Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,9,Mod(58,177)]
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, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(72.1060139808\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.3 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.9.c.a.58.78 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 29.8918i | − | 1.86824i | −0.356962 | − | 0.934119i | \(-0.616187\pi\) | ||
0.356962 | − | 0.934119i | \(-0.383813\pi\) | |||||||
\(3\) | 46.7654 | 0.577350 | ||||||||
\(4\) | −637.520 | −2.49031 | ||||||||
\(5\) | −247.630 | −0.396208 | −0.198104 | − | 0.980181i | \(-0.563478\pi\) | ||||
−0.198104 | + | 0.980181i | \(0.563478\pi\) | |||||||
\(6\) | − | 1397.90i | − | 1.07863i | ||||||
\(7\) | 4057.23 | 1.68981 | 0.844904 | − | 0.534918i | \(-0.179657\pi\) | ||||
0.844904 | + | 0.534918i | \(0.179657\pi\) | |||||||
\(8\) | 11404.3i | 2.78426i | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | 7402.10i | 0.740210i | ||||||||
\(11\) | − | 21197.9i | − | 1.44784i | −0.689882 | − | 0.723922i | \(-0.742338\pi\) | ||
0.689882 | − | 0.723922i | \(-0.257662\pi\) | |||||||
\(12\) | −29813.9 | −1.43778 | ||||||||
\(13\) | 21525.6i | 0.753669i | 0.926281 | + | 0.376835i | \(0.122988\pi\) | ||||
−0.926281 | + | 0.376835i | \(0.877012\pi\) | |||||||
\(14\) | − | 121278.i | − | 3.15696i | ||||||
\(15\) | −11580.5 | −0.228751 | ||||||||
\(16\) | 177691. | 2.71135 | ||||||||
\(17\) | −95116.6 | −1.13883 | −0.569417 | − | 0.822049i | \(-0.692831\pi\) | ||||
−0.569417 | + | 0.822049i | \(0.692831\pi\) | |||||||
\(18\) | − | 65373.4i | − | 0.622746i | ||||||
\(19\) | −41670.2 | −0.319750 | −0.159875 | − | 0.987137i | \(-0.551109\pi\) | ||||
−0.159875 | + | 0.987137i | \(0.551109\pi\) | |||||||
\(20\) | 157869. | 0.986681 | ||||||||
\(21\) | 189738. | 0.975611 | ||||||||
\(22\) | −633643. | −2.70492 | ||||||||
\(23\) | 492438.i | 1.75971i | 0.475246 | + | 0.879853i | \(0.342359\pi\) | ||||
−0.475246 | + | 0.879853i | \(0.657641\pi\) | |||||||
\(24\) | 533328.i | 1.60749i | ||||||||
\(25\) | −329304. | −0.843020 | ||||||||
\(26\) | 643438. | 1.40803 | ||||||||
\(27\) | 102276. | 0.192450 | ||||||||
\(28\) | −2.58657e6 | −4.20815 | ||||||||
\(29\) | −1.25263e6 | −1.77105 | −0.885523 | − | 0.464595i | \(-0.846200\pi\) | ||||
−0.885523 | + | 0.464595i | \(0.846200\pi\) | |||||||
\(30\) | 346162.i | 0.427361i | ||||||||
\(31\) | 1.66108e6i | 1.79864i | 0.437296 | + | 0.899318i | \(0.355936\pi\) | ||||
−0.437296 | + | 0.899318i | \(0.644064\pi\) | |||||||
\(32\) | − | 2.39199e6i | − | 2.28118i | ||||||
\(33\) | − | 991326.i | − | 0.835913i | ||||||
\(34\) | 2.84321e6i | 2.12761i | ||||||||
\(35\) | −1.00469e6 | −0.669515 | ||||||||
\(36\) | −1.39426e6 | −0.830104 | ||||||||
\(37\) | − | 889974.i | − | 0.474865i | −0.971404 | − | 0.237433i | \(-0.923694\pi\) | ||
0.971404 | − | 0.237433i | \(-0.0763059\pi\) | |||||||
\(38\) | 1.24560e6i | 0.597370i | ||||||||
\(39\) | 1.00665e6i | 0.435131i | ||||||||
\(40\) | − | 2.82405e6i | − | 1.10314i | ||||||
\(41\) | 1.19968e6 | 0.424552 | 0.212276 | − | 0.977210i | \(-0.431912\pi\) | ||||
0.212276 | + | 0.977210i | \(0.431912\pi\) | |||||||
\(42\) | − | 5.67161e6i | − | 1.82267i | ||||||
\(43\) | − | 2.01013e6i | − | 0.587963i | −0.955811 | − | 0.293981i | \(-0.905020\pi\) | ||
0.955811 | − | 0.293981i | \(-0.0949803\pi\) | |||||||
\(44\) | 1.35141e7i | 3.60558i | ||||||||
\(45\) | −541566. | −0.132069 | ||||||||
\(46\) | 1.47199e7 | 3.28755 | ||||||||
\(47\) | − | 2.76926e6i | − | 0.567508i | −0.958897 | − | 0.283754i | \(-0.908420\pi\) | ||
0.958897 | − | 0.283754i | \(-0.0915799\pi\) | |||||||
\(48\) | 8.30977e6 | 1.56540 | ||||||||
\(49\) | 1.06963e7 | 1.85545 | ||||||||
\(50\) | 9.84351e6i | 1.57496i | ||||||||
\(51\) | −4.44816e6 | −0.657506 | ||||||||
\(52\) | − | 1.37230e7i | − | 1.87687i | ||||||
\(53\) | −8.79299e6 | −1.11438 | −0.557190 | − | 0.830385i | \(-0.688120\pi\) | ||||
−0.557190 | + | 0.830385i | \(0.688120\pi\) | |||||||
\(54\) | − | 3.05721e6i | − | 0.359543i | ||||||
\(55\) | 5.24922e6i | 0.573647i | ||||||||
\(56\) | 4.62700e7i | 4.70486i | ||||||||
\(57\) | −1.94872e6 | −0.184608 | ||||||||
\(58\) | 3.74433e7i | 3.30874i | ||||||||
\(59\) | −1.17794e7 | + | 2.84185e6i | −0.972110 | + | 0.234527i | ||||
\(60\) | 7.38280e6 | 0.569661 | ||||||||
\(61\) | − | 1.24584e7i | − | 0.899793i | −0.893081 | − | 0.449896i | \(-0.851461\pi\) | ||
0.893081 | − | 0.449896i | \(-0.148539\pi\) | |||||||
\(62\) | 4.96526e7 | 3.36028 | ||||||||
\(63\) | 8.87316e6 | 0.563269 | ||||||||
\(64\) | −2.60121e7 | −1.55044 | ||||||||
\(65\) | − | 5.33037e6i | − | 0.298610i | ||||||
\(66\) | −2.96325e7 | −1.56168 | ||||||||
\(67\) | 2.43467e7i | 1.20820i | 0.796907 | + | 0.604102i | \(0.206468\pi\) | ||||
−0.796907 | + | 0.604102i | \(0.793532\pi\) | |||||||
\(68\) | 6.06387e7 | 2.83605 | ||||||||
\(69\) | 2.30290e7i | 1.01597i | ||||||||
\(70\) | 3.00320e7i | 1.25081i | ||||||||
\(71\) | −4.11384e7 | −1.61888 | −0.809439 | − | 0.587205i | \(-0.800228\pi\) | ||||
−0.809439 | + | 0.587205i | \(0.800228\pi\) | |||||||
\(72\) | 2.49413e7i | 0.928086i | ||||||||
\(73\) | 2.32169e7i | 0.817547i | 0.912636 | + | 0.408773i | \(0.134043\pi\) | ||||
−0.912636 | + | 0.408773i | \(0.865957\pi\) | |||||||
\(74\) | −2.66029e7 | −0.887161 | ||||||||
\(75\) | −1.54000e7 | −0.486718 | ||||||||
\(76\) | 2.65656e7 | 0.796279 | ||||||||
\(77\) | − | 8.60046e7i | − | 2.44658i | ||||||
\(78\) | 3.00906e7 | 0.812929 | ||||||||
\(79\) | 2.79916e6 | 0.0718652 | 0.0359326 | − | 0.999354i | \(-0.488560\pi\) | ||||
0.0359326 | + | 0.999354i | \(0.488560\pi\) | |||||||
\(80\) | −4.40015e7 | −1.07426 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | − | 3.58607e7i | − | 0.793165i | ||||||
\(83\) | − | 2.03547e6i | − | 0.0428896i | −0.999770 | − | 0.0214448i | \(-0.993173\pi\) | ||
0.999770 | − | 0.0214448i | \(-0.00682661\pi\) | |||||||
\(84\) | −1.20962e8 | −2.42958 | ||||||||
\(85\) | 2.35537e7 | 0.451215 | ||||||||
\(86\) | −6.00863e7 | −1.09845 | ||||||||
\(87\) | −5.85796e7 | −1.02251 | ||||||||
\(88\) | 2.41747e8 | 4.03117 | ||||||||
\(89\) | 2.00226e6i | 0.0319124i | 0.999873 | + | 0.0159562i | \(0.00507924\pi\) | ||||
−0.999873 | + | 0.0159562i | \(0.994921\pi\) | |||||||
\(90\) | 1.61884e7i | 0.246737i | ||||||||
\(91\) | 8.73341e7i | 1.27356i | ||||||||
\(92\) | − | 3.13939e8i | − | 4.38222i | ||||||
\(93\) | 7.76809e7i | 1.03844i | ||||||||
\(94\) | −8.27781e7 | −1.06024 | ||||||||
\(95\) | 1.03188e7 | 0.126688 | ||||||||
\(96\) | − | 1.11862e8i | − | 1.31704i | ||||||
\(97\) | − | 3.90744e7i | − | 0.441373i | −0.975345 | − | 0.220686i | \(-0.929170\pi\) | ||
0.975345 | − | 0.220686i | \(-0.0708297\pi\) | |||||||
\(98\) | − | 3.19732e8i | − | 3.46642i | ||||||
\(99\) | − | 4.63598e7i | − | 0.482614i | ||||||
\(100\) | 2.09938e8 | 2.09938 | ||||||||
\(101\) | 1.41791e8i | 1.36258i | 0.732012 | + | 0.681291i | \(0.238581\pi\) | ||||
−0.732012 | + | 0.681291i | \(0.761419\pi\) | |||||||
\(102\) | 1.32964e8i | 1.22838i | ||||||||
\(103\) | 2.84725e7i | 0.252975i | 0.991968 | + | 0.126487i | \(0.0403703\pi\) | ||||
−0.991968 | + | 0.126487i | \(0.959630\pi\) | |||||||
\(104\) | −2.45484e8 | −2.09841 | ||||||||
\(105\) | −4.69847e7 | −0.386545 | ||||||||
\(106\) | 2.62838e8i | 2.08193i | ||||||||
\(107\) | 1.77416e8 | 1.35350 | 0.676748 | − | 0.736215i | \(-0.263389\pi\) | ||||
0.676748 | + | 0.736215i | \(0.263389\pi\) | |||||||
\(108\) | −6.52029e7 | −0.479261 | ||||||||
\(109\) | 1.88778e8i | 1.33735i | 0.743555 | + | 0.668675i | \(0.233138\pi\) | ||||
−0.743555 | + | 0.668675i | \(0.766862\pi\) | |||||||
\(110\) | 1.56909e8 | 1.07171 | ||||||||
\(111\) | − | 4.16200e7i | − | 0.274164i | ||||||
\(112\) | 7.20932e8 | 4.58165 | ||||||||
