Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(63,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.63");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.n (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} + \cdots + 69451154208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{31}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(4.57273 - 4.57273i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.127 |
Dual form | 160.6.n.a.63.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −9.28112 | − | 9.28112i | −0.595384 | − | 0.595384i | 0.343697 | − | 0.939081i | \(-0.388321\pi\) |
−0.939081 | + | 0.343697i | \(0.888321\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 42.6946 | − | 36.0856i | 0.763744 | − | 0.645519i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 105.819 | − | 105.819i | 0.816242 | − | 0.816242i | −0.169319 | − | 0.985561i | \(-0.554157\pi\) |
0.985561 | + | 0.169319i | \(0.0541569\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 70.7216i | − | 0.291035i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 344.770i | 0.859108i | 0.903041 | + | 0.429554i | \(0.141329\pi\) | ||||
−0.903041 | + | 0.429554i | \(0.858671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 707.360 | − | 707.360i | 1.16087 | − | 1.16087i | 0.176579 | − | 0.984286i | \(-0.443497\pi\) |
0.984286 | − | 0.176579i | \(-0.0565031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −731.169 | − | 61.3385i | −0.839053 | − | 0.0703891i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1263.06 | + | 1263.06i | 1.05999 | + | 1.05999i | 0.998082 | + | 0.0619108i | \(0.0197194\pi\) |
0.0619108 | + | 0.998082i | \(0.480281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −438.382 | −0.278592 | −0.139296 | − | 0.990251i | \(-0.544484\pi\) | ||||
−0.139296 | + | 0.990251i | \(0.544484\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1964.24 | −0.971955 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1722.78 | + | 1722.78i | 0.679063 | + | 0.679063i | 0.959788 | − | 0.280725i | \(-0.0905750\pi\) |
−0.280725 | + | 0.959788i | \(0.590575\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 520.655 | − | 3081.32i | 0.166610 | − | 0.986023i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2911.69 | + | 2911.69i | −0.768662 | + | 0.768662i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2513.02i | − | 0.554881i | −0.960743 | − | 0.277441i | \(-0.910514\pi\) | ||
0.960743 | − | 0.277441i | \(-0.0894862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7145.63i | − | 1.33548i | −0.744396 | − | 0.667739i | \(-0.767262\pi\) | ||
0.744396 | − | 0.667739i | \(-0.232738\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3199.85 | − | 3199.85i | 0.511499 | − | 0.511499i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 699.354 | − | 8336.45i | 0.0964999 | − | 1.15030i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3361.24 | − | 3361.24i | −0.403641 | − | 0.403641i | 0.475873 | − | 0.879514i | \(-0.342132\pi\) |
−0.879514 | + | 0.475873i | \(0.842132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13130.2 | −1.38232 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6969.83 | 0.647534 | 0.323767 | − | 0.946137i | \(-0.395051\pi\) | ||||
0.323767 | + | 0.946137i | \(0.395051\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16311.3 | − | 16311.3i | −1.34530 | − | 1.34530i | −0.890695 | − | 0.454602i | \(-0.849781\pi\) |
−0.454602 | − | 0.890695i | \(-0.650219\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2552.03 | − | 3019.43i | −0.187869 | − | 0.222277i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13020.0 | + | 13020.0i | −0.859740 | + | 0.859740i | −0.991307 | − | 0.131567i | \(-0.957999\pi\) |
0.131567 | + | 0.991307i | \(0.457999\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5588.36i | − | 0.332502i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 23445.3i | − | 1.26221i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20029.3 | − | 20029.3i | 0.979436 | − | 0.979436i | −0.0203564 | − | 0.999793i | \(-0.506480\pi\) |
0.999793 | + | 0.0203564i | \(0.00648008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12441.2 | + | 14719.8i | 0.554571 | + | 0.656138i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4068.67 | + | 4068.67i | 0.165869 | + | 0.165869i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8416.00 | −0.314757 | −0.157379 | − | 0.987538i | \(-0.550304\pi\) | ||||
−0.157379 | + | 0.987538i | \(0.550304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2293.72 | −0.0789254 | −0.0394627 | − | 0.999221i | \(-0.512565\pi\) | ||||
−0.0394627 | + | 0.999221i | \(0.512565\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7483.70 | − | 7483.70i | −0.237555 | − | 0.237555i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4674.91 | − | 55725.9i | 0.137243 | − | 1.63596i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −395.619 | + | 395.619i | −0.0107669 | + | 0.0107669i | −0.712470 | − | 0.701703i | \(-0.752423\pi\) |
0.701703 | + | 0.712470i | \(0.252423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 31978.6i | − | 0.808606i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40844.5i | 0.961585i | 0.876834 | + | 0.480793i | \(0.159651\pi\) | ||||
−0.876834 | + | 0.480793i | \(0.840349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45689.8 | + | 45689.8i | −1.00349 | + | 1.00349i | −0.00349408 | + | 0.999994i | \(0.501112\pi\) |
−0.999994 | + | 0.00349408i | \(0.998888\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −33430.4 | + | 23765.9i | −0.686259 | + | 0.487866i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 36483.2 | + | 36483.2i | 0.701240 | + | 0.701240i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58457.5 | 1.05383 | 0.526917 | − | 0.849916i | \(-0.323348\pi\) | ||||
0.526917 | + | 0.849916i | \(0.323348\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 36862.1 | 0.624263 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −26914.9 | − | 26914.9i | −0.428843 | − | 0.428843i | 0.459391 | − | 0.888234i | \(-0.348068\pi\) |
−0.888234 | + | 0.459391i | \(0.848068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 99504.4 | + | 8347.53i | 1.49381 | + | 0.125317i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23323.6 | + | 23323.6i | −0.330368 | + | 0.330368i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 61939.2i | − | 0.828878i | −0.910077 | − | 0.414439i | \(-0.863978\pi\) | ||
0.910077 | − | 0.414439i | \(-0.136022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 149704.i | − | 1.89509i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −66319.5 | + | 66319.5i | −0.795122 | + | 0.795122i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18716.5 | + | 15819.3i | −0.212773 | + | 0.179836i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11097.0 | − | 11097.0i | −0.119751 | − | 0.119751i | 0.644692 | − | 0.764442i | \(-0.276986\pi\) |
−0.764442 | + | 0.644692i | \(0.776986\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24382.7 | 0.250031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −137921. | −1.34533 | −0.672664 | − | 0.739948i | \(-0.734850\pi\) | ||||
−0.672664 | + | 0.739948i | \(0.734850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 106930. | + | 106930.i | 0.993132 | + | 0.993132i | 0.999977 | − | 0.00684431i | \(-0.00217863\pi\) |
−0.00684431 | + | 0.999977i | \(0.502179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −83862.4 | + | 70880.8i | −0.742325 | + | 0.627416i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19347.9 | − | 19347.9i | 0.163371 | − | 0.163371i | −0.620687 | − | 0.784058i | \(-0.713146\pi\) |
0.784058 | + | 0.620687i | \(0.213146\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 155519.i | 1.25376i | 0.779114 | + | 0.626882i | \(0.215669\pi\) | ||||
