Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(307,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.p (of order \(4\), degree \(2\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 44 x^{14} - 160 x^{13} + 468 x^{12} - 1060 x^{11} + 2038 x^{10} - 3208 x^{9} + \cdots + 2468 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 433.8 | ||
Root | \(-0.961955 - 1.77607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.433 |
Dual form | 630.2.p.d.307.8 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.20245 | + | 0.386289i | 0.984965 | + | 0.172754i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.57763 | + | 2.12393i | −0.596289 | + | 0.802769i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.83051 | − | 1.28422i | 0.578859 | − | 0.406106i | ||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.66103 | − | 3.66103i | 1.01539 | − | 1.01539i | 0.0155066 | − | 0.999880i | \(-0.495064\pi\) |
0.999880 | − | 0.0155066i | \(-0.00493612\pi\) | |||||||
\(14\) | 0.386289 | + | 2.61740i | 0.103240 | + | 0.699529i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.58874 | + | 2.58874i | 0.627861 | + | 0.627861i | 0.947529 | − | 0.319668i | \(-0.103572\pi\) |
−0.319668 | + | 0.947529i | \(0.603572\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.75362 | 1.09055 | 0.545277 | − | 0.838256i | \(-0.316424\pi\) | ||||
0.545277 | + | 0.838256i | \(0.316424\pi\) | |||||||
\(20\) | 0.386289 | − | 2.20245i | 0.0863768 | − | 0.492483i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.00000i | 0.213201 | − | 0.213201i | ||||
\(23\) | −3.82059 | − | 3.82059i | −0.796647 | − | 0.796647i | 0.185918 | − | 0.982565i | \(-0.440474\pi\) |
−0.982565 | + | 0.185918i | \(0.940474\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.70156 | + | 1.70156i | 0.940312 | + | 0.340312i | ||||
\(26\) | − | 5.17748i | − | 1.01539i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.12393 | + | 1.57763i | 0.401385 | + | 0.298145i | ||||
\(29\) | 8.06323i | 1.49730i | 0.662963 | + | 0.748652i | \(0.269298\pi\) | ||||
−0.662963 | + | 0.748652i | \(0.730702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.89049i | − | 1.77639i | −0.459471 | − | 0.888193i | \(-0.651961\pi\) | ||
0.459471 | − | 0.888193i | \(-0.348039\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.66103 | 0.627861 | ||||||||
\(35\) | −4.29511 | + | 4.06842i | −0.726006 | + | 0.687689i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.701562 | + | 0.701562i | −0.115336 | + | 0.115336i | −0.762419 | − | 0.647083i | \(-0.775989\pi\) |
0.647083 | + | 0.762419i | \(0.275989\pi\) | |||||||
\(38\) | 3.36131 | − | 3.36131i | 0.545277 | − | 0.545277i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.28422 | − | 1.83051i | −0.203053 | − | 0.289430i | ||||
\(41\) | 10.3550i | 1.61717i | 0.588378 | + | 0.808586i | \(0.299767\pi\) | ||||
−0.588378 | + | 0.808586i | \(0.700233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | − | 2.00000i | −0.304997 | − | 0.304997i | 0.537968 | − | 0.842965i | \(-0.319192\pi\) |
−0.842965 | + | 0.537968i | \(0.819192\pi\) | |||||||
\(44\) | − | 1.41421i | − | 0.213201i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.40312 | −0.796647 | ||||||||
\(47\) | −1.54515 | − | 1.54515i | −0.225384 | − | 0.225384i | 0.585377 | − | 0.810761i | \(-0.300946\pi\) |
−0.810761 | + | 0.585377i | \(0.800946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.02214 | − | 6.70156i | −0.288878 | − | 0.957366i | ||||
\(50\) | 4.52769 | − | 2.12132i | 0.640312 | − | 0.300000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.66103 | − | 3.66103i | −0.507693 | − | 0.507693i | ||||
\(53\) | −6.64901 | − | 6.64901i | −0.913312 | − | 0.913312i | 0.0832191 | − | 0.996531i | \(-0.473480\pi\) |
−0.996531 | + | 0.0832191i | \(0.973480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.11473 | + | 0.546295i | 0.419991 | + | 0.0736624i | ||||
\(56\) | 2.61740 | − | 0.386289i | 0.349765 | − | 0.0516200i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.70156 | + | 5.70156i | 0.748652 | + | 0.748652i | ||||
\(59\) | −7.49521 | −0.975793 | −0.487896 | − | 0.872902i | \(-0.662236\pi\) | ||||
−0.487896 | + | 0.872902i | \(0.662236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.22947i | 0.797601i | 0.917038 | + | 0.398801i | \(0.130573\pi\) | ||||
−0.917038 | + | 0.398801i | \(0.869427\pi\) | |||||||
\(62\) | −6.99364 | − | 6.99364i | −0.888193 | − | 0.888193i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 9.47744 | − | 6.64901i | 1.17553 | − | 0.824709i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 4.00000i | −0.488678 | + | 0.488678i | −0.907889 | − | 0.419211i | \(-0.862307\pi\) |
0.419211 | + | 0.907889i | \(0.362307\pi\) | |||||||
\(68\) | 2.58874 | − | 2.58874i | 0.313931 | − | 0.313931i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.160291 | + | 5.91391i | −0.0191584 | + | 0.706847i | ||||
\(71\) | 0.992159 | 0.117748 | 0.0588738 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588738 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.59058 | − | 4.59058i | 0.537287 | − | 0.537287i | −0.385444 | − | 0.922731i | \(-0.625952\pi\) |
0.922731 | + | 0.385444i | \(0.125952\pi\) | |||||||
\(74\) | 0.992159i | 0.115336i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.75362i | − | 0.545277i | ||||||
\(77\) | −2.23111 | + | 3.00369i | −0.254259 | + | 0.342302i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.40312i | − | 0.832917i | −0.909155 | − | 0.416458i | \(-0.863271\pi\) | ||
0.909155 | − | 0.416458i | \(-0.136729\pi\) | |||||||
\(80\) | −2.20245 | − | 0.386289i | −0.246241 | − | 0.0431884i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.32206 | + | 7.32206i | 0.808586 | + | 0.808586i | ||||
\(83\) | −8.03722 | + | 8.03722i | −0.882199 | + | 0.882199i | −0.993758 | − | 0.111559i | \(-0.964416\pi\) |
0.111559 | + | 0.993758i | \(0.464416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.70156 | + | 6.70156i | 0.509956 | + | 0.726886i | ||||
\(86\) | −2.82843 | −0.304997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | − | 1.00000i | −0.106600 | − | 0.106600i | ||||
\(89\) | 12.4421 | 1.31886 | 0.659431 | − | 0.751765i | \(-0.270797\pi\) | ||||
0.659431 | + | 0.751765i | \(0.270797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 13.5515i | 0.209657 | + | 1.42059i | ||||
\(92\) | −3.82059 | + | 3.82059i | −0.398324 | + | 0.398324i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.18518 | −0.225384 | ||||||||
\(95\) | 10.4696 | + | 1.83627i | 1.07416 | + | 0.188397i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.63888 | − | 1.63888i | −0.166403 | − | 0.166403i | 0.618993 | − | 0.785396i | \(-0.287541\pi\) |
−0.785396 | + | 0.618993i | \(0.787541\pi\) | |||||||
\(98\) | −6.16859 | − | 3.30885i | −0.623122 | − | 0.334244i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.70156 | − | 4.70156i | 0.170156 | − | 0.470156i | ||||
\(101\) | − | 8.03722i | − | 0.799733i | −0.916573 | − | 0.399867i | \(-0.869056\pi\) | ||
0.916573 | − | 0.399867i | \(-0.130944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9126 | + | 11.9126i | −1.17379 | + | 1.17379i | −0.192488 | + | 0.981299i | \(0.561656\pi\) |
−0.981299 | + | 0.192488i | \(0.938344\pi\) | |||||||
\(104\) | −5.17748 | −0.507693 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.40312 | −0.913312 | ||||||||
\(107\) | −9.47744 | + | 9.47744i | −0.916219 | + | 0.916219i | −0.996752 | − | 0.0805332i | \(-0.974338\pi\) |
0.0805332 | + | 0.996752i | \(0.474338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.596876i | 0.0571703i | 0.999591 | + | 0.0285852i | \(0.00910018\pi\) | ||||
−0.999591 | + | 0.0285852i | \(0.990900\pi\) | |||||||
\(110\) | 2.58874 | − | 1.81616i | 0.246826 | − | 0.173164i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.57763 | − | 2.12393i | 0.149072 | − | 0.200692i | ||||
\(113\) | −6.22696 | − | 6.22696i | −0.585783 | − | 0.585783i | 0.350704 | − | 0.936487i | \(-0.385942\pi\) |
−0.936487 | + | 0.350704i | \(0.885942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.93880 | − | 9.89049i | −0.647046 | − | 0.922293i | ||||
\(116\) | 8.06323 | 0.748652 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.29991 | + | 5.29991i | −0.487896 | + | 0.487896i | ||||
