Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(121,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bd (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.7 | ||
Root | \(-2.62249i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.121 |
Dual form | 546.2.bd.b.361.7 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.27114 | − | 1.31124i | −1.01569 | − | 0.586406i | −0.102834 | − | 0.994699i | \(-0.532791\pi\) |
−0.912851 | + | 0.408292i | \(0.866124\pi\) | |||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −2.34750 | − | 1.22035i | −0.887271 | − | 0.461248i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.62249 | −0.829304 | ||||||||
\(11\) | − | 5.01074i | − | 1.51080i | −0.655267 | − | 0.755398i | \(-0.727444\pi\) | ||
0.655267 | − | 0.755398i | \(-0.272556\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 3.59427 | + | 0.285022i | 0.996871 | + | 0.0790510i | ||||
\(14\) | −2.64317 | + | 0.116897i | −0.706416 | + | 0.0312420i | ||||
\(15\) | −2.27114 | − | 1.31124i | −0.586406 | − | 0.338562i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.44859 | + | 5.97313i | −0.836406 | + | 1.44870i | 0.0564743 | + | 0.998404i | \(0.482014\pi\) |
−0.892880 | + | 0.450294i | \(0.851319\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | − | 3.03338i | − | 0.695906i | −0.937512 | − | 0.347953i | \(-0.886877\pi\) | ||
0.937512 | − | 0.347953i | \(-0.113123\pi\) | |||||||
\(20\) | −2.27114 | + | 1.31124i | −0.507843 | + | 0.293203i | ||||
\(21\) | −2.34750 | − | 1.22035i | −0.512266 | − | 0.266302i | ||||
\(22\) | −2.50537 | − | 4.33943i | −0.534147 | − | 0.925169i | ||||
\(23\) | −2.49983 | − | 4.32984i | −0.521251 | − | 0.902834i | −0.999695 | − | 0.0247154i | \(-0.992132\pi\) |
0.478443 | − | 0.878119i | \(-0.341201\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | 0.938722 | + | 1.62591i | 0.187744 | + | 0.325183i | ||||
\(26\) | 3.25524 | − | 1.55030i | 0.638405 | − | 0.304038i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.23060 | + | 1.42282i | −0.421544 | + | 0.268888i | ||||
\(29\) | 2.18859 | − | 3.79075i | 0.406411 | − | 0.703924i | −0.588074 | − | 0.808807i | \(-0.700113\pi\) |
0.994485 | + | 0.104883i | \(0.0334468\pi\) | |||||||
\(30\) | −2.62249 | −0.478799 | ||||||||
\(31\) | 4.93016 | − | 2.84643i | 0.885484 | − | 0.511234i | 0.0130211 | − | 0.999915i | \(-0.495855\pi\) |
0.872463 | + | 0.488681i | \(0.162522\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | − | 5.01074i | − | 0.872258i | ||||||
\(34\) | 6.89718i | 1.18286i | ||||||||
\(35\) | 3.73133 | + | 5.84973i | 0.630709 | + | 0.988784i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | −3.70976 | + | 2.14183i | −0.609881 | + | 0.352115i | −0.772919 | − | 0.634505i | \(-0.781204\pi\) |
0.163038 | + | 0.986620i | \(0.447871\pi\) | |||||||
\(38\) | −1.51669 | − | 2.62699i | −0.246040 | − | 0.426153i | ||||
\(39\) | 3.59427 | + | 0.285022i | 0.575543 | + | 0.0456401i | ||||
\(40\) | −1.31124 | + | 2.27114i | −0.207326 | + | 0.359099i | ||||
\(41\) | 4.95053 | + | 2.85819i | 0.773143 | + | 0.446374i | 0.833995 | − | 0.551772i | \(-0.186048\pi\) |
−0.0608516 | + | 0.998147i | \(0.519382\pi\) | |||||||
\(42\) | −2.64317 | + | 0.116897i | −0.407850 | + | 0.0180376i | ||||
\(43\) | 6.44053 | + | 11.1553i | 0.982172 | + | 1.70117i | 0.653886 | + | 0.756593i | \(0.273137\pi\) |
0.328285 | + | 0.944579i | \(0.393529\pi\) | |||||||
\(44\) | −4.33943 | − | 2.50537i | −0.654194 | − | 0.377699i | ||||
\(45\) | −2.27114 | − | 1.31124i | −0.338562 | − | 0.195469i | ||||
\(46\) | −4.32984 | − | 2.49983i | −0.638400 | − | 0.368580i | ||||
\(47\) | 0.499608 | + | 0.288449i | 0.0728753 | + | 0.0420746i | 0.535995 | − | 0.844221i | \(-0.319937\pi\) |
−0.463120 | + | 0.886296i | \(0.653270\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 4.02150 | + | 5.72953i | 0.574500 | + | 0.818505i | ||||
\(50\) | 1.62591 | + | 0.938722i | 0.229939 | + | 0.132755i | ||||
\(51\) | −3.44859 | + | 5.97313i | −0.482899 | + | 0.836406i | ||||
\(52\) | 2.04397 | − | 2.97022i | 0.283448 | − | 0.411895i | ||||
\(53\) | −3.49408 | − | 6.05193i | −0.479949 | − | 0.831296i | 0.519786 | − | 0.854296i | \(-0.326012\pi\) |
−0.999735 | + | 0.0229999i | \(0.992678\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −6.57031 | + | 11.3801i | −0.885940 | + | 1.53449i | ||||
\(56\) | −1.22035 | + | 2.34750i | −0.163076 | + | 0.313698i | ||||
\(57\) | − | 3.03338i | − | 0.401781i | ||||||
\(58\) | − | 4.37718i | − | 0.574752i | ||||||
\(59\) | 9.08332 | + | 5.24426i | 1.18255 | + | 0.682744i | 0.956603 | − | 0.291396i | \(-0.0941197\pi\) |
0.225945 | + | 0.974140i | \(0.427453\pi\) | |||||||
\(60\) | −2.27114 | + | 1.31124i | −0.293203 | + | 0.169281i | ||||
\(61\) | 14.3150 | 1.83285 | 0.916425 | − | 0.400206i | \(-0.131061\pi\) | ||||
0.916425 | + | 0.400206i | \(0.131061\pi\) | |||||||
\(62\) | 2.84643 | − | 4.93016i | 0.361497 | − | 0.626132i | ||||
\(63\) | −2.34750 | − | 1.22035i | −0.295757 | − | 0.153749i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −7.78936 | − | 5.36029i | −0.966151 | − | 0.664862i | ||||
\(66\) | −2.50537 | − | 4.33943i | −0.308390 | − | 0.534147i | ||||
\(67\) | − | 2.47913i | − | 0.302873i | −0.988467 | − | 0.151437i | \(-0.951610\pi\) | ||
0.988467 | − | 0.151437i | \(-0.0483900\pi\) | |||||||
\(68\) | 3.44859 | + | 5.97313i | 0.418203 | + | 0.724349i | ||||
\(69\) | −2.49983 | − | 4.32984i | −0.300945 | − | 0.521251i | ||||
\(70\) | 6.15629 | + | 3.20035i | 0.735817 | + | 0.382515i | ||||
\(71\) | 2.82667 | − | 1.63198i | 0.335463 | − | 0.193680i | −0.322801 | − | 0.946467i | \(-0.604624\pi\) |
0.658264 | + | 0.752787i | \(0.271291\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 4.20527 | − | 2.42791i | 0.492189 | − | 0.284166i | −0.233293 | − | 0.972406i | \(-0.574950\pi\) |
0.725482 | + | 0.688241i | \(0.241617\pi\) | |||||||
\(74\) | −2.14183 | + | 3.70976i | −0.248983 | + | 0.431251i | ||||
\(75\) | 0.938722 | + | 1.62591i | 0.108394 | + | 0.187744i | ||||
\(76\) | −2.62699 | − | 1.51669i | −0.301336 | − | 0.173976i | ||||
\(77\) | −6.11485 | + | 11.7627i | −0.696852 | + | 1.34049i | ||||
\(78\) | 3.25524 | − | 1.55030i | 0.368583 | − | 0.175537i | ||||
\(79\) | −3.69502 | + | 6.39996i | −0.415722 | + | 0.720052i | −0.995504 | − | 0.0947200i | \(-0.969804\pi\) |
0.579782 | + | 0.814772i | \(0.303138\pi\) | |||||||
\(80\) | 2.62249i | 0.293203i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.71638 | 0.631269 | ||||||||
\(83\) | − | 9.16995i | − | 1.00653i | −0.864131 | − | 0.503266i | \(-0.832131\pi\) | ||
0.864131 | − | 0.503266i | \(-0.167869\pi\) | |||||||
\(84\) | −2.23060 | + | 1.42282i | −0.243379 | + | 0.155242i | ||||
\(85\) | 15.6645 | − | 9.04389i | 1.69905 | − | 0.980947i | ||||
\(86\) | 11.1553 | + | 6.44053i | 1.20291 | + | 0.694500i | ||||
\(87\) | 2.18859 | − | 3.79075i | 0.234641 | − | 0.406411i | ||||
\(88\) | −5.01074 | −0.534147 | ||||||||
\(89\) | −13.3582 | + | 7.71235i | −1.41596 | + | 0.817507i | −0.995941 | − | 0.0900063i | \(-0.971311\pi\) |
−0.420023 | + | 0.907514i | \(0.637978\pi\) | |||||||
\(90\) | −2.62249 | −0.276435 | ||||||||
\(91\) | −8.08971 | − | 5.05535i | −0.848032 | − | 0.529945i | ||||
\(92\) | −4.99967 | −0.521251 | ||||||||
\(93\) | 4.93016 | − | 2.84643i | 0.511234 | − | 0.295161i | ||||
\(94\) | 0.576897 | 0.0595024 | ||||||||
\(95\) | −3.97750 | + | 6.88924i | −0.408083 | + | 0.706821i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | −12.1886 | + | 7.03709i | −1.23756 | + | 0.714508i | −0.968596 | − | 0.248641i | \(-0.920016\pi\) |
−0.268969 | + | 0.963149i | \(0.586683\pi\) | |||||||
\(98\) | 6.34749 | + | 2.95117i | 0.641193 | + | 0.298113i | ||||
\(99\) | − | 5.01074i | − | 0.503598i | ||||||
\(100\) | 1.87744 | 0.187744 | ||||||||
\(101\) | −9.23409 | −0.918826 | −0.459413 | − | 0.888223i | \(-0.651940\pi\) | ||||
−0.459413 | + | 0.888223i | \(0.651940\pi\) | |||||||
\(102\) | 6.89718i | 0.682923i | ||||||||
\(103\) | −2.43903 | + | 4.22453i | −0.240325 | + | 0.416255i | −0.960807 | − | 0.277219i | \(-0.910587\pi\) |
0.720482 | + | 0.693474i | \(0.243921\pi\) | |||||||
\(104\) | 0.285022 | − | 3.59427i | 0.0279487 | − | 0.352447i | ||||
\(105\) | 3.73133 | + | 5.84973i | 0.364140 | + | 0.570875i | ||||
\(106\) | −6.05193 | − | 3.49408i | −0.587815 | − | 0.339375i | ||||
\(107\) | 0.0863737 | + | 0.149604i | 0.00835006 | + | 0.0144627i | 0.870170 | − | 0.492751i | \(-0.164009\pi\) |
−0.861820 | + | 0.507214i | \(0.830675\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 10.9212 | − | 6.30538i | 1.04606 | − | 0.603946i | 0.124520 | − | 0.992217i | \(-0.460261\pi\) |
0.921545 | + | 0.388271i | \(0.126928\pi\) | |||||||
\(110\) | 13.1406i | 1.25291i | ||||||||
\(111\) | −3.70976 | + | 2.14183i | −0.352115 | + | 0.203294i | ||||
\(112\) | 0.116897 | + | 2.64317i | 0.0110457 | + | 0.249756i | ||||
\(113\) | −6.33262 | − | 10.9684i | −0.595722 | − | 1.03182i | −0.993444 | − | 0.114316i | \(-0.963533\pi\) |
0.397722 | − | 0.917506i | \(-0.369801\pi\) | |||||||
\(114\) | −1.51669 | − | 2.62699i | −0.142051 | − | 0.246040i | ||||
\(115\) | 13.1116i | 1.22266i | ||||||||
\(116\) | −2.18859 | − | 3.79075i | −0.203205 | − | 0.351962i | ||||
\(117\) | 3.59427 | + | 0.285022i | 0.332290 | + | 0.0263503i | ||||
\(118\) | 10.4885 | 0.965546 | ||||||||
\(119\) | 15.3849 | − | 9.81344i | 1.41033 | − | 0.899597i | ||||
\(120\) | −1.31124 | + | 2.27114i | −0.119700 | + | 0.207326i | ||||
\(121\) | −14.1075 | −1.28250 | ||||||||
\(122\) | 12.3972 | − | 7.15751i | 1.12239 | − | 0.648011i | ||||
\(123\) | 4.95053 | + | 2.85819i | 0.446374 | + | 0.257714i | ||||
\(124\) | − | 5.69286i | − | 0.511234i | ||||||
