Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.4252 | 0.946871 | 0.473435 | − | 0.880829i | \(-0.343014\pi\) | ||||
0.473435 | + | 0.880829i | \(0.343014\pi\) | |||||||
\(3\) | 32.0790 | 0.228652 | 0.114326 | − | 0.993443i | \(-0.463529\pi\) | ||||
0.114326 | + | 0.993443i | \(0.463529\pi\) | |||||||
\(4\) | −52.9591 | −0.103436 | ||||||||
\(5\) | 1493.58 | 1.06872 | 0.534359 | − | 0.845258i | \(-0.320553\pi\) | ||||
0.534359 | + | 0.845258i | \(0.320553\pi\) | |||||||
\(6\) | 687.300 | 0.216504 | ||||||||
\(7\) | 1220.42 | 0.192118 | 0.0960590 | − | 0.995376i | \(-0.469376\pi\) | ||||
0.0960590 | + | 0.995376i | \(0.469376\pi\) | |||||||
\(8\) | −12104.4 | −1.04481 | ||||||||
\(9\) | −18653.9 | −0.947718 | ||||||||
\(10\) | 32000.3 | 1.01194 | ||||||||
\(11\) | −59934.7 | −1.23427 | −0.617137 | − | 0.786856i | \(-0.711707\pi\) | ||||
−0.617137 | + | 0.786856i | \(0.711707\pi\) | |||||||
\(12\) | −1698.87 | −0.0236508 | ||||||||
\(13\) | 143048. | 1.38911 | 0.694554 | − | 0.719440i | \(-0.255602\pi\) | ||||
0.694554 | + | 0.719440i | \(0.255602\pi\) | |||||||
\(14\) | 26147.8 | 0.181911 | ||||||||
\(15\) | 47912.5 | 0.244364 | ||||||||
\(16\) | −232224. | −0.885865 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −399665. | −0.897367 | ||||||||
\(19\) | 897999. | 1.58083 | 0.790414 | − | 0.612573i | \(-0.209865\pi\) | ||||
0.790414 | + | 0.612573i | \(0.209865\pi\) | |||||||
\(20\) | −79098.5 | −0.110544 | ||||||||
\(21\) | 39149.8 | 0.0439282 | ||||||||
\(22\) | −1.28412e6 | −1.16870 | ||||||||
\(23\) | 1.66346e6 | 1.23947 | 0.619737 | − | 0.784810i | \(-0.287239\pi\) | ||||
0.619737 | + | 0.784810i | \(0.287239\pi\) | |||||||
\(24\) | −388297. | −0.238898 | ||||||||
\(25\) | 277651. | 0.142157 | ||||||||
\(26\) | 3.06483e6 | 1.31531 | ||||||||
\(27\) | −1.22981e6 | −0.445350 | ||||||||
\(28\) | −64632.3 | −0.0198719 | ||||||||
\(29\) | −4.05562e6 | −1.06480 | −0.532398 | − | 0.846494i | \(-0.678709\pi\) | ||||
−0.532398 | + | 0.846494i | \(0.678709\pi\) | |||||||
\(30\) | 1.02654e6 | 0.231382 | ||||||||
\(31\) | 488005. | 0.0949066 | 0.0474533 | − | 0.998873i | \(-0.484889\pi\) | ||||
0.0474533 | + | 0.998873i | \(0.484889\pi\) | |||||||
\(32\) | 1.22198e6 | 0.206011 | ||||||||
\(33\) | −1.92265e6 | −0.282219 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.82279e6 | 0.205320 | ||||||||
\(36\) | 987895. | 0.0980279 | ||||||||
\(37\) | −9.68561e6 | −0.849610 | −0.424805 | − | 0.905285i | \(-0.639657\pi\) | ||||
−0.424805 | + | 0.905285i | \(0.639657\pi\) | |||||||
\(38\) | 1.92399e7 | 1.49684 | ||||||||
\(39\) | 4.58883e6 | 0.317623 | ||||||||
\(40\) | −1.80788e7 | −1.11661 | ||||||||
\(41\) | −1.69156e7 | −0.934888 | −0.467444 | − | 0.884023i | \(-0.654825\pi\) | ||||
−0.467444 | + | 0.884023i | \(0.654825\pi\) | |||||||
\(42\) | 838795. | 0.0415943 | ||||||||
\(43\) | 6.52450e6 | 0.291031 | 0.145516 | − | 0.989356i | \(-0.453516\pi\) | ||||
0.145516 | + | 0.989356i | \(0.453516\pi\) | |||||||
\(44\) | 3.17409e6 | 0.127668 | ||||||||
\(45\) | −2.78611e7 | −1.01284 | ||||||||
\(46\) | 3.56400e7 | 1.17362 | ||||||||
\(47\) | −5.90622e7 | −1.76551 | −0.882753 | − | 0.469838i | \(-0.844312\pi\) | ||||
−0.882753 | + | 0.469838i | \(0.844312\pi\) | |||||||
\(48\) | −7.44952e6 | −0.202555 | ||||||||
\(49\) | −3.88642e7 | −0.963091 | ||||||||
\(50\) | 5.94873e6 | 0.134604 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.57568e6 | −0.143683 | ||||||||
\(53\) | −1.27513e7 | −0.221980 | −0.110990 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110990 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(54\) | −2.63490e7 | −0.421689 | ||||||||
\(55\) | −8.95172e7 | −1.31909 | ||||||||
\(56\) | −1.47724e7 | −0.200727 | ||||||||
\(57\) | 2.88069e7 | 0.361460 | ||||||||
\(58\) | −8.68927e7 | −1.00822 | ||||||||
\(59\) | −4.63714e7 | −0.498215 | −0.249107 | − | 0.968476i | \(-0.580137\pi\) | ||||
−0.249107 | + | 0.968476i | \(0.580137\pi\) | |||||||
\(60\) | −2.53740e6 | −0.0252760 | ||||||||
\(61\) | −4.21412e7 | −0.389693 | −0.194847 | − | 0.980834i | \(-0.562421\pi\) | ||||
−0.194847 | + | 0.980834i | \(0.562421\pi\) | |||||||
\(62\) | 1.04556e7 | 0.0898643 | ||||||||
\(63\) | −2.27656e7 | −0.182074 | ||||||||
\(64\) | 1.45080e8 | 1.08093 | ||||||||
\(65\) | 2.13653e8 | 1.48456 | ||||||||
\(66\) | −4.11931e7 | −0.267225 | ||||||||
\(67\) | −2.39406e8 | −1.45144 | −0.725719 | − | 0.687991i | \(-0.758493\pi\) | ||||
−0.725719 | + | 0.687991i | \(0.758493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.33622e7 | 0.283408 | ||||||||
\(70\) | 3.90538e7 | 0.194411 | ||||||||
\(71\) | 5.23949e7 | 0.244696 | 0.122348 | − | 0.992487i | \(-0.460958\pi\) | ||||
0.122348 | + | 0.992487i | \(0.460958\pi\) | |||||||
\(72\) | 2.25794e8 | 0.990186 | ||||||||
\(73\) | 1.27072e8 | 0.523719 | 0.261860 | − | 0.965106i | \(-0.415664\pi\) | ||||
0.261860 | + | 0.965106i | \(0.415664\pi\) | |||||||
\(74\) | −2.07517e8 | −0.804470 | ||||||||
\(75\) | 8.90675e6 | 0.0325045 | ||||||||
\(76\) | −4.75572e7 | −0.163514 | ||||||||
\(77\) | −7.31455e7 | −0.237126 | ||||||||
\(78\) | 9.83168e7 | 0.300748 | ||||||||
\(79\) | 1.16128e8 | 0.335439 | 0.167720 | − | 0.985835i | \(-0.446360\pi\) | ||||
0.167720 | + | 0.985835i | \(0.446360\pi\) | |||||||
\(80\) | −3.46845e8 | −0.946740 | ||||||||
\(81\) | 3.27714e8 | 0.845888 | ||||||||
\(82\) | −3.62420e8 | −0.885218 | ||||||||
\(83\) | 3.57245e8 | 0.826257 | 0.413128 | − | 0.910673i | \(-0.364436\pi\) | ||||
0.413128 | + | 0.910673i | \(0.364436\pi\) | |||||||
\(84\) | −2.07334e6 | −0.00454374 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.39789e8 | 0.275569 | ||||||||
\(87\) | −1.30100e8 | −0.243468 | ||||||||
\(88\) | 7.25473e8 | 1.28958 | ||||||||
\(89\) | −4.24226e8 | −0.716708 | −0.358354 | − | 0.933586i | \(-0.616662\pi\) | ||||
−0.358354 | + | 0.933586i | \(0.616662\pi\) | |||||||
\(90\) | −5.96931e8 | −0.959032 | ||||||||
\(91\) | 1.74578e8 | 0.266873 | ||||||||
\(92\) | −8.80954e7 | −0.128206 | ||||||||
\(93\) | 1.56547e7 | 0.0217006 | ||||||||
\(94\) | −1.26542e9 | −1.67171 | ||||||||
\(95\) | 1.34123e9 | 1.68946 | ||||||||
\(96\) | 3.92000e7 | 0.0471048 | ||||||||
\(97\) | −8.27894e8 | −0.949515 | −0.474757 | − | 0.880117i | \(-0.657464\pi\) | ||||
−0.474757 | + | 0.880117i | \(0.657464\pi\) | |||||||
\(98\) | −8.32674e8 | −0.911922 | ||||||||
\(99\) | 1.11802e9 | 1.16974 | ||||||||
\(100\) | −1.47041e7 | −0.0147041 | ||||||||
\(101\) | −1.39180e9 | −1.33085 | −0.665425 | − | 0.746465i | \(-0.731750\pi\) | ||||
−0.665425 | + | 0.746465i | \(0.731750\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.58618e8 | −0.138862 | −0.0694310 | − | 0.997587i | \(-0.522118\pi\) | ||||
−0.0694310 | + | 0.997587i | \(0.522118\pi\) | |||||||
\(104\) | −1.73151e9 | −1.45136 | ||||||||
\(105\) | 5.84733e7 | 0.0469468 | ||||||||
\(106\) | −2.73200e8 | −0.210186 | ||||||||
\(107\) | 2.29686e9 | 1.69398 | 0.846988 | − | 0.531612i | \(-0.178413\pi\) | ||||
0.846988 | + | 0.531612i | \(0.178413\pi\) | |||||||
\(108\) | 6.51296e7 | 0.0460651 | ||||||||
\(109\) | −2.49735e9 | −1.69457 | −0.847286 | − | 0.531136i | \(-0.821765\pi\) | ||||
−0.847286 | + | 0.531136i | \(0.821765\pi\) | |||||||
\(110\) | −1.91793e9 | −1.24901 | ||||||||
\(111\) | −3.10705e8 | −0.194265 | ||||||||
\(112\) | −2.83411e8 | −0.170191 | ||||||||
\(113\) | −1.12193e9 | −0.647310 | −0.323655 | − | 0.946175i | \(-0.604912\pi\) | ||||
−0.323655 | + | 0.946175i | \(0.604912\pi\) | |||||||
