Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.10 | ||
Root | \(-0.111613 - 1.72845i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.b.881.4 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.767566 | − | 1.55269i | 0.443154 | − | 0.896445i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.55269 | + | 0.767566i | 0.633883 | + | 0.313358i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.82168 | − | 2.38358i | −0.607228 | − | 0.794527i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | − | 2.30680i | − | 0.695527i | −0.937582 | − | 0.347763i | \(-0.886941\pi\) | ||
0.937582 | − | 0.347763i | \(-0.113059\pi\) | |||||||
\(12\) | −0.767566 | + | 1.55269i | −0.221577 | + | 0.448223i | ||||
\(13\) | 5.00084i | 1.38698i | 0.720464 | + | 0.693492i | \(0.243929\pi\) | ||||
−0.720464 | + | 0.693492i | \(0.756071\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.767566 | + | 1.55269i | −0.198185 | + | 0.400903i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.30230 | −1.52853 | −0.764266 | − | 0.644901i | \(-0.776898\pi\) | ||||
−0.764266 | + | 0.644901i | \(0.776898\pi\) | |||||||
\(18\) | 2.38358 | − | 1.82168i | 0.561816 | − | 0.429375i | ||||
\(19\) | − | 7.55717i | − | 1.73373i | −0.498539 | − | 0.866867i | \(-0.666130\pi\) | ||
0.498539 | − | 0.866867i | \(-0.333870\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.30680 | 0.491812 | ||||||||
\(23\) | 6.37256i | 1.32877i | 0.747390 | + | 0.664385i | \(0.231307\pi\) | ||||
−0.747390 | + | 0.664385i | \(0.768693\pi\) | |||||||
\(24\) | −1.55269 | − | 0.767566i | −0.316941 | − | 0.156679i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.00084 | −0.980746 | ||||||||
\(27\) | −5.09922 | + | 0.998953i | −0.981346 | + | 0.192249i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.83533i | 0.712204i | 0.934447 | + | 0.356102i | \(0.115894\pi\) | ||||
−0.934447 | + | 0.356102i | \(0.884106\pi\) | |||||||
\(30\) | −1.55269 | − | 0.767566i | −0.283481 | − | 0.140138i | ||||
\(31\) | − | 4.38153i | − | 0.786946i | −0.919336 | − | 0.393473i | \(-0.871273\pi\) | ||
0.919336 | − | 0.393473i | \(-0.128727\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −3.58174 | − | 1.77062i | −0.623501 | − | 0.308226i | ||||
\(34\) | − | 6.30230i | − | 1.08083i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.82168 | + | 2.38358i | 0.303614 | + | 0.397264i | ||||
\(37\) | −6.90930 | −1.13588 | −0.567941 | − | 0.823069i | \(-0.692260\pi\) | ||||
−0.567941 | + | 0.823069i | \(0.692260\pi\) | |||||||
\(38\) | 7.55717 | 1.22594 | ||||||||
\(39\) | 7.76475 | + | 3.83848i | 1.24335 | + | 0.614648i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −9.79371 | −1.52952 | −0.764760 | − | 0.644315i | \(-0.777143\pi\) | ||||
−0.764760 | + | 0.644315i | \(0.777143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.55278 | 0.389296 | 0.194648 | − | 0.980873i | \(-0.437644\pi\) | ||||
0.194648 | + | 0.980873i | \(0.437644\pi\) | |||||||
\(44\) | 2.30680i | 0.347763i | ||||||||
\(45\) | 1.82168 | + | 2.38358i | 0.271561 | + | 0.355323i | ||||
\(46\) | −6.37256 | −0.939583 | ||||||||
\(47\) | −1.65683 | −0.241674 | −0.120837 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120837 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(48\) | 0.767566 | − | 1.55269i | 0.110789 | − | 0.224111i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −4.83743 | + | 9.78550i | −0.677375 | + | 1.37024i | ||||
\(52\) | − | 5.00084i | − | 0.693492i | ||||||
\(53\) | 3.25278i | 0.446804i | 0.974726 | + | 0.223402i | \(0.0717163\pi\) | ||||
−0.974726 | + | 0.223402i | \(0.928284\pi\) | |||||||
\(54\) | −0.998953 | − | 5.09922i | −0.135940 | − | 0.693917i | ||||
\(55\) | 2.30680i | 0.311049i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.7339 | − | 5.80063i | −1.55420 | − | 0.768312i | ||||
\(58\) | −3.83533 | −0.503604 | ||||||||
\(59\) | −9.93145 | −1.29297 | −0.646483 | − | 0.762929i | \(-0.723761\pi\) | ||||
−0.646483 | + | 0.762929i | \(0.723761\pi\) | |||||||
\(60\) | 0.767566 | − | 1.55269i | 0.0990923 | − | 0.200451i | ||||
\(61\) | 5.98368i | 0.766131i | 0.923721 | + | 0.383066i | \(0.125132\pi\) | ||||
−0.923721 | + | 0.383066i | \(0.874868\pi\) | |||||||
\(62\) | 4.38153 | 0.556455 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 5.00084i | − | 0.620278i | ||||||
\(66\) | 1.77062 | − | 3.58174i | 0.217948 | − | 0.440882i | ||||
\(67\) | −2.76716 | −0.338063 | −0.169031 | − | 0.985611i | \(-0.554064\pi\) | ||||
−0.169031 | + | 0.985611i | \(0.554064\pi\) | |||||||
\(68\) | 6.30230 | 0.764266 | ||||||||
\(69\) | 9.89460 | + | 4.89136i | 1.19117 | + | 0.588851i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.85910i | − | 0.339312i | −0.985503 | − | 0.169656i | \(-0.945734\pi\) | ||
0.985503 | − | 0.169656i | \(-0.0542657\pi\) | |||||||
\(72\) | −2.38358 | + | 1.82168i | −0.280908 | + | 0.214688i | ||||
\(73\) | − | 3.68177i | − | 0.430919i | −0.976513 | − | 0.215459i | \(-0.930875\pi\) | ||
0.976513 | − | 0.215459i | \(-0.0691249\pi\) | |||||||
\(74\) | − | 6.90930i | − | 0.803190i | ||||||
\(75\) | 0.767566 | − | 1.55269i | 0.0886309 | − | 0.179289i | ||||
\(76\) | 7.55717i | 0.866867i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.83848 | + | 7.76475i | −0.434622 | + | 0.879185i | ||||
\(79\) | 2.55889 | 0.287898 | 0.143949 | − | 0.989585i | \(-0.454020\pi\) | ||||
0.143949 | + | 0.989585i | \(0.454020\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −2.36293 | + | 8.68427i | −0.262548 | + | 0.964919i | ||||
\(82\) | − | 9.79371i | − | 1.08153i | ||||||
\(83\) | 1.83743 | 0.201684 | 0.100842 | − | 0.994902i | \(-0.467846\pi\) | ||||
0.100842 | + | 0.994902i | \(0.467846\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.30230 | 0.683580 | ||||||||
\(86\) | 2.55278i | 0.275274i | ||||||||
\(87\) | 5.95508 | + | 2.94387i | 0.638452 | + | 0.315616i | ||||
\(88\) | −2.30680 | −0.245906 | ||||||||
\(89\) | −5.88774 | −0.624100 | −0.312050 | − | 0.950066i | \(-0.601016\pi\) | ||||
−0.312050 | + | 0.950066i | \(0.601016\pi\) | |||||||
\(90\) | −2.38358 | + | 1.82168i | −0.251252 | + | 0.192022i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 6.37256i | − | 0.664385i | ||||||
\(93\) | −6.80316 | − | 3.36311i | −0.705454 | − | 0.348739i | ||||
\(94\) | − | 1.65683i | − | 0.170889i | ||||||
\(95\) | 7.55717i | 0.775350i | ||||||||
\(96\) | 1.55269 | + | 0.767566i | 0.158471 | + | 0.0783394i | ||||
\(97\) | − | 4.61723i | − | 0.468808i | −0.972139 | − | 0.234404i | \(-0.924686\pi\) | ||
0.972139 | − | 0.234404i | \(-0.0753139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.49845 | + | 4.20226i | −0.552615 | + | 0.422343i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −11.3140 | −1.12579 | −0.562894 | − | 0.826529i | \(-0.690312\pi\) | ||||
−0.562894 | + | 0.826529i | \(0.690312\pi\) | |||||||
\(102\) | −9.78550 | − | 4.83743i | −0.968909 | − | 0.478977i | ||||
\(103\) | − | 7.36407i | − | 0.725603i | −0.931866 | − | 0.362802i | \(-0.881820\pi\) | ||
0.931866 | − | 0.362802i | \(-0.118180\pi\) | |||||||
\(104\) | 5.00084 | 0.490373 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.25278 | −0.315938 | ||||||||
\(107\) | − | 8.41874i | − | 0.813870i | −0.913457 | − | 0.406935i | \(-0.866598\pi\) | ||
0.913457 | − | 0.406935i | \(-0.133402\pi\) | |||||||
\(108\) | 5.09922 | − | 0.998953i | 0.490673 | − | 0.0961243i | ||||
\(109\) | −6.66311 | −0.638211 | −0.319105 | − | 0.947719i | \(-0.603382\pi\) | ||||
−0.319105 | + | 0.947719i | \(0.603382\pi\) | |||||||
\(110\) | −2.30680 | −0.219945 | ||||||||
\(111\) | −5.30334 | + | 10.7280i | −0.503371 | + | 1.01826i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.45505i | 0.419096i | 0.977798 | + | 0.209548i | \(0.0671992\pi\) | ||||
−0.977798 | + | 0.209548i | \(0.932801\pi\) | |||||||
\(114\) | 5.80063 | − | 11.7339i | 0.543279 | − | 1.09898i | ||||
\(115\) | − | 6.37256i | − | 0.594244i | ||||||
\(116\) | − | 3.83533i | − | 0.356102i | ||||||
\(117\) | 11.9199 | − | 9.10996i | 1.10200 | − | 0.842216i | ||||
\(118\) | − | 9.93145i | − | 0.914264i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.55269 | + | 0.767566i | 0.141740 | + | 0.0700689i | ||||
\(121\) | 5.67867 | 0.516243 | ||||||||
