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 | 1.13 | ||
Root | \(-14.0604\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 14.0604 | 1.24278 | 0.621388 | − | 0.783503i | \(-0.286569\pi\) | ||||
0.621388 | + | 0.783503i | \(0.286569\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 69.6949 | 0.544491 | ||||||||
\(5\) | 153.219 | 0.548173 | 0.274087 | − | 0.961705i | \(-0.411625\pi\) | ||||
0.274087 | + | 0.961705i | \(0.411625\pi\) | |||||||
\(6\) | −379.631 | −0.717517 | ||||||||
\(7\) | −215.221 | −0.237160 | −0.118580 | − | 0.992944i | \(-0.537834\pi\) | ||||
−0.118580 | + | 0.992944i | \(0.537834\pi\) | |||||||
\(8\) | −819.793 | −0.566095 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2154.32 | 0.681256 | ||||||||
\(11\) | 7869.22 | 1.78261 | 0.891307 | − | 0.453401i | \(-0.149789\pi\) | ||||
0.891307 | + | 0.453401i | \(0.149789\pi\) | |||||||
\(12\) | −1881.76 | −0.314362 | ||||||||
\(13\) | −14239.1 | −1.79754 | −0.898772 | − | 0.438416i | \(-0.855540\pi\) | ||||
−0.898772 | + | 0.438416i | \(0.855540\pi\) | |||||||
\(14\) | −3026.10 | −0.294737 | ||||||||
\(15\) | −4136.91 | −0.316488 | ||||||||
\(16\) | −20447.6 | −1.24802 | ||||||||
\(17\) | −14439.7 | −0.712830 | −0.356415 | − | 0.934328i | \(-0.616001\pi\) | ||||
−0.356415 | + | 0.934328i | \(0.616001\pi\) | |||||||
\(18\) | 10250.0 | 0.414259 | ||||||||
\(19\) | 52274.2 | 1.74844 | 0.874218 | − | 0.485533i | \(-0.161375\pi\) | ||||
0.874218 | + | 0.485533i | \(0.161375\pi\) | |||||||
\(20\) | 10678.6 | 0.298475 | ||||||||
\(21\) | 5810.97 | 0.136925 | ||||||||
\(22\) | 110644. | 2.21539 | ||||||||
\(23\) | −20917.2 | −0.358473 | −0.179237 | − | 0.983806i | \(-0.557363\pi\) | ||||
−0.179237 | + | 0.983806i | \(0.557363\pi\) | |||||||
\(24\) | 22134.4 | 0.326835 | ||||||||
\(25\) | −54648.9 | −0.699506 | ||||||||
\(26\) | −200207. | −2.23394 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −14999.8 | −0.129132 | ||||||||
\(29\) | −136874. | −1.04214 | −0.521070 | − | 0.853514i | \(-0.674467\pi\) | ||||
−0.521070 | + | 0.853514i | \(0.674467\pi\) | |||||||
\(30\) | −58166.7 | −0.393323 | ||||||||
\(31\) | 9325.59 | 0.0562225 | 0.0281113 | − | 0.999605i | \(-0.491051\pi\) | ||||
0.0281113 | + | 0.999605i | \(0.491051\pi\) | |||||||
\(32\) | −182567. | −0.984914 | ||||||||
\(33\) | −212469. | −1.02919 | ||||||||
\(34\) | −203028. | −0.885888 | ||||||||
\(35\) | −32976.0 | −0.130005 | ||||||||
\(36\) | 50807.6 | 0.181497 | ||||||||
\(37\) | −525467. | −1.70545 | −0.852726 | − | 0.522358i | \(-0.825052\pi\) | ||||
−0.852726 | + | 0.522358i | \(0.825052\pi\) | |||||||
\(38\) | 734996. | 2.17291 | ||||||||
\(39\) | 384455. | 1.03781 | ||||||||
\(40\) | −125608. | −0.310318 | ||||||||
\(41\) | 197767. | 0.448136 | 0.224068 | − | 0.974574i | \(-0.428066\pi\) | ||||
0.224068 | + | 0.974574i | \(0.428066\pi\) | |||||||
\(42\) | 81704.6 | 0.170166 | ||||||||
\(43\) | 410661. | 0.787669 | 0.393835 | − | 0.919181i | \(-0.371148\pi\) | ||||
0.393835 | + | 0.919181i | \(0.371148\pi\) | |||||||
\(44\) | 548444. | 0.970617 | ||||||||
\(45\) | 111697. | 0.182724 | ||||||||
\(46\) | −294105. | −0.445502 | ||||||||
\(47\) | −946517. | −1.32980 | −0.664899 | − | 0.746933i | \(-0.731525\pi\) | ||||
−0.664899 | + | 0.746933i | \(0.731525\pi\) | |||||||
\(48\) | 552084. | 0.720545 | ||||||||
\(49\) | −777223. | −0.943755 | ||||||||
\(50\) | −768386. | −0.869329 | ||||||||
\(51\) | 389871. | 0.411553 | ||||||||
\(52\) | −992389. | −0.978747 | ||||||||
\(53\) | −1.55829e6 | −1.43775 | −0.718873 | − | 0.695141i | \(-0.755342\pi\) | ||||
−0.718873 | + | 0.695141i | \(0.755342\pi\) | |||||||
\(54\) | −276751. | −0.239172 | ||||||||
\(55\) | 1.20571e6 | 0.977181 | ||||||||
\(56\) | 176437. | 0.134255 | ||||||||
\(57\) | −1.41140e6 | −1.00946 | ||||||||
\(58\) | −1.92450e6 | −1.29515 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −288322. | −0.172325 | ||||||||
\(61\) | −659307. | −0.371906 | −0.185953 | − | 0.982559i | \(-0.559537\pi\) | ||||
−0.185953 | + | 0.982559i | \(0.559537\pi\) | |||||||
\(62\) | 131121. | 0.0698720 | ||||||||
\(63\) | −156896. | −0.0790534 | ||||||||
\(64\) | 50317.0 | 0.0239930 | ||||||||
\(65\) | −2.18169e6 | −0.985365 | ||||||||
\(66\) | −2.98740e6 | −1.27906 | ||||||||
\(67\) | −2.30296e6 | −0.935457 | −0.467729 | − | 0.883872i | \(-0.654928\pi\) | ||||
−0.467729 | + | 0.883872i | \(0.654928\pi\) | |||||||
\(68\) | −1.00637e6 | −0.388130 | ||||||||
\(69\) | 564765. | 0.206965 | ||||||||
\(70\) | −463656. | −0.161567 | ||||||||
\(71\) | −1.68822e6 | −0.559788 | −0.279894 | − | 0.960031i | \(-0.590299\pi\) | ||||
−0.279894 | + | 0.960031i | \(0.590299\pi\) | |||||||
\(72\) | −597629. | −0.188698 | ||||||||
\(73\) | 2.53442e6 | 0.762514 | 0.381257 | − | 0.924469i | \(-0.375491\pi\) | ||||
0.381257 | + | 0.924469i | \(0.375491\pi\) | |||||||
\(74\) | −7.38828e6 | −2.11949 | ||||||||
\(75\) | 1.47552e6 | 0.403860 | ||||||||
\(76\) | 3.64324e6 | 0.952008 | ||||||||
\(77\) | −1.69362e6 | −0.422765 | ||||||||
\(78\) | 5.40559e6 | 1.28977 | ||||||||
\(79\) | −1.26627e6 | −0.288957 | −0.144478 | − | 0.989508i | \(-0.546150\pi\) | ||||
−0.144478 | + | 0.989508i | \(0.546150\pi\) | |||||||
\(80\) | −3.13296e6 | −0.684131 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 2.78068e6 | 0.556932 | ||||||||
\(83\) | 2.22258e6 | 0.426662 | 0.213331 | − | 0.976980i | \(-0.431569\pi\) | ||||
0.213331 | + | 0.976980i | \(0.431569\pi\) | |||||||
\(84\) | 404995. | 0.0745542 | ||||||||
\(85\) | −2.21243e6 | −0.390754 | ||||||||
\(86\) | 5.77406e6 | 0.978896 | ||||||||
\(87\) | 3.69558e6 | 0.601680 | ||||||||
\(88\) | −6.45113e6 | −1.00913 | ||||||||
\(89\) | −1.04798e7 | −1.57575 | −0.787876 | − | 0.615834i | \(-0.788819\pi\) | ||||
−0.787876 | + | 0.615834i | \(0.788819\pi\) | |||||||
\(90\) | 1.57050e6 | 0.227085 | ||||||||
\(91\) | 3.06455e6 | 0.426306 | ||||||||
\(92\) | −1.45782e6 | −0.195186 | ||||||||
\(93\) | −251791. | −0.0324601 | ||||||||
\(94\) | −1.33084e7 | −1.65264 | ||||||||
\(95\) | 8.00940e6 | 0.958446 | ||||||||
\(96\) | 4.92932e6 | 0.568641 | ||||||||
\(97\) | 5.41316e6 | 0.602212 | 0.301106 | − | 0.953591i | \(-0.402644\pi\) | ||||
0.301106 | + | 0.953591i | \(0.402644\pi\) | |||||||
\(98\) | −1.09281e7 | −1.17288 | ||||||||
\(99\) | 5.73666e6 | 0.594204 | ||||||||
\(100\) | −3.80875e6 | −0.380875 | ||||||||
\(101\) | −8.00726e6 | −0.773320 | −0.386660 | − | 0.922222i | \(-0.626371\pi\) | ||||
−0.386660 | + | 0.922222i | \(0.626371\pi\) | |||||||
\(102\) | 5.48174e6 | 0.511468 | ||||||||
\(103\) | 2.41569e6 | 0.217826 | 0.108913 | − | 0.994051i | \(-0.465263\pi\) | ||||
0.108913 | + | 0.994051i | \(0.465263\pi\) | |||||||
\(104\) | 1.16731e7 | 1.01758 | ||||||||
\(105\) | 890352. | 0.0750584 | ||||||||
\(106\) | −2.19102e7 | −1.78680 | ||||||||
\(107\) | 1.50841e7 | 1.19035 | 0.595175 | − | 0.803596i | \(-0.297083\pi\) | ||||
0.595175 | + | 0.803596i | \(0.297083\pi\) | |||||||
\(108\) | −1.37180e6 | −0.104787 | ||||||||
\(109\) | 1.30931e7 | 0.968386 | 0.484193 | − | 0.874961i | \(-0.339113\pi\) | ||||
0.484193 | + | 0.874961i | \(0.339113\pi\) | |||||||
\(110\) | 1.69528e7 | 1.21442 | ||||||||
\(111\) | 1.41876e7 | 0.984643 | ||||||||
\(112\) | 4.40075e6 | 0.295981 | ||||||||
\(113\) | −8.64628e6 | −0.563709 | −0.281854 | − | 0.959457i | \(-0.590950\pi\) | ||||
−0.281854 | + | 0.959457i | \(0.590950\pi\) | |||||||
\(114\) | −1.98449e7 | −1.25453 | ||||||||
