Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,3,Mod(577,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.577");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.6294988061\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 775.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.775 |
Dual form | 1014.3.f.d.577.1 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 4.73205 | + | 4.73205i | 0.946410 | + | 0.946410i | 0.998635 | − | 0.0522252i | \(-0.0166314\pi\) |
−0.0522252 | + | 0.998635i | \(0.516631\pi\) | |||||||
\(6\) | 1.73205 | + | 1.73205i | 0.288675 | + | 0.288675i | ||||
\(7\) | −1.83013 | + | 1.83013i | −0.261447 | + | 0.261447i | −0.825642 | − | 0.564195i | \(-0.809187\pi\) |
0.564195 | + | 0.825642i | \(0.309187\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 9.46410i | − | 0.946410i | ||||||
\(11\) | 10.7321 | − | 10.7321i | 0.975641 | − | 0.975641i | −0.0240693 | − | 0.999710i | \(-0.507662\pi\) |
0.999710 | + | 0.0240693i | \(0.00766224\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.66025 | 0.261447 | ||||||||
\(15\) | −8.19615 | − | 8.19615i | −0.546410 | − | 0.546410i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | − | 5.07180i | − | 0.298341i | −0.988811 | − | 0.149170i | \(-0.952340\pi\) | ||
0.988811 | − | 0.149170i | \(-0.0476603\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | 2.60770 | + | 2.60770i | 0.137247 | + | 0.137247i | 0.772393 | − | 0.635145i | \(-0.219060\pi\) |
−0.635145 | + | 0.772393i | \(0.719060\pi\) | |||||||
\(20\) | −9.46410 | + | 9.46410i | −0.473205 | + | 0.473205i | ||||
\(21\) | 3.16987 | − | 3.16987i | 0.150946 | − | 0.150946i | ||||
\(22\) | −21.4641 | −0.975641 | ||||||||
\(23\) | − | 31.8564i | − | 1.38506i | −0.721389 | − | 0.692531i | \(-0.756496\pi\) | ||
0.721389 | − | 0.692531i | \(-0.243504\pi\) | |||||||
\(24\) | −3.46410 | + | 3.46410i | −0.144338 | + | 0.144338i | ||||
\(25\) | 19.7846i | 0.791384i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −3.66025 | − | 3.66025i | −0.130723 | − | 0.130723i | ||||
\(29\) | 17.3205 | 0.597259 | 0.298629 | − | 0.954369i | \(-0.403471\pi\) | ||||
0.298629 | + | 0.954369i | \(0.403471\pi\) | |||||||
\(30\) | 16.3923i | 0.546410i | ||||||||
\(31\) | −30.8301 | − | 30.8301i | −0.994520 | − | 0.994520i | 0.00546484 | − | 0.999985i | \(-0.498260\pi\) |
−0.999985 | + | 0.00546484i | \(0.998260\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −18.5885 | + | 18.5885i | −0.563287 | + | 0.563287i | ||||
\(34\) | −5.07180 | + | 5.07180i | −0.149170 | + | 0.149170i | ||||
\(35\) | −17.3205 | −0.494872 | ||||||||
\(36\) | 6.00000i | 0.166667i | ||||||||
\(37\) | 36.1769 | − | 36.1769i | 0.977754 | − | 0.977754i | −0.0220034 | − | 0.999758i | \(-0.507004\pi\) |
0.999758 | + | 0.0220034i | \(0.00700448\pi\) | |||||||
\(38\) | − | 5.21539i | − | 0.137247i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 18.9282 | 0.473205 | ||||||||
\(41\) | −30.2487 | − | 30.2487i | −0.737773 | − | 0.737773i | 0.234373 | − | 0.972147i | \(-0.424696\pi\) |
−0.972147 | + | 0.234373i | \(0.924696\pi\) | |||||||
\(42\) | −6.33975 | −0.150946 | ||||||||
\(43\) | 32.6603i | 0.759541i | 0.925081 | + | 0.379770i | \(0.123997\pi\) | ||||
−0.925081 | + | 0.379770i | \(0.876003\pi\) | |||||||
\(44\) | 21.4641 | + | 21.4641i | 0.487820 | + | 0.487820i | ||||
\(45\) | 14.1962 | + | 14.1962i | 0.315470 | + | 0.315470i | ||||
\(46\) | −31.8564 | + | 31.8564i | −0.692531 | + | 0.692531i | ||||
\(47\) | −58.9808 | + | 58.9808i | −1.25491 | + | 1.25491i | −0.301418 | + | 0.953492i | \(0.597460\pi\) |
−0.953492 | + | 0.301418i | \(0.902540\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 42.3013i | 0.863291i | ||||||||
\(50\) | 19.7846 | − | 19.7846i | 0.395692 | − | 0.395692i | ||||
\(51\) | 8.78461i | 0.172247i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 97.6743 | 1.84291 | 0.921456 | − | 0.388483i | \(-0.127001\pi\) | ||||
0.921456 | + | 0.388483i | \(0.127001\pi\) | |||||||
\(54\) | 5.19615 | + | 5.19615i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 101.569 | 1.84671 | ||||||||
\(56\) | 7.32051i | 0.130723i | ||||||||
\(57\) | −4.51666 | − | 4.51666i | −0.0792397 | − | 0.0792397i | ||||
\(58\) | −17.3205 | − | 17.3205i | −0.298629 | − | 0.298629i | ||||
\(59\) | 43.2679 | − | 43.2679i | 0.733355 | − | 0.733355i | −0.237928 | − | 0.971283i | \(-0.576468\pi\) |
0.971283 | + | 0.237928i | \(0.0764682\pi\) | |||||||
\(60\) | 16.3923 | − | 16.3923i | 0.273205 | − | 0.273205i | ||||
\(61\) | 79.3013 | 1.30002 | 0.650010 | − | 0.759925i | \(-0.274765\pi\) | ||||
0.650010 | + | 0.759925i | \(0.274765\pi\) | |||||||
\(62\) | 61.6603i | 0.994520i | ||||||||
\(63\) | −5.49038 | + | 5.49038i | −0.0871489 | + | 0.0871489i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 37.1769 | 0.563287 | ||||||||
\(67\) | −46.7391 | − | 46.7391i | −0.697598 | − | 0.697598i | 0.266294 | − | 0.963892i | \(-0.414201\pi\) |
−0.963892 | + | 0.266294i | \(0.914201\pi\) | |||||||
\(68\) | 10.1436 | 0.149170 | ||||||||
\(69\) | 55.1769i | 0.799665i | ||||||||
\(70\) | 17.3205 | + | 17.3205i | 0.247436 | + | 0.247436i | ||||
\(71\) | 37.9474 | + | 37.9474i | 0.534471 | + | 0.534471i | 0.921900 | − | 0.387429i | \(-0.126637\pi\) |
−0.387429 | + | 0.921900i | \(0.626637\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 27.5814 | − | 27.5814i | 0.377828 | − | 0.377828i | −0.492490 | − | 0.870318i | \(-0.663913\pi\) |
0.870318 | + | 0.492490i | \(0.163913\pi\) | |||||||
\(74\) | −72.3538 | −0.977754 | ||||||||
\(75\) | − | 34.2679i | − | 0.456906i | ||||||
\(76\) | −5.21539 | + | 5.21539i | −0.0686236 | + | 0.0686236i | ||||
\(77\) | 39.2820i | 0.510156i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 36.1244 | 0.457270 | 0.228635 | − | 0.973512i | \(-0.426574\pi\) | ||||
0.228635 | + | 0.973512i | \(0.426574\pi\) | |||||||
\(80\) | −18.9282 | − | 18.9282i | −0.236603 | − | 0.236603i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 60.4974i | 0.737773i | ||||||||
\(83\) | −20.9667 | − | 20.9667i | −0.252611 | − | 0.252611i | 0.569430 | − | 0.822040i | \(-0.307164\pi\) |
−0.822040 | + | 0.569430i | \(0.807164\pi\) | |||||||
\(84\) | 6.33975 | + | 6.33975i | 0.0754732 | + | 0.0754732i | ||||
\(85\) | 24.0000 | − | 24.0000i | 0.282353 | − | 0.282353i | ||||
\(86\) | 32.6603 | − | 32.6603i | 0.379770 | − | 0.379770i | ||||
\(87\) | −30.0000 | −0.344828 | ||||||||
\(88\) | − | 42.9282i | − | 0.487820i | ||||||
\(89\) | 49.3590 | − | 49.3590i | 0.554595 | − | 0.554595i | −0.373168 | − | 0.927764i | \(-0.621729\pi\) |
0.927764 | + | 0.373168i | \(0.121729\pi\) | |||||||
\(90\) | − | 28.3923i | − | 0.315470i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 63.7128 | 0.692531 | ||||||||
\(93\) | 53.3993 | + | 53.3993i | 0.574187 | + | 0.574187i | ||||
\(94\) | 117.962 | 1.25491 | ||||||||
\(95\) | 24.6795i | 0.259784i | ||||||||
\(96\) | −6.92820 | − | 6.92820i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | −12.9878 | − | 12.9878i | −0.133895 | − | 0.133895i | 0.636983 | − | 0.770878i | \(-0.280182\pi\) |
−0.770878 | + | 0.636983i | \(0.780182\pi\) | |||||||
\(98\) | 42.3013 | − | 42.3013i | 0.431646 | − | 0.431646i | ||||
\(99\) | 32.1962 | − | 32.1962i | 0.325214 | − | 0.325214i | ||||
\(100\) | −39.5692 | −0.395692 | ||||||||
\(101\) | 138.813i | 1.37438i | 0.726476 | + | 0.687192i | \(0.241157\pi\) | ||||
−0.726476 | + | 0.687192i | \(0.758843\pi\) | |||||||
\(102\) | 8.78461 | − | 8.78461i | 0.0861236 | − | 0.0861236i | ||||
\(103\) | − | 107.263i | − | 1.04139i | −0.853744 | − | 0.520693i | \(-0.825674\pi\) | ||
0.853744 | − | 0.520693i | \(-0.174326\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.0000 | 0.285714 | ||||||||
\(106\) | −97.6743 | − | 97.6743i | −0.921456 | − | 0.921456i | ||||
\(107\) | 5.50258 | 0.0514260 | 0.0257130 | − | 0.999669i | \(-0.491814\pi\) | ||||
0.0257130 | + | 0.999669i | \(0.491814\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | −108.811 | − | 108.811i | −0.998265 | − | 0.998265i | 0.00173346 | − | 0.999998i | \(-0.499448\pi\) |
−0.999998 | + | 0.00173346i | \(0.999448\pi\) | |||||||
\(110\) | −101.569 | − | 101.569i | −0.923357 | − | 0.923357i | ||||
\(111\) | −62.6603 | + | 62.6603i | −0.564507 | + | 0.564507i | ||||
\(112\) | 7.32051 | − | 7.32051i | 0.0653617 | − | 0.0653617i | ||||
\(113\) | −86.7846 | −0.768005 | −0.384003 | − | 0.923332i | \(-0.625455\pi\) | ||||
−0.384003 | + | 0.923332i | \(0.625455\pi\) | |||||||
\(114\) | 9.03332i | 0.0792397i | ||||||||
\(115\) | 150.746 | − | 150.746i | 1.31084 | − | 1.31084i | ||||
\(116\) | 34.6410i | 0.298629i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −86.5359 | −0.733355 | ||||||||
\(119\) | 9.28203 | + | 9.28203i | 0.0780003 | + | 0.0780003i | ||||