\(122\) | −5.98368 | −0.541737 | ||||||||
\(123\) | −7.51732 | + | 15.2066i | −0.677814 | + | 1.37113i | ||||
\(124\) | 4.38153i | 0.393473i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.83694 | −0.163002 | −0.0815011 | − | 0.996673i | \(-0.525971\pi\) | ||||
−0.0815011 | + | 0.996673i | \(0.525971\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.95943 | − | 3.96368i | 0.172518 | − | 0.348982i | ||||
\(130\) | 5.00084 | 0.438603 | ||||||||
\(131\) | −5.53883 | −0.483930 | −0.241965 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241965 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(132\) | 3.58174 | + | 1.77062i | 0.311751 | + | 0.154113i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.76716i | − | 0.239047i | ||||||
\(135\) | 5.09922 | − | 0.998953i | 0.438871 | − | 0.0859762i | ||||
\(136\) | 6.30230i | 0.540417i | ||||||||
\(137\) | − | 1.24104i | − | 0.106029i | −0.998594 | − | 0.0530146i | \(-0.983117\pi\) | ||
0.998594 | − | 0.0530146i | \(-0.0168830\pi\) | |||||||
\(138\) | −4.89136 | + | 9.89460i | −0.416380 | + | 0.842285i | ||||
\(139\) | − | 12.5344i | − | 1.06315i | −0.847011 | − | 0.531576i | \(-0.821600\pi\) | ||
0.847011 | − | 0.531576i | \(-0.178400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.27173 | + | 2.57255i | −0.107099 | + | 0.216647i | ||||
\(142\) | 2.85910 | 0.239930 | ||||||||
\(143\) | 11.5359 | 0.964684 | ||||||||
\(144\) | −1.82168 | − | 2.38358i | −0.151807 | − | 0.198632i | ||||
\(145\) | − | 3.83533i | − | 0.318507i | ||||||
\(146\) | 3.68177 | 0.304706 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.90930 | 0.567941 | ||||||||
\(149\) | 15.5951i | 1.27760i | 0.769371 | + | 0.638802i | \(0.220570\pi\) | ||||
−0.769371 | + | 0.638802i | \(0.779430\pi\) | |||||||
\(150\) | 1.55269 | + | 0.767566i | 0.126777 | + | 0.0626715i | ||||
\(151\) | 3.03915 | 0.247323 | 0.123661 | − | 0.992324i | \(-0.460536\pi\) | ||||
0.123661 | + | 0.992324i | \(0.460536\pi\) | |||||||
\(152\) | −7.55717 | −0.612968 | ||||||||
\(153\) | 11.4808 | + | 15.0220i | 0.928168 | + | 1.21446i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.38153i | 0.351933i | ||||||||
\(156\) | −7.76475 | − | 3.83848i | −0.621677 | − | 0.307324i | ||||
\(157\) | 15.8252i | 1.26299i | 0.775381 | + | 0.631494i | \(0.217558\pi\) | ||||
−0.775381 | + | 0.631494i | \(0.782442\pi\) | |||||||
\(158\) | 2.55889i | 0.203575i | ||||||||
\(159\) | 5.05056 | + | 2.49673i | 0.400535 | + | 0.198003i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −8.68427 | − | 2.36293i | −0.682301 | − | 0.185649i | ||||
\(163\) | −8.61682 | −0.674921 | −0.337461 | − | 0.941340i | \(-0.609568\pi\) | ||||
−0.337461 | + | 0.941340i | \(0.609568\pi\) | |||||||
\(164\) | 9.79371 | 0.764760 | ||||||||
\(165\) | 3.58174 | + | 1.77062i | 0.278838 | + | 0.137843i | ||||
\(166\) | 1.83743i | 0.142612i | ||||||||
\(167\) | 8.64948 | 0.669317 | 0.334658 | − | 0.942339i | \(-0.391379\pi\) | ||||
0.334658 | + | 0.942339i | \(0.391379\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0084 | −0.923724 | ||||||||
\(170\) | 6.30230i | 0.483364i | ||||||||
\(171\) | −18.0131 | + | 13.7668i | −1.37750 | + | 1.05277i | ||||
\(172\) | −2.55278 | −0.194648 | ||||||||
\(173\) | 17.9315 | 1.36330 | 0.681652 | − | 0.731677i | \(-0.261262\pi\) | ||||
0.681652 | + | 0.731677i | \(0.261262\pi\) | |||||||
\(174\) | −2.94387 | + | 5.95508i | −0.223174 | + | 0.451454i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.30680i | − | 0.173882i | ||||||
\(177\) | −7.62305 | + | 15.4205i | −0.572983 | + | 1.15907i | ||||
\(178\) | − | 5.88774i | − | 0.441305i | ||||||
\(179\) | − | 12.0170i | − | 0.898190i | −0.893484 | − | 0.449095i | \(-0.851747\pi\) | ||
0.893484 | − | 0.449095i | \(-0.148253\pi\) | |||||||
\(180\) | −1.82168 | − | 2.38358i | −0.135780 | − | 0.177662i | ||||
\(181\) | − | 9.52612i | − | 0.708071i | −0.935232 | − | 0.354036i | \(-0.884809\pi\) | ||
0.935232 | − | 0.354036i | \(-0.115191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.29079 | + | 4.59287i | 0.686795 | + | 0.339514i | ||||
\(184\) | 6.37256 | 0.469791 | ||||||||
\(185\) | 6.90930 | 0.507982 | ||||||||
\(186\) | 3.36311 | − | 6.80316i | 0.246596 | − | 0.498832i | ||||
\(187\) | 14.5381i | 1.06313i | ||||||||
\(188\) | 1.65683 | 0.120837 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.55717 | −0.548255 | ||||||||
\(191\) | 4.97173i | 0.359741i | 0.983690 | + | 0.179871i | \(0.0575679\pi\) | ||||
−0.983690 | + | 0.179871i | \(0.942432\pi\) | |||||||
\(192\) | −0.767566 | + | 1.55269i | −0.0553943 | + | 0.112056i | ||||
\(193\) | 6.03321 | 0.434280 | 0.217140 | − | 0.976140i | \(-0.430327\pi\) | ||||
0.217140 | + | 0.976140i | \(0.430327\pi\) | |||||||
\(194\) | 4.61723 | 0.331498 | ||||||||
\(195\) | −7.76475 | − | 3.83848i | −0.556045 | − | 0.274879i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.2144i | − | 1.01273i | −0.862318 | − | 0.506366i | \(-0.830988\pi\) | ||
0.862318 | − | 0.506366i | \(-0.169012\pi\) | |||||||
\(198\) | −4.20226 | − | 5.49845i | −0.298642 | − | 0.390758i | ||||
\(199\) | 2.25088i | 0.159560i | 0.996812 | + | 0.0797802i | \(0.0254219\pi\) | ||||
−0.996812 | + | 0.0797802i | \(0.974578\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | −2.12398 | + | 4.29655i | −0.149814 | + | 0.303055i | ||||
\(202\) | − | 11.3140i | − | 0.796053i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.83743 | − | 9.78550i | 0.338688 | − | 0.685122i | ||||
\(205\) | 9.79371 | 0.684022 | ||||||||
\(206\) | 7.36407 | 0.513079 | ||||||||
\(207\) | 15.1895 | − | 11.6088i | 1.05574 | − | 0.806867i | ||||
\(208\) | 5.00084i | 0.346746i | ||||||||
\(209\) | −17.4329 | −1.20586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.6034 | 1.90029 | 0.950147 | − | 0.311804i | \(-0.100933\pi\) | ||||
0.950147 | + | 0.311804i | \(0.100933\pi\) | |||||||
\(212\) | − | 3.25278i | − | 0.223402i | ||||||
\(213\) | −4.43929 | − | 2.19455i | −0.304175 | − | 0.150368i | ||||
\(214\) | 8.41874 | 0.575493 | ||||||||
\(215\) | −2.55278 | −0.174098 | ||||||||
\(216\) | 0.998953 | + | 5.09922i | 0.0679701 | + | 0.346958i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 6.66311i | − | 0.451283i | ||||||
\(219\) | −5.71664 | − | 2.82600i | −0.386295 | − | 0.190964i | ||||
\(220\) | − | 2.30680i | − | 0.155524i | ||||||
\(221\) | − | 31.5168i | − | 2.12005i | ||||||
\(222\) | −10.7280 | − | 5.30334i | −0.720016 | − | 0.355937i | ||||
\(223\) | − | 23.0777i | − | 1.54539i | −0.634775 | − | 0.772697i | \(-0.718907\pi\) | ||
0.634775 | − | 0.772697i | \(-0.281093\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.82168 | − | 2.38358i | −0.121446 | − | 0.158905i | ||||
\(226\) | −4.45505 | −0.296345 | ||||||||
\(227\) | −20.0351 | −1.32977 | −0.664887 | − | 0.746944i | \(-0.731520\pi\) | ||||
−0.664887 | + | 0.746944i | \(0.731520\pi\) | |||||||
\(228\) | 11.7339 | + | 5.80063i | 0.777099 | + | 0.384156i | ||||
\(229\) | − | 28.7648i | − | 1.90083i | −0.310979 | − | 0.950417i | \(-0.600657\pi\) | ||
0.310979 | − | 0.950417i | \(-0.399343\pi\) | |||||||
\(230\) | 6.37256 | 0.420194 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.83533 | 0.251802 | ||||||||
\(233\) | − | 25.7115i | − | 1.68442i | −0.539151 | − | 0.842209i | \(-0.681255\pi\) | ||
0.539151 | − | 0.842209i | \(-0.318745\pi\) | |||||||
\(234\) | 9.10996 | + | 11.9199i | 0.595536 | + | 0.779229i | ||||
\(235\) | 1.65683 | 0.108080 | ||||||||
\(236\) | 9.93145 | 0.646483 | ||||||||
\(237\) | 1.96412 | − | 3.97317i | 0.127583 | − | 0.258085i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.7220i | − | 0.693551i | −0.937948 | − | 0.346776i | \(-0.887277\pi\) | ||
0.937948 | − | 0.346776i | \(-0.112723\pi\) | |||||||
\(240\) | −0.767566 | + | 1.55269i | −0.0495462 | + | 0.100226i | ||||
\(241\) | 1.18465i | 0.0763100i | 0.999272 | + | 0.0381550i | \(0.0121481\pi\) | ||||
−0.999272 | + | 0.0381550i | \(0.987852\pi\) | |||||||
\(242\) | 5.67867i | 0.365039i | ||||||||
\(243\) | 11.6703 | + | 10.3346i | 0.748648 | + | 0.662968i | ||||
\(244\) | − | 5.98368i | − | 0.383066i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.2066 | − | 7.51732i | −0.969536 | − | 0.479287i | ||||
\(247\) | 37.7922 | 2.40466 | ||||||||
\(248\) | −4.38153 | −0.278228 | ||||||||