\(114\) | 6.17195e8 | 0.342256 | ||||||||
\(115\) | 2.48451e9 | 1.32465 | ||||||||
\(116\) | 2.14782e8 | 0.110138 | ||||||||
\(117\) | −2.66841e9 | −1.31648 | ||||||||
\(118\) | −9.93519e8 | −0.471745 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.79951e8 | −0.255315 | ||||||||
\(121\) | 1.23422e9 | 0.523430 | ||||||||
\(122\) | −9.02886e8 | −0.368989 | ||||||||
\(123\) | −5.42635e8 | −0.213764 | ||||||||
\(124\) | −2.58443e7 | −0.00981674 | ||||||||
\(125\) | −2.50245e9 | −0.916792 | ||||||||
\(126\) | −4.87759e8 | −0.172400 | ||||||||
\(127\) | −1.24547e9 | −0.424830 | −0.212415 | − | 0.977180i | \(-0.568133\pi\) | ||||
−0.212415 | + | 0.977180i | \(0.568133\pi\) | |||||||
\(128\) | 2.48272e9 | 0.817491 | ||||||||
\(129\) | 2.09300e8 | 0.0665449 | ||||||||
\(130\) | 4.57757e9 | 1.40569 | ||||||||
\(131\) | −4.12512e9 | −1.22382 | −0.611908 | − | 0.790929i | \(-0.709598\pi\) | ||||
−0.611908 | + | 0.790929i | \(0.709598\pi\) | |||||||
\(132\) | 1.01822e8 | 0.0291915 | ||||||||
\(133\) | 1.09594e9 | 0.303706 | ||||||||
\(134\) | −5.12934e9 | −1.37433 | ||||||||
\(135\) | −1.83682e9 | −0.475953 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.46624e9 | −0.355600 | −0.177800 | − | 0.984067i | \(-0.556898\pi\) | ||||
−0.177800 | + | 0.984067i | \(0.556898\pi\) | |||||||
\(138\) | 1.14330e9 | 0.268351 | ||||||||
\(139\) | −2.87070e8 | −0.0652262 | −0.0326131 | − | 0.999468i | \(-0.510383\pi\) | ||||
−0.0326131 | + | 0.999468i | \(0.510383\pi\) | |||||||
\(140\) | −9.65334e7 | −0.0212374 | ||||||||
\(141\) | −1.89466e9 | −0.403686 | ||||||||
\(142\) | 1.12257e9 | 0.231695 | ||||||||
\(143\) | −8.57353e9 | −1.71454 | ||||||||
\(144\) | 4.33190e9 | 0.839551 | ||||||||
\(145\) | −6.05739e9 | −1.13797 | ||||||||
\(146\) | 2.72256e9 | 0.495895 | ||||||||
\(147\) | −1.24672e9 | −0.220213 | ||||||||
\(148\) | 5.12941e8 | 0.0878800 | ||||||||
\(149\) | −9.99209e9 | −1.66080 | −0.830401 | − | 0.557166i | \(-0.811889\pi\) | ||||
−0.830401 | + | 0.557166i | \(0.811889\pi\) | |||||||
\(150\) | 1.90829e8 | 0.0307776 | ||||||||
\(151\) | −1.36824e9 | −0.214174 | −0.107087 | − | 0.994250i | \(-0.534152\pi\) | ||||
−0.107087 | + | 0.994250i | \(0.534152\pi\) | |||||||
\(152\) | −1.08697e10 | −1.65167 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.56716e9 | −0.224528 | ||||||||
\(155\) | 7.28874e8 | 0.101428 | ||||||||
\(156\) | −2.43020e8 | −0.0328535 | ||||||||
\(157\) | 1.80109e9 | 0.236585 | 0.118293 | − | 0.992979i | \(-0.462258\pi\) | ||||
0.118293 | + | 0.992979i | \(0.462258\pi\) | |||||||
\(158\) | 2.48806e9 | 0.317618 | ||||||||
\(159\) | −4.09050e8 | −0.0507562 | ||||||||
\(160\) | 1.82513e9 | 0.220168 | ||||||||
\(161\) | 2.03012e9 | 0.238125 | ||||||||
\(162\) | 7.02136e9 | 0.800947 | ||||||||
\(163\) | 1.09895e10 | 1.21936 | 0.609681 | − | 0.792647i | \(-0.291298\pi\) | ||||
0.609681 | + | 0.792647i | \(0.291298\pi\) | |||||||
\(164\) | 8.95833e8 | 0.0967007 | ||||||||
\(165\) | −2.87162e9 | −0.301612 | ||||||||
\(166\) | 7.65406e9 | 0.782358 | ||||||||
\(167\) | −1.13053e10 | −1.12476 | −0.562378 | − | 0.826880i | \(-0.690113\pi\) | ||||
−0.562378 | + | 0.826880i | \(0.690113\pi\) | |||||||
\(168\) | −4.73885e8 | −0.0458966 | ||||||||
\(169\) | 9.85818e9 | 0.929623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.67512e10 | −1.49818 | ||||||||
\(172\) | −3.45532e8 | −0.0301030 | ||||||||
\(173\) | 1.48170e10 | 1.25763 | 0.628817 | − | 0.777553i | \(-0.283540\pi\) | ||||
0.628817 | + | 0.777553i | \(0.283540\pi\) | |||||||
\(174\) | −2.78743e9 | −0.230533 | ||||||||
\(175\) | 3.38850e8 | 0.0273109 | ||||||||
\(176\) | 1.39183e10 | 1.09340 | ||||||||
\(177\) | −1.48755e9 | −0.113918 | ||||||||
\(178\) | −9.08914e9 | −0.678630 | ||||||||
\(179\) | 7.88618e9 | 0.574154 | 0.287077 | − | 0.957908i | \(-0.407316\pi\) | ||||
0.287077 | + | 0.957908i | \(0.407316\pi\) | |||||||
\(180\) | 1.47550e9 | 0.104764 | ||||||||
\(181\) | 2.24536e10 | 1.55501 | 0.777505 | − | 0.628877i | \(-0.216485\pi\) | ||||
0.777505 | + | 0.628877i | \(0.216485\pi\) | |||||||
\(182\) | 3.74038e9 | 0.252694 | ||||||||
\(183\) | −1.35185e9 | −0.0891042 | ||||||||
\(184\) | −2.01352e10 | −1.29502 | ||||||||
\(185\) | −1.44662e10 | −0.907993 | ||||||||
\(186\) | 3.35406e8 | 0.0205477 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.12788e9 | 0.182616 | ||||||||
\(189\) | −1.50088e9 | −0.0855597 | ||||||||
\(190\) | 2.87362e10 | 1.59970 | ||||||||
\(191\) | −1.62873e10 | −0.885519 | −0.442759 | − | 0.896640i | \(-0.646000\pi\) | ||||
−0.442759 | + | 0.896640i | \(0.646000\pi\) | |||||||
\(192\) | 4.65402e9 | 0.247157 | ||||||||
\(193\) | −5.10953e9 | −0.265078 | −0.132539 | − | 0.991178i | \(-0.542313\pi\) | ||||
−0.132539 | + | 0.991178i | \(0.542313\pi\) | |||||||
\(194\) | −1.77378e10 | −0.899068 | ||||||||
\(195\) | 6.85378e9 | 0.339449 | ||||||||
\(196\) | 2.05821e9 | 0.0996180 | ||||||||
\(197\) | −2.46354e10 | −1.16536 | −0.582681 | − | 0.812701i | \(-0.697996\pi\) | ||||
−0.582681 | + | 0.812701i | \(0.697996\pi\) | |||||||
\(198\) | 2.39538e10 | 1.10760 | ||||||||
\(199\) | −1.69660e10 | −0.766901 | −0.383451 | − | 0.923561i | \(-0.625264\pi\) | ||||
−0.383451 | + | 0.923561i | \(0.625264\pi\) | |||||||
\(200\) | −3.36079e9 | −0.148527 | ||||||||
\(201\) | −7.67991e9 | −0.331875 | ||||||||
\(202\) | −2.98196e10 | −1.26014 | ||||||||
\(203\) | −4.94956e9 | −0.204567 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.52647e10 | −0.999131 | ||||||||
\(206\) | −3.39842e9 | −0.131484 | ||||||||
\(207\) | −3.10301e10 | −1.17467 | ||||||||
\(208\) | −3.32192e10 | −1.23056 | ||||||||
\(209\) | −5.38213e10 | −1.95117 | ||||||||
\(210\) | 1.25281e9 | 0.0444526 | ||||||||
\(211\) | 3.36381e10 | 1.16832 | 0.584158 | − | 0.811640i | \(-0.301425\pi\) | ||||
0.584158 | + | 0.811640i | \(0.301425\pi\) | |||||||
\(212\) | 6.75298e8 | 0.0229607 | ||||||||
\(213\) | 1.68078e9 | 0.0559502 | ||||||||
\(214\) | 4.92108e10 | 1.60398 | ||||||||
\(215\) | 9.74486e9 | 0.311030 | ||||||||
\(216\) | 1.48861e10 | 0.465306 | ||||||||
\(217\) | 5.95571e8 | 0.0182333 | ||||||||
\(218\) | −5.35063e10 | −1.60454 | ||||||||
\(219\) | 4.07636e9 | 0.119750 | ||||||||
\(220\) | 4.74075e9 | 0.136441 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.65692e9 | −0.183944 | ||||||||
\(223\) | 6.63366e10 | 1.79631 | 0.898155 | − | 0.439679i | \(-0.144908\pi\) | ||||
0.898155 | + | 0.439679i | \(0.144908\pi\) | |||||||
\(224\) | 1.49133e9 | 0.0395784 | ||||||||
\(225\) | −5.17928e9 | −0.134725 | ||||||||
\(226\) | −2.40376e10 | −0.612919 | ||||||||
\(227\) | −1.14996e10 | −0.287453 | −0.143727 | − | 0.989617i | \(-0.545909\pi\) | ||||
−0.143727 | + | 0.989617i | \(0.545909\pi\) | |||||||
\(228\) | −1.52559e9 | −0.0373878 | ||||||||
\(229\) | 3.93654e10 | 0.945920 | 0.472960 | − | 0.881084i | \(-0.343185\pi\) | ||||
0.472960 | + | 0.881084i | \(0.343185\pi\) | |||||||
\(230\) | 5.32312e10 | 1.25427 | ||||||||
\(231\) | −2.34643e9 | −0.0542194 | ||||||||
\(232\) | 4.90908e10 | 1.11251 | ||||||||
\(233\) | 4.79673e10 | 1.06621 | 0.533106 | − | 0.846049i | \(-0.321025\pi\) | ||||
0.533106 | + | 0.846049i | \(0.321025\pi\) | |||||||
\(234\) | −5.71712e10 | −1.24654 | ||||||||
\(235\) | −8.82140e10 | −1.88683 | ||||||||
\(236\) | 2.45579e9 | 0.0515332 | ||||||||
\(237\) | 3.72526e9 | 0.0766989 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.89651e10 | −1.76372 | −0.881859 | − | 0.471513i | \(-0.843708\pi\) | ||||