\(113\) | 1.94290e8i | 1.19162i | 0.803127 | + | 0.595808i | \(0.203168\pi\) | ||||
−0.803127 | + | 0.595808i | \(0.796832\pi\) | |||||||
\(114\) | 5.82508e7i | 0.344892i | ||||||||
\(115\) | − | 1.21942e8i | − | 0.697209i | ||||||
\(116\) | 7.98575e8 | 4.41046 | ||||||||
\(117\) | 4.70764e7i | 0.251223i | ||||||||
\(118\) | 8.49479e7 | + | 3.52108e8i | 0.438152 | + | 1.81613i | ||||
\(119\) | −3.85910e8 | −1.92441 | ||||||||
\(120\) | − | 1.32068e8i | − | 0.636901i | ||||||
\(121\) | −2.34991e8 | −1.09625 | ||||||||
\(122\) | −3.72404e8 | −1.68103 | ||||||||
\(123\) | 5.61037e7 | 0.245115 | ||||||||
\(124\) | − | 1.05897e9i | − | 4.47917i | ||||||
\(125\) | 1.78276e8 | 0.730218 | ||||||||
\(126\) | − | 2.65235e8i | − | 1.05232i | ||||||
\(127\) | 1.85538e8 | 0.713210 | 0.356605 | − | 0.934255i | \(-0.383934\pi\) | ||||
0.356605 | + | 0.934255i | \(0.383934\pi\) | |||||||
\(128\) | 1.65199e8i | 0.615413i | ||||||||
\(129\) | − | 9.40043e7i | − | 0.339460i | ||||||
\(130\) | −1.59334e8 | −0.557874 | ||||||||
\(131\) | − | 5.84623e8i | − | 1.98514i | −0.121683 | − | 0.992569i | \(-0.538829\pi\) | ||
0.121683 | − | 0.992569i | \(-0.461171\pi\) | |||||||
\(132\) | 6.31991e8i | 2.08168i | ||||||||
\(133\) | −1.69066e8 | −0.540317 | ||||||||
\(134\) | 7.27766e8 | 2.25721 | ||||||||
\(135\) | −2.53266e7 | −0.0762502 | ||||||||
\(136\) | − | 1.08474e9i | − | 3.17081i | ||||||
\(137\) | −3.84843e8 | −1.09245 | −0.546224 | − | 0.837639i | \(-0.683935\pi\) | ||||
−0.546224 | + | 0.837639i | \(0.683935\pi\) | |||||||
\(138\) | 6.88379e8 | 1.89807 | ||||||||
\(139\) | 1.34828e8 | 0.361179 | 0.180589 | − | 0.983559i | \(-0.442199\pi\) | ||||
0.180589 | + | 0.983559i | \(0.442199\pi\) | |||||||
\(140\) | 6.40511e8 | 1.66730 | ||||||||
\(141\) | − | 1.29505e8i | − | 0.327651i | ||||||
\(142\) | 1.22970e9i | 3.02445i | ||||||||
\(143\) | 4.56296e8 | 1.09120 | ||||||||
\(144\) | 3.88610e8 | 0.903782 | ||||||||
\(145\) | 3.10188e8 | 0.701702 | ||||||||
\(146\) | 6.93995e8 | 1.52737 | ||||||||
\(147\) | 5.00217e8 | 1.07125 | ||||||||
\(148\) | 5.67376e8i | 1.18256i | ||||||||
\(149\) | − | 4.99204e8i | − | 1.01282i | −0.862292 | − | 0.506411i | \(-0.830972\pi\) | ||
0.862292 | − | 0.506411i | \(-0.169028\pi\) | |||||||
\(150\) | 4.60335e8i | 0.909304i | ||||||||
\(151\) | − | 6.49690e8i | − | 1.24968i | −0.780754 | − | 0.624839i | \(-0.785165\pi\) | ||
0.780754 | − | 0.624839i | \(-0.214835\pi\) | |||||||
\(152\) | − | 4.75221e8i | − | 0.890268i | ||||||
\(153\) | −2.08020e8 | −0.379611 | ||||||||
\(154\) | −2.57083e9 | −4.57079 | ||||||||
\(155\) | − | 4.11332e8i | − | 0.712633i | ||||||
\(156\) | − | 6.41760e8i | − | 1.08361i | ||||||
\(157\) | 3.80148e8i | 0.625683i | 0.949805 | + | 0.312842i | \(0.101281\pi\) | ||||
−0.949805 | + | 0.312842i | \(0.898719\pi\) | |||||||
\(158\) | − | 8.36718e7i | − | 0.134261i | ||||||
\(159\) | −4.11207e8 | −0.643387 | ||||||||
\(160\) | 5.92328e8i | 0.903821i | ||||||||
\(161\) | 1.99793e9i | 2.97356i | ||||||||
\(162\) | − | 1.42972e8i | − | 0.207582i | ||||||
\(163\) | 4.70927e8 | 0.667119 | 0.333560 | − | 0.942729i | \(-0.391750\pi\) | ||||
0.333560 | + | 0.942729i | \(0.391750\pi\) | |||||||
\(164\) | −7.64823e8 | −1.05727 | ||||||||
\(165\) | 2.45482e8i | 0.331195i | ||||||||
\(166\) | −6.08438e7 | −0.0801280 | ||||||||
\(167\) | −1.19539e9 | −1.53689 | −0.768444 | − | 0.639917i | \(-0.778969\pi\) | ||||
−0.768444 | + | 0.639917i | \(0.778969\pi\) | |||||||
\(168\) | 2.16383e9i | 2.71635i | ||||||||
\(169\) | 3.52381e8 | 0.431982 | ||||||||
\(170\) | − | 7.04063e8i | − | 0.842977i | ||||||
\(171\) | −9.11327e7 | −0.106583 | ||||||||
\(172\) | 1.28150e9i | 1.46421i | ||||||||
\(173\) | − | 2.68426e8i | − | 0.299668i | −0.988711 | − | 0.149834i | \(-0.952126\pi\) | ||
0.988711 | − | 0.149834i | \(-0.0478740\pi\) | |||||||
\(174\) | 1.75105e9i | 1.91030i | ||||||||
\(175\) | −1.33606e9 | −1.42454 | ||||||||
\(176\) | − | 3.76667e9i | − | 3.92560i | ||||||
\(177\) | −5.50868e8 | + | 1.32900e8i | −0.561248 | + | 0.135404i | ||||
\(178\) | 5.98511e7 | 0.0596200 | ||||||||
\(179\) | 5.25010e8i | 0.511394i | 0.966757 | + | 0.255697i | \(0.0823049\pi\) | ||||
−0.966757 | + | 0.255697i | \(0.917695\pi\) | |||||||
\(180\) | 3.45259e8 | 0.328894 | ||||||||
\(181\) | 1.34593e9 | 1.25403 | 0.627017 | − | 0.779006i | \(-0.284276\pi\) | ||||
0.627017 | + | 0.779006i | \(0.284276\pi\) | |||||||
\(182\) | 2.61057e9 | 2.37931 | ||||||||
\(183\) | − | 5.82621e8i | − | 0.519496i | ||||||
\(184\) | −5.61592e9 | −4.89948 | ||||||||
\(185\) | 2.20384e8i | 0.188145i | ||||||||
\(186\) | 2.32202e9 | 1.94006 | ||||||||
\(187\) | 2.01627e9i | 1.64885i | ||||||||
\(188\) | 1.76546e9i | 1.41327i | ||||||||
\(189\) | 4.14957e8 | 0.325204 | ||||||||
\(190\) | − | 3.08447e8i | − | 0.236683i | ||||||
\(191\) | 3.31156e8i | 0.248828i | 0.992230 | + | 0.124414i | \(0.0397051\pi\) | ||||
−0.992230 | + | 0.124414i | \(0.960295\pi\) | |||||||
\(192\) | −1.21646e9 | −0.895148 | ||||||||
\(193\) | −2.19184e9 | −1.57972 | −0.789859 | − | 0.613289i | \(-0.789846\pi\) | ||||
−0.789859 | + | 0.613289i | \(0.789846\pi\) | |||||||
\(194\) | −1.16801e9 | −0.824590 | ||||||||
\(195\) | − | 2.49277e8i | − | 0.172402i | ||||||
\(196\) | −6.81911e9 | −4.62065 | ||||||||
\(197\) | 1.88008e9 | 1.24828 | 0.624139 | − | 0.781313i | \(-0.285450\pi\) | ||||
0.624139 | + | 0.781313i | \(0.285450\pi\) | |||||||
\(198\) | −1.38578e9 | −0.901639 | ||||||||
\(199\) | −1.84676e9 | −1.17760 | −0.588799 | − | 0.808279i | \(-0.700399\pi\) | ||||
−0.588799 | + | 0.808279i | \(0.700399\pi\) | |||||||
\(200\) | − | 3.75550e9i | − | 2.34718i | ||||||
\(201\) | 1.13858e9i | 0.697557i | ||||||||
\(202\) | 4.23839e9 | 2.54563 | ||||||||
\(203\) | −5.08220e9 | −2.99273 | ||||||||
\(204\) | 2.83579e9 | 1.63740 | ||||||||
\(205\) | −2.97077e8 | −0.168211 | ||||||||
\(206\) | 8.51096e8 | 0.472617 | ||||||||
\(207\) | 1.07696e9i | 0.586568i | ||||||||
\(208\) | 3.82489e9i | 2.04346i | ||||||||
\(209\) | 8.83320e8i | 0.462949i | ||||||||
\(210\) | 1.40446e9i | 0.722157i | ||||||||
\(211\) | 1.12595e9i | 0.568056i | 0.958816 | + | 0.284028i | \(0.0916708\pi\) | ||||
−0.958816 | + | 0.284028i | \(0.908329\pi\) | |||||||
\(212\) | 5.60571e9 | 2.77515 | ||||||||
\(213\) | −1.92385e9 | −0.934659 | ||||||||
\(214\) | − | 5.30328e9i | − | 2.52865i | ||||||
\(215\) | 4.97767e8i | 0.232955i | ||||||||
\(216\) | 1.16639e9i | 0.535831i | ||||||||
\(217\) | 6.73937e9i | 3.03935i | ||||||||
\(218\) | 5.64291e9 | 2.49849 | ||||||||
\(219\) | 1.08575e9i | 0.472011i | ||||||||
\(220\) | − | 3.34649e9i | − | 1.42856i | ||||||
\(221\) | − | 2.04744e9i | − | 0.858305i | ||||||
\(222\) | −1.24410e9 | −0.512203 | ||||||||
\(223\) | 1.27587e9 | 0.515924 | 0.257962 | − | 0.966155i | \(-0.416949\pi\) | ||||
0.257962 | + | 0.966155i | \(0.416949\pi\) | |||||||
\(224\) | − | 9.70485e9i | − | 3.85476i | ||||||
\(225\) | −7.20189e8 | −0.281007 | ||||||||
\(226\) | 5.80767e9 | 2.22622 | ||||||||
\(227\) | 1.10307e9i | 0.415433i | 0.978189 | + | 0.207716i | \(0.0666031\pi\) | ||||
−0.978189 | + | 0.207716i | \(0.933397\pi\) | |||||||
\(228\) | 1.24235e9 | 0.459732 | ||||||||
\(229\) | 1.07539e8i | 0.0391043i | 0.999809 | + | 0.0195521i | \(0.00622404\pi\) | ||||
−0.999809 | + | 0.0195521i | \(0.993776\pi\) | |||||||
\(230\) | −3.64507e9 | −1.30255 | ||||||||
\(231\) | − | 4.02204e9i | − | 1.41253i | ||||||
\(232\) | − | 1.42854e10i | − | 4.93105i | ||||||
\(233\) | 8.76987e8i | 0.297557i | 0.988871 | + | 0.148778i | \(0.0475341\pi\) | ||||
−0.988871 | + | 0.148778i | \(0.952466\pi\) | |||||||
\(234\) | 1.40720e9 | 0.469345 | ||||||||
\(235\) | 6.85751e8i | 0.224851i | ||||||||
\(236\) | 7.50961e9 | − | 1.81173e9i | 2.42086 | − | 0.584045i | ||||
\(237\) | 1.30904e8 | 0.0414914 | ||||||||
\(238\) | 1.15355e10i | 3.59526i | ||||||||
