Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(4.19214610612\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61803 | −1.85123 | −0.925615 | − | 0.378467i | \(-0.876451\pi\) | ||||
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.61803 | 1.06881 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.47214 | −2.64180 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.47214 | −1.64991 | −0.824956 | − | 0.565198i | \(-0.808800\pi\) | ||||
−0.824956 | + | 0.565198i | \(0.808800\pi\) | |||||||
\(12\) | −4.85410 | −1.40126 | ||||||||
\(13\) | −0.763932 | −0.211877 | −0.105938 | − | 0.994373i | \(-0.533785\pi\) | ||||
−0.105938 | + | 0.994373i | \(0.533785\pi\) | |||||||
\(14\) | −2.61803 | −0.699699 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | 7.70820 | 1.86951 | 0.934757 | − | 0.355288i | \(-0.115617\pi\) | ||||
0.934757 | + | 0.355288i | \(0.115617\pi\) | |||||||
\(18\) | −2.61803 | −0.617077 | ||||||||
\(19\) | −3.23607 | −0.742405 | −0.371202 | − | 0.928552i | \(-0.621054\pi\) | ||||
−0.371202 | + | 0.928552i | \(0.621054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 14.3262 | 3.05436 | ||||||||
\(23\) | −5.00000 | −1.04257 | −0.521286 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521286 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(24\) | 7.47214 | 1.52524 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.85410 | 0.917339 | ||||||||
\(29\) | 4.70820 | 0.874292 | 0.437146 | − | 0.899391i | \(-0.355989\pi\) | ||||
0.437146 | + | 0.899391i | \(0.355989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47214 | 0.803219 | 0.401610 | − | 0.915811i | \(-0.368451\pi\) | ||||
0.401610 | + | 0.915811i | \(0.368451\pi\) | |||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | 5.47214 | 0.952577 | ||||||||
\(34\) | −20.1803 | −3.46090 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.85410 | 0.809017 | ||||||||
\(37\) | −5.47214 | −0.899614 | −0.449807 | − | 0.893126i | \(-0.648507\pi\) | ||||
−0.449807 | + | 0.893126i | \(0.648507\pi\) | |||||||
\(38\) | 8.47214 | 1.37436 | ||||||||
\(39\) | 0.763932 | 0.122327 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 2.61803 | 0.403971 | ||||||||
\(43\) | −8.23607 | −1.25599 | −0.627994 | − | 0.778218i | \(-0.716124\pi\) | ||||
−0.627994 | + | 0.778218i | \(0.716124\pi\) | |||||||
\(44\) | −26.5623 | −4.00442 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 13.0902 | 1.93004 | ||||||||
\(47\) | −7.23607 | −1.05549 | −0.527744 | − | 0.849403i | \(-0.676962\pi\) | ||||
−0.527744 | + | 0.849403i | \(0.676962\pi\) | |||||||
\(48\) | −9.85410 | −1.42232 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.70820 | −1.07936 | ||||||||
\(52\) | −3.70820 | −0.514235 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 2.61803 | 0.356269 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.47214 | −0.998506 | ||||||||
\(57\) | 3.23607 | 0.428628 | ||||||||
\(58\) | −12.3262 | −1.61851 | ||||||||
\(59\) | −0.763932 | −0.0994555 | −0.0497277 | − | 0.998763i | \(-0.515835\pi\) | ||||
−0.0497277 | + | 0.998763i | \(0.515835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.4164 | −1.97387 | −0.986934 | − | 0.161123i | \(-0.948489\pi\) | ||||
−0.986934 | + | 0.161123i | \(0.948489\pi\) | |||||||
\(62\) | −11.7082 | −1.48694 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14.3262 | −1.76344 | ||||||||
\(67\) | 2.70820 | 0.330860 | 0.165430 | − | 0.986222i | \(-0.447099\pi\) | ||||
0.165430 | + | 0.986222i | \(0.447099\pi\) | |||||||
\(68\) | 37.4164 | 4.53741 | ||||||||
\(69\) | 5.00000 | 0.601929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.527864 | −0.0626459 | −0.0313230 | − | 0.999509i | \(-0.509972\pi\) | ||||
−0.0313230 | + | 0.999509i | \(0.509972\pi\) | |||||||
\(72\) | −7.47214 | −0.880600 | ||||||||
\(73\) | −1.23607 | −0.144671 | −0.0723354 | − | 0.997380i | \(-0.523045\pi\) | ||||
−0.0723354 | + | 0.997380i | \(0.523045\pi\) | |||||||
\(74\) | 14.3262 | 1.66539 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.7082 | −1.80185 | ||||||||
\(77\) | −5.47214 | −0.623608 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | 1.76393 | 0.198458 | 0.0992289 | − | 0.995065i | \(-0.468362\pi\) | ||||
0.0992289 | + | 0.995065i | \(0.468362\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.9443 | 2.31291 | ||||||||
\(83\) | −12.4721 | −1.36899 | −0.684497 | − | 0.729015i | \(-0.739978\pi\) | ||||
−0.684497 | + | 0.729015i | \(0.739978\pi\) | |||||||
\(84\) | −4.85410 | −0.529626 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 21.5623 | 2.32512 | ||||||||
\(87\) | −4.70820 | −0.504772 | ||||||||
\(88\) | 40.8885 | 4.35873 | ||||||||
\(89\) | −5.70820 | −0.605068 | −0.302534 | − | 0.953139i | \(-0.597833\pi\) | ||||
−0.302534 | + | 0.953139i | \(0.597833\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.763932 | −0.0800818 | ||||||||
\(92\) | −24.2705 | −2.53038 | ||||||||
\(93\) | −4.47214 | −0.463739 | ||||||||
\(94\) | 18.9443 | 1.95395 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.8541 | 1.10779 | ||||||||
\(97\) | −12.4721 | −1.26635 | −0.633177 | − | 0.774007i | \(-0.718249\pi\) | ||||
−0.633177 | + | 0.774007i | \(0.718249\pi\) | |||||||
\(98\) | −2.61803 | −0.264461 | ||||||||
\(99\) | −5.47214 | −0.549970 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.29180 | −0.427050 | −0.213525 | − | 0.976938i | \(-0.568494\pi\) | ||||
−0.213525 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(102\) | 20.1803 | 1.99815 | ||||||||
\(103\) | −9.70820 | −0.956578 | −0.478289 | − | 0.878203i | \(-0.658743\pi\) | ||||
−0.478289 | + | 0.878203i | \(0.658743\pi\) | |||||||
\(104\) | 5.70820 | 0.559735 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.23607 | 0.120058 | ||||||||
\(107\) | 4.94427 | 0.477981 | 0.238990 | − | 0.971022i | \(-0.423184\pi\) | ||||
0.238990 | + | 0.971022i | \(0.423184\pi\) | |||||||
\(108\) | −4.85410 | −0.467086 | ||||||||
\(109\) | −6.41641 | −0.614580 | −0.307290 | − | 0.951616i | \(-0.599422\pi\) | ||||
−0.307290 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.47214 | 0.519392 | ||||||||
\(112\) | 9.85410 | 0.931125 | ||||||||
\(113\) | 16.2361 | 1.52736 | 0.763680 | − | 0.645594i | \(-0.223390\pi\) | ||||
0.763680 | + | 0.645594i | \(0.223390\pi\) | |||||||
\(114\) | −8.47214 | −0.793488 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22.8541 | 2.12195 | ||||||||
\(117\) | −0.763932 | −0.0706255 | ||||||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | 7.70820 | 0.706610 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.9443 | 1.72221 | ||||||||
\(122\) | 40.3607 | 3.65408 | ||||||||
\(123\) | 8.00000 | 0.721336 | ||||||||
\(124\) | 21.7082 | 1.94945 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.61803 | −0.233233 | ||||||||