\(125\) | 8.18887i | 0.732434i | ||||||||
\(126\) | −2.64317 | + | 0.116897i | −0.235472 | + | 0.0104140i | ||||
\(127\) | 3.67120 | − | 6.35871i | 0.325767 | − | 0.564244i | −0.655901 | − | 0.754847i | \(-0.727711\pi\) |
0.981667 | + | 0.190603i | \(0.0610443\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 6.44053 | + | 11.1553i | 0.567057 | + | 0.982172i | ||||
\(130\) | −9.42593 | − | 0.747468i | −0.826708 | − | 0.0655573i | ||||
\(131\) | 5.41067 | − | 9.37156i | 0.472733 | − | 0.818797i | −0.526780 | − | 0.850001i | \(-0.676601\pi\) |
0.999513 | + | 0.0312046i | \(0.00993434\pi\) | |||||||
\(132\) | −4.33943 | − | 2.50537i | −0.377699 | − | 0.218065i | ||||
\(133\) | −3.70178 | + | 7.12086i | −0.320985 | + | 0.617457i | ||||
\(134\) | −1.23956 | − | 2.14699i | −0.107082 | − | 0.185471i | ||||
\(135\) | −2.27114 | − | 1.31124i | −0.195469 | − | 0.112854i | ||||
\(136\) | 5.97313 | + | 3.44859i | 0.512192 | + | 0.295714i | ||||
\(137\) | 11.9618 | + | 6.90614i | 1.02196 | + | 0.590031i | 0.914672 | − | 0.404196i | \(-0.132449\pi\) |
0.107292 | + | 0.994228i | \(0.465782\pi\) | |||||||
\(138\) | −4.32984 | − | 2.49983i | −0.368580 | − | 0.212800i | ||||
\(139\) | 5.75709 | + | 9.97158i | 0.488310 | + | 0.845778i | 0.999910 | − | 0.0134459i | \(-0.00428009\pi\) |
−0.511599 | + | 0.859224i | \(0.670947\pi\) | |||||||
\(140\) | 6.93168 | − | 0.306560i | 0.585834 | − | 0.0259091i | ||||
\(141\) | 0.499608 | + | 0.288449i | 0.0420746 | + | 0.0242918i | ||||
\(142\) | 1.63198 | − | 2.82667i | 0.136952 | − | 0.237209i | ||||
\(143\) | 1.42817 | − | 18.0099i | 0.119430 | − | 1.50607i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −9.94119 | + | 5.73955i | −0.825571 | + | 0.476644i | ||||
\(146\) | 2.42791 | − | 4.20527i | 0.200935 | − | 0.348030i | ||||
\(147\) | 4.02150 | + | 5.72953i | 0.331688 | + | 0.472564i | ||||
\(148\) | 4.28366i | 0.352115i | ||||||||
\(149\) | − | 16.5087i | − | 1.35245i | −0.736697 | − | 0.676223i | \(-0.763615\pi\) | ||
0.736697 | − | 0.676223i | \(-0.236385\pi\) | |||||||
\(150\) | 1.62591 | + | 0.938722i | 0.132755 | + | 0.0766463i | ||||
\(151\) | 5.69210 | − | 3.28634i | 0.463217 | − | 0.267438i | −0.250179 | − | 0.968200i | \(-0.580490\pi\) |
0.713396 | + | 0.700761i | \(0.247156\pi\) | |||||||
\(152\) | −3.03338 | −0.246040 | ||||||||
\(153\) | −3.44859 | + | 5.97313i | −0.278802 | + | 0.482899i | ||||
\(154\) | 0.585739 | + | 13.2442i | 0.0472002 | + | 1.06725i | ||||
\(155\) | −14.9295 | −1.19916 | ||||||||
\(156\) | 2.04397 | − | 2.97022i | 0.163649 | − | 0.237808i | ||||
\(157\) | 4.40621 | + | 7.63178i | 0.351654 | + | 0.609083i | 0.986539 | − | 0.163524i | \(-0.0522860\pi\) |
−0.634885 | + | 0.772606i | \(0.718953\pi\) | |||||||
\(158\) | 7.39004i | 0.587920i | ||||||||
\(159\) | −3.49408 | − | 6.05193i | −0.277099 | − | 0.479949i | ||||
\(160\) | 1.31124 | + | 2.27114i | 0.103663 | + | 0.179549i | ||||
\(161\) | 0.584445 | + | 13.2150i | 0.0460607 | + | 1.04148i | ||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | 9.36526i | 0.733544i | 0.930311 | + | 0.366772i | \(0.119537\pi\) | ||||
−0.930311 | + | 0.366772i | \(0.880463\pi\) | |||||||
\(164\) | 4.95053 | − | 2.85819i | 0.386572 | − | 0.223187i | ||||
\(165\) | −6.57031 | + | 11.3801i | −0.511498 | + | 0.885940i | ||||
\(166\) | −4.58497 | − | 7.94141i | −0.355863 | − | 0.616373i | ||||
\(167\) | −2.26138 | − | 1.30561i | −0.174991 | − | 0.101031i | 0.409946 | − | 0.912110i | \(-0.365547\pi\) |
−0.584937 | + | 0.811079i | \(0.698881\pi\) | |||||||
\(168\) | −1.22035 | + | 2.34750i | −0.0941519 | + | 0.181113i | ||||
\(169\) | 12.8375 | + | 2.04889i | 0.987502 | + | 0.157607i | ||||
\(170\) | 9.04389 | − | 15.6645i | 0.693635 | − | 1.20141i | ||||
\(171\) | − | 3.03338i | − | 0.231969i | ||||||
\(172\) | 12.8811 | 0.982172 | ||||||||
\(173\) | −4.99495 | −0.379759 | −0.189880 | − | 0.981807i | \(-0.560810\pi\) | ||||
−0.189880 | + | 0.981807i | \(0.560810\pi\) | |||||||
\(174\) | − | 4.37718i | − | 0.331833i | ||||||
\(175\) | −0.219467 | − | 4.96240i | −0.0165901 | − | 0.375122i | ||||
\(176\) | −4.33943 | + | 2.50537i | −0.327097 | + | 0.188849i | ||||
\(177\) | 9.08332 | + | 5.24426i | 0.682744 | + | 0.394183i | ||||
\(178\) | −7.71235 | + | 13.3582i | −0.578065 | + | 1.00124i | ||||
\(179\) | −7.52240 | −0.562251 | −0.281125 | − | 0.959671i | \(-0.590708\pi\) | ||||
−0.281125 | + | 0.959671i | \(0.590708\pi\) | |||||||
\(180\) | −2.27114 | + | 1.31124i | −0.169281 | + | 0.0977344i | ||||
\(181\) | −7.14351 | −0.530973 | −0.265487 | − | 0.964115i | \(-0.585533\pi\) | ||||
−0.265487 | + | 0.964115i | \(0.585533\pi\) | |||||||
\(182\) | −9.53357 | − | 0.333204i | −0.706675 | − | 0.0246987i | ||||
\(183\) | 14.3150 | 1.05820 | ||||||||
\(184\) | −4.32984 | + | 2.49983i | −0.319200 | + | 0.184290i | ||||
\(185\) | 11.2339 | 0.825929 | ||||||||
\(186\) | 2.84643 | − | 4.93016i | 0.208711 | − | 0.361497i | ||||
\(187\) | 29.9298 | + | 17.2800i | 2.18869 | + | 1.26364i | ||||
\(188\) | 0.499608 | − | 0.288449i | 0.0364376 | − | 0.0210373i | ||||
\(189\) | −2.34750 | − | 1.22035i | −0.170755 | − | 0.0887673i | ||||
\(190\) | 7.95501i | 0.577117i | ||||||||
\(191\) | 7.92903 | 0.573724 | 0.286862 | − | 0.957972i | \(-0.407388\pi\) | ||||
0.286862 | + | 0.957972i | \(0.407388\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − | 10.7806i | − | 0.776005i | −0.921658 | − | 0.388002i | \(-0.873165\pi\) | ||
0.921658 | − | 0.388002i | \(-0.126835\pi\) | |||||||
\(194\) | −7.03709 | + | 12.1886i | −0.505234 | + | 0.875090i | ||||
\(195\) | −7.78936 | − | 5.36029i | −0.557807 | − | 0.383858i | ||||
\(196\) | 6.97267 | − | 0.617955i | 0.498048 | − | 0.0441396i | ||||
\(197\) | −16.5289 | − | 9.54296i | −1.17763 | − | 0.679908i | −0.222169 | − | 0.975008i | \(-0.571314\pi\) |
−0.955466 | + | 0.295100i | \(0.904647\pi\) | |||||||
\(198\) | −2.50537 | − | 4.33943i | −0.178049 | − | 0.308390i | ||||
\(199\) | 11.7571 | − | 20.3638i | 0.833436 | − | 1.44355i | −0.0618609 | − | 0.998085i | \(-0.519704\pi\) |
0.895297 | − | 0.445469i | \(-0.146963\pi\) | |||||||
\(200\) | 1.62591 | − | 0.938722i | 0.114970 | − | 0.0663777i | ||||
\(201\) | − | 2.47913i | − | 0.174864i | ||||||
\(202\) | −7.99696 | + | 4.61704i | −0.562664 | + | 0.324854i | ||||
\(203\) | −9.76375 | + | 6.22794i | −0.685281 | + | 0.437115i | ||||
\(204\) | 3.44859 | + | 5.97313i | 0.241450 | + | 0.418203i | ||||
\(205\) | −7.49557 | − | 12.9827i | −0.523513 | − | 0.906752i | ||||
\(206\) | 4.87807i | 0.339871i | ||||||||
\(207\) | −2.49983 | − | 4.32984i | −0.173750 | − | 0.300945i | ||||
\(208\) | −1.55030 | − | 3.25524i | −0.107494 | − | 0.225710i | ||||
\(209\) | −15.1995 | −1.05137 | ||||||||
\(210\) | 6.15629 | + | 3.20035i | 0.424824 | + | 0.220845i | ||||
\(211\) | 2.44732 | − | 4.23888i | 0.168480 | − | 0.291816i | −0.769406 | − | 0.638761i | \(-0.779447\pi\) |
0.937886 | + | 0.346944i | \(0.112781\pi\) | |||||||
\(212\) | −6.98817 | −0.479949 | ||||||||
\(213\) | 2.82667 | − | 1.63198i | 0.193680 | − | 0.111821i | ||||
\(214\) | 0.149604 | + | 0.0863737i | 0.0102267 | + | 0.00590439i | ||||
\(215\) | − | 33.7804i | − | 2.30381i | ||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −15.0472 | + | 0.665477i | −1.02147 | + | 0.0451755i | ||||
\(218\) | 6.30538 | − | 10.9212i | 0.427054 | − | 0.739680i | ||||
\(219\) | 4.20527 | − | 2.42791i | 0.284166 | − | 0.164063i | ||||
\(220\) | 6.57031 | + | 11.3801i | 0.442970 | + | 0.767246i | ||||
\(221\) | −14.0976 | + | 20.4861i | −0.948310 | + | 1.37805i | ||||
\(222\) | −2.14183 | + | 3.70976i | −0.143750 | + | 0.248983i | ||||
\(223\) | −8.72547 | − | 5.03765i | −0.584301 | − | 0.337346i | 0.178540 | − | 0.983933i | \(-0.442863\pi\) |
−0.762841 | + | 0.646587i | \(0.776196\pi\) | |||||||
\(224\) | 1.42282 | + | 2.23060i | 0.0950661 | + | 0.149038i | ||||
\(225\) | 0.938722 | + | 1.62591i | 0.0625815 | + | 0.108394i | ||||
\(226\) | −10.9684 | − | 6.33262i | −0.729608 | − | 0.421239i | ||||
\(227\) | 12.3996 | + | 7.15891i | 0.822990 | + | 0.475154i | 0.851447 | − | 0.524441i | \(-0.175726\pi\) |
−0.0284563 | + | 0.999595i | \(0.509059\pi\) | |||||||
\(228\) | −2.62699 | − | 1.51669i | −0.173976 | − | 0.100445i | ||||
\(229\) | −13.3945 | − | 7.73332i | −0.885134 | − | 0.511032i | −0.0127863 | − | 0.999918i | \(-0.504070\pi\) |
−0.872348 | + | 0.488886i | \(0.837403\pi\) | |||||||
\(230\) | 6.55579 | + | 11.3550i | 0.432276 | + | 0.748723i | ||||
\(231\) | −6.11485 | + | 11.7627i | −0.402328 | + | 0.773929i | ||||
\(232\) | −3.79075 | − | 2.18859i | −0.248875 | − | 0.143688i | ||||
\(233\) | 2.31317 | − | 4.00653i | 0.151541 | − | 0.262477i | −0.780253 | − | 0.625464i | \(-0.784910\pi\) |
0.931794 | + | 0.362987i | \(0.118243\pi\) | |||||||
\(234\) | 3.25524 | − | 1.55030i | 0.212802 | − | 0.101346i | ||||
\(235\) | −0.756453 | − | 1.31022i | −0.0493456 | − | 0.0854690i | ||||
\(236\) | 9.08332 | − | 5.24426i | 0.591274 | − | 0.341372i | ||||
\(237\) | −3.69502 | + | 6.39996i | −0.240017 | + | 0.415722i | ||||
\(238\) | 8.41696 | − | 16.1911i | 0.545591 | − | 1.04951i | ||||
\(239\) | − | 8.48540i | − | 0.548875i | −0.961605 | − | 0.274437i | \(-0.911508\pi\) | ||
0.961605 | − | 0.274437i | \(-0.0884916\pi\) | |||||||
\(240\) | 2.62249i | 0.169281i | ||||||||
\(241\) | −3.68833 | − | 2.12946i | −0.237586 | − | 0.137170i | 0.376481 | − | 0.926425i | \(-0.377134\pi\) |
−0.614067 | + | 0.789254i | \(0.710467\pi\) | |||||||
\(242\) | −12.2175 | + | 7.05376i | −0.785369 | + | 0.453433i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.15751 | − | 12.3972i | 0.458213 | − | 0.793648i | ||||
\(245\) | −1.62058 | − | 18.2857i | −0.103535 | − | 1.16823i | ||||
\(246\) | 5.71638 | 0.364463 | ||||||||
