Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(88,273)]
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, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.88");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bl (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: | \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 88.4 | ||
Root | \(-0.915396i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.88 |
Dual form | 273.2.bl.d.121.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.792756 | − | 0.457698i | −0.560563 | − | 0.323641i | 0.192808 | − | 0.981236i | \(-0.438240\pi\) |
−0.753372 | + | 0.657595i | \(0.771574\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.581025 | − | 1.00636i | −0.290512 | − | 0.503182i | ||||
\(5\) | 2.26729 | − | 1.30902i | 1.01396 | − | 0.585412i | 0.101614 | − | 0.994824i | \(-0.467599\pi\) |
0.912350 | + | 0.409412i | \(0.134266\pi\) | |||||||
\(6\) | 0.792756 | + | 0.457698i | 0.323641 | + | 0.186854i | ||||
\(7\) | 1.81456 | + | 1.92545i | 0.685840 | + | 0.727752i | ||||
\(8\) | 2.89453i | 1.02337i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.39655 | −0.757854 | ||||||||
\(11\) | − | 2.54641i | − | 0.767772i | −0.923381 | − | 0.383886i | \(-0.874586\pi\) | ||
0.923381 | − | 0.383886i | \(-0.125414\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | 0.162771 | − | 0.281927i | 0.0406927 | − | 0.0704819i | ||||
\(17\) | −3.09980 | − | 5.36901i | −0.751812 | − | 1.30218i | −0.946944 | − | 0.321400i | \(-0.895847\pi\) |
0.195131 | − | 0.980777i | \(-0.437487\pi\) | |||||||
\(18\) | −0.792756 | − | 0.457698i | −0.186854 | − | 0.107880i | ||||
\(19\) | 2.73290i | 0.626969i | 0.949593 | + | 0.313485i | \(0.101496\pi\) | ||||
−0.949593 | + | 0.313485i | \(0.898504\pi\) | |||||||
\(20\) | −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 | ||||
\(23\) | 3.94513 | − | 6.83316i | 0.822616 | − | 1.42481i | −0.0811124 | − | 0.996705i | \(-0.525847\pi\) |
0.903728 | − | 0.428107i | \(-0.140819\pi\) | |||||||
\(24\) | − | 2.89453i | − | 0.590843i | ||||||
\(25\) | 0.927071 | − | 1.60573i | 0.185414 | − | 0.321147i | ||||
\(26\) | −2.04752 | + | 2.58863i | −0.401553 | + | 0.507672i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.883400 | − | 2.94485i | 0.166947 | − | 0.556524i | ||||
\(29\) | −1.77706 | − | 3.07796i | −0.329992 | − | 0.571562i | 0.652518 | − | 0.757773i | \(-0.273713\pi\) |
−0.982510 | + | 0.186211i | \(0.940379\pi\) | |||||||
\(30\) | 2.39655 | 0.437547 | ||||||||
\(31\) | 7.91220 | + | 4.56811i | 1.42107 | + | 0.820457i | 0.996391 | − | 0.0848850i | \(-0.0270523\pi\) |
0.424683 | + | 0.905342i | \(0.360386\pi\) | |||||||
\(32\) | 4.75540 | − | 2.74553i | 0.840643 | − | 0.485345i | ||||
\(33\) | 2.54641i | 0.443273i | ||||||||
\(34\) | 5.67509i | 0.973270i | ||||||||
\(35\) | 6.63460 | + | 1.99026i | 1.12145 | + | 0.336415i | ||||
\(36\) | −0.581025 | − | 1.00636i | −0.0968375 | − | 0.167727i | ||||
\(37\) | −7.52303 | − | 4.34342i | −1.23678 | − | 0.714054i | −0.268344 | − | 0.963323i | \(-0.586476\pi\) |
−0.968434 | + | 0.249269i | \(0.919810\pi\) | |||||||
\(38\) | 1.25084 | − | 2.16652i | 0.202913 | − | 0.351456i | ||||
\(39\) | −0.523154 | + | 3.56740i | −0.0837718 | + | 0.571240i | ||||
\(40\) | 3.78900 | + | 6.56274i | 0.599093 | + | 1.03766i | ||||
\(41\) | −3.98821 | + | 2.30259i | −0.622854 | + | 0.359605i | −0.777979 | − | 0.628290i | \(-0.783755\pi\) |
0.155125 | + | 0.987895i | \(0.450422\pi\) | |||||||
\(42\) | 0.557231 | + | 2.35694i | 0.0859826 | + | 0.363683i | ||||
\(43\) | −2.11228 | + | 3.65857i | −0.322119 | + | 0.557926i | −0.980925 | − | 0.194386i | \(-0.937728\pi\) |
0.658806 | + | 0.752313i | \(0.271062\pi\) | |||||||
\(44\) | −2.56262 | + | 1.47953i | −0.386329 | + | 0.223047i | ||||
\(45\) | 2.26729 | − | 1.30902i | 0.337988 | − | 0.195137i | ||||
\(46\) | −6.25505 | + | 3.61135i | −0.922257 | + | 0.532465i | ||||
