Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.2.e.i.271.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 0.633975i | 0.258819 | − | 0.448288i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.732051 | + | 1.26795i | 0.366025 | + | 0.633975i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.36603 | − | 4.09808i | 0.894274 | − | 1.54893i | 0.0595724 | − | 0.998224i | \(-0.481026\pi\) |
0.834701 | − | 0.550703i | \(-0.185640\pi\) | |||||||
\(8\) | 2.53590 | 0.896575 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.732051 | 0.231495 | ||||||||
\(11\) | −2.86603 | + | 4.96410i | −0.864139 | + | 1.49673i | 0.00376022 | + | 0.999993i | \(0.498803\pi\) |
−0.867899 | + | 0.496740i | \(0.834530\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.732051 | − | 1.26795i | −0.203034 | − | 0.351666i | 0.746470 | − | 0.665419i | \(-0.231747\pi\) |
−0.949505 | + | 0.313753i | \(0.898414\pi\) | |||||||
\(14\) | −1.73205 | − | 3.00000i | −0.462910 | − | 0.801784i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.535898 | + | 0.928203i | −0.133975 | + | 0.232051i | ||||
\(17\) | 2.73205 | 0.662620 | 0.331310 | − | 0.943522i | \(-0.392509\pi\) | ||||
0.331310 | + | 0.943522i | \(0.392509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46410 | 1.02414 | 0.512068 | − | 0.858945i | \(-0.328880\pi\) | ||||
0.512068 | + | 0.858945i | \(0.328880\pi\) | |||||||
\(20\) | −0.732051 | + | 1.26795i | −0.163692 | + | 0.283522i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.09808 | + | 3.63397i | 0.447311 | + | 0.774766i | ||||
\(23\) | −1.73205 | − | 3.00000i | −0.361158 | − | 0.625543i | 0.626994 | − | 0.779024i | \(-0.284285\pi\) |
−0.988152 | + | 0.153481i | \(0.950952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −1.07180 | −0.210197 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.92820 | 1.30931 | ||||||||
\(29\) | 1.59808 | − | 2.76795i | 0.296755 | − | 0.513995i | −0.678636 | − | 0.734474i | \(-0.737429\pi\) |
0.975392 | + | 0.220479i | \(0.0707621\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 2.59808i | 0.269408 | + | 0.466628i | 0.968709 | − | 0.248199i | \(-0.0798387\pi\) |
−0.699301 | + | 0.714827i | \(0.746505\pi\) | |||||||
\(32\) | 2.92820 | + | 5.07180i | 0.517638 | + | 0.896575i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | − | 1.73205i | 0.171499 | − | 0.297044i | ||||
\(35\) | 4.73205 | 0.799863 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.73205 | −0.449146 | −0.224573 | − | 0.974457i | \(-0.572099\pi\) | ||||
−0.224573 | + | 0.974457i | \(0.572099\pi\) | |||||||
\(38\) | 1.63397 | − | 2.83013i | 0.265066 | − | 0.459107i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.26795 | + | 2.19615i | 0.200480 | + | 0.347242i | ||||
\(41\) | −3.59808 | − | 6.23205i | −0.561925 | − | 0.973283i | −0.997328 | − | 0.0730473i | \(-0.976728\pi\) |
0.435403 | − | 0.900235i | \(-0.356606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0980762 | + | 0.169873i | −0.0149565 | + | 0.0259054i | −0.873407 | − | 0.486991i | \(-0.838094\pi\) |
0.858450 | + | 0.512897i | \(0.171428\pi\) | |||||||
\(44\) | −8.39230 | −1.26519 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.53590 | −0.373898 | ||||||||
\(47\) | −4.36603 | + | 7.56218i | −0.636850 | + | 1.10306i | 0.349270 | + | 0.937022i | \(0.386430\pi\) |
−0.986120 | + | 0.166035i | \(0.946904\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.69615 | − | 13.3301i | −1.09945 | − | 1.90430i | ||||
\(50\) | 0.366025 | + | 0.633975i | 0.0517638 | + | 0.0896575i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.07180 | − | 1.85641i | 0.148631 | − | 0.257437i | ||||
\(53\) | −6.73205 | −0.924718 | −0.462359 | − | 0.886693i | \(-0.652997\pi\) | ||||
−0.462359 | + | 0.886693i | \(0.652997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.73205 | −0.772910 | ||||||||
\(56\) | 6.00000 | − | 10.3923i | 0.801784 | − | 1.38873i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.16987 | − | 2.02628i | −0.153612 | − | 0.266064i | ||||
\(59\) | −4.13397 | − | 7.16025i | −0.538198 | − | 0.932186i | −0.999001 | − | 0.0446835i | \(-0.985772\pi\) |
0.460804 | − | 0.887502i | \(-0.347561\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | 2.19615 | 0.278912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.14359 | 0.267949 | ||||||||
\(65\) | 0.732051 | − | 1.26795i | 0.0907997 | − | 0.157270i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73205 | − | 3.00000i | −0.211604 | − | 0.366508i | 0.740613 | − | 0.671932i | \(-0.234535\pi\) |
−0.952217 | + | 0.305424i | \(0.901202\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.73205 | − | 3.00000i | 0.207020 | − | 0.358569i | ||||
\(71\) | 3.73205 | 0.442913 | 0.221456 | − | 0.975170i | \(-0.428919\pi\) | ||||
0.221456 | + | 0.975170i | \(0.428919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.66025 | −0.896565 | −0.448282 | − | 0.893892i | \(-0.647964\pi\) | ||||
−0.448282 | + | 0.893892i | \(0.647964\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.26795 | + | 5.66025i | 0.374859 | + | 0.649276i | ||||
\(77\) | 13.5622 | + | 23.4904i | 1.54555 | + | 2.67698i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.73205 | + | 13.3923i | −0.869924 | + | 1.50675i | −0.00784992 | + | 0.999969i | \(0.502499\pi\) |
−0.862074 | + | 0.506783i | \(0.830835\pi\) | |||||||
\(80\) | −1.07180 | −0.119831 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.26795 | −0.581748 | ||||||||
\(83\) | 1.09808 | − | 1.90192i | 0.120530 | − | 0.208763i | −0.799447 | − | 0.600737i | \(-0.794874\pi\) |
0.919977 | + | 0.391973i | \(0.128207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.36603 | + | 2.36603i | 0.148166 | + | 0.256631i | ||||
\(86\) | 0.0717968 | + | 0.124356i | 0.00774204 | + | 0.0134096i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.26795 | + | 12.5885i | −0.774766 | + | 1.34193i | ||||
\(89\) | −5.19615 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.92820 | −0.726273 | ||||||||
\(92\) | 2.53590 | − | 4.39230i | 0.264386 | − | 0.457929i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.19615 | + | 5.53590i | 0.329658 | + | 0.570984i | ||||
\(95\) | 2.23205 | + | 3.86603i | 0.229004 | + | 0.396646i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.83013 | − | 8.36603i | 0.490425 | − | 0.849441i | −0.509514 | − | 0.860462i | \(-0.670175\pi\) |
0.999939 | + | 0.0110211i | \(0.00350819\pi\) | |||||||
\(98\) | −11.2679 | −1.13823 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.46410 | −0.146410 | ||||||||
\(101\) | −1.33013 | + | 2.30385i | −0.132353 | + | 0.229241i | −0.924583 | − | 0.380981i | \(-0.875586\pi\) |
0.792230 | + | 0.610222i | \(0.208920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.267949 | + | 0.464102i | 0.0264018 | + | 0.0457293i | 0.878924 | − | 0.476961i | \(-0.158262\pi\) |
−0.852523 | + | 0.522690i | \(0.824928\pi\) | |||||||
\(104\) | −1.85641 | − | 3.21539i | −0.182036 | − | 0.315295i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.46410 | + | 4.26795i | −0.239335 | + | 0.414540i | ||||
\(107\) | 8.53590 | 0.825196 | 0.412598 | − | 0.910913i | \(-0.364621\pi\) | ||||
0.412598 | + | 0.910913i | \(0.364621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.07180 | −0.581573 | −0.290786 | − | 0.956788i | \(-0.593917\pi\) | ||||
−0.290786 | + | 0.956788i | \(0.593917\pi\) | |||||||
\(110\) | −2.09808 | + | 3.63397i | −0.200044 | + | 0.346486i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.53590 | + | 4.39230i | 0.239620 | + | 0.415034i | ||||
\(113\) | −9.56218 | − | 16.5622i | −0.899534 | − | 1.55804i | −0.828091 | − | 0.560594i | \(-0.810573\pi\) |
−0.0714432 | − | 0.997445i | \(-0.522760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.73205 | − | 3.00000i | 0.161515 | − | 0.279751i | ||||
\(116\) | 4.67949 | 0.434480 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.05256 | −0.557183 | ||||||||
\(119\) | 6.46410 | − | 11.1962i | 0.592563 | − | 1.02635i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9282 | − | 18.9282i | −0.993473 | − | 1.72075i | ||||
\(122\) | 1.46410 | + | 2.53590i | 0.132554 | + | 0.229589i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.19615 | + | 3.80385i | −0.197220 | + | 0.341596i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5885 | −1.29452 | −0.647258 | − | 0.762271i | \(-0.724084\pi\) | ||||