−0.881859 | + | 0.471513i | \(0.843708\pi\) | |||||||
\(240\) | −1.11264e10 | −0.216474 | ||||||||
\(241\) | 7.98752e10 | 1.52523 | 0.762615 | − | 0.646852i | \(-0.223915\pi\) | ||||
0.762615 | + | 0.646852i | \(0.223915\pi\) | |||||||
\(242\) | 2.64435e10 | 0.495621 | ||||||||
\(243\) | 3.47191e10 | 0.638764 | ||||||||
\(244\) | 2.23176e9 | 0.0403082 | ||||||||
\(245\) | −5.80467e10 | −1.02927 | ||||||||
\(246\) | −1.16261e10 | −0.202407 | ||||||||
\(247\) | 1.28457e11 | 2.19594 | ||||||||
\(248\) | −5.90700e9 | −0.0991595 | ||||||||
\(249\) | 1.14601e10 | 0.188925 | ||||||||
\(250\) | −5.36156e10 | −0.868083 | ||||||||
\(251\) | −8.42255e10 | −1.33941 | −0.669703 | − | 0.742629i | \(-0.733578\pi\) | ||||
−0.669703 | + | 0.742629i | \(0.733578\pi\) | |||||||
\(252\) | 1.20565e9 | 0.0188329 | ||||||||
\(253\) | −9.96990e10 | −1.52985 | ||||||||
\(254\) | −2.66844e10 | −0.402259 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.10881e10 | −0.306873 | ||||||||
\(257\) | 5.40709e10 | 0.773152 | 0.386576 | − | 0.922258i | \(-0.373658\pi\) | ||||
0.386576 | + | 0.922258i | \(0.373658\pi\) | |||||||
\(258\) | 4.48429e9 | 0.0630094 | ||||||||
\(259\) | −1.18205e10 | −0.163225 | ||||||||
\(260\) | −1.13149e10 | −0.153557 | ||||||||
\(261\) | 7.56534e10 | 1.00913 | ||||||||
\(262\) | −8.83818e10 | −1.15880 | ||||||||
\(263\) | −1.90882e10 | −0.246017 | −0.123008 | − | 0.992406i | \(-0.539254\pi\) | ||||
−0.123008 | + | 0.992406i | \(0.539254\pi\) | |||||||
\(264\) | 2.32724e10 | 0.294866 | ||||||||
\(265\) | −1.90451e10 | −0.237234 | ||||||||
\(266\) | 2.34807e10 | 0.287570 | ||||||||
\(267\) | −1.36087e10 | −0.163877 | ||||||||
\(268\) | 1.26787e10 | 0.150131 | ||||||||
\(269\) | 3.26919e10 | 0.380676 | 0.190338 | − | 0.981719i | \(-0.439042\pi\) | ||||
0.190338 | + | 0.981719i | \(0.439042\pi\) | |||||||
\(270\) | −3.93543e10 | −0.450666 | ||||||||
\(271\) | −4.55819e10 | −0.513370 | −0.256685 | − | 0.966495i | \(-0.582630\pi\) | ||||
−0.256685 | + | 0.966495i | \(0.582630\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.60030e9 | 0.0610210 | ||||||||
\(274\) | −3.14145e10 | −0.336707 | ||||||||
\(275\) | −1.66409e10 | −0.175461 | ||||||||
\(276\) | −2.82601e9 | −0.0293145 | ||||||||
\(277\) | −1.11315e10 | −0.113604 | −0.0568022 | − | 0.998385i | \(-0.518090\pi\) | ||||
−0.0568022 | + | 0.998385i | \(0.518090\pi\) | |||||||
\(278\) | −6.15055e9 | −0.0617607 | ||||||||
\(279\) | −9.10321e9 | −0.0899448 | ||||||||
\(280\) | −2.20638e10 | −0.214520 | ||||||||
\(281\) | −3.07136e10 | −0.293868 | −0.146934 | − | 0.989146i | \(-0.546940\pi\) | ||||
−0.146934 | + | 0.989146i | \(0.546940\pi\) | |||||||
\(282\) | −4.05934e10 | −0.382239 | ||||||||
\(283\) | 4.97422e10 | 0.460984 | 0.230492 | − | 0.973074i | \(-0.425966\pi\) | ||||
0.230492 | + | 0.973074i | \(0.425966\pi\) | |||||||
\(284\) | −2.77479e9 | −0.0253103 | ||||||||
\(285\) | 4.30254e10 | 0.386298 | ||||||||
\(286\) | −1.83690e11 | −1.62345 | ||||||||
\(287\) | −2.06441e10 | −0.179609 | ||||||||
\(288\) | −2.27948e10 | −0.195240 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1.29781e11 | −1.07751 | ||||||||
\(291\) | −2.65580e10 | −0.217109 | ||||||||
\(292\) | −6.72964e9 | −0.0541713 | ||||||||
\(293\) | −1.21705e11 | −0.964728 | −0.482364 | − | 0.875971i | \(-0.660222\pi\) | ||||
−0.482364 | + | 0.875971i | \(0.660222\pi\) | |||||||
\(294\) | −2.67114e10 | −0.208513 | ||||||||
\(295\) | −6.92594e10 | −0.532451 | ||||||||
\(296\) | 1.17238e11 | 0.887681 | ||||||||
\(297\) | 7.37083e10 | 0.549683 | ||||||||
\(298\) | −2.14083e11 | −1.57257 | ||||||||
\(299\) | 2.37954e11 | 1.72176 | ||||||||
\(300\) | −4.71693e8 | −0.00336213 | ||||||||
\(301\) | 7.96263e9 | 0.0559123 | ||||||||
\(302\) | −2.93150e10 | −0.202795 | ||||||||
\(303\) | −4.46474e10 | −0.304302 | ||||||||
\(304\) | −2.08537e11 | −1.40040 | ||||||||
\(305\) | −6.29412e10 | −0.416472 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.11287e11 | 0.715026 | 0.357513 | − | 0.933908i | \(-0.383625\pi\) | ||||
0.357513 | + | 0.933908i | \(0.383625\pi\) | |||||||
\(308\) | 3.87372e9 | 0.0245273 | ||||||||
\(309\) | −5.08829e9 | −0.0317511 | ||||||||
\(310\) | 1.56163e10 | 0.0960396 | ||||||||
\(311\) | −7.63765e10 | −0.462954 | −0.231477 | − | 0.972840i | \(-0.574356\pi\) | ||||
−0.231477 | + | 0.972840i | \(0.574356\pi\) | |||||||
\(312\) | −5.55450e10 | −0.331856 | ||||||||
\(313\) | −2.03210e11 | −1.19673 | −0.598364 | − | 0.801224i | \(-0.704182\pi\) | ||||
−0.598364 | + | 0.801224i | \(0.704182\pi\) | |||||||
\(314\) | 3.85889e10 | 0.224016 | ||||||||
\(315\) | −3.40022e10 | −0.194585 | ||||||||
\(316\) | −6.15002e9 | −0.0346964 | ||||||||
\(317\) | 3.45098e11 | 1.91945 | 0.959723 | − | 0.280949i | \(-0.0906493\pi\) | ||||
0.959723 | + | 0.280949i | \(0.0906493\pi\) | |||||||
\(318\) | −8.76399e9 | −0.0480595 | ||||||||
\(319\) | 2.43073e11 | 1.31425 | ||||||||
\(320\) | 2.16688e11 | 1.15521 | ||||||||
\(321\) | 7.36809e10 | 0.387331 | ||||||||
\(322\) | 4.34958e10 | 0.225474 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.73555e10 | −0.0874950 | ||||||||
\(325\) | 3.97173e10 | 0.197472 | ||||||||
\(326\) | 2.35452e11 | 1.15458 | ||||||||
\(327\) | −8.01125e10 | −0.387468 | ||||||||
\(328\) | 2.04753e11 | 0.976781 | ||||||||
\(329\) | −7.20806e10 | −0.339185 | ||||||||
\(330\) | −6.15252e10 | −0.285588 | ||||||||
\(331\) | −2.73355e11 | −1.25170 | −0.625852 | − | 0.779942i | \(-0.715249\pi\) | ||||
−0.625852 | + | 0.779942i | \(0.715249\pi\) | |||||||
\(332\) | −1.89194e10 | −0.0854644 | ||||||||
\(333\) | 1.80675e11 | 0.805190 | ||||||||
\(334\) | −2.42219e11 | −1.06500 | ||||||||
\(335\) | −3.57572e11 | −1.55118 | ||||||||
\(336\) | −9.09154e9 | −0.0389144 | ||||||||
\(337\) | 3.40769e11 | 1.43921 | 0.719606 | − | 0.694382i | \(-0.244322\pi\) | ||||
0.719606 | + | 0.694382i | \(0.244322\pi\) | |||||||
\(338\) | 2.11214e11 | 0.880233 | ||||||||
\(339\) | −3.59903e10 | −0.148009 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.92484e10 | −0.117141 | ||||||||
\(342\) | −3.58899e11 | −1.41858 | ||||||||
\(343\) | −9.66789e10 | −0.377145 | ||||||||
\(344\) | −7.89751e10 | −0.304073 | ||||||||
\(345\) | 7.97005e10 | 0.302883 | ||||||||
\(346\) | 3.17459e11 | 1.19082 | ||||||||
\(347\) | 6.65505e10 | 0.246416 | 0.123208 | − | 0.992381i | \(-0.460682\pi\) | ||||
0.123208 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(348\) | 6.88999e9 | 0.0251833 | ||||||||
\(349\) | −4.92387e10 | −0.177661 | −0.0888304 | − | 0.996047i | \(-0.528313\pi\) | ||||
−0.0888304 | + | 0.996047i | \(0.528313\pi\) | |||||||
\(350\) | 7.25995e9 | 0.0258599 | ||||||||
\(351\) | −1.75922e11 | −0.618639 | ||||||||
\(352\) | −7.32392e10 | −0.254274 | ||||||||
\(353\) | 2.30862e11 | 0.791346 | 0.395673 | − | 0.918391i | \(-0.370511\pi\) | ||||
0.395673 | + | 0.918391i | \(0.370511\pi\) | |||||||
\(354\) | −3.18711e10 | −0.107865 | ||||||||
\(355\) | 7.82559e10 | 0.261511 | ||||||||
\(356\) | 2.24666e10 | 0.0741332 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.68963e11 | 0.543649 | ||||||||
\(359\) | −2.04329e11 | −0.649241 | −0.324620 | − | 0.945844i | \(-0.605237\pi\) | ||||
−0.324620 | + | 0.945844i | \(0.605237\pi\) | |||||||
\(360\) | 3.37242e11 | 1.05823 | ||||||||
\(361\) | 4.83715e11 | 1.49902 | ||||||||
\(362\) | 4.81075e11 | 1.47239 | ||||||||
\(363\) | 3.95926e10 | 0.119683 | ||||||||
\(364\) | −9.24551e9 | −0.0276042 | ||||||||
\(365\) | 1.89793e11 | 0.559708 | ||||||||