−0.779114 | + | 0.626882i | \(0.784331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 62392.1i | 0.480643i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −88859.9 | + | 88859.9i | −0.654651 | + | 0.654651i | −0.954109 | − | 0.299459i | \(-0.903194\pi\) |
0.299459 | + | 0.954109i | \(0.403194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 135721. | + | 11385.8i | 0.956978 | + | 0.0802819i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −50025.6 | − | 50025.6i | −0.337853 | − | 0.337853i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 267312. | 1.73042 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 42184.7 | 0.261934 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −64687.9 | − | 64687.9i | −0.385532 | − | 0.385532i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −88962.3 | − | 150344.i | −0.509250 | − | 0.860619i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −147966. | + | 147966.i | −0.814052 | + | 0.814052i | −0.985239 | − | 0.171186i | \(-0.945240\pi\) |
0.171186 | + | 0.985239i | \(0.445240\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 302775.i | 1.60194i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 103447.i | − | 0.526670i | −0.964704 | − | 0.263335i | \(-0.915178\pi\) | ||
0.964704 | − | 0.263335i | \(-0.0848225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −46389.1 | + | 46389.1i | −0.227398 | + | 0.227398i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19243.2 | + | 229383.i | −0.0908748 | + | 1.08325i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 142659. | + | 142659.i | 0.649380 | + | 0.649380i | 0.952843 | − | 0.303463i | \(-0.0981430\pi\) |
−0.303463 | + | 0.952843i | \(0.598143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 147275. | 0.646534 | 0.323267 | − | 0.946308i | \(-0.395219\pi\) | ||||
0.323267 | + | 0.946308i | \(0.395219\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 241681. | 1.02375 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 243876. | + | 243876.i | 0.997309 | + | 0.997309i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −90683.7 | − | 107292.i | −0.358187 | − | 0.423787i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −51866.2 | + | 51866.2i | −0.197966 | + | 0.197966i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 312656.i | 1.15372i | 0.816842 | + | 0.576861i | \(0.195723\pi\) | ||||
−0.816842 | + | 0.576861i | \(0.804277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 91450.6i | − | 0.326396i | −0.986593 | − | 0.163198i | \(-0.947819\pi\) | ||
0.986593 | − | 0.163198i | \(-0.0521809\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 89325.9 | − | 89325.9i | 0.308495 | − | 0.308495i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −257855. | − | 305080.i | −0.862076 | − | 1.01996i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −215386. | − | 215386.i | −0.697377 | − | 0.697377i | 0.266467 | − | 0.963844i | \(-0.414144\pi\) |
−0.963844 | + | 0.266467i | \(0.914144\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −371789. | −1.16628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 364606. | 1.10856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 419280. | + | 419280.i | 1.23605 | + | 1.23605i | 0.961603 | + | 0.274444i | \(0.0884939\pi\) |
0.274444 | + | 0.961603i | \(0.411506\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21147.7 | − | 252085.i | 0.0604718 | − | 0.720837i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 396893. | − | 396893.i | 1.10124 | − | 1.10124i | 0.106978 | − | 0.994261i | \(-0.465883\pi\) |
0.994261 | − | 0.106978i | \(-0.0341174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 629422.i | − | 1.69522i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31003.1i | 0.0810801i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −46145.1 | + | 46145.1i | −0.117222 | + | 0.117222i | −0.763285 | − | 0.646062i | \(-0.776415\pi\) |
0.646062 | + | 0.763285i | \(0.276415\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −270967. | − | 381158.i | −0.668840 | − | 0.940827i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 78109.9 | + | 78109.9i | 0.187401 | + | 0.187401i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18040.3 | −0.0420834 | −0.0210417 | − | 0.999779i | \(-0.506698\pi\) | ||||
−0.0210417 | + | 0.999779i | \(0.506698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 125468. | 0.284667 | 0.142333 | − | 0.989819i | \(-0.454540\pi\) | ||||
0.142333 | + | 0.989819i | \(0.454540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21288.3 | + | 21288.3i | 0.0469909 | + | 0.0469909i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −264799. | − | 22214.3i | −0.568836 | − | 0.0477203i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −435466. | + | 435466.i | −0.910648 | + | 0.910648i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 616224.i | 1.25483i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 474723.i | − | 0.941579i | −0.882246 | − | 0.470789i | \(-0.843969\pi\) | ||
0.882246 | − | 0.470789i | \(-0.156031\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −345560. | + | 345560.i | −0.667776 | + | 0.667776i | −0.957201 | − | 0.289425i | \(-0.906536\pi\) |
0.289425 | + | 0.957201i | \(0.406536\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −560588. | + | 473811.i | −1.05574 | + | 0.892315i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −458847. | − | 458847.i | −0.842370 | − | 0.842370i | 0.146797 | − | 0.989167i | \(-0.453104\pi\) |
−0.989167 | + | 0.146797i | \(0.953104\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −362349. | −0.648627 | −0.324313 | − | 0.945950i | \(-0.605133\pi\) | ||||
−0.324313 | + | 0.945950i | \(0.605133\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7343.57 | 0.0128209 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −265925. | − | 265925.i | −0.452917 | − | 0.452917i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 297574. | − | 251511.i | 0.494550 | − | 0.417996i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 121838. | − | 121838.i | 0.197631 | − | 0.197631i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 151141.i | − | 0.239340i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 931084.i | − | 1.43974i | −0.694111 | − | 0.719868i | \(-0.744202\pi\) | ||
0.694111 | − | 0.719868i | \(-0.255798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 379083. | − | 379083.i | 0.572513 | − | 0.572513i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.28501e6 | − | 107801.i | −1.89588 | − | 0.159047i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −756144. | − | 756144.i | −1.09007 | − | 1.09007i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 848105. | 1.19492 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.78688e6 | 2.46102 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −517823. | − | 517823.i | −0.697299 | − | 0.697299i | 0.266528 | − | 0.963827i | \(-0.414123\pi\) |
−0.963827 | + | 0.266528i | \(0.914123\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −217916. | − | 36821.6i | −0.286968 | − | 0.0484893i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 62975.3 | − | 62975.3i | 0.0811158 | − | 0.0811158i | −0.665385 | − | 0.746501i | \(-0.731732\pi\) |
0.746501 | + | 0.665385i | \(0.231732\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 300417.i | − | 0.378560i | −0.981923 | − | 0.189280i | \(-0.939385\pi\) | ||
0.981923 | − | 0.189280i | \(-0.0606155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 677211.i | − | 0.835014i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 488904. | − | 488904.i | 0.589975 | − | 0.589975i | −0.347649 | − | 0.937625i | \(-0.613020\pi\) |