\(115\) | −3.20492e6 | −0.196505 | ||||||||
\(116\) | −9.53938e6 | −0.567437 | ||||||||
\(117\) | −1.03803e7 | −0.599181 | ||||||||
\(118\) | 2.88771e6 | 0.161796 | ||||||||
\(119\) | 3.10772e6 | 0.169055 | ||||||||
\(120\) | 3.39141e6 | 0.179162 | ||||||||
\(121\) | 4.24374e7 | 2.17771 | ||||||||
\(122\) | −9.27012e6 | −0.462196 | ||||||||
\(123\) | −5.33970e6 | −0.258731 | ||||||||
\(124\) | 649946. | 0.0306127 | ||||||||
\(125\) | −2.03435e7 | −0.931624 | ||||||||
\(126\) | −2.20602e6 | −0.0982457 | ||||||||
\(127\) | 2.77631e7 | 1.20269 | 0.601347 | − | 0.798988i | \(-0.294631\pi\) | ||||
0.601347 | + | 0.798988i | \(0.294631\pi\) | |||||||
\(128\) | 2.40761e7 | 1.01473 | ||||||||
\(129\) | −1.10878e7 | −0.454761 | ||||||||
\(130\) | −3.06755e7 | −1.22459 | ||||||||
\(131\) | 2.08878e7 | 0.811788 | 0.405894 | − | 0.913920i | \(-0.366960\pi\) | ||||
0.405894 | + | 0.913920i | \(0.366960\pi\) | |||||||
\(132\) | −1.48080e7 | −0.560386 | ||||||||
\(133\) | −1.12505e7 | −0.414660 | ||||||||
\(134\) | −3.23805e7 | −1.16256 | ||||||||
\(135\) | −3.01581e6 | −0.105496 | ||||||||
\(136\) | 1.18375e7 | 0.403530 | ||||||||
\(137\) | −1.47003e7 | −0.488432 | −0.244216 | − | 0.969721i | \(-0.578531\pi\) | ||||
−0.244216 | + | 0.969721i | \(0.578531\pi\) | |||||||
\(138\) | 7.94083e6 | 0.257211 | ||||||||
\(139\) | −3.38613e7 | −1.06943 | −0.534715 | − | 0.845033i | \(-0.679581\pi\) | ||||
−0.534715 | + | 0.845033i | \(0.679581\pi\) | |||||||
\(140\) | −2.29826e6 | −0.0707865 | ||||||||
\(141\) | 2.55559e7 | 0.767759 | ||||||||
\(142\) | −2.37370e7 | −0.695691 | ||||||||
\(143\) | −1.12050e8 | −3.20433 | ||||||||
\(144\) | −1.49063e7 | −0.416007 | ||||||||
\(145\) | −2.09716e7 | −0.571274 | ||||||||
\(146\) | 3.56349e7 | 0.947634 | ||||||||
\(147\) | 2.09850e7 | 0.544877 | ||||||||
\(148\) | −3.66224e7 | −0.928604 | ||||||||
\(149\) | −3.52382e7 | −0.872694 | −0.436347 | − | 0.899778i | \(-0.643728\pi\) | ||||
−0.436347 | + | 0.899778i | \(0.643728\pi\) | |||||||
\(150\) | 2.07464e7 | 0.501907 | ||||||||
\(151\) | 4.31481e7 | 1.01986 | 0.509932 | − | 0.860215i | \(-0.329671\pi\) | ||||
0.509932 | + | 0.860215i | \(0.329671\pi\) | |||||||
\(152\) | −4.28541e7 | −0.989781 | ||||||||
\(153\) | −1.05265e7 | −0.237610 | ||||||||
\(154\) | −2.38130e7 | −0.525402 | ||||||||
\(155\) | 1.42886e6 | 0.0308197 | ||||||||
\(156\) | 2.67945e7 | 0.565080 | ||||||||
\(157\) | 7.00495e6 | 0.144463 | 0.0722314 | − | 0.997388i | \(-0.476988\pi\) | ||||
0.0722314 | + | 0.997388i | \(0.476988\pi\) | |||||||
\(158\) | −1.78043e7 | −0.359108 | ||||||||
\(159\) | 4.20738e7 | 0.830083 | ||||||||
\(160\) | −2.79728e7 | −0.539904 | ||||||||
\(161\) | 4.50183e6 | 0.0850156 | ||||||||
\(162\) | 7.47227e6 | 0.138086 | ||||||||
\(163\) | 5.15447e7 | 0.932240 | 0.466120 | − | 0.884722i | \(-0.345652\pi\) | ||||
0.466120 | + | 0.884722i | \(0.345652\pi\) | |||||||
\(164\) | 1.37833e7 | 0.244006 | ||||||||
\(165\) | −3.25543e7 | −0.564176 | ||||||||
\(166\) | 3.12503e7 | 0.530245 | ||||||||
\(167\) | −8.79382e6 | −0.146107 | −0.0730533 | − | 0.997328i | \(-0.523274\pi\) | ||||
−0.0730533 | + | 0.997328i | \(0.523274\pi\) | |||||||
\(168\) | −4.76380e6 | −0.0775123 | ||||||||
\(169\) | 1.40002e8 | 2.23116 | ||||||||
\(170\) | −3.11077e7 | −0.485620 | ||||||||
\(171\) | 3.81079e7 | 0.582812 | ||||||||
\(172\) | 2.86210e7 | 0.428879 | ||||||||
\(173\) | 5.52334e7 | 0.811037 | 0.405518 | − | 0.914087i | \(-0.367091\pi\) | ||||
0.405518 | + | 0.914087i | \(0.367091\pi\) | |||||||
\(174\) | 5.19614e7 | 0.747754 | ||||||||
\(175\) | 1.17616e7 | 0.165895 | ||||||||
\(176\) | −1.60906e8 | −2.22474 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | −1.47350e8 | −1.95831 | ||||||||
\(179\) | 1.14162e8 | 1.48776 | 0.743882 | − | 0.668311i | \(-0.232982\pi\) | ||||
0.743882 | + | 0.668311i | \(0.232982\pi\) | |||||||
\(180\) | 7.78469e6 | 0.0994918 | ||||||||
\(181\) | 7.45147e6 | 0.0934044 | 0.0467022 | − | 0.998909i | \(-0.485129\pi\) | ||||
0.0467022 | + | 0.998909i | \(0.485129\pi\) | |||||||
\(182\) | 4.30888e7 | 0.529803 | ||||||||
\(183\) | 1.78013e7 | 0.214720 | ||||||||
\(184\) | 1.71478e7 | 0.202930 | ||||||||
\(185\) | −8.05116e7 | −0.934883 | ||||||||
\(186\) | −3.54028e6 | −0.0403406 | ||||||||
\(187\) | −1.13629e8 | −1.27070 | ||||||||
\(188\) | −6.59674e7 | −0.724063 | ||||||||
\(189\) | 4.23620e6 | 0.0456415 | ||||||||
\(190\) | 1.12615e8 | 1.19113 | ||||||||
\(191\) | −2.65020e7 | −0.275208 | −0.137604 | − | 0.990487i | \(-0.543940\pi\) | ||||
−0.137604 | + | 0.990487i | \(0.543940\pi\) | |||||||
\(192\) | −1.35856e6 | −0.0138524 | ||||||||
\(193\) | −7.95433e7 | −0.796440 | −0.398220 | − | 0.917290i | \(-0.630372\pi\) | ||||
−0.398220 | + | 0.917290i | \(0.630372\pi\) | |||||||
\(194\) | 7.61112e7 | 0.748415 | ||||||||
\(195\) | 5.89058e7 | 0.568901 | ||||||||
\(196\) | −5.41685e7 | −0.513866 | ||||||||
\(197\) | 6.69673e7 | 0.624067 | 0.312033 | − | 0.950071i | \(-0.398990\pi\) | ||||
0.312033 | + | 0.950071i | \(0.398990\pi\) | |||||||
\(198\) | 8.06597e7 | 0.738463 | ||||||||
\(199\) | −5.47720e7 | −0.492689 | −0.246345 | − | 0.969182i | \(-0.579229\pi\) | ||||
−0.246345 | + | 0.969182i | \(0.579229\pi\) | |||||||
\(200\) | 4.48008e7 | 0.395987 | ||||||||
\(201\) | 6.21798e7 | 0.540087 | ||||||||
\(202\) | −1.12585e8 | −0.961063 | ||||||||
\(203\) | 2.94581e7 | 0.247154 | ||||||||
\(204\) | 2.71720e7 | 0.224087 | ||||||||
\(205\) | 3.03016e7 | 0.245656 | ||||||||
\(206\) | 3.39655e7 | 0.270709 | ||||||||
\(207\) | −1.52487e7 | −0.119491 | ||||||||
\(208\) | 2.91154e8 | 2.24337 | ||||||||
\(209\) | 4.11357e8 | 3.11679 | ||||||||
\(210\) | 1.25187e7 | 0.0932807 | ||||||||
\(211\) | −6.45829e7 | −0.473292 | −0.236646 | − | 0.971596i | \(-0.576048\pi\) | ||||
−0.236646 | + | 0.971596i | \(0.576048\pi\) | |||||||
\(212\) | −1.08605e8 | −0.782840 | ||||||||
\(213\) | 4.55818e7 | 0.323194 | ||||||||
\(214\) | 2.12088e8 | 1.47934 | ||||||||
\(215\) | 6.29211e7 | 0.431779 | ||||||||
\(216\) | 1.61360e7 | 0.108945 | ||||||||
\(217\) | −2.00706e6 | −0.0133337 | ||||||||
\(218\) | 1.84094e8 | 1.20349 | ||||||||
\(219\) | −6.84292e7 | −0.440238 | ||||||||
\(220\) | 8.40321e7 | 0.532066 | ||||||||
\(221\) | 2.05607e8 | 1.28134 | ||||||||
\(222\) | 1.99484e8 | 1.22369 | ||||||||
\(223\) | −2.02022e8 | −1.21992 | −0.609961 | − | 0.792431i | \(-0.708815\pi\) | ||||
−0.609961 | + | 0.792431i | \(0.708815\pi\) | |||||||
\(224\) | 3.92924e7 | 0.233583 | ||||||||
\(225\) | −3.98391e7 | −0.233169 | ||||||||
\(226\) | −1.21570e8 | −0.700564 | ||||||||
\(227\) | −2.76130e8 | −1.56683 | −0.783416 | − | 0.621497i | \(-0.786525\pi\) | ||||
−0.783416 | + | 0.621497i | \(0.786525\pi\) | |||||||
\(228\) | −9.83676e7 | −0.549642 | ||||||||
\(229\) | −1.40164e8 | −0.771280 | −0.385640 | − | 0.922649i | \(-0.626019\pi\) | ||||
−0.385640 | + | 0.922649i | \(0.626019\pi\) | |||||||
\(230\) | −4.50624e7 | −0.244212 | ||||||||
\(231\) | 4.57278e7 | 0.244084 | ||||||||
\(232\) | 1.12208e8 | 0.589951 | ||||||||
\(233\) | 8.67302e7 | 0.449185 | 0.224592 | − | 0.974453i | \(-0.427895\pi\) | ||||
0.224592 | + | 0.974453i | \(0.427895\pi\) | |||||||
\(234\) | −1.45951e8 | −0.744648 | ||||||||
\(235\) | −1.45024e8 | −0.728960 | ||||||||
\(236\) | 1.43139e7 | 0.0708867 | ||||||||
\(237\) | 3.41894e7 | 0.166829 | ||||||||
\(238\) | 4.36958e7 | 0.210097 | ||||||||
