Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(129,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.129");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.c (of order \(2\), degree \(1\), 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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 165x^{10} + 9528x^{8} + 254984x^{6} + 3245664x^{4} + 15975501x^{2} + 588289 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{44}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.11 | ||
Root | \(4.23250i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.129 |
Dual form | 160.6.c.c.129.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 26.2718i | 1.68534i | 0.538434 | + | 0.842668i | \(0.319016\pi\) | ||||
−0.538434 | + | 0.842668i | \(0.680984\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 48.8634 | − | 27.1545i | 0.874095 | − | 0.485754i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 23.9306i | − | 0.184590i | −0.995732 | − | 0.0922952i | \(-0.970580\pi\) | ||
0.995732 | − | 0.0922952i | \(-0.0294203\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −447.206 | −1.84035 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 704.032 | 1.75433 | 0.877164 | − | 0.480191i | \(-0.159433\pi\) | ||||
0.877164 | + | 0.480191i | \(0.159433\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1037.56i | 1.70276i | 0.524549 | + | 0.851380i | \(0.324234\pi\) | ||||
−0.524549 | + | 0.851380i | \(0.675766\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 713.397 | + | 1283.73i | 0.818659 | + | 1.47314i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 217.433i | − | 0.182475i | −0.995829 | − | 0.0912375i | \(-0.970918\pi\) | ||
0.995829 | − | 0.0912375i | \(-0.0290823\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1290.13 | 0.819878 | 0.409939 | − | 0.912113i | \(-0.365550\pi\) | ||||
0.409939 | + | 0.912113i | \(0.365550\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 628.700 | 0.311097 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2806.24i | 1.10613i | 0.833138 | + | 0.553065i | \(0.186542\pi\) | ||||
−0.833138 | + | 0.553065i | \(0.813458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1650.27 | − | 2653.72i | 0.528086 | − | 0.849191i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5364.86i | − | 1.41628i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4905.42 | −1.08313 | −0.541566 | − | 0.840658i | \(-0.682168\pi\) | ||||
−0.541566 | + | 0.840658i | \(0.682168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 415.555 | 0.0776648 | 0.0388324 | − | 0.999246i | \(-0.487636\pi\) | ||||
0.0388324 | + | 0.999246i | \(0.487636\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18496.2i | 2.95663i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −649.824 | − | 1169.33i | −0.0896656 | − | 0.161350i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6450.71i | 0.774646i | 0.921944 | + | 0.387323i | \(0.126600\pi\) | ||||
−0.921944 | + | 0.387323i | \(0.873400\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −27258.5 | −2.86972 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −16402.5 | −1.52388 | −0.761940 | − | 0.647648i | \(-0.775753\pi\) | ||||
−0.761940 | + | 0.647648i | \(0.775753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 13772.3i | − | 1.13589i | −0.823067 | − | 0.567944i | \(-0.807739\pi\) | ||
0.823067 | − | 0.567944i | \(-0.192261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −21852.0 | + | 12143.7i | −1.60865 | + | 0.893960i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12942.4i | 0.854612i | 0.904107 | + | 0.427306i | \(0.140537\pi\) | ||||
−0.904107 | + | 0.427306i | \(0.859463\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16234.3 | 0.965926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5712.36 | 0.307532 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5239.24i | − | 0.256200i | −0.991761 | − | 0.128100i | \(-0.959112\pi\) | ||
0.991761 | − | 0.128100i | \(-0.0408878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 34401.4 | − | 19117.6i | 1.53345 | − | 0.852172i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 33894.0i | 1.38177i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −24042.4 | −0.899182 | −0.449591 | − | 0.893234i | \(-0.648430\pi\) | ||||
−0.449591 | + | 0.893234i | \(0.648430\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1037.24 | −0.0356908 | −0.0178454 | − | 0.999841i | \(-0.505681\pi\) | ||||
−0.0178454 | + | 0.999841i | \(0.505681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10701.9i | 0.339712i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 28174.3 | + | 50698.6i | 0.827123 | + | 1.48838i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47902.5i | 1.30368i | 0.758357 | + | 0.651840i | \(0.226002\pi\) | ||||
−0.758357 | + | 0.651840i | \(0.773998\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −73725.0 | −1.86420 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 74761.8 | 1.76009 | 0.880043 | − | 0.474893i | \(-0.157513\pi\) | ||||
0.880043 | + | 0.474893i | \(0.157513\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 22746.5i | − | 0.499582i | −0.968300 | − | 0.249791i | \(-0.919638\pi\) | ||
0.968300 | − | 0.249791i | \(-0.0803619\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 69718.0 | + | 43355.5i | 1.43117 | + | 0.890001i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 16847.9i | − | 0.323832i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64213.8 | −1.15761 | −0.578803 | − | 0.815468i | \(-0.696480\pi\) | ||||
−0.578803 | + | 0.815468i | \(0.696480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 32273.2 | 0.546550 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 22523.0i | 0.358865i | 0.983770 | + | 0.179432i | \(0.0574261\pi\) | ||||
−0.983770 | + | 0.179432i | \(0.942574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5904.29 | − | 10624.5i | −0.0886381 | − | 0.159501i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 128874.i | − | 1.82544i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 37886.4 | 0.507000 | 0.253500 | − | 0.967335i | \(-0.418418\pi\) | ||||
0.253500 | + | 0.967335i | \(0.418418\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24829.4 | 0.314313 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10917.4i | 0.130891i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 63040.1 | − | 35032.8i | 0.716651 | − | 0.398259i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 84119.7i | − | 0.907755i | −0.891064 | − | 0.453877i | \(-0.850040\pi\) | ||
0.891064 | − | 0.453877i | \(-0.149960\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −314847. | −3.22858 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −77492.2 | −0.755883 | −0.377941 | − | 0.925830i | \(-0.623368\pi\) | ||||
−0.377941 | + | 0.925830i | \(0.623368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 68641.0i | 0.637516i | 0.947836 | + | 0.318758i | \(0.103266\pi\) | ||||
−0.947836 | + | 0.318758i | \(0.896734\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30720.4 | − | 17072.0i | 0.271928 | − | 0.151117i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 84264.9i | − | 0.711520i | −0.934577 | − | 0.355760i | \(-0.884222\pi\) | ||
