ||||
−0.592231 | + | 0.805769i | \(0.701753\pi\) | |||||||
\(230\) | −3.47747 | −0.229298 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.40162 | −0.485940 | ||||||||
\(233\) | −18.4155 | −1.20644 | −0.603219 | − | 0.797576i | \(-0.706115\pi\) | ||||
−0.603219 | + | 0.797576i | \(0.706115\pi\) | |||||||
\(234\) | −5.47747 | −0.358073 | ||||||||
\(235\) | −41.7885 | −2.72598 | ||||||||
\(236\) | −7.84830 | −0.510881 | ||||||||
\(237\) | −13.4944 | −0.876556 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | −3.47747 | −0.224470 | ||||||||
\(241\) | 4.39853 | 0.283334 | 0.141667 | − | 0.989914i | \(-0.454754\pi\) | ||||
0.141667 | + | 0.989914i | \(0.454754\pi\) | |||||||
\(242\) | −9.38777 | −0.603469 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.92415 | −0.635329 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.50826 | −0.542467 | ||||||||
\(247\) | 10.9549 | 0.697046 | ||||||||
\(248\) | 9.57026 | 0.607712 | ||||||||
\(249\) | 5.10664 | 0.323620 | ||||||||
\(250\) | 7.27761 | 0.460277 | ||||||||
\(251\) | −4.29498 | −0.271097 | −0.135548 | − | 0.990771i | \(-0.543280\pi\) | ||||
−0.135548 | + | 0.990771i | \(0.543280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.26974 | 0.0798276 | ||||||||
\(254\) | 11.6149 | 0.728783 | ||||||||
\(255\) | 24.4493 | 1.53108 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.0451 | −0.813729 | −0.406864 | − | 0.913489i | \(-0.633378\pi\) | ||||
−0.406864 | + | 0.913489i | \(0.633378\pi\) | |||||||
\(258\) | 7.23852 | 0.450651 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −19.0477 | −1.18129 | ||||||||
\(261\) | −7.40162 | −0.458149 | ||||||||
\(262\) | 19.1405 | 1.18251 | ||||||||
\(263\) | 13.4016 | 0.826379 | 0.413190 | − | 0.910645i | \(-0.364415\pi\) | ||||
0.413190 | + | 0.910645i | \(0.364415\pi\) | |||||||
\(264\) | 1.26974 | 0.0781468 | ||||||||
\(265\) | 26.7251 | 1.64171 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.0308 | 0.675073 | ||||||||
\(268\) | −4.37637 | −0.267330 | ||||||||
\(269\) | 9.09236 | 0.554371 | 0.277186 | − | 0.960816i | \(-0.410598\pi\) | ||||
0.277186 | + | 0.960816i | \(0.410598\pi\) | |||||||
\(270\) | −3.47747 | −0.211632 | ||||||||
\(271\) | −15.9241 | −0.967323 | −0.483662 | − | 0.875255i | \(-0.660693\pi\) | ||||
−0.483662 | + | 0.875255i | \(0.660693\pi\) | |||||||
\(272\) | −7.03079 | −0.426304 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.86215 | 0.293733 | ||||||||
\(275\) | −9.00597 | −0.543080 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −18.7527 | −1.12674 | −0.563372 | − | 0.826204i | \(-0.690496\pi\) | ||||
−0.563372 | + | 0.826204i | \(0.690496\pi\) | |||||||
\(278\) | 16.5083 | 0.990099 | ||||||||
\(279\) | 9.57026 | 0.572956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4806 | −1.46039 | −0.730194 | − | 0.683240i | \(-0.760570\pi\) | ||||
−0.730194 | + | 0.683240i | \(0.760570\pi\) | |||||||
\(282\) | 12.0169 | 0.715598 | ||||||||
\(283\) | 6.18558 | 0.367695 | 0.183847 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183847 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(284\) | −10.0616 | −0.597045 | ||||||||
\(285\) | 6.95494 | 0.411975 | ||||||||
\(286\) | 6.95494 | 0.411254 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 32.4320 | 1.90776 | ||||||||
\(290\) | −25.7389 | −1.51144 | ||||||||
\(291\) | 14.5564 | 0.853312 | ||||||||
\(292\) | −13.4944 | −0.789701 | ||||||||
\(293\) | 32.0196 | 1.87061 | 0.935303 | − | 0.353849i | \(-0.115127\pi\) | ||||
0.935303 | + | 0.353849i | \(0.115127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.2922 | −1.58901 | ||||||||
\(296\) | 1.71642 | 0.0997647 | ||||||||
\(297\) | 1.26974 | 0.0736775 | ||||||||
\(298\) | 18.8257 | 1.09054 | ||||||||
\(299\) | 5.47747 | 0.316770 | ||||||||
\(300\) | −7.09279 | −0.409502 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.4632 | 0.889807 | ||||||||
\(303\) | −0.817512 | −0.0469648 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | −34.5109 | −1.97609 | ||||||||
\(306\) | −7.03079 | −0.401923 | ||||||||
\(307\) | 20.1710 | 1.15122 | 0.575609 | − | 0.817725i | \(-0.304765\pi\) | ||||
0.575609 | + | 0.817725i | \(0.304765\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.50826 | −0.256466 | ||||||||
\(310\) | 33.2803 | 1.89019 | ||||||||
\(311\) | −8.10973 | −0.459861 | −0.229930 | − | 0.973207i | \(-0.573850\pi\) | ||||
−0.229930 | + | 0.973207i | \(0.573850\pi\) | |||||||
\(312\) | 5.47747 | 0.310101 | ||||||||
\(313\) | −6.84521 | −0.386914 | −0.193457 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193457 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(314\) | −12.8791 | −0.726809 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4944 | 0.759120 | ||||||||
\(317\) | −0.598381 | −0.0336084 | −0.0168042 | − | 0.999859i | \(-0.505349\pi\) | ||||
−0.0168042 | + | 0.999859i | \(0.505349\pi\) | |||||||
\(318\) | −7.68520 | −0.430965 | ||||||||
\(319\) | 9.39810 | 0.526193 | ||||||||
\(320\) | 3.47747 | 0.194396 | ||||||||
\(321\) | 3.62363 | 0.202251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.0616 | 0.782407 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −38.8505 | −2.15504 | ||||||||