\(249\) | 1.41035 | − | 2.85295i | 0.0893771 | − | 0.180799i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 14.3689 | 0.906958 | 0.453479 | − | 0.891267i | \(-0.350183\pi\) | ||||
0.453479 | + | 0.891267i | \(0.350183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7002 | 0.924195 | ||||||||
\(254\) | − | 1.83694i | − | 0.115260i | ||||||
\(255\) | 4.83743 | − | 9.78550i | 0.302932 | − | 0.612792i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.5360 | 1.03149 | 0.515745 | − | 0.856742i | \(-0.327515\pi\) | ||||
0.515745 | + | 0.856742i | \(0.327515\pi\) | |||||||
\(258\) | 3.96368 | + | 1.95943i | 0.246768 | + | 0.121989i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.00084i | 0.310139i | ||||||||
\(261\) | 9.14184 | − | 6.98677i | 0.565865 | − | 0.432470i | ||||
\(262\) | − | 5.53883i | − | 0.342190i | ||||||
\(263\) | 30.9400i | 1.90784i | 0.300060 | + | 0.953920i | \(0.402993\pi\) | ||||
−0.300060 | + | 0.953920i | \(0.597007\pi\) | |||||||
\(264\) | −1.77062 | + | 3.58174i | −0.108974 | + | 0.220441i | ||||
\(265\) | − | 3.25278i | − | 0.199817i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.51923 | + | 9.14184i | −0.276573 | + | 0.559471i | ||||
\(268\) | 2.76716 | 0.169031 | ||||||||
\(269\) | −4.10422 | −0.250239 | −0.125119 | − | 0.992142i | \(-0.539931\pi\) | ||||
−0.125119 | + | 0.992142i | \(0.539931\pi\) | |||||||
\(270\) | 0.998953 | + | 5.09922i | 0.0607943 | + | 0.310329i | ||||
\(271\) | 9.07677i | 0.551374i | 0.961247 | + | 0.275687i | \(0.0889054\pi\) | ||||
−0.961247 | + | 0.275687i | \(0.911095\pi\) | |||||||
\(272\) | −6.30230 | −0.382133 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.24104 | 0.0749740 | ||||||||
\(275\) | − | 2.30680i | − | 0.139105i | ||||||
\(276\) | −9.89460 | − | 4.89136i | −0.595585 | − | 0.294425i | ||||
\(277\) | 0.216476 | 0.0130068 | 0.00650338 | − | 0.999979i | \(-0.497930\pi\) | ||||
0.00650338 | + | 0.999979i | \(0.497930\pi\) | |||||||
\(278\) | 12.5344 | 0.751761 | ||||||||
\(279\) | −10.4437 | + | 7.98177i | −0.625250 | + | 0.477856i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.8498i | − | 1.12448i | −0.826973 | − | 0.562241i | \(-0.809939\pi\) | ||
0.826973 | − | 0.562241i | \(-0.190061\pi\) | |||||||
\(282\) | −2.57255 | − | 1.27173i | −0.153193 | − | 0.0757303i | ||||
\(283\) | − | 1.99832i | − | 0.118788i | −0.998235 | − | 0.0593939i | \(-0.981083\pi\) | ||
0.998235 | − | 0.0593939i | \(-0.0189168\pi\) | |||||||
\(284\) | 2.85910i | 0.169656i | ||||||||
\(285\) | 11.7339 | + | 5.80063i | 0.695059 | + | 0.343600i | ||||
\(286\) | 11.5359i | 0.682135i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.38358 | − | 1.82168i | 0.140454 | − | 0.107344i | ||||
\(289\) | 22.7189 | 1.33641 | ||||||||
\(290\) | 3.83533 | 0.225219 | ||||||||
\(291\) | −7.16912 | − | 3.54403i | −0.420261 | − | 0.207755i | ||||
\(292\) | 3.68177i | 0.215459i | ||||||||
\(293\) | −9.28117 | −0.542212 | −0.271106 | − | 0.962550i | \(-0.587389\pi\) | ||||
−0.271106 | + | 0.962550i | \(0.587389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.93145 | 0.578232 | ||||||||
\(296\) | 6.90930i | 0.401595i | ||||||||
\(297\) | 2.30439 | + | 11.7629i | 0.133714 | + | 0.682552i | ||||
\(298\) | −15.5951 | −0.903403 | ||||||||
\(299\) | −31.8682 | −1.84298 | ||||||||
\(300\) | −0.767566 | + | 1.55269i | −0.0443154 | + | 0.0896445i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.03915i | 0.174883i | ||||||||
\(303\) | −8.68427 | + | 17.5672i | −0.498898 | + | 1.00921i | ||||
\(304\) | − | 7.55717i | − | 0.433434i | ||||||
\(305\) | − | 5.98368i | − | 0.342624i | ||||||
\(306\) | −15.0220 | + | 11.4808i | −0.858753 | + | 0.656314i | ||||
\(307\) | 26.9282i | 1.53687i | 0.639927 | + | 0.768436i | \(0.278965\pi\) | ||||
−0.639927 | + | 0.768436i | \(0.721035\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4341 | − | 5.65241i | −0.650464 | − | 0.321554i | ||||
\(310\) | −4.38153 | −0.248854 | ||||||||
\(311\) | 2.82130 | 0.159981 | 0.0799905 | − | 0.996796i | \(-0.474511\pi\) | ||||
0.0799905 | + | 0.996796i | \(0.474511\pi\) | |||||||
\(312\) | 3.83848 | − | 7.76475i | 0.217311 | − | 0.439592i | ||||
\(313\) | 11.4427i | 0.646780i | 0.946266 | + | 0.323390i | \(0.104823\pi\) | ||||
−0.946266 | + | 0.323390i | \(0.895177\pi\) | |||||||
\(314\) | −15.8252 | −0.893068 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.55889 | −0.143949 | ||||||||
\(317\) | − | 9.30982i | − | 0.522891i | −0.965218 | − | 0.261446i | \(-0.915801\pi\) | ||
0.965218 | − | 0.261446i | \(-0.0841992\pi\) | |||||||
\(318\) | −2.49673 | + | 5.05056i | −0.140009 | + | 0.283221i | ||||
\(319\) | 8.84735 | 0.495357 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −13.0717 | − | 6.46194i | −0.729590 | − | 0.360670i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.6275i | 2.65007i | ||||||||
\(324\) | 2.36293 | − | 8.68427i | 0.131274 | − | 0.482460i | ||||
\(325\) | 5.00084i | 0.277397i | ||||||||
\(326\) | − | 8.61682i | − | 0.477241i | ||||||
\(327\) | −5.11438 | + | 10.3457i | −0.282826 | + | 0.572121i | ||||
\(328\) | 9.79371i | 0.540767i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.77062 | + | 3.58174i | −0.0974695 | + | 0.197168i | ||||
\(331\) | 18.2960 | 1.00564 | 0.502820 | − | 0.864391i | \(-0.332296\pi\) | ||||
0.502820 | + | 0.864391i | \(0.332296\pi\) | |||||||
\(332\) | −1.83743 | −0.100842 | ||||||||
\(333\) | 12.5866 | + | 16.4689i | 0.689740 | + | 0.902489i | ||||
\(334\) | 8.64948i | 0.473279i | ||||||||
\(335\) | 2.76716 | 0.151186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.84516 | 0.427353 | 0.213676 | − | 0.976904i | \(-0.431456\pi\) | ||||
0.213676 | + | 0.976904i | \(0.431456\pi\) | |||||||
\(338\) | − | 12.0084i | − | 0.653171i | ||||||
\(339\) | 6.91730 | + | 3.41954i | 0.375696 | + | 0.185724i | ||||
\(340\) | −6.30230 | −0.341790 | ||||||||
\(341\) | −10.1073 | −0.547342 | ||||||||
\(342\) | −13.7668 | − | 18.0131i | −0.744423 | − | 0.974039i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 2.55278i | − | 0.137637i | ||||||
\(345\) | −9.89460 | − | 4.89136i | −0.532708 | − | 0.263342i | ||||
\(346\) | 17.9315i | 0.964001i | ||||||||
\(347\) | 0.232294i | 0.0124702i | 0.999981 | + | 0.00623509i | \(0.00198470\pi\) | ||||
−0.999981 | + | 0.00623509i | \(0.998015\pi\) | |||||||
\(348\) | −5.95508 | − | 2.94387i | −0.319226 | − | 0.157808i | ||||
\(349\) | 11.5685i | 0.619249i | 0.950859 | + | 0.309624i | \(0.100203\pi\) | ||||
−0.950859 | + | 0.309624i | \(0.899797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.99561 | − | 25.5004i | −0.266646 | − | 1.36111i | ||||
\(352\) | 2.30680 | 0.122953 | ||||||||
\(353\) | 34.7075 | 1.84729 | 0.923646 | − | 0.383247i | \(-0.125194\pi\) | ||||
0.923646 | + | 0.383247i | \(0.125194\pi\) | |||||||
\(354\) | −15.4205 | − | 7.62305i | −0.819588 | − | 0.405160i | ||||
\(355\) | 2.85910i | 0.151745i | ||||||||
\(356\) | 5.88774 | 0.312050 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0170 | 0.635116 | ||||||||
\(359\) | 17.5322i | 0.925316i | 0.886537 | + | 0.462658i | \(0.153104\pi\) | ||||
−0.886537 | + | 0.462658i | \(0.846896\pi\) | |||||||
\(360\) | 2.38358 | − | 1.82168i | 0.125626 | − | 0.0960112i | ||||
\(361\) | −38.1109 | −2.00584 | ||||||||
\(362\) | 9.52612 | 0.500682 | ||||||||
\(363\) | 4.35875 | − | 8.81721i | 0.228775 | − | 0.462783i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.68177i | 0.192713i | ||||||||
\(366\) | −4.59287 | + | 9.29079i | −0.240073 | + | 0.485637i | ||||
\(367\) | − | 10.0402i | − | 0.524093i | −0.965055 | − | 0.262047i | \(-0.915603\pi\) | ||
0.965055 | − | 0.262047i | \(-0.0843974\pi\) | |||||||
\(368\) | 6.37256i | 0.332193i | ||||||||
\(369\) | 17.8411 | + | 23.3441i | 0.928768 | + | 1.21525i | ||||
\(370\) | 6.90930i | 0.359197i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.80316 | + | 3.36311i | 0.352727 | + | 0.174369i | ||||
\(373\) | −0.00482067 | −0.000249605 | −0.000124803 | − | 1.00000i | \(-0.500040\pi\) | ||||
−0.000124803 | 1.00000i | \(0.500040\pi\) | ||||||||
\(374\) | −14.5381 | −0.751749 | ||||||||
\(375\) | −0.767566 | + | 1.55269i | −0.0396369 | + | 0.0801805i | ||||
\(376\) | 1.65683i | 0.0854446i | ||||||||