0.934577 | − | 0.355760i | \(-0.115778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 51640.6 | 0.416318 | 0.208159 | − | 0.978095i | \(-0.433253\pi\) | ||||
0.208159 | + | 0.978095i | \(0.433253\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −169472. | −1.30554 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 88744.4i | 0.653800i | 0.945059 | + | 0.326900i | \(0.106004\pi\) | ||||
−0.945059 | + | 0.326900i | \(0.893996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 76202.1 | + | 137123.i | 0.537307 | + | 0.966863i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 464002.i | − | 3.13368i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5203.31 | −0.0336832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 334610. | 2.07767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 430923.i | − | 2.56825i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8577.22 | − | 174482.i | 0.0490989 | − | 0.998794i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 178878.i | 0.984121i | 0.870561 | + | 0.492061i | \(0.163756\pi\) | ||||
−0.870561 | + | 0.492061i | \(0.836244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 361823. | 1.91435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 235194. | 1.19742 | 0.598711 | − | 0.800965i | \(-0.295680\pi\) | ||||
0.598711 | + | 0.800965i | \(0.295680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 30873.6i | − | 0.151342i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −145680. | − | 262145.i | −0.687963 | − | 1.23796i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 216936.i | − | 0.987486i | −0.869608 | − | 0.493743i | \(-0.835628\pi\) | ||
0.869608 | − | 0.493743i | \(-0.164372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 347938. | 1.52744 | 0.763721 | − | 0.645546i | \(-0.223370\pi\) | ||||
0.763721 | + | 0.645546i | \(0.223370\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −340019. | −1.44031 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 730473.i | 2.98720i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −239696. | + | 133204.i | −0.946760 | + | 0.526136i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 426505.i | 1.62791i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −136495. | −0.503677 | −0.251839 | − | 0.967769i | \(-0.581035\pi\) | ||||
−0.251839 | + | 0.967769i | \(0.581035\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 318940. | 1.13833 | 0.569163 | − | 0.822225i | \(-0.307267\pi\) | ||||
0.569163 | + | 0.822225i | \(0.307267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 97237.5i | 0.335819i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20305.4 | − | 11284.2i | 0.0678864 | − | 0.0377260i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 54247.3i | 0.175642i | 0.996136 | + | 0.0878211i | \(0.0279904\pi\) | ||||
−0.996136 | + | 0.0878211i | \(0.972010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 137644. | 0.431783 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67155.2 | 0.204181 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 504961.i | − | 1.48864i | −0.667825 | − | 0.744318i | \(-0.732775\pi\) | ||
0.667825 | − | 0.744318i | \(-0.267225\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 502254. | + | 903786.i | 1.43620 | + | 2.58438i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 264305.i | − | 0.733355i | −0.930348 | − | 0.366677i | \(-0.880495\pi\) | ||
0.930348 | − | 0.366677i | \(-0.119505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −705231. | −1.89939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −576953. | −1.50887 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 449650.i | − | 1.14225i | −0.820865 | − | 0.571123i | \(-0.806508\pi\) | ||
0.820865 | − | 0.571123i | \(-0.193492\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −63505.3 | − | 39491.9i | −0.156753 | − | 0.0974795i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 631636.i | − | 1.51542i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 657282. | 1.53327 | 0.766636 | − | 0.642082i | \(-0.221929\pi\) | ||||
0.766636 | + | 0.642082i | \(0.221929\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 640421. | 1.45301 | 0.726506 | − | 0.687160i | \(-0.241143\pi\) | ||||
0.726506 | + | 0.687160i | \(0.241143\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 27250.2i | − | 0.0601510i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 175166. | + | 315204.i | 0.376288 | + | 0.677115i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 153080.i | − | 0.320121i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −128384. | −0.261431 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −689612. | −1.36780 | −0.683898 | − | 0.729578i | \(-0.739717\pi\) | ||||
−0.683898 | + | 0.729578i | \(0.739717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 398342.i | 0.769773i | 0.922964 | + | 0.384887i | \(0.125759\pi\) | ||||
−0.922964 | + | 0.384887i | \(0.874241\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.33194e6 | + | 740190.i | −2.50841 | + | 1.39398i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19330.2i | 0.0354870i | 0.999843 | + | 0.0177435i | \(0.00564823\pi\) | ||||
−0.999843 | + | 0.0177435i | \(0.994352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 314706. | 0.563342 | 0.281671 | − | 0.959511i | \(-0.409111\pi\) | ||||
0.281671 | + | 0.959511i | \(0.409111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.25848e6 | −2.19714 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 117390.i | 0.199936i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −801482. | + | 445402.i | −1.33202 | + | 0.740231i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.25497e6i | − | 2.03567i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 908292. | 1.43833 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −478488. | −0.739885 | −0.369943 | − | 0.929055i | \(-0.620623\pi\) | ||||
−0.369943 | + | 0.929055i | \(0.620623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.96413e6i | 2.96634i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −373980. | − | 672962.i | −0.551762 | − | 0.992874i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9944.49i | − | 0.0143362i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 597590. | 0.841963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 225599. | 0.310711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 205163.i | 0.276273i | 0.990413 | + | 0.138136i | \(0.0441112\pi\) | ||||
−0.990413 | + | 0.138136i | \(0.955889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −738010. | + | 1.18676e6i | −0.971865 | + | 1.56281i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 409093.i | 0.526936i | 0.964668 | + | 0.263468i | \(0.0848663\pi\) | ||||
−0.964668 | + | 0.263468i | \(0.915134\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −405619. | −0.511128 | −0.255564 | − | 0.966792i | \(-0.582261\pi\) | ||||
−0.255564 | + | 0.966792i | \(0.582261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 442625. | 0.545766 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 64192.9i | 0.0774635i | 0.999250 | + | 0.0387318i | \(0.0123318\pi\) | ||||