\(326\) | −23.1405 | −1.28163 | ||||||||
\(327\) | −18.3175 | −1.01296 | ||||||||
\(328\) | 8.50826 | 0.469790 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.41547 | 0.243063 | ||||||||
\(331\) | 25.9099 | 1.42414 | 0.712068 | − | 0.702111i | \(-0.247759\pi\) | ||||
0.712068 | + | 0.702111i | \(0.247759\pi\) | |||||||
\(332\) | −5.10664 | −0.280263 | ||||||||
\(333\) | 1.71642 | 0.0940591 | ||||||||
\(334\) | 17.4186 | 0.953101 | ||||||||
\(335\) | −15.2187 | −0.831487 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.21328 | −0.447406 | −0.223703 | − | 0.974657i | \(-0.571815\pi\) | ||||
−0.223703 | + | 0.974657i | \(0.571815\pi\) | |||||||
\(338\) | 17.0027 | 0.924823 | ||||||||
\(339\) | 10.5083 | 0.570730 | ||||||||
\(340\) | −24.4493 | −1.32595 | ||||||||
\(341\) | −12.1517 | −0.658051 | ||||||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.23852 | −0.390275 | ||||||||
\(345\) | 3.47747 | 0.187221 | ||||||||
\(346\) | −2.84521 | −0.152959 | ||||||||
\(347\) | −15.4632 | −0.830108 | −0.415054 | − | 0.909797i | \(-0.636237\pi\) | ||||
−0.415054 | + | 0.909797i | \(0.636237\pi\) | |||||||
\(348\) | 7.40162 | 0.396768 | ||||||||
\(349\) | 11.9241 | 0.638285 | 0.319143 | − | 0.947707i | \(-0.396605\pi\) | ||||
0.319143 | + | 0.947707i | \(0.396605\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.47747 | 0.292366 | ||||||||
\(352\) | −1.26974 | −0.0676771 | ||||||||
\(353\) | −13.9688 | −0.743483 | −0.371742 | − | 0.928336i | \(-0.621239\pi\) | ||||
−0.371742 | + | 0.928336i | \(0.621239\pi\) | |||||||
\(354\) | 7.84830 | 0.417132 | ||||||||
\(355\) | −34.9888 | −1.85701 | ||||||||
\(356\) | −11.0308 | −0.584631 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.13785 | 0.0601374 | ||||||||
\(359\) | 6.56983 | 0.346743 | 0.173371 | − | 0.984857i | \(-0.444534\pi\) | ||||
0.173371 | + | 0.984857i | \(0.444534\pi\) | |||||||
\(360\) | 3.47747 | 0.183279 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −18.9407 | −0.995499 | ||||||||
\(363\) | 9.38777 | 0.492730 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −46.9264 | −2.45624 | ||||||||
\(366\) | 9.92415 | 0.518744 | ||||||||
\(367\) | 13.2499 | 0.691640 | 0.345820 | − | 0.938301i | \(-0.387601\pi\) | ||||
0.345820 | + | 0.938301i | \(0.387601\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 8.50826 | 0.442922 | ||||||||
\(370\) | 5.96879 | 0.310302 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.57026 | −0.496195 | ||||||||
\(373\) | 19.6852 | 1.01926 | 0.509631 | − | 0.860393i | \(-0.329782\pi\) | ||||
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(374\) | 8.92724 | 0.461617 | ||||||||
\(375\) | −7.27761 | −0.375814 | ||||||||
\(376\) | −12.0169 | −0.619726 | ||||||||
\(377\) | 40.5421 | 2.08803 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.77799 | 0.502262 | 0.251131 | − | 0.967953i | \(-0.419198\pi\) | ||||
0.251131 | + | 0.967953i | \(0.419198\pi\) | |||||||
\(380\) | −6.95494 | −0.356781 | ||||||||
\(381\) | −11.6149 | −0.595049 | ||||||||
\(382\) | −0.151700 | −0.00776166 | ||||||||
\(383\) | 2.80324 | 0.143239 | 0.0716194 | − | 0.997432i | \(-0.477183\pi\) | ||||
0.0716194 | + | 0.997432i | \(0.477183\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.9237 | 0.556003 | ||||||||
\(387\) | −7.23852 | −0.367955 | ||||||||
\(388\) | −14.5564 | −0.738990 | ||||||||
\(389\) | 1.06755 | 0.0541267 | 0.0270634 | − | 0.999634i | \(-0.491384\pi\) | ||||
0.0270634 | + | 0.999634i | \(0.491384\pi\) | |||||||
\(390\) | 19.0477 | 0.964519 | ||||||||
\(391\) | 7.03079 | 0.355562 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.1405 | −0.965511 | ||||||||
\(394\) | 13.6149 | 0.685909 | ||||||||
\(395\) | 46.9264 | 2.36112 | ||||||||
\(396\) | −1.26974 | −0.0638066 | ||||||||
\(397\) | 5.00309 | 0.251098 | 0.125549 | − | 0.992087i | \(-0.459931\pi\) | ||||
0.125549 | + | 0.992087i | \(0.459931\pi\) | |||||||
\(398\) | −22.5698 | −1.13132 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.09279 | 0.354640 | ||||||||
\(401\) | −22.7527 | −1.13622 | −0.568109 | − | 0.822953i | \(-0.692325\pi\) | ||||
−0.568109 | + | 0.822953i | \(0.692325\pi\) | |||||||
\(402\) | 4.37637 | 0.218274 | ||||||||
\(403\) | −52.4208 | −2.61127 | ||||||||
\(404\) | 0.817512 | 0.0406727 | ||||||||
\(405\) | 3.47747 | 0.172797 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.17940 | −0.108029 | ||||||||
\(408\) | 7.03079 | 0.348076 | ||||||||
\(409\) | −8.18558 | −0.404751 | −0.202375 | − | 0.979308i | \(-0.564866\pi\) | ||||
−0.202375 | + | 0.979308i | \(0.564866\pi\) | |||||||
\(410\) | 29.5872 | 1.46121 | ||||||||
\(411\) | −4.86215 | −0.239832 | ||||||||
\(412\) | 4.50826 | 0.222106 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −17.7582 | −0.871715 | ||||||||
\(416\) | −5.47747 | −0.268555 | ||||||||
\(417\) | −16.5083 | −0.808413 | ||||||||
\(418\) | 2.53947 | 0.124210 | ||||||||
\(419\) | −2.18558 | −0.106773 | −0.0533863 | − | 0.998574i | \(-0.517001\pi\) | ||||
−0.0533863 | + | 0.998574i | \(0.517001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.97475 | −0.242455 | −0.121227 | − | 0.992625i | \(-0.538683\pi\) | ||||
