Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(425,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.425");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 425.9 | ||
Character | \(\chi\) | \(=\) | 684.425 |
Dual form | 684.3.be.a.581.9 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.37911 | + | 1.82752i | −0.793037 | + | 0.609173i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.32501 | + | 3.07440i | 1.06500 | + | 0.614879i | 0.926812 | − | 0.375526i | \(-0.122538\pi\) |
0.138191 | + | 0.990406i | \(0.455871\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.67945 | + | 11.5692i | −0.954208 | + | 1.65274i | −0.218036 | + | 0.975941i | \(0.569965\pi\) |
−0.736171 | + | 0.676795i | \(0.763368\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.32035 | − | 8.69574i | 0.257817 | − | 0.966194i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.586623 | + | 0.338687i | 0.0533293 | + | 0.0307897i | 0.526428 | − | 0.850220i | \(-0.323531\pi\) |
−0.473098 | + | 0.881010i | \(0.656864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −21.9753 | −1.69041 | −0.845205 | − | 0.534442i | \(-0.820522\pi\) | ||||
−0.845205 | + | 0.534442i | \(0.820522\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.2873 | + | 2.41722i | −1.21915 | + | 0.161148i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −10.9425 | + | 6.31763i | −0.643674 | + | 0.371625i | −0.786028 | − | 0.618190i | \(-0.787866\pi\) |
0.142354 | + | 0.989816i | \(0.454533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.16635 | + | 17.5967i | 0.377176 | + | 0.926141i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.25168 | − | 39.7311i | −0.250080 | − | 1.89196i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 34.7581i | − | 1.51122i | −0.655022 | − | 0.755610i | \(-0.727341\pi\) | ||
0.655022 | − | 0.755610i | \(-0.272659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.40383 | + | 11.0918i | 0.256153 | + | 0.443670i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.3713 | + | 24.9286i | 0.384121 | + | 0.923283i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.0234 | − | 19.0661i | 1.13874 | − | 0.657450i | 0.192620 | − | 0.981273i | \(-0.438302\pi\) |
0.946118 | + | 0.323823i | \(0.104968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.7392 | + | 34.1893i | 0.636749 | + | 1.10288i | 0.986142 | + | 0.165905i | \(0.0530545\pi\) |
−0.349393 | + | 0.936976i | \(0.613612\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.01460 | + | 0.266290i | −0.0610484 | + | 0.00806940i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −71.1363 | + | 41.0706i | −2.03247 | + | 1.17345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.0074 | −0.648850 | −0.324425 | − | 0.945911i | \(-0.605171\pi\) | ||||
−0.324425 | + | 0.945911i | \(0.605171\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 52.2818 | − | 40.1603i | 1.34056 | − | 1.02975i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.866161 | + | 0.500078i | 0.0211259 | + | 0.0121970i | 0.510526 | − | 0.859862i | \(-0.329451\pi\) |
−0.489400 | + | 0.872060i | \(0.662784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.8150 | −0.274768 | −0.137384 | − | 0.990518i | \(-0.543870\pi\) | ||||
−0.137384 | + | 0.990518i | \(0.543870\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 39.0901 | − | 39.1713i | 0.868668 | − | 0.870473i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31.5282 | − | 18.2028i | 0.670813 | − | 0.387294i | −0.125572 | − | 0.992085i | \(-0.540077\pi\) |
0.796384 | + | 0.604791i | \(0.206743\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −64.7302 | − | 112.116i | −1.32102 | − | 2.28808i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.4877 | − | 35.0279i | 0.284073 | − | 0.686822i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −29.2948 | − | 16.9134i | −0.552732 | − | 0.319120i | 0.197491 | − | 0.980305i | \(-0.436721\pi\) |
−0.750223 | + | 0.661185i | \(0.770054\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.08251 | + | 3.60702i | 0.0378639 | + | 0.0655822i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −49.2078 | − | 28.7678i | −0.863295 | − | 0.504699i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 53.6084 | + | 30.9508i | 0.908617 | + | 0.524590i | 0.879986 | − | 0.475000i | \(-0.157552\pi\) |
0.0286309 | + | 0.999590i | \(0.490885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −49.9685 | − | 86.5480i | −0.819156 | − | 1.41882i | −0.906305 | − | 0.422625i | \(-0.861109\pi\) |
0.0871484 | − | 0.996195i | \(-0.472225\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 85.1037 | + | 84.9273i | 1.35085 | + | 1.34805i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −117.019 | − | 67.5609i | −1.80029 | − | 1.03940i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.6494 | −0.472379 | −0.236189 | − | 0.971707i | \(-0.575899\pi\) | ||||
−0.236189 | + | 0.971707i | \(0.575899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 63.5210 | + | 82.6933i | 0.920595 | + | 1.19845i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −104.178 | + | 60.1470i | −1.46729 | + | 0.847141i | −0.999330 | − | 0.0366080i | \(-0.988345\pi\) |
−0.467961 | + | 0.883749i | \(0.655011\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.08945 | + | 15.7434i | 0.124513 | + | 0.215663i | 0.921542 | − | 0.388278i | \(-0.126930\pi\) |
−0.797030 | + | 0.603940i | \(0.793596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −35.5058 | − | 14.6854i | −0.473411 | − | 0.195806i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.83664 | + | 4.52448i | −0.101774 | + | 0.0587595i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.21376 | 0.103972 | 0.0519858 | − | 0.998648i | \(-0.483445\pi\) | ||||
0.0519858 | + | 0.998648i | \(0.483445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −70.2320 | − | 40.3543i | −0.867061 | − | 0.498202i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −139.075 | − | 80.2951i | −1.67560 | − | 0.967410i | −0.964409 | − | 0.264416i | \(-0.914821\pi\) |
−0.711195 | − | 0.702995i | \(-0.751846\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −77.6916 | −0.914019 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −43.7227 | + | 105.711i | −0.502560 | + | 1.21507i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 91.8708 | + | 53.0416i | 1.03226 | + | 0.595973i | 0.917630 | − | 0.397436i | \(-0.130100\pi\) |
0.114626 | + | 0.993409i | \(0.463433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 146.783 | − | 254.236i | 1.61300 | − | 2.79380i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −109.443 | − | 45.2664i | −1.17681 | − | 0.486736i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.9383 | + | 115.735i | −0.167771 | + | 1.21826i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51.4195 | 0.530098 | 0.265049 | − | 0.964235i | \(-0.414612\pi\) | ||||
0.265049 | + | 0.964235i | \(0.414612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.30630 | − | 4.31525i | 0.0434980 | − | 0.0435884i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.56281 | + | 1.47964i | −0.0253744 | + | 0.0146499i | −0.512634 | − | 0.858608i | \(-0.671330\pi\) |
0.487259 | + | 0.873257i | \(0.337997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.46277 | + | 9.46179i | 0.0530366 | + | 0.0918620i | 0.891325 | − | 0.453365i | \(-0.149777\pi\) |
−0.838288 | + | 0.545227i | \(0.816443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 94.1840 | − | 227.714i | 0.896991 | − | 2.16871i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.7588i | 0.137933i | 0.997619 | + | 0.0689664i | \(0.0219701\pi\) | ||||
−0.997619 | + | 0.0689664i | \(0.978030\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.1494 | + | 27.9716i | 0.148160 | + | 0.256620i | 0.930547 | − | 0.366172i | \(-0.119332\pi\) |
−0.782388 | + | 0.622792i | \(0.785998\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 57.1164 | − | 43.8740i | 0.514562 | − | 0.395262i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −134.566 | + | 77.6917i | −1.19085 | + | 0.687537i | −0.958499 | − | 0.285095i | \(-0.907975\pi\) |