\(247\) | 0.864582 | − | 10.9028i | 0.0550120 | − | 0.693728i | ||||
\(248\) | −2.84643 | − | 4.93016i | −0.180749 | − | 0.313066i | ||||
\(249\) | − | 9.16995i | − | 0.581122i | ||||||
\(250\) | 4.09443 | + | 7.09177i | 0.258955 | + | 0.448523i | ||||
\(251\) | −1.00766 | − | 1.74531i | −0.0636027 | − | 0.110163i | 0.832471 | − | 0.554069i | \(-0.186926\pi\) |
−0.896073 | + | 0.443906i | \(0.853592\pi\) | |||||||
\(252\) | −2.23060 | + | 1.42282i | −0.140515 | + | 0.0896292i | ||||
\(253\) | −21.6957 | + | 12.5260i | −1.36400 | + | 0.787504i | ||||
\(254\) | − | 7.34240i | − | 0.460703i | ||||||
\(255\) | 15.6645 | − | 9.04389i | 0.980947 | − | 0.566350i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.4978 | + | 19.9147i | 0.717211 | + | 1.24225i | 0.962100 | + | 0.272695i | \(0.0879151\pi\) |
−0.244889 | + | 0.969551i | \(0.578752\pi\) | |||||||
\(258\) | 11.1553 | + | 6.44053i | 0.694500 | + | 0.400970i | ||||
\(259\) | 11.3224 | − | 0.500746i | 0.703542 | − | 0.0311148i | ||||
\(260\) | −8.53682 | + | 4.06564i | −0.529431 | + | 0.252140i | ||||
\(261\) | 2.18859 | − | 3.79075i | 0.135470 | − | 0.234641i | ||||
\(262\) | − | 10.8213i | − | 0.668545i | ||||||
\(263\) | 22.0383 | 1.35894 | 0.679470 | − | 0.733703i | \(-0.262210\pi\) | ||||
0.679470 | + | 0.733703i | \(0.262210\pi\) | |||||||
\(264\) | −5.01074 | −0.308390 | ||||||||
\(265\) | 18.3264i | 1.12578i | ||||||||
\(266\) | 0.354592 | + | 8.01774i | 0.0217415 | + | 0.491599i | ||||
\(267\) | −13.3582 | + | 7.71235i | −0.817507 | + | 0.471988i | ||||
\(268\) | −2.14699 | − | 1.23956i | −0.131148 | − | 0.0757184i | ||||
\(269\) | −2.18641 | + | 3.78698i | −0.133308 | + | 0.230896i | −0.924950 | − | 0.380089i | \(-0.875893\pi\) |
0.791642 | + | 0.610985i | \(0.209227\pi\) | |||||||
\(270\) | −2.62249 | −0.159600 | ||||||||
\(271\) | −13.4302 | + | 7.75390i | −0.815824 | + | 0.471016i | −0.848974 | − | 0.528434i | \(-0.822779\pi\) |
0.0331504 | + | 0.999450i | \(0.489446\pi\) | |||||||
\(272\) | 6.89718 | 0.418203 | ||||||||
\(273\) | −8.08971 | − | 5.05535i | −0.489612 | − | 0.305964i | ||||
\(274\) | 13.8123 | 0.834430 | ||||||||
\(275\) | 8.14704 | − | 4.70369i | 0.491285 | − | 0.283643i | ||||
\(276\) | −4.99967 | −0.300945 | ||||||||
\(277\) | −14.3794 | + | 24.9058i | −0.863972 | + | 1.49644i | 0.00409153 | + | 0.999992i | \(0.498698\pi\) |
−0.868064 | + | 0.496452i | \(0.834636\pi\) | |||||||
\(278\) | 9.97158 | + | 5.75709i | 0.598056 | + | 0.345288i | ||||
\(279\) | 4.93016 | − | 2.84643i | 0.295161 | − | 0.170411i | ||||
\(280\) | 5.84973 | − | 3.73133i | 0.349588 | − | 0.222989i | ||||
\(281\) | 13.5100i | 0.805941i | 0.915213 | + | 0.402970i | \(0.132022\pi\) | ||||
−0.915213 | + | 0.402970i | \(0.867978\pi\) | |||||||
\(282\) | 0.576897 | 0.0343537 | ||||||||
\(283\) | −19.0071 | −1.12986 | −0.564928 | − | 0.825140i | \(-0.691096\pi\) | ||||
−0.564928 | + | 0.825140i | \(0.691096\pi\) | |||||||
\(284\) | − | 3.26395i | − | 0.193680i | ||||||
\(285\) | −3.97750 | + | 6.88924i | −0.235607 | + | 0.408083i | ||||
\(286\) | −7.76814 | − | 16.3112i | −0.459340 | − | 0.964499i | ||||
\(287\) | −8.13338 | − | 12.7510i | −0.480098 | − | 0.752666i | ||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | −15.2856 | − | 26.4754i | −0.899150 | − | 1.55737i | ||||
\(290\) | −5.73955 | + | 9.94119i | −0.337038 | + | 0.583767i | ||||
\(291\) | −12.1886 | + | 7.03709i | −0.714508 | + | 0.412522i | ||||
\(292\) | − | 4.85582i | − | 0.284166i | ||||||
\(293\) | −7.14308 | + | 4.12406i | −0.417303 | + | 0.240930i | −0.693923 | − | 0.720049i | \(-0.744119\pi\) |
0.276620 | + | 0.960979i | \(0.410786\pi\) | |||||||
\(294\) | 6.34749 | + | 2.95117i | 0.370193 | + | 0.172116i | ||||
\(295\) | −13.7530 | − | 23.8209i | −0.800731 | − | 1.38691i | ||||
\(296\) | 2.14183 | + | 3.70976i | 0.124491 | + | 0.215625i | ||||
\(297\) | − | 5.01074i | − | 0.290753i | ||||||
\(298\) | −8.25436 | − | 14.2970i | −0.478162 | − | 0.828201i | ||||
\(299\) | −7.75097 | − | 16.2751i | −0.448250 | − | 0.941214i | ||||
\(300\) | 1.87744 | 0.108394 | ||||||||
\(301\) | −1.50575 | − | 34.0468i | −0.0867902 | − | 1.96243i | ||||
\(302\) | 3.28634 | − | 5.69210i | 0.189107 | − | 0.327544i | ||||
\(303\) | −9.23409 | −0.530485 | ||||||||
\(304\) | −2.62699 | + | 1.51669i | −0.150668 | + | 0.0869882i | ||||
\(305\) | −32.5114 | − | 18.7705i | −1.86160 | − | 1.07479i | ||||
\(306\) | 6.89718i | 0.394286i | ||||||||
\(307\) | 2.94195i | 0.167906i | 0.996470 | + | 0.0839531i | \(0.0267546\pi\) | ||||
−0.996470 | + | 0.0839531i | \(0.973245\pi\) | |||||||
\(308\) | 7.12938 | + | 11.1770i | 0.406234 | + | 0.636867i | ||||
\(309\) | −2.43903 | + | 4.22453i | −0.138752 | + | 0.240325i | ||||
\(310\) | −12.9293 | + | 7.46473i | −0.734335 | + | 0.423968i | ||||
\(311\) | 7.47126 | + | 12.9406i | 0.423656 | + | 0.733794i | 0.996294 | − | 0.0860145i | \(-0.0274131\pi\) |
−0.572638 | + | 0.819809i | \(0.694080\pi\) | |||||||
\(312\) | 0.285022 | − | 3.59427i | 0.0161362 | − | 0.203485i | ||||
\(313\) | 12.1929 | − | 21.1187i | 0.689182 | − | 1.19370i | −0.282921 | − | 0.959143i | \(-0.591303\pi\) |
0.972103 | − | 0.234555i | \(-0.0753632\pi\) | |||||||
\(314\) | 7.63178 | + | 4.40621i | 0.430686 | + | 0.248657i | ||||
\(315\) | 3.73133 | + | 5.84973i | 0.210236 | + | 0.329595i | ||||
\(316\) | 3.69502 | + | 6.39996i | 0.207861 | + | 0.360026i | ||||
\(317\) | 24.6493 | + | 14.2313i | 1.38444 | + | 0.799309i | 0.992682 | − | 0.120758i | \(-0.0385324\pi\) |
0.391762 | + | 0.920067i | \(0.371866\pi\) | |||||||
\(318\) | −6.05193 | − | 3.49408i | −0.339375 | − | 0.195938i | ||||
\(319\) | −18.9945 | − | 10.9665i | −1.06349 | − | 0.614004i | ||||
\(320\) | 2.27114 | + | 1.31124i | 0.126961 | + | 0.0733008i | ||||
\(321\) | 0.0863737 | + | 0.149604i | 0.00482091 | + | 0.00835006i | ||||
\(322\) | 7.11362 | + | 11.1523i | 0.396427 | + | 0.621492i | ||||
\(323\) | 18.1188 | + | 10.4609i | 1.00816 | + | 0.582060i | ||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 2.91060 | + | 6.11153i | 0.161451 | + | 0.339007i | ||||
\(326\) | 4.68263 | + | 8.11055i | 0.259347 | + | 0.449202i | ||||
\(327\) | 10.9212 | − | 6.30538i | 0.603946 | − | 0.348688i | ||||
\(328\) | 2.85819 | − | 4.95053i | 0.157817 | − | 0.273347i | ||||
\(329\) | −0.820821 | − | 1.28683i | −0.0452533 | − | 0.0709451i | ||||
\(330\) | 13.1406i | 0.723367i | ||||||||
\(331\) | 6.27684i | 0.345006i | 0.985009 | + | 0.172503i | \(0.0551855\pi\) | ||||
−0.985009 | + | 0.172503i | \(0.944815\pi\) | |||||||
\(332\) | −7.94141 | − | 4.58497i | −0.435841 | − | 0.251633i | ||||
\(333\) | −3.70976 | + | 2.14183i | −0.203294 | + | 0.117372i | ||||
\(334\) | −2.61122 | −0.142879 | ||||||||
\(335\) | −3.25074 | + | 5.63045i | −0.177607 | + | 0.307624i | ||||
\(336\) | 0.116897 | + | 2.64317i | 0.00637724 | + | 0.144197i | ||||
\(337\) | 9.99063 | 0.544224 | 0.272112 | − | 0.962266i | \(-0.412278\pi\) | ||||
0.272112 | + | 0.962266i | \(0.412278\pi\) | |||||||
\(338\) | 12.1421 | − | 4.64437i | 0.660441 | − | 0.252620i | ||||
\(339\) | −6.33262 | − | 10.9684i | −0.343941 | − | 0.595722i | ||||
\(340\) | − | 18.0878i | − | 0.980947i | ||||||
\(341\) | −14.2627 | − | 24.7038i | −0.772370 | − | 1.33778i | ||||
\(342\) | −1.51669 | − | 2.62699i | −0.0820133 | − | 0.142051i | ||||
\(343\) | −2.44844 | − | 18.3577i | −0.132203 | − | 0.991223i | ||||
\(344\) | 11.1553 | − | 6.44053i | 0.601455 | − | 0.347250i | ||||
\(345\) | 13.1116i | 0.705903i | ||||||||
\(346\) | −4.32576 | + | 2.49748i | −0.232554 | + | 0.134265i | ||||
\(347\) | 1.95465 | − | 3.38555i | 0.104931 | − | 0.181746i | −0.808779 | − | 0.588113i | \(-0.799871\pi\) |
0.913710 | + | 0.406367i | \(0.133204\pi\) | |||||||
\(348\) | −2.18859 | − | 3.79075i | −0.117321 | − | 0.203205i | ||||
\(349\) | 13.3325 | + | 7.69750i | 0.713671 | + | 0.412038i | 0.812419 | − | 0.583074i | \(-0.198150\pi\) |
−0.0987480 | + | 0.995112i | \(0.531484\pi\) | |||||||
\(350\) | −2.67126 | − | 4.18783i | −0.142785 | − | 0.223849i | ||||
\(351\) | 3.59427 | + | 0.285022i | 0.191848 | + | 0.0152134i | ||||
\(352\) | −2.50537 | + | 4.33943i | −0.133537 | + | 0.231292i | ||||
\(353\) | 30.0836i | 1.60119i | 0.599208 | + | 0.800594i | \(0.295482\pi\) | ||||
−0.599208 | + | 0.800594i | \(0.704518\pi\) | |||||||
\(354\) | 10.4885 | 0.557458 | ||||||||
\(355\) | −8.55968 | −0.454300 | ||||||||
\(356\) | 15.4247i | 0.817507i | ||||||||
\(357\) | 15.3849 | − | 9.81344i | 0.814254 | − | 0.519383i | ||||
\(358\) | −6.51459 | + | 3.76120i | −0.344307 | + | 0.198786i | ||||
\(359\) | −7.23357 | − | 4.17631i | −0.381773 | − | 0.220417i | 0.296816 | − | 0.954935i | \(-0.404075\pi\) |
−0.678590 | + | 0.734518i | \(0.737408\pi\) | |||||||
\(360\) | −1.31124 | + | 2.27114i | −0.0691086 | + | 0.119700i | ||||
\(361\) | 9.79859 | 0.515715 | ||||||||
\(362\) | −6.18646 | + | 3.57176i | −0.325153 | + | 0.187727i | ||||
\(363\) | −14.1075 | −0.740453 | ||||||||
\(364\) | −8.42292 | + | 4.47822i | −0.441481 | + | 0.234723i | ||||
\(365\) | −12.7343 | −0.666546 | ||||||||
\(366\) | 12.3972 | − | 7.15751i | 0.648011 | − | 0.374129i | ||||
\(367\) | 12.3640 | 0.645394 | 0.322697 | − | 0.946502i | \(-0.395410\pi\) | ||||
0.322697 | + | 0.946502i | \(0.395410\pi\) | |||||||
\(368\) | −2.49983 | + | 4.32984i | −0.130313 | + | 0.225708i | ||||
\(369\) | 4.95053 | + | 2.85819i | 0.257714 | + | 0.148791i | ||||
\(370\) | 9.72880 | − | 5.61693i | 0.505776 | − | 0.292010i | ||||
\(371\) | 0.816894 | + | 18.4709i | 0.0424110 | + | 0.958961i | ||||
\(372\) | − | 5.69286i | − | 0.295161i | ||||||
\(373\) | −22.6398 | −1.17224 | −0.586122 | − | 0.810223i | \(-0.699346\pi\) | ||||
−0.586122 | + | 0.810223i | \(0.699346\pi\) | |||||||
