Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(4.55626\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.55626 | −0.402720 | −0.201360 | − | 0.979517i | \(-0.564536\pi\) | ||||
−0.201360 | + | 0.979517i | \(0.564536\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | −107.241 | −0.837817 | ||||||||
\(5\) | −540.445 | −1.93355 | −0.966777 | − | 0.255623i | \(-0.917719\pi\) | ||||
−0.966777 | + | 0.255623i | \(0.917719\pi\) | |||||||
\(6\) | 123.019 | 0.232510 | ||||||||
\(7\) | −1238.10 | −1.36431 | −0.682154 | − | 0.731208i | \(-0.738957\pi\) | ||||
−0.682154 | + | 0.731208i | \(0.738957\pi\) | |||||||
\(8\) | 1071.82 | 0.740125 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2462.40 | 0.778680 | ||||||||
\(11\) | 3521.59 | 0.797745 | 0.398872 | − | 0.917006i | \(-0.369402\pi\) | ||||
0.398872 | + | 0.917006i | \(0.369402\pi\) | |||||||
\(12\) | 2895.49 | 0.483714 | ||||||||
\(13\) | −4832.75 | −0.610089 | −0.305044 | − | 0.952338i | \(-0.598671\pi\) | ||||
−0.305044 | + | 0.952338i | \(0.598671\pi\) | |||||||
\(14\) | 5641.10 | 0.549434 | ||||||||
\(15\) | 14592.0 | 1.11634 | ||||||||
\(16\) | 8843.32 | 0.539753 | ||||||||
\(17\) | 2243.59 | 0.110757 | 0.0553787 | − | 0.998465i | \(-0.482363\pi\) | ||||
0.0553787 | + | 0.998465i | \(0.482363\pi\) | |||||||
\(18\) | −3321.51 | −0.134240 | ||||||||
\(19\) | 53136.6 | 1.77728 | 0.888641 | − | 0.458603i | \(-0.151650\pi\) | ||||
0.888641 | + | 0.458603i | \(0.151650\pi\) | |||||||
\(20\) | 57957.6 | 1.61996 | ||||||||
\(21\) | 33428.7 | 0.787684 | ||||||||
\(22\) | −16045.3 | −0.321268 | ||||||||
\(23\) | −56390.0 | −0.966394 | −0.483197 | − | 0.875512i | \(-0.660525\pi\) | ||||
−0.483197 | + | 0.875512i | \(0.660525\pi\) | |||||||
\(24\) | −28939.0 | −0.427312 | ||||||||
\(25\) | 213955. | 2.73863 | ||||||||
\(26\) | 22019.3 | 0.245695 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 132774. | 1.14304 | ||||||||
\(29\) | −137347. | −1.04575 | −0.522874 | − | 0.852410i | \(-0.675140\pi\) | ||||
−0.522874 | + | 0.852410i | \(0.675140\pi\) | |||||||
\(30\) | −66484.9 | −0.449571 | ||||||||
\(31\) | −121430. | −0.732081 | −0.366041 | − | 0.930599i | \(-0.619287\pi\) | ||||
−0.366041 | + | 0.930599i | \(0.619287\pi\) | |||||||
\(32\) | −177485. | −0.957495 | ||||||||
\(33\) | −95082.8 | −0.460578 | ||||||||
\(34\) | −10222.4 | −0.0446042 | ||||||||
\(35\) | 669124. | 2.63796 | ||||||||
\(36\) | −78178.3 | −0.279272 | ||||||||
\(37\) | −476697. | −1.54716 | −0.773581 | − | 0.633697i | \(-0.781537\pi\) | ||||
−0.773581 | + | 0.633697i | \(0.781537\pi\) | |||||||
\(38\) | −242104. | −0.715747 | ||||||||
\(39\) | 130484. | 0.352235 | ||||||||
\(40\) | −579257. | −1.43107 | ||||||||
\(41\) | 140564. | 0.318516 | 0.159258 | − | 0.987237i | \(-0.449090\pi\) | ||||
0.159258 | + | 0.987237i | \(0.449090\pi\) | |||||||
\(42\) | −152310. | −0.317216 | ||||||||
\(43\) | 696919. | 1.33673 | 0.668363 | − | 0.743835i | \(-0.266995\pi\) | ||||
0.668363 | + | 0.743835i | \(0.266995\pi\) | |||||||
\(44\) | −377657. | −0.668364 | ||||||||
\(45\) | −393984. | −0.644518 | ||||||||
\(46\) | 256927. | 0.389186 | ||||||||
\(47\) | 783363. | 1.10058 | 0.550289 | − | 0.834974i | \(-0.314518\pi\) | ||||
0.550289 | + | 0.834974i | \(0.314518\pi\) | |||||||
\(48\) | −238770. | −0.311627 | ||||||||
\(49\) | 709348. | 0.861337 | ||||||||
\(50\) | −974835. | −1.10290 | ||||||||
\(51\) | −60577.0 | −0.0639458 | ||||||||
\(52\) | 518267. | 0.511142 | ||||||||
\(53\) | 1.05434e6 | 0.972781 | 0.486390 | − | 0.873742i | \(-0.338313\pi\) | ||||
0.486390 | + | 0.873742i | \(0.338313\pi\) | |||||||
\(54\) | 89680.8 | 0.0775035 | ||||||||
\(55\) | −1.90322e6 | −1.54248 | ||||||||
\(56\) | −1.32702e6 | −1.00976 | ||||||||
\(57\) | −1.43469e6 | −1.02611 | ||||||||
\(58\) | 625790. | 0.421144 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −1.56485e6 | −0.935286 | ||||||||
\(61\) | 378219. | 0.213348 | 0.106674 | − | 0.994294i | \(-0.465980\pi\) | ||||
0.106674 | + | 0.994294i | \(0.465980\pi\) | |||||||
\(62\) | 553265. | 0.294824 | ||||||||
\(63\) | −902575. | −0.454769 | ||||||||
\(64\) | −323278. | −0.154151 | ||||||||
\(65\) | 2.61184e6 | 1.17964 | ||||||||
\(66\) | 433222. | 0.185484 | ||||||||
\(67\) | −1.12190e6 | −0.455714 | −0.227857 | − | 0.973695i | \(-0.573172\pi\) | ||||
−0.227857 | + | 0.973695i | \(0.573172\pi\) | |||||||
\(68\) | −240604. | −0.0927943 | ||||||||
\(69\) | 1.52253e6 | 0.557948 | ||||||||
\(70\) | −3.04870e6 | −1.06236 | ||||||||
\(71\) | 3.82821e6 | 1.26938 | 0.634689 | − | 0.772767i | \(-0.281128\pi\) | ||||
0.634689 | + | 0.772767i | \(0.281128\pi\) | |||||||
\(72\) | 781354. | 0.246708 | ||||||||
\(73\) | −1.68355e6 | −0.506518 | −0.253259 | − | 0.967398i | \(-0.581503\pi\) | ||||
−0.253259 | + | 0.967398i | \(0.581503\pi\) | |||||||
\(74\) | 2.17195e6 | 0.623073 | ||||||||
\(75\) | −5.77679e6 | −1.58115 | ||||||||
\(76\) | −5.69840e6 | −1.48904 | ||||||||
\(77\) | −4.36008e6 | −1.08837 | ||||||||
\(78\) | −594520. | −0.141852 | ||||||||
\(79\) | 5.56662e6 | 1.27027 | 0.635136 | − | 0.772401i | \(-0.280944\pi\) | ||||
0.635136 | + | 0.772401i | \(0.280944\pi\) | |||||||
\(80\) | −4.77932e6 | −1.04364 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −640447. | −0.128273 | ||||||||
\(83\) | −1.80553e6 | −0.346602 | −0.173301 | − | 0.984869i | \(-0.555443\pi\) | ||||
−0.173301 | + | 0.984869i | \(0.555443\pi\) | |||||||
\(84\) | −3.58491e6 | −0.659935 | ||||||||
\(85\) | −1.21254e6 | −0.214155 | ||||||||
\(86\) | −3.17534e6 | −0.538327 | ||||||||
\(87\) | 3.70838e6 | 0.603763 | ||||||||
\(88\) | 3.77449e6 | 0.590431 | ||||||||
\(89\) | 8.26085e6 | 1.24211 | 0.621055 | − | 0.783767i | \(-0.286704\pi\) | ||||
0.621055 | + | 0.783767i | \(0.286704\pi\) | |||||||
\(90\) | 1.79509e6 | 0.259560 | ||||||||
\(91\) | 5.98343e6 | 0.832349 | ||||||||
\(92\) | 6.04729e6 | 0.809661 | ||||||||
\(93\) | 3.27860e6 | 0.422667 | ||||||||
\(94\) | −3.56920e6 | −0.443225 | ||||||||
\(95\) | −2.87174e7 | −3.43647 | ||||||||
\(96\) | 4.79209e6 | 0.552810 | ||||||||
\(97\) | −9.36799e6 | −1.04219 | −0.521093 | − | 0.853500i | \(-0.674476\pi\) | ||||
−0.521093 | + | 0.853500i | \(0.674476\pi\) | |||||||
\(98\) | −3.23197e6 | −0.346878 | ||||||||
\(99\) | 2.56724e6 | 0.265915 | ||||||||
\(100\) | −2.29447e7 | −2.29447 | ||||||||
\(101\) | 5.17821e6 | 0.500097 | 0.250049 | − | 0.968233i | \(-0.419553\pi\) | ||||
0.250049 | + | 0.968233i | \(0.419553\pi\) | |||||||
\(102\) | 276004. | 0.0257522 | ||||||||
\(103\) | −1.63595e7 | −1.47516 | −0.737579 | − | 0.675261i | \(-0.764031\pi\) | ||||
−0.737579 | + | 0.675261i | \(0.764031\pi\) | |||||||
\(104\) | −5.17982e6 | −0.451542 | ||||||||
\(105\) | −1.80664e7 | −1.52303 | ||||||||
\(106\) | −4.80384e6 | −0.391758 | ||||||||
\(107\) | −1.15281e7 | −0.909734 | −0.454867 | − | 0.890559i | \(-0.650313\pi\) | ||||
−0.454867 | + | 0.890559i | \(0.650313\pi\) | |||||||
\(108\) | 2.11082e6 | 0.161238 | ||||||||
\(109\) | −1.66988e6 | −0.123507 | −0.0617535 | − | 0.998091i | \(-0.519669\pi\) | ||||
−0.0617535 | + | 0.998091i | \(0.519669\pi\) | |||||||
\(110\) | 8.67157e6 | 0.621188 | ||||||||
\(111\) | 1.28708e7 | 0.893255 | ||||||||
\(112\) | −1.09489e7 | −0.736390 | ||||||||
\(113\) | −2.82765e6 | −0.184353 | −0.0921767 | − | 0.995743i | \(-0.529382\pi\) | ||||
−0.0921767 | + | 0.995743i | \(0.529382\pi\) | |||||||
\(114\) | 6.53681e6 | 0.413237 | ||||||||
