Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(100,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.i (of order \(3\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 133.1 | ||
Root | \(1.40131 + 2.42714i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.133 |
Dual form | 429.2.i.f.100.1 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.901309 | − | 1.56111i | −0.637322 | − | 1.10387i | −0.986018 | − | 0.166638i | \(-0.946709\pi\) |
0.348696 | − | 0.937236i | \(-0.386625\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.624717 | + | 1.08204i | −0.312359 | + | 0.541021i | ||||
\(5\) | −2.90617 | −1.29968 | −0.649839 | − | 0.760072i | \(-0.725164\pi\) | ||||
−0.649839 | + | 0.760072i | \(0.725164\pi\) | |||||||
\(6\) | −0.901309 | + | 1.56111i | −0.367958 | + | 0.637322i | ||||
\(7\) | −0.704431 | + | 1.22011i | −0.266250 | + | 0.461159i | −0.967890 | − | 0.251373i | \(-0.919118\pi\) |
0.701640 | + | 0.712531i | \(0.252451\pi\) | |||||||
\(8\) | −1.35298 | −0.478352 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.61936 | + | 4.53686i | 0.828313 | + | 1.43468i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 1.24943 | 0.360681 | ||||||||
\(13\) | 3.57513 | − | 0.467344i | 0.991564 | − | 0.129618i | ||||
\(14\) | 2.53964 | 0.678748 | ||||||||
\(15\) | 1.45308 | + | 2.51681i | 0.375185 | + | 0.649839i | ||||
\(16\) | 2.46889 | + | 4.27624i | 0.617223 | + | 1.06906i | ||||
\(17\) | −1.84007 | + | 3.18709i | −0.446282 | + | 0.772984i | −0.998141 | − | 0.0609543i | \(-0.980586\pi\) |
0.551858 | + | 0.833938i | \(0.313919\pi\) | |||||||
\(18\) | 1.80262 | 0.424881 | ||||||||
\(19\) | 1.19688 | − | 2.07305i | 0.274583 | − | 0.475591i | −0.695447 | − | 0.718577i | \(-0.744794\pi\) |
0.970030 | + | 0.242986i | \(0.0781270\pi\) | |||||||
\(20\) | 1.81553 | − | 3.14460i | 0.405966 | − | 0.703153i | ||||
\(21\) | 1.40886 | 0.307439 | ||||||||
\(22\) | −0.901309 | + | 1.56111i | −0.192160 | + | 0.332831i | ||||
\(23\) | 2.79585 | + | 4.84255i | 0.582975 | + | 1.00974i | 0.995125 | + | 0.0986256i | \(0.0314446\pi\) |
−0.412150 | + | 0.911116i | \(0.635222\pi\) | |||||||
\(24\) | 0.676492 | + | 1.17172i | 0.138088 | + | 0.239176i | ||||
\(25\) | 3.44581 | 0.689162 | ||||||||
\(26\) | −3.95188 | − | 5.15997i | −0.775027 | − | 1.01195i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.880141 | − | 1.52445i | −0.166331 | − | 0.288094i | ||||
\(29\) | 0.960637 | + | 1.66387i | 0.178386 | + | 0.308973i | 0.941328 | − | 0.337494i | \(-0.109579\pi\) |
−0.762942 | + | 0.646467i | \(0.776246\pi\) | |||||||
\(30\) | 2.61936 | − | 4.53686i | 0.478227 | − | 0.828313i | ||||
\(31\) | −7.17211 | −1.28815 | −0.644075 | − | 0.764963i | \(-0.722757\pi\) | ||||
−0.644075 | + | 0.764963i | \(0.722757\pi\) | |||||||
\(32\) | 3.09749 | − | 5.36500i | 0.547563 | − | 0.948408i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 6.63389 | 1.13770 | ||||||||
\(35\) | 2.04720 | − | 3.54585i | 0.346039 | − | 0.599357i | ||||
\(36\) | −0.624717 | − | 1.08204i | −0.104120 | − | 0.180340i | ||||
\(37\) | −0.171130 | − | 0.296407i | −0.0281337 | − | 0.0487290i | 0.851616 | − | 0.524167i | \(-0.175623\pi\) |
−0.879749 | + | 0.475438i | \(0.842290\pi\) | |||||||
\(38\) | −4.31503 | −0.699990 | ||||||||
\(39\) | −2.19230 | − | 2.86249i | −0.351049 | − | 0.458365i | ||||
\(40\) | 3.93200 | 0.621703 | ||||||||
\(41\) | 0.0680848 | + | 0.117926i | 0.0106331 | + | 0.0184170i | 0.871293 | − | 0.490763i | \(-0.163282\pi\) |
−0.860660 | + | 0.509180i | \(0.829949\pi\) | |||||||
\(42\) | −1.26982 | − | 2.19939i | −0.195938 | − | 0.339374i | ||||
\(43\) | −5.63932 | + | 9.76759i | −0.859988 | + | 1.48954i | 0.0119505 | + | 0.999929i | \(0.496196\pi\) |
−0.871939 | + | 0.489615i | \(0.837137\pi\) | |||||||
\(44\) | 1.24943 | 0.188359 | ||||||||
\(45\) | 1.45308 | − | 2.51681i | 0.216613 | − | 0.375185i | ||||
\(46\) | 5.03985 | − | 8.72927i | 0.743085 | − | 1.28706i | ||||
\(47\) | 2.74417 | 0.400278 | 0.200139 | − | 0.979767i | \(-0.435861\pi\) | ||||
0.200139 | + | 0.979767i | \(0.435861\pi\) | |||||||
\(48\) | 2.46889 | − | 4.27624i | 0.356354 | − | 0.617223i | ||||
\(49\) | 2.50755 | + | 4.34321i | 0.358222 | + | 0.620458i | ||||
\(50\) | −3.10574 | − | 5.37930i | −0.439218 | − | 0.760748i | ||||
\(51\) | 3.68014 | 0.515322 | ||||||||
\(52\) | −1.72776 | + | 4.16040i | −0.239598 | + | 0.576944i | ||||
\(53\) | −6.17071 | −0.847612 | −0.423806 | − | 0.905753i | \(-0.639306\pi\) | ||||
−0.423806 | + | 0.905753i | \(0.639306\pi\) | |||||||
\(54\) | −0.901309 | − | 1.56111i | −0.122653 | − | 0.212441i | ||||
\(55\) | 1.45308 | + | 2.51681i | 0.195934 | + | 0.339367i | ||||
\(56\) | 0.953084 | − | 1.65079i | 0.127361 | − | 0.220596i | ||||
\(57\) | −2.39376 | −0.317061 | ||||||||
\(58\) | 1.73166 | − | 2.99933i | 0.227378 | − | 0.393831i | ||||
\(59\) | 1.71613 | − | 2.97243i | 0.223422 | − | 0.386978i | −0.732423 | − | 0.680850i | \(-0.761611\pi\) |
0.955845 | + | 0.293872i | \(0.0949440\pi\) | |||||||
\(60\) | −3.63107 | −0.468769 | ||||||||
\(61\) | 0.380923 | − | 0.659778i | 0.0487722 | − | 0.0844759i | −0.840609 | − | 0.541643i | \(-0.817803\pi\) |
0.889381 | + | 0.457167i | \(0.151136\pi\) | |||||||
\(62\) | 6.46429 | + | 11.1965i | 0.820966 | + | 1.42195i | ||||
\(63\) | −0.704431 | − | 1.22011i | −0.0887500 | − | 0.153720i | ||||
\(64\) | −1.29161 | −0.161451 | ||||||||
\(65\) | −10.3899 | + | 1.35818i | −1.28871 | + | 0.168461i | ||||
\(66\) | 1.80262 | 0.221887 | ||||||||
\(67\) | 4.67939 | + | 8.10495i | 0.571679 | + | 0.990177i | 0.996394 | + | 0.0848496i | \(0.0270410\pi\) |
−0.424715 | + | 0.905327i | \(0.639626\pi\) | |||||||
\(68\) | −2.29905 | − | 3.98206i | −0.278800 | − | 0.482896i | ||||
\(69\) | 2.79585 | − | 4.84255i | 0.336581 | − | 0.582975i | ||||
\(70\) | −7.38063 | −0.882153 | ||||||||
\(71\) | 1.52645 | − | 2.64389i | 0.181156 | − | 0.313772i | −0.761118 | − | 0.648613i | \(-0.775349\pi\) |
0.942275 | + | 0.334841i | \(0.108683\pi\) | |||||||
\(72\) | 0.676492 | − | 1.17172i | 0.0797253 | − | 0.138088i | ||||
\(73\) | −2.98113 | −0.348914 | −0.174457 | − | 0.984665i | \(-0.555817\pi\) | ||||
−0.174457 | + | 0.984665i | \(0.555817\pi\) | |||||||
\(74\) | −0.308483 | + | 0.534308i | −0.0358604 | + | 0.0621121i | ||||
\(75\) | −1.72290 | − | 2.98416i | −0.198944 | − | 0.344581i | ||||
\(76\) | 1.49542 | + | 2.59015i | 0.171537 | + | 0.297110i | ||||
\(77\) | 1.40886 | 0.160555 | ||||||||
\(78\) | −2.49273 | + | 6.00241i | −0.282246 | + | 0.679639i | ||||
\(79\) | −10.6762 | −1.20117 | −0.600584 | − | 0.799561i | \(-0.705065\pi\) | ||||
−0.600584 | + | 0.799561i | \(0.705065\pi\) | |||||||
\(80\) | −7.17501 | − | 12.4275i | −0.802191 | − | 1.38943i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.122731 | − | 0.212576i | 0.0135534 | − | 0.0234751i | ||||
\(83\) | −16.9231 | −1.85755 | −0.928775 | − | 0.370644i | \(-0.879137\pi\) | ||||
−0.928775 | + | 0.370644i | \(0.879137\pi\) | |||||||
\(84\) | −0.880141 | + | 1.52445i | −0.0960312 | + | 0.166331i | ||||
\(85\) | 5.34755 | − | 9.26223i | 0.580023 | − | 1.00463i | ||||
\(86\) | 20.3311 | 2.19236 | ||||||||
\(87\) | 0.960637 | − | 1.66387i | 0.102991 | − | 0.178386i | ||||
\(88\) | 0.676492 | + | 1.17172i | 0.0721143 | + | 0.124906i | ||||
\(89\) | 7.51460 | + | 13.0157i | 0.796546 | + | 1.37966i | 0.921853 | + | 0.387541i | \(0.126675\pi\) |
−0.125306 | + | 0.992118i | \(0.539991\pi\) | |||||||
\(90\) | −5.23871 | −0.552209 | ||||||||
\(91\) | −1.94823 | + | 4.69127i | −0.204230 | + | 0.491779i | ||||
\(92\) | −6.98646 | −0.728389 | ||||||||
\(93\) | 3.58606 | + | 6.21123i | 0.371857 | + | 0.644075i | ||||
\(94\) | −2.47335 | − | 4.28396i | −0.255106 | − | 0.441857i | ||||
\(95\) | −3.47833 | + | 6.02464i | −0.356869 | + | 0.618115i | ||||
\(96\) | −6.19497 | −0.632272 | ||||||||
\(97\) | −7.85009 | + | 13.5968i | −0.797056 | + | 1.38054i | 0.124469 | + | 0.992223i | \(0.460277\pi\) |
−0.921525 | + | 0.388318i | \(0.873056\pi\) | |||||||
\(98\) | 4.52016 | − | 7.82915i | 0.456605 | − | 0.790864i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −2.15266 | + | 3.72851i | −0.215266 | + | 0.372851i | ||||
\(101\) | −0.548407 | − | 0.949869i | −0.0545685 | − | 0.0945155i | 0.837451 | − | 0.546513i | \(-0.184045\pi\) |
−0.892019 | + | 0.451997i | \(0.850712\pi\) | |||||||
\(102\) | −3.31694 | − | 5.74511i | −0.328426 | − | 0.568851i | ||||
\(103\) | −2.19361 | −0.216143 | −0.108072 | − | 0.994143i | \(-0.534468\pi\) | ||||
−0.108072 | + | 0.994143i | \(0.534468\pi\) | |||||||
\(104\) | −4.83710 | + | 0.632308i | −0.474316 | + | 0.0620029i | ||||
\(105\) | −4.09439 | −0.399572 | ||||||||
\(106\) | 5.56172 | + | 9.63318i | 0.540202 | + | 0.935657i | ||||
\(107\) | 3.17063 | + | 5.49169i | 0.306516 | + | 0.530901i | 0.977598 | − | 0.210482i | \(-0.0675033\pi\) |
−0.671082 | + | 0.741383i | \(0.734170\pi\) | |||||||
\(108\) | −0.624717 | + | 1.08204i | −0.0601135 | + | 0.104120i | ||||
\(109\) | −16.6691 | −1.59661 | −0.798307 | − | 0.602251i | \(-0.794271\pi\) | ||||
−0.798307 | + | 0.602251i | \(0.794271\pi\) | |||||||
\(110\) | 2.61936 | − | 4.53686i | 0.249746 | − | 0.432572i | ||||
\(111\) | −0.171130 | + | 0.296407i | −0.0162430 | + | 0.0281337i | ||||
\(112\) | −6.95666 | −0.657342 | ||||||||
\(113\) | −5.57921 | + | 9.66348i | −0.524848 | + | 0.909063i | 0.474733 | + | 0.880130i | \(0.342545\pi\) |
−0.999581 | + | 0.0289337i | \(0.990789\pi\) | |||||||
\(114\) | 2.15752 | + | 3.73693i | 0.202070 | + | 0.349995i | ||||
\(115\) | −8.12520 | − | 14.0733i | −0.757679 | − | 1.31234i | ||||