\(377\) | −19.1799 | −0.987815 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6572 | 0.958356 | 0.479178 | − | 0.877718i | \(-0.340935\pi\) | ||||
0.479178 | + | 0.877718i | \(0.340935\pi\) | |||||||
\(380\) | − | 7.55717i | − | 0.387675i | ||||||
\(381\) | −1.40997 | + | 2.85220i | −0.0722352 | + | 0.146123i | ||||
\(382\) | −4.97173 | −0.254376 | ||||||||
\(383\) | −18.8463 | −0.963002 | −0.481501 | − | 0.876446i | \(-0.659908\pi\) | ||||
−0.481501 | + | 0.876446i | \(0.659908\pi\) | |||||||
\(384\) | −1.55269 | − | 0.767566i | −0.0792353 | − | 0.0391697i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.03321i | 0.307082i | ||||||||
\(387\) | −4.65037 | − | 6.08477i | −0.236391 | − | 0.309306i | ||||
\(388\) | 4.61723i | 0.234404i | ||||||||
\(389\) | 10.8601i | 0.550627i | 0.961354 | + | 0.275314i | \(0.0887817\pi\) | ||||
−0.961354 | + | 0.275314i | \(0.911218\pi\) | |||||||
\(390\) | 3.83848 | − | 7.76475i | 0.194369 | − | 0.393183i | ||||
\(391\) | − | 40.1618i | − | 2.03107i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.25142 | + | 8.60008i | −0.214456 | + | 0.433817i | ||||
\(394\) | 14.2144 | 0.716110 | ||||||||
\(395\) | −2.55889 | −0.128752 | ||||||||
\(396\) | 5.49845 | − | 4.20226i | 0.276307 | − | 0.211172i | ||||
\(397\) | 27.0408i | 1.35714i | 0.734536 | + | 0.678570i | \(0.237400\pi\) | ||||
−0.734536 | + | 0.678570i | \(0.762600\pi\) | |||||||
\(398\) | −2.25088 | −0.112826 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − | 24.5254i | − | 1.22474i | −0.790571 | − | 0.612371i | \(-0.790216\pi\) | ||
0.790571 | − | 0.612371i | \(-0.209784\pi\) | |||||||
\(402\) | −4.29655 | − | 2.12398i | −0.214292 | − | 0.105935i | ||||
\(403\) | 21.9113 | 1.09148 | ||||||||
\(404\) | 11.3140 | 0.562894 | ||||||||
\(405\) | 2.36293 | − | 8.68427i | 0.117415 | − | 0.431525i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.9384i | 0.790036i | ||||||||
\(408\) | 9.78550 | + | 4.83743i | 0.484455 | + | 0.239488i | ||||
\(409\) | 5.40347i | 0.267184i | 0.991036 | + | 0.133592i | \(0.0426512\pi\) | ||||
−0.991036 | + | 0.133592i | \(0.957349\pi\) | |||||||
\(410\) | 9.79371i | 0.483677i | ||||||||
\(411\) | −1.92695 | − | 0.952581i | −0.0950494 | − | 0.0469873i | ||||
\(412\) | 7.36407i | 0.362802i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11.6088 | + | 15.1895i | 0.570541 | + | 0.746524i | ||||
\(415\) | −1.83743 | −0.0901958 | ||||||||
\(416\) | −5.00084 | −0.245186 | ||||||||
\(417\) | −19.4620 | − | 9.62095i | −0.953057 | − | 0.471140i | ||||
\(418\) | − | 17.4329i | − | 0.852671i | ||||||
\(419\) | 28.2930 | 1.38220 | 0.691101 | − | 0.722758i | \(-0.257126\pi\) | ||||
0.691101 | + | 0.722758i | \(0.257126\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.1687 | −1.22665 | −0.613323 | − | 0.789832i | \(-0.710168\pi\) | ||||
−0.613323 | + | 0.789832i | \(0.710168\pi\) | |||||||
\(422\) | 27.6034i | 1.34371i | ||||||||
\(423\) | 3.01823 | + | 3.94920i | 0.146751 | + | 0.192017i | ||||
\(424\) | 3.25278 | 0.157969 | ||||||||
\(425\) | −6.30230 | −0.305706 | ||||||||
\(426\) | 2.19455 | − | 4.43929i | 0.106326 | − | 0.215084i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.41874i | 0.406935i | ||||||||
\(429\) | 8.85460 | − | 17.9117i | 0.427504 | − | 0.864786i | ||||
\(430\) | − | 2.55278i | − | 0.123106i | ||||||
\(431\) | 11.2182i | 0.540361i | 0.962810 | + | 0.270181i | \(0.0870834\pi\) | ||||
−0.962810 | + | 0.270181i | \(0.912917\pi\) | |||||||
\(432\) | −5.09922 | + | 0.998953i | −0.245337 | + | 0.0480622i | ||||
\(433\) | − | 0.639592i | − | 0.0307368i | −0.999882 | − | 0.0153684i | \(-0.995108\pi\) | ||
0.999882 | − | 0.0153684i | \(-0.00489211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.95508 | − | 2.94387i | −0.285524 | − | 0.141148i | ||||
\(436\) | 6.66311 | 0.319105 | ||||||||
\(437\) | 48.1585 | 2.30374 | ||||||||
\(438\) | 2.82600 | − | 5.71664i | 0.135032 | − | 0.273152i | ||||
\(439\) | 13.1635i | 0.628259i | 0.949380 | + | 0.314129i | \(0.101713\pi\) | ||||
−0.949380 | + | 0.314129i | \(0.898287\pi\) | |||||||
\(440\) | 2.30680 | 0.109972 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.5168 | 1.49910 | ||||||||
\(443\) | − | 25.8446i | − | 1.22791i | −0.789339 | − | 0.613957i | \(-0.789577\pi\) | ||
0.789339 | − | 0.613957i | \(-0.210423\pi\) | |||||||
\(444\) | 5.30334 | − | 10.7280i | 0.251686 | − | 0.509128i | ||||
\(445\) | 5.88774 | 0.279106 | ||||||||
\(446\) | 23.0777 | 1.09276 | ||||||||
\(447\) | 24.2144 | + | 11.9703i | 1.14530 | + | 0.566176i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.3586i | 1.33833i | 0.743116 | + | 0.669163i | \(0.233347\pi\) | ||||
−0.743116 | + | 0.669163i | \(0.766653\pi\) | |||||||
\(450\) | 2.38358 | − | 1.82168i | 0.112363 | − | 0.0858750i | ||||
\(451\) | 22.5921i | 1.06382i | ||||||||
\(452\) | − | 4.45505i | − | 0.209548i | ||||||
\(453\) | 2.33275 | − | 4.71885i | 0.109602 | − | 0.221711i | ||||
\(454\) | − | 20.0351i | − | 0.940293i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.80063 | + | 11.7339i | −0.271639 | + | 0.549492i | ||||
\(457\) | −29.1905 | −1.36547 | −0.682737 | − | 0.730664i | \(-0.739211\pi\) | ||||
−0.682737 | + | 0.730664i | \(0.739211\pi\) | |||||||
\(458\) | 28.7648 | 1.34409 | ||||||||
\(459\) | 32.1368 | − | 6.29570i | 1.50002 | − | 0.293858i | ||||
\(460\) | 6.37256i | 0.297122i | ||||||||
\(461\) | −31.0968 | −1.44832 | −0.724162 | − | 0.689630i | \(-0.757773\pi\) | ||||
−0.724162 | + | 0.689630i | \(0.757773\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.4915 | −1.55648 | −0.778240 | − | 0.627967i | \(-0.783887\pi\) | ||||
−0.778240 | + | 0.627967i | \(0.783887\pi\) | |||||||
\(464\) | 3.83533i | 0.178051i | ||||||||
\(465\) | 6.80316 | + | 3.36311i | 0.315489 | + | 0.155961i | ||||
\(466\) | 25.7115 | 1.19106 | ||||||||
\(467\) | −14.8251 | −0.686023 | −0.343012 | − | 0.939331i | \(-0.611447\pi\) | ||||
−0.343012 | + | 0.939331i | \(0.611447\pi\) | |||||||
\(468\) | −11.9199 | + | 9.10996i | −0.550998 | + | 0.421108i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.65683i | 0.0764240i | ||||||||
\(471\) | 24.5716 | + | 12.1469i | 1.13220 | + | 0.559699i | ||||
\(472\) | 9.93145i | 0.457132i | ||||||||
\(473\) | − | 5.88876i | − | 0.270765i | ||||||
\(474\) | 3.97317 | + | 1.96412i | 0.182494 | + | 0.0902150i | ||||
\(475\) | − | 7.55717i | − | 0.346747i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.75328 | − | 5.92555i | 0.354998 | − | 0.271312i | ||||
\(478\) | 10.7220 | 0.490415 | ||||||||
\(479\) | −23.0447 | −1.05294 | −0.526469 | − | 0.850194i | \(-0.676484\pi\) | ||||
−0.526469 | + | 0.850194i | \(0.676484\pi\) | |||||||
\(480\) | −1.55269 | − | 0.767566i | −0.0708702 | − | 0.0350344i | ||||
\(481\) | − | 34.5523i | − | 1.57545i | ||||||
\(482\) | −1.18465 | −0.0539593 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.67867 | −0.258121 | ||||||||
\(485\) | 4.61723i | 0.209658i | ||||||||
\(486\) | −10.3346 | + | 11.6703i | −0.468789 | + | 0.529374i | ||||
\(487\) | −10.6277 | −0.481586 | −0.240793 | − | 0.970577i | \(-0.577407\pi\) | ||||
−0.240793 | + | 0.970577i | \(0.577407\pi\) | |||||||
\(488\) | 5.98368 | 0.270868 | ||||||||
\(489\) | −6.61397 | + | 13.3792i | −0.299094 | + | 0.605030i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.4687i | − | 1.01400i | −0.861947 | − | 0.506998i | \(-0.830755\pi\) | ||
0.861947 | − | 0.506998i | \(-0.169245\pi\) | |||||||
\(492\) | 7.51732 | − | 15.2066i | 0.338907 | − | 0.685566i | ||||
\(493\) | − | 24.1714i | − | 1.08863i | ||||||
\(494\) | 37.7922i | 1.70035i | ||||||||
\(495\) | 5.49845 | − | 4.20226i | 0.247137 | − | 0.188878i | ||||
\(496\) | − | 4.38153i | − | 0.196737i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.85295 | + | 1.41035i | 0.127844 | + | 0.0631992i | ||||
\(499\) | −39.7588 | −1.77985 | −0.889925 | − | 0.456107i | \(-0.849243\pi\) | ||||
−0.889925 | + | 0.456107i | \(0.849243\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 6.63905 | − | 13.4300i | 0.296611 | − | 0.600006i | ||||
\(502\) | 14.3689i | 0.641316i | ||||||||
\(503\) | −18.6717 | −0.832530 | −0.416265 | − | 0.909243i | \(-0.636661\pi\) | ||||
−0.416265 | + | 0.909243i | \(0.636661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.3140 | 0.503468 | ||||||||
