Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (of order \(6\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.7652750400000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} - 14 x^{9} + 21 x^{8} - 108 x^{7} + 368 x^{6} - 216 x^{5} + 84 x^{4} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.1 | ||
Root | \(-0.685661 - 0.685661i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.949 |
Dual form | 1470.2.n.j.79.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.20942 | + | 0.344208i | −0.988081 | + | 0.153935i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 1.74131 | − | 1.40280i | 0.550649 | − | 0.443605i | ||||
\(11\) | 2.39213 | − | 4.14329i | 0.721254 | − | 1.24925i | −0.239243 | − | 0.970960i | \(-0.576899\pi\) |
0.960497 | − | 0.278289i | \(-0.0897674\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | 3.17103i | 0.879485i | 0.898124 | + | 0.439743i | \(0.144930\pi\) | ||||
−0.898124 | + | 0.439743i | \(0.855070\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.08551 | − | 0.806615i | −0.538478 | − | 0.208267i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.52625 | − | 2.61323i | −1.09778 | − | 0.633801i | −0.162140 | − | 0.986768i | \(-0.551840\pi\) |
−0.935636 | + | 0.352966i | \(0.885173\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | 1.58551 | + | 2.74619i | 0.363742 | + | 0.630020i | 0.988573 | − | 0.150740i | \(-0.0481656\pi\) |
−0.624831 | + | 0.780760i | \(0.714832\pi\) | |||||||
\(20\) | −0.806615 | + | 2.08551i | −0.180365 | + | 0.466335i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.78426i | 1.02001i | ||||||||
\(23\) | 6.21029 | − | 3.58551i | 1.29494 | − | 0.747632i | 0.315411 | − | 0.948955i | \(-0.397858\pi\) |
0.979525 | + | 0.201324i | \(0.0645243\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 4.76304 | − | 1.52100i | 0.952608 | − | 0.304200i | ||||
\(26\) | −1.58551 | − | 2.74619i | −0.310945 | − | 0.538573i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.38677 | −0.443212 | −0.221606 | − | 0.975136i | \(-0.571130\pi\) | ||||
−0.221606 | + | 0.975136i | \(0.571130\pi\) | |||||||
\(30\) | 2.20942 | − | 0.344208i | 0.403382 | − | 0.0628436i | ||||
\(31\) | 2.08551 | − | 3.61222i | 0.374570 | − | 0.648773i | −0.615693 | − | 0.787986i | \(-0.711124\pi\) |
0.990263 | + | 0.139213i | \(0.0444572\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 4.14329 | − | 2.39213i | 0.721254 | − | 0.416416i | ||||
\(34\) | 5.22646 | 0.896330 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.21029 | + | 3.58551i | −1.02097 | + | 0.589455i | −0.914384 | − | 0.404849i | \(-0.867324\pi\) |
−0.106582 | + | 0.994304i | \(0.533991\pi\) | |||||||
\(38\) | −2.74619 | − | 1.58551i | −0.445491 | − | 0.257204i | ||||
\(39\) | −1.58551 | + | 2.74619i | −0.253886 | + | 0.439743i | ||||
\(40\) | −0.344208 | − | 2.20942i | −0.0544241 | − | 0.349339i | ||||
\(41\) | 2.05543 | 0.321004 | 0.160502 | − | 0.987035i | \(-0.448689\pi\) | ||||
0.160502 | + | 0.987035i | \(0.448689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −2.39213 | − | 4.14329i | −0.360627 | − | 0.624625i | ||||
\(45\) | −1.40280 | − | 1.74131i | −0.209117 | − | 0.259579i | ||||
\(46\) | −3.58551 | + | 6.21029i | −0.528655 | + | 0.915658i | ||||
\(47\) | 9.97063 | − | 5.75654i | 1.45437 | − | 0.839678i | 0.455641 | − | 0.890164i | \(-0.349410\pi\) |
0.998725 | + | 0.0504854i | \(0.0160768\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.36441 | + | 3.69874i | −0.475800 | + | 0.523081i | ||||
\(51\) | −2.61323 | − | 4.52625i | −0.365925 | − | 0.633801i | ||||
\(52\) | 2.74619 | + | 1.58551i | 0.380828 | + | 0.219871i | ||||
\(53\) | 7.02832 | + | 4.05780i | 0.965413 | + | 0.557382i | 0.897835 | − | 0.440332i | \(-0.145139\pi\) |
0.0675785 | + | 0.997714i | \(0.478473\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −3.85906 | + | 9.97764i | −0.520355 | + | 1.34539i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.17103i | 0.420013i | ||||||||
\(58\) | 2.06700 | − | 1.19339i | 0.271411 | − | 0.156699i | ||||
\(59\) | 5.36441 | − | 9.29144i | 0.698387 | − | 1.20964i | −0.270638 | − | 0.962681i | \(-0.587235\pi\) |
0.969025 | − | 0.246961i | \(-0.0794320\pi\) | |||||||
\(60\) | −1.74131 | + | 1.40280i | −0.224802 | + | 0.181101i | ||||
\(61\) | 3.55780 | + | 6.16229i | 0.455530 | + | 0.789000i | 0.998718 | − | 0.0506101i | \(-0.0161166\pi\) |
−0.543189 | + | 0.839611i | \(0.682783\pi\) | |||||||
\(62\) | 4.17103i | 0.529721i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.09150 | − | 7.00613i | −0.135383 | − | 0.869003i | ||||
\(66\) | −2.39213 | + | 4.14329i | −0.294451 | + | 0.510004i | ||||
\(67\) | 8.28658 | + | 4.78426i | 1.01237 | + | 0.584490i | 0.911884 | − | 0.410448i | \(-0.134628\pi\) |
0.100483 | + | 0.994939i | \(0.467961\pi\) | |||||||
\(68\) | −4.52625 | + | 2.61323i | −0.548888 | + | 0.316901i | ||||
\(69\) | 7.17103 | 0.863291 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 3.46410 | + | 2.00000i | 0.405442 | + | 0.234082i | 0.688830 | − | 0.724923i | \(-0.258125\pi\) |
−0.283387 | + | 0.959006i | \(0.591458\pi\) | |||||||
\(74\) | 3.58551 | − | 6.21029i | 0.416808 | − | 0.721932i | ||||
\(75\) | 4.88541 | + | 1.06430i | 0.564119 | + | 0.122894i | ||||
\(76\) | 3.17103 | 0.363742 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 3.17103i | − | 0.359048i | ||||||
\(79\) | 6.08551 | + | 10.5404i | 0.684674 | + | 1.18589i | 0.973539 | + | 0.228520i | \(0.0733887\pi\) |
−0.288865 | + | 0.957370i | \(0.593278\pi\) | |||||||
\(80\) | 1.40280 | + | 1.74131i | 0.156838 | + | 0.194684i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.78005 | + | 1.02771i | −0.196574 | + | 0.113492i | ||||
\(83\) | 3.39749i | 0.372923i | 0.982462 | + | 0.186461i | \(0.0597019\pi\) | ||||
−0.982462 | + | 0.186461i | \(0.940298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8999 | + | 4.21574i | 1.18226 | + | 0.457261i | ||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | −2.06700 | − | 1.19339i | −0.221606 | − | 0.127944i | ||||
\(88\) | 4.14329 | + | 2.39213i | 0.441676 | + | 0.255002i | ||||
\(89\) | −4.78426 | − | 8.28658i | −0.507131 | − | 0.878376i | −0.999966 | − | 0.00825326i | \(-0.997373\pi\) |
0.492835 | − | 0.870123i | \(-0.335960\pi\) | |||||||
\(90\) | 2.08551 | + | 0.806615i | 0.219833 | + | 0.0850247i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 7.17103i | − | 0.747632i | ||||||
\(93\) | 3.61222 | − | 2.08551i | 0.374570 | − | 0.216258i | ||||
\(94\) | −5.75654 | + | 9.97063i | −0.593742 | + | 1.02839i | ||||
\(95\) | −4.44833 | − | 5.52173i | −0.456389 | − | 0.566518i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 1.27117i | − | 0.129068i | −0.997916 | − | 0.0645339i | \(-0.979444\pi\) | ||
0.997916 | − | 0.0645339i | \(-0.0205561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.78426 | 0.480836 | ||||||||
\(100\) | 1.06430 | − | 4.88541i | 0.106430 | − | 0.488541i | ||||
\(101\) | −4.00000 | + | 6.92820i | −0.398015 | + | 0.689382i | −0.993481 | − | 0.113998i | \(-0.963634\pi\) |
0.595466 | + | 0.803380i | \(0.296967\pi\) | |||||||
\(102\) | 4.52625 | + | 2.61323i | 0.448165 | + | 0.258748i | ||||
\(103\) | 9.72240 | − | 5.61323i | 0.957976 | − | 0.553088i | 0.0624268 | − | 0.998050i | \(-0.480116\pi\) |
0.895550 | + | 0.444962i | \(0.146783\pi\) | |||||||
\(104\) | −3.17103 | −0.310945 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.11560 | −0.788257 | ||||||||
\(107\) | 1.21026 | − | 0.698745i | 0.117000 | − | 0.0675502i | −0.440358 | − | 0.897822i | \(-0.645148\pi\) |
0.557358 | + | 0.830272i | \(0.311815\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 6.22646 | − | 10.7845i | 0.596387 | − | 1.03297i | −0.396963 | − | 0.917835i | \(-0.629936\pi\) |
0.993350 | − | 0.115137i | \(-0.0367308\pi\) | |||||||
\(110\) | −1.64678 | − | 10.5704i | −0.157015 | − | 1.00785i | ||||
\(111\) | −7.17103 | −0.680644 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.34206i | 0.596611i | 0.954470 | + | 0.298305i | \(0.0964214\pi\) | ||||
−0.954470 | + | 0.298305i | \(0.903579\pi\) | |||||||
\(114\) | −1.58551 | − | 2.74619i | −0.148497 | − | 0.257204i | ||||
\(115\) | −12.4870 | + | 10.0595i | −1.16442 | + | 0.938056i | ||||
\(116\) | −1.19339 | + | 2.06700i | −0.110803 | + | 0.191916i | ||||
\(117\) | −2.74619 | + | 1.58551i | −0.253886 | + | 0.146581i | ||||
\(118\) | 10.7288i | 0.987669i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.806615 | − | 2.08551i | 0.0736335 | − | 0.190381i | ||||
\(121\) | −5.94457 | − | 10.2963i | −0.540415 | − | 0.936027i | ||||
\(122\) | −6.16229 | − | 3.55780i | −0.557908 | − | 0.322108i | ||||
\(123\) | 1.78005 | + | 1.02771i | 0.160502 | + | 0.0926659i | ||||
\(124\) | −2.08551 | − | 3.61222i | −0.187285 | − | 0.324387i | ||||
\(125\) | −10.0000 | + | 5.00000i | −0.894427 | + | 0.447214i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.0107i | − | 1.59819i | −0.601203 | − | 0.799096i | \(-0.705312\pi\) | ||
0.601203 | − | 0.799096i | \(-0.294688\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | 4.44833 | + | 5.52173i | 0.390144 | + | 0.484288i | ||||
\(131\) | −2.77890 | − | 4.81320i | −0.242794 | − | 0.420531i | 0.718715 | − | 0.695304i | \(-0.244730\pi\) |