\(47\) | 1.53652 | − | 0.887113i | 0.224125 | − | 0.129399i | −0.383734 | − | 0.923444i | \(-0.625362\pi\) |
0.607859 | + | 0.794045i | \(0.292029\pi\) | |||||||
\(48\) | −0.162771 | + | 0.281927i | −0.0234940 | + | 0.0406927i | ||||
\(49\) | −0.414724 | + | 6.98770i | −0.0592462 | + | 0.998243i | ||||
\(50\) | −1.46988 | + | 0.848638i | −0.207873 | + | 0.120015i | ||||
\(51\) | 3.09980 | + | 5.36901i | 0.434059 | + | 0.751812i | ||||
\(52\) | −3.89407 | + | 1.54626i | −0.540010 | + | 0.214428i | ||||
\(53\) | −3.42283 | + | 5.92852i | −0.470162 | + | 0.814345i | −0.999418 | − | 0.0341173i | \(-0.989138\pi\) |
0.529255 | + | 0.848463i | \(0.322471\pi\) | |||||||
\(54\) | 0.792756 | + | 0.457698i | 0.107880 | + | 0.0622848i | ||||
\(55\) | −3.33331 | − | 5.77345i | −0.449463 | − | 0.778492i | ||||
\(56\) | −5.57327 | + | 5.25230i | −0.744760 | + | 0.701869i | ||||
\(57\) | − | 2.73290i | − | 0.361981i | ||||||
\(58\) | 3.25343i | 0.427196i | ||||||||
\(59\) | 1.95579 | − | 1.12918i | 0.254622 | − | 0.147006i | −0.367257 | − | 0.930120i | \(-0.619703\pi\) |
0.621879 | + | 0.783113i | \(0.286370\pi\) | |||||||
\(60\) | 2.63470 | + | 1.52115i | 0.340139 | + | 0.196379i | ||||
\(61\) | 12.3720 | 1.58408 | 0.792038 | − | 0.610472i | \(-0.209020\pi\) | ||||
0.792038 | + | 0.610472i | \(0.209020\pi\) | |||||||
\(62\) | −4.18163 | − | 7.24280i | −0.531068 | − | 0.919837i | ||||
\(63\) | 1.81456 | + | 1.92545i | 0.228613 | + | 0.242584i | ||||
\(64\) | −5.67758 | −0.709697 | ||||||||
\(65\) | −3.48365 | − | 8.77314i | −0.432094 | − | 1.08817i | ||||
\(66\) | 1.16549 | − | 2.01868i | 0.143462 | − | 0.248483i | ||||
\(67\) | − | 0.619532i | − | 0.0756878i | −0.999284 | − | 0.0378439i | \(-0.987951\pi\) | ||
0.999284 | − | 0.0378439i | \(-0.0120490\pi\) | |||||||
\(68\) | −3.60212 | + | 6.23906i | −0.436821 | + | 0.756597i | ||||
\(69\) | −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 | 0.832554 | − | 0.553944i | \(-0.186878\pi\) |
−0.0634524 | + | 0.997985i | \(0.520211\pi\) | |||||||
\(72\) | 2.89453i | 0.341123i | ||||||||
\(73\) | 10.8250 | + | 6.24982i | 1.26697 | + | 0.731486i | 0.974414 | − | 0.224762i | \(-0.0721605\pi\) |
0.292557 | + | 0.956248i | \(0.405494\pi\) | |||||||
\(74\) | 3.97595 | + | 6.88655i | 0.462195 | + | 0.800545i | ||||
\(75\) | −0.927071 | + | 1.60573i | −0.107049 | + | 0.185414i | ||||
\(76\) | 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 | \(0.811049\pi\) | |||||||
\(80\) | − | 0.852282i | − | 0.0952880i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.21557 | 0.465532 | ||||||||
\(83\) | − | 2.10018i | − | 0.230524i | −0.993335 | − | 0.115262i | \(-0.963229\pi\) | ||
0.993335 | − | 0.115262i | \(-0.0367708\pi\) | |||||||
\(84\) | −0.883400 | + | 2.94485i | −0.0963868 | + | 0.321309i | ||||
\(85\) | −14.0563 | − | 8.11541i | −1.52462 | − | 0.880240i | ||||
\(86\) | 3.34904 | − | 1.93357i | 0.361136 | − | 0.208502i | ||||
\(87\) | 1.77706 | + | 3.07796i | 0.190521 | + | 0.329992i | ||||
\(88\) | 7.37066 | 0.785715 | ||||||||
\(89\) | 9.87880 | + | 5.70353i | 1.04715 | + | 0.604573i | 0.921850 | − | 0.387546i | \(-0.126677\pi\) |
0.125301 | + | 0.992119i | \(0.460010\pi\) | |||||||
\(90\) | −2.39655 | −0.252618 | ||||||||
\(91\) | 7.81814 | − | 5.46595i | 0.819564 | − | 0.572988i | ||||
\(92\) | −9.16886 | −0.955920 | ||||||||
\(93\) | −7.91220 | − | 4.56811i | −0.820457 | − | 0.473691i | ||||
\(94\) | −1.62412 | −0.167515 | ||||||||
\(95\) | 3.57742 | + | 6.19627i | 0.367035 | + | 0.635724i | ||||
\(96\) | −4.75540 | + | 2.74553i | −0.485345 | + | 0.280214i | ||||
\(97\) | −1.32935 | − | 0.767503i | −0.134975 | − | 0.0779281i | 0.430992 | − | 0.902356i | \(-0.358164\pi\) |
−0.565967 | + | 0.824428i | \(0.691497\pi\) | |||||||
\(98\) | 3.52703 | − | 5.34973i | 0.356284 | − | 0.540404i | ||||
\(99\) | − | 2.54641i | − | 0.255924i | ||||||
\(100\) | −2.15461 | −0.215461 | ||||||||
\(101\) | 0.504753 | 0.0502248 | 0.0251124 | − | 0.999685i | \(-0.492006\pi\) | ||||
