Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(4,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.t (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: | \(2.17991597518\) |
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: | \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + 27166 x^{4} + 6435 x^{2} + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4.4 | ||
Root | \(-0.915396i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.4 |
Dual form | 273.2.t.d.205.7 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.915396i | − | 0.647283i | −0.946180 | − | 0.323641i | \(-0.895093\pi\) | ||
0.946180 | − | 0.323641i | \(-0.104907\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.16205 | 0.581025 | ||||||||
\(5\) | −2.26729 | + | 1.30902i | −1.01396 | + | 0.585412i | −0.912350 | − | 0.409412i | \(-0.865734\pi\) |
−0.101614 | + | 0.994824i | \(0.532401\pi\) | |||||||
\(6\) | 0.792756 | − | 0.457698i | 0.323641 | − | 0.186854i | ||||
\(7\) | 2.57477 | − | 0.608732i | 0.973172 | − | 0.230079i | ||||
\(8\) | − | 2.89453i | − | 1.02337i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.19827 | + | 2.07547i | 0.378927 | + | 0.656321i | ||||
\(11\) | 2.20526 | − | 1.27321i | 0.664910 | − | 0.383886i | −0.129235 | − | 0.991614i | \(-0.541252\pi\) |
0.794145 | + | 0.607728i | \(0.207919\pi\) | |||||||
\(12\) | 0.581025 | + | 1.00636i | 0.167727 | + | 0.290512i | ||||
\(13\) | 0.523154 | + | 3.56740i | 0.145097 | + | 0.989417i | ||||
\(14\) | −0.557231 | − | 2.35694i | −0.148926 | − | 0.629918i | ||||
\(15\) | −2.26729 | − | 1.30902i | −0.585412 | − | 0.337988i | ||||
\(16\) | −0.325542 | −0.0813854 | ||||||||
\(17\) | 6.19960 | 1.50362 | 0.751812 | − | 0.659377i | \(-0.229180\pi\) | ||||
0.751812 | + | 0.659377i | \(0.229180\pi\) | |||||||
\(18\) | 0.792756 | + | 0.457698i | 0.186854 | + | 0.107880i | ||||
\(19\) | 2.36676 | + | 1.36645i | 0.542971 | + | 0.313485i | 0.746282 | − | 0.665630i | \(-0.231837\pi\) |
−0.203311 | + | 0.979114i | \(0.565170\pi\) | |||||||
\(20\) | −2.63470 | + | 1.52115i | −0.589138 | + | 0.340139i | ||||
\(21\) | 1.81456 | + | 1.92545i | 0.395970 | + | 0.420168i | ||||
\(22\) | −1.16549 | − | 2.01868i | −0.248483 | − | 0.430385i | ||||
\(23\) | −7.89025 | −1.64523 | −0.822616 | − | 0.568598i | \(-0.807486\pi\) | ||||
−0.822616 | + | 0.568598i | \(0.807486\pi\) | |||||||
\(24\) | 2.50674 | − | 1.44726i | 0.511685 | − | 0.295422i | ||||
\(25\) | 0.927071 | − | 1.60573i | 0.185414 | − | 0.321147i | ||||
\(26\) | 3.26558 | − | 0.478894i | 0.640433 | − | 0.0939188i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.99201 | − | 0.707377i | 0.565437 | − | 0.133682i | ||||
\(29\) | −1.77706 | + | 3.07796i | −0.329992 | + | 0.571562i | −0.982510 | − | 0.186211i | \(-0.940379\pi\) |
0.652518 | + | 0.757773i | \(0.273713\pi\) | |||||||
\(30\) | −1.19827 | + | 2.07547i | −0.218774 | + | 0.378927i | ||||
\(31\) | −7.91220 | − | 4.56811i | −1.42107 | − | 0.820457i | −0.424683 | − | 0.905342i | \(-0.639614\pi\) |
−0.996391 | + | 0.0848850i | \(0.972948\pi\) | |||||||
\(32\) | − | 5.49106i | − | 0.970691i | ||||||
\(33\) | 2.20526 | + | 1.27321i | 0.383886 | + | 0.221637i | ||||
\(34\) | − | 5.67509i | − | 0.973270i | ||||||
\(35\) | −5.04091 | + | 4.75060i | −0.852069 | + | 0.802998i | ||||
\(36\) | −0.581025 | + | 1.00636i | −0.0968375 | + | 0.167727i | ||||
\(37\) | − | 8.68684i | − | 1.42811i | −0.700091 | − | 0.714054i | \(-0.746857\pi\) | ||
0.700091 | − | 0.714054i | \(-0.253143\pi\) | |||||||
\(38\) | 1.25084 | − | 2.16652i | 0.202913 | − | 0.351456i | ||||
\(39\) | −2.82788 | + | 2.23676i | −0.452823 | + | 0.358169i | ||||
\(40\) | 3.78900 | + | 6.56274i | 0.599093 | + | 1.03766i | ||||
\(41\) | −3.98821 | − | 2.30259i | −0.622854 | − | 0.359605i | 0.155125 | − | 0.987895i | \(-0.450422\pi\) |
−0.777979 | + | 0.628290i | \(0.783755\pi\) | |||||||
\(42\) | 1.76255 | − | 1.66104i | 0.271967 | − | 0.256305i | ||||
\(43\) | −2.11228 | − | 3.65857i | −0.322119 | − | 0.557926i | 0.658806 | − | 0.752313i | \(-0.271062\pi\) |
−0.980925 | + | 0.194386i | \(0.937728\pi\) | |||||||
\(44\) | 2.56262 | − | 1.47953i | 0.386329 | − | 0.223047i | ||||
\(45\) | − | 2.61804i | − | 0.390275i | ||||||
\(46\) | 7.22271i | 1.06493i | ||||||||
\(47\) | −1.53652 | + | 0.887113i | −0.224125 | + | 0.129399i | −0.607859 | − | 0.794045i | \(-0.707971\pi\) |
0.383734 | + | 0.923444i | \(0.374638\pi\) | |||||||
\(48\) | −0.162771 | − | 0.281927i | −0.0234940 | − | 0.0406927i | ||||
\(49\) | 6.25889 | − | 3.13469i | 0.894127 | − | 0.447813i | ||||
\(50\) | −1.46988 | − | 0.848638i | −0.207873 | − | 0.120015i | ||||
\(51\) | 3.09980 | + | 5.36901i | 0.434059 | + | 0.751812i | ||||
\(52\) | 0.607931 | + | 4.14549i | 0.0843049 | + | 0.574876i | ||||
\(53\) | −3.42283 | + | 5.92852i | −0.470162 | + | 0.814345i | −0.999418 | − | 0.0341173i | \(-0.989138\pi\) |
0.529255 | + | 0.848463i | \(0.322471\pi\) | |||||||
\(54\) | 0.915396i | 0.124570i | ||||||||
\(55\) | −3.33331 | + | 5.77345i | −0.449463 | + | 0.778492i | ||||
\(56\) | −1.76199 | − | 7.45275i | −0.235456 | − | 0.995915i | ||||
\(57\) | 2.73290i | 0.361981i | ||||||||
\(58\) | 2.81755 | + | 1.62671i | 0.369962 | + | 0.213598i | ||||
\(59\) | − | 2.25835i | − | 0.294012i | −0.989136 | − | 0.147006i | \(-0.953036\pi\) | ||
0.989136 | − | 0.147006i | \(-0.0469637\pi\) | |||||||
\(60\) | −2.63470 | − | 1.52115i | −0.340139 | − | 0.196379i | ||||
\(61\) | −6.18601 | + | 10.7145i | −0.792038 | + | 1.37185i | 0.132666 | + | 0.991161i | \(0.457646\pi\) |
−0.924703 | + | 0.380688i | \(0.875687\pi\) | |||||||
\(62\) | −4.18163 | + | 7.24280i | −0.531068 | + | 0.919837i | ||||
\(63\) | −0.760208 | + | 2.53418i | −0.0957772 | + | 0.319277i | ||||
\(64\) | −5.67758 | −0.709697 | ||||||||
\(65\) | −5.85594 | − | 7.40350i | −0.726340 | − | 0.918291i | ||||
\(66\) | 1.16549 | − | 2.01868i | 0.143462 | − | 0.248483i | ||||
\(67\) | 0.536530 | − | 0.309766i | 0.0655476 | − | 0.0378439i | −0.466868 | − | 0.884327i | \(-0.654618\pi\) |
0.532416 | + | 0.846483i | \(0.321284\pi\) | |||||||
\(68\) | 7.20424 | 0.873643 | ||||||||
\(69\) | −3.94513 | − | 6.83316i | −0.474937 | − | 0.822616i | ||||
\(70\) | 4.34868 | + | 4.61443i | 0.519767 | + | 0.551530i | ||||
\(71\) | 6.48057 | − | 3.74156i | 0.769102 | − | 0.444041i | −0.0634524 | − | 0.997985i | \(-0.520211\pi\) |
0.832554 | + | 0.553944i | \(0.186878\pi\) | |||||||
\(72\) | 2.50674 | + | 1.44726i | 0.295422 | + | 0.170562i | ||||
\(73\) | −10.8250 | − | 6.24982i | −1.26697 | − | 0.731486i | −0.292557 | − | 0.956248i | \(-0.594506\pi\) |
−0.974414 | + | 0.224762i | \(0.927840\pi\) | |||||||
\(74\) | −7.95190 | −0.924390 | ||||||||
\(75\) | 1.85414 | 0.214098 | ||||||||
\(76\) | 2.75029 | + | 1.58788i | 0.315480 | + | 0.182142i | ||||
\(77\) | 4.90299 | − | 4.62062i | 0.558748 | − | 0.526569i | ||||
\(78\) | 2.04752 | + | 2.58863i | 0.231836 | + | 0.293105i | ||||
\(79\) | 0.621752 | + | 1.07691i | 0.0699526 | + | 0.121161i | 0.898880 | − | 0.438194i | \(-0.144382\pi\) |
−0.828928 | + | 0.559356i | \(0.811049\pi\) | |||||||
\(80\) | 0.738098 | − | 0.426141i | 0.0825218 | − | 0.0476440i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.10779 | + | 3.65079i | −0.232766 | + | 0.403163i | ||||
\(83\) | 2.10018i | 0.230524i | 0.993335 | + | 0.115262i | \(0.0367708\pi\) | ||||
−0.993335 | + | 0.115262i | \(0.963229\pi\) | |||||||
\(84\) | 2.10861 | + | 2.23747i | 0.230068 | + | 0.244128i | ||||
\(85\) | −14.0563 | + | 8.11541i | −1.52462 | + | 0.880240i | ||||
\(86\) | −3.34904 | + | 1.93357i | −0.361136 | + | 0.208502i | ||||
\(87\) | −3.55412 | −0.381041 | ||||||||
\(88\) | −3.68533 | − | 6.38318i | −0.392857 | − | 0.680449i | ||||
\(89\) | 11.4071i | 1.20915i | 0.796550 | + | 0.604573i | \(0.206656\pi\) | ||||
−0.796550 | + | 0.604573i | \(0.793344\pi\) | |||||||
\(90\) | −2.39655 | −0.252618 | ||||||||
\(91\) | 3.51859 | + | 8.86677i | 0.368848 | + | 0.929490i | ||||
\(92\) | −9.16886 | −0.955920 | ||||||||
\(93\) | − | 9.13622i | − | 0.947382i | ||||||
\(94\) | 0.812060 | + | 1.40653i | 0.0837576 | + | 0.145072i | ||||
\(95\) | −7.15484 | −0.734071 | ||||||||
\(96\) | 4.75540 | − | 2.74553i | 0.485345 | − | 0.280214i | ||||
\(97\) | −1.32935 | + | 0.767503i | −0.134975 | + | 0.0779281i | −0.565967 | − | 0.824428i | \(-0.691497\pi\) |
0.430992 | + | 0.902356i | \(0.358164\pi\) | |||||||
\(98\) | −2.86948 | − | 5.72937i | −0.289862 | − | 0.578753i | ||||
\(99\) | 2.54641i | 0.255924i | ||||||||
\(100\) | 1.07730 | − | 1.86594i | 0.107730 | − | 0.186594i | ||||
\(101\) | −0.252376 | − | 0.437129i | −0.0251124 | − | 0.0434959i | 0.853196 | − | 0.521590i | \(-0.174661\pi\) |
−0.878308 | + | 0.478094i | \(0.841328\pi\) | |||||||
\(102\) | 4.91477 | − | 2.83755i | 0.486635 | − | 0.280959i | ||||
\(103\) | −2.66915 | − | 4.62310i | −0.262999 | − | 0.455528i | 0.704038 | − | 0.710162i | \(-0.251378\pi\) |
−0.967038 | + | 0.254634i | \(0.918045\pi\) | |||||||
\(104\) | 10.3259 | − | 1.51429i | 1.01254 | − | 0.148488i | ||||
\(105\) | −6.63460 | − | 1.99026i | −0.647470 | − | 0.194229i | ||||
\(106\) | 5.42695 | + | 3.13325i | 0.527112 | + | 0.304328i | ||||
\(107\) | 17.8113 | 1.72189 | 0.860944 | − | 0.508700i | \(-0.169874\pi\) | ||||
0.860944 | + | 0.508700i | \(0.169874\pi\) | |||||||
\(108\) | −1.16205 | −0.111818 | ||||||||
\(109\) | 16.0930 | + | 9.29129i | 1.54143 | + | 0.889944i | 0.998749 | + | 0.0500036i | \(0.0159233\pi\) |
0.542679 | + | 0.839940i | \(0.317410\pi\) | |||||||
\(110\) | 5.28500 | + | 3.05130i | 0.503905 | + | 0.290930i | ||||
\(111\) | 7.52303 | − | 4.34342i | 0.714054 | − | 0.412259i | ||||
\(112\) | −0.838195 | + | 0.198168i | −0.0792020 | + | 0.0187251i | ||||
\(113\) | −3.61615 | − | 6.26336i | −0.340179 | − | 0.589207i | 0.644287 | − | 0.764784i | \(-0.277154\pi\) |
−0.984466 | + | 0.175577i | \(0.943821\pi\) | |||||||