\(366\) | −2.89637e10 | −0.0843701 | ||||||||
\(367\) | −2.97395e11 | −0.855729 | −0.427865 | − | 0.903843i | \(-0.640734\pi\) | ||||
−0.427865 | + | 0.903843i | \(0.640734\pi\) | |||||||
\(368\) | −3.86296e11 | −1.09801 | ||||||||
\(369\) | 3.15542e11 | 0.886010 | ||||||||
\(370\) | −3.09942e11 | −0.859752 | ||||||||
\(371\) | −1.55620e10 | −0.0426463 | ||||||||
\(372\) | −8.29059e8 | −0.00224462 | ||||||||
\(373\) | −6.65444e11 | −1.78001 | −0.890004 | − | 0.455952i | \(-0.849299\pi\) | ||||
−0.890004 | + | 0.455952i | \(0.849299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.02761e10 | −0.209626 | ||||||||
\(376\) | 7.14911e11 | 1.84462 | ||||||||
\(377\) | −5.80148e11 | −1.47912 | ||||||||
\(378\) | −3.21568e10 | −0.0810140 | ||||||||
\(379\) | −4.69183e11 | −1.16806 | −0.584031 | − | 0.811731i | \(-0.698525\pi\) | ||||
−0.584031 | + | 0.811731i | \(0.698525\pi\) | |||||||
\(380\) | −7.10304e10 | −0.174750 | ||||||||
\(381\) | −3.99533e10 | −0.0971382 | ||||||||
\(382\) | −3.48958e11 | −0.838472 | ||||||||
\(383\) | −2.89004e11 | −0.686293 | −0.343146 | − | 0.939282i | \(-0.611493\pi\) | ||||
−0.343146 | + | 0.939282i | \(0.611493\pi\) | |||||||
\(384\) | 7.96432e10 | 0.186921 | ||||||||
\(385\) | −1.09248e11 | −0.253421 | ||||||||
\(386\) | −1.09473e11 | −0.250994 | ||||||||
\(387\) | −1.21708e11 | −0.275815 | ||||||||
\(388\) | 4.38445e10 | 0.0982137 | ||||||||
\(389\) | −2.39881e11 | −0.531156 | −0.265578 | − | 0.964089i | \(-0.585563\pi\) | ||||
−0.265578 | + | 0.964089i | \(0.585563\pi\) | |||||||
\(390\) | 1.46844e11 | 0.321414 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 4.70427e11 | 1.00625 | ||||||||
\(393\) | −1.32330e11 | −0.279828 | ||||||||
\(394\) | −5.27819e11 | −1.10345 | ||||||||
\(395\) | 1.73446e11 | 0.358490 | ||||||||
\(396\) | −5.92092e10 | −0.120993 | ||||||||
\(397\) | −4.67123e11 | −0.943787 | −0.471894 | − | 0.881655i | \(-0.656429\pi\) | ||||
−0.471894 | + | 0.881655i | \(0.656429\pi\) | |||||||
\(398\) | −3.63500e11 | −0.726156 | ||||||||
\(399\) | 3.51565e10 | 0.0694429 | ||||||||
\(400\) | −6.44772e10 | −0.125932 | ||||||||
\(401\) | 9.49217e10 | 0.183323 | 0.0916613 | − | 0.995790i | \(-0.470782\pi\) | ||||
0.0916613 | + | 0.995790i | \(0.470782\pi\) | |||||||
\(402\) | −1.64544e11 | −0.314242 | ||||||||
\(403\) | 6.98081e10 | 0.131836 | ||||||||
\(404\) | 7.37082e10 | 0.137657 | ||||||||
\(405\) | 4.89467e11 | 0.904015 | ||||||||
\(406\) | −1.06046e11 | −0.193698 | ||||||||
\(407\) | 5.80504e11 | 1.04865 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.05913e11 | 1.07067 | 0.535334 | − | 0.844640i | \(-0.320186\pi\) | ||||
0.535334 | + | 0.844640i | \(0.320186\pi\) | |||||||
\(410\) | −5.41303e11 | −0.946048 | ||||||||
\(411\) | −4.70354e10 | −0.0813086 | ||||||||
\(412\) | 8.40024e9 | 0.0143633 | ||||||||
\(413\) | −5.65926e10 | −0.0957160 | ||||||||
\(414\) | −6.64827e11 | −1.11226 | ||||||||
\(415\) | 5.33574e11 | 0.883035 | ||||||||
\(416\) | 1.74802e11 | 0.286172 | ||||||||
\(417\) | −9.20893e9 | −0.0149141 | ||||||||
\(418\) | −1.15313e12 | −1.84751 | ||||||||
\(419\) | −2.42811e11 | −0.384862 | −0.192431 | − | 0.981311i | \(-0.561637\pi\) | ||||
−0.192431 | + | 0.981311i | \(0.561637\pi\) | |||||||
\(420\) | −3.09669e9 | −0.00485598 | ||||||||
\(421\) | 8.70105e10 | 0.134990 | 0.0674951 | − | 0.997720i | \(-0.478499\pi\) | ||||
0.0674951 | + | 0.997720i | \(0.478499\pi\) | |||||||
\(422\) | 7.20704e11 | 1.10624 | ||||||||
\(423\) | 1.10174e12 | 1.67320 | ||||||||
\(424\) | 1.54347e11 | 0.231927 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.60110e10 | 0.0529776 | ||||||||
\(427\) | −5.14300e10 | −0.0748671 | ||||||||
\(428\) | −1.21640e11 | −0.175218 | ||||||||
\(429\) | −2.75030e11 | −0.392033 | ||||||||
\(430\) | 2.08786e11 | 0.294505 | ||||||||
\(431\) | 3.68348e11 | 0.514175 | 0.257087 | − | 0.966388i | \(-0.417237\pi\) | ||||
0.257087 | + | 0.966388i | \(0.417237\pi\) | |||||||
\(432\) | 2.85592e11 | 0.394520 | ||||||||
\(433\) | 7.44038e10 | 0.101718 | 0.0508592 | − | 0.998706i | \(-0.483804\pi\) | ||||
0.0508592 | + | 0.998706i | \(0.483804\pi\) | |||||||
\(434\) | 1.27602e10 | 0.0172645 | ||||||||
\(435\) | −1.94315e11 | −0.260198 | ||||||||
\(436\) | 1.32257e11 | 0.175279 | ||||||||
\(437\) | 1.49379e12 | 1.95940 | ||||||||
\(438\) | 8.73369e10 | 0.113387 | ||||||||
\(439\) | 5.10991e11 | 0.656634 | 0.328317 | − | 0.944568i | \(-0.393519\pi\) | ||||
0.328317 | + | 0.944568i | \(0.393519\pi\) | |||||||
\(440\) | 1.08355e12 | 1.37820 | ||||||||
\(441\) | 7.24970e11 | 0.912739 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.03324e11 | −0.127462 | −0.0637312 | − | 0.997967i | \(-0.520300\pi\) | ||||
−0.0637312 | + | 0.997967i | \(0.520300\pi\) | |||||||
\(444\) | 1.64546e10 | 0.0200939 | ||||||||
\(445\) | −6.33615e11 | −0.765958 | ||||||||
\(446\) | 1.42128e12 | 1.70087 | ||||||||
\(447\) | −3.20536e11 | −0.379746 | ||||||||
\(448\) | 1.77059e11 | 0.207666 | ||||||||
\(449\) | 1.40092e12 | 1.62669 | 0.813346 | − | 0.581780i | \(-0.197643\pi\) | ||||
0.813346 | + | 0.581780i | \(0.197643\pi\) | |||||||
\(450\) | −1.10967e11 | −0.127567 | ||||||||
\(451\) | 1.01383e12 | 1.15391 | ||||||||
\(452\) | 5.94163e10 | 0.0669549 | ||||||||
\(453\) | −4.38919e10 | −0.0489714 | ||||||||
\(454\) | −2.46382e11 | −0.272181 | ||||||||
\(455\) | 2.60746e11 | 0.285212 | ||||||||
\(456\) | −3.48690e11 | −0.377657 | ||||||||
\(457\) | 8.90825e11 | 0.955366 | 0.477683 | − | 0.878532i | \(-0.341477\pi\) | ||||
0.477683 | + | 0.878532i | \(0.341477\pi\) | |||||||
\(458\) | 8.43412e11 | 0.895664 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.31577e11 | −0.137016 | ||||||||
\(461\) | 1.36094e12 | 1.40341 | 0.701707 | − | 0.712466i | \(-0.252422\pi\) | ||||
0.701707 | + | 0.712466i | \(0.252422\pi\) | |||||||
\(462\) | −5.02729e10 | −0.0513387 | ||||||||
\(463\) | −1.00418e12 | −1.01554 | −0.507770 | − | 0.861493i | \(-0.669530\pi\) | ||||
−0.507770 | + | 0.861493i | \(0.669530\pi\) | |||||||
\(464\) | 9.41814e11 | 0.943266 | ||||||||
\(465\) | 2.33815e10 | 0.0231918 | ||||||||
\(466\) | 1.02771e12 | 1.00956 | ||||||||
\(467\) | 6.55686e11 | 0.637926 | 0.318963 | − | 0.947767i | \(-0.396665\pi\) | ||||
0.318963 | + | 0.947767i | \(0.396665\pi\) | |||||||
\(468\) | 1.41316e11 | 0.136171 | ||||||||
\(469\) | −2.92176e11 | −0.278847 | ||||||||
\(470\) | −1.89001e12 | −1.78658 | ||||||||
\(471\) | 5.77773e10 | 0.0540957 | ||||||||
\(472\) | 5.61298e11 | 0.520540 | ||||||||
\(473\) | −3.91044e11 | −0.359212 | ||||||||
\(474\) | 7.98146e10 | 0.0726240 | ||||||||
\(475\) | 2.49330e11 | 0.224726 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.37862e11 | 0.210374 | ||||||||
\(478\) | −1.90610e12 | −1.67001 | ||||||||
\(479\) | 1.52667e12 | 1.32506 | 0.662531 | − | 0.749034i | \(-0.269482\pi\) | ||||
0.662531 | + | 0.749034i | \(0.269482\pi\) | |||||||
\(480\) | 5.85483e10 | 0.0503418 | ||||||||
\(481\) | −1.38551e12 | −1.18020 | ||||||||
\(482\) | 1.71135e12 | 1.44420 | ||||||||
\(483\) | 6.51242e10 | 0.0544478 | ||||||||
\(484\) | −6.53632e10 | −0.0541414 | ||||||||
\(485\) | −1.23652e12 | −1.01476 | ||||||||
\(486\) | 7.43865e11 | 0.604827 | ||||||||
\(487\) | −7.50120e11 | −0.604297 | −0.302149 | − | 0.953261i | \(-0.597704\pi\) | ||||
−0.302149 | + | 0.953261i | \(0.597704\pi\) | |||||||
\(488\) | 5.10094e11 | 0.407156 | ||||||||
\(489\) | 3.52531e11 | 0.278810 | ||||||||
\(490\) | −1.24366e12 | −0.974587 | ||||||||