0.937625 | + | 0.347649i | \(0.113020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −86048.8 | + | 1.02572e6i | −0.101642 | + | 1.21160i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −542551. | − | 542551.i | −0.627437 | − | 0.627437i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.06439e6 | 1.20533 | 0.602663 | − | 0.797996i | \(-0.294106\pi\) | ||||
0.602663 | + | 0.797996i | \(0.294106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.37049e6 | 1.51996 | 0.759981 | − | 0.649946i | \(-0.225208\pi\) | ||||
0.759981 | + | 0.649946i | \(0.225208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 365419. | + | 365419.i | 0.396986 | + | 0.396986i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −201659. | − | 238593.i | −0.214636 | − | 0.253946i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −310093. | + | 310093.i | −0.323408 | + | 0.323408i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 499602.i | 0.510652i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 483364.i | 0.484272i | 0.970242 | + | 0.242136i | \(0.0778481\pi\) | ||||
−0.970242 | + | 0.242136i | \(0.922152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −593962. | + | 593962.i | −0.583388 | + | 0.583388i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −846038. | − | 1.00099e6i | −0.814778 | − | 0.964002i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 244037. | + | 244037.i | 0.230474 | + | 0.230474i | 0.812891 | − | 0.582416i | \(-0.197893\pi\) |
−0.582416 | + | 0.812891i | \(0.697893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −711366. | −0.658937 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −177724. | −0.161490 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 660423. | + | 660423.i | 0.588752 | + | 0.588752i | 0.937293 | − | 0.348541i | \(-0.113323\pi\) |
−0.348541 | + | 0.937293i | \(0.613323\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 132373. | − | 1.57791e6i | 0.115793 | − | 1.38028i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −574865. | + | 574865.i | −0.493501 | + | 0.493501i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.08159e6i | 0.911344i | 0.890148 | + | 0.455672i | \(0.150601\pi\) | ||||
−0.890148 | + | 0.455672i | \(0.849399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 343393.i | 0.284032i | 0.989864 | + | 0.142016i | \(0.0453585\pi\) | ||||
−0.989864 | + | 0.142016i | \(0.954642\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.38942e6 | + | 1.38942e6i | −1.12831 | + | 1.12831i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.06235e6 | + | 179506.i | 0.847100 | + | 0.143136i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 335813. | + | 335813.i | 0.262965 | + | 0.262965i | 0.826258 | − | 0.563292i | \(-0.190465\pi\) |
−0.563292 | + | 0.826258i | \(0.690465\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −505351. | −0.388671 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.59679e6 | 1.20637 | 0.603187 | − | 0.797600i | \(-0.293897\pi\) | ||||
0.603187 | + | 0.797600i | \(0.293897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.31343e6 | + | 1.31343e6i | 0.974859 | + | 0.974859i | 0.999692 | − | 0.0248326i | \(-0.00790527\pi\) |
−0.0248326 | + | 0.999692i | \(0.507905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 320531. | + | 26889.7i | 0.233753 | + | 0.0196098i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 737541. | − | 737541.i | 0.528545 | − | 0.528545i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.77080e6i | 1.24717i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 205986.i | 0.142595i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −979199. | + | 979199.i | −0.666350 | + | 0.666350i | −0.956869 | − | 0.290520i | \(-0.906172\pi\) |
0.290520 | + | 0.956869i | \(0.406172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −359318. | + | 303697.i | −0.240394 | + | 0.203182i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00386e6 | − | 1.00386e6i | −0.660364 | − | 0.660364i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.43725e6 | 1.57660 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.45210e6 | −2.19618 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.28006e6 | + | 1.28006e6i | 0.800986 | + | 0.800986i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −97929.6 | + | 82770.5i | −0.0602788 | + | 0.0509478i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.37916e6 | + | 1.37916e6i | −0.835159 | + | 0.835159i | −0.988217 | − | 0.153058i | \(-0.951088\pi\) |
0.153058 | + | 0.988217i | \(0.451088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.98486e6i | − | 1.18259i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.40266e6i | − | 1.99488i | −0.0714984 | − | 0.997441i | \(-0.522778\pi\) | ||
0.0714984 | − | 0.997441i | \(-0.477222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.12834e6 | + | 1.12834e6i | −0.650997 | + | 0.650997i | −0.953233 | − | 0.302236i | \(-0.902267\pi\) |
0.302236 | + | 0.953233i | \(0.402267\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −589567. | − | 49459.4i | −0.334778 | − | 0.0280849i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.46256e6 | + | 2.46256e6i | 1.37638 | + | 1.37638i | 0.850657 | + | 0.525722i | \(0.176205\pi\) |
0.525722 | + | 0.850657i | \(0.323795\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 866412. | 0.476703 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −359141. | −0.194537 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −553704. | − | 553704.i | −0.295305 | − | 0.295305i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.81131e6 | − | 2.54789e6i | −0.951229 | − | 1.33805i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.44339e6 | − | 1.44339e6i | 0.746471 | − | 0.746471i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.75554e6i | 1.40351i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.84785e6i | − | 1.93041i | −0.261503 | − | 0.965203i | \(-0.584218\pi\) | ||
0.261503 | − | 0.965203i | \(-0.415782\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −237712. | + | 237712.i | −0.117474 | + | 0.117474i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2614.63 | + | 31166.9i | −0.00127291 | + | 0.0151734i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.14771e6 | + | 2.14771e6i | 1.03015 | + | 1.03015i | 0.999531 | + | 0.0306217i | \(0.00974872\pi\) |
0.0306217 | + | 0.999531i | \(0.490251\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.64944e6 | 0.779537 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.46360e6 | 1.14732 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.18715e6 | + | 1.18715e6i | 0.544840 | + | 0.544840i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.15397e6 | − | 1.36531e6i | −0.521971 | − | 0.617568i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.44660e6 | + | 2.44660e6i | −1.09078 | + | 1.09078i | −0.0953396 | + | 0.995445i | \(0.530394\pi\) |
−0.995445 | + | 0.0953396i | \(0.969606\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.21607e6i | 1.41339i | 0.707519 | + | 0.706694i | \(0.249814\pi\) | ||||
−0.707519 | + | 0.706694i | \(0.750186\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.11922e6i | 1.78463i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.20920e6 | − | 1.20920e6i | 0.516490 | − | 0.516490i | −0.400017 | − | 0.916508i | \(-0.630996\pi\) |
0.916508 | + | 0.400017i | \(0.130996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.47390e6 | + | 1.74384e6i | 0.620722 | + | 0.734405i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.48096e6 | − | 2.48096e6i | −1.03027 | − | 1.03027i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.56580e6 | −0.641211 | −0.320606 | − | 0.947213i | \(-0.603886\pi\) | ||||