\(114\) | 2.50168 | 0.234304 | ||||||||
\(115\) | 17.8895 | − | 10.3285i | 1.66820 | − | 0.963138i | ||||
\(116\) | −2.06503 | + | 3.57674i | −0.191733 | + | 0.332092i | ||||
\(117\) | −3.35103 | − | 1.33063i | −0.309803 | − | 0.123017i | ||||
\(118\) | −2.06729 | −0.190309 | ||||||||
\(119\) | 15.9626 | − | 3.77390i | 1.46328 | − | 0.345952i | ||||
\(120\) | −3.78900 | + | 6.56274i | −0.345887 | + | 0.599093i | ||||
\(121\) | −2.25790 | + | 3.91079i | −0.205263 | + | 0.355526i | ||||
\(122\) | 9.80800 | + | 5.66265i | 0.887975 | + | 0.512672i | ||||
\(123\) | − | 4.60519i | − | 0.415236i | ||||||
\(124\) | −9.19437 | − | 5.30837i | −0.825679 | − | 0.476706i | ||||
\(125\) | − | 8.23599i | − | 0.736649i | ||||||
\(126\) | 2.31978 | + | 0.695892i | 0.206663 | + | 0.0619950i | ||||
\(127\) | 4.21069 | − | 7.29312i | 0.373638 | − | 0.647160i | −0.616484 | − | 0.787367i | \(-0.711444\pi\) |
0.990122 | + | 0.140207i | \(0.0447769\pi\) | |||||||
\(128\) | − | 5.78488i | − | 0.511316i | ||||||
\(129\) | 2.11228 | − | 3.65857i | 0.185975 | − | 0.322119i | ||||
\(130\) | −6.77714 | + | 5.36050i | −0.594394 | + | 0.470147i | ||||
\(131\) | 8.26809 | + | 14.3207i | 0.722386 | + | 1.25121i | 0.960041 | + | 0.279860i | \(0.0902879\pi\) |
−0.237655 | + | 0.971350i | \(0.576379\pi\) | |||||||
\(132\) | 2.56262 | + | 1.47953i | 0.223047 | + | 0.128776i | ||||
\(133\) | 6.92566 | + | 2.07757i | 0.600531 | + | 0.180148i | ||||
\(134\) | −0.283559 | − | 0.491138i | −0.0244957 | − | 0.0424278i | ||||
\(135\) | 2.26729 | − | 1.30902i | 0.195137 | − | 0.112663i | ||||
\(136\) | − | 17.9449i | − | 1.53876i | ||||||
\(137\) | − | 1.91854i | − | 0.163912i | −0.996636 | − | 0.0819558i | \(-0.973883\pi\) | ||
0.996636 | − | 0.0819558i | \(-0.0261166\pi\) | |||||||
\(138\) | −6.25505 | + | 3.61135i | −0.532465 | + | 0.307419i | ||||
\(139\) | −11.0300 | − | 19.1046i | −0.935556 | − | 1.62043i | −0.773640 | − | 0.633626i | \(-0.781566\pi\) |
−0.161916 | − | 0.986805i | \(-0.551767\pi\) | |||||||
\(140\) | −5.85779 | + | 5.52043i | −0.495073 | + | 0.466562i | ||||
\(141\) | −1.53652 | − | 0.887113i | −0.129399 | − | 0.0747084i | ||||
\(142\) | −3.42501 | − | 5.93229i | −0.287420 | − | 0.497826i | ||||
\(143\) | 5.69572 | + | 7.20094i | 0.476300 | + | 0.602173i | ||||
\(144\) | 0.162771 | − | 0.281927i | 0.0135642 | − | 0.0234940i | ||||
\(145\) | − | 9.30483i | − | 0.772724i | ||||||
\(146\) | −5.72106 | + | 9.90917i | −0.473478 | + | 0.820089i | ||||
\(147\) | 5.84417 | + | 3.85301i | 0.482019 | + | 0.317791i | ||||
\(148\) | − | 10.0945i | − | 0.829766i | ||||||
\(149\) | −12.9855 | − | 7.49720i | −1.06382 | − | 0.614195i | −0.137331 | − | 0.990525i | \(-0.543852\pi\) |
−0.926485 | + | 0.376331i | \(0.877186\pi\) | |||||||
\(150\) | − | 1.69728i | − | 0.138582i | ||||||
\(151\) | 7.81993 | + | 4.51484i | 0.636377 | + | 0.367413i | 0.783218 | − | 0.621748i | \(-0.213577\pi\) |
−0.146840 | + | 0.989160i | \(0.546910\pi\) | |||||||
\(152\) | 3.95522 | − | 6.85065i | 0.320811 | − | 0.555661i | ||||
\(153\) | −3.09980 | + | 5.36901i | −0.250604 | + | 0.434059i | ||||
\(154\) | −4.22970 | − | 4.48818i | −0.340839 | − | 0.361668i | ||||
\(155\) | 23.9190 | 1.92122 | ||||||||
\(156\) | −3.28613 | + | 2.59923i | −0.263101 | + | 0.208105i | ||||
\(157\) | 0.0998014 | − | 0.172861i | 0.00796501 | − | 0.0137958i | −0.862015 | − | 0.506882i | \(-0.830798\pi\) |
0.869980 | + | 0.493086i | \(0.164131\pi\) | |||||||
\(158\) | 0.985797 | − | 0.569150i | 0.0784258 | − | 0.0452791i | ||||
\(159\) | −6.84567 | −0.542897 | ||||||||
\(160\) | 7.18791 | + | 12.4498i | 0.568254 | + | 0.984245i | ||||
\(161\) | −20.3156 | + | 4.80305i | −1.60109 | + | 0.378533i | ||||
\(162\) | −0.792756 | + | 0.457698i | −0.0622848 | + | 0.0359602i | ||||
\(163\) | −6.10731 | − | 3.52606i | −0.478362 | − | 0.276182i | 0.241372 | − | 0.970433i | \(-0.422403\pi\) |
−0.719733 | + | 0.694250i | \(0.755736\pi\) | |||||||
\(164\) | −4.63450 | − | 2.67573i | −0.361894 | − | 0.208939i | ||||
\(165\) | −6.66661 | −0.518995 | ||||||||
\(166\) | 1.92249 | 0.149214 | ||||||||
\(167\) | −1.55981 | − | 0.900559i | −0.120702 | − | 0.0696874i | 0.438433 | − | 0.898764i | \(-0.355534\pi\) |
−0.559135 | + | 0.829076i | \(0.688867\pi\) | |||||||
\(168\) | 5.57327 | − | 5.25230i | 0.429987 | − | 0.405224i | ||||
\(169\) | −12.4526 | + | 3.73260i | −0.957894 | + | 0.287123i | ||||
\(170\) | 7.42881 | + | 12.8671i | 0.569764 | + | 0.986860i | ||||
\(171\) | −2.36676 | + | 1.36645i | −0.180990 | + | 0.104495i | ||||
\(172\) | −2.45457 | − | 4.25144i | −0.187159 | − | 0.324169i | ||||
\(173\) | 5.96284 | − | 10.3279i | 0.453346 | − | 0.785219i | −0.545245 | − | 0.838277i | \(-0.683563\pi\) |
0.998591 | + | 0.0530578i | \(0.0168968\pi\) | |||||||
\(174\) | 3.25343i | 0.246642i | ||||||||
\(175\) | 1.40953 | − | 4.69874i | 0.106551 | − | 0.355191i | ||||
\(176\) | −0.717903 | + | 0.414482i | −0.0541140 | + | 0.0312427i | ||||
\(177\) | 1.95579 | − | 1.12918i | 0.147006 | − | 0.0848741i | ||||
\(178\) | 10.4420 | 0.782659 | ||||||||
\(179\) | 8.17000 | + | 14.1509i | 0.610655 | + | 1.05768i | 0.991130 | + | 0.132894i | \(0.0424269\pi\) |
−0.380476 | + | 0.924791i | \(0.624240\pi\) | |||||||
\(180\) | − | 3.04229i | − | 0.226759i | ||||||
\(181\) | 16.7748 | 1.24686 | 0.623429 | − | 0.781880i | \(-0.285739\pi\) | ||||
0.623429 | + | 0.781880i | \(0.285739\pi\) | |||||||
\(182\) | 8.11660 | − | 3.22090i | 0.601643 | − | 0.238749i | ||||
\(183\) | −12.3720 | −0.914566 | ||||||||
\(184\) | 22.8386i | 1.68368i | ||||||||
\(185\) | 11.3713 | + | 19.6956i | 0.836031 | + | 1.44805i | ||||
\(186\) | −8.36327 | −0.613224 | ||||||||
\(187\) | 13.6717 | − | 7.89337i | 0.999775 | − | 0.577220i | ||||
\(188\) | −1.78552 | + | 1.03087i | −0.130222 | + | 0.0751839i | ||||
\(189\) | −2.57477 | + | 0.608732i | −0.187287 | + | 0.0442787i | ||||
\(190\) | 6.54951i | 0.475151i | ||||||||
\(191\) | −3.74195 | + | 6.48125i | −0.270758 | + | 0.468967i | −0.969056 | − | 0.246840i | \(-0.920608\pi\) |
0.698298 | + | 0.715807i | \(0.253941\pi\) | |||||||
\(192\) | −2.83879 | − | 4.91693i | −0.204872 | − | 0.354849i | ||||
\(193\) | −10.1206 | + | 5.84311i | −0.728494 | + | 0.420596i | −0.817871 | − | 0.575402i | \(-0.804846\pi\) |
0.0893768 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(194\) | 0.702569 | + | 1.21689i | 0.0504416 | + | 0.0873673i | ||||
\(195\) | 3.48365 | − | 8.77314i | 0.249469 | − | 0.628258i | ||||
\(196\) | 7.27314 | − | 3.64267i | 0.519510 | − | 0.260190i | ||||
\(197\) | 0.388915 | + | 0.224540i | 0.0277091 | + | 0.0159978i | 0.513791 | − | 0.857916i | \(-0.328241\pi\) |
−0.486081 | + | 0.873913i | \(0.661574\pi\) | |||||||
\(198\) | 2.33098 | 0.165655 | ||||||||
\(199\) | −9.82331 | −0.696356 | −0.348178 | − | 0.937428i | \(-0.613200\pi\) | ||||
−0.348178 | + | 0.937428i | \(0.613200\pi\) | |||||||
\(200\) | −4.64784 | − | 2.68343i | −0.328652 | − | 0.189747i | ||||
\(201\) | 0.536530 | + | 0.309766i | 0.0378439 | + | 0.0218492i | ||||
\(202\) | −0.400146 | + | 0.231024i | −0.0281542 | + | 0.0162548i | ||||
\(203\) | −2.70187 | + | 9.00678i | −0.189634 | + | 0.632152i | ||||
\(204\) | 3.60212 | + | 6.23906i | 0.252199 | + | 0.436821i | ||||
\(205\) | 12.0566 | 0.842068 | ||||||||
\(206\) | −4.23197 | + | 2.44333i | −0.294856 | + | 0.170235i | ||||
\(207\) | 3.94513 | − | 6.83316i | 0.274205 | − | 0.474937i | ||||
\(208\) | −0.170309 | − | 1.16134i | −0.0118088 | − | 0.0805242i | ||||
\(209\) | 6.95908 | 0.481369 | ||||||||
\(210\) | −1.82187 | + | 6.07329i | −0.125721 | + | 0.419097i | ||||
\(211\) | 1.80752 | − | 3.13072i | 0.124435 | − | 0.215528i | −0.797077 | − | 0.603878i | \(-0.793621\pi\) |
0.921512 | + | 0.388350i | \(0.126955\pi\) | |||||||
\(212\) | −3.97750 | + | 6.88924i | −0.273176 | + | 0.473155i | ||||
\(213\) | 6.48057 | + | 3.74156i | 0.444041 | + | 0.256367i | ||||
\(214\) | − | 16.3044i | − | 1.11455i | ||||||
\(215\) | 9.57828 | + | 5.53002i | 0.653233 | + | 0.377145i | ||||
\(216\) | 2.89453i | 0.196948i | ||||||||
\(217\) | −23.1529 | − | 6.94543i | −1.57172 | − | 0.471487i | ||||
\(218\) | 8.50521 | − | 14.7315i | 0.576045 | − | 0.997740i | ||||
\(219\) | − | 12.4996i | − | 0.844647i | ||||||
\(220\) | −3.87347 | + | 6.70904i | −0.261149 | + | 0.452323i | ||||
\(221\) | 3.24335 | + | 22.1164i | 0.218171 | + | 1.48771i | ||||
\(222\) | −3.97595 | − | 6.88655i | −0.266848 | − | 0.462195i | ||||
\(223\) | 3.07998 | + | 1.77823i | 0.206251 | + | 0.119079i | 0.599568 | − | 0.800324i | \(-0.295339\pi\) |
−0.393317 | + | 0.919403i | \(0.628672\pi\) | |||||||
\(224\) | −3.34258 | − | 14.1382i | −0.223336 | − | 0.944649i | ||||
\(225\) | 0.927071 | + | 1.60573i | 0.0618047 | + | 0.107049i | ||||
\(226\) | −5.73345 | + | 3.31021i | −0.381384 | + | 0.220192i | ||||
\(227\) | 7.79500i | 0.517372i | 0.965961 | + | 0.258686i | \(0.0832895\pi\) | ||||
−0.965961 | + | 0.258686i | \(0.916711\pi\) | |||||||
\(228\) | 3.17576i | 0.210320i | ||||||||
\(229\) | −14.2182 | + | 8.20887i | −0.939563 | + | 0.542457i | −0.889823 | − | 0.456305i | \(-0.849173\pi\) |
−0.0497400 | + | 0.998762i | \(0.515839\pi\) | |||||||
\(230\) | −9.45467 | − | 16.3760i | −0.623423 | − | 1.07980i | ||||
\(231\) | 6.45307 | + | 1.93580i | 0.424581 | + | 0.127366i | ||||
\(232\) | 8.90923 | + | 5.14375i | 0.584920 | + | 0.337704i | ||||
\(233\) | −3.78863 | − | 6.56210i | −0.248201 | − | 0.429898i | 0.714825 | − | 0.699303i | \(-0.246506\pi\) |
−0.963027 | + | 0.269405i | \(0.913173\pi\) | |||||||
\(234\) | −1.21806 | + | 3.06752i | −0.0796268 | + | 0.200530i | ||||
\(235\) | 2.32250 | − | 4.02269i | 0.151503 | − | 0.262411i | ||||
\(236\) | − | 2.62432i | − | 0.170829i | ||||||
\(237\) | −0.621752 | + | 1.07691i | −0.0403872 | + | 0.0699526i | ||||
\(238\) | −3.45461 | − | 14.6121i | −0.223929 | − | 0.947159i | ||||
\(239\) | − | 4.68654i | − | 0.303147i | −0.988446 | − | 0.151574i | \(-0.951566\pi\) | ||