\(374\) | 34.5600 | 1.78705 | ||||||||
\(375\) | 8.18887i | 0.422871i | ||||||||
\(376\) | 0.288449 | − | 0.499608i | 0.0148756 | − | 0.0257653i | ||||
\(377\) | 8.94683 | − | 13.0012i | 0.460785 | − | 0.669594i | ||||
\(378\) | −2.64317 | + | 0.116897i | −0.135950 | + | 0.00601252i | ||||
\(379\) | 9.43601 | + | 5.44788i | 0.484695 | + | 0.279839i | 0.722371 | − | 0.691506i | \(-0.243052\pi\) |
−0.237676 | + | 0.971344i | \(0.576386\pi\) | |||||||
\(380\) | 3.97750 | + | 6.88924i | 0.204042 | + | 0.353411i | ||||
\(381\) | 3.67120 | − | 6.35871i | 0.188081 | − | 0.325767i | ||||
\(382\) | 6.86674 | − | 3.96451i | 0.351333 | − | 0.202842i | ||||
\(383\) | 1.26963i | 0.0648751i | 0.999474 | + | 0.0324375i | \(0.0103270\pi\) | ||||
−0.999474 | + | 0.0324375i | \(0.989673\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 29.3115 | − | 18.6967i | 1.49385 | − | 0.952873i | ||||
\(386\) | −5.39030 | − | 9.33627i | −0.274359 | − | 0.475204i | ||||
\(387\) | 6.44053 | + | 11.1553i | 0.327391 | + | 0.567057i | ||||
\(388\) | 14.0742i | 0.714508i | ||||||||
\(389\) | 15.3303 | + | 26.5529i | 0.777279 | + | 1.34629i | 0.933505 | + | 0.358565i | \(0.116734\pi\) |
−0.156226 | + | 0.987721i | \(0.549933\pi\) | |||||||
\(390\) | −9.42593 | − | 0.747468i | −0.477300 | − | 0.0378495i | ||||
\(391\) | 34.4836 | 1.74391 | ||||||||
\(392\) | 5.72953 | − | 4.02150i | 0.289385 | − | 0.203116i | ||||
\(393\) | 5.41067 | − | 9.37156i | 0.272932 | − | 0.472733i | ||||
\(394\) | −19.0859 | −0.961535 | ||||||||
\(395\) | 16.7838 | − | 9.69014i | 0.844486 | − | 0.487564i | ||||
\(396\) | −4.33943 | − | 2.50537i | −0.218065 | − | 0.125900i | ||||
\(397\) | − | 26.4480i | − | 1.32738i | −0.748006 | − | 0.663692i | \(-0.768988\pi\) | ||
0.748006 | − | 0.663692i | \(-0.231012\pi\) | |||||||
\(398\) | − | 23.5141i | − | 1.17866i | ||||||
\(399\) | −3.70178 | + | 7.12086i | −0.185321 | + | 0.356489i | ||||
\(400\) | 0.938722 | − | 1.62591i | 0.0469361 | − | 0.0812957i | ||||
\(401\) | −18.9775 | + | 10.9567i | −0.947693 | + | 0.547151i | −0.892364 | − | 0.451317i | \(-0.850954\pi\) |
−0.0553295 | + | 0.998468i | \(0.517621\pi\) | |||||||
\(402\) | −1.23956 | − | 2.14699i | −0.0618238 | − | 0.107082i | ||||
\(403\) | 18.5316 | − | 8.82563i | 0.923126 | − | 0.439636i | ||||
\(404\) | −4.61704 | + | 7.99696i | −0.229707 | + | 0.397863i | ||||
\(405\) | −2.27114 | − | 1.31124i | −0.112854 | − | 0.0651562i | ||||
\(406\) | −5.34168 | + | 10.2754i | −0.265103 | + | 0.509961i | ||||
\(407\) | 10.7322 | + | 18.5886i | 0.531973 | + | 0.921405i | ||||
\(408\) | 5.97313 | + | 3.44859i | 0.295714 | + | 0.170731i | ||||
\(409\) | −8.96270 | − | 5.17462i | −0.443177 | − | 0.255868i | 0.261767 | − | 0.965131i | \(-0.415695\pi\) |
−0.704944 | + | 0.709263i | \(0.749028\pi\) | |||||||
\(410\) | −12.9827 | − | 7.49557i | −0.641170 | − | 0.370180i | ||||
\(411\) | 11.9618 | + | 6.90614i | 0.590031 | + | 0.340655i | ||||
\(412\) | 2.43903 | + | 4.22453i | 0.120163 | + | 0.208128i | ||||
\(413\) | −14.9233 | − | 23.3957i | −0.734326 | − | 1.15123i | ||||
\(414\) | −4.32984 | − | 2.49983i | −0.212800 | − | 0.122860i | ||||
\(415\) | −12.0240 | + | 20.8262i | −0.590237 | + | 1.02232i | ||||
\(416\) | −2.97022 | − | 2.04397i | −0.145627 | − | 0.100214i | ||||
\(417\) | 5.75709 | + | 9.97158i | 0.281926 | + | 0.488310i | ||||
\(418\) | −13.1631 | + | 7.59975i | −0.643831 | + | 0.371716i | ||||
\(419\) | −8.98405 | + | 15.5608i | −0.438900 | + | 0.760197i | −0.997605 | − | 0.0691697i | \(-0.977965\pi\) |
0.558705 | + | 0.829366i | \(0.311298\pi\) | |||||||
\(420\) | 6.93168 | − | 0.306560i | 0.338231 | − | 0.0149586i | ||||
\(421\) | 7.16224i | 0.349066i | 0.984651 | + | 0.174533i | \(0.0558416\pi\) | ||||
−0.984651 | + | 0.174533i | \(0.944158\pi\) | |||||||
\(422\) | − | 4.89463i | − | 0.238267i | ||||||
\(423\) | 0.499608 | + | 0.288449i | 0.0242918 | + | 0.0140249i | ||||
\(424\) | −6.05193 | + | 3.49408i | −0.293908 | + | 0.169688i | ||||
\(425\) | −12.9491 | −0.628122 | ||||||||
\(426\) | 1.63198 | − | 2.82667i | 0.0790695 | − | 0.136952i | ||||
\(427\) | −33.6045 | − | 17.4693i | −1.62624 | − | 0.845399i | ||||
\(428\) | 0.172747 | 0.00835006 | ||||||||
\(429\) | 1.42817 | − | 18.0099i | 0.0689529 | − | 0.869528i | ||||
\(430\) | −16.8902 | − | 29.2547i | −0.814519 | − | 1.41079i | ||||
\(431\) | 31.7765i | 1.53062i | 0.643661 | + | 0.765311i | \(0.277415\pi\) | ||||
−0.643661 | + | 0.765311i | \(0.722585\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 2.56335 | + | 4.43985i | 0.123187 | + | 0.213365i | 0.921023 | − | 0.389509i | \(-0.127355\pi\) |
−0.797836 | + | 0.602874i | \(0.794022\pi\) | |||||||
\(434\) | −12.6985 | + | 8.09992i | −0.609548 | + | 0.388808i | ||||
\(435\) | −9.94119 | + | 5.73955i | −0.476644 | + | 0.275190i | ||||
\(436\) | − | 12.6108i | − | 0.603946i | ||||||
\(437\) | −13.1341 | + | 7.58295i | −0.628287 | + | 0.362742i | ||||
\(438\) | 2.42791 | − | 4.20527i | 0.116010 | − | 0.200935i | ||||
\(439\) | −18.1599 | − | 31.4539i | −0.866725 | − | 1.50121i | −0.865324 | − | 0.501212i | \(-0.832888\pi\) |
−0.00140016 | − | 0.999999i | \(-0.500446\pi\) | |||||||
\(440\) | 11.3801 | + | 6.57031i | 0.542525 | + | 0.313227i | ||||
\(441\) | 4.02150 | + | 5.72953i | 0.191500 | + | 0.272835i | ||||
\(442\) | −1.96585 | + | 24.7903i | −0.0935060 | + | 1.17916i | ||||
\(443\) | 7.15190 | − | 12.3874i | 0.339797 | − | 0.588545i | −0.644598 | − | 0.764522i | \(-0.722975\pi\) |
0.984394 | + | 0.175977i | \(0.0563084\pi\) | |||||||
\(444\) | 4.28366i | 0.203294i | ||||||||
\(445\) | 40.4511 | 1.91757 | ||||||||
\(446\) | −10.0753 | −0.477079 | ||||||||
\(447\) | − | 16.5087i | − | 0.780835i | ||||||
\(448\) | 2.34750 | + | 1.22035i | 0.110909 | + | 0.0576560i | ||||
\(449\) | −5.30462 | + | 3.06262i | −0.250340 | + | 0.144534i | −0.619920 | − | 0.784665i | \(-0.712835\pi\) |
0.369580 | + | 0.929199i | \(0.379502\pi\) | |||||||
\(450\) | 1.62591 | + | 0.938722i | 0.0766463 | + | 0.0442518i | ||||
\(451\) | 14.3217 | − | 24.8058i | 0.674380 | − | 1.16806i | ||||
\(452\) | −12.6652 | −0.595722 | ||||||||
\(453\) | 5.69210 | − | 3.28634i | 0.267438 | − | 0.154406i | ||||
\(454\) | 14.3178 | 0.671969 | ||||||||
\(455\) | 11.7441 | + | 22.0890i | 0.550571 | + | 1.03555i | ||||
\(456\) | −3.03338 | −0.142051 | ||||||||
\(457\) | −18.5805 | + | 10.7274i | −0.869157 | + | 0.501808i | −0.867068 | − | 0.498190i | \(-0.833998\pi\) |
−0.00208888 | + | 0.999998i | \(0.500665\pi\) | |||||||
\(458\) | −15.4666 | −0.722709 | ||||||||
\(459\) | −3.44859 | + | 5.97313i | −0.160966 | + | 0.278802i | ||||
\(460\) | 11.3550 | + | 6.55579i | 0.529427 | + | 0.305665i | ||||
\(461\) | −23.6097 | + | 13.6311i | −1.09961 | + | 0.634862i | −0.936120 | − | 0.351682i | \(-0.885610\pi\) |
−0.163494 | + | 0.986544i | \(0.552277\pi\) | |||||||
\(462\) | 0.585739 | + | 13.2442i | 0.0272510 | + | 0.616177i | ||||
\(463\) | − | 26.5768i | − | 1.23513i | −0.786521 | − | 0.617564i | \(-0.788120\pi\) | ||
0.786521 | − | 0.617564i | \(-0.211880\pi\) | |||||||
\(464\) | −4.37718 | −0.203205 | ||||||||
\(465\) | −14.9295 | −0.692337 | ||||||||
\(466\) | − | 4.62635i | − | 0.214311i | ||||||
\(467\) | −9.69582 | + | 16.7937i | −0.448669 | + | 0.777118i | −0.998300 | − | 0.0582902i | \(-0.981435\pi\) |
0.549631 | + | 0.835408i | \(0.314768\pi\) | |||||||
\(468\) | 2.04397 | − | 2.97022i | 0.0944826 | − | 0.137298i | ||||
\(469\) | −3.02540 | + | 5.81975i | −0.139700 | + | 0.268731i | ||||
\(470\) | −1.31022 | − | 0.756453i | −0.0604357 | − | 0.0348926i | ||||
\(471\) | 4.40621 | + | 7.63178i | 0.203028 | + | 0.351654i | ||||
\(472\) | 5.24426 | − | 9.08332i | 0.241387 | − | 0.418094i | ||||
\(473\) | 55.8965 | − | 32.2718i | 2.57012 | − | 1.48386i | ||||
\(474\) | 7.39004i | 0.339436i | ||||||||
\(475\) | 4.93202 | − | 2.84750i | 0.226297 | − | 0.130652i | ||||
\(476\) | −0.806258 | − | 18.2304i | −0.0369548 | − | 0.835589i | ||||
\(477\) | −3.49408 | − | 6.05193i | −0.159983 | − | 0.277099i | ||||
\(478\) | −4.24270 | − | 7.34857i | −0.194057 | − | 0.336116i | ||||
\(479\) | − | 24.6896i | − | 1.12810i | −0.825742 | − | 0.564048i | \(-0.809243\pi\) | ||
0.825742 | − | 0.564048i | \(-0.190757\pi\) | |||||||
\(480\) | 1.31124 | + | 2.27114i | 0.0598498 | + | 0.103663i | ||||
\(481\) | −13.9443 | + | 6.64095i | −0.635807 | + | 0.302801i | ||||
\(482\) | −4.25892 | −0.193988 | ||||||||
\(483\) | 0.584445 | + | 13.2150i | 0.0265932 | + | 0.601302i | ||||
\(484\) | −7.05376 | + | 12.2175i | −0.320626 | + | 0.555340i | ||||
\(485\) | 36.9094 | 1.67597 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −22.7389 | − | 13.1283i | −1.03040 | − | 0.594901i | −0.113300 | − | 0.993561i | \(-0.536142\pi\) |
−0.917099 | + | 0.398660i | \(0.869475\pi\) | |||||||
\(488\) | − | 14.3150i | − | 0.648011i | ||||||
\(489\) | 9.36526i | 0.423512i | ||||||||
\(490\) | −10.5463 | − | 15.0256i | −0.476435 | − | 0.678789i | ||||
\(491\) | −11.0510 | + | 19.1408i | −0.498723 | + | 0.863813i | −0.999999 | − | 0.00147433i | \(-0.999531\pi\) |
0.501276 | + | 0.865287i | \(0.332864\pi\) | |||||||
\(492\) | 4.95053 | − | 2.85819i | 0.223187 | − | 0.128857i | ||||
\(493\) | 15.0951 | + | 26.1455i | 0.679849 | + | 1.17753i | ||||
\(494\) | −4.70264 | − | 9.87438i | −0.211582 | − | 0.444270i | ||||
\(495\) | −6.57031 | + | 11.3801i | −0.295313 | + | 0.511498i | ||||
\(496\) | −4.93016 | − | 2.84643i | −0.221371 | − | 0.127809i | ||||
\(497\) | −8.62717 | + | 0.381545i | −0.386982 | + | 0.0171146i | ||||
\(498\) | −4.58497 | − | 7.94141i | −0.205458 | − | 0.355863i | ||||
\(499\) | 28.1585 | + | 16.2573i | 1.26055 | + | 0.727778i | 0.973181 | − | 0.230042i | \(-0.0738864\pi\) |