\(127\) | 12.2361 | 1.08578 | 0.542888 | − | 0.839805i | \(-0.317331\pi\) | ||||
0.542888 | + | 0.839805i | \(0.317331\pi\) | |||||||
\(128\) | −1.09017 | −0.0963583 | ||||||||
\(129\) | 8.23607 | 0.725145 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.29180 | −0.374976 | −0.187488 | − | 0.982267i | \(-0.560035\pi\) | ||||
−0.187488 | + | 0.982267i | \(0.560035\pi\) | |||||||
\(132\) | 26.5623 | 2.31195 | ||||||||
\(133\) | −3.23607 | −0.280603 | ||||||||
\(134\) | −7.09017 | −0.612497 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −57.5967 | −4.93888 | ||||||||
\(137\) | 0.472136 | 0.0403373 | 0.0201686 | − | 0.999797i | \(-0.493580\pi\) | ||||
0.0201686 | + | 0.999797i | \(0.493580\pi\) | |||||||
\(138\) | −13.0902 | −1.11431 | ||||||||
\(139\) | 3.70820 | 0.314526 | 0.157263 | − | 0.987557i | \(-0.449733\pi\) | ||||
0.157263 | + | 0.987557i | \(0.449733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.23607 | 0.609387 | ||||||||
\(142\) | 1.38197 | 0.115972 | ||||||||
\(143\) | 4.18034 | 0.349578 | ||||||||
\(144\) | 9.85410 | 0.821175 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.23607 | 0.267819 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −26.5623 | −2.18341 | ||||||||
\(149\) | 8.23607 | 0.674725 | 0.337362 | − | 0.941375i | \(-0.390465\pi\) | ||||
0.337362 | + | 0.941375i | \(0.390465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.29180 | 0.105125 | 0.0525624 | − | 0.998618i | \(-0.483261\pi\) | ||||
0.0525624 | + | 0.998618i | \(0.483261\pi\) | |||||||
\(152\) | 24.1803 | 1.96128 | ||||||||
\(153\) | 7.70820 | 0.623171 | ||||||||
\(154\) | 14.3262 | 1.15444 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.70820 | 0.296894 | ||||||||
\(157\) | −16.9443 | −1.35230 | −0.676150 | − | 0.736764i | \(-0.736353\pi\) | ||||
−0.676150 | + | 0.736764i | \(0.736353\pi\) | |||||||
\(158\) | −4.61803 | −0.367391 | ||||||||
\(159\) | 0.472136 | 0.0374428 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.00000 | −0.394055 | ||||||||
\(162\) | −2.61803 | −0.205692 | ||||||||
\(163\) | −18.4721 | −1.44685 | −0.723425 | − | 0.690403i | \(-0.757433\pi\) | ||||
−0.723425 | + | 0.690403i | \(0.757433\pi\) | |||||||
\(164\) | −38.8328 | −3.03233 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 32.6525 | 2.53432 | ||||||||
\(167\) | 6.29180 | 0.486874 | 0.243437 | − | 0.969917i | \(-0.421725\pi\) | ||||
0.243437 | + | 0.969917i | \(0.421725\pi\) | |||||||
\(168\) | 7.47214 | 0.576488 | ||||||||
\(169\) | −12.4164 | −0.955108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.23607 | −0.247468 | ||||||||
\(172\) | −39.9787 | −3.04835 | ||||||||
\(173\) | 3.81966 | 0.290403 | 0.145202 | − | 0.989402i | \(-0.453617\pi\) | ||||
0.145202 | + | 0.989402i | \(0.453617\pi\) | |||||||
\(174\) | 12.3262 | 0.934450 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −53.9230 | −4.06460 | ||||||||
\(177\) | 0.763932 | 0.0574206 | ||||||||
\(178\) | 14.9443 | 1.12012 | ||||||||
\(179\) | 4.94427 | 0.369552 | 0.184776 | − | 0.982781i | \(-0.440844\pi\) | ||||
0.184776 | + | 0.982781i | \(0.440844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.65248 | 0.345816 | 0.172908 | − | 0.984938i | \(-0.444684\pi\) | ||||
0.172908 | + | 0.984938i | \(0.444684\pi\) | |||||||
\(182\) | 2.00000 | 0.148250 | ||||||||
\(183\) | 15.4164 | 1.13961 | ||||||||
\(184\) | 37.3607 | 2.75427 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.7082 | 0.858487 | ||||||||
\(187\) | −42.1803 | −3.08453 | ||||||||
\(188\) | −35.1246 | −2.56173 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.4164 | −0.826062 | −0.413031 | − | 0.910717i | \(-0.635530\pi\) | ||||
−0.413031 | + | 0.910717i | \(0.635530\pi\) | |||||||
\(192\) | −8.70820 | −0.628460 | ||||||||
\(193\) | −0.416408 | −0.0299737 | −0.0149868 | − | 0.999888i | \(-0.504771\pi\) | ||||
−0.0149868 | + | 0.999888i | \(0.504771\pi\) | |||||||
\(194\) | 32.6525 | 2.34431 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.85410 | 0.346722 | ||||||||
\(197\) | 5.76393 | 0.410663 | 0.205332 | − | 0.978692i | \(-0.434173\pi\) | ||||
0.205332 | + | 0.978692i | \(0.434173\pi\) | |||||||
\(198\) | 14.3262 | 1.01812 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.70820 | −0.191022 | ||||||||
\(202\) | 11.2361 | 0.790567 | ||||||||
\(203\) | 4.70820 | 0.330451 | ||||||||
\(204\) | −37.4164 | −2.61967 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 25.4164 | 1.77085 | ||||||||
\(207\) | −5.00000 | −0.347524 | ||||||||
\(208\) | −7.52786 | −0.521963 | ||||||||
\(209\) | 17.7082 | 1.22490 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9443 | 0.891120 | 0.445560 | − | 0.895252i | \(-0.353005\pi\) | ||||
0.445560 | + | 0.895252i | \(0.353005\pi\) | |||||||
\(212\) | −2.29180 | −0.157401 | ||||||||
\(213\) | 0.527864 | 0.0361686 | ||||||||
\(214\) | −12.9443 | −0.884852 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.47214 | 0.508414 | ||||||||
\(217\) | 4.47214 | 0.303588 | ||||||||
\(218\) | 16.7984 | 1.13773 | ||||||||
\(219\) | 1.23607 | 0.0835257 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.88854 | −0.396106 | ||||||||
\(222\) | −14.3262 | −0.961514 | ||||||||
\(223\) | 1.23607 | 0.0827732 | 0.0413866 | − | 0.999143i | \(-0.486822\pi\) | ||||
0.0413866 | + | 0.999143i | \(0.486822\pi\) | |||||||
\(224\) | −10.8541 | −0.725220 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −42.5066 | −2.82750 | ||||||||
\(227\) | 4.76393 | 0.316193 | 0.158097 | − | 0.987424i | \(-0.449464\pi\) | ||||
0.158097 | + | 0.987424i | \(0.449464\pi\) | |||||||
\(228\) | 15.7082 | 1.04030 | ||||||||
\(229\) | 22.3607 | 1.47764 | 0.738818 | − | 0.673905i | \(-0.235384\pi\) | ||||
0.738818 | + | 0.673905i | \(0.235384\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.47214 | 0.360040 | ||||||||
\(232\) | −35.1803 | −2.30970 | ||||||||
\(233\) | −7.29180 | −0.477701 | −0.238851 | − | 0.971056i | \(-0.576771\pi\) | ||||
−0.238851 | + | 0.971056i | \(0.576771\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.70820 | −0.241384 | ||||||||
\(237\) | −1.76393 | −0.114580 | ||||||||
\(238\) | −20.1803 | −1.30810 | ||||||||
\(239\) | −28.3607 | −1.83450 | −0.917250 | − | 0.398312i | \(-0.869596\pi\) | ||||
−0.917250 | + | 0.398312i | \(0.869596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.2361 | 1.23910 | 0.619552 | − | 0.784956i | \(-0.287314\pi\) | ||||
0.619552 | + | 0.784956i | \(0.287314\pi\) | |||||||
\(242\) | −49.5967 | −3.18820 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −74.8328 | −4.79068 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.9443 | −1.33536 | ||||||||
\(247\) | 2.47214 | 0.157298 | ||||||||
\(248\) | −33.4164 | −2.12194 | ||||||||
\(249\) | 12.4721 | 0.790390 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.76393 | 0.174458 | 0.0872289 | − | 0.996188i | \(-0.472199\pi\) | ||||