\(115\) | 3.04756e7 | 1.86857 | ||||||||
\(116\) | 1.47292e7 | 0.876145 | ||||||||
\(117\) | −3.52308e6 | −0.203363 | ||||||||
\(118\) | −935759. | −0.0524297 | ||||||||
\(119\) | −2.77779e6 | −0.151107 | ||||||||
\(120\) | 1.56399e7 | 0.826230 | ||||||||
\(121\) | −7.08560e6 | −0.363603 | ||||||||
\(122\) | −1.72326e6 | −0.0859195 | ||||||||
\(123\) | −3.79524e6 | −0.183895 | ||||||||
\(124\) | 1.30222e7 | 0.613350 | ||||||||
\(125\) | −7.34087e7 | −3.36173 | ||||||||
\(126\) | 4.11236e6 | 0.183145 | ||||||||
\(127\) | 4.15154e7 | 1.79844 | 0.899221 | − | 0.437496i | \(-0.144134\pi\) | ||||
0.899221 | + | 0.437496i | \(0.144134\pi\) | |||||||
\(128\) | 2.41910e7 | 1.01957 | ||||||||
\(129\) | −1.88168e7 | −0.771760 | ||||||||
\(130\) | −1.19002e7 | −0.475064 | ||||||||
\(131\) | 4.63759e7 | 1.80237 | 0.901183 | − | 0.433438i | \(-0.142700\pi\) | ||||
0.901183 | + | 0.433438i | \(0.142700\pi\) | |||||||
\(132\) | 1.01967e7 | 0.385880 | ||||||||
\(133\) | −6.57885e7 | −2.42476 | ||||||||
\(134\) | 5.11167e6 | 0.183525 | ||||||||
\(135\) | 1.06376e7 | 0.372112 | ||||||||
\(136\) | 2.40472e6 | 0.0819743 | ||||||||
\(137\) | −3.20418e6 | −0.106462 | −0.0532310 | − | 0.998582i | \(-0.516952\pi\) | ||||
−0.0532310 | + | 0.998582i | \(0.516952\pi\) | |||||||
\(138\) | −6.93703e6 | −0.224697 | ||||||||
\(139\) | 3.74591e7 | 1.18306 | 0.591529 | − | 0.806284i | \(-0.298525\pi\) | ||||
0.591529 | + | 0.806284i | \(0.298525\pi\) | |||||||
\(140\) | −7.17572e7 | −2.21013 | ||||||||
\(141\) | −2.11508e7 | −0.635419 | ||||||||
\(142\) | −1.74423e7 | −0.511204 | ||||||||
\(143\) | −1.70190e7 | −0.486695 | ||||||||
\(144\) | 6.44678e6 | 0.179918 | ||||||||
\(145\) | 7.42286e7 | 2.02201 | ||||||||
\(146\) | 7.67067e6 | 0.203985 | ||||||||
\(147\) | −1.91524e7 | −0.497293 | ||||||||
\(148\) | 5.11212e7 | 1.29624 | ||||||||
\(149\) | 2.39531e7 | 0.593212 | 0.296606 | − | 0.955000i | \(-0.404145\pi\) | ||||
0.296606 | + | 0.955000i | \(0.404145\pi\) | |||||||
\(150\) | 2.63205e7 | 0.636760 | ||||||||
\(151\) | −6.59208e7 | −1.55813 | −0.779064 | − | 0.626945i | \(-0.784305\pi\) | ||||
−0.779064 | + | 0.626945i | \(0.784305\pi\) | |||||||
\(152\) | 5.69527e7 | 1.31541 | ||||||||
\(153\) | 1.63558e6 | 0.0369191 | ||||||||
\(154\) | 1.98656e7 | 0.438308 | ||||||||
\(155\) | 6.56261e7 | 1.41552 | ||||||||
\(156\) | −1.39932e7 | −0.295108 | ||||||||
\(157\) | −6.45045e7 | −1.33027 | −0.665137 | − | 0.746721i | \(-0.731627\pi\) | ||||
−0.665137 | + | 0.746721i | \(0.731627\pi\) | |||||||
\(158\) | −2.53629e7 | −0.511564 | ||||||||
\(159\) | −2.84672e7 | −0.561635 | ||||||||
\(160\) | 9.59207e7 | 1.85137 | ||||||||
\(161\) | 6.98164e7 | 1.31846 | ||||||||
\(162\) | −2.42138e6 | −0.0447467 | ||||||||
\(163\) | −3.88407e7 | −0.702474 | −0.351237 | − | 0.936287i | \(-0.614239\pi\) | ||||
−0.351237 | + | 0.936287i | \(0.614239\pi\) | |||||||
\(164\) | −1.50742e7 | −0.266858 | ||||||||
\(165\) | 5.13870e7 | 0.890552 | ||||||||
\(166\) | 8.22644e6 | 0.139583 | ||||||||
\(167\) | 2.62525e7 | 0.436178 | 0.218089 | − | 0.975929i | \(-0.430018\pi\) | ||||
0.218089 | + | 0.975929i | \(0.430018\pi\) | |||||||
\(168\) | 3.58294e7 | 0.582985 | ||||||||
\(169\) | −3.93930e7 | −0.627792 | ||||||||
\(170\) | 5.52463e6 | 0.0862446 | ||||||||
\(171\) | 3.87366e7 | 0.592428 | ||||||||
\(172\) | −7.47380e7 | −1.11993 | ||||||||
\(173\) | −9.81294e6 | −0.144091 | −0.0720457 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720457 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(174\) | −1.68963e7 | −0.243147 | ||||||||
\(175\) | −2.64898e8 | −3.73633 | ||||||||
\(176\) | 3.11425e7 | 0.430585 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | −3.76386e7 | −0.500222 | ||||||||
\(179\) | −3.88790e7 | −0.506675 | −0.253337 | − | 0.967378i | \(-0.581528\pi\) | ||||
−0.253337 | + | 0.967378i | \(0.581528\pi\) | |||||||
\(180\) | 4.22511e7 | 0.539988 | ||||||||
\(181\) | −5.75554e7 | −0.721458 | −0.360729 | − | 0.932671i | \(-0.617472\pi\) | ||||
−0.360729 | + | 0.932671i | \(0.617472\pi\) | |||||||
\(182\) | −2.72621e7 | −0.335204 | ||||||||
\(183\) | −1.02119e7 | −0.123177 | ||||||||
\(184\) | −6.04397e7 | −0.715253 | ||||||||
\(185\) | 2.57628e8 | 2.99152 | ||||||||
\(186\) | −1.49382e7 | −0.170217 | ||||||||
\(187\) | 7.90100e6 | 0.0883561 | ||||||||
\(188\) | −8.40083e7 | −0.922082 | ||||||||
\(189\) | 2.43695e7 | 0.262561 | ||||||||
\(190\) | 1.30844e8 | 1.38394 | ||||||||
\(191\) | 1.56708e8 | 1.62733 | 0.813663 | − | 0.581337i | \(-0.197470\pi\) | ||||
0.813663 | + | 0.581337i | \(0.197470\pi\) | |||||||
\(192\) | 8.72850e6 | 0.0889991 | ||||||||
\(193\) | 5.44941e7 | 0.545631 | 0.272816 | − | 0.962066i | \(-0.412045\pi\) | ||||
0.272816 | + | 0.962066i | \(0.412045\pi\) | |||||||
\(194\) | 4.26830e7 | 0.419709 | ||||||||
\(195\) | −7.05196e7 | −0.681065 | ||||||||
\(196\) | −7.60709e7 | −0.721642 | ||||||||
\(197\) | 1.46168e8 | 1.36213 | 0.681066 | − | 0.732222i | \(-0.261517\pi\) | ||||
0.681066 | + | 0.732222i | \(0.261517\pi\) | |||||||
\(198\) | −1.16970e7 | −0.107089 | ||||||||
\(199\) | 5.06585e7 | 0.455687 | 0.227843 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227843 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(200\) | 2.29321e8 | 2.02693 | ||||||||
\(201\) | 3.02913e7 | 0.263107 | ||||||||
\(202\) | −2.35932e7 | −0.201399 | ||||||||
\(203\) | 1.70050e8 | 1.42672 | ||||||||
\(204\) | 6.49631e6 | 0.0535748 | ||||||||
\(205\) | −7.59672e7 | −0.615868 | ||||||||
\(206\) | 7.45379e7 | 0.594076 | ||||||||
\(207\) | −4.11083e7 | −0.322131 | ||||||||
\(208\) | −4.27376e7 | −0.329297 | ||||||||
\(209\) | 1.87125e8 | 1.41782 | ||||||||
\(210\) | 8.23149e7 | 0.613354 | ||||||||
\(211\) | 3.36247e7 | 0.246416 | 0.123208 | − | 0.992381i | \(-0.460682\pi\) | ||||
0.123208 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(212\) | −1.13068e8 | −0.815012 | ||||||||
\(213\) | −1.03362e8 | −0.732876 | ||||||||
\(214\) | 5.25250e7 | 0.366368 | ||||||||
\(215\) | −3.76646e8 | −2.58463 | ||||||||
\(216\) | −2.10966e7 | −0.142437 | ||||||||
\(217\) | 1.50342e8 | 0.998784 | ||||||||
\(218\) | 7.60839e6 | 0.0497388 | ||||||||
\(219\) | 4.54558e7 | 0.292438 | ||||||||
\(220\) | 2.04103e8 | 1.29232 | ||||||||
\(221\) | −1.08427e7 | −0.0675718 | ||||||||
\(222\) | −5.86427e7 | −0.359732 | ||||||||
\(223\) | 8.68957e7 | 0.524725 | 0.262362 | − | 0.964969i | \(-0.415498\pi\) | ||||
0.262362 | + | 0.964969i | \(0.415498\pi\) | |||||||
\(224\) | 2.19744e8 | 1.30632 | ||||||||
\(225\) | 1.55973e8 | 0.912876 | ||||||||
\(226\) | 1.28835e7 | 0.0742428 | ||||||||
\(227\) | 3.64696e7 | 0.206938 | 0.103469 | − | 0.994633i | \(-0.467006\pi\) | ||||
0.103469 | + | 0.994633i | \(0.467006\pi\) | |||||||
\(228\) | 1.53857e8 | 0.859696 | ||||||||
\(229\) | 2.19546e8 | 1.20809 | 0.604047 | − | 0.796949i | \(-0.293554\pi\) | ||||
0.604047 | + | 0.796949i | \(0.293554\pi\) | |||||||
\(230\) | −1.38855e8 | −0.752512 | ||||||||
\(231\) | 1.17722e8 | 0.628371 | ||||||||
\(232\) | −1.47211e8 | −0.773985 | ||||||||
\(233\) | 1.19989e8 | 0.621435 | 0.310718 | − | 0.950502i | \(-0.399431\pi\) | ||||
0.310718 | + | 0.950502i | \(0.399431\pi\) | |||||||
\(234\) | 1.60520e7 | 0.0818983 | ||||||||
\(235\) | −4.23364e8 | −2.12803 | ||||||||
\(236\) | −2.20250e7 | −0.109074 | ||||||||
\(237\) | −1.50299e8 | −0.733391 | ||||||||
\(238\) | 1.26563e7 | 0.0608539 | ||||||||