\(116\) | −2.40051 | −0.222881 | ||||||||
\(117\) | −1.38284 | + | 3.32983i | −0.127843 | + | 0.307843i | ||||
\(118\) | −6.18707 | −0.569566 | ||||||||
\(119\) | −2.59240 | − | 4.49018i | −0.237645 | − | 0.411614i | ||||
\(120\) | −1.96600 | − | 3.40521i | −0.179470 | − | 0.310852i | ||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −1.37332 | −0.124334 | ||||||||
\(123\) | 0.0680848 | − | 0.117926i | 0.00613900 | − | 0.0106331i | ||||
\(124\) | 4.48054 | − | 7.76053i | 0.402365 | − | 0.696916i | ||||
\(125\) | 4.51674 | 0.403989 | ||||||||
\(126\) | −1.26982 | + | 2.19939i | −0.113125 | + | 0.195938i | ||||
\(127\) | −6.23779 | − | 10.8042i | −0.553514 | − | 0.958715i | −0.998017 | − | 0.0629374i | \(-0.979953\pi\) |
0.444503 | − | 0.895777i | \(-0.353380\pi\) | |||||||
\(128\) | −5.03083 | − | 8.71366i | −0.444667 | − | 0.770186i | ||||
\(129\) | 11.2786 | 0.993029 | ||||||||
\(130\) | 11.4848 | + | 14.9957i | 1.00729 | + | 1.31521i | ||||
\(131\) | 4.07537 | 0.356067 | 0.178033 | − | 0.984024i | \(-0.443027\pi\) | ||||
0.178033 | + | 0.984024i | \(0.443027\pi\) | |||||||
\(132\) | −0.624717 | − | 1.08204i | −0.0543747 | − | 0.0941797i | ||||
\(133\) | 1.68624 | + | 2.92065i | 0.146215 | + | 0.253252i | ||||
\(134\) | 8.43516 | − | 14.6101i | 0.728687 | − | 1.26212i | ||||
\(135\) | −2.90617 | −0.250123 | ||||||||
\(136\) | 2.48958 | − | 4.31208i | 0.213480 | − | 0.369758i | ||||
\(137\) | −2.72779 | + | 4.72467i | −0.233051 | + | 0.403656i | −0.958704 | − | 0.284404i | \(-0.908204\pi\) |
0.725653 | + | 0.688060i | \(0.241538\pi\) | |||||||
\(138\) | −10.0797 | −0.858041 | ||||||||
\(139\) | 8.68818 | − | 15.0484i | 0.736921 | − | 1.27639i | −0.216954 | − | 0.976182i | \(-0.569612\pi\) |
0.953875 | − | 0.300204i | \(-0.0970546\pi\) | |||||||
\(140\) | 2.55784 | + | 4.43030i | 0.216177 | + | 0.374429i | ||||
\(141\) | −1.37208 | − | 2.37652i | −0.115550 | − | 0.200139i | ||||
\(142\) | −5.50321 | −0.461819 | ||||||||
\(143\) | −2.19230 | − | 2.86249i | −0.183329 | − | 0.239373i | ||||
\(144\) | −4.93778 | −0.411482 | ||||||||
\(145\) | −2.79177 | − | 4.83549i | −0.231844 | − | 0.401566i | ||||
\(146\) | 2.68692 | + | 4.65388i | 0.222371 | + | 0.385158i | ||||
\(147\) | 2.50755 | − | 4.34321i | 0.206819 | − | 0.358222i | ||||
\(148\) | 0.427633 | 0.0351512 | ||||||||
\(149\) | 6.93673 | − | 12.0148i | 0.568279 | − | 0.984288i | −0.428457 | − | 0.903562i | \(-0.640943\pi\) |
0.996736 | − | 0.0807260i | \(-0.0257239\pi\) | |||||||
\(150\) | −3.10574 | + | 5.37930i | −0.253583 | + | 0.439218i | ||||
\(151\) | −18.6348 | −1.51648 | −0.758239 | − | 0.651977i | \(-0.773940\pi\) | ||||
−0.758239 | + | 0.651977i | \(0.773940\pi\) | |||||||
\(152\) | −1.61936 | + | 2.80481i | −0.131347 | + | 0.227500i | ||||
\(153\) | −1.84007 | − | 3.18709i | −0.148761 | − | 0.257661i | ||||
\(154\) | −1.26982 | − | 2.19939i | −0.102325 | − | 0.177232i | ||||
\(155\) | 20.8434 | 1.67418 | ||||||||
\(156\) | 4.46690 | − | 0.583916i | 0.357638 | − | 0.0467507i | ||||
\(157\) | 9.23600 | 0.737113 | 0.368557 | − | 0.929605i | \(-0.379852\pi\) | ||||
0.368557 | + | 0.929605i | \(0.379852\pi\) | |||||||
\(158\) | 9.62258 | + | 16.6668i | 0.765531 | + | 1.32594i | ||||
\(159\) | 3.08535 | + | 5.34399i | 0.244685 | + | 0.423806i | ||||
\(160\) | −9.00181 | + | 15.5916i | −0.711656 | + | 1.23262i | ||||
\(161\) | −7.87793 | −0.620868 | ||||||||
\(162\) | −0.901309 | + | 1.56111i | −0.0708136 | + | 0.122653i | ||||
\(163\) | −3.95485 | + | 6.85001i | −0.309768 | + | 0.536534i | −0.978312 | − | 0.207139i | \(-0.933585\pi\) |
0.668543 | + | 0.743673i | \(0.266918\pi\) | |||||||
\(164\) | −0.170135 | −0.0132853 | ||||||||
\(165\) | 1.45308 | − | 2.51681i | 0.113122 | − | 0.195934i | ||||
\(166\) | 15.2529 | + | 26.4189i | 1.18386 | + | 2.05050i | ||||
\(167\) | 10.3312 | + | 17.8941i | 0.799449 | + | 1.38469i | 0.919975 | + | 0.391977i | \(0.128209\pi\) |
−0.120526 | + | 0.992710i | \(0.538458\pi\) | |||||||
\(168\) | −1.90617 | −0.147064 | ||||||||
\(169\) | 12.5632 | − | 3.34163i | 0.966398 | − | 0.257049i | ||||
\(170\) | −19.2792 | −1.47865 | ||||||||
\(171\) | 1.19688 | + | 2.07305i | 0.0915276 | + | 0.158530i | ||||
\(172\) | −7.04596 | − | 12.2040i | −0.537250 | − | 0.930544i | ||||
\(173\) | −1.68737 | + | 2.92261i | −0.128288 | + | 0.222202i | −0.923013 | − | 0.384768i | \(-0.874282\pi\) |
0.794725 | + | 0.606969i | \(0.207615\pi\) | |||||||
\(174\) | −3.46332 | −0.262554 | ||||||||
\(175\) | −2.42734 | + | 4.20427i | −0.183489 | + | 0.317813i | ||||
\(176\) | 2.46889 | − | 4.27624i | 0.186100 | − | 0.322334i | ||||
\(177\) | −3.43227 | −0.257985 | ||||||||
\(178\) | 13.5460 | − | 23.4623i | 1.01531 | − | 1.75857i | ||||
\(179\) | −6.41737 | − | 11.1152i | −0.479657 | − | 0.830789i | 0.520071 | − | 0.854123i | \(-0.325905\pi\) |
−0.999728 | + | 0.0233334i | \(0.992572\pi\) | |||||||
\(180\) | 1.81553 | + | 3.14460i | 0.135322 | + | 0.234384i | ||||
\(181\) | 22.3924 | 1.66441 | 0.832206 | − | 0.554466i | \(-0.187078\pi\) | ||||
0.832206 | + | 0.554466i | \(0.187078\pi\) | |||||||
\(182\) | 9.07956 | − | 1.18689i | 0.673022 | − | 0.0879778i | ||||
\(183\) | −0.761846 | −0.0563173 | ||||||||
\(184\) | −3.78274 | − | 6.55189i | −0.278867 | − | 0.483012i | ||||
\(185\) | 0.497334 | + | 0.861408i | 0.0365647 | + | 0.0633319i | ||||
\(186\) | 6.46429 | − | 11.1965i | 0.473985 | − | 0.820966i | ||||
\(187\) | 3.68014 | 0.269118 | ||||||||
\(188\) | −1.71433 | + | 2.96931i | −0.125030 | + | 0.216559i | ||||
\(189\) | −0.704431 | + | 1.22011i | −0.0512398 | + | 0.0887500i | ||||
\(190\) | 12.5402 | 0.909762 | ||||||||
\(191\) | 1.68276 | − | 2.91463i | 0.121760 | − | 0.210895i | −0.798702 | − | 0.601727i | \(-0.794479\pi\) |
0.920462 | + | 0.390832i | \(0.127813\pi\) | |||||||
\(192\) | 0.645805 | + | 1.11857i | 0.0466070 | + | 0.0807256i | ||||
\(193\) | −9.42520 | − | 16.3249i | −0.678441 | − | 1.17509i | −0.975450 | − | 0.220219i | \(-0.929323\pi\) |
0.297010 | − | 0.954874i | \(-0.404011\pi\) | |||||||
\(194\) | 28.3015 | 2.03193 | ||||||||
\(195\) | 6.37119 | + | 8.31886i | 0.456250 | + | 0.595726i | ||||
\(196\) | −6.26605 | −0.447575 | ||||||||
\(197\) | 7.15007 | + | 12.3843i | 0.509422 | + | 0.882344i | 0.999940 | + | 0.0109134i | \(0.00347392\pi\) |
−0.490519 | + | 0.871431i | \(0.663193\pi\) | |||||||
\(198\) | −0.901309 | − | 1.56111i | −0.0640533 | − | 0.110944i | ||||
\(199\) | 11.7108 | − | 20.2837i | 0.830157 | − | 1.43787i | −0.0677572 | − | 0.997702i | \(-0.521584\pi\) |
0.897914 | − | 0.440171i | \(-0.145082\pi\) | |||||||
\(200\) | −4.66212 | −0.329662 | ||||||||
\(201\) | 4.67939 | − | 8.10495i | 0.330059 | − | 0.571679i | ||||
\(202\) | −0.988569 | + | 1.71225i | −0.0695555 | + | 0.120474i | ||||
\(203\) | −2.70681 | −0.189981 | ||||||||
\(204\) | −2.29905 | + | 3.98206i | −0.160965 | + | 0.278800i | ||||
\(205\) | −0.197866 | − | 0.342714i | −0.0138196 | − | 0.0239362i | ||||
\(206\) | 1.97712 | + | 3.42448i | 0.137753 | + | 0.238595i | ||||
\(207\) | −5.59170 | −0.388650 | ||||||||
\(208\) | 10.8251 | + | 14.1343i | 0.750585 | + | 0.980040i | ||||
\(209\) | −2.39376 | −0.165580 | ||||||||
\(210\) | 3.69031 | + | 6.39181i | 0.254656 | + | 0.441077i | ||||
\(211\) | −3.30355 | − | 5.72192i | −0.227426 | − | 0.393913i | 0.729619 | − | 0.683854i | \(-0.239698\pi\) |
−0.957044 | + | 0.289941i | \(0.906364\pi\) | |||||||
\(212\) | 3.85495 | − | 6.67697i | 0.264759 | − | 0.458576i | ||||
\(213\) | −3.05290 | −0.209181 | ||||||||
\(214\) | 5.71543 | − | 9.89942i | 0.390699 | − | 0.676710i | ||||
\(215\) | 16.3888 | − | 28.3863i | 1.11771 | − | 1.93593i | ||||
\(216\) | −1.35298 | −0.0920589 | ||||||||
\(217\) | 5.05226 | − | 8.75077i | 0.342970 | − | 0.594041i | ||||
\(218\) | 15.0240 | + | 26.0224i | 1.01756 | + | 1.76246i | ||||
\(219\) | 1.49056 | + | 2.58173i | 0.100723 | + | 0.174457i | ||||
\(220\) | −3.63107 | −0.244806 | ||||||||
\(221\) | −5.08903 | + | 12.2542i | −0.342325 | + | 0.824309i | ||||
\(222\) | 0.616966 | 0.0414081 | ||||||||
\(223\) | −0.176270 | − | 0.305309i | −0.0118039 | − | 0.0204450i | 0.860063 | − | 0.510188i | \(-0.170424\pi\) |
−0.871867 | + | 0.489743i | \(0.837091\pi\) | |||||||
\(224\) | 4.36393 | + | 7.55855i | 0.291578 | + | 0.505027i | ||||
\(225\) | −1.72290 | + | 2.98416i | −0.114860 | + | 0.198944i | ||||
\(226\) | 20.1144 | 1.33799 | ||||||||
\(227\) | 4.10506 | − | 7.11017i | 0.272462 | − | 0.471919i | −0.697029 | − | 0.717043i | \(-0.745495\pi\) |
0.969492 | + | 0.245124i | \(0.0788286\pi\) | |||||||
\(228\) | 1.49542 | − | 2.59015i | 0.0990367 | − | 0.171537i | ||||
\(229\) | 7.80991 | 0.516093 | 0.258047 | − | 0.966132i | \(-0.416921\pi\) | ||||
0.258047 | + | 0.966132i | \(0.416921\pi\) | |||||||
\(230\) | −14.6466 | + | 25.3687i | −0.965771 | + | 1.67276i | ||||
\(231\) | −0.704431 | − | 1.22011i | −0.0463482 | − | 0.0802774i | ||||
\(232\) | −1.29973 | − | 2.25119i | −0.0853312 | − | 0.147798i | ||||
\(233\) | −7.15319 | −0.468621 | −0.234311 | − | 0.972162i | \(-0.575283\pi\) | ||||
−0.234311 | + | 0.972162i | \(0.575283\pi\) | |||||||
\(234\) | 6.44461 | − | 0.842443i | 0.421297 | − | 0.0550722i | ||||
\(235\) | −7.97502 | −0.520233 | ||||||||
\(236\) | 2.14420 | + | 3.71386i | 0.139575 | + | 0.241752i | ||||
\(237\) | 5.33811 | + | 9.24588i | 0.346748 | + | 0.600584i | ||||
\(238\) | −4.67312 | + | 8.09408i | −0.302913 | + | 0.524661i | ||||
\(239\) | −12.8357 | −0.830275 | −0.415138 | − | 0.909759i | \(-0.636267\pi\) | ||||
−0.415138 | + | 0.909759i | \(0.636267\pi\) | |||||||