−0.320606 | + | 0.947213i | \(0.603886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.28392e6 | −0.922387 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −391521. | − | 391521.i | −0.155951 | − | 0.155951i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −301962. | + | 3.59945e6i | −0.118637 | + | 1.41418i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.29136e6 | + | 1.29136e6i | −0.500475 | + | 0.500475i | −0.911585 | − | 0.411111i | \(-0.865141\pi\) |
0.411111 | + | 0.911585i | \(0.365141\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 492918.i | − | 0.188455i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.23897e6i | − | 1.59891i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20034.2 | + | 20034.2i | −0.00745588 | + | 0.00745588i | −0.710825 | − | 0.703369i | \(-0.751678\pi\) |
0.703369 | + | 0.710825i | \(0.251678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −569690. | + | 2.22103e6i | −0.209200 | + | 0.815598i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.77761e6 | − | 1.77761e6i | −0.644143 | − | 0.644143i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.86453e6 | 1.38197 | 0.690985 | − | 0.722869i | \(-0.257177\pi\) | ||||
0.690985 | + | 0.722869i | \(0.257177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.74658e6 | 0.969348 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.42232e6 | + | 1.42232e6i | 0.495452 | + | 0.495452i | 0.910019 | − | 0.414567i | \(-0.136067\pi\) |
−0.414567 | + | 0.910019i | \(0.636067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.87416e6 | + | 241116.i | 0.988232 | + | 0.0829038i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.15356e6 | + | 1.15356e6i | −0.391529 | + | 0.391529i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.06571e6i | − | 1.02720i | −0.858029 | − | 0.513602i | \(-0.828311\pi\) | ||
0.858029 | − | 0.513602i | \(-0.171689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.35196e6i | 1.43960i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −960102. | + | 960102.i | −0.313571 | + | 0.313571i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.49582e6 | − | 2.10948e6i | 0.804860 | − | 0.680271i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.86964e6 | + | 2.86964e6i | 0.913800 | + | 0.913800i | 0.996569 | − | 0.0827685i | \(-0.0263762\pi\) |
−0.0827685 | + | 0.996569i | \(0.526376\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 861086. | 0.270779 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.30150e6 | −0.404187 | −0.202093 | − | 0.979366i | \(-0.564774\pi\) | ||||
−0.202093 | + | 0.979366i | \(0.564774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.05453e6 | − | 5.05453e6i | −1.55031 | − | 1.55031i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.57381e6 | − | 1.33019e6i | 0.476777 | − | 0.402974i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.15885e6 | − | 1.15885e6i | 0.346771 | − | 0.346771i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.91742e6i | − | 1.74914i | −0.484902 | − | 0.874569i | \(-0.661145\pi\) | ||
0.484902 | − | 0.874569i | \(-0.338855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.64808e6i | − | 0.773261i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −890573. | + | 890573.i | −0.256918 | + | 0.256918i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.12036e6 | − | 177880.i | −0.604352 | − | 0.0506998i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.36687e6 | − | 1.36687e6i | −0.384936 | − | 0.384936i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.36914e6 | −1.49407 | −0.747033 | − | 0.664788i | \(-0.768522\pi\) | ||||
−0.747033 | + | 0.664788i | \(0.768522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.11924e6 | 0.582740 | 0.291370 | − | 0.956610i | \(-0.405889\pi\) | ||||
0.291370 | + | 0.956610i | \(0.405889\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 920798. | + | 920798.i | 0.250215 | + | 0.250215i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.54952e6 | − | 3.23428e6i | 1.22178 | − | 0.868572i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −242720. | + | 242720.i | −0.0644222 | + | 0.0644222i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 4.52689e6i | − | 1.18756i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 469972.i | 0.121865i | 0.998142 | + | 0.0609325i | \(0.0194074\pi\) | ||||
−0.998142 | + | 0.0609325i | \(0.980593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 630785. | − | 630785.i | 0.161682 | − | 0.161682i | −0.621629 | − | 0.783311i | \(-0.713529\pi\) |
0.783311 | + | 0.621629i | \(0.213529\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −154145. | + | 1.83744e6i | −0.0390576 | + | 0.465575i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −755235. | − | 755235.i | −0.189181 | − | 0.189181i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −798304. | −0.197700 | −0.0988501 | − | 0.995102i | \(-0.531516\pi\) | ||||
−0.0988501 | + | 0.995102i | \(0.531516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −395218. | −0.0967698 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.62223e6 | − | 3.62223e6i | −0.876934 | − | 0.876934i | 0.116282 | − | 0.993216i | \(-0.462902\pi\) |
−0.993216 | + | 0.116282i | \(0.962902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.23512e6 | − | 2.64447e6i | −0.535057 | − | 0.633051i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.90180e6 | − | 2.90180e6i | 0.686908 | − | 0.686908i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.51152e6i | 1.75838i | 0.476474 | + | 0.879188i | \(0.341915\pi\) | ||||
−0.476474 | + | 0.879188i | \(0.658085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.40299e6i | 0.556302i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −848764. | + | 848764.i | −0.194331 | + | 0.194331i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.40217e6 | − | 6.39156e6i | −1.22332 | − | 1.44737i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −994327. | − | 994327.i | −0.222710 | − | 0.222710i | 0.586929 | − | 0.809638i | \(-0.300337\pi\) |
−0.809638 | + | 0.586929i | \(0.800337\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.35529e6 | −1.62955 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.47063e6 | 0.760600 | 0.380300 | − | 0.924863i | \(-0.375821\pi\) | ||||
0.380300 | + | 0.924863i | \(0.375821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.81963e6 | − | 2.81963e6i | −0.611280 | − | 0.611280i | 0.332000 | − | 0.943279i | \(-0.392277\pi\) |
−0.943279 | + | 0.332000i | \(0.892277\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −438303. | + | 5.22466e6i | −0.0940030 | + | 1.12054i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.53855e6 | − | 5.53855e6i | 1.17518 | − | 1.17518i | 0.194221 | − | 0.980958i | \(-0.437782\pi\) |
0.980958 | − | 0.194221i | \(-0.0622178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 83728.0i | 0.0175768i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.99804e6i | 0.830415i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.62365e6 | − | 5.62365e6i | 1.15575 | − | 1.15575i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −228246. | + | 1.35079e6i | −0.0464161 | + | 0.274698i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.41650e6 | − | 1.41650e6i | −0.285051 | − | 0.285051i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.72200e6 | −0.542063 | −0.271031 | − | 0.962571i | \(-0.587365\pi\) | ||||
−0.271031 | + | 0.962571i | \(0.587365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.75521e6 | −0.937145 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.38395e6 | − | 3.38395e6i | −0.660018 | − | 0.660018i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −874227. | − | 73339.8i | −0.168760 | − | 0.0141575i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.53481e6 | + | 1.53481e6i | −0.293246 | + | 0.293246i | −0.838361 | − | 0.545115i | \(-0.816486\pi\) |
