Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(191,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.191");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.f (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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 5192x^{16} + 8441320x^{12} + 4098006217x^{8} + 8949568544x^{4} + 8386816 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{87}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.17 | ||
Root | \(0.123732 - 0.123732i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.6.f.f.191.18 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 14.0881 | − | 6.67280i | 0.903750 | − | 0.428060i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −28.8990 | −0.516961 | −0.258481 | − | 0.966016i | \(-0.583222\pi\) | ||||
−0.258481 | + | 0.966016i | \(0.583222\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44.6454i | 0.344375i | 0.985064 | + | 0.172187i | \(0.0550835\pi\) | ||||
−0.985064 | + | 0.172187i | \(0.944917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 153.948 | − | 188.014i | 0.633529 | − | 0.773719i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 152.334i | − | 0.379591i | −0.981824 | − | 0.189796i | \(-0.939217\pi\) | ||
0.981824 | − | 0.189796i | \(-0.0607825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 578.038i | 0.948632i | 0.880355 | + | 0.474316i | \(0.157305\pi\) | ||||
−0.880355 | + | 0.474316i | \(0.842695\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −407.132 | + | 192.837i | −0.467204 | + | 0.221291i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82.5350i | 0.0692654i | 0.999400 | + | 0.0346327i | \(0.0110261\pi\) | ||||
−0.999400 | + | 0.0346327i | \(0.988974\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1232.16 | 0.783039 | 0.391519 | − | 0.920170i | \(-0.371950\pi\) | ||||
0.391519 | + | 0.920170i | \(0.371950\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 297.910 | + | 628.967i | 0.147413 | + | 0.311229i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2598.70 | 1.02432 | 0.512162 | − | 0.858889i | \(-0.328845\pi\) | ||||
0.512162 | + | 0.858889i | \(0.328845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2289.85 | −0.732751 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 914.247 | − | 3676.01i | 0.241354 | − | 0.970437i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −53.2122 | −0.0117494 | −0.00587471 | − | 0.999983i | \(-0.501870\pi\) | ||||
−0.00587471 | + | 0.999983i | \(0.501870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4031.95i | 0.753548i | 0.926305 | + | 0.376774i | \(0.122967\pi\) | ||||
−0.926305 | + | 0.376774i | \(0.877033\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1016.50 | − | 2146.10i | −0.162488 | − | 0.343056i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1290.21i | − | 0.178028i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3929.98i | − | 0.471940i | −0.971760 | − | 0.235970i | \(-0.924173\pi\) | ||
0.971760 | − | 0.235970i | \(-0.0758266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3857.13 | + | 8143.44i | 0.406072 | + | 0.857327i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4852.97i | − | 0.450867i | −0.974259 | − | 0.225433i | \(-0.927620\pi\) | ||
0.974259 | − | 0.225433i | \(-0.0723798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14593.3 | 1.20360 | 0.601800 | − | 0.798646i | \(-0.294450\pi\) | ||||
0.601800 | + | 0.798646i | \(0.294450\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4448.93 | + | 5433.41i | −0.327510 | + | 0.399983i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10997.2 | 0.726169 | 0.363084 | − | 0.931756i | \(-0.381724\pi\) | ||||
0.363084 | + | 0.931756i | \(0.381724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14813.8 | 0.881406 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 550.740 | + | 1162.76i | 0.0296497 | + | 0.0625986i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35748.6 | 1.74811 | 0.874057 | − | 0.485824i | \(-0.161480\pi\) | ||||
0.874057 | + | 0.485824i | \(0.161480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4402.31i | 0.196234i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17358.8 | − | 8221.95i | 0.707671 | − | 0.335188i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 20128.9i | − | 0.752818i | −0.926454 | − | 0.376409i | \(-0.877159\pi\) | ||
0.926454 | − | 0.376409i | \(-0.122841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28232.8i | 0.971471i | 0.874106 | + | 0.485736i | \(0.161448\pi\) | ||||
−0.874106 | + | 0.485736i | \(0.838552\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8393.94 | + | 6873.05i | 0.266449 | + | 0.218171i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 16704.7i | − | 0.490406i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1409.94 | 0.0383720 | 0.0191860 | − | 0.999816i | \(-0.493893\pi\) | ||||
0.0191860 | + | 0.999816i | \(0.493893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 36610.7 | − | 17340.6i | 0.925733 | − | 0.438472i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −44453.1 | −1.04654 | −0.523270 | − | 0.852167i | \(-0.675288\pi\) | ||||
−0.523270 | + | 0.852167i | \(0.675288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 17537.7 | 0.385181 | 0.192590 | − | 0.981279i | \(-0.438311\pi\) | ||||
0.192590 | + | 0.981279i | \(0.438311\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −32259.5 | + | 15279.7i | −0.662224 | + | 0.313661i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6801.02 | 0.130722 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 73476.1i | − | 1.32458i | −0.749247 | − | 0.662291i | \(-0.769584\pi\) | ||
0.749247 | − | 0.662291i | \(-0.230416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11649.3 | − | 57888.5i | −0.197282 | − | 0.980347i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 37013.3i | 0.589743i | 0.955537 | + | 0.294871i | \(0.0952768\pi\) | ||||
−0.955537 | + | 0.294871i | \(0.904723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2385.18i | − | 0.0358075i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −749.658 | + | 355.074i | −0.0106185 | + | 0.00502946i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 106980.i | − | 1.43162i | −0.698293 | − | 0.715812i | \(-0.746057\pi\) | ||
0.698293 | − | 0.715812i | \(-0.253943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25806.7 | −0.326685 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26904.4 | + | 56802.4i | 0.322564 | + | 0.681019i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −35608.2 | −0.404801 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 32885.5 | 0.354875 | 0.177438 | − | 0.984132i | \(-0.443219\pi\) | ||||
0.177438 | + | 0.984132i | \(0.443219\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −28640.9 | − | 23451.5i | −0.293697 | − | 0.240482i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 177795. | 1.73426 | 0.867131 | − | 0.498079i | \(-0.165961\pi\) | ||||
0.867131 | + | 0.498079i | \(0.165961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10133.0i | 0.0941118i | 0.998892 | + | 0.0470559i | \(0.0149839\pi\) | ||||
−0.998892 | + | 0.0470559i | \(0.985016\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8609.29 | − | 18176.5i | −0.0762069 | − | 0.160893i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 168254.i | 1.42072i | 0.703841 | + | 0.710358i | \(0.251467\pi\) | ||||