\(120\) | −32.7846 | −0.273205 | ||||||||
\(121\) | − | 109.354i | − | 0.903751i | ||||||
\(122\) | −79.3013 | − | 79.3013i | −0.650010 | − | 0.650010i | ||||
\(123\) | 52.3923 | + | 52.3923i | 0.425954 | + | 0.425954i | ||||
\(124\) | 61.6603 | − | 61.6603i | 0.497260 | − | 0.497260i | ||||
\(125\) | 24.6795 | − | 24.6795i | 0.197436 | − | 0.197436i | ||||
\(126\) | 10.9808 | 0.0871489 | ||||||||
\(127\) | − | 178.846i | − | 1.40824i | −0.710082 | − | 0.704118i | \(-0.751342\pi\) | ||
0.710082 | − | 0.704118i | \(-0.248658\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 56.5692i | − | 0.438521i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 53.6359 | 0.409434 | 0.204717 | − | 0.978821i | \(-0.434373\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434373\pi\) | |||||||
\(132\) | −37.1769 | − | 37.1769i | −0.281643 | − | 0.281643i | ||||
\(133\) | −9.54483 | −0.0717656 | ||||||||
\(134\) | 93.4782i | 0.697598i | ||||||||
\(135\) | −24.5885 | − | 24.5885i | −0.182137 | − | 0.182137i | ||||
\(136\) | −10.1436 | − | 10.1436i | −0.0745852 | − | 0.0745852i | ||||
\(137\) | −87.4641 | + | 87.4641i | −0.638424 | + | 0.638424i | −0.950167 | − | 0.311743i | \(-0.899087\pi\) |
0.311743 | + | 0.950167i | \(0.399087\pi\) | |||||||
\(138\) | 55.1769 | − | 55.1769i | 0.399833 | − | 0.399833i | ||||
\(139\) | 153.708 | 1.10581 | 0.552905 | − | 0.833244i | \(-0.313519\pi\) | ||||
0.552905 | + | 0.833244i | \(0.313519\pi\) | |||||||
\(140\) | − | 34.6410i | − | 0.247436i | ||||||
\(141\) | 102.158 | − | 102.158i | 0.724523 | − | 0.724523i | ||||
\(142\) | − | 75.8949i | − | 0.534471i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 81.9615 | + | 81.9615i | 0.565252 | + | 0.565252i | ||||
\(146\) | −55.1628 | −0.377828 | ||||||||
\(147\) | − | 73.2679i | − | 0.498421i | ||||||
\(148\) | 72.3538 | + | 72.3538i | 0.488877 | + | 0.488877i | ||||
\(149\) | 112.210 | + | 112.210i | 0.753089 | + | 0.753089i | 0.975054 | − | 0.221966i | \(-0.0712473\pi\) |
−0.221966 | + | 0.975054i | \(0.571247\pi\) | |||||||
\(150\) | −34.2679 | + | 34.2679i | −0.228453 | + | 0.228453i | ||||
\(151\) | 158.962 | − | 158.962i | 1.05273 | − | 1.05273i | 0.0541950 | − | 0.998530i | \(-0.482741\pi\) |
0.998530 | − | 0.0541950i | \(-0.0172592\pi\) | |||||||
\(152\) | 10.4308 | 0.0686236 | ||||||||
\(153\) | − | 15.2154i | − | 0.0994470i | ||||||
\(154\) | 39.2820 | − | 39.2820i | 0.255078 | − | 0.255078i | ||||
\(155\) | − | 291.779i | − | 1.88245i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 138.569 | 0.882606 | 0.441303 | − | 0.897358i | \(-0.354516\pi\) | ||||
0.441303 | + | 0.897358i | \(0.354516\pi\) | |||||||
\(158\) | −36.1244 | − | 36.1244i | −0.228635 | − | 0.228635i | ||||
\(159\) | −169.177 | −1.06401 | ||||||||
\(160\) | 37.8564i | 0.236603i | ||||||||
\(161\) | 58.3013 | + | 58.3013i | 0.362120 | + | 0.362120i | ||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 198.347 | − | 198.347i | 1.21685 | − | 1.21685i | 0.248123 | − | 0.968729i | \(-0.420186\pi\) |
0.968729 | − | 0.248123i | \(-0.0798137\pi\) | |||||||
\(164\) | 60.4974 | − | 60.4974i | 0.368887 | − | 0.368887i | ||||
\(165\) | −175.923 | −1.06620 | ||||||||
\(166\) | 41.9334i | 0.252611i | ||||||||
\(167\) | −197.569 | + | 197.569i | −1.18305 | + | 1.18305i | −0.204099 | + | 0.978950i | \(0.565426\pi\) |
−0.978950 | + | 0.204099i | \(0.934574\pi\) | |||||||
\(168\) | − | 12.6795i | − | 0.0754732i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −48.0000 | −0.282353 | ||||||||
\(171\) | 7.82309 | + | 7.82309i | 0.0457490 | + | 0.0457490i | ||||
\(172\) | −65.3205 | −0.379770 | ||||||||
\(173\) | − | 67.5411i | − | 0.390411i | −0.980762 | − | 0.195205i | \(-0.937463\pi\) | ||
0.980762 | − | 0.195205i | \(-0.0625373\pi\) | |||||||
\(174\) | 30.0000 | + | 30.0000i | 0.172414 | + | 0.172414i | ||||
\(175\) | −36.2083 | − | 36.2083i | −0.206905 | − | 0.206905i | ||||
\(176\) | −42.9282 | + | 42.9282i | −0.243910 | + | 0.243910i | ||||
\(177\) | −74.9423 | + | 74.9423i | −0.423403 | + | 0.423403i | ||||
\(178\) | −98.7180 | −0.554595 | ||||||||
\(179\) | − | 50.2205i | − | 0.280562i | −0.990112 | − | 0.140281i | \(-0.955199\pi\) | ||
0.990112 | − | 0.140281i | \(-0.0448005\pi\) | |||||||
\(180\) | −28.3923 | + | 28.3923i | −0.157735 | + | 0.157735i | ||||
\(181\) | 302.354i | 1.67046i | 0.549898 | + | 0.835232i | \(0.314666\pi\) | ||||
−0.549898 | + | 0.835232i | \(0.685334\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −137.354 | −0.750567 | ||||||||
\(184\) | −63.7128 | − | 63.7128i | −0.346265 | − | 0.346265i | ||||
\(185\) | 342.382 | 1.85071 | ||||||||
\(186\) | − | 106.799i | − | 0.574187i | ||||||
\(187\) | −54.4308 | − | 54.4308i | −0.291074 | − | 0.291074i | ||||
\(188\) | −117.962 | − | 117.962i | −0.627455 | − | 0.627455i | ||||
\(189\) | 9.50962 | − | 9.50962i | 0.0503154 | − | 0.0503154i | ||||
\(190\) | 24.6795 | − | 24.6795i | 0.129892 | − | 0.129892i | ||||
\(191\) | 162.679 | 0.851725 | 0.425863 | − | 0.904788i | \(-0.359971\pi\) | ||||
0.425863 | + | 0.904788i | \(0.359971\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −58.1506 | + | 58.1506i | −0.301299 | + | 0.301299i | −0.841522 | − | 0.540223i | \(-0.818340\pi\) |
0.540223 | + | 0.841522i | \(0.318340\pi\) | |||||||
\(194\) | 25.9756i | 0.133895i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −84.6025 | −0.431646 | ||||||||
\(197\) | 190.956 | + | 190.956i | 0.969322 | + | 0.969322i | 0.999543 | − | 0.0302216i | \(-0.00962128\pi\) |
−0.0302216 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(198\) | −64.3923 | −0.325214 | ||||||||
\(199\) | − | 63.7846i | − | 0.320526i | −0.987074 | − | 0.160263i | \(-0.948766\pi\) | ||
0.987074 | − | 0.160263i | \(-0.0512342\pi\) | |||||||
\(200\) | 39.5692 | + | 39.5692i | 0.197846 | + | 0.197846i | ||||
\(201\) | 80.9545 | + | 80.9545i | 0.402759 | + | 0.402759i | ||||
\(202\) | 138.813 | − | 138.813i | 0.687192 | − | 0.687192i | ||||
\(203\) | −31.6987 | + | 31.6987i | −0.156151 | + | 0.156151i | ||||
\(204\) | −17.5692 | −0.0861236 | ||||||||
\(205\) | − | 286.277i | − | 1.39647i | ||||||
\(206\) | −107.263 | + | 107.263i | −0.520693 | + | 0.520693i | ||||
\(207\) | − | 95.5692i | − | 0.461687i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 55.9718 | 0.267808 | ||||||||
\(210\) | −30.0000 | − | 30.0000i | −0.142857 | − | 0.142857i | ||||
\(211\) | 247.799 | 1.17440 | 0.587201 | − | 0.809441i | \(-0.300230\pi\) | ||||
0.587201 | + | 0.809441i | \(0.300230\pi\) | |||||||
\(212\) | 195.349i | 0.921456i | ||||||||
\(213\) | −65.7269 | − | 65.7269i | −0.308577 | − | 0.308577i | ||||
\(214\) | −5.50258 | − | 5.50258i | −0.0257130 | − | 0.0257130i | ||||
\(215\) | −154.550 | + | 154.550i | −0.718837 | + | 0.718837i | ||||
\(216\) | −10.3923 | + | 10.3923i | −0.0481125 | + | 0.0481125i | ||||
\(217\) | 112.846 | 0.520028 | ||||||||
\(218\) | 217.622i | 0.998265i | ||||||||
\(219\) | −47.7724 | + | 47.7724i | −0.218139 | + | 0.218139i | ||||
\(220\) | 203.138i | 0.923357i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 125.321 | 0.564507 | ||||||||
\(223\) | −32.5307 | − | 32.5307i | −0.145878 | − | 0.145878i | 0.630396 | − | 0.776274i | \(-0.282893\pi\) |
−0.776274 | + | 0.630396i | \(0.782893\pi\) | |||||||
\(224\) | −14.6410 | −0.0653617 | ||||||||
\(225\) | 59.3538i | 0.263795i | ||||||||
\(226\) | 86.7846 | + | 86.7846i | 0.384003 | + | 0.384003i | ||||
\(227\) | −9.71281 | − | 9.71281i | −0.0427877 | − | 0.0427877i | 0.685389 | − | 0.728177i | \(-0.259632\pi\) |
−0.728177 | + | 0.685389i | \(0.759632\pi\) | |||||||
\(228\) | 9.03332 | − | 9.03332i | 0.0396198 | − | 0.0396198i | ||||
\(229\) | −287.315 | + | 287.315i | −1.25465 | + | 1.25465i | −0.301041 | + | 0.953611i | \(0.597334\pi\) |
−0.953611 | + | 0.301041i | \(0.902666\pi\) | |||||||
\(230\) | −301.492 | −1.31084 | ||||||||
\(231\) | − | 68.0385i | − | 0.294539i | ||||||
\(232\) | 34.6410 | − | 34.6410i | 0.149315 | − | 0.149315i | ||||
\(233\) | 27.3308i | 0.117300i | 0.998279 | + | 0.0586498i | \(0.0186795\pi\) | ||||
−0.998279 | + | 0.0586498i | \(0.981320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −558.200 | −2.37532 | ||||||||
\(236\) | 86.5359 | + | 86.5359i | 0.366678 | + | 0.366678i | ||||
\(237\) | −62.5692 | −0.264005 | ||||||||
\(238\) | − | 18.5641i | − | 0.0780003i | ||||||
\(239\) | 0.861561 | + | 0.861561i | 0.00360486 | + | 0.00360486i | 0.708907 | − | 0.705302i | \(-0.249189\pi\) |
−0.705302 | + | 0.708907i | \(0.749189\pi\) | |||||||
\(240\) | 32.7846 | + | 32.7846i | 0.136603 | + | 0.136603i | ||||
\(241\) | 60.1769 | − | 60.1769i | 0.249697 | − | 0.249697i | −0.571149 | − | 0.820846i | \(-0.693502\pi\) |
0.820846 | + | 0.571149i | \(0.193502\pi\) | |||||||