\(240\) | −7.17501 | + | 12.4275i | −0.463145 | + | 0.802191i | ||||
\(241\) | −8.70249 | + | 15.0732i | −0.560577 | + | 0.970948i | 0.436869 | + | 0.899525i | \(0.356087\pi\) |
−0.997446 | + | 0.0714226i | \(0.977246\pi\) | |||||||
\(242\) | 1.80262 | 0.115877 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0.475938 | + | 0.824349i | 0.0304688 | + | 0.0527736i | ||||
\(245\) | −7.28737 | − | 12.6221i | −0.465573 | − | 0.806396i | ||||
\(246\) | −0.245462 | −0.0156501 | ||||||||
\(247\) | 3.31017 | − | 7.97080i | 0.210621 | − | 0.507170i | ||||
\(248\) | 9.70375 | 0.616188 | ||||||||
\(249\) | 8.46154 | + | 14.6558i | 0.536229 | + | 0.928775i | ||||
\(250\) | −4.07098 | − | 7.05114i | −0.257471 | − | 0.445953i | ||||
\(251\) | 6.83438 | − | 11.8375i | 0.431383 | − | 0.747176i | −0.565610 | − | 0.824673i | \(-0.691359\pi\) |
0.996993 | + | 0.0774964i | \(0.0246926\pi\) | |||||||
\(252\) | 1.76028 | 0.110887 | ||||||||
\(253\) | 2.79585 | − | 4.84255i | 0.175773 | − | 0.304449i | ||||
\(254\) | −11.2444 | + | 19.4758i | −0.705533 | + | 1.22202i | ||||
\(255\) | −10.6951 | −0.669753 | ||||||||
\(256\) | −10.3603 | + | 17.9445i | −0.647518 | + | 1.12153i | ||||
\(257\) | 10.6347 | + | 18.4198i | 0.663372 | + | 1.14899i | 0.979724 | + | 0.200353i | \(0.0642088\pi\) |
−0.316351 | + | 0.948642i | \(0.602458\pi\) | |||||||
\(258\) | −10.1655 | − | 17.6072i | −0.632879 | − | 1.09618i | ||||
\(259\) | 0.482199 | 0.0299624 | ||||||||
\(260\) | 5.02117 | − | 12.0908i | 0.311400 | − | 0.749842i | ||||
\(261\) | −1.92127 | −0.118924 | ||||||||
\(262\) | −3.67317 | − | 6.36212i | −0.226929 | − | 0.393053i | ||||
\(263\) | −7.32697 | − | 12.6907i | −0.451800 | − | 0.782541i | 0.546698 | − | 0.837330i | \(-0.315885\pi\) |
−0.998498 | + | 0.0547892i | \(0.982551\pi\) | |||||||
\(264\) | 0.676492 | − | 1.17172i | 0.0416352 | − | 0.0721143i | ||||
\(265\) | 17.9331 | 1.10162 | ||||||||
\(266\) | 3.03964 | − | 5.26481i | 0.186372 | − | 0.322806i | ||||
\(267\) | 7.51460 | − | 13.0157i | 0.459886 | − | 0.796546i | ||||
\(268\) | −11.6932 | −0.714275 | ||||||||
\(269\) | −8.39052 | + | 14.5328i | −0.511579 | + | 0.886081i | 0.488331 | + | 0.872658i | \(0.337606\pi\) |
−0.999910 | + | 0.0134221i | \(0.995727\pi\) | |||||||
\(270\) | 2.61936 | + | 4.53686i | 0.159409 | + | 0.276104i | ||||
\(271\) | −14.2006 | − | 24.5962i | −0.862626 | − | 1.49411i | −0.869386 | − | 0.494134i | \(-0.835485\pi\) |
0.00676017 | − | 0.999977i | \(-0.497848\pi\) | |||||||
\(272\) | −18.1717 | −1.10182 | ||||||||
\(273\) | 5.03687 | − | 0.658423i | 0.304845 | − | 0.0398496i | ||||
\(274\) | 9.83434 | 0.594114 | ||||||||
\(275\) | −1.72290 | − | 2.98416i | −0.103895 | − | 0.179952i | ||||
\(276\) | 3.49323 | + | 6.05045i | 0.210268 | + | 0.364194i | ||||
\(277\) | −4.74570 | + | 8.21980i | −0.285142 | + | 0.493880i | −0.972644 | − | 0.232303i | \(-0.925374\pi\) |
0.687502 | + | 0.726183i | \(0.258707\pi\) | |||||||
\(278\) | −31.3229 | −1.87863 | ||||||||
\(279\) | 3.58606 | − | 6.21123i | 0.214692 | − | 0.371857i | ||||
\(280\) | −2.76982 | + | 4.79747i | −0.165528 | + | 0.286704i | ||||
\(281\) | 21.7208 | 1.29575 | 0.647876 | − | 0.761746i | \(-0.275657\pi\) | ||||
0.647876 | + | 0.761746i | \(0.275657\pi\) | |||||||
\(282\) | −2.47335 | + | 4.28396i | −0.147286 | + | 0.255106i | ||||
\(283\) | −7.76918 | − | 13.4566i | −0.461830 | − | 0.799912i | 0.537223 | − | 0.843440i | \(-0.319473\pi\) |
−0.999052 | + | 0.0435283i | \(0.986140\pi\) | |||||||
\(284\) | 1.90720 | + | 3.30336i | 0.113171 | + | 0.196019i | ||||
\(285\) | 6.95666 | 0.412077 | ||||||||
\(286\) | −2.49273 | + | 6.00241i | −0.147398 | + | 0.354930i | ||||
\(287\) | −0.191844 | −0.0113242 | ||||||||
\(288\) | 3.09749 | + | 5.36500i | 0.182521 | + | 0.316136i | ||||
\(289\) | 1.72829 | + | 2.99349i | 0.101664 | + | 0.176088i | ||||
\(290\) | −5.03250 | + | 8.71655i | −0.295519 | + | 0.511853i | ||||
\(291\) | 15.7002 | 0.920361 | ||||||||
\(292\) | 1.86236 | − | 3.22570i | 0.108986 | − | 0.188770i | ||||
\(293\) | −2.07081 | + | 3.58674i | −0.120978 | + | 0.209540i | −0.920154 | − | 0.391558i | \(-0.871936\pi\) |
0.799176 | + | 0.601097i | \(0.205270\pi\) | |||||||
\(294\) | −9.04032 | −0.527242 | ||||||||
\(295\) | −4.98737 | + | 8.63838i | −0.290376 | + | 0.502946i | ||||
\(296\) | 0.231537 | + | 0.401033i | 0.0134578 | + | 0.0233096i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | −25.0086 | −1.44871 | ||||||||
\(299\) | 12.2587 | + | 16.0061i | 0.708937 | + | 0.925659i | ||||
\(300\) | 4.30531 | 0.248567 | ||||||||
\(301\) | −7.94503 | − | 13.7612i | −0.457944 | − | 0.793182i | ||||
\(302\) | 16.7957 | + | 29.0910i | 0.966484 | + | 1.67400i | ||||
\(303\) | −0.548407 | + | 0.949869i | −0.0315052 | + | 0.0545685i | ||||
\(304\) | 11.8198 | 0.677915 | ||||||||
\(305\) | −1.10703 | + | 1.91743i | −0.0633881 | + | 0.109791i | ||||
\(306\) | −3.31694 | + | 5.74511i | −0.189617 | + | 0.328426i | ||||
\(307\) | 28.0449 | 1.60061 | 0.800304 | − | 0.599595i | \(-0.204672\pi\) | ||||
0.800304 | + | 0.599595i | \(0.204672\pi\) | |||||||
\(308\) | −0.880141 | + | 1.52445i | −0.0501507 | + | 0.0868635i | ||||
\(309\) | 1.09681 | + | 1.89972i | 0.0623951 | + | 0.108072i | ||||
\(310\) | −18.7863 | − | 32.5388i | −1.06699 | − | 1.84808i | ||||
\(311\) | −21.4758 | −1.21778 | −0.608889 | − | 0.793255i | \(-0.708385\pi\) | ||||
−0.608889 | + | 0.793255i | \(0.708385\pi\) | |||||||
\(312\) | 2.96614 | + | 3.87290i | 0.167925 | + | 0.219260i | ||||
\(313\) | −23.8001 | −1.34526 | −0.672630 | − | 0.739979i | \(-0.734835\pi\) | ||||
−0.672630 | + | 0.739979i | \(0.734835\pi\) | |||||||
\(314\) | −8.32450 | − | 14.4185i | −0.469778 | − | 0.813680i | ||||
\(315\) | 2.04720 | + | 3.54585i | 0.115346 | + | 0.199786i | ||||
\(316\) | 6.66962 | − | 11.5521i | 0.375196 | − | 0.649858i | ||||
\(317\) | −16.3873 | −0.920401 | −0.460200 | − | 0.887815i | \(-0.652222\pi\) | ||||
−0.460200 | + | 0.887815i | \(0.652222\pi\) | |||||||
\(318\) | 5.56172 | − | 9.63318i | 0.311886 | − | 0.540202i | ||||
\(319\) | 0.960637 | − | 1.66387i | 0.0537853 | − | 0.0931589i | ||||
\(320\) | 3.75363 | 0.209835 | ||||||||
\(321\) | 3.17063 | − | 5.49169i | 0.176967 | − | 0.306516i | ||||
\(322\) | 7.10045 | + | 12.2983i | 0.395693 | + | 0.685360i | ||||
\(323\) | 4.40468 | + | 7.62912i | 0.245083 | + | 0.424496i | ||||
\(324\) | 1.24943 | 0.0694130 | ||||||||
\(325\) | 12.3192 | − | 1.61038i | 0.683348 | − | 0.0893277i | ||||
\(326\) | 14.2582 | 0.789688 | ||||||||
\(327\) | 8.33456 | + | 14.4359i | 0.460902 | + | 0.798307i | ||||
\(328\) | −0.0921176 | − | 0.159552i | −0.00508635 | − | 0.00880981i | ||||
\(329\) | −1.93308 | + | 3.34819i | −0.106574 | + | 0.184592i | ||||
\(330\) | −5.23871 | −0.288382 | ||||||||
\(331\) | −8.10697 | + | 14.0417i | −0.445599 | + | 0.771801i | −0.998094 | − | 0.0617158i | \(-0.980343\pi\) |
0.552494 | + | 0.833517i | \(0.313676\pi\) | |||||||
\(332\) | 10.5721 | − | 18.3115i | 0.580222 | − | 1.00497i | ||||
\(333\) | 0.342261 | 0.0187558 | ||||||||
\(334\) | 18.6231 | − | 32.2562i | 1.01901 | − | 1.76498i | ||||
\(335\) | −13.5991 | − | 23.5543i | −0.742998 | − | 1.28691i | ||||
\(336\) | 3.47833 | + | 6.02464i | 0.189758 | + | 0.328671i | ||||
\(337\) | 13.9667 | 0.760816 | 0.380408 | − | 0.924819i | \(-0.375784\pi\) | ||||
0.380408 | + | 0.924819i | \(0.375784\pi\) | |||||||
\(338\) | −16.5400 | − | 16.6007i | −0.899656 | − | 0.902959i | ||||
\(339\) | 11.1584 | 0.606042 | ||||||||
\(340\) | 6.68141 | + | 11.5725i | 0.362350 | + | 0.627609i | ||||
\(341\) | 3.58606 | + | 6.21123i | 0.194196 | + | 0.336357i | ||||
\(342\) | 2.15752 | − | 3.73693i | 0.116665 | − | 0.202070i | ||||
\(343\) | −16.9276 | −0.914006 | ||||||||
\(344\) | 7.62991 | − | 13.2154i | 0.411377 | − | 0.712526i | ||||
\(345\) | −8.12520 | + | 14.0733i | −0.437446 | + | 0.757679i | ||||
\(346\) | 6.08336 | 0.327044 | ||||||||
\(347\) | 2.18258 | − | 3.78034i | 0.117167 | − | 0.202940i | −0.801477 | − | 0.598026i | \(-0.795952\pi\) |
0.918644 | + | 0.395086i | \(0.129285\pi\) | |||||||
\(348\) | 1.20025 | + | 2.07890i | 0.0643403 | + | 0.111441i | ||||
\(349\) | 13.0950 | + | 22.6812i | 0.700958 | + | 1.21409i | 0.968131 | + | 0.250446i | \(0.0805772\pi\) |
−0.267173 | + | 0.963649i | \(0.586089\pi\) | |||||||
\(350\) | 8.75112 | 0.467767 | ||||||||
\(351\) | 3.57513 | − | 0.467344i | 0.190827 | − | 0.0249450i | ||||
\(352\) | −6.19497 | −0.330193 | ||||||||
\(353\) | −14.3710 | − | 24.8914i | −0.764894 | − | 1.32483i | −0.940303 | − | 0.340339i | \(-0.889458\pi\) |
0.175409 | − | 0.984496i | \(-0.443875\pi\) | |||||||
\(354\) | 3.09354 | + | 5.35816i | 0.164420 | + | 0.284783i | ||||
\(355\) | −4.43612 | + | 7.68358i | −0.235445 | + | 0.407802i | ||||
\(356\) | −18.7780 | −0.995233 | ||||||||
\(357\) | −2.59240 | + | 4.49018i | −0.137205 | + | 0.237645i | ||||
\(358\) | −11.5681 | + | 20.0365i | −0.611391 | + | 1.05896i | ||||
\(359\) | −32.8065 | −1.73146 | −0.865730 | − | 0.500511i | \(-0.833146\pi\) | ||||
−0.865730 | + | 0.500511i | \(0.833146\pi\) | |||||||
\(360\) | −1.96600 | + | 3.40521i | −0.103617 | + | 0.179470i | ||||
\(361\) | 6.63497 | + | 11.4921i | 0.349209 | + | 0.604847i | ||||
\(362\) | −20.1825 | − | 34.9570i | −1.06077 | − | 1.83730i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −3.85906 | − | 5.03878i | −0.202270 | − | 0.264104i | ||||
\(365\) | 8.66365 | 0.453476 | ||||||||
\(366\) | 0.686659 | + | 1.18933i | 0.0358922 | + | 0.0621672i | ||||