\(239\) | 1.11886e9 | 0.342913 | 0.171457 | − | 0.985192i | \(-0.445153\pi\) | ||||
0.171457 | + | 0.985192i | \(0.445153\pi\) | |||||||
\(240\) | −2.05775e9 | −0.620222 | ||||||||
\(241\) | 3.82849e9 | 1.13490 | 0.567452 | − | 0.823407i | \(-0.307929\pi\) | ||||
0.567452 | + | 0.823407i | \(0.307929\pi\) | |||||||
\(242\) | 7.02431e9i | 2.04806i | ||||||||
\(243\) | 2.23677e8 | 0.0641500 | ||||||||
\(244\) | 7.94247e9i | 2.24077i | ||||||||
\(245\) | −2.64872e9 | −0.735144 | ||||||||
\(246\) | − | 1.67704e9i | − | 0.457934i | ||||||
\(247\) | − | 8.96974e8i | − | 0.240986i | ||||||
\(248\) | −1.89435e10 | −5.00787 | ||||||||
\(249\) | − | 9.51894e7i | − | 0.0247623i | ||||||
\(250\) | − | 5.32899e9i | − | 1.36422i | ||||||
\(251\) | −4.29677e9 | −1.08255 | −0.541275 | − | 0.840846i | \(-0.682058\pi\) | ||||
−0.541275 | + | 0.840846i | \(0.682058\pi\) | |||||||
\(252\) | −5.65682e9 | −1.40272 | ||||||||
\(253\) | 1.04386e10 | 2.54778 | ||||||||
\(254\) | − | 5.54606e9i | − | 1.33245i | ||||||
\(255\) | 1.10150e9 | 0.260509 | ||||||||
\(256\) | −1.72101e9 | −0.400703 | ||||||||
\(257\) | 5.03295e9 | 1.15369 | 0.576847 | − | 0.816852i | \(-0.304283\pi\) | ||||
0.576847 | + | 0.816852i | \(0.304283\pi\) | |||||||
\(258\) | −2.80996e9 | −0.634193 | ||||||||
\(259\) | − | 3.61083e9i | − | 0.802431i | ||||||
\(260\) | 3.39822e9i | 0.743631i | ||||||||
\(261\) | −2.73950e9 | −0.590349 | ||||||||
\(262\) | −1.74754e10 | −3.70871 | ||||||||
\(263\) | 3.01837e8 | 0.0630884 | 0.0315442 | − | 0.999502i | \(-0.489957\pi\) | ||||
0.0315442 | + | 0.999502i | \(0.489957\pi\) | |||||||
\(264\) | 1.13054e10 | 2.32740 | ||||||||
\(265\) | 2.17741e9 | 0.441525 | ||||||||
\(266\) | 5.05368e9i | 1.00944i | ||||||||
\(267\) | 9.36364e7i | 0.0184247i | ||||||||
\(268\) | − | 1.55215e10i | − | 3.00881i | ||||||
\(269\) | − | 4.48283e9i | − | 0.856136i | −0.903747 | − | 0.428068i | \(-0.859194\pi\) | ||
0.903747 | − | 0.428068i | \(-0.140806\pi\) | |||||||
\(270\) | 7.57056e8i | 0.142454i | ||||||||
\(271\) | −2.34851e9 | −0.435427 | −0.217713 | − | 0.976013i | \(-0.569860\pi\) | ||||
−0.217713 | + | 0.976013i | \(0.569860\pi\) | |||||||
\(272\) | −1.69013e10 | −3.08777 | ||||||||
\(273\) | 4.08421e9i | 0.735288i | ||||||||
\(274\) | 1.15036e10i | 2.04095i | ||||||||
\(275\) | 6.98056e9i | 1.22056i | ||||||||
\(276\) | − | 1.46815e10i | − | 2.53007i | ||||||
\(277\) | −7.92826e9 | −1.34666 | −0.673331 | − | 0.739341i | \(-0.735137\pi\) | ||||
−0.673331 | + | 0.739341i | \(0.735137\pi\) | |||||||
\(278\) | − | 4.03026e9i | − | 0.674768i | ||||||
\(279\) | 3.63278e9i | 0.599545i | ||||||||
\(280\) | − | 1.14578e10i | − | 1.86410i | ||||||
\(281\) | −8.25964e9 | −1.32476 | −0.662378 | − | 0.749170i | \(-0.730453\pi\) | ||||
−0.662378 | + | 0.749170i | \(0.730453\pi\) | |||||||
\(282\) | −3.87115e9 | −0.612130 | ||||||||
\(283\) | 4.43696e8i | 0.0691736i | 0.999402 | + | 0.0345868i | \(0.0110115\pi\) | ||||
−0.999402 | + | 0.0345868i | \(0.988988\pi\) | |||||||
\(284\) | 2.62265e10 | 4.03151 | ||||||||
\(285\) | 4.82562e8 | 0.0731431 | ||||||||
\(286\) | − | 1.36395e10i | − | 2.03861i | ||||||
\(287\) | 4.86739e9 | 0.717412 | ||||||||
\(288\) | − | 5.23128e9i | − | 0.760393i | ||||||
\(289\) | 2.07141e9 | 0.296944 | ||||||||
\(290\) | − | 9.27208e9i | − | 1.31095i | ||||||
\(291\) | − | 1.82733e9i | − | 0.254827i | ||||||
\(292\) | − | 1.48012e10i | − | 2.03595i | ||||||
\(293\) | 3.14415e9 | 0.426612 | 0.213306 | − | 0.976985i | \(-0.431577\pi\) | ||||
0.213306 | + | 0.976985i | \(0.431577\pi\) | |||||||
\(294\) | − | 1.49524e10i | − | 2.00134i | ||||||
\(295\) | 2.91693e9 | − | 7.03726e8i | 0.385157 | − | 0.0929213i | ||||
\(296\) | 1.01496e10 | 1.32215 | ||||||||
\(297\) | − | 2.16803e9i | − | 0.278638i | ||||||
\(298\) | −1.49221e10 | −1.89219 | ||||||||
\(299\) | −1.06000e10 | −1.32624 | ||||||||
\(300\) | 9.81784e9 | 1.21208 | ||||||||
\(301\) | − | 8.15555e9i | − | 0.993544i | ||||||
\(302\) | −1.94204e10 | −2.33470 | ||||||||
\(303\) | 6.63091e9i | 0.786688i | ||||||||
\(304\) | −7.40441e9 | −0.866954 | ||||||||
\(305\) | 3.08507e9i | 0.356505i | ||||||||
\(306\) | 6.21809e9i | 0.709205i | ||||||||
\(307\) | −3.18785e9 | −0.358876 | −0.179438 | − | 0.983769i | \(-0.557428\pi\) | ||||
−0.179438 | + | 0.983769i | \(0.557428\pi\) | |||||||
\(308\) | 5.48297e10i | 6.09274i | ||||||||
\(309\) | 1.33153e9i | 0.146055i | ||||||||
\(310\) | −1.22955e10 | −1.33137 | ||||||||
\(311\) | −1.43538e10 | −1.53435 | −0.767176 | − | 0.641437i | \(-0.778339\pi\) | ||||
−0.767176 | + | 0.641437i | \(0.778339\pi\) | |||||||
\(312\) | −1.14802e10 | −1.21152 | ||||||||
\(313\) | 6.81720e9i | 0.710279i | 0.934813 | + | 0.355140i | \(0.115567\pi\) | ||||
−0.934813 | + | 0.355140i | \(0.884433\pi\) | |||||||
\(314\) | 1.13633e10 | 1.16892 | ||||||||
\(315\) | −2.19726e9 | −0.223172 | ||||||||
\(316\) | −1.78452e9 | −0.178967 | ||||||||
\(317\) | 5.79535e9 | 0.573909 | 0.286954 | − | 0.957944i | \(-0.407357\pi\) | ||||
0.286954 | + | 0.957944i | \(0.407357\pi\) | |||||||
\(318\) | 1.22917e10i | 1.20200i | ||||||||
\(319\) | 2.65530e10i | 2.56420i | ||||||||
\(320\) | 6.44137e9 | 0.614297 | ||||||||
\(321\) | 8.29691e9 | 0.781441 | ||||||||
\(322\) | 5.97218e10 | 5.55533 | ||||||||
\(323\) | 3.96353e9 | 0.364143 | ||||||||
\(324\) | −3.04924e9 | −0.276701 | ||||||||
\(325\) | − | 7.08846e9i | − | 0.635358i | ||||||
\(326\) | − | 1.40769e10i | − | 1.24634i | ||||||
\(327\) | 8.82826e9i | 0.772119i | ||||||||
\(328\) | 1.36816e10i | 1.18206i | ||||||||
\(329\) | − | 1.12355e10i | − | 0.958979i | ||||||
\(330\) | 7.33790e9 | 0.618751 | ||||||||
\(331\) | −1.65954e10 | −1.38253 | −0.691266 | − | 0.722601i | \(-0.742947\pi\) | ||||
−0.691266 | + | 0.722601i | \(0.742947\pi\) | |||||||
\(332\) | 1.29765e9i | 0.106809i | ||||||||
\(333\) | − | 1.94637e9i | − | 0.158288i | ||||||
\(334\) | 3.57322e10i | 2.87127i | ||||||||
\(335\) | − | 6.02896e9i | − | 0.478700i | ||||||
\(336\) | 3.37147e10 | 2.64522 | ||||||||
\(337\) | 1.80474e10i | 1.39925i | 0.714512 | + | 0.699623i | \(0.246649\pi\) | ||||
−0.714512 | + | 0.699623i | \(0.753351\pi\) | |||||||
\(338\) | − | 1.05333e10i | − | 0.807046i | ||||||
\(339\) | 9.08603e9i | 0.687979i | ||||||||
\(340\) | −1.50160e10 | −1.12367 | ||||||||
\(341\) | 3.52113e10 | 2.60414 | ||||||||
\(342\) | 2.72412e9i | 0.199123i | ||||||||
\(343\) | 2.00082e10 | 1.44555 | ||||||||
\(344\) | 2.29241e10 | 1.63704 | ||||||||
\(345\) | − | 5.70267e9i | − | 0.402534i | ||||||
\(346\) | −8.02375e9 | −0.559852 | ||||||||
\(347\) | − | 2.10020e10i | − | 1.44858i | −0.689494 | − | 0.724292i | \(-0.742167\pi\) | ||
0.689494 | − | 0.724292i | \(-0.257833\pi\) | |||||||
\(348\) | 3.73457e10 | 2.54638 | ||||||||
\(349\) | − | 4.85779e9i | − | 0.327444i | −0.986507 | − | 0.163722i | \(-0.947650\pi\) | ||
0.986507 | − | 0.163722i | \(-0.0523500\pi\) | |||||||
\(350\) | 3.99374e10i | 2.66138i | ||||||||
\(351\) | 2.20154e9i | 0.145044i | ||||||||
\(352\) | −5.07051e10 | −3.30279 | ||||||||
\(353\) | 1.90800e10i | 1.22879i | 0.788997 | + | 0.614397i | \(0.210601\pi\) | ||||
−0.788997 | + | 0.614397i | \(0.789399\pi\) | |||||||
\(354\) | 3.97262e9 | + | 1.64664e10i | 0.252967 | + | 1.04854i | ||||
\(355\) | 1.01871e10 | 0.641411 | ||||||||
\(356\) | − | 1.27648e9i | − | 0.0794720i | ||||||
\(357\) | −1.80472e10 | −1.11106 | ||||||||
\(358\) | 1.56935e10 | 0.955405 | ||||||||
\(359\) | −8.81861e9 | −0.530912 | −0.265456 | − | 0.964123i | \(-0.585522\pi\) | ||||
−0.265456 | + | 0.964123i | \(0.585522\pi\) | |||||||
\(360\) | − | 6.17620e9i | − | 0.367715i | ||||||
\(361\) | −1.52472e10 | −0.897760 | ||||||||
\(362\) | − | 4.02324e10i | − | 2.34283i | ||||||
\(363\) | −1.09894e10 | −0.632920 | ||||||||
\(364\) | − | 5.56772e10i | − | 3.17155i | ||||||