−0.121227 | + | 0.992625i | \(0.538683\pi\) | |||||||
\(422\) | 9.49441 | 0.462181 | ||||||||
\(423\) | −12.0169 | −0.584284 | ||||||||
\(424\) | 7.68520 | 0.373226 | ||||||||
\(425\) | −49.8679 | −2.41895 | ||||||||
\(426\) | 10.0616 | 0.487485 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.62363 | −0.175155 | ||||||||
\(429\) | −6.95494 | −0.335788 | ||||||||
\(430\) | −25.1717 | −1.21389 | ||||||||
\(431\) | −16.1267 | −0.776794 | −0.388397 | − | 0.921492i | \(-0.626971\pi\) | ||||
−0.388397 | + | 0.921492i | \(0.626971\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.5729 | −0.748387 | −0.374194 | − | 0.927351i | \(-0.622080\pi\) | ||||
−0.374194 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.7389 | 1.23409 | ||||||||
\(436\) | 18.3175 | 0.877247 | ||||||||
\(437\) | 2.00000 | 0.0956730 | ||||||||
\(438\) | 13.4944 | 0.644788 | ||||||||
\(439\) | 11.0308 | 0.526471 | 0.263235 | − | 0.964732i | \(-0.415210\pi\) | ||||
0.263235 | + | 0.964732i | \(0.415210\pi\) | |||||||
\(440\) | −4.41547 | −0.210499 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 38.5109 | 1.83178 | ||||||||
\(443\) | −12.6600 | −0.601493 | −0.300746 | − | 0.953704i | \(-0.597236\pi\) | ||||
−0.300746 | + | 0.953704i | \(0.597236\pi\) | |||||||
\(444\) | −1.71642 | −0.0814575 | ||||||||
\(445\) | −38.3592 | −1.81840 | ||||||||
\(446\) | −15.2946 | −0.724218 | ||||||||
\(447\) | −18.8257 | −0.890426 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.07894 | 0.145304 | 0.0726521 | − | 0.997357i | \(-0.476854\pi\) | ||||
0.0726521 | + | 0.997357i | \(0.476854\pi\) | |||||||
\(450\) | 7.09279 | 0.334357 | ||||||||
\(451\) | −10.8032 | −0.508705 | ||||||||
\(452\) | −10.5083 | −0.494267 | ||||||||
\(453\) | −15.4632 | −0.726524 | ||||||||
\(454\) | −1.42931 | −0.0670810 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | −15.4659 | −0.723462 | −0.361731 | − | 0.932282i | \(-0.617814\pi\) | ||||
−0.361731 | + | 0.932282i | \(0.617814\pi\) | |||||||
\(458\) | −17.9241 | −0.837541 | ||||||||
\(459\) | 7.03079 | 0.328169 | ||||||||
\(460\) | −3.47747 | −0.162138 | ||||||||
\(461\) | −14.0196 | −0.652958 | −0.326479 | − | 0.945204i | \(-0.605862\pi\) | ||||
−0.326479 | + | 0.945204i | \(0.605862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.72153 | 0.312376 | 0.156188 | − | 0.987727i | \(-0.450079\pi\) | ||||
0.156188 | + | 0.987727i | \(0.450079\pi\) | |||||||
\(464\) | −7.40162 | −0.343612 | ||||||||
\(465\) | −33.2803 | −1.54334 | ||||||||
\(466\) | −18.4155 | −0.853080 | ||||||||
\(467\) | 27.7104 | 1.28228 | 0.641141 | − | 0.767423i | \(-0.278461\pi\) | ||||
0.641141 | + | 0.767423i | \(0.278461\pi\) | |||||||
\(468\) | −5.47747 | −0.253196 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −41.7885 | −1.92756 | ||||||||
\(471\) | 12.8791 | 0.593437 | ||||||||
\(472\) | −7.84830 | −0.361247 | ||||||||
\(473\) | 9.19101 | 0.422603 | ||||||||
\(474\) | −13.4944 | −0.619819 | ||||||||
\(475\) | −14.1856 | −0.650879 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.68520 | 0.351881 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | −16.0339 | −0.732607 | −0.366303 | − | 0.930495i | \(-0.619377\pi\) | ||||
−0.366303 | + | 0.930495i | \(0.619377\pi\) | |||||||
\(480\) | −3.47747 | −0.158724 | ||||||||
\(481\) | −9.40162 | −0.428677 | ||||||||
\(482\) | 4.39853 | 0.200347 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.38777 | −0.426717 | ||||||||
\(485\) | −50.6195 | −2.29851 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 24.8794 | 1.12739 | 0.563697 | − | 0.825982i | \(-0.309379\pi\) | ||||
0.563697 | + | 0.825982i | \(0.309379\pi\) | |||||||
\(488\) | −9.92415 | −0.449245 | ||||||||
\(489\) | 23.1405 | 1.04645 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.9603 | 1.57773 | 0.788867 | − | 0.614563i | \(-0.210668\pi\) | ||||
0.788867 | + | 0.614563i | \(0.210668\pi\) | |||||||
\(492\) | −8.50826 | −0.383582 | ||||||||
\(493\) | 52.0392 | 2.34373 | ||||||||
\(494\) | 10.9549 | 0.492886 | ||||||||
\(495\) | −4.41547 | −0.198460 | ||||||||
\(496\) | 9.57026 | 0.429717 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.10664 | 0.228834 | ||||||||
\(499\) | 8.74166 | 0.391331 | 0.195665 | − | 0.980671i | \(-0.437313\pi\) | ||||
0.195665 | + | 0.980671i | \(0.437313\pi\) | |||||||
\(500\) | 7.27761 | 0.325465 | ||||||||
\(501\) | −17.4186 | −0.778204 | ||||||||
\(502\) | −4.29498 | −0.191694 | ||||||||
\(503\) | 6.76936 | 0.301831 | 0.150915 | − | 0.988547i | \(-0.451778\pi\) | ||||
0.150915 | + | 0.988547i | \(0.451778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.84287 | 0.126506 | ||||||||
\(506\) | 1.26974 | 0.0564466 | ||||||||
\(507\) | −17.0027 | −0.755115 | ||||||||
\(508\) | 11.6149 | 0.515328 | ||||||||
\(509\) | 0.906783 | 0.0401925 | 0.0200962 | − | 0.999798i | \(-0.493603\pi\) | ||||
0.0200962 | + | 0.999798i | \(0.493603\pi\) | |||||||
\(510\) | 24.4493 | 1.08264 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | −13.0451 | −0.575393 | ||||||||
\(515\) | 15.6773 | 0.690825 | ||||||||
\(516\) | 7.23852 | 0.318658 | ||||||||