\(506\) | 14.7002i | 0.653505i | ||||||||
\(507\) | −9.21725 | + | 18.6453i | −0.409352 | + | 0.828068i | ||||
\(508\) | 1.83694 | 0.0815011 | ||||||||
\(509\) | 4.03287 | 0.178754 | 0.0893768 | − | 0.995998i | \(-0.471512\pi\) | ||||
0.0893768 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(510\) | 9.78550 | + | 4.83743i | 0.433309 | + | 0.214205i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 7.54926 | + | 38.5357i | 0.333308 | + | 1.70139i | ||||
\(514\) | 16.5360i | 0.729374i | ||||||||
\(515\) | 7.36407i | 0.324500i | ||||||||
\(516\) | −1.95943 | + | 3.96368i | −0.0862591 | + | 0.174491i | ||||
\(517\) | 3.82198i | 0.168091i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.7636 | − | 27.8420i | 0.604154 | − | 1.22213i | ||||
\(520\) | −5.00084 | −0.219301 | ||||||||
\(521\) | −10.5547 | −0.462408 | −0.231204 | − | 0.972905i | \(-0.574266\pi\) | ||||
−0.231204 | + | 0.972905i | \(0.574266\pi\) | |||||||
\(522\) | 6.98677 | + | 9.14184i | 0.305803 | + | 0.400127i | ||||
\(523\) | 20.5323i | 0.897814i | 0.893579 | + | 0.448907i | \(0.148186\pi\) | ||||
−0.893579 | + | 0.448907i | \(0.851814\pi\) | |||||||
\(524\) | 5.53883 | 0.241965 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.9400 | −1.34905 | ||||||||
\(527\) | 27.6137i | 1.20287i | ||||||||
\(528\) | −3.58174 | − | 1.77062i | −0.155875 | − | 0.0770564i | ||||
\(529\) | −17.6095 | −0.765632 | ||||||||
\(530\) | 3.25278 | 0.141292 | ||||||||
\(531\) | 18.0920 | + | 23.6724i | 0.785125 | + | 1.02730i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 48.9768i | − | 2.12142i | ||||||
\(534\) | −9.14184 | − | 4.51923i | −0.395606 | − | 0.195566i | ||||
\(535\) | 8.41874i | 0.363974i | ||||||||
\(536\) | 2.76716i | 0.119523i | ||||||||
\(537\) | −18.6586 | − | 9.22381i | −0.805178 | − | 0.398037i | ||||
\(538\) | − | 4.10422i | − | 0.176946i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.09922 | + | 0.998953i | −0.219436 | + | 0.0429881i | ||||
\(541\) | −9.18511 | −0.394899 | −0.197449 | − | 0.980313i | \(-0.563266\pi\) | ||||
−0.197449 | + | 0.980313i | \(0.563266\pi\) | |||||||
\(542\) | −9.07677 | −0.389880 | ||||||||
\(543\) | −14.7911 | − | 7.31193i | −0.634747 | − | 0.313785i | ||||
\(544\) | − | 6.30230i | − | 0.270209i | ||||||
\(545\) | 6.66311 | 0.285416 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.21319 | −0.222900 | −0.111450 | − | 0.993770i | \(-0.535550\pi\) | ||||
−0.111450 | + | 0.993770i | \(0.535550\pi\) | |||||||
\(548\) | 1.24104i | 0.0530146i | ||||||||
\(549\) | 14.2626 | − | 10.9004i | 0.608712 | − | 0.465217i | ||||
\(550\) | 2.30680 | 0.0983623 | ||||||||
\(551\) | 28.9843 | 1.23477 | ||||||||
\(552\) | 4.89136 | − | 9.89460i | 0.208190 | − | 0.421142i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.216476i | 0.00919717i | ||||||||
\(555\) | 5.30334 | − | 10.7280i | 0.225114 | − | 0.455378i | ||||
\(556\) | 12.5344i | 0.531576i | ||||||||
\(557\) | − | 25.8133i | − | 1.09374i | −0.837216 | − | 0.546872i | \(-0.815818\pi\) | ||
0.837216 | − | 0.546872i | \(-0.184182\pi\) | |||||||
\(558\) | −7.98177 | − | 10.4437i | −0.337895 | − | 0.442119i | ||||
\(559\) | 12.7661i | 0.539947i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.5732 | + | 11.1590i | 0.953042 | + | 0.471133i | ||||
\(562\) | 18.8498 | 0.795129 | ||||||||
\(563\) | 37.4936 | 1.58017 | 0.790084 | − | 0.612999i | \(-0.210037\pi\) | ||||
0.790084 | + | 0.612999i | \(0.210037\pi\) | |||||||
\(564\) | 1.27173 | − | 2.57255i | 0.0535494 | − | 0.108324i | ||||
\(565\) | − | 4.45505i | − | 0.187425i | ||||||
\(566\) | 1.99832 | 0.0839956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.85910 | −0.119965 | ||||||||
\(569\) | − | 40.4552i | − | 1.69597i | −0.530020 | − | 0.847985i | \(-0.677815\pi\) | ||
0.530020 | − | 0.847985i | \(-0.322185\pi\) | |||||||
\(570\) | −5.80063 | + | 11.7339i | −0.242962 | + | 0.491481i | ||||
\(571\) | −29.1102 | −1.21822 | −0.609111 | − | 0.793085i | \(-0.708474\pi\) | ||||
−0.609111 | + | 0.793085i | \(0.708474\pi\) | |||||||
\(572\) | −11.5359 | −0.482342 | ||||||||
\(573\) | 7.71954 | + | 3.81613i | 0.322488 | + | 0.159421i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.37256i | 0.265754i | ||||||||
\(576\) | 1.82168 | + | 2.38358i | 0.0759035 | + | 0.0993159i | ||||
\(577\) | − | 15.1754i | − | 0.631759i | −0.948799 | − | 0.315880i | \(-0.897700\pi\) | ||
0.948799 | − | 0.315880i | \(-0.102300\pi\) | |||||||
\(578\) | 22.7189i | 0.944983i | ||||||||
\(579\) | 4.63088 | − | 9.36769i | 0.192453 | − | 0.389308i | ||||
\(580\) | 3.83533i | 0.159254i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.54403 | − | 7.16912i | 0.146905 | − | 0.297169i | ||||
\(583\) | 7.50352 | 0.310764 | ||||||||
\(584\) | −3.68177 | −0.152353 | ||||||||
\(585\) | −11.9199 | + | 9.10996i | −0.492828 | + | 0.376650i | ||||
\(586\) | − | 9.28117i | − | 0.383402i | ||||||
\(587\) | 3.22807 | 0.133237 | 0.0666183 | − | 0.997779i | \(-0.478779\pi\) | ||||
0.0666183 | + | 0.997779i | \(0.478779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.1120 | −1.36436 | ||||||||
\(590\) | 9.93145i | 0.408872i | ||||||||
\(591\) | −22.0705 | − | 10.9105i | −0.907859 | − | 0.448797i | ||||
\(592\) | −6.90930 | −0.283970 | ||||||||
\(593\) | 43.7305 | 1.79580 | 0.897899 | − | 0.440202i | \(-0.145093\pi\) | ||||
0.897899 | + | 0.440202i | \(0.145093\pi\) | |||||||
\(594\) | −11.7629 | + | 2.30439i | −0.482637 | + | 0.0945501i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 15.5951i | − | 0.638802i | ||||||
\(597\) | 3.49491 | + | 1.72770i | 0.143037 | + | 0.0707099i | ||||
\(598\) | − | 31.8682i | − | 1.30319i | ||||||
\(599\) | − | 8.04569i | − | 0.328738i | −0.986399 | − | 0.164369i | \(-0.947441\pi\) | ||
0.986399 | − | 0.164369i | \(-0.0525588\pi\) | |||||||
\(600\) | −1.55269 | − | 0.767566i | −0.0633883 | − | 0.0313358i | ||||
\(601\) | 8.38546i | 0.342050i | 0.985267 | + | 0.171025i | \(0.0547079\pi\) | ||||
−0.985267 | + | 0.171025i | \(0.945292\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.04090 | + | 6.59576i | 0.205281 | + | 0.268600i | ||||
\(604\) | −3.03915 | −0.123661 | ||||||||
\(605\) | −5.67867 | −0.230871 | ||||||||
\(606\) | −17.5672 | − | 8.68427i | −0.713618 | − | 0.352774i | ||||
\(607\) | − | 16.9336i | − | 0.687315i | −0.939095 | − | 0.343658i | \(-0.888334\pi\) | ||
0.939095 | − | 0.343658i | \(-0.111666\pi\) | |||||||
\(608\) | 7.55717 | 0.306484 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.98368 | 0.242272 | ||||||||
\(611\) | − | 8.28556i | − | 0.335198i | ||||||
\(612\) | −11.4808 | − | 15.0220i | −0.464084 | − | 0.607230i | ||||
\(613\) | 33.8863 | 1.36866 | 0.684328 | − | 0.729174i | \(-0.260096\pi\) | ||||
0.684328 | + | 0.729174i | \(0.260096\pi\) | |||||||
\(614\) | −26.9282 | −1.08673 | ||||||||
\(615\) | 7.51732 | − | 15.2066i | 0.303128 | − | 0.613189i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.5359i | 1.51114i | 0.655068 | + | 0.755570i | \(0.272640\pi\) | ||||
−0.655068 | + | 0.755570i | \(0.727360\pi\) | |||||||
\(618\) | 5.65241 | − | 11.4341i | 0.227373 | − | 0.459947i | ||||
\(619\) | 16.9160i | 0.679913i | 0.940441 | + | 0.339957i | \(0.110412\pi\) | ||||
−0.940441 | + | 0.339957i | \(0.889588\pi\) | |||||||
\(620\) | − | 4.38153i | − | 0.175967i | ||||||
\(621\) | −6.36589 | − | 32.4951i | −0.255454 | − | 1.30398i | ||||
\(622\) | 2.82130i | 0.113124i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.76475 | + | 3.83848i | 0.310839 | + | 0.153662i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.4427 | −0.457342 | ||||||||
\(627\) | −13.3809 | + | 27.0679i | −0.534381 | + | 1.08099i | ||||
\(628\) | − | 15.8252i | − | 0.631494i | ||||||
\(629\) | 43.5445 | 1.73623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.1879 | −1.16195 | −0.580977 | − | 0.813920i | \(-0.697329\pi\) | ||||
−0.580977 | + | 0.813920i | \(0.697329\pi\) | |||||||
\(632\) | − | 2.55889i | − | 0.101787i | ||||||
\(633\) | 21.1874 | − | 42.8594i | 0.842123 | − | 1.70351i | ||||
\(634\) | 9.30982 | 0.369740 | ||||||||
\(635\) | 1.83694 | 0.0728968 | ||||||||
\(636\) | −5.05056 | − | 2.49673i | −0.200268 | − | 0.0990016i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.84735i | 0.350270i | ||||||||