\(119\) | −9.58237 | + | 1.41421i | −0.878415 | + | 0.129641i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 4.40490 | + | 4.40490i | 0.398801 | + | 0.398801i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.89049 | −0.888193 | ||||||||
\(125\) | 9.69766 | + | 5.56376i | 0.867385 | + | 0.497638i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.70156 | + | 5.70156i | −0.505932 | + | 0.505932i | −0.913275 | − | 0.407343i | \(-0.866455\pi\) |
0.407343 | + | 0.913275i | \(0.366455\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 11.4031i | 0.175412 | − | 1.00012i | ||||
\(131\) | 4.40490i | 0.384858i | 0.981311 | + | 0.192429i | \(0.0616365\pi\) | ||||
−0.981311 | + | 0.192429i | \(0.938364\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.49947 | + | 10.0963i | −0.650286 | + | 0.875464i | ||||
\(134\) | 5.65685i | 0.488678i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.66103i | − | 0.313931i | ||||||
\(137\) | −11.8838 | + | 11.8838i | −1.01530 | + | 1.01530i | −0.0154215 | + | 0.999881i | \(0.504909\pi\) |
−0.999881 | + | 0.0154215i | \(0.995091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0757 | −1.02425 | −0.512123 | − | 0.858912i | \(-0.671141\pi\) | ||||
−0.512123 | + | 0.858912i | \(0.671141\pi\) | |||||||
\(140\) | 4.06842 | + | 4.29511i | 0.343844 | + | 0.363003i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.701562 | − | 0.701562i | 0.0588738 | − | 0.0588738i | ||||
\(143\) | 5.17748 | − | 5.17748i | 0.432962 | − | 0.432962i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.11473 | + | 17.7588i | −0.258665 | + | 1.47479i | ||||
\(146\) | − | 6.49206i | − | 0.537287i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.701562 | + | 0.701562i | 0.0576681 | + | 0.0576681i | ||||
\(149\) | 10.0475i | 0.823127i | 0.911381 | + | 0.411563i | \(0.135017\pi\) | ||||
−0.911381 | + | 0.411563i | \(0.864983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.8062 | 1.53043 | 0.765215 | − | 0.643774i | \(-0.222632\pi\) | ||||
0.765215 | + | 0.643774i | \(0.222632\pi\) | |||||||
\(152\) | −3.36131 | − | 3.36131i | −0.272639 | − | 0.272639i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.546295 | + | 3.70156i | 0.0440217 | + | 0.298280i | ||||
\(155\) | 3.82059 | − | 21.7833i | 0.306877 | − | 1.74968i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1683 | − | 13.1683i | −1.05094 | − | 1.05094i | −0.998631 | − | 0.0523109i | \(-0.983341\pi\) |
−0.0523109 | − | 0.998631i | \(-0.516659\pi\) | |||||||
\(158\) | −5.23480 | − | 5.23480i | −0.416458 | − | 0.416458i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.83051 | + | 1.28422i | −0.144715 | + | 0.101526i | ||||
\(161\) | 14.1421 | − | 2.08717i | 1.11456 | − | 0.164492i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.40312 | − | 1.40312i | −0.109901 | − | 0.109901i | 0.650018 | − | 0.759919i | \(-0.274761\pi\) |
−0.759919 | + | 0.650018i | \(0.774761\pi\) | |||||||
\(164\) | 10.3550 | 0.808586 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.3663i | 0.882199i | ||||||||
\(167\) | 3.63232 | + | 3.63232i | 0.281077 | + | 0.281077i | 0.833539 | − | 0.552461i | \(-0.186311\pi\) |
−0.552461 | + | 0.833539i | \(0.686311\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.8062i | − | 1.06202i | ||||||
\(170\) | 8.06323 | + | 1.41421i | 0.618421 | + | 0.108465i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | + | 2.00000i | −0.152499 | + | 0.152499i | ||||
\(173\) | 13.7163 | − | 13.7163i | 1.04283 | − | 1.04283i | 0.0437875 | − | 0.999041i | \(-0.486058\pi\) |
0.999041 | − | 0.0437875i | \(-0.0139424\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.0313 | + | 7.30134i | −0.833891 | + | 0.551929i | ||||
\(176\) | −1.41421 | −0.106600 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.79790 | − | 8.79790i | 0.659431 | − | 0.659431i | ||||
\(179\) | 3.39853i | 0.254018i | 0.991902 | + | 0.127009i | \(0.0405377\pi\) | ||||
−0.991902 | + | 0.127009i | \(0.959462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.27777i | 0.243635i | 0.992553 | + | 0.121817i | \(0.0388722\pi\) | ||||
−0.992553 | + | 0.121817i | \(0.961128\pi\) | |||||||
\(182\) | 10.9966 | + | 8.16816i | 0.815121 | + | 0.605464i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.40312i | 0.398324i | ||||||||
\(185\) | −1.81616 | + | 1.27415i | −0.133527 | + | 0.0936773i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.66103 | + | 3.66103i | 0.267721 | + | 0.267721i | ||||
\(188\) | −1.54515 | + | 1.54515i | −0.112692 | + | 0.112692i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.70156 | − | 6.10469i | 0.631278 | − | 0.442880i | ||||
\(191\) | 2.97648 | 0.215370 | 0.107685 | − | 0.994185i | \(-0.465656\pi\) | ||||
0.107685 | + | 0.994185i | \(0.465656\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | − | 11.0000i | −0.791797 | − | 0.791797i | 0.189989 | − | 0.981786i | \(-0.439155\pi\) |
−0.981786 | + | 0.189989i | \(0.939155\pi\) | |||||||
\(194\) | −2.31773 | −0.166403 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.70156 | + | 2.02214i | −0.478683 | + | 0.144439i | ||||
\(197\) | 7.49312 | − | 7.49312i | 0.533863 | − | 0.533863i | −0.387857 | − | 0.921720i | \(-0.626784\pi\) |
0.921720 | + | 0.387857i | \(0.126784\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7496 | 0.832907 | 0.416454 | − | 0.909157i | \(-0.363273\pi\) | ||||
0.416454 | + | 0.909157i | \(0.363273\pi\) | |||||||
\(200\) | −2.12132 | − | 4.52769i | −0.150000 | − | 0.320156i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.68317 | − | 5.68317i | −0.399867 | − | 0.399867i | ||||
\(203\) | −17.1257 | − | 12.7208i | −1.20199 | − | 0.892826i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | + | 22.8062i | −0.279372 | + | 1.59286i | ||||
\(206\) | 16.8470i | 1.17379i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.66103 | + | 3.66103i | −0.253847 | + | 0.253847i | ||||
\(209\) | 6.72263 | 0.465014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8062 | 1.01930 | 0.509652 | − | 0.860381i | \(-0.329774\pi\) | ||||
0.509652 | + | 0.860381i | \(0.329774\pi\) | |||||||
\(212\) | −6.64901 | + | 6.64901i | −0.456656 | + | 0.456656i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.4031i | 0.916219i | ||||||||
\(215\) | −3.63232 | − | 5.17748i | −0.247722 | − | 0.353101i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.0067 | + | 15.6036i | 1.42603 | + | 1.05924i | ||||
\(218\) | 0.422055 | + | 0.422055i | 0.0285852 | + | 0.0285852i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.546295 | − | 3.11473i | 0.0368312 | − | 0.209995i | ||||
\(221\) | 18.9549 | 1.27504 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.20732 | − | 4.20732i | 0.281743 | − | 0.281743i | −0.552061 | − | 0.833804i | \(-0.686158\pi\) |
0.833804 | + | 0.552061i | \(0.186158\pi\) | |||||||
\(224\) | −0.386289 | − | 2.61740i | −0.0258100 | − | 0.174882i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.80625 | −0.585783 | ||||||||
\(227\) | −17.0776 | − | 17.0776i | −1.13348 | − | 1.13348i | −0.989595 | − | 0.143884i | \(-0.954041\pi\) |
−0.143884 | − | 0.989595i | \(-0.545959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.85911 | −0.122853 | −0.0614267 | − | 0.998112i | \(-0.519565\pi\) | ||||
−0.0614267 | + | 0.998112i | \(0.519565\pi\) | |||||||
\(230\) | −11.9001 | − | 2.08717i | −0.784670 | − | 0.137624i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.70156 | − | 5.70156i | 0.374326 | − | 0.374326i | ||||
\(233\) | 4.24264 | + | 4.24264i | 0.277945 | + | 0.277945i | 0.832288 | − | 0.554343i | \(-0.187031\pi\) |
−0.554343 | + | 0.832288i | \(0.687031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.80625 | − | 4.00000i | −0.183059 | − | 0.260931i | ||||
\(236\) | 7.49521i | 0.487896i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.77576 | + | 7.77576i | −0.374387 | + | 0.504028i | ||||
\(239\) | 23.6196i | 1.52782i | 0.645321 | + | 0.763912i | \(0.276724\pi\) | ||||
−0.645321 | + | 0.763912i | \(0.723276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.8253i | − | 1.53472i | −0.641216 | − | 0.767360i | \(-0.721570\pi\) | ||
0.641216 | − | 0.767360i | \(-0.278430\pi\) | |||||||