−0.232350 | + | 0.972632i | \(0.574641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 106.860 | − | 185.087i | 0.929218 | − | 1.60945i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −50.9905 | + | 191.092i | −0.435816 | + | 1.63326i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 168.793i | − | 1.41843i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.2706 | − | 104.392i | −0.498104 | − | 0.862741i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.97460 | + | 0.393183i | −0.0241837 | + | 0.00319661i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 74.9682i | − | 0.599745i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.01913 | − | 10.4254i | 0.0473947 | − | 0.0820900i | −0.841355 | − | 0.540483i | \(-0.818241\pi\) |
0.888750 | + | 0.458393i | \(0.151575\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.1093 | − | 21.5922i | 0.217902 | − | 0.167382i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.17388 | − | 5.29654i | −0.0700296 | − | 0.0404316i | 0.464576 | − | 0.885533i | \(-0.346207\pi\) |
−0.534606 | + | 0.845101i | \(0.679540\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −251.446 | − | 34.6276i | −1.89057 | − | 0.260358i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.4134 | + | 164.631i | −0.158618 | + | 1.21949i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.0097 | + | 9.24323i | −0.116859 | + | 0.0674688i | −0.557290 | − | 0.830318i | \(-0.688159\pi\) |
0.440431 | + | 0.897786i | \(0.354826\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −127.233 | −0.915344 | −0.457672 | − | 0.889121i | \(-0.651317\pi\) | ||||
−0.457672 | + | 0.889121i | \(0.651317\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −41.7431 | + | 100.925i | −0.296051 | + | 0.715779i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.8912 | − | 7.44275i | −0.0901484 | − | 0.0520472i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 234.467 | 1.61701 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 358.894 | + | 148.441i | 2.44146 | + | 1.00980i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 172.812 | + | 99.7729i | 1.15981 | + | 0.669616i | 0.951258 | − | 0.308395i | \(-0.0997918\pi\) |
0.208551 | + | 0.978011i | \(0.433125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −86.0705 | + | 149.078i | −0.570003 | + | 0.987274i | 0.426562 | + | 0.904458i | \(0.359725\pi\) |
−0.996565 | + | 0.0828158i | \(0.973609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.5462 | + | 109.812i | 0.193112 | + | 0.717725i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 242.745i | 1.56609i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 63.0568 | − | 109.218i | 0.401636 | − | 0.695653i | −0.592288 | − | 0.805726i | \(-0.701775\pi\) |
0.993923 | + | 0.110073i | \(0.0351085\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 100.605 | − | 13.2980i | 0.632737 | − | 0.0836354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 402.121 | + | 232.165i | 2.49765 | + | 1.44202i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −130.019 | −0.797661 | −0.398831 | − | 0.917025i | \(-0.630584\pi\) | ||||
−0.398831 | + | 0.917025i | \(0.630584\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.5464 | − | 4.77567i | −0.0699784 | − | 0.0289435i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.5080i | 0.104838i | 0.998625 | + | 0.0524190i | \(0.0166931\pi\) | ||||
−0.998625 | + | 0.0524190i | \(0.983307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 313.915 | 1.85749 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 169.645 | − | 21.4863i | 0.992075 | − | 0.125651i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 259.825i | 1.50188i | 0.660370 | + | 0.750940i | \(0.270399\pi\) | ||||
−0.660370 | + | 0.750940i | \(0.729601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −171.096 | −0.977693 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −184.104 | + | 24.3349i | −1.04013 | + | 0.137485i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 120.898i | 0.675407i | 0.941252 | + | 0.337704i | \(0.109650\pi\) | ||||
−0.941252 | + | 0.337704i | \(0.890350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −110.148 | + | 190.783i | −0.608555 | + | 1.05405i | 0.382924 | + | 0.923780i | \(0.374917\pi\) |
−0.991479 | + | 0.130268i | \(0.958416\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 277.049 | + | 114.589i | 1.51393 | + | 0.626170i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −127.840 | − | 73.8084i | −0.691026 | − | 0.398964i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.55879 | −0.0457689 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −357.678 | − | 46.5229i | −1.89247 | − | 0.246153i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −87.7696 | − | 50.6738i | −0.459527 | − | 0.265308i | 0.252319 | − | 0.967644i | \(-0.418807\pi\) |
−0.711845 | + | 0.702336i | \(0.752140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 159.875 | − | 276.911i | 0.828367 | − | 1.43477i | −0.0709511 | − | 0.997480i | \(-0.522603\pi\) |
0.899318 | − | 0.437294i | \(-0.144063\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 401.870 | − | 53.1193i | 2.06087 | − | 0.272407i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 362.670i | 1.84096i | 0.390786 | + | 0.920482i | \(0.372203\pi\) | ||||
−0.390786 | + | 0.920482i | \(0.627797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −63.0213 | + | 109.156i | −0.316690 | + | 0.548523i | −0.979795 | − | 0.200003i | \(-0.935905\pi\) |
0.663105 | + | 0.748526i | \(0.269238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 75.2974 | − | 57.8398i | 0.374614 | − | 0.287760i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 509.403i | 2.50938i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.07488 | + | 5.32585i | 0.0149994 | + | 0.0259797i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −302.247 | − | 80.6508i | −1.46013 | − | 0.389618i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.75582 | + | 12.7498i | −0.00840105 | + | 0.0610036i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.3951 | + | 45.7177i | −0.125095 | + | 0.216672i | −0.921770 | − | 0.387737i | \(-0.873257\pi\) |
0.796675 | + | 0.604408i | \(0.206590\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 137.931 | − | 333.483i | 0.647561 | − | 1.56565i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −62.9152 | − | 36.3241i | −0.292629 | − | 0.168949i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −527.389 | −2.43036 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −50.3961 | − | 20.8441i | −0.230119 | − | 0.0951787i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 240.464 | − | 138.832i | 1.08807 | − | 0.628200i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.189234 | 0.000848582 | 0.000424291 | − | 1.00000i | \(-0.499865\pi\) | ||||
0.000424291 | 1.00000i | \(0.499865\pi\) | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 111.310 | − | 29.9493i | 0.494712 | − | 0.133108i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.0193 | − | 9.82612i | −0.0749751 | − | 0.0432869i | 0.462044 | − | 0.886857i | \(-0.347116\pi\) |
−0.537019 | + | 0.843570i | \(0.680450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 175.467 | + | 303.918i | 0.766233 | + | 1.32715i | 0.939592 | + | 0.342296i | \(0.111204\pi\) |
−0.173359 | + | 0.984859i | \(0.555462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.3757 | − | 25.0859i | 0.0449163 | − | 0.108597i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −212.611 | + | 122.751i | −0.912494 | + | 0.526829i | −0.881233 | − | 0.472683i | \(-0.843286\pi\) |
−0.0312613 | + | 0.999511i | \(0.509952\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 223.851 | 0.952556 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.5414 | + | 15.0108i | −0.0824534 | + | 0.0633367i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −215.150 | + | 124.217i | −0.900210 | + | 0.519736i | −0.877268 | − | 0.480000i | \(-0.840637\pi\) |
