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 | 191.10 | ||
Root | \(4.85801 + 4.85801i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.6.f.e.191.9 |
$q$-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 | ||||||||
\(3\) | −1.14396 | + | 15.5464i | −0.0733850 | + | 0.997304i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 71.6821 | 1.28229 | 0.641144 | − | 0.767420i | \(-0.278460\pi\) | ||||
0.641144 | + | 0.767420i | \(0.278460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 100.489i | − | 0.775129i | −0.921843 | − | 0.387565i | \(-0.873316\pi\) | ||
0.921843 | − | 0.387565i | \(-0.126684\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −240.383 | − | 35.5689i | −0.989229 | − | 0.146374i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 148.424i | − | 0.369848i | −0.982753 | − | 0.184924i | \(-0.940796\pi\) | ||
0.982753 | − | 0.184924i | \(-0.0592039\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 381.250i | − | 0.625678i | −0.949806 | − | 0.312839i | \(-0.898720\pi\) | ||
0.949806 | − | 0.312839i | \(-0.101280\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −82.0014 | + | 1114.40i | −0.0941008 | + | 1.27883i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2205.04i | 1.85052i | 0.379334 | + | 0.925260i | \(0.376153\pi\) | ||||
−0.379334 | + | 0.925260i | \(0.623847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1736.63 | −1.10363 | −0.551815 | − | 0.833967i | \(-0.686064\pi\) | ||||
−0.551815 | + | 0.833967i | \(0.686064\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1562.25 | + | 114.955i | 0.773039 | + | 0.0568829i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3556.80 | 1.40197 | 0.700987 | − | 0.713174i | \(-0.252743\pi\) | ||||
0.700987 | + | 0.713174i | \(0.252743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2013.33 | 0.644264 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 827.958 | − | 3696.40i | 0.218574 | − | 0.975820i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5772.58 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5121.78i | − | 0.957231i | −0.878025 | − | 0.478616i | \(-0.841139\pi\) | ||
0.878025 | − | 0.478616i | \(-0.158861\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2307.47 | + | 169.791i | 0.368851 | + | 0.0271413i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 7203.28i | − | 0.993939i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11029.0i | 1.32444i | 0.749312 | + | 0.662218i | \(0.230385\pi\) | ||||
−0.749312 | + | 0.662218i | \(0.769615\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5927.07 | + | 436.134i | 0.623991 | + | 0.0459154i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1457.33i | 0.135393i | 0.997706 | + | 0.0676967i | \(0.0215650\pi\) | ||||
−0.997706 | + | 0.0676967i | \(0.978435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18616.8 | 1.53545 | 0.767723 | − | 0.640782i | \(-0.221390\pi\) | ||||
0.767723 | + | 0.640782i | \(0.221390\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17231.1 | − | 2549.66i | −1.26848 | − | 0.187694i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12455.1 | 0.822434 | 0.411217 | − | 0.911537i | \(-0.365104\pi\) | ||||
0.411217 | + | 0.911537i | \(0.365104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6708.93 | 0.399175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −34280.5 | − | 2522.47i | −1.84553 | − | 0.135800i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4842.48 | −0.236798 | −0.118399 | − | 0.992966i | \(-0.537776\pi\) | ||||
−0.118399 | + | 0.992966i | \(0.537776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10639.4i | − | 0.474252i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1986.63 | − | 26998.4i | 0.0809898 | − | 1.10065i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 18265.7i | − | 0.683134i | −0.939857 | − | 0.341567i | \(-0.889042\pi\) | ||
0.939857 | − | 0.341567i | \(-0.110958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5459.70i | − | 0.187864i | −0.995579 | − | 0.0939322i | \(-0.970056\pi\) | ||
0.995579 | − | 0.0939322i | \(-0.0299437\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3574.29 | + | 24155.9i | −0.113459 | + | 0.766781i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 27328.8i | − | 0.802300i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 22202.1 | 0.604237 | 0.302118 | − | 0.953270i | \(-0.402306\pi\) | ||||
0.302118 | + | 0.953270i | \(0.402306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4068.83 | + | 55295.5i | −0.102884 | + | 1.39819i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10310.5 | −0.242736 | −0.121368 | − | 0.992608i | \(-0.538728\pi\) | ||||
−0.121368 | + | 0.992608i | \(0.538728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 61295.6 | 1.34624 | 0.673120 | − | 0.739533i | \(-0.264954\pi\) | ||||
0.673120 | + | 0.739533i | \(0.264954\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2303.16 | + | 31300.0i | −0.0472793 | + | 0.642527i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14915.0 | −0.286680 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 31323.4i | − | 0.564678i | −0.959315 | − | 0.282339i | \(-0.908890\pi\) | ||
0.959315 | − | 0.282339i | \(-0.0911104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 56518.7 | + | 17100.3i | 0.957149 | + | 0.289595i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 46611.6i | 0.742675i | 0.928498 | + | 0.371338i | \(0.121101\pi\) | ||||
−0.928498 | + | 0.371338i | \(0.878899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 158062.i | 2.37290i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6603.59 | + | 89742.9i | −0.0935367 | + | 1.27117i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 99794.6i | 1.33546i | 0.744402 | + | 0.667731i | \(0.232735\pi\) | ||||
−0.744402 | + | 0.667731i | \(0.767265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38311.5 | −0.484982 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 79625.4 | + | 5859.11i | 0.954650 | + | 0.0702464i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −124485. | −1.41517 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 115614. | 1.24762 | 0.623810 | − | 0.781576i | \(-0.285584\pi\) | ||||
0.623810 | + | 0.781576i | \(0.285584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5279.30 | + | 35678.6i | −0.0541362 | + | 0.365864i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 127872. | 1.24731 | 0.623653 | − | 0.781701i | \(-0.285648\pi\) | ||||
0.623653 | + | 0.781701i | \(0.285648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 109422.i | − | 1.01628i | −0.861275 | − | 0.508138i | \(-0.830334\pi\) | ||
0.861275 | − | 0.508138i | \(-0.169666\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 111985. | + | 8240.25i | 0.991259 | + | 0.0729403i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 102575.i | 0.866131i | 0.901362 | + | 0.433066i | \(0.142568\pi\) | ||||
−0.901362 | + | 0.433066i | \(0.857432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 77992.7i | 0.628764i | 0.949297 | + | 0.314382i | \(0.101797\pi\) | ||||
−0.949297 | + | 0.314382i | \(0.898203\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −171461. | − | 12616.7i | −1.32086 | − | 0.0971937i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 116524.i | − | 0.858462i | −0.903195 | − | 0.429231i | \(-0.858785\pi\) | ||