\(242\) | −6.36396 | + | 6.36396i | −0.409091 | + | 0.409091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.22947 | 0.398801 | ||||||||
\(245\) | −1.86493 | − | 15.5410i | −0.119146 | − | 0.992877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.4031 | − | 17.4031i | 1.10733 | − | 1.10733i | ||||
\(248\) | −6.99364 | + | 6.99364i | −0.444096 | + | 0.444096i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.7915 | − | 2.92310i | 0.682511 | − | 0.184873i | ||||
\(251\) | − | 0.230566i | − | 0.0145532i | −0.999974 | − | 0.00727661i | \(-0.997684\pi\) | ||
0.999974 | − | 0.00727661i | \(-0.00231624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.40312 | − | 5.40312i | −0.339692 | − | 0.339692i | ||||
\(254\) | 8.06323i | 0.505932i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.76621 | + | 7.76621i | 0.484443 | + | 0.484443i | 0.906547 | − | 0.422104i | \(-0.138708\pi\) |
−0.422104 | + | 0.906547i | \(0.638708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.383260 | − | 2.59688i | −0.0238146 | − | 0.161362i | ||||
\(260\) | −6.64901 | − | 9.47744i | −0.412354 | − | 0.587766i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.11473 | + | 3.11473i | 0.192429 | + | 0.192429i | ||||
\(263\) | −11.3137 | − | 11.3137i | −0.697633 | − | 0.697633i | 0.266266 | − | 0.963899i | \(-0.414210\pi\) |
−0.963899 | + | 0.266266i | \(0.914210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0757 | − | 17.2125i | −0.741803 | − | 1.05736i | ||||
\(266\) | 1.83627 | + | 12.4421i | 0.112589 | + | 0.762875i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | + | 4.00000i | 0.244339 | + | 0.244339i | ||||
\(269\) | 3.86289 | 0.235524 | 0.117762 | − | 0.993042i | \(-0.462428\pi\) | ||||
0.117762 | + | 0.993042i | \(0.462428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.1683i | 0.799915i | 0.916534 | + | 0.399957i | \(0.130975\pi\) | ||||
−0.916534 | + | 0.399957i | \(0.869025\pi\) | |||||||
\(272\) | −2.58874 | − | 2.58874i | −0.156965 | − | 0.156965i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.8062i | 1.01530i | ||||||||
\(275\) | 6.64901 | + | 2.40637i | 0.400951 | + | 0.145110i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1047 | + | 14.1047i | −0.847468 | + | 0.847468i | −0.989817 | − | 0.142348i | \(-0.954535\pi\) |
0.142348 | + | 0.989817i | \(0.454535\pi\) | |||||||
\(278\) | −8.53879 | + | 8.53879i | −0.512123 | + | 0.512123i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.91391 | + | 0.160291i | 0.353424 | + | 0.00957921i | ||||
\(281\) | −19.7990 | −1.18111 | −0.590554 | − | 0.806998i | \(-0.701091\pi\) | ||||
−0.590554 | + | 0.806998i | \(0.701091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8736 | − | 20.8736i | 1.24081 | − | 1.24081i | 0.281138 | − | 0.959667i | \(-0.409288\pi\) |
0.959667 | − | 0.281138i | \(-0.0907119\pi\) | |||||||
\(284\) | − | 0.992159i | − | 0.0588738i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 7.32206i | − | 0.432962i | ||||||
\(287\) | −21.9932 | − | 16.3363i | −1.29822 | − | 0.964302i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 3.59688i | − | 0.211581i | ||||||
\(290\) | 10.3550 | + | 14.7598i | 0.608064 | + | 0.866728i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.59058 | − | 4.59058i | −0.268643 | − | 0.268643i | ||||
\(293\) | 16.0340 | − | 16.0340i | 0.936716 | − | 0.936716i | −0.0613973 | − | 0.998113i | \(-0.519556\pi\) |
0.998113 | + | 0.0613973i | \(0.0195557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.5078 | − | 2.89531i | −0.961122 | − | 0.168572i | ||||
\(296\) | 0.992159 | 0.0576681 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.10469 | + | 7.10469i | 0.411563 | + | 0.411563i | ||||
\(299\) | −27.9745 | −1.61781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.40312 | − | 1.09259i | 0.426709 | − | 0.0629758i | ||||
\(302\) | 13.2980 | − | 13.2980i | 0.765215 | − | 0.765215i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.75362 | −0.272639 | ||||||||
\(305\) | −2.40637 | + | 13.7201i | −0.137788 | + | 0.785610i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.383260 | − | 0.383260i | −0.0218738 | − | 0.0218738i | 0.696085 | − | 0.717959i | \(-0.254924\pi\) |
−0.717959 | + | 0.696085i | \(0.754924\pi\) | |||||||
\(308\) | 3.00369 | + | 2.23111i | 0.171151 | + | 0.127129i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.7016 | − | 18.1047i | −0.721400 | − | 1.02828i | ||||
\(311\) | − | 19.1647i | − | 1.08673i | −0.839496 | − | 0.543367i | \(-0.817149\pi\) | ||
0.839496 | − | 0.543367i | \(-0.182851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0535 | − | 10.0535i | 0.568259 | − | 0.568259i | −0.363381 | − | 0.931640i | \(-0.618378\pi\) |
0.931640 | + | 0.363381i | \(0.118378\pi\) | |||||||
\(314\) | −18.6227 | −1.05094 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.40312 | −0.416458 | ||||||||
\(317\) | −1.41421 | + | 1.41421i | −0.0794301 | + | 0.0794301i | −0.745706 | − | 0.666276i | \(-0.767887\pi\) |
0.666276 | + | 0.745706i | \(0.267887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4031i | 0.638452i | ||||||||
\(320\) | −0.386289 | + | 2.20245i | −0.0215942 | + | 0.123121i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.52415 | − | 11.4758i | 0.475032 | − | 0.639524i | ||||
\(323\) | 12.3059 | + | 12.3059i | 0.684717 | + | 0.684717i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.4420 | − | 10.9831i | 1.30033 | − | 0.609232i | ||||
\(326\) | −1.98432 | −0.109901 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.32206 | − | 7.32206i | 0.404293 | − | 0.404293i | ||||
\(329\) | 5.71949 | − | 0.844110i | 0.315325 | − | 0.0465373i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.6125 | 1.40779 | 0.703895 | − | 0.710304i | \(-0.251443\pi\) | ||||
0.703895 | + | 0.710304i | \(0.251443\pi\) | |||||||
\(332\) | 8.03722 | + | 8.03722i | 0.441100 | + | 0.441100i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.13688 | 0.281077 | ||||||||
\(335\) | −10.3550 | + | 7.26464i | −0.565751 | + | 0.396910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.00000i | −0.0544735 | + | 0.0544735i | −0.733819 | − | 0.679345i | \(-0.762264\pi\) |
0.679345 | + | 0.733819i | \(0.262264\pi\) | |||||||
\(338\) | −9.76249 | − | 9.76249i | −0.531010 | − | 0.531010i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.70156 | − | 4.70156i | 0.363443 | − | 0.254978i | ||||
\(341\) | − | 13.9873i | − | 0.757453i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4238 | + | 6.27772i | 0.940799 | + | 0.338965i | ||||
\(344\) | 2.82843i | 0.152499i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 19.3977i | − | 1.04283i | ||||||
\(347\) | 10.0475 | − | 10.0475i | 0.539380 | − | 0.539380i | −0.383967 | − | 0.923347i | \(-0.625442\pi\) |
0.923347 | + | 0.383967i | \(0.125442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0588 | 1.23431 | 0.617153 | − | 0.786843i | \(-0.288286\pi\) | ||||
0.617153 | + | 0.786843i | \(0.288286\pi\) | |||||||
\(350\) | −2.63751 | + | 12.9632i | −0.140981 | + | 0.692910i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | + | 1.00000i | −0.0533002 | + | 0.0533002i | ||||
\(353\) | −14.4888 | + | 14.4888i | −0.771163 | + | 0.771163i | −0.978310 | − | 0.207147i | \(-0.933582\pi\) |
0.207147 | + | 0.978310i | \(0.433582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.18518 | + | 0.383260i | 0.115977 | + | 0.0203413i | ||||
\(356\) | − | 12.4421i | − | 0.659431i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.40312 | + | 2.40312i | 0.127009 | + | 0.127009i | ||||
\(359\) | − | 28.4323i | − | 1.50060i | −0.661097 | − | 0.750300i | \(-0.729909\pi\) | ||
0.661097 | − | 0.750300i | \(-0.270091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.59688 | 0.189309 | ||||||||
\(362\) | 2.31773 | + | 2.31773i | 0.121817 | + | 0.121817i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.5515 | − | 2.00000i | 0.710293 | − | 0.104828i | ||||
\(365\) | 11.8838 | − | 8.33723i | 0.622027 | − | 0.436391i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.25161 | − | 8.25161i | −0.430731 | − | 0.430731i | 0.458146 | − | 0.888877i | \(-0.348514\pi\) |
−0.888877 | + | 0.458146i | \(0.848514\pi\) | |||||||
\(368\) | 3.82059 | + | 3.82059i | 0.199162 | + | 0.199162i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.383260 | + | 2.18518i | −0.0199247 | + | 0.113602i | ||||