\(239\) | −2.23797e8 | −1.06038 | −0.530189 | − | 0.847879i | \(-0.677879\pi\) | ||||
−0.530189 | + | 0.847879i | \(0.677879\pi\) | |||||||
\(240\) | 1.29042e8 | 0.602547 | ||||||||
\(241\) | −1.78627e8 | −0.822030 | −0.411015 | − | 0.911629i | \(-0.634826\pi\) | ||||
−0.411015 | + | 0.911629i | \(0.634826\pi\) | |||||||
\(242\) | 3.22838e7 | 0.146430 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −4.05604e7 | −0.178746 | ||||||||
\(245\) | −3.83363e8 | −1.66544 | ||||||||
\(246\) | 1.72921e7 | 0.0740584 | ||||||||
\(247\) | −2.56796e8 | −1.08430 | ||||||||
\(248\) | −1.30150e8 | −0.541832 | ||||||||
\(249\) | 4.87492e7 | 0.200111 | ||||||||
\(250\) | 3.34469e8 | 1.35384 | ||||||||
\(251\) | −3.44628e8 | −1.37560 | −0.687800 | − | 0.725900i | \(-0.741423\pi\) | ||||
−0.687800 | + | 0.725900i | \(0.741423\pi\) | |||||||
\(252\) | 9.67926e7 | 0.381013 | ||||||||
\(253\) | −1.98582e8 | −0.770936 | ||||||||
\(254\) | −1.89155e8 | −0.724268 | ||||||||
\(255\) | 3.27385e7 | 0.123643 | ||||||||
\(256\) | −6.88409e7 | −0.256452 | ||||||||
\(257\) | −1.65611e7 | −0.0608588 | −0.0304294 | − | 0.999537i | \(-0.509687\pi\) | ||||
−0.0304294 | + | 0.999537i | \(0.509687\pi\) | |||||||
\(258\) | 8.57342e7 | 0.310803 | ||||||||
\(259\) | 5.90198e8 | 2.11081 | ||||||||
\(260\) | −2.80095e8 | −0.988321 | ||||||||
\(261\) | −1.00126e8 | −0.348583 | ||||||||
\(262\) | −2.11301e8 | −0.725849 | ||||||||
\(263\) | 3.89298e8 | 1.31958 | 0.659792 | − | 0.751448i | \(-0.270644\pi\) | ||||
0.659792 | + | 0.751448i | \(0.270644\pi\) | |||||||
\(264\) | −1.01911e8 | −0.340886 | ||||||||
\(265\) | −5.69812e8 | −1.88092 | ||||||||
\(266\) | 2.99749e8 | 0.976500 | ||||||||
\(267\) | −2.23043e8 | −0.717132 | ||||||||
\(268\) | 1.20313e8 | 0.381805 | ||||||||
\(269\) | −2.69260e8 | −0.843410 | −0.421705 | − | 0.906733i | \(-0.638568\pi\) | ||||
−0.421705 | + | 0.906733i | \(0.638568\pi\) | |||||||
\(270\) | −4.84675e7 | −0.149857 | ||||||||
\(271\) | −4.95264e8 | −1.51163 | −0.755813 | − | 0.654787i | \(-0.772758\pi\) | ||||
−0.755813 | + | 0.654787i | \(0.772758\pi\) | |||||||
\(272\) | 1.98408e7 | 0.0597816 | ||||||||
\(273\) | −1.61553e8 | −0.480557 | ||||||||
\(274\) | 1.45990e7 | 0.0428743 | ||||||||
\(275\) | 7.53462e8 | 2.18473 | ||||||||
\(276\) | −1.63277e8 | −0.467458 | ||||||||
\(277\) | 3.16965e8 | 0.896051 | 0.448025 | − | 0.894021i | \(-0.352127\pi\) | ||||
0.448025 | + | 0.894021i | \(0.352127\pi\) | |||||||
\(278\) | −1.70673e8 | −0.476441 | ||||||||
\(279\) | −8.85223e7 | −0.244027 | ||||||||
\(280\) | 7.17178e8 | 1.95242 | ||||||||
\(281\) | −4.50536e8 | −1.21132 | −0.605658 | − | 0.795725i | \(-0.707090\pi\) | ||||
−0.605658 | + | 0.795725i | \(0.707090\pi\) | |||||||
\(282\) | 9.63685e7 | 0.255896 | ||||||||
\(283\) | 4.67571e8 | 1.22629 | 0.613147 | − | 0.789969i | \(-0.289903\pi\) | ||||
0.613147 | + | 0.789969i | \(0.289903\pi\) | |||||||
\(284\) | −4.10539e8 | −1.06351 | ||||||||
\(285\) | 7.75370e8 | 1.98405 | ||||||||
\(286\) | 7.75428e7 | 0.196002 | ||||||||
\(287\) | −1.74033e8 | −0.434554 | ||||||||
\(288\) | −1.29386e8 | −0.319165 | ||||||||
\(289\) | −4.05305e8 | −0.987733 | ||||||||
\(290\) | −3.38205e8 | −0.814304 | ||||||||
\(291\) | 2.52936e8 | 0.601706 | ||||||||
\(292\) | 1.80544e8 | 0.424369 | ||||||||
\(293\) | −1.60508e7 | −0.0372786 | −0.0186393 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186393 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(294\) | 8.72632e7 | 0.200270 | ||||||||
\(295\) | −1.10996e8 | −0.251727 | ||||||||
\(296\) | −5.10931e8 | −1.14509 | ||||||||
\(297\) | −6.93154e7 | −0.153526 | ||||||||
\(298\) | −1.09136e8 | −0.238898 | ||||||||
\(299\) | 2.72519e8 | 0.589586 | ||||||||
\(300\) | 6.19506e8 | 1.32471 | ||||||||
\(301\) | −8.62855e8 | −1.82371 | ||||||||
\(302\) | 3.00352e8 | 0.627489 | ||||||||
\(303\) | −1.39812e8 | −0.288731 | ||||||||
\(304\) | 4.69904e8 | 0.959294 | ||||||||
\(305\) | −2.04406e8 | −0.412520 | ||||||||
\(306\) | −7.45211e6 | −0.0148681 | ||||||||
\(307\) | −6.56164e7 | −0.129428 | −0.0647140 | − | 0.997904i | \(-0.520614\pi\) | ||||
−0.0647140 | + | 0.997904i | \(0.520614\pi\) | |||||||
\(308\) | 4.67577e8 | 0.911854 | ||||||||
\(309\) | 4.41705e8 | 0.851683 | ||||||||
\(310\) | −2.99009e8 | −0.570057 | ||||||||
\(311\) | 4.44680e8 | 0.838275 | 0.419138 | − | 0.907923i | \(-0.362332\pi\) | ||||
0.419138 | + | 0.907923i | \(0.362332\pi\) | |||||||
\(312\) | 1.39855e8 | 0.260698 | ||||||||
\(313\) | 2.94757e8 | 0.543324 | 0.271662 | − | 0.962393i | \(-0.412427\pi\) | ||||
0.271662 | + | 0.962393i | \(0.412427\pi\) | |||||||
\(314\) | 2.93899e8 | 0.535728 | ||||||||
\(315\) | 4.87792e8 | 0.879321 | ||||||||
\(316\) | −5.96967e8 | −1.06425 | ||||||||
\(317\) | −3.97400e8 | −0.700682 | −0.350341 | − | 0.936622i | \(-0.613934\pi\) | ||||
−0.350341 | + | 0.936622i | \(0.613934\pi\) | |||||||
\(318\) | 1.29704e8 | 0.226182 | ||||||||
\(319\) | −4.83680e8 | −0.834240 | ||||||||
\(320\) | 1.74714e8 | 0.298059 | ||||||||
\(321\) | 3.11259e8 | 0.525235 | ||||||||
\(322\) | −3.18101e8 | −0.530970 | ||||||||
\(323\) | 1.19217e8 | 0.196847 | ||||||||
\(324\) | −5.69920e7 | −0.0930907 | ||||||||
\(325\) | −1.03399e9 | −1.67081 | ||||||||
\(326\) | 1.76968e8 | 0.282900 | ||||||||
\(327\) | 4.50867e7 | 0.0713069 | ||||||||
\(328\) | 1.50659e8 | 0.235742 | ||||||||
\(329\) | −9.69882e8 | −1.50153 | ||||||||
\(330\) | −2.34132e8 | −0.358643 | ||||||||
\(331\) | −1.15349e9 | −1.74830 | −0.874150 | − | 0.485656i | \(-0.838581\pi\) | ||||
−0.874150 | + | 0.485656i | \(0.838581\pi\) | |||||||
\(332\) | 1.93626e8 | 0.290389 | ||||||||
\(333\) | −3.47512e8 | −0.515721 | ||||||||
\(334\) | −1.19613e8 | −0.175658 | ||||||||
\(335\) | 6.06325e8 | 0.881148 | ||||||||
\(336\) | 2.95621e8 | 0.425155 | ||||||||
\(337\) | −1.00153e9 | −1.42547 | −0.712735 | − | 0.701434i | \(-0.752544\pi\) | ||||
−0.712735 | + | 0.701434i | \(0.752544\pi\) | |||||||
\(338\) | 1.79485e8 | 0.252824 | ||||||||
\(339\) | 7.63466e7 | 0.106437 | ||||||||
\(340\) | 1.30033e8 | 0.179423 | ||||||||
\(341\) | −4.27625e8 | −0.584014 | ||||||||
\(342\) | −1.76494e8 | −0.238582 | ||||||||
\(343\) | 1.41385e8 | 0.189179 | ||||||||
\(344\) | 7.46969e8 | 0.989346 | ||||||||
\(345\) | −8.22842e8 | −1.07882 | ||||||||
\(346\) | 4.47103e7 | 0.0580285 | ||||||||
\(347\) | −2.60064e8 | −0.334139 | −0.167069 | − | 0.985945i | \(-0.553430\pi\) | ||||
−0.167069 | + | 0.985945i | \(0.553430\pi\) | |||||||
\(348\) | −3.97688e8 | −0.505843 | ||||||||
\(349\) | −2.45544e8 | −0.309201 | −0.154600 | − | 0.987977i | \(-0.549409\pi\) | ||||
−0.154600 | + | 0.987977i | \(0.549409\pi\) | |||||||
\(350\) | 1.20694e9 | 1.50470 | ||||||||
\(351\) | 9.51231e7 | 0.117412 | ||||||||
\(352\) | −6.25028e8 | −0.763836 | ||||||||
\(353\) | −8.28455e8 | −1.00244 | −0.501219 | − | 0.865320i | \(-0.667115\pi\) | ||||
−0.501219 | + | 0.865320i | \(0.667115\pi\) | |||||||
\(354\) | 2.52655e7 | 0.0302703 | ||||||||
\(355\) | −2.06893e9 | −2.45441 | ||||||||
\(356\) | −8.85898e8 | −1.04066 | ||||||||
\(357\) | 7.50003e7 | 0.0872418 | ||||||||
\(358\) | 1.77143e8 | 0.204048 | ||||||||
\(359\) | 8.66890e8 | 0.988857 | 0.494428 | − | 0.869218i | \(-0.335377\pi\) | ||||
0.494428 | + | 0.869218i | \(0.335377\pi\) | |||||||
\(360\) | −4.22278e8 | −0.477024 | ||||||||
\(361\) | 1.92963e9 | 2.15873 | ||||||||
\(362\) | 2.62237e8 | 0.290546 | ||||||||
\(363\) | 1.91311e8 | 0.209927 | ||||||||