0.0872289 | + | 0.996188i | \(0.472199\pi\) | |||||||
\(252\) | 4.85410 | 0.305780 | ||||||||
\(253\) | 27.3607 | 1.72015 | ||||||||
\(254\) | −32.0344 | −2.01002 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | 8.47214 | 0.528477 | 0.264239 | − | 0.964457i | \(-0.414879\pi\) | ||||
0.264239 | + | 0.964457i | \(0.414879\pi\) | |||||||
\(258\) | −21.5623 | −1.34241 | ||||||||
\(259\) | −5.47214 | −0.340022 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.70820 | 0.291431 | ||||||||
\(262\) | 11.2361 | 0.694167 | ||||||||
\(263\) | −2.05573 | −0.126762 | −0.0633808 | − | 0.997989i | \(-0.520188\pi\) | ||||
−0.0633808 | + | 0.997989i | \(0.520188\pi\) | |||||||
\(264\) | −40.8885 | −2.51652 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.47214 | 0.519460 | ||||||||
\(267\) | 5.70820 | 0.349336 | ||||||||
\(268\) | 13.1459 | 0.803014 | ||||||||
\(269\) | −28.4721 | −1.73598 | −0.867988 | − | 0.496584i | \(-0.834587\pi\) | ||||
−0.867988 | + | 0.496584i | \(0.834587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.2361 | 1.41149 | 0.705745 | − | 0.708466i | \(-0.250612\pi\) | ||||
0.705745 | + | 0.708466i | \(0.250612\pi\) | |||||||
\(272\) | 75.9574 | 4.60560 | ||||||||
\(273\) | 0.763932 | 0.0462353 | ||||||||
\(274\) | −1.23607 | −0.0746736 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 24.2705 | 1.46091 | ||||||||
\(277\) | 15.8885 | 0.954650 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(278\) | −9.70820 | −0.582259 | ||||||||
\(279\) | 4.47214 | 0.267740 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6525 | 0.814438 | 0.407219 | − | 0.913330i | \(-0.366499\pi\) | ||||
0.407219 | + | 0.913330i | \(0.366499\pi\) | |||||||
\(282\) | −18.9443 | −1.12811 | ||||||||
\(283\) | 13.4164 | 0.797523 | 0.398761 | − | 0.917055i | \(-0.369440\pi\) | ||||
0.398761 | + | 0.917055i | \(0.369440\pi\) | |||||||
\(284\) | −2.56231 | −0.152045 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.9443 | −0.647148 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | −10.8541 | −0.639584 | ||||||||
\(289\) | 42.4164 | 2.49508 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.4721 | 0.731130 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 26.6525 | 1.55705 | 0.778527 | − | 0.627611i | \(-0.215967\pi\) | ||||
0.778527 | + | 0.627611i | \(0.215967\pi\) | |||||||
\(294\) | 2.61803 | 0.152687 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 40.8885 | 2.37660 | ||||||||
\(297\) | 5.47214 | 0.317526 | ||||||||
\(298\) | −21.5623 | −1.24907 | ||||||||
\(299\) | 3.81966 | 0.220897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.23607 | −0.474719 | ||||||||
\(302\) | −3.38197 | −0.194610 | ||||||||
\(303\) | 4.29180 | 0.246557 | ||||||||
\(304\) | −31.8885 | −1.82893 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −20.1803 | −1.15363 | ||||||||
\(307\) | −24.6525 | −1.40699 | −0.703496 | − | 0.710700i | \(-0.748379\pi\) | ||||
−0.703496 | + | 0.710700i | \(0.748379\pi\) | |||||||
\(308\) | −26.5623 | −1.51353 | ||||||||
\(309\) | 9.70820 | 0.552280 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.2361 | 0.750549 | 0.375274 | − | 0.926914i | \(-0.377549\pi\) | ||||
0.375274 | + | 0.926914i | \(0.377549\pi\) | |||||||
\(312\) | −5.70820 | −0.323163 | ||||||||
\(313\) | 5.70820 | 0.322647 | 0.161323 | − | 0.986902i | \(-0.448424\pi\) | ||||
0.161323 | + | 0.986902i | \(0.448424\pi\) | |||||||
\(314\) | 44.3607 | 2.50342 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.56231 | 0.481667 | ||||||||
\(317\) | −17.6525 | −0.991462 | −0.495731 | − | 0.868476i | \(-0.665100\pi\) | ||||
−0.495731 | + | 0.868476i | \(0.665100\pi\) | |||||||
\(318\) | −1.23607 | −0.0693153 | ||||||||
\(319\) | −25.7639 | −1.44250 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.94427 | −0.275962 | ||||||||
\(322\) | 13.0902 | 0.729487 | ||||||||
\(323\) | −24.9443 | −1.38794 | ||||||||
\(324\) | 4.85410 | 0.269672 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 48.3607 | 2.67845 | ||||||||
\(327\) | 6.41641 | 0.354828 | ||||||||
\(328\) | 59.7771 | 3.30064 | ||||||||
\(329\) | −7.23607 | −0.398937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7639 | 0.756534 | 0.378267 | − | 0.925697i | \(-0.376520\pi\) | ||||
0.378267 | + | 0.925697i | \(0.376520\pi\) | |||||||
\(332\) | −60.5410 | −3.32262 | ||||||||
\(333\) | −5.47214 | −0.299871 | ||||||||
\(334\) | −16.4721 | −0.901315 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.85410 | −0.537585 | ||||||||
\(337\) | 28.4721 | 1.55098 | 0.775488 | − | 0.631362i | \(-0.217504\pi\) | ||||
0.775488 | + | 0.631362i | \(0.217504\pi\) | |||||||
\(338\) | 32.5066 | 1.76812 | ||||||||
\(339\) | −16.2361 | −0.881822 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.4721 | −1.32524 | ||||||||
\(342\) | 8.47214 | 0.458121 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 61.5410 | 3.31807 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | −0.537603 | ||||||||
\(347\) | 13.0000 | 0.697877 | 0.348938 | − | 0.937146i | \(-0.386542\pi\) | ||||
0.348938 | + | 0.937146i | \(0.386542\pi\) | |||||||
\(348\) | −22.8541 | −1.22511 | ||||||||
\(349\) | 0.763932 | 0.0408923 | 0.0204462 | − | 0.999791i | \(-0.493491\pi\) | ||||
0.0204462 | + | 0.999791i | \(0.493491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.763932 | 0.0407757 | ||||||||
\(352\) | 59.3951 | 3.16577 | ||||||||
\(353\) | −1.05573 | −0.0561907 | −0.0280954 | − | 0.999605i | \(-0.508944\pi\) | ||||
−0.0280954 | + | 0.999605i | \(0.508944\pi\) | |||||||
\(354\) | −2.00000 | −0.106299 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −27.7082 | −1.46853 | ||||||||
\(357\) | −7.70820 | −0.407961 | ||||||||
\(358\) | −12.9443 | −0.684126 | ||||||||
\(359\) | 25.9443 | 1.36929 | 0.684643 | − | 0.728878i | \(-0.259958\pi\) | ||||
0.684643 | + | 0.728878i | \(0.259958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.52786 | −0.448835 | ||||||||
\(362\) | −12.1803 | −0.640184 | ||||||||
\(363\) | −18.9443 | −0.994316 | ||||||||
\(364\) | −3.70820 | −0.194363 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −40.3607 | −2.10969 | ||||||||
\(367\) | 8.94427 | 0.466887 | 0.233444 | − | 0.972370i | \(-0.425001\pi\) | ||||
0.233444 | + | 0.972370i | \(0.425001\pi\) | |||||||
\(368\) | −49.2705 | −2.56840 | ||||||||
\(369\) | −8.00000 | −0.416463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.472136 | −0.0245121 | ||||||||
\(372\) | −21.7082 | −1.12552 | ||||||||
\(373\) | 15.0000 | 0.776671 | 0.388335 | − | 0.921518i | \(-0.373050\pi\) | ||||
0.388335 | + | 0.921518i | \(0.373050\pi\) | |||||||
\(374\) | 110.430 | 5.71018 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 54.0689 | 2.78839 | ||||||||
\(377\) | −3.59675 | −0.185242 | ||||||||
\(378\) | 2.61803 | 0.134657 | ||||||||
