Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,3,Mod(161,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.l (of order \(2\), degree \(1\), 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: | \(6.53952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.681615360000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + 49x^{4} - 136x^{3} + 168x^{2} - 96x + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.8 | ||
Root | \(3.22255 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.161 |
Dual form | 240.3.l.d.161.7 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.87275 | + | 0.864473i | 0.957583 | + | 0.288158i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.02416 | −1.28917 | −0.644583 | − | 0.764535i | \(-0.722969\pi\) | ||||
−0.644583 | + | 0.764535i | \(0.722969\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.50537 | + | 4.96683i | 0.833930 | + | 0.551870i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.8827i | 1.98934i | 0.103119 | + | 0.994669i | \(0.467118\pi\) | ||||
−0.103119 | + | 0.994669i | \(0.532882\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.6599 | 1.66614 | 0.833071 | − | 0.553166i | \(-0.186580\pi\) | ||||
0.833071 | + | 0.553166i | \(0.186580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.93302 | + | 6.42366i | −0.128868 | + | 0.428244i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.1078i | 0.712221i | 0.934444 | + | 0.356111i | \(0.115897\pi\) | ||||
−0.934444 | + | 0.356111i | \(0.884103\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.03757 | −0.159872 | −0.0799361 | − | 0.996800i | \(-0.525472\pi\) | ||||
−0.0799361 | + | 0.996800i | \(0.525472\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −25.9241 | − | 7.80114i | −1.23448 | − | 0.371483i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 28.5735i | − | 1.24233i | −0.783681 | − | 0.621164i | \(-0.786660\pi\) | ||
0.783681 | − | 0.621164i | \(-0.213340\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.2674 | + | 20.7566i | 0.639532 | + | 0.768765i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 12.0364i | − | 0.415047i | −0.978230 | − | 0.207523i | \(-0.933460\pi\) | ||
0.978230 | − | 0.207523i | \(-0.0665403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.19085 | −0.0706725 | −0.0353363 | − | 0.999375i | \(-0.511250\pi\) | ||||
−0.0353363 | + | 0.999375i | \(0.511250\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18.9170 | + | 62.8636i | −0.573243 | + | 1.90496i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 20.1786i | − | 0.576532i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.839959 | 0.0227016 | 0.0113508 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113508 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 62.2233 | + | 18.7244i | 1.59547 | + | 0.480112i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 35.5690i | − | 0.867537i | −0.901024 | − | 0.433769i | \(-0.857184\pi\) | ||
0.901024 | − | 0.433769i | \(-0.142816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.7152 | 0.295702 | 0.147851 | − | 0.989010i | \(-0.452764\pi\) | ||||
0.147851 | + | 0.989010i | \(0.452764\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.1062 | + | 16.7825i | −0.246804 | + | 0.372945i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22.5481i | 0.479746i | 0.970804 | + | 0.239873i | \(0.0771058\pi\) | ||||
−0.970804 | + | 0.239873i | \(0.922894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 32.4354 | 0.661947 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.4668 | + | 34.7826i | −0.205232 | + | 0.682011i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.13775i | − | 0.172410i | −0.996277 | − | 0.0862052i | \(-0.972526\pi\) | ||
0.996277 | − | 0.0862052i | \(-0.0274741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −48.9312 | −0.889659 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.72618 | − | 2.62590i | −0.153091 | − | 0.0460684i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 80.4459i | − | 1.36349i | −0.731590 | − | 0.681745i | \(-0.761221\pi\) | ||
0.731590 | − | 0.681745i | \(-0.238779\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −57.8816 | −0.948878 | −0.474439 | − | 0.880288i | \(-0.657349\pi\) | ||||
−0.474439 | + | 0.880288i | \(0.657349\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −67.7297 | − | 44.8214i | −1.07507 | − | 0.711452i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 48.4329i | 0.745122i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 63.0560 | 0.941135 | 0.470567 | − | 0.882364i | \(-0.344049\pi\) | ||||
0.470567 | + | 0.882364i | \(0.344049\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.7011 | − | 82.0846i | 0.357986 | − | 1.18963i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17.0218i | 0.239743i | 0.992789 | + | 0.119872i | \(0.0382483\pi\) | ||||
−0.992789 | + | 0.119872i | \(0.961752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 52.1181 | 0.713947 | 0.356973 | − | 0.934115i | \(-0.383809\pi\) | ||||
0.356973 | + | 0.934115i | \(0.383809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.3637 | − | 4.32237i | −0.191517 | − | 0.0576316i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 197.473i | − | 2.56459i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.46224 | 0.0944588 | 0.0472294 | − | 0.998884i | \(-0.484961\pi\) | ||||
0.0472294 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31.6612 | + | 74.5558i | 0.390879 | + | 0.920442i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 82.3758i | − | 0.992480i | −0.868185 | − | 0.496240i | \(-0.834714\pi\) | ||
0.868185 | − | 0.496240i | \(-0.165286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27.0738 | −0.318515 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.4051 | − | 34.5774i | 0.119599 | − | 0.397442i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 27.5850i | 0.309944i | 0.987919 | + | 0.154972i | \(0.0495287\pi\) | ||||
−0.987919 | + | 0.154972i | \(0.950471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −195.462 | −2.14793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.29376 | − | 1.89393i | −0.0676748 | − | 0.0203648i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.79221i | − | 0.0714970i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 114.989 | 1.18545 | 0.592727 | − | 0.805404i | \(-0.298051\pi\) | ||||
0.592727 | + | 0.805404i | \(0.298051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −108.688 | + | 164.238i | −1.09786 | + | 1.65897i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 122.804i | − | 1.21588i | −0.793982 | − | 0.607941i | \(-0.791996\pi\) | ||
0.793982 | − | 0.607941i | \(-0.208004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 46.8275 | 0.454636 | 0.227318 | − | 0.973821i | \(-0.427004\pi\) | ||||
0.227318 | + | 0.973821i | \(0.427004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.4439 | − | 57.9681i | 0.166132 | − | 0.552077i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 105.086i | − | 0.982113i | −0.871128 | − | 0.491056i | \(-0.836611\pi\) | ||
0.871128 | − | 0.491056i | \(-0.163389\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −116.777 | −1.07135 | −0.535673 | − | 0.844426i | \(-0.679942\pi\) | ||||
−0.535673 | + | 0.844426i | \(0.679942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.41299 | + | 0.726122i | 0.0217387 | + | 0.00654164i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.8116i | − | 0.0956779i | −0.998855 | − | 0.0478389i | \(-0.984767\pi\) | ||