\(517\) | 15.2583 | 0.671061 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.84521 | 0.124891 | ||||||||
\(520\) | −19.0477 | −0.835298 | ||||||||
\(521\) | 29.4296 | 1.28934 | 0.644668 | − | 0.764463i | \(-0.276996\pi\) | ||||
0.644668 | + | 0.764463i | \(0.276996\pi\) | |||||||
\(522\) | −7.40162 | −0.323960 | ||||||||
\(523\) | 27.0789 | 1.18408 | 0.592040 | − | 0.805909i | \(-0.298323\pi\) | ||||
0.592040 | + | 0.805909i | \(0.298323\pi\) | |||||||
\(524\) | 19.1405 | 0.836157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.4016 | 0.584338 | ||||||||
\(527\) | −67.2865 | −2.93104 | ||||||||
\(528\) | 1.26974 | 0.0552582 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 26.7251 | 1.16086 | ||||||||
\(531\) | −7.84830 | −0.340587 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.6037 | −2.01863 | ||||||||
\(534\) | 11.0308 | 0.477349 | ||||||||
\(535\) | −12.6010 | −0.544791 | ||||||||
\(536\) | −4.37637 | −0.189031 | ||||||||
\(537\) | −1.13785 | −0.0491020 | ||||||||
\(538\) | 9.09236 | 0.392000 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.47747 | −0.149646 | ||||||||
\(541\) | 10.4440 | 0.449023 | 0.224512 | − | 0.974471i | \(-0.427921\pi\) | ||||
0.224512 | + | 0.974471i | \(0.427921\pi\) | |||||||
\(542\) | −15.9241 | −0.684001 | ||||||||
\(543\) | 18.9407 | 0.812822 | ||||||||
\(544\) | −7.03079 | −0.301443 | ||||||||
\(545\) | 63.6984 | 2.72854 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.72429 | 0.415781 | 0.207890 | − | 0.978152i | \(-0.433340\pi\) | ||||
0.207890 | + | 0.978152i | \(0.433340\pi\) | |||||||
\(548\) | 4.86215 | 0.207701 | ||||||||
\(549\) | −9.92415 | −0.423552 | ||||||||
\(550\) | −9.00597 | −0.384016 | ||||||||
\(551\) | 14.8032 | 0.630639 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.7527 | −0.796728 | ||||||||
\(555\) | −5.96879 | −0.253361 | ||||||||
\(556\) | 16.5083 | 0.700106 | ||||||||
\(557\) | −5.80921 | −0.246144 | −0.123072 | − | 0.992398i | \(-0.539275\pi\) | ||||
−0.123072 | + | 0.992398i | \(0.539275\pi\) | |||||||
\(558\) | 9.57026 | 0.405141 | ||||||||
\(559\) | 39.6488 | 1.67696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.92724 | −0.376908 | ||||||||
\(562\) | −24.4806 | −1.03265 | ||||||||
\(563\) | −9.55247 | −0.402588 | −0.201294 | − | 0.979531i | \(-0.564515\pi\) | ||||
−0.201294 | + | 0.979531i | \(0.564515\pi\) | |||||||
\(564\) | 12.0169 | 0.506004 | ||||||||
\(565\) | −36.5421 | −1.53734 | ||||||||
\(566\) | 6.18558 | 0.259999 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.0616 | −0.422174 | ||||||||
\(569\) | −43.5476 | −1.82561 | −0.912804 | − | 0.408397i | \(-0.866088\pi\) | ||||
−0.912804 | + | 0.408397i | \(0.866088\pi\) | |||||||
\(570\) | 6.95494 | 0.291310 | ||||||||
\(571\) | 17.5335 | 0.733754 | 0.366877 | − | 0.930269i | \(-0.380427\pi\) | ||||
0.366877 | + | 0.930269i | \(0.380427\pi\) | |||||||
\(572\) | 6.95494 | 0.290801 | ||||||||
\(573\) | 0.151700 | 0.00633737 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.09279 | −0.295790 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.4944 | 0.561780 | 0.280890 | − | 0.959740i | \(-0.409370\pi\) | ||||
0.280890 | + | 0.959740i | \(0.409370\pi\) | |||||||
\(578\) | 32.4320 | 1.34899 | ||||||||
\(579\) | −10.9237 | −0.453974 | ||||||||
\(580\) | −25.7389 | −1.06875 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.5564 | 0.603383 | ||||||||
\(583\) | −9.75818 | −0.404142 | ||||||||
\(584\) | −13.4944 | −0.558403 | ||||||||
\(585\) | −19.0477 | −0.787527 | ||||||||
\(586\) | 32.0196 | 1.32272 | ||||||||
\(587\) | −30.9264 | −1.27647 | −0.638234 | − | 0.769842i | \(-0.720335\pi\) | ||||
−0.638234 | + | 0.769842i | \(0.720335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.1405 | −0.788671 | ||||||||
\(590\) | −27.2922 | −1.12360 | ||||||||
\(591\) | −13.6149 | −0.560042 | ||||||||
\(592\) | 1.71642 | 0.0705443 | ||||||||
\(593\) | −33.6765 | −1.38293 | −0.691463 | − | 0.722411i | \(-0.743034\pi\) | ||||
−0.691463 | + | 0.722411i | \(0.743034\pi\) | |||||||
\(594\) | 1.26974 | 0.0520979 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.8257 | 0.771132 | ||||||||
\(597\) | 22.5698 | 0.923722 | ||||||||
\(598\) | 5.47747 | 0.223990 | ||||||||
\(599\) | 25.0165 | 1.02215 | 0.511074 | − | 0.859537i | \(-0.329248\pi\) | ||||
0.511074 | + | 0.859537i | \(0.329248\pi\) | |||||||
\(600\) | −7.09279 | −0.289562 | ||||||||
\(601\) | −9.73538 | −0.397114 | −0.198557 | − | 0.980089i | \(-0.563626\pi\) | ||||
−0.198557 | + | 0.980089i | \(0.563626\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.37637 | −0.178220 | ||||||||
\(604\) | 15.4632 | 0.629188 | ||||||||
\(605\) | −32.6457 | −1.32724 | ||||||||
\(606\) | −0.817512 | −0.0332091 | ||||||||
\(607\) | −3.69426 | −0.149946 | −0.0749728 | − | 0.997186i | \(-0.523887\pi\) | ||||
−0.0749728 | + | 0.997186i | \(0.523887\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −34.5109 | −1.39731 | ||||||||
\(611\) | 65.8224 | 2.66289 | ||||||||
\(612\) | −7.03079 | −0.284203 | ||||||||
\(613\) | −7.65484 | −0.309176 | −0.154588 | − | 0.987979i | \(-0.549405\pi\) | ||||
−0.154588 | + | 0.987979i | \(0.549405\pi\) | |||||||