\(379\) | 16.5967 | 0.852518 | 0.426259 | − | 0.904601i | \(-0.359831\pi\) | ||||
0.426259 | + | 0.904601i | \(0.359831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.2361 | −0.626873 | ||||||||
\(382\) | 29.8885 | 1.52923 | ||||||||
\(383\) | −25.1246 | −1.28381 | −0.641904 | − | 0.766785i | \(-0.721855\pi\) | ||||
−0.641904 | + | 0.766785i | \(0.721855\pi\) | |||||||
\(384\) | 1.09017 | 0.0556325 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.09017 | 0.0554882 | ||||||||
\(387\) | −8.23607 | −0.418663 | ||||||||
\(388\) | −60.5410 | −3.07350 | ||||||||
\(389\) | −1.76393 | −0.0894349 | −0.0447175 | − | 0.999000i | \(-0.514239\pi\) | ||||
−0.0447175 | + | 0.999000i | \(0.514239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.5410 | −1.94910 | ||||||||
\(392\) | −7.47214 | −0.377400 | ||||||||
\(393\) | 4.29180 | 0.216492 | ||||||||
\(394\) | −15.0902 | −0.760232 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −26.5623 | −1.33481 | ||||||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 41.8885 | 2.09968 | ||||||||
\(399\) | 3.23607 | 0.162006 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.7082 | −1.33374 | −0.666872 | − | 0.745172i | \(-0.732367\pi\) | ||||
−0.666872 | + | 0.745172i | \(0.732367\pi\) | |||||||
\(402\) | 7.09017 | 0.353626 | ||||||||
\(403\) | −3.41641 | −0.170183 | ||||||||
\(404\) | −20.8328 | −1.03647 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.3262 | −0.611741 | ||||||||
\(407\) | 29.9443 | 1.48428 | ||||||||
\(408\) | 57.5967 | 2.85146 | ||||||||
\(409\) | −8.18034 | −0.404492 | −0.202246 | − | 0.979335i | \(-0.564824\pi\) | ||||
−0.202246 | + | 0.979335i | \(0.564824\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.472136 | −0.0232887 | ||||||||
\(412\) | −47.1246 | −2.32166 | ||||||||
\(413\) | −0.763932 | −0.0375906 | ||||||||
\(414\) | 13.0902 | 0.643347 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8.29180 | 0.406539 | ||||||||
\(417\) | −3.70820 | −0.181592 | ||||||||
\(418\) | −46.3607 | −2.26757 | ||||||||
\(419\) | 9.05573 | 0.442401 | 0.221201 | − | 0.975228i | \(-0.429002\pi\) | ||||
0.221201 | + | 0.975228i | \(0.429002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.416408 | −0.0202945 | −0.0101472 | − | 0.999949i | \(-0.503230\pi\) | ||||
−0.0101472 | + | 0.999949i | \(0.503230\pi\) | |||||||
\(422\) | −33.8885 | −1.64967 | ||||||||
\(423\) | −7.23607 | −0.351830 | ||||||||
\(424\) | 3.52786 | 0.171328 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.38197 | −0.0669565 | ||||||||
\(427\) | −15.4164 | −0.746052 | ||||||||
\(428\) | 24.0000 | 1.16008 | ||||||||
\(429\) | −4.18034 | −0.201829 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.8885 | 1.63235 | 0.816177 | − | 0.577802i | \(-0.196089\pi\) | ||||
0.816177 | + | 0.577802i | \(0.196089\pi\) | |||||||
\(432\) | −9.85410 | −0.474106 | ||||||||
\(433\) | −37.3050 | −1.79276 | −0.896381 | − | 0.443285i | \(-0.853813\pi\) | ||||
−0.896381 | + | 0.443285i | \(0.853813\pi\) | |||||||
\(434\) | −11.7082 | −0.562012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.1459 | −1.49162 | ||||||||
\(437\) | 16.1803 | 0.774011 | ||||||||
\(438\) | −3.23607 | −0.154625 | ||||||||
\(439\) | −11.2361 | −0.536268 | −0.268134 | − | 0.963382i | \(-0.586407\pi\) | ||||
−0.268134 | + | 0.963382i | \(0.586407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 15.4164 | 0.733284 | ||||||||
\(443\) | −12.5836 | −0.597865 | −0.298932 | − | 0.954274i | \(-0.596630\pi\) | ||||
−0.298932 | + | 0.954274i | \(0.596630\pi\) | |||||||
\(444\) | 26.5623 | 1.26059 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.23607 | −0.153232 | ||||||||
\(447\) | −8.23607 | −0.389553 | ||||||||
\(448\) | 8.70820 | 0.411424 | ||||||||
\(449\) | 3.29180 | 0.155349 | 0.0776747 | − | 0.996979i | \(-0.475250\pi\) | ||||
0.0776747 | + | 0.996979i | \(0.475250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43.7771 | 2.06138 | ||||||||
\(452\) | 78.8115 | 3.70698 | ||||||||
\(453\) | −1.29180 | −0.0606939 | ||||||||
\(454\) | −12.4721 | −0.585346 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −24.1803 | −1.13235 | ||||||||
\(457\) | 29.4721 | 1.37865 | 0.689324 | − | 0.724453i | \(-0.257908\pi\) | ||||
0.689324 | + | 0.724453i | \(0.257908\pi\) | |||||||
\(458\) | −58.5410 | −2.73544 | ||||||||
\(459\) | −7.70820 | −0.359788 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.6525 | 0.496135 | 0.248068 | − | 0.968743i | \(-0.420204\pi\) | ||||
0.248068 | + | 0.968743i | \(0.420204\pi\) | |||||||
\(462\) | −14.3262 | −0.666517 | ||||||||
\(463\) | −28.3607 | −1.31803 | −0.659016 | − | 0.752129i | \(-0.729027\pi\) | ||||
−0.659016 | + | 0.752129i | \(0.729027\pi\) | |||||||
\(464\) | 46.3951 | 2.15384 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.0902 | 0.884335 | ||||||||
\(467\) | −23.8885 | −1.10543 | −0.552715 | − | 0.833370i | \(-0.686408\pi\) | ||||
−0.552715 | + | 0.833370i | \(0.686408\pi\) | |||||||
\(468\) | −3.70820 | −0.171412 | ||||||||
\(469\) | 2.70820 | 0.125053 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.9443 | 0.780751 | ||||||||
\(472\) | 5.70820 | 0.262741 | ||||||||
\(473\) | 45.0689 | 2.07227 | ||||||||
\(474\) | 4.61803 | 0.212113 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 37.4164 | 1.71498 | ||||||||
\(477\) | −0.472136 | −0.0216176 | ||||||||
\(478\) | 74.2492 | 3.39608 | ||||||||
\(479\) | −23.2361 | −1.06168 | −0.530842 | − | 0.847471i | \(-0.678124\pi\) | ||||
−0.530842 | + | 0.847471i | \(0.678124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.18034 | 0.190607 | ||||||||
\(482\) | −50.3607 | −2.29387 | ||||||||
\(483\) | 5.00000 | 0.227508 | ||||||||
\(484\) | 91.9574 | 4.17988 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.61803 | 0.118756 | ||||||||
\(487\) | 6.81966 | 0.309028 | 0.154514 | − | 0.987991i | \(-0.450619\pi\) | ||||
0.154514 | + | 0.987991i | \(0.450619\pi\) | |||||||
\(488\) | 115.193 | 5.21456 | ||||||||
\(489\) | 18.4721 | 0.835339 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.527864 | −0.0238222 | −0.0119111 | − | 0.999929i | \(-0.503792\pi\) | ||||
−0.0119111 | + | 0.999929i | \(0.503792\pi\) | |||||||
\(492\) | 38.8328 | 1.75072 | ||||||||
\(493\) | 36.2918 | 1.63450 | ||||||||
\(494\) | −6.47214 | −0.291195 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 44.0689 | 1.97875 | ||||||||
\(497\) | −0.527864 | −0.0236779 | ||||||||
\(498\) | −32.6525 | −1.46319 | ||||||||
\(499\) | −31.7771 | −1.42254 | −0.711269 | − | 0.702920i | \(-0.751879\pi\) | ||||
−0.711269 | + | 0.702920i | \(0.751879\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.29180 | −0.281097 | ||||||||
\(502\) | −7.23607 | −0.322962 | ||||||||
\(503\) | −17.4164 | −0.776559 | −0.388280 | − | 0.921542i | \(-0.626931\pi\) | ||||