\(639\) | −6.81489 | + | 5.20837i | −0.269593 | + | 0.206040i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 4.57113i | 0.180549i | 0.995917 | + | 0.0902743i | \(0.0287744\pi\) | ||||
−0.995917 | + | 0.0902743i | \(0.971226\pi\) | |||||||
\(642\) | 6.46194 | − | 13.0717i | 0.255032 | − | 0.515898i | ||||
\(643\) | 24.0758i | 0.949457i | 0.880132 | + | 0.474728i | \(0.157454\pi\) | ||||
−0.880132 | + | 0.474728i | \(0.842546\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.95943 | + | 3.96368i | −0.0771524 | + | 0.156070i | ||||
\(646\) | −47.6275 | −1.87388 | ||||||||
\(647\) | −17.4241 | −0.685012 | −0.342506 | − | 0.939516i | \(-0.611276\pi\) | ||||
−0.342506 | + | 0.939516i | \(0.611276\pi\) | |||||||
\(648\) | 8.68427 | + | 2.36293i | 0.341150 | + | 0.0928246i | ||||
\(649\) | 22.9099i | 0.899292i | ||||||||
\(650\) | −5.00084 | −0.196149 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.61682 | 0.337461 | ||||||||
\(653\) | − | 37.8911i | − | 1.48279i | −0.671068 | − | 0.741396i | \(-0.734164\pi\) | ||
0.671068 | − | 0.741396i | \(-0.265836\pi\) | |||||||
\(654\) | −10.3457 | − | 5.11438i | −0.404551 | − | 0.199988i | ||||
\(655\) | 5.53883 | 0.216420 | ||||||||
\(656\) | −9.79371 | −0.382380 | ||||||||
\(657\) | −8.77580 | + | 6.70703i | −0.342377 | + | 0.261666i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7262i | 0.963197i | 0.876392 | + | 0.481599i | \(0.159944\pi\) | ||||
−0.876392 | + | 0.481599i | \(0.840056\pi\) | |||||||
\(660\) | −3.58174 | − | 1.77062i | −0.139419 | − | 0.0689214i | ||||
\(661\) | − | 43.6879i | − | 1.69926i | −0.527378 | − | 0.849631i | \(-0.676825\pi\) | ||
0.527378 | − | 0.849631i | \(-0.323175\pi\) | |||||||
\(662\) | 18.2960i | 0.711095i | ||||||||
\(663\) | −48.9358 | − | 24.1912i | −1.90051 | − | 0.939509i | ||||
\(664\) | − | 1.83743i | − | 0.0713060i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.4689 | + | 12.5866i | −0.638156 | + | 0.487720i | ||||
\(667\) | −24.4409 | −0.946355 | ||||||||
\(668\) | −8.64948 | −0.334658 | ||||||||
\(669\) | −35.8324 | − | 17.7136i | −1.38536 | − | 0.684849i | ||||
\(670\) | 2.76716i | 0.106905i | ||||||||
\(671\) | 13.8031 | 0.532865 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.1588 | 1.31673 | 0.658363 | − | 0.752701i | \(-0.271249\pi\) | ||||
0.658363 | + | 0.752701i | \(0.271249\pi\) | |||||||
\(674\) | 7.84516i | 0.302184i | ||||||||
\(675\) | −5.09922 | + | 0.998953i | −0.196269 | + | 0.0384497i | ||||
\(676\) | 12.0084 | 0.461862 | ||||||||
\(677\) | −13.1326 | −0.504727 | −0.252364 | − | 0.967632i | \(-0.581208\pi\) | ||||
−0.252364 | + | 0.967632i | \(0.581208\pi\) | |||||||
\(678\) | −3.41954 | + | 6.91730i | −0.131327 | + | 0.265657i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 6.30230i | − | 0.241682i | ||||||
\(681\) | −15.3782 | + | 31.1082i | −0.589296 | + | 1.19207i | ||||
\(682\) | − | 10.1073i | − | 0.387029i | ||||||
\(683\) | − | 45.8823i | − | 1.75564i | −0.478994 | − | 0.877818i | \(-0.658998\pi\) | ||
0.478994 | − | 0.877818i | \(-0.341002\pi\) | |||||||
\(684\) | 18.0131 | − | 13.7668i | 0.688750 | − | 0.526386i | ||||
\(685\) | 1.24104i | 0.0474177i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −44.6628 | − | 22.0789i | −1.70399 | − | 0.842363i | ||||
\(688\) | 2.55278 | 0.0973239 | ||||||||
\(689\) | −16.2667 | −0.619710 | ||||||||
\(690\) | 4.89136 | − | 9.89460i | 0.186211 | − | 0.376681i | ||||
\(691\) | 17.5647i | 0.668191i | 0.942539 | + | 0.334096i | \(0.108431\pi\) | ||||
−0.942539 | + | 0.334096i | \(0.891569\pi\) | |||||||
\(692\) | −17.9315 | −0.681652 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.232294 | −0.00881775 | ||||||||
\(695\) | 12.5344i | 0.475456i | ||||||||
\(696\) | 2.94387 | − | 5.95508i | 0.111587 | − | 0.225727i | ||||
\(697\) | 61.7229 | 2.33792 | ||||||||
\(698\) | −11.5685 | −0.437875 | ||||||||
\(699\) | −39.9220 | − | 19.7353i | −1.50999 | − | 0.746458i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.2501i | − | 1.48246i | −0.671253 | − | 0.741228i | \(-0.734244\pi\) | ||
0.671253 | − | 0.741228i | \(-0.265756\pi\) | |||||||
\(702\) | 25.5004 | − | 4.99561i | 0.962451 | − | 0.188547i | ||||
\(703\) | 52.2148i | 1.96932i | ||||||||
\(704\) | 2.30680i | 0.0869408i | ||||||||
\(705\) | 1.27173 | − | 2.57255i | 0.0478961 | − | 0.0968877i | ||||
\(706\) | 34.7075i | 1.30623i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.62305 | − | 15.4205i | 0.286492 | − | 0.579536i | ||||
\(709\) | −47.6680 | −1.79021 | −0.895105 | − | 0.445854i | \(-0.852900\pi\) | ||||
−0.895105 | + | 0.445854i | \(0.852900\pi\) | |||||||
\(710\) | −2.85910 | −0.107300 | ||||||||
\(711\) | −4.66150 | − | 6.09933i | −0.174820 | − | 0.228743i | ||||
\(712\) | 5.88774i | 0.220653i | ||||||||
\(713\) | 27.9216 | 1.04567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.5359 | −0.431420 | ||||||||
\(716\) | 12.0170i | 0.449095i | ||||||||
\(717\) | −16.6480 | − | 8.22987i | −0.621731 | − | 0.307350i | ||||
\(718\) | −17.5322 | −0.654297 | ||||||||
\(719\) | −33.4214 | −1.24641 | −0.623205 | − | 0.782059i | \(-0.714170\pi\) | ||||
−0.623205 | + | 0.782059i | \(0.714170\pi\) | |||||||
\(720\) | 1.82168 | + | 2.38358i | 0.0678902 | + | 0.0888309i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 38.1109i | − | 1.41834i | ||||||
\(723\) | 1.83939 | + | 0.909297i | 0.0684077 | + | 0.0338171i | ||||
\(724\) | 9.52612i | 0.354036i | ||||||||
\(725\) | 3.83533i | 0.142441i | ||||||||
\(726\) | 8.81721 | + | 4.35875i | 0.327237 | + | 0.161769i | ||||
\(727\) | 31.9845i | 1.18624i | 0.805115 | + | 0.593119i | \(0.202104\pi\) | ||||
−0.805115 | + | 0.593119i | \(0.797896\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.0042 | − | 10.1878i | 0.926081 | − | 0.377325i | ||||
\(730\) | −3.68177 | −0.136268 | ||||||||
\(731\) | −16.0884 | −0.595051 | ||||||||
\(732\) | −9.29079 | − | 4.59287i | −0.343397 | − | 0.169757i | ||||
\(733\) | − | 39.2002i | − | 1.44789i | −0.689857 | − | 0.723945i | \(-0.742327\pi\) | ||
0.689857 | − | 0.723945i | \(-0.257673\pi\) | |||||||
\(734\) | 10.0402 | 0.370590 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.37256 | −0.234896 | ||||||||
\(737\) | 6.38330i | 0.235132i | ||||||||
\(738\) | −23.3441 | + | 17.8411i | −0.859309 | + | 0.656738i | ||||
\(739\) | −33.7628 | −1.24198 | −0.620992 | − | 0.783817i | \(-0.713270\pi\) | ||||
−0.620992 | + | 0.783817i | \(0.713270\pi\) | |||||||
\(740\) | −6.90930 | −0.253991 | ||||||||
\(741\) | 29.0080 | − | 58.6796i | 1.06564 | − | 2.15565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.3933i | 0.528038i | 0.964517 | + | 0.264019i | \(0.0850482\pi\) | ||||
−0.964517 | + | 0.264019i | \(0.914952\pi\) | |||||||
\(744\) | −3.36311 | + | 6.80316i | −0.123298 | + | 0.249416i | ||||
\(745\) | − | 15.5951i | − | 0.571362i | ||||||
\(746\) | − | 0.00482067i | − | 0.000176497i | ||||||
\(747\) | −3.34722 | − | 4.37966i | −0.122468 | − | 0.160243i | ||||
\(748\) | − | 14.5381i | − | 0.531567i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.55269 | − | 0.767566i | −0.0566962 | − | 0.0280275i | ||||
\(751\) | 17.8408 | 0.651020 | 0.325510 | − | 0.945539i | \(-0.394464\pi\) | ||||
0.325510 | + | 0.945539i | \(0.394464\pi\) | |||||||
\(752\) | −1.65683 | −0.0604185 | ||||||||
\(753\) | 11.0291 | − | 22.3104i | 0.401922 | − | 0.813038i | ||||
\(754\) | − | 19.1799i | − | 0.698491i | ||||||
\(755\) | −3.03915 | −0.110606 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.90604 | −0.0692760 | −0.0346380 | − | 0.999400i | \(-0.511028\pi\) | ||||
−0.0346380 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(758\) | 18.6572i | 0.677660i | ||||||||
\(759\) | 11.2834 | − | 22.8249i | 0.409561 | − | 0.828491i | ||||
\(760\) | 7.55717 | 0.274127 | ||||||||
\(761\) | −28.2729 | −1.02489 | −0.512445 | − | 0.858720i | \(-0.671260\pi\) | ||||
−0.512445 | + | 0.858720i | \(0.671260\pi\) | |||||||
\(762\) | −2.85220 | − | 1.40997i | −0.103324 | − | 0.0510780i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 4.97173i | − | 0.179871i | ||||||
\(765\) | −11.4808 | − | 15.0220i | −0.415089 | − | 0.543123i | ||||
\(766\) | − | 18.8463i | − | 0.680945i | ||||||
\(767\) | − | 49.6656i | − | 1.79332i | ||||||