0.903195 | − | 0.429231i | \(-0.141215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 254959. | 1.79774 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13560.7 | + | 91645.8i | −0.0915832 | + | 0.618939i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 221582. | 1.43439 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 139021. | 0.863213 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22656.2 | − | 1667.12i | −0.135028 | − | 0.00993585i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −79687.2 | −0.456156 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 141481.i | 0.778376i | 0.921158 | + | 0.389188i | \(0.127244\pi\) | ||||
−0.921158 | + | 0.389188i | \(0.872756\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21296.9 | + | 289425.i | −0.112679 | + | 1.53131i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 171204.i | − | 0.871637i | −0.900035 | − | 0.435818i | \(-0.856459\pi\) | ||
0.900035 | − | 0.435818i | \(-0.143541\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 174512.i | 0.855455i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 59349.8 | − | 264966.i | 0.280275 | − | 1.25128i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 138147.i | − | 0.628842i | −0.949284 | − | 0.314421i | \(-0.898190\pi\) | ||
0.949284 | − | 0.314421i | \(-0.101810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −300034. | −1.31714 | −0.658572 | − | 0.752518i | \(-0.728839\pi\) | ||||
−0.658572 | + | 0.752518i | \(0.728839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14248.1 | + | 193632.i | −0.0603543 | + | 0.820216i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −56586.7 | −0.231406 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 413790. | 1.63441 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7674.74 | + | 104300.i | −0.0292934 | + | 0.398098i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −383874. | −1.41652 | −0.708260 | − | 0.705952i | \(-0.750519\pi\) | ||||
−0.708260 | + | 0.705952i | \(0.750519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 481507.i | 1.71854i | 0.511522 | + | 0.859270i | \(0.329082\pi\) | ||||
−0.511522 | + | 0.859270i | \(0.670918\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 78430.9 | − | 530053.i | 0.270868 | − | 1.83059i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 367140.i | − | 1.22745i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 592981.i | 1.91996i | 0.280072 | + | 0.959979i | \(0.409642\pi\) | ||||
−0.280072 | + | 0.959979i | \(0.590358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5539.60 | − | 75283.2i | 0.0173774 | − | 0.236160i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 357420.i | − | 1.08671i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −482827. | −1.42339 | −0.711693 | − | 0.702490i | \(-0.752071\pi\) | ||||
−0.711693 | + | 0.702490i | \(0.752071\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 165404. | + | 12171.0i | 0.472973 | + | 0.0348030i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 710600. | 1.97167 | 0.985835 | − | 0.167719i | \(-0.0536400\pi\) | ||||
0.985835 | + | 0.167719i | \(0.0536400\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 225942. | 0.608527 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 417456. | + | 61770.1i | 1.09174 | + | 0.161543i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 208298. | 0.529140 | 0.264570 | − | 0.964366i | \(-0.414770\pi\) | ||||
0.264570 | + | 0.964366i | \(0.414770\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 202317.i | − | 0.499388i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 283966. | + | 20895.2i | 0.681292 | + | 0.0501318i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 294330.i | − | 0.686597i | −0.939226 | − | 0.343298i | \(-0.888456\pi\) | ||
0.939226 | − | 0.343298i | \(-0.111544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 442331.i | − | 1.00358i | −0.864990 | − | 0.501789i | \(-0.832675\pi\) | ||
0.864990 | − | 0.501789i | \(-0.167325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 84878.9 | + | 6245.68i | 0.187358 | + | 0.0137864i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 790580.i | 1.69831i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 327281. | 0.684411 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −371448. | − | 83200.8i | −0.756387 | − | 0.169423i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −311241. | −0.617325 | −0.308662 | − | 0.951172i | \(-0.599881\pi\) | ||||
−0.308662 | + | 0.951172i | \(0.599881\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −642830. | −1.24223 | −0.621116 | − | 0.783719i | \(-0.713320\pi\) | ||||
−0.621116 | + | 0.783719i | \(0.713320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 424865. | + | 31263.0i | 0.800137 | + | 0.0588768i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 269484. | 0.494729 | 0.247364 | − | 0.968923i | \(-0.420435\pi\) | ||||
0.247364 | + | 0.968923i | \(0.420435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 675602.i | − | 1.20937i | −0.796466 | − | 0.604683i | \(-0.793300\pi\) | ||
0.796466 | − | 0.604683i | \(-0.206700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25398.3 | + | 345163.i | −0.0443419 | + | 0.602608i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 580081.i | − | 0.987982i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 104464.i | 0.173614i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −854993. | − | 126512.i | −1.38687 | − | 0.205213i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 257758.i | 0.408175i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −897849. | −1.38834 | −0.694172 | − | 0.719809i | \(-0.744229\pi\) | ||||
−0.694172 | + | 0.719809i | \(0.744229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11794.8 | − | 160291.i | 0.0178132 | − | 0.242081i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.33449e6 | 1.96888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −514684. | −0.741978 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −70119.7 | + | 952928.i | −0.0987938 | + | 1.34261i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 840670. | 1.15783 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.05027e6i | 1.41429i | 0.707070 | + | 0.707144i | \(0.250017\pi\) | ||||
−0.707070 | + | 0.707144i | \(0.749983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −483969. | − | 71611.9i | −0.637325 | − | 0.0943037i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 23541.7i | − | 0.0303230i | −0.999885 | − | 0.0151615i | \(-0.995174\pi\) | ||
0.999885 | − | 0.0151615i | \(-0.00482624\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.18323e6i | − | 1.49101i | −0.666500 | − | 0.745505i | \(-0.732208\pi\) | ||
0.666500 | − | 0.745505i | \(-0.267792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17062.2 | − | 231875.i | 0.0210380 | − | 0.285907i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 97276.9i | − | 0.117387i | −0.998276 | − | 0.0586935i | \(-0.981307\pi\) | ||
0.998276 | − | 0.0586935i | \(-0.0186935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 892805. | 1.05460 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 486967. | + | 35832.7i | 0.563156 | + | 0.0414389i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.31214e6 | −1.48589 | −0.742943 | − | 0.669355i | \(-0.766571\pi\) | ||||