−0.388280 | + | 0.921542i | \(0.626931\pi\) | |||||||
\(504\) | −7.47214 | −0.332835 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −71.6312 | −3.18439 | ||||||||
\(507\) | 12.4164 | 0.551432 | ||||||||
\(508\) | 59.3951 | 2.63523 | ||||||||
\(509\) | −30.6525 | −1.35865 | −0.679324 | − | 0.733839i | \(-0.737727\pi\) | ||||
−0.679324 | + | 0.733839i | \(0.737727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.23607 | −0.0546804 | ||||||||
\(512\) | 40.3050 | 1.78124 | ||||||||
\(513\) | 3.23607 | 0.142876 | ||||||||
\(514\) | −22.1803 | −0.978333 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 39.9787 | 1.75996 | ||||||||
\(517\) | 39.5967 | 1.74146 | ||||||||
\(518\) | 14.3262 | 0.629459 | ||||||||
\(519\) | −3.81966 | −0.167664 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.7771 | −1.65504 | −0.827522 | − | 0.561433i | \(-0.810250\pi\) | ||||
−0.827522 | + | 0.561433i | \(0.810250\pi\) | |||||||
\(522\) | −12.3262 | −0.539505 | ||||||||
\(523\) | 35.7771 | 1.56442 | 0.782211 | − | 0.623013i | \(-0.214092\pi\) | ||||
0.782211 | + | 0.623013i | \(0.214092\pi\) | |||||||
\(524\) | −20.8328 | −0.910086 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.38197 | 0.234665 | ||||||||
\(527\) | 34.4721 | 1.50163 | ||||||||
\(528\) | 53.9230 | 2.34670 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.763932 | −0.0331518 | ||||||||
\(532\) | −15.7082 | −0.681037 | ||||||||
\(533\) | 6.11146 | 0.264717 | ||||||||
\(534\) | −14.9443 | −0.646702 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.2361 | −0.874065 | ||||||||
\(537\) | −4.94427 | −0.213361 | ||||||||
\(538\) | 74.5410 | 3.21369 | ||||||||
\(539\) | −5.47214 | −0.235702 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9443 | −0.771485 | −0.385742 | − | 0.922607i | \(-0.626055\pi\) | ||||
−0.385742 | + | 0.922607i | \(0.626055\pi\) | |||||||
\(542\) | −60.8328 | −2.61299 | ||||||||
\(543\) | −4.65248 | −0.199657 | ||||||||
\(544\) | −83.6656 | −3.58713 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | −0.0855921 | ||||||||
\(547\) | 35.0689 | 1.49944 | 0.749719 | − | 0.661757i | \(-0.230189\pi\) | ||||
0.749719 | + | 0.661757i | \(0.230189\pi\) | |||||||
\(548\) | 2.29180 | 0.0979007 | ||||||||
\(549\) | −15.4164 | −0.657956 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.2361 | −0.649078 | ||||||||
\(552\) | −37.3607 | −1.59018 | ||||||||
\(553\) | 1.76393 | 0.0750100 | ||||||||
\(554\) | −41.5967 | −1.76728 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.0000 | 0.763370 | ||||||||
\(557\) | 7.65248 | 0.324246 | 0.162123 | − | 0.986771i | \(-0.448166\pi\) | ||||
0.162123 | + | 0.986771i | \(0.448166\pi\) | |||||||
\(558\) | −11.7082 | −0.495648 | ||||||||
\(559\) | 6.29180 | 0.266115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.1803 | 1.78086 | ||||||||
\(562\) | −35.7426 | −1.50771 | ||||||||
\(563\) | −35.3050 | −1.48793 | −0.743963 | − | 0.668221i | \(-0.767056\pi\) | ||||
−0.743963 | + | 0.668221i | \(0.767056\pi\) | |||||||
\(564\) | 35.1246 | 1.47901 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −35.1246 | −1.47640 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 3.94427 | 0.165498 | ||||||||
\(569\) | −12.2361 | −0.512963 | −0.256481 | − | 0.966549i | \(-0.582563\pi\) | ||||
−0.256481 | + | 0.966549i | \(0.582563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.7082 | −1.70359 | −0.851793 | − | 0.523879i | \(-0.824484\pi\) | ||||
−0.851793 | + | 0.523879i | \(0.824484\pi\) | |||||||
\(572\) | 20.2918 | 0.848443 | ||||||||
\(573\) | 11.4164 | 0.476927 | ||||||||
\(574\) | 20.9443 | 0.874197 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.70820 | 0.362842 | ||||||||
\(577\) | −11.2361 | −0.467764 | −0.233882 | − | 0.972265i | \(-0.575143\pi\) | ||||
−0.233882 | + | 0.972265i | \(0.575143\pi\) | |||||||
\(578\) | −111.048 | −4.61897 | ||||||||
\(579\) | 0.416408 | 0.0173053 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.4721 | −0.517431 | ||||||||
\(582\) | −32.6525 | −1.35349 | ||||||||
\(583\) | 2.58359 | 0.107001 | ||||||||
\(584\) | 9.23607 | 0.382191 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −69.7771 | −2.88246 | ||||||||
\(587\) | 7.12461 | 0.294064 | 0.147032 | − | 0.989132i | \(-0.453028\pi\) | ||||
0.147032 | + | 0.989132i | \(0.453028\pi\) | |||||||
\(588\) | −4.85410 | −0.200180 | ||||||||
\(589\) | −14.4721 | −0.596314 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.76393 | −0.237096 | ||||||||
\(592\) | −53.9230 | −2.21622 | ||||||||
\(593\) | −25.3050 | −1.03915 | −0.519575 | − | 0.854425i | \(-0.673910\pi\) | ||||
−0.519575 | + | 0.854425i | \(0.673910\pi\) | |||||||
\(594\) | −14.3262 | −0.587813 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 39.9787 | 1.63759 | ||||||||
\(597\) | 16.0000 | 0.654836 | ||||||||
\(598\) | −10.0000 | −0.408930 | ||||||||
\(599\) | −45.9443 | −1.87723 | −0.938616 | − | 0.344964i | \(-0.887891\pi\) | ||||
−0.938616 | + | 0.344964i | \(0.887891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.3607 | −1.15686 | −0.578428 | − | 0.815733i | \(-0.696334\pi\) | ||||
−0.578428 | + | 0.815733i | \(0.696334\pi\) | |||||||
\(602\) | 21.5623 | 0.878814 | ||||||||
\(603\) | 2.70820 | 0.110287 | ||||||||
\(604\) | 6.27051 | 0.255143 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.2361 | −0.456434 | ||||||||
\(607\) | −2.29180 | −0.0930211 | −0.0465106 | − | 0.998918i | \(-0.514810\pi\) | ||||
−0.0465106 | + | 0.998918i | \(0.514810\pi\) | |||||||
\(608\) | 35.1246 | 1.42449 | ||||||||
\(609\) | −4.70820 | −0.190786 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.52786 | 0.223633 | ||||||||
\(612\) | 37.4164 | 1.51247 | ||||||||
\(613\) | −10.0557 | −0.406147 | −0.203074 | − | 0.979163i | \(-0.565093\pi\) | ||||
−0.203074 | + | 0.979163i | \(0.565093\pi\) | |||||||
\(614\) | 64.5410 | 2.60466 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 40.8885 | 1.64745 | ||||||||
\(617\) | 21.6525 | 0.871696 | 0.435848 | − | 0.900020i | \(-0.356449\pi\) | ||||
0.435848 | + | 0.900020i | \(0.356449\pi\) | |||||||
\(618\) | −25.4164 | −1.02240 | ||||||||
\(619\) | 25.1246 | 1.00984 | 0.504922 | − | 0.863165i | \(-0.331521\pi\) | ||||
0.504922 | + | 0.863165i | \(0.331521\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.00000 | 0.200643 | ||||||||
\(622\) | −34.6525 | −1.38944 | ||||||||
\(623\) | −5.70820 | −0.228694 | ||||||||
\(624\) | 7.52786 | 0.301356 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.9443 | −0.597293 | ||||||||
\(627\) | −17.7082 | −0.707198 | ||||||||
\(628\) | −82.2492 | −3.28210 | ||||||||
\(629\) | −42.1803 | −1.68184 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.1246 | −1.59734 | −0.798668 | − | 0.601772i | \(-0.794462\pi\) | ||||
−0.798668 | + | 0.601772i | \(0.794462\pi\) | |||||||