\(364\) | −6.41666e8 | −0.697356 | ||||||||
\(365\) | 9.09863e8 | 0.979380 | ||||||||
\(366\) | 4.65281e7 | 0.0496056 | ||||||||
\(367\) | −1.45949e9 | −1.54124 | −0.770620 | − | 0.637295i | \(-0.780053\pi\) | ||||
−0.770620 | + | 0.637295i | \(0.780053\pi\) | |||||||
\(368\) | −4.98674e8 | −0.521615 | ||||||||
\(369\) | 1.02471e8 | 0.106172 | ||||||||
\(370\) | −1.17382e9 | −1.20475 | ||||||||
\(371\) | −1.30538e9 | −1.32717 | ||||||||
\(372\) | −3.51599e8 | −0.354118 | ||||||||
\(373\) | −1.35964e9 | −1.35657 | −0.678287 | − | 0.734798i | \(-0.737277\pi\) | ||||
−0.678287 | + | 0.734798i | \(0.737277\pi\) | |||||||
\(374\) | −3.59990e7 | −0.0355828 | ||||||||
\(375\) | 1.98204e9 | 1.94090 | ||||||||
\(376\) | 8.39622e8 | 0.814566 | ||||||||
\(377\) | 6.63766e8 | 0.637999 | ||||||||
\(378\) | −1.11034e8 | −0.105739 | ||||||||
\(379\) | 1.81549e9 | 1.71300 | 0.856500 | − | 0.516147i | \(-0.172634\pi\) | ||||
0.856500 | + | 0.516147i | \(0.172634\pi\) | |||||||
\(380\) | 3.07967e9 | 2.87913 | ||||||||
\(381\) | −1.12092e9 | −1.03833 | ||||||||
\(382\) | −7.14002e8 | −0.655357 | ||||||||
\(383\) | −5.43039e8 | −0.493896 | −0.246948 | − | 0.969029i | \(-0.579428\pi\) | ||||
−0.246948 | + | 0.969029i | \(0.579428\pi\) | |||||||
\(384\) | −6.53157e8 | −0.588652 | ||||||||
\(385\) | 2.35638e9 | 2.10442 | ||||||||
\(386\) | −2.48289e8 | −0.219737 | ||||||||
\(387\) | 5.08054e8 | 0.445576 | ||||||||
\(388\) | 1.00463e9 | 0.873161 | ||||||||
\(389\) | 1.90428e9 | 1.64024 | 0.820121 | − | 0.572190i | \(-0.193906\pi\) | ||||
0.820121 | + | 0.572190i | \(0.193906\pi\) | |||||||
\(390\) | 3.21305e8 | 0.274278 | ||||||||
\(391\) | −1.26516e8 | −0.107035 | ||||||||
\(392\) | 7.60291e8 | 0.637498 | ||||||||
\(393\) | −1.25215e9 | −1.04060 | ||||||||
\(394\) | −6.65977e8 | −0.548558 | ||||||||
\(395\) | −3.00845e9 | −2.45614 | ||||||||
\(396\) | −2.75312e8 | −0.222788 | ||||||||
\(397\) | −2.75416e8 | −0.220913 | −0.110457 | − | 0.993881i | \(-0.535231\pi\) | ||||
−0.110457 | + | 0.993881i | \(0.535231\pi\) | |||||||
\(398\) | −2.30813e8 | −0.183514 | ||||||||
\(399\) | 1.77629e9 | 1.39994 | ||||||||
\(400\) | 1.89207e9 | 1.47818 | ||||||||
\(401\) | 1.17696e9 | 0.911501 | 0.455751 | − | 0.890108i | \(-0.349371\pi\) | ||||
0.455751 | + | 0.890108i | \(0.349371\pi\) | |||||||
\(402\) | −1.38015e8 | −0.105958 | ||||||||
\(403\) | 5.86840e8 | 0.446635 | ||||||||
\(404\) | −5.55314e8 | −0.418990 | ||||||||
\(405\) | −2.87214e8 | −0.214839 | ||||||||
\(406\) | −7.74790e8 | −0.574570 | ||||||||
\(407\) | −1.67873e9 | −1.23424 | ||||||||
\(408\) | −6.49274e7 | −0.0473279 | ||||||||
\(409\) | −1.75837e9 | −1.27080 | −0.635402 | − | 0.772181i | \(-0.719166\pi\) | ||||
−0.635402 | + | 0.772181i | \(0.719166\pi\) | |||||||
\(410\) | 3.46126e8 | 0.248022 | ||||||||
\(411\) | 8.65127e7 | 0.0614658 | ||||||||
\(412\) | 1.75440e9 | 1.23591 | ||||||||
\(413\) | −2.54280e8 | −0.177618 | ||||||||
\(414\) | 1.87300e8 | 0.129729 | ||||||||
\(415\) | 9.75787e8 | 0.670173 | ||||||||
\(416\) | 8.57741e8 | 0.584157 | ||||||||
\(417\) | −1.01140e9 | −0.683039 | ||||||||
\(418\) | −8.52591e8 | −0.570984 | ||||||||
\(419\) | 2.47153e9 | 1.64141 | 0.820705 | − | 0.571353i | \(-0.193581\pi\) | ||||
0.820705 | + | 0.571353i | \(0.193581\pi\) | |||||||
\(420\) | 1.93745e9 | 1.27602 | ||||||||
\(421\) | −1.28349e9 | −0.838313 | −0.419157 | − | 0.907914i | \(-0.637674\pi\) | ||||
−0.419157 | + | 0.907914i | \(0.637674\pi\) | |||||||
\(422\) | −1.53203e8 | −0.0992367 | ||||||||
\(423\) | 5.71072e8 | 0.366859 | ||||||||
\(424\) | 1.13006e9 | 0.719980 | ||||||||
\(425\) | 4.80028e8 | 0.303323 | ||||||||
\(426\) | 4.70942e8 | 0.295144 | ||||||||
\(427\) | −4.68272e8 | −0.291072 | ||||||||
\(428\) | 1.23628e9 | 0.762191 | ||||||||
\(429\) | 4.59512e8 | 0.280994 | ||||||||
\(430\) | 1.71610e9 | 1.04088 | ||||||||
\(431\) | 1.78192e9 | 1.07206 | 0.536030 | − | 0.844199i | \(-0.319923\pi\) | ||||
0.536030 | + | 0.844199i | \(0.319923\pi\) | |||||||
\(432\) | −1.74063e8 | −0.103876 | ||||||||
\(433\) | 8.17222e8 | 0.483763 | 0.241881 | − | 0.970306i | \(-0.422236\pi\) | ||||
0.241881 | + | 0.970306i | \(0.422236\pi\) | |||||||
\(434\) | −6.84998e8 | −0.402230 | ||||||||
\(435\) | −2.00417e9 | −1.16741 | ||||||||
\(436\) | 1.79079e8 | 0.103476 | ||||||||
\(437\) | −2.99637e9 | −1.71756 | ||||||||
\(438\) | −2.07108e8 | −0.117771 | ||||||||
\(439\) | −2.53136e9 | −1.42800 | −0.714001 | − | 0.700145i | \(-0.753119\pi\) | ||||
−0.714001 | + | 0.700145i | \(0.753119\pi\) | |||||||
\(440\) | −2.03990e9 | −1.14163 | ||||||||
\(441\) | 5.17115e8 | 0.287112 | ||||||||
\(442\) | 4.94022e7 | 0.0272125 | ||||||||
\(443\) | −7.10880e8 | −0.388493 | −0.194247 | − | 0.980953i | \(-0.562226\pi\) | ||||
−0.194247 | + | 0.980953i | \(0.562226\pi\) | |||||||
\(444\) | −1.38027e9 | −0.748384 | ||||||||
\(445\) | −4.46453e9 | −2.40169 | ||||||||
\(446\) | −3.95919e8 | −0.211317 | ||||||||
\(447\) | −6.46734e8 | −0.342491 | ||||||||
\(448\) | 4.00250e8 | 0.210309 | ||||||||
\(449\) | 1.22783e9 | 0.640139 | 0.320070 | − | 0.947394i | \(-0.396294\pi\) | ||||
0.320070 | + | 0.947394i | \(0.396294\pi\) | |||||||
\(450\) | −7.10655e8 | −0.367633 | ||||||||
\(451\) | 4.95009e8 | 0.254095 | ||||||||
\(452\) | 3.03239e8 | 0.154454 | ||||||||
\(453\) | 1.77986e9 | 0.899585 | ||||||||
\(454\) | −1.66165e8 | −0.0833382 | ||||||||
\(455\) | −3.23371e9 | −1.60939 | ||||||||
\(456\) | −1.53772e9 | −0.759454 | ||||||||
\(457\) | 3.07883e9 | 1.50897 | 0.754483 | − | 0.656319i | \(-0.227888\pi\) | ||||
0.754483 | + | 0.656319i | \(0.227888\pi\) | |||||||
\(458\) | −1.00031e9 | −0.486524 | ||||||||
\(459\) | −4.41606e7 | −0.0213153 | ||||||||
\(460\) | −3.26822e9 | −1.56552 | ||||||||
\(461\) | 1.77409e9 | 0.843379 | 0.421689 | − | 0.906740i | \(-0.361437\pi\) | ||||
0.421689 | + | 0.906740i | \(0.361437\pi\) | |||||||
\(462\) | −5.36372e8 | −0.253057 | ||||||||
\(463\) | 3.91361e9 | 1.83250 | 0.916249 | − | 0.400608i | \(-0.131201\pi\) | ||||
0.916249 | + | 0.400608i | \(0.131201\pi\) | |||||||
\(464\) | −1.21461e9 | −0.564446 | ||||||||
\(465\) | −1.77190e9 | −0.817250 | ||||||||
\(466\) | −5.46701e8 | −0.250264 | ||||||||
\(467\) | −3.15577e9 | −1.43383 | −0.716914 | − | 0.697162i | \(-0.754446\pi\) | ||||
−0.716914 | + | 0.697162i | \(0.754446\pi\) | |||||||
\(468\) | 3.77817e8 | 0.170381 | ||||||||
\(469\) | 1.38902e9 | 0.621735 | ||||||||
\(470\) | 1.92896e9 | 0.856998 | ||||||||
\(471\) | 1.74162e9 | 0.768034 | ||||||||
\(472\) | 2.20129e8 | 0.0963561 | ||||||||
\(473\) | 2.45426e9 | 1.06637 | ||||||||
\(474\) | 6.84799e8 | 0.295351 | ||||||||
\(475\) | 1.13689e10 | 4.86732 | ||||||||
\(476\) | 2.97892e8 | 0.126600 | ||||||||
\(477\) | 7.68614e8 | 0.324260 | ||||||||
\(478\) | 1.01967e9 | 0.427036 | ||||||||
\(479\) | −3.08907e9 | −1.28426 | −0.642130 | − | 0.766596i | \(-0.721949\pi\) | ||||
−0.642130 | + | 0.766596i | \(0.721949\pi\) | |||||||
\(480\) | −2.58986e9 | −1.06889 | ||||||||
\(481\) | 2.30376e9 | 0.943907 | ||||||||
\(482\) | 8.13870e8 | 0.331048 | ||||||||
\(483\) | −1.88504e9 | −0.761213 | ||||||||
\(484\) | 7.59864e8 | 0.304633 | ||||||||
\(485\) | 5.06288e9 | 2.01512 | ||||||||
\(486\) | 6.53773e7 | 0.0258345 | ||||||||
\(487\) | −8.99853e8 | −0.353037 | −0.176518 | − | 0.984297i | \(-0.556484\pi\) | ||||
−0.176518 | + | 0.984297i | \(0.556484\pi\) | |||||||
\(488\) | 4.05381e8 | 0.157904 | ||||||||