0.998855 | − | 0.0478389i | \(-0.0152334\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 63.8924 | 0.555586 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 162.565 | + | 107.581i | 1.38945 | + | 0.919494i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 109.262i | − | 0.918171i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −357.853 | −2.95747 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.7485 | − | 102.181i | 0.249988 | − | 0.830739i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 192.459 | 1.51543 | 0.757714 | − | 0.652587i | \(-0.226316\pi\) | ||||
0.757714 | + | 0.652587i | \(0.226316\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 36.5276 | + | 10.9919i | 0.283159 | + | 0.0852089i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 48.6360i | 0.371267i | 0.982619 | + | 0.185633i | \(0.0594337\pi\) | ||||
−0.982619 | + | 0.185633i | \(0.940566\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.4115 | 0.206102 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −46.4133 | + | 38.6110i | −0.343802 | + | 0.286007i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 157.869i | 1.15233i | 0.817335 | + | 0.576163i | \(0.195451\pi\) | ||||
−0.817335 | + | 0.576163i | \(0.804549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 164.752 | 1.18526 | 0.592632 | − | 0.805473i | \(-0.298089\pi\) | ||||
0.592632 | + | 0.805473i | \(0.298089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.4922 | + | 64.7749i | −0.138243 | + | 0.459397i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 473.977i | 3.31452i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.9141 | 0.185615 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 93.1788 | + | 28.0396i | 0.633869 | + | 0.190745i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 262.935i | 1.76467i | 0.470626 | + | 0.882333i | \(0.344028\pi\) | ||||
−0.470626 | + | 0.882333i | \(0.655972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8171 | −0.104749 | −0.0523745 | − | 0.998628i | \(-0.516679\pi\) | ||||
−0.0523745 | + | 0.998628i | \(0.516679\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −60.1372 | + | 90.8733i | −0.393054 | + | 0.593943i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.89889i | − | 0.0316057i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.11941 | −0.0389771 | −0.0194886 | − | 0.999810i | \(-0.506204\pi\) | ||||
−0.0194886 | + | 0.999810i | \(0.506204\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.89934 | − | 26.2505i | 0.0496814 | − | 0.165097i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 257.852i | 1.60157i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 170.444 | 1.04567 | 0.522833 | − | 0.852435i | \(-0.324875\pi\) | ||||
0.522833 | + | 0.852435i | \(0.324875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −140.567 | − | 42.2998i | −0.851922 | − | 0.256362i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 61.2668i | − | 0.366867i | −0.983032 | − | 0.183434i | \(-0.941279\pi\) | ||
0.983032 | − | 0.183434i | \(-0.0587212\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 300.149 | 1.77603 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.7981 | − | 15.0871i | −0.133322 | − | 0.0882286i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 262.548i | − | 1.51762i | −0.651312 | − | 0.758810i | \(-0.725781\pi\) | ||
0.651312 | − | 0.758810i | \(-0.274219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 45.1208 | 0.257833 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 69.5434 | − | 231.101i | 0.392900 | − | 1.30566i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.88752i | − | 0.0384778i | −0.999815 | − | 0.0192389i | \(-0.993876\pi\) | ||
0.999815 | − | 0.0192389i | \(-0.00612431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 218.536 | 1.20738 | 0.603691 | − | 0.797218i | \(-0.293696\pi\) | ||||
0.603691 | + | 0.797218i | \(0.293696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −166.279 | − | 50.0371i | −0.908630 | − | 0.273427i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.87821i | 0.0101525i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −264.951 | −1.41685 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −155.823 | − | 187.311i | −0.824462 | − | 0.991065i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 75.2506i | 0.393982i | 0.980405 | + | 0.196991i | \(0.0631170\pi\) | ||||
−0.980405 | + | 0.196991i | \(0.936883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −212.587 | −1.10149 | −0.550744 | − | 0.834674i | \(-0.685656\pi\) | ||||
−0.550744 | + | 0.834674i | \(0.685656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −41.8690 | + | 139.136i | −0.214713 | + | 0.713516i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 190.640i | 0.967718i | 0.875146 | + | 0.483859i | \(0.160765\pi\) | ||||
−0.875146 | + | 0.483859i | \(0.839235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −209.996 | −1.05526 | −0.527629 | − | 0.849475i | \(-0.676919\pi\) | ||||
−0.527629 | + | 0.849475i | \(0.676919\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 181.144 | + | 54.5102i | 0.901214 | + | 0.271195i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 108.618i | 0.535064i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 79.5348 | 0.387974 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 141.920 | − | 214.455i | 0.685603 | − | 1.03601i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 66.4703i | − | 0.318040i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −176.419 | −0.836110 | −0.418055 | − | 0.908422i | \(-0.637288\pi\) | ||||
−0.418055 | + | 0.908422i | \(0.637288\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.7149 | + | 48.8993i | −0.0690839 | + | 0.229574i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.4320i | 0.132242i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.7706 | 0.0911086 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 149.722 | + | 45.0547i | 0.683663 | + | 0.205729i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 262.252i | 1.18666i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −132.362 | −0.593552 | −0.296776 | − | 0.954947i | \(-0.595911\pi\) | ||||
−0.296776 | + | 0.954947i | \(0.595911\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −37.5269 | − | 24.8341i | −0.166786 | − | 0.110374i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 187.624i | 0.826537i | 0.910609 | + | 0.413268i | \(0.135613\pi\) | ||||
−0.910609 | + | 0.413268i | \(0.864387\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −178.571 | −0.779788 | −0.389894 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389894 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 170.710 | − | 567.291i | 0.739005 | − | 2.45580i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 296.711i | − | 1.27344i | −0.771097 | − | 0.636718i | \(-0.780292\pi\) | ||
0.771097 | − | 0.636718i | \(-0.219708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −50.4190 | −0.214549 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.4371 | + | 6.45091i | 0.0904521 | + | 0.0272190i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 137.976i | 0.577306i | 0.957434 | + | 0.288653i | \(0.0932074\pi\) | ||||
−0.957434 | + | 0.288653i | \(0.906793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 42.5687 | 0.176633 | 0.0883167 | − | 0.996092i | \(-0.471851\pi\) | ||||
