Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(881,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.q (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{6} - 2x^{5} + 48x^{4} - 7x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(0.232322 + 0.402393i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.961 |
Dual form | 1520.2.q.l.881.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.232322 | + | 0.402393i | −0.134131 | + | 0.232322i | −0.925265 | − | 0.379321i | \(-0.876158\pi\) |
0.791134 | + | 0.611643i | \(0.209491\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.83973 | 1.82925 | 0.914624 | − | 0.404306i | \(-0.132487\pi\) | ||||
0.914624 | + | 0.404306i | \(0.132487\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.39205 | + | 2.41111i | 0.464018 | + | 0.803702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.46464 | 0.743118 | 0.371559 | − | 0.928409i | \(-0.378823\pi\) | ||||
0.371559 | + | 0.928409i | \(0.378823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.23583 | + | 3.87256i | 0.620107 | + | 1.07406i | 0.989465 | + | 0.144769i | \(0.0462440\pi\) |
−0.369359 | + | 0.929287i | \(0.620423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.232322 | + | 0.402393i | 0.0599852 | + | 0.103897i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.30842 | + | 2.26624i | −0.317338 | + | 0.549645i | −0.979932 | − | 0.199334i | \(-0.936122\pi\) |
0.662594 | + | 0.748979i | \(0.269455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.851316 | − | 4.27496i | 0.195305 | − | 0.980743i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.12437 | + | 1.94747i | −0.245359 | + | 0.424974i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.927410 | − | 1.60632i | −0.193378 | − | 0.334941i | 0.752989 | − | 0.658033i | \(-0.228611\pi\) |
−0.946368 | + | 0.323092i | \(0.895278\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.68755 | −0.517218 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.19696 | + | 3.80525i | 0.407966 | + | 0.706618i | 0.994662 | − | 0.103190i | \(-0.0329048\pi\) |
−0.586696 | + | 0.809808i | \(0.699571\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.61683 | −1.54763 | −0.773814 | − | 0.633412i | \(-0.781654\pi\) | ||||
−0.773814 | + | 0.633412i | \(0.781654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.572590 | + | 0.991755i | −0.0996751 | + | 0.172642i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.41987 | − | 4.19133i | 0.409032 | − | 0.708465i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.76902 | −0.948421 | −0.474211 | − | 0.880411i | \(-0.657266\pi\) | ||||
−0.474211 | + | 0.880411i | \(0.657266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.07772 | −0.332702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.62034 | + | 4.53856i | −0.409228 | + | 0.708803i | −0.994803 | − | 0.101814i | \(-0.967535\pi\) |
0.585576 | + | 0.810618i | \(0.300869\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.74337 | − | 4.75165i | 0.418360 | − | 0.724621i | −0.577415 | − | 0.816451i | \(-0.695938\pi\) |
0.995775 | + | 0.0918304i | \(0.0292718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.78411 | 0.415030 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.20397 | + | 9.01355i | 0.759078 | + | 1.31476i | 0.943321 | + | 0.331880i | \(0.107683\pi\) |
−0.184244 | + | 0.982881i | \(0.558984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.4230 | 2.34615 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.607947 | − | 1.05299i | −0.0851296 | − | 0.147449i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.94033 | − | 5.09281i | −0.403886 | − | 0.699551i | 0.590305 | − | 0.807180i | \(-0.299007\pi\) |
−0.994191 | + | 0.107629i | \(0.965674\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.23232 | − | 2.13444i | 0.166166 | − | 0.287808i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.52243 | + | 1.33573i | 0.201651 | + | 0.176922i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.531852 | + | 0.921195i | −0.0692412 | + | 0.119929i | −0.898568 | − | 0.438835i | \(-0.855391\pi\) |
0.829326 | + | 0.558765i | \(0.188724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.07556 | − | 12.2552i | −0.905933 | − | 1.56912i | −0.819660 | − | 0.572850i | \(-0.805838\pi\) |
−0.0862726 | − | 0.996272i | \(-0.527496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.73717 | + | 11.6691i | 0.848804 | + | 1.47017i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47165 | 0.554640 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.98458 | − | 10.3656i | −0.731132 | − | 1.26636i | −0.956400 | − | 0.292061i | \(-0.905659\pi\) |
0.225267 | − | 0.974297i | \(-0.427674\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.861830 | 0.103752 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.201003 | − | 0.348147i | 0.0238546 | − | 0.0413175i | −0.853852 | − | 0.520516i | \(-0.825739\pi\) |
0.877706 | + | 0.479199i | \(0.159073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.49596 | + | 9.51929i | −0.643254 | + | 1.11415i | 0.341448 | + | 0.939901i | \(0.389083\pi\) |
−0.984702 | + | 0.174247i | \(0.944251\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.464643 | 0.0536524 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.9282 | 1.35935 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.76902 | − | 9.99224i | 0.649066 | − | 1.12421i | −0.334281 | − | 0.942474i | \(-0.608493\pi\) |
0.983346 | − | 0.181741i | \(-0.0581733\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.55179 | + | 6.15187i | −0.394643 | + | 0.683541i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.6050 | 1.71287 | 0.856436 | − | 0.516253i | \(-0.172674\pi\) | ||||
0.856436 | + | 0.516253i | \(0.172674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.30842 | + | 2.26624i | 0.141918 | + | 0.245809i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.04161 | −0.218884 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.30438 | + | 5.72335i | 0.350263 | + | 0.606674i | 0.986295 | − | 0.164989i | \(-0.0527587\pi\) |
−0.636032 | + | 0.771663i | \(0.719425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8208 | + | 18.7422i | 1.13433 | + | 1.96471i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00188 | − | 3.46735i | 0.207585 | − | 0.359548i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.27656 | − | 2.87474i | −0.336168 | − | 0.294942i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.60741 | − | 7.98027i | 0.467812 | − | 0.810274i | −0.531512 | − | 0.847051i | \(-0.678376\pi\) |
0.999323 | + | 0.0367770i | \(0.0117091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.43091 | + | 5.94252i | 0.344820 | + | 0.597246i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.46061 | + | 11.1901i | 0.642854 | + | 1.11346i | 0.984793 | + | 0.173734i | \(0.0555832\pi\) |
−0.341938 | + | 0.939722i | \(0.611083\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.32715 | −0.130768 | −0.0653840 | − | 0.997860i | \(-0.520827\pi\) | ||||
−0.0653840 | + | 0.997860i | \(0.520827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.12437 | + | 1.94747i | 0.109728 | + | 0.190054i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.30813 | −0.223135 | −0.111568 | − | 0.993757i | \(-0.535587\pi\) | ||||
−0.111568 | + | 0.993757i | \(0.535587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.888549 | − | 1.53901i | 0.0851075 | − | 0.147411i | −0.820330 | − | 0.571891i | \(-0.806210\pi\) |
0.905437 | + | 0.424481i | \(0.139543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.34027 | − | 2.32141i | 0.127213 | − | 0.220339i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0328566 | 0.00309089 | 0.00154544 | − | 0.999999i | \(-0.499508\pi\) | ||||