−0.742943 | + | 0.669355i | \(0.766571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 294315. | 0.326414 | 0.163207 | − | 0.986592i | \(-0.447816\pi\) | ||||
0.163207 | + | 0.986592i | \(0.447816\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −330504. | + | 859102.i | −0.359055 | + | 0.933316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 480910. | 0.511857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 662090.i | 0.690517i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −724644. | − | 53321.8i | −0.740673 | − | 0.0545012i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 683226.i | 0.684510i | 0.939607 | + | 0.342255i | \(0.111191\pi\) | ||||
−0.939607 | + | 0.342255i | \(0.888809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 527916.i | − | 0.518517i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.45730e6 | − | 180816.i | −2.36650 | − | 0.174135i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 400744.i | 0.378472i | 0.981932 | + | 0.189236i | \(0.0606011\pi\) | ||||
−0.981932 | + | 0.189236i | \(0.939399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.10829e6 | 1.02661 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.38763e6 | − | 205324.i | −1.26087 | − | 0.186569i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.33787e6 | 1.19269 | 0.596343 | − | 0.802730i | \(-0.296620\pi\) | ||||
0.596343 | + | 0.802730i | \(0.296620\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −347119. | −0.303643 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.55145e6 | − | 114161.i | −1.33186 | − | 0.0980029i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.23657e6 | −1.88452 | −0.942262 | − | 0.334878i | \(-0.891305\pi\) | ||||
−0.942262 | + | 0.334878i | \(0.891305\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.06106e6i | − | 0.877642i | −0.898574 | − | 0.438821i | \(-0.855396\pi\) | ||
0.898574 | − | 0.438821i | \(-0.144604\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 43826.7 | − | 595606.i | 0.0355904 | − | 0.483674i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 298826.i | − | 0.238280i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 423903.i | − | 0.331946i | −0.986130 | − | 0.165973i | \(-0.946924\pi\) | ||
0.986130 | − | 0.165973i | \(-0.0530764\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −182176. | + | 1.23119e6i | −0.140114 | + | 0.946921i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.17156e6i | − | 0.885115i | −0.896740 | − | 0.442558i | \(-0.854071\pi\) | ||
0.896740 | − | 0.442558i | \(-0.145929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −607065. | −0.450577 | −0.225289 | − | 0.974292i | \(-0.572332\pi\) | ||||
−0.225289 | + | 0.974292i | \(0.572332\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 142406. | − | 1.93530e6i | 0.103852 | − | 1.41136i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 146446. | 0.104947 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.44233e6 | −2.42442 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −132258. | + | 1.79739e6i | −0.0915566 | + | 1.24426i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −657552. | −0.447467 | −0.223734 | − | 0.974650i | \(-0.571825\pi\) | ||||
−0.223734 | + | 0.974650i | \(0.571825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.30932e6i | − | 0.875975i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −548636. | − | 122889.i | −0.360905 | − | 0.0808392i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.35603e6i | − | 0.877185i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.87079e6i | − | 1.19017i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −146281. | + | 1.98796e6i | −0.0915336 | + | 1.24394i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 391363.i | − | 0.240896i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.78991e6 | 1.08389 | 0.541944 | − | 0.840415i | \(-0.317688\pi\) | ||||
0.541944 | + | 0.840415i | \(0.317688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.70112e6 | + | 125174.i | 1.01354 | + | 0.0745795i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.83869e6 | 1.07797 | 0.538986 | − | 0.842314i | \(-0.318807\pi\) | ||||
0.538986 | + | 0.842314i | \(0.318807\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47967e6 | −1.43065 | −0.715324 | − | 0.698793i | \(-0.753721\pi\) | ||||
−0.715324 | + | 0.698793i | \(0.753721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −256213. | + | 1.73154e6i | −0.145487 | + | 0.983234i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −613487. | −0.342892 | −0.171446 | − | 0.985194i | \(-0.554844\pi\) | ||||
−0.171446 | + | 0.985194i | \(0.554844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 856790.i | − | 0.471409i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.59468e6 | − | 117342.i | −0.863796 | − | 0.0635610i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.82933e6i | − | 2.04229i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 767580.i | − | 0.403102i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.21251e6 | − | 89220.5i | −0.627069 | − | 0.0461419i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.25160e6i | − | 0.637493i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −685408. | −0.343858 | −0.171929 | − | 0.985109i | \(-0.555000\pi\) | ||||
−0.171929 | + | 0.985109i | \(0.555000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 392289. | − | 2.65117e6i | 0.193863 | − | 1.31017i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.59149e6 | 0.774806 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.57486e6 | 1.23504 | 0.617518 | − | 0.786557i | \(-0.288138\pi\) | ||||
0.617518 | + | 0.786557i | \(0.288138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.81154e6 | + | 133299.i | 0.856147 | + | 0.0629982i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −760197. | −0.354030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.36310e6i | − | 1.08454i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −291663. | + | 3.96370e6i | −0.131927 | + | 1.79289i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.51690e6i | − | 1.56797i | −0.620782 | − | 0.783984i | \(-0.713185\pi\) | ||
0.620782 | − | 0.783984i | \(-0.286815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.15782e6i | − | 0.508833i | −0.967095 | − | 0.254417i | \(-0.918117\pi\) | ||
0.967095 | − | 0.254417i | \(-0.0818835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.40925e6 | − | 315659.i | −0.610550 | − | 0.136757i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.87000e6i | 1.65301i | 0.562932 | + | 0.826503i | \(0.309673\pi\) | ||||
−0.562932 | + | 0.826503i | \(0.690327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −739078. | −0.311257 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −253481. | + | 3.44481e6i | −0.105263 | + | 1.43052i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.01806e6 | 1.64543 | 0.822716 | − | 0.568453i | \(-0.192458\pi\) | ||||
0.822716 | + | 0.568453i | \(0.192458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 539784. | 0.217998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −159035. | + | 2.16128e6i | −0.0633469 | + | 0.860885i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.39380e6 | 1.72627 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.02337e6i | − | 0.396612i | −0.980140 | − | 0.198306i | \(-0.936456\pi\) | ||