0.545115 | + | 0.838361i | \(0.316486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.78278e6i | − | 1.47185i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.17663e6i | − | 0.781848i | −0.920423 | − | 0.390924i | \(-0.872156\pi\) | ||
0.920423 | − | 0.390924i | \(-0.127844\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.17410e6 | − | 3.17410e6i | 0.588170 | − | 0.588170i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.04101e6 | − | 879865.i | 0.190960 | − | 0.161400i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.32213e6 | + | 4.32213e6i | 0.784886 | + | 0.784886i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.43895e6 | 0.977830 | 0.488915 | − | 0.872331i | \(-0.337393\pi\) | ||||
0.488915 | + | 0.872331i | \(0.337393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.36721e6 | −1.31132 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.20134e6 | + | 6.20134e6i | 1.09286 | + | 1.09286i | 0.995222 | + | 0.0976412i | \(0.0311298\pi\) |
0.0976412 | + | 0.995222i | \(0.468870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.88849e6 | + | 4.97698e6i | −1.02749 | + | 0.868435i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.84174e6 | + | 5.84174e6i | −1.00931 | + | 1.00931i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.07552e6i | 0.184003i | 0.995759 | + | 0.0920015i | \(0.0293265\pi\) | ||||
−0.995759 | + | 0.0920015i | \(0.970674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.66971e6i | 1.63818i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.27643e6 | − | 1.27643e6i | 0.214143 | − | 0.214143i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.42398e6 | + | 706697.i | 1.39958 | + | 0.117413i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.48892e6 | − | 4.48892e6i | −0.738610 | − | 0.738610i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 856557. | 0.139585 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 512247. | 0.0826770 | 0.0413385 | − | 0.999145i | \(-0.486838\pi\) | ||||
0.0413385 | + | 0.999145i | \(0.486838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.62407e6 | + | 1.62407e6i | 0.259627 | + | 0.259627i | 0.824902 | − | 0.565275i | \(-0.191230\pi\) |
−0.565275 | + | 0.824902i | \(0.691230\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.02269e6 | + | 6.05245e6i | −0.161937 | + | 0.958370i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.02539e6 | − | 9.02539e6i | 1.41560 | − | 1.41560i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 500411.i | − | 0.0777477i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 595193.i | 0.0916055i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.93018e6 | − | 4.93018e6i | 0.751700 | − | 0.751700i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 127870. | − | 1.52423e6i | 0.0193145 | − | 0.230233i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 167434. | + | 167434.i | 0.0250558 | + | 0.0250558i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.92670e6 | 0.285655 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.18839e6 | −0.321464 | −0.160732 | − | 0.986998i | \(-0.551385\pi\) | ||||
−0.160732 | + | 0.986998i | \(0.551385\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.16448e6 | − | 1.16448e6i | −0.169486 | − | 0.169486i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.61198e6 | + | 6.63980e6i | 0.809329 | + | 0.957555i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.08793e6 | + | 7.08793e6i | −1.01286 | + | 1.01286i | −0.0129482 | + | 0.999916i | \(0.504122\pi\) |
−0.999916 | + | 0.0129482i | \(0.995878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 162216.i | 0.0229701i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10166e6i | 0.154585i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.18592e6 | − | 6.18592e6i | 0.860184 | − | 0.860184i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.25146e6 | + | 2.66381e6i | 0.310264 | + | 0.367088i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.47008e6 | + | 8.47008e6i | 1.15678 | + | 1.15678i | 0.985165 | + | 0.171612i | \(0.0548975\pi\) |
0.171612 | + | 0.985165i | \(0.445102\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.30759e7 | −3.12342 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.08323e6 | 1.08437 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.30786e6 | + | 3.30786e6i | 0.439821 | + | 0.439821i | 0.891952 | − | 0.452131i | \(-0.149336\pi\) |
−0.452131 | + | 0.891952i | \(0.649336\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −587271. | + | 7.00040e6i | −0.0773958 | + | 0.922575i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.90071e6 | − | 3.90071e6i | 0.509550 | − | 0.509550i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.57983e6i | 0.722504i | 0.932468 | + | 0.361252i | \(0.117651\pi\) | ||||
−0.932468 | + | 0.361252i | \(0.882349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 119122.i | − | 0.0152898i | −0.999971 | − | 0.00764491i | \(-0.997567\pi\) | ||
0.999971 | − | 0.00764491i | \(-0.00243348\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.40596e6 | + | 4.40596e6i | −0.560601 | + | 0.560601i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.20541e6 | − | 4.41146e6i | 0.782710 | − | 0.556433i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.74821e6 | − | 5.74821e6i | −0.718775 | − | 0.718775i | 0.249579 | − | 0.968354i | \(-0.419708\pi\) |
−0.968354 | + | 0.249579i | \(0.919708\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.41438e6 | 0.795166 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.69623e6 | −0.700079 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.90550e6 | + | 6.90550e6i | 0.841442 | + | 0.841442i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.94103e6 | − | 330617.i | −0.476124 | − | 0.0399425i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.01460e6 | − | 1.01460e6i | 0.121535 | − | 0.121535i | −0.643724 | − | 0.765258i | \(-0.722611\pi\) |
0.765258 | + | 0.643724i | \(0.222611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.13252e6i | 0.372053i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.51724e6i | 1.00307i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.72430e6 | + | 5.72430e6i | −0.668476 | + | 0.668476i | −0.957363 | − | 0.288887i | \(-0.906715\pi\) |
0.288887 | + | 0.957363i | \(0.406715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.14128e7 | − | 9.64614e6i | 1.32160 | − | 1.11702i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.36301e6 | + | 3.36301e6i | 0.386182 | + | 0.386182i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.13903e6 | 0.585213 | 0.292606 | − | 0.956233i | \(-0.405477\pi\) | ||||
0.292606 | + | 0.956233i | \(0.405477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.24740e7 | −1.40871 | −0.704353 | − | 0.709850i | \(-0.748763\pi\) | ||||
−0.704353 | + | 0.709850i | \(0.748763\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27978.8 | + | 27978.8i | 0.00313354 | + | 0.00313354i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.80106e6 | − | 1.52226e6i | 0.200050 | − | 0.169083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.43385e6 | − | 9.43385e6i | 1.03924 | − | 1.03924i | 0.0400449 | − | 0.999198i | \(-0.487250\pi\) |
0.999198 | − | 0.0400449i | \(-0.0127501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.93616e6i | 0.539320i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.84197e7i | 1.99609i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.01442e6 | − | 5.01442e6i | 0.538976 | − | 0.538976i | −0.384252 | − | 0.923228i | \(-0.625541\pi\) |
0.923228 | + | 0.384252i | \(0.125541\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.09612e6 | − | 427519.i | −0.543316 | − | 0.0455793i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.22945e6 | + | 4.22945e6i | 0.447272 | + | 0.447272i | 0.894446 | − | 0.447175i | \(-0.147570\pi\) |