−0.703841 | + | 0.710358i | \(0.748533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171330.i | 1.38123i | 0.723220 | + | 0.690617i | \(0.242661\pi\) | ||||
−0.723220 | + | 0.690617i | \(0.757339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26224.0 | − | 55365.9i | −0.202018 | − | 0.426515i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 172128.i | − | 1.26811i | −0.773289 | − | 0.634054i | \(-0.781390\pi\) | ||
0.773289 | − | 0.634054i | \(-0.218610\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −75100.0 | −0.529536 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 108679. | + | 88987.5i | 0.733975 | + | 0.600986i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3684.81 | −0.0238532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 137845. | 0.855911 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −32382.9 | − | 68369.0i | −0.192998 | − | 0.407471i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 156484. | 0.895765 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 133394.i | − | 0.733882i | −0.930244 | − | 0.366941i | \(-0.880405\pi\) | ||
0.930244 | − | 0.366941i | \(-0.119595\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 205592. | − | 97378.2i | 1.08775 | − | 0.515214i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 53705.5i | − | 0.273426i | −0.990611 | − | 0.136713i | \(-0.956346\pi\) | ||
0.990611 | − | 0.136713i | \(-0.0436539\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 55010.3i | 0.269659i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −26420.9 | + | 106233.i | −0.124771 | + | 0.501679i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 352598.i | − | 1.60501i | −0.596643 | − | 0.802507i | \(-0.703499\pi\) | ||
0.596643 | − | 0.802507i | \(-0.296501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 60518.3 | 0.265674 | 0.132837 | − | 0.991138i | \(-0.457591\pi\) | ||||
0.132837 | + | 0.991138i | \(0.457591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 154929. | − | 73382.1i | 0.656275 | − | 0.310844i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 88055.0 | 0.360092 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1537.78 | 0.00607400 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 208698. | − | 98849.4i | 0.796571 | − | 0.377295i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 66567.9 | 0.245640 | 0.122820 | − | 0.992429i | \(-0.460806\pi\) | ||||
0.122820 | + | 0.992429i | \(0.460806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 496298.i | 1.77133i | 0.464323 | + | 0.885666i | \(0.346298\pi\) | ||||
−0.464323 | + | 0.885666i | \(0.653702\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15517.7 | + | 12706.1i | 0.0535919 | + | 0.0438816i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 116519.i | − | 0.389555i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 231714.i | − | 0.750245i | −0.926975 | − | 0.375123i | \(-0.877601\pi\) | ||
0.926975 | − | 0.375123i | \(-0.122399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 503629. | − | 238543.i | 1.57986 | − | 0.748298i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 116020.i | 0.352751i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 189838. | 0.559646 | 0.279823 | − | 0.960052i | \(-0.409724\pi\) | ||||
0.279823 | + | 0.960052i | \(0.409724\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 29375.7 | + | 62020.1i | 0.0839999 | + | 0.177346i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −475478. | −1.31929 | −0.659644 | − | 0.751578i | \(-0.729293\pi\) | ||||
−0.659644 | + | 0.751578i | \(0.729293\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37165.2 | 0.100097 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 189688. | − | 231663.i | 0.496078 | − | 0.605852i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 445145. | 1.13080 | 0.565400 | − | 0.824817i | \(-0.308722\pi\) | ||||
0.565400 | + | 0.824817i | \(0.308722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 102231.i | − | 0.252341i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −134316. | − | 283577.i | −0.322251 | − | 0.680360i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 183022.i | 0.426945i | 0.976949 | + | 0.213472i | \(0.0684773\pi\) | ||||
−0.976949 | + | 0.213472i | \(0.931523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 297588.i | 0.675180i | 0.941293 | + | 0.337590i | \(0.109612\pi\) | ||||
−0.941293 | + | 0.337590i | \(0.890388\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 188392. | + | 397746.i | 0.415848 | + | 0.877967i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 113573.i | 0.243975i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12572.9 | 0.0262925 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 164117. | + | 40816.9i | 0.334194 | + | 0.0831162i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 190595. | 0.378031 | 0.189016 | − | 0.981974i | \(-0.439470\pi\) | ||||
0.189016 | + | 0.981974i | \(0.439470\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 320590. | 0.619521 | 0.309761 | − | 0.950815i | \(-0.399751\pi\) | ||||
0.309761 | + | 0.950815i | \(0.399751\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −111467. | − | 235337.i | −0.209923 | − | 0.443205i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −508933. | −0.934319 | −0.467160 | − | 0.884173i | \(-0.654723\pi\) | ||||
−0.467160 | + | 0.884173i | \(0.654723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 738755.i | 1.32242i | 0.750203 | + | 0.661208i | \(0.229956\pi\) | ||||
−0.750203 | + | 0.661208i | \(0.770044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19863.4 | − | 9408.26i | 0.0346787 | − | 0.0164255i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2375.68i | − | 0.00404620i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 140246.i | 0.233081i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 400064. | − | 488592.i | 0.648939 | − | 0.792539i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 187700.i | − | 0.297235i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −358830. | −0.554858 | −0.277429 | − | 0.960746i | \(-0.589482\pi\) | ||||
−0.277429 | + | 0.960746i | \(0.589482\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −626258. | + | 296626.i | −0.945811 | + | 0.447982i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −421732. | −0.622215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −180008. | −0.259503 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 247072. | − | 117025.i | 0.348107 | − | 0.164880i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −47708.4 | −0.0657074 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.33973e6i | − | 1.80408i | −0.431658 | − | 0.902038i | \(-0.642071\pi\) | ||
0.431658 | − | 0.902038i | \(-0.357929\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −352516. | + | 430523.i | −0.464219 | + | 0.566943i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.11010e6i | 1.42987i | 0.699191 | + | 0.714935i | \(0.253544\pi\) | ||||
−0.699191 | + | 0.714935i | \(0.746456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 28453.2i | − | 0.0358544i | −0.999839 | − | 0.0179272i | \(-0.994293\pi\) | ||
0.999839 | − | 0.0179272i | \(-0.00570671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 95813.3 | − | 45381.8i | 0.118140 | − | 0.0559567i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 274080.i | 0.330741i | 0.986232 | + | 0.165370i | \(0.0528819\pi\) | ||||