−0.0229416 | + | 0.999737i | \(0.507303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.22517 | + | 12.5144i | 0.0299800 | + | 0.0519268i | 0.880626 | − | 0.473812i | \(-0.157122\pi\) |
−0.850646 | + | 0.525739i | \(0.823789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 240.838 | − | 32.3428i | 0.991103 | − | 0.133098i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 796.025i | − | 3.24908i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −157.483 | − | 386.693i | −0.637583 | − | 1.56556i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 477.616 | − | 63.1315i | 1.91814 | − | 0.253540i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 39.7299 | + | 22.9381i | 0.158286 | + | 0.0913867i | 0.577051 | − | 0.816708i | \(-0.304203\pi\) |
−0.418765 | + | 0.908095i | \(0.637537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.7721 | − | 20.3899i | 0.0465300 | − | 0.0805923i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 184.837 | − | 141.983i | 0.724851 | − | 0.556796i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 435.920i | − | 1.69619i | −0.529848 | − | 0.848093i | \(-0.677751\pi\) | ||
0.529848 | − | 0.848093i | \(-0.322249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 160.357 | − | 277.746i | 0.619137 | − | 1.07238i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −89.1678 | − | 331.403i | −0.341639 | − | 1.26974i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 206.601i | − | 0.785555i | −0.919634 | − | 0.392778i | \(-0.871514\pi\) | ||
0.919634 | − | 0.392778i | \(-0.128486\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −103.997 | − | 180.128i | −0.392441 | − | 0.679727i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −315.505 | + | 41.7036i | −1.18167 | + | 0.156193i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 250.230 | − | 144.470i | 0.930224 | − | 0.537065i | 0.0433415 | − | 0.999060i | \(-0.486200\pi\) |
0.886882 | + | 0.461995i | \(0.152866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 147.862 | + | 256.105i | 0.545618 | + | 0.945037i | 0.998568 | + | 0.0535016i | \(0.0170382\pi\) |
−0.452950 | + | 0.891536i | \(0.649628\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 115.407 | + | 873.105i | 0.422738 | + | 3.19819i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.67557i | 0.0315475i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −46.2692 | + | 80.1406i | −0.167037 | + | 0.289316i | −0.937377 | − | 0.348317i | \(-0.886753\pi\) |
0.770340 | + | 0.637633i | \(0.220087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 343.103 | − | 92.3160i | 1.22976 | − | 0.330882i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 45.6441 | − | 26.3526i | 0.162434 | − | 0.0937815i | −0.416579 | − | 0.909099i | \(-0.636771\pi\) |
0.579014 | + | 0.815318i | \(0.303438\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −189.282 | + | 327.846i | −0.668842 | + | 1.15847i | 0.309387 | + | 0.950936i | \(0.399876\pi\) |
−0.978228 | + | 0.207531i | \(0.933457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −173.589 | − | 304.474i | −0.609082 | − | 1.06833i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5710 | + | 6.68050i | −0.0403170 | + | 0.0232770i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −64.6750 | + | 112.020i | −0.223789 | + | 0.387614i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −122.333 | + | 93.9701i | −0.420388 | + | 0.322921i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −413.513 | + | 238.742i | −1.41131 | + | 0.814818i | −0.995512 | − | 0.0946404i | \(-0.969830\pi\) |
−0.415795 | + | 0.909458i | \(0.636497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 190.310 | + | 329.627i | 0.645119 | + | 1.11738i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.35898 | + | 18.1363i | −0.00794268 | + | 0.0610650i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 763.820i | 2.55458i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 78.9180 | − | 136.690i | 0.262186 | − | 0.454120i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.39314 | − | 8.20381i | 0.0111985 | − | 0.0270753i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 614.492i | − | 2.01473i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.3451 | + | 42.1669i | 0.0792999 | + | 0.137351i | 0.902948 | − | 0.429750i | \(-0.141398\pi\) |
−0.823648 | + | 0.567101i | \(0.808065\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.2881 | − | 12.5274i | −0.0980199 | − | 0.0405416i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 58.5917 | − | 33.8279i | 0.188398 | − | 0.108771i | −0.402835 | − | 0.915273i | \(-0.631975\pi\) |
0.591232 | + | 0.806501i | \(0.298642\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.36811 | + | 2.36963i | 0.00437095 | + | 0.00757071i | 0.868203 | − | 0.496210i | \(-0.165275\pi\) |
−0.863832 | + | 0.503781i | \(0.831942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 192.078 | + | 713.881i | 0.609772 | + | 2.26629i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −358.316 | + | 206.874i | −1.13034 | + | 0.652600i | −0.944019 | − | 0.329890i | \(-0.892988\pi\) |
−0.186316 | + | 0.982490i | \(0.559655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.8297 | 0.0809708 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.9720 | − | 35.1129i | −0.0840249 | − | 0.109386i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −189.587 | − | 147.277i | −0.586956 | − | 0.455965i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −140.726 | − | 243.745i | −0.433004 | − | 0.749985i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −89.5398 | − | 37.0342i | −0.273822 | − | 0.113254i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 486.339i | 1.47823i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 198.804 | − | 344.339i | 0.600617 | − | 1.04030i | −0.392110 | − | 0.919918i | \(-0.628255\pi\) |
0.992728 | − | 0.120382i | \(-0.0384118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −55.7056 | + | 208.763i | −0.167284 | + | 0.626915i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −168.533 | − | 97.3027i | −0.503084 | − | 0.290456i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0965 | − | 29.6119i | 0.0507313 | − | 0.0878692i | −0.839545 | − | 0.543291i | \(-0.817178\pi\) |
0.890276 | + | 0.455422i | \(0.150511\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 178.164 | − | 430.759i | 0.525559 | − | 1.27068i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.7416i | 0.0784212i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1074.86 | 3.13371 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 84.0180 | + | 635.632i | 0.243531 | + | 1.84241i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 103.128 | + | 59.5412i | 0.297200 | + | 0.171588i | 0.641184 | − | 0.767387i | \(-0.278443\pi\) |
−0.343984 | + | 0.938975i | \(0.611777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 196.268 | − | 339.946i | 0.562373 | − | 0.974059i | −0.434916 | − | 0.900471i | \(-0.643222\pi\) |
0.997289 | − | 0.0735875i | \(-0.0234448\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −227.912 | − | 547.815i | −0.649322 | − | 1.56073i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −285.889 | − | 165.058i | −0.809884 | − | 0.467587i | 0.0370318 | − | 0.999314i | \(-0.488210\pi\) |
−0.846915 | + | 0.531728i | \(0.821543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −739.663 | −2.08356 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 308.473 | + | 401.578i | 0.864070 | + | 1.12487i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 85.9500 | − | 49.6232i | 0.239415 | − | 0.138226i | −0.375493 | − | 0.926825i | \(-0.622527\pi\) |
0.614908 | + | 0.788599i | \(0.289193\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −258.287 | + | 252.208i | −0.715476 | + | 0.698638i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 334.168 | + | 138.214i | 0.920574 | + | 0.380755i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 111.778i | 0.306242i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.3195 | − | 57.7111i | −0.0907889 | − | 0.157251i | 0.817054 | − | 0.576561i | \(-0.195606\pi\) |