\(239\) | 2.22648e8 | 1.05494 | 0.527469 | − | 0.849574i | \(-0.323141\pi\) | ||||
0.527469 | + | 0.849574i | \(0.323141\pi\) | |||||||
\(240\) | 8.45898e7 | 0.394983 | ||||||||
\(241\) | 4.27798e8 | 1.96870 | 0.984350 | − | 0.176226i | \(-0.0563888\pi\) | ||||
0.984350 | + | 0.176226i | \(0.0563888\pi\) | |||||||
\(242\) | 5.96687e8 | 2.70641 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −4.59503e7 | −0.202500 | ||||||||
\(245\) | −1.19085e8 | −0.517341 | ||||||||
\(246\) | −7.50783e7 | −0.321545 | ||||||||
\(247\) | −7.44335e8 | −3.14289 | ||||||||
\(248\) | −7.64505e6 | −0.0318273 | ||||||||
\(249\) | −6.00096e7 | −0.246333 | ||||||||
\(250\) | −2.86038e8 | −1.15780 | ||||||||
\(251\) | 4.79689e7 | 0.191471 | 0.0957353 | − | 0.995407i | \(-0.469480\pi\) | ||||
0.0957353 | + | 0.995407i | \(0.469480\pi\) | |||||||
\(252\) | −1.09349e7 | −0.0430439 | ||||||||
\(253\) | −1.64602e8 | −0.639019 | ||||||||
\(254\) | 3.90360e8 | 1.49468 | ||||||||
\(255\) | 5.97357e7 | 0.225602 | ||||||||
\(256\) | 3.32079e8 | 1.23709 | ||||||||
\(257\) | 1.81282e8 | 0.666175 | 0.333087 | − | 0.942896i | \(-0.391910\pi\) | ||||
0.333087 | + | 0.942896i | \(0.391910\pi\) | |||||||
\(258\) | −1.55900e8 | −0.565166 | ||||||||
\(259\) | 1.13092e8 | 0.404466 | ||||||||
\(260\) | −1.52053e8 | −0.536523 | ||||||||
\(261\) | −9.97808e7 | −0.347380 | ||||||||
\(262\) | 2.93691e8 | 1.00887 | ||||||||
\(263\) | −2.00422e8 | −0.679359 | −0.339680 | − | 0.940541i | \(-0.610319\pi\) | ||||
−0.339680 | + | 0.940541i | \(0.610319\pi\) | |||||||
\(264\) | 1.74181e8 | 0.582621 | ||||||||
\(265\) | −2.38759e8 | −0.788134 | ||||||||
\(266\) | −1.58187e8 | −0.515329 | ||||||||
\(267\) | 2.82955e8 | 0.909761 | ||||||||
\(268\) | −1.60504e8 | −0.509348 | ||||||||
\(269\) | 2.62947e8 | 0.823637 | 0.411819 | − | 0.911266i | \(-0.364894\pi\) | ||||
0.411819 | + | 0.911266i | \(0.364894\pi\) | |||||||
\(270\) | −4.24035e7 | −0.131108 | ||||||||
\(271\) | 3.69328e8 | 1.12725 | 0.563625 | − | 0.826031i | \(-0.309406\pi\) | ||||
0.563625 | + | 0.826031i | \(0.309406\pi\) | |||||||
\(272\) | 2.95256e8 | 0.889627 | ||||||||
\(273\) | −8.27428e7 | −0.246128 | ||||||||
\(274\) | −2.06692e8 | −0.607011 | ||||||||
\(275\) | −4.30044e8 | −1.24695 | ||||||||
\(276\) | 3.93613e7 | 0.112690 | ||||||||
\(277\) | −2.94313e8 | −0.832014 | −0.416007 | − | 0.909361i | \(-0.636571\pi\) | ||||
−0.416007 | + | 0.909361i | \(0.636571\pi\) | |||||||
\(278\) | −4.76104e8 | −1.32906 | ||||||||
\(279\) | 6.79835e6 | 0.0187408 | ||||||||
\(280\) | 2.70335e7 | 0.0735951 | ||||||||
\(281\) | 4.33874e8 | 1.16652 | 0.583258 | − | 0.812287i | \(-0.301777\pi\) | ||||
0.583258 | + | 0.812287i | \(0.301777\pi\) | |||||||
\(282\) | 3.59327e8 | 0.954153 | ||||||||
\(283\) | −8.12492e7 | −0.213092 | −0.106546 | − | 0.994308i | \(-0.533979\pi\) | ||||
−0.106546 | + | 0.994308i | \(0.533979\pi\) | |||||||
\(284\) | −1.17660e8 | −0.304800 | ||||||||
\(285\) | −2.16254e8 | −0.553359 | ||||||||
\(286\) | −1.57547e9 | −3.98226 | ||||||||
\(287\) | −4.25636e7 | −0.106280 | ||||||||
\(288\) | −1.33092e8 | −0.328305 | ||||||||
\(289\) | −2.01835e8 | −0.491873 | ||||||||
\(290\) | −2.94869e8 | −0.709965 | ||||||||
\(291\) | −1.46155e8 | −0.347687 | ||||||||
\(292\) | 1.76636e8 | 0.415182 | ||||||||
\(293\) | −6.42476e8 | −1.49218 | −0.746089 | − | 0.665847i | \(-0.768071\pi\) | ||||
−0.746089 | + | 0.665847i | \(0.768071\pi\) | |||||||
\(294\) | 2.95058e8 | 0.677160 | ||||||||
\(295\) | 3.14680e7 | 0.0713661 | ||||||||
\(296\) | 4.30775e8 | 0.965448 | ||||||||
\(297\) | −1.54890e8 | −0.343064 | ||||||||
\(298\) | −4.95463e8 | −1.08456 | ||||||||
\(299\) | 2.97842e8 | 0.644372 | ||||||||
\(300\) | 1.02836e8 | 0.219898 | ||||||||
\(301\) | −8.83829e7 | −0.186804 | ||||||||
\(302\) | 6.06679e8 | 1.26746 | ||||||||
\(303\) | 2.16196e8 | 0.446477 | ||||||||
\(304\) | −1.06888e9 | −2.18208 | ||||||||
\(305\) | −1.01018e8 | −0.203869 | ||||||||
\(306\) | −1.48007e8 | −0.295296 | ||||||||
\(307\) | −6.93624e8 | −1.36817 | −0.684084 | − | 0.729403i | \(-0.739798\pi\) | ||||
−0.684084 | + | 0.729403i | \(0.739798\pi\) | |||||||
\(308\) | −1.18037e8 | −0.230192 | ||||||||
\(309\) | −6.52235e7 | −0.125762 | ||||||||
\(310\) | 2.00903e7 | 0.0383019 | ||||||||
\(311\) | −1.86724e8 | −0.351997 | −0.175999 | − | 0.984390i | \(-0.556315\pi\) | ||||
−0.175999 | + | 0.984390i | \(0.556315\pi\) | |||||||
\(312\) | −3.15173e8 | −0.587501 | ||||||||
\(313\) | 4.50446e8 | 0.830304 | 0.415152 | − | 0.909752i | \(-0.363728\pi\) | ||||
0.415152 | + | 0.909752i | \(0.363728\pi\) | |||||||
\(314\) | 9.84924e7 | 0.179535 | ||||||||
\(315\) | −2.40395e7 | −0.0433350 | ||||||||
\(316\) | −8.82527e7 | −0.157334 | ||||||||
\(317\) | −3.97194e8 | −0.700318 | −0.350159 | − | 0.936690i | \(-0.613872\pi\) | ||||
−0.350159 | + | 0.936690i | \(0.613872\pi\) | |||||||
\(318\) | 5.91574e8 | 1.03161 | ||||||||
\(319\) | −1.07709e9 | −1.85773 | ||||||||
\(320\) | 7.70953e6 | 0.0131523 | ||||||||
\(321\) | −4.07270e8 | −0.687249 | ||||||||
\(322\) | 6.32976e7 | 0.105655 | ||||||||
\(323\) | −7.54822e8 | −1.24634 | ||||||||
\(324\) | 3.70387e7 | 0.0604990 | ||||||||
\(325\) | 7.78149e8 | 1.25739 | ||||||||
\(326\) | 7.24740e8 | 1.15856 | ||||||||
\(327\) | −3.53513e8 | −0.559098 | ||||||||
\(328\) | −1.62128e8 | −0.253687 | ||||||||
\(329\) | 2.03710e8 | 0.315375 | ||||||||
\(330\) | −4.57726e8 | −0.701144 | ||||||||
\(331\) | −7.65695e8 | −1.16053 | −0.580267 | − | 0.814426i | \(-0.697052\pi\) | ||||
−0.580267 | + | 0.814426i | \(0.697052\pi\) | |||||||
\(332\) | 1.54902e8 | 0.232314 | ||||||||
\(333\) | −3.83066e8 | −0.568484 | ||||||||
\(334\) | −1.23645e8 | −0.181578 | ||||||||
\(335\) | −3.52857e8 | −0.512793 | ||||||||
\(336\) | −1.18820e8 | −0.170885 | ||||||||
\(337\) | 1.34277e8 | 0.191116 | 0.0955581 | − | 0.995424i | \(-0.469536\pi\) | ||||
0.0955581 | + | 0.995424i | \(0.469536\pi\) | |||||||
\(338\) | 1.96849e9 | 2.77284 | ||||||||
\(339\) | 2.33450e8 | 0.325457 | ||||||||
\(340\) | −1.54195e8 | −0.212762 | ||||||||
\(341\) | 7.33851e7 | 0.100223 | ||||||||
\(342\) | 5.35812e8 | 0.724305 | ||||||||
\(343\) | 3.44519e8 | 0.460981 | ||||||||
\(344\) | −3.36657e8 | −0.445896 | ||||||||
\(345\) | 8.65328e7 | 0.113452 | ||||||||
\(346\) | 7.76604e8 | 1.00794 | ||||||||
\(347\) | 1.31108e9 | 1.68451 | 0.842257 | − | 0.539076i | \(-0.181227\pi\) | ||||
0.842257 | + | 0.539076i | \(0.181227\pi\) | |||||||
\(348\) | 2.57563e8 | 0.327610 | ||||||||
\(349\) | −1.04850e9 | −1.32032 | −0.660160 | − | 0.751125i | \(-0.729511\pi\) | ||||
−0.660160 | + | 0.751125i | \(0.729511\pi\) | |||||||
\(350\) | 1.65373e8 | 0.206170 | ||||||||
\(351\) | 2.80267e8 | 0.345937 | ||||||||
\(352\) | −1.43666e9 | −1.75572 | ||||||||
\(353\) | −1.06498e9 | −1.28863 | −0.644317 | − | 0.764758i | \(-0.722858\pi\) | ||||
−0.644317 | + | 0.764758i | \(0.722858\pi\) | |||||||
\(354\) | −7.79682e7 | −0.0934127 | ||||||||
\(355\) | −2.58667e8 | −0.306861 | ||||||||
\(356\) | −7.30388e8 | −0.857983 | ||||||||
\(357\) | −8.39085e7 | −0.0976039 | ||||||||
\(358\) | 1.60516e9 | 1.84896 | ||||||||
\(359\) | −8.86207e8 | −1.01089 | −0.505446 | − | 0.862858i | \(-0.668672\pi\) | ||||
−0.505446 | + | 0.862858i | \(0.668672\pi\) | |||||||
\(360\) | −9.15682e7 | −0.103439 | ||||||||
\(361\) | 1.83872e9 | 2.05703 | ||||||||
\(362\) | 1.04771e8 | 0.116081 | ||||||||
\(363\) | −1.14581e9 | −1.25730 | ||||||||
\(364\) | 2.13583e8 | 0.232120 | ||||||||