0.980140 | − | 0.198306i | \(-0.0635440\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 51835.6 | − | 350317.i | 0.0198181 | − | 0.133935i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 486617.i | 0.183549i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 826829.i | − | 0.307711i | −0.988093 | − | 0.153856i | \(-0.950831\pi\) | ||
0.988093 | − | 0.153856i | \(-0.0491691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 91158.9 | − | 1.23885e6i | 0.0334750 | − | 0.454926i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.20079e6i | − | 0.797491i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.29909e6 | 0.464559 | 0.232279 | − | 0.972649i | \(-0.425382\pi\) | ||||
0.232279 | + | 0.972649i | \(0.425382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.19953e6 | − | 161849.i | −0.776278 | − | 0.0571212i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.14371e6 | 0.746740 | 0.373370 | − | 0.927683i | \(-0.378202\pi\) | ||||
0.373370 | + | 0.927683i | \(0.378202\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.06914e6 | −0.367606 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.47516e6 | − | 662181.i | −1.51891 | − | 0.224750i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.45427e6 | 0.822335 | 0.411167 | − | 0.911560i | \(-0.365121\pi\) | ||||
0.411167 | + | 0.911560i | \(0.365121\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.84288e6i | 2.59438i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.66161e6 | + | 195850.i | 0.869287 | + | 0.0639651i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2.24533e6i | − | 0.724081i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.55038e6i | 0.812136i | 0.913843 | + | 0.406068i | \(0.133100\pi\) | ||||
−0.913843 | + | 0.406068i | \(0.866900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.71305e6 | − | 199635.i | −0.853149 | − | 0.0627776i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 57308.6i | 0.0177975i | 0.999960 | + | 0.00889875i | \(0.00283260\pi\) | ||||
−0.999960 | + | 0.00889875i | \(0.997167\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.95268e6 | −0.598919 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.05138e6 | + | 1.22579e6i | 1.22734 | + | 0.371345i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.63697e6 | 0.489840 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −147846. | −0.0437020 | −0.0218510 | − | 0.999761i | \(-0.506956\pi\) | ||||
−0.0218510 | + | 0.999761i | \(0.506956\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.14770e6 | + | 158035.i | 0.627146 | + | 0.0461475i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.83550e6 | −0.529517 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.34122e6i | 0.952324i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 343226. | − | 4.66446e6i | 0.0966586 | − | 1.31359i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.93840e6i | − | 0.817666i | −0.912609 | − | 0.408833i | \(-0.865936\pi\) | ||
0.912609 | − | 0.408833i | \(-0.134064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 242806.i | − | 0.0667657i | −0.999443 | − | 0.0333829i | \(-0.989372\pi\) | ||
0.999443 | − | 0.0333829i | \(-0.0106281\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.99398e6 | − | 443013.i | −0.813576 | − | 0.120383i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.43946e6i | 1.19222i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −548641. | −0.145619 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 64732.9 | − | 879721.i | 0.0169817 | − | 0.230782i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.23003e6 | 0.318949 | 0.159474 | − | 0.987202i | \(-0.449020\pi\) | ||||
0.159474 | + | 0.987202i | \(0.449020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 965893. | 0.247577 | 0.123788 | − | 0.992309i | \(-0.460496\pi\) | ||||
0.123788 | + | 0.992309i | \(0.460496\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −473359. | + | 6.43296e6i | −0.119941 | + | 1.63000i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.17685e6 | −1.54726 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.17684e6i | − | 1.77735i | −0.458542 | − | 0.888673i | \(-0.651628\pi\) | ||
0.458542 | − | 0.888673i | \(-0.348372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.61271e6 | − | 238629.i | −0.394875 | − | 0.0584289i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.14564e6i | 0.277356i | 0.990338 | + | 0.138678i | \(0.0442853\pi\) | ||||
−0.990338 | + | 0.138678i | \(0.955715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.15348e6i | 1.71245i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 439136. | − | 5.96786e6i | 0.103951 | − | 1.41270i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.35308e6i | − | 1.01902i | −0.860466 | − | 0.509508i | \(-0.829827\pi\) | ||
0.860466 | − | 0.509508i | \(-0.170173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 216303. | 0.0500750 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.48571e6 | − | 550824.i | −1.71391 | − | 0.126115i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.74625e6 | −0.621886 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.73821e6 | 1.06126 | 0.530632 | − | 0.847602i | \(-0.321955\pi\) | ||||
0.530632 | + | 0.847602i | \(0.321955\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.15071e6 | + | 1.82568e6i | 1.80577 | + | 0.404476i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.48712e6 | −0.764214 | −0.382107 | − | 0.924118i | \(-0.624801\pi\) | ||||
−0.382107 | + | 0.924118i | \(0.624801\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.31702e6i | 1.15270i | 0.817203 | + | 0.576350i | \(0.195523\pi\) | ||||
−0.817203 | + | 0.576350i | \(0.804477\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.70772e6 | + | 419993.i | 1.22414 | + | 0.0900762i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.34272e6i | 0.709265i | 0.935006 | + | 0.354632i | \(0.115394\pi\) | ||||
−0.935006 | + | 0.354632i | \(0.884606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.23107e6i | − | 0.468362i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.21874e6 | − | 678346.i | −1.91478 | − | 0.140896i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.76319e6i | − | 0.567882i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.49640e6 | −0.711029 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.16405e6 | + | 172242.i | 0.234248 | + | 0.0346611i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.01866e6 | 0.601140 | 0.300570 | − | 0.953760i | \(-0.402823\pi\) | ||||
0.300570 | + | 0.953760i | \(0.402823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.20479e6 | 0.828670 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.55660e6 | + | 408874.i | 1.08378 | + | 0.0797483i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.28748e6 | 1.59981 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.35174e6i | 0.449332i | 0.974436 | + | 0.224666i | \(0.0721290\pi\) | ||||
−0.974436 | + | 0.224666i | \(0.927871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 552335. | − | 7.50624e6i | 0.104455 | − | 1.41955i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.24809e6i | 0.420832i | 0.977612 | + | 0.210416i | \(0.0674819\pi\) | ||||