0.0883167 | + | 0.996092i | \(0.471851\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 26.5032 | + | 241.550i | 0.109067 | + | 0.994034i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 72.5278i | 0.296032i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −65.7933 | −0.266370 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 71.2117 | − | 236.645i | 0.285991 | − | 0.950382i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 205.885i | − | 0.820259i | −0.912027 | − | 0.410130i | \(-0.865483\pi\) | ||
0.912027 | − | 0.410130i | \(-0.134517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 625.267 | 2.47141 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −77.7762 | − | 23.4046i | −0.305005 | − | 0.0917826i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 188.382i | − | 0.733004i | −0.930417 | − | 0.366502i | \(-0.880555\pi\) | ||
0.930417 | − | 0.366502i | \(-0.119445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.57992 | −0.0292661 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 59.7825 | − | 90.3373i | 0.229052 | − | 0.346120i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 188.745i | − | 0.717660i | −0.933403 | − | 0.358830i | \(-0.883176\pi\) | ||
0.933403 | − | 0.358830i | \(-0.116824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.4326 | 0.0771043 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.8465 | + | 79.2447i | −0.0893127 | + | 0.296797i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 333.372i | 1.23930i | 0.784878 | + | 0.619651i | \(0.212726\pi\) | ||||
−0.784878 | + | 0.619651i | \(0.787274\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −262.047 | −0.966964 | −0.483482 | − | 0.875354i | \(-0.660628\pi\) | ||||
−0.483482 | + | 0.875354i | \(0.660628\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −561.513 | − | 168.972i | −2.05682 | − | 0.618944i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 109.414i | − | 0.397868i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −400.100 | −1.44440 | −0.722202 | − | 0.691682i | \(-0.756870\pi\) | ||||
−0.722202 | + | 0.691682i | \(0.756870\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.4431 | − | 10.8816i | −0.0589360 | − | 0.0390020i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 350.698i | − | 1.24804i | −0.781410 | − | 0.624018i | \(-0.785499\pi\) | ||
0.781410 | − | 0.624018i | \(-0.214501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 464.015 | 1.63963 | 0.819814 | − | 0.572630i | \(-0.194077\pi\) | ||||
0.819814 | + | 0.572630i | \(0.194077\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.87169 | − | 19.5123i | 0.0206024 | − | 0.0684643i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 320.981i | 1.11840i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 142.402 | 0.492741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 330.334 | + | 99.4049i | 1.13517 | + | 0.341598i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 47.4080i | 0.161802i | 0.996722 | + | 0.0809009i | \(0.0257797\pi\) | ||||
−0.996722 | + | 0.0809009i | \(0.974220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 179.883 | 0.609771 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −454.212 | + | 377.857i | −1.52933 | + | 1.27224i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 618.899i | − | 2.06990i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −114.744 | −0.381209 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 106.161 | − | 352.785i | 0.350366 | − | 1.16431i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 129.427i | − | 0.424351i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −461.894 | −1.50454 | −0.752270 | − | 0.658855i | \(-0.771041\pi\) | ||||
−0.752270 | + | 0.658855i | \(0.771041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 134.524 | + | 40.4812i | 0.435352 | + | 0.131007i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 123.057i | 0.395681i | 0.980234 | + | 0.197841i | \(0.0633929\pi\) | ||||
−0.980234 | + | 0.197841i | \(0.936607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 97.4353 | 0.311295 | 0.155647 | − | 0.987813i | \(-0.450254\pi\) | ||||
0.155647 | + | 0.987813i | \(0.450254\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 100.224 | − | 151.448i | 0.318171 | − | 0.480788i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 252.388i | 0.796175i | 0.917347 | + | 0.398088i | \(0.130326\pi\) | ||||
−0.917347 | + | 0.398088i | \(0.869674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 263.388 | 0.825668 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 90.8441 | − | 301.886i | 0.283003 | − | 0.940454i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 36.7782i | − | 0.113864i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −108.299 | −0.333229 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −335.470 | − | 100.950i | −1.02590 | − | 0.308716i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 203.477i | − | 0.618472i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 303.273 | 0.916231 | 0.458116 | − | 0.888893i | \(-0.348525\pi\) | ||||
0.458116 | + | 0.888893i | \(0.348525\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.30420 | + | 4.17193i | 0.0189315 | + | 0.0125283i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 140.998i | 0.420888i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −352.738 | −1.04670 | −0.523350 | − | 0.852118i | \(-0.675318\pi\) | ||||
−0.523350 | + | 0.852118i | \(0.675318\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.34634 | − | 31.0590i | 0.0275703 | − | 0.0916195i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 47.9417i | − | 0.140592i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 149.481 | 0.435806 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 183.547 | + | 55.2332i | 0.532019 | + | 0.160096i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 280.382i | − | 0.808018i | −0.914755 | − | 0.404009i | \(-0.867616\pi\) | ||
0.914755 | − | 0.404009i | \(-0.132384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −586.721 | −1.68115 | −0.840575 | − | 0.541696i | \(-0.817783\pi\) | ||||
−0.840575 | + | 0.541696i | \(0.817783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 374.008 | + | 449.586i | 1.06555 | + | 1.28087i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 558.927i | 1.58336i | 0.610935 | + | 0.791681i | \(0.290794\pi\) | ||||
−0.610935 | + | 0.791681i | \(0.709206\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −38.0618 | −0.107216 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 94.4544 | − | 313.883i | 0.264578 | − | 0.879225i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 323.554i | 0.901264i | 0.892710 | + | 0.450632i | \(0.148801\pi\) | ||||
−0.892710 | + | 0.450632i | \(0.851199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −351.773 | −0.974441 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1028.02 | − | 309.355i | −2.83202 | − | 0.852217i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 116.540i | 0.319287i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −176.636 | −0.481296 | −0.240648 | − | 0.970612i | \(-0.577360\pi\) | ||||