\(614\) | 20.1710 | 0.814034 | ||||||||
\(615\) | −29.5872 | −1.19307 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.37116 | 0.0954594 | 0.0477297 | − | 0.998860i | \(-0.484801\pi\) | ||||
0.0477297 | + | 0.998860i | \(0.484801\pi\) | |||||||
\(618\) | −4.50826 | −0.181349 | ||||||||
\(619\) | 27.8474 | 1.11928 | 0.559642 | − | 0.828735i | \(-0.310939\pi\) | ||||
0.559642 | + | 0.828735i | \(0.310939\pi\) | |||||||
\(620\) | 33.2803 | 1.33657 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −8.10973 | −0.325171 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.47747 | 0.219274 | ||||||||
\(625\) | −10.1563 | −0.406251 | ||||||||
\(626\) | −6.84521 | −0.273589 | ||||||||
\(627\) | −2.53947 | −0.101417 | ||||||||
\(628\) | −12.8791 | −0.513932 | ||||||||
\(629\) | −12.0678 | −0.481173 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.8648 | −0.989853 | −0.494926 | − | 0.868935i | \(-0.664805\pi\) | ||||
−0.494926 | + | 0.868935i | \(0.664805\pi\) | |||||||
\(632\) | 13.4944 | 0.536779 | ||||||||
\(633\) | −9.49441 | −0.377369 | ||||||||
\(634\) | −0.598381 | −0.0237648 | ||||||||
\(635\) | 40.3904 | 1.60285 | ||||||||
\(636\) | −7.68520 | −0.304738 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.39810 | 0.372074 | ||||||||
\(639\) | −10.0616 | −0.398030 | ||||||||
\(640\) | 3.47747 | 0.137459 | ||||||||
\(641\) | 26.1267 | 1.03194 | 0.515971 | − | 0.856606i | \(-0.327431\pi\) | ||||
0.515971 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(642\) | 3.62363 | 0.143013 | ||||||||
\(643\) | 18.8309 | 0.742620 | 0.371310 | − | 0.928509i | \(-0.378909\pi\) | ||||
0.371310 | + | 0.928509i | \(0.378909\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.1717 | 0.991136 | ||||||||
\(646\) | 14.0616 | 0.553245 | ||||||||
\(647\) | 47.1539 | 1.85381 | 0.926906 | − | 0.375293i | \(-0.122458\pi\) | ||||
0.926906 | + | 0.375293i | \(0.122458\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 9.96527 | 0.391171 | ||||||||
\(650\) | −38.8505 | −1.52384 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.1405 | −0.906253 | ||||||||
\(653\) | 15.2610 | 0.597209 | 0.298605 | − | 0.954377i | \(-0.403479\pi\) | ||||
0.298605 | + | 0.954377i | \(0.403479\pi\) | |||||||
\(654\) | −18.3175 | −0.716270 | ||||||||
\(655\) | 66.5606 | 2.60074 | ||||||||
\(656\) | 8.50826 | 0.332192 | ||||||||
\(657\) | −13.4944 | −0.526467 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.9663 | −0.972550 | −0.486275 | − | 0.873806i | \(-0.661645\pi\) | ||||
−0.486275 | + | 0.873806i | \(0.661645\pi\) | |||||||
\(660\) | 4.41547 | 0.171872 | ||||||||
\(661\) | 7.09236 | 0.275861 | 0.137930 | − | 0.990442i | \(-0.455955\pi\) | ||||
0.137930 | + | 0.990442i | \(0.455955\pi\) | |||||||
\(662\) | 25.9099 | 1.00702 | ||||||||
\(663\) | −38.5109 | −1.49564 | ||||||||
\(664\) | −5.10664 | −0.198176 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.71642 | 0.0665098 | ||||||||
\(667\) | 7.40162 | 0.286592 | ||||||||
\(668\) | 17.4186 | 0.673944 | ||||||||
\(669\) | 15.2946 | 0.591322 | ||||||||
\(670\) | −15.2187 | −0.587950 | ||||||||
\(671\) | 12.6010 | 0.486458 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.0358 | −1.50472 | −0.752360 | − | 0.658753i | \(-0.771084\pi\) | ||||
−0.752360 | + | 0.658753i | \(0.771084\pi\) | |||||||
\(674\) | −8.21328 | −0.316364 | ||||||||
\(675\) | −7.09279 | −0.273002 | ||||||||
\(676\) | 17.0027 | 0.653949 | ||||||||
\(677\) | 13.9580 | 0.536451 | 0.268225 | − | 0.963356i | \(-0.413563\pi\) | ||||
0.268225 | + | 0.963356i | \(0.413563\pi\) | |||||||
\(678\) | 10.5083 | 0.403567 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −24.4493 | −0.937590 | ||||||||
\(681\) | 1.42931 | 0.0547714 | ||||||||
\(682\) | −12.1517 | −0.465313 | ||||||||
\(683\) | −27.4667 | −1.05098 | −0.525492 | − | 0.850798i | \(-0.676119\pi\) | ||||
−0.525492 | + | 0.850798i | \(0.676119\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 16.9080 | 0.646020 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.9241 | 0.683849 | ||||||||
\(688\) | −7.23852 | −0.275966 | ||||||||
\(689\) | −42.0955 | −1.60371 | ||||||||
\(690\) | 3.47747 | 0.132385 | ||||||||
\(691\) | 5.03046 | 0.191368 | 0.0956838 | − | 0.995412i | \(-0.469496\pi\) | ||||
0.0956838 | + | 0.995412i | \(0.469496\pi\) | |||||||
\(692\) | −2.84521 | −0.108159 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.4632 | −0.586975 | ||||||||
\(695\) | 57.4070 | 2.17757 | ||||||||
\(696\) | 7.40162 | 0.280558 | ||||||||
\(697\) | −59.8198 | −2.26583 | ||||||||
\(698\) | 11.9241 | 0.451336 | ||||||||
\(699\) | 18.4155 | 0.696537 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.56120 | 0.361121 | 0.180561 | − | 0.983564i | \(-0.442209\pi\) | ||||
0.180561 | + | 0.983564i | \(0.442209\pi\) | |||||||
\(702\) | 5.47747 | 0.206734 | ||||||||
\(703\) | −3.43283 | −0.129472 | ||||||||
\(704\) | −1.26974 | −0.0478550 | ||||||||
\(705\) | 41.7885 | 1.57385 | ||||||||
\(706\) | −13.9688 | −0.525722 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.84830 | 0.294957 | ||||||||
\(709\) | −31.5050 | −1.18319 | −0.591597 | − | 0.806234i | \(-0.701502\pi\) | ||||