\(365\) | 3.88321e8 | 0.417990 | ||||||||
\(366\) | 2.50293e8 | 0.266849 | ||||||||
\(367\) | −9.92035e8 | −1.04760 | −0.523801 | − | 0.851841i | \(-0.675486\pi\) | ||||
−0.523801 | + | 0.851841i | \(0.675486\pi\) | |||||||
\(368\) | 4.27707e8 | 0.447382 | ||||||||
\(369\) | 1.44172e8 | 0.149379 | ||||||||
\(370\) | −1.13203e9 | −1.16185 | ||||||||
\(371\) | 3.35377e8 | 0.340976 | ||||||||
\(372\) | −1.75485e7 | −0.0176742 | ||||||||
\(373\) | 9.84405e8 | 0.982184 | 0.491092 | − | 0.871108i | \(-0.336598\pi\) | ||||
0.491092 | + | 0.871108i | \(0.336598\pi\) | |||||||
\(374\) | −1.59767e9 | −1.57920 | ||||||||
\(375\) | 5.49274e8 | 0.537873 | ||||||||
\(376\) | 7.75948e8 | 0.752792 | ||||||||
\(377\) | 1.94895e9 | 1.87329 | ||||||||
\(378\) | 5.95627e7 | 0.0567222 | ||||||||
\(379\) | −1.03216e9 | −0.973888 | −0.486944 | − | 0.873433i | \(-0.661888\pi\) | ||||
−0.486944 | + | 0.873433i | \(0.661888\pi\) | |||||||
\(380\) | 5.58214e8 | 0.521865 | ||||||||
\(381\) | −7.49604e8 | −0.694375 | ||||||||
\(382\) | −3.72629e8 | −0.342022 | ||||||||
\(383\) | 1.11996e9 | 1.01861 | 0.509303 | − | 0.860587i | \(-0.329903\pi\) | ||||
0.509303 | + | 0.860587i | \(0.329903\pi\) | |||||||
\(384\) | −6.50055e8 | −0.585856 | ||||||||
\(385\) | −2.59495e8 | −0.231748 | ||||||||
\(386\) | −1.11841e9 | −0.989796 | ||||||||
\(387\) | 2.99372e8 | 0.262556 | ||||||||
\(388\) | 3.77269e8 | 0.327899 | ||||||||
\(389\) | −2.19361e9 | −1.88945 | −0.944725 | − | 0.327865i | \(-0.893671\pi\) | ||||
−0.944725 | + | 0.327865i | \(0.893671\pi\) | |||||||
\(390\) | 8.28239e8 | 0.707016 | ||||||||
\(391\) | 3.02038e8 | 0.255531 | ||||||||
\(392\) | 6.37162e8 | 0.534255 | ||||||||
\(393\) | −5.63970e8 | −0.468686 | ||||||||
\(394\) | 9.41587e8 | 0.775575 | ||||||||
\(395\) | −1.94017e8 | −0.158398 | ||||||||
\(396\) | 3.99816e8 | 0.323539 | ||||||||
\(397\) | −1.87970e9 | −1.50772 | −0.753862 | − | 0.657033i | \(-0.771811\pi\) | ||||
−0.753862 | + | 0.657033i | \(0.771811\pi\) | |||||||
\(398\) | −7.70117e8 | −0.612302 | ||||||||
\(399\) | 3.03764e8 | 0.239404 | ||||||||
\(400\) | 1.11744e9 | 0.872998 | ||||||||
\(401\) | 1.82808e9 | 1.41576 | 0.707881 | − | 0.706332i | \(-0.249651\pi\) | ||||
0.707881 | + | 0.706332i | \(0.249651\pi\) | |||||||
\(402\) | 8.74273e8 | 0.671206 | ||||||||
\(403\) | −1.32788e8 | −0.101062 | ||||||||
\(404\) | −5.58065e8 | −0.421066 | ||||||||
\(405\) | 8.14269e7 | 0.0609081 | ||||||||
\(406\) | 4.14192e8 | 0.307157 | ||||||||
\(407\) | −4.13502e9 | −3.04016 | ||||||||
\(408\) | −3.19614e8 | −0.232978 | ||||||||
\(409\) | −2.05110e9 | −1.48237 | −0.741183 | − | 0.671303i | \(-0.765735\pi\) | ||||
−0.741183 | + | 0.671303i | \(0.765735\pi\) | |||||||
\(410\) | 4.26053e8 | 0.305295 | ||||||||
\(411\) | 3.96908e8 | 0.281996 | ||||||||
\(412\) | 1.68361e8 | 0.118604 | ||||||||
\(413\) | −4.42019e7 | −0.0308756 | ||||||||
\(414\) | −2.14402e8 | −0.148501 | ||||||||
\(415\) | 3.40541e8 | 0.233884 | ||||||||
\(416\) | 2.59959e9 | 1.77043 | ||||||||
\(417\) | 9.14255e8 | 0.617435 | ||||||||
\(418\) | 5.78385e9 | 3.87347 | ||||||||
\(419\) | −1.07209e8 | −0.0712005 | −0.0356002 | − | 0.999366i | \(-0.511334\pi\) | ||||
−0.0356002 | + | 0.999366i | \(0.511334\pi\) | |||||||
\(420\) | 6.20530e7 | 0.0408686 | ||||||||
\(421\) | −2.81280e9 | −1.83718 | −0.918589 | − | 0.395213i | \(-0.870671\pi\) | ||||
−0.918589 | + | 0.395213i | \(0.870671\pi\) | |||||||
\(422\) | −9.08061e8 | −0.588195 | ||||||||
\(423\) | −6.90011e8 | −0.443266 | ||||||||
\(424\) | 1.27747e9 | 0.813901 | ||||||||
\(425\) | 7.89113e8 | 0.498629 | ||||||||
\(426\) | 6.40899e8 | 0.401657 | ||||||||
\(427\) | 1.41897e8 | 0.0882013 | ||||||||
\(428\) | 1.05128e9 | 0.648135 | ||||||||
\(429\) | 3.02536e9 | 1.85002 | ||||||||
\(430\) | 8.84696e8 | 0.536604 | ||||||||
\(431\) | 1.62988e9 | 0.980583 | 0.490292 | − | 0.871558i | \(-0.336890\pi\) | ||||
0.490292 | + | 0.871558i | \(0.336890\pi\) | |||||||
\(432\) | 4.02469e8 | 0.240182 | ||||||||
\(433\) | −8.30649e8 | −0.491711 | −0.245856 | − | 0.969306i | \(-0.579069\pi\) | ||||
−0.245856 | + | 0.969306i | \(0.579069\pi\) | |||||||
\(434\) | −2.82201e7 | −0.0165709 | ||||||||
\(435\) | 5.66234e8 | 0.329825 | ||||||||
\(436\) | 9.12520e8 | 0.527278 | ||||||||
\(437\) | −1.09343e9 | −0.626768 | ||||||||
\(438\) | −9.62142e8 | −0.547117 | ||||||||
\(439\) | 2.22387e9 | 1.25454 | 0.627270 | − | 0.778802i | \(-0.284172\pi\) | ||||
0.627270 | + | 0.778802i | \(0.284172\pi\) | |||||||
\(440\) | −9.88436e8 | −0.553177 | ||||||||
\(441\) | −5.66595e8 | −0.314585 | ||||||||
\(442\) | 2.89092e9 | 1.59242 | ||||||||
\(443\) | 1.30013e9 | 0.710516 | 0.355258 | − | 0.934768i | \(-0.384393\pi\) | ||||
0.355258 | + | 0.934768i | \(0.384393\pi\) | |||||||
\(444\) | 9.88804e8 | 0.536130 | ||||||||
\(445\) | −1.60570e9 | −0.863785 | ||||||||
\(446\) | −2.84052e9 | −1.51609 | ||||||||
\(447\) | 9.51432e8 | 0.503850 | ||||||||
\(448\) | −1.08293e7 | −0.00569019 | ||||||||
\(449\) | 1.41883e9 | 0.739720 | 0.369860 | − | 0.929088i | \(-0.379406\pi\) | ||||
0.369860 | + | 0.929088i | \(0.379406\pi\) | |||||||
\(450\) | −5.60153e8 | −0.289776 | ||||||||
\(451\) | 1.55627e9 | 0.798852 | ||||||||
\(452\) | −6.02602e8 | −0.306935 | ||||||||
\(453\) | −1.16500e9 | −0.588818 | ||||||||
\(454\) | −3.88249e9 | −1.94722 | ||||||||
\(455\) | 4.69547e8 | 0.233689 | ||||||||
\(456\) | 1.15706e9 | 0.571451 | ||||||||
\(457\) | −2.30832e9 | −1.13133 | −0.565664 | − | 0.824636i | \(-0.691380\pi\) | ||||
−0.565664 | + | 0.824636i | \(0.691380\pi\) | |||||||
\(458\) | −1.97076e9 | −0.958528 | ||||||||
\(459\) | 2.84216e8 | 0.137184 | ||||||||
\(460\) | −2.23366e8 | −0.106995 | ||||||||
\(461\) | −2.65874e8 | −0.126393 | −0.0631965 | − | 0.998001i | \(-0.520129\pi\) | ||||
−0.0631965 | + | 0.998001i | \(0.520129\pi\) | |||||||
\(462\) | 6.42951e8 | 0.303341 | ||||||||
\(463\) | −1.76799e9 | −0.827840 | −0.413920 | − | 0.910313i | \(-0.635841\pi\) | ||||
−0.413920 | + | 0.910313i | \(0.635841\pi\) | |||||||
\(464\) | 2.79873e9 | 1.30061 | ||||||||
\(465\) | −3.85792e7 | −0.0177937 | ||||||||
\(466\) | 1.21946e9 | 0.558236 | ||||||||
\(467\) | 3.74007e9 | 1.69930 | 0.849652 | − | 0.527344i | \(-0.176812\pi\) | ||||
0.849652 | + | 0.527344i | \(0.176812\pi\) | |||||||
\(468\) | −7.23452e8 | −0.326249 | ||||||||
\(469\) | 4.95645e8 | 0.221853 | ||||||||
\(470\) | −2.03910e9 | −0.905933 | ||||||||
\(471\) | −1.89134e8 | −0.0834057 | ||||||||
\(472\) | −1.68368e8 | −0.0736993 | ||||||||
\(473\) | 3.23158e9 | 1.40411 | ||||||||
\(474\) | 4.80716e8 | 0.207331 | ||||||||
\(475\) | −2.85673e9 | −1.22304 | ||||||||
\(476\) | 2.16592e8 | 0.0920490 | ||||||||
\(477\) | −1.13599e9 | −0.479249 | ||||||||
\(478\) | 3.13052e9 | 1.31105 | ||||||||
\(479\) | −4.49040e8 | −0.186686 | −0.0933428 | − | 0.995634i | \(-0.529755\pi\) | ||||
−0.0933428 | + | 0.995634i | \(0.529755\pi\) | |||||||
\(480\) | 7.55266e8 | 0.311713 | ||||||||
\(481\) | 7.48216e9 | 3.06563 | ||||||||
\(482\) | 6.01502e9 | 2.44665 | ||||||||
\(483\) | −1.21549e8 | −0.0490838 | ||||||||
\(484\) | 2.95767e9 | 1.18574 | ||||||||
\(485\) | 8.29399e8 | 0.330117 | ||||||||
\(486\) | −2.01751e8 | −0.0797241 | ||||||||
\(487\) | −3.09706e9 | −1.21506 | −0.607531 | − | 0.794296i | \(-0.707840\pi\) | ||||
−0.607531 | + | 0.794296i | \(0.707840\pi\) | |||||||
\(488\) | 5.40495e8 | 0.210534 | ||||||||
\(489\) | −1.39171e9 | −0.538229 | ||||||||