0.00154544 | + | 0.999999i | \(0.499508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.85482 | −0.172963 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.22478 | + | 10.7816i | −0.575481 | + | 0.996762i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.33239 | + | 10.9680i | −0.580489 | + | 1.00544i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.92553 | −0.447776 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.21752 | − | 2.10881i | −0.109780 | − | 0.190145i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.31245 | + | 2.27324i | 0.116461 | + | 0.201717i | 0.918363 | − | 0.395739i | \(-0.129512\pi\) |
−0.801902 | + | 0.597456i | \(0.796178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.27469 | + | 2.20782i | 0.112230 | + | 0.194388i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.24525 | + | 5.62093i | −0.283538 | + | 0.491103i | −0.972254 | − | 0.233929i | \(-0.924842\pi\) |
0.688715 | + | 0.725032i | \(0.258175\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.12014 | − | 20.6897i | 0.357262 | − | 1.79402i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.34377 | + | 2.32748i | −0.115654 | + | 0.200318i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.93683 | + | 3.35469i | 0.165474 | + | 0.286610i | 0.936824 | − | 0.349802i | \(-0.113751\pi\) |
−0.771349 | + | 0.636412i | \(0.780418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.596561 | − | 1.03327i | −0.0505996 | − | 0.0876411i | 0.839616 | − | 0.543180i | \(-0.182780\pi\) |
−0.890216 | + | 0.455539i | \(0.849447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.83598 | −0.407263 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.51051 | + | 9.54449i | 0.460812 | + | 0.798150i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.39393 | 0.364896 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.81543 | + | 6.60851i | −0.314691 | + | 0.545061i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.71152 | − | 6.42854i | 0.304059 | − | 0.526646i | −0.672992 | − | 0.739650i | \(-0.734991\pi\) |
0.977051 | + | 0.213003i | \(0.0683246\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.16727 | 0.339128 | 0.169564 | − | 0.985519i | \(-0.445764\pi\) | ||||
0.169564 | + | 0.985519i | \(0.445764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.28554 | −0.589001 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.30842 | + | 7.46240i | −0.346060 | + | 0.599394i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.51830 | − | 7.82593i | 0.360600 | − | 0.624577i | −0.627460 | − | 0.778649i | \(-0.715905\pi\) |
0.988060 | + | 0.154072i | \(0.0492386\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.73241 | 0.216694 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.48842 | − | 7.77417i | −0.353737 | − | 0.612690i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.15920 | 0.404100 | 0.202050 | − | 0.979375i | \(-0.435240\pi\) | ||||
0.202050 | + | 0.979375i | \(0.435240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.572590 | + | 0.991755i | 0.0445761 | + | 0.0772080i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.49058 | + | 7.77791i | 0.347492 | + | 0.601873i | 0.985803 | − | 0.167905i | \(-0.0537002\pi\) |
−0.638312 | + | 0.769778i | \(0.720367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.49784 | + | 6.05843i | −0.269064 | + | 0.466033i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.4925 | − | 3.89836i | 0.878850 | − | 0.298115i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0437 | − | 20.8603i | 0.915666 | − | 1.58598i | 0.109743 | − | 0.993960i | \(-0.464997\pi\) |
0.805923 | − | 0.592020i | \(-0.201670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.41987 | − | 4.19133i | −0.182925 | − | 0.316835i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.247121 | − | 0.428027i | −0.0185748 | − | 0.0321725i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7938 | −1.62895 | −0.814473 | − | 0.580202i | \(-0.802974\pi\) | ||||
−0.814473 | + | 0.580202i | \(0.802974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1014 | − | 17.4962i | −0.750832 | − | 1.30048i | −0.947420 | − | 0.319993i | \(-0.896320\pi\) |
0.196588 | − | 0.980486i | \(-0.437014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.57522 | 0.486054 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.88451 | + | 4.99612i | −0.212073 | + | 0.367322i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.22478 | + | 5.58548i | −0.235819 | + | 0.408451i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.0070 | −0.946121 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.5926 | −1.77946 | −0.889729 | − | 0.456489i | \(-0.849107\pi\) | ||||
−0.889729 | + | 0.456489i | \(0.849107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.71743 | + | 4.70673i | −0.195605 | + | 0.338798i | −0.947099 | − | 0.320943i | \(-0.896000\pi\) |
0.751494 | + | 0.659740i | \(0.229334\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.03886 | + | 1.79936i | −0.0743944 | + | 0.128855i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.30706 | 0.663101 | 0.331550 | − | 0.943438i | \(-0.392428\pi\) | ||||
0.331550 | + | 0.943438i | \(0.392428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.11145 | − | 10.5853i | −0.433229 | − | 0.750375i | 0.563920 | − | 0.825829i | \(-0.309293\pi\) |
−0.997149 | + | 0.0754543i | \(0.975959\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.56139 | 0.392270 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.6327 | + | 18.4164i | 0.746271 | + | 1.29258i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.62034 | + | 4.53856i | 0.183012 | + | 0.316987i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.58201 | − | 4.47217i | 0.179462 | − | 0.310837i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.09819 | − | 10.5362i | 0.145135 | − | 0.728807i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.56821 | + | 13.1085i | −0.521017 | + | 0.902428i | 0.478684 | + | 0.877987i | \(0.341114\pi\) |
−0.999701 | + | 0.0244412i | \(0.992219\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0933946 | + | 0.161764i | 0.00639929 | + | 0.0110839i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.74337 | − | 4.75165i | −0.187096 | − | 0.324060i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −41.7032 | −2.83100 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.55366 | − | 4.42307i | −0.172560 | − | 0.298883i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.7016 | −0.787132 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1532 | − | 22.7820i | 0.880803 | − | 1.52560i | 0.0303532 | − | 0.999539i | \(-0.490337\pi\) |
0.850450 | − | 0.526056i | \(-0.176330\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.39205 | − | 2.41111i | 0.0928036 | − | 0.160740i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.528347 | 0.0350677 | 0.0175338 | − | 0.999846i | \(-0.494419\pi\) | ||||
0.0175338 | + | 0.999846i | \(0.494419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.83906 | −0.518020 | −0.259010 | − | 0.965875i | \(-0.583396\pi\) | ||||
−0.259010 | + | 0.965875i | \(0.583396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.77118 | + | 4.79983i | −0.182330 | + | 0.315806i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0680 | − | 22.6345i | 0.856114 | − | 1.48283i | −0.0194930 | − | 0.999810i | \(-0.506205\pi\) |
0.875607 | − | 0.483024i | \(-0.160461\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4079 | 0.678940 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.68054 | + | 4.64283i | 0.174120 | + | 0.301584i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8785 | −1.15647 | −0.578233 | − | 0.815872i | \(-0.696258\pi\) | ||||