−0.591597 | + | 0.806234i | \(0.701502\pi\) | |||||||
\(710\) | −34.9888 | −1.31311 | ||||||||
\(711\) | 13.4944 | 0.506080 | ||||||||
\(712\) | −11.0308 | −0.413396 | ||||||||
\(713\) | −9.57026 | −0.358409 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.1856 | 0.904489 | ||||||||
\(716\) | 1.13785 | 0.0425235 | ||||||||
\(717\) | 8.00000 | 0.298765 | ||||||||
\(718\) | 6.56983 | 0.245184 | ||||||||
\(719\) | −3.38734 | −0.126327 | −0.0631633 | − | 0.998003i | \(-0.520119\pi\) | ||||
−0.0631633 | + | 0.998003i | \(0.520119\pi\) | |||||||
\(720\) | 3.47747 | 0.129598 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | −4.39853 | −0.163583 | ||||||||
\(724\) | −18.9407 | −0.703924 | ||||||||
\(725\) | −52.4981 | −1.94973 | ||||||||
\(726\) | 9.38777 | 0.348413 | ||||||||
\(727\) | 25.0504 | 0.929068 | 0.464534 | − | 0.885555i | \(-0.346222\pi\) | ||||
0.464534 | + | 0.885555i | \(0.346222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −46.9264 | −1.73682 | ||||||||
\(731\) | 50.8925 | 1.88233 | ||||||||
\(732\) | 9.92415 | 0.366807 | ||||||||
\(733\) | 15.3404 | 0.566610 | 0.283305 | − | 0.959030i | \(-0.408569\pi\) | ||||
0.283305 | + | 0.959030i | \(0.408569\pi\) | |||||||
\(734\) | 13.2499 | 0.489063 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 5.55684 | 0.204689 | ||||||||
\(738\) | 8.50826 | 0.313193 | ||||||||
\(739\) | −10.0616 | −0.370121 | −0.185061 | − | 0.982727i | \(-0.559248\pi\) | ||||
−0.185061 | + | 0.982727i | \(0.559248\pi\) | |||||||
\(740\) | 5.96879 | 0.219417 | ||||||||
\(741\) | −10.9549 | −0.402440 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5109 | 0.825846 | 0.412923 | − | 0.910766i | \(-0.364508\pi\) | ||||
0.412923 | + | 0.910766i | \(0.364508\pi\) | |||||||
\(744\) | −9.57026 | −0.350863 | ||||||||
\(745\) | 65.4659 | 2.39848 | ||||||||
\(746\) | 19.6852 | 0.720726 | ||||||||
\(747\) | −5.10664 | −0.186842 | ||||||||
\(748\) | 8.92724 | 0.326412 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.27761 | −0.265741 | ||||||||
\(751\) | 30.4770 | 1.11212 | 0.556062 | − | 0.831141i | \(-0.312312\pi\) | ||||
0.556062 | + | 0.831141i | \(0.312312\pi\) | |||||||
\(752\) | −12.0169 | −0.438213 | ||||||||
\(753\) | 4.29498 | 0.156518 | ||||||||
\(754\) | 40.5421 | 1.47646 | ||||||||
\(755\) | 53.7728 | 1.95699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.3652 | −0.921914 | −0.460957 | − | 0.887423i | \(-0.652494\pi\) | ||||
−0.460957 | + | 0.887423i | \(0.652494\pi\) | |||||||
\(758\) | 9.77799 | 0.355153 | ||||||||
\(759\) | −1.26974 | −0.0460885 | ||||||||
\(760\) | −6.95494 | −0.252282 | ||||||||
\(761\) | 43.4043 | 1.57340 | 0.786702 | − | 0.617333i | \(-0.211787\pi\) | ||||
0.786702 | + | 0.617333i | \(0.211787\pi\) | |||||||
\(762\) | −11.6149 | −0.420763 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.151700 | −0.00548832 | ||||||||
\(765\) | −24.4493 | −0.883968 | ||||||||
\(766\) | 2.80324 | 0.101285 | ||||||||
\(767\) | 42.9888 | 1.55224 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −9.32577 | −0.336296 | −0.168148 | − | 0.985762i | \(-0.553779\pi\) | ||||
−0.168148 | + | 0.985762i | \(0.553779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.0451 | 0.469806 | ||||||||
\(772\) | 10.9237 | 0.393153 | ||||||||
\(773\) | −12.6742 | −0.455860 | −0.227930 | − | 0.973677i | \(-0.573196\pi\) | ||||
−0.227930 | + | 0.973677i | \(0.573196\pi\) | |||||||
\(774\) | −7.23852 | −0.260183 | ||||||||
\(775\) | 67.8798 | 2.43832 | ||||||||
\(776\) | −14.5564 | −0.522545 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.06755 | 0.0382734 | ||||||||
\(779\) | −17.0165 | −0.609680 | ||||||||
\(780\) | 19.0477 | 0.682018 | ||||||||
\(781\) | 12.7755 | 0.457145 | ||||||||
\(782\) | 7.03079 | 0.251420 | ||||||||
\(783\) | 7.40162 | 0.264512 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.7866 | −1.59850 | ||||||||
\(786\) | −19.1405 | −0.682720 | ||||||||
\(787\) | 16.7408 | 0.596745 | 0.298373 | − | 0.954449i | \(-0.403556\pi\) | ||||
0.298373 | + | 0.954449i | \(0.403556\pi\) | |||||||
\(788\) | 13.6149 | 0.485011 | ||||||||
\(789\) | −13.4016 | −0.477110 | ||||||||
\(790\) | 46.9264 | 1.66957 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.26974 | −0.0451181 | ||||||||
\(793\) | 54.3592 | 1.93035 | ||||||||
\(794\) | 5.00309 | 0.177553 | ||||||||
\(795\) | −26.7251 | −0.947840 | ||||||||
\(796\) | −22.5698 | −0.799967 | ||||||||
\(797\) | 29.6622 | 1.05069 | 0.525344 | − | 0.850890i | \(-0.323936\pi\) | ||||
0.525344 | + | 0.850890i | \(0.323936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 84.4886 | 2.98899 | ||||||||
\(800\) | 7.09279 | 0.250768 | ||||||||
\(801\) | −11.0308 | −0.389754 | ||||||||
\(802\) | −22.7527 | −0.803427 | ||||||||
\(803\) | 17.1343 | 0.604657 | ||||||||
\(804\) | 4.37637 | 0.154343 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −52.4208 | −1.84644 | ||||||||
\(807\) | −9.09236 | −0.320066 | ||||||||
\(808\) | 0.817512 | 0.0287600 | ||||||||
\(809\) | 13.2187 | 0.464745 | 0.232372 | − | 0.972627i | \(-0.425351\pi\) | ||||
0.232372 | + | 0.972627i | \(0.425351\pi\) | |||||||
\(810\) | 3.47747 | 0.122186 | ||||||||