\(367\) | −11.9410 | − | 20.6824i | −0.623313 | − | 1.07961i | −0.988864 | − | 0.148819i | \(-0.952453\pi\) |
0.365551 | − | 0.930791i | \(-0.380880\pi\) | |||||||
\(368\) | −13.8053 | + | 23.9115i | −0.719650 | + | 1.24647i | ||||
\(369\) | −0.136170 | −0.00708871 | ||||||||
\(370\) | 0.896503 | − | 1.55279i | 0.0466070 | − | 0.0807257i | ||||
\(371\) | 4.34684 | − | 7.52895i | 0.225677 | − | 0.390883i | ||||
\(372\) | −8.96108 | −0.464611 | ||||||||
\(373\) | −10.4506 | + | 18.1010i | −0.541111 | + | 0.937232i | 0.457729 | + | 0.889092i | \(0.348663\pi\) |
−0.998841 | + | 0.0481406i | \(0.984670\pi\) | |||||||
\(374\) | −3.31694 | − | 5.74511i | −0.171515 | − | 0.297073i | ||||
\(375\) | −2.25837 | − | 3.91161i | −0.116622 | − | 0.201995i | ||||
\(376\) | −3.71282 | −0.191474 | ||||||||
\(377\) | 4.21201 | + | 5.49962i | 0.216929 | + | 0.283245i | ||||
\(378\) | 2.53964 | 0.130625 | ||||||||
\(379\) | 15.8980 | + | 27.5362i | 0.816628 | + | 1.41444i | 0.908153 | + | 0.418638i | \(0.137492\pi\) |
−0.0915258 | + | 0.995803i | \(0.529174\pi\) | |||||||
\(380\) | −4.34594 | − | 7.52740i | −0.222942 | − | 0.386147i | ||||
\(381\) | −6.23779 | + | 10.8042i | −0.319572 | + | 0.553514i | ||||
\(382\) | −6.06675 | −0.310402 | ||||||||
\(383\) | 11.5713 | − | 20.0421i | 0.591267 | − | 1.02410i | −0.402795 | − | 0.915290i | \(-0.631961\pi\) |
0.994062 | − | 0.108814i | \(-0.0347053\pi\) | |||||||
\(384\) | −5.03083 | + | 8.71366i | −0.256729 | + | 0.444667i | ||||
\(385\) | −4.09439 | −0.208669 | ||||||||
\(386\) | −16.9900 | + | 29.4276i | −0.864770 | + | 1.49783i | ||||
\(387\) | −5.63932 | − | 9.76759i | −0.286663 | − | 0.496514i | ||||
\(388\) | −9.80818 | − | 16.9883i | −0.497935 | − | 0.862448i | ||||
\(389\) | −22.3577 | −1.13358 | −0.566790 | − | 0.823862i | \(-0.691815\pi\) | ||||
−0.566790 | + | 0.823862i | \(0.691815\pi\) | |||||||
\(390\) | 7.24428 | − | 17.4440i | 0.366828 | − | 0.883312i | ||||
\(391\) | −20.5782 | −1.04068 | ||||||||
\(392\) | −3.39268 | − | 5.87629i | −0.171356 | − | 0.296797i | ||||
\(393\) | −2.03768 | − | 3.52937i | −0.102788 | − | 0.178033i | ||||
\(394\) | 12.8889 | − | 22.3241i | 0.649331 | − | 1.12467i | ||||
\(395\) | 31.0269 | 1.56113 | ||||||||
\(396\) | −0.624717 | + | 1.08204i | −0.0313932 | + | 0.0543747i | ||||
\(397\) | −11.3445 | + | 19.6492i | −0.569363 | + | 0.986166i | 0.427266 | + | 0.904126i | \(0.359477\pi\) |
−0.996629 | + | 0.0820403i | \(0.973856\pi\) | |||||||
\(398\) | −42.2202 | −2.11631 | ||||||||
\(399\) | 1.68624 | − | 2.92065i | 0.0844174 | − | 0.146215i | ||||
\(400\) | 8.50733 | + | 14.7351i | 0.425366 | + | 0.736756i | ||||
\(401\) | 16.1986 | + | 28.0568i | 0.808921 | + | 1.40109i | 0.913612 | + | 0.406587i | \(0.133281\pi\) |
−0.104691 | + | 0.994505i | \(0.533385\pi\) | |||||||
\(402\) | −16.8703 | −0.841415 | ||||||||
\(403\) | −25.6413 | + | 3.35184i | −1.27728 | + | 0.166967i | ||||
\(404\) | 1.37040 | 0.0681798 | ||||||||
\(405\) | 1.45308 | + | 2.51681i | 0.0722043 | + | 0.125062i | ||||
\(406\) | 2.43967 | + | 4.22564i | 0.121079 | + | 0.209715i | ||||
\(407\) | −0.171130 | + | 0.296407i | −0.00848262 | + | 0.0146923i | ||||
\(408\) | −4.97917 | −0.246505 | ||||||||
\(409\) | 13.4471 | − | 23.2911i | 0.664918 | − | 1.15167i | −0.314390 | − | 0.949294i | \(-0.601800\pi\) |
0.979308 | − | 0.202378i | \(-0.0648668\pi\) | |||||||
\(410\) | −0.356677 | + | 0.617782i | −0.0176150 | + | 0.0305101i | ||||
\(411\) | 5.45558 | 0.269104 | ||||||||
\(412\) | 1.37039 | − | 2.37358i | 0.0675142 | − | 0.116938i | ||||
\(413\) | 2.41780 | + | 4.18775i | 0.118972 | + | 0.206066i | ||||
\(414\) | 5.03985 | + | 8.72927i | 0.247695 | + | 0.429020i | ||||
\(415\) | 49.1813 | 2.41422 | ||||||||
\(416\) | 8.56663 | − | 20.6282i | 0.420014 | − | 1.01138i | ||||
\(417\) | −17.3764 | −0.850924 | ||||||||
\(418\) | 2.15752 | + | 3.73693i | 0.105528 | + | 0.182779i | ||||
\(419\) | −11.8033 | − | 20.4439i | −0.576628 | − | 0.998748i | −0.995863 | − | 0.0908706i | \(-0.971035\pi\) |
0.419235 | − | 0.907878i | \(-0.362298\pi\) | |||||||
\(420\) | 2.55784 | − | 4.43030i | 0.124810 | − | 0.216177i | ||||
\(421\) | 25.3078 | 1.23343 | 0.616714 | − | 0.787187i | \(-0.288463\pi\) | ||||
0.616714 | + | 0.787187i | \(0.288463\pi\) | |||||||
\(422\) | −5.95504 | + | 10.3144i | −0.289887 | + | 0.502099i | ||||
\(423\) | −1.37208 | + | 2.37652i | −0.0667130 | + | 0.115550i | ||||
\(424\) | 8.34887 | 0.405457 | ||||||||
\(425\) | −6.34053 | + | 10.9821i | −0.307561 | + | 0.532711i | ||||
\(426\) | 2.75161 | + | 4.76592i | 0.133316 | + | 0.230910i | ||||
\(427\) | 0.536668 | + | 0.929536i | 0.0259712 | + | 0.0449834i | ||||
\(428\) | −7.92298 | −0.382972 | ||||||||
\(429\) | −1.38284 | + | 3.32983i | −0.0667639 | + | 0.160766i | ||||
\(430\) | −59.0856 | −2.84936 | ||||||||
\(431\) | −6.79470 | − | 11.7688i | −0.327289 | − | 0.566881i | 0.654684 | − | 0.755903i | \(-0.272802\pi\) |
−0.981973 | + | 0.189021i | \(0.939468\pi\) | |||||||
\(432\) | 2.46889 | + | 4.27624i | 0.118785 | + | 0.205741i | ||||
\(433\) | −5.76282 | + | 9.98150i | −0.276944 | + | 0.479680i | −0.970624 | − | 0.240603i | \(-0.922655\pi\) |
0.693680 | + | 0.720283i | \(0.255988\pi\) | |||||||
\(434\) | −18.2146 | −0.874329 | ||||||||
\(435\) | −2.79177 | + | 4.83549i | −0.133855 | + | 0.231844i | ||||
\(436\) | 10.4135 | − | 18.0367i | 0.498716 | − | 0.863801i | ||||
\(437\) | 13.3852 | 0.640299 | ||||||||
\(438\) | 2.68692 | − | 4.65388i | 0.128386 | − | 0.222371i | ||||
\(439\) | −7.63403 | − | 13.2225i | −0.364353 | − | 0.631077i | 0.624320 | − | 0.781169i | \(-0.285376\pi\) |
−0.988672 | + | 0.150092i | \(0.952043\pi\) | |||||||
\(440\) | −1.96600 | − | 3.40521i | −0.0937253 | − | 0.162337i | ||||
\(441\) | −5.01511 | −0.238815 | ||||||||
\(442\) | 23.7170 | − | 3.10031i | 1.12810 | − | 0.147466i | ||||
\(443\) | 18.5447 | 0.881086 | 0.440543 | − | 0.897731i | \(-0.354786\pi\) | ||||
0.440543 | + | 0.897731i | \(0.354786\pi\) | |||||||
\(444\) | −0.213816 | − | 0.370341i | −0.0101473 | − | 0.0175756i | ||||
\(445\) | −21.8387 | − | 37.8257i | −1.03525 | − | 1.79311i | ||||
\(446\) | −0.317748 | + | 0.550356i | −0.0150458 | + | 0.0260601i | ||||
\(447\) | −13.8735 | −0.656192 | ||||||||
\(448\) | 0.909850 | − | 1.57591i | 0.0429864 | − | 0.0744546i | ||||
\(449\) | −6.02668 | + | 10.4385i | −0.284417 | + | 0.492624i | −0.972468 | − | 0.233038i | \(-0.925133\pi\) |
0.688051 | + | 0.725662i | \(0.258467\pi\) | |||||||
\(450\) | 6.21148 | 0.292812 | ||||||||
\(451\) | 0.0680848 | − | 0.117926i | 0.00320599 | − | 0.00555294i | ||||
\(452\) | −6.97086 | − | 12.0739i | −0.327882 | − | 0.567908i | ||||
\(453\) | 9.31739 | + | 16.1382i | 0.437769 | + | 0.758239i | ||||
\(454\) | −14.7997 | −0.694585 | ||||||||
\(455\) | 5.66187 | − | 13.6336i | 0.265433 | − | 0.639154i | ||||
\(456\) | 3.23871 | 0.151667 | ||||||||
\(457\) | −9.44307 | − | 16.3559i | −0.441728 | − | 0.765096i | 0.556090 | − | 0.831122i | \(-0.312301\pi\) |
−0.997818 | + | 0.0660266i | \(0.978968\pi\) | |||||||
\(458\) | −7.03915 | − | 12.1922i | −0.328918 | − | 0.569702i | ||||
\(459\) | −1.84007 | + | 3.18709i | −0.0858871 | + | 0.148761i | ||||
\(460\) | 20.3038 | 0.946670 | ||||||||
\(461\) | −4.94289 | + | 8.56134i | −0.230213 | + | 0.398741i | −0.957871 | − | 0.287199i | \(-0.907276\pi\) |
0.727657 | + | 0.685941i | \(0.240609\pi\) | |||||||
\(462\) | −1.26982 | + | 2.19939i | −0.0590774 | + | 0.102325i | ||||
\(463\) | 12.2452 | 0.569081 | 0.284540 | − | 0.958664i | \(-0.408159\pi\) | ||||
0.284540 | + | 0.958664i | \(0.408159\pi\) | |||||||
\(464\) | −4.74342 | + | 8.21584i | −0.220208 | + | 0.381411i | ||||
\(465\) | −10.4217 | − | 18.0509i | −0.483294 | − | 0.837089i | ||||
\(466\) | 6.44724 | + | 11.1669i | 0.298663 | + | 0.517299i | ||||
\(467\) | 42.4158 | 1.96277 | 0.981385 | − | 0.192051i | \(-0.0615139\pi\) | ||||
0.981385 | + | 0.192051i | \(0.0615139\pi\) | |||||||
\(468\) | −2.73913 | − | 3.57649i | −0.126617 | − | 0.165323i | ||||
\(469\) | −13.1852 | −0.608838 | ||||||||
\(470\) | 7.18796 | + | 12.4499i | 0.331556 | + | 0.574271i | ||||
\(471\) | −4.61800 | − | 7.99861i | −0.212786 | − | 0.368557i | ||||
\(472\) | −2.32190 | + | 4.02165i | −0.106874 | + | 0.185111i | ||||
\(473\) | 11.2786 | 0.518592 | ||||||||
\(474\) | 9.62258 | − | 16.6668i | 0.441980 | − | 0.765531i | ||||
\(475\) | 4.12421 | − | 7.14335i | 0.189232 | − | 0.327759i | ||||
\(476\) | 6.47808 | 0.296922 | ||||||||
\(477\) | 3.08535 | − | 5.34399i | 0.141269 | − | 0.244685i | ||||
\(478\) | 11.5690 | + | 20.0380i | 0.529153 | + | 0.916519i | ||||
\(479\) | 14.1978 | + | 24.5913i | 0.648715 | + | 1.12361i | 0.983430 | + | 0.181288i | \(0.0580266\pi\) |
−0.334715 | + | 0.942319i | \(0.608640\pi\) | |||||||
\(480\) | 18.0036 | 0.821749 | ||||||||
\(481\) | −0.750338 | − | 0.979717i | −0.0342125 | − | 0.0446713i | ||||
\(482\) | 31.3746 | 1.42907 | ||||||||
\(483\) | 3.93897 | + | 6.82249i | 0.179229 | + | 0.310434i | ||||
\(484\) | −0.624717 | − | 1.08204i | −0.0283962 | − | 0.0491837i | ||||
\(485\) | 22.8137 | − | 39.5145i | 1.03592 | − | 1.79426i | ||||
\(486\) | 1.80262 | 0.0817685 | ||||||||
\(487\) | −7.85330 | + | 13.6023i | −0.355867 | + | 0.616380i | −0.987266 | − | 0.159079i | \(-0.949148\pi\) |
0.631399 | + | 0.775458i | \(0.282481\pi\) | |||||||
\(488\) | −0.515382 | + | 0.892668i | −0.0233303 | + | 0.0404092i | ||||
\(489\) | 7.90971 | 0.357689 | ||||||||
\(490\) | −13.1363 | + | 22.7528i | −0.593440 | + | 1.02787i | ||||
\(491\) | 7.64508 | + | 13.2417i | 0.345018 | + | 0.597588i | 0.985357 | − | 0.170504i | \(-0.0545396\pi\) |