\(242\) | −109.354 | + | 109.354i | −0.451875 | + | 0.451875i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 158.603i | 0.650010i | ||||||||
\(245\) | −200.172 | + | 200.172i | −0.817028 | + | 0.817028i | ||||
\(246\) | − | 104.785i | − | 0.425954i | ||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −123.321 | −0.497260 | ||||||||
\(249\) | 36.3154 | + | 36.3154i | 0.145845 | + | 0.145845i | ||||
\(250\) | −49.3590 | −0.197436 | ||||||||
\(251\) | − | 40.7077i | − | 0.162182i | −0.996707 | − | 0.0810910i | \(-0.974160\pi\) | ||
0.996707 | − | 0.0810910i | \(-0.0258404\pi\) | |||||||
\(252\) | −10.9808 | − | 10.9808i | −0.0435745 | − | 0.0435745i | ||||
\(253\) | −341.885 | − | 341.885i | −1.35132 | − | 1.35132i | ||||
\(254\) | −178.846 | + | 178.846i | −0.704118 | + | 0.704118i | ||||
\(255\) | −41.5692 | + | 41.5692i | −0.163017 | + | 0.163017i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 309.779i | 1.20537i | 0.797980 | + | 0.602684i | \(0.205902\pi\) | ||||
−0.797980 | + | 0.602684i | \(0.794098\pi\) | |||||||
\(258\) | −56.5692 | + | 56.5692i | −0.219261 | + | 0.219261i | ||||
\(259\) | 132.417i | 0.511261i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 51.9615 | 0.199086 | ||||||||
\(262\) | −53.6359 | − | 53.6359i | −0.204717 | − | 0.204717i | ||||
\(263\) | −287.636 | −1.09367 | −0.546836 | − | 0.837240i | \(-0.684168\pi\) | ||||
−0.546836 | + | 0.837240i | \(0.684168\pi\) | |||||||
\(264\) | 74.3538i | 0.281643i | ||||||||
\(265\) | 462.200 | + | 462.200i | 1.74415 | + | 1.74415i | ||||
\(266\) | 9.54483 | + | 9.54483i | 0.0358828 | + | 0.0358828i | ||||
\(267\) | −85.4923 | + | 85.4923i | −0.320196 | + | 0.320196i | ||||
\(268\) | 93.4782 | − | 93.4782i | 0.348799 | − | 0.348799i | ||||
\(269\) | 163.741 | 0.608703 | 0.304351 | − | 0.952560i | \(-0.401560\pi\) | ||||
0.304351 | + | 0.952560i | \(0.401560\pi\) | |||||||
\(270\) | 49.1769i | 0.182137i | ||||||||
\(271\) | 229.954 | − | 229.954i | 0.848541 | − | 0.848541i | −0.141411 | − | 0.989951i | \(-0.545164\pi\) |
0.989951 | + | 0.141411i | \(0.0451637\pi\) | |||||||
\(272\) | 20.2872i | 0.0745852i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 174.928 | 0.638424 | ||||||||
\(275\) | 212.329 | + | 212.329i | 0.772107 | + | 0.772107i | ||||
\(276\) | −110.354 | −0.399833 | ||||||||
\(277\) | − | 134.985i | − | 0.487309i | −0.969862 | − | 0.243654i | \(-0.921654\pi\) | ||
0.969862 | − | 0.243654i | \(-0.0783463\pi\) | |||||||
\(278\) | −153.708 | − | 153.708i | −0.552905 | − | 0.552905i | ||||
\(279\) | −92.4904 | − | 92.4904i | −0.331507 | − | 0.331507i | ||||
\(280\) | −34.6410 | + | 34.6410i | −0.123718 | + | 0.123718i | ||||
\(281\) | −323.545 | + | 323.545i | −1.15141 | + | 1.15141i | −0.165134 | + | 0.986271i | \(0.552806\pi\) |
−0.986271 | + | 0.165134i | \(0.947194\pi\) | |||||||
\(282\) | −204.315 | −0.724523 | ||||||||
\(283\) | 141.354i | 0.499483i | 0.968312 | + | 0.249742i | \(0.0803457\pi\) | ||||
−0.968312 | + | 0.249742i | \(0.919654\pi\) | |||||||
\(284\) | −75.8949 | + | 75.8949i | −0.267236 | + | 0.267236i | ||||
\(285\) | − | 42.7461i | − | 0.149986i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 110.718 | 0.385777 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 263.277 | 0.910993 | ||||||||
\(290\) | − | 163.923i | − | 0.565252i | ||||||
\(291\) | 22.4955 | + | 22.4955i | 0.0773042 | + | 0.0773042i | ||||
\(292\) | 55.1628 | + | 55.1628i | 0.188914 | + | 0.188914i | ||||
\(293\) | 210.473 | − | 210.473i | 0.718338 | − | 0.718338i | −0.249927 | − | 0.968265i | \(-0.580407\pi\) |
0.968265 | + | 0.249927i | \(0.0804065\pi\) | |||||||
\(294\) | −73.2679 | + | 73.2679i | −0.249211 | + | 0.249211i | ||||
\(295\) | 409.492 | 1.38811 | ||||||||
\(296\) | − | 144.708i | − | 0.488877i | ||||||
\(297\) | −55.7654 | + | 55.7654i | −0.187762 | + | 0.187762i | ||||
\(298\) | − | 224.420i | − | 0.753089i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 68.5359 | 0.228453 | ||||||||
\(301\) | −59.7724 | − | 59.7724i | −0.198579 | − | 0.198579i | ||||
\(302\) | −317.923 | −1.05273 | ||||||||
\(303\) | − | 240.431i | − | 0.793501i | ||||||
\(304\) | −10.4308 | − | 10.4308i | −0.0343118 | − | 0.0343118i | ||||
\(305\) | 375.258 | + | 375.258i | 1.23035 | + | 1.23035i | ||||
\(306\) | −15.2154 | + | 15.2154i | −0.0497235 | + | 0.0497235i | ||||
\(307\) | 70.0685 | − | 70.0685i | 0.228236 | − | 0.228236i | −0.583719 | − | 0.811956i | \(-0.698403\pi\) |
0.811956 | + | 0.583719i | \(0.198403\pi\) | |||||||
\(308\) | −78.5641 | −0.255078 | ||||||||
\(309\) | 185.785i | 0.601245i | ||||||||
\(310\) | −291.779 | + | 291.779i | −0.941224 | + | 0.941224i | ||||
\(311\) | 140.238i | 0.450927i | 0.974252 | + | 0.225464i | \(0.0723897\pi\) | ||||
−0.974252 | + | 0.225464i | \(0.927610\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −550.286 | −1.75810 | −0.879051 | − | 0.476728i | \(-0.841823\pi\) | ||||
−0.879051 | + | 0.476728i | \(0.841823\pi\) | |||||||
\(314\) | −138.569 | − | 138.569i | −0.441303 | − | 0.441303i | ||||
\(315\) | −51.9615 | −0.164957 | ||||||||
\(316\) | 72.2487i | 0.228635i | ||||||||
\(317\) | 31.2923 | + | 31.2923i | 0.0987140 | + | 0.0987140i | 0.754739 | − | 0.656025i | \(-0.227763\pi\) |
−0.656025 | + | 0.754739i | \(0.727763\pi\) | |||||||
\(318\) | 169.177 | + | 169.177i | 0.532003 | + | 0.532003i | ||||
\(319\) | 185.885 | − | 185.885i | 0.582710 | − | 0.582710i | ||||
\(320\) | 37.8564 | − | 37.8564i | 0.118301 | − | 0.118301i | ||||
\(321\) | −9.53074 | −0.0296908 | ||||||||
\(322\) | − | 116.603i | − | 0.362120i | ||||||
\(323\) | 13.2257 | − | 13.2257i | 0.0409464 | − | 0.0409464i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −396.694 | −1.21685 | ||||||||
\(327\) | 188.466 | + | 188.466i | 0.576349 | + | 0.576349i | ||||
\(328\) | −120.995 | −0.368887 | ||||||||
\(329\) | − | 215.885i | − | 0.656184i | ||||||
\(330\) | 175.923 | + | 175.923i | 0.533100 | + | 0.533100i | ||||
\(331\) | 285.624 | + | 285.624i | 0.862911 | + | 0.862911i | 0.991675 | − | 0.128764i | \(-0.0411009\pi\) |
−0.128764 | + | 0.991675i | \(0.541101\pi\) | |||||||
\(332\) | 41.9334 | − | 41.9334i | 0.126305 | − | 0.126305i | ||||
\(333\) | 108.531 | − | 108.531i | 0.325918 | − | 0.325918i | ||||
\(334\) | 395.138 | 1.18305 | ||||||||
\(335\) | − | 442.344i | − | 1.32043i | ||||||
\(336\) | −12.6795 | + | 12.6795i | −0.0377366 | + | 0.0377366i | ||||
\(337\) | 638.492i | 1.89464i | 0.320295 | + | 0.947318i | \(0.396218\pi\) | ||||
−0.320295 | + | 0.947318i | \(0.603782\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 150.315 | 0.443408 | ||||||||
\(340\) | 48.0000 | + | 48.0000i | 0.141176 | + | 0.141176i | ||||
\(341\) | −661.741 | −1.94059 | ||||||||
\(342\) | − | 15.6462i | − | 0.0457490i | ||||||
\(343\) | −167.093 | − | 167.093i | −0.487151 | − | 0.487151i | ||||
\(344\) | 65.3205 | + | 65.3205i | 0.189885 | + | 0.189885i | ||||
\(345\) | −261.100 | + | 261.100i | −0.756811 | + | 0.756811i | ||||
\(346\) | −67.5411 | + | 67.5411i | −0.195205 | + | 0.195205i | ||||
\(347\) | −5.70250 | −0.0164337 | −0.00821686 | − | 0.999966i | \(-0.502616\pi\) | ||||
−0.00821686 | + | 0.999966i | \(0.502616\pi\) | |||||||
\(348\) | − | 60.0000i | − | 0.172414i | ||||||
\(349\) | −128.103 | + | 128.103i | −0.367058 | + | 0.367058i | −0.866403 | − | 0.499345i | \(-0.833574\pi\) |
0.499345 | + | 0.866403i | \(0.333574\pi\) | |||||||
\(350\) | 72.4167i | 0.206905i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 85.8564 | 0.243910 | ||||||||
\(353\) | −205.037 | − | 205.037i | −0.580842 | − | 0.580842i | 0.354293 | − | 0.935135i | \(-0.384722\pi\) |
−0.935135 | + | 0.354293i | \(0.884722\pi\) | |||||||
\(354\) | 149.885 | 0.423403 | ||||||||
\(355\) | 359.138i | 1.01166i | ||||||||
\(356\) | 98.7180 | + | 98.7180i | 0.277298 | + | 0.277298i | ||||
\(357\) | −16.0770 | − | 16.0770i | −0.0450335 | − | 0.0450335i | ||||
\(358\) | −50.2205 | + | 50.2205i | −0.140281 | + | 0.140281i | ||||
\(359\) | 268.277 | − | 268.277i | 0.747289 | − | 0.747289i | −0.226680 | − | 0.973969i | \(-0.572787\pi\) |
0.973969 | + | 0.226680i | \(0.0727871\pi\) | |||||||
\(360\) | 56.7846 | 0.157735 | ||||||||
\(361\) | − | 347.400i | − | 0.962326i | ||||||
\(362\) | 302.354 | − | 302.354i | 0.835232 | − | 0.835232i | ||||
\(363\) | 189.406i | 0.521781i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 261.033 | 0.715160 | ||||||||
\(366\) | 137.354 | + | 137.354i | 0.375284 | + | 0.375284i | ||||
\(367\) | −176.215 | −0.480151 | −0.240075 | − | 0.970754i | \(-0.577172\pi\) | ||||
−0.240075 | + | 0.970754i | \(0.577172\pi\) | |||||||
\(368\) | 127.426i | 0.346265i | ||||||||
\(369\) | −90.7461 | − | 90.7461i | −0.245924 | − | 0.245924i | ||||
\(370\) | −342.382 | − | 342.382i | −0.925357 | − | 0.925357i | ||||