\(365\) | − | 5.74919e9i | − | 0.323918i | ||||||
\(366\) | −1.74156e10 | −0.970541 | ||||||||
\(367\) | − | 1.46733e10i | − | 0.808840i | −0.914573 | − | 0.404420i | \(-0.867473\pi\) | ||
0.914573 | − | 0.404420i | \(-0.132527\pi\) | |||||||
\(368\) | 8.75016e10i | 4.77117i | ||||||||
\(369\) | 2.62371e9 | 0.141517 | ||||||||
\(370\) | 6.58768e9 | 0.351500 | ||||||||
\(371\) | −3.56752e10 | −1.88309 | ||||||||
\(372\) | − | 4.95232e10i | − | 2.58605i | ||||||
\(373\) | 4.10565e9 | 0.212103 | 0.106051 | − | 0.994361i | \(-0.466179\pi\) | ||||
0.106051 | + | 0.994361i | \(0.466179\pi\) | |||||||
\(374\) | 6.02699e10 | 3.08045 | ||||||||
\(375\) | 8.33714e9 | 0.421592 | ||||||||
\(376\) | 3.15815e10 | 1.58009 | ||||||||
\(377\) | − | 2.69635e10i | − | 1.33478i | ||||||
\(378\) | − | 1.24038e10i | − | 0.607558i | ||||||
\(379\) | −3.96543e10 | −1.92191 | −0.960955 | − | 0.276704i | \(-0.910758\pi\) | ||||
−0.960955 | + | 0.276704i | \(0.910758\pi\) | |||||||
\(380\) | −6.57843e9 | −0.315492 | ||||||||
\(381\) | 8.67674e9 | 0.411772 | ||||||||
\(382\) | 9.89885e9 | 0.464870 | ||||||||
\(383\) | 1.49720e10 | 0.695799 | 0.347899 | − | 0.937532i | \(-0.386895\pi\) | ||||
0.347899 | + | 0.937532i | \(0.386895\pi\) | |||||||
\(384\) | 7.72558e9i | 0.355309i | ||||||||
\(385\) | 2.12973e10i | 0.969353i | ||||||||
\(386\) | 6.55180e10i | 2.95129i | ||||||||
\(387\) | − | 4.39615e9i | − | 0.195988i | ||||||
\(388\) | 2.49107e10i | 1.09916i | ||||||||
\(389\) | 3.75472e9 | 0.163975 | 0.0819877 | − | 0.996633i | \(-0.473873\pi\) | ||||
0.0819877 | + | 0.996633i | \(0.473873\pi\) | |||||||
\(390\) | −7.45133e9 | −0.322089 | ||||||||
\(391\) | − | 4.68390e10i | − | 2.00401i | ||||||
\(392\) | 1.21984e11i | 5.16606i | ||||||||
\(393\) | − | 2.73401e10i | − | 1.14612i | ||||||
\(394\) | − | 5.61990e10i | − | 2.33208i | ||||||
\(395\) | −6.93154e8 | −0.0284735 | ||||||||
\(396\) | 2.95553e10i | 1.20186i | ||||||||
\(397\) | − | 5.89403e9i | − | 0.237274i | −0.992938 | − | 0.118637i | \(-0.962148\pi\) | ||
0.992938 | − | 0.118637i | \(-0.0378525\pi\) | |||||||
\(398\) | 5.52029e10i | 2.20003i | ||||||||
\(399\) | −7.90641e9 | −0.311952 | ||||||||
\(400\) | −5.85144e10 | −2.28572 | ||||||||
\(401\) | 3.30329e10i | 1.27752i | 0.769404 | + | 0.638762i | \(0.220553\pi\) | ||||
−0.769404 | + | 0.638762i | \(0.779447\pi\) | |||||||
\(402\) | 3.40343e10 | 1.30320 | ||||||||
\(403\) | −3.57556e10 | −1.35558 | ||||||||
\(404\) | − | 9.03946e10i | − | 3.39326i | ||||||
\(405\) | −1.18441e9 | −0.0440231 | ||||||||
\(406\) | 1.51916e11i | 5.59113i | ||||||||
\(407\) | −1.88656e10 | −0.687530 | ||||||||
\(408\) | − | 5.07283e10i | − | 1.83067i | ||||||
\(409\) | − | 3.04752e10i | − | 1.08906i | −0.838740 | − | 0.544532i | \(-0.816707\pi\) | ||
0.838740 | − | 0.544532i | \(-0.183293\pi\) | |||||||
\(410\) | 8.88018e9i | 0.314258i | ||||||||
\(411\) | −1.79973e10 | −0.630725 | ||||||||
\(412\) | − | 1.81518e10i | − | 0.629987i | ||||||
\(413\) | −4.77917e10 | + | 1.15300e10i | −1.64268 | + | 0.396305i | ||||
\(414\) | 3.21923e10 | 1.09585 | ||||||||
\(415\) | 5.04043e8i | 0.0169932i | ||||||||
\(416\) | 5.14889e10 | 1.71926 | ||||||||
\(417\) | 6.30530e9 | 0.208527 | ||||||||
\(418\) | 2.64040e10 | 0.864898 | ||||||||
\(419\) | − | 1.81306e9i | − | 0.0588241i | −0.999567 | − | 0.0294121i | \(-0.990637\pi\) | ||
0.999567 | − | 0.0294121i | \(-0.00936350\pi\) | |||||||
\(420\) | 2.99537e10 | 0.962617 | ||||||||
\(421\) | − | 3.79069e10i | − | 1.20667i | −0.797486 | − | 0.603337i | \(-0.793837\pi\) | ||
0.797486 | − | 0.603337i | \(-0.206163\pi\) | |||||||
\(422\) | 3.36568e10 | 1.06126 | ||||||||
\(423\) | − | 6.05637e9i | − | 0.189169i | ||||||
\(424\) | − | 1.00278e11i | − | 3.10272i | ||||||
\(425\) | 3.13223e10 | 0.960060 | ||||||||
\(426\) | 5.75074e10i | 1.74617i | ||||||||
\(427\) | − | 5.05465e10i | − | 1.52048i | ||||||
\(428\) | −1.13106e11 | −3.37063 | ||||||||
\(429\) | 2.13388e10 | 0.630002 | ||||||||
\(430\) | 1.48792e10 | 0.435216 | ||||||||
\(431\) | − | 6.06752e10i | − | 1.75834i | −0.476510 | − | 0.879169i | \(-0.658098\pi\) | ||
0.476510 | − | 0.879169i | \(-0.341902\pi\) | |||||||
\(432\) | 1.81735e10 | 0.521799 | ||||||||
\(433\) | −2.64222e10 | −0.751653 | −0.375826 | − | 0.926690i | \(-0.622641\pi\) | ||||
−0.375826 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(434\) | 2.01452e11 | 5.67823 | ||||||||
\(435\) | 1.45061e10 | 0.405128 | ||||||||
\(436\) | − | 1.20350e11i | − | 3.33042i | ||||||
\(437\) | − | 2.05200e10i | − | 0.562667i | ||||||
\(438\) | 3.24549e10 | 0.881829 | ||||||||
\(439\) | −6.36143e10 | −1.71276 | −0.856380 | − | 0.516347i | \(-0.827292\pi\) | ||||
−0.856380 | + | 0.516347i | \(0.827292\pi\) | |||||||
\(440\) | −5.98639e10 | −1.59718 | ||||||||
\(441\) | 2.33928e10 | 0.618484 | ||||||||
\(442\) | −6.12016e10 | −1.60352 | ||||||||
\(443\) | 3.79235e10i | 0.984677i | 0.870404 | + | 0.492338i | \(0.163858\pi\) | ||||
−0.870404 | + | 0.492338i | \(0.836142\pi\) | |||||||
\(444\) | 2.65336e10i | 0.682753i | ||||||||
\(445\) | − | 4.95819e8i | − | 0.0126440i | ||||||
\(446\) | − | 3.81380e10i | − | 0.963869i | ||||||
\(447\) | − | 2.33455e10i | − | 0.584753i | ||||||
\(448\) | −1.05537e11 | −2.61995 | ||||||||
\(449\) | −1.87339e10 | −0.460938 | −0.230469 | − | 0.973080i | \(-0.574026\pi\) | ||||
−0.230469 | + | 0.973080i | \(0.574026\pi\) | |||||||
\(450\) | 2.15277e10i | 0.524987i | ||||||||
\(451\) | − | 2.54307e10i | − | 0.614685i | ||||||
\(452\) | − | 1.23864e11i | − | 2.96749i | ||||||
\(453\) | − | 3.03830e10i | − | 0.721502i | ||||||
\(454\) | 3.29728e10 | 0.776127 | ||||||||
\(455\) | − | 2.16265e10i | − | 0.504593i | ||||||
\(456\) | − | 2.22239e10i | − | 0.513997i | ||||||
\(457\) | 1.55748e10i | 0.357074i | 0.983933 | + | 0.178537i | \(0.0571364\pi\) | ||||
−0.983933 | + | 0.178537i | \(0.942864\pi\) | |||||||
\(458\) | 3.21454e9 | 0.0730561 | ||||||||
\(459\) | −9.72813e9 | −0.219169 | ||||||||
\(460\) | 7.77406e10i | 1.73627i | ||||||||
\(461\) | 1.36617e10 | 0.302484 | 0.151242 | − | 0.988497i | \(-0.451673\pi\) | ||||
0.151242 | + | 0.988497i | \(0.451673\pi\) | |||||||
\(462\) | −1.20226e11 | −2.63895 | ||||||||
\(463\) | 2.90985e10i | 0.633209i | 0.948558 | + | 0.316604i | \(0.102543\pi\) | ||||
−0.948558 | + | 0.316604i | \(0.897457\pi\) | |||||||
\(464\) | −2.22580e11 | −4.80192 | ||||||||
\(465\) | − | 1.92361e10i | − | 0.411439i | ||||||
\(466\) | 2.62147e10 | 0.555906 | ||||||||
\(467\) | − | 9.71527e9i | − | 0.204262i | −0.994771 | − | 0.102131i | \(-0.967434\pi\) | ||
0.994771 | − | 0.102131i | \(-0.0325661\pi\) | |||||||
\(468\) | − | 3.00121e10i | − | 0.625624i | ||||||
\(469\) | 9.87800e10i | 2.04163i | ||||||||
\(470\) | 2.04983e10 | 0.420075 | ||||||||
\(471\) | 1.77778e10i | 0.361238i | ||||||||
\(472\) | −3.24093e10 | − | 1.34336e11i | −0.652984 | − | 2.70661i | ||||
\(473\) | −4.26104e10 | −0.851278 | ||||||||
\(474\) | − | 3.91294e9i | − | 0.0775158i | ||||||
\(475\) | 1.37222e10 | 0.269556 | ||||||||
\(476\) | 2.46025e11 | 4.79239 | ||||||||
\(477\) | −1.92303e10 | −0.371460 | ||||||||
\(478\) | − | 3.34448e10i | − | 0.640644i | ||||||
\(479\) | 5.28028e10 | 1.00303 | 0.501516 | − | 0.865148i | \(-0.332776\pi\) | ||||
0.501516 | + | 0.865148i | \(0.332776\pi\) | |||||||
\(480\) | 2.77004e10i | 0.521821i | ||||||||
\(481\) | 1.91572e10 | 0.357891 | ||||||||
\(482\) | − | 1.14440e11i | − | 2.12027i | ||||||
\(483\) | 9.34341e10i | 1.71679i | ||||||||
\(484\) | 1.49811e11 | 2.73001 | ||||||||
\(485\) | 9.67599e9i | 0.174875i | ||||||||
\(486\) | − | 6.68612e9i | − | 0.119848i | ||||||
\(487\) | 6.59238e10 | 1.17200 | 0.585998 | − | 0.810312i | \(-0.300703\pi\) | ||||
0.585998 | + | 0.810312i | \(0.300703\pi\) | |||||||
\(488\) | 1.42080e11 | 2.50526 | ||||||||
\(489\) | 2.20231e10 | 0.385162 | ||||||||