−0.640339 | + | 0.768092i | \(0.721206\pi\) | |||||||
\(492\) | 0.0850675 | + | 0.147341i | 0.00383514 | + | 0.00664266i | ||||
\(493\) | −7.07055 | −0.318442 | ||||||||
\(494\) | −15.4268 | + | 2.01660i | −0.694085 | + | 0.0907312i | ||||
\(495\) | −2.90617 | −0.130623 | ||||||||
\(496\) | −17.7072 | − | 30.6697i | −0.795075 | − | 1.37711i | ||||
\(497\) | 2.15056 | + | 3.72487i | 0.0964656 | + | 0.167083i | ||||
\(498\) | 15.2529 | − | 26.4189i | 0.683500 | − | 1.18386i | ||||
\(499\) | 16.8318 | 0.753496 | 0.376748 | − | 0.926316i | \(-0.377042\pi\) | ||||
0.376748 | + | 0.926316i | \(0.377042\pi\) | |||||||
\(500\) | −2.82168 | + | 4.88730i | −0.126190 | + | 0.218567i | ||||
\(501\) | 10.3312 | − | 17.8941i | 0.461562 | − | 0.799449i | ||||
\(502\) | −24.6396 | −1.09972 | ||||||||
\(503\) | −9.98757 | + | 17.2990i | −0.445324 | + | 0.771323i | −0.998075 | − | 0.0620231i | \(-0.980245\pi\) |
0.552751 | + | 0.833346i | \(0.313578\pi\) | |||||||
\(504\) | 0.953084 | + | 1.65079i | 0.0424537 | + | 0.0735320i | ||||
\(505\) | 1.59376 | + | 2.76048i | 0.0709215 | + | 0.122840i | ||||
\(506\) | −10.0797 | −0.448097 | ||||||||
\(507\) | −9.17553 | − | 9.20922i | −0.407500 | − | 0.408996i | ||||
\(508\) | 15.5874 | 0.691580 | ||||||||
\(509\) | −15.9912 | − | 27.6975i | −0.708796 | − | 1.22767i | −0.965304 | − | 0.261129i | \(-0.915905\pi\) |
0.256508 | − | 0.966542i | \(-0.417428\pi\) | |||||||
\(510\) | 9.63959 | + | 16.6963i | 0.426848 | + | 0.739323i | ||||
\(511\) | 2.10000 | − | 3.63730i | 0.0928984 | − | 0.160905i | ||||
\(512\) | 17.2280 | 0.761375 | ||||||||
\(513\) | 1.19688 | − | 2.07305i | 0.0528435 | − | 0.0915276i | ||||
\(514\) | 19.1703 | − | 33.2039i | 0.845564 | − | 1.46456i | ||||
\(515\) | 6.37501 | 0.280916 | ||||||||
\(516\) | −7.04596 | + | 12.2040i | −0.310181 | + | 0.537250i | ||||
\(517\) | −1.37208 | − | 2.37652i | −0.0603442 | − | 0.104519i | ||||
\(518\) | −0.434610 | − | 0.752767i | −0.0190957 | − | 0.0330747i | ||||
\(519\) | 3.37474 | 0.148134 | ||||||||
\(520\) | 14.0574 | − | 1.83759i | 0.616459 | − | 0.0805838i | ||||
\(521\) | −18.5052 | −0.810726 | −0.405363 | − | 0.914156i | \(-0.632855\pi\) | ||||
−0.405363 | + | 0.914156i | \(0.632855\pi\) | |||||||
\(522\) | 1.73166 | + | 2.99933i | 0.0757928 | + | 0.131277i | ||||
\(523\) | 13.2516 | + | 22.9524i | 0.579450 | + | 1.00364i | 0.995542 | + | 0.0943150i | \(0.0300661\pi\) |
−0.416092 | + | 0.909323i | \(0.636601\pi\) | |||||||
\(524\) | −2.54595 | + | 4.40972i | −0.111221 | + | 0.192640i | ||||
\(525\) | 4.85467 | 0.211875 | ||||||||
\(526\) | −13.2077 | + | 22.8765i | −0.575884 | + | 0.997461i | ||||
\(527\) | 13.1972 | − | 22.8582i | 0.574878 | − | 0.995718i | ||||
\(528\) | −4.93778 | −0.214889 | ||||||||
\(529\) | −4.13353 | + | 7.15948i | −0.179719 | + | 0.311282i | ||||
\(530\) | −16.1633 | − | 27.9956i | −0.702088 | − | 1.21605i | ||||
\(531\) | 1.71613 | + | 2.97243i | 0.0744739 | + | 0.128993i | ||||
\(532\) | −4.21369 | −0.182686 | ||||||||
\(533\) | 0.298525 | + | 0.389784i | 0.0129305 | + | 0.0168834i | ||||
\(534\) | −27.0919 | −1.17238 | ||||||||
\(535\) | −9.21437 | − | 15.9598i | −0.398372 | − | 0.690001i | ||||
\(536\) | −6.33114 | − | 10.9659i | −0.273464 | − | 0.473653i | ||||
\(537\) | −6.41737 | + | 11.1152i | −0.276930 | + | 0.479657i | ||||
\(538\) | 30.2498 | 1.30416 | ||||||||
\(539\) | 2.50755 | − | 4.34321i | 0.108008 | − | 0.187075i | ||||
\(540\) | 1.81553 | − | 3.14460i | 0.0781281 | − | 0.135322i | ||||
\(541\) | −19.6689 | −0.845633 | −0.422817 | − | 0.906215i | \(-0.638959\pi\) | ||||
−0.422817 | + | 0.906215i | \(0.638959\pi\) | |||||||
\(542\) | −25.5983 | + | 44.3375i | −1.09954 | + | 1.90446i | ||||
\(543\) | −11.1962 | − | 19.3924i | −0.480474 | − | 0.832206i | ||||
\(544\) | 11.3992 | + | 19.7440i | 0.488736 | + | 0.846515i | ||||
\(545\) | 48.4433 | 2.07508 | ||||||||
\(546\) | −5.56766 | − | 7.26969i | −0.238274 | − | 0.311114i | ||||
\(547\) | −7.89573 | −0.337597 | −0.168798 | − | 0.985651i | \(-0.553989\pi\) | ||||
−0.168798 | + | 0.985651i | \(0.553989\pi\) | |||||||
\(548\) | −3.40820 | − | 5.90317i | −0.145591 | − | 0.252171i | ||||
\(549\) | 0.380923 | + | 0.659778i | 0.0162574 | + | 0.0281586i | ||||
\(550\) | −3.10574 | + | 5.37930i | −0.132429 | + | 0.229374i | ||||
\(551\) | 4.59906 | 0.195927 | ||||||||
\(552\) | −3.78274 | + | 6.55189i | −0.161004 | + | 0.278867i | ||||
\(553\) | 7.52067 | − | 13.0262i | 0.319811 | − | 0.553929i | ||||
\(554\) | 17.1094 | 0.726908 | ||||||||
\(555\) | 0.497334 | − | 0.861408i | 0.0211106 | − | 0.0365647i | ||||
\(556\) | 10.8553 | + | 18.8019i | 0.460368 | + | 0.797380i | ||||
\(557\) | 20.9427 | + | 36.2738i | 0.887369 | + | 1.53697i | 0.842974 | + | 0.537955i | \(0.180803\pi\) |
0.0443955 | + | 0.999014i | \(0.485864\pi\) | |||||||
\(558\) | −12.9286 | −0.547311 | ||||||||
\(559\) | −15.5965 | + | 37.5560i | −0.659662 | + | 1.58845i | ||||
\(560\) | 20.2172 | 0.854333 | ||||||||
\(561\) | −1.84007 | − | 3.18709i | −0.0776878 | − | 0.134559i | ||||
\(562\) | −19.5771 | − | 33.9086i | −0.825812 | − | 1.43035i | ||||
\(563\) | 2.23717 | − | 3.87490i | 0.0942856 | − | 0.163308i | −0.815025 | − | 0.579426i | \(-0.803277\pi\) |
0.909310 | + | 0.416119i | \(0.136610\pi\) | |||||||
\(564\) | 3.42866 | 0.144373 | ||||||||
\(565\) | 16.2141 | − | 28.0837i | 0.682133 | − | 1.18149i | ||||
\(566\) | −14.0049 | + | 24.2571i | −0.588668 | + | 1.01960i | ||||
\(567\) | 1.40886 | 0.0591667 | ||||||||
\(568\) | −2.06526 | + | 3.57713i | −0.0866564 | + | 0.150093i | ||||
\(569\) | 15.7687 | + | 27.3123i | 0.661060 | + | 1.14499i | 0.980337 | + | 0.197328i | \(0.0632265\pi\) |
−0.319277 | + | 0.947661i | \(0.603440\pi\) | |||||||
\(570\) | −6.27010 | − | 10.8601i | −0.262626 | − | 0.454881i | ||||
\(571\) | 15.7405 | 0.658718 | 0.329359 | − | 0.944205i | \(-0.393167\pi\) | ||||
0.329359 | + | 0.944205i | \(0.393167\pi\) | |||||||
\(572\) | 4.46690 | − | 0.583916i | 0.186770 | − | 0.0244147i | ||||
\(573\) | −3.36552 | −0.140597 | ||||||||
\(574\) | 0.172911 | + | 0.299491i | 0.00721717 | + | 0.0125005i | ||||
\(575\) | 9.63396 | + | 16.6865i | 0.401764 | + | 0.695875i | ||||
\(576\) | 0.645805 | − | 1.11857i | 0.0269085 | − | 0.0466070i | ||||
\(577\) | 15.8739 | 0.660841 | 0.330421 | − | 0.943834i | \(-0.392809\pi\) | ||||
0.330421 | + | 0.943834i | \(0.392809\pi\) | |||||||
\(578\) | 3.11545 | − | 5.39612i | 0.129586 | − | 0.224449i | ||||
\(579\) | −9.42520 | + | 16.3249i | −0.391698 | + | 0.678441i | ||||
\(580\) | 6.97627 | 0.289674 | ||||||||
\(581\) | 11.9212 | − | 20.6480i | 0.494573 | − | 0.856625i | ||||
\(582\) | −14.1507 | − | 24.5098i | −0.586566 | − | 1.01596i | ||||
\(583\) | 3.08535 | + | 5.34399i | 0.127782 | + | 0.221325i | ||||
\(584\) | 4.03341 | 0.166904 | ||||||||
\(585\) | 4.01875 | − | 9.67704i | 0.166155 | − | 0.400096i | ||||
\(586\) | 7.46575 | 0.308407 | ||||||||
\(587\) | −7.52675 | − | 13.0367i | −0.310662 | − | 0.538083i | 0.667844 | − | 0.744302i | \(-0.267218\pi\) |
−0.978506 | + | 0.206219i | \(0.933884\pi\) | |||||||
\(588\) | 3.13302 | + | 5.42656i | 0.129204 | + | 0.223787i | ||||
\(589\) | −8.58414 | + | 14.8682i | −0.353703 | + | 0.612632i | ||||
\(590\) | 17.9807 | 0.740252 | ||||||||
\(591\) | 7.15007 | − | 12.3843i | 0.294115 | − | 0.509422i | ||||
\(592\) | 0.845005 | − | 1.46359i | 0.0347295 | − | 0.0601533i | ||||
\(593\) | 6.09765 | 0.250401 | 0.125200 | − | 0.992131i | \(-0.460043\pi\) | ||||
0.125200 | + | 0.992131i | \(0.460043\pi\) | |||||||
\(594\) | −0.901309 | + | 1.56111i | −0.0369812 | + | 0.0640533i | ||||
\(595\) | 7.53396 | + | 13.0492i | 0.308862 | + | 0.534965i | ||||
\(596\) | 8.66699 | + | 15.0117i | 0.355014 | + | 0.614902i | ||||
\(597\) | −23.4216 | −0.958582 | ||||||||
\(598\) | 13.9386 | − | 33.5637i | 0.569990 | − | 1.37252i | ||||
\(599\) | 28.9368 | 1.18232 | 0.591162 | − | 0.806553i | \(-0.298669\pi\) | ||||
0.591162 | + | 0.806553i | \(0.298669\pi\) | |||||||
\(600\) | 2.33106 | + | 4.03752i | 0.0951652 | + | 0.164831i | ||||
\(601\) | −3.68684 | − | 6.38579i | −0.150389 | − | 0.260482i | 0.780981 | − | 0.624554i | \(-0.214719\pi\) |
−0.931371 | + | 0.364073i | \(0.881386\pi\) | |||||||
\(602\) | −14.3219 | + | 24.8062i | −0.583715 | + | 1.01102i | ||||
\(603\) | −9.35878 | −0.381119 | ||||||||
\(604\) | 11.6415 | − | 20.1636i | 0.473685 | − | 0.820446i | ||||
\(605\) | 1.45308 | − | 2.51681i | 0.0590763 | − | 0.102323i | ||||
\(606\) | 1.97714 | 0.0803157 | ||||||||
\(607\) | −11.9548 | + | 20.7062i | −0.485229 | + | 0.840441i | −0.999856 | − | 0.0169733i | \(-0.994597\pi\) |
0.514627 | + | 0.857414i | \(0.327930\pi\) | |||||||
\(608\) | −7.41463 | − | 12.8425i | −0.300703 | − | 0.520833i | ||||
\(609\) | 1.35341 | + | 2.34417i | 0.0548428 | + | 0.0949904i | ||||
\(610\) | 3.99109 | 0.161595 | ||||||||
\(611\) | 9.81078 | − | 1.28247i | 0.396901 | − | 0.0518832i | ||||
\(612\) | 4.59809 | 0.185867 | ||||||||
\(613\) | −0.922977 | − | 1.59864i | −0.0372787 | − | 0.0645686i | 0.846784 | − | 0.531937i | \(-0.178536\pi\) |
−0.884063 | + | 0.467368i | \(0.845202\pi\) | |||||||
\(614\) | −25.2771 | − | 43.7813i | −1.02010 | − | 1.76687i | ||||
\(615\) | −0.197866 | + | 0.342714i | −0.00797872 | + | 0.0138196i | ||||
\(616\) | −1.90617 | −0.0768017 | ||||||||
\(617\) | 0.374827 | − | 0.649219i | 0.0150900 | − | 0.0261366i | −0.858382 | − | 0.513011i | \(-0.828530\pi\) |
0.873472 | + | 0.486875i | \(0.161863\pi\) | |||||||
\(618\) | 1.97712 | − | 3.42448i | 0.0795316 | − | 0.137753i | ||||