\(489\) | 1.04870e9 | 0.405574 | ||||||||
\(490\) | 1.74670e9 | 0.670706 | ||||||||
\(491\) | −8.98595e8 | −0.342593 | −0.171297 | − | 0.985220i | \(-0.554796\pi\) | ||||
−0.171297 | + | 0.985220i | \(0.554796\pi\) | |||||||
\(492\) | 4.07003e8 | 0.154071 | ||||||||
\(493\) | −3.08151e8 | −0.115824 | ||||||||
\(494\) | 1.17003e9 | 0.436669 | ||||||||
\(495\) | −1.38745e9 | −0.514161 | ||||||||
\(496\) | −1.07384e9 | −0.395143 | ||||||||
\(497\) | −4.73970e9 | −1.73182 | ||||||||
\(498\) | −2.22114e8 | −0.0805885 | ||||||||
\(499\) | −2.94063e8 | −0.105947 | −0.0529734 | − | 0.998596i | \(-0.516870\pi\) | ||||
−0.0529734 | + | 0.998596i | \(0.516870\pi\) | |||||||
\(500\) | 7.87239e9 | 2.81651 | ||||||||
\(501\) | −7.08819e8 | −0.251827 | ||||||||
\(502\) | 1.57021e9 | 0.553982 | ||||||||
\(503\) | −3.01250e9 | −1.05545 | −0.527727 | − | 0.849414i | \(-0.676956\pi\) | ||||
−0.527727 | + | 0.849414i | \(0.676956\pi\) | |||||||
\(504\) | −9.67394e8 | −0.336586 | ||||||||
\(505\) | −2.79853e9 | −0.966965 | ||||||||
\(506\) | 9.04791e8 | 0.310471 | ||||||||
\(507\) | 1.06361e9 | 0.362456 | ||||||||
\(508\) | −4.45213e9 | −1.50676 | ||||||||
\(509\) | 7.20984e8 | 0.242333 | 0.121167 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121167 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(510\) | −1.49165e8 | −0.0497933 | ||||||||
\(511\) | 2.08440e9 | 0.691047 | ||||||||
\(512\) | −2.78279e9 | −0.916296 | ||||||||
\(513\) | −1.04589e9 | −0.342038 | ||||||||
\(514\) | 7.54567e7 | 0.0245091 | ||||||||
\(515\) | 8.84138e9 | 2.85230 | ||||||||
\(516\) | 2.01792e9 | 0.646593 | ||||||||
\(517\) | 2.75868e9 | 0.877980 | ||||||||
\(518\) | −2.68909e9 | −0.850064 | ||||||||
\(519\) | 2.64949e8 | 0.0831912 | ||||||||
\(520\) | 2.79941e9 | 0.873081 | ||||||||
\(521\) | −3.99688e9 | −1.23820 | −0.619098 | − | 0.785314i | \(-0.712502\pi\) | ||||
−0.619098 | + | 0.785314i | \(0.712502\pi\) | |||||||
\(522\) | 4.56201e8 | 0.140381 | ||||||||
\(523\) | 2.17294e9 | 0.664190 | 0.332095 | − | 0.943246i | \(-0.392245\pi\) | ||||
0.332095 | + | 0.943246i | \(0.392245\pi\) | |||||||
\(524\) | −4.97338e9 | −1.51005 | ||||||||
\(525\) | 7.15225e9 | 2.15717 | ||||||||
\(526\) | −1.77374e9 | −0.531423 | ||||||||
\(527\) | −2.72439e8 | −0.0810834 | ||||||||
\(528\) | −8.40848e8 | −0.248599 | ||||||||
\(529\) | −2.24997e8 | −0.0660819 | ||||||||
\(530\) | 2.59621e9 | 0.757485 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 7.05519e9 | 2.03151 | ||||||||
\(533\) | −6.79313e8 | −0.194323 | ||||||||
\(534\) | 1.01624e9 | 0.288804 | ||||||||
\(535\) | 6.23030e9 | 1.75902 | ||||||||
\(536\) | −1.20247e9 | −0.337286 | ||||||||
\(537\) | 1.04973e9 | 0.292529 | ||||||||
\(538\) | 1.22682e9 | 0.339658 | ||||||||
\(539\) | 2.49803e9 | 0.687127 | ||||||||
\(540\) | −1.14078e9 | −0.311762 | ||||||||
\(541\) | −4.30836e9 | −1.16983 | −0.584914 | − | 0.811096i | \(-0.698872\pi\) | ||||
−0.584914 | + | 0.811096i | \(0.698872\pi\) | |||||||
\(542\) | 2.25655e9 | 0.608762 | ||||||||
\(543\) | 1.55400e9 | 0.416534 | ||||||||
\(544\) | −3.98204e8 | −0.106050 | ||||||||
\(545\) | 9.02476e8 | 0.238808 | ||||||||
\(546\) | 7.36075e8 | 0.193530 | ||||||||
\(547\) | 7.88729e8 | 0.206050 | 0.103025 | − | 0.994679i | \(-0.467148\pi\) | ||||
0.103025 | + | 0.994679i | \(0.467148\pi\) | |||||||
\(548\) | 3.43617e8 | 0.0891956 | ||||||||
\(549\) | 2.75721e8 | 0.0711160 | ||||||||
\(550\) | −3.43297e9 | −0.879833 | ||||||||
\(551\) | −7.29818e9 | −1.85859 | ||||||||
\(552\) | 1.63187e9 | 0.412952 | ||||||||
\(553\) | −6.89203e9 | −1.73304 | ||||||||
\(554\) | −1.44418e9 | −0.360858 | ||||||||
\(555\) | −6.95596e9 | −1.72716 | ||||||||
\(556\) | −4.01714e9 | −0.991186 | ||||||||
\(557\) | 5.29917e9 | 1.29932 | 0.649658 | − | 0.760226i | \(-0.274912\pi\) | ||||
0.649658 | + | 0.760226i | \(0.274912\pi\) | |||||||
\(558\) | 4.03330e8 | 0.0982746 | ||||||||
\(559\) | −3.36804e9 | −0.815522 | ||||||||
\(560\) | 5.91728e9 | 1.42385 | ||||||||
\(561\) | −2.13327e8 | −0.0510124 | ||||||||
\(562\) | 2.05276e9 | 0.487821 | ||||||||
\(563\) | −5.56156e9 | −1.31346 | −0.656731 | − | 0.754125i | \(-0.728061\pi\) | ||||
−0.656731 | + | 0.754125i | \(0.728061\pi\) | |||||||
\(564\) | 2.26822e9 | 0.532365 | ||||||||
\(565\) | 1.52819e9 | 0.356457 | ||||||||
\(566\) | −2.13037e9 | −0.493853 | ||||||||
\(567\) | −6.57977e8 | −0.151590 | ||||||||
\(568\) | 4.10314e9 | 0.939500 | ||||||||
\(569\) | 3.31033e9 | 0.753319 | 0.376659 | − | 0.926352i | \(-0.377073\pi\) | ||||
0.376659 | + | 0.926352i | \(0.377073\pi\) | |||||||
\(570\) | −3.53278e9 | −0.799015 | ||||||||
\(571\) | −3.86639e8 | −0.0869118 | −0.0434559 | − | 0.999055i | \(-0.513837\pi\) | ||||
−0.0434559 | + | 0.999055i | \(0.513837\pi\) | |||||||
\(572\) | 1.82512e9 | 0.407761 | ||||||||
\(573\) | −4.23112e9 | −0.939537 | ||||||||
\(574\) | 7.92938e8 | 0.175004 | ||||||||
\(575\) | −1.20649e10 | −2.64659 | ||||||||
\(576\) | −2.35670e8 | −0.0513836 | ||||||||
\(577\) | 3.94872e9 | 0.855739 | 0.427870 | − | 0.903840i | \(-0.359264\pi\) | ||||
0.427870 | + | 0.903840i | \(0.359264\pi\) | |||||||
\(578\) | 1.84667e9 | 0.397780 | ||||||||
\(579\) | −1.47134e9 | −0.315020 | ||||||||
\(580\) | −7.96031e9 | −1.69407 | ||||||||
\(581\) | 2.23542e9 | 0.472871 | ||||||||
\(582\) | −1.15244e9 | −0.242319 | ||||||||
\(583\) | 3.71295e9 | 0.776031 | ||||||||
\(584\) | −1.80445e9 | −0.374887 | ||||||||
\(585\) | 1.90403e9 | 0.393213 | ||||||||
\(586\) | 7.31315e7 | 0.0150128 | ||||||||
\(587\) | −1.13309e9 | −0.231223 | −0.115612 | − | 0.993294i | \(-0.536883\pi\) | ||||
−0.115612 | + | 0.993294i | \(0.536883\pi\) | |||||||
\(588\) | 2.05391e9 | 0.416640 | ||||||||
\(589\) | −6.45237e9 | −1.30112 | ||||||||
\(590\) | 5.05726e8 | 0.101376 | ||||||||
\(591\) | −3.94652e9 | −0.786427 | ||||||||
\(592\) | −4.21558e9 | −0.835086 | ||||||||
\(593\) | 6.61359e9 | 1.30240 | 0.651202 | − | 0.758904i | \(-0.274265\pi\) | ||||
0.651202 | + | 0.758904i | \(0.274265\pi\) | |||||||
\(594\) | 3.15819e8 | 0.0618280 | ||||||||
\(595\) | 1.50124e9 | 0.292174 | ||||||||
\(596\) | −2.56874e9 | −0.497003 | ||||||||
\(597\) | −1.36778e9 | −0.263091 | ||||||||
\(598\) | −1.24167e9 | −0.237438 | ||||||||
\(599\) | −2.36330e9 | −0.449289 | −0.224644 | − | 0.974441i | \(-0.572122\pi\) | ||||
−0.224644 | + | 0.974441i | \(0.572122\pi\) | |||||||
\(600\) | −6.19166e9 | −1.17025 | ||||||||
\(601\) | −4.40437e9 | −0.827605 | −0.413803 | − | 0.910367i | \(-0.635800\pi\) | ||||
−0.413803 | + | 0.910367i | \(0.635800\pi\) | |||||||
\(602\) | 3.93139e9 | 0.734443 | ||||||||
\(603\) | −8.17866e8 | −0.151905 | ||||||||
\(604\) | 7.06938e9 | 1.30543 | ||||||||
\(605\) | 3.82937e9 | 0.703047 | ||||||||
\(606\) | 6.37018e8 | 0.116278 | ||||||||
\(607\) | −2.71725e9 | −0.493138 | −0.246569 | − | 0.969125i | \(-0.579303\pi\) | ||||
−0.246569 | + | 0.969125i | \(0.579303\pi\) | |||||||
\(608\) | −9.43095e9 | −1.70174 | ||||||||
\(609\) | −4.59134e9 | −0.823719 | ||||||||
\(610\) | 9.31327e8 | 0.166130 | ||||||||
\(611\) | −3.78580e9 | −0.671450 | ||||||||
\(612\) | −1.75400e8 | −0.0309314 | ||||||||
\(613\) | −1.02118e10 | −1.79056 | −0.895282 | − | 0.445500i | \(-0.853026\pi\) | ||||
−0.895282 | + | 0.445500i | \(0.853026\pi\) | |||||||
\(614\) | 2.98965e8 | 0.0521233 | ||||||||
\(615\) | 2.05112e9 | 0.355572 | ||||||||
\(616\) | −4.67320e9 | −0.805530 | ||||||||