\(490\) | 7.91751e10i | 1.37342i | ||||||||
\(491\) | 1.08414e11 | 1.86535 | 0.932675 | − | 0.360719i | \(-0.117469\pi\) | ||||
0.932675 | + | 0.360719i | \(0.117469\pi\) | |||||||
\(492\) | −3.57672e10 | −0.610414 | ||||||||
\(493\) | 1.19146e11 | 2.01693 | ||||||||
\(494\) | −2.68122e10 | −0.450219 | ||||||||
\(495\) | 1.14801e10i | 0.191216i | ||||||||
\(496\) | 2.95158e11i | 4.87672i | ||||||||
\(497\) | −1.66908e11 | −2.73559 | ||||||||
\(498\) | −2.84538e9 | −0.0462619 | ||||||||
\(499\) | −2.38659e10 | −0.384925 | −0.192462 | − | 0.981304i | \(-0.561647\pi\) | ||||
−0.192462 | + | 0.981304i | \(0.561647\pi\) | |||||||
\(500\) | −1.13655e11 | −1.81847 | ||||||||
\(501\) | −5.59027e10 | −0.887323 | ||||||||
\(502\) | 1.28438e11i | 2.02246i | ||||||||
\(503\) | 1.22240e10i | 0.190960i | 0.995431 | + | 0.0954799i | \(0.0304386\pi\) | ||||
−0.995431 | + | 0.0954799i | \(0.969561\pi\) | |||||||
\(504\) | 1.01192e11i | 1.56829i | ||||||||
\(505\) | − | 3.51117e10i | − | 0.539866i | ||||||
\(506\) | − | 3.12030e11i | − | 4.75986i | ||||||
\(507\) | 1.64792e10 | 0.249405 | ||||||||
\(508\) | −1.18284e11 | −1.77612 | ||||||||
\(509\) | − | 3.81044e10i | − | 0.567680i | −0.958872 | − | 0.283840i | \(-0.908392\pi\) | ||
0.958872 | − | 0.283840i | \(-0.0916085\pi\) | |||||||
\(510\) | − | 3.29258e10i | − | 0.486693i | ||||||
\(511\) | 9.41963e10i | 1.38150i | ||||||||
\(512\) | 9.37349e10i | 1.36402i | ||||||||
\(513\) | −4.26186e9 | −0.0615360 | ||||||||
\(514\) | − | 1.50444e11i | − | 2.15537i | ||||||
\(515\) | − | 7.05065e9i | − | 0.100231i | ||||||
\(516\) | 5.99297e10i | 0.845363i | ||||||||
\(517\) | −5.87024e10 | −0.821662 | ||||||||
\(518\) | −1.07934e11 | −1.49913 | ||||||||
\(519\) | − | 1.25531e10i | − | 0.173014i | ||||||
\(520\) | 6.07892e10 | 0.831406 | ||||||||
\(521\) | −1.64846e10 | −0.223732 | −0.111866 | − | 0.993723i | \(-0.535683\pi\) | ||||
−0.111866 | + | 0.993723i | \(0.535683\pi\) | |||||||
\(522\) | 8.18885e10i | 1.10291i | ||||||||
\(523\) | 8.28989e9 | 0.110801 | 0.0554003 | − | 0.998464i | \(-0.482357\pi\) | ||||
0.0554003 | + | 0.998464i | \(0.482357\pi\) | |||||||
\(524\) | 3.72709e11i | 4.94362i | ||||||||
\(525\) | −6.24815e10 | −0.822459 | ||||||||
\(526\) | − | 9.02246e9i | − | 0.117864i | ||||||
\(527\) | − | 1.57996e11i | − | 2.04835i | ||||||
\(528\) | − | 1.76150e11i | − | 2.26645i | ||||||
\(529\) | −1.64184e11 | −2.09656 | ||||||||
\(530\) | − | 6.50866e10i | − | 0.824875i | ||||||
\(531\) | −2.57616e10 | + | 6.21512e9i | −0.324037 | + | 0.0781756i | ||||
\(532\) | 1.07783e11 | 1.34556 | ||||||||
\(533\) | 2.58239e10i | 0.319972i | ||||||||
\(534\) | 2.79896e9 | 0.0344216 | ||||||||
\(535\) | −4.39334e10 | −0.536265 | ||||||||
\(536\) | −2.77657e11 | −3.36395 | ||||||||
\(537\) | 2.45523e10i | 0.295253i | ||||||||
\(538\) | −1.34000e11 | −1.59947 | ||||||||
\(539\) | − | 2.26739e11i | − | 2.68640i | ||||||
\(540\) | 1.61462e10 | 0.189887 | ||||||||
\(541\) | − | 9.07595e10i | − | 1.05951i | −0.848152 | − | 0.529753i | \(-0.822285\pi\) | ||
0.848152 | − | 0.529753i | \(-0.177715\pi\) | |||||||
\(542\) | 7.02012e10i | 0.813481i | ||||||||
\(543\) | 6.29431e10 | 0.724017 | ||||||||
\(544\) | 2.27518e11i | 2.59789i | ||||||||
\(545\) | − | 4.67470e10i | − | 0.529868i | ||||||
\(546\) | 1.22084e11 | 1.37369 | ||||||||
\(547\) | −3.63083e10 | −0.405561 | −0.202781 | − | 0.979224i | \(-0.564998\pi\) | ||||
−0.202781 | + | 0.979224i | \(0.564998\pi\) | |||||||
\(548\) | 2.45345e11 | 2.72054 | ||||||||
\(549\) | − | 2.72465e10i | − | 0.299931i | ||||||
\(550\) | 2.08661e11 | 2.28030 | ||||||||
\(551\) | 5.21973e10 | 0.566293 | ||||||||
\(552\) | −2.62631e11 | −2.82871 | ||||||||
\(553\) | 1.13568e10 | 0.121438 | ||||||||
\(554\) | 2.36990e11i | 2.51589i | ||||||||
\(555\) | 1.03063e10i | 0.108626i | ||||||||
\(556\) | −8.59558e10 | −0.899448 | ||||||||
\(557\) | −1.36428e10 | −0.141737 | −0.0708684 | − | 0.997486i | \(-0.522577\pi\) | ||||
−0.0708684 | + | 0.997486i | \(0.522577\pi\) | |||||||
\(558\) | 1.08590e11 | 1.12009 | ||||||||
\(559\) | 4.32691e10 | 0.443129 | ||||||||
\(560\) | −1.78524e11 | −1.81529 | ||||||||
\(561\) | 9.42916e10i | 0.951966i | ||||||||
\(562\) | 2.46895e11i | 2.47496i | ||||||||
\(563\) | 9.41472e9i | 0.0937073i | 0.998902 | + | 0.0468537i | \(0.0149194\pi\) | ||||
−0.998902 | + | 0.0468537i | \(0.985081\pi\) | |||||||
\(564\) | 8.25623e10i | 0.815953i | ||||||||
\(565\) | − | 4.81119e10i | − | 0.472127i | ||||||
\(566\) | 1.32629e10 | 0.129233 | ||||||||
\(567\) | 1.94056e10 | 0.187756 | ||||||||
\(568\) | − | 4.69156e11i | − | 4.50737i | ||||||
\(569\) | − | 1.09073e11i | − | 1.04056i | −0.853995 | − | 0.520281i | \(-0.825827\pi\) | ||
0.853995 | − | 0.520281i | \(-0.174173\pi\) | |||||||
\(570\) | − | 1.44246e10i | − | 0.136649i | ||||||
\(571\) | 1.44117e11i | 1.35572i | 0.735189 | + | 0.677862i | \(0.237093\pi\) | ||||
−0.735189 | + | 0.677862i | \(0.762907\pi\) | |||||||
\(572\) | −2.90898e11 | −2.71742 | ||||||||
\(573\) | 1.54866e10i | 0.143661i | ||||||||
\(574\) | − | 1.45495e11i | − | 1.34030i | ||||||
\(575\) | − | 1.62162e11i | − | 1.48347i | ||||||
\(576\) | −5.68884e10 | −0.516814 | ||||||||
\(577\) | 2.14805e11 | 1.93794 | 0.968972 | − | 0.247172i | \(-0.0795013\pi\) | ||||
0.968972 | + | 0.247172i | \(0.0795013\pi\) | |||||||
\(578\) | − | 6.19181e10i | − | 0.554762i | ||||||
\(579\) | −1.02502e11 | −0.912050 | ||||||||
\(580\) | −1.97751e11 | −1.74746 | ||||||||
\(581\) | − | 8.25836e9i | − | 0.0724752i | ||||||
\(582\) | −5.46222e10 | −0.476077 | ||||||||
\(583\) | 1.86393e11i | 1.61345i | ||||||||
\(584\) | −2.64773e11 | −2.27626 | ||||||||
\(585\) | − | 1.16575e10i | − | 0.0995365i | ||||||
\(586\) | − | 9.39843e10i | − | 0.797012i | ||||||
\(587\) | − | 1.59442e11i | − | 1.34292i | −0.741039 | − | 0.671461i | \(-0.765667\pi\) | ||
0.741039 | − | 0.671461i | \(-0.234333\pi\) | |||||||
\(588\) | −3.18898e11 | −2.66774 | ||||||||
\(589\) | − | 6.92175e10i | − | 0.575115i | ||||||
\(590\) | −2.10356e10 | − | 8.71923e10i | −0.173599 | − | 0.719565i | ||||
\(591\) | 8.79227e10 | 0.720694 | ||||||||
\(592\) | − | 1.58140e11i | − | 1.28752i | ||||||
\(593\) | 1.49251e11 | 1.20698 | 0.603488 | − | 0.797372i | \(-0.293777\pi\) | ||||
0.603488 | + | 0.797372i | \(0.293777\pi\) | |||||||
\(594\) | −6.48064e10 | −0.520561 | ||||||||
\(595\) | 9.55628e10 | 0.762467 | ||||||||
\(596\) | 3.18253e11i | 2.52224i | ||||||||
\(597\) | −8.63642e10 | −0.679887 | ||||||||
\(598\) | 3.16853e11i | 2.47772i | ||||||||
\(599\) | 9.04429e9 | 0.0702533 | 0.0351267 | − | 0.999383i | \(-0.488817\pi\) | ||||
0.0351267 | + | 0.999383i | \(0.488817\pi\) | |||||||
\(600\) | − | 1.75627e11i | − | 1.35515i | ||||||
\(601\) | 3.45042e10i | 0.264469i | 0.991218 | + | 0.132234i | \(0.0422152\pi\) | ||||
−0.991218 | + | 0.132234i | \(0.957785\pi\) | |||||||
\(602\) | −2.43784e11 | −1.85618 | ||||||||
\(603\) | 5.32462e10i | 0.402735i | ||||||||
\(604\) | 4.14190e11i | 3.11209i | ||||||||
\(605\) | 5.81908e10 | 0.434343 | ||||||||
\(606\) | 1.98210e11 | 1.46972 | ||||||||
\(607\) | −1.49775e11 | −1.10328 | −0.551639 | − | 0.834083i | \(-0.685997\pi\) | ||||
−0.551639 | + | 0.834083i | \(0.685997\pi\) | |||||||
\(608\) | 9.96747e10i | 0.729408i | ||||||||
\(609\) | −2.37671e11 | −1.72785 | ||||||||
\(610\) | 9.22182e10 | 0.666036 | ||||||||
\(611\) | 5.96098e10 | 0.427713 | ||||||||
\(612\) | 1.32617e11 | 0.945351 | ||||||||
\(613\) | − | 7.52477e10i | − | 0.532907i | −0.963848 | − | 0.266453i | \(-0.914148\pi\) | ||
0.963848 | − | 0.266453i | \(-0.0858518\pi\) | |||||||
\(614\) | 9.52906e10i | 0.670465i | ||||||||
\(615\) | −1.38929e10 | −0.0971166 | ||||||||
\(616\) | 9.80825e11 | 6.81191 | ||||||||
\(617\) | −1.95339e11 | −1.34787 | −0.673934 | − | 0.738791i | \(-0.735397\pi\) | ||||