−0.647258 | + | 0.762271i | \(0.724084\pi\) | |||||||
\(128\) | −5.07180 | + | 8.78461i | −0.448288 | + | 0.776457i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.535898 | − | 0.928203i | −0.0470014 | − | 0.0814088i | ||||
\(131\) | 7.79423 | + | 13.5000i | 0.680985 | + | 1.17950i | 0.974681 | + | 0.223602i | \(0.0717814\pi\) |
−0.293696 | + | 0.955899i | \(0.594885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.5622 | − | 18.2942i | 0.915857 | − | 1.58631i | ||||
\(134\) | −2.53590 | −0.219068 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820 | 0.594089 | ||||||||
\(137\) | 1.26795 | − | 2.19615i | 0.108328 | − | 0.187630i | −0.806765 | − | 0.590873i | \(-0.798784\pi\) |
0.915093 | + | 0.403243i | \(0.132117\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.303848 | − | 0.526279i | −0.0257720 | − | 0.0446384i | 0.852852 | − | 0.522153i | \(-0.174871\pi\) |
−0.878624 | + | 0.477515i | \(0.841538\pi\) | |||||||
\(140\) | 3.46410 | + | 6.00000i | 0.292770 | + | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.36603 | − | 2.36603i | 0.114634 | − | 0.198552i | ||||
\(143\) | 8.39230 | 0.701800 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.19615 | 0.265426 | ||||||||
\(146\) | −2.80385 | + | 4.85641i | −0.232048 | + | 0.401919i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | − | 3.46410i | −0.164399 | − | 0.284747i | ||||
\(149\) | −4.00000 | − | 6.92820i | −0.327693 | − | 0.567581i | 0.654361 | − | 0.756182i | \(-0.272938\pi\) |
−0.982054 | + | 0.188602i | \(0.939604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.69615 | + | 4.66987i | −0.219410 | + | 0.380029i | −0.954628 | − | 0.297802i | \(-0.903746\pi\) |
0.735218 | + | 0.677831i | \(0.237080\pi\) | |||||||
\(152\) | 11.3205 | 0.918214 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.8564 | 1.60007 | ||||||||
\(155\) | −1.50000 | + | 2.59808i | −0.120483 | + | 0.208683i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.56218 | + | 16.5622i | 0.763145 | + | 1.32181i | 0.941222 | + | 0.337789i | \(0.109679\pi\) |
−0.178077 | + | 0.984017i | \(0.556988\pi\) | |||||||
\(158\) | 5.66025 | + | 9.80385i | 0.450306 | + | 0.779952i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.92820 | + | 5.07180i | −0.231495 | + | 0.400961i | ||||
\(161\) | −16.3923 | −1.29189 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7321 | 0.997251 | 0.498626 | − | 0.866817i | \(-0.333838\pi\) | ||||
0.498626 | + | 0.866817i | \(0.333838\pi\) | |||||||
\(164\) | 5.26795 | − | 9.12436i | 0.411358 | − | 0.712492i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.803848 | − | 1.39230i | −0.0623907 | − | 0.108064i | ||||
\(167\) | −8.83013 | − | 15.2942i | −0.683296 | − | 1.18350i | −0.973969 | − | 0.226681i | \(-0.927213\pi\) |
0.290673 | − | 0.956822i | \(-0.406121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.42820 | − | 9.40192i | 0.417554 | − | 0.723225i | ||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.287187 | −0.0218978 | ||||||||
\(173\) | 4.26795 | − | 7.39230i | 0.324486 | − | 0.562027i | −0.656922 | − | 0.753958i | \(-0.728142\pi\) |
0.981408 | + | 0.191932i | \(0.0614753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.36603 | + | 4.09808i | 0.178855 | + | 0.309785i | ||||
\(176\) | −3.07180 | − | 5.32051i | −0.231545 | − | 0.401048i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.90192 | + | 3.29423i | −0.142555 | + | 0.246913i | ||||
\(179\) | −8.12436 | −0.607243 | −0.303621 | − | 0.952793i | \(-0.598196\pi\) | ||||
−0.303621 | + | 0.952793i | \(0.598196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.4641 | 1.96706 | 0.983531 | − | 0.180742i | \(-0.0578498\pi\) | ||||
0.983531 | + | 0.180742i | \(0.0578498\pi\) | |||||||
\(182\) | −2.53590 | + | 4.39230i | −0.187973 | + | 0.325579i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.39230 | − | 7.60770i | −0.323805 | − | 0.560847i | ||||
\(185\) | −1.36603 | − | 2.36603i | −0.100432 | − | 0.173954i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.83013 | + | 13.5622i | −0.572596 | + | 0.991765i | ||||
\(188\) | −12.7846 | −0.932413 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.26795 | 0.237082 | ||||||||
\(191\) | −4.06218 | + | 7.03590i | −0.293929 | + | 0.509100i | −0.974735 | − | 0.223364i | \(-0.928296\pi\) |
0.680806 | + | 0.732464i | \(0.261630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.63397 | + | 4.56218i | 0.189598 | + | 0.328393i | 0.945116 | − | 0.326735i | \(-0.105948\pi\) |
−0.755519 | + | 0.655127i | \(0.772615\pi\) | |||||||
\(194\) | −3.53590 | − | 6.12436i | −0.253863 | − | 0.439703i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.2679 | − | 19.5167i | 0.804854 | − | 1.39405i | ||||
\(197\) | 13.8564 | 0.987228 | 0.493614 | − | 0.869681i | \(-0.335676\pi\) | ||||
0.493614 | + | 0.869681i | \(0.335676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | −1.26795 | + | 2.19615i | −0.0896575 | + | 0.155291i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.973721 | + | 1.68653i | 0.0685107 | + | 0.118664i | ||||
\(203\) | −7.56218 | − | 13.0981i | −0.530761 | − | 0.919305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.59808 | − | 6.23205i | 0.251301 | − | 0.435265i | ||||
\(206\) | 0.392305 | 0.0273332 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.56922 | 0.108806 | ||||||||
\(209\) | −12.7942 | + | 22.1603i | −0.884995 | + | 1.53286i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.42820 | + | 7.66987i | 0.304850 | + | 0.528016i | 0.977228 | − | 0.212192i | \(-0.0680603\pi\) |
−0.672378 | + | 0.740208i | \(0.734727\pi\) | |||||||
\(212\) | −4.92820 | − | 8.53590i | −0.338470 | − | 0.586248i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.12436 | − | 5.41154i | 0.213577 | − | 0.369925i | ||||
\(215\) | −0.196152 | −0.0133775 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.1962 | 0.963698 | ||||||||
\(218\) | −2.22243 | + | 3.84936i | −0.150522 | + | 0.260712i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.19615 | − | 7.26795i | −0.282905 | − | 0.490005i | ||||
\(221\) | −2.00000 | − | 3.46410i | −0.134535 | − | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.39230 | + | 14.5359i | −0.561990 | + | 0.973396i | 0.435332 | + | 0.900270i | \(0.356631\pi\) |
−0.997323 | + | 0.0731260i | \(0.976702\pi\) | |||||||
\(224\) | 27.7128 | 1.85164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | −9.02628 | + | 15.6340i | −0.599095 | + | 1.03766i | 0.393860 | + | 0.919171i | \(0.371140\pi\) |
−0.992955 | + | 0.118493i | \(0.962194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | + | 10.3923i | 0.396491 | + | 0.686743i | 0.993290 | − | 0.115648i | \(-0.0368944\pi\) |
−0.596799 | + | 0.802391i | \(0.703561\pi\) | |||||||
\(230\) | −1.26795 | − | 2.19615i | −0.0836061 | − | 0.144810i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.05256 | − | 7.01924i | 0.266064 | − | 0.460836i | ||||
\(233\) | 28.0526 | 1.83778 | 0.918892 | − | 0.394509i | \(-0.129085\pi\) | ||||
0.918892 | + | 0.394509i | \(0.129085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.73205 | −0.569616 | ||||||||
\(236\) | 6.05256 | − | 10.4833i | 0.393988 | − | 0.682407i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.73205 | − | 8.19615i | −0.306733 | − | 0.531278i | ||||
\(239\) | −0.267949 | − | 0.464102i | −0.0173322 | − | 0.0300202i | 0.857229 | − | 0.514935i | \(-0.172184\pi\) |
−0.874561 | + | 0.484915i | \(0.838851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.16025 | − | 14.1340i | 0.525648 | − | 0.910449i | −0.473906 | − | 0.880576i | \(-0.657156\pi\) |
0.999554 | − | 0.0298736i | \(-0.00951049\pi\) | |||||||
\(242\) | −16.0000 | −1.02852 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.85641 | −0.374918 | ||||||||
\(245\) | 7.69615 | − | 13.3301i | 0.491689 | − | 0.851631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.26795 | − | 5.66025i | −0.207935 | − | 0.360153i | ||||
\(248\) | 3.80385 | + | 6.58846i | 0.241545 | + | 0.418367i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.366025 | + | 0.633975i | −0.0231495 | + | 0.0400961i | ||||