−0.961509 | + | 0.274774i | \(0.911397\pi\) | |||||||
\(132\) | − | 4.78426i | − | 0.416416i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.56852 | −0.826594 | ||||||||
\(135\) | −0.344208 | − | 2.20942i | −0.0296247 | − | 0.190156i | ||||
\(136\) | 2.61323 | − | 4.52625i | 0.224083 | − | 0.388122i | ||||
\(137\) | −12.8128 | − | 7.39749i | −1.09467 | − | 0.632010i | −0.159857 | − | 0.987140i | \(-0.551103\pi\) |
−0.934817 | + | 0.355130i | \(0.884437\pi\) | |||||||
\(138\) | −6.21029 | + | 3.58551i | −0.528655 | + | 0.305219i | ||||
\(139\) | 3.65794 | 0.310262 | 0.155131 | − | 0.987894i | \(-0.450420\pi\) | ||||
0.155131 | + | 0.987894i | \(0.450420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5131 | 0.969577 | ||||||||
\(142\) | −5.19615 | + | 3.00000i | −0.436051 | + | 0.251754i | ||||
\(143\) | 13.1385 | + | 7.58551i | 1.09870 | + | 0.634333i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 5.27337 | − | 0.821546i | 0.437929 | − | 0.0682257i | ||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.17103i | 0.589455i | ||||||||
\(149\) | 11.1710 | + | 19.3488i | 0.915166 | + | 1.58511i | 0.806657 | + | 0.591019i | \(0.201274\pi\) |
0.108509 | + | 0.994095i | \(0.465392\pi\) | |||||||
\(150\) | −4.76304 | + | 1.52100i | −0.388901 | + | 0.124189i | ||||
\(151\) | −8.25654 | + | 14.3008i | −0.671908 | + | 1.16378i | 0.305454 | + | 0.952207i | \(0.401192\pi\) |
−0.977362 | + | 0.211572i | \(0.932142\pi\) | |||||||
\(152\) | −2.74619 | + | 1.58551i | −0.222746 | + | 0.128602i | ||||
\(153\) | − | 5.22646i | − | 0.422534i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.36441 | + | 8.69874i | −0.270236 | + | 0.698700i | ||||
\(156\) | 1.58551 | + | 2.74619i | 0.126943 | + | 0.219871i | ||||
\(157\) | −8.61225 | − | 4.97229i | −0.687332 | − | 0.396832i | 0.115280 | − | 0.993333i | \(-0.463224\pi\) |
−0.802612 | + | 0.596502i | \(0.796557\pi\) | |||||||
\(158\) | −10.5404 | − | 6.08551i | −0.838551 | − | 0.484138i | ||||
\(159\) | 4.05780 | + | 7.02832i | 0.321804 | + | 0.557382i | ||||
\(160\) | −2.08551 | − | 0.806615i | −0.164874 | − | 0.0637685i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 2.49796 | − | 1.44220i | 0.195656 | − | 0.112962i | −0.398972 | − | 0.916963i | \(-0.630633\pi\) |
0.594627 | + | 0.804001i | \(0.297300\pi\) | |||||||
\(164\) | 1.02771 | − | 1.78005i | 0.0802511 | − | 0.138999i | ||||
\(165\) | −8.33086 | + | 6.71137i | −0.648557 | + | 0.522479i | ||||
\(166\) | −1.69874 | − | 2.94231i | −0.131848 | − | 0.228368i | ||||
\(167\) | 4.05543i | 0.313819i | 0.987613 | + | 0.156909i | \(0.0501530\pi\) | ||||
−0.987613 | + | 0.156909i | \(0.949847\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.94457 | 0.226505 | ||||||||
\(170\) | −11.5474 | + | 1.79899i | −0.885647 | + | 0.137976i | ||||
\(171\) | −1.58551 | + | 2.74619i | −0.121247 | + | 0.210007i | ||||
\(172\) | −1.73205 | − | 1.00000i | −0.132068 | − | 0.0762493i | ||||
\(173\) | −5.54039 | + | 3.19874i | −0.421228 | + | 0.243196i | −0.695603 | − | 0.718427i | \(-0.744863\pi\) |
0.274375 | + | 0.961623i | \(0.411529\pi\) | |||||||
\(174\) | 2.38677 | 0.180941 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.78426 | −0.360627 | ||||||||
\(177\) | 9.29144 | − | 5.36441i | 0.698387 | − | 0.403214i | ||||
\(178\) | 8.28658 | + | 4.78426i | 0.621105 | + | 0.358595i | ||||
\(179\) | 9.75654 | − | 16.8988i | 0.729238 | − | 1.26308i | −0.227967 | − | 0.973669i | \(-0.573208\pi\) |
0.957206 | − | 0.289409i | \(-0.0934588\pi\) | |||||||
\(180\) | −2.20942 | + | 0.344208i | −0.164680 | + | 0.0256558i | ||||
\(181\) | 23.0262 | 1.71152 | 0.855761 | − | 0.517371i | \(-0.173089\pi\) | ||||
0.855761 | + | 0.517371i | \(0.173089\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.11560i | 0.526000i | ||||||||
\(184\) | 3.58551 | + | 6.21029i | 0.264328 | + | 0.457829i | ||||
\(185\) | 12.4870 | − | 10.0595i | 0.918060 | − | 0.739591i | ||||
\(186\) | −2.08551 | + | 3.61222i | −0.152917 | + | 0.264861i | ||||
\(187\) | −21.6547 | + | 12.5024i | −1.58355 | + | 0.914264i | ||||
\(188\) | − | 11.5131i | − | 0.839678i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.61323 | + | 2.55780i | 0.479774 | + | 0.185562i | ||||
\(191\) | 5.11560 | + | 8.86048i | 0.370152 | + | 0.641122i | 0.989589 | − | 0.143925i | \(-0.0459723\pi\) |
−0.619437 | + | 0.785047i | \(0.712639\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 10.0574 | + | 5.80661i | 0.723944 | + | 0.417969i | 0.816203 | − | 0.577766i | \(-0.196075\pi\) |
−0.0922586 | + | 0.995735i | \(0.529409\pi\) | |||||||
\(194\) | 0.635585 | + | 1.10087i | 0.0456324 | + | 0.0790376i | ||||
\(195\) | 2.55780 | − | 6.61323i | 0.183168 | − | 0.473583i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.39749i | 0.170814i | 0.996346 | + | 0.0854070i | \(0.0272191\pi\) | ||||
−0.996346 | + | 0.0854070i | \(0.972781\pi\) | |||||||
\(198\) | −4.14329 | + | 2.39213i | −0.294451 | + | 0.170001i | ||||
\(199\) | 9.17103 | − | 15.8847i | 0.650117 | − | 1.12604i | −0.332977 | − | 0.942935i | \(-0.608053\pi\) |
0.983094 | − | 0.183101i | \(-0.0586135\pi\) | |||||||
\(200\) | 1.52100 | + | 4.76304i | 0.107551 | + | 0.336798i | ||||
\(201\) | 4.78426 | + | 8.28658i | 0.337456 | + | 0.584490i | ||||
\(202\) | − | 8.00000i | − | 0.562878i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.22646 | −0.365925 | ||||||||
\(205\) | −4.54130 | + | 0.707496i | −0.317178 | + | 0.0494137i | ||||
\(206\) | −5.61323 | + | 9.72240i | −0.391092 | + | 0.677392i | ||||
\(207\) | 6.21029 | + | 3.58551i | 0.431645 | + | 0.249211i | ||||
\(208\) | 2.74619 | − | 1.58551i | 0.190414 | − | 0.109936i | ||||
\(209\) | 15.1710 | 1.04940 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.82897 | −0.194754 | −0.0973772 | − | 0.995248i | \(-0.531045\pi\) | ||||
−0.0973772 | + | 0.995248i | \(0.531045\pi\) | |||||||
\(212\) | 7.02832 | − | 4.05780i | 0.482707 | − | 0.278691i | ||||
\(213\) | 5.19615 | + | 3.00000i | 0.356034 | + | 0.205557i | ||||
\(214\) | −0.698745 | + | 1.21026i | −0.0477652 | + | 0.0827318i | ||||
\(215\) | 0.688417 | + | 4.41883i | 0.0469496 | + | 0.301362i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.4529i | 0.843418i | ||||||||
\(219\) | 2.00000 | + | 3.46410i | 0.135147 | + | 0.234082i | ||||
\(220\) | 6.71137 | + | 8.33086i | 0.452480 | + | 0.561667i | ||||
\(221\) | 8.28663 | − | 14.3529i | 0.557419 | − | 0.965478i | ||||
\(222\) | 6.21029 | − | 3.58551i | 0.416808 | − | 0.240644i | ||||
\(223\) | − | 14.2973i | − | 0.957421i | −0.877973 | − | 0.478711i | \(-0.841104\pi\) | ||
0.877973 | − | 0.478711i | \(-0.158896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.69874 | + | 3.36441i | 0.246583 | + | 0.224294i | ||||
\(226\) | −3.17103 | − | 5.49238i | −0.210934 | − | 0.365348i | ||||
\(227\) | −9.57428 | − | 5.52771i | −0.635467 | − | 0.366887i | 0.147399 | − | 0.989077i | \(-0.452910\pi\) |
−0.782866 | + | 0.622190i | \(0.786243\pi\) | |||||||
\(228\) | 2.74619 | + | 1.58551i | 0.181871 | + | 0.105003i | ||||
\(229\) | 9.22646 | + | 15.9807i | 0.609702 | + | 1.05603i | 0.991289 | + | 0.131702i | \(0.0420441\pi\) |
−0.381588 | + | 0.924333i | \(0.624623\pi\) | |||||||
\(230\) | 5.78426 | − | 14.9553i | 0.381403 | − | 0.986123i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2.38677i | − | 0.156699i | ||||||
\(233\) | −7.89434 | + | 4.55780i | −0.517175 | + | 0.298591i | −0.735778 | − | 0.677223i | \(-0.763183\pi\) |
0.218603 | + | 0.975814i | \(0.429850\pi\) | |||||||
\(234\) | 1.58551 | − | 2.74619i | 0.103648 | − | 0.179524i | ||||
\(235\) | −20.0478 | + | 16.1506i | −1.30778 | + | 1.05355i | ||||
\(236\) | −5.36441 | − | 9.29144i | −0.349194 | − | 0.604821i | ||||
\(237\) | 12.1710i | 0.790593i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.1156 | −0.848378 | −0.424189 | − | 0.905574i | \(-0.639441\pi\) | ||||
−0.424189 | + | 0.905574i | \(0.639441\pi\) | |||||||
\(240\) | 0.344208 | + | 2.20942i | 0.0222186 | + | 0.142617i | ||||
\(241\) | −2.67103 | + | 4.62636i | −0.172056 | + | 0.298010i | −0.939139 | − | 0.343539i | \(-0.888374\pi\) |
0.767082 | + | 0.641549i | \(0.221708\pi\) | |||||||
\(242\) | 10.2963 | + | 5.94457i | 0.661871 | + | 0.382131i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 7.11560 | 0.455530 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.05543 | −0.131049 | ||||||||
\(247\) | −8.70826 | + | 5.02771i | −0.554093 | + | 0.319906i | ||||
\(248\) | 3.61222 | + | 2.08551i | 0.229376 | + | 0.132430i | ||||
\(249\) | −1.69874 | + | 2.94231i | −0.107654 | + | 0.186461i | ||||
\(250\) | 6.16025 | − | 9.33013i | 0.389609 | − | 0.590089i | ||||
\(251\) | −27.9213 | −1.76238 | −0.881188 | − | 0.472765i | \(-0.843256\pi\) | ||||
−0.881188 | + | 0.472765i | \(0.843256\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 34.3081i | − | 2.15693i | ||||||
\(254\) | 9.00536 | + | 15.5977i | 0.565047 | + | 0.978689i | ||||
\(255\) | 7.33169 | + | 9.10087i | 0.459128 | + | 0.569918i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −18.3052 | + | 10.5685i | −1.14185 | + | 0.659246i | −0.946887 | − | 0.321565i | \(-0.895791\pi\) |