−0.578233 | + | 0.815872i | \(0.696258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2631 | + | 26.4365i | 0.983183 | + | 1.70292i | 0.649747 | + | 0.760150i | \(0.274875\pi\) |
0.333436 | + | 0.942773i | \(0.391792\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.68163 | − | 9.84087i | −0.364477 | − | 0.631292i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.21152 | − | 14.2228i | 0.524615 | − | 0.908659i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.4584 | − | 6.26129i | 1.17448 | − | 0.398396i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.62538 | + | 6.27934i | −0.229749 | + | 0.397937i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.16862 | − | 10.6844i | −0.389360 | − | 0.674391i | 0.603004 | − | 0.797738i | \(-0.293970\pi\) |
−0.992364 | + | 0.123348i | \(0.960637\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.28574 | − | 3.95901i | −0.143703 | − | 0.248901i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.21589 | −0.0761422 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.82331 | + | 11.8183i | 0.425626 | + | 0.737206i | 0.996479 | − | 0.0838465i | \(-0.0267205\pi\) |
−0.570853 | + | 0.821053i | \(0.693387\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.9205 | −1.73490 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.11658 | + | 10.5942i | −0.378607 | + | 0.655767i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2407 | − | 19.4694i | 0.693130 | − | 1.20054i | −0.277678 | − | 0.960674i | \(-0.589565\pi\) |
0.970807 | − | 0.239861i | \(-0.0771020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.88067 | −0.361247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.07071 | −0.187925 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.52944 | − | 4.38112i | 0.154223 | − | 0.267122i | −0.778553 | − | 0.627579i | \(-0.784046\pi\) |
0.932776 | + | 0.360457i | \(0.117379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.76715 | − | 8.25694i | 0.289583 | − | 0.501573i | −0.684127 | − | 0.729363i | \(-0.739817\pi\) |
0.973710 | + | 0.227790i | \(0.0731499\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.0556 | −0.608594 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.23232 | − | 2.13444i | −0.0743118 | − | 0.128712i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.70099 | −0.582876 | −0.291438 | − | 0.956590i | \(-0.594134\pi\) | ||||
−0.291438 | + | 0.956590i | \(0.594134\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.9951 | − | 20.7761i | −0.718127 | − | 1.24383i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4619 | − | 21.5847i | −0.743417 | − | 1.28764i | −0.950930 | − | 0.309405i | \(-0.899870\pi\) |
0.207513 | − | 0.978232i | \(-0.433463\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.26922 | − | 7.39450i | 0.253779 | − | 0.439557i | −0.710784 | − | 0.703410i | \(-0.751660\pi\) |
0.964563 | + | 0.263852i | \(0.0849932\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.91799 | − | 0.650602i | 0.113612 | − | 0.0385383i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.6817 | + | 21.9654i | −0.748579 | + | 1.29658i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.07609 | + | 8.79205i | 0.298594 | + | 0.517180i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.14080 | + | 3.70798i | 0.125496 | + | 0.217366i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.5698 | 1.49381 | 0.746903 | − | 0.664933i | \(-0.231540\pi\) | ||||
0.746903 | + | 0.664933i | \(0.231540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.531852 | + | 0.921195i | 0.0309656 | + | 0.0536340i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.62384 | −0.384354 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.14706 | − | 7.18291i | 0.239830 | − | 0.415399i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.2772 | − | 22.9967i | 0.765284 | − | 1.32551i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.00375 | −0.344907 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.1511 | −0.810291 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.86424 | + | 10.1572i | −0.334690 | + | 0.579700i | −0.983425 | − | 0.181314i | \(-0.941965\pi\) |
0.648735 | + | 0.761014i | \(0.275298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.308326 | − | 0.534035i | 0.0175400 | − | 0.0303802i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.2238 | −1.43031 | −0.715157 | − | 0.698964i | \(-0.753645\pi\) | ||||
−0.715157 | + | 0.698964i | \(0.753645\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.95360 | + | 6.84783i | 0.223470 | + | 0.387062i | 0.955859 | − | 0.293824i | \(-0.0949280\pi\) |
−0.732389 | + | 0.680886i | \(0.761595\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.4743 | 0.759193 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.6387 | − | 21.8909i | −0.709862 | − | 1.22952i | −0.964908 | − | 0.262588i | \(-0.915424\pi\) |
0.255046 | − | 0.966929i | \(-0.417909\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.41473 | + | 9.37860i | 0.303167 | + | 0.525101i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.536229 | − | 0.928775i | 0.0299294 | − | 0.0518392i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.57422 | + | 7.52271i | 0.477082 | + | 0.418575i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.23583 | − | 3.87256i | 0.124021 | − | 0.214811i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.412858 | + | 0.715091i | 0.0228311 | + | 0.0395446i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.1859 | + | 43.6232i | 1.38854 | + | 2.40502i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9915 | 1.04387 | 0.521935 | − | 0.852986i | \(-0.325211\pi\) | ||||
0.521935 | + | 0.852986i | \(0.325211\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.03079 | − | 13.9097i | −0.440084 | − | 0.762248i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.9692 | −0.653945 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.75091 | + | 3.03267i | −0.0953782 | + | 0.165200i | −0.909766 | − | 0.415121i | \(-0.863739\pi\) |
0.814388 | + | 0.580321i | \(0.197073\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.00763330 | + | 0.0132213i | −0.000414584 | + | 0.000718080i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.2374 | −1.15007 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.6050 | 2.46244 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.430915 | − | 0.746366i | 0.0231997 | − | 0.0401830i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.83219 | − | 3.17345i | 0.0983572 | − | 0.170360i | −0.812648 | − | 0.582755i | \(-0.801975\pi\) |
0.911005 | + | 0.412396i | \(0.135308\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.66438 | 0.142621 | 0.0713106 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713106 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.00889 | − | 10.4077i | −0.320731 | − | 0.555522i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2866 | 1.02652 | 0.513261 | − | 0.858232i | \(-0.328437\pi\) | ||||
0.513261 | + | 0.858232i | \(0.328437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.201003 | − | 0.348147i | −0.0106681 | − | 0.0184777i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.94230 | − | 5.09621i | −0.155723 | − | 0.269720i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.26355 | + | 16.0449i | −0.488911 | + | 0.846819i | −0.999919 | − | 0.0127570i | \(-0.995939\pi\) |