−0.986232 | + | 0.165370i | \(0.947118\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −317808. | −0.375401 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −490291. | − | 1.03514e6i | −0.567000 | − | 1.19709i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −736307. | −0.833805 | −0.416902 | − | 0.908951i | \(-0.636884\pi\) | ||||
−0.416902 | + | 0.908951i | \(0.636884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.01712e6 | −1.12805 | −0.564027 | − | 0.825757i | \(-0.690748\pi\) | ||||
−0.564027 | + | 0.825757i | \(0.690748\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −550394. | − | 737804.i | −0.597941 | − | 0.801540i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −428104. | −0.455653 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 712235.i | 0.742816i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 246982. | + | 521446.i | 0.252445 | + | 0.532980i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.60216e6i | 1.60517i | 0.596540 | + | 0.802584i | \(0.296542\pi\) | ||||
−0.596540 | + | 0.802584i | \(0.703458\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 395872.i | − | 0.388824i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15915.8 | − | 33602.6i | −0.0153278 | − | 0.0323611i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.78274e6i | 1.68366i | 0.539739 | + | 0.841832i | \(0.318523\pi\) | ||||
−0.539739 | + | 0.841832i | \(0.681477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 175456. | 0.162524 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8191.89 | + | 10004.6i | −0.00744360 | + | 0.00909075i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.84815e6 | −1.64759 | −0.823793 | − | 0.566891i | \(-0.808146\pi\) | ||||
−0.823793 | + | 0.566891i | \(0.808146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.03310e6 | −0.903707 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −713858. | − | 1.50715e6i | −0.612821 | − | 1.29383i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.48588e6 | −1.25200 | −0.625999 | − | 0.779824i | \(-0.715308\pi\) | ||||
−0.625999 | + | 0.779824i | \(0.715308\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.00499e6i | − | 1.65840i | −0.558950 | − | 0.829201i | \(-0.688796\pi\) | ||
0.558950 | − | 0.829201i | \(-0.311204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −363567. | + | 172203.i | −0.295242 | + | 0.139841i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 348822.i | 0.278146i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.23674e6i | − | 1.75152i | −0.482745 | − | 0.875761i | \(-0.660360\pi\) | ||
0.482745 | − | 0.875761i | \(-0.339640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 758062. | + | 620709.i | 0.583034 | + | 0.477394i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.98583e6i | 1.50029i | 0.661272 | + | 0.750146i | \(0.270017\pi\) | ||||
−0.661272 | + | 0.750146i | \(0.729983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −562336. | −0.417379 | −0.208689 | − | 0.977982i | \(-0.566920\pi\) | ||||
−0.208689 | + | 0.977982i | \(0.566920\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −501651. | + | 237606.i | −0.365839 | + | 0.173279i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 216663. | 0.155267 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.41304e6 | 0.995202 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 463294. | − | 219439.i | 0.320719 | − | 0.151908i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −868343. | −0.590911 | −0.295456 | − | 0.955356i | \(-0.595471\pi\) | ||||
−0.295456 | + | 0.955356i | \(0.595471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 581706.i | 0.389178i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −559983. | − | 139271.i | −0.368369 | − | 0.0916158i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.50215e6i | 0.971707i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 651524.i | 0.414490i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.50478e6 | − | 1.18639e6i | 1.56734 | − | 0.742369i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 815901.i | − | 0.502213i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 655310. | 0.396827 | 0.198413 | − | 0.980118i | \(-0.436421\pi\) | ||||
0.198413 | + | 0.980118i | \(0.436421\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 67615.3 | + | 142754.i | 0.0402855 | + | 0.0850535i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.43617e6 | −1.42826 | −0.714130 | − | 0.700013i | \(-0.753178\pi\) | ||||
−0.714130 | + | 0.700013i | \(0.753178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 538383. | 0.310621 | 0.155310 | − | 0.987866i | \(-0.450362\pi\) | ||||
0.155310 | + | 0.987866i | \(0.450362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −242577. | − | 198624.i | −0.137744 | − | 0.112786i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.44244e6 | −1.36514 | −0.682568 | − | 0.730822i | \(-0.739137\pi\) | ||||
−0.682568 | + | 0.730822i | \(0.739137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8106.05i | 0.00445998i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.12273e6 | + | 2.37038e6i | 0.608152 | + | 1.28397i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 101696.i | 0.0542374i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.32362e6i | − | 0.695111i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.14325e6 | + | 2.41371e6i | 0.591252 | + | 1.24829i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 490974.i | 0.250074i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.40659e6 | 0.705662 | 0.352831 | − | 0.935687i | \(-0.385219\pi\) | ||||
0.352831 | + | 0.935687i | \(0.385219\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −738891. | − | 605011.i | −0.365149 | − | 0.298987i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −40745.9 | −0.0198368 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.23749e6 | −1.55287 | −0.776433 | − | 0.630200i | \(-0.782973\pi\) | ||||
−0.776433 | + | 0.630200i | \(0.782973\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.14858e6 | − | 2.42496e6i | −0.542827 | − | 1.14605i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 614204. | 0.286040 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.41172e6i | 0.647909i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.05801e6 | + | 501127.i | −0.478568 | + | 0.226673i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 734757.i | − | 0.327582i | −0.986495 | − | 0.163791i | \(-0.947628\pi\) | ||
0.986495 | − | 0.163791i | \(-0.0523722\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.99425e6i | 0.876426i | 0.898871 | + | 0.438213i | \(0.144388\pi\) | ||||
−0.898871 | + | 0.438213i | \(0.855612\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.12487e6 | + | 528470.i | 0.920588 | + | 0.228956i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.67494e6i | 0.715423i | 0.933832 | + | 0.357712i | \(0.116443\pi\) | ||||
−0.933832 | + | 0.357712i | \(0.883557\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.28465e6 | 0.541021 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −51911.8 | + | 24588.0i | −0.0215574 | + | 0.0102106i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 131434. | 0.0538233 | 0.0269116 | − | 0.999638i | \(-0.491433\pi\) | ||||