0.287368 | + | 0.957820i | \(0.407220\pi\) | |||||||
\(500\) | 7.09177 | + | 4.09443i | 0.317153 | + | 0.183109i | ||||
\(501\) | −2.26138 | − | 1.30561i | −0.101031 | − | 0.0583303i | ||||
\(502\) | −1.74531 | − | 1.00766i | −0.0778971 | − | 0.0449739i | ||||
\(503\) | 9.95552 | + | 17.2435i | 0.443895 | + | 0.768848i | 0.997974 | − | 0.0636154i | \(-0.0202631\pi\) |
−0.554080 | + | 0.832464i | \(0.686930\pi\) | |||||||
\(504\) | −1.22035 | + | 2.34750i | −0.0543586 | + | 0.104566i | ||||
\(505\) | 20.9719 | + | 12.1081i | 0.933238 | + | 0.538805i | ||||
\(506\) | −12.5260 | + | 21.6957i | −0.556850 | + | 0.964492i | ||||
\(507\) | 12.8375 | + | 2.04889i | 0.570134 | + | 0.0909946i | ||||
\(508\) | −3.67120 | − | 6.35871i | −0.162883 | − | 0.282122i | ||||
\(509\) | −2.34934 | + | 1.35639i | −0.104133 | + | 0.0601209i | −0.551162 | − | 0.834398i | \(-0.685815\pi\) |
0.447029 | + | 0.894519i | \(0.352482\pi\) | |||||||
\(510\) | 9.04389 | − | 15.6645i | 0.400470 | − | 0.693635i | ||||
\(511\) | −12.8348 | + | 0.567630i | −0.567776 | + | 0.0251105i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 3.03338i | − | 0.133927i | ||||||
\(514\) | 19.9147 | + | 11.4978i | 0.878401 | + | 0.507145i | ||||
\(515\) | 11.0788 | − | 6.39634i | 0.488189 | − | 0.281856i | ||||
\(516\) | 12.8811 | 0.567057 | ||||||||
\(517\) | 1.44534 | − | 2.50341i | 0.0635660 | − | 0.110100i | ||||
\(518\) | 9.55514 | − | 6.09488i | 0.419829 | − | 0.267793i | ||||
\(519\) | −4.99495 | −0.219254 | ||||||||
\(520\) | −5.36029 | + | 7.78936i | −0.235064 | + | 0.341586i | ||||
\(521\) | −2.90626 | − | 5.03379i | −0.127326 | − | 0.220534i | 0.795314 | − | 0.606198i | \(-0.207306\pi\) |
−0.922640 | + | 0.385663i | \(0.873973\pi\) | |||||||
\(522\) | − | 4.37718i | − | 0.191584i | ||||||
\(523\) | 19.6486 | + | 34.0323i | 0.859172 | + | 1.48813i | 0.872719 | + | 0.488222i | \(0.162354\pi\) |
−0.0135471 | + | 0.999908i | \(0.504312\pi\) | |||||||
\(524\) | −5.41067 | − | 9.37156i | −0.236366 | − | 0.409398i | ||||
\(525\) | −0.219467 | − | 4.96240i | −0.00957833 | − | 0.216577i | ||||
\(526\) | 19.0857 | − | 11.0191i | 0.832177 | − | 0.480458i | ||||
\(527\) | 39.2647i | 1.71040i | ||||||||
\(528\) | −4.33943 | + | 2.50537i | −0.188849 | + | 0.109032i | ||||
\(529\) | −0.998341 | + | 1.72918i | −0.0434062 | + | 0.0751817i | ||||
\(530\) | 9.16319 | + | 15.8711i | 0.398024 | + | 0.689397i | ||||
\(531\) | 9.08332 | + | 5.24426i | 0.394183 | + | 0.227581i | ||||
\(532\) | 4.31596 | + | 6.76627i | 0.187120 | + | 0.293355i | ||||
\(533\) | 16.9789 | + | 11.6841i | 0.735437 | + | 0.506095i | ||||
\(534\) | −7.71235 | + | 13.3582i | −0.333746 | + | 0.578065i | ||||
\(535\) | − | 0.453028i | − | 0.0195861i | ||||||
\(536\) | −2.47913 | −0.107082 | ||||||||
\(537\) | −7.52240 | −0.324616 | ||||||||
\(538\) | 4.37283i | 0.188526i | ||||||||
\(539\) | 28.7092 | − | 20.1507i | 1.23659 | − | 0.867952i | ||||
\(540\) | −2.27114 | + | 1.31124i | −0.0977344 | + | 0.0564270i | ||||
\(541\) | 20.1625 | + | 11.6408i | 0.866854 | + | 0.500478i | 0.866301 | − | 0.499522i | \(-0.166491\pi\) |
0.000552417 | 1.00000i | \(0.499824\pi\) | ||||||||
\(542\) | −7.75390 | + | 13.4302i | −0.333059 | + | 0.576875i | ||||
\(543\) | −7.14351 | −0.306557 | ||||||||
\(544\) | 5.97313 | − | 3.44859i | 0.256096 | − | 0.147857i | ||||
\(545\) | −33.0716 | −1.41663 | ||||||||
\(546\) | −9.53357 | − | 0.333204i | −0.407999 | − | 0.0142598i | ||||
\(547\) | −9.23824 | −0.394999 | −0.197499 | − | 0.980303i | \(-0.563282\pi\) | ||||
−0.197499 | + | 0.980303i | \(0.563282\pi\) | |||||||
\(548\) | 11.9618 | − | 6.90614i | 0.510982 | − | 0.295016i | ||||
\(549\) | 14.3150 | 0.610950 | ||||||||
\(550\) | 4.70369 | − | 8.14704i | 0.200566 | − | 0.347391i | ||||
\(551\) | −11.4988 | − | 6.63883i | −0.489865 | − | 0.282824i | ||||
\(552\) | −4.32984 | + | 2.49983i | −0.184290 | + | 0.106400i | ||||
\(553\) | 16.4842 | − | 10.5147i | 0.700981 | − | 0.447130i | ||||
\(554\) | 28.7587i | 1.22184i | ||||||||
\(555\) | 11.2339 | 0.476850 | ||||||||
\(556\) | 11.5142 | 0.488310 | ||||||||
\(557\) | − | 23.8434i | − | 1.01028i | −0.863038 | − | 0.505139i | \(-0.831441\pi\) | ||
0.863038 | − | 0.505139i | \(-0.168559\pi\) | |||||||
\(558\) | 2.84643 | − | 4.93016i | 0.120499 | − | 0.208711i | ||||
\(559\) | 19.9695 | + | 41.9309i | 0.844619 | + | 1.77349i | ||||
\(560\) | 3.20035 | − | 6.15629i | 0.135239 | − | 0.260151i | ||||
\(561\) | 29.9298 | + | 17.2800i | 1.26364 | + | 0.729562i | ||||
\(562\) | 6.75501 | + | 11.7000i | 0.284943 | + | 0.493536i | ||||
\(563\) | 1.04048 | − | 1.80217i | 0.0438511 | − | 0.0759523i | −0.843267 | − | 0.537495i | \(-0.819371\pi\) |
0.887118 | + | 0.461543i | \(0.152704\pi\) | |||||||
\(564\) | 0.499608 | − | 0.288449i | 0.0210373 | − | 0.0121459i | ||||
\(565\) | 33.2144i | 1.39734i | ||||||||
\(566\) | −16.4607 | + | 9.50356i | −0.691893 | + | 0.399465i | ||||
\(567\) | −2.34750 | − | 1.22035i | −0.0985857 | − | 0.0512498i | ||||
\(568\) | −1.63198 | − | 2.82667i | −0.0684762 | − | 0.118604i | ||||
\(569\) | 17.6844 | + | 30.6303i | 0.741370 | + | 1.28409i | 0.951872 | + | 0.306497i | \(0.0991568\pi\) |
−0.210502 | + | 0.977593i | \(0.567510\pi\) | |||||||
\(570\) | 7.95501i | 0.333199i | ||||||||
\(571\) | 18.0174 | + | 31.2071i | 0.754006 | + | 1.30598i | 0.945867 | + | 0.324555i | \(0.105214\pi\) |
−0.191861 | + | 0.981422i | \(0.561452\pi\) | |||||||
\(572\) | −14.8830 | − | 10.2418i | −0.622289 | − | 0.428232i | ||||
\(573\) | 7.92903 | 0.331240 | ||||||||
\(574\) | −13.4192 | − | 6.97598i | −0.560107 | − | 0.291172i | ||||
\(575\) | 4.69330 | − | 8.12903i | 0.195724 | − | 0.339004i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −34.4738 | + | 19.9034i | −1.43516 | + | 0.828591i | −0.997508 | − | 0.0705519i | \(-0.977524\pi\) |
−0.437654 | + | 0.899143i | \(0.644191\pi\) | |||||||
\(578\) | −26.4754 | − | 15.2856i | −1.10123 | − | 0.635795i | ||||
\(579\) | − | 10.7806i | − | 0.448026i | ||||||
\(580\) | 11.4791i | 0.476644i | ||||||||
\(581\) | −11.1905 | + | 21.5264i | −0.464261 | + | 0.893067i | ||||
\(582\) | −7.03709 | + | 12.1886i | −0.291697 | + | 0.505234i | ||||
\(583\) | −30.3247 | + | 17.5079i | −1.25592 | + | 0.725105i | ||||
\(584\) | −2.42791 | − | 4.20527i | −0.100468 | − | 0.174015i | ||||
\(585\) | −7.78936 | − | 5.36029i | −0.322050 | − | 0.221621i | ||||
\(586\) | −4.12406 | + | 7.14308i | −0.170363 | + | 0.295078i | ||||
\(587\) | 12.1473 | + | 7.01325i | 0.501373 | + | 0.289468i | 0.729280 | − | 0.684215i | \(-0.239855\pi\) |
−0.227907 | + | 0.973683i | \(0.573188\pi\) | |||||||
\(588\) | 6.97267 | − | 0.617955i | 0.287548 | − | 0.0254840i | ||||
\(589\) | −8.63432 | − | 14.9551i | −0.355771 | − | 0.616213i | ||||
\(590\) | −23.8209 | − | 13.7530i | −0.980691 | − | 0.566202i | ||||
\(591\) | −16.5289 | − | 9.54296i | −0.679908 | − | 0.392545i | ||||
\(592\) | 3.70976 | + | 2.14183i | 0.152470 | + | 0.0880287i | ||||
\(593\) | 15.5416 | + | 8.97292i | 0.638215 | + | 0.368474i | 0.783927 | − | 0.620853i | \(-0.213214\pi\) |
−0.145711 | + | 0.989327i | \(0.546547\pi\) | |||||||
\(594\) | −2.50537 | − | 4.33943i | −0.102797 | − | 0.178049i | ||||
\(595\) | −47.8090 | + | 2.11440i | −1.95998 | + | 0.0866820i | ||||
\(596\) | −14.2970 | − | 8.25436i | −0.585627 | − | 0.338112i | ||||
\(597\) | 11.7571 | − | 20.3638i | 0.481185 | − | 0.833436i | ||||
\(598\) | −14.8501 | − | 10.2192i | −0.607266 | − | 0.417893i | ||||
\(599\) | 15.2420 | + | 26.4000i | 0.622772 | + | 1.07867i | 0.988967 | + | 0.148135i | \(0.0473270\pi\) |
−0.366195 | + | 0.930538i | \(0.619340\pi\) | |||||||
\(600\) | 1.62591 | − | 0.938722i | 0.0663777 | − | 0.0383232i | ||||
\(601\) | −7.94423 | + | 13.7598i | −0.324052 | + | 0.561274i | −0.981320 | − | 0.192383i | \(-0.938379\pi\) |
0.657268 | + | 0.753657i | \(0.271712\pi\) | |||||||
\(602\) | −18.3274 | − | 28.7325i | −0.746970 | − | 1.17105i | ||||
\(603\) | − | 2.47913i | − | 0.100958i | ||||||
\(604\) | − | 6.57267i | − | 0.267438i | ||||||
\(605\) | 32.0402 | + | 18.4984i | 1.30262 | + | 0.752067i | ||||
\(606\) | −7.99696 | + | 4.61704i | −0.324854 | + | 0.187555i | ||||
\(607\) | 4.29143 | 0.174184 | 0.0870919 | − | 0.996200i | \(-0.472243\pi\) | ||||
0.0870919 | + | 0.996200i | \(0.472243\pi\) | |||||||
\(608\) | −1.51669 | + | 2.62699i | −0.0615100 | + | 0.106538i | ||||
\(609\) | −9.76375 | + | 6.22794i | −0.395647 | + | 0.252369i | ||||
\(610\) | −37.5410 | −1.51999 | ||||||||
\(611\) | 1.71351 | + | 1.17916i | 0.0693212 | + | 0.0477038i | ||||
\(612\) | 3.44859 | + | 5.97313i | 0.139401 | + | 0.241450i | ||||
\(613\) | 8.36726i | 0.337950i | 0.985620 | + | 0.168975i | \(0.0540458\pi\) | ||||
−0.985620 | + | 0.168975i | \(0.945954\pi\) | |||||||
\(614\) | 1.47098 | + | 2.54781i | 0.0593638 | + | 0.102821i | ||||
\(615\) | −7.49557 | − | 12.9827i | −0.302251 | − | 0.523513i | ||||
\(616\) | 11.7627 | + | 6.11485i | 0.473933 | + | 0.246374i | ||||
\(617\) | 22.4455 | − | 12.9589i | 0.903621 | − | 0.521706i | 0.0252476 | − | 0.999681i | \(-0.491963\pi\) |
0.878373 | + | 0.477976i | \(0.158629\pi\) | |||||||
\(618\) | 4.87807i | 0.196225i | ||||||||
\(619\) | −4.60270 | + | 2.65737i | −0.184998 | + | 0.106809i | −0.589639 | − | 0.807667i | \(-0.700730\pi\) |
0.404641 | + | 0.914476i | \(0.367397\pi\) | |||||||
\(620\) | −7.46473 | + | 12.9293i | −0.299791 | + | 0.519253i | ||||
\(621\) | −2.49983 | − | 4.32984i | −0.100315 | − | 0.173750i | ||||
\(622\) | 12.9406 | + | 7.47126i | 0.518871 | + | 0.299570i | ||||
\(623\) | 40.7701 | − | 1.80310i | 1.63342 | − | 0.0722395i | ||||
\(624\) | −1.55030 | − | 3.25524i | −0.0620616 | − | 0.130314i | ||||