−0.907843 | + | 0.419310i | \(0.862272\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.35835 | − | 6.37156i | 0.0172313 | − | 0.0172671i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 391.347 | − | 225.944i | 1.05484 | − | 0.609014i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 163.975 | + | 284.013i | 0.439611 | + | 0.761429i | 0.997659 | − | 0.0683793i | \(-0.0217828\pi\) |
−0.558048 | + | 0.829809i | \(0.688449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 137.006 | + | 178.358i | 0.365349 | + | 0.475621i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −725.700 | + | 418.983i | −1.92493 | + | 1.11136i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −588.049 | −1.55158 | −0.775790 | − | 0.630991i | \(-0.782649\pi\) | ||||
−0.775790 | + | 0.630991i | \(0.782649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.73250 | + | 35.8033i | 0.0124213 | + | 0.0939720i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 314.491 | + | 181.571i | 0.821124 | + | 0.474076i | 0.850804 | − | 0.525483i | \(-0.176115\pi\) |
−0.0296797 | + | 0.999559i | \(0.509449\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −55.6402 | −0.144520 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.4150 | + | 102.741i | −0.0708399 | + | 0.265480i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 363.165 | − | 209.673i | 0.933585 | − | 0.539006i | 0.0456415 | − | 0.998958i | \(-0.485467\pi\) |
0.887944 | + | 0.459952i | \(0.152133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 219.589 | + | 380.339i | 0.561608 | + | 0.972733i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.5052 | − | 4.16437i | 0.0801659 | − | 0.0105964i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.7383 | + | 25.2523i | 0.110730 | + | 0.0639300i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4059 | + | 31.8800i | 0.0463625 | + | 0.0803022i | 0.888275 | − | 0.459311i | \(-0.151904\pi\) |
−0.841913 | + | 0.539613i | \(0.818570\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 661.501 | − | 377.139i | 1.65790 | − | 0.945212i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −479.111 | − | 276.615i | −1.19479 | − | 0.689813i | −0.235402 | − | 0.971898i | \(-0.575641\pi\) |
−0.959389 | + | 0.282085i | \(0.908974\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −433.776 | − | 751.322i | −1.07637 | − | 1.86432i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −249.921 | − | 430.808i | −0.617088 | − | 1.06372i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0833 | − | 8.13100i | −0.0346027 | − | 0.0199779i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −228.124 | −0.557760 | −0.278880 | − | 0.960326i | \(-0.589963\pi\) | ||||
−0.278880 | + | 0.960326i | \(0.589963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1968 | − | 51.2488i | 0.0515737 | − | 0.124693i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −716.149 | + | 413.469i | −1.73402 | + | 1.00114i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −493.718 | − | 855.144i | −1.18968 | − | 2.06059i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 302.701 | − | 232.520i | 0.725902 | − | 0.557603i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −427.551 | + | 246.847i | −1.02041 | + | 0.589133i | −0.914222 | − | 0.405213i | \(-0.867197\pi\) |
−0.106187 | + | 0.994346i | \(0.533864\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 174.161 | 0.413684 | 0.206842 | − | 0.978374i | \(-0.433681\pi\) | ||||
0.206842 | + | 0.978374i | \(0.433681\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −85.1306 | − | 316.398i | −0.201254 | − | 0.747986i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −140.147 | − | 80.9141i | −0.329758 | − | 0.190386i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1335.05 | 3.12658 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 44.2714 | − | 5.85182i | 0.103197 | − | 0.0136406i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −183.318 | − | 105.838i | −0.425331 | − | 0.245565i | 0.272025 | − | 0.962290i | \(-0.412307\pi\) |
−0.697356 | + | 0.716725i | \(0.745640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 98.5927 | − | 170.768i | 0.227697 | − | 0.394382i | −0.729428 | − | 0.684057i | \(-0.760214\pi\) |
0.957125 | + | 0.289675i | \(0.0935472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −557.822 | + | 428.492i | −1.28235 | + | 0.985039i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 611.627 | − | 249.089i | 1.39960 | − | 0.569997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −614.810 | −1.40048 | −0.700239 | − | 0.713908i | \(-0.746923\pi\) | ||||
−0.700239 | + | 0.713908i | \(0.746923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1125.13 | + | 302.729i | −2.55131 | + | 0.686460i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 481.861 | − | 278.203i | 1.08772 | − | 0.627997i | 0.154754 | − | 0.987953i | \(-0.450542\pi\) |
0.932969 | + | 0.359956i | \(0.117208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 326.142 | + | 564.894i | 0.732903 | + | 1.26943i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −593.475 | + | 78.4458i | −1.32768 | + | 0.175494i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 257.610i | 0.573742i | 0.957969 | + | 0.286871i | \(0.0926150\pi\) | ||||
−0.957969 | + | 0.286871i | \(0.907385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.338740 | + | 0.586715i | 0.000751086 | + | 0.00130092i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −67.6723 | − | 511.970i | −0.149387 | − | 1.13018i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1563.24 | − | 902.540i | 3.43570 | − | 1.98360i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 215.637 | − | 373.494i | 0.471853 | − | 0.817273i | −0.527629 | − | 0.849475i | \(-0.676919\pi\) |
0.999481 | + | 0.0322025i | \(0.0102521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −270.977 | − | 207.259i | −0.590364 | − | 0.451544i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 151.493i | 0.328617i | 0.986409 | + | 0.164309i | \(0.0525393\pi\) | ||||
−0.986409 | + | 0.164309i | \(0.947461\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −125.351 | − | 217.114i | −0.270736 | − | 0.468928i | 0.698315 | − | 0.715791i | \(-0.253934\pi\) |
−0.969050 | + | 0.246863i | \(0.920600\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −443.620 | − | 577.517i | −0.954022 | − | 1.24197i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 263.024i | 0.563220i | 0.959529 | + | 0.281610i | \(0.0908685\pi\) | ||||
−0.959529 | + | 0.281610i | \(0.909132\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 211.400 | − | 366.156i | 0.450747 | − | 0.780717i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 49.5780 | + | 375.078i | 0.105261 | + | 0.796344i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.93097 | − | 4.00160i | −0.0146532 | − | 0.00846004i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −149.286 | + | 192.174i | −0.314287 | + | 0.404576i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −215.048 | + | 215.495i | −0.450835 | + | 0.451772i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −552.766 | + | 319.140i | −1.15400 | + | 0.666262i | −0.949859 | − | 0.312679i | \(-0.898773\pi\) |
−0.204141 | + | 0.978941i | \(0.565440\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 527.572 | 1.09682 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1380.98 | + | 182.538i | −2.85917 | + | 0.377926i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 273.809 | + | 158.084i | 0.564556 | + | 0.325946i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −780.042 | −1.60173 | −0.800864 | − | 0.598846i | \(-0.795626\pi\) | ||||
−0.800864 | + | 0.598846i | \(0.795626\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 309.329 | − | 237.612i | 0.632575 | − | 0.485914i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 502.452 | + | 290.091i | 1.02332 | + | 0.590816i | 0.915065 | − | 0.403307i | \(-0.132139\pi\) |