0.0269116 | + | 0.999638i | \(0.491433\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −957880. | −0.386851 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94197e6 | − | 919813.i | 0.773529 | − | 0.366381i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −506821. | −0.199123 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.39215e6i | 0.539535i | 0.962925 | + | 0.269768i | \(0.0869469\pi\) | ||||
−0.962925 | + | 0.269768i | \(0.913053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −912425. | − | 747103.i | −0.348844 | − | 0.285637i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.59601e6i | 0.602006i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.31485e6i | − | 0.489333i | −0.969607 | − | 0.244667i | \(-0.921321\pi\) | ||
0.969607 | − | 0.244667i | \(-0.0786785\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.20455e6 | − | 1.04418e6i | 0.809548 | − | 0.383441i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 30758.7i | − | 0.0111459i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.11465e6 | 0.398602 | 0.199301 | − | 0.979938i | \(-0.436133\pi\) | ||||
0.199301 | + | 0.979938i | \(0.436133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −890110. | − | 1.87926e6i | −0.314146 | − | 0.663246i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.84613e6 | −0.991419 | −0.495710 | − | 0.868488i | \(-0.665092\pi\) | ||||
−0.495710 | + | 0.868488i | \(0.665092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −196543. | −0.0675780 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.24660e6 | − | 2.74374e6i | 0.762516 | − | 0.931249i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 226921. | 0.0760328 | 0.0380164 | − | 0.999277i | \(-0.487896\pi\) | ||||
0.0380164 | + | 0.999277i | \(0.487896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 214484.i | 0.0709502i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −358366. | − | 756607.i | −0.117043 | − | 0.247109i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.12339e6i | 0.684757i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.18565e6i | 0.695992i | 0.937496 | + | 0.347996i | \(0.113138\pi\) | ||||
−0.937496 | + | 0.347996i | \(0.886862\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 367072. | + | 774988.i | 0.115430 | + | 0.243704i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.78893e6i | − | 1.17667i | −0.808616 | − | 0.588336i | \(-0.799783\pi\) | ||
0.808616 | − | 0.588336i | \(-0.200217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.33062e6 | −0.714840 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 336653. | + | 1.67292e6i | 0.101987 | + | 0.506801i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −598671. | −0.179144 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.94246e6 | 0.869765 | 0.434882 | − | 0.900487i | \(-0.356790\pi\) | ||||
0.434882 | + | 0.900487i | \(0.356790\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.35282e6 | − | 4.96743e6i | −0.687042 | − | 1.45053i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 898663. | 0.259252 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.06965e6i | − | 0.304874i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 852586. | − | 403826.i | 0.240103 | − | 0.113725i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.05386e6i | 1.40633i | 0.711026 | + | 0.703166i | \(0.248231\pi\) | ||||
−0.711026 | + | 0.703166i | \(0.751769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.45462e6i | − | 0.399984i | −0.979798 | − | 0.199992i | \(-0.935908\pi\) | ||
0.979798 | − | 0.199992i | \(-0.0640917\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.69299e6 | − | 2.06762e6i | 0.460049 | − | 0.561850i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 188993.i | − | 0.0507543i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.26047e6 | −0.334550 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.24053e6 | − | 587573.i | 0.325434 | − | 0.154141i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.82711e6 | −0.992380 | −0.496190 | − | 0.868214i | \(-0.665268\pi\) | ||||
−0.496190 | + | 0.868214i | \(0.665268\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.03269e6 | 1.03365 | 0.516827 | − | 0.856090i | \(-0.327113\pi\) | ||||
0.516827 | + | 0.856090i | \(0.327113\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21664.4 | − | 10261.3i | 0.00548938 | − | 0.00260004i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.20202e6 | 0.802085 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.40698e6i | − | 0.596090i | −0.954552 | − | 0.298045i | \(-0.903665\pi\) | ||
0.954552 | − | 0.298045i | \(-0.0963345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.28055e6 | − | 2.78520e6i | 0.558396 | − | 0.681960i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.08258e6i | 0.262090i | 0.991376 | + | 0.131045i | \(0.0418332\pi\) | ||||
−0.991376 | + | 0.131045i | \(0.958167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.09163e6i | 0.740094i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 937813. | − | 444194.i | 0.221997 | − | 0.105149i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 521460.i | − | 0.122069i | −0.998136 | − | 0.0610344i | \(-0.980560\pi\) | ||
0.998136 | − | 0.0610344i | \(-0.0194399\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −739274. | −0.171145 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.31169e6 | + | 6.99188e6i | 0.758237 | + | 1.60084i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 745789. | 0.168884 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.05419e6 | 0.236117 | 0.118058 | − | 0.993007i | \(-0.462333\pi\) | ||||
0.118058 | + | 0.993007i | \(0.462333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 303400. | + | 75457.4i | 0.0672177 | + | 0.0167175i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.05120e6 | 1.54529 | 0.772647 | − | 0.634836i | \(-0.218933\pi\) | ||||
0.772647 | + | 0.634836i | \(0.218933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.69949e6i | 1.01882i | 0.860523 | + | 0.509411i | \(0.170137\pi\) | ||||
−0.860523 | + | 0.509411i | \(0.829863\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −777510. | − | 1.64153e6i | −0.166753 | − | 0.352061i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.38535e6i | 0.293946i | 0.989140 | + | 0.146973i | \(0.0469531\pi\) | ||||
−0.989140 | + | 0.146973i | \(0.953047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 62947.4i | 0.0132143i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.54618e6 | − | 3.26440e6i | −0.321150 | − | 0.678034i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.22306e6i | − | 0.456876i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.82146e6 | −0.573772 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.50341e6 | − | 6.72123e6i | 1.10748 | − | 1.35255i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.72473e6 | −0.741748 | −0.370874 | − | 0.928683i | \(-0.620942\pi\) | ||||
−0.370874 | + | 0.928683i | \(0.620942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.27168e6 | 0.447697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 774179. | + | 1.63450e6i | 0.150999 | + | 0.318799i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −950360. | −0.183457 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.89476e6i | − | 0.935209i | −0.883938 | − | 0.467605i | \(-0.845117\pi\) | ||