\(371\) | 24.6117 | − | 3.63232i | 1.27778 | − | 0.188581i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.70156 | + | 2.70156i | 0.139882 | + | 0.139882i | 0.773580 | − | 0.633699i | \(-0.218464\pi\) |
−0.633699 | + | 0.773580i | \(0.718464\pi\) | |||||||
\(374\) | 5.17748 | 0.267721 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.18518i | 0.112692i | ||||||||
\(377\) | 29.5197 | + | 29.5197i | 1.52034 | + | 1.52034i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.6125i | 1.72656i | 0.504727 | + | 0.863279i | \(0.331593\pi\) | ||||
−0.504727 | + | 0.863279i | \(0.668407\pi\) | |||||||
\(380\) | 1.83627 | − | 10.4696i | 0.0941986 | − | 0.537079i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.10469 | − | 2.10469i | 0.107685 | − | 0.107685i | ||||
\(383\) | −21.2519 | + | 21.2519i | −1.08592 | + | 1.08592i | −0.0899782 | + | 0.995944i | \(0.528680\pi\) |
−0.995944 | + | 0.0899782i | \(0.971320\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.07420 | + | 5.75362i | −0.309570 | + | 0.293231i | ||||
\(386\) | −15.5563 | −0.791797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.63888 | + | 1.63888i | −0.0832017 | + | 0.0832017i | ||||
\(389\) | − | 22.2054i | − | 1.12586i | −0.826506 | − | 0.562928i | \(-0.809675\pi\) | ||
0.826506 | − | 0.562928i | \(-0.190325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.7810i | − | 1.00037i | ||||||
\(392\) | −3.30885 | + | 6.16859i | −0.167122 | + | 0.311561i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 10.5969i | − | 0.533863i | ||||||
\(395\) | 2.85974 | − | 16.3050i | 0.143889 | − | 0.820394i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.75362 | + | 4.75362i | 0.238577 | + | 0.238577i | 0.816261 | − | 0.577684i | \(-0.196043\pi\) |
−0.577684 | + | 0.816261i | \(0.696043\pi\) | |||||||
\(398\) | 8.30822 | − | 8.30822i | 0.416454 | − | 0.416454i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.70156 | − | 1.70156i | −0.235078 | − | 0.0850781i | ||||
\(401\) | −31.4088 | −1.56848 | −0.784240 | − | 0.620457i | \(-0.786947\pi\) | ||||
−0.784240 | + | 0.620457i | \(0.786947\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.2094 | − | 36.2094i | −1.80372 | − | 1.80372i | ||||
\(404\) | −8.03722 | −0.399867 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.1047 | + | 3.11473i | −1.04741 | + | 0.154582i | ||||
\(407\) | −0.992159 | + | 0.992159i | −0.0491795 | + | 0.0491795i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.22947 | −0.308027 | −0.154014 | − | 0.988069i | \(-0.549220\pi\) | ||||
−0.154014 | + | 0.988069i | \(0.549220\pi\) | |||||||
\(410\) | 13.2980 | + | 18.9549i | 0.656743 | + | 0.936115i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.9126 | + | 11.9126i | 0.586894 | + | 0.586894i | ||||
\(413\) | 11.8247 | − | 15.9193i | 0.581855 | − | 0.783337i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.8062 | + | 14.5969i | −1.02134 | + | 0.716532i | ||||
\(416\) | 5.17748i | 0.253847i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.75362 | − | 4.75362i | 0.232507 | − | 0.232507i | ||||
\(419\) | 23.5696 | 1.15145 | 0.575726 | − | 0.817643i | \(-0.304719\pi\) | ||||
0.575726 | + | 0.817643i | \(0.304719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4031 | 0.945650 | 0.472825 | − | 0.881156i | \(-0.343234\pi\) | ||||
0.472825 | + | 0.881156i | \(0.343234\pi\) | |||||||
\(422\) | 10.4696 | − | 10.4696i | 0.509652 | − | 0.509652i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.40312i | 0.456656i | ||||||||
\(425\) | 7.76621 | + | 16.5760i | 0.376717 | + | 0.804055i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2309 | − | 9.82782i | −0.640290 | − | 0.475601i | ||||
\(428\) | 9.47744 | + | 9.47744i | 0.458109 | + | 0.458109i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.22947 | − | 1.09259i | −0.300412 | − | 0.0526893i | ||||
\(431\) | −0.148049 | −0.00713126 | −0.00356563 | − | 0.999994i | \(-0.501135\pi\) | ||||
−0.00356563 | + | 0.999994i | \(0.501135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.96094 | + | 8.96094i | −0.430635 | + | 0.430635i | −0.888844 | − | 0.458209i | \(-0.848491\pi\) |
0.458209 | + | 0.888844i | \(0.348491\pi\) | |||||||
\(434\) | 25.8874 | − | 3.82059i | 1.24263 | − | 0.183394i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.596876 | 0.0285852 | ||||||||
\(437\) | −18.1616 | − | 18.1616i | −0.868787 | − | 0.868787i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.47585 | 0.0704384 | 0.0352192 | − | 0.999380i | \(-0.488787\pi\) | ||||
0.0352192 | + | 0.999380i | \(0.488787\pi\) | |||||||
\(440\) | −1.81616 | − | 2.58874i | −0.0865820 | − | 0.123413i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.4031 | − | 13.4031i | 0.637522 | − | 0.637522i | ||||
\(443\) | 16.5485 | + | 16.5485i | 0.786243 | + | 0.786243i | 0.980876 | − | 0.194633i | \(-0.0623515\pi\) |
−0.194633 | + | 0.980876i | \(0.562352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.4031 | + | 4.80625i | 1.29903 | + | 0.227838i | ||||
\(446\) | − | 5.95005i | − | 0.281743i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.12393 | − | 1.57763i | −0.100346 | − | 0.0745362i | ||||
\(449\) | 17.8147i | 0.840726i | 0.907356 | + | 0.420363i | \(0.138097\pi\) | ||||
−0.907356 | + | 0.420363i | \(0.861903\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6441i | 0.689564i | ||||||||
\(452\) | −6.22696 | + | 6.22696i | −0.292891 | + | 0.292891i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.1513 | −1.13348 | ||||||||
\(455\) | −0.829902 | + | 30.6191i | −0.0389064 | + | 1.43545i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.80625 | + | 5.80625i | −0.271605 | + | 0.271605i | −0.829746 | − | 0.558141i | \(-0.811515\pi\) |
0.558141 | + | 0.829746i | \(0.311515\pi\) | |||||||
\(458\) | −1.31459 | + | 1.31459i | −0.0614267 | + | 0.0614267i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.89049 | + | 6.93880i | −0.461147 | + | 0.323523i | ||||
\(461\) | 1.31459i | 0.0612265i | 0.999531 | + | 0.0306132i | \(0.00974602\pi\) | ||||
−0.999531 | + | 0.0306132i | \(0.990254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1047 | − | 13.1047i | −0.609026 | − | 0.609026i | 0.333665 | − | 0.942692i | \(-0.391714\pi\) |
−0.942692 | + | 0.333665i | \(0.891714\pi\) | |||||||
\(464\) | − | 8.06323i | − | 0.374326i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 5.40804 | + | 5.40804i | 0.250254 | + | 0.250254i | 0.821075 | − | 0.570821i | \(-0.193375\pi\) |
−0.570821 | + | 0.821075i | \(0.693375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.18518 | − | 14.8062i | −0.100902 | − | 0.683689i | ||||
\(470\) | −4.81274 | − | 0.844110i | −0.221995 | − | 0.0389359i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.29991 | + | 5.29991i | 0.243948 | + | 0.243948i | ||||
\(473\) | −2.82843 | − | 2.82843i | −0.130051 | − | 0.130051i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.3494 | + | 8.08857i | 1.02546 | + | 0.371129i | ||||
\(476\) | 1.41421 | + | 9.58237i | 0.0648204 | + | 0.439207i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.7016 | + | 16.7016i | 0.763912 | + | 0.763912i | ||||
\(479\) | −4.63546 | −0.211800 | −0.105900 | − | 0.994377i | \(-0.533772\pi\) | ||||
−0.105900 | + | 0.994377i | \(0.533772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.13688i | 0.234221i | ||||||||
\(482\) | −16.8470 | − | 16.8470i | −0.767360 | − | 0.767360i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00000i | 0.409091i | ||||||||
\(485\) | −2.97648 | − | 4.24264i | −0.135155 | − | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5078 | − | 16.5078i | 0.748040 | − | 0.748040i | −0.226071 | − | 0.974111i | \(-0.572588\pi\) |
0.974111 | + | 0.226071i | \(0.0725880\pi\) | |||||||
\(488\) | 4.40490 | − | 4.40490i | 0.199400 | − | 0.199400i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.3078 | − | 9.67043i | −0.556011 | − | 0.436865i | ||||
\(491\) | −40.1681 | −1.81276 | −0.906380 | − | 0.422463i | \(-0.861166\pi\) | ||||
−0.906380 | + | 0.422463i | \(0.861166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.8736 | + | 20.8736i | −0.940099 | + | 0.940099i | ||||