0.988446 | − | 0.151574i | \(-0.0484341\pi\) | |||||||
\(240\) | 0.738098 | + | 0.426141i | 0.0476440 | + | 0.0275073i | ||||
\(241\) | 10.7233i | 0.690748i | 0.938465 | + | 0.345374i | \(0.112248\pi\) | ||||
−0.938465 | + | 0.345374i | \(0.887752\pi\) | |||||||
\(242\) | 3.57992 | + | 2.06687i | 0.230126 | + | 0.132863i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −7.18845 | + | 12.4508i | −0.460193 | + | 0.797078i | ||||
\(245\) | −10.0873 | + | 15.3003i | −0.644457 | + | 0.977499i | ||||
\(246\) | −4.21557 | −0.268775 | ||||||||
\(247\) | −3.63648 | + | 9.15802i | −0.231384 | + | 0.582711i | ||||
\(248\) | −13.2225 | + | 22.9021i | −0.839632 | + | 1.45428i | ||||
\(249\) | −1.81881 | + | 1.05009i | −0.115262 | + | 0.0665466i | ||||
\(250\) | −7.53919 | −0.476820 | ||||||||
\(251\) | 5.93135 | + | 10.2734i | 0.374384 | + | 0.648452i | 0.990235 | − | 0.139411i | \(-0.0445209\pi\) |
−0.615851 | + | 0.787863i | \(0.711188\pi\) | |||||||
\(252\) | −0.883400 | + | 2.94485i | −0.0556489 | + | 0.185508i | ||||
\(253\) | −17.4000 | + | 10.0459i | −1.09393 | + | 0.631581i | ||||
\(254\) | −6.67610 | − | 3.85445i | −0.418896 | − | 0.241849i | ||||
\(255\) | −14.0563 | − | 8.11541i | −0.880240 | − | 0.508207i | ||||
\(256\) | −16.6506 | −1.04066 | ||||||||
\(257\) | 9.34756 | 0.583085 | 0.291542 | − | 0.956558i | \(-0.405832\pi\) | ||||
0.291542 | + | 0.956558i | \(0.405832\pi\) | |||||||
\(258\) | −3.34904 | − | 1.93357i | −0.208502 | − | 0.120379i | ||||
\(259\) | −5.28796 | − | 22.3666i | −0.328578 | − | 1.38979i | ||||
\(260\) | −6.80489 | − | 8.60324i | −0.422021 | − | 0.533550i | ||||
\(261\) | −1.77706 | − | 3.07796i | −0.109997 | − | 0.190521i | ||||
\(262\) | 13.1092 | − | 7.56858i | 0.809886 | − | 0.467588i | ||||
\(263\) | −0.471710 | − | 0.817026i | −0.0290869 | − | 0.0503800i | 0.851116 | − | 0.524978i | \(-0.175927\pi\) |
−0.880202 | + | 0.474598i | \(0.842593\pi\) | |||||||
\(264\) | 3.68533 | − | 6.38318i | 0.226816 | − | 0.392857i | ||||
\(265\) | − | 17.9222i | − | 1.10095i | ||||||
\(266\) | 1.90180 | − | 6.33972i | 0.116607 | − | 0.388713i | ||||
\(267\) | −9.87880 | + | 5.70353i | −0.604573 | + | 0.349050i | ||||
\(268\) | 0.623475 | − | 0.359963i | 0.0380848 | − | 0.0219883i | ||||
\(269\) | −7.58306 | −0.462347 | −0.231174 | − | 0.972913i | \(-0.574257\pi\) | ||||
−0.231174 | + | 0.972913i | \(0.574257\pi\) | |||||||
\(270\) | −1.19827 | − | 2.07547i | −0.0729246 | − | 0.126309i | ||||
\(271\) | 20.5902i | 1.25077i | 0.780317 | + | 0.625384i | \(0.215058\pi\) | ||||
−0.780317 | + | 0.625384i | \(0.784942\pi\) | |||||||
\(272\) | −2.01823 | −0.122373 | ||||||||
\(273\) | −5.91955 | + | 7.48057i | −0.358267 | + | 0.452745i | ||||
\(274\) | −1.75622 | −0.106097 | ||||||||
\(275\) | − | 4.72141i | − | 0.284712i | ||||||
\(276\) | −4.58443 | − | 7.94047i | −0.275950 | − | 0.477960i | ||||
\(277\) | 20.4256 | 1.22726 | 0.613628 | − | 0.789595i | \(-0.289710\pi\) | ||||
0.613628 | + | 0.789595i | \(0.289710\pi\) | |||||||
\(278\) | −17.4883 | + | 10.0969i | −1.04888 | + | 0.605569i | ||||
\(279\) | 7.91220 | − | 4.56811i | 0.473691 | − | 0.273486i | ||||
\(280\) | 13.7508 | + | 14.5911i | 0.821765 | + | 0.871983i | ||||
\(281\) | − | 10.8703i | − | 0.648466i | −0.945977 | − | 0.324233i | \(-0.894894\pi\) | ||
0.945977 | − | 0.324233i | \(-0.105106\pi\) | |||||||
\(282\) | −0.812060 | + | 1.40653i | −0.0483575 | + | 0.0837576i | ||||
\(283\) | −1.91077 | − | 3.30955i | −0.113583 | − | 0.196732i | 0.803629 | − | 0.595130i | \(-0.202900\pi\) |
−0.917213 | + | 0.398398i | \(0.869566\pi\) | |||||||
\(284\) | 7.53074 | − | 4.34787i | 0.446867 | − | 0.257999i | ||||
\(285\) | −3.57742 | − | 6.19627i | −0.211908 | − | 0.367035i | ||||
\(286\) | 6.59171 | − | 5.21384i | 0.389776 | − | 0.308301i | ||||
\(287\) | −11.6704 | − | 3.50090i | −0.688882 | − | 0.206652i | ||||
\(288\) | 4.75540 | + | 2.74553i | 0.280214 | + | 0.161782i | ||||
\(289\) | 21.4351 | 1.26089 | ||||||||
\(290\) | −8.51760 | −0.500171 | ||||||||
\(291\) | −1.32935 | − | 0.767503i | −0.0779281 | − | 0.0449918i | ||||
\(292\) | −12.5792 | − | 7.26260i | −0.736141 | − | 0.425011i | ||||
\(293\) | 15.6392 | − | 9.02929i | 0.913651 | − | 0.527497i | 0.0320472 | − | 0.999486i | \(-0.489797\pi\) |
0.881604 | + | 0.471989i | \(0.156464\pi\) | |||||||
\(294\) | 3.52703 | − | 5.34973i | 0.205701 | − | 0.312003i | ||||
\(295\) | 2.95623 | + | 5.12034i | 0.172118 | + | 0.298118i | ||||
\(296\) | −25.1443 | −1.46148 | ||||||||
\(297\) | −2.20526 | + | 1.27321i | −0.127962 | + | 0.0738789i | ||||
\(298\) | −6.86291 | + | 11.8869i | −0.397558 | + | 0.688590i | ||||
\(299\) | −4.12782 | − | 28.1476i | −0.238718 | − | 1.62782i | ||||
\(300\) | 2.15461 | 0.124396 | ||||||||
\(301\) | −7.66571 | − | 8.13416i | −0.441844 | − | 0.468845i | ||||
\(302\) | 4.13287 | − | 7.15834i | 0.237820 | − | 0.411916i | ||||
\(303\) | 0.252376 | − | 0.437129i | 0.0144986 | − | 0.0251124i | ||||
\(304\) | −0.770478 | − | 0.444836i | −0.0441900 | − | 0.0255131i | ||||
\(305\) | − | 32.3905i | − | 1.85467i | ||||||
\(306\) | 4.91477 | + | 2.83755i | 0.280959 | + | 0.162212i | ||||
\(307\) | − | 8.88791i | − | 0.507260i | −0.967301 | − | 0.253630i | \(-0.918375\pi\) | ||
0.967301 | − | 0.253630i | \(-0.0816246\pi\) | |||||||
\(308\) | 5.69752 | − | 5.36939i | 0.324646 | − | 0.305950i | ||||
\(309\) | 2.66915 | − | 4.62310i | 0.151843 | − | 0.262999i | ||||
\(310\) | − | 21.8954i | − | 1.24357i | ||||||
\(311\) | −8.24533 | + | 14.2813i | −0.467550 | + | 0.809820i | −0.999313 | − | 0.0370736i | \(-0.988196\pi\) |
0.531763 | + | 0.846893i | \(0.321530\pi\) | |||||||
\(312\) | 6.47437 | + | 8.18537i | 0.366539 | + | 0.463405i | ||||
\(313\) | −11.0236 | − | 19.0935i | −0.623092 | − | 1.07923i | −0.988907 | − | 0.148539i | \(-0.952543\pi\) |
0.365815 | − | 0.930688i | \(-0.380790\pi\) | |||||||
\(314\) | −0.158236 | − | 0.0913578i | −0.00892979 | − | 0.00515562i | ||||
\(315\) | −1.59369 | − | 6.74086i | −0.0897940 | − | 0.379804i | ||||
\(316\) | 0.722507 | + | 1.25142i | 0.0406442 | + | 0.0703978i | ||||
\(317\) | −19.7541 | + | 11.4050i | −1.10950 | + | 0.640569i | −0.938699 | − | 0.344737i | \(-0.887968\pi\) |
−0.170799 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(318\) | 6.26650i | 0.351408i | ||||||||
\(319\) | 9.05024i | 0.506716i | ||||||||
\(320\) | 12.8727 | − | 7.43207i | 0.719607 | − | 0.415465i | ||||
\(321\) | 8.90567 | + | 15.4251i | 0.497066 | + | 0.860944i | ||||
\(322\) | 4.39669 | + | 18.5968i | 0.245018 | + | 1.03636i | ||||
\(323\) | 14.6730 | + | 8.47143i | 0.816425 | + | 0.471363i | ||||
\(324\) | −0.581025 | − | 1.00636i | −0.0322792 | − | 0.0559091i | ||||
\(325\) | 6.21329 | + | 2.46718i | 0.344651 | + | 0.136855i | ||||
\(326\) | −3.22774 | + | 5.59061i | −0.178768 | + | 0.309635i | ||||
\(327\) | 18.5826i | 1.02762i | ||||||||
\(328\) | −6.66493 | + | 11.5440i | −0.368009 | + | 0.637410i | ||||
\(329\) | −3.41619 | + | 3.21944i | −0.188340 | + | 0.177494i | ||||
\(330\) | 6.10259i | 0.335937i | ||||||||
\(331\) | 27.7264 | + | 16.0079i | 1.52398 | + | 0.879871i | 0.999597 | + | 0.0283898i | \(0.00903797\pi\) |
0.524385 | + | 0.851481i | \(0.324295\pi\) | |||||||
\(332\) | 2.44051i | 0.133940i | ||||||||
\(333\) | 7.52303 | + | 4.34342i | 0.412259 | + | 0.238018i | ||||
\(334\) | −0.824369 | + | 1.42785i | −0.0451074 | + | 0.0781284i | ||||
\(335\) | −0.810980 | + | 1.40466i | −0.0443086 | + | 0.0767447i | ||||
\(336\) | −0.590716 | − | 0.626815i | −0.0322262 | − | 0.0341955i | ||||
\(337\) | 4.99719 | 0.272214 | 0.136107 | − | 0.990694i | \(-0.456541\pi\) | ||||
0.136107 | + | 0.990694i | \(0.456541\pi\) | |||||||
\(338\) | 3.41681 | + | 11.3991i | 0.185850 | + | 0.620028i | ||||
\(339\) | 3.61615 | − | 6.26336i | 0.196402 | − | 0.340179i | ||||
\(340\) | −16.3341 | + | 9.43051i | −0.885842 | + | 0.511441i | ||||
\(341\) | −23.2646 | −1.25985 | ||||||||
\(342\) | 1.25084 | + | 2.16652i | 0.0676378 | + | 0.117152i | ||||
\(343\) | 14.2070 | − | 11.8811i | 0.767107 | − | 0.641519i | ||||
\(344\) | −10.5898 | + | 6.11404i | −0.570965 | + | 0.329647i | ||||
\(345\) | 17.8895 | + | 10.3285i | 0.963138 | + | 0.556068i | ||||
\(346\) | −9.45416 | − | 5.45836i | −0.508259 | − | 0.293443i | ||||
\(347\) | 34.3420 | 1.84358 | 0.921789 | − | 0.387692i | \(-0.126728\pi\) | ||||
0.921789 | + | 0.387692i | \(0.126728\pi\) | |||||||
\(348\) | −4.13006 | −0.221394 | ||||||||
\(349\) | 8.51580 | + | 4.91660i | 0.455841 | + | 0.263180i | 0.710294 | − | 0.703905i | \(-0.248562\pi\) |
−0.254453 | + | 0.967085i | \(0.581895\pi\) | |||||||
\(350\) | −4.30121 | − | 1.29028i | −0.229909 | − | 0.0689685i | ||||
\(351\) | −0.523154 | − | 3.56740i | −0.0279239 | − | 0.190413i | ||||
\(352\) | −6.99124 | − | 12.1092i | −0.372635 | − | 0.645422i | ||||
\(353\) | 13.2871 | − | 7.67129i | 0.707199 | − | 0.408302i | −0.102824 | − | 0.994700i | \(-0.532788\pi\) |
0.810023 | + | 0.586398i | \(0.199454\pi\) | |||||||
\(354\) | −1.03364 | − | 1.79032i | −0.0549375 | − | 0.0951546i | ||||
\(355\) | −9.79555 | + | 16.9664i | −0.519894 | + | 0.900483i | ||||
\(356\) | 13.2556i | 0.702544i | ||||||||
\(357\) | 11.2496 | + | 11.9370i | 0.595390 | + | 0.631775i | ||||
\(358\) | 12.9536 | − | 7.47879i | 0.684621 | − | 0.395266i | ||||
\(359\) | 25.1701 | − | 14.5319i | 1.32842 | − | 0.766966i | 0.343369 | − | 0.939201i | \(-0.388432\pi\) |
0.985056 | + | 0.172235i | \(0.0550987\pi\) | |||||||
\(360\) | −7.57800 | −0.399395 | ||||||||
\(361\) | −5.76564 | − | 9.98638i | −0.303455 | − | 0.525599i | ||||
\(362\) | − | 15.3555i | − | 0.807070i | ||||||
\(363\) | −4.51579 | −0.237018 | ||||||||
\(364\) | 4.08878 | + | 10.3036i | 0.214310 | + | 0.540056i | ||||
\(365\) | 32.7246 | 1.71288 | ||||||||
\(366\) | 11.3253i | 0.591983i | ||||||||
\(367\) | −9.15105 | − | 15.8501i | −0.477681 | − | 0.827368i | 0.521992 | − | 0.852950i | \(-0.325189\pi\) |