−0.240648 | + | 0.970612i | \(0.577360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 176.665 | − | 266.959i | 0.478768 | − | 0.723466i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 82.4605i | 0.222265i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 367.327 | 0.984790 | 0.492395 | − | 0.870372i | \(-0.336122\pi\) | ||||
0.492395 | + | 0.870372i | \(0.336122\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.66511 | − | 32.1183i | 0.0257736 | − | 0.0856488i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 260.706i | − | 0.691527i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −611.014 | −1.61217 | −0.806087 | − | 0.591798i | \(-0.798418\pi\) | ||||
−0.806087 | + | 0.591798i | \(0.798418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 552.887 | + | 166.376i | 1.45115 | + | 0.436682i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6994i | 0.0357687i | 0.999840 | + | 0.0178844i | \(0.00569307\pi\) | ||||
−0.999840 | + | 0.0178844i | \(0.994307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 441.563 | 1.14692 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 95.4322 | + | 63.1542i | 0.246595 | + | 0.163189i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 379.601i | − | 0.975838i | −0.872889 | − | 0.487919i | \(-0.837756\pi\) | ||
0.872889 | − | 0.487919i | \(-0.162244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 345.962 | 0.884812 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −42.0445 | + | 139.719i | −0.106983 | + | 0.355519i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.6861i | 0.0422432i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 450.560 | 1.13491 | 0.567456 | − | 0.823404i | \(-0.307928\pi\) | ||||
0.567456 | + | 0.823404i | \(0.307928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 78.7464 | + | 23.6965i | 0.197359 | + | 0.0593898i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 503.683i | − | 1.25607i | −0.778186 | − | 0.628034i | \(-0.783860\pi\) | ||
0.778186 | − | 0.628034i | \(-0.216140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −47.4535 | −0.117751 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −166.712 | + | 70.7966i | −0.411634 | + | 0.174806i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.3806i | 0.0451611i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 240.726 | 0.588573 | 0.294286 | − | 0.955717i | \(-0.404918\pi\) | ||||
0.294286 | + | 0.955717i | \(0.404918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −136.473 | + | 453.517i | −0.332051 | + | 1.10345i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 725.957i | 1.75776i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 184.198 | 0.443850 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 473.290 | + | 142.423i | 1.13499 | + | 0.341543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 676.873i | 1.61545i | 0.589561 | + | 0.807724i | \(0.299301\pi\) | ||||
−0.589561 | + | 0.807724i | \(0.700699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 683.755 | 1.62412 | 0.812061 | − | 0.583572i | \(-0.198346\pi\) | ||||
0.812061 | + | 0.583572i | \(0.198346\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −111.992 | + | 169.232i | −0.264757 | + | 0.400075i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 60.5388i | − | 0.142444i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 522.332 | 1.22326 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −409.740 | + | 1361.62i | −0.955105 | + | 3.17393i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 213.608i | 0.495610i | 0.968810 | + | 0.247805i | \(0.0797092\pi\) | ||||
−0.968810 | + | 0.247805i | \(0.920291\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −383.579 | −0.885864 | −0.442932 | − | 0.896555i | \(-0.646062\pi\) | ||||
−0.442932 | + | 0.896555i | \(0.646062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 77.3175 | + | 23.2665i | 0.177741 | + | 0.0534863i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 86.7941i | 0.198614i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −523.900 | −1.19340 | −0.596698 | − | 0.802466i | \(-0.703521\pi\) | ||||
−0.596698 | + | 0.802466i | \(0.703521\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 243.440 | + | 161.101i | 0.552018 | + | 0.365309i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 391.277i | − | 0.883243i | −0.897201 | − | 0.441622i | \(-0.854403\pi\) | ||
0.897201 | − | 0.441622i | \(-0.145597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −61.6819 | −0.138611 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −227.301 | + | 755.347i | −0.508502 | + | 1.68981i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 375.014i | 0.835220i | 0.908626 | + | 0.417610i | \(0.137132\pi\) | ||||
−0.908626 | + | 0.417610i | \(0.862868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 778.347 | 1.72582 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −45.4386 | − | 13.6735i | −0.100306 | − | 0.0301843i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 437.066i | − | 0.960585i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −734.032 | −1.60620 | −0.803098 | − | 0.595847i | \(-0.796817\pi\) | ||||
−0.803098 | + | 0.595847i | \(0.796817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −251.317 | + | 209.069i | −0.547531 | + | 0.455488i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 775.239i | − | 1.68165i | −0.541310 | − | 0.840823i | \(-0.682072\pi\) | ||
0.541310 | − | 0.840823i | \(-0.317928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 323.967 | 0.699714 | 0.349857 | − | 0.936803i | \(-0.386230\pi\) | ||||
0.349857 | + | 0.936803i | \(0.386230\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.23496 | − | 14.0733i | 0.00910743 | − | 0.0302651i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 160.785i | 0.344294i | 0.985071 | + | 0.172147i | \(0.0550704\pi\) | ||||
−0.985071 | + | 0.172147i | \(0.944930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −569.027 | −1.21328 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.5795 | − | 5.29007i | −0.0373239 | − | 0.0112316i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 278.243i | 0.588252i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.1879 | 0.0319744 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 45.3856 | − | 68.5822i | 0.0951481 | − | 0.143778i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 61.7565i | 0.128928i | 0.997920 | + | 0.0644640i | \(0.0205338\pi\) | ||||
−0.997920 | + | 0.0644640i | \(0.979466\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1934 | 0.0378241 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −222.906 | + | 740.744i | −0.461504 | + | 1.53363i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 257.123i | 0.530151i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −129.969 | −0.266876 | −0.133438 | − | 0.991057i | \(-0.542602\pi\) | ||||
−0.133438 | + | 0.991057i | \(0.542602\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 489.642 | + | 147.344i | 1.00131 | + | 0.301317i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 810.511i | − | 1.65074i | −0.564595 | − | 0.825368i | \(-0.690968\pi\) | ||
0.564595 | − | 0.825368i | \(-0.309032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 145.733 | 0.295605 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −367.247 | − | 243.033i | −0.741914 | − | 0.490976i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 153.607i | − | 0.309069i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 600.897 | 1.20420 | 0.602101 | − | 0.798420i | \(-0.294330\pi\) | ||||