0.108258 | + | 0.994123i | \(0.465473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −240.905 | + | 417.259i | −0.488651 | + | 0.846368i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36.1979 | − | 9.73947i | 0.0731271 | − | 0.0196757i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1607.00i | − | 3.23339i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.2604 | + | 48.9485i | −0.0566341 | + | 0.0980931i | −0.892952 | − | 0.450151i | \(-0.851370\pi\) |
0.836318 | + | 0.548244i | \(0.184704\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.9961 | − | 41.6534i | −0.0638645 | − | 0.0831405i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −144.369 | − | 83.3516i | −0.287016 | − | 0.165709i | 0.349579 | − | 0.936907i | \(-0.386325\pi\) |
−0.636596 | + | 0.771198i | \(0.719658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1960 | −0.0360317 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −746.840 | + | 573.686i | −1.47306 | + | 1.13153i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 300.193i | − | 0.589770i | −0.955533 | − | 0.294885i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294885i | \(-0.0952813\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −242.850 | −0.475245 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −364.337 | + | 361.147i | −0.710209 | + | 0.703991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 67.1789i | 0.130444i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.6602 | 0.0476986 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −474.836 | − | 618.154i | −0.914905 | − | 1.19105i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 209.742i | 0.402575i | 0.979532 | + | 0.201288i | \(0.0645126\pi\) | ||||
−0.979532 | + | 0.201288i | \(0.935487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −492.016 | + | 852.197i | −0.940758 | + | 1.62944i | −0.176727 | + | 0.984260i | \(0.556551\pi\) |
−0.764031 | + | 0.645180i | \(0.776782\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 407.057 | − | 312.682i | 0.775347 | − | 0.595584i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −431.991 | − | 249.410i | −0.819717 | − | 0.473264i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −679.123 | −1.28379 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 393.531 | − | 394.348i | 0.741112 | − | 0.742652i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.0342 | − | 10.9894i | −0.0357114 | − | 0.0206180i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −45.3744 | + | 78.5908i | −0.0848120 | + | 0.146899i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −220.943 | − | 287.630i | −0.411440 | − | 0.535623i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 87.6930i | − | 0.162696i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −486.250 | + | 842.210i | −0.898799 | + | 1.55677i | −0.0697678 | + | 0.997563i | \(0.522226\pi\) |
−0.829031 | + | 0.559202i | \(0.811107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −86.6035 | − | 655.192i | −0.159491 | − | 1.20661i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 198.599i | 0.364401i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 531.315 | + | 920.265i | 0.971326 | + | 1.68239i | 0.691563 | + | 0.722316i | \(0.256923\pi\) |
0.279763 | + | 0.960069i | \(0.409744\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −868.544 | + | 233.692i | −1.58205 | + | 0.425668i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 572.157 | + | 444.468i | 1.03840 | + | 0.806657i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54.8634 | + | 95.0262i | −0.0992105 | + | 0.171838i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 439.032 | − | 58.0314i | 0.791048 | − | 0.104561i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 719.310 | + | 415.294i | 1.29140 | + | 0.745590i | 0.978902 | − | 0.204329i | \(-0.0655011\pi\) |
0.312497 | + | 0.949919i | \(0.398834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 259.640 | 0.464471 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.3623 | − | 15.6414i | 0.0362965 | − | 0.0278812i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 530.247 | − | 306.138i | 0.941824 | − | 0.543762i | 0.0512923 | − | 0.998684i | \(-0.483666\pi\) |
0.890532 | + | 0.454921i | \(0.150333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −955.420 | −1.69101 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 935.976 | − | 542.979i | 1.65075 | − | 0.957636i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 177.066 | + | 102.229i | 0.311188 | + | 0.179665i | 0.647458 | − | 0.762101i | \(-0.275832\pi\) |
−0.336270 | + | 0.941766i | \(0.609165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −244.282 | − | 423.109i | −0.427814 | − | 0.740996i | 0.568865 | − | 0.822431i | \(-0.307383\pi\) |
−0.996679 | + | 0.0814355i | \(0.974050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 301.421 | − | 39.8419i | 0.526040 | − | 0.0695322i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 385.528 | − | 222.585i | 0.670484 | − | 0.387104i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 856.457 | 1.48433 | 0.742164 | − | 0.670219i | \(-0.233800\pi\) | ||||
0.742164 | + | 0.670219i | \(0.233800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 125.701 | + | 950.978i | 0.217099 | + | 1.64245i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1857.89 | − | 1072.65i | 3.19775 | − | 1.84622i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.4567 | − | 19.8435i | −0.0196512 | − | 0.0340369i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −859.017 | + | 860.802i | −1.46841 | + | 1.47146i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 586.816i | − | 0.999686i | −0.866116 | − | 0.499843i | \(-0.833391\pi\) | ||
0.866116 | − | 0.499843i | \(-0.166609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −460.161 | + | 592.357i | −0.781257 | + | 1.00570i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −662.786 | − | 862.832i | −1.12146 | − | 1.45995i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −316.266 | − | 182.596i | −0.533331 | − | 0.307919i | 0.209041 | − | 0.977907i | \(-0.432966\pi\) |
−0.742372 | + | 0.669988i | \(0.766299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 518.938 | − | 898.826i | 0.872164 | − | 1.51063i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.5501 | − | 374.867i | −0.0829985 | − | 0.627919i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 448.395i | 0.748573i | 0.927313 | + | 0.374287i | \(0.122112\pi\) | ||||
−0.927313 | + | 0.374287i | \(0.877888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 323.504 | − | 560.326i | 0.538277 | − | 0.932323i | −0.460720 | − | 0.887545i | \(-0.652409\pi\) |
0.998997 | − | 0.0447773i | \(-0.0142578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −73.4376 | + | 275.215i | −0.121787 | + | 0.456409i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 741.183i | − | 1.22510i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 413.907 | + | 716.909i | 0.681890 | + | 1.18107i | 0.974403 | + | 0.224807i | \(0.0721753\pi\) |
−0.292513 | + | 0.956262i | \(0.594491\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −930.944 | − | 1211.93i | −1.52864 | − | 1.99003i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −692.843 | + | 400.013i | −1.13395 | + | 0.654686i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 420.668 | + | 728.618i | 0.686244 | + | 1.18861i | 0.973044 | + | 0.230619i | \(0.0740752\pi\) |
−0.286800 | + | 0.957991i | \(0.592591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.0486 | − | 7.05139i | −0.0277212 | − | 0.0114657i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1004.65i | − | 1.62828i | −0.580669 | − | 0.814139i | \(-0.697209\pi\) | ||
0.580669 | − | 0.814139i | \(-0.302791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.19386 | − | 15.9242i | 0.0148528 | − | 0.0257257i | −0.858503 | − | 0.512808i | \(-0.828605\pi\) |