\(619\) | −40.6177 | −1.63256 | −0.816282 | − | 0.577654i | \(-0.803968\pi\) | ||||
−0.816282 | + | 0.577654i | \(0.803968\pi\) | |||||||
\(620\) | −13.0212 | + | 22.5534i | −0.522944 | + | 0.905766i | ||||
\(621\) | 2.79585 | + | 4.84255i | 0.112194 | + | 0.194325i | ||||
\(622\) | 19.3563 | + | 33.5261i | 0.776117 | + | 1.34427i | ||||
\(623\) | −21.1741 | −0.848322 | ||||||||
\(624\) | 6.82814 | − | 16.4420i | 0.273344 | − | 0.658206i | ||||
\(625\) | −30.3554 | −1.21422 | ||||||||
\(626\) | 21.4512 | + | 37.1546i | 0.857363 | + | 1.48500i | ||||
\(627\) | 1.19688 | + | 2.07305i | 0.0477987 | + | 0.0827898i | ||||
\(628\) | −5.76989 | + | 9.99374i | −0.230244 | + | 0.398794i | ||||
\(629\) | 1.25957 | 0.0502222 | ||||||||
\(630\) | 3.69031 | − | 6.39181i | 0.147026 | − | 0.254656i | ||||
\(631\) | −6.96959 | + | 12.0717i | −0.277455 | + | 0.480566i | −0.970752 | − | 0.240086i | \(-0.922824\pi\) |
0.693296 | + | 0.720652i | \(0.256158\pi\) | |||||||
\(632\) | 14.4448 | 0.574581 | ||||||||
\(633\) | −3.30355 | + | 5.72192i | −0.131304 | + | 0.227426i | ||||
\(634\) | 14.7700 | + | 25.5824i | 0.586592 | + | 1.01601i | ||||
\(635\) | 18.1281 | + | 31.3987i | 0.719390 | + | 1.24602i | ||||
\(636\) | −7.70990 | −0.305717 | ||||||||
\(637\) | 10.9946 | + | 14.3557i | 0.435622 | + | 0.568792i | ||||
\(638\) | −3.46332 | −0.137114 | ||||||||
\(639\) | 1.52645 | + | 2.64389i | 0.0603854 | + | 0.104591i | ||||
\(640\) | 14.6204 | + | 25.3233i | 0.577924 | + | 1.00099i | ||||
\(641\) | −19.9399 | + | 34.5370i | −0.787580 | + | 1.36413i | 0.139865 | + | 0.990171i | \(0.455333\pi\) |
−0.927445 | + | 0.373959i | \(0.878000\pi\) | |||||||
\(642\) | −11.4309 | −0.451140 | ||||||||
\(643\) | −4.08268 | + | 7.07141i | −0.161005 | + | 0.278869i | −0.935229 | − | 0.354042i | \(-0.884807\pi\) |
0.774224 | + | 0.632911i | \(0.218140\pi\) | |||||||
\(644\) | 4.92148 | − | 8.52425i | 0.193933 | − | 0.335903i | ||||
\(645\) | −32.7776 | −1.29062 | ||||||||
\(646\) | 7.93995 | − | 13.7524i | 0.312393 | − | 0.541081i | ||||
\(647\) | −7.49759 | − | 12.9862i | −0.294761 | − | 0.510540i | 0.680169 | − | 0.733056i | \(-0.261907\pi\) |
−0.974929 | + | 0.222515i | \(0.928573\pi\) | |||||||
\(648\) | 0.676492 | + | 1.17172i | 0.0265751 | + | 0.0460294i | ||||
\(649\) | −3.43227 | −0.134728 | ||||||||
\(650\) | −13.6174 | − | 17.7803i | −0.534119 | − | 0.697400i | ||||
\(651\) | −10.1045 | −0.396027 | ||||||||
\(652\) | −4.94133 | − | 8.55864i | −0.193517 | − | 0.335182i | ||||
\(653\) | −10.4219 | − | 18.0513i | −0.407841 | − | 0.706401i | 0.586807 | − | 0.809727i | \(-0.300385\pi\) |
−0.994648 | + | 0.103326i | \(0.967051\pi\) | |||||||
\(654\) | 15.0240 | − | 26.0224i | 0.587487 | − | 1.01756i | ||||
\(655\) | −11.8437 | −0.462772 | ||||||||
\(656\) | −0.336188 | + | 0.582295i | −0.0131259 | + | 0.0227348i | ||||
\(657\) | 1.49056 | − | 2.58173i | 0.0581524 | − | 0.100723i | ||||
\(658\) | 6.96921 | 0.271688 | ||||||||
\(659\) | −14.7195 | + | 25.4948i | −0.573389 | + | 0.993138i | 0.422826 | + | 0.906211i | \(0.361038\pi\) |
−0.996215 | + | 0.0869272i | \(0.972295\pi\) | |||||||
\(660\) | 1.81553 | + | 3.14460i | 0.0706695 | + | 0.122403i | ||||
\(661\) | 15.5971 | + | 27.0150i | 0.606657 | + | 1.05076i | 0.991787 | + | 0.127899i | \(0.0408232\pi\) |
−0.385130 | + | 0.922862i | \(0.625843\pi\) | |||||||
\(662\) | 29.2276 | 1.13596 | ||||||||
\(663\) | 13.1570 | − | 1.71989i | 0.510975 | − | 0.0667950i | ||||
\(664\) | 22.8967 | 0.888563 | ||||||||
\(665\) | −4.90049 | − | 8.48789i | −0.190033 | − | 0.329146i | ||||
\(666\) | −0.308483 | − | 0.534308i | −0.0119535 | − | 0.0207040i | ||||
\(667\) | −5.37159 | + | 9.30387i | −0.207989 | + | 0.360247i | ||||
\(668\) | −25.8162 | −0.998860 | ||||||||
\(669\) | −0.176270 | + | 0.305309i | −0.00681501 | + | 0.0118039i | ||||
\(670\) | −24.5140 | + | 42.4595i | −0.947058 | + | 1.64035i | ||||
\(671\) | −0.761846 | −0.0294107 | ||||||||
\(672\) | 4.36393 | − | 7.55855i | 0.168342 | − | 0.291578i | ||||
\(673\) | 0.693334 | + | 1.20089i | 0.0267261 | + | 0.0462909i | 0.879079 | − | 0.476676i | \(-0.158158\pi\) |
−0.852353 | + | 0.522967i | \(0.824825\pi\) | |||||||
\(674\) | −12.5883 | − | 21.8036i | −0.484884 | − | 0.839845i | ||||
\(675\) | 3.44581 | 0.132629 | ||||||||
\(676\) | −4.23265 | + | 15.6815i | −0.162794 | + | 0.603133i | ||||
\(677\) | 23.5904 | 0.906654 | 0.453327 | − | 0.891344i | \(-0.350237\pi\) | ||||
0.453327 | + | 0.891344i | \(0.350237\pi\) | |||||||
\(678\) | −10.0572 | − | 17.4196i | −0.386244 | − | 0.668994i | ||||
\(679\) | −11.0597 | − | 19.1560i | −0.424432 | − | 0.735139i | ||||
\(680\) | −7.23514 | + | 12.5316i | −0.277455 | + | 0.480566i | ||||
\(681\) | −8.21012 | −0.314613 | ||||||||
\(682\) | 6.46429 | − | 11.1965i | 0.247530 | − | 0.428735i | ||||
\(683\) | −9.73997 | + | 16.8701i | −0.372690 | + | 0.645517i | −0.989978 | − | 0.141219i | \(-0.954898\pi\) |
0.617289 | + | 0.786737i | \(0.288231\pi\) | |||||||
\(684\) | −2.99084 | −0.114358 | ||||||||
\(685\) | 7.92742 | − | 13.7307i | 0.302891 | − | 0.524623i | ||||
\(686\) | 15.2570 | + | 26.4260i | 0.582516 | + | 1.00895i | ||||
\(687\) | −3.90496 | − | 6.76358i | −0.148983 | − | 0.258047i | ||||
\(688\) | −55.6915 | −2.12322 | ||||||||
\(689\) | −22.0611 | + | 2.88384i | −0.840462 | + | 0.109866i | ||||
\(690\) | 29.2933 | 1.11518 | ||||||||
\(691\) | 16.9880 | + | 29.4241i | 0.646254 | + | 1.11935i | 0.984010 | + | 0.178112i | \(0.0569988\pi\) |
−0.337756 | + | 0.941234i | \(0.609668\pi\) | |||||||
\(692\) | −2.10826 | − | 3.65161i | −0.0801438 | − | 0.138813i | ||||
\(693\) | −0.704431 | + | 1.22011i | −0.0267591 | + | 0.0463482i | ||||
\(694\) | −7.86873 | −0.298693 | ||||||||
\(695\) | −25.2493 | + | 43.7331i | −0.957760 | + | 1.65889i | ||||
\(696\) | −1.29973 | + | 2.25119i | −0.0492660 | + | 0.0853312i | ||||
\(697\) | −0.501123 | −0.0189814 | ||||||||
\(698\) | 23.6052 | − | 40.8855i | 0.893472 | − | 1.54754i | ||||
\(699\) | 3.57660 | + | 6.19485i | 0.135279 | + | 0.234311i | ||||
\(700\) | −3.03280 | − | 5.25296i | −0.114629 | − | 0.198543i | ||||
\(701\) | −4.91282 | −0.185555 | −0.0927773 | − | 0.995687i | \(-0.529574\pi\) | ||||
−0.0927773 | + | 0.995687i | \(0.529574\pi\) | |||||||
\(702\) | −3.95188 | − | 5.15997i | −0.149154 | − | 0.194751i | ||||
\(703\) | −0.819289 | −0.0309001 | ||||||||
\(704\) | 0.645805 | + | 1.11857i | 0.0243397 | + | 0.0421576i | ||||
\(705\) | 3.98751 | + | 6.90657i | 0.150178 | + | 0.260116i | ||||
\(706\) | −25.9055 | + | 44.8697i | −0.974967 | + | 1.68869i | ||||
\(707\) | 1.54526 | 0.0581155 | ||||||||
\(708\) | 2.14420 | − | 3.71386i | 0.0805839 | − | 0.139575i | ||||
\(709\) | −4.41523 | + | 7.64740i | −0.165817 | + | 0.287204i | −0.936945 | − | 0.349476i | \(-0.886360\pi\) |
0.771128 | + | 0.636680i | \(0.219693\pi\) | |||||||
\(710\) | 15.9933 | 0.600216 | ||||||||
\(711\) | 5.33811 | − | 9.24588i | 0.200195 | − | 0.346748i | ||||
\(712\) | −10.1671 | − | 17.6100i | −0.381029 | − | 0.659962i | ||||
\(713\) | −20.0521 | − | 34.7313i | −0.750958 | − | 1.30070i | ||||
\(714\) | 9.34623 | 0.349774 | ||||||||
\(715\) | 6.37119 | + | 8.31886i | 0.238269 | + | 0.311108i | ||||
\(716\) | 16.0362 | 0.599299 | ||||||||
\(717\) | 6.41787 | + | 11.1161i | 0.239680 | + | 0.415138i | ||||
\(718\) | 29.5688 | + | 51.2147i | 1.10350 | + | 1.91131i | ||||
\(719\) | 13.1970 | − | 22.8578i | 0.492164 | − | 0.852453i | −0.507795 | − | 0.861478i | \(-0.669539\pi\) |
0.999959 | + | 0.00902447i | \(0.00287262\pi\) | |||||||
\(720\) | 14.3500 | 0.534794 | ||||||||
\(721\) | 1.54525 | − | 2.67645i | 0.0575481 | − | 0.0996762i | ||||
\(722\) | 11.9603 | − | 20.7159i | 0.445117 | − | 0.770965i | ||||
\(723\) | 17.4050 | 0.647298 | ||||||||
\(724\) | −13.9889 | + | 24.2295i | −0.519894 | + | 0.900482i | ||||
\(725\) | 3.31017 | + | 5.73339i | 0.122937 | + | 0.212933i | ||||
\(726\) | −0.901309 | − | 1.56111i | −0.0334507 | − | 0.0579384i | ||||
\(727\) | 18.0047 | 0.667756 | 0.333878 | − | 0.942616i | \(-0.391643\pi\) | ||||
0.333878 | + | 0.942616i | \(0.391643\pi\) | |||||||
\(728\) | 2.63592 | − | 6.34721i | 0.0976936 | − | 0.235243i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.80863 | − | 13.5249i | −0.289010 | − | 0.500581i | ||||
\(731\) | −20.7535 | − | 35.9461i | −0.767595 | − | 1.32951i | ||||
\(732\) | 0.475938 | − | 0.824349i | 0.0175912 | − | 0.0304688i | ||||
\(733\) | 7.43903 | 0.274767 | 0.137383 | − | 0.990518i | \(-0.456131\pi\) | ||||
0.137383 | + | 0.990518i | \(0.456131\pi\) | |||||||
\(734\) | −21.5250 | + | 37.2824i | −0.794502 | + | 1.37612i | ||||
\(735\) | −7.28737 | + | 12.6221i | −0.268799 | + | 0.465573i | ||||
\(736\) | 34.6404 | 1.27686 | ||||||||
\(737\) | 4.67939 | − | 8.10495i | 0.172368 | − | 0.298549i | ||||
\(738\) | 0.122731 | + | 0.212576i | 0.00451779 | + | 0.00782504i | ||||
\(739\) | 6.52566 | + | 11.3028i | 0.240050 | + | 0.415779i | 0.960728 | − | 0.277490i | \(-0.0895027\pi\) |
−0.720678 | + | 0.693270i | \(0.756169\pi\) | |||||||
\(740\) | −1.24277 | −0.0456852 | ||||||||
\(741\) | −8.55800 | + | 1.11871i | −0.314386 | + | 0.0410967i | ||||
\(742\) | −15.6714 | −0.575315 | ||||||||
\(743\) | 1.89661 | + | 3.28502i | 0.0695797 | + | 0.120516i | 0.898716 | − | 0.438530i | \(-0.144501\pi\) |
−0.829137 | + | 0.559046i | \(0.811168\pi\) | |||||||
\(744\) | −4.85187 | − | 8.40369i | −0.177878 | − | 0.308094i | ||||
\(745\) | −20.1593 | + | 34.9169i | −0.738579 | + | 1.27926i | ||||
\(746\) | 37.6769 | 1.37945 | ||||||||
\(747\) | 8.46154 | − | 14.6558i | 0.309592 | − | 0.536229i | ||||