0.602101 | + | 0.798420i | \(0.294330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 52.9635 | − | 176.004i | 0.105716 | − | 0.351306i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 688.332i | − | 1.36845i | −0.729270 | − | 0.684226i | \(-0.760140\pi\) | ||
0.729270 | − | 0.684226i | \(-0.239860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 274.598 | 0.543759 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 862.254 | + | 259.471i | 1.70070 | + | 0.511777i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 823.791i | − | 1.61845i | −0.587498 | − | 0.809225i | \(-0.699887\pi\) | ||
0.587498 | − | 0.809225i | \(-0.300113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −470.322 | −0.920395 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −52.4508 | − | 63.0498i | −0.102243 | − | 0.122904i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 104.710i | 0.203320i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −493.413 | −0.954377 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 226.966 | − | 754.235i | 0.437314 | − | 1.45325i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 964.525i | 1.85130i | 0.378386 | + | 0.925648i | \(0.376479\pi\) | ||||
−0.378386 | + | 0.925648i | \(0.623521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −462.679 | −0.884664 | −0.442332 | − | 0.896851i | \(-0.645849\pi\) | ||||
−0.442332 | + | 0.896851i | \(0.645849\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 129.621 | + | 39.0057i | 0.246897 | + | 0.0742966i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 26.5263i | − | 0.0503345i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −287.447 | −0.543378 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 399.561 | − | 603.777i | 0.752469 | − | 1.13706i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 770.420i | − | 1.44544i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 234.980 | 0.439214 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.95408 | − | 19.7861i | 0.0110877 | − | 0.0368457i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 709.775i | 1.31684i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −516.752 | −0.955180 | −0.477590 | − | 0.878583i | \(-0.658490\pi\) | ||||
−0.477590 | + | 0.878583i | \(0.658490\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 627.800 | + | 188.919i | 1.15617 | + | 0.347917i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 261.120i | − | 0.479120i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −478.953 | −0.875599 | −0.437799 | − | 0.899073i | \(-0.644242\pi\) | ||||
−0.437799 | + | 0.899073i | \(0.644242\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −434.423 | − | 287.488i | −0.791298 | − | 0.523657i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.5613i | 0.0663544i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −67.3404 | −0.121773 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.62366 | + | 5.39561i | −0.00292551 | + | 0.00972182i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 343.982i | − | 0.617561i | −0.951133 | − | 0.308781i | \(-0.900079\pi\) | ||
0.951133 | − | 0.308781i | \(-0.0999209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 275.409 | 0.492682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −761.137 | − | 229.043i | −1.35675 | − | 0.408276i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 394.056i | − | 0.699922i | −0.936764 | − | 0.349961i | \(-0.886195\pi\) | ||
0.936764 | − | 0.349961i | \(-0.113805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.1755 | 0.0427885 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −285.716 | − | 672.803i | −0.503908 | − | 1.18660i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 537.452i | − | 0.944556i | −0.881450 | − | 0.472278i | \(-0.843432\pi\) | ||
0.881450 | − | 0.472278i | \(-0.156568\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −710.555 | −1.24440 | −0.622202 | − | 0.782856i | \(-0.713762\pi\) | ||||
−0.622202 | + | 0.782856i | \(0.713762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −65.0521 | + | 216.176i | −0.113529 | + | 0.377271i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 142.868i | 0.248466i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 452.846 | 0.784828 | 0.392414 | − | 0.919789i | \(-0.371640\pi\) | ||||
0.392414 | + | 0.919789i | \(0.371640\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −610.709 | − | 183.776i | −1.05477 | − | 0.317402i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 743.372i | 1.27947i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 199.959 | 0.342983 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −240.558 | + | 363.507i | −0.411210 | + | 0.621379i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1103.34i | − | 1.87963i | −0.341690 | − | 0.939813i | \(-0.610999\pi\) | ||
0.341690 | − | 0.939813i | \(-0.389001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.65486 | 0.0112986 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −164.804 | + | 547.662i | −0.278855 | + | 0.926670i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 249.474i | 0.420698i | 0.977626 | + | 0.210349i | \(0.0674601\pi\) | ||||
−0.977626 | + | 0.210349i | \(0.932540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 244.318 | 0.410619 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −603.267 | − | 181.536i | −1.01050 | − | 0.304081i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 596.120i | − | 0.995191i | −0.867409 | − | 0.497596i | \(-0.834216\pi\) | ||
0.867409 | − | 0.497596i | \(-0.165784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 476.515 | 0.792871 | 0.396435 | − | 0.918063i | \(-0.370247\pi\) | ||||
0.396435 | + | 0.918063i | \(0.370247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 473.259 | + | 313.188i | 0.784841 | + | 0.519384i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 800.185i | − | 1.32262i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.8813 | −0.0459329 | −0.0229664 | − | 0.999736i | \(-0.507311\pi\) | ||||
−0.0229664 | + | 0.999736i | \(0.507311\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −93.8973 | + | 312.032i | −0.154183 | + | 0.512368i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 488.388i | 0.799325i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 465.472 | 0.759334 | 0.379667 | − | 0.925123i | \(-0.376039\pi\) | ||||
0.379667 | + | 0.925123i | \(0.376039\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 228.483 | + | 68.7557i | 0.371518 | + | 0.111798i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 48.6709i | − | 0.0788832i | −0.999222 | − | 0.0394416i | \(-0.987442\pi\) | ||
0.999222 | − | 0.0394416i | \(-0.0125579\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 213.318 | 0.344617 | 0.172309 | − | 0.985043i | \(-0.444877\pi\) | ||||
0.172309 | + | 0.985043i | \(0.444877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 593.091 | − | 493.389i | 0.955058 | − | 0.794508i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 248.931i | − | 0.399569i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 57.4618 | − | 190.953i | 0.0916456 | − | 0.304549i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1700i | 0.0161686i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −582.489 | −0.923121 | −0.461560 | − | 0.887109i | \(-0.652710\pi\) | ||||