\(768\) | 0.767566 | − | 1.55269i | 0.0276972 | − | 0.0560278i | ||||
\(769\) | − | 1.43146i | − | 0.0516197i | −0.999667 | − | 0.0258098i | \(-0.991784\pi\) | ||
0.999667 | − | 0.0258098i | \(-0.00821644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.6925 | − | 25.6753i | 0.457109 | − | 0.924675i | ||||
\(772\) | −6.03321 | −0.217140 | ||||||||
\(773\) | −34.8175 | −1.25230 | −0.626149 | − | 0.779703i | \(-0.715370\pi\) | ||||
−0.626149 | + | 0.779703i | \(0.715370\pi\) | |||||||
\(774\) | 6.08477 | − | 4.65037i | 0.218712 | − | 0.167154i | ||||
\(775\) | − | 4.38153i | − | 0.157389i | ||||||
\(776\) | −4.61723 | −0.165749 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.8601 | −0.389352 | ||||||||
\(779\) | 74.0128i | 2.65178i | ||||||||
\(780\) | 7.76475 | + | 3.83848i | 0.278023 | + | 0.137439i | ||||
\(781\) | −6.59537 | −0.236001 | ||||||||
\(782\) | 40.1618 | 1.43618 | ||||||||
\(783\) | −3.83132 | − | 19.5572i | −0.136920 | − | 0.698918i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 15.8252i | − | 0.564826i | ||||||
\(786\) | −8.60008 | − | 4.25142i | −0.306755 | − | 0.151643i | ||||
\(787\) | − | 49.7082i | − | 1.77191i | −0.463775 | − | 0.885953i | \(-0.653505\pi\) | ||
0.463775 | − | 0.885953i | \(-0.346495\pi\) | |||||||
\(788\) | 14.2144i | 0.506366i | ||||||||
\(789\) | 48.0402 | + | 23.7485i | 1.71027 | + | 0.845468i | ||||
\(790\) | − | 2.55889i | − | 0.0910414i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.20226 | + | 5.49845i | 0.149321 | + | 0.195379i | ||||
\(793\) | −29.9234 | −1.06261 | ||||||||
\(794\) | −27.0408 | −0.959643 | ||||||||
\(795\) | −5.05056 | − | 2.49673i | −0.179125 | − | 0.0885497i | ||||
\(796\) | − | 2.25088i | − | 0.0797802i | ||||||
\(797\) | −8.43295 | −0.298710 | −0.149355 | − | 0.988784i | \(-0.547720\pi\) | ||||
−0.149355 | + | 0.988784i | \(0.547720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.4419 | 0.369406 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 10.7256 | + | 14.0339i | 0.378971 | + | 0.495864i | ||||
\(802\) | 24.5254 | 0.866023 | ||||||||
\(803\) | −8.49311 | −0.299715 | ||||||||
\(804\) | 2.12398 | − | 4.29655i | 0.0749070 | − | 0.151527i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.9113i | 0.771794i | ||||||||
\(807\) | −3.15026 | + | 6.37258i | −0.110894 | + | 0.224325i | ||||
\(808\) | 11.3140i | 0.398026i | ||||||||
\(809\) | 38.9747i | 1.37028i | 0.728413 | + | 0.685138i | \(0.240258\pi\) | ||||
−0.728413 | + | 0.685138i | \(0.759742\pi\) | |||||||
\(810\) | 8.68427 | + | 2.36293i | 0.305134 | + | 0.0830248i | ||||
\(811\) | − | 29.5668i | − | 1.03823i | −0.854704 | − | 0.519116i | \(-0.826261\pi\) | ||
0.854704 | − | 0.519116i | \(-0.173739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0934 | + | 6.96702i | 0.494277 | + | 0.244344i | ||||
\(814\) | −15.9384 | −0.558640 | ||||||||
\(815\) | 8.61682 | 0.301834 | ||||||||
\(816\) | −4.83743 | + | 9.78550i | −0.169344 | + | 0.342561i | ||||
\(817\) | − | 19.2918i | − | 0.674935i | ||||||
\(818\) | −5.40347 | −0.188928 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.79371 | −0.342011 | ||||||||
\(821\) | − | 33.6571i | − | 1.17464i | −0.809355 | − | 0.587320i | \(-0.800183\pi\) | ||
0.809355 | − | 0.587320i | \(-0.199817\pi\) | |||||||
\(822\) | 0.952581 | − | 1.92695i | 0.0332251 | − | 0.0672101i | ||||
\(823\) | −12.5405 | −0.437134 | −0.218567 | − | 0.975822i | \(-0.570138\pi\) | ||||
−0.218567 | + | 0.975822i | \(0.570138\pi\) | |||||||
\(824\) | −7.36407 | −0.256540 | ||||||||
\(825\) | −3.58174 | − | 1.77062i | −0.124700 | − | 0.0616451i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.6875i | − | 0.545506i | −0.962084 | − | 0.272753i | \(-0.912066\pi\) | ||
0.962084 | − | 0.272753i | \(-0.0879342\pi\) | |||||||
\(828\) | −15.1895 | + | 11.6088i | −0.527872 | + | 0.403434i | ||||
\(829\) | − | 5.67186i | − | 0.196992i | −0.995137 | − | 0.0984959i | \(-0.968597\pi\) | ||
0.995137 | − | 0.0984959i | \(-0.0314031\pi\) | |||||||
\(830\) | − | 1.83743i | − | 0.0637781i | ||||||
\(831\) | 0.166159 | − | 0.336119i | 0.00576400 | − | 0.0116598i | ||||
\(832\) | − | 5.00084i | − | 0.173373i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.62095 | − | 19.4620i | 0.333146 | − | 0.673913i | ||||
\(835\) | −8.64948 | −0.299328 | ||||||||
\(836\) | 17.4329 | 0.602929 | ||||||||
\(837\) | 4.37694 | + | 22.3424i | 0.151289 | + | 0.772267i | ||||
\(838\) | 28.2930i | 0.977364i | ||||||||
\(839\) | 14.5217 | 0.501346 | 0.250673 | − | 0.968072i | \(-0.419348\pi\) | ||||
0.250673 | + | 0.968072i | \(0.419348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2902 | 0.492766 | ||||||||
\(842\) | − | 25.1687i | − | 0.867370i | ||||||
\(843\) | −29.2678 | − | 14.4684i | −1.00804 | − | 0.498319i | ||||
\(844\) | −27.6034 | −0.950147 | ||||||||
\(845\) | 12.0084 | 0.413102 | ||||||||
\(846\) | −3.94920 | + | 3.01823i | −0.135776 | + | 0.103769i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.25278i | 0.111701i | ||||||||
\(849\) | −3.10277 | − | 1.53384i | −0.106487 | − | 0.0526413i | ||||
\(850\) | − | 6.30230i | − | 0.216167i | ||||||
\(851\) | − | 44.0299i | − | 1.50933i | ||||||
\(852\) | 4.43929 | + | 2.19455i | 0.152087 | + | 0.0751839i | ||||
\(853\) | 3.66698i | 0.125555i | 0.998028 | + | 0.0627775i | \(0.0199958\pi\) | ||||
−0.998028 | + | 0.0627775i | \(0.980004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.0131 | − | 13.7668i | 0.616037 | − | 0.470814i | ||||
\(856\) | −8.41874 | −0.287747 | ||||||||
\(857\) | 11.5630 | 0.394984 | 0.197492 | − | 0.980305i | \(-0.436720\pi\) | ||||
0.197492 | + | 0.980305i | \(0.436720\pi\) | |||||||
\(858\) | 17.9117 | + | 8.85460i | 0.611496 | + | 0.302291i | ||||
\(859\) | 14.9665i | 0.510650i | 0.966855 | + | 0.255325i | \(0.0821825\pi\) | ||||
−0.966855 | + | 0.255325i | \(0.917818\pi\) | |||||||
\(860\) | 2.55278 | 0.0870492 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.2182 | −0.382093 | ||||||||
\(863\) | 9.37277i | 0.319053i | 0.987194 | + | 0.159526i | \(0.0509967\pi\) | ||||
−0.987194 | + | 0.159526i | \(0.949003\pi\) | |||||||
\(864\) | −0.998953 | − | 5.09922i | −0.0339851 | − | 0.173479i | ||||
\(865\) | −17.9315 | −0.609688 | ||||||||
\(866\) | 0.639592 | 0.0217342 | ||||||||
\(867\) | 17.4383 | − | 35.2754i | 0.592235 | − | 1.19802i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.90286i | − | 0.200241i | ||||||
\(870\) | 2.94387 | − | 5.95508i | 0.0998066 | − | 0.201896i | ||||
\(871\) | − | 13.8381i | − | 0.468888i | ||||||
\(872\) | 6.66311i | 0.225642i | ||||||||
\(873\) | −11.0055 | + | 8.41113i | −0.372481 | + | 0.284674i | ||||
\(874\) | 48.1585i | 1.62899i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.71664 | + | 2.82600i | 0.193148 | + | 0.0954818i | ||||
\(877\) | −15.6223 | −0.527529 | −0.263764 | − | 0.964587i | \(-0.584964\pi\) | ||||
−0.263764 | + | 0.964587i | \(0.584964\pi\) | |||||||
\(878\) | −13.1635 | −0.444246 | ||||||||
\(879\) | −7.12391 | + | 14.4108i | −0.240284 | + | 0.486063i | ||||
\(880\) | 2.30680i | 0.0777622i | ||||||||
\(881\) | −4.54709 | −0.153195 | −0.0765977 | − | 0.997062i | \(-0.524406\pi\) | ||||
−0.0765977 | + | 0.997062i | \(0.524406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.8190 | −1.64289 | −0.821445 | − | 0.570288i | \(-0.806831\pi\) | ||||
−0.821445 | + | 0.570288i | \(0.806831\pi\) | |||||||
\(884\) | 31.5168i | 1.06002i | ||||||||
\(885\) | 7.62305 | − | 15.4205i | 0.256246 | − | 0.518353i | ||||
\(886\) | 25.8446 | 0.868267 | ||||||||
\(887\) | 7.28336 | 0.244551 | 0.122276 | − | 0.992496i | \(-0.460981\pi\) | ||||
0.122276 | + | 0.992496i | \(0.460981\pi\) | |||||||
\(888\) | 10.7280 | + | 5.30334i | 0.360008 | + | 0.177969i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.88774i | 0.197358i | ||||||||
\(891\) | 20.0329 | + | 5.45080i | 0.671127 | + | 0.182609i | ||||
\(892\) | 23.0777i | 0.772697i | ||||||||
\(893\) | 12.5210i | 0.418998i | ||||||||
\(894\) | −11.9703 | + | 24.2144i | −0.400347 | + | 0.809851i | ||||
\(895\) | 12.0170i | 0.401683i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.4609 | + | 49.4813i | −0.816726 | + | 1.65213i | ||||
\(898\) | −28.3586 | −0.946339 | ||||||||