−0.673934 | + | 0.738791i | \(0.735397\pi\) | |||||||
\(618\) | 3.98018e10 | 0.272866 | ||||||||
\(619\) | −3.92472e10 | −0.267329 | −0.133664 | − | 0.991027i | \(-0.542674\pi\) | ||||
−0.133664 | + | 0.991027i | \(0.542674\pi\) | |||||||
\(620\) | 2.62233e11i | 1.77468i | ||||||||
\(621\) | 5.03645e10i | 0.338655i | ||||||||
\(622\) | 4.29060e11i | 2.86653i | ||||||||
\(623\) | 8.12362e9i | 0.0539259i | ||||||||
\(624\) | 1.78872e11i | 1.17979i | ||||||||
\(625\) | 8.44881e10 | 0.553701 | ||||||||
\(626\) | 2.03779e11 | 1.32697 | ||||||||
\(627\) | 4.13088e10i | 0.267284i | ||||||||
\(628\) | − | 2.42352e11i | − | 1.55815i | ||||||
\(629\) | 8.46513e10i | 0.540793i | ||||||||
\(630\) | 6.56800e10i | 0.416938i | ||||||||
\(631\) | −1.90888e11 | −1.20410 | −0.602048 | − | 0.798460i | \(-0.705648\pi\) | ||||
−0.602048 | + | 0.798460i | \(0.705648\pi\) | |||||||
\(632\) | 3.19225e10i | 0.200091i | ||||||||
\(633\) | 5.26557e10i | 0.327967i | ||||||||
\(634\) | − | 1.73234e11i | − | 1.07220i | ||||||
\(635\) | −4.59447e10 | −0.282579 | ||||||||
\(636\) | 2.62153e11 | 1.60224 | ||||||||
\(637\) | 2.30244e11i | 1.39840i | ||||||||
\(638\) | 7.93718e11 | 4.79053 | ||||||||
\(639\) | −8.99697e10 | −0.539626 | ||||||||
\(640\) | − | 4.09081e10i | − | 0.243831i | ||||||
\(641\) | 1.74358e11 | 1.03278 | 0.516392 | − | 0.856352i | \(-0.327275\pi\) | ||||
0.516392 | + | 0.856352i | \(0.327275\pi\) | |||||||
\(642\) | − | 2.48010e11i | − | 1.45992i | ||||||
\(643\) | −1.55791e10 | −0.0911376 | −0.0455688 | − | 0.998961i | \(-0.514510\pi\) | ||||
−0.0455688 | + | 0.998961i | \(0.514510\pi\) | |||||||
\(644\) | − | 1.27372e12i | − | 7.40511i | ||||||
\(645\) | 2.32783e10i | 0.134497i | ||||||||
\(646\) | − | 1.18477e11i | − | 0.680306i | ||||||
\(647\) | 8.29547e10 | 0.473395 | 0.236697 | − | 0.971583i | \(-0.423935\pi\) | ||||
0.236697 | + | 0.971583i | \(0.423935\pi\) | |||||||
\(648\) | 5.45465e10i | 0.309362i | ||||||||
\(649\) | 6.02411e10 | + | 2.49698e11i | 0.339558 | + | 1.40746i | ||||
\(650\) | −2.11887e11 | −1.18700 | ||||||||
\(651\) | 3.15169e11i | 1.75477i | ||||||||
\(652\) | −3.00226e11 | −1.66134 | ||||||||
\(653\) | −2.11139e10 | −0.116122 | −0.0580612 | − | 0.998313i | \(-0.518492\pi\) | ||||
−0.0580612 | + | 0.998313i | \(0.518492\pi\) | |||||||
\(654\) | 2.63893e11 | 1.44250 | ||||||||
\(655\) | 1.44770e11i | 0.786527i | ||||||||
\(656\) | 2.13173e11 | 1.15111 | ||||||||
\(657\) | 5.07753e10i | 0.272516i | ||||||||
\(658\) | −3.35850e11 | −1.79160 | ||||||||
\(659\) | − | 2.40511e11i | − | 1.27524i | −0.770350 | − | 0.637622i | \(-0.779918\pi\) | ||
0.770350 | − | 0.637622i | \(-0.220082\pi\) | |||||||
\(660\) | − | 1.56500e11i | − | 0.824779i | ||||||
\(661\) | 4.97787e10 | 0.260758 | 0.130379 | − | 0.991464i | \(-0.458381\pi\) | ||||
0.130379 | + | 0.991464i | \(0.458381\pi\) | |||||||
\(662\) | 4.96066e11i | 2.58290i | ||||||||
\(663\) | − | 9.57492e10i | − | 0.495542i | ||||||
\(664\) | 2.32131e10 | 0.119416 | ||||||||
\(665\) | 4.18657e10 | 0.214078 | ||||||||
\(666\) | −5.81806e10 | −0.295720 | ||||||||
\(667\) | − | 6.16841e11i | − | 3.11652i | ||||||
\(668\) | 7.62083e11 | 3.82733 | ||||||||
\(669\) | 5.96664e10 | 0.297869 | ||||||||
\(670\) | −1.80217e11 | −0.894325 | ||||||||
\(671\) | −2.64091e11 | −1.30276 | ||||||||
\(672\) | − | 4.53851e11i | − | 2.22554i | ||||||
\(673\) | 3.50853e9i | 0.0171027i | 0.999963 | + | 0.00855136i | \(0.00272201\pi\) | ||||
−0.999963 | + | 0.00855136i | \(0.997278\pi\) | |||||||
\(674\) | 5.39468e11 | 2.61412 | ||||||||
\(675\) | −3.36799e10 | −0.162239 | ||||||||
\(676\) | −2.24650e11 | −1.07577 | ||||||||
\(677\) | −1.33644e11 | −0.636200 | −0.318100 | − | 0.948057i | \(-0.603045\pi\) | ||||
−0.318100 | + | 0.948057i | \(0.603045\pi\) | |||||||
\(678\) | 2.71598e11 | 1.28531 | ||||||||
\(679\) | − | 1.58534e11i | − | 0.745835i | ||||||
\(680\) | 2.68614e11i | 1.25630i | ||||||||
\(681\) | 5.15856e10i | 0.239850i | ||||||||
\(682\) | − | 1.05253e12i | − | 4.86516i | ||||||
\(683\) | 2.61051e11i | 1.19962i | 0.800144 | + | 0.599808i | \(0.204756\pi\) | ||||
−0.800144 | + | 0.599808i | \(0.795244\pi\) | |||||||
\(684\) | 5.80990e10 | 0.265426 | ||||||||
\(685\) | 9.52985e10 | 0.432836 | ||||||||
\(686\) | − | 5.98083e11i | − | 2.70063i | ||||||
\(687\) | 5.02911e9i | 0.0225769i | ||||||||
\(688\) | − | 3.57181e11i | − | 1.59417i | ||||||
\(689\) | − | 1.89274e11i | − | 0.839873i | ||||||
\(690\) | −1.70463e11 | −0.752029 | ||||||||
\(691\) | 1.53433e11i | 0.672987i | 0.941686 | + | 0.336493i | \(0.109241\pi\) | ||||
−0.941686 | + | 0.336493i | \(0.890759\pi\) | |||||||
\(692\) | 1.71127e11i | 0.746268i | ||||||||
\(693\) | − | 1.88092e11i | − | 0.815526i | ||||||
\(694\) | −6.27789e11 | −2.70630 | ||||||||
\(695\) | −3.33875e10 | −0.143102 | ||||||||
\(696\) | − | 6.68061e11i | − | 2.84695i | ||||||
\(697\) | −1.14110e11 | −0.483495 | ||||||||
\(698\) | −1.45208e11 | −0.611743 | ||||||||
\(699\) | 4.10126e10i | 0.171794i | ||||||||
\(700\) | 8.51768e11 | 3.54755 | ||||||||
\(701\) | − | 8.71726e10i | − | 0.361001i | −0.983575 | − | 0.180500i | \(-0.942228\pi\) | ||
0.983575 | − | 0.180500i | \(-0.0577717\pi\) | |||||||
\(702\) | 6.58081e10 | 0.270976 | ||||||||
\(703\) | 3.70854e10i | 0.151838i | ||||||||
\(704\) | 5.51401e11i | 2.24480i | ||||||||
\(705\) | 3.20694e10i | 0.129818i | ||||||||
\(706\) | 5.70335e11 | 2.29568 | ||||||||
\(707\) | 5.75278e11i | 2.30250i | ||||||||
\(708\) | 3.51190e11 | − | 8.47264e10i | 1.39768 | − | 0.337199i | ||||
\(709\) | 3.33405e10 | 0.131943 | 0.0659717 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659717 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(710\) | − | 3.04511e11i | − | 1.19831i | ||||||
\(711\) | 6.12175e9 | 0.0239551 | ||||||||
\(712\) | −2.28344e10 | −0.0888525 | ||||||||
\(713\) | −8.17977e11 | −3.16507 | ||||||||
\(714\) | 5.39464e11i | 2.07572i | ||||||||
\(715\) | −1.12992e11 | −0.432340 | ||||||||
\(716\) | − | 3.34704e11i | − | 1.27353i | ||||||
\(717\) | 5.23239e10 | 0.197981 | ||||||||
\(718\) | 2.63604e11i | 0.991870i | ||||||||
\(719\) | − | 9.49106e10i | − | 0.355140i | −0.984108 | − | 0.177570i | \(-0.943176\pi\) | ||
0.984108 | − | 0.177570i | \(-0.0568236\pi\) | |||||||
\(720\) | −9.62313e10 | −0.358085 | ||||||||
\(721\) | 1.15520e11i | 0.427479i | ||||||||
\(722\) | 4.55765e11i | 1.67723i | ||||||||
\(723\) | 1.79041e11 | 0.655237 | ||||||||
\(724\) | −8.58059e11 | −3.12294 | ||||||||
\(725\) | 4.12496e11 | 1.49303 | ||||||||
\(726\) | 3.28494e11i | 1.18245i | ||||||||
\(727\) | −1.53628e11 | −0.549963 | −0.274981 | − | 0.961450i | \(-0.588672\pi\) | ||||
−0.274981 | + | 0.961450i | \(0.588672\pi\) | |||||||
\(728\) | −9.95987e11 | −3.54591 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | −1.71854e11 | −0.605156 | ||||||||
\(731\) | 1.91196e11i | 0.669592i | ||||||||
\(732\) | 3.71433e11i | 1.29371i | ||||||||
\(733\) | 4.52962e10 | 0.156908 | 0.0784541 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784541 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(734\) | −4.38611e11 | −1.51111 | ||||||||
\(735\) | −1.23869e11 | −0.424436 | ||||||||
\(736\) | 1.17791e12 | 4.01420 | ||||||||
\(737\) | 5.16098e11 | 1.74929 | ||||||||
\(738\) | − | 7.84274e10i | − | 0.264388i | ||||||
\(739\) | 3.89715e11i | 1.30668i | 0.757065 | + | 0.653340i | \(0.226633\pi\) | ||||
−0.757065 | + | 0.653340i | \(0.773367\pi\) | |||||||
\(740\) | − | 1.40499e11i | − | 0.468541i | ||||||
\(741\) | − | 4.19473e10i | − | 0.139133i | ||||||
\(742\) | 1.06640e12i | 3.51805i | ||||||||
\(743\) | −2.21515e10 | −0.0726854 | −0.0363427 | − | 0.999339i | \(-0.511571\pi\) | ||||
−0.0363427 | + | 0.999339i | \(0.511571\pi\) | |||||||
\(744\) | −8.85899e11 | −2.89129 | ||||||||
\(745\) | 1.23618e11i | 0.401288i | ||||||||