0.511007 | + | 0.859576i | \(0.329273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5505 | − | 7.27868i | −0.923712 | − | 0.383088i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.14431 | − | 1.98200i | 0.0600606 | − | 0.104028i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.49596 | + | 9.51929i | 0.287672 | + | 0.498262i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.7782 | − | 18.6684i | −0.562617 | − | 0.974481i | −0.997267 | − | 0.0738819i | \(-0.976461\pi\) |
0.434650 | − | 0.900599i | \(-0.356872\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.5906 | −0.759556 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.2304 | − | 24.6478i | −0.738807 | − | 1.27965i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1257 | −0.834955 | −0.417478 | − | 0.908687i | \(-0.637086\pi\) | ||||
−0.417478 | + | 0.908687i | \(0.637086\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.232322 | − | 0.402393i | 0.0119970 | − | 0.0207795i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.82406 | + | 17.0158i | −0.505965 | + | 0.876357i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.3342 | −0.736296 | −0.368148 | − | 0.929767i | \(-0.620008\pi\) | ||||
−0.368148 | + | 0.929767i | \(0.620008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.21965 | −0.0624843 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.86163 | + | 11.8847i | −0.350613 | + | 0.607280i | −0.986357 | − | 0.164620i | \(-0.947360\pi\) |
0.635744 | + | 0.771900i | \(0.280693\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.96411 | − | 10.3301i | 0.303959 | − | 0.526473i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.2757 | 0.776506 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.97516 | + | 17.2775i | 0.505761 | + | 0.876003i | 0.999978 | + | 0.00666453i | \(0.00212140\pi\) |
−0.494217 | + | 0.869338i | \(0.664545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.85375 | 0.245465 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.50788 | − | 2.61173i | −0.0760625 | − | 0.131744i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.76902 | − | 9.99224i | −0.290271 | − | 0.502764i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.70647 | − | 6.41980i | 0.186023 | − | 0.322201i | −0.757898 | − | 0.652373i | \(-0.773774\pi\) |
0.943921 | + | 0.330172i | \(0.107107\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.36817 | + | 6.46457i | 0.368870 | + | 0.323633i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8241 | + | 27.4082i | −0.790219 | + | 1.36870i | 0.135613 | + | 0.990762i | \(0.456700\pi\) |
−0.925831 | + | 0.377937i | \(0.876634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.2657 | − | 33.3692i | −0.959695 | − | 1.66224i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.55179 | + | 6.15187i | 0.176490 | + | 0.305689i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.2186 | −0.704789 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.95685 | + | 5.12142i | 0.146207 | + | 0.253238i | 0.929823 | − | 0.368008i | \(-0.119960\pi\) |
−0.783616 | + | 0.621246i | \(0.786627\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.79987 | −0.0887810 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.57402 | + | 4.45834i | −0.126659 | + | 0.219381i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.80250 | − | 13.5143i | 0.383010 | − | 0.663392i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.554376 | 0.0271479 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.3620 | 0.994750 | 0.497375 | − | 0.867536i | \(-0.334297\pi\) | ||||
0.497375 | + | 0.867536i | \(0.334297\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.1203 | + | 27.9212i | −0.785657 | + | 1.36080i | 0.142949 | + | 0.989730i | \(0.454342\pi\) |
−0.928606 | + | 0.371068i | \(0.878992\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.4884 | + | 25.0947i | −0.704451 | + | 1.22015i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.61683 | 0.126935 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.2438 | − | 59.3121i | −1.65718 | − | 2.87031i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.12085 | −0.247237 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.08858 | + | 5.34957i | 0.148771 | + | 0.257680i | 0.930774 | − | 0.365596i | \(-0.119135\pi\) |
−0.782002 | + | 0.623276i | \(0.785801\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.5651 | + | 28.6916i | 0.796067 | + | 1.37883i | 0.922160 | + | 0.386810i | \(0.126423\pi\) |
−0.126093 | + | 0.992018i | \(0.540244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.02080 | + | 1.76809i | −0.0489438 | + | 0.0847732i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.65647 | + | 2.59715i | −0.366259 | + | 0.124239i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6735 | − | 25.4152i | 0.700326 | − | 1.21300i | −0.268026 | − | 0.963412i | \(-0.586371\pi\) |
0.968352 | − | 0.249589i | \(-0.0802955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.8617 | + | 39.5977i | 1.08865 | + | 1.88560i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.66520 | − | 2.88422i | −0.0791162 | − | 0.137033i | 0.823753 | − | 0.566949i | \(-0.191876\pi\) |
−0.902869 | + | 0.429916i | \(0.858543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.60876 | 0.313285 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.72453 | + | 2.98698i | 0.0815675 | + | 0.141279i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.8153 | −1.12391 | −0.561957 | − | 0.827166i | \(-0.689951\pi\) | ||||
−0.561957 | + | 0.827166i | \(0.689951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.45820 | + | 11.1859i | −0.304105 | + | 0.526725i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.968148 | + | 1.67688i | −0.0454876 | + | 0.0787868i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.6416 | 1.01457 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.1100 | 0.660038 | 0.330019 | − | 0.943974i | \(-0.392945\pi\) | ||||
0.330019 | + | 0.943974i | \(0.392945\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.51643 | − | 6.09063i | 0.164133 | − | 0.284286i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.0028 | + | 19.0574i | −0.512450 | + | 0.887590i | 0.487445 | + | 0.873153i | \(0.337929\pi\) |
−0.999896 | + | 0.0144366i | \(0.995405\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5860 | −1.00319 | −0.501593 | − | 0.865104i | \(-0.667252\pi\) | ||||
−0.501593 | + | 0.865104i | \(0.667252\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00188 | − | 3.46735i | −0.0928348 | − | 0.160795i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.8705 | −1.33597 | −0.667983 | − | 0.744177i | \(-0.732842\pi\) | ||||
−0.667983 | + | 0.744177i | \(0.732842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.9638 | − | 50.1667i | −1.33742 | − | 2.31648i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.09940 | + | 3.63627i | 0.0967352 | + | 0.167550i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.76143 | − | 11.7111i | 0.310891 | − | 0.538478i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.12788 | + | 1.40022i | −0.189400 | + | 0.0642464i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.18620 | − | 14.1789i | 0.374820 | − | 0.649208i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0121 | + | 19.0734i | 0.503153 | + | 0.871487i | 0.999993 | + | 0.00364517i | \(0.00116030\pi\) |
−0.496840 | + | 0.867842i | \(0.665506\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.8985 | − | 22.3409i | −0.588122 | − | 1.01866i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.17103 | 0.189788 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.60741 | − | 7.98027i | −0.209212 | − | 0.362366i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.28228 | 0.194049 | 0.0970244 | − | 0.995282i | \(-0.469068\pi\) | ||||