\(490\) | −1.67439e9 | −0.642939 | ||||||||
\(491\) | −2.15480e9 | −0.821527 | −0.410763 | − | 0.911742i | \(-0.634738\pi\) | ||||
−0.410763 | + | 0.911742i | \(0.634738\pi\) | |||||||
\(492\) | −3.72150e8 | −0.140877 | ||||||||
\(493\) | 1.97641e9 | 0.742869 | ||||||||
\(494\) | −1.04657e10 | −3.90591 | ||||||||
\(495\) | 8.78965e8 | 0.325727 | ||||||||
\(496\) | −1.90686e8 | −0.0701669 | ||||||||
\(497\) | 3.63340e8 | 0.132759 | ||||||||
\(498\) | −8.43759e8 | −0.306137 | ||||||||
\(499\) | 5.11219e9 | 1.84185 | 0.920926 | − | 0.389738i | \(-0.127434\pi\) | ||||
0.920926 | + | 0.389738i | \(0.127434\pi\) | |||||||
\(500\) | −1.41784e9 | −0.507261 | ||||||||
\(501\) | 2.37433e8 | 0.0843547 | ||||||||
\(502\) | 6.74462e8 | 0.237955 | ||||||||
\(503\) | −3.11720e9 | −1.09214 | −0.546069 | − | 0.837740i | \(-0.683876\pi\) | ||||
−0.546069 | + | 0.837740i | \(0.683876\pi\) | |||||||
\(504\) | 1.28623e8 | 0.0447518 | ||||||||
\(505\) | −1.22687e9 | −0.423913 | ||||||||
\(506\) | −2.31437e9 | −0.794158 | ||||||||
\(507\) | −3.78006e9 | −1.28816 | ||||||||
\(508\) | 1.93495e9 | 0.654856 | ||||||||
\(509\) | −3.33182e9 | −1.11988 | −0.559938 | − | 0.828535i | \(-0.689175\pi\) | ||||
−0.559938 | + | 0.828535i | \(0.689175\pi\) | |||||||
\(510\) | 8.39908e8 | 0.280373 | ||||||||
\(511\) | −5.45460e8 | −0.180838 | ||||||||
\(512\) | 1.58742e9 | 0.522695 | ||||||||
\(513\) | −1.02891e9 | −0.336487 | ||||||||
\(514\) | 2.54889e9 | 0.827905 | ||||||||
\(515\) | 3.70129e8 | 0.119406 | ||||||||
\(516\) | −7.72766e8 | −0.247613 | ||||||||
\(517\) | −7.44834e9 | −2.37052 | ||||||||
\(518\) | 1.59011e9 | 0.502660 | ||||||||
\(519\) | −1.49130e9 | −0.468252 | ||||||||
\(520\) | 1.78854e9 | 0.557811 | ||||||||
\(521\) | −1.20322e8 | −0.0372745 | −0.0186373 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186373 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(522\) | −1.40296e9 | −0.431716 | ||||||||
\(523\) | 1.56158e9 | 0.477318 | 0.238659 | − | 0.971103i | \(-0.423292\pi\) | ||||
0.238659 | + | 0.971103i | \(0.423292\pi\) | |||||||
\(524\) | 1.45577e9 | 0.442012 | ||||||||
\(525\) | −3.17563e8 | −0.0957796 | ||||||||
\(526\) | −2.81801e9 | −0.844291 | ||||||||
\(527\) | −1.34658e8 | −0.0400771 | ||||||||
\(528\) | 4.34447e9 | 1.28445 | ||||||||
\(529\) | −2.96729e9 | −0.871497 | ||||||||
\(530\) | −3.35705e9 | −0.979473 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | −7.84103e8 | −0.225779 | ||||||||
\(533\) | −2.81601e9 | −0.805543 | ||||||||
\(534\) | 3.97845e9 | 1.13063 | ||||||||
\(535\) | 2.31116e9 | 0.652518 | ||||||||
\(536\) | 1.88795e9 | 0.529558 | ||||||||
\(537\) | −3.08236e9 | −0.858961 | ||||||||
\(538\) | 3.69715e9 | 1.02360 | ||||||||
\(539\) | −6.11614e9 | −1.68235 | ||||||||
\(540\) | −2.10187e8 | −0.0574416 | ||||||||
\(541\) | 2.94601e9 | 0.799914 | 0.399957 | − | 0.916534i | \(-0.369025\pi\) | ||||
0.399957 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(542\) | 5.19290e9 | 1.40092 | ||||||||
\(543\) | −2.01190e8 | −0.0539270 | ||||||||
\(544\) | 2.63621e9 | 0.702077 | ||||||||
\(545\) | 2.00611e9 | 0.530843 | ||||||||
\(546\) | −1.16340e9 | −0.305882 | ||||||||
\(547\) | 5.07000e9 | 1.32450 | 0.662251 | − | 0.749282i | \(-0.269601\pi\) | ||||
0.662251 | + | 0.749282i | \(0.269601\pi\) | |||||||
\(548\) | −1.02453e9 | −0.265947 | ||||||||
\(549\) | −4.80635e8 | −0.123969 | ||||||||
\(550\) | −6.04659e9 | −1.54968 | ||||||||
\(551\) | −7.15495e9 | −1.82212 | ||||||||
\(552\) | −4.62991e8 | −0.117162 | ||||||||
\(553\) | 2.72529e8 | 0.0685290 | ||||||||
\(554\) | −4.13816e9 | −1.03401 | ||||||||
\(555\) | 2.17381e9 | 0.539755 | ||||||||
\(556\) | −2.35996e9 | −0.582295 | ||||||||
\(557\) | 7.03628e9 | 1.72524 | 0.862621 | − | 0.505851i | \(-0.168821\pi\) | ||||
0.862621 | + | 0.505851i | \(0.168821\pi\) | |||||||
\(558\) | 9.55876e7 | 0.0232907 | ||||||||
\(559\) | −5.84742e9 | −1.41587 | ||||||||
\(560\) | 6.74279e8 | 0.162249 | ||||||||
\(561\) | 3.06798e9 | 0.733639 | ||||||||
\(562\) | 6.10044e9 | 1.44972 | ||||||||
\(563\) | −4.94078e9 | −1.16685 | −0.583426 | − | 0.812166i | \(-0.698288\pi\) | ||||
−0.583426 | + | 0.812166i | \(0.698288\pi\) | |||||||
\(564\) | 1.78112e9 | 0.418038 | ||||||||
\(565\) | −1.32478e9 | −0.309010 | ||||||||
\(566\) | −1.14240e9 | −0.264825 | ||||||||
\(567\) | −1.14377e8 | −0.0263511 | ||||||||
\(568\) | 1.38399e9 | 0.316893 | ||||||||
\(569\) | 2.66776e9 | 0.607090 | 0.303545 | − | 0.952817i | \(-0.401830\pi\) | ||||
0.303545 | + | 0.952817i | \(0.401830\pi\) | |||||||
\(570\) | −3.04062e9 | −0.687701 | ||||||||
\(571\) | 6.77696e9 | 1.52338 | 0.761690 | − | 0.647941i | \(-0.224370\pi\) | ||||
0.761690 | + | 0.647941i | \(0.224370\pi\) | |||||||
\(572\) | −7.80933e9 | −1.74473 | ||||||||
\(573\) | 7.15554e8 | 0.158892 | ||||||||
\(574\) | −5.98461e8 | −0.132082 | ||||||||
\(575\) | 1.14310e9 | 0.250754 | ||||||||
\(576\) | 3.66811e7 | 0.00799768 | ||||||||
\(577\) | −5.53458e9 | −1.19941 | −0.599707 | − | 0.800219i | \(-0.704716\pi\) | ||||
−0.599707 | + | 0.800219i | \(0.704716\pi\) | |||||||
\(578\) | −2.83787e9 | −0.611288 | ||||||||
\(579\) | 2.14767e9 | 0.459825 | ||||||||
\(580\) | −1.46162e9 | −0.311053 | ||||||||
\(581\) | −4.78346e8 | −0.101187 | ||||||||
\(582\) | −2.05500e9 | −0.432098 | ||||||||
\(583\) | −1.22625e10 | −2.56294 | ||||||||
\(584\) | −2.07770e9 | −0.431655 | ||||||||
\(585\) | −1.59046e9 | −0.328455 | ||||||||
\(586\) | −9.03347e9 | −1.85444 | ||||||||
\(587\) | 5.22919e9 | 1.06709 | 0.533545 | − | 0.845771i | \(-0.320859\pi\) | ||||
0.533545 | + | 0.845771i | \(0.320859\pi\) | |||||||
\(588\) | 1.46255e9 | 0.296681 | ||||||||
\(589\) | 4.87488e8 | 0.0983015 | ||||||||
\(590\) | 4.42452e8 | 0.0886920 | ||||||||
\(591\) | −1.80812e9 | −0.360305 | ||||||||
\(592\) | 1.07445e10 | 2.12844 | ||||||||
\(593\) | 8.33930e8 | 0.164224 | 0.0821122 | − | 0.996623i | \(-0.473833\pi\) | ||||
0.0821122 | + | 0.996623i | \(0.473833\pi\) | |||||||
\(594\) | −2.17781e9 | −0.426352 | ||||||||
\(595\) | 4.76162e8 | 0.0926714 | ||||||||
\(596\) | −2.45592e9 | −0.475174 | ||||||||
\(597\) | 1.47884e9 | 0.284454 | ||||||||
\(598\) | 4.18777e9 | 0.800809 | ||||||||
\(599\) | 3.80759e9 | 0.723863 | 0.361931 | − | 0.932205i | \(-0.382117\pi\) | ||||
0.361931 | + | 0.932205i | \(0.382117\pi\) | |||||||
\(600\) | −1.20962e9 | −0.228623 | ||||||||
\(601\) | 8.81584e9 | 1.65654 | 0.828272 | − | 0.560326i | \(-0.189324\pi\) | ||||
0.828272 | + | 0.560326i | \(0.189324\pi\) | |||||||
\(602\) | −1.24270e9 | −0.232155 | ||||||||
\(603\) | −1.67886e9 | −0.311819 | ||||||||
\(604\) | 3.00720e9 | 0.555307 | ||||||||
\(605\) | 6.50222e9 | 1.19376 | ||||||||
\(606\) | 3.03980e9 | 0.554870 | ||||||||
\(607\) | 3.12869e9 | 0.567809 | 0.283904 | − | 0.958853i | \(-0.408370\pi\) | ||||
0.283904 | + | 0.958853i | \(0.408370\pi\) | |||||||
\(608\) | −9.54357e9 | −1.72206 | ||||||||
\(609\) | −7.95368e8 | −0.142695 | ||||||||
\(610\) | −1.42036e9 | −0.253363 | ||||||||
\(611\) | 1.34775e10 | 2.39037 | ||||||||
\(612\) | −7.33645e8 | −0.129377 | ||||||||
\(613\) | 6.07990e9 | 1.06607 | 0.533034 | − | 0.846094i | \(-0.321052\pi\) | ||||
0.533034 | + | 0.846094i | \(0.321052\pi\) | |||||||
\(614\) | −9.75263e9 | −1.70033 | ||||||||
\(615\) | −8.18143e8 | −0.141829 | ||||||||
\(616\) | 1.38842e9 | 0.239325 | ||||||||
\(617\) | −1.45081e9 | −0.248664 | −0.124332 | − | 0.992241i | \(-0.539679\pi\) | ||||