\(494\) | − | 24.6117i | − | 1.10733i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.89049i | 0.444096i | ||||||||
\(497\) | −1.56526 | + | 2.10727i | −0.0702116 | + | 0.0945242i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00000i | 0.358129i | 0.983837 | + | 0.179065i | \(0.0573071\pi\) | ||||
−0.983837 | + | 0.179065i | \(0.942693\pi\) | |||||||
\(500\) | 5.56376 | − | 9.69766i | 0.248819 | − | 0.433692i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.163035 | − | 0.163035i | −0.00727661 | − | 0.00727661i | ||||
\(503\) | 13.9873 | − | 13.9873i | 0.623662 | − | 0.623662i | −0.322804 | − | 0.946466i | \(-0.604626\pi\) |
0.946466 | + | 0.322804i | \(0.104626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.10469 | − | 17.7016i | 0.138157 | − | 0.787709i | ||||
\(506\) | −7.64117 | −0.339692 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.70156 | + | 5.70156i | 0.252966 | + | 0.252966i | ||||
\(509\) | 20.9405 | 0.928170 | 0.464085 | − | 0.885791i | \(-0.346383\pi\) | ||||
0.464085 | + | 0.885791i | \(0.346383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.50781 | + | 16.9923i | 0.110939 | + | 0.751696i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.9831 | 0.484443 | ||||||||
\(515\) | −30.8387 | + | 21.6353i | −1.35892 | + | 0.953363i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.18518 | − | 2.18518i | −0.0961041 | − | 0.0961041i | ||||
\(518\) | −2.10727 | − | 1.56526i | −0.0925883 | − | 0.0687737i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.4031 | − | 2.00000i | −0.500060 | − | 0.0877058i | ||||
\(521\) | 39.3326i | 1.72319i | 0.507593 | + | 0.861597i | \(0.330535\pi\) | ||||
−0.507593 | + | 0.861597i | \(0.669465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.84621 | + | 5.84621i | −0.255637 | + | 0.255637i | −0.823277 | − | 0.567640i | \(-0.807857\pi\) |
0.567640 | + | 0.823277i | \(0.307857\pi\) | |||||||
\(524\) | 4.40490 | 0.192429 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0000 | −0.697633 | ||||||||
\(527\) | 25.6039 | − | 25.6039i | 1.11532 | − | 1.11532i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.19375i | 0.269294i | ||||||||
\(530\) | −20.7099 | − | 3.63232i | −0.899581 | − | 0.157778i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.0963 | + | 7.49947i | 0.437732 | + | 0.325143i | ||||
\(533\) | 37.9098 | + | 37.9098i | 1.64205 | + | 1.64205i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.5346 | + | 17.2125i | −1.06072 | + | 0.744163i | ||||
\(536\) | 5.65685 | 0.244339 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.73147 | − | 2.73147i | 0.117762 | − | 0.117762i | ||||
\(539\) | −2.85974 | − | 9.47744i | −0.123178 | − | 0.408222i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 9.31137 | + | 9.31137i | 0.399957 | + | 0.399957i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.66103 | −0.156965 | ||||||||
\(545\) | −0.230566 | + | 1.31459i | −0.00987638 | + | 0.0563108i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.5969 | + | 16.5969i | −0.709631 | + | 0.709631i | −0.966458 | − | 0.256826i | \(-0.917323\pi\) |
0.256826 | + | 0.966458i | \(0.417323\pi\) | |||||||
\(548\) | 11.8838 | + | 11.8838i | 0.507651 | + | 0.507651i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.40312 | − | 3.00000i | 0.273030 | − | 0.127920i | ||||
\(551\) | 38.3295i | 1.63289i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.7237 | + | 11.6794i | 0.668640 | + | 0.496659i | ||||
\(554\) | 19.9470i | 0.847468i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.0757i | 0.512123i | ||||||||
\(557\) | −1.83627 | + | 1.83627i | −0.0778052 | + | 0.0778052i | −0.744938 | − | 0.667133i | \(-0.767521\pi\) |
0.667133 | + | 0.744938i | \(0.267521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6441 | −0.619380 | ||||||||
\(560\) | 4.29511 | − | 4.06842i | 0.181501 | − | 0.171922i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.0000 | + | 14.0000i | −0.590554 | + | 0.590554i | ||||
\(563\) | 14.5293 | − | 14.5293i | 0.612336 | − | 0.612336i | −0.331218 | − | 0.943554i | \(-0.607460\pi\) |
0.943554 | + | 0.331218i | \(0.107460\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3092 | − | 16.1200i | −0.475780 | − | 0.678172i | ||||
\(566\) | − | 29.5197i | − | 1.24081i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.701562 | − | 0.701562i | −0.0294369 | − | 0.0294369i | ||||
\(569\) | − | 8.78138i | − | 0.368135i | −0.982914 | − | 0.184067i | \(-0.941074\pi\) | ||
0.982914 | − | 0.184067i | \(-0.0589264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | −5.17748 | − | 5.17748i | −0.216481 | − | 0.216481i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27.1030 | + | 4.00000i | −1.13126 | + | 0.166957i | ||||
\(575\) | −11.4618 | − | 24.4637i | −0.477988 | − | 1.02021i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8200 | + | 10.8200i | 0.450445 | + | 0.450445i | 0.895502 | − | 0.445057i | \(-0.146817\pi\) |
−0.445057 | + | 0.895502i | \(0.646817\pi\) | |||||||
\(578\) | −2.54338 | − | 2.54338i | −0.105790 | − | 0.105790i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.7588 | + | 3.11473i | 0.737396 | + | 0.129332i | ||||
\(581\) | −4.39069 | − | 29.7503i | −0.182156 | − | 1.23425i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.40312 | − | 9.40312i | −0.389438 | − | 0.389438i | ||||
\(584\) | −6.49206 | −0.268643 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 22.6755i | − | 0.936716i | ||||||
\(587\) | 11.6695 | + | 11.6695i | 0.481653 | + | 0.481653i | 0.905659 | − | 0.424006i | \(-0.139376\pi\) |
−0.424006 | + | 0.905659i | \(0.639376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 47.0156i | − | 1.93724i | ||||||
\(590\) | −13.7201 | + | 9.62549i | −0.564847 | + | 0.396275i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.701562 | − | 0.701562i | 0.0288340 | − | 0.0288340i | ||||
\(593\) | −19.1243 | + | 19.1243i | −0.785341 | + | 0.785341i | −0.980727 | − | 0.195385i | \(-0.937404\pi\) |
0.195385 | + | 0.980727i | \(0.437404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.6510 | − | 0.586829i | −0.887604 | − | 0.0240576i | ||||
\(596\) | 10.0475 | 0.411563 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.7810 | + | 19.7810i | −0.808905 | + | 0.808905i | ||||
\(599\) | − | 20.7911i | − | 0.849503i | −0.905310 | − | 0.424752i | \(-0.860361\pi\) | ||
0.905310 | − | 0.424752i | \(-0.139639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8696i | 1.13682i | 0.822744 | + | 0.568412i | \(0.192442\pi\) | ||||
−0.822744 | + | 0.568412i | \(0.807558\pi\) | |||||||
\(602\) | 4.46222 | − | 6.00738i | 0.181867 | − | 0.244842i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 18.8062i | − | 0.765215i | ||||||
\(605\) | −19.8220 | − | 3.47660i | −0.805881 | − | 0.141344i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.02214 | + | 2.02214i | 0.0820763 | + | 0.0820763i | 0.746953 | − | 0.664877i | \(-0.231516\pi\) |
−0.664877 | + | 0.746953i | \(0.731516\pi\) | |||||||
\(608\) | −3.36131 | + | 3.36131i | −0.136319 | + | 0.136319i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.00000 | + | 11.4031i | 0.323911 | + | 0.461699i | ||||
\(611\) | −11.3137 | −0.457704 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2984 | − | 15.2984i | −0.617898 | − | 0.617898i | 0.327094 | − | 0.944992i | \(-0.393931\pi\) |
−0.944992 | + | 0.327094i | \(0.893931\pi\) | |||||||
\(614\) | −0.542011 | −0.0218738 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.70156 | − | 0.546295i | 0.149140 | − | 0.0220108i | ||||
\(617\) | 30.8387 | − | 30.8387i | 1.24152 | − | 1.24152i | 0.282148 | − | 0.959371i | \(-0.408953\pi\) |
0.959371 | − | 0.282148i | \(-0.0910470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.8084 | −1.39907 | −0.699533 | − | 0.714600i | \(-0.746609\pi\) | ||||
−0.699533 | + | 0.714600i | \(0.746609\pi\) | |||||||
\(620\) | −21.7833 | − | 3.82059i | −0.874839 | − | 0.153438i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.5515 | − | 13.5515i | −0.543367 | − | 0.543367i | ||||
\(623\) | −19.6291 | + | 26.4262i | −0.786423 | + | 1.05874i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.2094 | + | 16.0000i | 0.768375 | + | 0.640000i | ||||
\(626\) | − | 14.2178i | − | 0.568259i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.1683 | + | 13.1683i | −0.525471 | + | 0.525471i | ||||