\(251\) | 10.3923 | 0.655956 | 0.327978 | − | 0.944685i | \(-0.393633\pi\) | ||||
0.327978 | + | 0.944685i | \(0.393633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.8564 | 1.24836 | ||||||||
\(254\) | −5.33975 | + | 9.24871i | −0.335045 | + | 0.580316i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.85641 | + | 10.1436i | 0.366025 | + | 0.633975i | ||||
\(257\) | 5.19615 | + | 9.00000i | 0.324127 | + | 0.561405i | 0.981335 | − | 0.192304i | \(-0.0615961\pi\) |
−0.657208 | + | 0.753709i | \(0.728263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.46410 | + | 11.1962i | −0.401660 | + | 0.695695i | ||||
\(260\) | 2.14359 | 0.132940 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.4115 | 0.705007 | ||||||||
\(263\) | 10.6603 | − | 18.4641i | 0.657339 | − | 1.13855i | −0.323962 | − | 0.946070i | \(-0.605015\pi\) |
0.981302 | − | 0.192475i | \(-0.0616515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.36603 | − | 5.83013i | −0.206773 | − | 0.358142i | ||||
\(266\) | −7.73205 | − | 13.3923i | −0.474082 | − | 0.821135i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.53590 | − | 4.39230i | 0.154905 | − | 0.268303i | ||||
\(269\) | −10.6603 | −0.649967 | −0.324984 | − | 0.945720i | \(-0.605359\pi\) | ||||
−0.324984 | + | 0.945720i | \(0.605359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.92820 | −0.177876 | −0.0889378 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889378 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(272\) | −1.46410 | + | 2.53590i | −0.0887742 | + | 0.153761i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.928203 | − | 1.60770i | −0.0560748 | − | 0.0971244i | ||||
\(275\) | −2.86603 | − | 4.96410i | −0.172828 | − | 0.299347i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.90192 | + | 3.29423i | −0.114276 | + | 0.197931i | −0.917490 | − | 0.397759i | \(-0.869788\pi\) |
0.803214 | + | 0.595690i | \(0.203121\pi\) | |||||||
\(278\) | −0.444864 | −0.0266812 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0000 | 0.717137 | ||||||||
\(281\) | 7.73205 | − | 13.3923i | 0.461255 | − | 0.798918i | −0.537768 | − | 0.843093i | \(-0.680732\pi\) |
0.999024 | + | 0.0441747i | \(0.0140658\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6603 | + | 25.3923i | 0.871462 | + | 1.50942i | 0.860485 | + | 0.509476i | \(0.170161\pi\) |
0.0109768 | + | 0.999940i | \(0.496506\pi\) | |||||||
\(284\) | 2.73205 | + | 4.73205i | 0.162117 | + | 0.280796i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.07180 | − | 5.32051i | 0.181639 | − | 0.314608i | ||||
\(287\) | −34.0526 | −2.01006 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.53590 | −0.560935 | ||||||||
\(290\) | 1.16987 | − | 2.02628i | 0.0686973 | − | 0.118987i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.60770 | − | 9.71281i | −0.328166 | − | 0.568399i | ||||
\(293\) | 14.3660 | + | 24.8827i | 0.839272 | + | 1.45366i | 0.890504 | + | 0.454975i | \(0.150352\pi\) |
−0.0512319 | + | 0.998687i | \(0.516315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.13397 | − | 7.16025i | 0.240689 | − | 0.416886i | ||||
\(296\) | −6.92820 | −0.402694 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.85641 | −0.339253 | ||||||||
\(299\) | −2.53590 | + | 4.39230i | −0.146655 | + | 0.254014i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.464102 | + | 0.803848i | 0.0267504 | + | 0.0463330i | ||||
\(302\) | 1.97372 | + | 3.41858i | 0.113575 | + | 0.196717i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.39230 | + | 4.14359i | −0.137208 | + | 0.237651i | ||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0526 | 0.802022 | 0.401011 | − | 0.916073i | \(-0.368659\pi\) | ||||
0.401011 | + | 0.916073i | \(0.368659\pi\) | |||||||
\(308\) | −19.8564 | + | 34.3923i | −1.13142 | + | 1.95968i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.09808 | + | 1.90192i | 0.0623665 | + | 0.108022i | ||||
\(311\) | 9.86603 | + | 17.0885i | 0.559451 | + | 0.968998i | 0.997542 | + | 0.0700670i | \(0.0223213\pi\) |
−0.438091 | + | 0.898930i | \(0.644345\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.53590 | − | 7.85641i | 0.256384 | − | 0.444070i | −0.708886 | − | 0.705323i | \(-0.750802\pi\) |
0.965271 | + | 0.261252i | \(0.0841355\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.6410 | −1.27366 | ||||||||
\(317\) | 3.09808 | − | 5.36603i | 0.174005 | − | 0.301386i | −0.765811 | − | 0.643065i | \(-0.777662\pi\) |
0.939817 | + | 0.341679i | \(0.110996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.16025 | + | 15.8660i | 0.512876 | + | 0.888327i | ||||
\(320\) | 1.07180 | + | 1.85641i | 0.0599153 | + | 0.103776i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | + | 10.3923i | −0.334367 | + | 0.579141i | ||||
\(323\) | 12.1962 | 0.678612 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46410 | 0.0812137 | ||||||||
\(326\) | 4.66025 | − | 8.07180i | 0.258108 | − | 0.447055i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.12436 | − | 15.8038i | −0.503808 | − | 0.872622i | ||||
\(329\) | 20.6603 | + | 35.7846i | 1.13904 | + | 1.97287i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.232051 | − | 0.401924i | 0.0127547 | − | 0.0220917i | −0.859578 | − | 0.511005i | \(-0.829273\pi\) |
0.872332 | + | 0.488913i | \(0.162607\pi\) | |||||||
\(332\) | 3.21539 | 0.176467 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.9282 | −0.707400 | ||||||||
\(335\) | 1.73205 | − | 3.00000i | 0.0946320 | − | 0.163908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.6603 | − | 23.6603i | −0.744121 | − | 1.28886i | −0.950604 | − | 0.310406i | \(-0.899535\pi\) |
0.206483 | − | 0.978450i | \(-0.433798\pi\) | |||||||
\(338\) | −3.97372 | − | 6.88269i | −0.216142 | − | 0.374369i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00000 | + | 3.46410i | −0.108465 | + | 0.187867i | ||||
\(341\) | −17.1962 | −0.931224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −39.7128 | −2.14429 | ||||||||
\(344\) | −0.248711 | + | 0.430781i | −0.0134096 | + | 0.0232261i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.12436 | − | 5.41154i | −0.167966 | − | 0.290926i | ||||
\(347\) | −14.2942 | − | 24.7583i | −0.767354 | − | 1.32910i | −0.938993 | − | 0.343937i | \(-0.888239\pi\) |
0.171638 | − | 0.985160i | \(-0.445094\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.42820 | − | 16.3301i | 0.504680 | − | 0.874132i | −0.495305 | − | 0.868719i | \(-0.664944\pi\) |
0.999985 | − | 0.00541263i | \(-0.00172290\pi\) | |||||||
\(350\) | 3.46410 | 0.185164 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −33.5692 | −1.78925 | ||||||||
\(353\) | 12.7583 | − | 22.0981i | 0.679057 | − | 1.17616i | −0.296208 | − | 0.955124i | \(-0.595722\pi\) |
0.975265 | − | 0.221038i | \(-0.0709446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.86603 | + | 3.23205i | 0.0990383 | + | 0.171539i | ||||
\(356\) | −3.80385 | − | 6.58846i | −0.201604 | − | 0.349188i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.97372 | + | 5.15064i | −0.157166 | + | 0.272220i | ||||
\(359\) | 6.12436 | 0.323231 | 0.161616 | − | 0.986854i | \(-0.448330\pi\) | ||||
0.161616 | + | 0.986854i | \(0.448330\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.928203 | 0.0488528 | ||||||||
\(362\) | 9.68653 | − | 16.7776i | 0.509113 | − | 0.881809i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.07180 | − | 8.78461i | −0.265834 | − | 0.460439i | ||||
\(365\) | −3.83013 | − | 6.63397i | −0.200478 | − | 0.347238i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5885 | + | 27.0000i | −0.813711 | + | 1.40939i | 0.0965390 | + | 0.995329i | \(0.469223\pi\) |
−0.910250 | + | 0.414059i | \(0.864111\pi\) | |||||||
\(368\) | 3.71281 | 0.193544 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.00000 | −0.103975 | ||||||||
\(371\) | −15.9282 | + | 27.5885i | −0.826951 | + | 1.43232i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0263 | − | 17.3660i | −0.519141 | − | 0.899179i | −0.999753 | − | 0.0222451i | \(-0.992919\pi\) |
0.480611 | − | 0.876934i | \(-0.340415\pi\) | |||||||
\(374\) | 5.73205 | + | 9.92820i | 0.296397 | + | 0.513375i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.0718 | + | 19.1769i | −0.570984 | + | 0.988974i | ||||