−0.999673 | + | 0.0255830i | \(0.991856\pi\) | |||||||
\(368\) | 2.56861 | 0.133898 | ||||||||
\(369\) | 3.98821 | − | 2.30259i | 0.207618 | − | 0.119868i | ||||
\(370\) | 18.0293 | − | 10.4092i | 0.937297 | − | 0.541149i | ||||
\(371\) | −5.20413 | + | 17.3482i | −0.270185 | + | 0.900672i | ||||
\(372\) | − | 10.6167i | − | 0.550453i | ||||||
\(373\) | −6.43274 | + | 11.1418i | −0.333074 | + | 0.576902i | −0.983113 | − | 0.182999i | \(-0.941419\pi\) |
0.650039 | + | 0.759901i | \(0.274753\pi\) | |||||||
\(374\) | −7.22556 | − | 12.5150i | −0.373625 | − | 0.647137i | ||||
\(375\) | 7.13257 | − | 4.11799i | 0.368325 | − | 0.212652i | ||||
\(376\) | 2.56777 | + | 4.44752i | 0.132423 | + | 0.229363i | ||||
\(377\) | −11.9100 | − | 4.72922i | −0.613394 | − | 0.243567i | ||||
\(378\) | 0.557231 | + | 2.35694i | 0.0286609 | + | 0.121228i | ||||
\(379\) | 22.8080 | + | 13.1682i | 1.17157 | + | 0.676405i | 0.954049 | − | 0.299651i | \(-0.0968703\pi\) |
0.217519 | + | 0.976056i | \(0.430204\pi\) | |||||||
\(380\) | −8.31427 | −0.426513 | ||||||||
\(381\) | 8.42137 | 0.431440 | ||||||||
\(382\) | 5.93291 | + | 3.42537i | 0.303554 | + | 0.175257i | ||||
\(383\) | −12.4747 | − | 7.20224i | −0.637425 | − | 0.368017i | 0.146197 | − | 0.989255i | \(-0.453297\pi\) |
−0.783622 | + | 0.621238i | \(0.786630\pi\) | |||||||
\(384\) | 5.00985 | − | 2.89244i | 0.255658 | − | 0.147604i | ||||
\(385\) | −5.06801 | + | 16.8944i | −0.258290 | + | 0.861019i | ||||
\(386\) | 5.34876 | + | 9.26433i | 0.272245 | + | 0.471542i | ||||
\(387\) | 4.22455 | 0.214746 | ||||||||
\(388\) | −1.54478 | + | 0.891877i | −0.0784241 | + | 0.0452782i | ||||
\(389\) | 3.30891 | − | 5.73120i | 0.167768 | − | 0.290584i | −0.769866 | − | 0.638205i | \(-0.779677\pi\) |
0.937635 | + | 0.347621i | \(0.113011\pi\) | |||||||
\(390\) | −8.03090 | − | 3.18892i | −0.406661 | − | 0.161477i | ||||
\(391\) | −48.9164 | −2.47381 | ||||||||
\(392\) | −9.07345 | − | 18.1165i | −0.458279 | − | 0.915023i | ||||
\(393\) | −8.26809 | + | 14.3207i | −0.417070 | + | 0.722386i | ||||
\(394\) | 0.205543 | − | 0.356012i | 0.0103551 | − | 0.0179356i | ||||
\(395\) | −2.81939 | − | 1.62777i | −0.141859 | − | 0.0819022i | ||||
\(396\) | 2.95906i | 0.148698i | ||||||||
\(397\) | −19.6031 | − | 11.3178i | −0.983851 | − | 0.568027i | −0.0804203 | − | 0.996761i | \(-0.525626\pi\) |
−0.903431 | + | 0.428734i | \(0.858960\pi\) | |||||||
\(398\) | 8.99222i | 0.450739i | ||||||||
\(399\) | 1.66360 | + | 7.03658i | 0.0832842 | + | 0.352270i | ||||
\(400\) | −0.301800 | + | 0.522734i | −0.0150900 | + | 0.0261367i | ||||
\(401\) | 0.450563i | 0.0225000i | 0.999937 | + | 0.0112500i | \(0.00358107\pi\) | ||||
−0.999937 | + | 0.0112500i | \(0.996419\pi\) | |||||||
\(402\) | 0.283559 | − | 0.491138i | 0.0141426 | − | 0.0244957i | ||||
\(403\) | 12.1570 | − | 30.6158i | 0.605581 | − | 1.52508i | ||||
\(404\) | −0.293274 | − | 0.507965i | −0.0145909 | − | 0.0252722i | ||||
\(405\) | 2.26729 | + | 1.30902i | 0.112663 | + | 0.0650458i | ||||
\(406\) | 8.24478 | + | 2.47328i | 0.409181 | + | 0.122747i | ||||
\(407\) | −11.0601 | − | 19.1567i | −0.548231 | − | 0.949563i | ||||
\(408\) | 15.5408 | − | 8.97246i | 0.769382 | − | 0.444203i | ||||
\(409\) | 34.4616i | 1.70402i | 0.523529 | + | 0.852008i | \(0.324615\pi\) | ||||
−0.523529 | + | 0.852008i | \(0.675385\pi\) | |||||||
\(410\) | − | 11.0365i | − | 0.545056i | ||||||
\(411\) | 1.66150 | − | 0.959268i | 0.0819558 | − | 0.0473172i | ||||
\(412\) | −3.10169 | − | 5.37228i | −0.152809 | − | 0.264673i | ||||
\(413\) | −1.37473 | − | 5.81474i | −0.0676461 | − | 0.286125i | ||||
\(414\) | −6.25505 | − | 3.61135i | −0.307419 | − | 0.177488i | ||||
\(415\) | −2.74917 | − | 4.76171i | −0.134952 | − | 0.233743i | ||||
\(416\) | 19.5888 | − | 2.87267i | 0.960419 | − | 0.140844i | ||||
\(417\) | 11.0300 | − | 19.1046i | 0.540143 | − | 0.935556i | ||||
\(418\) | − | 6.37031i | − | 0.311582i | ||||||
\(419\) | 0.195021 | − | 0.337787i | 0.00952742 | − | 0.0165020i | −0.861222 | − | 0.508228i | \(-0.830301\pi\) |
0.870750 | + | 0.491726i | \(0.163634\pi\) | |||||||
\(420\) | −7.70973 | − | 2.31278i | −0.376196 | − | 0.112852i | ||||
\(421\) | 24.5494i | 1.19646i | 0.801323 | + | 0.598232i | \(0.204130\pi\) | ||||
−0.801323 | + | 0.598232i | \(0.795870\pi\) | |||||||
\(422\) | −2.86585 | − | 1.65460i | −0.139507 | − | 0.0805447i | ||||
\(423\) | − | 1.77423i | − | 0.0862658i | ||||||
\(424\) | 17.1603 | + | 9.90749i | 0.833377 | + | 0.481150i | ||||
\(425\) | 5.74747 | − | 9.95491i | 0.278793 | − | 0.482884i | ||||
\(426\) | 3.42501 | − | 5.93229i | 0.165942 | − | 0.287420i | ||||
\(427\) | −9.40531 | + | 31.3530i | −0.455155 | + | 1.51728i | ||||
\(428\) | 20.6977 | 1.00046 | ||||||||
\(429\) | −3.38834 | + | 8.53311i | −0.163590 | + | 0.411982i | ||||
\(430\) | 5.06216 | − | 8.76793i | 0.244119 | − | 0.422827i | ||||
\(431\) | −0.983361 | + | 0.567744i | −0.0473668 | + | 0.0273473i | −0.523496 | − | 0.852028i | \(-0.675373\pi\) |
0.476130 | + | 0.879375i | \(0.342039\pi\) | |||||||
\(432\) | 0.325542 | 0.0156626 | ||||||||
\(433\) | 10.1233 | + | 17.5341i | 0.486495 | + | 0.842634i | 0.999879 | − | 0.0155250i | \(-0.00494195\pi\) |
−0.513385 | + | 0.858159i | \(0.671609\pi\) | |||||||
\(434\) | −6.35782 | + | 21.1940i | −0.305185 | + | 1.01735i | ||||
\(435\) | 8.05822 | − | 4.65241i | 0.386362 | − | 0.223066i | ||||
\(436\) | 18.7008 | + | 10.7969i | 0.895608 | + | 0.517079i | ||||
\(437\) | −18.6743 | − | 10.7816i | −0.893313 | − | 0.515755i | ||||
\(438\) | −11.4421 | −0.546726 | ||||||||
\(439\) | 27.9764 | 1.33524 | 0.667621 | − | 0.744501i | \(-0.267313\pi\) | ||||
0.667621 | + | 0.744501i | \(0.267313\pi\) | |||||||
\(440\) | 16.7114 | + | 9.64835i | 0.796686 | + | 0.459967i | ||||
\(441\) | −0.414724 | + | 6.98770i | −0.0197487 | + | 0.332748i | ||||
\(442\) | 20.2453 | − | 2.96895i | 0.962971 | − | 0.141219i | ||||
\(443\) | 10.7712 | + | 18.6562i | 0.511755 | + | 0.886385i | 0.999907 | + | 0.0136266i | \(0.00433761\pi\) |
−0.488153 | + | 0.872758i | \(0.662329\pi\) | |||||||
\(444\) | 8.74213 | − | 5.04727i | 0.414883 | − | 0.239533i | ||||
\(445\) | −14.9321 | − | 25.8631i | −0.707848 | − | 1.22603i | ||||
\(446\) | 1.62778 | − | 2.81941i | 0.0770778 | − | 0.133503i | ||||
\(447\) | − | 14.9944i | − | 0.709211i | ||||||
\(448\) | −14.6185 | + | 3.45612i | −0.690657 | + | 0.163286i | ||||
\(449\) | −2.50177 | + | 1.44440i | −0.118066 | + | 0.0681652i | −0.557870 | − | 0.829928i | \(-0.688381\pi\) |
0.439804 | + | 0.898094i | \(0.355048\pi\) | |||||||
\(450\) | 1.46988 | − | 0.848638i | 0.0692910 | − | 0.0400052i | ||||
\(451\) | −11.7267 | −0.552189 | ||||||||
\(452\) | −4.20215 | − | 7.27833i | −0.197652 | − | 0.342344i | ||||
\(453\) | 9.02968i | 0.424251i | ||||||||
\(454\) | 7.13551 | 0.334886 | ||||||||
\(455\) | −19.5844 | − | 15.4976i | −0.918133 | − | 0.726540i | ||||
\(456\) | 7.91045 | 0.370441 | ||||||||
\(457\) | − | 32.6685i | − | 1.52817i | −0.645118 | − | 0.764083i | \(-0.723192\pi\) | ||
0.645118 | − | 0.764083i | \(-0.276808\pi\) | |||||||
\(458\) | 7.51437 | + | 13.0153i | 0.351123 | + | 0.608163i | ||||
\(459\) | −6.19960 | −0.289373 | ||||||||
\(460\) | 20.7885 | − | 12.0022i | 0.969268 | − | 0.559607i | ||||
\(461\) | −32.7978 | + | 18.9358i | −1.52755 | + | 0.881930i | −0.528084 | + | 0.849192i | \(0.677089\pi\) |
−0.999464 | + | 0.0327376i | \(0.989577\pi\) | |||||||
\(462\) | 1.77203 | − | 5.90712i | 0.0824421 | − | 0.274824i | ||||
\(463\) | 20.8936i | 0.971006i | 0.874235 | + | 0.485503i | \(0.161364\pi\) | ||||
−0.874235 | + | 0.485503i | \(0.838636\pi\) | |||||||
\(464\) | 0.578507 | − | 1.00200i | 0.0268565 | − | 0.0465168i | ||||
\(465\) | 11.9595 | + | 20.7145i | 0.554609 | + | 0.960611i | ||||
\(466\) | −6.00692 | + | 3.46810i | −0.278265 | + | 0.160657i | ||||
\(467\) | −10.8858 | − | 18.8548i | −0.503735 | − | 0.872494i | −0.999991 | − | 0.00431766i | \(-0.998626\pi\) |
0.496256 | − | 0.868176i | \(-0.334708\pi\) | |||||||
\(468\) | −3.89407 | − | 1.54626i | −0.180003 | − | 0.0714759i | ||||
\(469\) | 1.19288 | − | 1.12418i | 0.0550820 | − | 0.0519098i | ||||
\(470\) | −3.68235 | − | 2.12601i | −0.169854 | − | 0.0980654i | ||||
\(471\) | 0.199603 | 0.00919721 | ||||||||
\(472\) | −6.53687 | −0.300884 | ||||||||
\(473\) | −9.31622 | − | 5.37872i | −0.428360 | − | 0.247314i | ||||
\(474\) | 0.985797 | + | 0.569150i | 0.0452791 | + | 0.0261419i | ||||
\(475\) | 4.38830 | − | 2.53359i | 0.201349 | − | 0.116249i | ||||
\(476\) | 18.5493 | − | 4.38545i | 0.850205 | − | 0.201007i | ||||
\(477\) | −3.42283 | − | 5.92852i | −0.156721 | − | 0.271448i | ||||
\(478\) | −4.29004 | −0.196222 | ||||||||
\(479\) | −9.43952 | + | 5.44991i | −0.431303 | + | 0.249013i | −0.699901 | − | 0.714239i | \(-0.746773\pi\) |
0.268599 | + | 0.963252i | \(0.413439\pi\) | |||||||
\(480\) | −7.18791 | + | 12.4498i | −0.328082 | + | 0.568254i | ||||
\(481\) | 30.9894 | − | 4.54456i | 1.41299 | − | 0.207214i | ||||
\(482\) | 9.81606 | 0.447109 | ||||||||
\(483\) | −14.3174 | − | 15.1923i | −0.651462 | − | 0.691273i | ||||
\(484\) | −2.62379 | + | 4.54453i | −0.119263 | + | 0.206570i | ||||
\(485\) | 2.00936 | − | 3.48031i | 0.0912401 | − | 0.158033i | ||||
\(486\) | −0.792756 | − | 0.457698i | −0.0359602 | − | 0.0207616i | ||||
\(487\) | − | 6.15209i | − | 0.278778i | −0.990238 | − | 0.139389i | \(-0.955486\pi\) | ||
0.990238 | − | 0.139389i | \(-0.0445138\pi\) | |||||||
\(488\) | 31.0134 | + | 17.9056i | 1.40391 | + | 0.810548i | ||||
\(489\) | − | 7.05212i | − | 0.318908i | ||||||
\(490\) | 14.0058 | + | 9.23392i | 0.632718 | + | 0.417146i | ||||
\(491\) | 5.40015 | − | 9.35334i | 0.243705 | − | 0.422110i | −0.718061 | − | 0.695980i | \(-0.754970\pi\) |
0.961767 | + | 0.273869i | \(0.0883036\pi\) | |||||||
\(492\) | − | 5.35146i | − | 0.241262i | ||||||