\(625\) | 15.4312 | − | 26.7276i | 0.617248 | − | 1.06911i | ||||
\(626\) | − | 24.3857i | − | 0.974650i | ||||||
\(627\) | −15.1995 | −0.607009 | ||||||||
\(628\) | 8.81242 | 0.351654 | ||||||||
\(629\) | − | 29.5452i | − | 1.17804i | ||||||
\(630\) | 6.15629 | + | 3.20035i | 0.245272 | + | 0.127505i | ||||
\(631\) | 4.21716 | − | 2.43478i | 0.167883 | − | 0.0969271i | −0.413704 | − | 0.910411i | \(-0.635765\pi\) |
0.581587 | + | 0.813484i | \(0.302432\pi\) | |||||||
\(632\) | 6.39996 | + | 3.69502i | 0.254577 | + | 0.146980i | ||||
\(633\) | 2.44732 | − | 4.23888i | 0.0972721 | − | 0.168480i | ||||
\(634\) | 28.4626 | 1.13039 | ||||||||
\(635\) | −16.6756 | + | 9.62768i | −0.661753 | + | 0.382063i | ||||
\(636\) | −6.98817 | −0.277099 | ||||||||
\(637\) | 12.8213 | + | 21.7397i | 0.507999 | + | 0.861358i | ||||
\(638\) | −21.9329 | −0.868333 | ||||||||
\(639\) | 2.82667 | − | 1.63198i | 0.111821 | − | 0.0645600i | ||||
\(640\) | 2.62249 | 0.103663 | ||||||||
\(641\) | 9.60785 | − | 16.6413i | 0.379487 | − | 0.657291i | −0.611500 | − | 0.791244i | \(-0.709434\pi\) |
0.990988 | + | 0.133953i | \(0.0427671\pi\) | |||||||
\(642\) | 0.149604 | + | 0.0863737i | 0.00590439 | + | 0.00340890i | ||||
\(643\) | −12.2082 | + | 7.04841i | −0.481444 | + | 0.277962i | −0.721018 | − | 0.692916i | \(-0.756326\pi\) |
0.239574 | + | 0.970878i | \(0.422992\pi\) | |||||||
\(644\) | 11.7367 | + | 6.10134i | 0.462491 | + | 0.240426i | ||||
\(645\) | − | 33.7804i | − | 1.33010i | ||||||
\(646\) | 20.9218 | 0.823157 | ||||||||
\(647\) | −28.1839 | −1.10802 | −0.554012 | − | 0.832509i | \(-0.686904\pi\) | ||||
−0.554012 | + | 0.832509i | \(0.686904\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 26.2776 | − | 45.5142i | 1.03149 | − | 1.78659i | ||||
\(650\) | 5.57642 | + | 3.83744i | 0.218725 | + | 0.150517i | ||||
\(651\) | −15.0472 | + | 0.665477i | −0.589746 | + | 0.0260821i | ||||
\(652\) | 8.11055 | + | 4.68263i | 0.317634 | + | 0.183386i | ||||
\(653\) | 22.2048 | + | 38.4599i | 0.868941 | + | 1.50505i | 0.863080 | + | 0.505068i | \(0.168533\pi\) |
0.00586180 | + | 0.999983i | \(0.498134\pi\) | |||||||
\(654\) | 6.30538 | − | 10.9212i | 0.246560 | − | 0.427054i | ||||
\(655\) | −24.5768 | + | 14.1894i | −0.960295 | + | 0.554427i | ||||
\(656\) | − | 5.71638i | − | 0.223187i | ||||||
\(657\) | 4.20527 | − | 2.42791i | 0.164063 | − | 0.0947218i | ||||
\(658\) | −1.35427 | − | 0.704016i | −0.0527948 | − | 0.0274454i | ||||
\(659\) | −8.69801 | − | 15.0654i | −0.338826 | − | 0.586864i | 0.645386 | − | 0.763857i | \(-0.276697\pi\) |
−0.984212 | + | 0.176992i | \(0.943363\pi\) | |||||||
\(660\) | 6.57031 | + | 11.3801i | 0.255749 | + | 0.442970i | ||||
\(661\) | 0.791848i | 0.0307993i | 0.999881 | + | 0.0153997i | \(0.00490206\pi\) | ||||
−0.999881 | + | 0.0153997i | \(0.995098\pi\) | |||||||
\(662\) | 3.13842 | + | 5.43590i | 0.121978 | + | 0.211272i | ||||
\(663\) | −14.0976 | + | 20.4861i | −0.547507 | + | 0.795615i | ||||
\(664\) | −9.16995 | −0.355863 | ||||||||
\(665\) | 17.7445 | − | 11.3185i | 0.688101 | − | 0.438914i | ||||
\(666\) | −2.14183 | + | 3.70976i | −0.0829943 | + | 0.143750i | ||||
\(667\) | −21.8844 | −0.847369 | ||||||||
\(668\) | −2.26138 | + | 1.30561i | −0.0874954 | + | 0.0505155i | ||||
\(669\) | −8.72547 | − | 5.03765i | −0.337346 | − | 0.194767i | ||||
\(670\) | 6.50148i | 0.251174i | ||||||||
\(671\) | − | 71.7289i | − | 2.76906i | ||||||
\(672\) | 1.42282 | + | 2.23060i | 0.0548864 | + | 0.0860473i | ||||
\(673\) | 10.4137 | − | 18.0371i | 0.401420 | − | 0.695280i | −0.592477 | − | 0.805587i | \(-0.701850\pi\) |
0.993898 | + | 0.110307i | \(0.0351834\pi\) | |||||||
\(674\) | 8.65214 | − | 4.99532i | 0.333268 | − | 0.192412i | ||||
\(675\) | 0.938722 | + | 1.62591i | 0.0361314 | + | 0.0625815i | ||||
\(676\) | 8.19316 | − | 10.0932i | 0.315121 | − | 0.388199i | ||||
\(677\) | −14.2416 | + | 24.6671i | −0.547347 | + | 0.948034i | 0.451108 | + | 0.892470i | \(0.351029\pi\) |
−0.998455 | + | 0.0555641i | \(0.982304\pi\) | |||||||
\(678\) | −10.9684 | − | 6.33262i | −0.421239 | − | 0.243203i | ||||
\(679\) | 37.2004 | − | 1.64523i | 1.42762 | − | 0.0631379i | ||||
\(680\) | −9.04389 | − | 15.6645i | −0.346817 | − | 0.600705i | ||||
\(681\) | 12.3996 | + | 7.15891i | 0.475154 | + | 0.274330i | ||||
\(682\) | −24.7038 | − | 14.2627i | −0.945957 | − | 0.546148i | ||||
\(683\) | 7.08612 | + | 4.09118i | 0.271143 | + | 0.156544i | 0.629407 | − | 0.777076i | \(-0.283298\pi\) |
−0.358264 | + | 0.933620i | \(0.616631\pi\) | |||||||
\(684\) | −2.62699 | − | 1.51669i | −0.100445 | − | 0.0579921i | ||||
\(685\) | −18.1113 | − | 31.3696i | −0.691996 | − | 1.19857i | ||||
\(686\) | −11.2993 | − | 14.6740i | −0.431408 | − | 0.560256i | ||||
\(687\) | −13.3945 | − | 7.73332i | −0.511032 | − | 0.295045i | ||||
\(688\) | 6.44053 | − | 11.1553i | 0.245543 | − | 0.425293i | ||||
\(689\) | −10.8337 | − | 22.7481i | −0.412732 | − | 0.866635i | ||||
\(690\) | 6.55579 | + | 11.3550i | 0.249574 | + | 0.432276i | ||||
\(691\) | 1.10054 | − | 0.635398i | 0.0418666 | − | 0.0241717i | −0.478921 | − | 0.877858i | \(-0.658972\pi\) |
0.520787 | + | 0.853687i | \(0.325638\pi\) | |||||||
\(692\) | −2.49748 | + | 4.32576i | −0.0949398 | + | 0.164441i | ||||
\(693\) | −6.11485 | + | 11.7627i | −0.232284 | + | 0.446828i | ||||
\(694\) | − | 3.90930i | − | 0.148395i | ||||||
\(695\) | − | 30.1958i | − | 1.14539i | ||||||
\(696\) | −3.79075 | − | 2.18859i | −0.143688 | − | 0.0829583i | ||||
\(697\) | −34.1447 | + | 19.7135i | −1.29332 | + | 0.746701i | ||||
\(698\) | 15.3950 | 0.582710 | ||||||||
\(699\) | 2.31317 | − | 4.00653i | 0.0874922 | − | 0.151541i | ||||
\(700\) | −4.40730 | − | 2.29114i | −0.166580 | − | 0.0865968i | ||||
\(701\) | 13.9585 | 0.527207 | 0.263604 | − | 0.964631i | \(-0.415089\pi\) | ||||
0.263604 | + | 0.964631i | \(0.415089\pi\) | |||||||
\(702\) | 3.25524 | − | 1.55030i | 0.122861 | − | 0.0585122i | ||||
\(703\) | 6.49699 | + | 11.2531i | 0.245039 | + | 0.424419i | ||||
\(704\) | 5.01074i | 0.188849i | ||||||||
\(705\) | −0.756453 | − | 1.31022i | −0.0284897 | − | 0.0493456i | ||||
\(706\) | 15.0418 | + | 26.0531i | 0.566105 | + | 0.980523i | ||||
\(707\) | 21.6770 | + | 11.2688i | 0.815248 | + | 0.423807i | ||||
\(708\) | 9.08332 | − | 5.24426i | 0.341372 | − | 0.197091i | ||||
\(709\) | − | 2.21567i | − | 0.0832113i | −0.999134 | − | 0.0416057i | \(-0.986753\pi\) | ||
0.999134 | − | 0.0416057i | \(-0.0132473\pi\) | |||||||
\(710\) | −7.41290 | + | 4.27984i | −0.278201 | + | 0.160619i | ||||
\(711\) | −3.69502 | + | 6.39996i | −0.138574 | + | 0.240017i | ||||
\(712\) | 7.71235 | + | 13.3582i | 0.289032 | + | 0.500619i | ||||
\(713\) | −24.6492 | − | 14.2312i | −0.923119 | − | 0.532963i | ||||
\(714\) | 8.41696 | − | 16.1911i | 0.314997 | − | 0.605938i | ||||
\(715\) | −26.8590 | + | 39.0305i | −1.00447 | + | 1.45966i | ||||
\(716\) | −3.76120 | + | 6.51459i | −0.140563 | + | 0.243462i | ||||
\(717\) | − | 8.48540i | − | 0.316893i | ||||||
\(718\) | −8.35261 | −0.311717 | ||||||||
\(719\) | 6.10672 | 0.227742 | 0.113871 | − | 0.993496i | \(-0.463675\pi\) | ||||
0.113871 | + | 0.993496i | \(0.463675\pi\) | |||||||
\(720\) | 2.62249i | 0.0977344i | ||||||||
\(721\) | 10.8810 | − | 6.94061i | 0.405231 | − | 0.258482i | ||||
\(722\) | 8.48583 | − | 4.89930i | 0.315810 | − | 0.182333i | ||||
\(723\) | −3.68833 | − | 2.12946i | −0.137170 | − | 0.0791954i | ||||
\(724\) | −3.57176 | + | 6.18646i | −0.132743 | + | 0.229918i | ||||
\(725\) | 8.21791 | 0.305206 | ||||||||
\(726\) | −12.2175 | + | 7.05376i | −0.453433 | + | 0.261790i | ||||
\(727\) | 6.95455 | 0.257930 | 0.128965 | − | 0.991649i | \(-0.458835\pi\) | ||||
0.128965 | + | 0.991649i | \(0.458835\pi\) | |||||||
\(728\) | −5.05535 | + | 8.08971i | −0.187364 | + | 0.299825i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.0283 | + | 6.36717i | −0.408174 | + | 0.235660i | ||||
\(731\) | −88.8430 | −3.28598 | ||||||||
\(732\) | 7.15751 | − | 12.3972i | 0.264549 | − | 0.458213i | ||||
\(733\) | 13.1539 | + | 7.59443i | 0.485852 | + | 0.280506i | 0.722852 | − | 0.691003i | \(-0.242831\pi\) |
−0.237000 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(734\) | 10.7075 | − | 6.18199i | 0.395222 | − | 0.228181i | ||||
\(735\) | −1.62058 | − | 18.2857i | −0.0597760 | − | 0.674480i | ||||
\(736\) | 4.99967i | 0.184290i | ||||||||
\(737\) | −12.4223 | −0.457580 | ||||||||
\(738\) | 5.71638 | 0.210423 | ||||||||
\(739\) | − | 48.1214i | − | 1.77018i | −0.465424 | − | 0.885088i | \(-0.654098\pi\) | ||
0.465424 | − | 0.885088i | \(-0.345902\pi\) | |||||||
\(740\) | 5.61693 | − | 9.72880i | 0.206482 | − | 0.357638i | ||||
\(741\) | 0.864582 | − | 10.9028i | 0.0317612 | − | 0.400524i | ||||
\(742\) | 9.94290 | + | 15.5878i | 0.365015 | + | 0.572247i | ||||
\(743\) | 35.6831 | + | 20.6017i | 1.30909 | + | 0.755802i | 0.981944 | − | 0.189173i | \(-0.0605807\pi\) |
0.327143 | + | 0.944975i | \(0.393914\pi\) | |||||||
\(744\) | −2.84643 | − | 4.93016i | −0.104355 | − | 0.180749i | ||||
\(745\) | −21.6470 | + | 37.4936i | −0.793083 | + | 1.37366i | ||||
\(746\) | −19.6066 | + | 11.3199i | −0.717849 | + | 0.414451i | ||||
\(747\) | − | 9.16995i | − | 0.335511i | ||||||
\(748\) | 29.9298 | − | 17.2800i | 1.09434 | − | 0.631819i | ||||
\(749\) | −0.0201936 | − | 0.456600i | −0.000737858 | − | 0.0166838i | ||||
\(750\) | 4.09443 | + | 7.09177i | 0.149508 | + | 0.258955i | ||||
\(751\) | −21.3607 | − | 36.9979i | −0.779465 | − | 1.35007i | −0.932251 | − | 0.361813i | \(-0.882158\pi\) |
0.152786 | − | 0.988259i | \(-0.451176\pi\) | |||||||
\(752\) | − | 0.576897i | − | 0.0210373i | ||||||
\(753\) | −1.00766 | − | 1.74531i | −0.0367210 | − | 0.0636027i | ||||