\(371\) | −178.756 | + | 178.756i | −0.481823 | + | 0.481823i | ||||
\(372\) | −106.799 | + | 106.799i | −0.287093 | + | 0.287093i | ||||
\(373\) | 483.606 | 1.29653 | 0.648266 | − | 0.761414i | \(-0.275495\pi\) | ||||
0.648266 | + | 0.761414i | \(0.275495\pi\) | |||||||
\(374\) | 108.862i | 0.291074i | ||||||||
\(375\) | −42.7461 | + | 42.7461i | −0.113990 | + | 0.113990i | ||||
\(376\) | 235.923i | 0.627455i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −19.0192 | −0.0503154 | ||||||||
\(379\) | 204.107 | + | 204.107i | 0.538541 | + | 0.538541i | 0.923100 | − | 0.384559i | \(-0.125647\pi\) |
−0.384559 | + | 0.923100i | \(0.625647\pi\) | |||||||
\(380\) | −49.3590 | −0.129892 | ||||||||
\(381\) | 309.771i | 0.813046i | ||||||||
\(382\) | −162.679 | − | 162.679i | −0.425863 | − | 0.425863i | ||||
\(383\) | 186.249 | + | 186.249i | 0.486289 | + | 0.486289i | 0.907133 | − | 0.420844i | \(-0.138266\pi\) |
−0.420844 | + | 0.907133i | \(0.638266\pi\) | |||||||
\(384\) | 13.8564 | − | 13.8564i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | −185.885 | + | 185.885i | −0.482817 | + | 0.482817i | ||||
\(386\) | 116.301 | 0.301299 | ||||||||
\(387\) | 97.9808i | 0.253180i | ||||||||
\(388\) | 25.9756 | − | 25.9756i | 0.0669474 | − | 0.0669474i | ||||
\(389\) | − | 66.2487i | − | 0.170305i | −0.996368 | − | 0.0851526i | \(-0.972862\pi\) | ||
0.996368 | − | 0.0851526i | \(-0.0271378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −161.569 | −0.413221 | ||||||||
\(392\) | 84.6025 | + | 84.6025i | 0.215823 | + | 0.215823i | ||||
\(393\) | −92.9000 | −0.236387 | ||||||||
\(394\) | − | 381.913i | − | 0.969322i | ||||||
\(395\) | 170.942 | + | 170.942i | 0.432765 | + | 0.432765i | ||||
\(396\) | 64.3923 | + | 64.3923i | 0.162607 | + | 0.162607i | ||||
\(397\) | −95.6429 | + | 95.6429i | −0.240914 | + | 0.240914i | −0.817228 | − | 0.576314i | \(-0.804490\pi\) |
0.576314 | + | 0.817228i | \(0.304490\pi\) | |||||||
\(398\) | −63.7846 | + | 63.7846i | −0.160263 | + | 0.160263i | ||||
\(399\) | 16.5321 | 0.0414339 | ||||||||
\(400\) | − | 79.1384i | − | 0.197846i | ||||||
\(401\) | 135.415 | − | 135.415i | 0.337694 | − | 0.337694i | −0.517805 | − | 0.855499i | \(-0.673251\pi\) |
0.855499 | + | 0.517805i | \(0.173251\pi\) | |||||||
\(402\) | − | 161.909i | − | 0.402759i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −277.626 | −0.687192 | ||||||||
\(405\) | 42.5885 | + | 42.5885i | 0.105157 | + | 0.105157i | ||||
\(406\) | 63.3975 | 0.156151 | ||||||||
\(407\) | − | 776.505i | − | 1.90787i | ||||||
\(408\) | 17.5692 | + | 17.5692i | 0.0430618 | + | 0.0430618i | ||||
\(409\) | −392.974 | − | 392.974i | −0.960816 | − | 0.960816i | 0.0384448 | − | 0.999261i | \(-0.487760\pi\) |
−0.999261 | + | 0.0384448i | \(0.987760\pi\) | |||||||
\(410\) | −286.277 | + | 286.277i | −0.698236 | + | 0.698236i | ||||
\(411\) | 151.492 | − | 151.492i | 0.368594 | − | 0.368594i | ||||
\(412\) | 214.526 | 0.520693 | ||||||||
\(413\) | 158.372i | 0.383467i | ||||||||
\(414\) | −95.5692 | + | 95.5692i | −0.230844 | + | 0.230844i | ||||
\(415\) | − | 198.431i | − | 0.478146i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −266.229 | −0.638440 | ||||||||
\(418\) | −55.9718 | − | 55.9718i | −0.133904 | − | 0.133904i | ||||
\(419\) | −657.646 | −1.56956 | −0.784781 | − | 0.619774i | \(-0.787224\pi\) | ||||
−0.784781 | + | 0.619774i | \(0.787224\pi\) | |||||||
\(420\) | 60.0000i | 0.142857i | ||||||||
\(421\) | −328.035 | − | 328.035i | −0.779181 | − | 0.779181i | 0.200511 | − | 0.979692i | \(-0.435740\pi\) |
−0.979692 | + | 0.200511i | \(0.935740\pi\) | |||||||
\(422\) | −247.799 | − | 247.799i | −0.587201 | − | 0.587201i | ||||
\(423\) | −176.942 | + | 176.942i | −0.418303 | + | 0.418303i | ||||
\(424\) | 195.349 | − | 195.349i | 0.460728 | − | 0.460728i | ||||
\(425\) | 100.344 | 0.236102 | ||||||||
\(426\) | 131.454i | 0.308577i | ||||||||
\(427\) | −145.131 | + | 145.131i | −0.339886 | + | 0.339886i | ||||
\(428\) | 11.0052i | 0.0257130i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 309.100 | 0.718837 | ||||||||
\(431\) | −22.6898 | − | 22.6898i | −0.0526446 | − | 0.0526446i | 0.680294 | − | 0.732939i | \(-0.261852\pi\) |
−0.732939 | + | 0.680294i | \(0.761852\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 196.215i | 0.453153i | 0.973993 | + | 0.226577i | \(0.0727534\pi\) | ||||
−0.973993 | + | 0.226577i | \(0.927247\pi\) | |||||||
\(434\) | −112.846 | − | 112.846i | −0.260014 | − | 0.260014i | ||||
\(435\) | −141.962 | − | 141.962i | −0.326348 | − | 0.326348i | ||||
\(436\) | 217.622 | − | 217.622i | 0.499133 | − | 0.499133i | ||||
\(437\) | 83.0718 | − | 83.0718i | 0.190096 | − | 0.190096i | ||||
\(438\) | 95.5448 | 0.218139 | ||||||||
\(439\) | − | 41.4627i | − | 0.0944481i | −0.998884 | − | 0.0472241i | \(-0.984963\pi\) | ||
0.998884 | − | 0.0472241i | \(-0.0150375\pi\) | |||||||
\(440\) | 203.138 | − | 203.138i | 0.461678 | − | 0.461678i | ||||
\(441\) | 126.904i | 0.287764i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.9718 | −0.0450831 | −0.0225416 | − | 0.999746i | \(-0.507176\pi\) | ||||
−0.0225416 | + | 0.999746i | \(0.507176\pi\) | |||||||
\(444\) | −125.321 | − | 125.321i | −0.282253 | − | 0.282253i | ||||
\(445\) | 467.138 | 1.04975 | ||||||||
\(446\) | 65.0615i | 0.145878i | ||||||||
\(447\) | −194.354 | − | 194.354i | −0.434796 | − | 0.434796i | ||||
\(448\) | 14.6410 | + | 14.6410i | 0.0326808 | + | 0.0326808i | ||||
\(449\) | 93.3064 | − | 93.3064i | 0.207809 | − | 0.207809i | −0.595526 | − | 0.803336i | \(-0.703056\pi\) |
0.803336 | + | 0.595526i | \(0.203056\pi\) | |||||||
\(450\) | 59.3538 | − | 59.3538i | 0.131897 | − | 0.131897i | ||||
\(451\) | −649.261 | −1.43960 | ||||||||
\(452\) | − | 173.569i | − | 0.384003i | ||||||
\(453\) | −275.329 | + | 275.329i | −0.607791 | + | 0.607791i | ||||
\(454\) | 19.4256i | 0.0427877i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0666 | −0.0396198 | ||||||||
\(457\) | −208.519 | − | 208.519i | −0.456277 | − | 0.456277i | 0.441154 | − | 0.897431i | \(-0.354569\pi\) |
−0.897431 | + | 0.441154i | \(0.854569\pi\) | |||||||
\(458\) | 574.631 | 1.25465 | ||||||||
\(459\) | 26.3538i | 0.0574157i | ||||||||
\(460\) | 301.492 | + | 301.492i | 0.655418 | + | 0.655418i | ||||
\(461\) | −332.123 | − | 332.123i | −0.720440 | − | 0.720440i | 0.248255 | − | 0.968695i | \(-0.420143\pi\) |
−0.968695 | + | 0.248255i | \(0.920143\pi\) | |||||||
\(462\) | −68.0385 | + | 68.0385i | −0.147269 | + | 0.147269i | ||||
\(463\) | −462.599 | + | 462.599i | −0.999134 | + | 0.999134i | −1.00000 | 0.000865128i | \(-0.999725\pi\) | |
0.000865128 | 1.00000i | \(0.499725\pi\) | ||||||||
\(464\) | −69.2820 | −0.149315 | ||||||||
\(465\) | 505.377i | 1.08683i | ||||||||
\(466\) | 27.3308 | − | 27.3308i | 0.0586498 | − | 0.0586498i | ||||
\(467\) | − | 396.649i | − | 0.849355i | −0.905345 | − | 0.424677i | \(-0.860388\pi\) | ||
0.905345 | − | 0.424677i | \(-0.139612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 171.077 | 0.364770 | ||||||||
\(470\) | 558.200 | + | 558.200i | 1.18766 | + | 1.18766i | ||||
\(471\) | −240.009 | −0.509573 | ||||||||
\(472\) | − | 173.072i | − | 0.366678i | ||||||
\(473\) | 350.512 | + | 350.512i | 0.741039 | + | 0.741039i | ||||
\(474\) | 62.5692 | + | 62.5692i | 0.132003 | + | 0.132003i | ||||
\(475\) | −51.5922 | + | 51.5922i | −0.108615 | + | 0.108615i | ||||
\(476\) | −18.5641 | + | 18.5641i | −0.0390001 | + | 0.0390001i | ||||
\(477\) | 293.023 | 0.614304 | ||||||||
\(478\) | − | 1.72312i | − | 0.00360486i | ||||||
\(479\) | −254.536 | + | 254.536i | −0.531390 | + | 0.531390i | −0.920986 | − | 0.389596i | \(-0.872615\pi\) |
0.389596 | + | 0.920986i | \(0.372615\pi\) | |||||||
\(480\) | − | 65.5692i | − | 0.136603i | ||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −120.354 | −0.249697 | ||||||||
\(483\) | −100.981 | − | 100.981i | −0.209070 | − | 0.209070i | ||||
\(484\) | 218.708 | 0.451875 | ||||||||
\(485\) | − | 122.918i | − | 0.253439i | ||||||
\(486\) | 15.5885 | + | 15.5885i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 137.000 | + | 137.000i | 0.281314 | + | 0.281314i | 0.833633 | − | 0.552319i | \(-0.186257\pi\) |
−0.552319 | + | 0.833633i | \(0.686257\pi\) | |||||||
\(488\) | 158.603 | − | 158.603i | 0.325005 | − | 0.325005i | ||||
\(489\) | −343.547 | + | 343.547i | −0.702550 | + | 0.702550i | ||||
\(490\) | 400.344 | 0.817028 | ||||||||
\(491\) | − | 23.0718i | − | 0.0469894i | −0.999724 | − | 0.0234947i | \(-0.992521\pi\) | ||
0.999724 | − | 0.0234947i | \(-0.00747928\pi\) | |||||||
\(492\) | −104.785 | + | 104.785i | −0.212977 | + | 0.212977i | ||||
\(493\) | − | 87.8461i | − | 0.178187i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 304.708 | 0.615571 | ||||||||