\(493\) | −11.0171 | + | 19.0821i | −0.496183 | + | 0.859415i | ||||
\(494\) | 8.38322 | + | 3.32882i | 0.377179 | + | 0.149771i | ||||
\(495\) | −3.33331 | − | 5.77345i | −0.149821 | − | 0.259497i | ||||
\(496\) | 2.57575 | + | 1.48711i | 0.115655 | + | 0.0667733i | ||||
\(497\) | 14.4084 | − | 13.5786i | 0.646304 | − | 0.609082i | ||||
\(498\) | 0.961247 | + | 1.66493i | 0.0430745 | + | 0.0746072i | ||||
\(499\) | −1.85936 | + | 1.07350i | −0.0832362 | + | 0.0480565i | −0.541040 | − | 0.840997i | \(-0.681969\pi\) |
0.457804 | + | 0.889053i | \(0.348636\pi\) | |||||||
\(500\) | − | 9.57062i | − | 0.428011i | ||||||
\(501\) | − | 1.80112i | − | 0.0804680i | ||||||
\(502\) | 9.40424 | − | 5.42954i | 0.419732 | − | 0.242332i | ||||
\(503\) | −3.07639 | − | 5.32846i | −0.137169 | − | 0.237584i | 0.789255 | − | 0.614066i | \(-0.210467\pi\) |
−0.926424 | + | 0.376482i | \(0.877134\pi\) | |||||||
\(504\) | 7.33527 | + | 2.20044i | 0.326739 | + | 0.0980156i | ||||
\(505\) | 1.14442 | + | 0.660732i | 0.0509261 | + | 0.0294022i | ||||
\(506\) | 9.19599 | + | 15.9279i | 0.408812 | + | 0.708083i | ||||
\(507\) | −9.45883 | − | 8.91799i | −0.420082 | − | 0.396062i | ||||
\(508\) | 4.89302 | − | 8.47497i | 0.217093 | − | 0.376016i | ||||
\(509\) | − | 4.58685i | − | 0.203309i | −0.994820 | − | 0.101654i | \(-0.967586\pi\) | ||
0.994820 | − | 0.101654i | \(-0.0324136\pi\) | |||||||
\(510\) | −7.42881 | + | 12.8671i | −0.328953 | + | 0.569764i | ||||
\(511\) | −31.6764 | − | 9.50233i | −1.40128 | − | 0.420358i | ||||
\(512\) | 3.67215i | 0.162288i | ||||||||
\(513\) | −2.36676 | − | 1.36645i | −0.104495 | − | 0.0603302i | ||||
\(514\) | − | 8.55672i | − | 0.377421i | ||||||
\(515\) | 12.1035 | + | 6.98795i | 0.533343 | + | 0.307926i | ||||
\(516\) | 2.45457 | − | 4.25144i | 0.108056 | − | 0.187159i | ||||
\(517\) | −2.25895 | + | 3.91262i | −0.0993487 | + | 0.172077i | ||||
\(518\) | −20.4743 | + | 4.84058i | −0.899590 | + | 0.212683i | ||||
\(519\) | 11.9257 | 0.523479 | ||||||||
\(520\) | −21.4296 | + | 16.9502i | −0.939752 | + | 0.743315i | ||||
\(521\) | 10.7536 | − | 18.6258i | 0.471123 | − | 0.816009i | −0.528331 | − | 0.849038i | \(-0.677182\pi\) |
0.999454 | + | 0.0330292i | \(0.0105154\pi\) | |||||||
\(522\) | −2.81755 | + | 1.62671i | −0.123321 | + | 0.0711993i | ||||
\(523\) | −12.0380 | −0.526387 | −0.263193 | − | 0.964743i | \(-0.584776\pi\) | ||||
−0.263193 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(524\) | 9.60793 | + | 16.6414i | 0.419724 | + | 0.726984i | ||||
\(525\) | 4.77399 | − | 1.12868i | 0.208354 | − | 0.0492594i | ||||
\(526\) | −0.747902 | + | 0.431802i | −0.0326101 | + | 0.0188274i | ||||
\(527\) | −49.0525 | − | 28.3205i | −2.13676 | − | 1.23366i | ||||
\(528\) | −0.717903 | − | 0.414482i | −0.0312427 | − | 0.0180380i | ||||
\(529\) | 39.2561 | 1.70679 | ||||||||
\(530\) | −16.4060 | −0.712629 | ||||||||
\(531\) | 1.95579 | + | 1.12918i | 0.0848741 | + | 0.0490021i | ||||
\(532\) | 8.04796 | + | 2.41424i | 0.348923 | + | 0.104671i | ||||
\(533\) | 6.12782 | − | 15.4321i | 0.265425 | − | 0.668440i | ||||
\(534\) | 5.22099 | + | 9.04302i | 0.225934 | + | 0.391330i | ||||
\(535\) | −40.3835 | + | 23.3154i | −1.74593 | + | 1.00801i | ||||
\(536\) | −0.896626 | − | 1.55300i | −0.0387283 | − | 0.0670795i | ||||
\(537\) | −8.17000 | + | 14.1509i | −0.352562 | + | 0.610655i | ||||
\(538\) | 6.94150i | 0.299269i | ||||||||
\(539\) | 9.81135 | − | 14.8817i | 0.422605 | − | 0.640998i | ||||
\(540\) | 2.63470 | − | 1.52115i | 0.113380 | − | 0.0654597i | ||||
\(541\) | −1.68945 | + | 0.975405i | −0.0726352 | + | 0.0419360i | −0.535878 | − | 0.844296i | \(-0.680019\pi\) |
0.463243 | + | 0.886232i | \(0.346686\pi\) | |||||||
\(542\) | 18.8482 | 0.809601 | ||||||||
\(543\) | 8.38738 | + | 14.5274i | 0.359937 | + | 0.623429i | ||||
\(544\) | − | 34.0424i | − | 1.45955i | ||||||
\(545\) | −48.6500 | −2.08393 | ||||||||
\(546\) | 6.84769 | + | 5.41873i | 0.293054 | + | 0.231900i | ||||
\(547\) | 4.27037 | 0.182588 | 0.0912940 | − | 0.995824i | \(-0.470900\pi\) | ||||
0.0912940 | + | 0.995824i | \(0.470900\pi\) | |||||||
\(548\) | − | 2.22943i | − | 0.0952367i | ||||||
\(549\) | −6.18601 | − | 10.7145i | −0.264013 | − | 0.457283i | ||||
\(550\) | −4.32196 | −0.184289 | ||||||||
\(551\) | −8.41173 | + | 4.85652i | −0.358352 | + | 0.206895i | ||||
\(552\) | −19.7788 | + | 11.4193i | −0.841840 | + | 0.486037i | ||||
\(553\) | 2.25642 | + | 2.39431i | 0.0959527 | + | 0.101816i | ||||
\(554\) | − | 18.6975i | − | 0.794382i | ||||||
\(555\) | −11.3713 | + | 19.6956i | −0.482683 | + | 0.836031i | ||||
\(556\) | −12.8175 | − | 22.2005i | −0.543581 | − | 0.941510i | ||||
\(557\) | −34.6266 | + | 19.9917i | −1.46718 | + | 0.847075i | −0.999325 | − | 0.0367316i | \(-0.988305\pi\) |
−0.467852 | + | 0.883807i | \(0.654972\pi\) | |||||||
\(558\) | −4.18163 | − | 7.24280i | −0.177023 | − | 0.306612i | ||||
\(559\) | 11.9465 | − | 9.44932i | 0.505284 | − | 0.399663i | ||||
\(560\) | 1.64103 | − | 1.54652i | 0.0693460 | − | 0.0653524i | ||||
\(561\) | 13.6717 | + | 7.89337i | 0.577220 | + | 0.333258i | ||||
\(562\) | −9.95061 | −0.419741 | ||||||||
\(563\) | 33.5147 | 1.41248 | 0.706239 | − | 0.707974i | \(-0.250391\pi\) | ||||
0.706239 | + | 0.707974i | \(0.250391\pi\) | |||||||
\(564\) | −1.78552 | − | 1.03087i | −0.0751839 | − | 0.0434074i | ||||
\(565\) | 16.3977 | + | 9.46723i | 0.689858 | + | 0.398290i | ||||
\(566\) | −3.02955 | + | 1.74911i | −0.127342 | + | 0.0735207i | ||||
\(567\) | −1.81456 | − | 1.92545i | −0.0762045 | − | 0.0808613i | ||||
\(568\) | −10.8300 | − | 18.7582i | −0.454418 | − | 0.787076i | ||||
\(569\) | −38.8836 | −1.63009 | −0.815043 | − | 0.579401i | \(-0.803287\pi\) | ||||
−0.815043 | + | 0.579401i | \(0.803287\pi\) | |||||||
\(570\) | −5.67204 | + | 3.27476i | −0.237576 | + | 0.137164i | ||||
\(571\) | 11.3324 | − | 19.6282i | 0.474245 | − | 0.821417i | −0.525320 | − | 0.850905i | \(-0.676054\pi\) |
0.999565 | + | 0.0294882i | \(0.00938774\pi\) | |||||||
\(572\) | 6.61871 | + | 8.36785i | 0.276742 | + | 0.349877i | ||||
\(573\) | −7.48391 | −0.312645 | ||||||||
\(574\) | −3.20471 | + | 10.6830i | −0.133762 | + | 0.445901i | ||||
\(575\) | −7.31482 | + | 12.6696i | −0.305049 | + | 0.528361i | ||||
\(576\) | 2.83879 | − | 4.91693i | 0.118283 | − | 0.204872i | ||||
\(577\) | 20.1472 | + | 11.6320i | 0.838740 | + | 0.484247i | 0.856836 | − | 0.515589i | \(-0.172427\pi\) |
−0.0180956 | + | 0.999836i | \(0.505760\pi\) | |||||||
\(578\) | − | 19.6216i | − | 0.816150i | ||||||
\(579\) | −10.1206 | − | 5.84311i | −0.420596 | − | 0.242831i | ||||
\(580\) | − | 10.8127i | − | 0.448972i | ||||||
\(581\) | 1.27844 | + | 5.40747i | 0.0530388 | + | 0.224340i | ||||
\(582\) | −0.702569 | + | 1.21689i | −0.0291224 | + | 0.0504416i | ||||
\(583\) | 17.4319i | 0.721955i | ||||||||
\(584\) | −18.0903 | + | 31.3333i | −0.748581 | + | 1.29658i | ||||
\(585\) | 9.33959 | − | 1.36964i | 0.386145 | − | 0.0566276i | ||||
\(586\) | −8.26538 | − | 14.3161i | −0.341440 | − | 0.591391i | ||||
\(587\) | −11.6230 | − | 6.71057i | −0.479734 | − | 0.276975i | 0.240571 | − | 0.970631i | \(-0.422665\pi\) |
−0.720306 | + | 0.693657i | \(0.755998\pi\) | |||||||
\(588\) | 6.79121 | + | 4.47739i | 0.280065 | + | 0.184645i | ||||
\(589\) | −12.4842 | − | 21.6232i | −0.514402 | − | 0.890970i | ||||
\(590\) | 4.68714 | − | 2.70612i | 0.192967 | − | 0.111409i | ||||
\(591\) | 0.449081i | 0.0184727i | ||||||||
\(592\) | 2.82793i | 0.116227i | ||||||||
\(593\) | −7.76746 | + | 4.48455i | −0.318972 | + | 0.184158i | −0.650934 | − | 0.759134i | \(-0.725623\pi\) |
0.331963 | + | 0.943293i | \(0.392289\pi\) | |||||||
\(594\) | 1.16549 | + | 2.01868i | 0.0478205 | + | 0.0828276i | ||||
\(595\) | −31.2516 | + | 29.4518i | −1.28119 | + | 1.20741i | ||||
\(596\) | −15.0898 | − | 8.71212i | −0.618104 | − | 0.356862i | ||||
\(597\) | −4.91166 | − | 8.50724i | −0.201021 | − | 0.348178i | ||||
\(598\) | −25.7663 | + | 3.77859i | −1.05366 | + | 0.154518i | ||||
\(599\) | −17.2505 | + | 29.8787i | −0.704836 | + | 1.22081i | 0.261914 | + | 0.965091i | \(0.415646\pi\) |
−0.966751 | + | 0.255721i | \(0.917687\pi\) | |||||||
\(600\) | − | 5.36687i | − | 0.219101i | ||||||
\(601\) | 10.6843 | − | 18.5058i | 0.435824 | − | 0.754869i | −0.561539 | − | 0.827450i | \(-0.689791\pi\) |
0.997362 | + | 0.0725818i | \(0.0231238\pi\) | |||||||
\(602\) | −7.44598 | + | 7.01716i | −0.303476 | + | 0.285998i | ||||
\(603\) | 0.619532i | 0.0252293i | ||||||||
\(604\) | 9.08715 | + | 5.24647i | 0.369751 | + | 0.213476i | ||||
\(605\) | − | 11.8225i | − | 0.480654i | ||||||
\(606\) | −0.400146 | − | 0.231024i | −0.0162548 | − | 0.00938472i | ||||
\(607\) | 0.563082 | − | 0.975286i | 0.0228548 | − | 0.0395857i | −0.854372 | − | 0.519662i | \(-0.826058\pi\) |
0.877227 | + | 0.480077i | \(0.159391\pi\) | |||||||
\(608\) | 7.50324 | − | 12.9960i | 0.304297 | − | 0.527057i | ||||
\(609\) | −9.15104 | + | 2.16350i | −0.370819 | + | 0.0876696i | ||||
\(610\) | −29.6501 | −1.20050 | ||||||||
\(611\) | −3.96852 | − | 5.01729i | −0.160549 | − | 0.202978i | ||||
\(612\) | −3.60212 | + | 6.23906i | −0.145607 | + | 0.252199i | ||||
\(613\) | −25.0649 | + | 14.4712i | −1.01236 | + | 0.584486i | −0.911882 | − | 0.410453i | \(-0.865371\pi\) |
−0.100478 | + | 0.994939i | \(0.532037\pi\) | |||||||
\(614\) | −8.13596 | −0.328341 | ||||||||
\(615\) | 6.02829 | + | 10.4413i | 0.243084 | + | 0.421034i | ||||
\(616\) | −13.3745 | − | 14.1918i | −0.538875 | − | 0.571806i | ||||
\(617\) | −3.55424 | + | 2.05204i | −0.143088 | + | 0.0826120i | −0.569835 | − | 0.821759i | \(-0.692993\pi\) |
0.426747 | + | 0.904371i | \(0.359660\pi\) | |||||||
\(618\) | −4.23197 | − | 2.44333i | −0.170235 | − | 0.0982852i | ||||
\(619\) | 9.06150 | + | 5.23166i | 0.364212 | + | 0.210278i | 0.670927 | − | 0.741523i | \(-0.265896\pi\) |