0.0970244 | + | 0.995282i | \(0.469068\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.19859 | + | 2.07602i | −0.0542023 | + | 0.0938811i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.78598 | − | 8.28957i | 0.215988 | − | 0.374103i | −0.737589 | − | 0.675249i | \(-0.764036\pi\) |
0.953578 | + | 0.301147i | \(0.0973693\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.4982 | −0.517852 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.86183 | 0.308416 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.972800 | − | 1.68494i | 0.0436361 | − | 0.0755799i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.23045 | + | 9.05940i | −0.234147 | + | 0.405554i | −0.959024 | − | 0.283323i | \(-0.908563\pi\) |
0.724878 | + | 0.688878i | \(0.241896\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.17304 | −0.186437 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.4398 | − | 33.6707i | −0.866778 | − | 1.50130i | −0.865271 | − | 0.501304i | \(-0.832854\pi\) |
−0.00150688 | − | 0.999999i | \(-0.500480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.9212 | 0.574986 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.62525 | − | 2.81501i | −0.0721797 | − | 0.125019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.0656 | − | 20.8982i | −0.534799 | − | 0.926299i | −0.999173 | − | 0.0406595i | \(-0.987054\pi\) |
0.464374 | − | 0.885639i | \(-0.346279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.5990 | + | 46.0708i | −1.17667 | + | 2.03805i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.28795 | + | 11.4891i | −0.101015 | + | 0.507258i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.663575 | + | 1.14935i | −0.0292406 | + | 0.0506462i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.8259 | + | 22.2152i | 0.564084 | + | 0.977022i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.59603 | + | 9.69260i | 0.245638 | + | 0.425458i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.9350 | −1.31148 | −0.655739 | − | 0.754988i | \(-0.727643\pi\) | ||||
−0.655739 | + | 0.754988i | \(0.727643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8964 | + | 22.3372i | 0.563919 | + | 0.976736i | 0.997149 | + | 0.0754529i | \(0.0240402\pi\) |
−0.433231 | + | 0.901283i | \(0.642626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.24875 | 0.0981435 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.2744 | − | 19.5278i | 0.491121 | − | 0.850646i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.77982 | − | 16.9391i | 0.425210 | − | 0.736485i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.96147 | −0.128517 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.4345 | −1.01506 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.15407 | + | 1.99890i | −0.0498946 | + | 0.0864200i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.06317 | − | 8.76967i | 0.218492 | − | 0.378439i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 40.4769 | 1.74346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.61703 | − | 6.26487i | −0.155508 | − | 0.269348i | 0.777736 | − | 0.628591i | \(-0.216368\pi\) |
−0.933244 | + | 0.359243i | \(0.883035\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.38710 | 0.402839 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.888549 | − | 1.53901i | −0.0380612 | − | 0.0659240i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2966 | + | 28.2265i | 0.696792 | + | 1.20688i | 0.969573 | + | 0.244803i | \(0.0787232\pi\) |
−0.272781 | + | 0.962076i | \(0.587943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.6991 | − | 34.1199i | 0.840738 | − | 1.45620i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.1376 | − | 6.15246i | 0.772688 | − | 0.262104i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.9205 | − | 48.3598i | 1.18730 | − | 2.05647i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.34027 | − | 2.32141i | −0.0568912 | − | 0.0985385i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.09637 | + | 7.09511i | 0.173569 | + | 0.300630i | 0.939665 | − | 0.342096i | \(-0.111137\pi\) |
−0.766096 | + | 0.642726i | \(0.777804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.5348 | 1.03771 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.49837 | − | 2.59526i | −0.0632613 | − | 0.109572i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.8105 | −0.666334 | −0.333167 | − | 0.942868i | \(-0.608117\pi\) | ||||
−0.333167 | + | 0.942868i | \(0.608117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.0164283 | − | 0.0284546i | 0.000691144 | − | 0.00119710i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.1897 | + | 29.7734i | −0.721899 | + | 1.25037i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.25519 | 0.387998 | 0.193999 | − | 0.981002i | \(-0.437854\pi\) | ||||
0.193999 | + | 0.981002i | \(0.437854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.4297 | −1.14790 | −0.573948 | − | 0.818892i | \(-0.694589\pi\) | ||||
−0.573948 | + | 0.818892i | \(0.694589\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.71339 | − | 9.89589i | 0.238680 | − | 0.413407i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.927410 | + | 1.60632i | −0.0386757 | + | 0.0669882i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0723 | −1.16867 | −0.584333 | − | 0.811514i | \(-0.698644\pi\) | ||||
−0.584333 | + | 0.811514i | \(0.698644\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.26264 | − | 2.18695i | −0.0524734 | − | 0.0908865i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 75.5241 | 3.13327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.24687 | − | 12.5520i | −0.300135 | − | 0.519849i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.22478 | + | 10.7816i | 0.257363 | + | 0.445766i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.79684 | − | 15.2366i | 0.363084 | − | 0.628880i | −0.625383 | − | 0.780318i | \(-0.715057\pi\) |
0.988467 | + | 0.151438i | \(0.0483904\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.33564 | + | 36.8366i | −0.302260 | + | 1.51783i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.16223 | + | 3.74510i | −0.0889423 | + | 0.154053i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.8011 | + | 41.2248i | 0.977396 | + | 1.69290i | 0.671790 | + | 0.740742i | \(0.265526\pi\) |
0.305606 | + | 0.952158i | \(0.401141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.33239 | + | 10.9680i | 0.259603 | + | 0.449645i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.67929 | 0.232438 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.863420 | + | 1.49549i | 0.0352784 | + | 0.0611040i | 0.883126 | − | 0.469137i | \(-0.155435\pi\) |
−0.847847 | + | 0.530241i | \(0.822102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.8558 | 1.62575 | 0.812875 | − | 0.582438i | \(-0.197901\pi\) | ||||
0.812875 | + | 0.582438i | \(0.197901\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.6617 | − | 28.8589i | 0.678517 | − | 1.17523i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.46277 | + | 4.26564i | −0.100126 | + | 0.173423i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.9801 | −1.54156 | −0.770782 | − | 0.637099i | \(-0.780134\pi\) | ||||
−0.770782 | + | 0.637099i | \(0.780134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.88085 | −0.400392 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.2704 | + | 40.3055i | −0.941418 | + | 1.63058i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.7374 | + | 25.5259i | −0.595237 | + | 1.03098i | 0.398277 | + | 0.917265i | \(0.369608\pi\) |
−0.993513 | + | 0.113715i | \(0.963725\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.43504 | −0.0981904 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4949 | − | 25.1059i | −0.583543 | − | 1.01073i | −0.995055 | − | 0.0993213i | \(-0.968333\pi\) |