\(629\) | −3.63232 | −0.144830 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.59688 | 0.342236 | 0.171118 | − | 0.985251i | \(-0.445262\pi\) | ||||
0.171118 | + | 0.985251i | \(0.445262\pi\) | |||||||
\(632\) | −5.23480 | + | 5.23480i | −0.208229 | + | 0.208229i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.00000i | 0.0794301i | ||||||||
\(635\) | −14.7598 | + | 10.3550i | −0.585727 | + | 0.410924i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.9377 | − | 17.1315i | −1.26542 | − | 0.678774i | ||||
\(638\) | 8.06323 | + | 8.06323i | 0.319226 | + | 0.319226i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.28422 | + | 1.83051i | 0.0507632 | + | 0.0723574i | ||||
\(641\) | 47.2392 | 1.86583 | 0.932917 | − | 0.360091i | \(-0.117254\pi\) | ||||
0.932917 | + | 0.360091i | \(0.117254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.9831 | + | 10.9831i | −0.433131 | + | 0.433131i | −0.889692 | − | 0.456561i | \(-0.849081\pi\) |
0.456561 | + | 0.889692i | \(0.349081\pi\) | |||||||
\(644\) | −2.08717 | − | 14.1421i | −0.0822459 | − | 0.557278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.4031 | 0.684717 | ||||||||
\(647\) | 22.7971 | + | 22.7971i | 0.896245 | + | 0.896245i | 0.995102 | − | 0.0988565i | \(-0.0315185\pi\) |
−0.0988565 | + | 0.995102i | \(0.531518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5998 | −0.416079 | ||||||||
\(650\) | 8.80980 | − | 24.3422i | 0.345549 | − | 0.954780i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.40312 | + | 1.40312i | −0.0549506 | + | 0.0549506i | ||||
\(653\) | 0.570104 | + | 0.570104i | 0.0223099 | + | 0.0223099i | 0.718174 | − | 0.695864i | \(-0.244978\pi\) |
−0.695864 | + | 0.718174i | \(0.744978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.70156 | + | 9.70156i | −0.0664855 | + | 0.379071i | ||||
\(656\) | − | 10.3550i | − | 0.404293i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.44741 | − | 4.64116i | 0.134394 | − | 0.180931i | ||||
\(659\) | − | 15.8524i | − | 0.617524i | −0.951139 | − | 0.308762i | \(-0.900085\pi\) | ||
0.951139 | − | 0.308762i | \(-0.0999146\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.1473i | 1.21149i | 0.795659 | + | 0.605745i | \(0.207125\pi\) | ||||
−0.795659 | + | 0.605745i | \(0.792875\pi\) | |||||||
\(662\) | 18.1108 | − | 18.1108i | 0.703895 | − | 0.703895i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.3663 | 0.441100 | ||||||||
\(665\) | −20.4173 | + | 19.3397i | −0.791749 | + | 0.749962i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.8062 | − | 30.8062i | 1.19282 | − | 1.19282i | ||||
\(668\) | 3.63232 | − | 3.63232i | 0.140539 | − | 0.140539i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.18518 | + | 12.4589i | −0.0844208 | + | 0.481331i | ||||
\(671\) | 8.80980i | 0.340098i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.8062 | + | 33.8062i | 1.30314 | + | 1.30314i | 0.926267 | + | 0.376868i | \(0.122999\pi\) |
0.376868 | + | 0.926267i | \(0.377001\pi\) | |||||||
\(674\) | 1.41421i | 0.0544735i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.8062 | −0.531010 | ||||||||
\(677\) | −18.3517 | − | 18.3517i | −0.705314 | − | 0.705314i | 0.260232 | − | 0.965546i | \(-0.416201\pi\) |
−0.965546 | + | 0.260232i | \(0.916201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.06643 | − | 0.895314i | 0.232808 | − | 0.0343590i | ||||
\(680\) | 1.41421 | − | 8.06323i | 0.0542326 | − | 0.309211i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.89049 | − | 9.89049i | −0.378727 | − | 0.378727i | ||||
\(683\) | 12.4539 | + | 12.4539i | 0.476536 | + | 0.476536i | 0.904022 | − | 0.427486i | \(-0.140601\pi\) |
−0.427486 | + | 0.904022i | \(0.640601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.7641 | + | 21.5829i | −1.17543 | + | 0.824640i | ||||
\(686\) | 16.7595 | − | 7.88150i | 0.639882 | − | 0.300917i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 2.00000i | 0.0762493 | + | 0.0762493i | ||||
\(689\) | −48.6844 | −1.85473 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.3494i | − | 0.850212i | −0.905144 | − | 0.425106i | \(-0.860237\pi\) | ||
0.905144 | − | 0.425106i | \(-0.139763\pi\) | |||||||
\(692\) | −13.7163 | − | 13.7163i | −0.521414 | − | 0.521414i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 14.2094i | − | 0.539380i | ||||||
\(695\) | −26.5961 | − | 4.66470i | −1.00885 | − | 0.176942i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.8062 | + | 26.8062i | −1.01536 | + | 1.01536i | ||||
\(698\) | 16.3050 | − | 16.3050i | 0.617153 | − | 0.617153i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.30134 | + | 11.0313i | 0.275965 | + | 0.416945i | ||||
\(701\) | −52.4740 | −1.98191 | −0.990957 | − | 0.134181i | \(-0.957160\pi\) | ||||
−0.990957 | + | 0.134181i | \(0.957160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.33496 | + | 3.33496i | −0.125780 | + | 0.125780i | ||||
\(704\) | 1.41421i | 0.0533002i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.4903i | 0.771163i | ||||||||
\(707\) | 17.0705 | + | 12.6798i | 0.642001 | + | 0.476872i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 41.0156i | − | 1.54037i | −0.637818 | − | 0.770187i | \(-0.720163\pi\) | ||
0.637818 | − | 0.770187i | \(-0.279837\pi\) | |||||||
\(710\) | 1.81616 | − | 1.27415i | 0.0681593 | − | 0.0478180i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.79790 | − | 8.79790i | −0.329715 | − | 0.329715i | ||||
\(713\) | −37.7875 | + | 37.7875i | −1.41515 | + | 1.41515i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.4031 | − | 9.40312i | 0.501248 | − | 0.351657i | ||||
\(716\) | 3.39853 | 0.127009 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.1047 | − | 20.1047i | −0.750300 | − | 0.750300i | ||||
\(719\) | −4.17433 | −0.155676 | −0.0778381 | − | 0.996966i | \(-0.524802\pi\) | ||||
−0.0778381 | + | 0.996966i | \(0.524802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.50781 | − | 44.0954i | −0.242364 | − | 1.64220i | ||||
\(722\) | 2.54338 | − | 2.54338i | 0.0946546 | − | 0.0946546i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.27777 | 0.121817 | ||||||||
\(725\) | −13.7201 | + | 37.9098i | −0.509551 | + | 1.40793i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.7105 | + | 20.7105i | 0.768111 | + | 0.768111i | 0.977774 | − | 0.209662i | \(-0.0672365\pi\) |
−0.209662 | + | 0.977774i | \(0.567236\pi\) | |||||||
\(728\) | 8.16816 | − | 10.9966i | 0.302732 | − | 0.407561i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.50781 | − | 14.2984i | 0.0928182 | − | 0.529209i | ||||
\(731\) | − | 10.3550i | − | 0.382992i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.80192 | + | 1.80192i | −0.0665554 | + | 0.0665554i | −0.739601 | − | 0.673046i | \(-0.764986\pi\) |
0.673046 | + | 0.739601i | \(0.264986\pi\) | |||||||
\(734\) | −11.6695 | −0.430731 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.40312 | 0.199162 | ||||||||
\(737\) | −5.65685 | + | 5.65685i | −0.208373 | + | 0.208373i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.8062i | 1.28037i | 0.768221 | + | 0.640184i | \(0.221142\pi\) | ||||
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(740\) | 1.27415 | + | 1.81616i | 0.0468387 | + | 0.0667634i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.8347 | − | 19.9716i | 0.544598 | − | 0.733179i | ||||
\(743\) | 22.6274 | + | 22.6274i | 0.830119 | + | 0.830119i | 0.987533 | − | 0.157413i | \(-0.0503155\pi\) |
−0.157413 | + | 0.987533i | \(0.550316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.88125 | + | 22.1292i | −0.142198 | + | 0.810751i | ||||
\(746\) | 3.82059 | 0.139882 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.66103 | − | 3.66103i | 0.133860 | − | 0.133860i | ||||
\(749\) | −5.17748 | − | 35.0813i | −0.189181 | − | 1.28184i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.2094 | −1.24832 | −0.624159 | − | 0.781297i | \(-0.714558\pi\) | ||||
−0.624159 | + | 0.781297i | \(0.714558\pi\) | |||||||
\(752\) | 1.54515 | + | 1.54515i | 0.0563460 | + | 0.0563460i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 41.7472 | 1.52034 | ||||||||