−0.461560 | + | 0.887109i | \(0.652710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −506.808 | − | 152.510i | −0.800644 | − | 0.240931i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 430.352i | 0.677720i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 702.546 | 1.10290 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −84.5442 | + | 127.755i | −0.132307 | + | 0.199929i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 319.635i | 0.498650i | 0.968420 | + | 0.249325i | \(0.0802088\pi\) | ||||
−0.968420 | + | 0.249325i | \(0.919791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −458.627 | −0.713261 | −0.356630 | − | 0.934246i | \(-0.616074\pi\) | ||||
−0.356630 | + | 0.934246i | \(0.616074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.5787 | + | 81.6781i | −0.0381066 | + | 0.126633i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 507.599i | 0.784543i | 0.919850 | + | 0.392271i | \(0.128311\pi\) | ||||
−0.919850 | + | 0.392271i | \(0.871689\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1760.38 | 2.71244 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 56.7959 | + | 17.0911i | 0.0872440 | + | 0.0262536i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1197.20i | − | 1.83339i | −0.399591 | − | 0.916694i | \(-0.630848\pi\) | ||
0.399591 | − | 0.916694i | \(-0.369152\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −108.753 | −0.166036 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 391.166 | + | 258.862i | 0.595382 | + | 0.394006i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 632.173i | − | 0.959291i | −0.877462 | − | 0.479645i | \(-0.840765\pi\) | ||
0.877462 | − | 0.479645i | \(-0.159235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −565.316 | −0.855243 | −0.427622 | − | 0.903958i | \(-0.640648\pi\) | ||||
−0.427622 | + | 0.903958i | \(0.640648\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −226.710 | + | 753.385i | −0.341946 | + | 1.13633i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 61.2940i | 0.0921715i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −343.921 | −0.515624 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −380.243 | − | 114.423i | −0.568375 | − | 0.171036i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1266.61i | − | 1.88764i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −306.607 | −0.455582 | −0.227791 | − | 0.973710i | \(-0.573150\pi\) | ||||
−0.227791 | + | 0.973710i | \(0.573150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −86.3368 | − | 103.783i | −0.127906 | − | 0.153753i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 546.672i | 0.807491i | 0.914871 | + | 0.403746i | \(0.132292\pi\) | ||||
−0.914871 | + | 0.403746i | \(0.867708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1037.68 | −1.52824 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −162.196 | + | 538.996i | −0.238173 | + | 0.791478i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 812.204i | 1.18917i | 0.804032 | + | 0.594586i | \(0.202684\pi\) | ||||
−0.804032 | + | 0.594586i | \(0.797316\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −353.005 | −0.515335 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −512.991 | − | 154.370i | −0.746712 | − | 0.224702i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 197.922i | − | 0.287260i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.9358 | 0.0664773 | 0.0332387 | − | 0.999447i | \(-0.489418\pi\) | ||||
0.0332387 | + | 0.999447i | \(0.489418\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 980.815 | − | 1482.11i | 1.41532 | − | 2.13869i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 368.396i | 0.530066i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 430.661 | 0.617879 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 256.498 | − | 852.375i | 0.366950 | − | 1.21942i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 674.615i | − | 0.962360i | −0.876622 | − | 0.481180i | \(-0.840208\pi\) | ||
0.876622 | − | 0.481180i | \(-0.159792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.55143 | −0.00362935 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −144.841 | − | 43.5859i | −0.205448 | − | 0.0618240i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1108.20i | 1.56747i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 656.626 | 0.926129 | 0.463065 | − | 0.886324i | \(-0.346750\pi\) | ||||
0.463065 | + | 0.886324i | \(0.346750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 56.0069 | + | 37.0637i | 0.0787720 | + | 0.0521290i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 62.6003i | 0.0877984i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1059.84 | −1.48230 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −119.277 | + | 396.371i | −0.166355 | + | 0.552819i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 644.279i | 0.896076i | 0.894014 | + | 0.448038i | \(0.147877\pi\) | ||||
−0.894014 | + | 0.448038i | \(0.852123\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −422.579 | −0.586101 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 122.289 | + | 36.7995i | 0.169141 | + | 0.0508983i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 60.1818i | 0.0830094i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 981.269 | 1.34975 | 0.674875 | − | 0.737932i | \(-0.264197\pi\) | ||||
0.674875 | + | 0.737932i | \(0.264197\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −132.677 | + | 716.825i | −0.181998 | + | 0.983299i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 153.953i | 0.210605i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −127.756 | −0.174292 | −0.0871460 | − | 0.996196i | \(-0.527775\pi\) | ||||
−0.0871460 | + | 0.996196i | \(0.527775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −62.6983 | + | 208.354i | −0.0853039 | + | 0.283475i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1379.84i | 1.87223i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1401.59 | 1.89660 | 0.948302 | − | 0.317368i | \(-0.102799\pi\) | ||||
0.948302 | + | 0.317368i | \(0.102799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −189.008 | − | 56.8766i | −0.255071 | − | 0.0767565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6734i | 0.0157112i | 0.999969 | + | 0.00785561i | \(0.00250055\pi\) | ||||
−0.999969 | + | 0.00785561i | \(0.997499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −587.941 | −0.789183 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 409.147 | − | 618.261i | 0.547720 | − | 0.827659i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 948.313i | 1.26611i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −380.403 | −0.506529 | −0.253264 | − | 0.967397i | \(-0.581504\pi\) | ||||
−0.253264 | + | 0.967397i | \(0.581504\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 177.982 | − | 591.456i | 0.236364 | − | 0.785466i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 35.3681i | − | 0.0468452i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 63.6621 | 0.0840979 | 0.0420490 | − | 0.999116i | \(-0.486611\pi\) | ||||
0.0420490 | + | 0.999116i | \(0.486611\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1796.23 | + | 540.526i | 2.36658 | + | 0.712156i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 377.891i | 0.496571i | 0.968687 | + | 0.248286i | \(0.0798671\pi\) | ||||