\(746\) | − | 1.22725e11i | − | 0.396259i | ||||||
\(747\) | − | 4.45157e9i | − | 0.0142965i | ||||||
\(748\) | − | 1.28541e12i | − | 4.10616i | ||||||
\(749\) | 7.19816e11 | 2.28715 | ||||||||
\(750\) | − | 2.49212e11i | − | 0.787634i | ||||||
\(751\) | − | 1.70755e10i | − | 0.0536803i | −0.999640 | − | 0.0268401i | \(-0.991455\pi\) | ||
0.999640 | − | 0.0268401i | \(-0.00854450\pi\) | |||||||
\(752\) | − | 4.92071e11i | − | 1.53871i | ||||||
\(753\) | −2.00940e11 | −0.625010 | ||||||||
\(754\) | −8.05988e11 | −2.49369 | ||||||||
\(755\) | 1.60882e11i | 0.495132i | ||||||||
\(756\) | −2.64543e11 | −0.809859 | ||||||||
\(757\) | −3.31538e10 | −0.100960 | −0.0504800 | − | 0.998725i | \(-0.516075\pi\) | ||||
−0.0504800 | + | 0.998725i | \(0.516075\pi\) | |||||||
\(758\) | 1.18534e12i | 3.59059i | ||||||||
\(759\) | 4.88167e11 | 1.47096 | ||||||||
\(760\) | 1.17679e11i | 0.352731i | ||||||||
\(761\) | −5.71126e11 | −1.70292 | −0.851458 | − | 0.524423i | \(-0.824281\pi\) | ||||
−0.851458 | + | 0.524423i | \(0.824281\pi\) | |||||||
\(762\) | − | 2.59363e11i | − | 0.769288i | ||||||
\(763\) | 7.65915e11i | 2.25986i | ||||||||
\(764\) | − | 2.11119e11i | − | 0.619659i | ||||||
\(765\) | 5.15119e10 | 0.150405 | ||||||||
\(766\) | − | 4.47539e11i | − | 1.29992i | ||||||
\(767\) | −6.11723e10 | − | 2.53558e11i | −0.176756 | − | 0.732649i | ||||
\(768\) | −8.04836e10 | −0.231346 | ||||||||
\(769\) | − | 8.44024e10i | − | 0.241351i | −0.992692 | − | 0.120676i | \(-0.961494\pi\) | ||
0.992692 | − | 0.120676i | \(-0.0385061\pi\) | |||||||
\(770\) | 6.36615e11 | 1.81098 | ||||||||
\(771\) | 2.35368e11 | 0.666085 | ||||||||
\(772\) | 1.39734e12 | 3.93399 | ||||||||
\(773\) | − | 2.74428e11i | − | 0.768618i | −0.923205 | − | 0.384309i | \(-0.874440\pi\) | ||
0.923205 | − | 0.384309i | \(-0.125560\pi\) | |||||||
\(774\) | −1.31409e11 | −0.366151 | ||||||||
\(775\) | − | 5.47000e11i | − | 1.51628i | ||||||
\(776\) | 4.45617e11 | 1.22890 | ||||||||
\(777\) | − | 1.68862e11i | − | 0.463284i | ||||||
\(778\) | − | 1.12235e11i | − | 0.306345i | ||||||
\(779\) | −4.99911e10 | −0.135751 | ||||||||
\(780\) | 1.58919e11i | 0.429336i | ||||||||
\(781\) | 8.72046e11i | 2.34388i | ||||||||
\(782\) | −1.40010e12 | −3.74397 | ||||||||
\(783\) | −1.28114e11 | −0.340838 | ||||||||
\(784\) | 1.90063e12 | 5.03077 | ||||||||
\(785\) | − | 9.41360e10i | − | 0.247900i | ||||||
\(786\) | −8.17245e11 | −2.14122 | ||||||||
\(787\) | −1.65013e11 | −0.430148 | −0.215074 | − | 0.976598i | \(-0.568999\pi\) | ||||
−0.215074 | + | 0.976598i | \(0.568999\pi\) | |||||||
\(788\) | −1.19859e12 | −3.10860 | ||||||||
\(789\) | 1.41155e10 | 0.0364241 | ||||||||
\(790\) | 2.07196e10i | 0.0531954i | ||||||||
\(791\) | 7.88278e11i | 2.01360i | ||||||||
\(792\) | 5.28702e11 | 1.34372 | ||||||||
\(793\) | 2.68174e11 | 0.678146 | ||||||||
\(794\) | −1.76183e11 | −0.443284 | ||||||||
\(795\) | 1.01827e11 | 0.254915 | ||||||||
\(796\) | 1.17734e12 | 2.93259 | ||||||||
\(797\) | − | 2.42268e11i | − | 0.600430i | −0.953872 | − | 0.300215i | \(-0.902942\pi\) | ||
0.953872 | − | 0.300215i | \(-0.0970585\pi\) | |||||||
\(798\) | 2.36337e11i | 0.582801i | ||||||||
\(799\) | 2.63402e11i | 0.646297i | ||||||||
\(800\) | 7.87693e11i | 1.92308i | ||||||||
\(801\) | 4.37894e9i | 0.0106375i | ||||||||
\(802\) | 9.87413e11 | 2.38672 | ||||||||
\(803\) | 4.92149e11 | 1.18368 | ||||||||
\(804\) | − | 7.25868e11i | − | 1.73714i | ||||||
\(805\) | − | 4.94748e11i | − | 1.17815i | ||||||
\(806\) | 1.06880e12i | 2.53254i | ||||||||
\(807\) | − | 2.09641e11i | − | 0.494290i | ||||||
\(808\) | −1.61703e12 | −3.79378 | ||||||||
\(809\) | 4.60332e11i | 1.07467i | 0.843368 | + | 0.537337i | \(0.180570\pi\) | ||||
−0.843368 | + | 0.537337i | \(0.819430\pi\) | |||||||
\(810\) | 3.54040e10i | 0.0822456i | ||||||||
\(811\) | − | 2.57768e11i | − | 0.595861i | −0.954588 | − | 0.297931i | \(-0.903704\pi\) | ||
0.954588 | − | 0.297931i | \(-0.0962964\pi\) | |||||||
\(812\) | 3.24000e12 | 7.45283 | ||||||||
\(813\) | −1.09829e11 | −0.251394 | ||||||||
\(814\) | 5.63926e11i | 1.28447i | ||||||||
\(815\) | −1.16616e11 | −0.264318 | ||||||||
\(816\) | −7.90397e11 | −1.78273 | ||||||||
\(817\) | 8.37624e10i | 0.188001i | ||||||||
\(818\) | −9.10959e11 | −2.03463 | ||||||||
\(819\) | 1.91000e11i | 0.424519i | ||||||||
\(820\) | 1.89393e11 | 0.418898 | ||||||||
\(821\) | − | 1.74887e11i | − | 0.384933i | −0.981304 | − | 0.192466i | \(-0.938351\pi\) | ||
0.981304 | − | 0.192466i | \(-0.0616486\pi\) | |||||||
\(822\) | 5.37972e11i | 1.17835i | ||||||||
\(823\) | 3.23459e11i | 0.705049i | 0.935803 | + | 0.352525i | \(0.114677\pi\) | ||||
−0.935803 | + | 0.352525i | \(0.885323\pi\) | |||||||
\(824\) | −3.24710e11 | −0.704348 | ||||||||
\(825\) | 3.26448e11i | 0.704691i | ||||||||
\(826\) | 3.44653e11 | + | 1.42858e12i | 0.740393 | + | 3.06891i | ||||
\(827\) | 4.56032e11 | 0.974929 | 0.487465 | − | 0.873143i | \(-0.337922\pi\) | ||||
0.487465 | + | 0.873143i | \(0.337922\pi\) | |||||||
\(828\) | − | 6.86585e11i | − | 1.46074i | ||||||
\(829\) | 3.65235e11 | 0.773310 | 0.386655 | − | 0.922224i | \(-0.373630\pi\) | ||||
0.386655 | + | 0.922224i | \(0.373630\pi\) | |||||||
\(830\) | 1.50667e10 | 0.0317473 | ||||||||
\(831\) | −3.70768e11 | −0.777496 | ||||||||
\(832\) | − | 5.59924e11i | − | 1.16852i | ||||||
\(833\) | −1.01740e12 | −2.11305 | ||||||||
\(834\) | − | 1.88477e11i | − | 0.389577i | ||||||
\(835\) | 2.96013e11 | 0.608927 | ||||||||
\(836\) | − | 5.63134e11i | − | 1.15289i | ||||||
\(837\) | 1.69888e11i | 0.346148i | ||||||||
\(838\) | −5.41956e10 | −0.109897 | ||||||||
\(839\) | 2.76165e11i | 0.557342i | 0.960387 | + | 0.278671i | \(0.0898938\pi\) | ||||
−0.960387 | + | 0.278671i | \(0.910106\pi\) | |||||||
\(840\) | − | 5.35829e11i | − | 1.07624i | ||||||
\(841\) | 1.06883e12 | 2.13661 | ||||||||
\(842\) | −1.13311e12 | −2.25436 | ||||||||
\(843\) | −3.86265e11 | −0.764848 | ||||||||
\(844\) | − | 7.17818e11i | − | 1.41464i | ||||||
\(845\) | −8.72601e10 | −0.171155 | ||||||||
\(846\) | −1.81036e11 | −0.353413 | ||||||||
\(847\) | −9.53412e11 | −1.85245 | ||||||||
\(848\) | −1.56243e12 | −3.02147 | ||||||||
\(849\) | 2.07496e10i | 0.0399374i | ||||||||
\(850\) | − | 9.36281e11i | − | 1.79362i | ||||||
\(851\) | 4.38257e11 | 0.835623 | ||||||||
\(852\) | 1.22649e12 | 2.32759 | ||||||||
\(853\) | 1.17242e11 | 0.221456 | 0.110728 | − | 0.993851i | \(-0.464682\pi\) | ||||
0.110728 | + | 0.993851i | \(0.464682\pi\) | |||||||
\(854\) | −1.51093e12 | −2.84061 | ||||||||
\(855\) | 2.25672e10 | 0.0422292 | ||||||||
\(856\) | 2.02331e12i | 3.76848i | ||||||||
\(857\) | − | 1.39151e11i | − | 0.257966i | −0.991647 | − | 0.128983i | \(-0.958829\pi\) | ||
0.991647 | − | 0.128983i | \(-0.0411713\pi\) | |||||||
\(858\) | − | 6.37857e11i | − | 1.17699i | ||||||
\(859\) | 1.96043e11i | 0.360064i | 0.983661 | + | 0.180032i | \(0.0576201\pi\) | ||||
−0.983661 | + | 0.180032i | \(0.942380\pi\) | |||||||
\(860\) | − | 3.17337e11i | − | 0.580132i | ||||||
\(861\) | 2.27625e11 | 0.414198 | ||||||||
\(862\) | −1.81369e12 | −3.28499 | ||||||||
\(863\) | 2.32620e11i | 0.419376i | 0.977768 | + | 0.209688i | \(0.0672449\pi\) | ||||
−0.977768 | + | 0.209688i | \(0.932755\pi\) | |||||||
\(864\) | − | 2.44643e11i | − | 0.439013i | ||||||
\(865\) | 6.64704e10i | 0.118731i | ||||||||
\(866\) | 7.89807e11i | 1.40427i | ||||||||
\(867\) | 9.68702e10 | 0.171441 | ||||||||
\(868\) | − | 4.29649e12i | − | 7.56893i | ||||||
\(869\) | − | 5.93362e10i | − | 0.104050i | ||||||
\(870\) | − | 4.33612e11i | − | 0.756875i | ||||||
\(871\) | −5.24076e11 | −0.910587 | ||||||||
\(872\) | −2.15288e12 | −3.72353 | ||||||||
\(873\) | − | 8.54558e10i | − | 0.147124i | ||||||
\(874\) | −6.13379e11 | −1.05120 | ||||||||
\(875\) | 7.23306e11 | 1.23393 | ||||||||