\(899\) | 16.8046 | 0.560466 | ||||||||
\(900\) | 1.82168 | + | 2.38358i | 0.0607228 | + | 0.0794527i | ||||
\(901\) | − | 20.5000i | − | 0.682954i | ||||||
\(902\) | −22.5921 | −0.752236 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.45505 | 0.148173 | ||||||||
\(905\) | 9.52612i | 0.316659i | ||||||||
\(906\) | 4.71885 | + | 2.33275i | 0.156773 | + | 0.0775004i | ||||
\(907\) | −26.8962 | −0.893074 | −0.446537 | − | 0.894765i | \(-0.647343\pi\) | ||||
−0.446537 | + | 0.894765i | \(0.647343\pi\) | |||||||
\(908\) | 20.0351 | 0.664887 | ||||||||
\(909\) | 20.6106 | + | 26.9679i | 0.683611 | + | 0.894470i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.4059i | 1.53750i | 0.639552 | + | 0.768748i | \(0.279120\pi\) | ||||
−0.639552 | + | 0.768748i | \(0.720880\pi\) | |||||||
\(912\) | −11.7339 | − | 5.80063i | −0.388550 | − | 0.192078i | ||||
\(913\) | − | 4.23858i | − | 0.140277i | ||||||
\(914\) | − | 29.1905i | − | 0.965536i | ||||||
\(915\) | −9.29079 | − | 4.59287i | −0.307144 | − | 0.151835i | ||||
\(916\) | 28.7648i | 0.950417i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.29570 | + | 32.1368i | 0.207789 | + | 1.06067i | ||||
\(919\) | −4.52146 | −0.149149 | −0.0745746 | − | 0.997215i | \(-0.523760\pi\) | ||||
−0.0745746 | + | 0.997215i | \(0.523760\pi\) | |||||||
\(920\) | −6.37256 | −0.210097 | ||||||||
\(921\) | 41.8111 | + | 20.6691i | 1.37772 | + | 0.681071i | ||||
\(922\) | − | 31.0968i | − | 1.02412i | ||||||
\(923\) | 14.2979 | 0.470621 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.90930 | −0.227176 | ||||||||
\(926\) | − | 33.4915i | − | 1.10060i | ||||||
\(927\) | −17.5529 | + | 13.4150i | −0.576512 | + | 0.440607i | ||||
\(928\) | −3.83533 | −0.125901 | ||||||||
\(929\) | −16.6094 | −0.544938 | −0.272469 | − | 0.962165i | \(-0.587840\pi\) | ||||
−0.272469 | + | 0.962165i | \(0.587840\pi\) | |||||||
\(930\) | −3.36311 | + | 6.80316i | −0.110281 | + | 0.223084i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25.7115i | 0.842209i | ||||||||
\(933\) | 2.16553 | − | 4.38059i | 0.0708963 | − | 0.143414i | ||||
\(934\) | − | 14.8251i | − | 0.485092i | ||||||
\(935\) | − | 14.5381i | − | 0.475448i | ||||||
\(936\) | −9.10996 | − | 11.9199i | −0.297768 | − | 0.389615i | ||||
\(937\) | 20.5347i | 0.670839i | 0.942069 | + | 0.335419i | \(0.108878\pi\) | ||||
−0.942069 | + | 0.335419i | \(0.891122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.7670 | + | 8.78303i | 0.579803 | + | 0.286623i | ||||
\(940\) | −1.65683 | −0.0540399 | ||||||||
\(941\) | 24.3984 | 0.795364 | 0.397682 | − | 0.917523i | \(-0.369815\pi\) | ||||
0.397682 | + | 0.917523i | \(0.369815\pi\) | |||||||
\(942\) | −12.1469 | + | 24.5716i | −0.395767 | + | 0.800586i | ||||
\(943\) | − | 62.4110i | − | 2.03238i | ||||||
\(944\) | −9.93145 | −0.323241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.88876 | 0.191460 | ||||||||
\(947\) | 19.1133i | 0.621100i | 0.950557 | + | 0.310550i | \(0.100513\pi\) | ||||
−0.950557 | + | 0.310550i | \(0.899487\pi\) | |||||||
\(948\) | −1.96412 | + | 3.97317i | −0.0637917 | + | 0.129042i | ||||
\(949\) | 18.4120 | 0.597677 | ||||||||
\(950\) | 7.55717 | 0.245187 | ||||||||
\(951\) | −14.4553 | − | 7.14590i | −0.468744 | − | 0.231722i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.20297i | − | 0.233327i | −0.993171 | − | 0.116664i | \(-0.962780\pi\) | ||
0.993171 | − | 0.116664i | \(-0.0372199\pi\) | |||||||
\(954\) | 5.92555 | + | 7.75328i | 0.191847 | + | 0.251022i | ||||
\(955\) | − | 4.97173i | − | 0.160881i | ||||||
\(956\) | 10.7220i | 0.346776i | ||||||||
\(957\) | 6.79093 | − | 13.7372i | 0.219519 | − | 0.444060i | ||||
\(958\) | − | 23.0447i | − | 0.744540i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.767566 | − | 1.55269i | 0.0247731 | − | 0.0501128i | ||||
\(961\) | 11.8022 | 0.380715 | ||||||||
\(962\) | 34.5523 | 1.11401 | ||||||||
\(963\) | −20.0668 | + | 15.3363i | −0.646642 | + | 0.494205i | ||||
\(964\) | − | 1.18465i | − | 0.0381550i | ||||||
\(965\) | −6.03321 | −0.194216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.2448 | −0.393765 | −0.196883 | − | 0.980427i | \(-0.563082\pi\) | ||||
−0.196883 | + | 0.980427i | \(0.563082\pi\) | |||||||
\(968\) | − | 5.67867i | − | 0.182519i | ||||||
\(969\) | 73.9508 | + | 36.5573i | 2.37564 | + | 1.17439i | ||||
\(970\) | −4.61723 | −0.148250 | ||||||||
\(971\) | −26.8777 | −0.862546 | −0.431273 | − | 0.902221i | \(-0.641935\pi\) | ||||
−0.431273 | + | 0.902221i | \(0.641935\pi\) | |||||||
\(972\) | −11.6703 | − | 10.3346i | −0.374324 | − | 0.331484i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 10.6277i | − | 0.340533i | ||||||
\(975\) | 7.76475 | + | 3.83848i | 0.248671 | + | 0.122930i | ||||
\(976\) | 5.98368i | 0.191533i | ||||||||
\(977\) | 36.7539i | 1.17586i | 0.808911 | + | 0.587931i | \(0.200057\pi\) | ||||
−0.808911 | + | 0.587931i | \(0.799943\pi\) | |||||||
\(978\) | −13.3792 | − | 6.61397i | −0.427821 | − | 0.211492i | ||||
\(979\) | 13.5819i | 0.434078i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.1381 | + | 15.8821i | 0.387540 | + | 0.507076i | ||||
\(982\) | 22.4687 | 0.717004 | ||||||||
\(983\) | 13.3704 | 0.426449 | 0.213224 | − | 0.977003i | \(-0.431603\pi\) | ||||
0.213224 | + | 0.977003i | \(0.431603\pi\) | |||||||
\(984\) | 15.2066 | + | 7.51732i | 0.484768 | + | 0.239643i | ||||
\(985\) | 14.2144i | 0.452908i | ||||||||
\(986\) | 24.1714 | 0.769775 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.7922 | −1.20233 | ||||||||
\(989\) | 16.2678i | 0.517285i | ||||||||
\(990\) | 4.20226 | + | 5.49845i | 0.133557 | + | 0.174752i | ||||
\(991\) | 16.6969 | 0.530393 | 0.265197 | − | 0.964194i | \(-0.414563\pi\) | ||||
0.265197 | + | 0.964194i | \(0.414563\pi\) | |||||||
\(992\) | 4.38153 | 0.139114 | ||||||||
\(993\) | 14.0434 | − | 28.4080i | 0.445654 | − | 0.901501i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.25088i | − | 0.0713576i | ||||||
\(996\) | −1.41035 | + | 2.85295i | −0.0446886 | + | 0.0903993i | ||||
\(997\) | 49.1853i | 1.55771i | 0.627201 | + | 0.778857i | \(0.284200\pi\) | ||||
−0.627201 | + | 0.778857i | \(0.715800\pi\) | |||||||
\(998\) | − | 39.7588i | − | 1.25854i | ||||||
\(999\) | 35.2321 | − | 6.90207i | 1.11469 | − | 0.218372i |
(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 | 1470.2.b.b.881.10 | 12 | ||
3.2 | odd | 2 | 1470.2.b.a.881.3 | 12 | |||
7.4 | even | 3 | 210.2.r.a.131.1 | yes | 12 | ||
7.5 | odd | 6 | 210.2.r.b.101.4 | yes | 12 | ||
7.6 | odd | 2 | 1470.2.b.a.881.9 | 12 | |||
21.5 | even | 6 | 210.2.r.a.101.1 | ✓ | 12 | ||
21.11 | odd | 6 | 210.2.r.b.131.4 | yes | 12 | ||
21.20 | even | 2 | inner | 1470.2.b.b.881.4 | 12 | ||
35.4 | even | 6 | 1050.2.s.g.551.6 | 12 | |||
35.12 | even | 12 | 1050.2.u.h.899.1 | 12 | |||
35.18 | odd | 12 | 1050.2.u.f.299.3 | 12 | |||
35.19 | odd | 6 | 1050.2.s.f.101.3 | 12 | |||
35.32 | odd | 12 | 1050.2.u.g.299.4 | 12 | |||
35.33 | even | 12 | 1050.2.u.e.899.6 | 12 | |||
105.32 | even | 12 | 1050.2.u.e.299.6 | 12 | |||
105.47 | odd | 12 | 1050.2.u.f.899.3 | 12 | |||
105.53 | even | 12 | 1050.2.u.h.299.1 | 12 | |||
105.68 | odd | 12 | 1050.2.u.g.899.4 | 12 | |||
105.74 | odd | 6 | 1050.2.s.f.551.3 | 12 | |||
105.89 | even | 6 | 1050.2.s.g.101.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.r.a.101.1 | ✓ | 12 | 21.5 | even | 6 | ||
210.2.r.a.131.1 | yes | 12 | 7.4 | even | 3 | ||
210.2.r.b.101.4 | yes | 12 | 7.5 | odd | 6 | ||
210.2.r.b.131.4 | yes | 12 | 21.11 | odd | 6 | ||
1050.2.s.f.101.3 | 12 | 35.19 | odd | 6 | |||
1050.2.s.f.551.3 | 12 | 105.74 | odd | 6 | |||
1050.2.s.g.101.6 | 12 | 105.89 | even | 6 | |||
1050.2.s.g.551.6 | 12 | 35.4 | even | 6 | |||
1050.2.u.e.299.6 | 12 | 105.32 | even | 12 | |||
1050.2.u.e.899.6 | 12 | 35.33 | even | 12 | |||
1050.2.u.f.299.3 | 12 | 35.18 | odd | 12 | |||
1050.2.u.f.899.3 | 12 | 105.47 | odd | 12 | |||
1050.2.u.g.299.4 | 12 | 35.32 | odd | 12 | |||
1050.2.u.g.899.4 | 12 | 105.68 | odd | 12 | |||
1050.2.u.h.299.1 | 12 | 105.53 | even | 12 | |||
1050.2.u.h.899.1 | 12 | 35.12 | even | 12 | |||
1470.2.b.a.881.3 | 12 | 3.2 | odd | 2 | |||
1470.2.b.a.881.9 | 12 | 7.6 | odd | 2 | |||
1470.2.b.b.881.4 | 12 | 21.20 | even | 2 | inner | ||
1470.2.b.b.881.10 | 12 | 1.1 | even | 1 | trivial |