0.411513 | − | 0.911404i | \(-0.365001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.61577 | 0.145330 | 0.0726649 | − | 0.997356i | \(-0.476850\pi\) | ||||
0.0726649 | + | 0.997356i | \(0.476850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.49246 | + | 4.31706i | 0.100019 | + | 0.173238i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.9923 | + | 27.6995i | 0.640719 | + | 1.10976i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.75225 | + | 3.29209i | 0.149851 | + | 0.131474i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.54828 | − | 13.0740i | 0.300970 | − | 0.521295i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7603 | + | 34.2258i | 0.786644 | + | 1.36251i | 0.928012 | + | 0.372550i | \(0.121517\pi\) |
−0.141368 | + | 0.989957i | \(0.545150\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.51652 | − | 6.09079i | −0.139769 | − | 0.242087i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.62491 | 0.104166 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.7191 | + | 63.5993i | 1.45486 | + | 2.51989i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.11923 | 0.0442759 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.02540 | − | 6.97221i | 0.158994 | − | 0.275386i | −0.775512 | − | 0.631333i | \(-0.782508\pi\) |
0.934506 | + | 0.355947i | \(0.115842\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.170779 | + | 0.295798i | −0.00673487 | + | 0.0116651i | −0.869373 | − | 0.494156i | \(-0.835477\pi\) |
0.862638 | + | 0.505821i | \(0.168810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.54938 | 0.100382 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.2796 | 0.757959 | 0.378980 | − | 0.925405i | \(-0.376275\pi\) | ||||
0.378980 | + | 0.925405i | \(0.376275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.31083 | + | 2.27042i | −0.0514544 | + | 0.0891217i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.68855 | − | 16.7811i | 0.379724 | − | 0.657702i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.7026 | −0.966689 | −0.483344 | − | 0.875430i | \(-0.660578\pi\) | ||||
−0.483344 | + | 0.875430i | \(0.660578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.24525 | + | 5.62093i | 0.126802 | + | 0.219628i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.6027 | −1.19392 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.96834 | + | 13.8016i | 0.310403 | + | 0.537633i | 0.978450 | − | 0.206486i | \(-0.0662028\pi\) |
−0.668047 | + | 0.744119i | \(0.732869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.7533 | − | 20.3574i | −0.457152 | − | 0.791811i | 0.541657 | − | 0.840600i | \(-0.317797\pi\) |
−0.998809 | + | 0.0487887i | \(0.984464\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.71853 | − | 4.70863i | 0.105579 | − | 0.182868i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.8577 | − | 13.9130i | −0.614935 | − | 0.539522i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.07497 | − | 7.05806i | 0.157784 | − | 0.273289i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.11154 | + | 10.5855i | 0.236286 | + | 0.409259i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.4387 | − | 30.2048i | −0.673215 | − | 1.16604i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.8634 | 0.495850 | 0.247925 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247925 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.34377 | + | 2.32748i | 0.0517218 | + | 0.0895849i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.7369 | 1.68095 | 0.840473 | − | 0.541853i | \(-0.182277\pi\) | ||||
0.840473 | + | 0.541853i | \(0.182277\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.2987 | − | 38.6224i | 0.855744 | − | 1.48219i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.122747 | + | 0.212603i | −0.00470366 | + | 0.00814697i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.6409 | −0.560220 | −0.280110 | − | 0.959968i | \(-0.590371\pi\) | ||||
−0.280110 | + | 0.959968i | \(0.590371\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.87366 | 0.148005 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.82118 | − | 3.15438i | 0.0694824 | − | 0.120347i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.1482 | − | 22.7733i | 0.500905 | − | 0.867592i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.83609 | −0.374182 | −0.187091 | − | 0.982343i | \(-0.559906\pi\) | ||||
−0.187091 | + | 0.982343i | \(0.559906\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.6047 | + | 28.7602i | 0.630761 | + | 1.09251i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.19312 | −0.0452577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.85698 | − | 11.8766i | −0.259727 | − | 0.449860i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.07197 | + | 10.5170i | 0.229663 | + | 0.397788i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.19212 | − | 12.4571i | 0.271643 | − | 0.470499i | −0.697640 | − | 0.716448i | \(-0.745767\pi\) |
0.969283 | + | 0.245950i | \(0.0790998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.91126 | + | 24.6623i | −0.185232 | + | 0.930157i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.41799 | + | 4.18808i | −0.0910668 | + | 0.157732i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.2676 | + | 54.1571i | 1.17594 | + | 2.03679i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.3849 | − | 38.7717i | −0.840682 | − | 1.45610i | −0.889319 | − | 0.457287i | \(-0.848821\pi\) |
0.0486375 | − | 0.998816i | \(-0.484512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.1231 | 1.20471 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.99134 | + | 13.8414i | 0.299278 | + | 0.518365i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.0210 | 0.412163 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.15357 | − | 7.19419i | 0.155118 | − | 0.268672i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.55798 | + | 14.8228i | −0.319159 | + | 0.552799i | −0.980313 | − | 0.197451i | \(-0.936734\pi\) |
0.661154 | + | 0.750250i | \(0.270067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.42305 | −0.239207 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.1838 | −0.527501 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.19696 | − | 3.80525i | 0.0815932 | − | 0.141324i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.77998 | − | 13.4753i | 0.288543 | − | 0.499772i | −0.684919 | − | 0.728619i | \(-0.740162\pi\) |
0.973462 | + | 0.228847i | \(0.0734957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.0308 | −0.593735 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.17894 | + | 12.4343i | 0.265523 | + | 0.459899i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3218 | −0.528986 | −0.264493 | − | 0.964388i | \(-0.585205\pi\) | ||||
−0.264493 | + | 0.964388i | \(0.585205\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.81543 | + | 6.60851i | 0.140734 | + | 0.243759i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.7498 | − | 25.5475i | −0.543318 | − | 0.941054i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.93692 | − | 13.7471i | 0.291964 | − | 0.505697i | −0.682310 | − | 0.731063i | \(-0.739024\pi\) |
0.974274 | + | 0.225366i | \(0.0723578\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.76880 | + | 8.88218i | −0.0649784 | + | 0.326295i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.86539 | + | 13.6233i | −0.288553 | + | 0.499789i | −0.973465 | − | 0.228838i | \(-0.926508\pi\) |