−0.447175 | + | 0.894446i | \(0.647570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.02116e6 | 0.631617 | 0.315808 | − | 0.948823i | \(-0.397724\pi\) | ||||
0.315808 | + | 0.948823i | \(0.397724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00324e7 | −1.04394 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.55435e6 | − | 6.55435e6i | −0.676565 | − | 0.676565i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.22346e6 | − | 3.20861e6i | −0.944482 | − | 0.328562i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.40276e6 | + | 1.40276e6i | −0.142499 | + | 0.142499i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8.49092e6i | − | 0.855713i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.59184e6i | − | 0.259141i | −0.991570 | − | 0.129570i | \(-0.958640\pi\) | ||
0.991570 | − | 0.129570i | \(-0.0413598\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.64150e6 | + | 8.64150e6i | −0.857196 | + | 0.857196i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −977900. | + | 1.16568e7i | −0.0962410 | + | 1.14721i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.95298e6 | − | 3.95298e6i | −0.385990 | − | 0.385990i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.88859e6 | 0.279855 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.99741e6 | −0.576526 | −0.288263 | − | 0.957551i | \(-0.593078\pi\) | ||||
−0.288263 | + | 0.957551i | \(0.593078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −841642. | − | 841642.i | −0.0802786 | − | 0.0802786i | 0.665827 | − | 0.746106i | \(-0.268079\pi\) |
−0.746106 | + | 0.665827i | \(0.768079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.09258e7 | + | 1.29268e7i | 1.03408 | + | 1.22347i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.18127e7 | − | 1.18127e7i | 1.10940 | − | 1.10940i | 0.116170 | − | 0.993229i | \(-0.462938\pi\) |
0.993229 | − | 0.116170i | \(-0.0370618\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.90158e6i | − | 0.270410i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.40357e7i | 1.29802i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.22862e6 | − | 1.22862e6i | 0.112755 | − | 0.112755i | −0.648478 | − | 0.761233i | \(-0.724594\pi\) |
0.761233 | + | 0.648478i | \(0.224594\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.73294e6 | − | 4.41662e6i | −0.339976 | − | 0.402241i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.23126e6 | + | 3.23126e6i | 0.292051 | + | 0.292051i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.69732e6 | −0.421343 | −0.210672 | − | 0.977557i | \(-0.567565\pi\) | ||||
−0.210672 | + | 0.977557i | \(0.567565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.07325e7 | −0.955423 | −0.477712 | − | 0.878517i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878517i | \(0.658534\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.65842e7 | − | 1.65842e7i | −1.46525 | − | 1.46525i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −306584. | + | 3.65455e6i | −0.0268841 | + | 0.320464i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.32937e6 | − | 4.32937e6i | 0.376799 | − | 0.376799i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.61195e6i | 0.830322i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 790807.i | − | 0.0678054i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.62488e6 | + | 6.62488e6i | −0.563820 | + | 0.563820i | −0.930390 | − | 0.366571i | \(-0.880532\pi\) |
0.366571 | + | 0.930390i | \(0.380532\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.45586e6 | + | 1.04878e7i | 0.629852 | + | 0.885985i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.62424e6 | + | 5.62424e6i | 0.471620 | + | 0.471620i | 0.902438 | − | 0.430819i | \(-0.141775\pi\) |
−0.430819 | + | 0.902438i | \(0.641775\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.34856e6 | −0.195491 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.16896e6 | −0.0965902 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.92168e6 | − | 6.92168e6i | −0.567754 | − | 0.567754i | 0.363745 | − | 0.931499i | \(-0.381498\pi\) |
−0.931499 | + | 0.363745i | \(0.881498\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.12387e7 | + | 942829.i | 0.915147 | + | 0.0767727i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.78820e6 | + | 2.78820e6i | −0.225389 | + | 0.225389i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.83358e7i | − | 2.27399i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.49915e6i | 0.756815i | 0.925639 | + | 0.378407i | \(0.123528\pi\) | ||||
−0.925639 | + | 0.378407i | \(0.876472\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.58015e6 | − | 2.58015e6i | 0.204086 | − | 0.204086i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.28783e6 | − | 5.31450e6i | 0.493786 | − | 0.417350i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.80334e6 | + | 8.80334e6i | 0.686381 | + | 0.686381i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.07516e6 | −0.702524 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.94148e6 | 0.149224 | 0.0746120 | − | 0.997213i | \(-0.476228\pi\) | ||||
0.0746120 | + | 0.997213i | \(0.476228\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.47351e6 | + | 1.47351e6i | 0.112451 | + | 0.112451i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.03185e7 | − | 8.72121e6i | 0.781884 | − | 0.660852i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.45947e7 | + | 1.45947e7i | −1.09811 | + | 1.09811i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.89625e6i | − | 0.216382i | −0.994130 | − | 0.108191i | \(-0.965494\pi\) | ||
0.994130 | − | 0.108191i | \(-0.0345057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4.13421e6i | − | 0.306703i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.23103e7 | − | 1.23103e7i | 0.906873 | − | 0.906873i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.92126e7 | + | 1.61177e6i | 1.40547 | + | 0.117906i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.87870e6 | − | 9.87870e6i | −0.717632 | − | 0.717632i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 751266. | 0.0541965 | 0.0270983 | − | 0.999633i | \(-0.491373\pi\) | ||||
0.0270983 | + | 0.999633i | \(0.491373\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.26305e7 | 1.62127 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.27197e7 | − | 1.27197e7i | −0.904961 | − | 0.904961i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.74341e6 | − | 1.30841e6i | −0.547126 | − | 0.0924486i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.73454e7 | + | 1.73454e7i | −1.21716 | + | 1.21716i | −0.248536 | + | 0.968623i | \(0.579949\pi\) |
−0.968623 | + | 0.248536i | \(0.920051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.57405e7i | − | 1.09698i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.12045e7i | − | 2.85201i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.21536e7 | − | 1.21536e7i | 0.835496 | − | 0.835496i | −0.152766 | − | 0.988262i | \(-0.548818\pi\) |
0.988262 | + | 0.152766i | \(0.0488181\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −342782. | + | 4.08603e6i | −0.0234045 | + | 0.278987i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −136397. | − | 136397.i | −0.00924991 | − | 0.00924991i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −888631. | −0.0598564 | −0.0299282 | − | 0.999552i | \(-0.509528\pi\) | ||||
−0.0299282 | + | 0.999552i | \(0.509528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.75603e6 | 0.385104 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.63933e6 | − | 3.63933e6i | −0.241852 | − | 0.241852i | 0.575764 | − | 0.817616i | \(-0.304705\pi\) |