\(876\) | − | 6.92185e11i | − | 1.17545i | ||||||
\(877\) | 3.48906e11 | 0.589807 | 0.294903 | − | 0.955527i | \(-0.404713\pi\) | ||||
0.294903 | + | 0.955527i | \(0.404713\pi\) | |||||||
\(878\) | 1.90155e12i | 3.19984i | ||||||||
\(879\) | 1.47037e11 | 0.246304 | ||||||||
\(880\) | 9.32739e11i | 1.55535i | ||||||||
\(881\) | 1.10103e12i | 1.82766i | 0.406101 | + | 0.913828i | \(0.366888\pi\) | ||||
−0.406101 | + | 0.913828i | \(0.633112\pi\) | |||||||
\(882\) | − | 6.99254e11i | − | 1.15547i | ||||||
\(883\) | 3.90643e11 | 0.642595 | 0.321298 | − | 0.946978i | \(-0.395881\pi\) | ||||
0.321298 | + | 0.946978i | \(0.395881\pi\) | |||||||
\(884\) | 1.30528e12i | 2.13745i | ||||||||
\(885\) | 1.36411e11 | − | 3.29100e10i | 0.222371 | − | 0.0536482i | ||||
\(886\) | 1.13360e12 | 1.83961 | ||||||||
\(887\) | 3.64372e11i | 0.588641i | 0.955707 | + | 0.294321i | \(0.0950933\pi\) | ||||
−0.955707 | + | 0.294321i | \(0.904907\pi\) | |||||||
\(888\) | 4.74648e11 | 0.763343 | ||||||||
\(889\) | 7.52769e11 | 1.20519 | ||||||||
\(890\) | −1.48209e10 | −0.0236219 | ||||||||
\(891\) | − | 1.01389e11i | − | 0.160871i | ||||||
\(892\) | −8.13391e11 | −1.28481 | ||||||||
\(893\) | 1.15396e11i | 0.181461i | ||||||||
\(894\) | −6.97838e11 | −1.09246 | ||||||||
\(895\) | − | 1.30008e11i | − | 0.202618i | ||||||
\(896\) | 6.70249e11i | 1.03993i | ||||||||
\(897\) | −4.95713e11 | −0.765703 | ||||||||
\(898\) | 5.59989e11i | 0.861141i | ||||||||
\(899\) | − | 2.08071e12i | − | 3.18547i | ||||||
\(900\) | 4.59135e11 | 0.699794 | ||||||||
\(901\) | 8.36359e11 | 1.26909 | ||||||||
\(902\) | −7.60171e11 | −1.14838 | ||||||||
\(903\) | − | 3.81397e11i | − | 0.573623i | ||||||
\(904\) | −2.21574e12 | −3.31777 | ||||||||
\(905\) | −3.33293e11 | −0.496858 | ||||||||
\(906\) | −9.08202e11 | −1.34794 | ||||||||
\(907\) | 6.73147e11 | 0.994673 | 0.497337 | − | 0.867558i | \(-0.334311\pi\) | ||||
0.497337 | + | 0.867558i | \(0.334311\pi\) | |||||||
\(908\) | − | 7.03231e11i | − | 1.03456i | ||||||
\(909\) | 3.10097e11i | 0.454194i | ||||||||
\(910\) | −6.46456e11 | −0.942700 | ||||||||
\(911\) | −1.11052e11 | −0.161232 | −0.0806160 | − | 0.996745i | \(-0.525689\pi\) | ||||
−0.0806160 | + | 0.996745i | \(0.525689\pi\) | |||||||
\(912\) | −3.46270e11 | −0.500536 | ||||||||
\(913\) | −4.31476e10 | −0.0620974 | ||||||||
\(914\) | 4.65560e11 | 0.667099 | ||||||||
\(915\) | 1.44274e11i | 0.205828i | ||||||||
\(916\) | − | 6.85583e10i | − | 0.0973819i | ||||||
\(917\) | − | 2.37195e12i | − | 3.35450i | ||||||
\(918\) | 2.90791e11i | 0.409459i | ||||||||
\(919\) | − | 8.37123e11i | − | 1.17362i | −0.809725 | − | 0.586809i | \(-0.800384\pi\) | ||
0.809725 | − | 0.586809i | \(-0.199616\pi\) | |||||||
\(920\) | 1.39067e12 | 1.94121 | ||||||||
\(921\) | −1.49081e11 | −0.207197 | ||||||||
\(922\) | − | 4.08374e11i | − | 0.565112i | ||||||
\(923\) | − | 8.85526e11i | − | 1.22010i | ||||||
\(924\) | 2.56413e12i | 3.51765i | ||||||||
\(925\) | 2.93072e11i | 0.400321i | ||||||||
\(926\) | 8.69807e11 | 1.18298 | ||||||||
\(927\) | 6.22695e10i | 0.0843250i | ||||||||
\(928\) | 2.99627e12i | 4.04008i | ||||||||
\(929\) | − | 1.13432e12i | − | 1.52290i | −0.648224 | − | 0.761449i | \(-0.724488\pi\) | ||
0.648224 | − | 0.761449i | \(-0.275512\pi\) | |||||||
\(930\) | −5.75002e11 | −0.768666 | ||||||||
\(931\) | −4.45717e11 | −0.593281 | ||||||||
\(932\) | − | 5.59097e11i | − | 0.741009i | ||||||
\(933\) | −6.71260e11 | −0.885858 | ||||||||
\(934\) | −2.90407e11 | −0.381610 | ||||||||
\(935\) | − | 4.99288e11i | − | 0.653288i | ||||||
\(936\) | −5.36874e11 | −0.699470 | ||||||||
\(937\) | 1.22246e12i | 1.58590i | 0.609285 | + | 0.792952i | \(0.291457\pi\) | ||||
−0.609285 | + | 0.792952i | \(0.708543\pi\) | |||||||
\(938\) | 2.95271e12 | 3.81426 | ||||||||
\(939\) | 3.18809e11i | 0.410080i | ||||||||
\(940\) | − | 4.37180e11i | − | 0.559949i | ||||||
\(941\) | − | 1.07347e11i | − | 0.136909i | −0.997654 | − | 0.0684543i | \(-0.978193\pi\) | ||
0.997654 | − | 0.0684543i | \(-0.0218067\pi\) | |||||||
\(942\) | 5.31410e11 | 0.674879 | ||||||||
\(943\) | 5.90770e11i | 0.747087i | ||||||||
\(944\) | −2.09309e12 | + | 5.04970e11i | −2.63573 | + | 0.635883i | ||||
\(945\) | −1.02756e11 | −0.128848 | ||||||||
\(946\) | 1.27370e12i | 1.59039i | ||||||||
\(947\) | 2.49539e11 | 0.310270 | 0.155135 | − | 0.987893i | \(-0.450419\pi\) | ||||
0.155135 | + | 0.987893i | \(0.450419\pi\) | |||||||
\(948\) | −8.34537e10 | −0.103327 | ||||||||
\(949\) | −4.99756e11 | −0.616160 | ||||||||
\(950\) | − | 4.10181e11i | − | 0.503595i | ||||||
\(951\) | 2.71022e11 | 0.331346 | ||||||||
\(952\) | − | 4.40104e12i | − | 5.35806i | ||||||
\(953\) | 1.01884e12 | 1.23519 | 0.617594 | − | 0.786497i | \(-0.288108\pi\) | ||||
0.617594 | + | 0.786497i | \(0.288108\pi\) | |||||||
\(954\) | 5.74827e11i | 0.693975i | ||||||||
\(955\) | − | 8.20040e10i | − | 0.0985875i | ||||||
\(956\) | −7.13296e11 | −0.853962 | ||||||||
\(957\) | 1.24176e12i | 1.48044i | ||||||||
\(958\) | − | 1.57837e12i | − | 1.87390i | ||||||
\(959\) | −1.56139e12 | −1.84603 | ||||||||
\(960\) | 3.01233e11 | 0.354664 | ||||||||
\(961\) | −1.90629e12 | −2.23509 | ||||||||
\(962\) | − | 5.72643e11i | − | 0.668626i | ||||||
\(963\) | 3.88008e11 | 0.451165 | ||||||||
\(964\) | −2.44074e12 | −2.82626 | ||||||||
\(965\) | 5.42764e11 | 0.625896 | ||||||||
\(966\) | 2.79291e12 | 3.20737 | ||||||||
\(967\) | − | 2.25546e11i | − | 0.257946i | −0.991648 | − | 0.128973i | \(-0.958832\pi\) | ||
0.991648 | − | 0.128973i | \(-0.0411680\pi\) | |||||||
\(968\) | − | 2.67991e12i | − | 3.05225i | ||||||
\(969\) | 1.85356e11 | 0.210238 | ||||||||
\(970\) | 2.89233e11 | 0.326709 | ||||||||
\(971\) | −1.33335e12 | −1.49992 | −0.749960 | − | 0.661484i | \(-0.769927\pi\) | ||||
−0.749960 | + | 0.661484i | \(0.769927\pi\) | |||||||
\(972\) | −1.42599e11 | −0.159754 | ||||||||
\(973\) | 5.47030e11 | 0.610323 | ||||||||
\(974\) | − | 1.97058e12i | − | 2.18957i | ||||||
\(975\) | − | 3.31495e11i | − | 0.366824i | ||||||
\(976\) | − | 2.21374e12i | − | 2.43965i | ||||||
\(977\) | − | 1.06416e12i | − | 1.16796i | −0.811767 | − | 0.583982i | \(-0.801494\pi\) | ||
0.811767 | − | 0.583982i | \(-0.198506\pi\) | |||||||
\(978\) | − | 6.58310e11i | − | 0.719573i | ||||||
\(979\) | 4.24436e10 | 0.0462042 | ||||||||
\(980\) | 1.68861e12 | 1.83074 | ||||||||
\(981\) | 4.12857e11i | 0.445783i | ||||||||
\(982\) | − | 3.24070e12i | − | 3.48492i | ||||||
\(983\) | − | 2.83765e9i | − | 0.00303910i | −0.999999 | − | 0.00151955i | \(-0.999516\pi\) | ||
0.999999 | − | 0.00151955i | \(-0.000483688\pi\) | |||||||
\(984\) | 6.39824e11i | 0.682465i | ||||||||
\(985\) | −4.65564e11 | −0.494578 | ||||||||
\(986\) | − | 3.56148e12i | − | 3.76810i | ||||||
\(987\) | − | 5.25433e11i | − | 0.553667i | ||||||
\(988\) | 5.71839e11i | 0.600131i | ||||||||
\(989\) | 9.89862e11 | 1.03464 | ||||||||
\(990\) | 3.43160e11 | 0.357236 | ||||||||
\(991\) | − | 1.14914e12i | − | 1.19146i | −0.803186 | − | 0.595728i | \(-0.796864\pi\) | ||
0.803186 | − | 0.595728i | \(-0.203136\pi\) | |||||||
\(992\) | 3.97328e12 | 4.10301 | ||||||||
\(993\) | −7.76089e11 | −0.798205 | ||||||||
\(994\) | 4.98918e12i | 5.11074i | ||||||||
\(995\) | 4.57312e11 | 0.466574 | ||||||||
\(996\) | 6.06852e10i | 0.0616659i | ||||||||
\(997\) | −1.40469e12 | −1.42167 | −0.710834 | − | 0.703360i | \(-0.751682\pi\) | ||||
−0.710834 | + | 0.703360i | \(0.751682\pi\) | |||||||
\(998\) | 7.13395e11i | 0.719131i | ||||||||
\(999\) | − | 9.10229e10i | − | 0.0913879i |
(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 | 177.9.c.a.58.3 | ✓ | 80 | |
59.58 | odd | 2 | inner | 177.9.c.a.58.78 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.9.c.a.58.3 | ✓ | 80 | 1.1 | even | 1 | trivial | |
177.9.c.a.58.78 | yes | 80 | 59.58 | odd | 2 | inner |