−0.999250 | + | 0.0387318i | \(0.987668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 351443. | + | 632408.i | 0.415131 | + | 0.747012i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.68701e6i | − | 1.95095i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.36063e6 | 1.54080 | 0.770401 | − | 0.637560i | \(-0.220056\pi\) | ||||
0.770401 | + | 0.637560i | \(0.220056\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34482e6 | −1.49149 | −0.745745 | − | 0.666231i | \(-0.767906\pi\) | ||||
−0.745745 | + | 0.666231i | \(0.767906\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 455786.i | − | 0.495159i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 793265. | − | 440835.i | 0.844312 | − | 0.469203i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.33858e6i | 1.39605i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −591719. | −0.604808 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 171857. | 0.172180 | 0.0860898 | − | 0.996287i | \(-0.472563\pi\) | ||||
0.0860898 | + | 0.996287i | \(0.472563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.97569e6i | 1.94051i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 279125. | − | 155116.i | 0.268812 | − | 0.149385i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.78486e6i | − | 1.68567i | −0.538173 | − | 0.842834i | \(-0.680885\pi\) | ||
0.538173 | − | 0.842834i | \(-0.319115\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 154370. | 0.142992 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.19373e6 | 1.99335 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.23207e6i | 1.09836i | 0.835703 | + | 0.549182i | \(0.185060\pi\) | ||||
−0.835703 | + | 0.549182i | \(0.814940\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −142269. | − | 256007.i | −0.124450 | − | 0.223943i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 995343.i | 0.854466i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 309231. | 0.260557 | 0.130278 | − | 0.991477i | \(-0.458413\pi\) | ||||
0.130278 | + | 0.991477i | \(0.458413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −143525. | −0.118714 | −0.0593572 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593572 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 652312.i | 0.529723i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.16184e6 | − | 1.86831e6i | 0.926435 | − | 1.48976i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 635705.i | − | 0.497802i | −0.968529 | − | 0.248901i | \(-0.919931\pi\) | ||
0.968529 | − | 0.248901i | \(-0.0800693\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −185839. | −0.142931 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −240440. | −0.181652 | −0.0908262 | − | 0.995867i | \(-0.528951\pi\) | ||||
−0.0908262 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 442548.i | − | 0.328469i | −0.986421 | − | 0.164234i | \(-0.947485\pi\) | ||
0.986421 | − | 0.164234i | \(-0.0525153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 920373. | + | 1.65618e6i | 0.671200 | + | 1.20780i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 392522.i | 0.281293i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.37258e6 | 0.966703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.20997e6 | 1.52987 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.02835e6i | − | 1.38030i | −0.723667 | − | 0.690149i | \(-0.757545\pi\) | ||
0.723667 | − | 0.690149i | \(-0.242455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17479e6 | + | 652859.i | −0.785971 | + | 0.436782i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.77703e6i | − | 2.48462i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.91164e6 | −1.88347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −329580. | −0.209674 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.03586e6i | − | 1.27392i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −50683.3 | + | 28165.8i | −0.0311972 | + | 0.0173370i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.31899e6i | − | 1.40427i | −0.712042 | − | 0.702137i | \(-0.752229\pi\) | ||
0.712042 | − | 0.702137i | \(-0.247771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.80332e6 | −1.07443 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.17253e6 | −1.27369 | −0.636846 | − | 0.770991i | \(-0.719761\pi\) | ||||
−0.636846 | + | 0.770991i | \(0.719761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.93017e6i | − | 1.11362i | −0.830641 | − | 0.556808i | \(-0.812026\pi\) | ||
0.830641 | − | 0.556808i | \(-0.187974\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 290605. | + | 522933.i | 0.165016 | + | 0.296940i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.16542e6i | − | 1.21030i | −0.796111 | − | 0.605151i | \(-0.793113\pi\) | ||
0.796111 | − | 0.605151i | \(-0.206887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.45357e6 | −1.90017 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.21379e6 | 1.19915 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 280517.i | − | 0.149607i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.75339e6 | + | 1.71225e6i | 1.44597 | + | 0.899203i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.35669e6i | 0.701635i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 309719. | 0.157753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.27143e6 | −0.637857 | −0.318929 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318929 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.88480e6i | − | 1.42562i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.30077e6 | + | 2.34068e6i | 0.633268 | + | 1.13954i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.23785e6i | 1.07338i | 0.843778 | + | 0.536692i | \(0.180326\pi\) | ||||
−0.843778 | + | 0.536692i | \(0.819674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.33147e6 | −1.10187 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 292564. | 0.136250 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 790700.i | − | 0.362891i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.60246e6 | + | 2.00197e6i | −1.62949 | + | 0.905542i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4.29048e6i | − | 1.91285i | −0.291971 | − | 0.956427i | \(-0.594311\pi\) | ||
0.291971 | − | 0.956427i | \(-0.405689\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −907418. | −0.398790 | −0.199395 | − | 0.979919i | \(-0.563898\pi\) | ||||
−0.199395 | + | 0.979919i | \(0.563898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.56634e6 | 2.41158 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 383963.i | − | 0.164003i | −0.996632 | − | 0.0820017i | \(-0.973869\pi\) | ||
0.996632 | − | 0.0820017i | \(-0.0261313\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.65312e6 | − | 2.03012e6i | 1.53848 | − | 0.854970i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 136700.i | − | 0.0567674i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.38837e6 | −0.978060 | −0.489030 | − | 0.872267i | \(-0.662649\pi\) | ||||