\(491\) | 9.77091e11 | 0.758697 | 0.379348 | − | 0.925254i | \(-0.376148\pi\) | ||||
0.379348 | + | 0.925254i | \(0.376148\pi\) | |||||||
\(492\) | 2.87374e10 | 0.0221108 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.75222e12 | 2.07927 | ||||||||
\(495\) | 1.66985e12 | 1.25012 | ||||||||
\(496\) | −1.13327e11 | −0.0840745 | ||||||||
\(497\) | 6.39438e10 | 0.0470105 | ||||||||
\(498\) | 2.45535e11 | 0.178888 | ||||||||
\(499\) | 3.34485e11 | 0.241504 | 0.120752 | − | 0.992683i | \(-0.461469\pi\) | ||||
0.120752 | + | 0.992683i | \(0.461469\pi\) | |||||||
\(500\) | 1.32528e11 | 0.0948290 | ||||||||
\(501\) | −3.62663e11 | −0.257178 | ||||||||
\(502\) | −1.80455e12 | −1.26824 | ||||||||
\(503\) | −8.94503e11 | −0.623054 | −0.311527 | − | 0.950237i | \(-0.600840\pi\) | ||||
−0.311527 | + | 0.950237i | \(0.600840\pi\) | |||||||
\(504\) | 2.75564e11 | 0.190233 | ||||||||
\(505\) | −2.07876e12 | −1.42230 | ||||||||
\(506\) | −2.13608e12 | −1.44857 | ||||||||
\(507\) | 3.16241e11 | 0.212560 | ||||||||
\(508\) | 6.59587e10 | 0.0439426 | ||||||||
\(509\) | 2.06105e12 | 1.36100 | 0.680500 | − | 0.732748i | \(-0.261763\pi\) | ||||
0.680500 | + | 0.732748i | \(0.261763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.55082e11 | 0.100616 | ||||||||
\(512\) | −1.72297e12 | −1.10806 | ||||||||
\(513\) | −1.10437e12 | −0.704022 | ||||||||
\(514\) | 1.15848e12 | 0.732075 | ||||||||
\(515\) | −2.36908e11 | −0.148404 | ||||||||
\(516\) | −1.10843e10 | −0.00688311 | ||||||||
\(517\) | 3.53987e12 | 2.17912 | ||||||||
\(518\) | −2.53257e11 | −0.154553 | ||||||||
\(519\) | 4.75316e11 | 0.287561 | ||||||||
\(520\) | −2.58614e12 | −1.55109 | ||||||||
\(521\) | 8.82079e11 | 0.524491 | 0.262245 | − | 0.965001i | \(-0.415537\pi\) | ||||
0.262245 | + | 0.965001i | \(0.415537\pi\) | |||||||
\(522\) | 1.62089e12 | 0.955513 | ||||||||
\(523\) | 1.84775e12 | 1.07990 | 0.539952 | − | 0.841696i | \(-0.318442\pi\) | ||||
0.539952 | + | 0.841696i | \(0.318442\pi\) | |||||||
\(524\) | 2.18463e11 | 0.126586 | ||||||||
\(525\) | 1.08700e10 | 0.00624470 | ||||||||
\(526\) | −4.08970e11 | −0.232946 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.46485e11 | 0.250008 | ||||||||
\(529\) | 9.65949e11 | 0.536295 | ||||||||
\(530\) | −4.08046e11 | −0.224630 | ||||||||
\(531\) | 8.65010e11 | 0.472167 | ||||||||
\(532\) | −5.80398e10 | −0.0314140 | ||||||||
\(533\) | −2.41974e12 | −1.29866 | ||||||||
\(534\) | −2.91571e11 | −0.155170 | ||||||||
\(535\) | 3.43054e12 | 1.81038 | ||||||||
\(536\) | 2.89786e12 | 1.51648 | ||||||||
\(537\) | 2.52981e11 | 0.131281 | ||||||||
\(538\) | 7.00432e11 | 0.360451 | ||||||||
\(539\) | 2.32931e12 | 1.18872 | ||||||||
\(540\) | 9.72762e10 | 0.0492305 | ||||||||
\(541\) | 1.98969e12 | 0.998616 | 0.499308 | − | 0.866424i | \(-0.333588\pi\) | ||||
0.499308 | + | 0.866424i | \(0.333588\pi\) | |||||||
\(542\) | −9.76604e11 | −0.486095 | ||||||||
\(543\) | 7.20290e11 | 0.355556 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.72999e12 | −1.81102 | ||||||||
\(546\) | 1.19988e11 | 0.0577790 | ||||||||
\(547\) | −2.90319e12 | −1.38654 | −0.693270 | − | 0.720678i | \(-0.743831\pi\) | ||||
−0.693270 | + | 0.720678i | \(0.743831\pi\) | |||||||
\(548\) | 7.76505e10 | 0.0367817 | ||||||||
\(549\) | 7.86100e11 | 0.369319 | ||||||||
\(550\) | −3.56535e11 | −0.166139 | ||||||||
\(551\) | −3.64195e12 | −1.68326 | ||||||||
\(552\) | −6.45916e11 | −0.296108 | ||||||||
\(553\) | 1.41725e11 | 0.0644439 | ||||||||
\(554\) | −2.38495e11 | −0.107569 | ||||||||
\(555\) | −4.64062e11 | −0.207614 | ||||||||
\(556\) | 1.52030e10 | 0.00674671 | ||||||||
\(557\) | −7.01764e11 | −0.308918 | −0.154459 | − | 0.987999i | \(-0.549363\pi\) | ||||
−0.154459 | + | 0.987999i | \(0.549363\pi\) | |||||||
\(558\) | −1.95039e11 | −0.0851661 | ||||||||
\(559\) | 9.33316e11 | 0.404274 | ||||||||
\(560\) | −4.23297e11 | −0.181886 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.58045e11 | −0.278255 | ||||||||
\(563\) | 1.39790e10 | 0.00586393 | 0.00293196 | − | 0.999996i | \(-0.499067\pi\) | ||||
0.00293196 | + | 0.999996i | \(0.499067\pi\) | |||||||
\(564\) | 1.00339e11 | 0.0417556 | ||||||||
\(565\) | −1.67569e12 | −0.691791 | ||||||||
\(566\) | 1.06574e12 | 0.436493 | ||||||||
\(567\) | 3.99949e11 | 0.162510 | ||||||||
\(568\) | −6.34208e11 | −0.255661 | ||||||||
\(569\) | −2.78982e12 | −1.11576 | −0.557880 | − | 0.829922i | \(-0.688385\pi\) | ||||
−0.557880 | + | 0.829922i | \(0.688385\pi\) | |||||||
\(570\) | 9.21829e11 | 0.365775 | ||||||||
\(571\) | 3.89052e12 | 1.53160 | 0.765800 | − | 0.643079i | \(-0.222343\pi\) | ||||
0.765800 | + | 0.643079i | \(0.222343\pi\) | |||||||
\(572\) | 4.54046e11 | 0.177345 | ||||||||
\(573\) | −5.22479e11 | −0.202476 | ||||||||
\(574\) | −4.42305e11 | −0.170066 | ||||||||
\(575\) | 4.61861e11 | 0.176200 | ||||||||
\(576\) | −2.70632e12 | −1.02442 | ||||||||
\(577\) | −2.43855e12 | −0.915883 | −0.457942 | − | 0.888982i | \(-0.651413\pi\) | ||||
−0.457942 | + | 0.888982i | \(0.651413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.63909e11 | −0.0606106 | ||||||||
\(580\) | 3.20794e11 | 0.117706 | ||||||||
\(581\) | 4.35989e11 | 0.158739 | ||||||||
\(582\) | −5.69012e11 | −0.205574 | ||||||||
\(583\) | 7.64247e11 | 0.273984 | ||||||||
\(584\) | −1.53813e12 | −0.547188 | ||||||||
\(585\) | −3.98547e12 | −1.40695 | ||||||||
\(586\) | −2.60756e12 | −0.913473 | ||||||||
\(587\) | −3.11396e12 | −1.08254 | −0.541268 | − | 0.840850i | \(-0.682056\pi\) | ||||
−0.541268 | + | 0.840850i | \(0.682056\pi\) | |||||||
\(588\) | 6.60254e10 | 0.0227779 | ||||||||
\(589\) | 4.38228e11 | 0.150031 | ||||||||
\(590\) | −1.48390e12 | −0.504162 | ||||||||
\(591\) | −7.90278e11 | −0.266463 | ||||||||
\(592\) | 2.24923e12 | 0.752640 | ||||||||
\(593\) | −7.59897e11 | −0.252353 | −0.126177 | − | 0.992008i | \(-0.540271\pi\) | ||||
−0.126177 | + | 0.992008i | \(0.540271\pi\) | |||||||
\(594\) | 1.57922e12 | 0.520479 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.29172e11 | 0.171786 | ||||||||
\(597\) | −5.44251e11 | −0.175354 | ||||||||
\(598\) | 5.09823e12 | 1.63029 | ||||||||
\(599\) | −8.96263e11 | −0.284456 | −0.142228 | − | 0.989834i | \(-0.545427\pi\) | ||||
−0.142228 | + | 0.989834i | \(0.545427\pi\) | |||||||
\(600\) | −1.07811e11 | −0.0339611 | ||||||||
\(601\) | 3.76154e12 | 1.17606 | 0.588032 | − | 0.808838i | \(-0.299903\pi\) | ||||
0.588032 | + | 0.808838i | \(0.299903\pi\) | |||||||
\(602\) | 1.70601e11 | 0.0529417 | ||||||||
\(603\) | 4.46587e12 | 1.37556 | ||||||||
\(604\) | 7.24609e10 | 0.0221533 | ||||||||
\(605\) | 1.84340e12 | 0.559399 | ||||||||
\(606\) | −9.56581e11 | −0.288134 | ||||||||
\(607\) | −1.60985e12 | −0.481323 | −0.240662 | − | 0.970609i | \(-0.577364\pi\) | ||||
−0.240662 | + | 0.970609i | \(0.577364\pi\) | |||||||
\(608\) | 1.09734e12 | 0.325668 | ||||||||
\(609\) | −1.58777e11 | −0.0467746 | ||||||||
\(610\) | −1.34853e12 | −0.394345 | ||||||||
\(611\) | −8.44872e12 | −2.45248 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.46562e11 | 0.270755 | 0.135378 | − | 0.990794i | \(-0.456775\pi\) | ||||
0.135378 | + | 0.990794i | \(0.456775\pi\) | |||||||
\(614\) | 2.38435e12 | 0.677037 | ||||||||
\(615\) | −8.10467e11 | −0.228453 | ||||||||
\(616\) | 8.85381e11 | 0.247752 | ||||||||
\(617\) | −6.21655e12 | −1.72690 | −0.863448 | − | 0.504438i | \(-0.831700\pi\) | ||||
−0.863448 | + | 0.504438i | \(0.831700\pi\) | |||||||
\(618\) | −1.09018e11 | −0.0300642 | ||||||||