−0.124332 | + | 0.992241i | \(0.539679\pi\) | |||||||
\(618\) | −9.17069e8 | −0.156294 | ||||||||
\(619\) | −3.93245e9 | −0.666416 | −0.333208 | − | 0.942853i | \(-0.608131\pi\) | ||||
−0.333208 | + | 0.942853i | \(0.608131\pi\) | |||||||
\(620\) | 9.95841e7 | 0.0167810 | ||||||||
\(621\) | 4.11714e8 | 0.0689882 | ||||||||
\(622\) | −2.62542e9 | −0.437454 | ||||||||
\(623\) | 2.25547e9 | 0.373706 | ||||||||
\(624\) | −7.86116e9 | −1.29521 | ||||||||
\(625\) | 1.15244e9 | 0.188815 | ||||||||
\(626\) | 6.33345e9 | 1.03188 | ||||||||
\(627\) | −1.11066e10 | −1.79948 | ||||||||
\(628\) | 4.88209e8 | 0.0786588 | ||||||||
\(629\) | 7.58757e9 | 1.21570 | ||||||||
\(630\) | −3.38005e8 | −0.0538556 | ||||||||
\(631\) | 9.82173e9 | 1.55627 | 0.778135 | − | 0.628097i | \(-0.216166\pi\) | ||||
0.778135 | + | 0.628097i | \(0.216166\pi\) | |||||||
\(632\) | 1.03808e9 | 0.163577 | ||||||||
\(633\) | 1.74374e9 | 0.273255 | ||||||||
\(634\) | −5.58470e9 | −0.870338 | ||||||||
\(635\) | 4.25383e9 | 0.659284 | ||||||||
\(636\) | 2.93233e9 | 0.451973 | ||||||||
\(637\) | 1.10669e10 | 1.69644 | ||||||||
\(638\) | −1.51443e10 | −2.30875 | ||||||||
\(639\) | −1.23071e9 | −0.186596 | ||||||||
\(640\) | 3.68892e9 | 0.556249 | ||||||||
\(641\) | −7.96630e9 | −1.19469 | −0.597343 | − | 0.801986i | \(-0.703777\pi\) | ||||
−0.597343 | + | 0.801986i | \(0.703777\pi\) | |||||||
\(642\) | −5.72637e9 | −0.854097 | ||||||||
\(643\) | 7.54836e9 | 1.11973 | 0.559866 | − | 0.828583i | \(-0.310852\pi\) | ||||
0.559866 | + | 0.828583i | \(0.310852\pi\) | |||||||
\(644\) | 3.13755e8 | 0.0462903 | ||||||||
\(645\) | −1.69887e9 | −0.249288 | ||||||||
\(646\) | −1.06131e10 | −1.54892 | ||||||||
\(647\) | 1.12209e10 | 1.62878 | 0.814388 | − | 0.580321i | \(-0.197073\pi\) | ||||
0.814388 | + | 0.580321i | \(0.197073\pi\) | |||||||
\(648\) | −4.35672e8 | −0.0628995 | ||||||||
\(649\) | 1.61617e9 | 0.232076 | ||||||||
\(650\) | 1.09411e10 | 1.56266 | ||||||||
\(651\) | 5.41907e7 | 0.00769824 | ||||||||
\(652\) | 3.59240e9 | 0.507596 | ||||||||
\(653\) | −6.06010e9 | −0.851694 | −0.425847 | − | 0.904795i | \(-0.640024\pi\) | ||||
−0.425847 | + | 0.904795i | \(0.640024\pi\) | |||||||
\(654\) | −4.97053e9 | −0.694834 | ||||||||
\(655\) | 3.20041e9 | 0.445001 | ||||||||
\(656\) | −4.04385e9 | −0.559282 | ||||||||
\(657\) | 1.84759e9 | 0.254171 | ||||||||
\(658\) | 2.86425e9 | 0.391941 | ||||||||
\(659\) | −1.39437e10 | −1.89792 | −0.948960 | − | 0.315398i | \(-0.897862\pi\) | ||||
−0.948960 | + | 0.315398i | \(0.897862\pi\) | |||||||
\(660\) | −2.26887e9 | −0.307189 | ||||||||
\(661\) | −8.46218e9 | −1.13966 | −0.569832 | − | 0.821761i | \(-0.692992\pi\) | ||||
−0.569832 | + | 0.821761i | \(0.692992\pi\) | |||||||
\(662\) | −1.07660e10 | −1.44228 | ||||||||
\(663\) | −5.55140e9 | −0.739784 | ||||||||
\(664\) | −1.82205e9 | −0.241531 | ||||||||
\(665\) | −1.72379e9 | −0.227305 | ||||||||
\(666\) | −5.38606e9 | −0.706498 | ||||||||
\(667\) | 2.86302e9 | 0.373580 | ||||||||
\(668\) | −6.12884e8 | −0.0795538 | ||||||||
\(669\) | 5.45460e9 | 0.704323 | ||||||||
\(670\) | −4.96131e9 | −0.637286 | ||||||||
\(671\) | −5.18823e9 | −0.662965 | ||||||||
\(672\) | −1.06089e9 | −0.134859 | ||||||||
\(673\) | 2.59986e9 | 0.328773 | 0.164387 | − | 0.986396i | \(-0.447436\pi\) | ||||
0.164387 | + | 0.986396i | \(0.447436\pi\) | |||||||
\(674\) | 1.88799e9 | 0.237514 | ||||||||
\(675\) | 1.07565e9 | 0.134620 | ||||||||
\(676\) | 9.75744e9 | 1.21485 | ||||||||
\(677\) | 2.24286e8 | 0.0277807 | 0.0138903 | − | 0.999904i | \(-0.495578\pi\) | ||||
0.0138903 | + | 0.999904i | \(0.495578\pi\) | |||||||
\(678\) | 3.28240e9 | 0.404471 | ||||||||
\(679\) | −1.16503e9 | −0.142821 | ||||||||
\(680\) | 1.81374e9 | 0.221204 | ||||||||
\(681\) | 7.45550e9 | 0.904611 | ||||||||
\(682\) | 1.03182e9 | 0.124555 | ||||||||
\(683\) | −1.29921e9 | −0.156029 | −0.0780146 | − | 0.996952i | \(-0.524858\pi\) | ||||
−0.0780146 | + | 0.996952i | \(0.524858\pi\) | |||||||
\(684\) | 2.65593e9 | 0.317336 | ||||||||
\(685\) | −2.25236e9 | −0.267745 | ||||||||
\(686\) | 4.84407e9 | 0.572896 | ||||||||
\(687\) | 3.78443e9 | 0.445299 | ||||||||
\(688\) | −8.39702e9 | −0.983027 | ||||||||
\(689\) | 2.21886e10 | 2.58441 | ||||||||
\(690\) | 1.21669e9 | 0.140996 | ||||||||
\(691\) | −1.09890e10 | −1.26703 | −0.633514 | − | 0.773732i | \(-0.718388\pi\) | ||||
−0.633514 | + | 0.773732i | \(0.718388\pi\) | |||||||
\(692\) | 3.84949e9 | 0.441602 | ||||||||
\(693\) | −1.23465e9 | −0.140922 | ||||||||
\(694\) | 1.84342e10 | 2.09347 | ||||||||
\(695\) | −5.18820e9 | −0.586232 | ||||||||
\(696\) | −3.02962e9 | −0.340608 | ||||||||
\(697\) | −2.85568e9 | −0.319445 | ||||||||
\(698\) | −1.47423e10 | −1.64086 | ||||||||
\(699\) | −2.34172e9 | −0.259337 | ||||||||
\(700\) | 8.19724e8 | 0.0903284 | ||||||||
\(701\) | 1.12676e10 | 1.23543 | 0.617715 | − | 0.786402i | \(-0.288059\pi\) | ||||
0.617715 | + | 0.786402i | \(0.288059\pi\) | |||||||
\(702\) | 3.94067e9 | 0.429923 | ||||||||
\(703\) | −2.74684e10 | −2.98188 | ||||||||
\(704\) | 3.95956e8 | 0.0427703 | ||||||||
\(705\) | 3.91566e9 | 0.420865 | ||||||||
\(706\) | −1.49740e10 | −1.60148 | ||||||||
\(707\) | 1.72333e9 | 0.183401 | ||||||||
\(708\) | −3.86474e8 | −0.0409265 | ||||||||
\(709\) | −8.10979e9 | −0.854571 | −0.427285 | − | 0.904117i | \(-0.640530\pi\) | ||||
−0.427285 | + | 0.904117i | \(0.640530\pi\) | |||||||
\(710\) | −3.63696e9 | −0.381359 | ||||||||
\(711\) | −9.23113e8 | −0.0963188 | ||||||||
\(712\) | 8.59127e9 | 0.892026 | ||||||||
\(713\) | −1.95065e8 | −0.0201543 | ||||||||
\(714\) | −1.17979e9 | −0.121300 | ||||||||
\(715\) | −1.71682e10 | −1.75653 | ||||||||
\(716\) | 7.95647e9 | 0.810075 | ||||||||
\(717\) | −6.01150e9 | −0.609069 | ||||||||
\(718\) | −1.24604e10 | −1.25631 | ||||||||
\(719\) | 1.37914e10 | 1.38375 | 0.691873 | − | 0.722019i | \(-0.256786\pi\) | ||||
0.691873 | + | 0.722019i | \(0.256786\pi\) | |||||||
\(720\) | −2.28393e9 | −0.228044 | ||||||||
\(721\) | −5.19907e8 | −0.0516597 | ||||||||
\(722\) | 2.58532e10 | 2.55643 | ||||||||
\(723\) | −1.15506e10 | −1.13663 | ||||||||
\(724\) | 5.19330e8 | 0.0508579 | ||||||||
\(725\) | 7.47999e9 | 0.728984 | ||||||||
\(726\) | −1.61105e10 | −1.56254 | ||||||||
\(727\) | −8.25616e9 | −0.796907 | −0.398454 | − | 0.917189i | \(-0.630453\pi\) | ||||
−0.398454 | + | 0.917189i | \(0.630453\pi\) | |||||||
\(728\) | −2.51230e9 | −0.241330 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 5.45994e9 | 0.519467 | ||||||||
\(731\) | −5.92981e9 | −0.561474 | ||||||||
\(732\) | 1.24066e9 | 0.116913 | ||||||||
\(733\) | 1.14387e10 | 1.07279 | 0.536395 | − | 0.843967i | \(-0.319786\pi\) | ||||
0.536395 | + | 0.843967i | \(0.319786\pi\) | |||||||
\(734\) | −1.39484e10 | −1.30193 | ||||||||
\(735\) | 3.21530e9 | 0.298687 | ||||||||
\(736\) | 3.81881e9 | 0.353065 | ||||||||
\(737\) | −1.81225e10 | −1.66756 | ||||||||
\(738\) | 2.02711e9 | 0.185644 | ||||||||
\(739\) | 1.48024e10 | 1.34920 | 0.674598 | − | 0.738185i | \(-0.264317\pi\) | ||||
0.674598 | + | 0.738185i | \(0.264317\pi\) | |||||||
\(740\) | −5.61125e9 | −0.509036 | ||||||||
\(741\) | 2.00971e10 | 1.81455 | ||||||||
\(742\) | 4.71553e9 | 0.423757 | ||||||||
\(743\) | 1.21140e10 | 1.08349 | 0.541746 | − | 0.840542i | \(-0.317764\pi\) | ||||
0.541746 | + | 0.840542i | \(0.317764\pi\) | |||||||
\(744\) | 2.06416e8 | 0.0183755 | ||||||||