\(617\) | 3.23817e9 | 0.555011 | 0.277506 | − | 0.960724i | \(-0.410492\pi\) | ||||
0.277506 | + | 0.960724i | \(0.410492\pi\) | |||||||
\(618\) | −2.01252e9 | −0.342990 | ||||||||
\(619\) | −1.72870e9 | −0.292956 | −0.146478 | − | 0.989214i | \(-0.546794\pi\) | ||||
−0.146478 | + | 0.989214i | \(0.546794\pi\) | |||||||
\(620\) | −7.03777e9 | −1.18594 | ||||||||
\(621\) | 1.10992e9 | 0.185983 | ||||||||
\(622\) | −2.02608e9 | −0.337590 | ||||||||
\(623\) | −1.02278e10 | −1.69462 | ||||||||
\(624\) | 1.15391e9 | 0.190120 | ||||||||
\(625\) | 2.29581e10 | 3.76145 | ||||||||
\(626\) | −1.34299e9 | −0.218807 | ||||||||
\(627\) | −5.05238e9 | −0.818578 | ||||||||
\(628\) | 6.91750e9 | 1.11453 | ||||||||
\(629\) | −1.06951e9 | −0.171360 | ||||||||
\(630\) | −2.22250e9 | −0.354120 | ||||||||
\(631\) | 7.57564e9 | 1.20037 | 0.600187 | − | 0.799859i | \(-0.295093\pi\) | ||||
0.600187 | + | 0.799859i | \(0.295093\pi\) | |||||||
\(632\) | 5.96639e9 | 0.940160 | ||||||||
\(633\) | −9.07866e8 | −0.142268 | ||||||||
\(634\) | 1.81066e9 | 0.282179 | ||||||||
\(635\) | −2.24368e10 | −3.47738 | ||||||||
\(636\) | 3.05283e9 | 0.470547 | ||||||||
\(637\) | −3.42811e9 | −0.525492 | ||||||||
\(638\) | 2.20377e9 | 0.335965 | ||||||||
\(639\) | 2.79076e9 | 0.423126 | ||||||||
\(640\) | −1.30739e10 | −1.97140 | ||||||||
\(641\) | −5.56603e9 | −0.834723 | −0.417362 | − | 0.908740i | \(-0.637045\pi\) | ||||
−0.417362 | + | 0.908740i | \(0.637045\pi\) | |||||||
\(642\) | −1.41817e9 | −0.211523 | ||||||||
\(643\) | −7.76877e9 | −1.15243 | −0.576214 | − | 0.817299i | \(-0.695471\pi\) | ||||
−0.576214 | + | 0.817299i | \(0.695471\pi\) | |||||||
\(644\) | −7.48715e9 | −1.10463 | ||||||||
\(645\) | 1.01694e10 | 1.49224 | ||||||||
\(646\) | −5.43183e8 | −0.0792743 | ||||||||
\(647\) | 6.50327e9 | 0.943989 | 0.471994 | − | 0.881602i | \(-0.343534\pi\) | ||||
0.471994 | + | 0.881602i | \(0.343534\pi\) | |||||||
\(648\) | 5.69607e8 | 0.0822362 | ||||||||
\(649\) | 7.23260e8 | 0.103858 | ||||||||
\(650\) | 4.71114e9 | 0.672867 | ||||||||
\(651\) | −4.05924e9 | −0.576648 | ||||||||
\(652\) | 4.16530e9 | 0.588545 | ||||||||
\(653\) | −9.96747e9 | −1.40084 | −0.700420 | − | 0.713731i | \(-0.747004\pi\) | ||||
−0.700420 | + | 0.713731i | \(0.747004\pi\) | |||||||
\(654\) | −2.05427e8 | −0.0287167 | ||||||||
\(655\) | −2.50636e10 | −3.48497 | ||||||||
\(656\) | 1.24306e9 | 0.171920 | ||||||||
\(657\) | −1.22731e9 | −0.168839 | ||||||||
\(658\) | 4.41903e9 | 0.604695 | ||||||||
\(659\) | 1.28708e10 | 1.75189 | 0.875946 | − | 0.482410i | \(-0.160238\pi\) | ||||
0.875946 | + | 0.482410i | \(0.160238\pi\) | |||||||
\(660\) | −5.51077e9 | −0.746119 | ||||||||
\(661\) | −4.36910e9 | −0.588420 | −0.294210 | − | 0.955741i | \(-0.595056\pi\) | ||||
−0.294210 | + | 0.955741i | \(0.595056\pi\) | |||||||
\(662\) | 5.25560e9 | 0.704075 | ||||||||
\(663\) | 2.92754e8 | 0.0390126 | ||||||||
\(664\) | −1.93519e9 | −0.256529 | ||||||||
\(665\) | 3.55550e10 | 4.68841 | ||||||||
\(666\) | 1.58335e9 | 0.207691 | ||||||||
\(667\) | 7.74501e9 | 1.01061 | ||||||||
\(668\) | −2.81534e9 | −0.365437 | ||||||||
\(669\) | −2.34618e9 | −0.302950 | ||||||||
\(670\) | −2.76257e9 | −0.354856 | ||||||||
\(671\) | 1.33193e9 | 0.170197 | ||||||||
\(672\) | −5.93309e9 | −0.754203 | ||||||||
\(673\) | −2.50718e9 | −0.317053 | −0.158527 | − | 0.987355i | \(-0.550674\pi\) | ||||
−0.158527 | + | 0.987355i | \(0.550674\pi\) | |||||||
\(674\) | 4.56321e9 | 0.574065 | ||||||||
\(675\) | −4.21128e9 | −0.527049 | ||||||||
\(676\) | 4.22453e9 | 0.525974 | ||||||||
\(677\) | 4.46850e9 | 0.553479 | 0.276739 | − | 0.960945i | \(-0.410746\pi\) | ||||
0.276739 | + | 0.960945i | \(0.410746\pi\) | |||||||
\(678\) | −3.47855e8 | −0.0428641 | ||||||||
\(679\) | 1.15985e10 | 1.42186 | ||||||||
\(680\) | −1.29962e9 | −0.158502 | ||||||||
\(681\) | −9.84680e8 | −0.119476 | ||||||||
\(682\) | 1.94837e9 | 0.235194 | ||||||||
\(683\) | −3.36244e9 | −0.403815 | −0.201908 | − | 0.979405i | \(-0.564714\pi\) | ||||
−0.201908 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(684\) | −4.15413e9 | −0.496346 | ||||||||
\(685\) | 1.73168e9 | 0.205850 | ||||||||
\(686\) | −6.44185e8 | −0.0761862 | ||||||||
\(687\) | −5.92773e9 | −0.697493 | ||||||||
\(688\) | 6.16308e9 | 0.721503 | ||||||||
\(689\) | −5.09536e9 | −0.593483 | ||||||||
\(690\) | 3.74908e9 | 0.434463 | ||||||||
\(691\) | 1.73704e9 | 0.200279 | 0.100140 | − | 0.994973i | \(-0.468071\pi\) | ||||
0.100140 | + | 0.994973i | \(0.468071\pi\) | |||||||
\(692\) | 1.05235e9 | 0.120722 | ||||||||
\(693\) | −3.17849e9 | −0.362790 | ||||||||
\(694\) | 1.18492e9 | 0.134564 | ||||||||
\(695\) | −2.02446e10 | −2.28751 | ||||||||
\(696\) | 3.97470e9 | 0.446860 | ||||||||
\(697\) | 3.15369e8 | 0.0352780 | ||||||||
\(698\) | 1.11876e9 | 0.124521 | ||||||||
\(699\) | −3.23971e9 | −0.358786 | ||||||||
\(700\) | 2.84078e10 | 3.13036 | ||||||||
\(701\) | 7.43794e9 | 0.815529 | 0.407764 | − | 0.913087i | \(-0.366308\pi\) | ||||
0.407764 | + | 0.913087i | \(0.366308\pi\) | |||||||
\(702\) | −4.33405e8 | −0.0472840 | ||||||||
\(703\) | −2.53301e10 | −2.74975 | ||||||||
\(704\) | −1.13845e9 | −0.122973 | ||||||||
\(705\) | 1.14308e10 | 1.22862 | ||||||||
\(706\) | 3.77465e9 | 0.403702 | ||||||||
\(707\) | −6.41114e9 | −0.682287 | ||||||||
\(708\) | 5.94674e8 | 0.0629742 | ||||||||
\(709\) | −3.13976e9 | −0.330853 | −0.165426 | − | 0.986222i | \(-0.552900\pi\) | ||||
−0.165426 | + | 0.986222i | \(0.552900\pi\) | |||||||
\(710\) | 9.42659e9 | 0.988441 | ||||||||
\(711\) | 4.05806e9 | 0.423424 | ||||||||
\(712\) | 8.85412e9 | 0.919317 | ||||||||
\(713\) | 6.84742e9 | 0.707479 | ||||||||
\(714\) | −3.41721e8 | −0.0351340 | ||||||||
\(715\) | 9.19780e9 | 0.941051 | ||||||||
\(716\) | 4.16940e9 | 0.424501 | ||||||||
\(717\) | 6.04251e9 | 0.612210 | ||||||||
\(718\) | −3.94977e9 | −0.398232 | ||||||||
\(719\) | −1.62139e10 | −1.62680 | −0.813402 | − | 0.581701i | \(-0.802387\pi\) | ||||
−0.813402 | + | 0.581701i | \(0.802387\pi\) | |||||||
\(720\) | −3.48413e9 | −0.347881 | ||||||||
\(721\) | 2.02546e10 | 2.01257 | ||||||||
\(722\) | −8.79190e9 | −0.869365 | ||||||||
\(723\) | 4.82293e9 | 0.474599 | ||||||||
\(724\) | 6.17227e9 | 0.604449 | ||||||||
\(725\) | −2.93862e10 | −2.86392 | ||||||||
\(726\) | −8.71663e8 | −0.0845416 | ||||||||
\(727\) | 1.44572e10 | 1.39545 | 0.697725 | − | 0.716366i | \(-0.254196\pi\) | ||||
0.697725 | + | 0.716366i | \(0.254196\pi\) | |||||||
\(728\) | 6.41314e9 | 0.616043 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −4.14557e9 | −0.394416 | ||||||||
\(731\) | 1.56360e9 | 0.148052 | ||||||||
\(732\) | 1.09513e9 | 0.103199 | ||||||||
\(733\) | 8.79960e9 | 0.825275 | 0.412638 | − | 0.910895i | \(-0.364608\pi\) | ||||
0.412638 | + | 0.910895i | \(0.364608\pi\) | |||||||
\(734\) | 6.64982e9 | 0.620688 | ||||||||
\(735\) | 1.03508e10 | 0.961543 | ||||||||
\(736\) | 1.00084e10 | 0.925318 | ||||||||
\(737\) | −3.95087e9 | −0.363544 | ||||||||
\(738\) | −4.66886e8 | −0.0427576 | ||||||||
\(739\) | 1.06478e10 | 0.970523 | 0.485262 | − | 0.874369i | \(-0.338724\pi\) | ||||
0.485262 | + | 0.874369i | \(0.338724\pi\) | |||||||
\(740\) | −2.76282e10 | −2.50635 | ||||||||
\(741\) | 6.93350e9 | 0.626021 | ||||||||
\(742\) | 5.94764e9 | 0.534479 | ||||||||
\(743\) | −6.58260e9 | −0.588758 | −0.294379 | − | 0.955689i | \(-0.595113\pi\) | ||||
−0.294379 | + | 0.955689i | \(0.595113\pi\) | |||||||