0.684912 | + | 0.728626i | \(0.259841\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.71152 | − | 6.42854i | −0.135979 | − | 0.235523i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.7230 | + | 37.6253i | 0.794803 | + | 1.37664i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.1707 | −0.408170 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.66593 | + | 2.88548i | 0.0607907 | + | 0.105293i | 0.894819 | − | 0.446429i | \(-0.147304\pi\) |
−0.834028 | + | 0.551722i | \(0.813971\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.73241 | 0.208901 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.08364 | − | 3.60897i | 0.0758313 | − | 0.131344i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3582 | − | 23.1371i | 0.485513 | − | 0.840934i | −0.514348 | − | 0.857581i | \(-0.671966\pi\) |
0.999861 | + | 0.0166478i | \(0.00529941\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.12410 | 0.0771000 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.8029 | 0.464106 | 0.232053 | − | 0.972703i | \(-0.425456\pi\) | ||||
0.232053 | + | 0.972703i | \(0.425456\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.30034 | − | 7.44841i | 0.155683 | − | 0.269650i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.64277 | + | 6.30946i | −0.131705 | + | 0.228119i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.75652 | −0.171748 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.95216 | + | 8.57740i | 0.178580 | + | 0.309309i | 0.941394 | − | 0.337308i | \(-0.109516\pi\) |
−0.762815 | + | 0.646617i | \(0.776183\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.34081 | −0.228359 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.5442 | + | 26.9233i | 0.559084 | + | 0.968362i | 0.997573 | + | 0.0696258i | \(0.0221805\pi\) |
−0.438489 | + | 0.898737i | \(0.644486\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.30842 | + | 7.46240i | 0.154763 | + | 0.268057i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.48654 | − | 11.2350i | 0.232703 | − | 0.403054i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.1714 | + | 15.0656i | 0.615229 | + | 0.539780i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.495400 | − | 0.858058i | 0.0177268 | − | 0.0307037i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.90444 | − | 10.2268i | −0.211008 | − | 0.365476i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.51830 | − | 7.82593i | −0.161265 | − | 0.279320i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2780 | 1.04365 | 0.521823 | − | 0.853054i | \(-0.325252\pi\) | ||||
0.521823 | + | 0.853054i | \(0.325252\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.22290 | + | 9.04633i | 0.185940 | + | 0.322058i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.159017 | 0.00565400 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.6395 | − | 54.8011i | 1.12355 | − | 1.94605i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.36621 | − | 2.36634i | 0.0484543 | − | 0.0839254i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.8850 | −1.30653 | −0.653266 | − | 0.757128i | \(-0.726602\pi\) | ||||
−0.653266 | + | 0.757128i | \(0.726602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2359 | −0.963535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.19974 | + | 15.9344i | −0.325057 | + | 0.563015i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.5456 | + | 23.4616i | −0.478013 | + | 0.827943i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.97684 | −0.316392 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.17529 | + | 2.03566i | 0.0413721 | + | 0.0716586i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.3738 | 1.03273 | 0.516365 | − | 0.856369i | \(-0.327285\pi\) | ||||
0.516365 | + | 0.856369i | \(0.327285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8261 | − | 25.6796i | −0.520616 | − | 0.901733i | −0.999713 | − | 0.0239712i | \(-0.992369\pi\) |
0.479097 | − | 0.877762i | \(-0.340964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.21502 | + | 3.83653i | 0.0776842 | + | 0.134553i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.57960 | − | 4.46800i | 0.0903594 | − | 0.156507i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.9776 | − | 15.7729i | −0.628958 | − | 0.551825i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −30.1263 | + | 52.1802i | −1.05270 | + | 1.82333i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.61919 | + | 4.53657i | 0.0914103 | + | 0.158327i | 0.908105 | − | 0.418743i | \(-0.137529\pi\) |
−0.816694 | + | 0.577070i | \(0.804196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.3302 | − | 26.5527i | −0.534378 | − | 0.925570i | −0.999193 | − | 0.0401622i | \(-0.987213\pi\) |
0.464815 | − | 0.885408i | \(-0.346121\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.14518 | 0.0398700 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.0898 | + | 24.4043i | 0.489951 | + | 0.848621i | 0.999933 | − | 0.0115646i | \(-0.00368121\pi\) |
−0.509982 | + | 0.860185i | \(0.670348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.5194 | −0.434817 | −0.217409 | − | 0.976081i | \(-0.569760\pi\) | ||||
−0.217409 | + | 0.976081i | \(0.569760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.25375 | − | 3.90361i | 0.0781817 | − | 0.135415i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.4882 | + | 37.2186i | −0.744521 | + | 1.28955i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.98116 | 0.310806 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.1581 | 0.800462 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.93658 | − | 15.4786i | 0.308525 | − | 0.534381i | −0.669515 | − | 0.742799i | \(-0.733498\pi\) |
0.978040 | + | 0.208418i | \(0.0668313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.84669 | − | 8.39472i | 0.167127 | − | 0.289473i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.5807 | 0.398861 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.49784 | + | 6.05843i | 0.120329 | + | 0.208416i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.8383 | −0.819093 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.98366 | + | 3.43580i | 0.0680791 | + | 0.117916i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.35025 | + | 9.26690i | 0.183404 | + | 0.317665i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5959 | − | 39.1373i | 0.773670 | − | 1.34004i | −0.161869 | − | 0.986812i | \(-0.551752\pi\) |
0.935539 | − | 0.353224i | \(-0.114915\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.37015 | − | 11.9019i | 0.0810575 | − | 0.407038i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.30144 | + | 5.71827i | −0.112775 | + | 0.195332i | −0.916888 | − | 0.399144i | \(-0.869307\pi\) |
0.804113 | + | 0.594476i | \(0.202641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.0508 | + | 36.4610i | 0.718243 | + | 1.24403i | 0.961695 | + | 0.274121i | \(0.0883867\pi\) |
−0.243452 | + | 0.969913i | \(0.578280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.89248 | − | 10.2061i | −0.200815 | − | 0.347822i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.6952 | −0.534272 | −0.267136 | − | 0.963659i | \(-0.586077\pi\) | ||||
−0.267136 | + | 0.963659i | \(0.586077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0437 | − | 20.8603i | −0.409498 | − | 0.709272i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.71715 | −0.160203 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.2186 | − | 24.6273i | 0.482332 | − | 0.835424i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.7609 | − | 46.3513i | 0.906760 | − | 1.57055i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.6551 | 0.868292 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.83973 | −0.163613 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.5532 | + | 25.2069i | −0.491427 | + | 0.851177i | −0.999951 | − | 0.00987081i | \(-0.996858\pi\) |