\(377\) | −4.67949 | −0.241006 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.39230 | 0.122884 | 0.0614422 | − | 0.998111i | \(-0.480430\pi\) | ||||
0.0614422 | + | 0.998111i | \(0.480430\pi\) | |||||||
\(380\) | −3.26795 | + | 5.66025i | −0.167642 | + | 0.290365i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.97372 | + | 5.15064i | 0.152149 | + | 0.263529i | ||||
\(383\) | 1.26795 | + | 2.19615i | 0.0647892 | + | 0.112218i | 0.896600 | − | 0.442840i | \(-0.146029\pi\) |
−0.831811 | + | 0.555059i | \(0.812696\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.5622 | + | 23.4904i | −0.691193 | + | 1.19718i | ||||
\(386\) | 3.85641 | 0.196286 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.1436 | 0.718032 | ||||||||
\(389\) | 13.7321 | − | 23.7846i | 0.696243 | − | 1.20593i | −0.273517 | − | 0.961867i | \(-0.588187\pi\) |
0.969760 | − | 0.244061i | \(-0.0784796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.73205 | − | 8.19615i | −0.239310 | − | 0.414497i | ||||
\(392\) | −19.5167 | − | 33.8038i | −0.985740 | − | 1.70735i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.07180 | − | 8.78461i | 0.255513 | − | 0.442562i | ||||
\(395\) | −15.4641 | −0.778083 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3923 | 0.722329 | 0.361165 | − | 0.932502i | \(-0.382379\pi\) | ||||
0.361165 | + | 0.932502i | \(0.382379\pi\) | |||||||
\(398\) | −0.732051 | + | 1.26795i | −0.0366944 | + | 0.0635566i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.535898 | − | 0.928203i | −0.0267949 | − | 0.0464102i | ||||
\(401\) | 12.4641 | + | 21.5885i | 0.622428 | + | 1.07808i | 0.989032 | + | 0.147699i | \(0.0471868\pi\) |
−0.366605 | + | 0.930377i | \(0.619480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.19615 | − | 3.80385i | 0.109398 | − | 0.189483i | ||||
\(404\) | −3.89488 | −0.193778 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.0718 | −0.549484 | ||||||||
\(407\) | 7.83013 | − | 13.5622i | 0.388125 | − | 0.672252i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.92820 | + | 15.4641i | 0.441471 | + | 0.764651i | 0.997799 | − | 0.0663124i | \(-0.0211234\pi\) |
−0.556328 | + | 0.830963i | \(0.687790\pi\) | |||||||
\(410\) | −2.63397 | − | 4.56218i | −0.130083 | − | 0.225310i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.392305 | + | 0.679492i | −0.0193275 | + | 0.0334762i | ||||
\(413\) | −39.1244 | −1.92518 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.19615 | 0.107805 | ||||||||
\(416\) | 4.28719 | − | 7.42563i | 0.210197 | − | 0.364071i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.36603 | + | 16.2224i | 0.458107 | + | 0.793465i | ||||
\(419\) | 10.1962 | + | 17.6603i | 0.498115 | + | 0.862760i | 0.999998 | − | 0.00217566i | \(-0.000692534\pi\) |
−0.501883 | + | 0.864936i | \(0.667359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8923 | + | 29.2583i | −0.823281 | + | 1.42596i | 0.0799458 | + | 0.996799i | \(0.474525\pi\) |
−0.903226 | + | 0.429165i | \(0.858808\pi\) | |||||||
\(422\) | 6.48334 | 0.315604 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.0718 | −0.829080 | ||||||||
\(425\) | −1.36603 | + | 2.36603i | −0.0662620 | + | 0.114769i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.46410 | + | 16.3923i | 0.458000 | + | 0.793279i | ||||
\(428\) | 6.24871 | + | 10.8231i | 0.302043 | + | 0.523154i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0717968 | + | 0.124356i | −0.00346235 | + | 0.00599696i | ||||
\(431\) | 21.3397 | 1.02790 | 0.513950 | − | 0.857820i | \(-0.328182\pi\) | ||||
0.513950 | + | 0.857820i | \(0.328182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.4641 | −1.70430 | −0.852148 | − | 0.523301i | \(-0.824700\pi\) | ||||
−0.852148 | + | 0.523301i | \(0.824700\pi\) | |||||||
\(434\) | 5.19615 | − | 9.00000i | 0.249423 | − | 0.432014i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.44486 | − | 7.69873i | −0.212870 | − | 0.368702i | ||||
\(437\) | −7.73205 | − | 13.3923i | −0.369874 | − | 0.640641i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.69615 | + | 4.66987i | −0.128680 | + | 0.222881i | −0.923166 | − | 0.384403i | \(-0.874407\pi\) |
0.794485 | + | 0.607284i | \(0.207741\pi\) | |||||||
\(440\) | −14.5359 | −0.692972 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.92820 | −0.139280 | ||||||||
\(443\) | −0.169873 | + | 0.294229i | −0.00807091 | + | 0.0139792i | −0.870033 | − | 0.492994i | \(-0.835902\pi\) |
0.861962 | + | 0.506973i | \(0.169236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.59808 | − | 4.50000i | −0.123161 | − | 0.213320i | ||||
\(446\) | 6.14359 | + | 10.6410i | 0.290908 | + | 0.503867i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.07180 | − | 8.78461i | 0.239620 | − | 0.415034i | ||||
\(449\) | −8.12436 | −0.383412 | −0.191706 | − | 0.981452i | \(-0.561402\pi\) | ||||
−0.191706 | + | 0.981452i | \(0.561402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.2487 | 1.94233 | ||||||||
\(452\) | 14.0000 | − | 24.2487i | 0.658505 | − | 1.14056i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.60770 | + | 11.4449i | 0.310114 | + | 0.537134i | ||||
\(455\) | −3.46410 | − | 6.00000i | −0.162400 | − | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.36603 | + | 2.36603i | −0.0639000 | + | 0.110678i | −0.896206 | − | 0.443639i | \(-0.853687\pi\) |
0.832306 | + | 0.554317i | \(0.187021\pi\) | |||||||
\(458\) | 8.78461 | 0.410478 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.07180 | 0.236474 | ||||||||
\(461\) | −18.5263 | + | 32.0885i | −0.862855 | + | 1.49451i | 0.00630665 | + | 0.999980i | \(0.497993\pi\) |
−0.869162 | + | 0.494528i | \(0.835341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.19615 | + | 9.00000i | 0.241486 | + | 0.418265i | 0.961138 | − | 0.276069i | \(-0.0890320\pi\) |
−0.719652 | + | 0.694335i | \(0.755699\pi\) | |||||||
\(464\) | 1.71281 | + | 2.96668i | 0.0795153 | + | 0.137725i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2679 | − | 17.7846i | 0.475654 | − | 0.823856i | ||||
\(467\) | −37.3731 | −1.72942 | −0.864710 | − | 0.502272i | \(-0.832498\pi\) | ||||
−0.864710 | + | 0.502272i | \(0.832498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3923 | −0.756926 | ||||||||
\(470\) | −3.19615 | + | 5.53590i | −0.147428 | + | 0.255352i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.4833 | − | 18.1577i | −0.482535 | − | 0.835775i | ||||
\(473\) | −0.562178 | − | 0.973721i | −0.0258490 | − | 0.0447717i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.23205 | + | 3.86603i | −0.102414 | + | 0.177385i | ||||
\(476\) | 18.9282 | 0.867573 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.392305 | −0.0179436 | ||||||||
\(479\) | −5.93782 | + | 10.2846i | −0.271306 | + | 0.469916i | −0.969197 | − | 0.246289i | \(-0.920789\pi\) |
0.697890 | + | 0.716204i | \(0.254122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | −5.97372 | − | 10.3468i | −0.272096 | − | 0.471283i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.0000 | − | 27.7128i | 0.727273 | − | 1.25967i | ||||
\(485\) | 9.66025 | 0.438650 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3923 | 1.10532 | 0.552660 | − | 0.833407i | \(-0.313613\pi\) | ||||
0.552660 | + | 0.833407i | \(0.313613\pi\) | |||||||
\(488\) | −5.07180 | + | 8.78461i | −0.229589 | + | 0.397661i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.63397 | − | 9.75833i | −0.254517 | − | 0.440836i | ||||
\(491\) | −6.93782 | − | 12.0167i | −0.313100 | − | 0.542304i | 0.665932 | − | 0.746012i | \(-0.268034\pi\) |
−0.979032 | + | 0.203708i | \(0.934701\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.36603 | − | 7.56218i | 0.196636 | − | 0.340583i | ||||
\(494\) | −4.78461 | −0.215270 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.21539 | −0.144375 | ||||||||
\(497\) | 8.83013 | − | 15.2942i | 0.396085 | − | 0.686040i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1603 | − | 21.0622i | −0.544368 | − | 0.942873i | −0.998646 | − | 0.0520129i | \(-0.983436\pi\) |
0.454279 | − | 0.890860i | \(-0.349897\pi\) | |||||||
\(500\) | −0.732051 | − | 1.26795i | −0.0327383 | − | 0.0567044i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.80385 | − | 6.58846i | 0.169774 | − | 0.294057i | ||||