\(619\) | −6.25622e11 | −0.171279 | −0.0856395 | − | 0.996326i | \(-0.527293\pi\) | ||||
−0.0856395 | + | 0.996326i | \(0.527293\pi\) | |||||||
\(620\) | −3.86005e10 | −0.0104913 | ||||||||
\(621\) | −2.04574e12 | −0.551999 | ||||||||
\(622\) | −1.63639e12 | −0.438358 | ||||||||
\(623\) | −5.17734e11 | −0.137692 | ||||||||
\(624\) | −1.06564e12 | −0.281371 | ||||||||
\(625\) | −4.27989e12 | −1.12195 | ||||||||
\(626\) | −4.35382e12 | −1.13315 | ||||||||
\(627\) | −1.72653e12 | −0.446140 | ||||||||
\(628\) | −9.53842e10 | −0.0244714 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −7.28506e11 | −0.184247 | ||||||||
\(631\) | −2.47719e12 | −0.622053 | −0.311026 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311026 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(632\) | −1.40565e12 | −0.350471 | ||||||||
\(633\) | 1.07908e12 | 0.267138 | ||||||||
\(634\) | 7.39381e12 | 1.81747 | ||||||||
\(635\) | −1.86020e12 | −0.454023 | ||||||||
\(636\) | 2.16629e10 | 0.00525000 | ||||||||
\(637\) | −5.55944e12 | −1.33784 | ||||||||
\(638\) | 5.20789e12 | 1.24442 | ||||||||
\(639\) | −9.77372e11 | −0.231903 | ||||||||
\(640\) | 3.70814e12 | 0.873667 | ||||||||
\(641\) | −6.99847e12 | −1.63735 | −0.818675 | − | 0.574257i | \(-0.805291\pi\) | ||||
−0.818675 | + | 0.574257i | \(0.805291\pi\) | |||||||
\(642\) | 1.57863e12 | 0.366753 | ||||||||
\(643\) | −7.69131e12 | −1.77440 | −0.887199 | − | 0.461387i | \(-0.847352\pi\) | ||||
−0.887199 | + | 0.461387i | \(0.847352\pi\) | |||||||
\(644\) | −1.07513e11 | −0.0246306 | ||||||||
\(645\) | 3.12605e11 | 0.0711177 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.23210e11 | 0.0500777 | 0.0250389 | − | 0.999686i | \(-0.492029\pi\) | ||||
0.0250389 | + | 0.999686i | \(0.492029\pi\) | |||||||
\(648\) | −3.96678e12 | −0.883793 | ||||||||
\(649\) | 2.77926e12 | 0.614933 | ||||||||
\(650\) | 8.50953e11 | 0.186980 | ||||||||
\(651\) | 1.91053e10 | 0.00416907 | ||||||||
\(652\) | −5.81992e11 | −0.126126 | ||||||||
\(653\) | −3.47267e11 | −0.0747402 | −0.0373701 | − | 0.999301i | \(-0.511898\pi\) | ||||
−0.0373701 | + | 0.999301i | \(0.511898\pi\) | |||||||
\(654\) | −1.71643e12 | −0.366882 | ||||||||
\(655\) | −6.16120e12 | −1.30791 | ||||||||
\(656\) | 3.92821e12 | 0.828184 | ||||||||
\(657\) | −2.37040e12 | −0.496338 | ||||||||
\(658\) | −1.54434e12 | −0.321165 | ||||||||
\(659\) | 6.95963e12 | 1.43748 | 0.718740 | − | 0.695279i | \(-0.244719\pi\) | ||||
0.718740 | + | 0.695279i | \(0.244719\pi\) | |||||||
\(660\) | 1.52078e11 | 0.0311975 | ||||||||
\(661\) | −5.93268e12 | −1.20877 | −0.604386 | − | 0.796692i | \(-0.706581\pi\) | ||||
−0.604386 | + | 0.796692i | \(0.706581\pi\) | |||||||
\(662\) | −5.85671e12 | −1.18520 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.32423e12 | −0.863282 | ||||||||
\(665\) | 1.63687e12 | 0.324575 | ||||||||
\(666\) | 3.87100e12 | 0.762411 | ||||||||
\(667\) | −6.74637e12 | −1.31979 | ||||||||
\(668\) | 5.98719e11 | 0.116340 | ||||||||
\(669\) | 2.12801e12 | 0.410730 | ||||||||
\(670\) | −7.66106e12 | −1.46877 | ||||||||
\(671\) | 2.52572e12 | 0.480988 | ||||||||
\(672\) | 4.78404e10 | 0.00904969 | ||||||||
\(673\) | 9.27751e12 | 1.74327 | 0.871633 | − | 0.490158i | \(-0.163061\pi\) | ||||
0.871633 | + | 0.490158i | \(0.163061\pi\) | |||||||
\(674\) | 7.30105e12 | 1.36275 | ||||||||
\(675\) | −3.41458e11 | −0.0633096 | ||||||||
\(676\) | −5.22080e11 | −0.0961562 | ||||||||
\(677\) | 6.80134e12 | 1.24436 | 0.622179 | − | 0.782875i | \(-0.286248\pi\) | ||||
0.622179 | + | 0.782875i | \(0.286248\pi\) | |||||||
\(678\) | −7.71102e11 | −0.140145 | ||||||||
\(679\) | −1.01038e12 | −0.182419 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.68897e11 | −0.0657268 | ||||||||
\(682\) | −6.26655e11 | −0.110917 | ||||||||
\(683\) | 8.67042e12 | 1.52457 | 0.762284 | − | 0.647242i | \(-0.224078\pi\) | ||||
0.762284 | + | 0.647242i | \(0.224078\pi\) | |||||||
\(684\) | 8.87129e11 | 0.154965 | ||||||||
\(685\) | −2.18994e12 | −0.380036 | ||||||||
\(686\) | −2.07137e12 | −0.357108 | ||||||||
\(687\) | 1.26280e12 | 0.216287 | ||||||||
\(688\) | −1.51515e12 | −0.257814 | ||||||||
\(689\) | −1.82405e12 | −0.308354 | ||||||||
\(690\) | 1.70760e12 | 0.286791 | ||||||||
\(691\) | 1.03357e13 | 1.72461 | 0.862304 | − | 0.506390i | \(-0.169020\pi\) | ||||
0.862304 | + | 0.506390i | \(0.169020\pi\) | |||||||
\(692\) | −7.84697e11 | −0.130084 | ||||||||
\(693\) | 1.36445e12 | 0.224729 | ||||||||
\(694\) | 1.42586e12 | 0.233324 | ||||||||
\(695\) | −4.28762e11 | −0.0697083 | ||||||||
\(696\) | 1.57478e12 | 0.254378 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.05495e12 | −0.168222 | ||||||||
\(699\) | 1.53874e12 | 0.243791 | ||||||||
\(700\) | −1.79452e10 | −0.00282492 | ||||||||
\(701\) | −1.00027e13 | −1.56453 | −0.782267 | − | 0.622944i | \(-0.785937\pi\) | ||||
−0.782267 | + | 0.622944i | \(0.785937\pi\) | |||||||
\(702\) | −3.76917e12 | −0.585771 | ||||||||
\(703\) | −8.69767e12 | −1.34309 | ||||||||
\(704\) | −8.69533e12 | −1.33416 | ||||||||
\(705\) | −2.82982e12 | −0.431427 | ||||||||
\(706\) | 4.94628e12 | 0.749302 | ||||||||
\(707\) | −1.69857e12 | −0.255680 | ||||||||
\(708\) | 7.87793e10 | 0.0117832 | ||||||||
\(709\) | 7.69309e12 | 1.14339 | 0.571693 | − | 0.820467i | \(-0.306287\pi\) | ||||
0.571693 | + | 0.820467i | \(0.306287\pi\) | |||||||
\(710\) | 1.67665e12 | 0.247617 | ||||||||
\(711\) | −2.16624e12 | −0.317902 | ||||||||
\(712\) | 5.13499e12 | 0.748824 | ||||||||
\(713\) | 8.11777e11 | 0.117634 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.28052e13 | −1.83236 | ||||||||
\(716\) | −4.17645e11 | −0.0593880 | ||||||||
\(717\) | −2.85391e12 | −0.403278 | ||||||||
\(718\) | −4.37781e12 | −0.614747 | ||||||||
\(719\) | −3.98924e12 | −0.556686 | −0.278343 | − | 0.960482i | \(-0.589785\pi\) | ||||
−0.278343 | + | 0.960482i | \(0.589785\pi\) | |||||||
\(720\) | 6.47003e12 | 0.897243 | ||||||||
\(721\) | −1.93580e11 | −0.0266779 | ||||||||
\(722\) | 1.03637e13 | 1.41938 | ||||||||
\(723\) | 2.56232e12 | 0.348747 | ||||||||
\(724\) | −1.18912e12 | −0.160844 | ||||||||
\(725\) | −1.12605e12 | −0.151368 | ||||||||
\(726\) | 8.48280e11 | 0.113325 | ||||||||
\(727\) | −1.39684e13 | −1.85456 | −0.927279 | − | 0.374370i | \(-0.877859\pi\) | ||||
−0.927279 | + | 0.374370i | \(0.877859\pi\) | |||||||
\(728\) | −2.11316e12 | −0.278832 | ||||||||
\(729\) | −5.33665e12 | −0.699833 | ||||||||
\(730\) | 4.06635e12 | 0.529971 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 7.15926e10 | 0.00921655 | ||||||||
\(733\) | 8.88183e12 | 1.13641 | 0.568204 | − | 0.822887i | \(-0.307638\pi\) | ||||
0.568204 | + | 0.822887i | \(0.307638\pi\) | |||||||
\(734\) | −6.37176e12 | −0.810265 | ||||||||
\(735\) | −1.86208e12 | −0.235345 | ||||||||
\(736\) | 2.03272e12 | 0.255345 | ||||||||
\(737\) | 1.43487e13 | 1.79147 | ||||||||
\(738\) | 6.76056e12 | 0.838937 | ||||||||
\(739\) | −4.12811e12 | −0.509156 | −0.254578 | − | 0.967052i | \(-0.581937\pi\) | ||||
−0.254578 | + | 0.967052i | \(0.581937\pi\) | |||||||
\(740\) | 7.66118e11 | 0.0939188 | ||||||||
\(741\) | 4.12077e12 | 0.502107 | ||||||||
\(742\) | −3.33419e11 | −0.0403806 | ||||||||
\(743\) | 1.16810e13 | 1.40615 | 0.703073 | − | 0.711118i | \(-0.251811\pi\) | ||||
0.703073 | + | 0.711118i | \(0.251811\pi\) | |||||||
\(744\) | −1.89491e11 | −0.0226730 | ||||||||
\(745\) | −1.49240e13 | −1.77493 | ||||||||
\(746\) | −1.42573e13 | −1.68544 | ||||||||