−0.194960 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(258\) | 2.00000i | 0.124515i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.61323 | − | 2.55780i | −0.410135 | − | 0.158628i | ||||
\(261\) | −1.19339 | − | 2.06700i | −0.0738687 | − | 0.127944i | ||||
\(262\) | 4.81320 | + | 2.77890i | 0.297360 | + | 0.171681i | ||||
\(263\) | −10.3149 | − | 5.95529i | −0.636042 | − | 0.367219i | 0.147046 | − | 0.989130i | \(-0.453023\pi\) |
−0.783088 | + | 0.621911i | \(0.786357\pi\) | |||||||
\(264\) | 2.39213 | + | 4.14329i | 0.147225 | + | 0.255002i | ||||
\(265\) | −16.9252 | − | 6.54616i | −1.03971 | − | 0.402128i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 9.56852i | − | 0.585584i | ||||||
\(268\) | 8.28658 | − | 4.78426i | 0.506183 | − | 0.292245i | ||||
\(269\) | 1.63559 | − | 2.83292i | 0.0997234 | − | 0.172726i | −0.811847 | − | 0.583871i | \(-0.801538\pi\) |
0.911570 | + | 0.411145i | \(0.134871\pi\) | |||||||
\(270\) | 1.40280 | + | 1.74131i | 0.0853718 | + | 0.105973i | ||||
\(271\) | 0.311975 | + | 0.540356i | 0.0189511 | + | 0.0328243i | 0.875345 | − | 0.483498i | \(-0.160634\pi\) |
−0.856394 | + | 0.516322i | \(0.827301\pi\) | |||||||
\(272\) | 5.22646i | 0.316901i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.7950 | 0.893797 | ||||||||
\(275\) | 5.09187 | − | 23.3731i | 0.307051 | − | 1.40945i | ||||
\(276\) | 3.58551 | − | 6.21029i | 0.215823 | − | 0.373816i | ||||
\(277\) | −24.9372 | − | 14.3975i | −1.49833 | − | 0.865061i | −0.498332 | − | 0.866986i | \(-0.666054\pi\) |
−0.999998 | + | 0.00192499i | \(0.999387\pi\) | |||||||
\(278\) | −3.16787 | + | 1.82897i | −0.189996 | + | 0.109694i | ||||
\(279\) | 4.17103 | 0.249713 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.82897 | 0.168762 | 0.0843811 | − | 0.996434i | \(-0.473109\pi\) | ||||
0.0843811 | + | 0.996434i | \(0.473109\pi\) | |||||||
\(282\) | −9.97063 | + | 5.75654i | −0.593742 | + | 0.342797i | ||||
\(283\) | −21.7693 | − | 12.5685i | −1.29405 | − | 0.747121i | −0.314682 | − | 0.949197i | \(-0.601898\pi\) |
−0.979370 | + | 0.202076i | \(0.935231\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | −1.09150 | − | 7.00613i | −0.0646546 | − | 0.415007i | ||||
\(286\) | −15.1710 | −0.897082 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 5.15794 | + | 8.93381i | 0.303408 | + | 0.525519i | ||||
\(290\) | −4.15610 | + | 3.34816i | −0.244054 | + | 0.196611i | ||||
\(291\) | 0.635585 | − | 1.10087i | 0.0372587 | − | 0.0645339i | ||||
\(292\) | 3.46410 | − | 2.00000i | 0.202721 | − | 0.117041i | ||||
\(293\) | − | 10.2265i | − | 0.597436i | −0.954341 | − | 0.298718i | \(-0.903441\pi\) | ||
0.954341 | − | 0.298718i | \(-0.0965590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.65403 | + | 22.3751i | −0.503857 | + | 1.30273i | ||||
\(296\) | −3.58551 | − | 6.21029i | −0.208404 | − | 0.360966i | ||||
\(297\) | 4.14329 | + | 2.39213i | 0.240418 | + | 0.138805i | ||||
\(298\) | −19.3488 | − | 11.1710i | −1.12085 | − | 0.647120i | ||||
\(299\) | 11.3698 | + | 19.6930i | 0.657531 | + | 1.13888i | ||||
\(300\) | 3.36441 | − | 3.69874i | 0.194245 | − | 0.213547i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 16.5131i | − | 0.950222i | ||||||
\(303\) | −6.92820 | + | 4.00000i | −0.398015 | + | 0.229794i | ||||
\(304\) | 1.58551 | − | 2.74619i | 0.0909355 | − | 0.157505i | ||||
\(305\) | −9.98177 | − | 12.3904i | −0.571555 | − | 0.709475i | ||||
\(306\) | 2.61323 | + | 4.52625i | 0.149388 | + | 0.258748i | ||||
\(307\) | − | 23.4577i | − | 1.33880i | −0.742902 | − | 0.669400i | \(-0.766551\pi\) | ||
0.742902 | − | 0.669400i | \(-0.233449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2265 | 0.638651 | ||||||||
\(310\) | −1.43570 | − | 9.21554i | −0.0815425 | − | 0.523408i | ||||
\(311\) | −2.82897 | + | 4.89992i | −0.160416 | + | 0.277849i | −0.935018 | − | 0.354600i | \(-0.884617\pi\) |
0.774602 | + | 0.632449i | \(0.217950\pi\) | |||||||
\(312\) | −2.74619 | − | 1.58551i | −0.155473 | − | 0.0897621i | ||||
\(313\) | 14.1914 | − | 8.19339i | 0.802143 | − | 0.463118i | −0.0420769 | − | 0.999114i | \(-0.513397\pi\) |
0.844220 | + | 0.535997i | \(0.180064\pi\) | |||||||
\(314\) | 9.94457 | 0.561205 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1710 | 0.684674 | ||||||||
\(317\) | −3.90845 | + | 2.25654i | −0.219520 | + | 0.126740i | −0.605728 | − | 0.795672i | \(-0.707118\pi\) |
0.386208 | + | 0.922412i | \(0.373785\pi\) | |||||||
\(318\) | −7.02832 | − | 4.05780i | −0.394128 | − | 0.227550i | ||||
\(319\) | −5.70946 | + | 9.88908i | −0.319669 | + | 0.553682i | ||||
\(320\) | 2.20942 | − | 0.344208i | 0.123510 | − | 0.0192418i | ||||
\(321\) | 1.39749 | 0.0780003 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 16.5733i | − | 0.922161i | ||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 4.82313 | + | 15.1037i | 0.267539 | + | 0.837805i | ||||
\(326\) | −1.44220 | + | 2.49796i | −0.0798761 | + | 0.138349i | ||||
\(327\) | 10.7845 | − | 6.22646i | 0.596387 | − | 0.344324i | ||||
\(328\) | 2.05543i | 0.113492i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.85906 | − | 9.97764i | 0.212434 | − | 0.549251i | ||||
\(331\) | 6.54080 | + | 11.3290i | 0.359515 | + | 0.622698i | 0.987880 | − | 0.155220i | \(-0.0496088\pi\) |
−0.628365 | + | 0.777919i | \(0.716275\pi\) | |||||||
\(332\) | 2.94231 | + | 1.69874i | 0.161480 | + | 0.0932307i | ||||
\(333\) | −6.21029 | − | 3.58551i | −0.340322 | − | 0.196485i | ||||
\(334\) | −2.02771 | − | 3.51211i | −0.110952 | − | 0.192174i | ||||
\(335\) | −19.9553 | − | 7.71811i | −1.09027 | − | 0.421685i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.2973i | − | 1.10567i | −0.833292 | − | 0.552834i | \(-0.813547\pi\) | ||
0.833292 | − | 0.552834i | \(-0.186453\pi\) | |||||||
\(338\) | −2.55007 | + | 1.47229i | −0.138706 | + | 0.0800817i | ||||
\(339\) | −3.17103 | + | 5.49238i | −0.172227 | + | 0.298305i | ||||
\(340\) | 9.10087 | − | 7.33169i | 0.493564 | − | 0.397616i | ||||
\(341\) | −9.97764 | − | 17.2818i | −0.540320 | − | 0.935861i | ||||
\(342\) | − | 3.17103i | − | 0.171470i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | −15.8438 | + | 2.46833i | −0.853001 | + | 0.132890i | ||||
\(346\) | 3.19874 | − | 5.54039i | 0.171966 | − | 0.297853i | ||||
\(347\) | 12.5166 | + | 7.22646i | 0.671926 | + | 0.387937i | 0.796806 | − | 0.604235i | \(-0.206521\pi\) |
−0.124880 | + | 0.992172i | \(0.539855\pi\) | |||||||
\(348\) | −2.06700 | + | 1.19339i | −0.110803 | + | 0.0639722i | ||||
\(349\) | 13.8891 | 0.743469 | 0.371734 | − | 0.928339i | \(-0.378763\pi\) | ||||
0.371734 | + | 0.928339i | \(0.378763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.17103 | −0.169257 | ||||||||
\(352\) | 4.14329 | − | 2.39213i | 0.220838 | − | 0.127501i | ||||
\(353\) | −5.58839 | − | 3.22646i | −0.297440 | − | 0.171727i | 0.343852 | − | 0.939024i | \(-0.388268\pi\) |
−0.641292 | + | 0.767297i | \(0.721601\pi\) | |||||||
\(354\) | −5.36441 | + | 9.29144i | −0.285115 | + | 0.493834i | ||||
\(355\) | −13.2565 | + | 2.06525i | −0.703582 | + | 0.109612i | ||||
\(356\) | −9.56852 | −0.507131 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.5131i | 1.03130i | ||||||||
\(359\) | 3.61323 | + | 6.25830i | 0.190699 | + | 0.330300i | 0.945482 | − | 0.325674i | \(-0.105591\pi\) |
−0.754783 | + | 0.655974i | \(0.772258\pi\) | |||||||
\(360\) | 1.74131 | − | 1.40280i | 0.0917749 | − | 0.0739341i | ||||
\(361\) | 4.47229 | − | 7.74622i | 0.235383 | − | 0.407696i | ||||
\(362\) | −19.9413 | + | 11.5131i | −1.04809 | + | 0.605115i | ||||
\(363\) | − | 11.8891i | − | 0.624018i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.34206 | − | 3.22646i | −0.436643 | − | 0.168881i | ||||
\(366\) | −3.55780 | − | 6.16229i | −0.185969 | − | 0.322108i | ||||
\(367\) | 1.81878 | + | 1.05007i | 0.0949393 | + | 0.0548132i | 0.546718 | − | 0.837317i | \(-0.315877\pi\) |
−0.451779 | + | 0.892130i | \(0.649210\pi\) | |||||||
\(368\) | −6.21029 | − | 3.58551i | −0.323734 | − | 0.186908i | ||||
\(369\) | 1.02771 | + | 1.78005i | 0.0535007 | + | 0.0926659i | ||||
\(370\) | −5.78426 | + | 14.9553i | −0.300709 | + | 0.777488i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 4.17103i | − | 0.216258i | ||||||
\(373\) | −20.1333 | + | 11.6239i | −1.04246 | + | 0.601865i | −0.920529 | − | 0.390673i | \(-0.872242\pi\) |
−0.121932 | + | 0.992538i | \(0.538909\pi\) | |||||||
\(374\) | 12.5024 | − | 21.6547i | 0.646482 | − | 1.11974i | ||||
\(375\) | −11.1603 | − | 0.669873i | −0.576313 | − | 0.0345921i | ||||
\(376\) | 5.75654 | + | 9.97063i | 0.296871 | + | 0.514196i | ||||
\(377\) | − | 7.56852i | − | 0.389799i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.16629 | −0.111275 | −0.0556374 | − | 0.998451i | \(-0.517719\pi\) | ||||
−0.0556374 | + | 0.998451i | \(0.517719\pi\) | |||||||
\(380\) | −7.00613 | + | 1.09150i | −0.359407 | + | 0.0559925i | ||||
\(381\) | 9.00536 | − | 15.5977i | 0.461359 | − | 0.799096i | ||||
\(382\) | −8.86048 | − | 5.11560i | −0.453342 | − | 0.261737i | ||||
\(383\) | 6.97621 | − | 4.02771i | 0.356468 | − | 0.205807i | −0.311063 | − | 0.950389i | \(-0.600685\pi\) |
0.667530 | + | 0.744583i | \(0.267352\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.6132 | −0.591098 | ||||||||