\(632\) | −13.1803 | −0.524286 | ||||||||
\(633\) | −12.9443 | −0.514489 | ||||||||
\(634\) | 46.2148 | 1.83542 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.29180 | 0.0908756 | ||||||||
\(637\) | −0.763932 | −0.0302681 | ||||||||
\(638\) | 67.4508 | 2.67040 | ||||||||
\(639\) | −0.527864 | −0.0208820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.2918 | −0.603990 | −0.301995 | − | 0.953310i | \(-0.597653\pi\) | ||||
−0.301995 | + | 0.953310i | \(0.597653\pi\) | |||||||
\(642\) | 12.9443 | 0.510870 | ||||||||
\(643\) | 44.7214 | 1.76364 | 0.881819 | − | 0.471588i | \(-0.156319\pi\) | ||||
0.881819 | + | 0.471588i | \(0.156319\pi\) | |||||||
\(644\) | −24.2705 | −0.956392 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 65.3050 | 2.56939 | ||||||||
\(647\) | 1.05573 | 0.0415050 | 0.0207525 | − | 0.999785i | \(-0.493394\pi\) | ||||
0.0207525 | + | 0.999785i | \(0.493394\pi\) | |||||||
\(648\) | −7.47214 | −0.293533 | ||||||||
\(649\) | 4.18034 | 0.164093 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.47214 | −0.175277 | ||||||||
\(652\) | −89.6656 | −3.51158 | ||||||||
\(653\) | −25.4164 | −0.994621 | −0.497310 | − | 0.867573i | \(-0.665679\pi\) | ||||
−0.497310 | + | 0.867573i | \(0.665679\pi\) | |||||||
\(654\) | −16.7984 | −0.656868 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −78.8328 | −3.07790 | ||||||||
\(657\) | −1.23607 | −0.0482236 | ||||||||
\(658\) | 18.9443 | 0.738525 | ||||||||
\(659\) | 40.9443 | 1.59496 | 0.797481 | − | 0.603344i | \(-0.206165\pi\) | ||||
0.797481 | + | 0.603344i | \(0.206165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.18034 | 0.318178 | 0.159089 | − | 0.987264i | \(-0.449144\pi\) | ||||
0.159089 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(662\) | −36.0344 | −1.40052 | ||||||||
\(663\) | 5.88854 | 0.228692 | ||||||||
\(664\) | 93.1935 | 3.61661 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.3262 | 0.555130 | ||||||||
\(667\) | −23.5410 | −0.911512 | ||||||||
\(668\) | 30.5410 | 1.18167 | ||||||||
\(669\) | −1.23607 | −0.0477891 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 84.3607 | 3.25671 | ||||||||
\(672\) | 10.8541 | 0.418706 | ||||||||
\(673\) | 6.00000 | 0.231283 | 0.115642 | − | 0.993291i | \(-0.463108\pi\) | ||||
0.115642 | + | 0.993291i | \(0.463108\pi\) | |||||||
\(674\) | −74.5410 | −2.87121 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −60.2705 | −2.31810 | ||||||||
\(677\) | −43.3050 | −1.66434 | −0.832172 | − | 0.554517i | \(-0.812903\pi\) | ||||
−0.832172 | + | 0.554517i | \(0.812903\pi\) | |||||||
\(678\) | 42.5066 | 1.63246 | ||||||||
\(679\) | −12.4721 | −0.478637 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.76393 | −0.182554 | ||||||||
\(682\) | 64.0689 | 2.45332 | ||||||||
\(683\) | −5.11146 | −0.195584 | −0.0977922 | − | 0.995207i | \(-0.531178\pi\) | ||||
−0.0977922 | + | 0.995207i | \(0.531178\pi\) | |||||||
\(684\) | −15.7082 | −0.600618 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.61803 | −0.0999570 | ||||||||
\(687\) | −22.3607 | −0.853113 | ||||||||
\(688\) | −81.1591 | −3.09416 | ||||||||
\(689\) | 0.360680 | 0.0137408 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3607 | −0.470222 | −0.235111 | − | 0.971968i | \(-0.575545\pi\) | ||||
−0.235111 | + | 0.971968i | \(0.575545\pi\) | |||||||
\(692\) | 18.5410 | 0.704824 | ||||||||
\(693\) | −5.47214 | −0.207869 | ||||||||
\(694\) | −34.0344 | −1.29193 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 35.1803 | 1.33351 | ||||||||
\(697\) | −61.6656 | −2.33575 | ||||||||
\(698\) | −2.00000 | −0.0757011 | ||||||||
\(699\) | 7.29180 | 0.275801 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.4164 | 1.26212 | 0.631060 | − | 0.775734i | \(-0.282620\pi\) | ||||
0.631060 | + | 0.775734i | \(0.282620\pi\) | |||||||
\(702\) | −2.00000 | −0.0754851 | ||||||||
\(703\) | 17.7082 | 0.667878 | ||||||||
\(704\) | −47.6525 | −1.79597 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.76393 | 0.104022 | ||||||||
\(707\) | −4.29180 | −0.161410 | ||||||||
\(708\) | 3.70820 | 0.139363 | ||||||||
\(709\) | 43.8885 | 1.64827 | 0.824134 | − | 0.566394i | \(-0.191662\pi\) | ||||
0.824134 | + | 0.566394i | \(0.191662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.76393 | 0.0661526 | ||||||||
\(712\) | 42.6525 | 1.59847 | ||||||||
\(713\) | −22.3607 | −0.837414 | ||||||||
\(714\) | 20.1803 | 0.755230 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0000 | 0.896922 | ||||||||
\(717\) | 28.3607 | 1.05915 | ||||||||
\(718\) | −67.9230 | −2.53486 | ||||||||
\(719\) | 42.2492 | 1.57563 | 0.787815 | − | 0.615912i | \(-0.211212\pi\) | ||||
0.787815 | + | 0.615912i | \(0.211212\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.70820 | −0.361552 | ||||||||
\(722\) | 22.3262 | 0.830897 | ||||||||
\(723\) | −19.2361 | −0.715397 | ||||||||
\(724\) | 22.5836 | 0.839313 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 49.5967 | 1.84071 | ||||||||
\(727\) | 18.5410 | 0.687648 | 0.343824 | − | 0.939034i | \(-0.388278\pi\) | ||||
0.343824 | + | 0.939034i | \(0.388278\pi\) | |||||||
\(728\) | 5.70820 | 0.211560 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −63.4853 | −2.34809 | ||||||||
\(732\) | 74.8328 | 2.76590 | ||||||||
\(733\) | −12.0000 | −0.443230 | −0.221615 | − | 0.975134i | \(-0.571133\pi\) | ||||
−0.221615 | + | 0.975134i | \(0.571133\pi\) | |||||||
\(734\) | −23.4164 | −0.864315 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 54.2705 | 2.00044 | ||||||||
\(737\) | −14.8197 | −0.545889 | ||||||||
\(738\) | 20.9443 | 0.770969 | ||||||||
\(739\) | 3.76393 | 0.138458 | 0.0692292 | − | 0.997601i | \(-0.477946\pi\) | ||||
0.0692292 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.47214 | −0.0908162 | ||||||||
\(742\) | 1.23607 | 0.0453775 | ||||||||
\(743\) | 30.2492 | 1.10974 | 0.554868 | − | 0.831938i | \(-0.312769\pi\) | ||||
0.554868 | + | 0.831938i | \(0.312769\pi\) | |||||||
\(744\) | 33.4164 | 1.22510 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −39.2705 | −1.43780 | ||||||||
\(747\) | −12.4721 | −0.456332 | ||||||||
\(748\) | −204.748 | −7.48632 | ||||||||
\(749\) | 4.94427 | 0.180660 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.3607 | 1.47278 | 0.736391 | − | 0.676556i | \(-0.236528\pi\) | ||||
0.736391 | + | 0.676556i | \(0.236528\pi\) | |||||||
\(752\) | −71.3050 | −2.60022 | ||||||||
\(753\) | −2.76393 | −0.100723 | ||||||||
\(754\) | 9.41641 | 0.342925 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.85410 | −0.176542 | ||||||||
\(757\) | 13.9443 | 0.506813 | 0.253407 | − | 0.967360i | \(-0.418449\pi\) | ||||
0.253407 | + | 0.967360i | \(0.418449\pi\) | |||||||
\(758\) | −43.4508 | −1.57821 | ||||||||
\(759\) | −27.3607 | −0.993130 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.30495 | 0.337304 | 0.168652 | − | 0.985676i | \(-0.446059\pi\) | ||||