−0.489030 | + | 0.872267i | \(0.662649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −811667. | −0.327801 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.79080e6i | 3.50156i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −617668. | − | 1.11147e6i | −0.242674 | − | 0.436682i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.80989e6i | − | 1.08899i | −0.838764 | − | 0.544495i | \(-0.816721\pi\) | ||
0.838764 | − | 0.544495i | \(-0.183279\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.33530e6 | 2.80448 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −125378. | −0.0472920 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 602108.i | 0.224080i | 0.993704 | + | 0.112040i | \(0.0357384\pi\) | ||||
−0.993704 | + | 0.112040i | \(0.964262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.58395e6 | + | 225339.i | 1.68330 | + | 0.0827481i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.08965e6i | − | 1.84431i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 153274. | 0.0548115 | 0.0274057 | − | 0.999624i | \(-0.491275\pi\) | ||||
0.0274057 | + | 0.999624i | \(0.491275\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.69945e6 | −1.65857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.29677e6i | − | 1.49673i | −0.663285 | − | 0.748367i | \(-0.730838\pi\) | ||
0.663285 | − | 0.748367i | \(-0.269162\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −457497. | − | 823248.i | −0.157303 | − | 0.283060i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.15906e6i | 2.09044i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.29468e6 | 0.433800 | 0.216900 | − | 0.976194i | \(-0.430405\pi\) | ||||
0.216900 | + | 0.976194i | \(0.430405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 610171. | 0.201841 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.17895e6i | 2.01806i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.13771e6 | + | 1.74369e6i | −1.01186 | + | 0.562312i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.41262e6i | − | 0.768266i | −0.923278 | − | 0.384133i | \(-0.874500\pi\) | ||
0.923278 | − | 0.384133i | \(-0.125500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 811104. | 0.255061 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.88260e6 | 1.82687 | 0.913437 | − | 0.406980i | \(-0.133418\pi\) | ||||
0.913437 | + | 0.406980i | \(0.133418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 431162.i | 0.132245i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.57698e6 | − | 876363.i | 0.477737 | − | 0.265489i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.54151e6i | 1.35898i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −166944. | −0.0493473 | −0.0246737 | − | 0.999696i | \(-0.507855\pi\) | ||||
−0.0246737 | + | 0.999696i | \(0.507855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.69930e6 | 1.66424 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 575350.i | 0.165980i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 611601. | + | 1.10055e6i | 0.174320 | + | 0.313682i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.14095e6i | 2.57425i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.19513e6 | 0.610838 | 0.305419 | − | 0.952218i | \(-0.401204\pi\) | ||||
0.305419 | + | 0.952218i | \(0.401204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.54531e6 | −0.424924 | −0.212462 | − | 0.977169i | \(-0.568148\pi\) | ||||
−0.212462 | + | 0.977169i | \(0.568148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.78790e6i | − | 1.57279i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −577007. | − | 358823.i | −0.154956 | − | 0.0963625i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24821.9i | 0.00658818i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.91908e7 | −5.03443 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.05590e6 | −0.792402 | −0.396201 | − | 0.918164i | \(-0.629672\pi\) | ||||
−0.396201 | + | 0.918164i | \(0.629672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.34883e6i | 1.37100i | 0.728071 | + | 0.685502i | \(0.240417\pi\) | ||||
−0.728071 | + | 0.685502i | \(0.759583\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.49951e6 | − | 6.29723e6i | −0.886715 | − | 1.59561i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.62042e6i | 0.906891i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.65736e6 | −0.410446 | −0.205223 | − | 0.978715i | \(-0.565792\pi\) | ||||
−0.205223 | + | 0.978715i | \(0.565792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.26009e6 | −1.77765 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.02478e6i | − | 0.248098i | −0.992276 | − | 0.124049i | \(-0.960412\pi\) | ||
0.992276 | − | 0.124049i | \(-0.0395880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.85126e6 | − | 1.02879e6i | 0.443167 | − | 0.246278i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 3.58598e6i | − | 0.848865i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.87947e6 | 0.439966 | 0.219983 | − | 0.975504i | \(-0.429400\pi\) | ||||
0.219983 | + | 0.975504i | \(0.429400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.15479e7 | −2.67338 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.37912e6i | 1.91846i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.21325e6 | − | 674230.i | 0.274740 | − | 0.152679i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.51688e6i | 1.01169i | 0.862624 | + | 0.505846i | \(0.168820\pi\) | ||||
−0.862624 | + | 0.505846i | \(0.831180\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.16650e6 | −0.258436 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.74712e6 | 1.47865 | 0.739326 | − | 0.673348i | \(-0.235144\pi\) | ||||
0.739326 | + | 0.673348i | \(0.235144\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.43370e6i | 0.744407i | 0.928151 | + | 0.372203i | \(0.121398\pi\) | ||||
−0.928151 | + | 0.372203i | \(0.878602\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 296456. | + | 533460.i | 0.0635810 | + | 0.114411i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 791564.i | 0.167955i | 0.996468 | + | 0.0839777i | \(0.0267625\pi\) | ||||
−0.996468 | + | 0.0839777i | \(0.973238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.14634e6 | 0.240647 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.42517e6 | −0.296016 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.69614e6i | − | 1.99272i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.12906e6 | − | 3.42364e6i | 0.432965 | − | 0.696233i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.34302e6i | 0.471499i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 799322. | 0.159178 | 0.0795890 | − | 0.996828i | \(-0.474639\pi\) | ||||
0.0795890 | + | 0.996828i | \(0.474639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.69298e6 | −1.31904 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.76429e6i | 0.344113i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.28423e6 | − | 4.11038e6i | −0.440946 | − | 0.793464i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.68591e6i | 1.27743i | 0.769442 | + | 0.638717i | \(0.220534\pi\) | ||||
−0.769442 | + | 0.638717i | \(0.779466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.32662e7 | 2.50885 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 235143. | 0.0440179 | 0.0220089 | − | 0.999758i | \(-0.492994\pi\) | ||||