−0.968687 | + | 0.248286i | \(0.920133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1053.81 | 1.38114 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −203.199 | − | 134.471i | −0.265619 | − | 0.175779i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1742.45i | − | 2.27177i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 231.920 | 0.301586 | 0.150793 | − | 0.988565i | \(-0.451817\pi\) | ||||
0.150793 | + | 0.988565i | \(0.451817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 162.851 | − | 541.174i | 0.211221 | − | 0.701912i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1509.05i | 1.95220i | 0.217320 | + | 0.976101i | \(0.430269\pi\) | ||||
−0.217320 | + | 0.976101i | \(0.569731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9542 | 0.0141345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.7752 | − | 6.55264i | −0.0280247 | − | 0.00843326i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 108.043i | 0.138695i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −372.483 | −0.476930 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 249.834 | − | 207.836i | 0.319073 | − | 0.265436i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 13.6834i | − | 0.0174311i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1171.43 | −1.48848 | −0.744240 | − | 0.667912i | \(-0.767188\pi\) | ||||
−0.744240 | + | 0.667912i | \(0.767188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 163.165 | − | 542.216i | 0.206799 | − | 0.687219i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 97.5656i | 0.123345i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1253.71 | −1.58097 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 58.6978 | + | 17.6635i | 0.0738337 | + | 0.0222182i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 988.589i | − | 1.24039i | −0.784448 | − | 0.620194i | \(-0.787054\pi\) | ||
0.784448 | − | 0.620194i | \(-0.212946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −273.007 | −0.341685 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −137.010 | + | 207.036i | −0.171049 | + | 0.258471i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1140.49i | 1.42028i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −576.575 | −0.716242 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −288.191 | + | 957.694i | −0.357114 | + | 1.18673i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1334.53i | − | 1.64961i | −0.565419 | − | 0.824804i | \(-0.691286\pi\) | ||
0.565419 | − | 0.824804i | \(-0.308714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −610.590 | −0.752885 | −0.376443 | − | 0.926440i | \(-0.622853\pi\) | ||||
−0.376443 | + | 0.926440i | \(0.622853\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −752.796 | − | 226.533i | −0.925949 | − | 0.278638i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 381.123i | 0.467636i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.6233 | −0.0472745 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1467.01 | − | 970.826i | −1.79123 | − | 1.18538i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 877.538i | 1.06887i | 0.845211 | + | 0.534433i | \(0.179475\pi\) | ||||
−0.845211 | + | 0.534433i | \(0.820525\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −230.855 | −0.280504 | −0.140252 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140252 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 94.5851 | − | 314.318i | 0.114649 | − | 0.380991i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 969.434i | 1.17223i | 0.810228 | + | 0.586115i | \(0.199343\pi\) | ||||
−0.810228 | + | 0.586115i | \(0.800657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1049.09 | −1.26549 | −0.632746 | − | 0.774360i | \(-0.718072\pi\) | ||||
−0.632746 | + | 0.774360i | \(0.718072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1149.39 | − | 345.876i | −1.38314 | − | 0.416216i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 392.720i | 0.471453i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 136.997 | 0.164068 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −37.8302 | − | 45.4747i | −0.0451973 | − | 0.0543305i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1214.62i | 1.44770i | 0.689959 | + | 0.723849i | \(0.257629\pi\) | ||||
−0.689959 | + | 0.723849i | \(0.742371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 696.126 | 0.827736 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 303.169 | − | 1007.47i | 0.359631 | − | 1.19510i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 671.154i | 0.794265i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3229.33 | 3.81266 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1333.00 | + | 401.128i | 1.57008 | + | 0.472472i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 24.0006i | − | 0.0282028i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 190.704 | 0.223569 | 0.111784 | − | 0.993732i | \(-0.464343\pi\) | ||||
0.111784 | + | 0.993732i | \(0.464343\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.7358 | − | 50.9781i | 0.0394570 | − | 0.0596235i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 351.238i | 0.409846i | 0.978778 | + | 0.204923i | \(0.0656944\pi\) | ||||
−0.978778 | + | 0.204923i | \(0.934306\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1233.74 | 1.43625 | 0.718123 | − | 0.695916i | \(-0.245002\pi\) | ||||
0.718123 | + | 0.695916i | \(0.245002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −277.479 | + | 922.096i | −0.322275 | + | 1.07096i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 463.404i | 0.536968i | 0.963284 | + | 0.268484i | \(0.0865227\pi\) | ||||
−0.963284 | + | 0.268484i | \(0.913477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 587.076 | 0.678700 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 409.085 | + | 123.103i | 0.471840 | + | 0.141987i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 163.294i | 0.187910i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1365.78 | 1.56806 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 863.035 | + | 571.130i | 0.988585 | + | 0.654216i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 100.893i | 0.115306i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 777.195 | 0.886197 | 0.443099 | − | 0.896473i | \(-0.353879\pi\) | ||||
0.443099 | + | 0.896473i | \(0.353879\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.9829 | + | 136.191i | −0.0466245 | + | 0.154939i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1609.50i | 1.82690i | 0.406951 | + | 0.913450i | \(0.366592\pi\) | ||||
−0.406951 | + | 0.913450i | \(0.633408\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −331.153 | −0.375032 | −0.187516 | − | 0.982262i | \(-0.560044\pi\) | ||||
−0.187516 | + | 0.982262i | \(0.560044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 516.757 | + | 155.504i | 0.583907 | + | 0.175710i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 365.778i | 0.412377i | 0.978512 | + | 0.206188i | \(0.0661060\pi\) | ||||
−0.978512 | + | 0.206188i | \(0.933894\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1736.78 | −1.95364 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1631.48 | + | 692.833i | −1.83107 | + | 0.777591i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 68.4913i | − | 0.0766980i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4010 | 0.0172078 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 535.021 | − | 1777.94i | 0.596456 | − | 1.98210i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.3698i | 0.0293324i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 110.638 | 0.122794 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −329.630 | − | 99.1930i | −0.365039 | − | 0.109848i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 488.662i | 0.539958i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 270.791 | 0.298556 | 0.149278 | − | 0.988795i | \(-0.452305\pi\) | ||||