\(755\) | 41.4198 | + | 7.26464i | 1.50742 | + | 0.264387i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.5078 | + | 31.5078i | −1.14517 | + | 1.14517i | −0.157681 | + | 0.987490i | \(0.550402\pi\) |
−0.987490 | + | 0.157681i | \(0.949598\pi\) | |||||||
\(758\) | 23.7676 | + | 23.7676i | 0.863279 | + | 0.863279i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.10469 | − | 8.70156i | −0.221440 | − | 0.315639i | ||||
\(761\) | 2.62918i | 0.0953076i | 0.998864 | + | 0.0476538i | \(0.0151744\pi\) | ||||
−0.998864 | + | 0.0476538i | \(0.984826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.26772 | − | 0.941651i | −0.0458946 | − | 0.0340901i | ||||
\(764\) | − | 2.97648i | − | 0.107685i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0547i | 1.08592i | ||||||||
\(767\) | −27.4402 | + | 27.4402i | −0.990807 | + | 0.990807i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.5217 | 1.02852 | 0.514259 | − | 0.857635i | \(-0.328067\pi\) | ||||
0.514259 | + | 0.857635i | \(0.328067\pi\) | |||||||
\(770\) | −0.226685 | + | 8.36353i | −0.00816918 | + | 0.301401i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.0000 | + | 11.0000i | −0.395899 | + | 0.395899i | ||||
\(773\) | −14.2583 | + | 14.2583i | −0.512835 | + | 0.512835i | −0.915394 | − | 0.402559i | \(-0.868121\pi\) |
0.402559 | + | 0.915394i | \(0.368121\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.8293 | − | 46.5008i | 0.604526 | − | 1.67036i | ||||
\(776\) | 2.31773i | 0.0832017i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.7016 | − | 15.7016i | −0.562928 | − | 0.562928i | ||||
\(779\) | 49.2235i | 1.76361i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.40312 | 0.0502077 | ||||||||
\(782\) | −13.9873 | − | 13.9873i | −0.500184 | − | 0.500184i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.02214 | + | 6.70156i | 0.0722194 | + | 0.239342i | ||||
\(785\) | −23.9157 | − | 34.0892i | −0.853587 | − | 1.21669i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.1344 | + | 35.1344i | 1.25241 | + | 1.25241i | 0.954638 | + | 0.297769i | \(0.0962426\pi\) |
0.297769 | + | 0.954638i | \(0.403757\pi\) | |||||||
\(788\) | −7.49312 | − | 7.49312i | −0.266931 | − | 0.266931i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.50723 | − | 13.5515i | −0.338252 | − | 0.482142i | ||||
\(791\) | 23.0495 | − | 3.40175i | 0.819545 | − | 0.120952i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.8062 | + | 22.8062i | 0.809874 | + | 0.809874i | ||||
\(794\) | 6.72263 | 0.238577 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 11.7496i | − | 0.416454i | ||||||
\(797\) | −14.2583 | − | 14.2583i | −0.505054 | − | 0.505054i | 0.407950 | − | 0.913004i | \(-0.366244\pi\) |
−0.913004 | + | 0.407950i | \(0.866244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.00000i | − | 0.283020i | ||||||
\(800\) | −4.52769 | + | 2.12132i | −0.160078 | + | 0.0750000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.2094 | + | 22.2094i | −0.784240 | + | 0.784240i | ||||
\(803\) | 6.49206 | − | 6.49206i | 0.229100 | − | 0.229100i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.9536 | + | 0.866071i | 1.12622 | + | 0.0305250i | ||||
\(806\) | −51.2078 | −1.80372 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.68317 | + | 5.68317i | −0.199933 | + | 0.199933i | ||||
\(809\) | − | 34.2372i | − | 1.20372i | −0.798603 | − | 0.601858i | \(-0.794427\pi\) | ||
0.798603 | − | 0.601858i | \(-0.205573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.3494i | − | 0.784794i | −0.919796 | − | 0.392397i | \(-0.871646\pi\) | ||
0.919796 | − | 0.392397i | \(-0.128354\pi\) | |||||||
\(812\) | −12.7208 | + | 17.1257i | −0.446413 | + | 0.600995i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.40312i | 0.0491795i | ||||||||
\(815\) | −2.54830 | − | 3.63232i | −0.0892630 | − | 0.127235i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.50723 | − | 9.50723i | −0.332616 | − | 0.332616i | ||||
\(818\) | −4.40490 | + | 4.40490i | −0.154014 | + | 0.154014i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.8062 | + | 4.00000i | 0.796429 | + | 0.139686i | ||||
\(821\) | 16.8446 | 0.587881 | 0.293940 | − | 0.955824i | \(-0.405033\pi\) | ||||
0.293940 | + | 0.955824i | \(0.405033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.9109 | + | 27.9109i | 0.972914 | + | 0.972914i | 0.999643 | − | 0.0267287i | \(-0.00850902\pi\) |
−0.0267287 | + | 0.999643i | \(0.508509\pi\) | |||||||
\(824\) | 16.8470 | 0.586894 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.89531 | − | 19.6180i | −0.100741 | − | 0.682596i | ||||
\(827\) | 26.0259 | − | 26.0259i | 0.905011 | − | 0.905011i | −0.0908534 | − | 0.995864i | \(-0.528959\pi\) |
0.995864 | + | 0.0908534i | \(0.0289595\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.4774 | 0.850136 | 0.425068 | − | 0.905161i | \(-0.360250\pi\) | ||||
0.425068 | + | 0.905161i | \(0.360250\pi\) | |||||||
\(830\) | −4.39069 | + | 25.0338i | −0.152403 | + | 0.868936i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.66103 | + | 3.66103i | 0.126923 | + | 0.126923i | ||||
\(833\) | 12.1138 | − | 22.5834i | 0.419718 | − | 0.782468i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.59688 | + | 9.40312i | 0.228294 | + | 0.325409i | ||||
\(836\) | − | 6.72263i | − | 0.232507i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.6663 | − | 16.6663i | 0.575726 | − | 0.575726i | ||||
\(839\) | 23.8002 | 0.821674 | 0.410837 | − | 0.911709i | \(-0.365236\pi\) | ||||
0.410837 | + | 0.911709i | \(0.365236\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −36.0156 | −1.24192 | ||||||||
\(842\) | 13.7201 | − | 13.7201i | 0.472825 | − | 0.472825i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 14.8062i | − | 0.509652i | ||||||
\(845\) | 5.33320 | − | 30.4076i | 0.183468 | − | 1.04605i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.1987 | − | 19.1154i | 0.487873 | − | 0.656811i | ||||
\(848\) | 6.64901 | + | 6.64901i | 0.228328 | + | 0.228328i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.2125 | + | 6.22947i | 0.590386 | + | 0.213669i | ||||
\(851\) | 5.36076 | 0.183764 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9050 | − | 28.9050i | 0.989687 | − | 0.989687i | −0.0102603 | − | 0.999947i | \(-0.503266\pi\) |
0.999947 | + | 0.0102603i | \(0.00326601\pi\) | |||||||
\(854\) | −16.3050 | + | 2.40637i | −0.557946 | + | 0.0823444i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.4031 | 0.458109 | ||||||||
\(857\) | 4.13389 | + | 4.13389i | 0.141211 | + | 0.141211i | 0.774178 | − | 0.632967i | \(-0.218163\pi\) |
−0.632967 | + | 0.774178i | \(0.718163\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.12397 | −0.311306 | −0.155653 | − | 0.987812i | \(-0.549748\pi\) | ||||
−0.155653 | + | 0.987812i | \(0.549748\pi\) | |||||||
\(860\) | −5.17748 | + | 3.63232i | −0.176550 | + | 0.123861i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.104686 | + | 0.104686i | −0.00356563 | + | 0.00356563i | ||||
\(863\) | 25.6039 | + | 25.6039i | 0.871567 | + | 0.871567i | 0.992643 | − | 0.121077i | \(-0.0386346\pi\) |
−0.121077 | + | 0.992643i | \(0.538635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.5078 | − | 24.9109i | 1.20730 | − | 0.846997i | ||||
\(866\) | 12.6727i | 0.430635i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.6036 | − | 21.0067i | 0.529620 | − | 0.713014i | ||||
\(869\) | − | 10.4696i | − | 0.355157i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.2882i | 0.992394i | ||||||||
\(872\) | 0.422055 | − | 0.422055i | 0.0142926 | − | 0.0142926i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −25.6844 | −0.868787 | ||||||||
\(875\) | −27.1164 | + | 11.8195i | −0.916701 | + | 0.399574i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.49219 | − | 6.49219i | 0.219226 | − | 0.219226i | −0.588946 | − | 0.808172i | \(-0.700457\pi\) |
0.808172 | + | 0.588946i | \(0.200457\pi\) | |||||||
\(878\) | 1.04358 | − | 1.04358i | 0.0352192 | − | 0.0352192i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.11473 | − | 0.546295i | −0.104998 | − | 0.0184156i | ||||
\(881\) | 43.5070i | 1.46579i | 0.680343 | + | 0.732893i | \(0.261831\pi\) | ||||
−0.680343 | + | 0.732893i | \(0.738169\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.19375 | − | 1.19375i | −0.0401729 | − | 0.0401729i | 0.686735 | − | 0.726908i | \(-0.259043\pi\) |