0.0220089 | + | 0.999758i | \(0.492994\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.06660e6i | 0.197644i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.53845e7 | + | 8.54952e6i | −2.82209 | + | 1.56830i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.78910e6i | − | 0.324895i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.20861e6 | 1.29599 | 0.647993 | − | 0.761646i | \(-0.275609\pi\) | ||||
0.647993 | + | 0.761646i | \(0.275609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.94376e6 | 1.23595 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.24297e6i | − | 1.27643i | −0.769858 | − | 0.638215i | \(-0.779673\pi\) | ||
0.769858 | − | 0.638215i | \(-0.220327\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.78653e6 | + | 2.10426e6i | −0.660714 | + | 0.367173i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.85277e7i | − | 3.20111i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.34344e6 | −0.914169 | −0.457085 | − | 0.889423i | \(-0.651106\pi\) | ||||
−0.457085 | + | 0.889423i | \(0.651106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −544337. | −0.0922180 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 6.92135e6i | − | 1.16118i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.86391e6 | + | 3.35404e6i | 0.309676 | + | 0.557249i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.11184e6i | 1.49927i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.18131e7 | 1.92507 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.91899e6 | −0.632529 | −0.316264 | − | 0.948671i | \(-0.602429\pi\) | ||||
−0.316264 | + | 0.948671i | \(0.602429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.74591e6i | 0.598829i | 0.954123 | + | 0.299414i | \(0.0967913\pi\) | ||||
−0.954123 | + | 0.299414i | \(0.903209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.03752e6 | − | 1.66840e6i | 0.164286 | − | 0.264181i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 90355.5i | − | 0.0141719i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.43866e6 | −0.223522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.07519e7 | 1.65481 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.70185e7i | − | 2.59480i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.28817e6 | − | 4.11747e6i | −0.345624 | − | 0.621937i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.72680e7i | 2.58408i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.14295e7 | 1.69455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.32207e6 | −0.194206 | −0.0971031 | − | 0.995274i | \(-0.530958\pi\) | ||||
−0.0971031 | + | 0.995274i | \(0.530958\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.68250e7i | 2.44881i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.52334e6 | − | 1.40227e6i | 0.363901 | − | 0.202228i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.82591e6i | 1.26122i | 0.776100 | + | 0.630610i | \(0.217195\pi\) | ||||
−0.776100 | + | 0.630610i | \(0.782805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 463862. | 0.0656837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.32862e6 | −0.888035 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.53668e6i | 0.213683i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.28097e6 | + | 4.60192e6i | −1.14117 | + | 0.634171i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 446795.i | − | 0.0610197i | −0.999534 | − | 0.0305099i | \(-0.990287\pi\) | ||
0.999534 | − | 0.0305099i | \(-0.00971310\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.42895e7 | 1.93414 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.02168e6 | 0.539511 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.61652e6i | − | 0.214937i | −0.994208 | − | 0.107468i | \(-0.965726\pi\) | ||
0.994208 | − | 0.107468i | \(-0.0342745\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.40981e6 | + | 4.33636e6i | 0.317586 | + | 0.571484i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 772318.i | − | 0.100888i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.25416e7 | 1.62395 | 0.811974 | − | 0.583693i | \(-0.198393\pi\) | ||||
0.811974 | + | 0.583693i | \(0.198393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.19556e6 | −0.153455 | −0.0767276 | − | 0.997052i | \(-0.524447\pi\) | ||||
−0.0767276 | + | 0.997052i | \(0.524447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.81173e7i | − | 2.30519i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.44699e6 | + | 4.63105e6i | 0.939315 | + | 0.584131i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.15431e7i | − | 1.44339i | −0.692211 | − | 0.721695i | \(-0.743363\pi\) | ||
0.692211 | − | 0.721695i | \(-0.256637\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.04652e7 | −1.29733 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 538990. | 0.0662430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.68860e6i | − | 0.449459i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.25997e7 | − | 2.26727e7i | −1.52220 | − | 2.73914i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.96527e6i | 0.594768i | 0.954758 | + | 0.297384i | \(0.0961142\pi\) | ||||
−0.954758 | + | 0.297384i | \(0.903886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 536119. | 0.0636756 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −507837. | −0.0598076 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.44208e6i | 0.401962i | 0.979595 | + | 0.200981i | \(0.0644129\pi\) | ||||
−0.979595 | + | 0.200981i | \(0.935587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −254252. | + | 141293.i | −0.0294423 | + | 0.0163617i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.26787e6i | 0.949419i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.32967e6 | 0.834675 | 0.417338 | − | 0.908752i | \(-0.362963\pi\) | ||||
0.417338 | + | 0.908752i | \(0.362963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.96589e6 | −0.673735 | −0.336868 | − | 0.941552i | \(-0.609368\pi\) | ||||
−0.336868 | + | 0.941552i | \(0.609368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.14223e7i | − | 2.39923i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.63502e7 | − | 9.08617e6i | 1.81608 | − | 1.00924i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.35750e7i | − | 1.49543i | −0.664018 | − | 0.747716i | \(-0.731150\pi\) | ||
0.664018 | − | 0.747716i | \(-0.268850\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.08404e6 | −0.336959 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.34284e7 | −1.45520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.11070e7i | 1.19384i | 0.802302 | + | 0.596918i | \(0.203608\pi\) | ||||
−0.802302 | + | 0.596918i | \(0.796392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.17015e7 | − | 2.10564e7i | −1.24754 | − | 2.24489i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 5.62274e6i | − | 0.594614i | −0.954782 | − | 0.297307i | \(-0.903912\pi\) | ||
0.954782 | − | 0.297307i | \(-0.0960884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.37545e6 | −0.249184 | −0.124592 | − | 0.992208i | \(-0.539762\pi\) | ||||