\(387\) | 1.73205 | − | 1.00000i | 0.0880451 | − | 0.0508329i | ||||
\(388\) | −1.10087 | − | 0.635585i | −0.0558880 | − | 0.0322669i | ||||
\(389\) | 5.94457 | − | 10.2963i | 0.301402 | − | 0.522043i | −0.675052 | − | 0.737770i | \(-0.735879\pi\) |
0.976454 | + | 0.215727i | \(0.0692122\pi\) | |||||||
\(390\) | 1.09150 | + | 7.00613i | 0.0552700 | + | 0.354769i | ||||
\(391\) | −37.4791 | −1.89540 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.55780i | − | 0.280354i | ||||||
\(394\) | −1.19874 | − | 2.07629i | −0.0603919 | − | 0.104602i | ||||
\(395\) | −17.0735 | − | 21.1935i | −0.859063 | − | 1.06636i | ||||
\(396\) | 2.39213 | − | 4.14329i | 0.120209 | − | 0.208208i | ||||
\(397\) | −13.9524 | + | 8.05543i | −0.700252 | + | 0.404290i | −0.807441 | − | 0.589948i | \(-0.799148\pi\) |
0.107190 | + | 0.994239i | \(0.465815\pi\) | |||||||
\(398\) | 18.3421i | 0.919404i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.69874 | − | 3.36441i | −0.184937 | − | 0.168221i | ||||
\(401\) | −12.4854 | − | 21.6253i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(402\) | −8.28658 | − | 4.78426i | −0.413297 | − | 0.238617i | ||||
\(403\) | 11.4545 | + | 6.61323i | 0.570587 | + | 0.329428i | ||||
\(404\) | 4.00000 | + | 6.92820i | 0.199007 | + | 0.344691i | ||||
\(405\) | 0.806615 | − | 2.08551i | 0.0400810 | − | 0.103630i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.3081i | 1.70059i | ||||||||
\(408\) | 4.52625 | − | 2.61323i | 0.224083 | − | 0.129374i | ||||
\(409\) | −1.52771 | + | 2.64608i | −0.0755406 | + | 0.130840i | −0.901321 | − | 0.433151i | \(-0.857402\pi\) |
0.825781 | + | 0.563991i | \(0.190735\pi\) | |||||||
\(410\) | 3.57913 | − | 2.88336i | 0.176761 | − | 0.142399i | ||||
\(411\) | −7.39749 | − | 12.8128i | −0.364891 | − | 0.632010i | ||||
\(412\) | − | 11.2265i | − | 0.553088i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.17103 | −0.352437 | ||||||||
\(415\) | −1.16944 | − | 7.50647i | −0.0574058 | − | 0.368478i | ||||
\(416\) | −1.58551 | + | 2.74619i | −0.0777363 | + | 0.134643i | ||||
\(417\) | 3.16787 | + | 1.82897i | 0.155131 | + | 0.0895651i | ||||
\(418\) | −13.1385 | + | 7.58551i | −0.642625 | + | 0.371020i | ||||
\(419\) | −20.1972 | −0.986698 | −0.493349 | − | 0.869831i | \(-0.664227\pi\) | ||||
−0.493349 | + | 0.869831i | \(0.664227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.3635 | −1.47983 | −0.739913 | − | 0.672702i | \(-0.765133\pi\) | ||||
−0.739913 | + | 0.672702i | \(0.765133\pi\) | |||||||
\(422\) | 2.44996 | − | 1.41449i | 0.119262 | − | 0.0688561i | ||||
\(423\) | 9.97063 | + | 5.75654i | 0.484789 | + | 0.279893i | ||||
\(424\) | −4.05780 | + | 7.02832i | −0.197064 | + | 0.341325i | ||||
\(425\) | −25.5334 | − | 5.56250i | −1.23855 | − | 0.269821i | ||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 1.39749i | − | 0.0675502i | ||||||
\(429\) | 7.58551 | + | 13.1385i | 0.366232 | + | 0.634333i | ||||
\(430\) | −2.80560 | − | 3.48261i | −0.135298 | − | 0.167947i | ||||
\(431\) | −12.2866 | + | 21.2811i | −0.591826 | + | 1.02507i | 0.402160 | + | 0.915569i | \(0.368259\pi\) |
−0.993986 | + | 0.109504i | \(0.965074\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 4.68412i | − | 0.225104i | −0.993646 | − | 0.112552i | \(-0.964097\pi\) | ||
0.993646 | − | 0.112552i | \(-0.0359026\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.97764 | + | 1.92520i | 0.238660 | + | 0.0923065i | ||||
\(436\) | −6.22646 | − | 10.7845i | −0.298193 | − | 0.516486i | ||||
\(437\) | 19.6930 | + | 11.3698i | 0.942045 | + | 0.543890i | ||||
\(438\) | −3.46410 | − | 2.00000i | −0.165521 | − | 0.0955637i | ||||
\(439\) | 15.2565 | + | 26.4251i | 0.728155 | + | 1.26120i | 0.957662 | + | 0.287895i | \(0.0929553\pi\) |
−0.229507 | + | 0.973307i | \(0.573711\pi\) | |||||||
\(440\) | −9.97764 | − | 3.85906i | −0.475666 | − | 0.183973i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.5733i | 0.788310i | ||||||||
\(443\) | −8.23447 | + | 4.75417i | −0.391232 | + | 0.225878i | −0.682694 | − | 0.730705i | \(-0.739192\pi\) |
0.291462 | + | 0.956582i | \(0.405858\pi\) | |||||||
\(444\) | −3.58551 | + | 6.21029i | −0.170161 | + | 0.294728i | ||||
\(445\) | 13.4227 | + | 16.6617i | 0.636299 | + | 0.789841i | ||||
\(446\) | 7.14867 | + | 12.3819i | 0.338500 | + | 0.586298i | ||||
\(447\) | 22.3421i | 1.05674i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.6239 | −0.831726 | −0.415863 | − | 0.909427i | \(-0.636520\pi\) | ||||
−0.415863 | + | 0.909427i | \(0.636520\pi\) | |||||||
\(450\) | −4.88541 | − | 1.06430i | −0.230301 | − | 0.0501714i | ||||
\(451\) | 4.91686 | − | 8.51624i | 0.231526 | − | 0.401014i | ||||
\(452\) | 5.49238 | + | 3.17103i | 0.258340 | + | 0.149153i | ||||
\(453\) | −14.3008 | + | 8.25654i | −0.671908 | + | 0.387926i | ||||
\(454\) | 11.0554 | 0.518857 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.17103 | −0.148497 | ||||||||
\(457\) | −0.334953 | + | 0.193385i | −0.0156684 | + | 0.00904617i | −0.507814 | − | 0.861467i | \(-0.669546\pi\) |
0.492145 | + | 0.870513i | \(0.336213\pi\) | |||||||
\(458\) | −15.9807 | − | 9.22646i | −0.746729 | − | 0.431124i | ||||
\(459\) | 2.61323 | − | 4.52625i | 0.121975 | − | 0.211267i | ||||
\(460\) | 2.46833 | + | 15.8438i | 0.115086 | + | 0.738721i | ||||
\(461\) | 37.3682 | 1.74041 | 0.870206 | − | 0.492688i | \(-0.163986\pi\) | ||||
0.870206 | + | 0.492688i | \(0.163986\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3081i | 1.12969i | 0.825196 | + | 0.564846i | \(0.191064\pi\) | ||||
−0.825196 | + | 0.564846i | \(0.808936\pi\) | |||||||
\(464\) | 1.19339 | + | 2.06700i | 0.0554015 | + | 0.0959582i | ||||
\(465\) | −7.26304 | + | 5.85113i | −0.336815 | + | 0.271339i | ||||
\(466\) | 4.55780 | − | 7.89434i | 0.211136 | − | 0.365698i | ||||
\(467\) | 24.7452 | − | 14.2866i | 1.14507 | − | 0.661106i | 0.197389 | − | 0.980325i | \(-0.436754\pi\) |
0.947681 | + | 0.319219i | \(0.103421\pi\) | |||||||
\(468\) | 3.17103i | 0.146581i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.28663 | − | 24.0107i | 0.428360 | − | 1.10753i | ||||
\(471\) | −4.97229 | − | 8.61225i | −0.229111 | − | 0.396832i | ||||
\(472\) | 9.29144 | + | 5.36441i | 0.427673 | + | 0.246917i | ||||
\(473\) | −8.28658 | − | 4.78426i | −0.381017 | − | 0.219980i | ||||
\(474\) | −6.08551 | − | 10.5404i | −0.279517 | − | 0.484138i | ||||
\(475\) | 11.7288 | + | 10.6687i | 0.538156 | + | 0.489512i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.11560i | 0.371588i | ||||||||
\(478\) | 11.3584 | − | 6.55780i | 0.519523 | − | 0.299947i | ||||
\(479\) | 4.28189 | − | 7.41645i | 0.195645 | − | 0.338866i | −0.751467 | − | 0.659771i | \(-0.770653\pi\) |
0.947112 | + | 0.320904i | \(0.103987\pi\) | |||||||
\(480\) | −1.40280 | − | 1.74131i | −0.0640288 | − | 0.0794794i | ||||
\(481\) | −11.3698 | − | 19.6930i | −0.518417 | − | 0.897925i | ||||
\(482\) | − | 5.34206i | − | 0.243324i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.8891 | −0.540415 | ||||||||
\(485\) | 0.437548 | + | 2.80854i | 0.0198680 | + | 0.127529i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −27.5781 | − | 15.9222i | −1.24968 | − | 0.721504i | −0.278636 | − | 0.960397i | \(-0.589882\pi\) |
−0.971046 | + | 0.238892i | \(0.923216\pi\) | |||||||
\(488\) | −6.16229 | + | 3.55780i | −0.278954 | + | 0.161054i | ||||
\(489\) | 2.88440 | 0.130437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.49763 | 0.202975 | 0.101488 | − | 0.994837i | \(-0.467640\pi\) | ||||
0.101488 | + | 0.994837i | \(0.467640\pi\) | |||||||
\(492\) | 1.78005 | − | 1.02771i | 0.0802511 | − | 0.0463330i | ||||
\(493\) | 10.8031 | + | 6.23718i | 0.486548 | + | 0.280908i | ||||
\(494\) | 5.02771 | − | 8.70826i | 0.226208 | − | 0.391803i | ||||
\(495\) | −10.5704 | + | 1.64678i | −0.475105 | + | 0.0740174i | ||||
\(496\) | −4.17103 | −0.187285 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 3.39749i | − | 0.152245i | ||||||
\(499\) | −0.171030 | − | 0.296232i | −0.00765634 | − | 0.0132612i | 0.862172 | − | 0.506616i | \(-0.169104\pi\) |
−0.869828 | + | 0.493355i | \(0.835770\pi\) | |||||||
\(500\) | −0.669873 | + | 11.1603i | −0.0299576 | + | 0.499102i | ||||
\(501\) | −2.02771 | + | 3.51211i | −0.0905916 | + | 0.156909i | ||||
\(502\) | 24.1806 | − | 13.9606i | 1.07923 | − | 0.623094i | ||||
\(503\) | 7.56852i | 0.337464i | 0.985662 | + | 0.168732i | \(0.0539672\pi\) | ||||
−0.985662 | + | 0.168732i | \(0.946033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.45292 | − | 16.6841i | 0.287151 | − | 0.742434i | ||||
\(506\) | 17.1540 | + | 29.7117i | 0.762590 | + | 1.32084i | ||||
\(507\) | 2.55007 | + | 1.47229i | 0.113253 | + | 0.0653865i | ||||
\(508\) | −15.5977 | − | 9.00536i | −0.692038 | − | 0.399548i | ||||
\(509\) | −15.4800 | − | 26.8122i | −0.686140 | − | 1.18843i | −0.973077 | − | 0.230479i | \(-0.925971\pi\) |
0.286938 | − | 0.957949i | \(-0.407363\pi\) | |||||||
\(510\) | −10.8999 | − | 4.21574i | −0.482654 | − | 0.186676i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −2.74619 | + | 1.58551i | −0.121247 | + | 0.0700022i | ||||
\(514\) | 10.5685 | − | 18.3052i | 0.466157 | − | 0.807408i | ||||