\(745\) | −5.39917e9 | −0.478387 | ||||||||
\(746\) | 1.38411e10 | 1.22063 | ||||||||
\(747\) | 1.62026e9 | 0.142221 | ||||||||
\(748\) | −7.91935e9 | −0.691885 | ||||||||
\(749\) | −3.24641e9 | −0.282304 | ||||||||
\(750\) | 7.72302e9 | 0.668456 | ||||||||
\(751\) | −3.71223e9 | −0.319812 | −0.159906 | − | 0.987132i | \(-0.551119\pi\) | ||||
−0.159906 | + | 0.987132i | \(0.551119\pi\) | |||||||
\(752\) | 1.93540e10 | 1.65962 | ||||||||
\(753\) | −1.29516e9 | −0.110546 | ||||||||
\(754\) | 2.74030e10 | 2.32808 | ||||||||
\(755\) | 6.61111e9 | 0.559062 | ||||||||
\(756\) | 2.95241e8 | 0.0248514 | ||||||||
\(757\) | 2.68089e9 | 0.224617 | 0.112309 | − | 0.993673i | \(-0.464175\pi\) | ||||
0.112309 | + | 0.993673i | \(0.464175\pi\) | |||||||
\(758\) | −1.45126e10 | −1.21032 | ||||||||
\(759\) | 4.44426e9 | 0.368938 | ||||||||
\(760\) | −6.56606e9 | −0.542572 | ||||||||
\(761\) | −8.48234e9 | −0.697701 | −0.348850 | − | 0.937178i | \(-0.613428\pi\) | ||||
−0.348850 | + | 0.937178i | \(0.613428\pi\) | |||||||
\(762\) | −1.05397e10 | −0.862953 | ||||||||
\(763\) | −2.81791e9 | −0.229663 | ||||||||
\(764\) | −1.84705e9 | −0.149849 | ||||||||
\(765\) | −1.61286e9 | −0.130251 | ||||||||
\(766\) | 1.57471e10 | 1.26590 | ||||||||
\(767\) | −2.92440e9 | −0.234020 | ||||||||
\(768\) | −8.96614e9 | −0.714235 | ||||||||
\(769\) | 4.34767e9 | 0.344758 | 0.172379 | − | 0.985031i | \(-0.444855\pi\) | ||||
0.172379 | + | 0.985031i | \(0.444855\pi\) | |||||||
\(770\) | −3.64861e9 | −0.288011 | ||||||||
\(771\) | −4.89461e9 | −0.384616 | ||||||||
\(772\) | −5.54376e9 | −0.433655 | ||||||||
\(773\) | −1.06536e10 | −0.829601 | −0.414800 | − | 0.909912i | \(-0.636149\pi\) | ||||
−0.414800 | + | 0.909912i | \(0.636149\pi\) | |||||||
\(774\) | 4.20929e9 | 0.326299 | ||||||||
\(775\) | −5.09633e8 | −0.0393280 | ||||||||
\(776\) | −4.43767e9 | −0.340910 | ||||||||
\(777\) | −3.05348e9 | −0.233518 | ||||||||
\(778\) | −3.08430e10 | −2.34816 | ||||||||
\(779\) | 1.03381e10 | 0.783537 | ||||||||
\(780\) | 4.10543e9 | 0.309762 | ||||||||
\(781\) | −1.32849e10 | −0.997886 | ||||||||
\(782\) | 4.24678e9 | 0.317567 | ||||||||
\(783\) | 2.69408e9 | 0.200560 | ||||||||
\(784\) | 1.58923e10 | 1.17783 | ||||||||
\(785\) | 1.07329e9 | 0.0791907 | ||||||||
\(786\) | −7.92965e9 | −0.582472 | ||||||||
\(787\) | 2.49085e9 | 0.182153 | 0.0910763 | − | 0.995844i | \(-0.470969\pi\) | ||||
0.0910763 | + | 0.995844i | \(0.470969\pi\) | |||||||
\(788\) | 4.66728e9 | 0.339799 | ||||||||
\(789\) | 5.41138e9 | 0.392228 | ||||||||
\(790\) | −2.72796e9 | −0.196853 | ||||||||
\(791\) | 1.86086e9 | 0.133689 | ||||||||
\(792\) | −4.70288e9 | −0.336376 | ||||||||
\(793\) | 9.38791e9 | 0.668517 | ||||||||
\(794\) | −2.64293e10 | −1.87376 | ||||||||
\(795\) | 6.44650e9 | 0.455029 | ||||||||
\(796\) | −3.81733e9 | −0.268265 | ||||||||
\(797\) | 6.71594e9 | 0.469897 | 0.234949 | − | 0.972008i | \(-0.424508\pi\) | ||||
0.234949 | + | 0.972008i | \(0.424508\pi\) | |||||||
\(798\) | 4.27104e9 | 0.297525 | ||||||||
\(799\) | 1.36674e10 | 0.947920 | ||||||||
\(800\) | 9.97712e9 | 0.688954 | ||||||||
\(801\) | −7.63977e9 | −0.525251 | ||||||||
\(802\) | 2.57036e10 | 1.75947 | ||||||||
\(803\) | 1.99439e10 | 1.35927 | ||||||||
\(804\) | 4.33362e9 | 0.294072 | ||||||||
\(805\) | 6.89766e8 | 0.0466033 | ||||||||
\(806\) | −1.86705e9 | −0.125598 | ||||||||
\(807\) | −7.09958e9 | −0.475527 | ||||||||
\(808\) | 6.56430e9 | 0.437773 | ||||||||
\(809\) | −5.26318e9 | −0.349485 | −0.174743 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174743 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(810\) | 1.14489e9 | 0.0756951 | ||||||||
\(811\) | 1.05418e10 | 0.693971 | 0.346985 | − | 0.937870i | \(-0.387205\pi\) | ||||
0.346985 | + | 0.937870i | \(0.387205\pi\) | |||||||
\(812\) | 2.05308e9 | 0.134573 | ||||||||
\(813\) | −9.97186e9 | −0.650818 | ||||||||
\(814\) | −5.81400e10 | −3.77824 | ||||||||
\(815\) | 7.89763e9 | 0.511029 | ||||||||
\(816\) | −7.97192e9 | −0.513626 | ||||||||
\(817\) | 2.14670e10 | 1.37719 | ||||||||
\(818\) | −2.88393e10 | −1.84225 | ||||||||
\(819\) | 2.23405e9 | 0.142102 | ||||||||
\(820\) | 2.11187e9 | 0.133757 | ||||||||
\(821\) | 2.59089e10 | 1.63399 | 0.816994 | − | 0.576646i | \(-0.195639\pi\) | ||||
0.816994 | + | 0.576646i | \(0.195639\pi\) | |||||||
\(822\) | 5.58068e9 | 0.350458 | ||||||||
\(823\) | −8.31491e9 | −0.519946 | −0.259973 | − | 0.965616i | \(-0.583714\pi\) | ||||
−0.259973 | + | 0.965616i | \(0.583714\pi\) | |||||||
\(824\) | −1.98036e9 | −0.123310 | ||||||||
\(825\) | 1.16112e10 | 0.719926 | ||||||||
\(826\) | −6.21497e8 | −0.0383715 | ||||||||
\(827\) | −6.36168e9 | −0.391113 | −0.195557 | − | 0.980692i | \(-0.562651\pi\) | ||||
−0.195557 | + | 0.980692i | \(0.562651\pi\) | |||||||
\(828\) | −1.06275e9 | −0.0650619 | ||||||||
\(829\) | −2.31191e10 | −1.40938 | −0.704692 | − | 0.709513i | \(-0.748915\pi\) | ||||
−0.704692 | + | 0.709513i | \(0.748915\pi\) | |||||||
\(830\) | 4.78815e9 | 0.290666 | ||||||||
\(831\) | 7.94646e9 | 0.480364 | ||||||||
\(832\) | −7.16467e8 | −0.0431285 | ||||||||
\(833\) | 1.12228e10 | 0.672737 | ||||||||
\(834\) | 1.28548e10 | 0.767333 | ||||||||
\(835\) | −1.34738e9 | −0.0800918 | ||||||||
\(836\) | 2.86695e10 | 1.69706 | ||||||||
\(837\) | −1.83556e8 | −0.0108200 | ||||||||
\(838\) | −1.50740e9 | −0.0884862 | ||||||||
\(839\) | 1.96736e10 | 1.15005 | 0.575026 | − | 0.818135i | \(-0.304992\pi\) | ||||
0.575026 | + | 0.818135i | \(0.304992\pi\) | |||||||
\(840\) | −7.29904e8 | −0.0424902 | ||||||||
\(841\) | 1.48448e9 | 0.0860574 | ||||||||
\(842\) | −3.95491e10 | −2.28320 | ||||||||
\(843\) | −1.17146e10 | −0.673489 | ||||||||
\(844\) | −4.50110e9 | −0.257703 | ||||||||
\(845\) | 2.14510e10 | 1.22306 | ||||||||
\(846\) | −9.70183e9 | −0.550880 | ||||||||
\(847\) | −9.13343e9 | −0.516466 | ||||||||
\(848\) | 3.18632e10 | 1.79434 | ||||||||
\(849\) | 2.19373e9 | 0.123029 | ||||||||
\(850\) | 1.10952e10 | 0.619684 | ||||||||
\(851\) | 1.09913e10 | 0.611359 | ||||||||
\(852\) | 3.17682e9 | 0.175976 | ||||||||
\(853\) | −2.05583e10 | −1.13413 | −0.567067 | − | 0.823671i | \(-0.691922\pi\) | ||||
−0.567067 | + | 0.823671i | \(0.691922\pi\) | |||||||
\(854\) | 1.99513e9 | 0.109614 | ||||||||
\(855\) | 5.83886e9 | 0.319482 | ||||||||
\(856\) | −1.23658e10 | −0.673852 | ||||||||
\(857\) | −1.22990e10 | −0.667476 | −0.333738 | − | 0.942666i | \(-0.608310\pi\) | ||||
−0.333738 | + | 0.942666i | \(0.608310\pi\) | |||||||
\(858\) | 4.25377e10 | 2.29916 | ||||||||
\(859\) | 6.11395e9 | 0.329114 | 0.164557 | − | 0.986368i | \(-0.447381\pi\) | ||||
0.164557 | + | 0.986368i | \(0.447381\pi\) | |||||||
\(860\) | 4.38528e9 | 0.235100 | ||||||||
\(861\) | 1.14922e9 | 0.0613608 | ||||||||
\(862\) | 2.29167e10 | 1.21864 | ||||||||
\(863\) | −5.85317e9 | −0.309994 | −0.154997 | − | 0.987915i | \(-0.549537\pi\) | ||||
−0.154997 | + | 0.987915i | \(0.549537\pi\) | |||||||
\(864\) | 3.59348e9 | 0.189547 | ||||||||
\(865\) | 8.46281e9 | 0.444589 | ||||||||
\(866\) | −1.16793e10 | −0.611087 | ||||||||
\(867\) | 5.44953e9 | 0.283983 | ||||||||
\(868\) | −1.39882e8 | −0.00726011 | ||||||||
\(869\) | −9.96458e9 | −0.515098 | ||||||||
\(870\) | 7.96148e9 | 0.409898 | ||||||||
\(871\) | 3.27919e10 | 1.68153 | ||||||||
\(872\) | −1.07336e10 | −0.548199 | ||||||||
\(873\) | 3.94619e9 | 0.200737 | ||||||||
\(874\) | −1.53741e10 | −0.778932 | ||||||||
\(875\) | 4.37835e9 | 0.220944 | ||||||||