\(811\) | −22.7554 | −0.799051 | −0.399525 | − | 0.916722i | \(-0.630825\pi\) | ||||
−0.399525 | + | 0.916722i | \(0.630825\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.9241 | 0.558484 | ||||||||
\(814\) | −2.17940 | −0.0763878 | ||||||||
\(815\) | −80.4704 | −2.81876 | ||||||||
\(816\) | 7.03079 | 0.246127 | ||||||||
\(817\) | 14.4770 | 0.506488 | ||||||||
\(818\) | −8.18558 | −0.286202 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29.5872 | 1.03323 | ||||||||
\(821\) | −21.6184 | −0.754488 | −0.377244 | − | 0.926114i | \(-0.623128\pi\) | ||||
−0.377244 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(822\) | −4.86215 | −0.169587 | ||||||||
\(823\) | −19.4008 | −0.676268 | −0.338134 | − | 0.941098i | \(-0.609796\pi\) | ||||
−0.338134 | + | 0.941098i | \(0.609796\pi\) | |||||||
\(824\) | 4.50826 | 0.157053 | ||||||||
\(825\) | 9.00597 | 0.313548 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.5388 | −1.30535 | −0.652677 | − | 0.757637i | \(-0.726354\pi\) | ||||
−0.652677 | + | 0.757637i | \(0.726354\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 33.6823 | 1.16984 | 0.584918 | − | 0.811093i | \(-0.301127\pi\) | ||||
0.584918 | + | 0.811093i | \(0.301127\pi\) | |||||||
\(830\) | −17.7582 | −0.616395 | ||||||||
\(831\) | 18.7527 | 0.650526 | ||||||||
\(832\) | −5.47747 | −0.189897 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.5083 | −0.571634 | ||||||||
\(835\) | 60.5725 | 2.09620 | ||||||||
\(836\) | 2.53947 | 0.0878295 | ||||||||
\(837\) | −9.57026 | −0.330797 | ||||||||
\(838\) | −2.18558 | −0.0754996 | ||||||||
\(839\) | −34.0330 | −1.17495 | −0.587475 | − | 0.809242i | \(-0.699878\pi\) | ||||
−0.587475 | + | 0.809242i | \(0.699878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.7840 | 0.889102 | ||||||||
\(842\) | −4.97475 | −0.171441 | ||||||||
\(843\) | 24.4806 | 0.843155 | ||||||||
\(844\) | 9.49441 | 0.326811 | ||||||||
\(845\) | 59.1262 | 2.03400 | ||||||||
\(846\) | −12.0169 | −0.413151 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.68520 | 0.263911 | ||||||||
\(849\) | −6.18558 | −0.212289 | ||||||||
\(850\) | −49.8679 | −1.71046 | ||||||||
\(851\) | −1.71642 | −0.0588380 | ||||||||
\(852\) | 10.0616 | 0.344704 | ||||||||
\(853\) | −29.6630 | −1.01564 | −0.507822 | − | 0.861462i | \(-0.669549\pi\) | ||||
−0.507822 | + | 0.861462i | \(0.669549\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.95494 | −0.237854 | ||||||||
\(856\) | −3.62363 | −0.123853 | ||||||||
\(857\) | −37.0200 | −1.26458 | −0.632290 | − | 0.774732i | \(-0.717885\pi\) | ||||
−0.632290 | + | 0.774732i | \(0.717885\pi\) | |||||||
\(858\) | −6.95494 | −0.237438 | ||||||||
\(859\) | −1.24992 | −0.0426467 | −0.0213233 | − | 0.999773i | \(-0.506788\pi\) | ||||
−0.0213233 | + | 0.999773i | \(0.506788\pi\) | |||||||
\(860\) | −25.1717 | −0.858349 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.1267 | −0.549277 | ||||||||
\(863\) | −56.5953 | −1.92653 | −0.963263 | − | 0.268559i | \(-0.913452\pi\) | ||||
−0.963263 | + | 0.268559i | \(0.913452\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −9.89412 | −0.336410 | ||||||||
\(866\) | −15.5729 | −0.529190 | ||||||||
\(867\) | −32.4320 | −1.10145 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.1343 | −0.581242 | ||||||||
\(870\) | 25.7389 | 0.872630 | ||||||||
\(871\) | 23.9715 | 0.812242 | ||||||||
\(872\) | 18.3175 | 0.620308 | ||||||||
\(873\) | −14.5564 | −0.492660 | ||||||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.4944 | 0.455934 | ||||||||
\(877\) | −35.7139 | −1.20597 | −0.602986 | − | 0.797752i | \(-0.706022\pi\) | ||||
−0.602986 | + | 0.797752i | \(0.706022\pi\) | |||||||
\(878\) | 11.0308 | 0.372271 | ||||||||
\(879\) | −32.0196 | −1.07999 | ||||||||
\(880\) | −4.41547 | −0.148845 | ||||||||
\(881\) | 37.5306 | 1.26444 | 0.632219 | − | 0.774789i | \(-0.282144\pi\) | ||||
0.632219 | + | 0.774789i | \(0.282144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7242 | −1.10126 | −0.550629 | − | 0.834750i | \(-0.685612\pi\) | ||||
−0.550629 | + | 0.834750i | \(0.685612\pi\) | |||||||
\(884\) | 38.5109 | 1.29526 | ||||||||
\(885\) | 27.2922 | 0.917418 | ||||||||
\(886\) | −12.6600 | −0.425320 | ||||||||
\(887\) | −4.18792 | −0.140616 | −0.0703082 | − | 0.997525i | \(-0.522398\pi\) | ||||
−0.0703082 | + | 0.997525i | \(0.522398\pi\) | |||||||
\(888\) | −1.71642 | −0.0575992 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −38.3592 | −1.28580 | ||||||||
\(891\) | −1.26974 | −0.0425377 | ||||||||
\(892\) | −15.2946 | −0.512100 | ||||||||
\(893\) | 24.0339 | 0.804263 | ||||||||
\(894\) | −18.8257 | −0.629626 | ||||||||
\(895\) | 3.95685 | 0.132263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.47747 | −0.182887 | ||||||||
\(898\) | 3.07894 | 0.102746 | ||||||||
\(899\) | −70.8354 | −2.36249 | ||||||||
\(900\) | 7.09279 | 0.236426 | ||||||||
\(901\) | −54.0330 | −1.80010 | ||||||||
\(902\) | −10.8032 | −0.359708 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.5083 | −0.349499 | ||||||||
\(905\) | −65.8656 | −2.18945 | ||||||||
\(906\) | −15.4632 | −0.513730 | ||||||||
\(907\) | 39.6097 | 1.31522 | 0.657609 | − | 0.753359i | \(-0.271568\pi\) | ||||