−0.977612 | + | 0.210416i | \(0.932518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.27287e7i | 2.35868i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −378431. | + | 2.55752e6i | −0.0694183 | + | 0.469144i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.03609e6i | 0.188152i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.93445e6 | −0.887131 | −0.443565 | − | 0.896242i | \(-0.646287\pi\) | ||||
−0.443565 | + | 0.896242i | \(0.646287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −812898. | + | 1.10473e7i | −0.144691 | + | 1.96635i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.42902e6 | −1.48545 | −0.742724 | − | 0.669598i | \(-0.766466\pi\) | ||||
−0.742724 | + | 0.669598i | \(0.766466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.16616e6 | 1.59941 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −258468. | + | 3.51259e6i | −0.0446567 | + | 0.606886i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.54347e6 | 1.11947 | 0.559737 | − | 0.828670i | \(-0.310902\pi\) | ||||
0.559737 | + | 0.828670i | \(0.310902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.15955e6i | − | 1.04351i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.43786e6 | + | 6.41928e6i | −0.241225 | + | 1.07694i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.84361e6i | − | 1.30316i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.84863e6i | − | 0.304176i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −238285. | + | 3.23830e6i | −0.0388310 | + | 0.527713i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 388674.i | − | 0.0627323i | −0.999508 | − | 0.0313661i | \(-0.990014\pi\) | ||
0.999508 | − | 0.0313661i | \(-0.00998579\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −252292. | −0.0403319 | −0.0201659 | − | 0.999797i | \(-0.506419\pi\) | ||||
−0.0201659 | + | 0.999797i | \(0.506419\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.14531e6 | + | 231443.i | 0.498041 | + | 0.0366476i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.12937e7 | 1.77138 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.21449e6 | 0.965531 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −649691. | + | 4.39075e6i | −0.0999932 | + | 0.675776i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 555606. | 0.0847128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.35282e6i | 1.11063i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.57578e6 | + | 336701.i | 0.684745 | + | 0.0503859i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 995768.i | − | 0.147634i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.20507e6i | 1.35218i | 0.736820 | + | 0.676089i | \(0.236327\pi\) | ||||
−0.736820 | + | 0.676089i | \(0.763673\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.87667e6 | + | 506009.i | 1.00087 | + | 0.0736476i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.59068e6i | 0.806257i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.73723e6 | 0.819850 | 0.409925 | − | 0.912119i | \(-0.365555\pi\) | ||||
0.409925 | + | 0.912119i | \(0.365555\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −194196. | + | 1.31242e6i | −0.0274985 | + | 0.185841i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00248e7 | −1.40669 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.14766e6 | −0.437699 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.22907e7 | − | 904391.i | −1.69373 | − | 0.124630i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.94218e6 | −0.948108 | −0.474054 | − | 0.880496i | \(-0.657210\pi\) | ||||
−0.474054 | + | 0.880496i | \(0.657210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.09766e6i | − | 0.960695i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −374396. | + | 5.08805e6i | −0.0502255 | + | 0.682565i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.89782e6i | 0.651226i | 0.945503 | + | 0.325613i | \(0.105571\pi\) | ||||
−0.945503 | + | 0.325613i | \(0.894429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.35272e6i | − | 1.10080i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.71840e6 | − | 5.67952e6i | 0.224474 | − | 0.741914i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.24106e6i | 0.808123i | 0.914732 | + | 0.404062i | \(0.132402\pi\) | ||||
−0.914732 | + | 0.404062i | \(0.867598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.53464e6 | −0.453685 | −0.226842 | − | 0.973931i | \(-0.572840\pi\) | ||||
−0.226842 | + | 0.973931i | \(0.572840\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 356047. | − | 4.83869e6i | 0.0453024 | − | 0.615660i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.16100e6 | 0.903241 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.23801e6 | 0.279848 | 0.139924 | − | 0.990162i | \(-0.455314\pi\) | ||||
0.139924 | + | 0.990162i | \(0.455314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 735371. | − | 9.99371e6i | 0.0911612 | − | 1.23888i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.68396e6 | 0.575669 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 718741.i | 0.0875793i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −972056. | + | 6.56937e6i | −0.117436 | + | 0.793659i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.22958e7i | − | 1.47287i | −0.676510 | − | 0.736433i | \(-0.736509\pi\) | ||
0.676510 | − | 0.736433i | \(-0.263491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.89464e6i | 1.05643i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −308279. | + | 4.18951e6i | −0.0363057 | + | 0.493395i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.06803e7i | − | 1.24723i | −0.781733 | − | 0.623614i | \(-0.785664\pi\) | ||
0.781733 | − | 0.623614i | \(-0.214336\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.58835e7 | 1.83930 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.05032e7 | + | 772861.i | 1.20611 | + | 0.0887494i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.78335e6 | 0.544710 | 0.272355 | − | 0.962197i | \(-0.412198\pi\) | ||||
0.272355 | + | 0.962197i | \(0.412198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −894944. | −0.101067 | −0.0505335 | − | 0.998722i | \(-0.516092\pi\) | ||||
−0.0505335 | + | 0.998722i | \(0.516092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.33700e6 | − | 789705.i | −0.597729 | − | 0.0884447i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.96534e6 | 1.10689 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.19696e7i | 1.31858i | 0.751888 | + | 0.659291i | \(0.229144\pi\) | ||||
−0.751888 | + | 0.659291i | \(0.770856\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.01819e6 | + | 663589.i | 0.985318 | + | 0.0725030i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.74849e6i | − | 0.514579i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 4.89530e6i | − | 0.526172i | −0.964772 | − | 0.263086i | \(-0.915260\pi\) | ||
0.964772 | − | 0.263086i | \(-0.0847403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.62405e6 | − | 119503.i | −0.173145 | − | 0.0127406i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.29935e6i | 0.243160i | 0.992582 | + | 0.121580i | \(0.0387961\pi\) | ||||
−0.992582 | + | 0.121580i | \(0.961204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.34773e6 | 0.246275 | 0.123138 | − | 0.992390i | \(-0.460704\pi\) | ||||