0.168652 | + | 0.985676i | \(0.446059\pi\) | |||||||
\(762\) | 32.0344 | 1.16049 | ||||||||
\(763\) | −6.41641 | −0.232290 | ||||||||
\(764\) | −55.4164 | −2.00490 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 65.7771 | 2.37662 | ||||||||
\(767\) | 0.583592 | 0.0210723 | ||||||||
\(768\) | 14.5623 | 0.525472 | ||||||||
\(769\) | 35.4164 | 1.27715 | 0.638574 | − | 0.769560i | \(-0.279525\pi\) | ||||
0.638574 | + | 0.769560i | \(0.279525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.47214 | −0.305117 | ||||||||
\(772\) | −2.02129 | −0.0727477 | ||||||||
\(773\) | 34.9443 | 1.25686 | 0.628429 | − | 0.777867i | \(-0.283698\pi\) | ||||
0.628429 | + | 0.777867i | \(0.283698\pi\) | |||||||
\(774\) | 21.5623 | 0.775041 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 93.1935 | 3.34545 | ||||||||
\(777\) | 5.47214 | 0.196312 | ||||||||
\(778\) | 4.61803 | 0.165565 | ||||||||
\(779\) | 25.8885 | 0.927553 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.88854 | 0.103360 | ||||||||
\(782\) | 100.902 | 3.60824 | ||||||||
\(783\) | −4.70820 | −0.168257 | ||||||||
\(784\) | 9.85410 | 0.351932 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.2361 | −0.400777 | ||||||||
\(787\) | −38.7639 | −1.38178 | −0.690892 | − | 0.722958i | \(-0.742782\pi\) | ||||
−0.690892 | + | 0.722958i | \(0.742782\pi\) | |||||||
\(788\) | 27.9787 | 0.996700 | ||||||||
\(789\) | 2.05573 | 0.0731859 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.2361 | 0.577288 | ||||||||
\(792\) | 40.8885 | 1.45291 | ||||||||
\(793\) | 11.7771 | 0.418217 | ||||||||
\(794\) | −47.1246 | −1.67239 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −77.6656 | −2.75279 | ||||||||
\(797\) | 40.0689 | 1.41931 | 0.709656 | − | 0.704548i | \(-0.248850\pi\) | ||||
0.709656 | + | 0.704548i | \(0.248850\pi\) | |||||||
\(798\) | −8.47214 | −0.299910 | ||||||||
\(799\) | −55.7771 | −1.97325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.70820 | −0.201689 | ||||||||
\(802\) | 69.9230 | 2.46907 | ||||||||
\(803\) | 6.76393 | 0.238694 | ||||||||
\(804\) | −13.1459 | −0.463620 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.94427 | 0.315049 | ||||||||
\(807\) | 28.4721 | 1.00227 | ||||||||
\(808\) | 32.0689 | 1.12818 | ||||||||
\(809\) | −6.81966 | −0.239766 | −0.119883 | − | 0.992788i | \(-0.538252\pi\) | ||||
−0.119883 | + | 0.992788i | \(0.538252\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.00000 | −0.210688 | −0.105344 | − | 0.994436i | \(-0.533594\pi\) | ||||
−0.105344 | + | 0.994436i | \(0.533594\pi\) | |||||||
\(812\) | 22.8541 | 0.802022 | ||||||||
\(813\) | −23.2361 | −0.814924 | ||||||||
\(814\) | −78.3951 | −2.74775 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −75.9574 | −2.65904 | ||||||||
\(817\) | 26.6525 | 0.932452 | ||||||||
\(818\) | 21.4164 | 0.748807 | ||||||||
\(819\) | −0.763932 | −0.0266939 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.9443 | −0.381958 | −0.190979 | − | 0.981594i | \(-0.561166\pi\) | ||||
−0.190979 | + | 0.981594i | \(0.561166\pi\) | |||||||
\(822\) | 1.23607 | 0.0431128 | ||||||||
\(823\) | 44.0132 | 1.53420 | 0.767101 | − | 0.641526i | \(-0.221698\pi\) | ||||
0.767101 | + | 0.641526i | \(0.221698\pi\) | |||||||
\(824\) | 72.5410 | 2.52709 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.00000 | 0.0695889 | ||||||||
\(827\) | −31.9443 | −1.11081 | −0.555406 | − | 0.831580i | \(-0.687437\pi\) | ||||
−0.555406 | + | 0.831580i | \(0.687437\pi\) | |||||||
\(828\) | −24.2705 | −0.843459 | ||||||||
\(829\) | 26.7639 | 0.929550 | 0.464775 | − | 0.885429i | \(-0.346135\pi\) | ||||
0.464775 | + | 0.885429i | \(0.346135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.8885 | −0.551167 | ||||||||
\(832\) | −6.65248 | −0.230633 | ||||||||
\(833\) | 7.70820 | 0.267073 | ||||||||
\(834\) | 9.70820 | 0.336168 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 85.9574 | 2.97290 | ||||||||
\(837\) | −4.47214 | −0.154580 | ||||||||
\(838\) | −23.7082 | −0.818986 | ||||||||
\(839\) | 27.1246 | 0.936446 | 0.468223 | − | 0.883610i | \(-0.344894\pi\) | ||||
0.468223 | + | 0.883610i | \(0.344894\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.83282 | −0.235614 | ||||||||
\(842\) | 1.09017 | 0.0375697 | ||||||||
\(843\) | −13.6525 | −0.470216 | ||||||||
\(844\) | 62.8328 | 2.16279 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.9443 | 0.651317 | ||||||||
\(847\) | 18.9443 | 0.650933 | ||||||||
\(848\) | −4.65248 | −0.159767 | ||||||||
\(849\) | −13.4164 | −0.460450 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.3607 | 0.937912 | ||||||||
\(852\) | 2.56231 | 0.0877832 | ||||||||
\(853\) | −52.3607 | −1.79280 | −0.896398 | − | 0.443251i | \(-0.853825\pi\) | ||||
−0.896398 | + | 0.443251i | \(0.853825\pi\) | |||||||
\(854\) | 40.3607 | 1.38111 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.9443 | −1.26273 | ||||||||
\(857\) | −39.4164 | −1.34644 | −0.673219 | − | 0.739443i | \(-0.735089\pi\) | ||||
−0.673219 | + | 0.739443i | \(0.735089\pi\) | |||||||
\(858\) | 10.9443 | 0.373631 | ||||||||
\(859\) | −0.472136 | −0.0161091 | −0.00805454 | − | 0.999968i | \(-0.502564\pi\) | ||||
−0.00805454 | + | 0.999968i | \(0.502564\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.00000 | 0.272639 | ||||||||
\(862\) | −88.7214 | −3.02186 | ||||||||
\(863\) | −2.05573 | −0.0699778 | −0.0349889 | − | 0.999388i | \(-0.511140\pi\) | ||||
−0.0349889 | + | 0.999388i | \(0.511140\pi\) | |||||||
\(864\) | 10.8541 | 0.369264 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 97.6656 | 3.31881 | ||||||||
\(867\) | −42.4164 | −1.44054 | ||||||||
\(868\) | 21.7082 | 0.736824 | ||||||||
\(869\) | −9.65248 | −0.327438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.06888 | −0.0701015 | ||||||||
\(872\) | 47.9443 | 1.62360 | ||||||||
\(873\) | −12.4721 | −0.422118 | ||||||||
\(874\) | −42.3607 | −1.43287 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | −6.00000 | −0.202606 | −0.101303 | − | 0.994856i | \(-0.532301\pi\) | ||||
−0.101303 | + | 0.994856i | \(0.532301\pi\) | |||||||
\(878\) | 29.4164 | 0.992756 | ||||||||
\(879\) | −26.6525 | −0.898966 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.3607 | −1.29240 | −0.646202 | − | 0.763166i | \(-0.723644\pi\) | ||||
−0.646202 | + | 0.763166i | \(0.723644\pi\) | |||||||
\(882\) | −2.61803 | −0.0881538 | ||||||||
\(883\) | −34.2361 | −1.15214 | −0.576068 | − | 0.817402i | \(-0.695414\pi\) | ||||
−0.576068 | + | 0.817402i | \(0.695414\pi\) | |||||||
\(884\) | −28.5836 | −0.961370 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.9443 | 1.10678 | ||||||||
\(887\) | 15.4164 | 0.517632 | 0.258816 | − | 0.965927i | \(-0.416668\pi\) | ||||
0.258816 | + | 0.965927i | \(0.416668\pi\) | |||||||