0.873356 | + | 0.487082i | \(0.161939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 866.471 | − | 360.485i | 1.39528 | − | 0.580491i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1227.29 | + | 708.578i | −1.96997 | + | 1.13736i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.578 | − | 676.500i | 0.624924 | − | 1.08240i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.1231 | − | 33.5419i | −0.0304994 | − | 0.0534959i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 262.700 | − | 151.670i | 0.417648 | − | 0.241129i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 511.523 | − | 885.984i | 0.810655 | − | 1.40410i | −0.101752 | − | 0.994810i | \(-0.532445\pi\) |
0.912406 | − | 0.409285i | \(-0.134222\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.7530 | − | 157.005i | −0.0327852 | − | 0.248034i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 64.1038 | − | 37.0104i | 0.100951 | − | 0.0582841i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1422.47 | + | 2463.79i | 2.23307 | + | 3.86780i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 281.294 | + | 1045.46i | 0.440210 | + | 1.63609i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 549.016i | − | 0.856499i | −0.903660 | − | 0.428250i | \(-0.859130\pi\) | ||
0.903660 | − | 0.428250i | \(-0.140870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 275.137 | − | 476.551i | 0.427896 | − | 0.741137i | −0.568790 | − | 0.822483i | \(-0.692588\pi\) |
0.996686 | + | 0.0813455i | \(0.0259217\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 216.065 | − | 28.5596i | 0.334985 | − | 0.0442785i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 246.104i | 0.380376i | 0.981748 | + | 0.190188i | \(0.0609098\pi\) | ||||
−0.981748 | + | 0.190188i | \(0.939090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.9653 | + | 36.3129i | 0.0323039 | + | 0.0559521i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1254.72 | − | 963.812i | 1.92737 | − | 1.48051i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 70.4998 | − | 40.7031i | 0.107963 | − | 0.0623324i | −0.445046 | − | 0.895508i | \(-0.646813\pi\) |
0.553009 | + | 0.833175i | \(0.313479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.5673 | − | 56.4083i | −0.0497211 | − | 0.0861195i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 157.991 | − | 42.5094i | 0.240474 | − | 0.0647022i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −492.796 | + | 284.516i | −0.747793 | + | 0.431738i | −0.824896 | − | 0.565285i | \(-0.808766\pi\) |
0.0771029 | + | 0.997023i | \(0.475433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 183.113 | 0.277025 | 0.138512 | − | 0.990361i | \(-0.455768\pi\) | ||||
0.138512 | + | 0.990361i | \(0.455768\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −318.373 | + | 769.750i | −0.480201 | + | 1.16101i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1232.49 | − | 957.437i | −1.85337 | − | 1.43976i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −662.699 | − | 1147.83i | −0.993552 | − | 1.72088i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.450208 | + | 0.345828i | −0.000672957 | + | 0.000516933i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 67.6947i | − | 0.100886i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 120.295 | − | 208.356i | 0.178744 | − | 0.309593i | −0.762707 | − | 0.646744i | \(-0.776130\pi\) |
0.941451 | + | 0.337151i | \(0.109463\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −210.087 | + | 274.674i | −0.311239 | + | 0.406925i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 497.193 | + | 287.055i | 0.734407 | + | 0.424010i | 0.820032 | − | 0.572317i | \(-0.193955\pi\) |
−0.0856253 | + | 0.996327i | \(0.527289\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −343.454 | + | 594.880i | −0.505824 | + | 0.876112i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 58.4483 | − | 7.72572i | 0.0858272 | − | 0.0113447i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1104.28i | 1.61681i | 0.588628 | + | 0.808404i | \(0.299668\pi\) | ||||
−0.588628 | + | 0.808404i | \(0.700332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −113.669 | −0.165941 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −972.873 | − | 402.386i | −1.41612 | − | 0.585715i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 643.763 | + | 371.677i | 0.934344 | + | 0.539444i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −182.004 | + | 315.241i | −0.263393 | + | 0.456210i | −0.967141 | − | 0.254239i | \(-0.918175\pi\) |
0.703748 | + | 0.710449i | \(0.251508\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21.1600 | + | 78.6438i | 0.0305339 | + | 0.113483i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −677.516 | − | 391.164i | −0.974844 | − | 0.562826i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.6372 | −0.0181309 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 281.496 | − | 680.589i | 0.402712 | − | 0.973662i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −629.268 | + | 363.308i | −0.897672 | + | 0.518271i | −0.876444 | − | 0.481503i | \(-0.840091\pi\) |
−0.0212278 | + | 0.999775i | \(0.506758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −172.046 | − | 422.451i | −0.244731 | − | 0.600927i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −532.566 | + | 409.091i | −0.755412 | + | 0.580271i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 39.5327i | − | 0.0559162i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.0021 | + | 27.7164i | 0.0225699 | + | 0.0390922i | 0.877090 | − | 0.480327i | \(-0.159482\pi\) |
−0.854520 | + | 0.519419i | \(0.826148\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.0588 | − | 71.4247i | 0.0268056 | − | 0.100457i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1188.35 | − | 686.097i | 1.66670 | − | 0.962268i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45.7640 | − | 79.2655i | −0.0640055 | − | 0.110861i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 284.857 | − | 688.717i | 0.397291 | − | 0.960554i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −737.472 | + | 425.780i | −1.02569 | + | 0.592183i | −0.915747 | − | 0.401755i | \(-0.868400\pi\) |
−0.109944 | + | 0.993938i | \(0.535067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −145.953 | −0.202432 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −40.0597 | − | 16.5689i | −0.0554077 | − | 0.0229169i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 422.952 | + | 244.192i | 0.583382 | + | 0.336816i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 572.256 | 0.787147 | 0.393574 | − | 0.919293i | \(-0.371239\pi\) | ||||
0.393574 | + | 0.919293i | \(0.371239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −513.874 | + | 517.083i | −0.704902 | + | 0.709305i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 129.286 | − | 74.6431i | 0.176861 | − | 0.102111i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −388.675 | − | 673.206i | −0.530253 | − | 0.918425i | −0.999377 | − | 0.0352927i | \(-0.988764\pi\) |
0.469124 | − | 0.883132i | \(-0.344570\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1454.75 | + | 1893.83i | 1.97925 | + | 2.57664i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.5662 | − | 10.7192i | −0.0251916 | − | 0.0145444i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 186.632 | + | 323.256i | 0.252546 | + | 0.437423i | 0.964226 | − | 0.265081i | \(-0.0853987\pi\) |
−0.711680 | + | 0.702504i | \(0.752065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1081.36 | + | 632.183i | 1.45932 | + | 0.853149i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 561.225 | + | 324.023i | 0.755349 | + | 0.436101i | 0.827623 | − | 0.561284i | \(-0.189692\pi\) |
−0.0722742 | + | 0.997385i | \(0.523026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 613.483 | + | 1062.58i | 0.823467 | + | 1.42629i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1020.93 | + | 1023.05i | −1.36670 | + | 1.36954i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −170.747 | − | 98.5808i | −0.227967 | − | 0.131617i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −405.165 | −0.539501 | −0.269750 | − | 0.962930i | \(-0.586941\pi\) | ||||