\(744\) | 3.51406e9 | 0.312827 | ||||||||
\(745\) | −1.29453e10 | −1.14701 | ||||||||
\(746\) | 6.19487e9 | 0.546319 | ||||||||
\(747\) | −1.31623e9 | −0.115534 | ||||||||
\(748\) | −8.47307e8 | −0.0740262 | ||||||||
\(749\) | 1.42729e10 | 1.24116 | ||||||||
\(750\) | −9.03066e9 | −0.781637 | ||||||||
\(751\) | −8.17849e9 | −0.704585 | −0.352293 | − | 0.935890i | \(-0.614598\pi\) | ||||
−0.352293 | + | 0.935890i | \(0.614598\pi\) | |||||||
\(752\) | 6.92753e9 | 0.594040 | ||||||||
\(753\) | 9.30495e9 | 0.794203 | ||||||||
\(754\) | −3.02429e9 | −0.256935 | ||||||||
\(755\) | 3.56265e10 | 3.01272 | ||||||||
\(756\) | −2.61340e9 | −0.219978 | ||||||||
\(757\) | 1.76129e10 | 1.47569 | 0.737844 | − | 0.674972i | \(-0.235844\pi\) | ||||
0.737844 | + | 0.674972i | \(0.235844\pi\) | |||||||
\(758\) | −8.27185e9 | −0.689860 | ||||||||
\(759\) | 5.36172e9 | 0.445100 | ||||||||
\(760\) | −3.07798e10 | −2.54342 | ||||||||
\(761\) | −1.93708e10 | −1.59331 | −0.796657 | − | 0.604431i | \(-0.793400\pi\) | ||||
−0.796657 | + | 0.604431i | \(0.793400\pi\) | |||||||
\(762\) | 5.10718e9 | 0.418156 | ||||||||
\(763\) | 2.06748e9 | 0.168502 | ||||||||
\(764\) | −1.68055e10 | −1.36340 | ||||||||
\(765\) | −8.83939e8 | −0.0713851 | ||||||||
\(766\) | 2.47423e9 | 0.198902 | ||||||||
\(767\) | −9.92546e8 | −0.0794268 | ||||||||
\(768\) | 1.85870e9 | 0.148063 | ||||||||
\(769\) | 9.07869e9 | 0.719915 | 0.359957 | − | 0.932969i | \(-0.382791\pi\) | ||||
0.359957 | + | 0.932969i | \(0.382791\pi\) | |||||||
\(770\) | −1.07363e10 | −0.847492 | ||||||||
\(771\) | 4.47150e8 | 0.0351369 | ||||||||
\(772\) | −5.84398e9 | −0.457139 | ||||||||
\(773\) | −1.79639e10 | −1.39886 | −0.699428 | − | 0.714703i | \(-0.746562\pi\) | ||||
−0.699428 | + | 0.714703i | \(0.746562\pi\) | |||||||
\(774\) | −2.31482e9 | −0.179442 | ||||||||
\(775\) | −2.59805e10 | −2.00490 | ||||||||
\(776\) | −1.00408e10 | −0.771348 | ||||||||
\(777\) | −1.59353e10 | −1.21867 | ||||||||
\(778\) | −8.67641e9 | −0.660558 | ||||||||
\(779\) | 7.46912e9 | 0.566093 | ||||||||
\(780\) | 7.56256e9 | 0.570607 | ||||||||
\(781\) | 1.34814e10 | 1.01264 | ||||||||
\(782\) | 5.76440e8 | 0.0431052 | ||||||||
\(783\) | 2.70341e9 | 0.201254 | ||||||||
\(784\) | 6.27299e9 | 0.464909 | ||||||||
\(785\) | 3.48611e10 | 2.57216 | ||||||||
\(786\) | 5.70512e9 | 0.419069 | ||||||||
\(787\) | −9.95896e9 | −0.728287 | −0.364143 | − | 0.931343i | \(-0.618638\pi\) | ||||
−0.364143 | + | 0.931343i | \(0.618638\pi\) | |||||||
\(788\) | −1.56751e10 | −1.14122 | ||||||||
\(789\) | −1.05110e10 | −0.761862 | ||||||||
\(790\) | 1.37073e10 | 0.989135 | ||||||||
\(791\) | 3.50092e9 | 0.251515 | ||||||||
\(792\) | 2.75161e9 | 0.196810 | ||||||||
\(793\) | −1.82784e9 | −0.130161 | ||||||||
\(794\) | 1.25486e9 | 0.0889662 | ||||||||
\(795\) | 1.53849e10 | 1.08595 | ||||||||
\(796\) | −5.43264e9 | −0.381782 | ||||||||
\(797\) | 2.78445e10 | 1.94821 | 0.974105 | − | 0.226095i | \(-0.0725959\pi\) | ||||
0.974105 | + | 0.226095i | \(0.0725959\pi\) | |||||||
\(798\) | −8.09323e9 | −0.563783 | ||||||||
\(799\) | 1.75755e9 | 0.121897 | ||||||||
\(800\) | −3.79738e10 | −2.62222 | ||||||||
\(801\) | 6.02216e9 | 0.414037 | ||||||||
\(802\) | −5.36254e9 | −0.367080 | ||||||||
\(803\) | −5.92875e9 | −0.404072 | ||||||||
\(804\) | −3.24846e9 | −0.220435 | ||||||||
\(805\) | −3.77319e10 | −2.54931 | ||||||||
\(806\) | −2.67380e9 | −0.179869 | ||||||||
\(807\) | 7.27002e9 | 0.486943 | ||||||||
\(808\) | 5.55009e9 | 0.370135 | ||||||||
\(809\) | 6.81852e9 | 0.452762 | 0.226381 | − | 0.974039i | \(-0.427311\pi\) | ||||
0.226381 | + | 0.974039i | \(0.427311\pi\) | |||||||
\(810\) | 1.30862e9 | 0.0865201 | ||||||||
\(811\) | 3.94141e9 | 0.259465 | 0.129732 | − | 0.991549i | \(-0.458588\pi\) | ||||
0.129732 | + | 0.991549i | \(0.458588\pi\) | |||||||
\(812\) | −1.82362e10 | −1.19533 | ||||||||
\(813\) | 1.33721e10 | 0.872738 | ||||||||
\(814\) | 7.64872e9 | 0.497053 | ||||||||
\(815\) | 2.09912e10 | 1.35827 | ||||||||
\(816\) | −5.35701e8 | −0.0345149 | ||||||||
\(817\) | 3.70319e10 | 2.37574 | ||||||||
\(818\) | 8.01159e9 | 0.511778 | ||||||||
\(819\) | 4.36192e9 | 0.277450 | ||||||||
\(820\) | 8.14676e9 | 0.515985 | ||||||||
\(821\) | 2.49119e10 | 1.57111 | 0.785553 | − | 0.618795i | \(-0.212379\pi\) | ||||
0.785553 | + | 0.618795i | \(0.212379\pi\) | |||||||
\(822\) | −3.94174e8 | −0.0247535 | ||||||||
\(823\) | −2.21681e9 | −0.138621 | −0.0693105 | − | 0.997595i | \(-0.522080\pi\) | ||||
−0.0693105 | + | 0.997595i | \(0.522080\pi\) | |||||||
\(824\) | −1.75343e10 | −1.09180 | ||||||||
\(825\) | −2.03435e10 | −1.26135 | ||||||||
\(826\) | 1.15856e9 | 0.0715302 | ||||||||
\(827\) | −1.70597e10 | −1.04882 | −0.524410 | − | 0.851466i | \(-0.675714\pi\) | ||||
−0.524410 | + | 0.851466i | \(0.675714\pi\) | |||||||
\(828\) | 4.40847e9 | 0.269887 | ||||||||
\(829\) | −5.39778e9 | −0.329060 | −0.164530 | − | 0.986372i | \(-0.552611\pi\) | ||||
−0.164530 | + | 0.986372i | \(0.552611\pi\) | |||||||
\(830\) | −4.44594e9 | −0.269892 | ||||||||
\(831\) | −8.55806e9 | −0.517335 | ||||||||
\(832\) | 1.56232e9 | 0.0940457 | ||||||||
\(833\) | 1.59149e9 | 0.0953994 | ||||||||
\(834\) | 4.60818e9 | 0.275073 | ||||||||
\(835\) | −1.41880e10 | −0.843373 | ||||||||
\(836\) | −2.00674e10 | −1.18787 | ||||||||
\(837\) | 2.39010e9 | 0.140889 | ||||||||
\(838\) | −1.12609e10 | −0.661028 | ||||||||
\(839\) | 1.48286e10 | 0.866830 | 0.433415 | − | 0.901194i | \(-0.357308\pi\) | ||||
0.433415 | + | 0.901194i | \(0.357308\pi\) | |||||||
\(840\) | −1.93638e10 | −1.12723 | ||||||||
\(841\) | 1.61441e9 | 0.0935895 | ||||||||
\(842\) | 5.84793e9 | 0.337606 | ||||||||
\(843\) | 1.21645e10 | 0.699353 | ||||||||
\(844\) | −3.60593e9 | −0.206452 | ||||||||
\(845\) | 2.12897e10 | 1.21387 | ||||||||
\(846\) | −2.60195e9 | −0.147742 | ||||||||
\(847\) | 8.77268e9 | 0.496067 | ||||||||
\(848\) | 9.32386e9 | 0.525062 | ||||||||
\(849\) | −1.26244e10 | −0.708001 | ||||||||
\(850\) | −2.18713e9 | −0.122154 | ||||||||
\(851\) | 2.68809e10 | 1.49517 | ||||||||
\(852\) | 1.10846e10 | 0.614016 | ||||||||
\(853\) | 1.65358e10 | 0.912227 | 0.456114 | − | 0.889922i | \(-0.349241\pi\) | ||||
0.456114 | + | 0.889922i | \(0.349241\pi\) | |||||||
\(854\) | 2.13357e9 | 0.117221 | ||||||||
\(855\) | −2.09350e10 | −1.14549 | ||||||||
\(856\) | −1.23560e10 | −0.673318 | ||||||||
\(857\) | 1.32332e10 | 0.718176 | 0.359088 | − | 0.933304i | \(-0.383088\pi\) | ||||
0.359088 | + | 0.933304i | \(0.383088\pi\) | |||||||
\(858\) | −2.09365e9 | −0.113162 | ||||||||
\(859\) | −4.23318e9 | −0.227872 | −0.113936 | − | 0.993488i | \(-0.536346\pi\) | ||||
−0.113936 | + | 0.993488i | \(0.536346\pi\) | |||||||
\(860\) | 4.03917e10 | 2.16545 | ||||||||
\(861\) | 4.69888e9 | 0.250890 | ||||||||
\(862\) | −8.11891e9 | −0.431740 | ||||||||
\(863\) | 3.99379e8 | 0.0211518 | 0.0105759 | − | 0.999944i | \(-0.496634\pi\) | ||||
0.0105759 | + | 0.999944i | \(0.496634\pi\) | |||||||
\(864\) | 3.49344e9 | 0.184270 | ||||||||
\(865\) | 5.30335e9 | 0.278608 | ||||||||
\(866\) | −3.72347e9 | −0.194821 | ||||||||
\(867\) | 1.09432e10 | 0.570268 | ||||||||
\(868\) | −1.61228e10 | −0.836798 | ||||||||
\(869\) | 1.96033e10 | 1.01335 | ||||||||
\(870\) | 9.13152e9 | 0.470139 | ||||||||
\(871\) | 5.42187e9 | 0.278026 | ||||||||
\(872\) | −1.78980e9 | −0.0914108 | ||||||||
\(873\) | −6.82926e9 | −0.347395 | ||||||||
\(874\) | 1.36522e10 | 0.691694 | ||||||||