\(515\) | −19.5487 | + | 15.7485i | −0.861419 | + | 0.693962i | ||||
\(516\) | −1.00000 | − | 1.73205i | −0.0440225 | − | 0.0762493i | ||||
\(517\) | − | 55.0816i | − | 2.42249i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.39749 | −0.280819 | ||||||||
\(520\) | 7.00613 | − | 1.09150i | 0.307239 | − | 0.0478652i | ||||
\(521\) | 2.42520 | − | 4.20058i | 0.106250 | − | 0.184031i | −0.807998 | − | 0.589185i | \(-0.799449\pi\) |
0.914248 | + | 0.405154i | \(0.132782\pi\) | |||||||
\(522\) | 2.06700 | + | 1.19339i | 0.0904703 | + | 0.0522330i | ||||
\(523\) | −3.68289 | + | 2.12632i | −0.161042 | + | 0.0929774i | −0.578355 | − | 0.815785i | \(-0.696305\pi\) |
0.417313 | + | 0.908763i | \(0.362972\pi\) | |||||||
\(524\) | −5.55780 | −0.242794 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.9106 | 0.519326 | ||||||||
\(527\) | −18.8791 | + | 10.8999i | −0.822387 | + | 0.474805i | ||||
\(528\) | −4.14329 | − | 2.39213i | −0.180314 | − | 0.104104i | ||||
\(529\) | 14.2118 | − | 24.6156i | 0.617906 | − | 1.07024i | ||||
\(530\) | 17.9307 | − | 2.79346i | 0.778862 | − | 0.121340i | ||||
\(531\) | 10.7288 | 0.465592 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.51783i | 0.282319i | ||||||||
\(534\) | 4.78426 | + | 8.28658i | 0.207035 | + | 0.358595i | ||||
\(535\) | −2.43346 | + | 1.96040i | −0.105208 | + | 0.0847555i | ||||
\(536\) | −4.78426 | + | 8.28658i | −0.206649 | + | 0.357926i | ||||
\(537\) | 16.8988 | − | 9.75654i | 0.729238 | − | 0.421026i | ||||
\(538\) | 3.27117i | 0.141030i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.08551 | − | 0.806615i | −0.0897463 | − | 0.0347112i | ||||
\(541\) | −19.1817 | − | 33.2238i | −0.824688 | − | 1.42840i | −0.902158 | − | 0.431406i | \(-0.858017\pi\) |
0.0774699 | − | 0.996995i | \(-0.475316\pi\) | |||||||
\(542\) | −0.540356 | − | 0.311975i | −0.0232103 | − | 0.0134005i | ||||
\(543\) | 19.9413 | + | 11.5131i | 0.855761 | + | 0.494074i | ||||
\(544\) | −2.61323 | − | 4.52625i | −0.112041 | − | 0.194061i | ||||
\(545\) | −10.0447 | + | 25.9707i | −0.430268 | + | 1.11246i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.44818i | 0.0619197i | 0.999521 | + | 0.0309598i | \(0.00985640\pi\) | ||||
−0.999521 | + | 0.0309598i | \(0.990144\pi\) | |||||||
\(548\) | −12.8128 | + | 7.39749i | −0.547337 | + | 0.316005i | ||||
\(549\) | −3.55780 | + | 6.16229i | −0.151843 | + | 0.263000i | ||||
\(550\) | 7.27686 | + | 22.7876i | 0.310286 | + | 0.971668i | ||||
\(551\) | −3.78426 | − | 6.55453i | −0.161215 | − | 0.279232i | ||||
\(552\) | 7.17103i | 0.305219i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 28.7950 | 1.22338 | ||||||||
\(555\) | 15.8438 | − | 2.46833i | 0.672531 | − | 0.104775i | ||||
\(556\) | 1.82897 | − | 3.16787i | 0.0775656 | − | 0.134348i | ||||
\(557\) | 11.2769 | + | 6.51072i | 0.477817 | + | 0.275868i | 0.719506 | − | 0.694486i | \(-0.244368\pi\) |
−0.241689 | + | 0.970354i | \(0.577701\pi\) | |||||||
\(558\) | −3.61222 | + | 2.08551i | −0.152917 | + | 0.0882869i | ||||
\(559\) | 6.34206 | 0.268241 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.0047 | −1.05570 | ||||||||
\(562\) | −2.44996 | + | 1.41449i | −0.103345 | + | 0.0596665i | ||||
\(563\) | 5.06660 | + | 2.92520i | 0.213532 | + | 0.123283i | 0.602952 | − | 0.797778i | \(-0.293991\pi\) |
−0.389420 | + | 0.921060i | \(0.627324\pi\) | |||||||
\(564\) | 5.75654 | − | 9.97063i | 0.242394 | − | 0.419839i | ||||
\(565\) | −2.18299 | − | 14.0123i | −0.0918391 | − | 0.589500i | ||||
\(566\) | 25.1370 | 1.05659 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | −20.3251 | − | 35.2040i | −0.852071 | − | 1.47583i | −0.879336 | − | 0.476202i | \(-0.842013\pi\) |
0.0272649 | − | 0.999628i | \(-0.491320\pi\) | |||||||
\(570\) | 4.44833 | + | 5.52173i | 0.186320 | + | 0.231280i | ||||
\(571\) | 1.61323 | − | 2.79420i | 0.0675116 | − | 0.116933i | −0.830294 | − | 0.557326i | \(-0.811827\pi\) |
0.897805 | + | 0.440393i | \(0.145161\pi\) | |||||||
\(572\) | 13.1385 | − | 7.58551i | 0.549348 | − | 0.317166i | ||||
\(573\) | 10.2312i | 0.427415i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.1263 | − | 26.5238i | 1.00614 | − | 1.10612i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −10.0759 | − | 5.81733i | −0.419466 | − | 0.242179i | 0.275383 | − | 0.961335i | \(-0.411195\pi\) |
−0.694849 | + | 0.719156i | \(0.744529\pi\) | |||||||
\(578\) | −8.93381 | − | 5.15794i | −0.371598 | − | 0.214542i | ||||
\(579\) | 5.80661 | + | 10.0574i | 0.241315 | + | 0.417969i | ||||
\(580\) | 1.92520 | − | 4.97764i | 0.0799398 | − | 0.206685i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.27117i | 0.0526917i | ||||||||
\(583\) | 33.6253 | − | 19.4136i | 1.39262 | − | 0.804028i | ||||
\(584\) | −2.00000 | + | 3.46410i | −0.0827606 | + | 0.143346i | ||||
\(585\) | 5.52173 | − | 4.44833i | 0.228296 | − | 0.183916i | ||||
\(586\) | 5.11323 | + | 8.85637i | 0.211226 | + | 0.365853i | ||||
\(587\) | 28.9446i | 1.19467i | 0.801992 | + | 0.597335i | \(0.203774\pi\) | ||||
−0.801992 | + | 0.597335i | \(0.796226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.2265 | 0.544987 | ||||||||
\(590\) | −3.69295 | − | 23.7045i | −0.152036 | − | 0.975897i | ||||
\(591\) | −1.19874 | + | 2.07629i | −0.0493098 | + | 0.0854070i | ||||
\(592\) | 6.21029 | + | 3.58551i | 0.255242 | + | 0.147364i | ||||
\(593\) | 9.92262 | − | 5.72883i | 0.407473 | − | 0.235255i | −0.282230 | − | 0.959347i | \(-0.591074\pi\) |
0.689704 | + | 0.724092i | \(0.257741\pi\) | |||||||
\(594\) | −4.78426 | −0.196301 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.3421 | 0.915166 | ||||||||
\(597\) | 15.8847 | − | 9.17103i | 0.650117 | − | 0.375345i | ||||
\(598\) | −19.6930 | − | 11.3698i | −0.805308 | − | 0.464945i | ||||
\(599\) | −1.50237 | + | 2.60218i | −0.0613852 | + | 0.106322i | −0.895085 | − | 0.445896i | \(-0.852885\pi\) |
0.833700 | + | 0.552218i | \(0.186218\pi\) | |||||||
\(600\) | −1.06430 | + | 4.88541i | −0.0434497 | + | 0.199446i | ||||
\(601\) | −40.0816 | −1.63496 | −0.817481 | − | 0.575955i | \(-0.804630\pi\) | ||||
−0.817481 | + | 0.575955i | \(0.804630\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.56852i | 0.389660i | ||||||||
\(604\) | 8.25654 | + | 14.3008i | 0.335954 | + | 0.581889i | ||||
\(605\) | 16.6781 | + | 20.7026i | 0.678061 | + | 0.841682i | ||||
\(606\) | 4.00000 | − | 6.92820i | 0.162489 | − | 0.281439i | ||||
\(607\) | −22.6220 | + | 13.0608i | −0.918197 | + | 0.530121i | −0.883059 | − | 0.469261i | \(-0.844520\pi\) |
−0.0351374 | + | 0.999382i | \(0.511187\pi\) | |||||||
\(608\) | 3.17103i | 0.128602i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.8397 | + | 5.73955i | 0.600841 | + | 0.232388i | ||||
\(611\) | 18.2542 | + | 31.6172i | 0.738485 | + | 1.27909i | ||||
\(612\) | −4.52625 | − | 2.61323i | −0.182963 | − | 0.105634i | ||||
\(613\) | 35.9514 | + | 20.7565i | 1.45206 | + | 0.838349i | 0.998598 | − | 0.0529254i | \(-0.0168546\pi\) |
0.453464 | + | 0.891274i | \(0.350188\pi\) | |||||||
\(614\) | 11.7288 | + | 20.3149i | 0.473337 | + | 0.819844i | ||||
\(615\) | −4.28663 | − | 1.65794i | −0.172854 | − | 0.0668546i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1156i | 1.25267i | 0.779555 | + | 0.626333i | \(0.215445\pi\) | ||||
−0.779555 | + | 0.626333i | \(0.784555\pi\) | |||||||
\(618\) | −9.72240 | + | 5.61323i | −0.391092 | + | 0.225797i | ||||
\(619\) | −16.4961 | + | 28.5721i | −0.663034 | + | 1.14841i | 0.316780 | + | 0.948499i | \(0.397398\pi\) |
−0.979814 | + | 0.199910i | \(0.935935\pi\) | |||||||
\(620\) | 5.85113 | + | 7.26304i | 0.234987 | + | 0.291691i | ||||
\(621\) | 3.58551 | + | 6.21029i | 0.143882 | + | 0.249211i | ||||
\(622\) | − | 5.65794i | − | 0.226863i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.17103 | 0.126943 | ||||||||
\(625\) | 20.3731 | − | 14.4892i | 0.814925 | − | 0.579567i | ||||
\(626\) | −8.19339 | + | 14.1914i | −0.327474 | + | 0.567201i | ||||
\(627\) | 13.1385 | + | 7.58551i | 0.524701 | + | 0.302936i | ||||
\(628\) | −8.61225 | + | 4.97229i | −0.343666 | + | 0.198416i | ||||
\(629\) | 37.4791 | 1.49439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.6501 | 1.89692 | 0.948461 | − | 0.316894i | \(-0.102640\pi\) | ||||
0.948461 | + | 0.316894i | \(0.102640\pi\) | |||||||
\(632\) | −10.5404 | + | 6.08551i | −0.419275 | + | 0.242069i | ||||
\(633\) | −2.44996 | − | 1.41449i | −0.0973772 | − | 0.0562207i | ||||
\(634\) | 2.25654 | − | 3.90845i | 0.0896188 | − | 0.155224i | ||||
\(635\) | 6.19944 | + | 39.7932i | 0.246017 | + | 1.57914i | ||||
\(636\) | 8.11560 | 0.321804 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 11.4189i | − | 0.452080i | ||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | −1.74131 | + | 1.40280i | −0.0688312 | + | 0.0554506i | ||||
\(641\) | −5.14331 | + | 8.90848i | −0.203149 | + | 0.351864i | −0.949541 | − | 0.313642i | \(-0.898451\pi\) |
0.746393 | + | 0.665506i | \(0.231784\pi\) | |||||||
\(642\) | −1.21026 | + | 0.698745i | −0.0477652 | + | 0.0275773i | ||||
\(643\) | 38.9368i | 1.53552i | 0.640740 | + | 0.767758i | \(0.278628\pi\) | ||||
−0.640740 | + | 0.767758i | \(0.721372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.61323 | + | 4.17103i | −0.0635209 | + | 0.164234i | ||||