−0.817616 | + | 0.575764i | \(0.804705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.12824e7 | + | 1.33487e7i | 0.744750 | + | 0.881148i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.90347e6 | + | 1.90347e6i | −0.124808 | + | 0.124808i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4.09476e6i | − | 0.266700i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 202134.i | − | 0.0130779i | −0.999979 | − | 0.00653897i | \(-0.997919\pi\) | ||
0.999979 | − | 0.00653897i | \(-0.00208143\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.48616e6 | − | 4.48616e6i | 0.288328 | − | 0.288328i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.30005e6 | − | 3.90445e6i | −0.210695 | − | 0.249283i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.73504e6 | − | 8.73504e6i | −0.554020 | − | 0.554020i | 0.373579 | − | 0.927599i | \(-0.378131\pi\) |
−0.927599 | + | 0.373579i | \(0.878131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.10253e7 | 0.694680 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.57714e7 | −0.987208 | −0.493604 | − | 0.869687i | \(-0.664321\pi\) | ||||
−0.493604 | + | 0.869687i | \(0.664321\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.64568e7 | + | 1.64568e7i | 1.02337 | + | 1.02337i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 590351. | − | 7.03711e6i | 0.0364717 | − | 0.434751i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.95314e6 | + | 5.95314e6i | −0.365391 | + | 0.365391i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.82867e6i | − | 0.355430i | −0.984082 | − | 0.177715i | \(-0.943130\pi\) | ||
0.984082 | − | 0.177715i | \(-0.0568705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 4.52986e6i | − | 0.274441i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.64656e6 | + | 3.64656e6i | −0.219500 | + | 0.219500i | −0.808288 | − | 0.588788i | \(-0.799605\pi\) |
0.588788 | + | 0.808288i | \(0.299605\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.20180e7 | − | 3.72041e6i | −1.31681 | − | 0.222503i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.60228e6 | + | 6.60228e6i | 0.392321 | + | 0.392321i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.05545e6 | −0.180398 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.40820e7 | −0.826105 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.31712e6 | + | 7.31712e6i | 0.426516 | + | 0.426516i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.69681e7 | − | 1.42348e6i | −0.982788 | − | 0.0824472i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.07036e7 | − | 1.07036e7i | 0.616016 | − | 0.616016i | −0.328491 | − | 0.944507i | \(-0.606540\pi\) |
0.944507 | + | 0.328491i | \(0.106540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.22589e7i | − | 0.701068i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.88061e7i | 1.06871i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.62249e6 | + | 1.62249e6i | −0.0916217 | + | 0.0916217i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.58734e7 | + | 1.34162e7i | −0.890741 | + | 0.752857i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.51227e6 | + | 3.51227e6i | 0.195858 | + | 0.195858i | 0.798222 | − | 0.602364i | \(-0.205774\pi\) |
−0.602364 | + | 0.798222i | \(0.705774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.28902e7 | −1.82264 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.38044e6 | −0.241233 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.57525e7 | − | 1.57525e7i | −0.862104 | − | 0.862104i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.55667e7 | − | 1.31570e7i | 0.846655 | − | 0.715596i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00384e7 | − | 1.00384e7i | 0.542600 | − | 0.542600i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.21162e7i | 1.72525i | 0.505840 | + | 0.862627i | \(0.331183\pi\) | ||||
−0.505840 | + | 0.862627i | \(0.668817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.71193e6i | − | 0.358340i | −0.983818 | − | 0.179170i | \(-0.942659\pi\) | ||
0.983818 | − | 0.179170i | \(-0.0573412\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.18707e6 | − | 3.18707e6i | 0.169108 | − | 0.169108i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.30310e7 | + | 2.77100e6i | 1.74192 | + | 0.146131i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.15059e6 | + | 7.15059e6i | 0.374789 | + | 0.374789i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.05873e7 | −0.551540 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.61048e6 | 0.135164 | 0.0675821 | − | 0.997714i | \(-0.478472\pi\) | ||||
0.0675821 | + | 0.997714i | \(0.478472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.89694e6 | − | 7.89694e6i | −0.406405 | − | 0.406405i | 0.474078 | − | 0.880483i | \(-0.342782\pi\) |
−0.880483 | + | 0.474078i | \(0.842782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.19375e6 | − | 1.15258e7i | −0.419129 | − | 0.589571i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.87602e7 | + | 1.87602e7i | −0.953834 | + | 0.953834i | −0.998980 | − | 0.0451462i | \(-0.985625\pi\) |
0.0451462 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.06101e6i | 0.154696i | 0.997004 | + | 0.0773480i | \(0.0246452\pi\) | ||||
−0.997004 | + | 0.0773480i | \(0.975355\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 6.23345e6i | − | 0.313131i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.05845e6 | − | 7.05845e6i | 0.352449 | − | 0.352449i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.62305e6 | − | 3.12673e7i | 0.130194 | − | 1.55194i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.08059e7 | + | 2.08059e7i | 1.02653 | + | 1.02653i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.88579e6 | −0.141534 | −0.0707668 | − | 0.997493i | \(-0.522545\pi\) | ||||
−0.0707668 | + | 0.997493i | \(0.522545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.41959e7 | 0.692107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.48200e7 | − | 1.48200e7i | −0.718256 | − | 0.718256i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.27131e7 | − | 2.68729e7i | −1.09430 | − | 1.29471i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.46395e6 | − | 4.46395e6i | 0.213801 | − | 0.213801i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 2.43803e7i | − | 1.16083i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.15813e7i | − | 0.548195i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.27693e7 | + | 2.27693e7i | −1.07146 | + | 1.07146i | −0.0742217 | + | 0.997242i | \(0.523647\pi\) |
−0.997242 | + | 0.0742217i | \(0.976353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.11876e6 | + | 1.32366e6i | 0.0523388 | + | 0.0619244i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 709645. | + | 709645.i | 0.0330057 | + | 0.0330057i | 0.723417 | − | 0.690411i | \(-0.242570\pi\) |
−0.690411 | + | 0.723417i | \(0.742570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.46778e7 | 1.14110 | 0.570549 | − | 0.821264i | \(-0.306731\pi\) | ||||
0.570549 | + | 0.821264i | \(0.306731\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.36904e7 | −0.629374 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.20888e7 | + | 1.20888e7i | 0.552532 | + | 0.552532i | 0.927171 | − | 0.374639i | \(-0.122233\pi\) |
−0.374639 | + | 0.927171i | \(0.622233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −304971. | + | 3.63532e6i | −0.0138586 | + | 0.165197i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.64350e7 | − | 1.64350e7i | 0.742544 | − | 0.742544i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.01544e7i | 0.905358i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 559690.i | 0.0249978i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −784800. | + | 784800.i | −0.0348517 | + | 0.0348517i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.53232e7 | − | 6.49535e6i | −1.11814 | − | 0.286802i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.57595e6 | − | 5.57595e6i | −0.244805 | − | 0.244805i | 0.574030 | − | 0.818834i | \(-0.305379\pi\) |