\(496\) | 123.321 | + | 123.321i | 0.248630 | + | 0.248630i | ||||
\(497\) | −138.897 | −0.279471 | ||||||||
\(498\) | − | 72.6307i | − | 0.145845i | ||||||
\(499\) | 160.769 | + | 160.769i | 0.322183 | + | 0.322183i | 0.849604 | − | 0.527421i | \(-0.176841\pi\) |
−0.527421 | + | 0.849604i | \(0.676841\pi\) | |||||||
\(500\) | 49.3590 | + | 49.3590i | 0.0987180 | + | 0.0987180i | ||||
\(501\) | 342.200 | − | 342.200i | 0.683034 | − | 0.683034i | ||||
\(502\) | −40.7077 | + | 40.7077i | −0.0810910 | + | 0.0810910i | ||||
\(503\) | −601.244 | −1.19532 | −0.597658 | − | 0.801751i | \(-0.703902\pi\) | ||||
−0.597658 | + | 0.801751i | \(0.703902\pi\) | |||||||
\(504\) | 21.9615i | 0.0435745i | ||||||||
\(505\) | −656.869 | + | 656.869i | −1.30073 | + | 1.30073i | ||||
\(506\) | 683.769i | 1.35132i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 357.692 | 0.704118 | ||||||||
\(509\) | −347.745 | − | 347.745i | −0.683192 | − | 0.683192i | 0.277526 | − | 0.960718i | \(-0.410486\pi\) |
−0.960718 | + | 0.277526i | \(0.910486\pi\) | |||||||
\(510\) | 83.1384 | 0.163017 | ||||||||
\(511\) | 100.955i | 0.197564i | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −13.5500 | − | 13.5500i | −0.0264132 | − | 0.0264132i | ||||
\(514\) | 309.779 | − | 309.779i | 0.602684 | − | 0.602684i | ||||
\(515\) | 507.573 | − | 507.573i | 0.985579 | − | 0.985579i | ||||
\(516\) | 113.138 | 0.219261 | ||||||||
\(517\) | 1265.97i | 2.44868i | ||||||||
\(518\) | 132.417 | − | 132.417i | 0.255631 | − | 0.255631i | ||||
\(519\) | 116.985i | 0.225404i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 647.951 | 1.24367 | 0.621834 | − | 0.783149i | \(-0.286388\pi\) | ||||
0.621834 | + | 0.783149i | \(0.286388\pi\) | |||||||
\(522\) | −51.9615 | − | 51.9615i | −0.0995431 | − | 0.0995431i | ||||
\(523\) | −165.923 | −0.317252 | −0.158626 | − | 0.987339i | \(-0.550706\pi\) | ||||
−0.158626 | + | 0.987339i | \(0.550706\pi\) | |||||||
\(524\) | 107.272i | 0.204717i | ||||||||
\(525\) | 62.7147 | + | 62.7147i | 0.119457 | + | 0.119457i | ||||
\(526\) | 287.636 | + | 287.636i | 0.546836 | + | 0.546836i | ||||
\(527\) | −156.364 | + | 156.364i | −0.296706 | + | 0.296706i | ||||
\(528\) | 74.3538 | − | 74.3538i | 0.140822 | − | 0.140822i | ||||
\(529\) | −485.831 | −0.918394 | ||||||||
\(530\) | − | 924.400i | − | 1.74415i | ||||||
\(531\) | 129.804 | − | 129.804i | 0.244452 | − | 0.244452i | ||||
\(532\) | − | 19.0897i | − | 0.0358828i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 170.985 | 0.320196 | ||||||||
\(535\) | 26.0385 | + | 26.0385i | 0.0486700 | + | 0.0486700i | ||||
\(536\) | −186.956 | −0.348799 | ||||||||
\(537\) | 86.9845i | 0.161982i | ||||||||
\(538\) | −163.741 | − | 163.741i | −0.304351 | − | 0.304351i | ||||
\(539\) | 453.979 | + | 453.979i | 0.842262 | + | 0.842262i | ||||
\(540\) | 49.1769 | − | 49.1769i | 0.0910684 | − | 0.0910684i | ||||
\(541\) | 210.557 | − | 210.557i | 0.389200 | − | 0.389200i | −0.485202 | − | 0.874402i | \(-0.661254\pi\) |
0.874402 | + | 0.485202i | \(0.161254\pi\) | |||||||
\(542\) | −459.909 | −0.848541 | ||||||||
\(543\) | − | 523.692i | − | 0.964442i | ||||||
\(544\) | 20.2872 | − | 20.2872i | 0.0372926 | − | 0.0372926i | ||||
\(545\) | − | 1029.80i | − | 1.88954i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −392.492 | −0.717536 | −0.358768 | − | 0.933427i | \(-0.616803\pi\) | ||||
−0.358768 | + | 0.933427i | \(0.616803\pi\) | |||||||
\(548\) | −174.928 | − | 174.928i | −0.319212 | − | 0.319212i | ||||
\(549\) | 237.904 | 0.433340 | ||||||||
\(550\) | − | 424.659i | − | 0.772107i | ||||||
\(551\) | 45.1666 | + | 45.1666i | 0.0819721 | + | 0.0819721i | ||||
\(552\) | 110.354 | + | 110.354i | 0.199916 | + | 0.199916i | ||||
\(553\) | −66.1122 | + | 66.1122i | −0.119552 | + | 0.119552i | ||||
\(554\) | −134.985 | + | 134.985i | −0.243654 | + | 0.243654i | ||||
\(555\) | −593.023 | −1.06851 | ||||||||
\(556\) | 307.415i | 0.552905i | ||||||||
\(557\) | −50.1539 | + | 50.1539i | −0.0900429 | + | 0.0900429i | −0.750694 | − | 0.660651i | \(-0.770280\pi\) |
0.660651 | + | 0.750694i | \(0.270280\pi\) | |||||||
\(558\) | 184.981i | 0.331507i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 69.2820 | 0.123718 | ||||||||
\(561\) | 94.2769 | + | 94.2769i | 0.168051 | + | 0.168051i | ||||
\(562\) | 647.090 | 1.15141 | ||||||||
\(563\) | 832.726i | 1.47909i | 0.673109 | + | 0.739543i | \(0.264958\pi\) | ||||
−0.673109 | + | 0.739543i | \(0.735042\pi\) | |||||||
\(564\) | 204.315 | + | 204.315i | 0.362261 | + | 0.362261i | ||||
\(565\) | −410.669 | − | 410.669i | −0.726848 | − | 0.726848i | ||||
\(566\) | 141.354 | − | 141.354i | 0.249742 | − | 0.249742i | ||||
\(567\) | −16.4711 | + | 16.4711i | −0.0290496 | + | 0.0290496i | ||||
\(568\) | 151.790 | 0.267236 | ||||||||
\(569\) | − | 348.431i | − | 0.612356i | −0.951974 | − | 0.306178i | \(-0.900950\pi\) | ||
0.951974 | − | 0.306178i | \(-0.0990503\pi\) | |||||||
\(570\) | −42.7461 | + | 42.7461i | −0.0749932 | + | 0.0749932i | ||||
\(571\) | 411.892i | 0.721352i | 0.932691 | + | 0.360676i | \(0.117454\pi\) | ||||
−0.932691 | + | 0.360676i | \(0.882546\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −281.769 | −0.491744 | ||||||||
\(574\) | −110.718 | − | 110.718i | −0.192888 | − | 0.192888i | ||||
\(575\) | 630.267 | 1.09612 | ||||||||
\(576\) | − | 24.0000i | − | 0.0416667i | ||||||
\(577\) | −39.6692 | − | 39.6692i | −0.0687507 | − | 0.0687507i | 0.671895 | − | 0.740646i | \(-0.265480\pi\) |
−0.740646 | + | 0.671895i | \(0.765480\pi\) | |||||||
\(578\) | −263.277 | − | 263.277i | −0.455496 | − | 0.455496i | ||||
\(579\) | 100.720 | − | 100.720i | 0.173955 | − | 0.173955i | ||||
\(580\) | −163.923 | + | 163.923i | −0.282626 | + | 0.282626i | ||||
\(581\) | 76.7434 | 0.132088 | ||||||||
\(582\) | − | 44.9911i | − | 0.0773042i | ||||||
\(583\) | 1048.25 | − | 1048.25i | 1.79802 | − | 1.79802i | ||||
\(584\) | − | 110.326i | − | 0.188914i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −420.946 | −0.718338 | ||||||||
\(587\) | −370.004 | − | 370.004i | −0.630330 | − | 0.630330i | 0.317821 | − | 0.948151i | \(-0.397049\pi\) |
−0.948151 | + | 0.317821i | \(0.897049\pi\) | |||||||
\(588\) | 146.536 | 0.249211 | ||||||||
\(589\) | − | 160.791i | − | 0.272990i | ||||||
\(590\) | −409.492 | − | 409.492i | −0.694055 | − | 0.694055i | ||||
\(591\) | −330.746 | − | 330.746i | −0.559638 | − | 0.559638i | ||||
\(592\) | −144.708 | + | 144.708i | −0.244439 | + | 0.244439i | ||||
\(593\) | −234.771 | + | 234.771i | −0.395903 | + | 0.395903i | −0.876785 | − | 0.480882i | \(-0.840316\pi\) |
0.480882 | + | 0.876785i | \(0.340316\pi\) | |||||||
\(594\) | 111.531 | 0.187762 | ||||||||
\(595\) | 87.8461i | 0.147640i | ||||||||
\(596\) | −224.420 | + | 224.420i | −0.376544 | + | 0.376544i | ||||
\(597\) | 110.478i | 0.185056i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −652.908 | −1.09000 | −0.544998 | − | 0.838437i | \(-0.683470\pi\) | ||||
−0.544998 | + | 0.838437i | \(0.683470\pi\) | |||||||
\(600\) | −68.5359 | − | 68.5359i | −0.114226 | − | 0.114226i | ||||
\(601\) | 65.5692 | 0.109100 | 0.0545501 | − | 0.998511i | \(-0.482628\pi\) | ||||
0.0545501 | + | 0.998511i | \(0.482628\pi\) | |||||||
\(602\) | 119.545i | 0.198579i | ||||||||
\(603\) | −140.217 | − | 140.217i | −0.232533 | − | 0.232533i | ||||
\(604\) | 317.923 | + | 317.923i | 0.526363 | + | 0.526363i | ||||
\(605\) | 517.468 | − | 517.468i | 0.855319 | − | 0.855319i | ||||
\(606\) | −240.431 | + | 240.431i | −0.396750 | + | 0.396750i | ||||
\(607\) | −776.600 | −1.27941 | −0.639703 | − | 0.768622i | \(-0.720943\pi\) | ||||
−0.639703 | + | 0.768622i | \(0.720943\pi\) | |||||||
\(608\) | 20.8616i | 0.0343118i | ||||||||
\(609\) | 54.9038 | − | 54.9038i | 0.0901540 | − | 0.0901540i | ||||
\(610\) | − | 750.515i | − | 1.23035i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 30.4308 | 0.0497235 | ||||||||
\(613\) | −300.757 | − | 300.757i | −0.490631 | − | 0.490631i | 0.417874 | − | 0.908505i | \(-0.362775\pi\) |
−0.908505 | + | 0.417874i | \(0.862775\pi\) | |||||||
\(614\) | −140.137 | −0.228236 | ||||||||
\(615\) | 495.846i | 0.806254i | ||||||||
\(616\) | 78.5641 | + | 78.5641i | 0.127539 | + | 0.127539i | ||||
\(617\) | 95.6603 | + | 95.6603i | 0.155041 | + | 0.155041i | 0.780365 | − | 0.625324i | \(-0.215033\pi\) |
−0.625324 | + | 0.780365i | \(0.715033\pi\) | |||||||
\(618\) | 185.785 | − | 185.785i | 0.300622 | − | 0.300622i | ||||
\(619\) | 661.030 | − | 661.030i | 1.06790 | − | 1.06790i | 0.0703796 | − | 0.997520i | \(-0.477579\pi\) |
0.997520 | − | 0.0703796i | \(-0.0224211\pi\) | |||||||
\(620\) | 583.559 | 0.941224 | ||||||||
\(621\) | 165.531i | 0.266555i | ||||||||
\(622\) | 140.238 | − | 140.238i | 0.225464 | − | 0.225464i | ||||