0.149278 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 609.947 | − | 921.690i | 0.671008 | − | 1.01396i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1238.74i | 1.35976i | 0.733324 | + | 0.679879i | \(0.237968\pi\) | ||||
−0.733324 | + | 0.679879i | \(0.762032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1802.61 | 1.97438 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 111.886 | − | 371.812i | 0.122280 | − | 0.406352i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 438.898i | − | 0.478624i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −578.894 | −0.629918 | −0.314959 | − | 0.949105i | \(-0.601991\pi\) | ||||
−0.314959 | + | 0.949105i | \(0.601991\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1326.91 | − | 399.295i | −1.44072 | − | 0.433545i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 368.689i | 0.399447i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.19979 | −0.00454032 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 351.458 | + | 232.584i | 0.379135 | + | 0.250900i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1307.58i | 1.40752i | 0.710440 | + | 0.703758i | \(0.248496\pi\) | ||||
−0.710440 | + | 0.703758i | \(0.751504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −98.5249 | −0.105827 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −106.379 | + | 353.511i | −0.114019 | + | 0.378898i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 592.448i | − | 0.633634i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −693.314 | −0.739929 | −0.369965 | − | 0.929046i | \(-0.620630\pi\) | ||||
−0.369965 | + | 0.929046i | \(0.620630\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 279.907 | + | 84.2302i | 0.298091 | + | 0.0897020i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 783.592i | 0.832723i | 0.909199 | + | 0.416362i | \(0.136695\pi\) | ||||
−0.909199 | + | 0.416362i | \(0.863305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1016.33 | −1.07777 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 418.841 | − | 348.432i | 0.443218 | − | 0.368711i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1621.44i | − | 1.71219i | −0.516820 | − | 0.856094i | \(-0.672884\pi\) | ||
0.516820 | − | 0.856094i | \(-0.327116\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1128.87 | 1.18954 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −218.182 | + | 725.046i | −0.229424 | + | 0.762404i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1105.90i | − | 1.16044i | −0.814461 | − | 0.580218i | \(-0.802967\pi\) | ||
0.814461 | − | 0.580218i | \(-0.197033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −168.265 | −0.176194 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 756.648 | + | 227.692i | 0.790646 | + | 0.237923i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1424.63i | − | 1.48554i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −956.200 | −0.995005 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 521.945 | − | 788.710i | 0.541998 | − | 0.819013i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 475.359i | − | 0.492600i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1307.89 | −1.35253 | −0.676264 | − | 0.736659i | \(-0.736402\pi\) | ||||
−0.676264 | + | 0.736659i | \(0.736402\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.7938 | − | 105.655i | 0.0328109 | − | 0.109035i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 749.988i | 0.772387i | 0.922418 | + | 0.386194i | \(0.126210\pi\) | ||||
−0.922418 | + | 0.386194i | \(0.873790\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1486.75 | −1.52800 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −311.117 | − | 93.6218i | −0.319094 | − | 0.0960224i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 373.792i | − | 0.382591i | −0.981532 | − | 0.191296i | \(-0.938731\pi\) | ||
0.981532 | − | 0.191296i | \(-0.0612690\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −603.634 | −0.616583 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −876.452 | − | 580.009i | −0.893427 | − | 0.591243i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 27.7025i | − | 0.0281815i | −0.999901 | − | 0.0140908i | \(-0.995515\pi\) | ||
0.999901 | − | 0.0140908i | \(-0.00448538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −426.285 | −0.432777 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 175.901 | − | 584.539i | 0.178218 | − | 0.592238i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 363.318i | − | 0.367359i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1030.34 | −1.03970 | −0.519850 | − | 0.854258i | \(-0.674012\pi\) | ||||
−0.519850 | + | 0.854258i | \(0.674012\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 871.226 | + | 262.171i | 0.877367 | + | 0.264019i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 469.566i | − | 0.471926i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1217.62 | 1.22128 | 0.610640 | − | 0.791909i | \(-0.290912\pi\) | ||||
0.610640 | + | 0.791909i | \(0.290912\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.5039 | + | 17.4347i | 0.0145184 | + | 0.0174522i |
(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 | 240.3.l.d.161.8 | 8 | ||
3.2 | odd | 2 | inner | 240.3.l.d.161.7 | 8 | ||
4.3 | odd | 2 | 120.3.l.a.41.1 | ✓ | 8 | ||
5.2 | odd | 4 | 1200.3.c.m.449.11 | 16 | |||
5.3 | odd | 4 | 1200.3.c.m.449.6 | 16 | |||
5.4 | even | 2 | 1200.3.l.x.401.1 | 8 | |||
8.3 | odd | 2 | 960.3.l.h.641.8 | 8 | |||
8.5 | even | 2 | 960.3.l.g.641.1 | 8 | |||
12.11 | even | 2 | 120.3.l.a.41.2 | yes | 8 | ||
15.2 | even | 4 | 1200.3.c.m.449.5 | 16 | |||
15.8 | even | 4 | 1200.3.c.m.449.12 | 16 | |||
15.14 | odd | 2 | 1200.3.l.x.401.2 | 8 | |||
20.3 | even | 4 | 600.3.c.d.449.11 | 16 | |||
20.7 | even | 4 | 600.3.c.d.449.6 | 16 | |||
20.19 | odd | 2 | 600.3.l.f.401.8 | 8 | |||
24.5 | odd | 2 | 960.3.l.g.641.2 | 8 | |||
24.11 | even | 2 | 960.3.l.h.641.7 | 8 | |||
60.23 | odd | 4 | 600.3.c.d.449.5 | 16 | |||
60.47 | odd | 4 | 600.3.c.d.449.12 | 16 | |||
60.59 | even | 2 | 600.3.l.f.401.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.1 | ✓ | 8 | 4.3 | odd | 2 | ||
120.3.l.a.41.2 | yes | 8 | 12.11 | even | 2 | ||
240.3.l.d.161.7 | 8 | 3.2 | odd | 2 | inner | ||
240.3.l.d.161.8 | 8 | 1.1 | even | 1 | trivial | ||
600.3.c.d.449.5 | 16 | 60.23 | odd | 4 | |||
600.3.c.d.449.6 | 16 | 20.7 | even | 4 | |||
600.3.c.d.449.11 | 16 | 20.3 | even | 4 | |||
600.3.c.d.449.12 | 16 | 60.47 | odd | 4 | |||
600.3.l.f.401.7 | 8 | 60.59 | even | 2 | |||
600.3.l.f.401.8 | 8 | 20.19 | odd | 2 | |||
960.3.l.g.641.1 | 8 | 8.5 | even | 2 | |||
960.3.l.g.641.2 | 8 | 24.5 | odd | 2 | |||
960.3.l.h.641.7 | 8 | 24.11 | even | 2 | |||
960.3.l.h.641.8 | 8 | 8.3 | odd | 2 | |||
1200.3.c.m.449.5 | 16 | 15.2 | even | 4 | |||
1200.3.c.m.449.6 | 16 | 5.3 | odd | 4 | |||
1200.3.c.m.449.11 | 16 | 5.2 | odd | 4 | |||
1200.3.c.m.449.12 | 16 | 15.8 | even | 4 | |||
1200.3.l.x.401.1 | 8 | 5.4 | even | 2 | |||
1200.3.l.x.401.2 | 8 | 15.14 | odd | 2 |