0.0251124 | + | 0.999685i | \(0.492006\pi\) | |||||||
\(102\) | − | 5.67509i | − | 0.561918i | ||||||
\(103\) | −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 | ||||
\(107\) | −8.90567 | + | 15.4251i | −0.860944 | + | 1.49120i | 0.0100752 | + | 0.999949i | \(0.496793\pi\) |
−0.871019 | + | 0.491249i | \(0.836540\pi\) | |||||||
\(108\) | 0.581025 | + | 1.00636i | 0.0559091 | + | 0.0968375i | ||||
\(109\) | −16.0930 | − | 9.29129i | −1.54143 | − | 0.889944i | −0.998749 | − | 0.0500036i | \(-0.984077\pi\) |
−0.542679 | − | 0.839940i | \(-0.682590\pi\) | |||||||
\(110\) | 6.10259i | 0.581859i | ||||||||
\(111\) | 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 | −0.984466 | − | 0.175577i | \(-0.943821\pi\) |
0.644287 | + | 0.764784i | \(0.277154\pi\) | |||||||
\(114\) | −1.25084 | + | 2.16652i | −0.117152 | + | 0.202913i | ||||
\(115\) | − | 20.6570i | − | 1.92628i | ||||||
\(116\) | −2.06503 | + | 3.57674i | −0.191733 | + | 0.332092i | ||||
\(117\) | 0.523154 | − | 3.56740i | 0.0483656 | − | 0.329806i | ||||
\(118\) | −2.06729 | −0.190309 | ||||||||
\(119\) | 4.71299 | − | 15.7109i | 0.432039 | − | 1.44022i | ||||
\(120\) | −3.78900 | − | 6.56274i | −0.345887 | − | 0.599093i | ||||
\(121\) | 4.51579 | 0.410526 | ||||||||
\(122\) | −9.80800 | − | 5.66265i | −0.887975 | − | 0.512672i | ||||
\(123\) | 3.98821 | − | 2.30259i | 0.359605 | − | 0.207618i | ||||
\(124\) | − | 10.6167i | − | 0.953412i | ||||||
\(125\) | 8.23599i | 0.736649i | ||||||||
\(126\) | −0.557231 | − | 2.35694i | −0.0496421 | − | 0.209973i | ||||
\(127\) | 4.21069 | + | 7.29312i | 0.373638 | + | 0.647160i | 0.990122 | − | 0.140207i | \(-0.0447769\pi\) |
−0.616484 | + | 0.787367i | \(0.711444\pi\) | |||||||
\(128\) | −5.00985 | − | 2.89244i | −0.442813 | − | 0.255658i | ||||
\(129\) | 2.11228 | − | 3.65857i | 0.185975 | − | 0.322119i | ||||
\(130\) | −1.25376 | + | 8.54943i | −0.109962 | + | 0.749834i | ||||
\(131\) | 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 | ||||
\(133\) | −5.26206 | + | 4.95901i | −0.456278 | + | 0.430001i | ||||
\(134\) | −0.283559 | + | 0.491138i | −0.0244957 | + | 0.0424278i | ||||
\(135\) | −2.26729 | + | 1.30902i | −0.195137 | + | 0.112663i | ||||
\(136\) | 15.5408 | − | 8.97246i | 1.33261 | − | 0.769382i | ||||
\(137\) | 1.66150 | − | 0.959268i | 0.141952 | − | 0.0819558i | −0.427342 | − | 0.904090i | \(-0.640550\pi\) |
0.569294 | + | 0.822134i | \(0.307217\pi\) | |||||||
\(138\) | 6.25505 | − | 3.61135i | 0.532465 | − | 0.307419i | ||||
\(139\) | −11.0300 | + | 19.1046i | −0.935556 | + | 1.62043i | −0.161916 | + | 0.986805i | \(0.551767\pi\) |
−0.773640 | + | 0.633626i | \(0.781566\pi\) | |||||||
\(140\) | −1.85194 | − | 7.83321i | −0.156518 | − | 0.662027i | ||||
\(141\) | −1.53652 | + | 0.887113i | −0.129399 | + | 0.0747084i | ||||
\(142\) | −3.42501 | − | 5.93229i | −0.287420 | − | 0.497826i | ||||
\(143\) | −9.08405 | − | 1.33217i | −0.759647 | − | 0.111401i | ||||
\(144\) | 0.162771 | − | 0.281927i | 0.0135642 | − | 0.0234940i | ||||
\(145\) | −8.05822 | − | 4.65241i | −0.669198 | − | 0.386362i | ||||
\(146\) | −5.72106 | − | 9.90917i | −0.473478 | − | 0.820089i | ||||
\(147\) | 0.414724 | − | 6.98770i | 0.0342058 | − | 0.576336i | ||||
\(148\) | 10.0945i | 0.829766i | ||||||||
\(149\) | − | 14.9944i | − | 1.22839i | −0.789155 | − | 0.614195i | \(-0.789481\pi\) | ||
0.789155 | − | 0.614195i | \(-0.210519\pi\) | |||||||
\(150\) | 1.46988 | − | 0.848638i | 0.120015 | − | 0.0692910i | ||||
\(151\) | −7.81993 | − | 4.51484i | −0.636377 | − | 0.367413i | 0.146840 | − | 0.989160i | \(-0.453090\pi\) |
−0.783218 | + | 0.621748i | \(0.786423\pi\) | |||||||
\(152\) | −7.91045 | −0.641622 | ||||||||
\(153\) | −3.09980 | − | 5.36901i | −0.250604 | − | 0.434059i | ||||
\(154\) | −6.00173 | + | 1.41894i | −0.483633 | + | 0.114341i | ||||
\(155\) | 23.9190 | 1.92122 | ||||||||
\(156\) | 3.89407 | − | 1.54626i | 0.311775 | − | 0.123800i | ||||