\(503\) | 7.32051 | 0.326405 | 0.163203 | − | 0.986593i | \(-0.447818\pi\) | ||||
0.163203 | + | 0.986593i | \(0.447818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.66025 | −0.118380 | ||||||||
\(506\) | 7.26795 | − | 12.5885i | 0.323100 | − | 0.559625i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.6795 | − | 18.4974i | −0.473826 | − | 0.820690i | ||||
\(509\) | −3.39230 | − | 5.87564i | −0.150361 | − | 0.260433i | 0.780999 | − | 0.624532i | \(-0.214710\pi\) |
−0.931360 | + | 0.364099i | \(0.881377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.1244 | + | 31.3923i | −0.801774 | + | 1.38871i | ||||
\(512\) | −11.7128 | −0.517638 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.60770 | 0.335561 | ||||||||
\(515\) | −0.267949 | + | 0.464102i | −0.0118073 | + | 0.0204508i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.0263 | − | 43.3468i | −1.10065 | − | 1.90639i | ||||
\(518\) | 4.73205 | + | 8.19615i | 0.207914 | + | 0.360118i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.85641 | − | 3.21539i | 0.0814088 | − | 0.141004i | ||||
\(521\) | −19.4641 | −0.852738 | −0.426369 | − | 0.904549i | \(-0.640207\pi\) | ||||
−0.426369 | + | 0.904549i | \(0.640207\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2487 | 0.972868 | 0.486434 | − | 0.873717i | \(-0.338297\pi\) | ||||
0.486434 | + | 0.873717i | \(0.338297\pi\) | |||||||
\(524\) | −11.4115 | + | 19.7654i | −0.498516 | + | 0.863454i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.80385 | − | 13.5167i | −0.340264 | − | 0.589354i | ||||
\(527\) | 4.09808 | + | 7.09808i | 0.178515 | + | 0.309197i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | − | 9.52628i | 0.239130 | − | 0.414186i | ||||
\(530\) | −4.92820 | −0.214067 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 30.9282 | 1.34091 | ||||||||
\(533\) | −5.26795 | + | 9.12436i | −0.228180 | + | 0.395220i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.26795 | + | 7.39230i | 0.184520 | + | 0.319597i | ||||
\(536\) | −4.39230 | − | 7.60770i | −0.189719 | − | 0.328602i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.90192 | + | 6.75833i | −0.168224 | + | 0.291372i | ||||
\(539\) | 88.2295 | 3.80031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.4641 | −1.05179 | −0.525897 | − | 0.850548i | \(-0.676270\pi\) | ||||
−0.525897 | + | 0.850548i | \(0.676270\pi\) | |||||||
\(542\) | −1.07180 | + | 1.85641i | −0.0460376 | + | 0.0797395i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.00000 | + | 13.8564i | 0.342997 | + | 0.594089i | ||||
\(545\) | −3.03590 | − | 5.25833i | −0.130044 | − | 0.225242i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9282 | − | 29.3205i | 0.723798 | − | 1.25365i | −0.235669 | − | 0.971833i | \(-0.575728\pi\) |
0.959467 | − | 0.281821i | \(-0.0909385\pi\) | |||||||
\(548\) | 3.71281 | 0.158604 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.19615 | −0.178925 | ||||||||
\(551\) | 7.13397 | − | 12.3564i | 0.303918 | − | 0.526401i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.5885 | + | 63.3731i | 1.55590 | + | 2.69490i | ||||
\(554\) | 1.39230 | + | 2.41154i | 0.0591534 | + | 0.102457i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.444864 | − | 0.770527i | 0.0188664 | − | 0.0326776i | ||||
\(557\) | 2.53590 | 0.107449 | 0.0537247 | − | 0.998556i | \(-0.482891\pi\) | ||||
0.0537247 | + | 0.998556i | \(0.482891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.287187 | 0.0121467 | ||||||||
\(560\) | −2.53590 | + | 4.39230i | −0.107161 | + | 0.185609i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.66025 | − | 9.80385i | −0.238763 | − | 0.413550i | ||||
\(563\) | −8.36603 | − | 14.4904i | −0.352586 | − | 0.610697i | 0.634116 | − | 0.773238i | \(-0.281364\pi\) |
−0.986702 | + | 0.162541i | \(0.948031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.56218 | − | 16.5622i | 0.402284 | − | 0.696776i | ||||
\(566\) | 21.4641 | 0.902203 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.46410 | 0.397105 | ||||||||
\(569\) | −16.4545 | + | 28.5000i | −0.689808 | + | 1.19478i | 0.282092 | + | 0.959387i | \(0.408972\pi\) |
−0.971900 | + | 0.235395i | \(0.924362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.8923 | + | 34.4545i | 0.832467 | + | 1.44188i | 0.896076 | + | 0.443900i | \(0.146406\pi\) |
−0.0636091 | + | 0.997975i | \(0.520261\pi\) | |||||||
\(572\) | 6.14359 | + | 10.6410i | 0.256877 | + | 0.444923i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.4641 | + | 21.5885i | −0.520242 | + | 0.901085i | ||||
\(575\) | 3.46410 | 0.144463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2679 | 0.635613 | 0.317807 | − | 0.948156i | \(-0.397054\pi\) | ||||
0.317807 | + | 0.948156i | \(0.397054\pi\) | |||||||
\(578\) | −3.49038 | + | 6.04552i | −0.145181 | + | 0.251460i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.33975 | + | 4.05256i | 0.0971527 | + | 0.168273i | ||||
\(581\) | −5.19615 | − | 9.00000i | −0.215573 | − | 0.373383i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.2942 | − | 33.4186i | 0.799085 | − | 1.38406i | ||||
\(584\) | −19.4256 | −0.803838 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0333 | 0.868878 | ||||||||
\(587\) | −5.83013 | + | 10.0981i | −0.240635 | + | 0.416792i | −0.960895 | − | 0.276912i | \(-0.910689\pi\) |
0.720260 | + | 0.693704i | \(0.244022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.69615 | + | 11.5981i | 0.275910 | + | 0.477890i | ||||
\(590\) | −3.02628 | − | 5.24167i | −0.124590 | − | 0.215796i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.46410 | − | 2.53590i | 0.0601742 | − | 0.104225i | ||||
\(593\) | 0.143594 | 0.00589668 | 0.00294834 | − | 0.999996i | \(-0.499062\pi\) | ||||
0.00294834 | + | 0.999996i | \(0.499062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.9282 | 0.530005 | ||||||||
\(596\) | 5.85641 | − | 10.1436i | 0.239888 | − | 0.415498i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.85641 | + | 3.21539i | 0.0759141 | + | 0.131487i | ||||
\(599\) | 13.5981 | + | 23.5526i | 0.555602 | + | 0.962331i | 0.997856 | + | 0.0654417i | \(0.0208456\pi\) |
−0.442254 | + | 0.896890i | \(0.645821\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6244 | − | 27.0622i | 0.637331 | − | 1.10389i | −0.348685 | − | 0.937240i | \(-0.613372\pi\) |
0.986016 | − | 0.166649i | \(-0.0532948\pi\) | |||||||
\(602\) | 0.679492 | 0.0276940 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.89488 | −0.321238 | ||||||||
\(605\) | 10.9282 | − | 18.9282i | 0.444295 | − | 0.769541i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.09808 | + | 14.0263i | 0.328691 | + | 0.569309i | 0.982252 | − | 0.187564i | \(-0.0600593\pi\) |
−0.653562 | + | 0.756873i | \(0.726726\pi\) | |||||||
\(608\) | 13.0718 | + | 22.6410i | 0.530131 | + | 0.918214i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.46410 | + | 2.53590i | −0.0592797 | + | 0.102676i | ||||
\(611\) | 12.7846 | 0.517210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.46410 | 0.0591345 | 0.0295673 | − | 0.999563i | \(-0.490587\pi\) | ||||
0.0295673 | + | 0.999563i | \(0.490587\pi\) | |||||||
\(614\) | 5.14359 | − | 8.90897i | 0.207579 | − | 0.359537i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 34.3923 | + | 59.5692i | 1.38571 | + | 2.40011i | ||||
\(617\) | −3.46410 | − | 6.00000i | −0.139459 | − | 0.241551i | 0.787833 | − | 0.615889i | \(-0.211203\pi\) |
−0.927292 | + | 0.374338i | \(0.877870\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.92820 | − | 10.2679i | 0.238275 | − | 0.412704i | −0.721945 | − | 0.691951i | \(-0.756752\pi\) |
0.960219 | + | 0.279247i | \(0.0900848\pi\) | |||||||
\(620\) | −4.39230 | −0.176399 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.4449 | 0.579186 | ||||||||
\(623\) | −12.2942 | + | 21.2942i | −0.492558 | + | 0.853135i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −3.32051 | − | 5.75129i | −0.132714 | − | 0.229868i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | + | 24.2487i | −0.558661 | + | 0.967629i | ||||
\(629\) | −7.46410 | −0.297613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.7128 | −1.30228 | −0.651138 | − | 0.758959i | \(-0.725708\pi\) | ||||
−0.651138 | + | 0.758959i | \(0.725708\pi\) | |||||||