\(646\) | 8.28663 | + | 14.3529i | 0.326033 | + | 0.564706i | ||||
\(647\) | 29.3194 | + | 16.9276i | 1.15267 | + | 0.665492i | 0.949535 | − | 0.313660i | \(-0.101555\pi\) |
0.203130 | + | 0.979152i | \(0.434889\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | −25.6648 | − | 44.4527i | −1.00743 | − | 1.74492i | ||||
\(650\) | −11.7288 | − | 10.6687i | −0.460043 | − | 0.418459i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 2.88440i | − | 0.112962i | ||||||
\(653\) | 4.64493 | − | 2.68175i | 0.181770 | − | 0.104945i | −0.406354 | − | 0.913716i | \(-0.633200\pi\) |
0.588124 | + | 0.808771i | \(0.299867\pi\) | |||||||
\(654\) | −6.22646 | + | 10.7845i | −0.243474 | + | 0.421709i | ||||
\(655\) | 7.79649 | + | 9.67783i | 0.304634 | + | 0.378144i | ||||
\(656\) | −1.02771 | − | 1.78005i | −0.0401255 | − | 0.0694995i | ||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.2265 | −0.904774 | −0.452387 | − | 0.891822i | \(-0.649427\pi\) | ||||
−0.452387 | + | 0.891822i | \(0.649427\pi\) | |||||||
\(660\) | 1.64678 | + | 10.5704i | 0.0641009 | + | 0.411453i | ||||
\(661\) | −18.2973 | + | 31.6919i | −0.711684 | + | 1.23267i | 0.252540 | + | 0.967586i | \(0.418734\pi\) |
−0.964224 | + | 0.265087i | \(0.914599\pi\) | |||||||
\(662\) | −11.3290 | − | 6.54080i | −0.440314 | − | 0.254216i | ||||
\(663\) | 14.3529 | − | 8.28663i | 0.557419 | − | 0.321826i | ||||
\(664\) | −3.39749 | −0.131848 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.17103 | 0.277872 | ||||||||
\(667\) | −14.8225 | + | 8.55780i | −0.573931 | + | 0.331359i | ||||
\(668\) | 3.51211 | + | 2.02771i | 0.135887 | + | 0.0784546i | ||||
\(669\) | 7.14867 | − | 12.3819i | 0.276384 | − | 0.478711i | ||||
\(670\) | 21.1408 | − | 3.29357i | 0.816742 | − | 0.127242i | ||||
\(671\) | 34.0429 | 1.31421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17.7336i | − | 0.683579i | −0.939777 | − | 0.341789i | \(-0.888967\pi\) | ||
0.939777 | − | 0.341789i | \(-0.111033\pi\) | |||||||
\(674\) | 10.1487 | + | 17.5780i | 0.390912 | + | 0.677080i | ||||
\(675\) | 1.52100 | + | 4.76304i | 0.0585433 | + | 0.183330i | ||||
\(676\) | 1.47229 | − | 2.55007i | 0.0566263 | − | 0.0980797i | ||||
\(677\) | 22.7128 | − | 13.1132i | 0.872923 | − | 0.503982i | 0.00460456 | − | 0.999989i | \(-0.498534\pi\) |
0.868319 | + | 0.496007i | \(0.165201\pi\) | |||||||
\(678\) | − | 6.34206i | − | 0.243565i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.21574 | + | 10.8999i | −0.161666 | + | 0.417991i | ||||
\(681\) | −5.52771 | − | 9.57428i | −0.211822 | − | 0.366887i | ||||
\(682\) | 17.2818 | + | 9.97764i | 0.661754 | + | 0.382064i | ||||
\(683\) | 42.6246 | + | 24.6093i | 1.63098 | + | 0.941650i | 0.983790 | + | 0.179325i | \(0.0573914\pi\) |
0.647195 | + | 0.762324i | \(0.275942\pi\) | |||||||
\(684\) | 1.58551 | + | 2.74619i | 0.0606237 | + | 0.105003i | ||||
\(685\) | 30.8551 | + | 11.9339i | 1.17891 | + | 0.455969i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4529i | 0.704023i | ||||||||
\(688\) | −1.73205 | + | 1.00000i | −0.0660338 | + | 0.0381246i | ||||
\(689\) | −12.8674 | + | 22.2870i | −0.490209 | + | 0.849067i | ||||
\(690\) | 12.4870 | − | 10.0595i | 0.475370 | − | 0.382960i | ||||
\(691\) | 4.45292 | + | 7.71268i | 0.169397 | + | 0.293404i | 0.938208 | − | 0.346072i | \(-0.112485\pi\) |
−0.768811 | + | 0.639476i | \(0.779151\pi\) | |||||||
\(692\) | 6.39749i | 0.243196i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.4529 | −0.548625 | ||||||||
\(695\) | −8.08191 | + | 1.25909i | −0.306564 | + | 0.0477602i | ||||
\(696\) | 1.19339 | − | 2.06700i | 0.0452351 | − | 0.0783496i | ||||
\(697\) | −9.30338 | − | 5.37131i | −0.352391 | − | 0.203453i | ||||
\(698\) | −12.0283 | + | 6.94457i | −0.455280 | + | 0.262856i | ||||
\(699\) | −9.11560 | −0.344784 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9553 | 0.451545 | 0.225773 | − | 0.974180i | \(-0.427509\pi\) | ||||
0.225773 | + | 0.974180i | \(0.427509\pi\) | |||||||
\(702\) | 2.74619 | − | 1.58551i | 0.103648 | − | 0.0598414i | ||||
\(703\) | −19.6930 | − | 11.3698i | −0.742737 | − | 0.428819i | ||||
\(704\) | −2.39213 | + | 4.14329i | −0.0901568 | + | 0.156156i | ||||
\(705\) | −25.4372 | + | 3.96290i | −0.958021 | + | 0.149252i | ||||
\(706\) | 6.45292 | 0.242859 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 10.7288i | − | 0.403214i | ||||||
\(709\) | 26.0816 | + | 45.1747i | 0.979515 | + | 1.69657i | 0.664149 | + | 0.747600i | \(0.268794\pi\) |
0.315367 | + | 0.948970i | \(0.397872\pi\) | |||||||
\(710\) | 10.4478 | − | 8.41681i | 0.392100 | − | 0.315877i | ||||
\(711\) | −6.08551 | + | 10.5404i | −0.228225 | + | 0.395297i | ||||
\(712\) | 8.28658 | − | 4.78426i | 0.310553 | − | 0.179298i | ||||
\(713\) | − | 29.9106i | − | 1.12016i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.6394 | − | 12.2372i | −1.18325 | − | 0.457645i | ||||
\(716\) | −9.75654 | − | 16.8988i | −0.364619 | − | 0.631539i | ||||
\(717\) | −11.3584 | − | 6.55780i | −0.424189 | − | 0.244906i | ||||
\(718\) | −6.25830 | − | 3.61323i | −0.233558 | − | 0.134845i | ||||
\(719\) | −12.8951 | − | 22.3350i | −0.480907 | − | 0.832955i | 0.518853 | − | 0.854863i | \(-0.326359\pi\) |
−0.999760 | + | 0.0219083i | \(0.993026\pi\) | |||||||
\(720\) | −0.806615 | + | 2.08551i | −0.0300608 | + | 0.0777226i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.94457i | 0.332882i | ||||||||
\(723\) | −4.62636 | + | 2.67103i | −0.172056 | + | 0.0993367i | ||||
\(724\) | 11.5131 | − | 19.9413i | 0.427881 | − | 0.741111i | ||||
\(725\) | −11.3683 | + | 3.63028i | −0.422207 | + | 0.134825i | ||||
\(726\) | 5.94457 | + | 10.2963i | 0.220624 | + | 0.382131i | ||||
\(727\) | 34.6054i | 1.28344i | 0.766937 | + | 0.641722i | \(0.221780\pi\) | ||||
−0.766937 | + | 0.641722i | \(0.778220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 8.83767 | − | 1.37683i | 0.327097 | − | 0.0509589i | ||||
\(731\) | −5.22646 | + | 9.05249i | −0.193308 | + | 0.334819i | ||||
\(732\) | 6.16229 | + | 3.55780i | 0.227765 | + | 0.131500i | ||||
\(733\) | 26.8215 | − | 15.4854i | 0.990673 | − | 0.571965i | 0.0851976 | − | 0.996364i | \(-0.472848\pi\) |
0.905475 | + | 0.424399i | \(0.139515\pi\) | |||||||
\(734\) | −2.10014 | −0.0775176 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.17103 | 0.264328 | ||||||||
\(737\) | 39.6452 | − | 22.8891i | 1.46035 | − | 0.843132i | ||||
\(738\) | −1.78005 | − | 1.02771i | −0.0655247 | − | 0.0378307i | ||||
\(739\) | −1.08788 | + | 1.88427i | −0.0400185 | + | 0.0693141i | −0.885341 | − | 0.464942i | \(-0.846075\pi\) |
0.845322 | + | 0.534257i | \(0.179408\pi\) | |||||||
\(740\) | −2.46833 | − | 15.8438i | −0.0907376 | − | 0.582429i | ||||
\(741\) | −10.0554 | −0.369395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31.9446i | − | 1.17193i | −0.810335 | − | 0.585966i | \(-0.800715\pi\) | ||
0.810335 | − | 0.585966i | \(-0.199285\pi\) | |||||||
\(744\) | 2.08551 | + | 3.61222i | 0.0764587 | + | 0.132430i | ||||
\(745\) | −31.3415 | − | 38.9044i | −1.14826 | − | 1.42535i | ||||
\(746\) | 11.6239 | − | 20.1333i | 0.425583 | − | 0.737131i | ||||
\(747\) | −2.94231 | + | 1.69874i | −0.107654 | + | 0.0621538i | ||||
\(748\) | 25.0047i | 0.914264i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.0000 | − | 5.00000i | 0.365148 | − | 0.182574i | ||||
\(751\) | 2.80363 | + | 4.85602i | 0.102306 | + | 0.177199i | 0.912634 | − | 0.408777i | \(-0.134045\pi\) |
−0.810329 | + | 0.585976i | \(0.800711\pi\) | |||||||
\(752\) | −9.97063 | − | 5.75654i | −0.363591 | − | 0.209920i | ||||
\(753\) | −24.1806 | − | 13.9606i | −0.881188 | − | 0.508754i | ||||
\(754\) | 3.78426 | + | 6.55453i | 0.137815 | + | 0.238702i | ||||
\(755\) | 13.3197 | − | 34.4383i | 0.484754 | − | 1.25334i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.2312i | 0.880698i | 0.897827 | + | 0.440349i | \(0.145145\pi\) | ||||
−0.897827 | + | 0.440349i | \(0.854855\pi\) | |||||||
\(758\) | 1.87606 | − | 1.08314i | 0.0681416 | − | 0.0393416i | ||||
\(759\) | 17.1540 | − | 29.7117i | 0.622652 | − | 1.07846i | ||||
\(760\) | 5.52173 | − | 4.44833i | 0.200294 | − | 0.161358i | ||||
\(761\) | 19.9276 | + | 34.5156i | 0.722374 | + | 1.25119i | 0.960046 | + | 0.279843i | \(0.0902824\pi\) |
−0.237672 | + | 0.971346i | \(0.576384\pi\) | |||||||
\(762\) | 18.0107i | 0.652460i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.2312 | 0.370152 | ||||||||
\(765\) | 1.79899 | + | 11.5474i | 0.0650427 | + | 0.417498i | ||||
\(766\) | −4.02771 | + | 6.97621i | −0.145527 | + | 0.252061i | ||||
\(767\) | 29.4634 | + | 17.0107i | 1.06386 | + | 0.614221i | ||||
\(768\) | −0.866025 | + | 0.500000i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | 29.7950 | 1.07443 | 0.537217 | − | 0.843444i | \(-0.319476\pi\) | ||||
0.537217 | + | 0.843444i | \(0.319476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.1370 | −0.761232 | ||||||||
\(772\) | 10.0574 | − | 5.80661i | 0.361972 | − | 0.208985i | ||||
\(773\) | 0.144011 | + | 0.0831449i | 0.00517972 | + | 0.00299051i | 0.502588 | − | 0.864526i | \(-0.332381\pi\) |
−0.497408 | + | 0.867517i | \(0.665715\pi\) | |||||||