\(157\) | 0.0998014 | − | 0.172861i | 0.00796501 | − | 0.0137958i | −0.862015 | − | 0.506882i | \(-0.830798\pi\) |
0.869980 | + | 0.493086i | \(0.164131\pi\) | |||||||
\(158\) | − | 1.13830i | − | 0.0905583i | ||||||
\(159\) | 3.42283 | − | 5.92852i | 0.271448 | − | 0.470162i | ||||
\(160\) | 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 | ||||
\(163\) | − | 7.05212i | − | 0.552364i | −0.961105 | − | 0.276182i | \(-0.910931\pi\) | ||
0.961105 | − | 0.276182i | \(-0.0890693\pi\) | |||||||
\(164\) | 4.63450 | + | 2.67573i | 0.361894 | + | 0.208939i | ||||
\(165\) | 3.33331 | + | 5.77345i | 0.259497 | + | 0.449463i | ||||
\(166\) | −0.961247 | + | 1.66493i | −0.0746072 | + | 0.129223i | ||||
\(167\) | −1.55981 | + | 0.900559i | −0.120702 | + | 0.0696874i | −0.559135 | − | 0.829076i | \(-0.688867\pi\) |
0.438433 | + | 0.898764i | \(0.355534\pi\) | |||||||
\(168\) | 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 | ||||
\(171\) | 2.73290i | 0.208990i | ||||||||
\(172\) | 4.90914 | 0.374318 | ||||||||
\(173\) | −11.9257 | −0.906693 | −0.453346 | − | 0.891334i | \(-0.649770\pi\) | ||||
−0.453346 | + | 0.891334i | \(0.649770\pi\) | |||||||
\(174\) | − | 3.25343i | − | 0.246642i | ||||||
\(175\) | 4.77399 | − | 1.12868i | 0.360880 | − | 0.0853199i | ||||
\(176\) | −0.717903 | − | 0.414482i | −0.0541140 | − | 0.0312427i | ||||
\(177\) | −1.95579 | + | 1.12918i | −0.147006 | + | 0.0848741i | ||||
\(178\) | −5.22099 | − | 9.04302i | −0.391330 | − | 0.677803i | ||||
\(179\) | −16.3400 | −1.22131 | −0.610655 | − | 0.791897i | \(-0.709094\pi\) | ||||
−0.610655 | + | 0.791897i | \(0.709094\pi\) | |||||||
\(180\) | −2.63470 | − | 1.52115i | −0.196379 | − | 0.113380i | ||||
\(181\) | 16.7748 | 1.24686 | 0.623429 | − | 0.781880i | \(-0.285739\pi\) | ||||
0.623429 | + | 0.781880i | \(0.285739\pi\) | |||||||
\(182\) | −8.69964 | + | 0.754822i | −0.644860 | + | 0.0559511i | ||||
\(183\) | −12.3720 | −0.914566 | ||||||||
\(184\) | 19.7788 | + | 11.4193i | 1.45811 | + | 0.841840i | ||||
\(185\) | −22.7425 | −1.67206 | ||||||||
\(186\) | 4.18163 | + | 7.24280i | 0.306612 | + | 0.531068i | ||||
\(187\) | −13.6717 | + | 7.89337i | −0.999775 | + | 0.577220i | ||||
\(188\) | −1.78552 | − | 1.03087i | −0.130222 | − | 0.0751839i | ||||
\(189\) | −1.81456 | − | 1.92545i | −0.131990 | − | 0.140056i | ||||
\(190\) | − | 6.54951i | − | 0.475151i | ||||||
\(191\) | 7.48391 | 0.541516 | 0.270758 | − | 0.962647i | \(-0.412726\pi\) | ||||
0.270758 | + | 0.962647i | \(0.412726\pi\) | |||||||
\(192\) | 5.67758 | 0.409744 | ||||||||
\(193\) | 11.6862i | 0.841193i | 0.907248 | + | 0.420596i | \(0.138179\pi\) | ||||
−0.907248 | + | 0.420596i | \(0.861821\pi\) | |||||||
\(194\) | 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 | −0.486081 | − | 0.873913i | \(-0.661574\pi\) |
0.513791 | + | 0.857916i | \(0.328241\pi\) | |||||||
\(198\) | −1.16549 | + | 2.01868i | −0.0828276 | + | 0.143462i | ||||
\(199\) | 4.91166 | + | 8.50724i | 0.348178 | + | 0.603062i | 0.985926 | − | 0.167183i | \(-0.0534671\pi\) |
−0.637748 | + | 0.770245i | \(0.720134\pi\) | |||||||
\(200\) | 4.64784 | + | 2.68343i | 0.328652 | + | 0.189747i | ||||
\(201\) | 0.619532i | 0.0436984i | ||||||||
\(202\) | −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 | ||||
\(205\) | −6.02829 | + | 10.4413i | −0.421034 | + | 0.729252i | ||||
\(206\) | 4.88666i | 0.340470i | ||||||||
\(207\) | 3.94513 | − | 6.83316i | 0.274205 | − | 0.474937i | ||||
\(208\) | −0.920592 | − | 0.728160i | −0.0638316 | − | 0.0504888i | ||||
\(209\) | 6.95908 | 0.481369 | ||||||||
\(210\) | 4.34868 | + | 4.61443i | 0.300088 | + | 0.318426i | ||||
\(211\) | 1.80752 | + | 3.13072i | 0.124435 | + | 0.215528i | 0.921512 | − | 0.388350i | \(-0.126955\pi\) |
−0.797077 | + | 0.603878i | \(0.793621\pi\) | |||||||
\(212\) | 7.95501 | 0.546352 | ||||||||
\(213\) | −6.48057 | − | 3.74156i | −0.444041 | − | 0.256367i | ||||
\(214\) | 14.1201 | − | 8.15222i | 0.965227 | − | 0.557274i | ||||