\(632\) | −19.6077 | + | 33.9615i | −0.779952 | + | 1.35092i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.26795 | − | 3.92820i | −0.0900718 | − | 0.156009i | ||||
\(635\) | −7.29423 | − | 12.6340i | −0.289463 | − | 0.501364i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.2679 | + | 19.5167i | −0.446452 | + | 0.773278i | ||||
\(638\) | 13.4115 | 0.530968 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.1436 | −0.400961 | ||||||||
\(641\) | 4.66987 | − | 8.08846i | 0.184449 | − | 0.319475i | −0.758942 | − | 0.651158i | \(-0.774283\pi\) |
0.943391 | + | 0.331684i | \(0.107617\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.8301 | − | 36.0788i | −0.821460 | − | 1.42281i | −0.904595 | − | 0.426272i | \(-0.859827\pi\) |
0.0831349 | − | 0.996538i | \(-0.473507\pi\) | |||||||
\(644\) | −12.0000 | − | 20.7846i | −0.472866 | − | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.46410 | − | 7.73205i | 0.175638 | − | 0.304213i | ||||
\(647\) | −11.4641 | −0.450700 | −0.225350 | − | 0.974278i | \(-0.572353\pi\) | ||||
−0.225350 | + | 0.974278i | \(0.572353\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.3923 | 1.86031 | ||||||||
\(650\) | 0.535898 | − | 0.928203i | 0.0210197 | − | 0.0364071i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.32051 | + | 16.1436i | 0.365019 | + | 0.632232i | ||||
\(653\) | −8.73205 | − | 15.1244i | −0.341712 | − | 0.591862i | 0.643039 | − | 0.765833i | \(-0.277673\pi\) |
−0.984751 | + | 0.173972i | \(0.944340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.79423 | + | 13.5000i | −0.304546 | + | 0.527489i | ||||
\(656\) | 7.71281 | 0.301135 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.2487 | 1.17922 | ||||||||
\(659\) | −0.732051 | + | 1.26795i | −0.0285167 | + | 0.0493923i | −0.879932 | − | 0.475101i | \(-0.842412\pi\) |
0.851415 | + | 0.524493i | \(0.175745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.16025 | − | 15.8660i | −0.356293 | − | 0.617117i | 0.631046 | − | 0.775746i | \(-0.282626\pi\) |
−0.987338 | + | 0.158629i | \(0.949293\pi\) | |||||||
\(662\) | −0.169873 | − | 0.294229i | −0.00660230 | − | 0.0114355i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.78461 | − | 4.82309i | 0.108064 | − | 0.187172i | ||||
\(665\) | 21.1244 | 0.819167 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0718 | −0.428702 | ||||||||
\(668\) | 12.9282 | − | 22.3923i | 0.500207 | − | 0.866384i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.26795 | − | 2.19615i | −0.0489852 | − | 0.0848448i | ||||
\(671\) | −11.4641 | − | 19.8564i | −0.442567 | − | 0.766548i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.19615 | − | 9.00000i | 0.200297 | − | 0.346925i | −0.748327 | − | 0.663330i | \(-0.769143\pi\) |
0.948624 | + | 0.316405i | \(0.102476\pi\) | |||||||
\(674\) | −20.0000 | −0.770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.8949 | 0.611342 | ||||||||
\(677\) | −9.00000 | + | 15.5885i | −0.345898 | + | 0.599113i | −0.985517 | − | 0.169580i | \(-0.945759\pi\) |
0.639618 | + | 0.768693i | \(0.279092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.8564 | − | 39.5885i | −0.877148 | − | 1.51927i | ||||
\(680\) | 3.46410 | + | 6.00000i | 0.132842 | + | 0.230089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.29423 | + | 10.9019i | −0.241018 | + | 0.417456i | ||||
\(683\) | 19.6077 | 0.750268 | 0.375134 | − | 0.926971i | \(-0.377597\pi\) | ||||
0.375134 | + | 0.926971i | \(0.377597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.53590 | 0.0968917 | ||||||||
\(686\) | −14.5359 | + | 25.1769i | −0.554983 | + | 0.961259i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.105118 | − | 0.182069i | −0.00400758 | − | 0.00694133i | ||||
\(689\) | 4.92820 | + | 8.53590i | 0.187750 | + | 0.325192i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.85641 | − | 15.3397i | 0.336914 | − | 0.583551i | −0.646937 | − | 0.762544i | \(-0.723950\pi\) |
0.983851 | + | 0.178992i | \(0.0572836\pi\) | |||||||
\(692\) | 12.4974 | 0.475081 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.9282 | −0.794424 | ||||||||
\(695\) | 0.303848 | − | 0.526279i | 0.0115256 | − | 0.0199629i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.83013 | − | 17.0263i | −0.372343 | − | 0.644916i | ||||
\(698\) | −6.90192 | − | 11.9545i | −0.261242 | − | 0.452484i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.46410 | + | 6.00000i | −0.130931 | + | 0.226779i | ||||
\(701\) | 20.8038 | 0.785750 | 0.392875 | − | 0.919592i | \(-0.371480\pi\) | ||||
0.392875 | + | 0.919592i | \(0.371480\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.1962 | −0.459987 | ||||||||
\(704\) | −6.14359 | + | 10.6410i | −0.231545 | + | 0.401048i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.33975 | − | 16.1769i | −0.351506 | − | 0.608826i | ||||
\(707\) | 6.29423 | + | 10.9019i | 0.236719 | + | 0.410009i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2679 | − | 19.5167i | 0.423177 | − | 0.732964i | −0.573072 | − | 0.819505i | \(-0.694248\pi\) |
0.996248 | + | 0.0865418i | \(0.0275816\pi\) | |||||||
\(710\) | 2.73205 | 0.102532 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.1769 | −0.493826 | ||||||||
\(713\) | 5.19615 | − | 9.00000i | 0.194597 | − | 0.337053i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.19615 | + | 7.26795i | 0.156927 | + | 0.271806i | ||||
\(716\) | −5.94744 | − | 10.3013i | −0.222266 | − | 0.384977i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.24167 | − | 3.88269i | 0.0836584 | − | 0.144901i | ||||
\(719\) | −8.41154 | −0.313698 | −0.156849 | − | 0.987623i | \(-0.550134\pi\) | ||||
−0.156849 | + | 0.987623i | \(0.550134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.53590 | 0.0944418 | ||||||||
\(722\) | 0.339746 | − | 0.588457i | 0.0126440 | − | 0.0219001i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.3731 | + | 33.5551i | 0.719994 | + | 1.24707i | ||||
\(725\) | 1.59808 | + | 2.76795i | 0.0593511 | + | 0.102799i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.19615 | − | 7.26795i | 0.155627 | − | 0.269553i | −0.777660 | − | 0.628685i | \(-0.783594\pi\) |
0.933287 | + | 0.359131i | \(0.116927\pi\) | |||||||
\(728\) | −17.5692 | −0.651159 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.60770 | −0.207550 | ||||||||
\(731\) | −0.267949 | + | 0.464102i | −0.00991046 | + | 0.0171654i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3923 | − | 30.1244i | −0.642399 | − | 1.11267i | −0.984896 | − | 0.173149i | \(-0.944606\pi\) |
0.342496 | − | 0.939519i | \(-0.388728\pi\) | |||||||
\(734\) | 11.4115 | + | 19.7654i | 0.421208 | + | 0.729553i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.1436 | − | 17.5692i | 0.373898 | − | 0.647610i | ||||
\(737\) | 19.8564 | 0.731420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.4641 | 0.826355 | 0.413178 | − | 0.910650i | \(-0.364419\pi\) | ||||
0.413178 | + | 0.910650i | \(0.364419\pi\) | |||||||
\(740\) | 2.00000 | − | 3.46410i | 0.0735215 | − | 0.127343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.6603 | + | 20.1962i | 0.428061 | + | 0.741424i | ||||
\(743\) | 9.95448 | + | 17.2417i | 0.365195 | + | 0.632536i | 0.988807 | − | 0.149198i | \(-0.0476691\pi\) |
−0.623613 | + | 0.781733i | \(0.714336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | − | 6.92820i | 0.146549 | − | 0.253830i | ||||
\(746\) | −14.6795 | −0.537454 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.9282 | −0.838338 | ||||||||
\(749\) | 20.1962 | − | 34.9808i | 0.737951 | − | 1.27817i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3923 | − | 42.2487i | −0.890088 | − | 1.54168i | −0.839769 | − | 0.542944i | \(-0.817310\pi\) |
−0.0503191 | − | 0.998733i | \(-0.516024\pi\) | |||||||
\(752\) | −4.67949 | − | 8.10512i | −0.170644 | − | 0.295563i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.71281 | + | 2.96668i | −0.0623770 | + | 0.108040i | ||||
\(755\) | −5.39230 | −0.196246 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.17691 | −0.333541 | −0.166770 | − | 0.985996i | \(-0.553334\pi\) | ||||
−0.166770 | + | 0.985996i | \(0.553334\pi\) | |||||||
\(758\) | 0.875644 | − | 1.51666i | 0.0318048 | − | 0.0550876i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.66025 | + | 9.80385i | 0.205319 | + | 0.355623i | ||||