\(623\) | 180.666i | 0.289994i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 728.184 | 1.16510 | ||||||||
\(626\) | 550.286 | + | 550.286i | 0.879051 | + | 0.879051i | ||||
\(627\) | −96.9461 | −0.154619 | ||||||||
\(628\) | 277.138i | 0.441303i | ||||||||
\(629\) | −183.482 | − | 183.482i | −0.291704 | − | 0.291704i | ||||
\(630\) | 51.9615 | + | 51.9615i | 0.0824786 | + | 0.0824786i | ||||
\(631\) | 274.445 | − | 274.445i | 0.434937 | − | 0.434937i | −0.455367 | − | 0.890304i | \(-0.650492\pi\) |
0.890304 | + | 0.455367i | \(0.150492\pi\) | |||||||
\(632\) | 72.2487 | − | 72.2487i | 0.114318 | − | 0.114318i | ||||
\(633\) | −429.200 | −0.678041 | ||||||||
\(634\) | − | 62.5847i | − | 0.0987140i | ||||||
\(635\) | 846.309 | − | 846.309i | 1.33277 | − | 1.33277i | ||||
\(636\) | − | 338.354i | − | 0.532003i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −371.769 | −0.582710 | ||||||||
\(639\) | 113.842 | + | 113.842i | 0.178157 | + | 0.178157i | ||||
\(640\) | −75.7128 | −0.118301 | ||||||||
\(641\) | 623.387i | 0.972523i | 0.873813 | + | 0.486261i | \(0.161640\pi\) | ||||
−0.873813 | + | 0.486261i | \(0.838360\pi\) | |||||||
\(642\) | 9.53074 | + | 9.53074i | 0.0148454 | + | 0.0148454i | ||||
\(643\) | −578.270 | − | 578.270i | −0.899331 | − | 0.899331i | 0.0960459 | − | 0.995377i | \(-0.469380\pi\) |
−0.995377 | + | 0.0960459i | \(0.969380\pi\) | |||||||
\(644\) | −116.603 | + | 116.603i | −0.181060 | + | 0.181060i | ||||
\(645\) | 267.688 | − | 267.688i | 0.415021 | − | 0.415021i | ||||
\(646\) | −26.4514 | −0.0409464 | ||||||||
\(647\) | 286.841i | 0.443340i | 0.975122 | + | 0.221670i | \(0.0711508\pi\) | ||||
−0.975122 | + | 0.221670i | \(0.928849\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 928.708i | − | 1.43098i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −195.455 | −0.300238 | ||||||||
\(652\) | 396.694 | + | 396.694i | 0.608426 | + | 0.608426i | ||||
\(653\) | 648.848 | 0.993642 | 0.496821 | − | 0.867853i | \(-0.334500\pi\) | ||||
0.496821 | + | 0.867853i | \(0.334500\pi\) | |||||||
\(654\) | − | 376.932i | − | 0.576349i | ||||||
\(655\) | 253.808 | + | 253.808i | 0.387493 | + | 0.387493i | ||||
\(656\) | 120.995 | + | 120.995i | 0.184443 | + | 0.184443i | ||||
\(657\) | 82.7442 | − | 82.7442i | 0.125943 | − | 0.125943i | ||||
\(658\) | −215.885 | + | 215.885i | −0.328092 | + | 0.328092i | ||||
\(659\) | 456.315 | 0.692436 | 0.346218 | − | 0.938154i | \(-0.387466\pi\) | ||||
0.346218 | + | 0.938154i | \(0.387466\pi\) | |||||||
\(660\) | − | 351.846i | − | 0.533100i | ||||||
\(661\) | 229.988 | − | 229.988i | 0.347939 | − | 0.347939i | −0.511402 | − | 0.859341i | \(-0.670874\pi\) |
0.859341 | + | 0.511402i | \(0.170874\pi\) | |||||||
\(662\) | − | 571.247i | − | 0.862911i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −83.8667 | −0.126305 | ||||||||
\(665\) | −45.1666 | − | 45.1666i | −0.0679197 | − | 0.0679197i | ||||
\(666\) | −217.061 | −0.325918 | ||||||||
\(667\) | − | 551.769i | − | 0.827240i | ||||||
\(668\) | −395.138 | − | 395.138i | −0.591525 | − | 0.591525i | ||||
\(669\) | 56.3449 | + | 56.3449i | 0.0842226 | + | 0.0842226i | ||||
\(670\) | −442.344 | + | 442.344i | −0.660214 | + | 0.660214i | ||||
\(671\) | 851.065 | − | 851.065i | 1.26835 | − | 1.26835i | ||||
\(672\) | 25.3590 | 0.0377366 | ||||||||
\(673\) | − | 1044.01i | − | 1.55128i | −0.631178 | − | 0.775638i | \(-0.717428\pi\) | ||
0.631178 | − | 0.775638i | \(-0.282572\pi\) | |||||||
\(674\) | 638.492 | − | 638.492i | 0.947318 | − | 0.947318i | ||||
\(675\) | − | 102.804i | − | 0.152302i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −193.408 | −0.285684 | −0.142842 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142842 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(678\) | −150.315 | − | 150.315i | −0.221704 | − | 0.221704i | ||||
\(679\) | 47.5387 | 0.0700128 | ||||||||
\(680\) | − | 96.0000i | − | 0.141176i | ||||||
\(681\) | 16.8231 | + | 16.8231i | 0.0247035 | + | 0.0247035i | ||||
\(682\) | 661.741 | + | 661.741i | 0.970295 | + | 0.970295i | ||||
\(683\) | −587.678 | + | 587.678i | −0.860436 | + | 0.860436i | −0.991389 | − | 0.130952i | \(-0.958197\pi\) |
0.130952 | + | 0.991389i | \(0.458197\pi\) | |||||||
\(684\) | −15.6462 | + | 15.6462i | −0.0228745 | + | 0.0228745i | ||||
\(685\) | −827.769 | −1.20842 | ||||||||
\(686\) | 334.186i | 0.487151i | ||||||||
\(687\) | 497.645 | − | 497.645i | 0.724374 | − | 0.724374i | ||||
\(688\) | − | 130.641i | − | 0.189885i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 522.200 | 0.756811 | ||||||||
\(691\) | 164.030 | + | 164.030i | 0.237381 | + | 0.237381i | 0.815765 | − | 0.578384i | \(-0.196316\pi\) |
−0.578384 | + | 0.815765i | \(0.696316\pi\) | |||||||
\(692\) | 135.082 | 0.195205 | ||||||||
\(693\) | 117.846i | 0.170052i | ||||||||
\(694\) | 5.70250 | + | 5.70250i | 0.00821686 | + | 0.00821686i | ||||
\(695\) | 727.352 | + | 727.352i | 1.04655 | + | 1.04655i | ||||
\(696\) | −60.0000 | + | 60.0000i | −0.0862069 | + | 0.0862069i | ||||
\(697\) | −153.415 | + | 153.415i | −0.220108 | + | 0.220108i | ||||
\(698\) | 256.206 | 0.367058 | ||||||||
\(699\) | − | 47.3384i | − | 0.0677230i | ||||||
\(700\) | 72.4167 | − | 72.4167i | 0.103452 | − | 0.103452i | ||||
\(701\) | − | 55.6565i | − | 0.0793958i | −0.999212 | − | 0.0396979i | \(-0.987360\pi\) | ||
0.999212 | − | 0.0396979i | \(-0.0126396\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 188.677 | 0.268388 | ||||||||
\(704\) | −85.8564 | − | 85.8564i | −0.121955 | − | 0.121955i | ||||
\(705\) | 966.831 | 1.37139 | ||||||||
\(706\) | 410.074i | 0.580842i | ||||||||
\(707\) | −254.045 | − | 254.045i | −0.359328 | − | 0.359328i | ||||
\(708\) | −149.885 | − | 149.885i | −0.211701 | − | 0.211701i | ||||
\(709\) | −219.581 | + | 219.581i | −0.309706 | + | 0.309706i | −0.844795 | − | 0.535090i | \(-0.820278\pi\) |
0.535090 | + | 0.844795i | \(0.320278\pi\) | |||||||
\(710\) | 359.138 | − | 359.138i | 0.505829 | − | 0.505829i | ||||
\(711\) | 108.373 | 0.152423 | ||||||||
\(712\) | − | 197.436i | − | 0.277298i | ||||||
\(713\) | −982.137 | + | 982.137i | −1.37747 | + | 1.37747i | ||||
\(714\) | 32.1539i | 0.0450335i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 100.441 | 0.140281 | ||||||||
\(717\) | −1.49227 | − | 1.49227i | −0.00208127 | − | 0.00208127i | ||||
\(718\) | −536.554 | −0.747289 | ||||||||
\(719\) | 311.520i | 0.433269i | 0.976253 | + | 0.216635i | \(0.0695080\pi\) | ||||
−0.976253 | + | 0.216635i | \(0.930492\pi\) | |||||||
\(720\) | −56.7846 | − | 56.7846i | −0.0788675 | − | 0.0788675i | ||||
\(721\) | 196.305 | + | 196.305i | 0.272267 | + | 0.272267i | ||||
\(722\) | −347.400 | + | 347.400i | −0.481163 | + | 0.481163i | ||||
\(723\) | −104.229 | + | 104.229i | −0.144162 | + | 0.144162i | ||||
\(724\) | −604.708 | −0.835232 | ||||||||
\(725\) | 342.679i | 0.472661i | ||||||||
\(726\) | 189.406 | − | 189.406i | 0.260890 | − | 0.260890i | ||||
\(727\) | − | 379.585i | − | 0.522125i | −0.965322 | − | 0.261062i | \(-0.915927\pi\) | ||
0.965322 | − | 0.261062i | \(-0.0840728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −261.033 | − | 261.033i | −0.357580 | − | 0.357580i | ||||
\(731\) | 165.646 | 0.226602 | ||||||||
\(732\) | − | 274.708i | − | 0.375284i | ||||||
\(733\) | −769.627 | − | 769.627i | −1.04997 | − | 1.04997i | −0.998684 | − | 0.0512852i | \(-0.983668\pi\) |
−0.0512852 | − | 0.998684i | \(-0.516332\pi\) | |||||||
\(734\) | 176.215 | + | 176.215i | 0.240075 | + | 0.240075i | ||||
\(735\) | 346.708 | − | 346.708i | 0.471711 | − | 0.471711i | ||||
\(736\) | 127.426 | − | 127.426i | 0.173133 | − | 0.173133i | ||||
\(737\) | −1003.21 | −1.36121 | ||||||||
\(738\) | 181.492i | 0.245924i | ||||||||
\(739\) | −189.161 | + | 189.161i | −0.255969 | + | 0.255969i | −0.823413 | − | 0.567443i | \(-0.807933\pi\) |
0.567443 | + | 0.823413i | \(0.307933\pi\) | |||||||
\(740\) | 684.764i | 0.925357i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 357.513 | 0.481823 | ||||||||
\(743\) | −783.640 | − | 783.640i | −1.05470 | − | 1.05470i | −0.998415 | − | 0.0562818i | \(-0.982075\pi\) |
−0.0562818 | − | 0.998415i | \(-0.517925\pi\) | |||||||
\(744\) | 213.597 | 0.287093 | ||||||||
\(745\) | 1061.97i | 1.42546i | ||||||||
\(746\) | −483.606 | − | 483.606i | −0.648266 | − | 0.648266i | ||||
\(747\) | −62.9000 | − | 62.9000i | −0.0842035 | − | 0.0842035i | ||||
\(748\) | 108.862 | − | 108.862i | 0.145537 | − | 0.145537i | ||||
\(749\) | −10.0704 | + | 10.0704i | −0.0134451 | + | 0.0134451i | ||||
\(750\) | 85.4923 | 0.113990 | ||||||||
\(751\) | − | 367.923i | − | 0.489911i | −0.969534 | − | 0.244955i | \(-0.921227\pi\) | ||
0.969534 | − | 0.244955i | \(-0.0787733\pi\) | |||||||