−0.306715 | + | 0.951802i | \(0.599230\pi\) | |||||||
\(620\) | 27.7951 | 1.11628 | ||||||||
\(621\) | 7.89025 | 0.316625 | ||||||||
\(622\) | 13.0731 | + | 7.54774i | 0.524182 | + | 0.302637i | ||||
\(623\) | 6.94384 | + | 29.3706i | 0.278199 | + | 1.17671i | ||||
\(624\) | 0.920592 | − | 0.728160i | 0.0368532 | − | 0.0291497i | ||||
\(625\) | 15.4164 | + | 26.7020i | 0.616657 | + | 1.06808i | ||||
\(626\) | −17.4781 | + | 10.0910i | −0.698565 | + | 0.403317i | ||||
\(627\) | 3.47954 | + | 6.02674i | 0.138959 | + | 0.240685i | ||||
\(628\) | 0.115974 | − | 0.200873i | 0.00462787 | − | 0.00801571i | ||||
\(629\) | − | 53.8550i | − | 2.14734i | ||||||
\(630\) | −6.17056 | + | 1.45885i | −0.245841 | + | 0.0581221i | ||||
\(631\) | 24.3336 | − | 14.0490i | 0.968704 | − | 0.559281i | 0.0698630 | − | 0.997557i | \(-0.477744\pi\) |
0.898841 | + | 0.438275i | \(0.144410\pi\) | |||||||
\(632\) | 3.11714 | − | 1.79968i | 0.123993 | − | 0.0715874i | ||||
\(633\) | 3.61505 | 0.143685 | ||||||||
\(634\) | 10.4401 | + | 18.0828i | 0.414629 | + | 0.718159i | ||||
\(635\) | 22.0475i | 0.874928i | ||||||||
\(636\) | −7.95501 | −0.315437 | ||||||||
\(637\) | 14.4570 | + | 20.6880i | 0.572809 | + | 0.819689i | ||||
\(638\) | 8.28456 | 0.327989 | ||||||||
\(639\) | 7.48311i | 0.296027i | ||||||||
\(640\) | 7.57253 | + | 13.1160i | 0.299331 | + | 0.518456i | ||||
\(641\) | −28.6276 | −1.13072 | −0.565362 | − | 0.824843i | \(-0.691263\pi\) | ||||
−0.565362 | + | 0.824843i | \(0.691263\pi\) | |||||||
\(642\) | 14.1201 | − | 8.15222i | 0.557274 | − | 0.321742i | ||||
\(643\) | −7.81711 | + | 4.51321i | −0.308277 | + | 0.177984i | −0.646155 | − | 0.763206i | \(-0.723624\pi\) |
0.337878 | + | 0.941190i | \(0.390291\pi\) | |||||||
\(644\) | −23.6077 | + | 5.58138i | −0.930275 | + | 0.219937i | ||||
\(645\) | 11.0600i | 0.435489i | ||||||||
\(646\) | 7.75472 | − | 13.4316i | 0.305105 | − | 0.528458i | ||||
\(647\) | 13.1024 | + | 22.6940i | 0.515109 | + | 0.892195i | 0.999846 | + | 0.0175353i | \(0.00558194\pi\) |
−0.484737 | + | 0.874660i | \(0.661085\pi\) | |||||||
\(648\) | −2.50674 | + | 1.44726i | −0.0984739 | + | 0.0568539i | ||||
\(649\) | −2.87535 | − | 4.98025i | −0.112867 | − | 0.195492i | ||||
\(650\) | 2.25845 | − | 5.68762i | 0.0885837 | − | 0.223087i | ||||
\(651\) | −5.56151 | − | 23.5237i | −0.217973 | − | 0.921966i | ||||
\(652\) | −7.09700 | − | 4.09745i | −0.277940 | − | 0.160469i | ||||
\(653\) | 45.4789 | 1.77973 | 0.889864 | − | 0.456226i | \(-0.150799\pi\) | ||||
0.889864 | + | 0.456226i | \(0.150799\pi\) | |||||||
\(654\) | 17.0104 | 0.665160 | ||||||||
\(655\) | −37.4923 | − | 21.6462i | −1.46495 | − | 0.845787i | ||||
\(656\) | 1.29833 | + | 0.749591i | 0.0506912 | + | 0.0292666i | ||||
\(657\) | 10.8250 | − | 6.24982i | 0.422324 | − | 0.243829i | ||||
\(658\) | 2.94707 | + | 3.12716i | 0.114889 | + | 0.121910i | ||||
\(659\) | 10.1806 | + | 17.6334i | 0.396581 | + | 0.686899i | 0.993302 | − | 0.115550i | \(-0.0368632\pi\) |
−0.596720 | + | 0.802449i | \(0.703530\pi\) | |||||||
\(660\) | −7.74693 | −0.301549 | ||||||||
\(661\) | 34.7308 | − | 20.0518i | 1.35087 | − | 0.779926i | 0.362501 | − | 0.931984i | \(-0.381923\pi\) |
0.988372 | + | 0.152057i | \(0.0485898\pi\) | |||||||
\(662\) | 14.6535 | − | 25.3807i | 0.569526 | − | 0.986447i | ||||
\(663\) | −17.5317 | + | 13.8670i | −0.680875 | + | 0.538551i | ||||
\(664\) | 6.07902 | 0.235912 | ||||||||
\(665\) | −18.4221 | + | 4.35538i | −0.714377 | + | 0.168894i | ||||
\(666\) | 3.97595 | − | 6.88655i | 0.154065 | − | 0.266848i | ||||
\(667\) | 14.0214 | − | 24.2858i | 0.542912 | − | 0.940352i | ||||
\(668\) | −1.81258 | − | 1.04649i | −0.0701309 | − | 0.0404901i | ||||
\(669\) | 3.55646i | 0.137501i | ||||||||
\(670\) | 1.28582 | + | 0.742368i | 0.0496755 | + | 0.0286802i | ||||
\(671\) | 31.5043i | 1.21621i | ||||||||
\(672\) | 10.5728 | − | 9.96387i | 0.407853 | − | 0.384365i | ||||
\(673\) | 10.2385 | − | 17.7336i | 0.394666 | − | 0.683581i | −0.598393 | − | 0.801203i | \(-0.704194\pi\) |
0.993058 | + | 0.117622i | \(0.0375270\pi\) | |||||||
\(674\) | − | 4.57441i | − | 0.176200i | ||||||
\(675\) | −0.927071 | + | 1.60573i | −0.0356830 | + | 0.0618047i | ||||
\(676\) | −14.4706 | + | 4.33746i | −0.556560 | + | 0.166825i | ||||
\(677\) | 18.6224 | + | 32.2549i | 0.715717 | + | 1.23966i | 0.962682 | + | 0.270634i | \(0.0872332\pi\) |
−0.246966 | + | 0.969024i | \(0.579433\pi\) | |||||||
\(678\) | −5.73345 | − | 3.31021i | −0.220192 | − | 0.127128i | ||||
\(679\) | −2.95558 | + | 2.78537i | −0.113425 | + | 0.106893i | ||||
\(680\) | 23.4903 | + | 40.6864i | 0.900811 | + | 1.56025i | ||||
\(681\) | −6.75066 | + | 3.89750i | −0.258686 | + | 0.149352i | ||||
\(682\) | 21.2963i | 0.815478i | ||||||||
\(683\) | − | 5.92465i | − | 0.226700i | −0.993555 | − | 0.113350i | \(-0.963842\pi\) | ||
0.993555 | − | 0.113350i | \(-0.0361582\pi\) | |||||||
\(684\) | −2.75029 | + | 1.58788i | −0.105160 | + | 0.0607141i | ||||
\(685\) | 2.51140 | + | 4.34988i | 0.0959558 | + | 0.166200i | ||||
\(686\) | −10.8759 | − | 13.0051i | −0.415244 | − | 0.496535i | ||||
\(687\) | −14.2182 | − | 8.20887i | −0.542457 | − | 0.313188i | ||||
\(688\) | 0.687634 | + | 1.19102i | 0.0262158 | + | 0.0454071i | ||||
\(689\) | −22.9401 | − | 9.10907i | −0.873946 | − | 0.347028i | ||||
\(690\) | 9.45467 | − | 16.3760i | 0.359933 | − | 0.623423i | ||||
\(691\) | − | 3.05713i | − | 0.116299i | −0.998308 | − | 0.0581493i | \(-0.981480\pi\) | ||
0.998308 | − | 0.0581493i | \(-0.0185199\pi\) | |||||||
\(692\) | 6.92912 | − | 12.0016i | 0.263405 | − | 0.456232i | ||||
\(693\) | 1.55008 | + | 6.55643i | 0.0588827 | + | 0.249058i | ||||
\(694\) | − | 31.4366i | − | 1.19332i | ||||||
\(695\) | 50.0166 | + | 28.8771i | 1.89724 | + | 1.09537i | ||||
\(696\) | 10.2875i | 0.389946i | ||||||||
\(697\) | −24.7253 | − | 14.2752i | −0.936538 | − | 0.540711i | ||||
\(698\) | 4.50064 | − | 7.79534i | 0.170352 | − | 0.295058i | ||||
\(699\) | 3.78863 | − | 6.56210i | 0.143299 | − | 0.248201i | ||||
\(700\) | 1.63795 | − | 5.46016i | 0.0619086 | − | 0.206375i | ||||
\(701\) | −2.81064 | −0.106156 | −0.0530782 | − | 0.998590i | \(-0.516903\pi\) | ||||
−0.0530782 | + | 0.998590i | \(0.516903\pi\) | |||||||
\(702\) | −3.26558 | + | 0.478894i | −0.123251 | + | 0.0180747i | ||||
\(703\) | 11.8701 | − | 20.5596i | 0.447690 | − | 0.775422i | ||||
\(704\) | −12.5205 | + | 7.22872i | −0.471885 | + | 0.272443i | ||||
\(705\) | 4.64500 | 0.174941 | ||||||||
\(706\) | −7.02227 | − | 12.1629i | −0.264287 | − | 0.457758i | ||||
\(707\) | −0.915906 | − | 0.971877i | −0.0344462 | − | 0.0365512i | ||||
\(708\) | 2.27273 | − | 1.31216i | 0.0854143 | − | 0.0493139i | ||||
\(709\) | −33.2799 | − | 19.2141i | −1.24985 | − | 0.721602i | −0.278772 | − | 0.960357i | \(-0.589927\pi\) |
−0.971080 | + | 0.238755i | \(0.923261\pi\) | |||||||
\(710\) | 15.5310 | + | 8.96681i | 0.582867 | + | 0.336518i | ||||
\(711\) | −1.24350 | −0.0466351 | ||||||||
\(712\) | 33.0181 | 1.23740 | ||||||||
\(713\) | 62.4293 | + | 36.0436i | 2.33799 | + | 1.34984i | ||||
\(714\) | 10.9271 | − | 10.2978i | 0.408937 | − | 0.385386i | ||||
\(715\) | −22.3400 | − | 8.87081i | −0.835470 | − | 0.331749i | ||||
\(716\) | 9.49395 | + | 16.4440i | 0.354805 | + | 0.614541i | ||||
\(717\) | 4.05866 | − | 2.34327i | 0.151574 | − | 0.0875111i | ||||
\(718\) | −13.3025 | − | 23.0406i | −0.496444 | − | 0.859867i | ||||
\(719\) | 13.2943 | − | 23.0263i | 0.495792 | − | 0.858737i | −0.504196 | − | 0.863589i | \(-0.668211\pi\) |
0.999988 | + | 0.00485212i | \(0.00154448\pi\) | |||||||
\(720\) | 0.852282i | 0.0317627i | ||||||||
\(721\) | −9.68668 | − | 10.2786i | −0.360751 | − | 0.382797i | ||||
\(722\) | −9.14150 | + | 5.27785i | −0.340211 | + | 0.196421i | ||||
\(723\) | −9.28664 | + | 5.36164i | −0.345374 | + | 0.199402i | ||||
\(724\) | 19.4931 | 0.724455 | ||||||||
\(725\) | 3.29492 | + | 5.70697i | 0.122370 | + | 0.211951i | ||||
\(726\) | 4.13374i | 0.153417i | ||||||||
\(727\) | −26.5203 | −0.983583 | −0.491792 | − | 0.870713i | \(-0.663658\pi\) | ||||
−0.491792 | + | 0.870713i | \(0.663658\pi\) | |||||||
\(728\) | 25.6651 | − | 10.1847i | 0.951212 | − | 0.377469i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 29.9560i | − | 1.10872i | ||||||
\(731\) | −13.0953 | − | 22.6817i | −0.484346 | − | 0.838912i | ||||
\(732\) | −14.3769 | −0.531386 | ||||||||
\(733\) | −22.0215 | + | 12.7141i | −0.813384 | + | 0.469607i | −0.848130 | − | 0.529789i | \(-0.822271\pi\) |
0.0347458 | + | 0.999396i | \(0.488938\pi\) | |||||||
\(734\) | −14.5091 | + | 8.37684i | −0.535541 | + | 0.309195i | ||||
\(735\) | −18.2941 | − | 1.08576i | −0.674788 | − | 0.0400490i | ||||
\(736\) | 43.3258i | 1.59701i | ||||||||
\(737\) | 0.788791 | − | 1.36623i | 0.0290555 | − | 0.0503256i | ||||
\(738\) | −2.10779 | − | 3.65079i | −0.0775887 | − | 0.134388i | ||||
\(739\) | −25.3568 | + | 14.6397i | −0.932763 | + | 0.538531i | −0.887684 | − | 0.460452i | \(-0.847687\pi\) |
−0.0450789 | + | 0.998983i | \(0.514354\pi\) | |||||||
\(740\) | 13.2140 | + | 22.8873i | 0.485755 | + | 0.841352i | ||||
\(741\) | −9.74932 | + | 1.42973i | −0.358150 | + | 0.0525223i | ||||
\(742\) | 15.8805 | + | 4.76384i | 0.582990 | + | 0.174886i | ||||
\(743\) | 11.9142 | + | 6.87868i | 0.437090 | + | 0.252354i | 0.702363 | − | 0.711819i | \(-0.252129\pi\) |
−0.265272 | + | 0.964174i | \(0.585462\pi\) | |||||||
\(744\) | −26.4451 | −0.969523 | ||||||||
\(745\) | 39.2560 | 1.43823 | ||||||||
\(746\) | 10.1992 | + | 5.88850i | 0.373419 | + | 0.215593i | ||||
\(747\) | −1.81881 | − | 1.05009i | −0.0665466 | − | 0.0384207i | ||||
\(748\) | 15.8872 | − | 9.17248i | 0.580894 | − | 0.335379i | ||||
\(749\) | 45.8601 | − | 10.8423i | 1.67569 | − | 0.396170i | ||||
\(750\) | −3.76960 | − | 6.52913i | −0.137646 | − | 0.238410i | ||||
\(751\) | 31.4688 | 1.14831 | 0.574156 | − | 0.818746i | \(-0.305330\pi\) | ||||