\(215\) | 11.0600i | 0.754289i | ||||||||
\(216\) | − | 2.89453i | − | 0.196948i | ||||||
\(217\) | 5.56151 | + | 23.5237i | 0.377540 | + | 1.59689i | ||||
\(218\) | 8.50521 | + | 14.7315i | 0.576045 | + | 0.997740i | ||||
\(219\) | −10.8250 | − | 6.24982i | −0.731486 | − | 0.422324i | ||||
\(220\) | −3.87347 | + | 6.70904i | −0.261149 | + | 0.452323i | ||||
\(221\) | −20.7751 | + | 8.24939i | −1.39748 | + | 0.554914i | ||||
\(222\) | −3.97595 | − | 6.88655i | −0.266848 | − | 0.462195i | ||||
\(223\) | 3.07998 | − | 1.77823i | 0.206251 | − | 0.119079i | −0.393317 | − | 0.919403i | \(-0.628672\pi\) |
0.599568 | + | 0.800324i | \(0.295339\pi\) | |||||||
\(224\) | 13.9153 | + | 4.17435i | 0.929758 | + | 0.278910i | ||||
\(225\) | 0.927071 | − | 1.60573i | 0.0618047 | − | 0.107049i | ||||
\(226\) | 5.73345 | − | 3.31021i | 0.381384 | − | 0.220192i | ||||
\(227\) | −6.75066 | + | 3.89750i | −0.448057 | + | 0.258686i | −0.707009 | − | 0.707204i | \(-0.749956\pi\) |
0.258952 | + | 0.965890i | \(0.416623\pi\) | |||||||
\(228\) | −2.75029 | + | 1.58788i | −0.182142 | + | 0.105160i | ||||
\(229\) | 14.2182 | − | 8.20887i | 0.939563 | − | 0.542457i | 0.0497400 | − | 0.998762i | \(-0.484161\pi\) |
0.889823 | + | 0.456305i | \(0.150827\pi\) | |||||||
\(230\) | −9.45467 | + | 16.3760i | −0.623423 | + | 1.07980i | ||||
\(231\) | −4.90299 | + | 4.62062i | −0.322593 | + | 0.304015i | ||||
\(232\) | 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 | \(0.913173\pi\) | |||||||
\(234\) | −2.04752 | + | 2.58863i | −0.133851 | + | 0.169224i | ||||
\(235\) | 2.32250 | − | 4.02269i | 0.151503 | − | 0.262411i | ||||
\(236\) | −2.27273 | − | 1.31216i | −0.147942 | − | 0.0854143i | ||||
\(237\) | −0.621752 | − | 1.07691i | −0.0403872 | − | 0.0699526i | ||||
\(238\) | −10.9271 | + | 10.2978i | −0.708300 | + | 0.667508i | ||||
\(239\) | 4.68654i | 0.303147i | 0.988446 | + | 0.151574i | \(0.0484341\pi\) | ||||
−0.988446 | + | 0.151574i | \(0.951566\pi\) | |||||||
\(240\) | 0.852282i | 0.0550146i | ||||||||
\(241\) | −9.28664 | + | 5.36164i | −0.598205 | + | 0.345374i | −0.768335 | − | 0.640048i | \(-0.778915\pi\) |
0.170130 | + | 0.985422i | \(0.445581\pi\) | |||||||
\(242\) | −3.57992 | − | 2.06687i | −0.230126 | − | 0.132863i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.18845 | − | 12.4508i | −0.460193 | − | 0.797078i | ||||
\(245\) | 8.20675 | + | 16.3860i | 0.524310 | + | 1.04687i | ||||
\(246\) | −4.21557 | −0.268775 | ||||||||
\(247\) | 9.74932 | + | 1.42973i | 0.620334 | + | 0.0909713i | ||||
\(248\) | −13.2225 | + | 22.9021i | −0.839632 | + | 1.45428i | ||||
\(249\) | 2.10018i | 0.133093i | ||||||||
\(250\) | 3.76960 | − | 6.52913i | 0.238410 | − | 0.412939i | ||||
\(251\) | 5.93135 | − | 10.2734i | 0.374384 | − | 0.648452i | −0.615851 | − | 0.787863i | \(-0.711188\pi\) |
0.990235 | + | 0.139411i | \(0.0445209\pi\) | |||||||
\(252\) | 0.883400 | − | 2.94485i | 0.0556489 | − | 0.185508i | ||||
\(253\) | −17.4000 | − | 10.0459i | −1.09393 | − | 0.631581i | ||||
\(254\) | − | 7.70889i | − | 0.483699i | ||||||
\(255\) | 14.0563 | + | 8.11541i | 0.880240 | + | 0.508207i | ||||
\(256\) | 8.32531 | + | 14.4199i | 0.520332 | + | 0.901241i | ||||
\(257\) | −4.67378 | + | 8.09523i | −0.291542 | + | 0.504966i | −0.974175 | − | 0.225796i | \(-0.927502\pi\) |
0.682632 | + | 0.730762i | \(0.260835\pi\) | |||||||
\(258\) | −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 | ||||
\(262\) | − | 15.1372i | − | 0.935176i | ||||||
\(263\) | 0.943420 | 0.0581738 | 0.0290869 | − | 0.999577i | \(-0.490740\pi\) | ||||
0.0290869 | + | 0.999577i | \(0.490740\pi\) | |||||||
\(264\) | −7.37066 | −0.453633 | ||||||||
\(265\) | 17.9222i | 1.10095i | ||||||||
\(266\) | 6.44126 | − | 1.52285i | 0.394939 | − | 0.0933722i | ||||
\(267\) | −9.87880 | − | 5.70353i | −0.604573 | − | 0.349050i | ||||
\(268\) | −0.623475 | + | 0.359963i | −0.0380848 | + | 0.0219883i | ||||