\(752\) | 235.923 | − | 235.923i | 0.313727 | − | 0.313727i | ||||
\(753\) | 70.5077i | 0.0936358i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1504.43 | 1.99262 | ||||||||
\(756\) | 19.0192 | + | 19.0192i | 0.0251577 | + | 0.0251577i | ||||
\(757\) | 195.384 | 0.258104 | 0.129052 | − | 0.991638i | \(-0.458807\pi\) | ||||
0.129052 | + | 0.991638i | \(0.458807\pi\) | |||||||
\(758\) | − | 408.214i | − | 0.538541i | ||||||
\(759\) | 592.161 | + | 592.161i | 0.780186 | + | 0.780186i | ||||
\(760\) | 49.3590 | + | 49.3590i | 0.0649460 | + | 0.0649460i | ||||
\(761\) | 861.367 | − | 861.367i | 1.13189 | − | 1.13189i | 0.142025 | − | 0.989863i | \(-0.454639\pi\) |
0.989863 | − | 0.142025i | \(-0.0453612\pi\) | |||||||
\(762\) | 309.771 | − | 309.771i | 0.406523 | − | 0.406523i | ||||
\(763\) | 398.275 | 0.521986 | ||||||||
\(764\) | 325.359i | 0.425863i | ||||||||
\(765\) | 72.0000 | − | 72.0000i | 0.0941176 | − | 0.0941176i | ||||
\(766\) | − | 372.497i | − | 0.486289i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | −732.685 | − | 732.685i | −0.952776 | − | 0.952776i | 0.0461583 | − | 0.998934i | \(-0.485302\pi\) |
−0.998934 | + | 0.0461583i | \(0.985302\pi\) | |||||||
\(770\) | 371.769 | 0.482817 | ||||||||
\(771\) | − | 536.554i | − | 0.695919i | ||||||
\(772\) | −116.301 | − | 116.301i | −0.150649 | − | 0.150649i | ||||
\(773\) | −662.232 | − | 662.232i | −0.856704 | − | 0.856704i | 0.134245 | − | 0.990948i | \(-0.457139\pi\) |
−0.990948 | + | 0.134245i | \(0.957139\pi\) | |||||||
\(774\) | 97.9808 | − | 97.9808i | 0.126590 | − | 0.126590i | ||||
\(775\) | 609.962 | − | 609.962i | 0.787048 | − | 0.787048i | ||||
\(776\) | −51.9512 | −0.0669474 | ||||||||
\(777\) | − | 229.352i | − | 0.295177i | ||||||
\(778\) | −66.2487 | + | 66.2487i | −0.0851526 | + | 0.0851526i | ||||
\(779\) | − | 157.759i | − | 0.202515i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 814.508 | 1.04290 | ||||||||
\(782\) | 161.569 | + | 161.569i | 0.206610 | + | 0.206610i | ||||
\(783\) | −90.0000 | −0.114943 | ||||||||
\(784\) | − | 169.205i | − | 0.215823i | ||||||
\(785\) | 655.717 | + | 655.717i | 0.835308 | + | 0.835308i | ||||
\(786\) | 92.9000 | + | 92.9000i | 0.118193 | + | 0.118193i | ||||
\(787\) | −677.547 | + | 677.547i | −0.860923 | + | 0.860923i | −0.991445 | − | 0.130522i | \(-0.958335\pi\) |
0.130522 | + | 0.991445i | \(0.458335\pi\) | |||||||
\(788\) | −381.913 | + | 381.913i | −0.484661 | + | 0.484661i | ||||
\(789\) | 498.200 | 0.631432 | ||||||||
\(790\) | − | 341.885i | − | 0.432765i | ||||||
\(791\) | 158.827 | − | 158.827i | 0.200792 | − | 0.200792i | ||||
\(792\) | − | 128.785i | − | 0.162607i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 191.286 | 0.240914 | ||||||||
\(795\) | −800.554 | − | 800.554i | −1.00699 | − | 1.00699i | ||||
\(796\) | 127.569 | 0.160263 | ||||||||
\(797\) | 375.118i | 0.470662i | 0.971915 | + | 0.235331i | \(0.0756175\pi\) | ||||
−0.971915 | + | 0.235331i | \(0.924383\pi\) | |||||||
\(798\) | −16.5321 | − | 16.5321i | −0.0207169 | − | 0.0207169i | ||||
\(799\) | 299.138 | + | 299.138i | 0.374391 | + | 0.374391i | ||||
\(800\) | −79.1384 | + | 79.1384i | −0.0989230 | + | 0.0989230i | ||||
\(801\) | 148.077 | − | 148.077i | 0.184865 | − | 0.184865i | ||||
\(802\) | −270.831 | −0.337694 | ||||||||
\(803\) | − | 592.010i | − | 0.737248i | ||||||
\(804\) | −161.909 | + | 161.909i | −0.201379 | + | 0.201379i | ||||
\(805\) | 551.769i | 0.685428i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −283.608 | −0.351435 | ||||||||
\(808\) | 277.626 | + | 277.626i | 0.343596 | + | 0.343596i | ||||
\(809\) | 752.554 | 0.930227 | 0.465114 | − | 0.885251i | \(-0.346013\pi\) | ||||
0.465114 | + | 0.885251i | \(0.346013\pi\) | |||||||
\(810\) | − | 85.1769i | − | 0.105157i | ||||||
\(811\) | 49.8071 | + | 49.8071i | 0.0614144 | + | 0.0614144i | 0.737147 | − | 0.675732i | \(-0.236173\pi\) |
−0.675732 | + | 0.737147i | \(0.736173\pi\) | |||||||
\(812\) | −63.3975 | − | 63.3975i | −0.0780757 | − | 0.0780757i | ||||
\(813\) | −398.293 | + | 398.293i | −0.489905 | + | 0.489905i | ||||
\(814\) | −776.505 | + | 776.505i | −0.953937 | + | 0.953937i | ||||
\(815\) | 1877.17 | 2.30328 | ||||||||
\(816\) | − | 35.1384i | − | 0.0430618i | ||||||
\(817\) | −85.1680 | + | 85.1680i | −0.104245 | + | 0.104245i | ||||
\(818\) | 785.947i | 0.960816i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 572.554 | 0.698236 | ||||||||
\(821\) | 268.750 | + | 268.750i | 0.327345 | + | 0.327345i | 0.851576 | − | 0.524231i | \(-0.175647\pi\) |
−0.524231 | + | 0.851576i | \(0.675647\pi\) | |||||||
\(822\) | −302.985 | −0.368594 | ||||||||
\(823\) | 1326.83i | 1.61219i | 0.591788 | + | 0.806094i | \(0.298422\pi\) | ||||
−0.591788 | + | 0.806094i | \(0.701578\pi\) | |||||||
\(824\) | −214.526 | − | 214.526i | −0.260347 | − | 0.260347i | ||||
\(825\) | −367.765 | − | 367.765i | −0.445776 | − | 0.445776i | ||||
\(826\) | 158.372 | − | 158.372i | 0.191733 | − | 0.191733i | ||||
\(827\) | 178.410 | − | 178.410i | 0.215732 | − | 0.215732i | −0.590965 | − | 0.806697i | \(-0.701253\pi\) |
0.806697 | + | 0.590965i | \(0.201253\pi\) | |||||||
\(828\) | 191.138 | 0.230844 | ||||||||
\(829\) | 969.092i | 1.16899i | 0.811398 | + | 0.584495i | \(0.198707\pi\) | ||||
−0.811398 | + | 0.584495i | \(0.801293\pi\) | |||||||
\(830\) | −198.431 | + | 198.431i | −0.239073 | + | 0.239073i | ||||
\(831\) | 233.800i | 0.281348i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 214.543 | 0.257555 | ||||||||
\(834\) | 266.229 | + | 266.229i | 0.319220 | + | 0.319220i | ||||
\(835\) | −1869.82 | −2.23930 | ||||||||
\(836\) | 111.944i | 0.133904i | ||||||||
\(837\) | 160.198 | + | 160.198i | 0.191396 | + | 0.191396i | ||||
\(838\) | 657.646 | + | 657.646i | 0.784781 | + | 0.784781i | ||||
\(839\) | −154.070 | + | 154.070i | −0.183636 | + | 0.183636i | −0.792938 | − | 0.609302i | \(-0.791450\pi\) |
0.609302 | + | 0.792938i | \(0.291450\pi\) | |||||||
\(840\) | 60.0000 | − | 60.0000i | 0.0714286 | − | 0.0714286i | ||||
\(841\) | −541.000 | −0.643282 | ||||||||
\(842\) | 656.070i | 0.779181i | ||||||||
\(843\) | 560.396 | − | 560.396i | 0.664764 | − | 0.664764i | ||||
\(844\) | 495.597i | 0.587201i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 353.885 | 0.418303 | ||||||||
\(847\) | 200.131 | + | 200.131i | 0.236283 | + | 0.236283i | ||||
\(848\) | −390.697 | −0.460728 | ||||||||
\(849\) | − | 244.832i | − | 0.288377i | ||||||
\(850\) | −100.344 | − | 100.344i | −0.118051 | − | 0.118051i | ||||
\(851\) | −1152.47 | − | 1152.47i | −1.35425 | − | 1.35425i | ||||
\(852\) | 131.454 | − | 131.454i | 0.154288 | − | 0.154288i | ||||
\(853\) | 173.527 | − | 173.527i | 0.203432 | − | 0.203432i | −0.598037 | − | 0.801469i | \(-0.704052\pi\) |
0.801469 | + | 0.598037i | \(0.204052\pi\) | |||||||
\(854\) | 290.263 | 0.339886 | ||||||||
\(855\) | 74.0385i | 0.0865947i | ||||||||
\(856\) | 11.0052 | − | 11.0052i | 0.0128565 | − | 0.0128565i | ||||
\(857\) | 616.543i | 0.719421i | 0.933064 | + | 0.359710i | \(0.117124\pi\) | ||||
−0.933064 | + | 0.359710i | \(0.882876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 566.398 | 0.659370 | 0.329685 | − | 0.944091i | \(-0.393058\pi\) | ||||
0.329685 | + | 0.944091i | \(0.393058\pi\) | |||||||
\(860\) | −309.100 | − | 309.100i | −0.359419 | − | 0.359419i | ||||
\(861\) | −191.769 | −0.222728 | ||||||||
\(862\) | 45.3796i | 0.0526446i | ||||||||
\(863\) | −656.627 | − | 656.627i | −0.760866 | − | 0.760866i | 0.215613 | − | 0.976479i | \(-0.430825\pi\) |
−0.976479 | + | 0.215613i | \(0.930825\pi\) | |||||||
\(864\) | −20.7846 | − | 20.7846i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | 319.608 | − | 319.608i | 0.369489 | − | 0.369489i | ||||
\(866\) | 196.215 | − | 196.215i | 0.226577 | − | 0.226577i | ||||
\(867\) | −456.009 | −0.525962 | ||||||||
\(868\) | 225.692i | 0.260014i | ||||||||
\(869\) | 387.688 | − | 387.688i | 0.446132 | − | 0.446132i | ||||
\(870\) | 283.923i | 0.326348i | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −435.244 | −0.499133 | ||||||||
\(873\) | −38.9634 | − | 38.9634i | −0.0446316 | − | 0.0446316i | ||||
\(874\) | −166.144 | −0.190096 | ||||||||
\(875\) | 90.3332i | 0.103238i | ||||||||
\(876\) | −95.5448 | − | 95.5448i | −0.109069 | − | 0.109069i | ||||
\(877\) | −472.069 | − | 472.069i | −0.538277 | − | 0.538277i | 0.384746 | − | 0.923023i | \(-0.374289\pi\) |
−0.923023 | + | 0.384746i | \(0.874289\pi\) | |||||||
\(878\) | −41.4627 | + | 41.4627i | −0.0472241 | + | 0.0472241i | ||||
\(879\) | −364.550 | + | 364.550i | −0.414733 | + | 0.414733i | ||||
\(880\) | −406.277 | −0.461678 | ||||||||
\(881\) | 1016.34i | 1.15362i | 0.816880 | + | 0.576808i | \(0.195702\pi\) | ||||
−0.816880 | + | 0.576808i | \(0.804298\pi\) | |||||||