−0.124592 | + | 0.992208i | \(0.539762\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.50551e7 | 1.56659 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 906646.i | − | 0.0935874i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.31886e6 | − | 8.75870e6i | −0.442251 | − | 0.896891i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.38624e7i | 2.42407i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.40260e6 | 0.141354 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.70995e6 | 0.370932 | 0.185466 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185466 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.25707e7i | − | 1.24695i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.85735e6 | + | 8.74061e6i | 0.478041 | + | 0.860216i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68440e7i | 1.64474i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.34340e7 | −3.23918 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.35252e6 | 0.706791 | 0.353396 | − | 0.935474i | \(-0.385027\pi\) | ||||
0.353396 | + | 0.935474i | \(0.385027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.03451e6i | 0.289442i | 0.989473 | + | 0.144721i | \(0.0462284\pi\) | ||||
−0.989473 | + | 0.144721i | \(0.953772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.76799e7 | − | 9.82511e6i | 1.67333 | − | 0.929904i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.69808e6i | 0.441224i | 0.975362 | + | 0.220612i | \(0.0708055\pi\) | ||||
−0.975362 | + | 0.220612i | \(0.929194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.69266e7 | −1.57746 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 261259. | 0.0241613 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.29779e7i | 1.19103i | 0.803346 | + | 0.595513i | \(0.203051\pi\) | ||||
−0.803346 | + | 0.595513i | \(0.796949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.14924e7 | − | 6.38656e6i | 1.04666 | − | 0.581653i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.01724e7i | 0.919407i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.46461e6 | −0.131374 | −0.0656868 | − | 0.997840i | \(-0.520924\pi\) | ||||
−0.0656868 | + | 0.997840i | \(0.520924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.06947e7 | 0.952061 | 0.476031 | − | 0.879429i | \(-0.342075\pi\) | ||||
0.476031 | + | 0.879429i | \(0.342075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.92689e6i | 0.523653i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −838357. | − | 1.50859e6i | −0.0735148 | − | 0.132287i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.37658e7i | − | 1.19808i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.39001e6 | −0.465612 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −730253. | −0.0626134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.91777e6i | − | 0.758959i | −0.925200 | − | 0.379480i | \(-0.876103\pi\) | ||
0.925200 | − | 0.379480i | \(-0.123897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.42368e7 | − | 8.85345e6i | −1.20269 | − | 0.747916i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.93032e7i | − | 1.61867i | −0.587349 | − | 0.809334i | \(-0.699828\pi\) | ||
0.587349 | − | 0.809334i | \(-0.300172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.01304e6 | −0.167563 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.07476e7 | −0.888063 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.15277e7i | 0.945565i | 0.881179 | + | 0.472783i | \(0.156750\pi\) | ||||
−0.881179 | + | 0.472783i | \(0.843250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.89079e6 | − | 1.06002e7i | −0.479675 | − | 0.863157i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.06563e7i | − | 0.861421i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.43601e6 | 0.436247 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.95573e6 | 0.315160 | 0.157580 | − | 0.987506i | \(-0.449631\pi\) | ||||
0.157580 | + | 0.987506i | \(0.449631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.53450e6i | 0.595966i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.70014e7 | − | 9.44808e6i | 1.33513 | − | 0.741962i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.56645e6i | 0.278070i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.68646e6 | −0.130552 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.05492e7 | −1.57943 | −0.789715 | − | 0.613474i | \(-0.789771\pi\) | ||||
−0.789715 | + | 0.613474i | \(0.789771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.32225e6i | 0.635115i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.66145e7 | + | 9.23304e6i | −1.25897 | + | 0.699636i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.85444e6i | 0.139529i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.07226e7 | 0.801100 | 0.400550 | − | 0.916275i | \(-0.368819\pi\) | ||||
0.400550 | + | 0.916275i | \(0.368819\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.87168e7 | 2.13040 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.16615e6i | 0.0859073i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.98356e7 | + | 3.56934e7i | 1.45105 | + | 2.61110i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.57463e7i | 2.59677i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.12405e6 | 0.586071 | 0.293035 | − | 0.956102i | \(-0.405335\pi\) | ||||
0.293035 | + | 0.956102i | \(0.405335\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.64262e6 | 0.117679 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 3.53307e7i | − | 2.51366i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.09525e6 | + | 1.30176e7i | −0.571986 | + | 0.919786i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.87419e7i | 1.31516i | 0.753386 | + | 0.657578i | \(0.228419\pi\) | ||||
−0.753386 | + | 0.657578i | \(0.771581\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.98167e7 | 1.38106 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.99456e6 | −0.207271 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.43325e6i | 0.0985284i | 0.998786 | + | 0.0492642i | \(0.0156876\pi\) | ||||
−0.998786 | + | 0.0492642i | \(0.984312\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.15815e7 | + | 2.08405e7i | 0.790764 | + | 1.42295i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.37249e7i | 2.28708i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.87933e6 | 0.261304 | 0.130652 | − | 0.991428i | \(-0.458293\pi\) | ||||
0.130652 | + | 0.991428i | \(0.458293\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.51669e7 | −2.35282 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.51128e7i | 1.66887i | 0.551104 | + | 0.834437i | \(0.314207\pi\) | ||||
−0.551104 | + | 0.834437i | \(0.685793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.66963e6 | + | 3.70646e6i | −0.440262 | + | 0.244663i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.00724e7i | − | 0.660439i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.01651e6 | −0.131340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.68579e7 | −1.09070 | −0.545349 | − | 0.838209i | \(-0.683603\pi\) | ||||
−0.545349 | + | 0.838209i | \(0.683603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.51498e6i | 0.290180i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.55845e7 | − | 8.66065e6i | 0.995005 | − | 0.552946i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.64597e6i | 0.167821i | 0.996473 | + | 0.0839104i | \(0.0267410\pi\) | ||||