\(876\) | −4.76917e9 | −0.239705 | ||||||||
\(877\) | −5.35250e9 | −0.267953 | −0.133976 | − | 0.990985i | \(-0.542775\pi\) | ||||
−0.133976 | + | 0.990985i | \(0.542775\pi\) | |||||||
\(878\) | 3.12686e10 | 1.55911 | ||||||||
\(879\) | 1.73469e10 | 0.861509 | ||||||||
\(880\) | −2.46539e10 | −1.21954 | ||||||||
\(881\) | −9.28115e9 | −0.457284 | −0.228642 | − | 0.973511i | \(-0.573429\pi\) | ||||
−0.228642 | + | 0.973511i | \(0.573429\pi\) | |||||||
\(882\) | −7.96656e9 | −0.390959 | ||||||||
\(883\) | −1.19702e10 | −0.585114 | −0.292557 | − | 0.956248i | \(-0.594506\pi\) | ||||
−0.292557 | + | 0.956248i | \(0.594506\pi\) | |||||||
\(884\) | 1.43298e10 | 0.697680 | ||||||||
\(885\) | −8.49635e8 | −0.0412032 | ||||||||
\(886\) | 1.82804e10 | 0.883012 | ||||||||
\(887\) | 2.48052e10 | 1.19347 | 0.596734 | − | 0.802439i | \(-0.296465\pi\) | ||||
0.596734 | + | 0.802439i | \(0.296465\pi\) | |||||||
\(888\) | −1.16309e10 | −0.557402 | ||||||||
\(889\) | −5.97521e9 | −0.285231 | ||||||||
\(890\) | −2.25769e10 | −1.07349 | ||||||||
\(891\) | 4.18202e9 | 0.198068 | ||||||||
\(892\) | −1.40799e10 | −0.664237 | ||||||||
\(893\) | −4.94784e10 | −2.32507 | ||||||||
\(894\) | 1.33775e10 | 0.626173 | ||||||||
\(895\) | 1.74917e10 | 0.815552 | ||||||||
\(896\) | −5.18169e9 | −0.240654 | ||||||||
\(897\) | −8.04173e9 | −0.372028 | ||||||||
\(898\) | 1.99493e10 | 0.919306 | ||||||||
\(899\) | −1.27643e9 | −0.0585918 | ||||||||
\(900\) | −2.77658e9 | −0.126958 | ||||||||
\(901\) | 2.25012e10 | 1.02487 | ||||||||
\(902\) | 2.18818e10 | 0.992794 | ||||||||
\(903\) | 2.38634e9 | 0.107851 | ||||||||
\(904\) | 7.08816e9 | 0.319113 | ||||||||
\(905\) | 1.14171e9 | 0.0512018 | ||||||||
\(906\) | −1.63803e10 | −0.731769 | ||||||||
\(907\) | 9.90452e9 | 0.440766 | 0.220383 | − | 0.975413i | \(-0.429269\pi\) | ||||
0.220383 | + | 0.975413i | \(0.429269\pi\) | |||||||
\(908\) | −1.92448e10 | −0.853127 | ||||||||
\(909\) | −5.83730e9 | −0.257773 | ||||||||
\(910\) | 6.60202e9 | 0.290424 | ||||||||
\(911\) | −8.15910e8 | −0.0357543 | −0.0178771 | − | 0.999840i | \(-0.505691\pi\) | ||||
−0.0178771 | + | 0.999840i | \(0.505691\pi\) | |||||||
\(912\) | 2.88598e10 | 1.25983 | ||||||||
\(913\) | 1.74899e10 | 0.760573 | ||||||||
\(914\) | −3.24559e10 | −1.40599 | ||||||||
\(915\) | 2.72750e9 | 0.117704 | ||||||||
\(916\) | −9.76871e9 | −0.419955 | ||||||||
\(917\) | −4.49549e9 | −0.192524 | ||||||||
\(918\) | 3.99619e9 | 0.170489 | ||||||||
\(919\) | −3.65375e9 | −0.155287 | −0.0776434 | − | 0.996981i | \(-0.524740\pi\) | ||||
−0.0776434 | + | 0.996981i | \(0.524740\pi\) | |||||||
\(920\) | 2.62737e9 | 0.111241 | ||||||||
\(921\) | 1.87278e10 | 0.789912 | ||||||||
\(922\) | −3.73830e9 | −0.157078 | ||||||||
\(923\) | 2.40386e10 | 1.00624 | ||||||||
\(924\) | 3.18699e9 | 0.132901 | ||||||||
\(925\) | 2.87162e10 | 1.19297 | ||||||||
\(926\) | −2.48587e10 | −1.02882 | ||||||||
\(927\) | 1.76103e9 | 0.0726087 | ||||||||
\(928\) | 2.49886e10 | 1.02642 | ||||||||
\(929\) | 3.46180e10 | 1.41660 | 0.708299 | − | 0.705913i | \(-0.249463\pi\) | ||||
0.708299 | + | 0.705913i | \(0.249463\pi\) | |||||||
\(930\) | −5.42438e8 | −0.0221136 | ||||||||
\(931\) | −4.06287e10 | −1.65010 | ||||||||
\(932\) | 6.04465e9 | 0.244577 | ||||||||
\(933\) | 5.04155e9 | 0.203226 | ||||||||
\(934\) | 5.25869e10 | 2.11185 | ||||||||
\(935\) | −1.74101e10 | −0.696564 | ||||||||
\(936\) | 8.50968e9 | 0.339194 | ||||||||
\(937\) | −1.64978e10 | −0.655143 | −0.327572 | − | 0.944826i | \(-0.606230\pi\) | ||||
−0.327572 | + | 0.944826i | \(0.606230\pi\) | |||||||
\(938\) | 6.96897e9 | 0.275714 | ||||||||
\(939\) | −1.21620e10 | −0.479376 | ||||||||
\(940\) | −1.01075e10 | −0.396912 | ||||||||
\(941\) | −2.07806e10 | −0.813009 | −0.406504 | − | 0.913649i | \(-0.633252\pi\) | ||||
−0.406504 | + | 0.913649i | \(0.633252\pi\) | |||||||
\(942\) | −2.65930e9 | −0.103655 | ||||||||
\(943\) | −4.13673e9 | −0.160645 | ||||||||
\(944\) | −4.19950e9 | −0.162478 | ||||||||
\(945\) | 6.49066e8 | 0.0250195 | ||||||||
\(946\) | 4.54373e10 | 1.74499 | ||||||||
\(947\) | −3.39662e10 | −1.29964 | −0.649818 | − | 0.760090i | \(-0.725155\pi\) | ||||
−0.649818 | + | 0.760090i | \(0.725155\pi\) | |||||||
\(948\) | 2.38282e9 | 0.0908370 | ||||||||
\(949\) | −3.60877e10 | −1.37065 | ||||||||
\(950\) | −4.01668e10 | −1.51997 | ||||||||
\(951\) | 1.07242e10 | 0.404329 | ||||||||
\(952\) | −2.54769e9 | −0.0957012 | ||||||||
\(953\) | 1.25066e9 | 0.0468074 | 0.0234037 | − | 0.999726i | \(-0.492550\pi\) | ||||
0.0234037 | + | 0.999726i | \(0.492550\pi\) | |||||||
\(954\) | −1.59725e10 | −0.595599 | ||||||||
\(955\) | −4.06061e9 | −0.150862 | ||||||||
\(956\) | 1.55174e10 | 0.574404 | ||||||||
\(957\) | 2.90814e10 | 1.07256 | ||||||||
\(958\) | −6.31369e9 | −0.232008 | ||||||||
\(959\) | 3.16381e9 | 0.115837 | ||||||||
\(960\) | −2.08157e8 | −0.00759351 | ||||||||
\(961\) | −2.74256e10 | −0.996839 | ||||||||
\(962\) | 1.05202e11 | 3.80989 | ||||||||
\(963\) | 1.09963e10 | 0.396784 | ||||||||
\(964\) | 2.98154e10 | 1.07194 | ||||||||
\(965\) | −1.21876e10 | −0.436587 | ||||||||
\(966\) | −1.70903e9 | −0.0610001 | ||||||||
\(967\) | 1.99659e10 | 0.710063 | 0.355032 | − | 0.934854i | \(-0.384470\pi\) | ||||
0.355032 | + | 0.934854i | \(0.384470\pi\) | |||||||
\(968\) | −3.47899e10 | −1.23279 | ||||||||
\(969\) | 2.03802e10 | 0.719574 | ||||||||
\(970\) | 1.16617e10 | 0.410261 | ||||||||
\(971\) | −5.02413e10 | −1.76114 | −0.880569 | − | 0.473919i | \(-0.842839\pi\) | ||||
−0.880569 | + | 0.473919i | \(0.842839\pi\) | |||||||
\(972\) | −1.00005e9 | −0.0349291 | ||||||||
\(973\) | 7.28767e9 | 0.253626 | ||||||||
\(974\) | −4.35459e10 | −1.51005 | ||||||||
\(975\) | −2.10100e10 | −0.725956 | ||||||||
\(976\) | 1.34812e10 | 0.464146 | ||||||||
\(977\) | −5.76202e10 | −1.97671 | −0.988357 | − | 0.152155i | \(-0.951379\pi\) | ||||
−0.988357 | + | 0.152155i | \(0.951379\pi\) | |||||||
\(978\) | −1.95680e10 | −0.668898 | ||||||||
\(979\) | −8.24678e10 | −2.80896 | ||||||||
\(980\) | −8.29964e9 | −0.281688 | ||||||||
\(981\) | 9.54485e9 | 0.322795 | ||||||||
\(982\) | −3.02974e10 | −1.02097 | ||||||||
\(983\) | 1.60520e10 | 0.539003 | 0.269502 | − | 0.963000i | \(-0.413141\pi\) | ||||
0.269502 | + | 0.963000i | \(0.413141\pi\) | |||||||
\(984\) | 4.37745e9 | 0.146466 | ||||||||
\(985\) | 1.02607e10 | 0.342096 | ||||||||
\(986\) | 2.77891e10 | 0.923220 | ||||||||
\(987\) | −5.50018e9 | −0.182082 | ||||||||
\(988\) | −5.18764e10 | −1.71128 | ||||||||
\(989\) | −8.58989e9 | −0.282358 | ||||||||
\(990\) | 1.23586e10 | 0.404805 | ||||||||
\(991\) | −8.99460e9 | −0.293578 | −0.146789 | − | 0.989168i | \(-0.546894\pi\) | ||||
−0.146789 | + | 0.989168i | \(0.546894\pi\) | |||||||
\(992\) | −1.70255e9 | −0.0553744 | ||||||||
\(993\) | 2.06738e10 | 0.670034 | ||||||||
\(994\) | 5.10870e9 | 0.164990 | ||||||||
\(995\) | −8.39212e9 | −0.270079 | ||||||||
\(996\) | −4.18236e9 | −0.134126 | ||||||||
\(997\) | 1.62638e9 | 0.0519744 | 0.0259872 | − | 0.999662i | \(-0.491727\pi\) | ||||
0.0259872 | + | 0.999662i | \(0.491727\pi\) | |||||||
\(998\) | 7.18794e10 | 2.28901 | ||||||||
\(999\) | 1.03428e10 | 0.328214 |
(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.1.13 | ✓ | 16 | |
3.2 | odd | 2 | 531.8.a.b.1.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.13 | ✓ | 16 | 1.1 | even | 1 | trivial | |
531.8.a.b.1.4 | 16 | 3.2 | odd | 2 |