\(269\) | 3.79153 | + | 6.56712i | 0.231174 | + | 0.400404i | 0.958154 | − | 0.286254i | \(-0.0924101\pi\) |
−0.726980 | + | 0.686658i | \(0.759077\pi\) | |||||||
\(270\) | 2.39655 | 0.145849 | ||||||||
\(271\) | 17.8317 | + | 10.2951i | 1.08320 | + | 0.625384i | 0.931757 | − | 0.363083i | \(-0.118276\pi\) |
0.151440 | + | 0.988466i | \(0.451609\pi\) | |||||||
\(272\) | −2.01823 | −0.122373 | ||||||||
\(273\) | −7.81814 | + | 5.46595i | −0.473175 | + | 0.330815i | ||||
\(274\) | −1.75622 | −0.106097 | ||||||||
\(275\) | −4.08886 | − | 2.36070i | −0.246568 | − | 0.142356i | ||||
\(276\) | 9.16886 | 0.551901 | ||||||||
\(277\) | −10.2128 | − | 17.6891i | −0.613628 | − | 1.06283i | −0.990624 | − | 0.136620i | \(-0.956376\pi\) |
0.376996 | − | 0.926215i | \(-0.376957\pi\) | |||||||
\(278\) | 17.4883 | − | 10.0969i | 1.04888 | − | 0.605569i | ||||
\(279\) | 7.91220 | + | 4.56811i | 0.473691 | + | 0.273486i | ||||
\(280\) | −5.76085 | + | 19.2040i | −0.344277 | + | 1.14766i | ||||
\(281\) | 10.8703i | 0.648466i | 0.945977 | + | 0.324233i | \(0.105106\pi\) | ||||
−0.945977 | + | 0.324233i | \(0.894894\pi\) | |||||||
\(282\) | 1.62412 | 0.0967149 | ||||||||
\(283\) | 3.82154 | 0.227167 | 0.113583 | − | 0.993528i | \(-0.463767\pi\) | ||||
0.113583 | + | 0.993528i | \(0.463767\pi\) | |||||||
\(284\) | − | 8.69575i | − | 0.515998i | ||||||
\(285\) | −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 | ||||
\(289\) | −10.7175 | + | 18.5633i | −0.630443 | + | 1.09196i | ||||
\(290\) | 4.25880 | + | 7.37646i | 0.250085 | + | 0.433161i | ||||
\(291\) | 1.32935 | + | 0.767503i | 0.0779281 | + | 0.0449918i | ||||
\(292\) | − | 14.5252i | − | 0.850023i | ||||||
\(293\) | 15.6392 | + | 9.02929i | 0.913651 | + | 0.527497i | 0.881604 | − | 0.471989i | \(-0.156464\pi\) |
0.0320472 | + | 0.999486i | \(0.489797\pi\) | |||||||
\(294\) | −3.52703 | + | 5.34973i | −0.205701 | + | 0.312003i | ||||
\(295\) | 2.95623 | − | 5.12034i | 0.172118 | − | 0.298118i | ||||
\(296\) | 12.5722 | − | 21.7756i | 0.730742 | − | 1.26568i | ||||
\(297\) | 2.54641i | 0.147758i | ||||||||
\(298\) | −6.86291 | + | 11.8869i | −0.397558 | + | 0.688590i | ||||
\(299\) | −22.3127 | − | 17.6486i | −1.29037 | − | 1.02065i | ||||
\(300\) | 2.15461 | 0.124396 | ||||||||
\(301\) | −10.8772 | + | 2.57162i | −0.626954 | + | 0.148226i | ||||
\(302\) | 4.13287 | + | 7.15834i | 0.237820 | + | 0.411916i | ||||
\(303\) | −0.504753 | −0.0289973 | ||||||||
\(304\) | 0.770478 | + | 0.444836i | 0.0441900 | + | 0.0255131i | ||||
\(305\) | 28.0510 | − | 16.1952i | 1.60619 | − | 0.927336i | ||||
\(306\) | 5.67509i | 0.324423i | ||||||||
\(307\) | 8.88791i | 0.507260i | 0.967301 | + | 0.253630i | \(0.0816246\pi\) | ||||
−0.967301 | + | 0.253630i | \(0.918375\pi\) | |||||||
\(308\) | −7.49879 | − | 2.24950i | −0.427283 | − | 0.128177i | ||||
\(309\) | 2.66915 | + | 4.62310i | 0.151843 | + | 0.262999i | ||||
\(310\) | −18.9620 | − | 10.9477i | −1.07697 | − | 0.621787i | ||||
\(311\) | −8.24533 | + | 14.2813i | −0.467550 | + | 0.809820i | −0.999313 | − | 0.0370736i | \(-0.988196\pi\) |
0.531763 | + | 0.846893i | \(0.321530\pi\) | |||||||
\(312\) | −10.3259 | − | 1.51429i | −0.584591 | − | 0.0857295i | ||||
\(313\) | −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 | ||||
\(315\) | 6.63460 | + | 1.99026i | 0.373817 | + | 0.112138i | ||||
\(316\) | 0.722507 | − | 1.25142i | 0.0406442 | − | 0.0703978i | ||||
\(317\) | 19.7541 | − | 11.4050i | 1.10950 | − | 0.640569i | 0.170799 | − | 0.985306i | \(-0.445365\pi\) |
0.938699 | + | 0.344737i | \(0.112032\pi\) | |||||||
\(318\) | −5.42695 | + | 3.13325i | −0.304328 | + | 0.175704i | ||||
\(319\) | −7.83774 | + | 4.52512i | −0.438829 | + | 0.253358i | ||||
\(320\) | −12.8727 | + | 7.43207i | −0.719607 | + | 0.415465i | ||||
\(321\) | 8.90567 | − | 15.4251i | 0.497066 | − | 0.860944i | ||||
\(322\) | −18.3037 | − | 5.49076i | −1.02002 | − | 0.305988i | ||||
\(323\) | 14.6730 | − | 8.47143i | 0.816425 | − | 0.471363i | ||||