0.123138 | + | 0.992390i | \(0.460704\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.94488e6 | − | 1.31474e7i | 0.306435 | − | 1.36807i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.00283e7 | 1.03516 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20038e7 | −1.22919 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.00722e6 | − | 294865.i | −0.407074 | − | 0.0299539i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.43193e7 | −2.45089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.32907e7i | − | 1.32885i | −0.747356 | − | 0.664424i | \(-0.768677\pi\) | ||
0.747356 | − | 0.664424i | \(-0.231323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.02710e6 | − | 1.39583e7i | 0.101884 | − | 1.38460i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.01417e7i | 0.998103i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.55778e6i | − | 0.249755i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.47847e6 | + | 366734.i | 0.240121 | + | 0.0355303i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.68877e7i | − | 1.62340i | −0.584078 | − | 0.811698i | \(-0.698544\pi\) | ||
0.584078 | − | 0.811698i | \(-0.301456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.77198e7 | −1.69017 | −0.845086 | − | 0.534631i | \(-0.820451\pi\) | ||||
−0.845086 | + | 0.534631i | \(0.820451\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.52661e6 | + | 2.07466e7i | −0.144487 | + | 1.96358i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.19463e6 | −0.206111 | −0.103056 | − | 0.994676i | \(-0.532862\pi\) | ||||
−0.103056 | + | 0.994676i | \(0.532862\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.71107e6 | −0.252656 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 588777. | − | 8.00149e6i | 0.0544501 | − | 0.739977i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.02224e7 | −0.938141 | −0.469071 | − | 0.883161i | \(-0.655411\pi\) | ||||
−0.469071 | + | 0.883161i | \(0.655411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.22723e7i | − | 1.11769i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.47344e7 | − | 2.18022e6i | −1.33174 | − | 0.197055i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.14626e7i | 1.02818i | 0.857736 | + | 0.514090i | \(0.171870\pi\) | ||||
−0.857736 | + | 0.514090i | \(0.828130\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.12139e6i | − | 0.0998278i | −0.998754 | − | 0.0499139i | \(-0.984105\pi\) | ||
0.998754 | − | 0.0499139i | \(-0.0158947\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −961692. | + | 1.30694e7i | −0.0849674 | + | 1.15471i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.25094e7i | 1.09694i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.05319e7 | 1.78696 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.63279e7 | − | 1.20146e6i | −1.41047 | − | 0.103787i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −810353. | −0.0694813 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.05752e6 | 0.600640 | 0.300320 | − | 0.953838i | \(-0.402907\pi\) | ||||
0.300320 | + | 0.953838i | \(0.402907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.66695e6 | − | 7.44206e6i | 0.140819 | − | 0.628686i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.09408e6 | 0.259454 | 0.129727 | − | 0.991550i | \(-0.458590\pi\) | ||||
0.129727 | + | 0.991550i | \(0.458590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.16180e7i | − | 0.967067i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 365989. | + | 26930.7i | 0.0302413 | + | 0.00222526i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 8.19357e6i | − | 0.672080i | −0.941848 | − | 0.336040i | \(-0.890912\pi\) | ||
0.941848 | − | 0.336040i | \(-0.109088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.90270e6i | − | 0.806357i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.83950e7 | + | 1.35357e6i | 1.48699 | + | 0.109418i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.84619e6i | 0.148159i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.08153e6 | 0.564199 | 0.282099 | − | 0.959385i | \(-0.408969\pi\) | ||||
0.282099 | + | 0.959385i | \(0.408969\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.58532e6 | + | 530512.i | 0.283592 | + | 0.0419626i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.15071e7 | −1.68896 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.21346e6 | −0.250548 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.51231e6 | + | 111281.i | 0.117070 | + | 0.00861445i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 57414.8 | 0.00441295 | 0.00220647 | − | 0.999998i | \(-0.499298\pi\) | ||||
0.00220647 | + | 0.999998i | \(0.499298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.91532e7i | − | 1.46169i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.02133e6 | + | 1.38799e7i | −0.0773917 | + | 1.05175i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.28498e7i | − | 0.966824i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.30024e7i | − | 0.971419i | −0.874120 | − | 0.485710i | \(-0.838561\pi\) | ||
0.874120 | − | 0.485710i | \(-0.161439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.11414e6 | + | 7.52960e6i | −0.0826544 | + | 0.558596i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.82172e7i | − | 1.34201i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.05625e6 | −0.296729 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.50103e6 | − | 2.03991e7i | 0.109042 | − | 1.48188i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.03530e7 | −0.746868 | −0.373434 | − | 0.927657i | \(-0.621820\pi\) | ||||
−0.373434 | + | 0.927657i | \(0.621820\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.09957e7 | −0.787746 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −336684. | + | 4.57554e6i | −0.0239539 | + | 0.325534i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.16221e7 | 0.821180 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.30522e7i | 1.61762i | 0.588072 | + | 0.808809i | \(0.299887\pi\) | ||||
−0.588072 | + | 0.808809i | \(0.700113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.29779e7 | − | 6.12093e6i | −0.904451 | − | 0.426578i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.10508e7i | 2.84137i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.18210e7i | − | 0.812634i | −0.913732 | − | 0.406317i | \(-0.866813\pi\) | ||
0.913732 | − | 0.406317i | \(-0.133187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −550141. | + | 7.47643e6i | −0.0375626 | + | 0.510477i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.29533e6i | − | 0.223476i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.69579e7 | −1.14225 | −0.571123 | − | 0.820864i | \(-0.693492\pi\) | ||||
−0.571123 | + | 0.820864i | \(0.693492\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.02931e7 | − | 757403.i | −0.688655 | − | 0.0506736i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.53213e7 | −1.01817 | −0.509087 | − | 0.860715i | \(-0.670017\pi\) | ||||
−0.509087 | + | 0.860715i | \(0.670017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.75169e7 | −1.81639 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.65793e6 | − | 1.12046e7i | 0.108709 | − | 0.734676i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.03077e7 | 0.671364 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.38132e7i | 1.54070i | 0.637620 | + | 0.770351i | \(0.279919\pi\) | ||||