0.883938 | − | 0.467605i | \(-0.154883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.67445e6 | − | 1.26675e6i | 0.505781 | − | 0.239562i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.81907e6i | 1.27650i | 0.769829 | + | 0.638250i | \(0.220342\pi\) | ||||
−0.769829 | + | 0.638250i | \(0.779658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4391.87i | − | 0.000813828i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 827695. | + | 677725.i | 0.151830 | + | 0.124320i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.98462e6i | − | 0.360402i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.21107e6 | −1.47621 | −0.738105 | − | 0.674686i | \(-0.764279\pi\) | ||||
−0.738105 | + | 0.674686i | \(0.764279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.69857e6 | + | 3.17277e6i | −1.19231 | + | 0.564734i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.77094e6 | −1.01701 | −0.508507 | − | 0.861058i | \(-0.669802\pi\) | ||||
−0.508507 | + | 0.861058i | \(0.669802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.13809e6 | −0.896547 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 523586. | − | 247996.i | 0.0904624 | − | 0.0428474i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.52490e6 | 1.28738 | 0.643689 | − | 0.765287i | \(-0.277403\pi\) | ||||
0.643689 | + | 0.765287i | \(0.277403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 782975.i | 0.132646i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.12650e6 | − | 4.52943e6i | 0.188989 | − | 0.759890i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 292833.i | − | 0.0486522i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.67525e6i | − | 0.275647i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.27123e6 | − | 2.97036e6i | 1.02196 | − | 0.484050i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.63123e6i | − | 1.55449i | −0.629199 | − | 0.777244i | \(-0.716617\pi\) | ||
0.629199 | − | 0.777244i | \(-0.283383\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.69103e6 | 0.590057 | 0.295028 | − | 0.955488i | \(-0.404671\pi\) | ||||
0.295028 | + | 0.955488i | \(0.404671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −682167. | − | 1.44024e6i | −0.108017 | − | 0.228053i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −332777. | −0.0521948 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 316921. | 0.0492394 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.78451e6 | − | 3.09880e6i | −0.582470 | − | 0.476932i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.80520e6 | 0.427707 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.86239e6i | − | 0.734455i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.22127e6 | + | 2.57843e6i | 0.182758 | + | 0.385851i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2.25665e6i | − | 0.334574i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.19936e6i | 1.05755i | 0.848762 | + | 0.528775i | \(0.177348\pi\) | ||||
−0.848762 | + | 0.528775i | \(0.822652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.98575e6 | + | 4.19245e6i | 0.289018 | + | 0.610194i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.95127e6i | − | 0.714045i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.16775e7 | 1.66871 | 0.834353 | − | 0.551230i | \(-0.185841\pi\) | ||||
0.834353 | + | 0.551230i | \(0.185841\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.30816e6 | + | 4.34638e6i | 0.751646 | + | 0.615455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −65566.0 | −0.00920025 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.28037e6 | 0.456152 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 757847. | + | 1.60002e6i | 0.104436 | + | 0.220492i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.59886e6 | 0.354932 | 0.177466 | − | 0.984127i | \(-0.443210\pi\) | ||||
0.177466 | + | 0.984127i | \(0.443210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.43548e6i | 1.14177i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 177128. | − | 83896.5i | 0.0237619 | − | 0.0112548i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 6.44592e6i | − | 0.857065i | −0.903526 | − | 0.428533i | \(-0.859031\pi\) | ||
0.903526 | − | 0.428533i | \(-0.140969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.97434e6i | 0.655563i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.58445e6 | − | 520087.i | 0.337607 | − | 0.0679389i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.43660e6i | − | 0.444988i | −0.974934 | − | 0.222494i | \(-0.928580\pi\) | ||
0.974934 | − | 0.222494i | \(-0.0714198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.87411e6 | −0.882320 | −0.441160 | − | 0.897429i | \(-0.645433\pi\) | ||||
−0.441160 | + | 0.897429i | \(0.645433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.68511e6 | − | 1.27180e6i | 0.341646 | − | 0.161820i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.95063e6 | −0.750574 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 929033. | 0.116169 | 0.0580847 | − | 0.998312i | \(-0.481501\pi\) | ||||
0.0580847 | + | 0.998312i | \(0.481501\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.51649e6 | − | 2.13923e6i | 0.559892 | − | 0.265192i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.65247e6 | −0.203092 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.44574e6i | − | 0.663568i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.14072e6 | − | 2.57165e6i | −0.379437 | − | 0.310687i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.26726e6i | − | 0.750728i | −0.926878 | − | 0.375364i | \(-0.877518\pi\) | ||
0.926878 | − | 0.375364i | \(-0.122482\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.96801e6i | 0.590057i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.16989e6 | + | 3.39601e6i | −0.844391 | + | 0.399945i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.55168e6i | 0.414760i | 0.978260 | + | 0.207380i | \(0.0664936\pi\) | ||||
−0.978260 | + | 0.207380i | \(0.933506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 106487. | 0.0123312 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.92956e6 | + | 1.04076e7i | 0.566073 | + | 1.19513i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.62084e7 | 1.84575 | 0.922876 | − | 0.385098i | \(-0.125832\pi\) | ||||
0.922876 | + | 0.385098i | \(0.125832\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.56876e6 | 0.741818 | 0.370909 | − | 0.928669i | \(-0.379046\pi\) | ||||
0.370909 | + | 0.928669i | \(0.379046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 217057. | − | 265088.i | 0.0243098 | − | 0.0296891i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.98359e6 | −0.442473 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.54789e7i | 1.70518i | 0.522584 | + | 0.852588i | \(0.324968\pi\) | ||||
−0.522584 | + | 0.852588i | \(0.675032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15852.4 | − | 33468.7i | −0.00173202 | − | 0.00365676i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.35680e6i | 0.688867i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.23906e7i | − | 1.33181i | −0.746038 | − | 0.665903i | \(-0.768046\pi\) | ||
0.746038 | − | 0.665903i | \(-0.231954\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 935834. | + | 1.97580e6i | 0.0997725 | + | 0.210647i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.76077e6i | 0.609211i | 0.952479 | + | 0.304606i | \(0.0985247\pi\) | ||||
−0.952479 | + | 0.304606i | \(0.901475\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.06686e7 | 1.11913 | 0.559564 | − | 0.828787i | \(-0.310969\pi\) | ||||