−0.726908 | + | 0.686735i | \(0.759043\pi\) | |||||||
\(884\) | − | 18.9549i | − | 0.637522i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.4031 | 0.786243 | ||||||||
\(887\) | 26.8905 | + | 26.8905i | 0.902895 | + | 0.902895i | 0.995686 | − | 0.0927904i | \(-0.0295786\pi\) |
−0.0927904 | + | 0.995686i | \(0.529579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.11473 | − | 21.1047i | −0.104465 | − | 0.707828i | ||||
\(890\) | 22.7755 | − | 15.9784i | 0.763435 | − | 0.535597i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.20732 | − | 4.20732i | −0.140872 | − | 0.140872i | ||||
\(893\) | −7.34507 | − | 7.34507i | −0.245794 | − | 0.245794i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.31281 | + | 7.48509i | −0.0438825 | + | 0.250199i | ||||
\(896\) | −2.61740 | + | 0.386289i | −0.0874412 | + | 0.0129050i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.5969 | + | 12.5969i | 0.420363 | + | 0.420363i | ||||
\(899\) | 79.7493 | 2.65979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 34.4251i | − | 1.14687i | ||||||
\(902\) | 10.3550 | + | 10.3550i | 0.344782 | + | 0.344782i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.80625i | 0.292891i | ||||||||
\(905\) | −1.26616 | + | 7.21912i | −0.0420887 | + | 0.239972i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.5969 | − | 16.5969i | 0.551090 | − | 0.551090i | −0.375665 | − | 0.926755i | \(-0.622586\pi\) |
0.926755 | + | 0.375665i | \(0.122586\pi\) | |||||||
\(908\) | −17.0776 | + | 17.0776i | −0.566739 | + | 0.566739i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 21.0642 | + | 22.2378i | 0.698270 | + | 0.737176i | ||||
\(911\) | −30.1205 | −0.997938 | −0.498969 | − | 0.866620i | \(-0.666288\pi\) | ||||
−0.498969 | + | 0.866620i | \(0.666288\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3663 | + | 11.3663i | −0.376171 | + | 0.376171i | ||||
\(914\) | 8.21128i | 0.271605i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.85911i | 0.0614267i | ||||||||
\(917\) | −9.35569 | − | 6.94932i | −0.308952 | − | 0.229487i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.8219i | 1.31360i | 0.754064 | + | 0.656801i | \(0.228091\pi\) | ||||
−0.754064 | + | 0.656801i | \(0.771909\pi\) | |||||||
\(920\) | −2.08717 | + | 11.9001i | −0.0688118 | + | 0.392335i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.929554 | + | 0.929554i | 0.0306132 | + | 0.0306132i | ||||
\(923\) | 3.63232 | − | 3.63232i | 0.119559 | − | 0.119559i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.49219 | + | 2.10469i | −0.147702 | + | 0.0692017i | ||||
\(926\) | −18.5328 | −0.609026 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.70156 | − | 5.70156i | −0.187163 | − | 0.187163i | ||||
\(929\) | 17.1585 | 0.562951 | 0.281475 | − | 0.959568i | \(-0.409176\pi\) | ||||
0.281475 | + | 0.959568i | \(0.409176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.61250 | − | 31.8567i | −0.315037 | − | 1.04406i | ||||
\(932\) | 4.24264 | − | 4.24264i | 0.138972 | − | 0.138972i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.64813 | 0.250254 | ||||||||
\(935\) | 6.64901 | + | 9.47744i | 0.217446 | + | 0.309945i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.6453 | − | 34.6453i | −1.13181 | − | 1.13181i | −0.989876 | − | 0.141938i | \(-0.954667\pi\) |
−0.141938 | − | 0.989876i | \(-0.545333\pi\) | |||||||
\(938\) | −12.0148 | − | 8.92444i | −0.392296 | − | 0.291393i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.00000 | + | 2.80625i | −0.130466 | + | 0.0915297i | ||||
\(941\) | − | 25.1148i | − | 0.818719i | −0.912373 | − | 0.409360i | \(-0.865752\pi\) | ||
0.912373 | − | 0.409360i | \(-0.134248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.5620 | − | 39.5620i | 1.28832 | − | 1.28832i | ||||
\(944\) | 7.49521 | 0.243948 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | 1.26616 | − | 1.26616i | 0.0411448 | − | 0.0411448i | −0.686235 | − | 0.727380i | \(-0.740738\pi\) |
0.727380 | + | 0.686235i | \(0.240738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 33.6125i | − | 1.09111i | ||||||
\(950\) | 21.5229 | − | 10.0839i | 0.698296 | − | 0.327166i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.77576 | + | 5.77576i | 0.252014 | + | 0.187193i | ||||
\(953\) | 32.5269 | + | 32.5269i | 1.05365 | + | 1.05365i | 0.998477 | + | 0.0551732i | \(0.0175711\pi\) |
0.0551732 | + | 0.998477i | \(0.482429\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.55554 | + | 1.14978i | 0.212132 | + | 0.0372060i | ||||
\(956\) | 23.6196 | 0.763912 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.27777 | + | 3.27777i | −0.105900 | + | 0.105900i | ||||
\(959\) | −6.49206 | − | 43.9887i | −0.209640 | − | 1.42047i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −66.8219 | −2.15554 | ||||||||
\(962\) | 3.63232 | + | 3.63232i | 0.117111 | + | 0.117111i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.8253 | −0.767360 | ||||||||
\(965\) | −19.9778 | − | 28.4761i | −0.643107 | − | 0.916679i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.1047 | − | 15.1047i | 0.485734 | − | 0.485734i | −0.421223 | − | 0.906957i | \(-0.638399\pi\) |
0.906957 | + | 0.421223i | \(0.138399\pi\) | |||||||
\(968\) | 6.36396 | + | 6.36396i | 0.204545 | + | 0.204545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.10469 | − | 0.895314i | −0.163902 | − | 0.0287468i | ||||
\(971\) | − | 35.0086i | − | 1.12348i | −0.827314 | − | 0.561740i | \(-0.810132\pi\) | ||
0.827314 | − | 0.561740i | \(-0.189868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.0510 | − | 25.6479i | 0.610747 | − | 0.822233i | ||||
\(974\) | − | 23.3456i | − | 0.748040i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 6.22947i | − | 0.199400i | ||||||
\(977\) | 8.21128 | − | 8.21128i | 0.262702 | − | 0.262702i | −0.563449 | − | 0.826151i | \(-0.690526\pi\) |
0.826151 | + | 0.563449i | \(0.190526\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5958 | 0.562364 | ||||||||
\(980\) | −15.5410 | + | 1.86493i | −0.496438 | + | 0.0595730i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.4031 | + | 28.4031i | −0.906380 | + | 0.906380i | ||||
\(983\) | 35.2392 | − | 35.2392i | 1.12396 | − | 1.12396i | 0.132814 | − | 0.991141i | \(-0.457599\pi\) |
0.991141 | − | 0.132814i | \(-0.0424014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.3977 | − | 13.6087i | 0.618063 | − | 0.433610i | ||||
\(986\) | 29.5197i | 0.940099i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.4031 | − | 17.4031i | −0.553667 | − | 0.553667i | ||||
\(989\) | 15.2823i | 0.485950i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.80625 | 0.0891434 | 0.0445717 | − | 0.999006i | \(-0.485808\pi\) | ||||
0.0445717 | + | 0.999006i | \(0.485808\pi\) | |||||||
\(992\) | 6.99364 | + | 6.99364i | 0.222048 | + | 0.222048i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.383260 | + | 2.59688i | 0.0121563 | + | 0.0823679i | ||||
\(995\) | 25.8779 | + | 4.53874i | 0.820385 | + | 0.143888i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.3534 | + | 15.3534i | 0.486248 | + | 0.486248i | 0.907120 | − | 0.420872i | \(-0.138276\pi\) |
−0.420872 | + | 0.907120i | \(0.638276\pi\) | |||||||
\(998\) | 5.65685 | + | 5.65685i | 0.179065 | + | 0.179065i | ||||
\(999\) | 0 | 0 |
(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 | 630.2.p.d.433.8 | yes | 16 | |
3.2 | odd | 2 | inner | 630.2.p.d.433.1 | yes | 16 | |
5.2 | odd | 4 | inner | 630.2.p.d.307.5 | yes | 16 | |
7.6 | odd | 2 | inner | 630.2.p.d.433.5 | yes | 16 | |
15.2 | even | 4 | inner | 630.2.p.d.307.4 | yes | 16 | |
21.20 | even | 2 | inner | 630.2.p.d.433.4 | yes | 16 | |
35.27 | even | 4 | inner | 630.2.p.d.307.8 | yes | 16 | |
105.62 | odd | 4 | inner | 630.2.p.d.307.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.p.d.307.1 | ✓ | 16 | 105.62 | odd | 4 | inner | |
630.2.p.d.307.4 | yes | 16 | 15.2 | even | 4 | inner | |
630.2.p.d.307.5 | yes | 16 | 5.2 | odd | 4 | inner | |
630.2.p.d.307.8 | yes | 16 | 35.27 | even | 4 | inner | |
630.2.p.d.433.1 | yes | 16 | 3.2 | odd | 2 | inner | |
630.2.p.d.433.4 | yes | 16 | 21.20 | even | 2 | inner | |
630.2.p.d.433.5 | yes | 16 | 7.6 | odd | 2 | inner | |
630.2.p.d.433.8 | yes | 16 | 1.1 | even | 1 | trivial |