−0.269750 | + | 0.962930i | \(0.586941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −136.442 | + | 18.0349i | −0.181197 | + | 0.0239507i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −916.652 | + | 529.229i | −1.21411 | + | 0.700966i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 473.100 | + | 819.433i | 0.624966 | + | 1.08247i | 0.988547 | + | 0.150911i | \(0.0482207\pi\) |
−0.363581 | + | 0.931563i | \(0.618446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.25573 | + | 70.0235i | 0.0121946 | + | 0.0922576i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −646.639 | + | 373.337i | −0.849722 | + | 0.490588i | −0.860557 | − | 0.509354i | \(-0.829884\pi\) |
0.0108347 | + | 0.999941i | \(0.496551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −431.476 | −0.565500 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −180.272 | + | 675.587i | −0.235649 | + | 0.883120i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1178.06 | − | 680.155i | −1.53594 | − | 0.886773i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −680.159 | −0.884472 | −0.442236 | − | 0.896899i | \(-0.645815\pi\) | ||||
−0.442236 | + | 0.896899i | \(0.645815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 796.651 | + | 1037.10i | 1.03327 | + | 1.34514i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 334.968 | + | 193.394i | 0.433335 | + | 0.250186i | 0.700766 | − | 0.713391i | \(-0.252842\pi\) |
−0.267431 | + | 0.963577i | \(0.586175\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −252.813 | + | 437.885i | −0.326210 | + | 0.565013i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 126.079 | + | 953.843i | 0.162264 | + | 1.22760i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.59251 | + | 18.8253i | −0.00332799 | + | 0.0241660i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −81.4840 | −0.104333 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 817.785 | + | 625.489i | 1.04443 | + | 0.798836i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 671.556 | − | 387.723i | 0.855486 | − | 0.493915i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 150.489 | + | 260.655i | 0.191219 | + | 0.331201i | 0.945654 | − | 0.325173i | \(-0.105423\pi\) |
−0.754436 | + | 0.656374i | \(0.772089\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 377.567 | + | 491.527i | 0.478539 | + | 0.622975i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2075.75i | − | 2.62421i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1098.08 | + | 1901.92i | 1.38471 | + | 2.39839i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 576.607 | + | 238.488i | 0.725291 | + | 0.299985i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 252.290 | − | 145.660i | 0.316550 | − | 0.182760i | −0.333304 | − | 0.942820i | \(-0.608163\pi\) |
0.649854 | + | 0.760059i | \(0.274830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −229.997 | + | 398.367i | −0.287856 | + | 0.498582i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 674.409 | − | 675.810i | 0.841958 | − | 0.843707i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.3139i | 0.0153349i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1427.53 | + | 2472.56i | 1.77333 | + | 3.07150i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −331.303 | + | 801.012i | −0.410537 | + | 0.992580i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1049.66i | − | 1.29748i | −0.761011 | − | 0.648739i | \(-0.775297\pi\) | ||
0.761011 | − | 0.648739i | \(-0.224703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 208.027 | − | 360.313i | 0.256506 | − | 0.444282i | −0.708797 | − | 0.705412i | \(-0.750762\pi\) |
0.965304 | + | 0.261130i | \(0.0840952\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −819.818 | − | 339.082i | −1.00839 | − | 0.417074i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −692.351 | − | 399.729i | −0.849511 | − | 0.490465i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −84.6708 | − | 207.906i | −0.103636 | − | 0.254474i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1870.18 | − | 1866.31i | −2.28350 | − | 2.27876i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 72.6869 | − | 41.9658i | 0.0885345 | − | 0.0511154i | −0.455079 | − | 0.890451i | \(-0.650389\pi\) |
0.543614 | + | 0.839336i | \(0.317056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 765.989 | 0.930728 | 0.465364 | − | 0.885119i | \(-0.345923\pi\) | ||||
0.465364 | + | 0.885119i | \(0.345923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.8548 | − | 20.6401i | −0.0192179 | − | 0.0250184i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1372.99 | − | 792.695i | −1.66020 | − | 0.958518i | −0.972617 | − | 0.232415i | \(-0.925337\pi\) |
−0.687586 | − | 0.726103i | \(-0.741329\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −543.934 | −0.656133 | −0.328067 | − | 0.944655i | \(-0.606397\pi\) | ||||
−0.328067 | + | 0.944655i | \(0.606397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.3788 | − | 275.221i | −0.0437772 | − | 0.331193i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1416.62 | + | 817.883i | 1.70062 | + | 0.981852i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −53.8264 | + | 93.2301i | −0.0644628 | + | 0.111653i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −647.572 | + | 846.658i | −0.773683 | + | 1.01154i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 344.007i | − | 0.410020i | −0.978760 | − | 0.205010i | \(-0.934277\pi\) | ||
0.978760 | − | 0.205010i | \(-0.0657227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 306.529 | − | 530.924i | 0.364482 | − | 0.631301i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −60.4324 | + | 146.111i | −0.0716874 | + | 0.173323i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1671.60 | + | 965.101i | 1.97823 | + | 1.14213i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1610.30 | 1.90118 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −148.822 | − | 1125.90i | −0.175291 | − | 1.32615i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 834.452i | 0.980555i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −583.024 | −0.683499 | −0.341749 | − | 0.939791i | \(-0.611019\pi\) | ||||
−0.341749 | + | 0.939791i | \(0.611019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 969.418 | + | 407.140i | 1.13382 | + | 0.476188i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1404.53i | 1.63889i | 0.573156 | + | 0.819446i | \(0.305719\pi\) | ||||
−0.573156 | + | 0.819446i | \(0.694281\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1087.44 | −1.26593 | −0.632967 | − | 0.774179i | \(-0.718163\pi\) | ||||
−0.632967 | + | 0.774179i | \(0.718163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.3199 | − | 37.0398i | 0.0177931 | − | 0.0430195i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1009.86i | 1.17018i | 0.810970 | + | 0.585088i | \(0.198940\pi\) | ||||
−0.810970 | + | 0.585088i | \(0.801060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −798.806 | + | 1383.57i | −0.923475 | + | 1.59951i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −50.8503 | − | 384.704i | −0.0586509 | − | 0.443719i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.81837 | + | 2.78189i | 0.00554473 | + | 0.00320125i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 695.505 | 0.798514 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 119.311 | − | 447.131i | 0.136668 | − | 0.512177i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 867.318 | + | 500.746i | 0.991221 | + | 0.572282i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 303.466 | − | 525.619i | 0.346028 | − | 0.599337i | −0.639512 | − | 0.768781i | \(-0.720864\pi\) |
0.985540 | + | 0.169443i | \(0.0541970\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 547.488 | − | 1323.70i | 0.622853 | − | 1.50591i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1319.04i | − | 1.49721i | −0.663015 | − | 0.748606i | \(-0.730723\pi\) | ||