0.559564 | + | 0.828787i | \(0.310969\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.37586e6 | − | 9.55287e6i | 0.247225 | − | 0.994042i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.77618e6 | 0.493015 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.63354e6 | 0.269675 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.25249e6 | − | 2.64434e6i | −0.127234 | − | 0.268626i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 324361. | 0.0326891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.14991e7i | − | 1.14972i | −0.818253 | − | 0.574858i | \(-0.805057\pi\) | ||
0.818253 | − | 0.574858i | \(-0.194943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.05522e6 | + | 2.39440e6i | −0.501453 | + | 0.237513i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.85495e6i | 0.379389i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.56293e6i | 0.836130i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.84344e6 | + | 8.35778e6i | −0.663013 | + | 0.809728i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.17687e6i | − | 0.209261i | −0.994511 | − | 0.104630i | \(-0.966634\pi\) | ||
0.994511 | − | 0.104630i | \(-0.0333660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.45127e7 | 1.38427 | 0.692133 | − | 0.721770i | \(-0.256671\pi\) | ||||
0.692133 | + | 0.721770i | \(0.256671\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.94139e6 | + | 2.81413e6i | −0.562327 | + | 0.266346i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.07629e7 | 1.01081 | 0.505405 | − | 0.862882i | \(-0.331343\pi\) | ||||
0.505405 | + | 0.862882i | \(0.331343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.06632e6 | −0.285763 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.53596e6 | + | 1.20116e6i | −0.234526 | + | 0.111083i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.99624e6 | −0.825616 | −0.412808 | − | 0.910818i | \(-0.635452\pi\) | ||||
−0.412808 | + | 0.910818i | \(0.635452\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.55204e6i | 0.141351i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.69988e6 | − | 3.29732e6i | 0.244023 | − | 0.298021i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.19620e7i | − | 1.07298i | −0.843908 | − | 0.536488i | \(-0.819751\pi\) | ||
0.843908 | − | 0.536488i | \(-0.180249\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.07936e7i | − | 1.85109i | −0.378640 | − | 0.925544i | \(-0.623608\pi\) | ||
0.378640 | − | 0.925544i | \(-0.376392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −672119. | + | 318348.i | −0.0593830 | + | 0.0281267i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.58974e6i | − | 0.139403i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −138283. | −0.0120352 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.93974e6 | − | 1.88742e7i | −0.772253 | − | 1.63043i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.30083e6 | 0.368762 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.54212e7 | −1.31244 | −0.656221 | − | 0.754569i | \(-0.727846\pi\) | ||||
−0.656221 | + | 0.754569i | \(0.727846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.09349e6 | + | 8.41750e6i | −0.176852 | + | 0.711089i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.02029e6 | 0.0855565 | 0.0427783 | − | 0.999085i | \(-0.486379\pi\) | ||||
0.0427783 | + | 0.999085i | \(0.486379\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.46819e6i | 0.122210i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.40746e6 | + | 1.56391e7i | 0.612070 | + | 1.29225i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.00685e7i | − | 0.825873i | −0.910760 | − | 0.412936i | \(-0.864503\pi\) | ||
0.910760 | − | 0.412936i | \(-0.135497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.01897e7i | 0.829730i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −189862. | − | 400851.i | −0.0153478 | − | 0.0324034i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.06641e7i | 1.65832i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.49758e7 | −1.98987 | −0.994934 | − | 0.100531i | \(-0.967946\pi\) | ||||
−0.994934 | + | 0.100531i | \(0.967946\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.04700e6 | − | 1.27869e6i | 0.0828160 | − | 0.101142i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.74892e6 | −0.137343 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 400540. | 0.0312294 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.82888e6 | + | 3.86126e6i | 0.141577 | + | 0.298907i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.23032e7 | −0.945631 | −0.472816 | − | 0.881161i | \(-0.656762\pi\) | ||||
−0.472816 | + | 0.881161i | \(0.656762\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.84237e6i | − | 0.369547i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.47731e6 | + | 2.12067e6i | −0.339269 | + | 0.160694i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.93770e6i | 0.597236i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.44444e7i | − | 1.07915i | −0.841936 | − | 0.539577i | \(-0.818584\pi\) | ||
0.841936 | − | 0.539577i | \(-0.181416\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.38145e7 | − | 1.13115e7i | −1.02485 | − | 0.839161i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.04778e7i | 0.771877i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.54470e6 | −0.186154 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.03732e7 | + | 4.91323e6i | −0.753551 | + | 0.356919i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.61863e6 | −0.333189 | −0.166595 | − | 0.986025i | \(-0.553277\pi\) | ||||
−0.166595 | + | 0.986025i | \(0.553277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −452391. | −0.0324097 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.43293e7 | + | 6.78704e6i | −1.01948 | + | 0.482875i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 121848. | 0.00860940 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 681858.i | − | 0.0478473i | −0.999714 | − | 0.0239237i | \(-0.992384\pi\) | ||
0.999714 | − | 0.0239237i | \(-0.00761587\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.26772e7 | − | 6.72157e6i | −0.883497 | − | 0.468438i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.20446e6i | 0.0833679i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.19274e7i | 0.819945i | 0.912098 | + | 0.409972i | \(0.134462\pi\) | ||||
−0.912098 | + | 0.409972i | \(0.865538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.03116e6 | + | 2.85665e6i | −0.411796 | + | 0.195047i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 214783.i | − | 0.0145657i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.82646e7 | 1.23027 | 0.615133 | − | 0.788424i | \(-0.289103\pi\) | ||||
0.615133 | + | 0.788424i | \(0.289103\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.75260e6 | + | 1.00340e7i | 0.317970 | + | 0.671320i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.74762e6 | −0.647778 | −0.323889 | − | 0.946095i | \(-0.604990\pi\) | ||||
−0.323889 | + | 0.946095i | \(0.604990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.92375e6 | −0.126986 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.95900e6 | + | 5.69811e6i | 0.456295 | + | 0.373619i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.51178e6 | −0.489259 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.40856e7i | − | 0.911330i | −0.890151 | − | 0.455665i | \(-0.849402\pi\) | ||