0.574156 | + | 0.818746i | \(0.305330\pi\) | |||||||
\(752\) | 0.500203 | − | 0.288792i | 0.0182405 | − | 0.0105312i | ||||
\(753\) | −5.93135 | + | 10.2734i | −0.216151 | + | 0.374384i | ||||
\(754\) | −4.32911 | + | 10.9023i | −0.157657 | + | 0.397040i | ||||
\(755\) | −23.6401 | −0.860351 | ||||||||
\(756\) | −2.99201 | + | 0.707377i | −0.108818 | + | 0.0257270i | ||||
\(757\) | −20.2956 | + | 35.1531i | −0.737657 | + | 1.27766i | 0.215890 | + | 0.976418i | \(0.430735\pi\) |
−0.953548 | + | 0.301243i | \(0.902599\pi\) | |||||||
\(758\) | 12.0541 | − | 20.8784i | 0.437825 | − | 0.758336i | ||||
\(759\) | −17.4000 | − | 10.0459i | −0.631581 | − | 0.364644i | ||||
\(760\) | 20.7099i | 0.751226i | ||||||||
\(761\) | −35.0760 | − | 20.2511i | −1.27150 | − | 0.734103i | −0.296232 | − | 0.955116i | \(-0.595730\pi\) |
−0.975271 | + | 0.221013i | \(0.929064\pi\) | |||||||
\(762\) | − | 7.70889i | − | 0.279264i | ||||||
\(763\) | 47.0916 | + | 14.1266i | 1.70483 | + | 0.511418i | ||||
\(764\) | −4.34833 | + | 7.53154i | −0.157317 | + | 0.272481i | ||||
\(765\) | − | 16.2308i | − | 0.586826i | ||||||
\(766\) | −6.59291 | + | 11.4193i | −0.238211 | + | 0.412594i | ||||
\(767\) | 8.05644 | − | 1.18147i | 0.290901 | − | 0.0426603i | ||||
\(768\) | −8.32531 | − | 14.4199i | −0.300414 | − | 0.520332i | ||||
\(769\) | 25.2026 | + | 14.5507i | 0.908828 | + | 0.524712i | 0.880054 | − | 0.474874i | \(-0.157506\pi\) |
0.0287743 | + | 0.999586i | \(0.490840\pi\) | |||||||
\(770\) | 15.4651 | + | 4.63924i | 0.557323 | + | 0.167187i | ||||
\(771\) | 4.67378 | + | 8.09523i | 0.168322 | + | 0.291542i | ||||
\(772\) | −11.7606 | + | 6.78998i | −0.423273 | + | 0.244377i | ||||
\(773\) | − | 10.3478i | − | 0.372186i | −0.982532 | − | 0.186093i | \(-0.940417\pi\) | ||
0.982532 | − | 0.186093i | \(-0.0595825\pi\) | |||||||
\(774\) | − | 3.86714i | − | 0.139001i | ||||||
\(775\) | −14.6704 | + | 8.46993i | −0.526975 | + | 0.304249i | ||||
\(776\) | 2.22156 | + | 3.84785i | 0.0797493 | + | 0.138130i | ||||
\(777\) | 16.7261 | − | 15.7628i | 0.600045 | − | 0.565488i | ||||
\(778\) | −5.24632 | − | 3.02897i | −0.188090 | − | 0.108594i | ||||
\(779\) | −6.29275 | − | 10.8994i | −0.225461 | − | 0.390510i | ||||
\(780\) | 4.04818 | − | 10.1948i | 0.144948 | − | 0.365033i | ||||
\(781\) | 9.52754 | − | 16.5022i | 0.340922 | − | 0.590495i | ||||
\(782\) | 44.7779i | 1.60125i | ||||||||
\(783\) | 1.77706 | − | 3.07796i | 0.0635069 | − | 0.109997i | ||||
\(784\) | −2.03753 | + | 1.02047i | −0.0727689 | + | 0.0364455i | ||||
\(785\) | 0.522568i | 0.0186513i | ||||||||
\(786\) | 13.1092 | + | 7.56858i | 0.467588 | + | 0.269962i | ||||
\(787\) | − | 29.1016i | − | 1.03736i | −0.854968 | − | 0.518680i | \(-0.826423\pi\) | ||
0.854968 | − | 0.518680i | \(-0.173577\pi\) | |||||||
\(788\) | 0.451939 | + | 0.260927i | 0.0160997 | + | 0.00929514i | ||||
\(789\) | 0.471710 | − | 0.817026i | 0.0167933 | − | 0.0290869i | ||||
\(790\) | −1.49006 | + | 2.58086i | −0.0530139 | + | 0.0918228i | ||||
\(791\) | −13.1235 | − | 13.9254i | −0.466617 | − | 0.495132i | ||||
\(792\) | 7.37066 | 0.261905 | ||||||||
\(793\) | −41.4590 | − | 16.4626i | −1.47225 | − | 0.584605i | ||||
\(794\) | −10.3603 | + | 17.9446i | −0.367674 | + | 0.636830i | ||||
\(795\) | 15.5211 | − | 8.96112i | 0.550477 | − | 0.317818i | ||||
\(796\) | −11.4152 | −0.404600 | ||||||||
\(797\) | −14.9812 | − | 25.9482i | −0.530661 | − | 0.919131i | −0.999360 | − | 0.0357733i | \(-0.988611\pi\) |
0.468699 | − | 0.883358i | \(-0.344723\pi\) | |||||||
\(798\) | 6.44126 | − | 1.52285i | 0.228018 | − | 0.0539085i | ||||
\(799\) | −9.52584 | + | 5.49975i | −0.337000 | + | 0.194567i | ||||
\(800\) | −8.81718 | − | 5.09060i | −0.311734 | − | 0.179980i | ||||
\(801\) | −9.87880 | − | 5.70353i | −0.349050 | − | 0.201524i | ||||
\(802\) | 0.412443 | 0.0145639 | ||||||||
\(803\) | −31.8292 | −1.12323 | ||||||||
\(804\) | 0.623475 | + | 0.359963i | 0.0219883 | + | 0.0126949i | ||||
\(805\) | 39.7741 | − | 37.4834i | 1.40185 | − | 1.32112i | ||||
\(806\) | −28.0256 | − | 11.1284i | −0.987159 | − | 0.391982i | ||||
\(807\) | −3.79153 | − | 6.56712i | −0.133468 | − | 0.231174i | ||||
\(808\) | −1.26528 | + | 0.730511i | −0.0445124 | + | 0.0256993i | ||||
\(809\) | 8.03836 | + | 13.9228i | 0.282614 | + | 0.489501i | 0.972028 | − | 0.234866i | \(-0.0754653\pi\) |
−0.689414 | + | 0.724367i | \(0.742132\pi\) | |||||||
\(810\) | 1.19827 | − | 2.07547i | 0.0421030 | − | 0.0729246i | ||||
\(811\) | 41.5793i | 1.46005i | 0.683423 | + | 0.730023i | \(0.260491\pi\) | ||||
−0.683423 | + | 0.730023i | \(0.739509\pi\) | |||||||
\(812\) | −3.13971 | + | 10.4663i | −0.110182 | + | 0.367296i | ||||
\(813\) | −17.8317 | + | 10.2951i | −0.625384 | + | 0.361066i | ||||
\(814\) | −17.5360 | + | 10.1244i | −0.614636 | + | 0.354860i | ||||
\(815\) | 18.4627 | 0.646721 | ||||||||
\(816\) | −1.00911 | − | 1.74784i | −0.0353261 | − | 0.0611866i | ||||
\(817\) | − | 11.5453i | − | 0.403917i | ||||||
\(818\) | 31.5460 | 1.10298 | ||||||||
\(819\) | −9.43814 | − | 1.38619i | −0.329795 | − | 0.0484375i | ||||
\(820\) | 14.0103 | 0.489262 | ||||||||
\(821\) | − | 4.07383i | − | 0.142178i | −0.997470 | − | 0.0710888i | \(-0.977353\pi\) | ||
0.997470 | − | 0.0710888i | \(-0.0226474\pi\) | |||||||
\(822\) | −0.878110 | − | 1.52093i | −0.0306276 | − | 0.0530486i | ||||
\(823\) | 42.6371 | 1.48624 | 0.743118 | − | 0.669160i | \(-0.233346\pi\) | ||||
0.743118 | + | 0.669160i | \(0.233346\pi\) | |||||||
\(824\) | −13.3817 | + | 7.72593i | −0.466174 | + | 0.269146i | ||||
\(825\) | 4.08886 | − | 2.36070i | 0.142356 | − | 0.0821892i | ||||
\(826\) | −5.32279 | + | 1.25842i | −0.185204 | + | 0.0437862i | ||||
\(827\) | 21.7244i | 0.755431i | 0.925922 | + | 0.377716i | \(0.123290\pi\) | ||||
−0.925922 | + | 0.377716i | \(0.876710\pi\) | |||||||
\(828\) | 4.58443 | − | 7.94047i | 0.159320 | − | 0.275950i | ||||
\(829\) | −0.461472 | − | 0.799293i | −0.0160276 | − | 0.0277606i | 0.857900 | − | 0.513816i | \(-0.171769\pi\) |
−0.873928 | + | 0.486055i | \(0.838435\pi\) | |||||||
\(830\) | −4.35885 | + | 2.51658i | −0.151298 | + | 0.0873519i | ||||
\(831\) | 10.2128 | + | 17.6891i | 0.354278 | + | 0.613628i | ||||
\(832\) | −2.97025 | − | 20.2542i | −0.102975 | − | 0.702187i | ||||
\(833\) | 38.8026 | − | 19.4338i | 1.34443 | − | 0.673342i | ||||
\(834\) | −17.4883 | − | 10.0969i | −0.605569 | − | 0.349626i | ||||
\(835\) | 4.71540 | 0.163183 | ||||||||
\(836\) | 8.08679 | 0.279688 | ||||||||
\(837\) | 7.91220 | + | 4.56811i | 0.273486 | + | 0.157897i | ||||
\(838\) | −0.309209 | − | 0.178522i | −0.0106814 | − | 0.00616693i | ||||
\(839\) | 10.4845 | − | 6.05325i | 0.361966 | − | 0.208981i | −0.307977 | − | 0.951394i | \(-0.599652\pi\) |
0.669943 | + | 0.742413i | \(0.266319\pi\) | |||||||
\(840\) | −5.76085 | + | 19.2040i | −0.198768 | + | 0.662602i | ||||
\(841\) | 8.18413 | + | 14.1753i | 0.282211 | + | 0.488804i | ||||
\(842\) | 22.4724 | 0.774451 | ||||||||
\(843\) | 9.41393 | − | 5.43514i | 0.324233 | − | 0.187196i | ||||
\(844\) | 2.10043 | − | 3.63805i | 0.0722998 | − | 0.125227i | ||||
\(845\) | 23.3477 | − | 24.7636i | 0.803184 | − | 0.851894i | ||||
\(846\) | −1.62412 | −0.0558384 | ||||||||
\(847\) | −3.43294 | + | 11.4438i | −0.117957 | + | 0.393215i | ||||
\(848\) | 1.11428 | − | 1.92998i | 0.0382644 | − | 0.0662758i | ||||
\(849\) | 1.91077 | − | 3.30955i | 0.0655775 | − | 0.113583i | ||||
\(850\) | −9.11269 | − | 5.26121i | −0.312563 | − | 0.180458i | ||||
\(851\) | 68.5414i | 2.34957i | ||||||||
\(852\) | 7.53074 | + | 4.34787i | 0.257999 | + | 0.148956i | ||||
\(853\) | − | 25.9127i | − | 0.887233i | −0.896217 | − | 0.443616i | \(-0.853695\pi\) | ||
0.896217 | − | 0.443616i | \(-0.146305\pi\) | |||||||
\(854\) | 28.7004 | + | 8.60959i | 0.982107 | + | 0.294614i | ||||
\(855\) | 3.57742 | − | 6.19627i | 0.122345 | − | 0.211908i | ||||
\(856\) | − | 51.5554i | − | 1.76213i | ||||||
\(857\) | −7.12117 | + | 12.3342i | −0.243255 | + | 0.421329i | −0.961639 | − | 0.274317i | \(-0.911548\pi\) |
0.718385 | + | 0.695646i | \(0.244882\pi\) | |||||||
\(858\) | 7.81117 | + | 3.10167i | 0.266669 | + | 0.105889i | ||||
\(859\) | −7.79426 | − | 13.5001i | −0.265937 | − | 0.460616i | 0.701872 | − | 0.712303i | \(-0.252348\pi\) |
−0.967809 | + | 0.251687i | \(0.919015\pi\) | |||||||
\(860\) | 11.1304 | + | 6.42616i | 0.379545 | + | 0.219130i | ||||
\(861\) | −2.80333 | − | 11.8573i | −0.0955371 | − | 0.404096i | ||||
\(862\) | 0.519711 | + | 0.900165i | 0.0177014 | + | 0.0306597i | ||||
\(863\) | 18.3943 | − | 10.6200i | 0.626150 | − | 0.361508i | −0.153109 | − | 0.988209i | \(-0.548929\pi\) |
0.779260 | + | 0.626701i | \(0.215595\pi\) | |||||||
\(864\) | 5.49106i | 0.186810i | ||||||||
\(865\) | 31.2219i | 1.06158i | ||||||||
\(866\) | 16.0506 | − | 9.26683i | 0.545422 | − | 0.314900i | ||||
\(867\) | 10.7175 | + | 18.5633i | 0.363986 | + | 0.630443i | ||||
\(868\) | −26.9048 | − | 8.07094i | −0.913208 | − | 0.273945i | ||||
\(869\) | 2.74225 | + | 1.58324i | 0.0930244 | + | 0.0537077i | ||||
\(870\) | −4.25880 | − | 7.37646i | −0.144387 | − | 0.250085i | ||||
\(871\) | 1.38575 | + | 1.75196i | 0.0469542 | + | 0.0593629i | ||||
\(872\) | 26.8939 | − | 46.5816i | 0.910742 | − | 1.57745i | ||||
\(873\) | − | 1.53501i | − | 0.0519521i | ||||||
\(874\) | −9.86945 | + | 17.0944i | −0.333839 | + | 0.578227i | ||||
\(875\) | −5.01351 | − | 21.2058i | −0.169488 | − | 0.716886i | ||||
\(876\) | − | 14.5252i | − | 0.490761i | ||||||
\(877\) | 26.0572 | + | 15.0441i | 0.879889 | + | 0.508004i | 0.870622 | − | 0.491953i | \(-0.163717\pi\) |
0.00926688 | + | 0.999957i | \(0.497050\pi\) | |||||||
\(878\) | − | 25.6095i | − | 0.864280i | ||||||
\(879\) | 15.6392 | + | 9.02929i | 0.527497 | + | 0.304550i | ||||
\(880\) | 1.08513 | − | 1.87950i | 0.0365797 | − | 0.0633579i | ||||