\(754\) | 1.24759 | − | 15.7328i | 0.0454347 | − | 0.572953i | ||||
\(755\) | −17.2368 | −0.627310 | ||||||||
\(756\) | −2.23060 | + | 1.42282i | −0.0811262 | + | 0.0517474i | ||||
\(757\) | −21.7752 | + | 37.7157i | −0.791432 | + | 1.37080i | 0.133648 | + | 0.991029i | \(0.457331\pi\) |
−0.925080 | + | 0.379772i | \(0.876003\pi\) | |||||||
\(758\) | 10.8958 | 0.395752 | ||||||||
\(759\) | −21.6957 | + | 12.5260i | −0.787504 | + | 0.454666i | ||||
\(760\) | 6.88924 | + | 3.97750i | 0.249899 | + | 0.144279i | ||||
\(761\) | 9.54931i | 0.346162i | 0.984908 | + | 0.173081i | \(0.0553723\pi\) | ||||
−0.984908 | + | 0.173081i | \(0.944628\pi\) | |||||||
\(762\) | − | 7.34240i | − | 0.265987i | ||||||
\(763\) | −33.3324 | + | 1.47416i | −1.20671 | + | 0.0533680i | ||||
\(764\) | 3.96451 | − | 6.86674i | 0.143431 | − | 0.248430i | ||||
\(765\) | 15.6645 | − | 9.04389i | 0.566350 | − | 0.326982i | ||||
\(766\) | 0.634815 | + | 1.09953i | 0.0229368 | + | 0.0397277i | ||||
\(767\) | 31.1532 | + | 21.4382i | 1.12488 | + | 0.774089i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −22.0605 | − | 12.7366i | −0.795521 | − | 0.459294i | 0.0463817 | − | 0.998924i | \(-0.485231\pi\) |
−0.841903 | + | 0.539630i | \(0.818564\pi\) | |||||||
\(770\) | 16.0361 | − | 30.8476i | 0.577902 | − | 1.11167i | ||||
\(771\) | 11.4978 | + | 19.9147i | 0.414082 | + | 0.717211i | ||||
\(772\) | −9.33627 | − | 5.39030i | −0.336020 | − | 0.194001i | ||||
\(773\) | 14.7720 | + | 8.52865i | 0.531314 | + | 0.306754i | 0.741551 | − | 0.670896i | \(-0.234090\pi\) |
−0.210238 | + | 0.977650i | \(0.567424\pi\) | |||||||
\(774\) | 11.1553 | + | 6.44053i | 0.400970 | + | 0.231500i | ||||
\(775\) | 9.25611 | + | 5.34402i | 0.332489 | + | 0.191963i | ||||
\(776\) | 7.03709 | + | 12.1886i | 0.252617 | + | 0.437545i | ||||
\(777\) | 11.3224 | − | 0.500746i | 0.406190 | − | 0.0179642i | ||||
\(778\) | 26.5529 | + | 15.3303i | 0.951968 | + | 0.549619i | ||||
\(779\) | 8.66999 | − | 15.0169i | 0.310634 | − | 0.538035i | ||||
\(780\) | −8.53682 | + | 4.06564i | −0.305667 | + | 0.145573i | ||||
\(781\) | −8.17741 | − | 14.1637i | −0.292611 | − | 0.506817i | ||||
\(782\) | 29.8637 | − | 17.2418i | 1.06792 | − | 0.616566i | ||||
\(783\) | 2.18859 | − | 3.79075i | 0.0782138 | − | 0.135470i | ||||
\(784\) | 2.95117 | − | 6.34749i | 0.105399 | − | 0.226696i | ||||
\(785\) | − | 23.1105i | − | 0.824848i | ||||||
\(786\) | − | 10.8213i | − | 0.385984i | ||||||
\(787\) | −34.2123 | − | 19.7525i | −1.21954 | − | 0.704099i | −0.254717 | − | 0.967016i | \(-0.581982\pi\) |
−0.964818 | + | 0.262917i | \(0.915316\pi\) | |||||||
\(788\) | −16.5289 | + | 9.54296i | −0.588817 | + | 0.339954i | ||||
\(789\) | 22.0383 | 0.784584 | ||||||||
\(790\) | 9.69014 | − | 16.7838i | 0.344760 | − | 0.597141i | ||||
\(791\) | 1.48052 | + | 33.4763i | 0.0526414 | + | 1.19028i | ||||
\(792\) | −5.01074 | −0.178049 | ||||||||
\(793\) | 51.4520 | + | 4.08010i | 1.82711 | + | 0.144889i | ||||
\(794\) | −13.2240 | − | 22.9046i | −0.469301 | − | 0.812854i | ||||
\(795\) | 18.3264i | 0.649970i | ||||||||
\(796\) | −11.7571 | − | 20.3638i | −0.416718 | − | 0.721777i | ||||
\(797\) | −8.76369 | − | 15.1792i | −0.310426 | − | 0.537673i | 0.668029 | − | 0.744135i | \(-0.267138\pi\) |
−0.978455 | + | 0.206462i | \(0.933805\pi\) | |||||||
\(798\) | 0.354592 | + | 8.01774i | 0.0125524 | + | 0.283825i | ||||
\(799\) | −3.44589 | + | 1.98948i | −0.121907 | + | 0.0703828i | ||||
\(800\) | − | 1.87744i | − | 0.0663777i | ||||||
\(801\) | −13.3582 | + | 7.71235i | −0.471988 | + | 0.272502i | ||||
\(802\) | −10.9567 | + | 18.9775i | −0.386894 | + | 0.670120i | ||||
\(803\) | −12.1656 | − | 21.0715i | −0.429316 | − | 0.743597i | ||||
\(804\) | −2.14699 | − | 1.23956i | −0.0757184 | − | 0.0437160i | ||||
\(805\) | 16.0007 | − | 30.7794i | 0.563950 | − | 1.08483i | ||||
\(806\) | 11.6360 | − | 16.9090i | 0.409862 | − | 0.595595i | ||||
\(807\) | −2.18641 | + | 3.78698i | −0.0769654 | + | 0.133308i | ||||
\(808\) | 9.23409i | 0.324854i | ||||||||
\(809\) | 7.21823 | 0.253779 | 0.126890 | − | 0.991917i | \(-0.459501\pi\) | ||||
0.126890 | + | 0.991917i | \(0.459501\pi\) | |||||||
\(810\) | −2.62249 | −0.0921448 | ||||||||
\(811\) | − | 33.6889i | − | 1.18298i | −0.806314 | − | 0.591488i | \(-0.798541\pi\) | ||
0.806314 | − | 0.591488i | \(-0.201459\pi\) | |||||||
\(812\) | 0.511678 | + | 11.5696i | 0.0179564 | + | 0.406014i | ||||
\(813\) | −13.4302 | + | 7.75390i | −0.471016 | + | 0.271941i | ||||
\(814\) | 18.5886 | + | 10.7322i | 0.651532 | + | 0.376162i | ||||
\(815\) | 12.2801 | − | 21.2698i | 0.430155 | − | 0.745050i | ||||
\(816\) | 6.89718 | 0.241450 | ||||||||
\(817\) | 33.8384 | − | 19.5366i | 1.18385 | − | 0.683499i | ||||
\(818\) | −10.3492 | −0.361852 | ||||||||
\(819\) | −8.08971 | − | 5.05535i | −0.282677 | − | 0.176648i | ||||
\(820\) | −14.9911 | −0.523513 | ||||||||
\(821\) | −5.50808 | + | 3.18009i | −0.192233 | + | 0.110986i | −0.593028 | − | 0.805182i | \(-0.702068\pi\) |
0.400794 | + | 0.916168i | \(0.368734\pi\) | |||||||
\(822\) | 13.8123 | 0.481759 | ||||||||
\(823\) | 4.94605 | − | 8.56680i | 0.172408 | − | 0.298620i | −0.766853 | − | 0.641823i | \(-0.778178\pi\) |
0.939261 | + | 0.343203i | \(0.111512\pi\) | |||||||
\(824\) | 4.22453 | + | 2.43903i | 0.147168 | + | 0.0849678i | ||||
\(825\) | 8.14704 | − | 4.70369i | 0.283643 | − | 0.163762i | ||||
\(826\) | −24.6218 | − | 12.7996i | −0.856701 | − | 0.445357i | ||||
\(827\) | 0.161968i | 0.00563219i | 0.999996 | + | 0.00281610i | \(0.000896393\pi\) | ||||
−0.999996 | + | 0.00281610i | \(0.999104\pi\) | |||||||
\(828\) | −4.99967 | −0.173750 | ||||||||
\(829\) | 2.49876 | 0.0867857 | 0.0433928 | − | 0.999058i | \(-0.486183\pi\) | ||||
0.0433928 | + | 0.999058i | \(0.486183\pi\) | |||||||
\(830\) | 24.0481i | 0.834721i | ||||||||
\(831\) | −14.3794 | + | 24.9058i | −0.498815 | + | 0.863972i | ||||
\(832\) | −3.59427 | − | 0.285022i | −0.124609 | − | 0.00988137i | ||||
\(833\) | −48.0918 | + | 4.26215i | −1.66628 | + | 0.147675i | ||||
\(834\) | 9.97158 | + | 5.75709i | 0.345288 | + | 0.199352i | ||||
\(835\) | 3.42394 | + | 5.93044i | 0.118490 | + | 0.205231i | ||||
\(836\) | −7.59975 | + | 13.1631i | −0.262843 | + | 0.455257i | ||||
\(837\) | 4.93016 | − | 2.84643i | 0.170411 | − | 0.0983871i | ||||
\(838\) | 17.9681i | 0.620698i | ||||||||
\(839\) | 33.8670 | − | 19.5531i | 1.16922 | − | 0.675048i | 0.215722 | − | 0.976455i | \(-0.430790\pi\) |
0.953496 | + | 0.301407i | \(0.0974563\pi\) | |||||||
\(840\) | 5.84973 | − | 3.73133i | 0.201835 | − | 0.128743i | ||||
\(841\) | 4.92015 | + | 8.52195i | 0.169660 | + | 0.293860i | ||||
\(842\) | 3.58112 | + | 6.20268i | 0.123413 | + | 0.213758i | ||||
\(843\) | 13.5100i | 0.465310i | ||||||||
\(844\) | −2.44732 | − | 4.23888i | −0.0842401 | − | 0.145908i | ||||
\(845\) | −26.4692 | − | 21.4865i | −0.910569 | − | 0.739157i | ||||
\(846\) | 0.576897 | 0.0198341 | ||||||||
\(847\) | 33.1174 | + | 17.2161i | 1.13793 | + | 0.591552i | ||||
\(848\) | −3.49408 | + | 6.05193i | −0.119987 | + | 0.207824i | ||||
\(849\) | −19.0071 | −0.652323 | ||||||||
\(850\) | −11.2142 | + | 6.47454i | −0.384645 | + | 0.222075i | ||||
\(851\) | 18.5476 | + | 10.7084i | 0.635802 | + | 0.367081i | ||||
\(852\) | − | 3.26395i | − | 0.111821i | ||||||
\(853\) | 3.18625i | 0.109095i | 0.998511 | + | 0.0545476i | \(0.0173717\pi\) | ||||
−0.998511 | + | 0.0545476i | \(0.982628\pi\) | |||||||
\(854\) | −37.8370 | + | 1.67338i | −1.29476 | + | 0.0572618i | ||||
\(855\) | −3.97750 | + | 6.88924i | −0.136028 | + | 0.235607i | ||||
\(856\) | 0.149604 | − | 0.0863737i | 0.00511335 | − | 0.00295219i | ||||
\(857\) | −21.1932 | − | 36.7078i | −0.723947 | − | 1.25391i | −0.959406 | − | 0.282029i | \(-0.908993\pi\) |
0.235459 | − | 0.971884i | \(-0.424341\pi\) | |||||||
\(858\) | −7.76814 | − | 16.3112i | −0.265200 | − | 0.556854i | ||||
\(859\) | 6.71141 | − | 11.6245i | 0.228990 | − | 0.396623i | −0.728519 | − | 0.685026i | \(-0.759791\pi\) |
0.957509 | + | 0.288403i | \(0.0931242\pi\) | |||||||
\(860\) | −29.2547 | − | 16.8902i | −0.997577 | − | 0.575952i | ||||
\(861\) | −8.13338 | − | 12.7510i | −0.277185 | − | 0.434552i | ||||
\(862\) | 15.8883 | + | 27.5193i | 0.541157 | + | 0.937311i | ||||
\(863\) | −34.2623 | − | 19.7813i | −1.16630 | − | 0.673365i | −0.213496 | − | 0.976944i | \(-0.568485\pi\) |
−0.952806 | + | 0.303579i | \(0.901818\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 11.3442 | + | 6.54960i | 0.385716 | + | 0.222693i | ||||
\(866\) | 4.43985 | + | 2.56335i | 0.150872 | + | 0.0871061i | ||||
\(867\) | −15.2856 | − | 26.4754i | −0.519125 | − | 0.899150i | ||||
\(868\) | −6.94728 | + | 13.3640i | −0.235806 | + | 0.453603i | ||||
\(869\) | 32.0685 | + | 18.5148i | 1.08785 | + | 0.628071i | ||||
\(870\) | −5.73955 | + | 9.94119i | −0.194589 | + | 0.337038i | ||||
\(871\) | 0.706606 | − | 8.91064i | 0.0239424 | − | 0.301926i | ||||
\(872\) | −6.30538 | − | 10.9212i | −0.213527 | − | 0.369840i | ||||
\(873\) | −12.1886 | + | 7.03709i | −0.412522 | + | 0.238169i | ||||
\(874\) | −7.58295 | + | 13.1341i | −0.256497 | + | 0.444266i | ||||
\(875\) | 9.99327 | − | 19.2234i | 0.337834 | − | 0.649868i | ||||
\(876\) | − | 4.85582i | − | 0.164063i | ||||||
\(877\) | 27.7042i | 0.935503i | 0.883860 | + | 0.467752i | \(0.154936\pi\) | ||||
−0.883860 | + | 0.467752i | \(0.845064\pi\) | |||||||
\(878\) | −31.4539 | − | 18.1599i | −1.06152 | − | 0.612867i | ||||
\(879\) | −7.14308 | + | 4.12406i | −0.240930 | + | 0.139101i | ||||
\(880\) | 13.1406 | 0.442970 | ||||||||
\(881\) | 18.7398 | − | 32.4583i | 0.631360 | − | 1.09355i | −0.355914 | − | 0.934519i | \(-0.615830\pi\) |