\(747\) | −6.66403e12 | −0.783059 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.80313e12 | 0.325443 | ||||||||
\(750\) | −1.71994e12 | −0.198489 | ||||||||
\(751\) | 8.87631e11 | 0.101825 | 0.0509123 | − | 0.998703i | \(-0.483787\pi\) | ||||
0.0509123 | + | 0.998703i | \(0.483787\pi\) | |||||||
\(752\) | 1.37157e13 | 1.56400 | ||||||||
\(753\) | −2.70187e12 | −0.306258 | ||||||||
\(754\) | −1.24298e13 | −1.40053 | ||||||||
\(755\) | −2.04358e12 | −0.228892 | ||||||||
\(756\) | 7.94855e10 | 0.00884993 | ||||||||
\(757\) | 1.30648e13 | 1.44602 | 0.723008 | − | 0.690840i | \(-0.242759\pi\) | ||||
0.723008 | + | 0.690840i | \(0.242759\pi\) | |||||||
\(758\) | −1.00524e13 | −1.10600 | ||||||||
\(759\) | −3.19824e12 | −0.349803 | ||||||||
\(760\) | −1.62348e13 | −1.76517 | ||||||||
\(761\) | −1.23220e12 | −0.133183 | −0.0665915 | − | 0.997780i | \(-0.521212\pi\) | ||||
−0.0665915 | + | 0.997780i | \(0.521212\pi\) | |||||||
\(762\) | −8.56009e11 | −0.0919773 | ||||||||
\(763\) | −3.04781e12 | −0.325558 | ||||||||
\(764\) | 8.62558e11 | 0.0915943 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.19198e12 | −0.649831 | ||||||||
\(767\) | −6.63333e12 | −0.692074 | ||||||||
\(768\) | −6.76486e11 | −0.0701671 | ||||||||
\(769\) | 1.35515e13 | 1.39739 | 0.698697 | − | 0.715417i | \(-0.253763\pi\) | ||||
0.698697 | + | 0.715417i | \(0.253763\pi\) | |||||||
\(770\) | −2.34067e12 | −0.239957 | ||||||||
\(771\) | 1.73454e12 | 0.176783 | ||||||||
\(772\) | 2.70596e11 | 0.0274185 | ||||||||
\(773\) | 4.78823e12 | 0.482355 | 0.241178 | − | 0.970481i | \(-0.422466\pi\) | ||||
0.241178 | + | 0.970481i | \(0.422466\pi\) | |||||||
\(774\) | −2.60762e12 | −0.261162 | ||||||||
\(775\) | 1.35495e11 | 0.0134917 | ||||||||
\(776\) | 1.00211e13 | 0.992064 | ||||||||
\(777\) | −3.79190e11 | −0.0373218 | ||||||||
\(778\) | −5.13950e12 | −0.502936 | ||||||||
\(779\) | −1.51902e13 | −1.47790 | ||||||||
\(780\) | −3.62970e11 | −0.0351111 | ||||||||
\(781\) | −3.14027e12 | −0.302022 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.98765e12 | 0.474207 | ||||||||
\(784\) | 9.02521e12 | 0.853169 | ||||||||
\(785\) | 2.69007e12 | 0.252843 | ||||||||
\(786\) | −2.83520e12 | −0.264961 | ||||||||
\(787\) | 1.01965e13 | 0.947470 | 0.473735 | − | 0.880668i | \(-0.342906\pi\) | ||||
0.473735 | + | 0.880668i | \(0.342906\pi\) | |||||||
\(788\) | 1.30467e12 | 0.120540 | ||||||||
\(789\) | −6.12331e11 | −0.0562522 | ||||||||
\(790\) | 3.71612e12 | 0.339444 | ||||||||
\(791\) | −1.36922e12 | −0.124360 | ||||||||
\(792\) | −1.35329e13 | −1.22216 | ||||||||
\(793\) | −6.02821e12 | −0.541326 | ||||||||
\(794\) | −1.00082e13 | −0.893645 | ||||||||
\(795\) | −6.10947e11 | −0.0542440 | ||||||||
\(796\) | 8.98501e11 | 0.0793250 | ||||||||
\(797\) | −2.90050e11 | −0.0254631 | −0.0127315 | − | 0.999919i | \(-0.504053\pi\) | ||||
−0.0127315 | + | 0.999919i | \(0.504053\pi\) | |||||||
\(798\) | 7.53237e11 | 0.0657535 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.39284e11 | 0.0292859 | ||||||||
\(801\) | 7.91348e12 | 0.679237 | ||||||||
\(802\) | 2.03372e12 | 0.173583 | ||||||||
\(803\) | −7.61605e12 | −0.646413 | ||||||||
\(804\) | 4.06721e11 | 0.0343277 | ||||||||
\(805\) | 3.03214e12 | 0.254488 | ||||||||
\(806\) | 1.49565e12 | 0.124831 | ||||||||
\(807\) | 1.04872e12 | 0.0870422 | ||||||||
\(808\) | 1.68468e13 | 1.39049 | ||||||||
\(809\) | 8.66799e12 | 0.711459 | 0.355730 | − | 0.934589i | \(-0.384232\pi\) | ||||
0.355730 | + | 0.934589i | \(0.384232\pi\) | |||||||
\(810\) | 1.04869e13 | 0.855986 | ||||||||
\(811\) | 1.70242e13 | 1.38189 | 0.690943 | − | 0.722909i | \(-0.257196\pi\) | ||||
0.690943 | + | 0.722909i | \(0.257196\pi\) | |||||||
\(812\) | 2.62124e11 | 0.0211595 | ||||||||
\(813\) | −1.46222e12 | −0.117383 | ||||||||
\(814\) | 1.24374e13 | 0.992936 | ||||||||
\(815\) | 1.64136e13 | 1.30315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.85900e12 | 0.460070 | ||||||||
\(818\) | 1.29818e13 | 1.01379 | ||||||||
\(819\) | −3.25657e12 | −0.252920 | ||||||||
\(820\) | 1.33800e12 | 0.103346 | ||||||||
\(821\) | −4.27376e12 | −0.328296 | −0.164148 | − | 0.986436i | \(-0.552488\pi\) | ||||
−0.164148 | + | 0.986436i | \(0.552488\pi\) | |||||||
\(822\) | −1.00774e12 | −0.0769887 | ||||||||
\(823\) | 1.34081e13 | 1.01875 | 0.509376 | − | 0.860544i | \(-0.329876\pi\) | ||||
0.509376 | + | 0.860544i | \(0.329876\pi\) | |||||||
\(824\) | 1.91997e12 | 0.145085 | ||||||||
\(825\) | −5.33823e11 | −0.0401194 | ||||||||
\(826\) | −1.21251e12 | −0.0906307 | ||||||||
\(827\) | −1.90577e13 | −1.41676 | −0.708378 | − | 0.705833i | \(-0.750573\pi\) | ||||
−0.708378 | + | 0.705833i | \(0.750573\pi\) | |||||||
\(828\) | 1.64333e12 | 0.121503 | ||||||||
\(829\) | −2.19283e13 | −1.61253 | −0.806267 | − | 0.591551i | \(-0.798516\pi\) | ||||
−0.806267 | + | 0.591551i | \(0.798516\pi\) | |||||||
\(830\) | 1.14319e13 | 0.836120 | ||||||||
\(831\) | −3.57088e11 | −0.0259759 | ||||||||
\(832\) | 2.07534e13 | 1.50153 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.97304e11 | −0.0141217 | ||||||||
\(835\) | −1.68854e13 | −1.20205 | ||||||||
\(836\) | 2.85033e12 | 0.201821 | ||||||||
\(837\) | −6.00154e11 | −0.0422667 | ||||||||
\(838\) | −5.20228e12 | −0.364414 | ||||||||
\(839\) | 2.60613e13 | 1.81580 | 0.907898 | − | 0.419192i | \(-0.137687\pi\) | ||||
0.907898 | + | 0.419192i | \(0.137687\pi\) | |||||||
\(840\) | −7.07784e11 | −0.0490505 | ||||||||
\(841\) | 1.94094e12 | 0.133792 | ||||||||
\(842\) | 1.86422e12 | 0.127818 | ||||||||
\(843\) | −9.85260e11 | −0.0671934 | ||||||||
\(844\) | −1.78144e12 | −0.120846 | ||||||||
\(845\) | 1.47240e13 | 0.993504 | ||||||||
\(846\) | 2.36051e13 | 1.58431 | ||||||||
\(847\) | 1.50627e12 | 0.100560 | ||||||||
\(848\) | 2.96117e12 | 0.196644 | ||||||||
\(849\) | 1.59568e12 | 0.105405 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.61116e13 | −1.05307 | ||||||||
\(852\) | −8.90124e10 | −0.00578725 | ||||||||
\(853\) | −1.12348e13 | −0.726598 | −0.363299 | − | 0.931673i | \(-0.618350\pi\) | ||||
−0.363299 | + | 0.931673i | \(0.618350\pi\) | |||||||
\(854\) | −1.10190e12 | −0.0708894 | ||||||||
\(855\) | −2.50193e13 | −1.60113 | ||||||||
\(856\) | −2.78021e13 | −1.76989 | ||||||||
\(857\) | 1.22547e13 | 0.776046 | 0.388023 | − | 0.921650i | \(-0.373158\pi\) | ||||
0.388023 | + | 0.921650i | \(0.373158\pi\) | |||||||
\(858\) | −5.89259e12 | −0.371205 | ||||||||
\(859\) | −4.30100e12 | −0.269526 | −0.134763 | − | 0.990878i | \(-0.543027\pi\) | ||||
−0.134763 | + | 0.990878i | \(0.543027\pi\) | |||||||
\(860\) | −5.16079e11 | −0.0321716 | ||||||||
\(861\) | −6.62242e11 | −0.0410679 | ||||||||
\(862\) | 7.89195e12 | 0.486857 | ||||||||
\(863\) | 2.80501e12 | 0.172141 | 0.0860707 | − | 0.996289i | \(-0.472569\pi\) | ||||
0.0860707 | + | 0.996289i | \(0.472569\pi\) | |||||||
\(864\) | −1.50281e12 | −0.0917470 | ||||||||
\(865\) | 2.21304e13 | 1.34406 | ||||||||
\(866\) | 1.59412e12 | 0.0963142 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.15409e10 | −0.00188597 | ||||||||
\(869\) | −6.96008e12 | −0.414024 | ||||||||
\(870\) | −4.16325e12 | −0.246374 | ||||||||
\(871\) | −3.42465e13 | −2.01621 | ||||||||
\(872\) | 3.02289e13 | 1.77051 | ||||||||
\(873\) | 1.54435e13 | 0.899873 | ||||||||
\(874\) | 3.20047e13 | 1.85529 | ||||||||
\(875\) | −3.05404e12 | −0.176132 | ||||||||
\(876\) | −2.15880e11 | −0.0123864 | ||||||||
\(877\) | 1.65539e13 | 0.944937 | 0.472468 | − | 0.881348i | \(-0.343363\pi\) | ||||