0.890151 | − | 0.455665i | \(-0.150598\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.06909e7 | + | 2.25713e7i | 0.687108 | + | 1.45067i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.43425e7i | − | 0.915710i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.59982e7i | − | 1.01469i | −0.861744 | − | 0.507344i | \(-0.830627\pi\) | ||
0.861744 | − | 0.507344i | \(-0.169373\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.64157e6 | − | 5.57707e6i | −0.166440 | − | 0.351400i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.23238e6i | 0.390115i | 0.980792 | + | 0.195057i | \(0.0624893\pi\) | ||||
−0.980792 | + | 0.195057i | \(0.937511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.64910e6 | −0.475663 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −448447. | − | 367193.i | −0.0277050 | − | 0.0226851i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.16353e7 | 0.714148 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.40292e6 | −0.390447 | −0.195224 | − | 0.980759i | \(-0.562543\pi\) | ||||
−0.195224 | + | 0.980759i | \(0.562543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.18959e7 | + | 2.51154e7i | 0.720710 | + | 1.52161i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.25165e7 | −0.753416 | −0.376708 | − | 0.926332i | \(-0.622944\pi\) | ||||
−0.376708 | + | 0.926332i | \(0.622944\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.23255e6i | − | 0.552163i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.47183e6 | − | 1.17078e6i | 0.146881 | − | 0.0695701i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.97964e6i | − | 0.353046i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.77173e6i | 0.397257i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48649.1 | + | 195609.i | −0.00283577 | + | 0.0114021i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.69631e6i | 0.387848i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.29675e7 | −1.32183 | −0.660917 | − | 0.750459i | \(-0.729832\pi\) | ||||
−0.660917 | + | 0.750459i | \(0.729832\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.60369e7 | + | 1.23323e7i | −1.48901 | + | 0.705266i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.68474e6 | 0.436705 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.63196e7 | −0.921569 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.45544e7 | + | 6.89367e6i | −0.816726 | + | 0.386841i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.69135e7 | −0.943164 | −0.471582 | − | 0.881822i | \(-0.656317\pi\) | ||||
−0.471582 | + | 0.881822i | \(0.656317\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 907654.i | 0.0502983i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.01138e7 | − | 1.64694e7i | −1.10767 | − | 0.906975i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.67159e6i | − | 0.146211i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 3.35287e6i | − | 0.182359i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.09332e7 | + | 9.91498e6i | −1.13149 | + | 0.535930i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.09637e7i | 1.12615i | 0.826406 | + | 0.563075i | \(0.190382\pi\) | ||||
−0.826406 | + | 0.563075i | \(0.809618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.01493e6 | −0.267740 | −0.133870 | − | 0.990999i | \(-0.542740\pi\) | ||||
−0.133870 | + | 0.990999i | \(0.542740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.33789e7 | − | 2.82465e7i | −0.709896 | − | 1.49878i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.48613e6 | −0.289316 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.79813e7 | 0.942466 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.97288e6 | + | 4.85202e6i | −0.206965 | + | 0.252762i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.05082e6 | −0.157964 | −0.0789821 | − | 0.996876i | \(-0.525167\pi\) | ||||
−0.0789821 | + | 0.996876i | \(0.525167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.19672e7i | 1.13051i | 0.824916 | + | 0.565255i | \(0.191222\pi\) | ||||
−0.824916 | + | 0.565255i | \(0.808778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.32762e6 | + | 4.91423e6i | 0.119063 | + | 0.251374i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.60374e7i | − | 1.32384i | −0.749576 | − | 0.661918i | \(-0.769743\pi\) | ||
0.749576 | − | 0.661918i | \(-0.230257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.21363e7i | − | 0.613336i | −0.951817 | − | 0.306668i | \(-0.900786\pi\) | ||
0.951817 | − | 0.306668i | \(-0.0992141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.49253e7 | − | 3.15113e7i | −0.749756 | − | 1.58294i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.22266e6i | 0.0610509i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.37409e7 | 0.682021 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.48215e7 | + | 3.68620e6i | 0.731271 | + | 0.181872i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.94937e7 | 0.956069 | 0.478034 | − | 0.878341i | \(-0.341349\pi\) | ||||
0.478034 | + | 0.878341i | \(0.341349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05083e7 | −0.999862 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.32510e7 | + | 2.79765e7i | 0.642215 | + | 1.35589i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.07404e6 | −0.0517461 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.15415e6i | 0.294754i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.92224e6 | + | 3.75236e6i | −0.377206 | + | 0.178663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.02129e7i | − | 0.483419i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.87188e7i | − | 0.880858i | −0.897788 | − | 0.440429i | \(-0.854826\pi\) | ||
0.897788 | − | 0.440429i | \(-0.145174\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48180e6 | + | 6.69483e6i | −0.256453 | + | 0.313202i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.40764e6i | 0.251510i | 0.992061 | + | 0.125755i | \(0.0401354\pi\) | ||||
−0.992061 | + | 0.125755i | \(0.959865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.14398e7 | −0.528977 | −0.264489 | − | 0.964389i | \(-0.585203\pi\) | ||||
−0.264489 | + | 0.964389i | \(0.585203\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.05236e6 | − | 1.44575e6i | 0.140323 | − | 0.0664637i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.07572e7 | 1.40579 | 0.702895 | − | 0.711294i | \(-0.251890\pi\) | ||||
0.702895 | + | 0.711294i | \(0.251890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.28642e7 | −0.584580 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.99071e7 | − | 9.42896e6i | 0.899414 | − | 0.426006i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.11929e7 | −0.502799 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 815000.i | 0.0364009i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.06265e6 | − | 6.18293e6i | 0.224824 | − | 0.274574i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.98628e6i | 0.308479i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.93601e7i | 0.849981i | 0.905198 | + | 0.424991i | \(0.139723\pi\) | ||||
−0.905198 | + | 0.424991i | \(0.860277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.22333e7 | + | 5.79428e6i | −0.534036 | + | 0.252946i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.36498e7i | 1.02657i | 0.858219 | + | 0.513284i | \(0.171571\pi\) | ||||
−0.858219 | + | 0.513284i | \(0.828429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.50443e7 | −0.649336 | −0.324668 | − | 0.945828i | \(-0.605253\pi\) | ||||