0.987274 | − | 0.159029i | \(-0.0508364\pi\) | |||||||
\(882\) | 6.34749 | + | 2.95117i | 0.213731 | + | 0.0993711i | ||||
\(883\) | 25.4665 | 0.857015 | 0.428508 | − | 0.903538i | \(-0.359040\pi\) | ||||
0.428508 | + | 0.903538i | \(0.359040\pi\) | |||||||
\(884\) | 10.6927 | + | 22.4520i | 0.359634 | + | 0.755142i | ||||
\(885\) | −13.7530 | − | 23.8209i | −0.462302 | − | 0.800731i | ||||
\(886\) | − | 14.3038i | − | 0.480545i | ||||||
\(887\) | 14.8882 | + | 25.7871i | 0.499896 | + | 0.865846i | 1.00000 | 0.000119786i | \(-3.81289e-5\pi\) | |
−0.500104 | + | 0.865966i | \(0.666705\pi\) | |||||||
\(888\) | 2.14183 | + | 3.70976i | 0.0718751 | + | 0.124491i | ||||
\(889\) | −16.3780 | + | 10.4469i | −0.549300 | + | 0.350378i | ||||
\(890\) | 35.0317 | − | 20.2255i | 1.17426 | − | 0.677962i | ||||
\(891\) | − | 5.01074i | − | 0.167866i | ||||||
\(892\) | −8.72547 | + | 5.03765i | −0.292150 | + | 0.168673i | ||||
\(893\) | 0.874975 | − | 1.51550i | 0.0292799 | − | 0.0507143i | ||||
\(894\) | −8.25436 | − | 14.2970i | −0.276067 | − | 0.478162i | ||||
\(895\) | 17.0844 | + | 9.86371i | 0.571070 | + | 0.329707i | ||||
\(896\) | 2.64317 | − | 0.116897i | 0.0883020 | − | 0.00390524i | ||||
\(897\) | −7.75097 | − | 16.2751i | −0.258797 | − | 0.543410i | ||||
\(898\) | −3.06262 | + | 5.30462i | −0.102201 | + | 0.177017i | ||||
\(899\) | − | 24.9187i | − | 0.831085i | ||||||
\(900\) | 1.87744 | 0.0625815 | ||||||||
\(901\) | 48.1987 | 1.60573 | ||||||||
\(902\) | − | 28.6433i | − | 0.953718i | ||||||
\(903\) | −1.50575 | − | 34.0468i | −0.0501083 | − | 1.13301i | ||||
\(904\) | −10.9684 | + | 6.33262i | −0.364804 | + | 0.210620i | ||||
\(905\) | 16.2239 | + | 9.36689i | 0.539302 | + | 0.311366i | ||||
\(906\) | 3.28634 | − | 5.69210i | 0.109181 | − | 0.189107i | ||||
\(907\) | 45.3138 | 1.50462 | 0.752311 | − | 0.658808i | \(-0.228939\pi\) | ||||
0.752311 | + | 0.658808i | \(0.228939\pi\) | |||||||
\(908\) | 12.3996 | − | 7.15891i | 0.411495 | − | 0.237577i | ||||
\(909\) | −9.23409 | −0.306275 | ||||||||
\(910\) | 21.2152 | + | 13.2576i | 0.703276 | + | 0.439485i | ||||
\(911\) | −44.3887 | −1.47066 | −0.735332 | − | 0.677707i | \(-0.762974\pi\) | ||||
−0.735332 | + | 0.677707i | \(0.762974\pi\) | |||||||
\(912\) | −2.62699 | + | 1.51669i | −0.0869882 | + | 0.0502227i | ||||
\(913\) | −45.9482 | −1.52066 | ||||||||
\(914\) | −10.7274 | + | 18.5805i | −0.354832 | + | 0.614587i | ||||
\(915\) | −32.5114 | − | 18.7705i | −1.07479 | − | 0.620533i | ||||
\(916\) | −13.3945 | + | 7.73332i | −0.442567 | + | 0.255516i | ||||
\(917\) | −24.1381 | + | 15.3968i | −0.797111 | + | 0.508448i | ||||
\(918\) | 6.89718i | 0.227641i | ||||||||
\(919\) | −29.3318 | −0.967568 | −0.483784 | − | 0.875188i | \(-0.660738\pi\) | ||||
−0.483784 | + | 0.875188i | \(0.660738\pi\) | |||||||
\(920\) | 13.1116 | 0.432276 | ||||||||
\(921\) | 2.94195i | 0.0969407i | ||||||||
\(922\) | −13.6311 | + | 23.6097i | −0.448915 | + | 0.777544i | ||||
\(923\) | 10.6249 | − | 5.06010i | 0.349724 | − | 0.166555i | ||||
\(924\) | 7.12938 | + | 11.1770i | 0.234539 | + | 0.367695i | ||||
\(925\) | −6.96487 | − | 4.02117i | −0.229003 | − | 0.132215i | ||||
\(926\) | −13.2884 | − | 23.0162i | −0.436684 | − | 0.756358i | ||||
\(927\) | −2.43903 | + | 4.22453i | −0.0801084 | + | 0.138752i | ||||
\(928\) | −3.79075 | + | 2.18859i | −0.124437 | + | 0.0718440i | ||||
\(929\) | − | 27.9191i | − | 0.915995i | −0.888954 | − | 0.457997i | \(-0.848567\pi\) | ||
0.888954 | − | 0.457997i | \(-0.151433\pi\) | |||||||
\(930\) | −12.9293 | + | 7.46473i | −0.423968 | + | 0.244778i | ||||
\(931\) | 17.3799 | − | 12.1987i | 0.569602 | − | 0.399798i | ||||
\(932\) | −2.31317 | − | 4.00653i | −0.0757705 | − | 0.131238i | ||||
\(933\) | 7.47126 | + | 12.9406i | 0.244598 | + | 0.423656i | ||||
\(934\) | 19.3916i | 0.634514i | ||||||||
\(935\) | −45.3166 | − | 78.4906i | −1.48201 | − | 2.56692i | ||||
\(936\) | 0.285022 | − | 3.59427i | 0.00931625 | − | 0.117482i | ||||
\(937\) | −38.6927 | −1.26404 | −0.632018 | − | 0.774953i | \(-0.717773\pi\) | ||||
−0.632018 | + | 0.774953i | \(0.717773\pi\) | |||||||
\(938\) | 0.289802 | + | 6.55275i | 0.00946236 | + | 0.213955i | ||||
\(939\) | 12.1929 | − | 21.1187i | 0.397899 | − | 0.689182i | ||||
\(940\) | −1.51291 | −0.0493456 | ||||||||
\(941\) | 2.94391 | − | 1.69967i | 0.0959688 | − | 0.0554076i | −0.451247 | − | 0.892399i | \(-0.649021\pi\) |
0.547216 | + | 0.836991i | \(0.315688\pi\) | |||||||
\(942\) | 7.63178 | + | 4.40621i | 0.248657 | + | 0.143562i | ||||
\(943\) | − | 28.5800i | − | 0.930693i | ||||||
\(944\) | − | 10.4885i | − | 0.341372i | ||||||
\(945\) | 3.73133 | + | 5.84973i | 0.121380 | + | 0.190292i | ||||
\(946\) | 32.2718 | − | 55.8965i | 1.04925 | − | 1.81735i | ||||
\(947\) | −18.0395 | + | 10.4151i | −0.586206 | + | 0.338446i | −0.763596 | − | 0.645694i | \(-0.776568\pi\) |
0.177390 | + | 0.984141i | \(0.443235\pi\) | |||||||
\(948\) | 3.69502 | + | 6.39996i | 0.120009 | + | 0.207861i | ||||
\(949\) | 15.8069 | − | 7.52797i | 0.513112 | − | 0.244368i | ||||
\(950\) | 2.84750 | − | 4.93202i | 0.0923852 | − | 0.160016i | ||||
\(951\) | 24.6493 | + | 14.2313i | 0.799309 | + | 0.461481i | ||||
\(952\) | −9.81344 | − | 15.3849i | −0.318056 | − | 0.498626i | ||||
\(953\) | −12.1372 | − | 21.0222i | −0.393162 | − | 0.680977i | 0.599703 | − | 0.800223i | \(-0.295286\pi\) |
−0.992865 | + | 0.119246i | \(0.961952\pi\) | |||||||
\(954\) | −6.05193 | − | 3.49408i | −0.195938 | − | 0.113125i | ||||
\(955\) | −18.0079 | − | 10.3969i | −0.582723 | − | 0.336435i | ||||
\(956\) | −7.34857 | − | 4.24270i | −0.237670 | − | 0.137219i | ||||
\(957\) | −18.9945 | − | 10.9665i | −0.614004 | − | 0.354495i | ||||
\(958\) | −12.3448 | − | 21.3818i | −0.398842 | − | 0.690815i | ||||
\(959\) | −19.6524 | − | 30.8097i | −0.634609 | − | 0.994897i | ||||
\(960\) | 2.27114 | + | 1.31124i | 0.0733008 | + | 0.0423202i | ||||
\(961\) | 0.704348 | − | 1.21997i | 0.0227209 | − | 0.0393537i | ||||
\(962\) | −8.75568 | + | 12.7234i | −0.282294 | + | 0.410219i | ||||
\(963\) | 0.0863737 | + | 0.149604i | 0.00278335 | + | 0.00482091i | ||||
\(964\) | −3.68833 | + | 2.12946i | −0.118793 | + | 0.0685852i | ||||
\(965\) | −14.1360 | + | 24.4843i | −0.455054 | + | 0.788176i | ||||
\(966\) | 7.11362 | + | 11.1523i | 0.228877 | + | 0.358818i | ||||
\(967\) | 47.4200i | 1.52492i | 0.647033 | + | 0.762462i | \(0.276010\pi\) | ||||
−0.647033 | + | 0.762462i | \(0.723990\pi\) | |||||||
\(968\) | 14.1075i | 0.453433i | ||||||||
\(969\) | 18.1188 | + | 10.4609i | 0.582060 | + | 0.336052i | ||||
\(970\) | 31.9645 | − | 18.4547i | 1.02632 | − | 0.592544i | ||||
\(971\) | 32.9127 | 1.05622 | 0.528110 | − | 0.849176i | \(-0.322901\pi\) | ||||
0.528110 | + | 0.849176i | \(0.322901\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −1.34597 | − | 30.4339i | −0.0431498 | − | 0.975667i | ||||
\(974\) | −26.2566 | −0.841317 | ||||||||
\(975\) | 2.91060 | + | 6.11153i | 0.0932137 | + | 0.195726i | ||||
\(976\) | −7.15751 | − | 12.3972i | −0.229106 | − | 0.396824i | ||||
\(977\) | − | 47.6840i | − | 1.52555i | −0.646667 | − | 0.762773i | \(-0.723837\pi\) | ||
0.646667 | − | 0.762773i | \(-0.276163\pi\) | |||||||
\(978\) | 4.68263 | + | 8.11055i | 0.149734 | + | 0.259347i | ||||
\(979\) | 38.6446 | + | 66.9344i | 1.23509 | + | 2.13923i | ||||
\(980\) | −16.6462 | − | 7.73941i | −0.531744 | − | 0.247226i | ||||
\(981\) | 10.9212 | − | 6.30538i | 0.348688 | − | 0.201315i | ||||
\(982\) | 22.1019i | 0.705300i | ||||||||
\(983\) | 24.8943 | − | 14.3727i | 0.794003 | − | 0.458418i | −0.0473666 | − | 0.998878i | \(-0.515083\pi\) |
0.841370 | + | 0.540459i | \(0.181750\pi\) | |||||||
\(984\) | 2.85819 | − | 4.95053i | 0.0911158 | − | 0.157817i | ||||
\(985\) | 25.0263 | + | 43.3468i | 0.797404 | + | 1.38114i | ||||
\(986\) | 26.1455 | + | 15.0951i | 0.832642 | + | 0.480726i | ||||
\(987\) | −0.820821 | − | 1.28683i | −0.0261270 | − | 0.0409602i | ||||
\(988\) | −9.00980 | − | 6.20014i | −0.286640 | − | 0.197253i | ||||
\(989\) | 32.2005 | − | 55.7729i | 1.02392 | − | 1.77348i | ||||
\(990\) | 13.1406i | 0.417636i | ||||||||
\(991\) | 8.72038 | 0.277012 | 0.138506 | − | 0.990362i | \(-0.455770\pi\) | ||||
0.138506 | + | 0.990362i | \(0.455770\pi\) | |||||||
\(992\) | −5.69286 | −0.180749 | ||||||||
\(993\) | 6.27684i | 0.199189i | ||||||||
\(994\) | −7.28058 | + | 4.64401i | −0.230926 | + | 0.147299i | ||||
\(995\) | −53.4039 | + | 30.8328i | −1.69302 | + | 0.977464i | ||||
\(996\) | −7.94141 | − | 4.58497i | −0.251633 | − | 0.145280i | ||||
\(997\) | 0.441010 | − | 0.763851i | 0.0139669 | − | 0.0241914i | −0.858957 | − | 0.512047i | \(-0.828887\pi\) |
0.872924 | + | 0.487856i | \(0.162221\pi\) | |||||||
\(998\) | 32.5147 | 1.02923 | ||||||||
\(999\) | −3.70976 | + | 2.14183i | −0.117372 | + | 0.0677645i |
(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 | 546.2.bd.b.121.7 | ✓ | 20 | |
3.2 | odd | 2 | 1638.2.cr.b.667.4 | 20 | |||
7.4 | even | 3 | 546.2.bm.b.277.9 | yes | 20 | ||
13.10 | even | 6 | 546.2.bm.b.205.4 | yes | 20 | ||
21.11 | odd | 6 | 1638.2.dt.b.1369.2 | 20 | |||
39.23 | odd | 6 | 1638.2.dt.b.1297.7 | 20 | |||
91.88 | even | 6 | inner | 546.2.bd.b.361.7 | yes | 20 | |
273.179 | odd | 6 | 1638.2.cr.b.361.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bd.b.121.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
546.2.bd.b.361.7 | yes | 20 | 91.88 | even | 6 | inner | |
546.2.bm.b.205.4 | yes | 20 | 13.10 | even | 6 | ||
546.2.bm.b.277.9 | yes | 20 | 7.4 | even | 3 | ||
1638.2.cr.b.361.4 | 20 | 273.179 | odd | 6 | |||
1638.2.cr.b.667.4 | 20 | 3.2 | odd | 2 | |||
1638.2.dt.b.1297.7 | 20 | 39.23 | odd | 6 | |||
1638.2.dt.b.1369.2 | 20 | 21.11 | odd | 6 |