0.508524 | + | 0.861048i | \(0.330191\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.94042 | + | 10.2891i | −0.200366 | + | 0.347043i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.20417 | −0.242715 | −0.121357 | − | 0.992609i | \(-0.538725\pi\) | ||||
−0.121357 | + | 0.992609i | \(0.538725\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.07393 | − | 15.7165i | −0.305362 | − | 0.528903i | 0.671980 | − | 0.740570i | \(-0.265444\pi\) |
−0.977342 | + | 0.211667i | \(0.932111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.494243 | −0.0166138 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.9630 | − | 31.1129i | −0.603140 | − | 1.04467i | −0.992342 | − | 0.123517i | \(-0.960583\pi\) |
0.389203 | − | 0.921152i | \(-0.372751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.35193 | + | 11.0019i | 0.213037 | + | 0.368991i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.75388 | + | 15.1622i | −0.293266 | + | 0.507952i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.9628 | − | 14.5734i | 1.43769 | − | 0.487680i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.8969 | + | 18.8740i | −0.364243 | + | 0.630888i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.92690 | + | 3.33749i | 0.0643374 | + | 0.111436i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.9309 | − | 32.7892i | −0.631380 | − | 1.09358i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3887 | 0.512673 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.16915 | + | 10.6853i | 0.205296 | + | 0.355584i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.2028 | −0.671564 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.64896 | − | 9.78429i | 0.187571 | − | 0.324882i | −0.756869 | − | 0.653567i | \(-0.773272\pi\) |
0.944440 | + | 0.328685i | \(0.106605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.9870 | + | 31.1544i | −0.596592 | + | 1.03333i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.0643 | 1.29426 | 0.647128 | − | 0.762381i | \(-0.275970\pi\) | ||||
0.647128 | + | 0.762381i | \(0.275970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.4608 | 1.27287 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.28761 | − | 5.69431i | 0.108685 | − | 0.188248i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.7061 | + | 27.2038i | −0.518662 | + | 0.898349i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.92535 | 0.228446 | 0.114223 | − | 0.993455i | \(-0.463562\pi\) | ||||
0.114223 | + | 0.993455i | \(0.463562\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.72478 | − | 4.71946i | −0.0897845 | − | 0.155511i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.79763 | 0.0591697 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.88451 | + | 4.99612i | 0.0948421 | + | 0.164271i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.84746 | − | 3.19990i | −0.0606787 | − | 0.105099i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.16242 | + | 14.1377i | −0.267800 | + | 0.463844i | −0.968293 | − | 0.249815i | \(-0.919630\pi\) |
0.700493 | + | 0.713659i | \(0.252963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.9812 | − | 70.2078i | 0.458215 | − | 2.30097i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.86004 | − | 10.1499i | 0.191849 | − | 0.332293i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.22478 | + | 5.58548i | 0.105462 | + | 0.182665i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.25845 | + | 14.3041i | 0.269792 | + | 0.467293i | 0.968808 | − | 0.247813i | \(-0.0797117\pi\) |
−0.699016 | + | 0.715106i | \(0.746378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.67402 | −0.119897 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.2963 | − | 29.9581i | −0.563843 | − | 0.976605i | −0.997156 | − | 0.0753618i | \(-0.975989\pi\) |
0.433313 | − | 0.901244i | \(-0.357344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.72051 | 0.316543 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.50350 | + | 11.2644i | −0.211559 | + | 0.366431i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.1858 | + | 52.2833i | −0.980906 | + | 1.69898i | −0.322024 | + | 0.946731i | \(0.604363\pi\) |
−0.658881 | + | 0.752247i | \(0.728970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.1521 | −1.59554 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.7450 | 0.380858 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.3138 | + | 24.7922i | −0.463669 | + | 0.803099i | −0.999140 | − | 0.0414547i | \(-0.986801\pi\) |
0.535471 | + | 0.844554i | \(0.320134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.2963 | + | 21.2978i | −0.397899 | + | 0.689181i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.03184 | −0.162656 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.37374 | + | 16.2358i | 0.302694 | + | 0.524281i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.2498 | 1.39515 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.21304 | − | 5.56515i | −0.103539 | − | 0.179334i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.71743 | + | 4.70673i | 0.0874772 | + | 0.151515i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.4268 | − | 21.5238i | 0.399619 | − | 0.692160i | −0.594060 | − | 0.804421i | \(-0.702476\pi\) |
0.993679 | + | 0.112261i | \(0.0358093\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.01906 | + | 1.70252i | −0.161235 | + | 0.0546927i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.1635 | + | 33.1922i | −0.614986 | + | 1.06519i | 0.375401 | + | 0.926863i | \(0.377505\pi\) |
−0.990387 | + | 0.138325i | \(0.955828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.88720 | − | 5.00077i | −0.0925593 | − | 0.160317i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.03886 | + | 1.79936i | 0.0332702 | + | 0.0576257i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.91834 | −0.157352 | −0.0786759 | − | 0.996900i | \(-0.525069\pi\) | ||||
−0.0786759 | + | 0.996900i | \(0.525069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.14411 | + | 14.1060i | 0.260287 | + | 0.450830i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.94763 | 0.157966 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.8685 | − | 36.1452i | 0.665601 | − | 1.15285i | −0.313522 | − | 0.949581i | \(-0.601509\pi\) |
0.979122 | − | 0.203273i | \(-0.0651579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.65353 | − | 8.06015i | 0.148274 | − | 0.256818i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.4049 | −0.744985 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.1769 | −0.323607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.20081 | − | 7.27601i | 0.133443 | − | 0.231130i | −0.791559 | − | 0.611093i | \(-0.790730\pi\) |
0.925002 | + | 0.379963i | \(0.124063\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.41214 | + | 7.64206i | −0.140015 | + | 0.242513i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.2229 | −0.387492 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.6756 | + | 42.7393i | 0.781483 | + | 1.35357i | 0.931078 | + | 0.364821i | \(0.118870\pi\) |
−0.149595 | + | 0.988747i | \(0.547797\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.5045 | 0.490541 |
(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 | 1520.2.q.l.961.2 | 8 | ||
4.3 | odd | 2 | 760.2.q.e.201.3 | yes | 8 | ||
19.7 | even | 3 | inner | 1520.2.q.l.881.2 | 8 | ||
76.7 | odd | 6 | 760.2.q.e.121.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.q.e.121.3 | ✓ | 8 | 76.7 | odd | 6 | ||
760.2.q.e.201.3 | yes | 8 | 4.3 | odd | 2 | ||
1520.2.q.l.881.2 | 8 | 19.7 | even | 3 | inner | ||
1520.2.q.l.961.2 | 8 | 1.1 | even | 1 | trivial |