−0.996473 | + | 0.0839104i | \(0.973259\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.19048e7 | −3.27042 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 778479. | 0.0487288 | 0.0243644 | − | 0.999703i | \(-0.492244\pi\) | ||||
0.0243644 | + | 0.999703i | \(0.492244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.23579e6i | − | 0.0768483i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.64043e6 | + | 4.75135e6i | 0.163125 | + | 0.293538i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.49454e7i | − | 1.53109i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.11827e7 | −0.681919 | −0.340959 | − | 0.940078i | \(-0.610752\pi\) | ||||
−0.340959 | + | 0.940078i | \(0.610752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.68915e7 | 2.84092 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.00821e7i | − | 1.20882i | −0.796675 | − | 0.604408i | \(-0.793410\pi\) | ||
0.796675 | − | 0.604408i | \(-0.206590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 685777. | − | 1.10277e6i | 0.0410137 | − | 0.0659523i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.05556e6i | 0.240990i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.11613e7 | −1.24939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.26347e7 | 3.08777 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.63169e7i | 1.53402i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.47306e6 | + | 2.65071e6i | 0.0853190 | + | 0.153528i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.62920e6i | 0.151317i | 0.997134 | + | 0.0756584i | \(0.0241059\pi\) | ||||
−0.997134 | + | 0.0756584i | \(0.975894\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.23687e7 | −1.85111 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.12371e6 | 0.120685 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.07620e6i | − | 0.0607729i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.72577e6 | − | 3.73766e6i | 0.377419 | − | 0.209740i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.44461e6i | − | 0.359377i | −0.983724 | − | 0.179689i | \(-0.942491\pi\) | ||
0.983724 | − | 0.179689i | \(-0.0575090\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.81410e6 | 0.155945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.69430e7 | −0.933061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.60142e7i | − | 0.876430i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.28143e6 | − | 1.82357e6i | 0.178474 | − | 0.0991817i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.12405e6i | 0.439126i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.59388e6 | −0.193060 | −0.0965299 | − | 0.995330i | \(-0.530774\pi\) | ||||
−0.0965299 | + | 0.995330i | \(0.530774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.79497e7 | −1.49220 | −0.746098 | − | 0.665837i | \(-0.768075\pi\) | ||||
−0.746098 | + | 0.665837i | \(0.768075\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.77065e6i | − | 0.200074i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.37120e7 | − | 2.46741e7i | −0.723111 | − | 1.30121i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.77680e7i | − | 0.931289i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.11039e7 | −0.578448 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.41956e6 | −0.435945 | −0.217972 | − | 0.975955i | \(-0.569944\pi\) | ||||
−0.217972 | + | 0.975955i | \(0.569944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.51378e7i | − | 0.779048i | −0.921016 | − | 0.389524i | \(-0.872640\pi\) | ||
0.921016 | − | 0.389524i | \(-0.127360\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.90837e7 | + | 3.05236e7i | 2.51074 | + | 1.56135i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.14412e6i | − | 0.261545i | −0.991412 | − | 0.130773i | \(-0.958254\pi\) | ||
0.991412 | − | 0.130773i | \(-0.0417458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00711e7 | 0.508970 | 0.254485 | − | 0.967077i | \(-0.418094\pi\) | ||||
0.254485 | + | 0.967077i | \(0.418094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.67011e7 | 0.838963 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.52988e6i | − | 0.176258i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.17706e6 | − | 1.29148e7i | −0.356230 | − | 0.641022i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2.22939e6i | − | 0.109995i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −933470. | −0.0457821 | −0.0228910 | − | 0.999738i | \(-0.507287\pi\) | ||||
−0.0228910 | + | 0.999738i | \(0.507287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.55199e6 | 0.173173 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 6.31679e6i | − | 0.306145i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.44600e7 | + | 1.91502e7i | −1.66025 | + | 0.922638i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.00743e6i | − | 0.383517i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.16265e7 | 0.553580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.81023e7 | −0.856859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.96289e7i | 0.923682i | 0.886963 | + | 0.461841i | \(0.152811\pi\) | ||||
−0.886963 | + | 0.461841i | \(0.847189\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.81919e7 | + | 1.56669e7i | −1.31889 | + | 0.732938i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.93615e7i | 1.36561i | 0.730601 | + | 0.682805i | \(0.239240\pi\) | ||||
−0.730601 | + | 0.682805i | \(0.760760\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.22206e7 | −1.02748 | −0.513739 | − | 0.857947i | \(-0.671740\pi\) | ||||
−0.513739 | + | 0.857947i | \(0.671740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.03123e7 | −0.474074 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.40411e7i | − | 0.641763i | −0.947119 | − | 0.320881i | \(-0.896021\pi\) | ||
0.947119 | − | 0.320881i | \(-0.103979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.22100e7 | − | 2.19714e7i | −0.554851 | − | 0.998432i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.60601e7i | 1.62922i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.52086e7 | −2.03082 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.97015e7 | −2.21985 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.76189e7i | 1.67059i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.17547e6 | − | 205258.i | −0.184368 | − | 0.00906318i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 3.11419e7i | − | 1.36724i | −0.729836 | − | 0.683622i | \(-0.760404\pi\) | ||
0.729836 | − | 0.683622i | \(-0.239596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.32882e7 | 2.32626 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.80425e6 | −0.295352 | −0.147676 | − | 0.989036i | \(-0.547179\pi\) | ||||
−0.147676 | + | 0.989036i | \(0.547179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.02459e7i | − | 0.442230i | −0.975248 | − | 0.221115i | \(-0.929030\pi\) | ||
0.975248 | − | 0.221115i | \(-0.0709697\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.71518e7 | − | 3.08639e7i | −0.736123 | − | 1.32462i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.03507e7i | 1.29527i | 0.761951 | + | 0.647635i | \(0.224242\pi\) | ||||