\(761\) | 11.7224 | + | 20.3038i | 0.424938 | + | 0.736014i | 0.996415 | − | 0.0846043i | \(-0.0269626\pi\) |
−0.571477 | + | 0.820618i | \(0.693629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.3660 | + | 24.8827i | −0.520085 | + | 0.900814i | ||||
\(764\) | −11.8949 | −0.430342 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.85641 | 0.0670747 | ||||||||
\(767\) | −6.05256 | + | 10.4833i | −0.218545 | + | 0.378531i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.76795 | + | 8.25833i | 0.171937 | + | 0.297803i | 0.939097 | − | 0.343653i | \(-0.111664\pi\) |
−0.767160 | + | 0.641456i | \(0.778331\pi\) | |||||||
\(770\) | 9.92820 | + | 17.1962i | 0.357788 | + | 0.619706i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.85641 | + | 6.67949i | −0.138795 | + | 0.240400i | ||||
\(773\) | −1.51666 | −0.0545505 | −0.0272752 | − | 0.999628i | \(-0.508683\pi\) | ||||
−0.0272752 | + | 0.999628i | \(0.508683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.00000 | −0.107763 | ||||||||
\(776\) | 12.2487 | − | 21.2154i | 0.439703 | − | 0.761588i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0526 | − | 17.4115i | −0.360402 | − | 0.624234i | ||||
\(779\) | −16.0622 | − | 27.8205i | −0.575487 | − | 0.996773i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.6962 | + | 18.5263i | −0.382738 | + | 0.662922i | ||||
\(782\) | −6.92820 | −0.247752 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.4974 | 0.589194 | ||||||||
\(785\) | −9.56218 | + | 16.5622i | −0.341289 | + | 0.591129i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.0263 | + | 41.6147i | 0.856444 | + | 1.48341i | 0.875299 | + | 0.483583i | \(0.160665\pi\) |
−0.0188542 | + | 0.999822i | \(0.506002\pi\) | |||||||
\(788\) | 10.1436 | + | 17.5692i | 0.361351 | + | 0.625878i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.66025 | + | 9.80385i | −0.201383 | + | 0.348805i | ||||
\(791\) | −90.4974 | −3.21772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.85641 | 0.207967 | ||||||||
\(794\) | 5.26795 | − | 9.12436i | 0.186953 | − | 0.323811i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.46410 | − | 2.53590i | −0.0518937 | − | 0.0898825i | ||||
\(797\) | −7.80385 | − | 13.5167i | −0.276426 | − | 0.478785i | 0.694068 | − | 0.719910i | \(-0.255817\pi\) |
−0.970494 | + | 0.241125i | \(0.922484\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.9282 | + | 20.6603i | −0.421989 | + | 0.730907i | ||||
\(800\) | −5.85641 | −0.207055 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.2487 | 0.644384 | ||||||||
\(803\) | 21.9545 | − | 38.0263i | 0.774757 | − | 1.34192i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.19615 | − | 14.1962i | −0.288876 | − | 0.500349i | ||||
\(806\) | −1.60770 | − | 2.78461i | −0.0566286 | − | 0.0980837i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.37307 | + | 5.84232i | −0.118664 | + | 0.205532i | ||||
\(809\) | −45.4449 | −1.59776 | −0.798878 | − | 0.601493i | \(-0.794573\pi\) | ||||
−0.798878 | + | 0.601493i | \(0.794573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4641 | −0.648362 | −0.324181 | − | 0.945995i | \(-0.605089\pi\) | ||||
−0.324181 | + | 0.945995i | \(0.605089\pi\) | |||||||
\(812\) | 11.0718 | − | 19.1769i | 0.388544 | − | 0.672978i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.73205 | − | 9.92820i | −0.200908 | − | 0.347983i | ||||
\(815\) | 6.36603 | + | 11.0263i | 0.222992 | + | 0.386234i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.437822 | + | 0.758330i | −0.0153175 | + | 0.0265306i | ||||
\(818\) | 13.0718 | 0.457045 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.5359 | 0.367930 | ||||||||
\(821\) | −18.8660 | + | 32.6769i | −0.658429 | + | 1.14043i | 0.322594 | + | 0.946538i | \(0.395445\pi\) |
−0.981022 | + | 0.193895i | \(0.937888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.92820 | − | 3.33975i | −0.0672129 | − | 0.116416i | 0.830461 | − | 0.557077i | \(-0.188077\pi\) |
−0.897673 | + | 0.440661i | \(0.854744\pi\) | |||||||
\(824\) | 0.679492 | + | 1.17691i | 0.0236712 | + | 0.0409998i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.3205 | + | 24.8038i | −0.498274 | + | 0.863036i | ||||
\(827\) | 11.6077 | 0.403639 | 0.201820 | − | 0.979423i | \(-0.435315\pi\) | ||||
0.201820 | + | 0.979423i | \(0.435315\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.7846 | −0.826074 | −0.413037 | − | 0.910714i | \(-0.635532\pi\) | ||||
−0.413037 | + | 0.910714i | \(0.635532\pi\) | |||||||
\(830\) | 0.803848 | − | 1.39230i | 0.0279020 | − | 0.0483276i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.56922 | − | 2.71797i | −0.0544029 | − | 0.0942286i | ||||
\(833\) | −21.0263 | − | 36.4186i | −0.728517 | − | 1.26183i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.83013 | − | 15.2942i | 0.305579 | − | 0.529279i | ||||
\(836\) | −37.4641 | −1.29572 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.9282 | 0.515686 | ||||||||
\(839\) | 16.5981 | − | 28.7487i | 0.573029 | − | 0.992516i | −0.423223 | − | 0.906025i | \(-0.639101\pi\) |
0.996253 | − | 0.0864904i | \(-0.0275652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.39230 | + | 16.2679i | 0.323873 | + | 0.560964i | ||||
\(842\) | 12.3660 | + | 21.4186i | 0.426161 | + | 0.738133i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.48334 | + | 11.2295i | −0.223166 | + | 0.386534i | ||||
\(845\) | 10.8564 | 0.373472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −103.426 | −3.55375 | ||||||||
\(848\) | 3.60770 | − | 6.24871i | 0.123889 | − | 0.214582i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.00000 | + | 1.73205i | 0.0342997 | + | 0.0594089i | ||||
\(851\) | 4.73205 | + | 8.19615i | 0.162213 | + | 0.280960i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.24167 | + | 9.07884i | −0.179471 | + | 0.310854i | −0.941700 | − | 0.336455i | \(-0.890772\pi\) |
0.762228 | + | 0.647308i | \(0.224105\pi\) | |||||||
\(854\) | 13.8564 | 0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.6462 | 0.739851 | ||||||||
\(857\) | 22.2487 | − | 38.5359i | 0.760002 | − | 1.31636i | −0.182848 | − | 0.983141i | \(-0.558531\pi\) |
0.942849 | − | 0.333220i | \(-0.108135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.50000 | + | 9.52628i | 0.187658 | + | 0.325032i | 0.944469 | − | 0.328601i | \(-0.106577\pi\) |
−0.756811 | + | 0.653633i | \(0.773244\pi\) | |||||||
\(860\) | −0.143594 | − | 0.248711i | −0.00489650 | − | 0.00848099i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.81089 | − | 13.5289i | 0.266040 | − | 0.460795i | ||||
\(863\) | 23.1244 | 0.787162 | 0.393581 | − | 0.919290i | \(-0.371236\pi\) | ||||
0.393581 | + | 0.919290i | \(0.371236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.53590 | 0.290229 | ||||||||
\(866\) | −12.9808 | + | 22.4833i | −0.441104 | + | 0.764015i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.3923 | + | 18.0000i | 0.352738 | + | 0.610960i | ||||
\(869\) | −44.3205 | − | 76.7654i | −1.50347 | − | 2.60409i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.53590 | + | 4.39230i | −0.0859256 | + | 0.148828i | ||||
\(872\) | −15.3975 | −0.521424 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.3205 | −0.382922 | ||||||||
\(875\) | −2.36603 | + | 4.09808i | −0.0799863 | + | 0.138540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7321 | − | 28.9808i | −0.565001 | − | 0.978611i | −0.997050 | − | 0.0767604i | \(-0.975542\pi\) |
0.432048 | − | 0.901850i | \(-0.357791\pi\) | |||||||
\(878\) | 1.97372 | + | 3.41858i | 0.0666098 | + | 0.115372i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.07180 | − | 5.32051i | 0.103550 | − | 0.179354i | ||||
\(881\) | 47.0526 | 1.58524 | 0.792620 | − | 0.609715i | \(-0.208716\pi\) | ||||
0.792620 | + | 0.609715i | \(0.208716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.1962 | −1.01618 | −0.508091 | − | 0.861304i | \(-0.669649\pi\) | ||||
−0.508091 | + | 0.861304i | \(0.669649\pi\) | |||||||
\(884\) | 2.92820 | − | 5.07180i | 0.0984861 | − | 0.170583i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.124356 | + | 0.215390i | 0.00417781 | + | 0.00723618i | ||||
\(887\) | 16.9019 | + | 29.2750i | 0.567511 | + | 0.982958i | 0.996811 | + | 0.0797961i | \(0.0254269\pi\) |