−0.637620 | + | 0.770351i | \(0.720081\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.06217e7 | − | 781582.i | −0.682665 | − | 0.0502328i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.45154e7i | 2.20367i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.77331e6i | − | 0.619872i | −0.950757 | − | 0.309936i | \(-0.899692\pi\) | ||
0.950757 | − | 0.309936i | \(-0.100308\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.20720e6 | + | 603914.i | 0.517119 | + | 0.0380514i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.77488e6i | 0.611857i | 0.952054 | + | 0.305928i | \(0.0989668\pi\) | ||||
−0.952054 | + | 0.305928i | \(0.901033\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.83742e6 | 0.487374 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.62209e6 | − | 3.79953e7i | 0.347332 | − | 2.34734i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.96379e6 | −0.427422 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.19002e6 | −0.377465 | −0.188732 | − | 0.982029i | \(-0.560438\pi\) | ||||
−0.188732 | + | 0.982029i | \(0.560438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.23013e6 | − | 458434.i | −0.377452 | − | 0.0277742i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.56139e7 | 0.939860 | 0.469930 | − | 0.882704i | \(-0.344279\pi\) | ||||
0.469930 | + | 0.882704i | \(0.344279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.03118e7i | − | 0.616710i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.26784e6 | + | 1.72300e7i | −0.0753377 | + | 1.02384i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 2.53084e6i | − | 0.149424i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.53033e6i | 0.0897753i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.77945e6 | − | 2.13378e7i | 0.278595 | − | 1.24378i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.25061e7i | 2.46194i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.87295e7 | −1.65345 | −0.826725 | − | 0.562607i | \(-0.809798\pi\) | ||||
−0.826725 | + | 0.562607i | \(0.809798\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.53047e6 | + | 2.07992e7i | −0.0875252 | + | 1.18947i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.17094e7 | −0.665419 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.08151e6 | −0.117543 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 397090. | − | 5.39646e6i | 0.0222829 | − | 0.302825i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.60767e7 | −0.896503 | −0.448251 | − | 0.893907i | \(-0.647953\pi\) | ||||
−0.448251 | + | 0.893907i | \(0.647953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.74639e7i | 1.52193i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.54959e6 | − | 2.39889e7i | 0.195477 | − | 1.32108i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.09776e6i | − | 0.497904i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 2.56206e7i | − | 1.39348i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.55854e6 | − | 3.47706e7i | 0.138296 | − | 1.87944i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.95204e7i | 1.04862i | 0.851528 | + | 0.524309i | \(0.175676\pi\) | ||||
−0.851528 | + | 0.524309i | \(0.824324\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.99009e6 | 0.479968 | 0.239984 | − | 0.970777i | \(-0.422858\pi\) | ||||
0.239984 | + | 0.970777i | \(0.422858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.64957e7 | + | 1.21381e6i | 0.875276 | + | 0.0644058i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.46101e7 | −1.82519 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.23305e7 | −1.69456 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.20941e6 | + | 1.36270e6i | 0.479758 | + | 0.0709888i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.64087e6 | 0.188516 | 0.0942578 | − | 0.995548i | \(-0.469952\pi\) | ||||
0.0942578 | + | 0.995548i | \(0.469952\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.60705e7i | 0.827048i | 0.910493 | + | 0.413524i | \(0.135702\pi\) | ||||
−0.910493 | + | 0.413524i | \(0.864298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.64568e6 | + | 341845.i | 0.237637 | + | 0.0174862i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.68243e6i | − | 0.339759i | −0.985465 | − | 0.169879i | \(-0.945662\pi\) | ||
0.985465 | − | 0.169879i | \(-0.0543378\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.43981e7i | 1.23302i | 0.787348 | + | 0.616509i | \(0.211454\pi\) | ||||
−0.787348 | + | 0.616509i | \(0.788546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.59017e6 | + | 484928.i | 0.331051 | + | 0.0243598i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.47934e7i | 0.738680i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.09373e7 | 2.52825 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.89322e7 | − | 4.24062e6i | −0.934086 | − | 0.209226i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.26116e7 | 0.618535 | 0.309267 | − | 0.950975i | \(-0.399916\pi\) | ||||
0.309267 | + | 0.950975i | \(0.399916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28115e7 | 0.624611 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.82136e7 | + | 1.34022e6i | 0.882729 | + | 0.0649542i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.61960e7 | 0.780307 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.39701e7i | − | 0.669101i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 694457. | − | 9.43769e6i | 0.0330656 | − | 0.449362i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.92279e7i | 1.85682i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.53134e7i | − | 1.19118i | −0.803289 | − | 0.595590i | \(-0.796918\pi\) | ||
0.803289 | − | 0.595590i | \(-0.203082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.99241e7 | + | 4.42781e6i | 1.39993 | + | 0.207145i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 4.08243e7i | − | 1.89874i | −0.314155 | − | 0.949372i | \(-0.601721\pi\) | ||
0.314155 | − | 0.949372i | \(-0.398279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.83562e7 | −1.77359 | −0.886793 | − | 0.462167i | \(-0.847072\pi\) | ||||
−0.886793 | + | 0.462167i | \(0.847072\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −167528. | + | 2.27671e6i | −0.00770157 | + | 0.104664i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.90424e6 | −0.452683 | −0.226342 | − | 0.974048i | \(-0.572677\pi\) | ||||
−0.226342 | + | 0.974048i | \(0.572677\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.49313e7 | 0.678510 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.93789e6 | − | 5.35160e7i | 0.177916 | − | 2.41789i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.64915e6 | −0.208845 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.46455e6i | − | 0.378058i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.77917e7 | − | 4.11228e6i | −1.23418 | − | 0.182620i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.00770e6i | 0.353580i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.33103e6i | 0.234052i | 0.993129 | + | 0.117026i | \(0.0373361\pi\) | ||||
−0.993129 | + | 0.117026i | \(0.962664\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 752213. | − | 1.02226e7i | 0.0328374 | − | 0.446261i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.41429e7i | − | 1.04797i | −0.851726 | − | 0.523987i | \(-0.824444\pi\) | ||
0.851726 | − | 0.523987i | \(-0.175556\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.51549e6 | 0.151734 | 0.0758672 | − | 0.997118i | \(-0.475828\pi\) | ||||