\(875\) | 9.08873e10 | 4.58643 | ||||||||
\(876\) | −4.87470e9 | −0.245010 | ||||||||
\(877\) | 9.41245e9 | 0.471199 | 0.235599 | − | 0.971850i | \(-0.424295\pi\) | ||||
0.235599 | + | 0.971850i | \(0.424295\pi\) | |||||||
\(878\) | 1.15335e10 | 0.575085 | ||||||||
\(879\) | 4.33371e8 | 0.0215228 | ||||||||
\(880\) | −1.68308e10 | −0.832560 | ||||||||
\(881\) | −6.45929e8 | −0.0318250 | −0.0159125 | − | 0.999873i | \(-0.505065\pi\) | ||||
−0.0159125 | + | 0.999873i | \(0.505065\pi\) | |||||||
\(882\) | −2.35611e9 | −0.115626 | ||||||||
\(883\) | 3.76342e10 | 1.83959 | 0.919793 | − | 0.392403i | \(-0.128356\pi\) | ||||
0.919793 | + | 0.392403i | \(0.128356\pi\) | |||||||
\(884\) | 1.16278e9 | 0.0566128 | ||||||||
\(885\) | 2.99689e9 | 0.145335 | ||||||||
\(886\) | 3.23895e9 | 0.156454 | ||||||||
\(887\) | −1.95731e10 | −0.941732 | −0.470866 | − | 0.882205i | \(-0.656059\pi\) | ||||
−0.470866 | + | 0.882205i | \(0.656059\pi\) | |||||||
\(888\) | 1.37951e10 | 0.661121 | ||||||||
\(889\) | −5.14002e10 | −2.45363 | ||||||||
\(890\) | 2.03416e10 | 0.967207 | ||||||||
\(891\) | 1.87152e9 | 0.0886383 | ||||||||
\(892\) | −9.31874e9 | −0.439623 | ||||||||
\(893\) | 4.16253e10 | 1.95604 | ||||||||
\(894\) | 2.94668e9 | 0.137928 | ||||||||
\(895\) | 2.10119e10 | 0.979683 | ||||||||
\(896\) | −2.99509e10 | −1.39101 | ||||||||
\(897\) | −7.35801e9 | −0.340398 | ||||||||
\(898\) | −5.59429e9 | −0.257797 | ||||||||
\(899\) | 1.66781e10 | 0.765573 | ||||||||
\(900\) | −1.67267e10 | −0.764823 | ||||||||
\(901\) | 2.36551e9 | 0.107743 | ||||||||
\(902\) | −2.25539e9 | −0.102329 | ||||||||
\(903\) | 2.32971e10 | 1.05292 | ||||||||
\(904\) | −3.03072e9 | −0.136445 | ||||||||
\(905\) | 3.11055e10 | 1.39498 | ||||||||
\(906\) | −8.10950e9 | −0.362281 | ||||||||
\(907\) | −2.68155e10 | −1.19333 | −0.596665 | − | 0.802491i | \(-0.703508\pi\) | ||||
−0.596665 | + | 0.802491i | \(0.703508\pi\) | |||||||
\(908\) | −3.91102e9 | −0.173376 | ||||||||
\(909\) | 3.77491e9 | 0.166699 | ||||||||
\(910\) | 1.47336e10 | 0.648134 | ||||||||
\(911\) | −3.43001e10 | −1.50307 | −0.751537 | − | 0.659690i | \(-0.770687\pi\) | ||||
−0.751537 | + | 0.659690i | \(0.770687\pi\) | |||||||
\(912\) | −1.26874e10 | −0.553849 | ||||||||
\(913\) | −6.35832e9 | −0.276500 | ||||||||
\(914\) | −1.40280e10 | −0.607691 | ||||||||
\(915\) | 5.51897e9 | 0.238168 | ||||||||
\(916\) | −2.35442e10 | −1.01216 | ||||||||
\(917\) | −5.74180e10 | −2.45898 | ||||||||
\(918\) | 2.01207e8 | 0.00858408 | ||||||||
\(919\) | 1.59456e10 | 0.677698 | 0.338849 | − | 0.940841i | \(-0.389962\pi\) | ||||
0.338849 | + | 0.940841i | \(0.389962\pi\) | |||||||
\(920\) | 3.26643e10 | 1.38298 | ||||||||
\(921\) | 1.77164e9 | 0.0747253 | ||||||||
\(922\) | −8.08321e9 | −0.339645 | ||||||||
\(923\) | −1.85008e10 | −0.774434 | ||||||||
\(924\) | −1.26246e10 | −0.526459 | ||||||||
\(925\) | −1.01992e11 | −4.23710 | ||||||||
\(926\) | −1.78314e10 | −0.737984 | ||||||||
\(927\) | −1.19260e10 | −0.491720 | ||||||||
\(928\) | 2.43771e10 | 1.00130 | ||||||||
\(929\) | 1.42285e9 | 0.0582242 | 0.0291121 | − | 0.999576i | \(-0.490732\pi\) | ||||
0.0291121 | + | 0.999576i | \(0.490732\pi\) | |||||||
\(930\) | 8.07325e9 | 0.329123 | ||||||||
\(931\) | 3.76924e10 | 1.53084 | ||||||||
\(932\) | −1.28677e10 | −0.520649 | ||||||||
\(933\) | −1.20064e10 | −0.483978 | ||||||||
\(934\) | 1.43785e10 | 0.577431 | ||||||||
\(935\) | −4.27005e9 | −0.170841 | ||||||||
\(936\) | −3.77609e9 | −0.150514 | ||||||||
\(937\) | −2.31807e10 | −0.920532 | −0.460266 | − | 0.887781i | \(-0.652246\pi\) | ||||
−0.460266 | + | 0.887781i | \(0.652246\pi\) | |||||||
\(938\) | −6.32875e9 | −0.250385 | ||||||||
\(939\) | −7.95843e9 | −0.313688 | ||||||||
\(940\) | 4.54018e10 | 1.78290 | ||||||||
\(941\) | 3.37421e10 | 1.32010 | 0.660052 | − | 0.751220i | \(-0.270534\pi\) | ||||
0.660052 | + | 0.751220i | \(0.270534\pi\) | |||||||
\(942\) | −7.93527e9 | −0.309303 | ||||||||
\(943\) | −7.92642e9 | −0.307812 | ||||||||
\(944\) | 1.81623e9 | 0.0702699 | ||||||||
\(945\) | −1.31704e10 | −0.507676 | ||||||||
\(946\) | −1.11822e10 | −0.429447 | ||||||||
\(947\) | 2.26076e10 | 0.865029 | 0.432514 | − | 0.901627i | \(-0.357626\pi\) | ||||
0.432514 | + | 0.901627i | \(0.357626\pi\) | |||||||
\(948\) | 1.61181e10 | 0.614448 | ||||||||
\(949\) | 8.13617e9 | 0.309021 | ||||||||
\(950\) | −5.17995e10 | −1.96017 | ||||||||
\(951\) | 1.07298e10 | 0.404539 | ||||||||
\(952\) | −2.97728e9 | −0.111838 | ||||||||
\(953\) | 1.78597e10 | 0.668420 | 0.334210 | − | 0.942499i | \(-0.391531\pi\) | ||||
0.334210 | + | 0.942499i | \(0.391531\pi\) | |||||||
\(954\) | −3.50200e9 | −0.130586 | ||||||||
\(955\) | −8.46920e10 | −3.14652 | ||||||||
\(956\) | 2.40001e10 | 0.888403 | ||||||||
\(957\) | 1.30594e10 | 0.481649 | ||||||||
\(958\) | 1.40746e10 | 0.517197 | ||||||||
\(959\) | 3.96709e9 | 0.145247 | ||||||||
\(960\) | −4.71727e9 | −0.172084 | ||||||||
\(961\) | −1.27674e10 | −0.464057 | ||||||||
\(962\) | −1.04965e10 | −0.380130 | ||||||||
\(963\) | −8.40399e9 | −0.303245 | ||||||||
\(964\) | 1.91561e10 | 0.688710 | ||||||||
\(965\) | −2.94511e10 | −1.05501 | ||||||||
\(966\) | 8.58874e9 | 0.306556 | ||||||||
\(967\) | −1.61338e8 | −0.00573778 | −0.00286889 | − | 0.999996i | \(-0.500913\pi\) | ||||
−0.00286889 | + | 0.999996i | \(0.500913\pi\) | |||||||
\(968\) | −7.59446e9 | −0.269112 | ||||||||
\(969\) | −3.21886e9 | −0.113650 | ||||||||
\(970\) | −2.30678e10 | −0.811530 | ||||||||
\(971\) | −4.94599e10 | −1.73375 | −0.866874 | − | 0.498527i | \(-0.833875\pi\) | ||||
−0.866874 | + | 0.498527i | \(0.833875\pi\) | |||||||
\(972\) | 1.53878e9 | 0.0537460 | ||||||||
\(973\) | −4.63782e10 | −1.61406 | ||||||||
\(974\) | 4.09996e9 | 0.142175 | ||||||||
\(975\) | 2.79178e10 | 0.964640 | ||||||||
\(976\) | 3.34471e9 | 0.115155 | ||||||||
\(977\) | −1.43208e10 | −0.491290 | −0.245645 | − | 0.969360i | \(-0.579000\pi\) | ||||
−0.245645 | + | 0.969360i | \(0.579000\pi\) | |||||||
\(978\) | −4.77814e9 | −0.163333 | ||||||||
\(979\) | 2.90913e10 | 0.990886 | ||||||||
\(980\) | 4.11121e10 | 1.39533 | ||||||||
\(981\) | −1.21734e9 | −0.0411690 | ||||||||
\(982\) | 4.09423e9 | 0.137969 | ||||||||
\(983\) | −5.16305e10 | −1.73368 | −0.866840 | − | 0.498587i | \(-0.833852\pi\) | ||||
−0.866840 | + | 0.498587i | \(0.833852\pi\) | |||||||
\(984\) | −4.06780e9 | −0.136106 | ||||||||
\(985\) | −7.89955e10 | −2.63375 | ||||||||
\(986\) | 1.40402e9 | 0.0466448 | ||||||||
\(987\) | 2.61868e10 | 0.866907 | ||||||||
\(988\) | 2.75390e10 | 0.908445 | ||||||||
\(989\) | −3.92992e10 | −1.29181 | ||||||||
\(990\) | 6.32157e9 | 0.207063 | ||||||||
\(991\) | −4.70999e10 | −1.53731 | −0.768656 | − | 0.639662i | \(-0.779074\pi\) | ||||
−0.768656 | + | 0.639662i | \(0.779074\pi\) | |||||||
\(992\) | 2.15520e10 | 0.700964 | ||||||||
\(993\) | 3.11442e10 | 1.00938 | ||||||||
\(994\) | 2.15953e10 | 0.697440 | ||||||||
\(995\) | −2.73781e10 | −0.881094 | ||||||||
\(996\) | −5.22789e9 | −0.167656 | ||||||||
\(997\) | −5.20068e10 | −1.66198 | −0.830992 | − | 0.556284i | \(-0.812227\pi\) | ||||
−0.830992 | + | 0.556284i | \(0.812227\pi\) | |||||||
\(998\) | 1.33982e9 | 0.0426669 | ||||||||
\(999\) | 9.38282e9 | 0.297752 |
(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 | 177.8.a.a.1.7 | ✓ | 16 | |
3.2 | odd | 2 | 531.8.a.b.1.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
531.8.a.b.1.10 | 16 | 3.2 | odd | 2 |