\(774\) | −1.00000 | + | 1.73205i | −0.0359443 | + | 0.0622573i | ||||
\(775\) | 4.43921 | − | 20.3772i | 0.159461 | − | 0.731971i | ||||
\(776\) | 1.27117 | 0.0456324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.8891i | 0.426246i | ||||||||
\(779\) | 3.25891 | + | 5.64461i | 0.116763 | + | 0.202239i | ||||
\(780\) | −4.44833 | − | 5.52173i | −0.159276 | − | 0.197710i | ||||
\(781\) | 14.3528 | − | 24.8597i | 0.513583 | − | 0.889552i | ||||
\(782\) | 32.4579 | − | 18.7395i | 1.16069 | − | 0.670125i | ||||
\(783\) | − | 2.38677i | − | 0.0852962i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.7395 | + | 8.02144i | 0.740226 | + | 0.286297i | ||||
\(786\) | 2.77890 | + | 4.81320i | 0.0991201 | + | 0.171681i | ||||
\(787\) | 24.6410 | + | 14.2265i | 0.878355 | + | 0.507119i | 0.870116 | − | 0.492848i | \(-0.164044\pi\) |
0.00823936 | + | 0.999966i | \(0.497377\pi\) | |||||||
\(788\) | 2.07629 | + | 1.19874i | 0.0739647 | + | 0.0427035i | ||||
\(789\) | −5.95529 | − | 10.3149i | −0.212014 | − | 0.367219i | ||||
\(790\) | 25.3829 | + | 9.81733i | 0.903082 | + | 0.349285i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.78426i | 0.170001i | ||||||||
\(793\) | −19.5408 | + | 11.2819i | −0.693914 | + | 0.400632i | ||||
\(794\) | 8.05543 | − | 13.9524i | 0.285877 | − | 0.495153i | ||||
\(795\) | −11.3846 | − | 14.1317i | −0.403769 | − | 0.501201i | ||||
\(796\) | −9.17103 | − | 15.8847i | −0.325059 | − | 0.563018i | ||||
\(797\) | 36.6334i | 1.29762i | 0.760949 | + | 0.648811i | \(0.224734\pi\) | ||||
−0.760949 | + | 0.648811i | \(0.775266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.1727 | −2.12876 | ||||||||
\(800\) | 4.88541 | + | 1.06430i | 0.172725 | + | 0.0376286i | ||||
\(801\) | 4.78426 | − | 8.28658i | 0.169044 | − | 0.292792i | ||||
\(802\) | 21.6253 | + | 12.4854i | 0.763616 | + | 0.440874i | ||||
\(803\) | 16.5732 | − | 9.56852i | 0.584854 | − | 0.337666i | ||||
\(804\) | 9.56852 | 0.337456 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2265 | −0.465882 | ||||||||
\(807\) | 2.83292 | − | 1.63559i | 0.0997234 | − | 0.0575753i | ||||
\(808\) | −6.92820 | − | 4.00000i | −0.243733 | − | 0.140720i | ||||
\(809\) | −10.1433 | + | 17.5687i | −0.356620 | + | 0.617684i | −0.987394 | − | 0.158283i | \(-0.949404\pi\) |
0.630774 | + | 0.775967i | \(0.282738\pi\) | |||||||
\(810\) | 0.344208 | + | 2.20942i | 0.0120943 | + | 0.0776310i | ||||
\(811\) | −1.38079 | −0.0484861 | −0.0242431 | − | 0.999706i | \(-0.507718\pi\) | ||||
−0.0242431 | + | 0.999706i | \(0.507718\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.623949i | 0.0218829i | ||||||||
\(814\) | −17.1540 | − | 29.7117i | −0.601249 | − | 1.04139i | ||||
\(815\) | −5.02262 | + | 4.04624i | −0.175935 | + | 0.141734i | ||||
\(816\) | −2.61323 | + | 4.52625i | −0.0914813 | + | 0.158450i | ||||
\(817\) | 5.49238 | − | 3.17103i | 0.192154 | − | 0.110940i | ||||
\(818\) | − | 3.05543i | − | 0.106831i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.65794 | + | 4.28663i | −0.0578978 | + | 0.149696i | ||||
\(821\) | 8.70647 | + | 15.0801i | 0.303858 | + | 0.526298i | 0.977006 | − | 0.213210i | \(-0.0683918\pi\) |
−0.673148 | + | 0.739507i | \(0.735058\pi\) | |||||||
\(822\) | 12.8128 | + | 7.39749i | 0.446899 | + | 0.258017i | ||||
\(823\) | −17.8355 | − | 10.2973i | −0.621708 | − | 0.358943i | 0.155826 | − | 0.987785i | \(-0.450196\pi\) |
−0.777534 | + | 0.628842i | \(0.783529\pi\) | |||||||
\(824\) | 5.61323 | + | 9.72240i | 0.195546 | + | 0.338696i | ||||
\(825\) | 16.0962 | − | 17.6958i | 0.560399 | − | 0.616087i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.8504i | − | 0.481626i | −0.970572 | − | 0.240813i | \(-0.922586\pi\) | ||
0.970572 | − | 0.240813i | \(-0.0774140\pi\) | |||||||
\(828\) | 6.21029 | − | 3.58551i | 0.215823 | − | 0.124605i | ||||
\(829\) | 0.613230 | − | 1.06215i | 0.0212984 | − | 0.0368898i | −0.855180 | − | 0.518331i | \(-0.826553\pi\) |
0.876478 | + | 0.481442i | \(0.159887\pi\) | |||||||
\(830\) | 4.76600 | + | 5.91607i | 0.165430 | + | 0.205350i | ||||
\(831\) | −14.3975 | − | 24.9372i | −0.499443 | − | 0.865061i | ||||
\(832\) | − | 3.17103i | − | 0.109936i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.65794 | −0.126664 | ||||||||
\(835\) | −1.39591 | − | 8.96013i | −0.0483076 | − | 0.310078i | ||||
\(836\) | 7.58551 | − | 13.1385i | 0.262351 | − | 0.454404i | ||||
\(837\) | 3.61222 | + | 2.08551i | 0.124857 | + | 0.0720859i | ||||
\(838\) | 17.4913 | − | 10.0986i | 0.604227 | − | 0.348850i | ||||
\(839\) | 29.9106 | 1.03263 | 0.516314 | − | 0.856399i | \(-0.327304\pi\) | ||||
0.516314 | + | 0.856399i | \(0.327304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3033 | −0.803563 | ||||||||
\(842\) | 26.2956 | − | 15.1817i | 0.906205 | − | 0.523198i | ||||
\(843\) | 2.44996 | + | 1.41449i | 0.0843811 | + | 0.0487175i | ||||
\(844\) | −1.41449 | + | 2.44996i | −0.0486886 | + | 0.0843311i | ||||
\(845\) | −6.50578 | + | 1.01355i | −0.223806 | + | 0.0348670i | ||||
\(846\) | −11.5131 | −0.395828 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 8.11560i | − | 0.278691i | ||||||
\(849\) | −12.5685 | − | 21.7693i | −0.431350 | − | 0.747121i | ||||
\(850\) | 24.8938 | − | 7.94944i | 0.853852 | − | 0.272664i | ||||
\(851\) | −25.7118 | + | 44.5342i | −0.881390 | + | 1.52661i | ||||
\(852\) | 5.19615 | − | 3.00000i | 0.178017 | − | 0.102778i | ||||
\(853\) | 10.7181i | 0.366981i | 0.983021 | + | 0.183491i | \(0.0587397\pi\) | ||||
−0.983021 | + | 0.183491i | \(0.941260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.55780 | − | 6.61323i | 0.0874749 | − | 0.226168i | ||||
\(856\) | 0.698745 | + | 1.21026i | 0.0238826 | + | 0.0413659i | ||||
\(857\) | −34.3716 | − | 19.8444i | −1.17411 | − | 0.677873i | −0.219465 | − | 0.975620i | \(-0.570431\pi\) |
−0.954645 | + | 0.297747i | \(0.903765\pi\) | |||||||
\(858\) | −13.1385 | − | 7.58551i | −0.448541 | − | 0.258965i | ||||
\(859\) | −5.50237 | − | 9.53038i | −0.187738 | − | 0.325173i | 0.756757 | − | 0.653696i | \(-0.226782\pi\) |
−0.944496 | + | 0.328523i | \(0.893449\pi\) | |||||||
\(860\) | 4.17103 | + | 1.61323i | 0.142231 | + | 0.0550107i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 24.5733i | − | 0.836969i | ||||||
\(863\) | 7.47266 | − | 4.31434i | 0.254372 | − | 0.146862i | −0.367392 | − | 0.930066i | \(-0.619749\pi\) |
0.621765 | + | 0.783204i | \(0.286416\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 11.1400 | − | 8.97441i | 0.378771 | − | 0.305139i | ||||
\(866\) | 2.34206 | + | 4.05657i | 0.0795864 | + | 0.137848i | ||||
\(867\) | 10.3159i | 0.350346i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.2294 | 1.97530 | ||||||||
\(870\) | −5.27337 | + | 0.821546i | −0.178784 | + | 0.0278530i | ||||
\(871\) | −15.1710 | + | 26.2770i | −0.514051 | + | 0.890362i | ||||
\(872\) | 10.7845 | + | 6.22646i | 0.365211 | + | 0.210855i | ||||
\(873\) | 1.10087 | − | 0.635585i | 0.0372587 | − | 0.0215113i | ||||
\(874\) | −22.7395 | −0.769177 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | 33.5494 | − | 19.3698i | 1.13288 | − | 0.654071i | 0.188225 | − | 0.982126i | \(-0.439726\pi\) |
0.944659 | + | 0.328055i | \(0.106393\pi\) | |||||||
\(878\) | −26.4251 | − | 15.2565i | −0.891804 | − | 0.514883i | ||||
\(879\) | 5.11323 | − | 8.85637i | 0.172465 | − | 0.298718i | ||||
\(880\) | 10.5704 | − | 1.64678i | 0.356329 | − | 0.0555130i | ||||
\(881\) | 6.03399 | 0.203290 | 0.101645 | − | 0.994821i | \(-0.467589\pi\) | ||||
0.101645 | + | 0.994821i | \(0.467589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.77828i | 0.261760i | 0.991398 | + | 0.130880i | \(0.0417803\pi\) | ||||
−0.991398 | + | 0.130880i | \(0.958220\pi\) | |||||||
\(884\) | −8.28663 | − | 14.3529i | −0.278710 | − | 0.482739i | ||||
\(885\) | −18.6822 | + | 15.0504i | −0.627995 | + | 0.505914i | ||||
\(886\) | 4.75417 | − | 8.23447i | 0.159720 | − | 0.276642i | ||||
\(887\) | −21.5587 | + | 12.4469i | −0.723871 | + | 0.417927i | −0.816176 | − | 0.577803i | \(-0.803910\pi\) |
0.0923045 | + | 0.995731i | \(0.470577\pi\) | |||||||
\(888\) | − | 7.17103i | − | 0.240644i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19.9553 | − | 7.71811i | −0.668903 | − | 0.258712i | ||||
\(891\) | 2.39213 | + | 4.14329i | 0.0801394 | + | 0.138805i | ||||
\(892\) | −12.3819 | − | 7.14867i | −0.414576 | − | 0.239355i | ||||
\(893\) | 31.6172 | + | 18.2542i | 1.05803 | + | 0.610853i | ||||
\(894\) | −11.1710 | − | 19.3488i | −0.373615 | − | 0.647120i | ||||
\(895\) | −15.7395 | + | 40.6948i | −0.526115 | + | 1.36028i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.7395i | 0.759251i | ||||||||
\(898\) | 15.2628 | − | 8.81197i | 0.509326 | − | 0.294059i | ||||
\(899\) | −4.97764 | + | 8.62153i | −0.166014 | + | 0.287544i | ||||
\(900\) | 4.76304 | − | 1.52100i | 0.158768 | − | 0.0507000i | ||||
\(901\) | −21.2079 | − | 36.7332i | −0.706539 | − | 1.22376i | ||||
\(902\) | 9.83371i | 0.327427i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.34206 | −0.210934 | ||||||||
\(905\) | −50.8744 | + | 7.92580i | −1.69112 | + | 0.263463i | ||||
\(906\) | 8.25654 | − | 14.3008i | 0.274305 | − | 0.475111i | ||||