\(748\) | −2.29905 | + | 3.98206i | −0.0840614 | + | 0.145599i | ||||
\(749\) | −8.93396 | −0.326440 | ||||||||
\(750\) | −4.07098 | + | 7.05114i | −0.148651 | + | 0.257471i | ||||
\(751\) | −7.10884 | − | 12.3129i | −0.259405 | − | 0.449303i | 0.706677 | − | 0.707536i | \(-0.250193\pi\) |
−0.966083 | + | 0.258233i | \(0.916860\pi\) | |||||||
\(752\) | 6.77506 | + | 11.7347i | 0.247061 | + | 0.427922i | ||||
\(753\) | −13.6688 | −0.498118 | ||||||||
\(754\) | 4.78921 | − | 11.5323i | 0.174413 | − | 0.419981i | ||||
\(755\) | 54.1558 | 1.97093 | ||||||||
\(756\) | −0.880141 | − | 1.52445i | −0.0320104 | − | 0.0554437i | ||||
\(757\) | −11.5235 | − | 19.9593i | −0.418830 | − | 0.725434i | 0.576992 | − | 0.816749i | \(-0.304226\pi\) |
−0.995822 | + | 0.0913154i | \(0.970893\pi\) | |||||||
\(758\) | 28.6581 | − | 49.6373i | 1.04091 | − | 1.80291i | ||||
\(759\) | −5.59170 | −0.202966 | ||||||||
\(760\) | 4.70612 | − | 8.15124i | 0.170709 | − | 0.295677i | ||||
\(761\) | 16.8109 | − | 29.1173i | 0.609394 | − | 1.05550i | −0.381947 | − | 0.924184i | \(-0.624746\pi\) |
0.991340 | − | 0.131317i | \(-0.0419205\pi\) | |||||||
\(762\) | 22.4887 | 0.814680 | ||||||||
\(763\) | 11.7423 | − | 20.3382i | 0.425098 | − | 0.736292i | ||||
\(764\) | 2.10250 | + | 3.64163i | 0.0760657 | + | 0.131750i | ||||
\(765\) | 5.34755 | + | 9.26223i | 0.193341 | + | 0.334876i | ||||
\(766\) | −41.7174 | −1.50731 | ||||||||
\(767\) | 4.74626 | − | 11.4289i | 0.171378 | − | 0.412672i | ||||
\(768\) | 20.7206 | 0.747689 | ||||||||
\(769\) | −12.4722 | − | 21.6025i | −0.449760 | − | 0.779007i | 0.548610 | − | 0.836078i | \(-0.315157\pi\) |
−0.998370 | + | 0.0570715i | \(0.981824\pi\) | |||||||
\(770\) | 3.69031 | + | 6.39181i | 0.132990 | + | 0.230345i | ||||
\(771\) | 10.6347 | − | 18.4198i | 0.382998 | − | 0.663372i | ||||
\(772\) | 23.5523 | 0.847667 | ||||||||
\(773\) | 23.7783 | − | 41.1853i | 0.855247 | − | 1.48133i | −0.0211691 | − | 0.999776i | \(-0.506739\pi\) |
0.876416 | − | 0.481555i | \(-0.159928\pi\) | |||||||
\(774\) | −10.1655 | + | 17.6072i | −0.365393 | + | 0.632879i | ||||
\(775\) | −24.7137 | −0.887743 | ||||||||
\(776\) | 10.6210 | − | 18.3962i | 0.381273 | − | 0.660385i | ||||
\(777\) | −0.241099 | − | 0.417596i | −0.00864939 | − | 0.0149812i | ||||
\(778\) | 20.1512 | + | 34.9029i | 0.722455 | + | 1.25133i | ||||
\(779\) | 0.325957 | 0.0116786 | ||||||||
\(780\) | −12.9816 | + | 1.69696i | −0.464814 | + | 0.0607608i | ||||
\(781\) | −3.05290 | −0.109241 | ||||||||
\(782\) | 18.5473 | + | 32.1249i | 0.663251 | + | 1.14879i | ||||
\(783\) | 0.960637 | + | 1.66387i | 0.0343304 | + | 0.0594619i | ||||
\(784\) | −12.3818 | + | 21.4458i | −0.442205 | + | 0.765922i | ||||
\(785\) | −26.8414 | −0.958010 | ||||||||
\(786\) | −3.67317 | + | 6.36212i | −0.131018 | + | 0.226929i | ||||
\(787\) | −0.521877 | + | 0.903918i | −0.0186029 | + | 0.0322212i | −0.875177 | − | 0.483803i | \(-0.839255\pi\) |
0.856574 | + | 0.516024i | \(0.172589\pi\) | |||||||
\(788\) | −17.8671 | −0.636489 | ||||||||
\(789\) | −7.32697 | + | 12.6907i | −0.260847 | + | 0.451800i | ||||
\(790\) | −27.9648 | − | 48.4365i | −0.994944 | − | 1.72329i | ||||
\(791\) | −7.86034 | − | 13.6145i | −0.279482 | − | 0.484076i | ||||
\(792\) | −1.35298 | −0.0480762 | ||||||||
\(793\) | 1.05351 | − | 2.53682i | 0.0374112 | − | 0.0900850i | ||||
\(794\) | 40.8996 | 1.45147 | ||||||||
\(795\) | −8.96656 | − | 15.5305i | −0.318011 | − | 0.550811i | ||||
\(796\) | 14.6319 | + | 25.3432i | 0.518613 | + | 0.898264i | ||||
\(797\) | 17.0522 | − | 29.5353i | 0.604020 | − | 1.04619i | −0.388185 | − | 0.921581i | \(-0.626898\pi\) |
0.992206 | − | 0.124612i | \(-0.0397687\pi\) | |||||||
\(798\) | −6.07928 | −0.215204 | ||||||||
\(799\) | −5.04946 | + | 8.74592i | −0.178637 | + | 0.309408i | ||||
\(800\) | 10.6733 | − | 18.4868i | 0.377360 | − | 0.653606i | ||||
\(801\) | −15.0292 | −0.531031 | ||||||||
\(802\) | 29.2000 | − | 50.5758i | 1.03109 | − | 1.78589i | ||||
\(803\) | 1.49056 | + | 2.58173i | 0.0526008 | + | 0.0911073i | ||||
\(804\) | 5.84659 | + | 10.1266i | 0.206193 | + | 0.357138i | ||||
\(805\) | 22.8946 | 0.806928 | ||||||||
\(806\) | 28.3433 | + | 37.0079i | 0.998351 | + | 1.30355i | ||||
\(807\) | 16.7810 | 0.590720 | ||||||||
\(808\) | 0.741986 | + | 1.28516i | 0.0261030 | + | 0.0452117i | ||||
\(809\) | 13.7471 | + | 23.8107i | 0.483322 | + | 0.837139i | 0.999817 | − | 0.0191519i | \(-0.00609661\pi\) |
−0.516494 | + | 0.856291i | \(0.672763\pi\) | |||||||
\(810\) | 2.61936 | − | 4.53686i | 0.0920348 | − | 0.159409i | ||||
\(811\) | 27.9591 | 0.981778 | 0.490889 | − | 0.871222i | \(-0.336672\pi\) | ||||
0.490889 | + | 0.871222i | \(0.336672\pi\) | |||||||
\(812\) | 1.69099 | − | 2.92888i | 0.0593422 | − | 0.102784i | ||||
\(813\) | −14.2006 | + | 24.5962i | −0.498037 | + | 0.862626i | ||||
\(814\) | 0.616966 | 0.0216246 | ||||||||
\(815\) | 11.4935 | − | 19.9073i | 0.402599 | − | 0.697321i | ||||
\(816\) | 9.08586 | + | 15.7372i | 0.318069 | + | 0.550911i | ||||
\(817\) | 13.4992 | + | 23.3812i | 0.472276 | + | 0.818006i | ||||
\(818\) | −48.4801 | −1.69507 | ||||||||
\(819\) | −3.08865 | − | 4.03285i | −0.107926 | − | 0.140919i | ||||
\(820\) | 0.494441 | 0.0172666 | ||||||||
\(821\) | −20.9045 | − | 36.2077i | −0.729574 | − | 1.26366i | −0.957064 | − | 0.289878i | \(-0.906385\pi\) |
0.227490 | − | 0.973780i | \(-0.426948\pi\) | |||||||
\(822\) | −4.91717 | − | 8.51679i | −0.171506 | − | 0.297057i | ||||
\(823\) | 8.70855 | − | 15.0836i | 0.303561 | − | 0.525783i | −0.673379 | − | 0.739297i | \(-0.735158\pi\) |
0.976940 | + | 0.213515i | \(0.0684911\pi\) | |||||||
\(824\) | 2.96792 | 0.103392 | ||||||||
\(825\) | −1.72290 | + | 2.98416i | −0.0599838 | + | 0.103895i | ||||
\(826\) | 4.35837 | − | 7.54891i | 0.151647 | − | 0.262660i | ||||
\(827\) | −34.9915 | −1.21677 | −0.608387 | − | 0.793641i | \(-0.708183\pi\) | ||||
−0.608387 | + | 0.793641i | \(0.708183\pi\) | |||||||
\(828\) | 3.49323 | − | 6.05045i | 0.121398 | − | 0.210268i | ||||
\(829\) | −1.73570 | − | 3.00632i | −0.0602834 | − | 0.104414i | 0.834309 | − | 0.551298i | \(-0.185867\pi\) |
−0.894592 | + | 0.446884i | \(0.852534\pi\) | |||||||
\(830\) | −44.3276 | − | 76.7776i | −1.53863 | − | 2.66499i | ||||
\(831\) | 9.49141 | 0.329253 | ||||||||
\(832\) | −4.61768 | + | 0.603626i | −0.160089 | + | 0.0209270i | ||||
\(833\) | −18.4563 | −0.639472 | ||||||||
\(834\) | 15.6615 | + | 27.1265i | 0.542312 | + | 0.939313i | ||||
\(835\) | −30.0241 | − | 52.0032i | −1.03903 | − | 1.79965i | ||||
\(836\) | 1.49542 | − | 2.59015i | 0.0517202 | − | 0.0895820i | ||||
\(837\) | −7.17211 | −0.247904 | ||||||||
\(838\) | −21.2768 | + | 36.8525i | −0.734995 | + | 1.27305i | ||||
\(839\) | −27.5672 | + | 47.7479i | −0.951727 | + | 1.64844i | −0.210041 | + | 0.977693i | \(0.567360\pi\) |
−0.741686 | + | 0.670747i | \(0.765974\pi\) | |||||||
\(840\) | 5.53964 | 0.191136 | ||||||||
\(841\) | 12.6544 | − | 21.9180i | 0.436357 | − | 0.755793i | ||||
\(842\) | −22.8102 | − | 39.5084i | −0.786091 | − | 1.36155i | ||||
\(843\) | −10.8604 | − | 18.8107i | −0.374052 | − | 0.647876i | ||||
\(844\) | 8.25514 | 0.284154 | ||||||||
\(845\) | −36.5107 | + | 9.71135i | −1.25601 | + | 0.334081i | ||||
\(846\) | 4.94669 | 0.170071 | ||||||||
\(847\) | −0.704431 | − | 1.22011i | −0.0242045 | − | 0.0419235i | ||||
\(848\) | −15.2348 | − | 26.3875i | −0.523165 | − | 0.906149i | ||||
\(849\) | −7.76918 | + | 13.4566i | −0.266637 | + | 0.461830i | ||||
\(850\) | 22.8591 | 0.784061 | ||||||||
\(851\) | 0.956910 | − | 1.65742i | 0.0328024 | − | 0.0568155i | ||||
\(852\) | 1.90720 | − | 3.30336i | 0.0653395 | − | 0.113171i | ||||
\(853\) | 34.9221 | 1.19571 | 0.597855 | − | 0.801604i | \(-0.296020\pi\) | ||||
0.597855 | + | 0.801604i | \(0.296020\pi\) | |||||||
\(854\) | 0.967408 | − | 1.67560i | 0.0331040 | − | 0.0573378i | ||||
\(855\) | −3.47833 | − | 6.02464i | −0.118956 | − | 0.206038i | ||||
\(856\) | −4.28981 | − | 7.43016i | −0.146623 | − | 0.253958i | ||||
\(857\) | −23.2086 | −0.792790 | −0.396395 | − | 0.918080i | \(-0.629739\pi\) | ||||
−0.396395 | + | 0.918080i | \(0.629739\pi\) | |||||||
\(858\) | 6.44461 | − | 0.842443i | 0.220015 | − | 0.0287605i | ||||
\(859\) | 26.8142 | 0.914889 | 0.457444 | − | 0.889238i | \(-0.348765\pi\) | ||||
0.457444 | + | 0.889238i | \(0.348765\pi\) | |||||||
\(860\) | 20.4767 | + | 35.4668i | 0.698251 | + | 1.20941i | ||||
\(861\) | 0.0959222 | + | 0.166142i | 0.00326902 | + | 0.00566211i | ||||
\(862\) | −12.2483 | + | 21.2146i | −0.417177 | + | 0.722572i | ||||
\(863\) | −26.5007 | −0.902096 | −0.451048 | − | 0.892500i | \(-0.648950\pi\) | ||||
−0.451048 | + | 0.892500i | \(0.648950\pi\) | |||||||
\(864\) | 3.09749 | − | 5.36500i | 0.105379 | − | 0.182521i | ||||
\(865\) | 4.90377 | − | 8.49358i | 0.166733 | − | 0.288791i | ||||
\(866\) | 20.7763 | 0.706009 | ||||||||
\(867\) | 1.72829 | − | 2.99349i | 0.0586959 | − | 0.101664i | ||||
\(868\) | 6.31247 | + | 10.9335i | 0.214259 | + | 0.371108i | ||||
\(869\) | 5.33811 | + | 9.24588i | 0.181083 | + | 0.313645i | ||||
\(870\) | 10.0650 | 0.341235 | ||||||||
\(871\) | 20.5173 | + | 26.7894i | 0.695201 | + | 0.907724i | ||||
\(872\) | 22.5531 | 0.763743 | ||||||||
\(873\) | −7.85009 | − | 13.5968i | −0.265685 | − | 0.460181i | ||||
\(874\) | −12.0642 | − | 20.8958i | −0.408077 | − | 0.706809i | ||||
\(875\) | −3.18173 | + | 5.51092i | −0.107562 | + | 0.186303i | ||||
\(876\) | −3.72472 | −0.125847 | ||||||||