\(324\) | −0.581025 | − | 1.00636i | −0.0322792 | − | 0.0559091i | ||||
\(325\) | −5.24329 | − | 4.14728i | −0.290845 | − | 0.230049i | ||||
\(326\) | −3.22774 | + | 5.59061i | −0.178768 | + | 0.309635i | ||||
\(327\) | 16.0930 | + | 9.29129i | 0.889944 | + | 0.513809i | ||||
\(328\) | −6.66493 | − | 11.5440i | −0.368009 | − | 0.637410i | ||||
\(329\) | 4.49621 | + | 1.34878i | 0.247884 | + | 0.0743607i | ||||
\(330\) | − | 6.10259i | − | 0.335937i | ||||||
\(331\) | 32.0157i | 1.75974i | 0.475212 | + | 0.879871i | \(0.342371\pi\) | ||||
−0.475212 | + | 0.879871i | \(0.657629\pi\) | |||||||
\(332\) | −2.11354 | + | 1.22025i | −0.115996 | + | 0.0669702i | ||||
\(333\) | −7.52303 | − | 4.34342i | −0.412259 | − | 0.238018i | ||||
\(334\) | 1.64874 | 0.0902149 | ||||||||
\(335\) | −0.810980 | − | 1.40466i | −0.0443086 | − | 0.0767447i | ||||
\(336\) | −0.838195 | + | 0.198168i | −0.0457273 | + | 0.0108109i | ||||
\(337\) | 4.99719 | 0.272214 | 0.136107 | − | 0.990694i | \(-0.456541\pi\) | ||||
0.136107 | + | 0.990694i | \(0.456541\pi\) | |||||||
\(338\) | 8.16349 | + | 8.65858i | 0.444035 | + | 0.470965i | ||||
\(339\) | 3.61615 | − | 6.26336i | 0.196402 | − | 0.340179i | ||||
\(340\) | 18.8610i | 1.02288i | ||||||||
\(341\) | 11.6323 | − | 20.1477i | 0.629924 | − | 1.09106i | ||||
\(342\) | 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 | ||||
\(345\) | 20.6570i | 1.11214i | ||||||||
\(346\) | 9.45416 | + | 5.45836i | 0.508259 | + | 0.293443i | ||||
\(347\) | −17.1710 | − | 29.7411i | −0.921789 | − | 1.59659i | −0.796646 | − | 0.604446i | \(-0.793394\pi\) |
−0.125143 | − | 0.992139i | \(-0.539939\pi\) | |||||||
\(348\) | 2.06503 | − | 3.57674i | 0.110697 | − | 0.191733i | ||||
\(349\) | 8.51580 | − | 4.91660i | 0.455841 | − | 0.263180i | −0.254453 | − | 0.967085i | \(-0.581895\pi\) |
0.710294 | + | 0.703905i | \(0.248562\pi\) | |||||||
\(350\) | −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 | ||||
\(353\) | − | 15.3426i | − | 0.816603i | −0.912847 | − | 0.408302i | \(-0.866121\pi\) | ||
0.912847 | − | 0.408302i | \(-0.133879\pi\) | |||||||
\(354\) | 2.06729 | 0.109875 | ||||||||
\(355\) | 19.5911 | 1.03979 | ||||||||
\(356\) | − | 13.2556i | − | 0.702544i | ||||||
\(357\) | −4.71299 | + | 15.7109i | −0.249438 | + | 0.831510i | ||||
\(358\) | 12.9536 | + | 7.47879i | 0.684621 | + | 0.395266i | ||||
\(359\) | −25.1701 | + | 14.5319i | −1.32842 | + | 0.766966i | −0.985056 | − | 0.172235i | \(-0.944901\pi\) |
−0.343369 | + | 0.939201i | \(0.611568\pi\) | |||||||
\(360\) | 3.78900 | + | 6.56274i | 0.199698 | + | 0.345887i | ||||
\(361\) | 11.5313 | 0.606909 | ||||||||
\(362\) | −13.2983 | − | 7.67777i | −0.698943 | − | 0.403535i | ||||
\(363\) | −4.51579 | −0.237018 | ||||||||
\(364\) | −10.0433 | − | 4.69204i | −0.526411 | − | 0.245930i | ||||
\(365\) | 32.7246 | 1.71288 | ||||||||
\(366\) | 9.80800 | + | 5.66265i | 0.512672 | + | 0.295992i | ||||
\(367\) | 18.3021 | 0.955362 | 0.477681 | − | 0.878533i | \(-0.341478\pi\) | ||||
0.477681 | + | 0.878533i | \(0.341478\pi\) | |||||||
\(368\) | −1.28430 | − | 2.22448i | −0.0669489 | − | 0.115959i | ||||
\(369\) | −3.98821 | + | 2.30259i | −0.207618 | + | 0.119868i | ||||
\(370\) | 18.0293 | + | 10.4092i | 0.937297 | + | 0.541149i | ||||
\(371\) | −17.6260 | + | 4.16718i | −0.915098 | + | 0.216349i | ||||
\(372\) | 10.6167i | 0.550453i | ||||||||
\(373\) | 12.8655 | 0.666149 | 0.333074 | − | 0.942901i | \(-0.391914\pi\) | ||||
0.333074 | + | 0.942901i | \(0.391914\pi\) | |||||||
\(374\) | 14.4511 | 0.747250 | ||||||||
\(375\) | − | 8.23599i | − | 0.425305i | ||||||
\(376\) | 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 | 0.217519 | − | 0.976056i | \(-0.430204\pi\) |
0.954049 | + | 0.299651i | \(0.0968703\pi\) | |||||||
\(380\) | 4.15714 | − | 7.20037i | 0.213257 | − | 0.369371i | ||||
\(381\) | −4.21069 | − | 7.29312i | −0.215720 | − | 0.373638i | ||||