0.472468 | + | 0.881348i | \(0.343363\pi\) | |||||||
\(878\) | 1.09481e13 | 0.621747 | ||||||||
\(879\) | −3.90418e12 | −0.220587 | ||||||||
\(880\) | 2.07881e13 | 1.16854 | ||||||||
\(881\) | 5.47621e12 | 0.306259 | 0.153129 | − | 0.988206i | \(-0.451065\pi\) | ||||
0.153129 | + | 0.988206i | \(0.451065\pi\) | |||||||
\(882\) | 1.55327e13 | 0.864246 | ||||||||
\(883\) | −1.05997e13 | −0.586775 | −0.293387 | − | 0.955994i | \(-0.594783\pi\) | ||||
−0.293387 | + | 0.955994i | \(0.594783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.22177e12 | −0.121746 | ||||||||
\(886\) | −2.21373e12 | −0.120691 | ||||||||
\(887\) | −4.63428e12 | −0.251377 | −0.125689 | − | 0.992070i | \(-0.540114\pi\) | ||||
−0.125689 | + | 0.992070i | \(0.540114\pi\) | |||||||
\(888\) | 3.76089e12 | 0.202970 | ||||||||
\(889\) | −1.51999e12 | −0.0816174 | ||||||||
\(890\) | −1.35753e13 | −0.725263 | ||||||||
\(891\) | −1.96415e13 | −1.04406 | ||||||||
\(892\) | −3.51313e12 | −0.185803 | ||||||||
\(893\) | −5.30378e13 | −2.79096 | ||||||||
\(894\) | −6.86757e12 | −0.359570 | ||||||||
\(895\) | 1.17786e13 | 0.613608 | ||||||||
\(896\) | 3.02996e12 | 0.157055 | ||||||||
\(897\) | 7.63334e12 | 0.393685 | ||||||||
\(898\) | 3.00151e13 | 1.54027 | ||||||||
\(899\) | −1.97916e12 | −0.101056 | ||||||||
\(900\) | 2.74290e11 | 0.0139354 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.17215e13 | 1.09260 | ||||||||
\(903\) | 2.55433e11 | 0.0127845 | ||||||||
\(904\) | 1.35803e13 | 0.676316 | ||||||||
\(905\) | 3.35363e13 | 1.66187 | ||||||||
\(906\) | −9.40394e11 | −0.0463696 | ||||||||
\(907\) | −2.01528e13 | −0.988789 | −0.494395 | − | 0.869238i | \(-0.664610\pi\) | ||||
−0.494395 | + | 0.869238i | \(0.664610\pi\) | |||||||
\(908\) | 6.09010e11 | 0.0297330 | ||||||||
\(909\) | 2.59625e13 | 1.26127 | ||||||||
\(910\) | 5.58655e12 | 0.270058 | ||||||||
\(911\) | −2.42307e13 | −1.16556 | −0.582778 | − | 0.812632i | \(-0.698034\pi\) | ||||
−0.582778 | + | 0.812632i | \(0.698034\pi\) | |||||||
\(912\) | −6.68967e12 | −0.320205 | ||||||||
\(913\) | −2.14114e13 | −1.01983 | ||||||||
\(914\) | 1.90861e13 | 0.904608 | ||||||||
\(915\) | −2.01909e12 | −0.0952272 | ||||||||
\(916\) | −2.08475e12 | −0.0978419 | ||||||||
\(917\) | −5.03438e12 | −0.235117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.39352e13 | 1.56939 | 0.784695 | − | 0.619881i | \(-0.212819\pi\) | ||||
0.784695 | + | 0.619881i | \(0.212819\pi\) | |||||||
\(920\) | −3.00734e13 | −1.38401 | ||||||||
\(921\) | 3.56998e12 | 0.163492 | ||||||||
\(922\) | 2.91585e13 | 1.32885 | ||||||||
\(923\) | 7.49498e12 | 0.339909 | ||||||||
\(924\) | 1.24265e11 | 0.00560822 | ||||||||
\(925\) | −2.68922e12 | −0.120778 | ||||||||
\(926\) | −2.15148e13 | −0.961585 | ||||||||
\(927\) | 2.95884e12 | 0.131602 | ||||||||
\(928\) | −4.95590e12 | −0.219360 | ||||||||
\(929\) | −4.44344e13 | −1.95726 | −0.978629 | − | 0.205632i | \(-0.934075\pi\) | ||||
−0.978629 | + | 0.205632i | \(0.934075\pi\) | |||||||
\(930\) | 5.00955e11 | 0.0219596 | ||||||||
\(931\) | −3.49000e13 | −1.52248 | ||||||||
\(932\) | −2.54030e12 | −0.110284 | ||||||||
\(933\) | −2.45008e12 | −0.105855 | ||||||||
\(934\) | 1.40482e13 | 0.604033 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.22994e13 | 1.37548 | ||||||||
\(937\) | 1.07753e13 | 0.456669 | 0.228335 | − | 0.973583i | \(-0.426672\pi\) | ||||
0.228335 | + | 0.973583i | \(0.426672\pi\) | |||||||
\(938\) | −6.25994e12 | −0.264033 | ||||||||
\(939\) | −6.51877e12 | −0.273634 | ||||||||
\(940\) | 4.67173e12 | 0.195165 | ||||||||
\(941\) | −7.03292e12 | −0.292403 | −0.146202 | − | 0.989255i | \(-0.546705\pi\) | ||||
−0.146202 | + | 0.989255i | \(0.546705\pi\) | |||||||
\(942\) | 1.23789e12 | 0.0512217 | ||||||||
\(943\) | −2.81384e13 | −1.15877 | ||||||||
\(944\) | 1.07686e13 | 0.441351 | ||||||||
\(945\) | −2.24169e12 | −0.0914391 | ||||||||
\(946\) | −8.37821e12 | −0.340127 | ||||||||
\(947\) | −2.60497e13 | −1.05251 | −0.526257 | − | 0.850325i | \(-0.676405\pi\) | ||||
−0.526257 | + | 0.850325i | \(0.676405\pi\) | |||||||
\(948\) | −1.97286e11 | −0.00793341 | ||||||||
\(949\) | 1.81774e13 | 0.727503 | ||||||||
\(950\) | 5.34196e12 | 0.212787 | ||||||||
\(951\) | 1.10704e13 | 0.438885 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.63568e13 | 1.03508 | 0.517541 | − | 0.855658i | \(-0.326847\pi\) | ||||
0.517541 | + | 0.855658i | \(0.326847\pi\) | |||||||
\(954\) | 5.09626e12 | 0.199197 | ||||||||
\(955\) | −2.43263e13 | −0.946370 | ||||||||
\(956\) | 4.71151e12 | 0.182431 | ||||||||
\(957\) | 7.79752e12 | 0.300506 | ||||||||
\(958\) | 3.27093e13 | 1.25466 | ||||||||
\(959\) | −1.78942e12 | −0.0683171 | ||||||||
\(960\) | 6.95115e12 | 0.264141 | ||||||||
\(961\) | −2.62015e13 | −0.990993 | ||||||||
\(962\) | −2.96848e13 | −1.11750 | ||||||||
\(963\) | −4.28455e13 | −1.60541 | ||||||||
\(964\) | −4.23012e12 | −0.157763 | ||||||||
\(965\) | −7.63149e12 | −0.283293 | ||||||||
\(966\) | 1.39530e12 | 0.0515550 | ||||||||
\(967\) | 3.86295e13 | 1.42069 | 0.710347 | − | 0.703852i | \(-0.248538\pi\) | ||||
0.710347 | + | 0.703852i | \(0.248538\pi\) | |||||||
\(968\) | −1.49395e13 | −0.546885 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.64928e13 | −0.960850 | ||||||||
\(971\) | 5.64860e12 | 0.203917 | 0.101959 | − | 0.994789i | \(-0.467489\pi\) | ||||
0.101959 | + | 0.994789i | \(0.467489\pi\) | |||||||
\(972\) | −1.83869e12 | −0.0660710 | ||||||||
\(973\) | −3.50346e11 | −0.0125311 | ||||||||
\(974\) | −1.60715e13 | −0.572191 | ||||||||
\(975\) | 1.27409e12 | 0.0451523 | ||||||||
\(976\) | 9.78622e12 | 0.345216 | ||||||||
\(977\) | 1.04338e13 | 0.366368 | 0.183184 | − | 0.983079i | \(-0.441360\pi\) | ||||
0.183184 | + | 0.983079i | \(0.441360\pi\) | |||||||
\(978\) | 7.55306e12 | 0.263997 | ||||||||
\(979\) | 2.54259e13 | 0.884613 | ||||||||
\(980\) | 3.07410e12 | 0.106463 | ||||||||
\(981\) | 4.65854e13 | 1.60598 | ||||||||
\(982\) | 2.09344e13 | 0.718388 | ||||||||
\(983\) | 3.49221e13 | 1.19292 | 0.596458 | − | 0.802644i | \(-0.296574\pi\) | ||||
0.596458 | + | 0.802644i | \(0.296574\pi\) | |||||||
\(984\) | 6.56826e12 | 0.223343 | ||||||||
\(985\) | −3.67949e13 | −1.24544 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.31227e12 | −0.0775554 | ||||||||
\(988\) | −6.80296e12 | −0.227139 | ||||||||
\(989\) | 1.08533e13 | 0.360725 | ||||||||
\(990\) | 3.57769e13 | 1.18371 | ||||||||
\(991\) | 2.80238e13 | 0.922986 | 0.461493 | − | 0.887144i | \(-0.347314\pi\) | ||||
0.461493 | + | 0.887144i | \(0.347314\pi\) | |||||||
\(992\) | 5.96334e11 | 0.0195518 | ||||||||
\(993\) | −8.76897e12 | −0.286205 | ||||||||
\(994\) | 1.37001e12 | 0.0445128 | ||||||||
\(995\) | −2.53400e13 | −0.819601 | ||||||||
\(996\) | −6.06915e11 | −0.0195416 | ||||||||
\(997\) | −1.82363e13 | −0.584532 | −0.292266 | − | 0.956337i | \(-0.594409\pi\) | ||||
−0.292266 | + | 0.956337i | \(0.594409\pi\) | |||||||
\(998\) | 7.16643e12 | 0.228673 | ||||||||
\(999\) | 1.19115e13 | 0.378373 |
(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 | 289.10.a.f.1.18 | 24 | ||
17.2 | even | 8 | 17.10.c.a.4.9 | ✓ | 24 | ||
17.9 | even | 8 | 17.10.c.a.13.4 | yes | 24 | ||
17.16 | even | 2 | inner | 289.10.a.f.1.17 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.9 | ✓ | 24 | 17.2 | even | 8 | ||
17.10.c.a.13.4 | yes | 24 | 17.9 | even | 8 | ||
289.10.a.f.1.17 | 24 | 17.16 | even | 2 | inner | ||
289.10.a.f.1.18 | 24 | 1.1 | even | 1 | trivial |