−0.324668 | + | 0.945828i | \(0.605253\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.88160e6 | + | 8.19511e6i | 0.166592 | + | 0.351720i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.89243e7 | 0.807628 | 0.403814 | − | 0.914841i | \(-0.367684\pi\) | ||||
0.403814 | + | 0.914841i | \(0.367684\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.95542e6 | 0.252731 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.81841e6 | + | 1.77459e6i | −0.372131 | + | 0.0748864i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.35503e7 | 0.568618 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.28917e6i | − | 0.220714i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.00235e7 | + | 2.11624e7i | 0.415949 | + | 0.878180i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 214549.i | − | 0.00885375i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.95051e6i | 0.121084i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.34748e6 | + | 9.17871e6i | 0.177427 | + | 0.374595i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.60001e6i | − | 0.349042i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.26513e7 | 1.72153 | 0.860765 | − | 0.509003i | \(-0.169986\pi\) | ||||
0.860765 | + | 0.509003i | \(0.169986\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.73710e7 | − | 3.34278e7i | 1.09871 | − | 1.34183i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.50247e7 | 0.999018 | 0.499509 | − | 0.866309i | \(-0.333514\pi\) | ||||
0.499509 | + | 0.866309i | \(0.333514\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.63839e6 | 0.223861 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.44434e6 | − | 1.14945e7i | −0.214977 | − | 0.453875i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.39770e6 | 0.0941612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.02276e7i | 1.18063i | 0.807172 | + | 0.590316i | \(0.200997\pi\) | ||||
−0.807172 | + | 0.590316i | \(0.799003\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.23206e6 | − | 4.37275e6i | 0.358632 | − | 0.169866i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.56955e7i | − | 0.992781i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.99906e6i | 0.345814i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.90514e6 | + | 1.55995e6i | 0.0728161 | + | 0.0596225i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.85644e7i | − | 1.46604i | −0.680204 | − | 0.733022i | \(-0.738109\pi\) | ||
0.680204 | − | 0.733022i | \(-0.261891\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.82530e7 | 0.690175 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.43210e7 | + | 1.62561e7i | −1.29079 | + | 0.611381i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −363345. | −0.0135922 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.10429e7 | 1.52717 | 0.763587 | − | 0.645705i | \(-0.223436\pi\) | ||||
0.763587 | + | 0.645705i | \(0.223436\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.58478e6 | − | 3.59252e6i | 0.280724 | − | 0.132964i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.86355e7 | 1.05422 | 0.527110 | − | 0.849797i | \(-0.323276\pi\) | ||||
0.527110 | + | 0.849797i | \(0.323276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.26114e7i | − | 0.461833i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.74282e6 | − | 1.17957e6i | −0.172765 | − | 0.0429679i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 4.29903e7i | − | 1.55774i | −0.627183 | − | 0.778872i | \(-0.715792\pi\) | ||
0.627183 | − | 0.778872i | \(-0.284208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.01374e7i | 0.365395i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.44093e7 | + | 1.62979e7i | −1.23374 | + | 0.584360i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.53032e7i | − | 0.545822i | −0.962039 | − | 0.272911i | \(-0.912014\pi\) | ||
0.962039 | − | 0.272911i | \(-0.0879864\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.50800e6 | −0.195428 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 54090.0 | + | 114199.i | 0.00190914 | + | 0.00403070i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.57419e7 | 0.552726 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.23725e7 | 0.432166 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.16341e7 | + | 2.59024e7i | 1.09923 | + | 0.900064i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.26472e6 | −0.320268 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.08678e7i | 1.74935i | 0.484711 | + | 0.874674i | \(0.338925\pi\) | ||||
−0.484711 | + | 0.874674i | \(0.661075\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 678599. | + | 1.43271e6i | 0.0232169 | + | 0.0490171i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.01232e7i | 1.02530i | 0.858597 | + | 0.512652i | \(0.171337\pi\) | ||||
−0.858597 | + | 0.512652i | \(0.828663\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.70186e6i | 0.0914916i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.83223e6 | − | 1.86472e7i | −0.297549 | − | 0.628207i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.06872e7i | − | 1.69888i | −0.527689 | − | 0.849438i | \(-0.676941\pi\) | ||
0.527689 | − | 0.849438i | \(-0.323059\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.62968e7 | −0.543432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.22124e7 | + | 2.63759e7i | 1.06869 | + | 0.875052i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.20972e6 | −0.171961 | −0.0859806 | − | 0.996297i | \(-0.527402\pi\) | ||||
−0.0859806 | + | 0.996297i | \(0.527402\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.47077e7 | 0.483007 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.27617e6 | + | 6.91688e6i | 0.107047 | + | 0.226005i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.79237e7 | 1.23288 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.30327e7i | − | 1.06846i | −0.845338 | − | 0.534232i | \(-0.820601\pi\) | ||
0.845338 | − | 0.534232i | \(-0.179399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.98161e7 | − | 9.38588e6i | 0.637743 | − | 0.302066i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.13493e7i | − | 0.683638i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 700904.i | 0.0223316i | 0.999938 | + | 0.0111658i | \(0.00355426\pi\) | ||||
−0.999938 | + | 0.0111658i | \(0.996446\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.44467e7 | − | 3.59298e6i | −0.457988 | − | 0.113904i |
(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 | 384.6.f.f.191.17 | yes | 20 | |
3.2 | odd | 2 | 384.6.f.e.191.18 | yes | 20 | ||
4.3 | odd | 2 | 384.6.f.e.191.4 | yes | 20 | ||
8.3 | odd | 2 | 384.6.f.e.191.17 | yes | 20 | ||
8.5 | even | 2 | inner | 384.6.f.f.191.4 | yes | 20 | |
12.11 | even | 2 | inner | 384.6.f.f.191.3 | yes | 20 | |
24.5 | odd | 2 | 384.6.f.e.191.3 | ✓ | 20 | ||
24.11 | even | 2 | inner | 384.6.f.f.191.18 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.f.e.191.3 | ✓ | 20 | 24.5 | odd | 2 | ||
384.6.f.e.191.4 | yes | 20 | 4.3 | odd | 2 | ||
384.6.f.e.191.17 | yes | 20 | 8.3 | odd | 2 | ||
384.6.f.e.191.18 | yes | 20 | 3.2 | odd | 2 | ||
384.6.f.f.191.3 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.f.f.191.4 | yes | 20 | 8.5 | even | 2 | inner | |
384.6.f.f.191.17 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.f.f.191.18 | yes | 20 | 24.11 | even | 2 | inner |