0.0758672 | + | 0.997118i | \(0.475828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.03553e7 | + | 1.49781e6i | 0.873613 | + | 0.0642834i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.61885e7 | 1.54441 | 0.772204 | − | 0.635375i | \(-0.219154\pi\) | ||||
0.772204 | + | 0.635375i | \(0.219154\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.42173e7 | 0.603342 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.53810e6 | − | 8.38875e6i | 0.107106 | − | 0.354000i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.16298e7 | −0.907662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.10982e7i | − | 0.880415i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.10814e7 | + | 1.55124e6i | 0.874820 | + | 0.0643722i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.95659e7i | − | 1.22009i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.06778e7i | − | 0.438199i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90841e7 | + | 2.14011e6i | 1.18696 | + | 0.0873406i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.17073e7i | − | 1.28688i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.36597e7 | −1.76223 | −0.881115 | − | 0.472902i | \(-0.843206\pi\) | ||||
−0.881115 | + | 0.472902i | \(0.843206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.07383e7 | − | 4.54829e6i | −1.23387 | − | 0.182574i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.48211e7 | −1.39010 | −0.695051 | − | 0.718960i | \(-0.744618\pi\) | ||||
−0.695051 | + | 0.718960i | \(0.744618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.91830e6 | 0.274677 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.08430e6 | + | 447703.i | 0.240247 | + | 0.0176782i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.72041e7 | −0.675631 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.48938e7i | 0.972305i | 0.873874 | + | 0.486152i | \(0.161600\pi\) | ||||
−0.873874 | + | 0.486152i | \(0.838400\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.04758e6 | + | 2.78267e7i | −0.0795411 | + | 1.08097i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.93087e6i | 0.151875i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.22049e7i | 0.853286i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.89203e6 | + | 2.63032e7i | −0.148757 | + | 1.00533i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.53134e6i | 0.286308i | 0.989700 | + | 0.143154i | \(0.0457243\pi\) | ||||
−0.989700 | + | 0.143154i | \(0.954276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.16509e7 | −0.440541 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.10339e6 | + | 2.85851e7i | −0.0791070 | + | 1.07507i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.34602e7 | 0.877612 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.35884e7 | −1.24980 | −0.624899 | − | 0.780706i | \(-0.714860\pi\) | ||||
−0.624899 | + | 0.780706i | \(0.714860\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.83664e6 | − | 3.85500e7i | 0.104988 | − | 1.42679i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.89573e7 | −0.697915 | −0.348958 | − | 0.937138i | \(-0.613464\pi\) | ||||
−0.348958 | + | 0.937138i | \(0.613464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.18343e6i | 0.189818i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.66262e7 | − | 5.96401e6i | −0.969906 | − | 0.217250i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.39256e7i | 1.22929i | 0.788806 | + | 0.614643i | \(0.210700\pi\) | ||||
−0.788806 | + | 0.614643i | \(0.789300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.33689e7i | − | 0.842313i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 701804. | − | 9.53753e6i | 0.0251631 | − | 0.341967i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.08981e7i | 0.745373i | 0.927957 | + | 0.372687i | \(0.121563\pi\) | ||||
−0.927957 | + | 0.372687i | \(0.878437\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.23104e7 | −0.791588 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.33200e7 | + | 980133.i | 0.470138 | + | 0.0345944i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.38823e7 | −0.487434 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.39649e6 | 0.0837082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.64850e6 | − | 2.46573e7i | 0.126779 | − | 0.856802i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.60794e7 | −1.59290 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.33064e6i | − | 0.320882i | −0.987045 | − | 0.160441i | \(-0.948708\pi\) | ||
0.987045 | − | 0.160441i | \(-0.0512916\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.95324e7 | + | 4.38060e6i | 2.03678 | + | 0.149873i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.63366e7i | 0.896419i | 0.893929 | + | 0.448209i | \(0.147938\pi\) | ||||
−0.893929 | + | 0.448209i | \(0.852062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.01502e7i | 1.02096i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.19331e7 | + | 878080.i | 0.402015 | + | 0.0295816i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.77880e7i | − | 0.931366i | −0.884952 | − | 0.465683i | \(-0.845809\pi\) | ||
0.884952 | − | 0.465683i | \(-0.154191\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.48119e7 | 0.493918 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.77412e6 | − | 1.87481e7i | 0.0920349 | − | 0.621992i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.72065e6 | −0.221834 | −0.110917 | − | 0.993830i | \(-0.535379\pi\) | ||||
−0.110917 | + | 0.993830i | \(0.535379\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.93172e7 | 0.634385 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.94579e7 | + | 1.43178e6i | 0.635774 | + | 0.0467824i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.62163e7 | 2.15266 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.58678e7i | 0.513254i | 0.966510 | + | 0.256627i | \(0.0826112\pi\) | ||||
−0.966510 | + | 0.256627i | \(0.917389\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 784079. | − | 1.06557e7i | 0.0252340 | − | 0.342931i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.84286e7i | − | 1.55076i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.44639e7i | 0.779451i | 0.920931 | + | 0.389725i | \(0.127430\pi\) | ||||
−0.920931 | + | 0.389725i | \(0.872570\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.07675e7 | + | 9.13152e6i | 1.29241 | + | 0.289487i |
(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.e.191.10 | yes | 20 | |
3.2 | odd | 2 | 384.6.f.f.191.9 | yes | 20 | ||
4.3 | odd | 2 | 384.6.f.f.191.11 | yes | 20 | ||
8.3 | odd | 2 | 384.6.f.f.191.10 | yes | 20 | ||
8.5 | even | 2 | inner | 384.6.f.e.191.11 | yes | 20 | |
12.11 | even | 2 | inner | 384.6.f.e.191.12 | yes | 20 | |
24.5 | odd | 2 | 384.6.f.f.191.12 | yes | 20 | ||
24.11 | even | 2 | inner | 384.6.f.e.191.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.f.e.191.9 | ✓ | 20 | 24.11 | even | 2 | inner | |
384.6.f.e.191.10 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.f.e.191.11 | yes | 20 | 8.5 | even | 2 | inner | |
384.6.f.e.191.12 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.f.f.191.9 | yes | 20 | 3.2 | odd | 2 | ||
384.6.f.f.191.10 | yes | 20 | 8.3 | odd | 2 | ||
384.6.f.f.191.11 | yes | 20 | 4.3 | odd | 2 | ||
384.6.f.f.191.12 | yes | 20 | 24.5 | odd | 2 |