\(877\) | 10.2439 | − | 17.7429i | 0.345911 | − | 0.599136i | −0.639608 | − | 0.768701i | \(-0.720903\pi\) |
0.985519 | + | 0.169566i | \(0.0542365\pi\) | |||||||
\(878\) | −13.7613 | + | 23.8352i | −0.464420 | + | 0.804399i | ||||
\(879\) | 4.14161 | 0.139693 | ||||||||
\(880\) | −7.17501 | + | 12.4275i | −0.241870 | + | 0.418930i | ||||
\(881\) | −22.6724 | − | 39.2697i | −0.763852 | − | 1.32303i | −0.940851 | − | 0.338820i | \(-0.889972\pi\) |
0.176999 | − | 0.984211i | \(-0.443361\pi\) | |||||||
\(882\) | 4.52016 | + | 7.82915i | 0.152202 | + | 0.263621i | ||||
\(883\) | −31.1709 | −1.04898 | −0.524491 | − | 0.851416i | \(-0.675745\pi\) | ||||
−0.524491 | + | 0.851416i | \(0.675745\pi\) | |||||||
\(884\) | −10.0804 | − | 13.1620i | −0.339040 | − | 0.442685i | ||||
\(885\) | 9.97474 | 0.335297 | ||||||||
\(886\) | −16.7145 | − | 28.9504i | −0.561536 | − | 0.972608i | ||||
\(887\) | −19.5965 | − | 33.9422i | −0.657987 | − | 1.13967i | −0.981136 | − | 0.193319i | \(-0.938075\pi\) |
0.323149 | − | 0.946348i | \(-0.395258\pi\) | |||||||
\(888\) | 0.231537 | − | 0.401033i | 0.00776986 | − | 0.0134578i | ||||
\(889\) | 17.5764 | 0.589493 | ||||||||
\(890\) | −39.3668 | + | 68.1854i | −1.31958 | + | 2.28558i | ||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | 0.440477 | 0.0147482 | ||||||||
\(893\) | 3.28444 | − | 5.68881i | 0.109909 | − | 0.190369i | ||||
\(894\) | 12.5043 | + | 21.6580i | 0.418206 | + | 0.724353i | ||||
\(895\) | 18.6499 | + | 32.3026i | 0.623399 | + | 1.07976i | ||||
\(896\) | 14.1755 | 0.473570 | ||||||||
\(897\) | 7.73240 | − | 18.6194i | 0.258177 | − | 0.621683i | ||||
\(898\) | 21.7276 | 0.725060 | ||||||||
\(899\) | −6.88979 | − | 11.9335i | −0.229788 | − | 0.398004i | ||||
\(900\) | −2.15266 | − | 3.72851i | −0.0717552 | − | 0.124284i | ||||
\(901\) | 11.3545 | − | 19.6666i | 0.378274 | − | 0.655190i | ||||
\(902\) | −0.245462 | −0.00817299 | ||||||||
\(903\) | −7.94503 | + | 13.7612i | −0.264394 | + | 0.457944i | ||||
\(904\) | 7.54858 | − | 13.0745i | 0.251062 | − | 0.434852i | ||||
\(905\) | −65.0760 | −2.16320 | ||||||||
\(906\) | 16.7957 | − | 29.0910i | 0.558000 | − | 0.966484i | ||||
\(907\) | −13.6017 | − | 23.5589i | −0.451638 | − | 0.782259i | 0.546850 | − | 0.837230i | \(-0.315827\pi\) |
−0.998488 | + | 0.0549710i | \(0.982493\pi\) | |||||||
\(908\) | 5.12901 | + | 8.88370i | 0.170212 | + | 0.294816i | ||||
\(909\) | 1.09681 | 0.0363790 | ||||||||
\(910\) | −26.3867 | + | 3.44929i | −0.874712 | + | 0.114343i | ||||
\(911\) | 6.55704 | 0.217244 | 0.108622 | − | 0.994083i | \(-0.465356\pi\) | ||||
0.108622 | + | 0.994083i | \(0.465356\pi\) | |||||||
\(912\) | −5.90992 | − | 10.2363i | −0.195697 | − | 0.338957i | ||||
\(913\) | 8.46154 | + | 14.6558i | 0.280036 | + | 0.485037i | ||||
\(914\) | −17.0223 | + | 29.4834i | −0.563046 | + | 0.975225i | ||||
\(915\) | 2.21405 | 0.0731943 | ||||||||
\(916\) | −4.87899 | + | 8.45065i | −0.161206 | + | 0.279217i | ||||
\(917\) | −2.87082 | + | 4.97240i | −0.0948028 | + | 0.164203i | ||||
\(918\) | 6.63389 | 0.218951 | ||||||||
\(919\) | −8.99063 | + | 15.5722i | −0.296573 | + | 0.513680i | −0.975350 | − | 0.220665i | \(-0.929177\pi\) |
0.678776 | + | 0.734345i | \(0.262511\pi\) | |||||||
\(920\) | 10.9933 | + | 19.0409i | 0.362437 | + | 0.627760i | ||||
\(921\) | −14.0225 | − | 24.2876i | −0.462056 | − | 0.800304i | ||||
\(922\) | 17.8203 | 0.586880 | ||||||||
\(923\) | 4.22166 | − | 10.1656i | 0.138958 | − | 0.334606i | ||||
\(924\) | 1.76028 | 0.0579090 | ||||||||
\(925\) | −0.589683 | − | 1.02136i | −0.0193887 | − | 0.0335821i | ||||
\(926\) | −11.0367 | − | 19.1161i | −0.362688 | − | 0.628193i | ||||
\(927\) | 1.09681 | − | 1.89972i | 0.0360239 | − | 0.0623951i | ||||
\(928\) | 11.9022 | 0.390710 | ||||||||
\(929\) | 3.40346 | − | 5.89497i | 0.111664 | − | 0.193408i | −0.804777 | − | 0.593577i | \(-0.797715\pi\) |
0.916441 | + | 0.400169i | \(0.131049\pi\) | |||||||
\(930\) | −18.7863 | + | 32.5388i | −0.616027 | + | 1.06699i | ||||
\(931\) | 12.0049 | 0.393446 | ||||||||
\(932\) | 4.46872 | − | 7.74006i | 0.146378 | − | 0.253534i | ||||
\(933\) | 10.7379 | + | 18.5986i | 0.351543 | + | 0.608889i | ||||
\(934\) | −38.2298 | − | 66.2159i | −1.25092 | − | 2.16665i | ||||
\(935\) | −10.6951 | −0.349767 | ||||||||
\(936\) | 1.87095 | − | 4.50520i | 0.0611540 | − | 0.147257i | ||||
\(937\) | 16.8541 | 0.550600 | 0.275300 | − | 0.961358i | \(-0.411223\pi\) | ||||
0.275300 | + | 0.961358i | \(0.411223\pi\) | |||||||
\(938\) | 11.8840 | + | 20.5837i | 0.388026 | + | 0.672080i | ||||
\(939\) | 11.9000 | + | 20.6115i | 0.388343 | + | 0.672630i | ||||
\(940\) | 4.98213 | − | 8.62930i | 0.162499 | − | 0.281457i | ||||
\(941\) | −41.9816 | −1.36856 | −0.684280 | − | 0.729219i | \(-0.739883\pi\) | ||||
−0.684280 | + | 0.729219i | \(0.739883\pi\) | |||||||
\(942\) | −8.32450 | + | 14.4185i | −0.271227 | + | 0.469778i | ||||
\(943\) | −0.380710 | + | 0.659408i | −0.0123976 | + | 0.0214733i | ||||
\(944\) | 16.9478 | 0.551604 | ||||||||
\(945\) | 2.04720 | − | 3.54585i | 0.0665953 | − | 0.115346i | ||||
\(946\) | −10.1655 | − | 17.6072i | −0.330510 | − | 0.572461i | ||||
\(947\) | −4.91811 | − | 8.51841i | −0.159817 | − | 0.276811i | 0.774986 | − | 0.631979i | \(-0.217757\pi\) |
−0.934803 | + | 0.355168i | \(0.884424\pi\) | |||||||
\(948\) | −13.3392 | −0.433238 | ||||||||
\(949\) | −10.6579 | + | 1.39321i | −0.345971 | + | 0.0452255i | ||||
\(950\) | −14.8688 | −0.482407 | ||||||||
\(951\) | 8.19364 | + | 14.1918i | 0.265697 | + | 0.460200i | ||||
\(952\) | 3.50748 | + | 6.07513i | 0.113678 | + | 0.196896i | ||||
\(953\) | 19.1147 | − | 33.1077i | 0.619187 | − | 1.07246i | −0.370448 | − | 0.928853i | \(-0.620796\pi\) |
0.989634 | − | 0.143610i | \(-0.0458709\pi\) | |||||||
\(954\) | −11.1234 | −0.360135 | ||||||||
\(955\) | −4.89038 | + | 8.47039i | −0.158249 | + | 0.274095i | ||||
\(956\) | 8.01871 | − | 13.8888i | 0.259344 | − | 0.449196i | ||||
\(957\) | −1.92127 | −0.0621060 | ||||||||
\(958\) | 25.5933 | − | 44.3288i | 0.826881 | − | 1.43220i | ||||
\(959\) | −3.84308 | − | 6.65642i | −0.124100 | − | 0.214947i | ||||
\(960\) | −1.87682 | − | 3.25074i | −0.0605740 | − | 0.104917i | ||||
\(961\) | 20.4392 | 0.659328 | ||||||||
\(962\) | −0.853163 | + | 2.05439i | −0.0275071 | + | 0.0662363i | ||||
\(963\) | −6.34125 | −0.204344 | ||||||||
\(964\) | −10.8732 | − | 18.8329i | −0.350202 | − | 0.606568i | ||||
\(965\) | 27.3912 | + | 47.4430i | 0.881754 | + | 1.52724i | ||||
\(966\) | 7.10045 | − | 12.2983i | 0.228453 | − | 0.395693i | ||||
\(967\) | −21.0319 | −0.676341 | −0.338170 | − | 0.941085i | \(-0.609808\pi\) | ||||
−0.338170 | + | 0.941085i | \(0.609808\pi\) | |||||||
\(968\) | 0.676492 | − | 1.17172i | 0.0217433 | − | 0.0376604i | ||||
\(969\) | 4.40468 | − | 7.62912i | 0.141499 | − | 0.245083i | ||||
\(970\) | −82.2488 | −2.64085 | ||||||||
\(971\) | −19.7620 | + | 34.2288i | −0.634194 | + | 1.09846i | 0.352492 | + | 0.935815i | \(0.385335\pi\) |
−0.986685 | + | 0.162641i | \(0.947999\pi\) | |||||||
\(972\) | −0.624717 | − | 1.08204i | −0.0200378 | − | 0.0347065i | ||||
\(973\) | 12.2404 | + | 21.2011i | 0.392411 | + | 0.679675i | ||||
\(974\) | 28.3130 | 0.907207 | ||||||||
\(975\) | −7.55425 | − | 9.86358i | −0.241929 | − | 0.315887i | ||||
\(976\) | 3.76183 | 0.120413 | ||||||||
\(977\) | 21.4732 | + | 37.1926i | 0.686987 | + | 1.18990i | 0.972808 | + | 0.231614i | \(0.0744006\pi\) |
−0.285820 | + | 0.958283i | \(0.592266\pi\) | |||||||
\(978\) | −7.12909 | − | 12.3480i | −0.227963 | − | 0.394844i | ||||
\(979\) | 7.51460 | − | 13.0157i | 0.240168 | − | 0.415983i | ||||
\(980\) | 18.2102 | 0.581703 | ||||||||
\(981\) | 8.33456 | − | 14.4359i | 0.266102 | − | 0.460902i | ||||
\(982\) | 13.7812 | − | 23.8697i | 0.439775 | − | 0.761712i | ||||
\(983\) | −38.9916 | −1.24364 | −0.621819 | − | 0.783161i | \(-0.713606\pi\) | ||||
−0.621819 | + | 0.783161i | \(0.713606\pi\) | |||||||
\(984\) | −0.0921176 | + | 0.159552i | −0.00293660 | + | 0.00508635i | ||||
\(985\) | −20.7793 | − | 35.9908i | −0.662084 | − | 1.14676i | ||||
\(986\) | 6.37276 | + | 11.0379i | 0.202950 | + | 0.351520i | ||||
\(987\) | 3.86616 | 0.123061 | ||||||||
\(988\) | 6.55682 | + | 8.56124i | 0.208600 | + | 0.272369i | ||||
\(989\) | −63.0667 | −2.00541 | ||||||||
\(990\) | 2.61936 | + | 4.53686i | 0.0832486 | + | 0.144191i | ||||
\(991\) | 25.3523 | + | 43.9115i | 0.805344 | + | 1.39490i | 0.916059 | + | 0.401044i | \(0.131353\pi\) |
−0.110715 | + | 0.993852i | \(0.535314\pi\) | |||||||
\(992\) | −22.2155 | + | 38.4784i | −0.705343 | + | 1.22169i | ||||
\(993\) | 16.2139 | 0.514534 | ||||||||
\(994\) | 3.87663 | − | 6.71453i | 0.122959 | − | 0.212972i | ||||
\(995\) | −34.0335 | + | 58.9478i | −1.07894 | + | 1.86877i | ||||
\(996\) | −21.1443 | −0.669982 | ||||||||
\(997\) | 20.1395 | − | 34.8826i | 0.637823 | − | 1.10474i | −0.348086 | − | 0.937463i | \(-0.613168\pi\) |
0.985909 | − | 0.167280i | \(-0.0534983\pi\) | |||||||
\(998\) | −15.1707 | − | 26.2764i | −0.480220 | − | 0.831765i | ||||
\(999\) | −0.171130 | − | 0.296407i | −0.00541433 | − | 0.00937789i |
(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 | 429.2.i.f.133.1 | yes | 10 | |
13.3 | even | 3 | 5577.2.a.n.1.5 | 5 | |||
13.9 | even | 3 | inner | 429.2.i.f.100.1 | ✓ | 10 | |
13.10 | even | 6 | 5577.2.a.w.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.i.f.100.1 | ✓ | 10 | 13.9 | even | 3 | inner | |
429.2.i.f.133.1 | yes | 10 | 1.1 | even | 1 | trivial | |
5577.2.a.n.1.5 | 5 | 13.3 | even | 3 | |||
5577.2.a.w.1.1 | 5 | 13.10 | even | 6 |