0.663015 | − | 0.748606i | \(-0.269277\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 632.552 | − | 1095.61i | 0.716367 | − | 1.24078i | −0.246063 | − | 0.969254i | \(-0.579137\pi\) |
0.962430 | − | 0.271530i | \(-0.0875295\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1055.17 | − | 436.424i | −1.19228 | − | 0.493134i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 485.196i | − | 0.547008i | −0.961871 | − | 0.273504i | \(-0.911817\pi\) | ||
0.961871 | − | 0.273504i | \(-0.0881827\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 80.4090 | + | 139.272i | 0.0904488 | + | 0.156662i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.5322 | − | 47.4594i | −0.0309003 | − | 0.0532653i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 546.251 | + | 424.344i | 0.611704 | + | 0.475189i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −371.688 | + | 643.783i | −0.415294 | + | 0.719310i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1395.90 | − | 1817.21i | −1.55618 | − | 2.02588i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1303.71 | + | 752.698i | 1.45018 | + | 0.837261i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 427.410 | 0.474372 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 62.0488 | + | 469.425i | 0.0687140 | + | 0.519851i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1173.08 | + | 677.280i | −1.29622 | + | 0.748375i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 443.540 | 0.489018 | 0.244509 | − | 0.969647i | \(-0.421373\pi\) | ||||
0.244509 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.91995 | + | 25.7188i | 0.00761271 | + | 0.0282935i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −162.124 | − | 93.6021i | −0.177962 | − | 0.102747i | 0.408373 | − | 0.912815i | \(-0.366096\pi\) |
−0.586335 | + | 0.810069i | \(0.699430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.3897 | − | 94.2058i | −0.0595725 | − | 0.103183i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1123.00 | + | 1461.95i | 1.22732 | + | 1.59776i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 122.553 | − | 70.7560i | 0.133646 | − | 0.0771603i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −829.412 | −0.902516 | −0.451258 | − | 0.892394i | \(-0.649025\pi\) | ||||
−0.451258 | + | 0.892394i | \(0.649025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −134.980 | − | 55.8287i | −0.146559 | − | 0.0606175i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2289.34 | − | 1321.75i | 2.48032 | − | 1.43202i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −153.740 | − | 266.285i | −0.166205 | − | 0.287875i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 94.9528 | − | 25.5482i | 0.102430 | − | 0.0275601i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.7942i | 0.0385298i | 0.999814 | + | 0.0192649i | \(0.00613259\pi\) | ||||
−0.999814 | + | 0.0192649i | \(0.993867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1508.99 | − | 1942.50i | 1.62083 | − | 2.08647i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −77.5750 | + | 187.558i | −0.0831458 | + | 0.201027i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45.5757 | − | 26.3131i | −0.0487440 | − | 0.0281424i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −678.876 | + | 1175.85i | −0.724521 | + | 1.25491i | 0.234650 | + | 0.972080i | \(0.424606\pi\) |
−0.959171 | + | 0.282827i | \(0.908728\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.58543 | − | 3.13738i | −0.00807820 | − | 0.00334119i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1169.98i | 1.24334i | 0.783279 | + | 0.621670i | \(0.213545\pi\) | ||||
−0.783279 | + | 0.621670i | \(0.786455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.3818 | − | 30.1061i | 0.0184324 | − | 0.0319259i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1761.61 | − | 1347.38i | −1.86413 | − | 1.42580i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1036.15i | − | 1.09414i | −0.837086 | − | 0.547072i | \(-0.815742\pi\) | ||
0.837086 | − | 0.547072i | \(-0.184258\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −199.744 | − | 345.966i | −0.210478 | − | 0.364559i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 474.409 | − | 1147.01i | 0.498852 | − | 1.20611i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.9587 | + | 12.6779i | −0.0230416 | + | 0.0133031i | −0.511477 | − | 0.859297i | \(-0.670901\pi\) |
0.488435 | + | 0.872600i | \(0.337568\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −311.583 | − | 539.677i | −0.326265 | − | 0.565107i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −61.4517 | + | 47.2042i | −0.0642129 | + | 0.0493252i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 246.959i | − | 0.257517i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −298.773 | + | 517.490i | −0.310898 | + | 0.538491i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 128.339 | + | 34.2456i | 0.133270 | + | 0.0355614i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1702.67 | − | 983.038i | 1.76443 | − | 1.01869i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 597.003 | − | 1034.04i | 0.617376 | − | 1.06933i | −0.372587 | − | 0.927997i | \(-0.621529\pi\) |
0.989963 | − | 0.141329i | \(-0.0451376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 720.199 | + | 3.91398i | 0.743240 | + | 0.00403920i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 903.364 | − | 521.557i | 0.930344 | − | 0.537134i | 0.0434236 | − | 0.999057i | \(-0.486173\pi\) |
0.886920 | + | 0.461922i | \(0.152840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 849.846 | − | 1471.98i | 0.873429 | − | 1.51282i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 780.253 | + | 322.717i | 0.800259 | + | 0.330992i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.5462 | + | 13.0171i | −0.0230770 | + | 0.0133235i | −0.511494 | − | 0.859287i | \(-0.670908\pi\) |
0.488417 | + | 0.872610i | \(0.337574\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.9290 | + | 62.2308i | 0.0366997 | + | 0.0635657i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 280.706 | − | 75.5272i | 0.286143 | − | 0.0769900i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 327.709i | 0.333376i | 0.986010 | + | 0.166688i | \(0.0533073\pi\) | ||||
−0.986010 | + | 0.166688i | \(0.946693\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1114.99 | + | 1931.22i | −1.13197 | + | 1.96063i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −888.794 | − | 1157.06i | −0.900501 | − | 1.17230i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 410.668i | 0.415236i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −559.358 | − | 968.836i | −0.564438 | − | 0.977635i | −0.997102 | − | 0.0760795i | \(-0.975760\pi\) |
0.432664 | − | 0.901555i | \(-0.357574\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 156.309 | + | 1182.54i | 0.157411 | + | 1.19088i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −671.179 | + | 387.505i | −0.674551 | + | 0.389452i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 408.943 | + | 708.310i | 0.410174 | + | 0.710441i | 0.994908 | − | 0.100783i | \(-0.0321348\pi\) |
−0.584735 | + | 0.811224i | \(0.698801\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −248.988 | − | 598.473i | −0.249237 | − | 0.599072i |
(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 | 684.3.be.a.425.9 | yes | 80 | |
3.2 | odd | 2 | 2052.3.be.a.197.9 | 80 | |||
9.4 | even | 3 | 2052.3.m.a.881.9 | 80 | |||
9.5 | odd | 6 | 684.3.m.a.653.35 | yes | 80 | ||
19.11 | even | 3 | 684.3.m.a.353.35 | ✓ | 80 | ||
57.11 | odd | 6 | 2052.3.m.a.1493.32 | 80 | |||
171.49 | even | 3 | 2052.3.be.a.125.9 | 80 | |||
171.68 | odd | 6 | inner | 684.3.be.a.581.9 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.35 | ✓ | 80 | 19.11 | even | 3 | ||
684.3.m.a.653.35 | yes | 80 | 9.5 | odd | 6 | ||
684.3.be.a.425.9 | yes | 80 | 1.1 | even | 1 | trivial | |
684.3.be.a.581.9 | yes | 80 | 171.68 | odd | 6 | inner | |
2052.3.m.a.881.9 | 80 | 9.4 | even | 3 | |||
2052.3.m.a.1493.32 | 80 | 57.11 | odd | 6 | |||
2052.3.be.a.125.9 | 80 | 171.49 | even | 3 | |||
2052.3.be.a.197.9 | 80 | 3.2 | odd | 2 |