−0.818834 | + | 0.574030i | \(0.805379\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.81761e7 | 0.793468 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00694e7 | −1.30522 | −0.652611 | − | 0.757693i | \(-0.726326\pi\) | ||||
−0.652611 | + | 0.757693i | \(0.726326\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.38514e6 | + | 9.38514e6i | 0.405078 | + | 0.405078i | 0.880018 | − | 0.474940i | \(-0.157530\pi\) |
−0.474940 | + | 0.880018i | \(0.657530\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.15351e6 | + | 516225.i | 0.264098 | + | 0.0221555i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.96936e7 | + | 1.96936e7i | −0.840458 | + | 0.840458i | −0.988918 | − | 0.148461i | \(-0.952568\pi\) |
0.148461 | + | 0.988918i | \(0.452568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.13152e7i | 1.32893i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.27089e7i | 0.536309i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.70774e6 | − | 5.70774e6i | 0.239517 | − | 0.239517i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −770222. | + | 650995.i | −0.0321409 | + | 0.0271656i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.26204e7 | − | 2.26204e7i | −0.938683 | − | 0.938683i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.79571e7 | −0.741032 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.05966e7 | 2.07639 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.20393e7 | + | 3.20393e7i | 1.30757 | + | 1.30757i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.35680e6 | − | 4.52759e6i | 0.217412 | − | 0.183758i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.14154e7 | − | 2.14154e7i | 0.864388 | − | 0.864388i | −0.127456 | − | 0.991844i | \(-0.540681\pi\) |
0.991844 | + | 0.127456i | \(0.0406813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.75402e6i | 0.391538i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.69457e6i | 0.147492i | 0.997277 | + | 0.0737459i | \(0.0234954\pi\) | ||||
−0.997277 | + | 0.0737459i | \(0.976505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.27946e6 | − | 9.27946e6i | 0.368422 | − | 0.368422i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.67710e6 | + | 140694.i | 0.0662226 | + | 0.00555548i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.09466e7 | − | 1.09466e7i | −0.429890 | − | 0.429890i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.06290e7 | 0.805731 | 0.402865 | − | 0.915259i | \(-0.368014\pi\) | ||||
0.402865 | + | 0.915259i | \(0.368014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.56003e7 | 0.994481 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.88918e7 | + | 2.88918e7i | 1.11627 | + | 1.11627i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.21071e7 | + | 8.60701e6i | −0.465250 | + | 0.330749i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.56227e6 | − | 7.56227e6i | 0.289037 | − | 0.289037i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.31010e6i | − | 0.277897i | −0.990300 | − | 0.138948i | \(-0.955628\pi\) | ||
0.990300 | − | 0.138948i | \(-0.0443722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.44983e6i | 0.0926323i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.15805e7 | + | 3.15805e7i | −1.18772 | + | 1.18772i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.87798e6 | + | 3.43061e7i | −0.107661 | + | 1.28334i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.32850e6 | − | 6.32850e6i | −0.235479 | − | 0.235479i | 0.579496 | − | 0.814975i | \(-0.303249\pi\) |
−0.814975 | + | 0.579496i | \(0.803249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.09445e7 | 0.775187 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.14005e7 | 1.52416 | 0.762082 | − | 0.647481i | \(-0.224177\pi\) | ||||
0.762082 | + | 0.647481i | \(0.224177\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.20075e7 | + | 1.20075e7i | 0.439716 | + | 0.439716i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.22368e7 | + | 2.63094e7i | 0.810016 | + | 0.958368i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.01051e7 | + | 2.01051e7i | −0.728503 | + | 0.728503i | −0.970322 | − | 0.241818i | \(-0.922256\pi\) |
0.241818 | + | 0.970322i | \(0.422256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.46382e7i | 2.32983i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.57105e7i | − | 1.63895i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.97014e7 | + | 2.97014e7i | −1.05936 | + | 1.05936i | −0.0612391 | + | 0.998123i | \(0.519505\pi\) |
−0.998123 | + | 0.0612391i | \(0.980495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.71307e7 | − | 2.02681e7i | −0.607807 | − | 0.719125i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.04127e6 | − | 8.04127e6i | −0.283821 | − | 0.283821i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.01922e7 | 1.06010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.24309e7 | −0.783500 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.36832e6 | − | 1.36832e6i | −0.0475467 | − | 0.0475467i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.28379e6 | + | 2.72233e7i | −0.0789475 | + | 0.941072i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.21695e7 | + | 3.21695e7i | −1.10631 | + | 1.10631i | −0.112681 | + | 0.993631i | \(0.535944\pi\) |
−0.993631 | + | 0.112681i | \(0.964056\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.02780e7i | 0.351640i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.27877e7i | 1.11600i | 0.829842 | + | 0.557998i | \(0.188430\pi\) | ||||
−0.829842 | + | 0.557998i | \(0.811570\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.55845e7 | − | 1.55845e7i | 0.527728 | − | 0.527728i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.83629e6 | + | 4.04583e7i | −0.230308 | + | 1.36300i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.68706e7 | − | 2.68706e7i | −0.900618 | − | 0.900618i | 0.0948719 | − | 0.995489i | \(-0.469756\pi\) |
−0.995489 | + | 0.0948719i | \(0.969756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.13548e7 | 0.712096 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.09985e7 | 0.364890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.96745e7 | + | 1.96745e7i | 0.649412 | + | 0.649412i | 0.952851 | − | 0.303439i | \(-0.0981349\pi\) |
−0.303439 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.61481e7 | − | 3.03250e6i | −1.18712 | − | 0.0995888i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.55745e7 | − | 2.55745e7i | 0.835629 | − | 0.835629i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.62016e7i | − | 1.82708i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.01223e7i | 0.974324i | 0.873312 | + | 0.487162i | \(0.161968\pi\) | ||||
−0.873312 | + | 0.487162i | \(0.838032\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.57124e7 | + | 3.57124e7i | −1.14933 | + | 1.14933i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.54704e7 | + | 1.30756e7i | −0.495385 | + | 0.418701i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.86509e6 | − | 4.86509e6i | −0.155008 | − | 0.155008i | 0.625343 | − | 0.780350i | \(-0.284959\pi\) |
−0.780350 | + | 0.625343i | \(0.784959\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.95738e7 | 0.620527 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 160.6.n.a.127.3 | yes | 14 | |
4.3 | odd | 2 | 160.6.n.b.127.5 | yes | 14 | ||
5.3 | odd | 4 | 160.6.n.b.63.5 | yes | 14 | ||
20.3 | even | 4 | inner | 160.6.n.a.63.3 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.n.a.63.3 | ✓ | 14 | 20.3 | even | 4 | inner | |
160.6.n.a.127.3 | yes | 14 | 1.1 | even | 1 | trivial | |
160.6.n.b.63.5 | yes | 14 | 5.3 | odd | 4 | ||
160.6.n.b.127.5 | yes | 14 | 4.3 | odd | 2 |