−0.761951 | + | 0.647635i | \(0.775758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.28067e6 | 0.181659 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.27214e7 | 0.958827 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.66973e7i | 0.700677i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.21171e7 | − | 1.78482e7i | 1.34023 | − | 0.744794i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 7.64939e7i | − | 3.17428i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.03847e6 | −0.0841212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.13919e6 | −0.0467501 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 8.65865e6i | − | 0.353371i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.12932e7 | − | 1.73903e7i | 1.27007 | − | 0.705807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.03000e6i | 0.203025i | 0.994834 | + | 0.101513i | \(0.0323682\pi\) | ||||
−0.994834 | + | 0.101513i | \(0.967632\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.46550e7 | 1.39109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.17959e6 | −0.246697 | −0.123348 | − | 0.992363i | \(-0.539363\pi\) | ||||
−0.123348 | + | 0.992363i | \(0.539363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.58569e7i | 0.629567i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −739966. | − | 1.33154e6i | −0.0292186 | − | 0.0525777i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 5.62833e6i | − | 0.221033i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.27546e7 | 1.66992 | 0.834958 | − | 0.550314i | \(-0.185492\pi\) | ||||
0.834958 | + | 0.550314i | \(0.185492\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.09239e7 | 2.36667 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.75697e7i | 2.99701i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.71184e7 | + | 1.06454e7i | 0.657823 | + | 0.409080i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 3.06967e7i | − | 1.17325i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.75757e7 | 0.668151 | 0.334075 | − | 0.942546i | \(-0.391576\pi\) | ||||
0.334075 | + | 0.942546i | \(0.391576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.09444e7 | 0.791941 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 5.70761e7i | − | 2.14660i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.15681e6 | − | 7.48001e6i | −0.155500 | − | 0.279816i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.25313e7i | − | 1.58256i | −0.611455 | − | 0.791279i | \(-0.709415\pi\) | ||
0.611455 | − | 0.791279i | \(-0.290585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.07091e7 | 1.87682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.23345e7 | 0.454095 | 0.227047 | − | 0.973884i | \(-0.427093\pi\) | ||||
0.227047 | + | 0.973884i | \(0.427093\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.60294e7i | − | 1.68561i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.27330e6 | + | 3.48621e6i | −0.228516 | + | 0.126991i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.28532e7i | − | 0.828081i | −0.910259 | − | 0.414040i | \(-0.864117\pi\) | ||
0.910259 | − | 0.414040i | \(-0.135883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.36007e7 | 0.850668 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.68894e7 | 2.03976 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.08757e7i | 1.10125i | 0.834754 | + | 0.550623i | \(0.185610\pi\) | ||||
−0.834754 | + | 0.550623i | \(0.814390\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.36968e7 | + | 1.87261e7i | −1.19558 | + | 0.664413i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 9.07315e7i | − | 3.20242i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.19142e6 | −0.182280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.84565e7 | −0.993968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.76838e7i | 1.30945i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.08168e7 | + | 1.94644e7i | 0.373921 | + | 0.672855i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.99276e7i | 0.685313i | 0.939461 | + | 0.342657i | \(0.111327\pi\) | ||||
−0.939461 | + | 0.342657i | \(0.888673\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.36967e6 | 0.252138 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.53795e7 | −1.20421 | −0.602107 | − | 0.798415i | \(-0.705672\pi\) | ||||
−0.602107 | + | 0.798415i | \(0.705672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.32638e6i | − | 0.281951i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.49837e7 | + | 7.23364e7i | −1.51546 | + | 2.43694i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.28357e7i | 1.10055i | 0.834983 | + | 0.550275i | \(0.185477\pi\) | ||||
−0.834983 | + | 0.550275i | \(0.814523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.66732e7 | 0.889445 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.30940e7 | −0.766172 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.83290e7i | − | 0.935077i | −0.883973 | − | 0.467539i | \(-0.845141\pi\) | ||
0.883973 | − | 0.467539i | \(-0.154859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 524900. | + | 944537.i | 0.0172380 | + | 0.0310191i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.13687e6i | 0.265867i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.86484e7 | 1.25644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.98087e6 | −0.193455 | −0.0967276 | − | 0.995311i | \(-0.530838\pi\) | ||||
−0.0967276 | + | 0.995311i | \(0.530838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.34028e7i | − | 1.07500i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.53776e7 | − | 8.54567e6i | 0.492414 | − | 0.273646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.87665e6i | 0.0597922i | 0.999553 | + | 0.0298961i | \(0.00951764\pi\) | ||||
−0.999553 | + | 0.0298961i | \(0.990482\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.46072e7 | 1.09711 |
(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 | 160.6.c.c.129.11 | yes | 12 | |
4.3 | odd | 2 | inner | 160.6.c.c.129.1 | ✓ | 12 | |
5.2 | odd | 4 | 800.6.a.ba.1.6 | 6 | |||
5.3 | odd | 4 | 800.6.a.z.1.1 | 6 | |||
5.4 | even | 2 | inner | 160.6.c.c.129.2 | yes | 12 | |
8.3 | odd | 2 | 320.6.c.k.129.12 | 12 | |||
8.5 | even | 2 | 320.6.c.k.129.2 | 12 | |||
20.3 | even | 4 | 800.6.a.z.1.6 | 6 | |||
20.7 | even | 4 | 800.6.a.ba.1.1 | 6 | |||
20.19 | odd | 2 | inner | 160.6.c.c.129.12 | yes | 12 | |
40.19 | odd | 2 | 320.6.c.k.129.1 | 12 | |||
40.29 | even | 2 | 320.6.c.k.129.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.c.c.129.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
160.6.c.c.129.2 | yes | 12 | 5.4 | even | 2 | inner | |
160.6.c.c.129.11 | yes | 12 | 1.1 | even | 1 | trivial | |
160.6.c.c.129.12 | yes | 12 | 20.19 | odd | 2 | inner | |
320.6.c.k.129.1 | 12 | 40.19 | odd | 2 | |||
320.6.c.k.129.2 | 12 | 8.5 | even | 2 | |||
320.6.c.k.129.11 | 12 | 40.29 | even | 2 | |||
320.6.c.k.129.12 | 12 | 8.3 | odd | 2 | |||
800.6.a.z.1.1 | 6 | 5.3 | odd | 4 | |||
800.6.a.z.1.6 | 6 | 20.3 | even | 4 | |||
800.6.a.ba.1.1 | 6 | 20.7 | even | 4 | |||
800.6.a.ba.1.6 | 6 | 5.2 | odd | 4 |