\(881\) | 22.2785 | − | 38.5876i | 0.750583 | − | 1.30005i | −0.196957 | − | 0.980412i | \(-0.563106\pi\) |
0.947540 | − | 0.319636i | \(-0.103561\pi\) | |||||||
\(882\) | 6.39652 | + | 0.379636i | 0.215382 | + | 0.0127830i | ||||
\(883\) | −1.96438 | −0.0661066 | −0.0330533 | − | 0.999454i | \(-0.510523\pi\) | ||||
−0.0330533 | + | 0.999454i | \(0.510523\pi\) | |||||||
\(884\) | 3.76893 | + | 25.7004i | 0.126763 | + | 0.864398i | ||||
\(885\) | −2.95623 | + | 5.12034i | −0.0993726 | + | 0.172118i | ||||
\(886\) | 17.0779 | − | 9.85991i | 0.573742 | − | 0.331250i | ||||
\(887\) | 4.61734 | 0.155035 | 0.0775175 | − | 0.996991i | \(-0.475301\pi\) | ||||
0.0775175 | + | 0.996991i | \(0.475301\pi\) | |||||||
\(888\) | −12.5722 | − | 21.7756i | −0.421894 | − | 0.730742i | ||||
\(889\) | 6.40199 | − | 21.3413i | 0.214716 | − | 0.715764i | ||||
\(890\) | −23.6750 | + | 13.6688i | −0.793588 | + | 0.458178i | ||||
\(891\) | −2.20526 | − | 1.27321i | −0.0738789 | − | 0.0426540i | ||||
\(892\) | 3.57909 | + | 2.06639i | 0.119837 | + | 0.0691879i | ||||
\(893\) | −4.84878 | −0.162258 | ||||||||
\(894\) | −13.7258 | −0.459060 | ||||||||
\(895\) | −37.0475 | − | 21.3894i | −1.23836 | − | 0.714969i | ||||
\(896\) | −3.52144 | − | 14.8947i | −0.117643 | − | 0.497598i | ||||
\(897\) | 22.3127 | − | 17.6486i | 0.744998 | − | 0.589270i | ||||
\(898\) | 1.32219 | + | 2.29011i | 0.0441222 | + | 0.0764219i | ||||
\(899\) | 28.1209 | − | 16.2356i | 0.937884 | − | 0.541488i | ||||
\(900\) | 1.07730 | + | 1.86594i | 0.0359101 | + | 0.0621981i | ||||
\(901\) | −21.2202 | + | 36.7545i | −0.706948 | + | 1.22447i | ||||
\(902\) | 10.7346i | 0.357423i | ||||||||
\(903\) | 3.21154 | − | 10.7058i | 0.106873 | − | 0.356266i | ||||
\(904\) | −18.1295 | + | 10.4671i | −0.602977 | + | 0.348129i | ||||
\(905\) | −38.0332 | + | 21.9585i | −1.26427 | + | 0.729925i | ||||
\(906\) | 8.26574 | 0.274611 | ||||||||
\(907\) | 10.3823 | + | 17.9827i | 0.344740 | + | 0.597107i | 0.985306 | − | 0.170796i | \(-0.0546338\pi\) |
−0.640567 | + | 0.767903i | \(0.721300\pi\) | |||||||
\(908\) | 9.05817i | 0.300606i | ||||||||
\(909\) | 0.504753 | 0.0167416 | ||||||||
\(910\) | −14.1865 | + | 17.9275i | −0.470277 | + | 0.594292i | ||||
\(911\) | −49.6547 | −1.64513 | −0.822567 | − | 0.568669i | \(-0.807459\pi\) | ||||
−0.822567 | + | 0.568669i | \(0.807459\pi\) | |||||||
\(912\) | − | 0.889672i | − | 0.0294600i | ||||||
\(913\) | 2.67396 | + | 4.63143i | 0.0884950 | + | 0.153278i | ||||
\(914\) | −29.9046 | −0.989156 | ||||||||
\(915\) | 28.0510 | − | 16.1952i | 0.927336 | − | 0.535398i | ||||
\(916\) | −16.5222 | + | 9.53911i | −0.545910 | + | 0.315181i | ||||
\(917\) | 30.0059 | + | 31.8396i | 0.990883 | + | 1.05144i | ||||
\(918\) | 5.67509i | 0.187306i | ||||||||
\(919\) | −27.5731 | + | 47.7580i | −0.909553 | + | 1.57539i | −0.0948669 | + | 0.995490i | \(0.530243\pi\) |
−0.814686 | + | 0.579902i | \(0.803091\pi\) | |||||||
\(920\) | −29.8961 | − | 51.7817i | −0.985647 | − | 1.70719i | ||||
\(921\) | 7.69716 | − | 4.44396i | 0.253630 | − | 0.146433i | ||||
\(922\) | 17.3338 | + | 30.0230i | 0.570858 | + | 0.988756i | ||||
\(923\) | 16.7379 | + | 21.1613i | 0.550936 | + | 0.696534i | ||||
\(924\) | 7.49879 | + | 2.24950i | 0.246692 | + | 0.0740031i | ||||
\(925\) | −13.9488 | − | 8.05332i | −0.458632 | − | 0.264792i | ||||
\(926\) | 19.1259 | 0.628516 | ||||||||
\(927\) | 5.33830 | 0.175333 | ||||||||
\(928\) | 16.9012 | + | 9.75793i | 0.554810 | + | 0.320320i | ||||
\(929\) | −3.77027 | − | 2.17677i | −0.123699 | − | 0.0714174i | 0.436874 | − | 0.899523i | \(-0.356086\pi\) |
−0.560573 | + | 0.828105i | \(0.689419\pi\) | |||||||
\(930\) | 18.9620 | − | 10.9477i | 0.621787 | − | 0.358989i | ||||
\(931\) | 19.0967 | + | 1.13340i | 0.625868 | + | 0.0371456i | ||||
\(932\) | −4.40258 | − | 7.62549i | −0.144211 | − | 0.249781i | ||||
\(933\) | −16.4907 | −0.539880 | ||||||||
\(934\) | −17.2596 | + | 9.96482i | −0.564750 | + | 0.326059i | ||||
\(935\) | −20.6652 | + | 35.7931i | −0.675823 | + | 1.17056i | ||||
\(936\) | −3.85155 | + | 9.69966i | −0.125892 | + | 0.317043i | ||||
\(937\) | 0.712633 | 0.0232807 | 0.0116404 | − | 0.999932i | \(-0.496295\pi\) | ||||
0.0116404 | + | 0.999932i | \(0.496295\pi\) | |||||||
\(938\) | −1.02907 | − | 1.09196i | −0.0336003 | − | 0.0356536i | ||||
\(939\) | 11.0236 | − | 19.0935i | 0.359742 | − | 0.623092i | ||||
\(940\) | 2.69886 | − | 4.67456i | 0.0880271 | − | 0.152467i | ||||
\(941\) | −10.1930 | − | 5.88493i | −0.332282 | − | 0.191843i | 0.324572 | − | 0.945861i | \(-0.394780\pi\) |
−0.656854 | + | 0.754018i | \(0.728113\pi\) | |||||||
\(942\) | − | 0.182716i | − | 0.00595320i | ||||||
\(943\) | 31.4680 | + | 18.1681i | 1.02474 | + | 0.591633i | ||||
\(944\) | 0.735188i | 0.0239283i | ||||||||
\(945\) | 5.04091 | − | 4.75060i | 0.163981 | − | 0.154537i | ||||
\(946\) | −4.92366 | + | 8.52803i | −0.160082 | + | 0.277270i | ||||
\(947\) | − | 30.7176i | − | 0.998187i | −0.866548 | − | 0.499093i | \(-0.833666\pi\) | ||
0.866548 | − | 0.499093i | \(-0.166334\pi\) | |||||||
\(948\) | −0.722507 | + | 1.25142i | −0.0234659 | + | 0.0406442i | ||||
\(949\) | 16.6324 | − | 41.8867i | 0.539911 | − | 1.35970i | ||||
\(950\) | −2.31924 | − | 4.01704i | −0.0752460 | − | 0.130330i | ||||
\(951\) | −19.7541 | − | 11.4050i | −0.640569 | − | 0.369833i | ||||
\(952\) | −10.9236 | − | 46.2041i | −0.354037 | − | 1.49748i | ||||
\(953\) | −13.0794 | − | 22.6542i | −0.423684 | − | 0.733843i | 0.572612 | − | 0.819826i | \(-0.305930\pi\) |
−0.996297 | + | 0.0859835i | \(0.972597\pi\) | |||||||
\(954\) | −5.42695 | + | 3.13325i | −0.175704 | + | 0.101443i | ||||
\(955\) | − | 19.5932i | − | 0.634020i | ||||||
\(956\) | − | 5.44599i | − | 0.176136i | ||||||
\(957\) | −7.83774 | + | 4.52512i | −0.253358 | + | 0.146276i | ||||
\(958\) | 4.98883 | + | 8.64090i | 0.161182 | + | 0.279175i | ||||
\(959\) | −1.16787 | − | 4.93979i | −0.0377126 | − | 0.159514i | ||||
\(960\) | 12.8727 | + | 7.43207i | 0.415465 | + | 0.239869i | ||||
\(961\) | 26.2353 | + | 45.4409i | 0.846300 | + | 1.46583i | ||||
\(962\) | −4.16007 | − | 28.3676i | −0.134126 | − | 0.914608i | ||||
\(963\) | −8.90567 | + | 15.4251i | −0.286981 | + | 0.497066i | ||||
\(964\) | 12.4610i | 0.401342i | ||||||||
\(965\) | 15.2975 | − | 26.4961i | 0.492444 | − | 0.852938i | ||||
\(966\) | −13.9070 | + | 13.1061i | −0.447449 | + | 0.421680i | ||||
\(967\) | − | 2.99020i | − | 0.0961582i | −0.998844 | − | 0.0480791i | \(-0.984690\pi\) | ||
0.998844 | − | 0.0480791i | \(-0.0153100\pi\) | |||||||
\(968\) | 11.3199 | + | 6.53554i | 0.363835 | + | 0.210060i | ||||
\(969\) | 16.9429i | 0.544283i | ||||||||
\(970\) | −3.18586 | − | 1.83936i | −0.102292 | − | 0.0590582i | ||||
\(971\) | 9.27532 | − | 16.0653i | 0.297659 | − | 0.515561i | −0.677941 | − | 0.735116i | \(-0.737127\pi\) |
0.975600 | + | 0.219556i | \(0.0704608\pi\) | |||||||
\(972\) | 0.581025 | − | 1.00636i | 0.0186364 | − | 0.0322792i | ||||
\(973\) | −40.0294 | − | 42.4756i | −1.28328 | − | 1.36171i | ||||
\(974\) | −5.63160 | −0.180448 | ||||||||
\(975\) | 0.970003 | + | 6.61446i | 0.0310649 | + | 0.211832i | ||||
\(976\) | 2.01380 | − | 3.48801i | 0.0644603 | − | 0.111649i | ||||
\(977\) | 3.31539 | − | 1.91414i | 0.106069 | − | 0.0612387i | −0.446027 | − | 0.895019i | \(-0.647162\pi\) |
0.552096 | + | 0.833781i | \(0.313828\pi\) | |||||||
\(978\) | −6.45548 | −0.206424 | ||||||||
\(979\) | 14.5235 | + | 25.1555i | 0.464174 | + | 0.803973i | ||||
\(980\) | −11.7220 | + | 17.7797i | −0.374446 | + | 0.567951i | ||||
\(981\) | −16.0930 | + | 9.29129i | −0.513809 | + | 0.296648i | ||||
\(982\) | −8.56201 | − | 4.94328i | −0.273225 | − | 0.157746i | ||||
\(983\) | −27.0572 | − | 15.6215i | −0.862992 | − | 0.498248i | 0.00202132 | − | 0.999998i | \(-0.499357\pi\) |
−0.865013 | + | 0.501749i | \(0.832690\pi\) | |||||||
\(984\) | −13.3299 | −0.424940 | ||||||||
\(985\) | −1.17571 | −0.0374613 | ||||||||
\(986\) | 17.4677 | + | 10.0850i | 0.556284 | + | 0.321171i | ||||
\(987\) | −4.49621 | − | 1.34878i | −0.143116 | − | 0.0429322i | ||||
\(988\) | −4.22577 | + | 10.6421i | −0.134440 | + | 0.338570i | ||||
\(989\) | 16.6664 | + | 28.8670i | 0.529960 | + | 0.917918i | ||||
\(990\) | −5.28500 | + | 3.05130i | −0.167968 | + | 0.0969765i | ||||
\(991\) | −2.96796 | − | 5.14066i | −0.0942805 | − | 0.163299i | 0.815028 | − | 0.579422i | \(-0.196722\pi\) |
−0.909308 | + | 0.416124i | \(0.863388\pi\) | |||||||
\(992\) | −25.0838 | + | 43.4464i | −0.796410 | + | 1.37942i | ||||
\(993\) | 32.0157i | 1.01599i | ||||||||
\(994\) | −12.4298 | − | 13.1894i | −0.394249 | − | 0.418341i | ||||
\(995\) | 22.2723 | − | 12.8589i | 0.706079 | − | 0.407655i | ||||
\(996\) | −2.11354 | + | 1.22025i | −0.0669702 | + | 0.0386652i | ||||
\(997\) | −7.84640 | −0.248498 | −0.124249 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124249 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(998\) | 0.982678 | + | 1.70205i | 0.0311061 | + | 0.0538774i | ||||
\(999\) | 8.68684i | 0.274840i |
(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 | 273.2.t.d.4.4 | ✓ | 20 | |
3.2 | odd | 2 | 819.2.bm.g.550.7 | 20 | |||
7.2 | even | 3 | 273.2.bl.d.121.4 | yes | 20 | ||
13.10 | even | 6 | 273.2.bl.d.88.4 | yes | 20 | ||
21.2 | odd | 6 | 819.2.do.g.667.7 | 20 | |||
39.23 | odd | 6 | 819.2.do.g.361.7 | 20 | |||
91.23 | even | 6 | inner | 273.2.t.d.205.7 | yes | 20 | |
273.23 | odd | 6 | 819.2.bm.g.478.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.d.4.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
273.2.t.d.205.7 | yes | 20 | 91.23 | even | 6 | inner | |
273.2.bl.d.88.4 | yes | 20 | 13.10 | even | 6 | ||
273.2.bl.d.121.4 | yes | 20 | 7.2 | even | 3 | ||
819.2.bm.g.478.4 | 20 | 273.23 | odd | 6 | |||
819.2.bm.g.550.7 | 20 | 3.2 | odd | 2 | |||
819.2.do.g.361.7 | 20 | 39.23 | odd | 6 | |||
819.2.do.g.667.7 | 20 | 21.2 | odd | 6 |