\(882\) | 126.904 | − | 126.904i | 0.143882 | − | 0.143882i | ||||
\(883\) | − | 785.277i | − | 0.889328i | −0.895697 | − | 0.444664i | \(-0.853323\pi\) | ||
0.895697 | − | 0.444664i | \(-0.146677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −709.261 | −0.801425 | ||||||||
\(886\) | 19.9718 | + | 19.9718i | 0.0225416 | + | 0.0225416i | ||||
\(887\) | 1285.06 | 1.44877 | 0.724386 | − | 0.689394i | \(-0.242123\pi\) | ||||
0.724386 | + | 0.689394i | \(0.242123\pi\) | |||||||
\(888\) | 250.641i | 0.282253i | ||||||||
\(889\) | 327.311 | + | 327.311i | 0.368179 | + | 0.368179i | ||||
\(890\) | −467.138 | − | 467.138i | −0.524875 | − | 0.524875i | ||||
\(891\) | 96.5885 | − | 96.5885i | 0.108405 | − | 0.108405i | ||||
\(892\) | 65.0615 | − | 65.0615i | 0.0729389 | − | 0.0729389i | ||||
\(893\) | −307.608 | −0.344466 | ||||||||
\(894\) | 388.708i | 0.434796i | ||||||||
\(895\) | 237.646 | − | 237.646i | 0.265526 | − | 0.265526i | ||||
\(896\) | − | 29.2820i | − | 0.0326808i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −186.613 | −0.207809 | ||||||||
\(899\) | −533.993 | − | 533.993i | −0.593986 | − | 0.593986i | ||||
\(900\) | −118.708 | −0.131897 | ||||||||
\(901\) | − | 495.384i | − | 0.549816i | ||||||
\(902\) | 649.261 | + | 649.261i | 0.719802 | + | 0.719802i | ||||
\(903\) | 103.529 | + | 103.529i | 0.114650 | + | 0.114650i | ||||
\(904\) | −173.569 | + | 173.569i | −0.192001 | + | 0.192001i | ||||
\(905\) | −1430.75 | + | 1430.75i | −1.58094 | + | 1.58094i | ||||
\(906\) | 550.659 | 0.607791 | ||||||||
\(907\) | 278.862i | 0.307455i | 0.988113 | + | 0.153727i | \(0.0491278\pi\) | ||||
−0.988113 | + | 0.153727i | \(0.950872\pi\) | |||||||
\(908\) | 19.4256 | − | 19.4256i | 0.0213939 | − | 0.0213939i | ||||
\(909\) | 416.438i | 0.458128i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 86.7668 | 0.0952434 | 0.0476217 | − | 0.998865i | \(-0.484836\pi\) | ||||
0.0476217 | + | 0.998865i | \(0.484836\pi\) | |||||||
\(912\) | 18.0666 | + | 18.0666i | 0.0198099 | + | 0.0198099i | ||||
\(913\) | −450.031 | −0.492914 | ||||||||
\(914\) | 417.037i | 0.456277i | ||||||||
\(915\) | −649.965 | − | 649.965i | −0.710345 | − | 0.710345i | ||||
\(916\) | −574.631 | − | 574.631i | −0.627326 | − | 0.627326i | ||||
\(917\) | −98.1604 | + | 98.1604i | −0.107045 | + | 0.107045i | ||||
\(918\) | 26.3538 | − | 26.3538i | 0.0287079 | − | 0.0287079i | ||||
\(919\) | 576.862 | 0.627706 | 0.313853 | − | 0.949472i | \(-0.398380\pi\) | ||||
0.313853 | + | 0.949472i | \(0.398380\pi\) | |||||||
\(920\) | − | 602.985i | − | 0.655418i | ||||||
\(921\) | −121.362 | + | 121.362i | −0.131772 | + | 0.131772i | ||||
\(922\) | 664.246i | 0.720440i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 136.077 | 0.147269 | ||||||||
\(925\) | 715.746 | + | 715.746i | 0.773780 | + | 0.773780i | ||||
\(926\) | 925.199 | 0.999134 | ||||||||
\(927\) | − | 321.788i | − | 0.347129i | ||||||
\(928\) | 69.2820 | + | 69.2820i | 0.0746574 | + | 0.0746574i | ||||
\(929\) | −10.5434 | − | 10.5434i | −0.0113492 | − | 0.0113492i | 0.701409 | − | 0.712759i | \(-0.252555\pi\) |
−0.712759 | + | 0.701409i | \(0.752555\pi\) | |||||||
\(930\) | 505.377 | − | 505.377i | 0.543416 | − | 0.543416i | ||||
\(931\) | −110.309 | + | 110.309i | −0.118484 | + | 0.118484i | ||||
\(932\) | −54.6616 | −0.0586498 | ||||||||
\(933\) | − | 242.900i | − | 0.260343i | ||||||
\(934\) | −396.649 | + | 396.649i | −0.424677 | + | 0.424677i | ||||
\(935\) | − | 515.138i | − | 0.550950i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 700.477 | 0.747574 | 0.373787 | − | 0.927515i | \(-0.378059\pi\) | ||||
0.373787 | + | 0.927515i | \(0.378059\pi\) | |||||||
\(938\) | −171.077 | − | 171.077i | −0.182385 | − | 0.182385i | ||||
\(939\) | 953.123 | 1.01504 | ||||||||
\(940\) | − | 1116.40i | − | 1.18766i | ||||||
\(941\) | 1147.05 | + | 1147.05i | 1.21897 | + | 1.21897i | 0.967992 | + | 0.250983i | \(0.0807538\pi\) |
0.250983 | + | 0.967992i | \(0.419246\pi\) | |||||||
\(942\) | 240.009 | + | 240.009i | 0.254787 | + | 0.254787i | ||||
\(943\) | −963.615 | + | 963.615i | −1.02186 | + | 1.02186i | ||||
\(944\) | −173.072 | + | 173.072i | −0.183339 | + | 0.183339i | ||||
\(945\) | 90.0000 | 0.0952381 | ||||||||
\(946\) | − | 701.023i | − | 0.741039i | ||||||
\(947\) | −868.526 | + | 868.526i | −0.917134 | + | 0.917134i | −0.996820 | − | 0.0796863i | \(-0.974608\pi\) |
0.0796863 | + | 0.996820i | \(0.474608\pi\) | |||||||
\(948\) | − | 125.138i | − | 0.132003i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 103.184 | 0.108615 | ||||||||
\(951\) | −54.1999 | − | 54.1999i | −0.0569926 | − | 0.0569926i | ||||
\(952\) | 37.1281 | 0.0390001 | ||||||||
\(953\) | − | 1086.62i | − | 1.14021i | −0.821573 | − | 0.570104i | \(-0.806903\pi\) | ||
0.821573 | − | 0.570104i | \(-0.193097\pi\) | |||||||
\(954\) | −293.023 | − | 293.023i | −0.307152 | − | 0.307152i | ||||
\(955\) | 769.808 | + | 769.808i | 0.806081 | + | 0.806081i | ||||
\(956\) | −1.72312 | + | 1.72312i | −0.00180243 | + | 0.00180243i | ||||
\(957\) | −321.962 | + | 321.962i | −0.336428 | + | 0.336428i | ||||
\(958\) | 509.072 | 0.531390 | ||||||||
\(959\) | − | 320.141i | − | 0.333828i | ||||||
\(960\) | −65.5692 | + | 65.5692i | −0.0683013 | + | 0.0683013i | ||||
\(961\) | 939.993i | 0.978141i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.5077 | 0.0171420 | ||||||||
\(964\) | 120.354 | + | 120.354i | 0.124848 | + | 0.124848i | ||||
\(965\) | −550.344 | −0.570304 | ||||||||
\(966\) | 201.962i | 0.209070i | ||||||||
\(967\) | −827.831 | − | 827.831i | −0.856081 | − | 0.856081i | 0.134793 | − | 0.990874i | \(-0.456963\pi\) |
−0.990874 | + | 0.134793i | \(0.956963\pi\) | |||||||
\(968\) | −218.708 | − | 218.708i | −0.225938 | − | 0.225938i | ||||
\(969\) | −22.9076 | + | 22.9076i | −0.0236404 | + | 0.0236404i | ||||
\(970\) | −122.918 | + | 122.918i | −0.126719 | + | 0.126719i | ||||
\(971\) | −1143.70 | −1.17786 | −0.588929 | − | 0.808185i | \(-0.700450\pi\) | ||||
−0.588929 | + | 0.808185i | \(0.700450\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −281.305 | + | 281.305i | −0.289111 | + | 0.289111i | ||||
\(974\) | − | 274.000i | − | 0.281314i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −317.205 | −0.325005 | ||||||||
\(977\) | 243.033 | + | 243.033i | 0.248755 | + | 0.248755i | 0.820459 | − | 0.571705i | \(-0.193718\pi\) |
−0.571705 | + | 0.820459i | \(0.693718\pi\) | |||||||
\(978\) | 687.093 | 0.702550 | ||||||||
\(979\) | − | 1059.45i | − | 1.08217i | ||||||
\(980\) | −400.344 | − | 400.344i | −0.408514 | − | 0.408514i | ||||
\(981\) | −326.433 | − | 326.433i | −0.332755 | − | 0.332755i | ||||
\(982\) | −23.0718 | + | 23.0718i | −0.0234947 | + | 0.0234947i | ||||
\(983\) | −630.073 | + | 630.073i | −0.640970 | + | 0.640970i | −0.950794 | − | 0.309824i | \(-0.899730\pi\) |
0.309824 | + | 0.950794i | \(0.399730\pi\) | |||||||
\(984\) | 209.569 | 0.212977 | ||||||||
\(985\) | 1807.23i | 1.83475i | ||||||||
\(986\) | −87.8461 | + | 87.8461i | −0.0890934 | + | 0.0890934i | ||||
\(987\) | 373.923i | 0.378848i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1040.44 | 1.05201 | ||||||||
\(990\) | −304.708 | − | 304.708i | −0.307786 | − | 0.307786i | ||||
\(991\) | −956.739 | −0.965427 | −0.482714 | − | 0.875778i | \(-0.660349\pi\) | ||||
−0.482714 | + | 0.875778i | \(0.660349\pi\) | |||||||
\(992\) | − | 246.641i | − | 0.248630i | ||||||
\(993\) | −494.715 | − | 494.715i | −0.498202 | − | 0.498202i | ||||
\(994\) | 138.897 | + | 138.897i | 0.139736 | + | 0.139736i | ||||
\(995\) | 301.832 | − | 301.832i | 0.303349 | − | 0.303349i | ||||
\(996\) | −72.6307 | + | 72.6307i | −0.0729224 | + | 0.0729224i | ||||
\(997\) | −167.169 | −0.167672 | −0.0838360 | − | 0.996480i | \(-0.526717\pi\) | ||||
−0.0838360 | + | 0.996480i | \(0.526717\pi\) | |||||||
\(998\) | − | 321.538i | − | 0.322183i | ||||||
\(999\) | −187.981 | + | 187.981i | −0.188169 | + | 0.188169i |
(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 | 1014.3.f.d.775.1 | 4 | ||
13.5 | odd | 4 | inner | 1014.3.f.d.577.1 | 4 | ||
13.7 | odd | 12 | 78.3.l.a.67.1 | yes | 4 | ||
13.8 | odd | 4 | 1014.3.f.e.577.1 | 4 | |||
13.10 | even | 6 | 78.3.l.a.7.1 | ✓ | 4 | ||
13.12 | even | 2 | 1014.3.f.e.775.1 | 4 | |||
39.20 | even | 12 | 234.3.bb.c.145.1 | 4 | |||
39.23 | odd | 6 | 234.3.bb.c.163.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.l.a.7.1 | ✓ | 4 | 13.10 | even | 6 | ||
78.3.l.a.67.1 | yes | 4 | 13.7 | odd | 12 | ||
234.3.bb.c.145.1 | 4 | 39.20 | even | 12 | |||
234.3.bb.c.163.1 | 4 | 39.23 | odd | 6 | |||
1014.3.f.d.577.1 | 4 | 13.5 | odd | 4 | inner | ||
1014.3.f.d.775.1 | 4 | 1.1 | even | 1 | trivial | ||
1014.3.f.e.577.1 | 4 | 13.8 | odd | 4 | |||
1014.3.f.e.775.1 | 4 | 13.12 | even | 2 |