−0.429300 | + | 0.903162i | \(0.641240\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.5167 | + | 59.7846i | −1.15765 | + | 2.00511i | ||||
\(890\) | −3.80385 | −0.127505 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.5744 | −0.822811 | ||||||||
\(893\) | −19.4904 | + | 33.7583i | −0.652221 | + | 1.12968i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.06218 | − | 7.03590i | −0.135784 | − | 0.235184i | ||||
\(896\) | 24.0000 | + | 41.5692i | 0.801784 | + | 1.38873i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.97372 | + | 5.15064i | −0.0992343 | + | 0.171879i | ||||
\(899\) | 9.58846 | 0.319793 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.3923 | −0.612737 | ||||||||
\(902\) | 15.0981 | − | 26.1506i | 0.502711 | − | 0.870721i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.2487 | − | 42.0000i | −0.806500 | − | 1.39690i | ||||
\(905\) | 13.2321 | + | 22.9186i | 0.439848 | + | 0.761840i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0000 | − | 25.9808i | 0.498067 | − | 0.862677i | −0.501931 | − | 0.864908i | \(-0.667377\pi\) |
0.999998 | + | 0.00223080i | \(0.000710087\pi\) | |||||||
\(908\) | −26.4308 | −0.877136 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.07180 | −0.168128 | ||||||||
\(911\) | 11.7942 | − | 20.4282i | 0.390760 | − | 0.676817i | −0.601790 | − | 0.798655i | \(-0.705545\pi\) |
0.992550 | + | 0.121838i | \(0.0388788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.29423 | + | 10.9019i | 0.208309 | + | 0.360801i | ||||
\(914\) | 1.00000 | + | 1.73205i | 0.0330771 | + | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.78461 | + | 15.2154i | −0.290252 | + | 0.502731i | ||||
\(917\) | 73.7654 | 2.43595 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.9615 | −1.87899 | −0.939494 | − | 0.342566i | \(-0.888704\pi\) | ||||
−0.939494 | + | 0.342566i | \(0.888704\pi\) | |||||||
\(920\) | 4.39230 | − | 7.60770i | 0.144810 | − | 0.250818i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.5622 | + | 23.4904i | 0.446647 | + | 0.773615i | ||||
\(923\) | −2.73205 | − | 4.73205i | −0.0899265 | − | 0.155757i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.36603 | − | 2.36603i | 0.0449146 | − | 0.0777944i | ||||
\(926\) | 7.60770 | 0.250004 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18.7180 | 0.614447 | ||||||||
\(929\) | −22.1865 | + | 38.4282i | −0.727917 | + | 1.26079i | 0.229846 | + | 0.973227i | \(0.426178\pi\) |
−0.957762 | + | 0.287561i | \(0.907155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.3564 | − | 59.5070i | −1.12599 | − | 1.95026i | ||||
\(932\) | 20.5359 | + | 35.5692i | 0.672676 | + | 1.16511i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.6795 | + | 23.6936i | −0.447607 | + | 0.775277i | ||||
\(935\) | −15.6603 | −0.512145 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.14359 | −0.135365 | −0.0676827 | − | 0.997707i | \(-0.521561\pi\) | ||||
−0.0676827 | + | 0.997707i | \(0.521561\pi\) | |||||||
\(938\) | −6.00000 | + | 10.3923i | −0.195907 | + | 0.339321i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.39230 | − | 11.0718i | −0.208494 | − | 0.361122i | ||||
\(941\) | 17.5885 | + | 30.4641i | 0.573367 | + | 0.993101i | 0.996217 | + | 0.0869015i | \(0.0276965\pi\) |
−0.422850 | + | 0.906200i | \(0.638970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.4641 | + | 21.5885i | −0.405887 | + | 0.703017i | ||||
\(944\) | 8.86156 | 0.288419 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.823085 | −0.0267608 | ||||||||
\(947\) | −28.8564 | + | 49.9808i | −0.937707 | + | 1.62416i | −0.167973 | + | 0.985792i | \(0.553722\pi\) |
−0.769734 | + | 0.638365i | \(0.779611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.60770 | + | 9.71281i | 0.182033 | + | 0.315291i | ||||
\(950\) | 1.63397 | + | 2.83013i | 0.0530131 | + | 0.0918214i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.3923 | − | 28.3923i | 0.531278 | − | 0.920200i | ||||
\(953\) | −36.3923 | −1.17886 | −0.589431 | − | 0.807819i | \(-0.700648\pi\) | ||||
−0.589431 | + | 0.807819i | \(0.700648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.12436 | −0.262898 | ||||||||
\(956\) | 0.392305 | − | 0.679492i | 0.0126880 | − | 0.0219763i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.34679 | + | 7.52886i | 0.140438 | + | 0.243246i | ||||
\(959\) | −6.00000 | − | 10.3923i | −0.193750 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 2.92820 | 0.0944091 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.8949 | 0.769602 | ||||||||
\(965\) | −2.63397 | + | 4.56218i | −0.0847906 | + | 0.146862i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.9019 | + | 22.3468i | 0.414898 | + | 0.718624i | 0.995418 | − | 0.0956219i | \(-0.0304840\pi\) |
−0.580520 | + | 0.814246i | \(0.697151\pi\) | |||||||
\(968\) | −27.7128 | − | 48.0000i | −0.890724 | − | 1.54278i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.53590 | − | 6.12436i | 0.113531 | − | 0.196641i | ||||
\(971\) | −17.4449 | −0.559832 | −0.279916 | − | 0.960024i | \(-0.590307\pi\) | ||||
−0.279916 | + | 0.960024i | \(0.590307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.87564 | −0.0921889 | ||||||||
\(974\) | 8.92820 | − | 15.4641i | 0.286078 | − | 0.495502i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.14359 | − | 3.71281i | −0.0686148 | − | 0.118844i | ||||
\(977\) | 2.73205 | + | 4.73205i | 0.0874060 | + | 0.151392i | 0.906414 | − | 0.422391i | \(-0.138809\pi\) |
−0.819008 | + | 0.573782i | \(0.805476\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8923 | − | 25.7942i | 0.475960 | − | 0.824387i | ||||
\(980\) | 22.5359 | 0.719883 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.1577 | −0.324144 | ||||||||
\(983\) | 24.2942 | − | 42.0788i | 0.774866 | − | 1.34211i | −0.160004 | − | 0.987116i | \(-0.551151\pi\) |
0.934870 | − | 0.354990i | \(-0.115516\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.92820 | + | 12.0000i | 0.220751 | + | 0.382352i | ||||
\(986\) | −3.19615 | − | 5.53590i | −0.101786 | − | 0.176299i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.78461 | − | 8.28719i | 0.152219 | − | 0.263651i | ||||
\(989\) | 0.679492 | 0.0216066 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.8564 | 0.980186 | 0.490093 | − | 0.871670i | \(-0.336963\pi\) | ||||
0.490093 | + | 0.871670i | \(0.336963\pi\) | |||||||
\(992\) | −8.78461 | + | 15.2154i | −0.278912 | + | 0.483089i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.46410 | − | 11.1962i | −0.205029 | − | 0.355120i | ||||
\(995\) | −1.00000 | − | 1.73205i | −0.0317021 | − | 0.0549097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.7583 | + | 22.0981i | −0.404060 | + | 0.699853i | −0.994212 | − | 0.107440i | \(-0.965735\pi\) |
0.590151 | + | 0.807293i | \(0.299068\pi\) | |||||||
\(998\) | −17.8038 | −0.563571 | ||||||||
\(999\) | 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 | 405.2.e.i.136.2 | 4 | ||
3.2 | odd | 2 | 405.2.e.l.136.1 | 4 | |||
9.2 | odd | 6 | 405.2.a.g.1.2 | ✓ | 2 | ||
9.4 | even | 3 | inner | 405.2.e.i.271.2 | 4 | ||
9.5 | odd | 6 | 405.2.e.l.271.1 | 4 | |||
9.7 | even | 3 | 405.2.a.h.1.1 | yes | 2 | ||
36.7 | odd | 6 | 6480.2.a.bi.1.2 | 2 | |||
36.11 | even | 6 | 6480.2.a.br.1.2 | 2 | |||
45.2 | even | 12 | 2025.2.b.g.649.3 | 4 | |||
45.7 | odd | 12 | 2025.2.b.h.649.2 | 4 | |||
45.29 | odd | 6 | 2025.2.a.m.1.1 | 2 | |||
45.34 | even | 6 | 2025.2.a.g.1.2 | 2 | |||
45.38 | even | 12 | 2025.2.b.g.649.2 | 4 | |||
45.43 | odd | 12 | 2025.2.b.h.649.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.a.g.1.2 | ✓ | 2 | 9.2 | odd | 6 | ||
405.2.a.h.1.1 | yes | 2 | 9.7 | even | 3 | ||
405.2.e.i.136.2 | 4 | 1.1 | even | 1 | trivial | ||
405.2.e.i.271.2 | 4 | 9.4 | even | 3 | inner | ||
405.2.e.l.136.1 | 4 | 3.2 | odd | 2 | |||
405.2.e.l.271.1 | 4 | 9.5 | odd | 6 | |||
2025.2.a.g.1.2 | 2 | 45.34 | even | 6 | |||
2025.2.a.m.1.1 | 2 | 45.29 | odd | 6 | |||
2025.2.b.g.649.2 | 4 | 45.38 | even | 12 | |||
2025.2.b.g.649.3 | 4 | 45.2 | even | 12 | |||
2025.2.b.h.649.2 | 4 | 45.7 | odd | 12 | |||
2025.2.b.h.649.3 | 4 | 45.43 | odd | 12 | |||
6480.2.a.bi.1.2 | 2 | 36.7 | odd | 6 | |||
6480.2.a.br.1.2 | 2 | 36.11 | even | 6 |