\(907\) | −40.4482 | − | 23.3528i | −1.34306 | − | 0.775416i | −0.355805 | − | 0.934560i | \(-0.615793\pi\) |
−0.987255 | + | 0.159144i | \(0.949127\pi\) | |||||||
\(908\) | −9.57428 | + | 5.52771i | −0.317734 | + | 0.183444i | ||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 2.74619 | − | 1.58551i | 0.0909355 | − | 0.0525016i | ||||
\(913\) | 14.0768 | + | 8.12724i | 0.465874 | + | 0.268972i | ||||
\(914\) | 0.193385 | − | 0.334953i | 0.00639661 | − | 0.0110793i | ||||
\(915\) | −2.44925 | − | 15.7213i | −0.0809697 | − | 0.519731i | ||||
\(916\) | 18.4529 | 0.609702 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.22646i | 0.172499i | ||||||||
\(919\) | −17.1156 | − | 29.6451i | −0.564592 | − | 0.977901i | −0.997088 | − | 0.0762654i | \(-0.975700\pi\) |
0.432496 | − | 0.901636i | \(-0.357633\pi\) | |||||||
\(920\) | −10.0595 | − | 12.4870i | −0.331653 | − | 0.411683i | ||||
\(921\) | 11.7288 | − | 20.3149i | 0.386478 | − | 0.669400i | ||||
\(922\) | −32.3618 | + | 18.6841i | −1.06578 | + | 0.615329i | ||||
\(923\) | 19.0262i | 0.626254i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.1263 | + | 26.5238i | −0.793268 | + | 0.872097i | ||||
\(926\) | −12.1540 | − | 21.0514i | −0.399406 | − | 0.691792i | ||||
\(927\) | 9.72240 | + | 5.61323i | 0.319325 | + | 0.184363i | ||||
\(928\) | −2.06700 | − | 1.19339i | −0.0678527 | − | 0.0391748i | ||||
\(929\) | 13.8274 | + | 23.9498i | 0.453663 | + | 0.785768i | 0.998610 | − | 0.0527025i | \(-0.0167835\pi\) |
−0.544947 | + | 0.838471i | \(0.683450\pi\) | |||||||
\(930\) | 3.36441 | − | 8.69874i | 0.110324 | − | 0.285243i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.11560i | 0.298591i | ||||||||
\(933\) | −4.89992 | + | 2.82897i | −0.160416 | + | 0.0926163i | ||||
\(934\) | −14.2866 | + | 24.7452i | −0.467473 | + | 0.809687i | ||||
\(935\) | 43.5409 | − | 35.0767i | 1.42394 | − | 1.14713i | ||||
\(936\) | −1.58551 | − | 2.74619i | −0.0518242 | − | 0.0897621i | ||||
\(937\) | − | 38.8397i | − | 1.26884i | −0.772990 | − | 0.634419i | \(-0.781240\pi\) | ||
0.772990 | − | 0.634419i | \(-0.218760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.3868 | 0.534762 | ||||||||
\(940\) | 3.96290 | + | 25.4372i | 0.129256 | + | 0.829670i | ||||
\(941\) | −9.87750 | + | 17.1083i | −0.321997 | + | 0.557716i | −0.980900 | − | 0.194512i | \(-0.937688\pi\) |
0.658903 | + | 0.752228i | \(0.271021\pi\) | |||||||
\(942\) | 8.61225 | + | 4.97229i | 0.280602 | + | 0.162006i | ||||
\(943\) | 12.7648 | − | 7.36977i | 0.415680 | − | 0.239993i | ||||
\(944\) | −10.7288 | −0.349194 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.56852 | 0.311099 | ||||||||
\(947\) | 32.9543 | − | 19.0262i | 1.07087 | − | 0.618268i | 0.142452 | − | 0.989802i | \(-0.454501\pi\) |
0.928419 | + | 0.371534i | \(0.121168\pi\) | |||||||
\(948\) | 10.5404 | + | 6.08551i | 0.342337 | + | 0.197648i | ||||
\(949\) | −6.34206 | + | 10.9848i | −0.205872 | + | 0.356581i | ||||
\(950\) | −15.4918 | − | 3.37492i | −0.502620 | − | 0.109497i | ||||
\(951\) | −4.51309 | −0.146347 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.5947i | 1.70371i | 0.523778 | + | 0.851855i | \(0.324522\pi\) | ||||
−0.523778 | + | 0.851855i | \(0.675478\pi\) | |||||||
\(954\) | −4.05780 | − | 7.02832i | −0.131376 | − | 0.227550i | ||||
\(955\) | −14.3523 | − | 17.8157i | −0.464431 | − | 0.576501i | ||||
\(956\) | −6.55780 | + | 11.3584i | −0.212094 | + | 0.367358i | ||||
\(957\) | −9.88908 | + | 5.70946i | −0.319669 | + | 0.184561i | ||||
\(958\) | 8.56378i | 0.276683i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.08551 | + | 0.806615i | 0.0673097 | + | 0.0260334i | ||||
\(961\) | 6.80126 | + | 11.7801i | 0.219395 | + | 0.380004i | ||||
\(962\) | 19.6930 | + | 11.3698i | 0.634929 | + | 0.366576i | ||||
\(963\) | 1.21026 | + | 0.698745i | 0.0390001 | + | 0.0225167i | ||||
\(964\) | 2.67103 | + | 4.62636i | 0.0860281 | + | 0.149005i | ||||
\(965\) | −24.2196 | − | 9.36740i | −0.779655 | − | 0.301547i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.61797i | 0.148504i | 0.997240 | + | 0.0742520i | \(0.0236569\pi\) | ||||
−0.997240 | + | 0.0742520i | \(0.976343\pi\) | |||||||
\(968\) | 10.2963 | − | 5.94457i | 0.330936 | − | 0.191066i | ||||
\(969\) | 8.28663 | − | 14.3529i | 0.266205 | − | 0.461080i | ||||
\(970\) | −1.78320 | − | 2.21350i | −0.0572551 | − | 0.0710711i | ||||
\(971\) | 19.4523 | + | 33.6924i | 0.624254 | + | 1.08124i | 0.988685 | + | 0.150009i | \(0.0479303\pi\) |
−0.364431 | + | 0.931231i | \(0.618736\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.8444 | 1.02036 | ||||||||
\(975\) | −3.37492 | + | 15.4918i | −0.108084 | + | 0.496134i | ||||
\(976\) | 3.55780 | − | 6.16229i | 0.113882 | − | 0.197250i | ||||
\(977\) | −13.8750 | − | 8.01072i | −0.443900 | − | 0.256286i | 0.261351 | − | 0.965244i | \(-0.415832\pi\) |
−0.705250 | + | 0.708958i | \(0.749165\pi\) | |||||||
\(978\) | −2.49796 | + | 1.44220i | −0.0798761 | + | 0.0461165i | ||||
\(979\) | −45.7783 | −1.46308 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.4529 | 0.397591 | ||||||||
\(982\) | −3.89506 | + | 2.24881i | −0.124296 | + | 0.0717626i | ||||
\(983\) | −1.78005 | − | 1.02771i | −0.0567749 | − | 0.0327790i | 0.471344 | − | 0.881950i | \(-0.343769\pi\) |
−0.528119 | + | 0.849171i | \(0.677102\pi\) | |||||||
\(984\) | −1.02771 | + | 1.78005i | −0.0327624 | + | 0.0567461i | ||||
\(985\) | −0.825236 | − | 5.29705i | −0.0262942 | − | 0.168778i | ||||
\(986\) | −12.4744 | −0.397264 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.0554i | 0.319906i | ||||||||
\(989\) | −7.17103 | − | 12.4206i | −0.228025 | − | 0.394952i | ||||
\(990\) | 8.33086 | − | 6.71137i | 0.264772 | − | 0.213301i | ||||
\(991\) | 13.5986 | − | 23.5535i | 0.431974 | − | 0.748201i | −0.565069 | − | 0.825043i | \(-0.691151\pi\) |
0.997043 | + | 0.0768427i | \(0.0244839\pi\) | |||||||
\(992\) | 3.61222 | − | 2.08551i | 0.114688 | − | 0.0662152i | ||||
\(993\) | 13.0816i | 0.415132i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.7950 | + | 38.2526i | −0.469032 | + | 1.21269i | ||||
\(996\) | 1.69874 | + | 2.94231i | 0.0538268 | + | 0.0932307i | ||||
\(997\) | 15.9993 | + | 9.23718i | 0.506702 | + | 0.292544i | 0.731477 | − | 0.681866i | \(-0.238831\pi\) |
−0.224775 | + | 0.974411i | \(0.572165\pi\) | |||||||
\(998\) | 0.296232 | + | 0.171030i | 0.00937707 | + | 0.00541385i | ||||
\(999\) | −3.58551 | − | 6.21029i | −0.113441 | − | 0.196485i |
(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 | 1470.2.n.j.949.1 | 12 | ||
5.4 | even | 2 | inner | 1470.2.n.j.949.6 | 12 | ||
7.2 | even | 3 | inner | 1470.2.n.j.79.6 | 12 | ||
7.3 | odd | 6 | 1470.2.g.i.589.2 | 6 | |||
7.4 | even | 3 | 1470.2.g.h.589.2 | 6 | |||
7.5 | odd | 6 | 210.2.n.b.79.4 | yes | 12 | ||
7.6 | odd | 2 | 210.2.n.b.109.3 | yes | 12 | ||
21.5 | even | 6 | 630.2.u.f.289.3 | 12 | |||
21.20 | even | 2 | 630.2.u.f.109.4 | 12 | |||
28.19 | even | 6 | 1680.2.di.c.289.1 | 12 | |||
28.27 | even | 2 | 1680.2.di.c.529.6 | 12 | |||
35.3 | even | 12 | 7350.2.a.dn.1.1 | 3 | |||
35.4 | even | 6 | 1470.2.g.h.589.5 | 6 | |||
35.9 | even | 6 | inner | 1470.2.n.j.79.1 | 12 | ||
35.12 | even | 12 | 1050.2.i.u.751.2 | 6 | |||
35.13 | even | 4 | 1050.2.i.v.151.2 | 6 | |||
35.17 | even | 12 | 7350.2.a.dq.1.1 | 3 | |||
35.18 | odd | 12 | 7350.2.a.do.1.1 | 3 | |||
35.19 | odd | 6 | 210.2.n.b.79.3 | ✓ | 12 | ||
35.24 | odd | 6 | 1470.2.g.i.589.5 | 6 | |||
35.27 | even | 4 | 1050.2.i.u.151.2 | 6 | |||
35.32 | odd | 12 | 7350.2.a.dp.1.1 | 3 | |||
35.33 | even | 12 | 1050.2.i.v.751.2 | 6 | |||
35.34 | odd | 2 | 210.2.n.b.109.4 | yes | 12 | ||
105.89 | even | 6 | 630.2.u.f.289.4 | 12 | |||
105.104 | even | 2 | 630.2.u.f.109.3 | 12 | |||
140.19 | even | 6 | 1680.2.di.c.289.6 | 12 | |||
140.139 | even | 2 | 1680.2.di.c.529.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.b.79.3 | ✓ | 12 | 35.19 | odd | 6 | ||
210.2.n.b.79.4 | yes | 12 | 7.5 | odd | 6 | ||
210.2.n.b.109.3 | yes | 12 | 7.6 | odd | 2 | ||
210.2.n.b.109.4 | yes | 12 | 35.34 | odd | 2 | ||
630.2.u.f.109.3 | 12 | 105.104 | even | 2 | |||
630.2.u.f.109.4 | 12 | 21.20 | even | 2 | |||
630.2.u.f.289.3 | 12 | 21.5 | even | 6 | |||
630.2.u.f.289.4 | 12 | 105.89 | even | 6 | |||
1050.2.i.u.151.2 | 6 | 35.27 | even | 4 | |||
1050.2.i.u.751.2 | 6 | 35.12 | even | 12 | |||
1050.2.i.v.151.2 | 6 | 35.13 | even | 4 | |||
1050.2.i.v.751.2 | 6 | 35.33 | even | 12 | |||
1470.2.g.h.589.2 | 6 | 7.4 | even | 3 | |||
1470.2.g.h.589.5 | 6 | 35.4 | even | 6 | |||
1470.2.g.i.589.2 | 6 | 7.3 | odd | 6 | |||
1470.2.g.i.589.5 | 6 | 35.24 | odd | 6 | |||
1470.2.n.j.79.1 | 12 | 35.9 | even | 6 | inner | ||
1470.2.n.j.79.6 | 12 | 7.2 | even | 3 | inner | ||
1470.2.n.j.949.1 | 12 | 1.1 | even | 1 | trivial | ||
1470.2.n.j.949.6 | 12 | 5.4 | even | 2 | inner | ||
1680.2.di.c.289.1 | 12 | 28.19 | even | 6 | |||
1680.2.di.c.289.6 | 12 | 140.19 | even | 6 | |||
1680.2.di.c.529.1 | 12 | 140.139 | even | 2 | |||
1680.2.di.c.529.6 | 12 | 28.27 | even | 2 | |||
7350.2.a.dn.1.1 | 3 | 35.3 | even | 12 | |||
7350.2.a.do.1.1 | 3 | 35.18 | odd | 12 | |||
7350.2.a.dp.1.1 | 3 | 35.32 | odd | 12 | |||
7350.2.a.dq.1.1 | 3 | 35.17 | even | 12 |