0.657609 | + | 0.753359i | \(0.271568\pi\) | |||||||
\(908\) | −1.42931 | −0.0474335 | ||||||||
\(909\) | 0.817512 | 0.0271152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.3843 | −0.741623 | −0.370812 | − | 0.928708i | \(-0.620920\pi\) | ||||
−0.370812 | + | 0.928708i | \(0.620920\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | 6.48408 | 0.214592 | ||||||||
\(914\) | −15.4659 | −0.511565 | ||||||||
\(915\) | 34.5109 | 1.14090 | ||||||||
\(916\) | −17.9241 | −0.592231 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.03079 | 0.232051 | ||||||||
\(919\) | −32.6010 | −1.07541 | −0.537705 | − | 0.843133i | \(-0.680708\pi\) | ||||
−0.537705 | + | 0.843133i | \(0.680708\pi\) | |||||||
\(920\) | −3.47747 | −0.114649 | ||||||||
\(921\) | −20.1710 | −0.664656 | ||||||||
\(922\) | −14.0196 | −0.461711 | ||||||||
\(923\) | 55.1120 | 1.81403 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.1742 | 0.400285 | ||||||||
\(926\) | 6.72153 | 0.220883 | ||||||||
\(927\) | 4.50826 | 0.148071 | ||||||||
\(928\) | −7.40162 | −0.242970 | ||||||||
\(929\) | −58.4235 | −1.91681 | −0.958406 | − | 0.285409i | \(-0.907871\pi\) | ||||
−0.958406 | + | 0.285409i | \(0.907871\pi\) | |||||||
\(930\) | −33.2803 | −1.09130 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18.4155 | −0.603219 | ||||||||
\(933\) | 8.10973 | 0.265501 | ||||||||
\(934\) | 27.7104 | 0.906710 | ||||||||
\(935\) | 31.0442 | 1.01525 | ||||||||
\(936\) | −5.47747 | −0.179037 | ||||||||
\(937\) | −20.3431 | −0.664581 | −0.332291 | − | 0.943177i | \(-0.607821\pi\) | ||||
−0.332291 | + | 0.943177i | \(0.607821\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.84521 | 0.223385 | ||||||||
\(940\) | −41.7885 | −1.36299 | ||||||||
\(941\) | 39.4221 | 1.28512 | 0.642562 | − | 0.766234i | \(-0.277872\pi\) | ||||
0.642562 | + | 0.766234i | \(0.277872\pi\) | |||||||
\(942\) | 12.8791 | 0.419623 | ||||||||
\(943\) | −8.50826 | −0.277067 | ||||||||
\(944\) | −7.84830 | −0.255440 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.19101 | 0.298825 | ||||||||
\(947\) | −45.5587 | −1.48046 | −0.740229 | − | 0.672355i | \(-0.765283\pi\) | ||||
−0.740229 | + | 0.672355i | \(0.765283\pi\) | |||||||
\(948\) | −13.4944 | −0.438278 | ||||||||
\(949\) | 73.9152 | 2.39939 | ||||||||
\(950\) | −14.1856 | −0.460241 | ||||||||
\(951\) | 0.598381 | 0.0194038 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0782 | 0.456037 | 0.228019 | − | 0.973657i | \(-0.426775\pi\) | ||||
0.228019 | + | 0.973657i | \(0.426775\pi\) | |||||||
\(954\) | 7.68520 | 0.248818 | ||||||||
\(955\) | −0.527533 | −0.0170706 | ||||||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | −9.39810 | −0.303797 | ||||||||
\(958\) | −16.0339 | −0.518031 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.47747 | −0.112235 | ||||||||
\(961\) | 60.5899 | 1.95451 | ||||||||
\(962\) | −9.40162 | −0.303120 | ||||||||
\(963\) | −3.62363 | −0.116770 | ||||||||
\(964\) | 4.39853 | 0.141667 | ||||||||
\(965\) | 37.9869 | 1.22284 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.5102 | 1.46351 | 0.731754 | − | 0.681569i | \(-0.238702\pi\) | ||||
0.731754 | + | 0.681569i | \(0.238702\pi\) | |||||||
\(968\) | −9.38777 | −0.301734 | ||||||||
\(969\) | −14.0616 | −0.451723 | ||||||||
\(970\) | −50.6195 | −1.62529 | ||||||||
\(971\) | −30.0053 | −0.962917 | −0.481458 | − | 0.876469i | \(-0.659893\pi\) | ||||
−0.481458 | + | 0.876469i | \(0.659893\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.8794 | 0.797188 | ||||||||
\(975\) | 38.8505 | 1.24421 | ||||||||
\(976\) | −9.92415 | −0.317664 | ||||||||
\(977\) | 49.0531 | 1.56935 | 0.784673 | − | 0.619910i | \(-0.212831\pi\) | ||||
0.784673 | + | 0.619910i | \(0.212831\pi\) | |||||||
\(978\) | 23.1405 | 0.739952 | ||||||||
\(979\) | 14.0062 | 0.447640 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.3175 | 0.584832 | ||||||||
\(982\) | 34.9603 | 1.11563 | ||||||||
\(983\) | −25.7582 | −0.821558 | −0.410779 | − | 0.911735i | \(-0.634743\pi\) | ||||
−0.410779 | + | 0.911735i | \(0.634743\pi\) | |||||||
\(984\) | −8.50826 | −0.271233 | ||||||||
\(985\) | 47.3454 | 1.50855 | ||||||||
\(986\) | 52.0392 | 1.65727 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.9549 | 0.348523 | ||||||||
\(989\) | 7.23852 | 0.230172 | ||||||||
\(990\) | −4.41547 | −0.140333 | ||||||||
\(991\) | −15.9715 | −0.507350 | −0.253675 | − | 0.967290i | \(-0.581639\pi\) | ||||
−0.253675 | + | 0.967290i | \(0.581639\pi\) | |||||||
\(992\) | 9.57026 | 0.303856 | ||||||||
\(993\) | −25.9099 | −0.822225 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −78.4859 | −2.48817 | ||||||||
\(996\) | 5.10664 | 0.161810 | ||||||||
\(997\) | 15.8956 | 0.503419 | 0.251709 | − | 0.967803i | \(-0.419007\pi\) | ||||
0.251709 | + | 0.967803i | \(0.419007\pi\) | |||||||
\(998\) | 8.74166 | 0.276712 | ||||||||
\(999\) | −1.71642 | −0.0543050 |
(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 | 6762.2.a.cj.1.4 | ✓ | 4 | |
7.6 | odd | 2 | 6762.2.a.cs.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.cj.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6762.2.a.cs.1.1 | yes | 4 | 7.6 | odd | 2 |