\(888\) | −40.8885 | −1.37213 | ||||||||
\(889\) | 12.2361 | 0.410385 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.47214 | −0.183323 | ||||||||
\(892\) | 6.00000 | 0.200895 | ||||||||
\(893\) | 23.4164 | 0.783600 | ||||||||
\(894\) | 21.5623 | 0.721151 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.09017 | −0.0364200 | ||||||||
\(897\) | −3.81966 | −0.127535 | ||||||||
\(898\) | −8.61803 | −0.287588 | ||||||||
\(899\) | 21.0557 | 0.702248 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.63932 | −0.121243 | ||||||||
\(902\) | −114.610 | −3.81609 | ||||||||
\(903\) | 8.23607 | 0.274079 | ||||||||
\(904\) | −121.318 | −4.03498 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.38197 | 0.112358 | ||||||||
\(907\) | 16.3607 | 0.543247 | 0.271624 | − | 0.962404i | \(-0.412439\pi\) | ||||
0.271624 | + | 0.962404i | \(0.412439\pi\) | |||||||
\(908\) | 23.1246 | 0.767417 | ||||||||
\(909\) | −4.29180 | −0.142350 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.58359 | 0.251256 | 0.125628 | − | 0.992077i | \(-0.459905\pi\) | ||||
0.125628 | + | 0.992077i | \(0.459905\pi\) | |||||||
\(912\) | 31.8885 | 1.05594 | ||||||||
\(913\) | 68.2492 | 2.25872 | ||||||||
\(914\) | −77.1591 | −2.55219 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 108.541 | 3.58630 | ||||||||
\(917\) | −4.29180 | −0.141728 | ||||||||
\(918\) | 20.1803 | 0.666050 | ||||||||
\(919\) | 36.0132 | 1.18796 | 0.593982 | − | 0.804478i | \(-0.297555\pi\) | ||||
0.593982 | + | 0.804478i | \(0.297555\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.6525 | 0.812327 | ||||||||
\(922\) | −27.8885 | −0.918460 | ||||||||
\(923\) | 0.403252 | 0.0132732 | ||||||||
\(924\) | 26.5623 | 0.873836 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 74.2492 | 2.43998 | ||||||||
\(927\) | −9.70820 | −0.318859 | ||||||||
\(928\) | −51.1033 | −1.67755 | ||||||||
\(929\) | −30.1803 | −0.990185 | −0.495092 | − | 0.868840i | \(-0.664866\pi\) | ||||
−0.495092 | + | 0.868840i | \(0.664866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.23607 | −0.106058 | ||||||||
\(932\) | −35.3951 | −1.15941 | ||||||||
\(933\) | −13.2361 | −0.433329 | ||||||||
\(934\) | 62.5410 | 2.04640 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.70820 | 0.186578 | ||||||||
\(937\) | −4.36068 | −0.142457 | −0.0712286 | − | 0.997460i | \(-0.522692\pi\) | ||||
−0.0712286 | + | 0.997460i | \(0.522692\pi\) | |||||||
\(938\) | −7.09017 | −0.231502 | ||||||||
\(939\) | −5.70820 | −0.186280 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.8328 | 1.46151 | 0.730754 | − | 0.682641i | \(-0.239169\pi\) | ||||
0.730754 | + | 0.682641i | \(0.239169\pi\) | |||||||
\(942\) | −44.3607 | −1.44535 | ||||||||
\(943\) | 40.0000 | 1.30258 | ||||||||
\(944\) | −7.52786 | −0.245011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −117.992 | −3.83625 | ||||||||
\(947\) | −32.9443 | −1.07054 | −0.535272 | − | 0.844679i | \(-0.679791\pi\) | ||||
−0.535272 | + | 0.844679i | \(0.679791\pi\) | |||||||
\(948\) | −8.56231 | −0.278091 | ||||||||
\(949\) | 0.944272 | 0.0306524 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.6525 | 0.572421 | ||||||||
\(952\) | −57.5967 | −1.86672 | ||||||||
\(953\) | −16.1246 | −0.522327 | −0.261164 | − | 0.965295i | \(-0.584106\pi\) | ||||
−0.261164 | + | 0.965295i | \(0.584106\pi\) | |||||||
\(954\) | 1.23607 | 0.0400192 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −137.666 | −4.45242 | ||||||||
\(957\) | 25.7639 | 0.832830 | ||||||||
\(958\) | 60.8328 | 1.96542 | ||||||||
\(959\) | 0.472136 | 0.0152461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0000 | −0.354839 | ||||||||
\(962\) | −10.9443 | −0.352857 | ||||||||
\(963\) | 4.94427 | 0.159327 | ||||||||
\(964\) | 93.3738 | 3.00737 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.0902 | −0.421169 | ||||||||
\(967\) | 2.11146 | 0.0678999 | 0.0339499 | − | 0.999424i | \(-0.489191\pi\) | ||||
0.0339499 | + | 0.999424i | \(0.489191\pi\) | |||||||
\(968\) | −141.554 | −4.54972 | ||||||||
\(969\) | 24.9443 | 0.801325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.5967 | 0.372157 | 0.186079 | − | 0.982535i | \(-0.440422\pi\) | ||||
0.186079 | + | 0.982535i | \(0.440422\pi\) | |||||||
\(972\) | −4.85410 | −0.155695 | ||||||||
\(973\) | 3.70820 | 0.118880 | ||||||||
\(974\) | −17.8541 | −0.572082 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −151.915 | −4.86268 | ||||||||
\(977\) | −3.29180 | −0.105314 | −0.0526569 | − | 0.998613i | \(-0.516769\pi\) | ||||
−0.0526569 | + | 0.998613i | \(0.516769\pi\) | |||||||
\(978\) | −48.3607 | −1.54640 | ||||||||
\(979\) | 31.2361 | 0.998309 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.41641 | −0.204860 | ||||||||
\(982\) | 1.38197 | 0.0441003 | ||||||||
\(983\) | 2.58359 | 0.0824038 | 0.0412019 | − | 0.999151i | \(-0.486881\pi\) | ||||
0.0412019 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(984\) | −59.7771 | −1.90562 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −95.0132 | −3.02584 | ||||||||
\(987\) | 7.23607 | 0.230327 | ||||||||
\(988\) | 12.0000 | 0.381771 | ||||||||
\(989\) | 41.1803 | 1.30946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.59675 | 0.273085 | 0.136542 | − | 0.990634i | \(-0.456401\pi\) | ||||
0.136542 | + | 0.990634i | \(0.456401\pi\) | |||||||
\(992\) | −48.5410 | −1.54118 | ||||||||
\(993\) | −13.7639 | −0.436785 | ||||||||
\(994\) | 1.38197 | 0.0438333 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 60.5410 | 1.91832 | ||||||||
\(997\) | −52.5410 | −1.66399 | −0.831995 | − | 0.554783i | \(-0.812801\pi\) | ||||
−0.831995 | + | 0.554783i | \(0.812801\pi\) | |||||||
\(998\) | 83.1935 | 2.63344 | ||||||||
\(999\) | 5.47214 | 0.173131 |
(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 | 525.2.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1575.2.a.v.1.2 | 2 | |||
4.3 | odd | 2 | 8400.2.a.da.1.2 | 2 | |||
5.2 | odd | 4 | 525.2.d.e.274.1 | 4 | |||
5.3 | odd | 4 | 525.2.d.e.274.4 | 4 | |||
5.4 | even | 2 | 525.2.a.i.1.2 | yes | 2 | ||
7.6 | odd | 2 | 3675.2.a.r.1.1 | 2 | |||
15.2 | even | 4 | 1575.2.d.f.1324.4 | 4 | |||
15.8 | even | 4 | 1575.2.d.f.1324.1 | 4 | |||
15.14 | odd | 2 | 1575.2.a.l.1.1 | 2 | |||
20.19 | odd | 2 | 8400.2.a.cy.1.2 | 2 | |||
35.34 | odd | 2 | 3675.2.a.bh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
525.2.a.i.1.2 | yes | 2 | 5.4 | even | 2 | ||
525.2.d.e.274.1 | 4 | 5.2 | odd | 4 | |||
525.2.d.e.274.4 | 4 | 5.3 | odd | 4 | |||
1575.2.a.l.1.1 | 2 | 15.14 | odd | 2 | |||
1575.2.a.v.1.2 | 2 | 3.2 | odd | 2 | |||
1575.2.d.f.1324.1 | 4 | 15.8 | even | 4 | |||
1575.2.d.f.1324.4 | 4 | 15.2 | even | 4 | |||
3675.2.a.r.1.1 | 2 | 7.6 | odd | 2 | |||
3675.2.a.bh.1.2 | 2 | 35.34 | odd | 2 | |||
8400.2.a.cy.1.2 | 2 | 20.19 | odd | 2 | |||
8400.2.a.da.1.2 | 2 | 4.3 | odd | 2 |