\(382\) | −5.93291 | − | 3.42537i | −0.303554 | − | 0.175257i | ||||
\(383\) | − | 14.4045i | − | 0.736035i | −0.929819 | − | 0.368017i | \(-0.880037\pi\) | ||
0.929819 | − | 0.368017i | \(-0.119963\pi\) | |||||||
\(384\) | 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 | ||||
\(387\) | −2.11228 | + | 3.65857i | −0.107373 | + | 0.185975i | ||||
\(388\) | 1.78375i | 0.0905563i | ||||||||
\(389\) | 3.30891 | − | 5.73120i | 0.167768 | − | 0.290584i | −0.769866 | − | 0.638205i | \(-0.779677\pi\) |
0.937635 | + | 0.347621i | \(0.113011\pi\) | |||||||
\(390\) | 1.25376 | − | 8.54943i | 0.0634868 | − | 0.432917i | ||||
\(391\) | −48.9164 | −2.47381 | ||||||||
\(392\) | −20.2261 | − | 1.20043i | −1.02157 | − | 0.0606308i | ||||
\(393\) | −8.26809 | − | 14.3207i | −0.417070 | − | 0.722386i | ||||
\(394\) | −0.411087 | −0.0207103 | ||||||||
\(395\) | 2.81939 | + | 1.62777i | 0.141859 | + | 0.0819022i | ||||
\(396\) | −2.56262 | + | 1.47953i | −0.128776 | + | 0.0743491i | ||||
\(397\) | − | 22.6357i | − | 1.13605i | −0.823010 | − | 0.568027i | \(-0.807707\pi\) | ||
0.823010 | − | 0.568027i | \(-0.192293\pi\) | |||||||
\(398\) | − | 8.99222i | − | 0.450739i | ||||||
\(399\) | 5.26206 | − | 4.95901i | 0.263432 | − | 0.248261i | ||||
\(400\) | −0.301800 | − | 0.522734i | −0.0150900 | − | 0.0261367i | ||||
\(401\) | 0.390199 | + | 0.225281i | 0.0194856 | + | 0.0112500i | 0.509711 | − | 0.860346i | \(-0.329752\pi\) |
−0.490226 | + | 0.871596i | \(0.663086\pi\) | |||||||
\(402\) | 0.283559 | − | 0.491138i | 0.0141426 | − | 0.0244957i | ||||
\(403\) | 20.4356 | − | 25.8361i | 1.01797 | − | 1.28699i | ||||
\(404\) | −0.293274 | − | 0.507965i | −0.0145909 | − | 0.0252722i | ||||
\(405\) | 2.26729 | − | 1.30902i | 0.112663 | − | 0.0650458i | ||||
\(406\) | −6.26431 | + | 5.90355i | −0.310893 | + | 0.292988i | ||||
\(407\) | −11.0601 | + | 19.1567i | −0.548231 | + | 0.949563i | ||||
\(408\) | −15.5408 | + | 8.97246i | −0.769382 | + | 0.444203i | ||||
\(409\) | −29.8446 | + | 17.2308i | −1.47572 | + | 0.852008i | −0.999625 | − | 0.0273852i | \(-0.991282\pi\) |
−0.476096 | + | 0.879393i | \(0.657949\pi\) | |||||||
\(410\) | 9.55793 | − | 5.51827i | 0.472033 | − | 0.272528i | ||||
\(411\) | −1.66150 | + | 0.959268i | −0.0819558 | + | 0.0473172i | ||||
\(412\) | −3.10169 | + | 5.37228i | −0.152809 | + | 0.264673i | ||||
\(413\) | 5.72308 | + | 1.71682i | 0.281614 | + | 0.0844791i | ||||
\(414\) | −6.25505 | + | 3.61135i | −0.307419 | + | 0.177488i | ||||
\(415\) | −2.74917 | − | 4.76171i | −0.134952 | − | 0.233743i | ||||
\(416\) | −7.30658 | − | 18.4007i | −0.358235 | − | 0.902169i | ||||
\(417\) | 11.0300 | − | 19.1046i | 0.540143 | − | 0.935556i | ||||
\(418\) | −5.51685 | − | 3.18516i | −0.269838 | − | 0.155791i | ||||
\(419\) | 0.195021 | + | 0.337787i | 0.00952742 | + | 0.0165020i | 0.870750 | − | 0.491726i | \(-0.163634\pi\) |
−0.861222 | + | 0.508228i | \(0.830301\pi\) | |||||||
\(420\) | 1.85194 | + | 7.83321i | 0.0903655 | + | 0.382222i | ||||
\(421\) | − | 24.5494i | − | 1.19646i | −0.801323 | − | 0.598232i | \(-0.795870\pi\) | ||
0.801323 | − | 0.598232i | \(-0.204130\pi\) | |||||||
\(422\) | − | 3.30920i | − | 0.161089i | ||||||
\(423\) | 1.53652 | − | 0.887113i | 0.0747084 | − | 0.0431329i | ||||
\(424\) | −17.1603 | − | 9.90749i | −0.833377 | − | 0.481150i | ||||
\(425\) | −11.4949 | −0.557587 | ||||||||
\(426\) | 3.42501 | + | 5.93229i | 0.165942 | + | 0.287420i | ||||
\(427\) | 22.4498 | + | 23.8217i | 1.08642 | + | 1.15281i | ||||
\(428\) | 20.6977 | 1.00046 | ||||||||
\(429\) | 9.08405 | + | 1.33217i | 0.438582 | + | 0.0643176i | ||||
\(430\) | 5.06216 | − | 8.76793i | 0.244119 | − | 0.422827i | ||||
\(431\) | 1.13549i | 0.0546945i | 0.999626 | + | 0.0273473i | \(0.00870599\pi\) | ||||
−0.999626 | + | 0.0273473i | \(0.991294\pi\) | |||||||
\(432\) | −0.162771 | + | 0.281927i | −0.00783132 | + | 0.0135642i | ||||
\(433\) | 10.1233 | − | 17.5341i | 0.486495 | − | 0.842634i | −0.513385 | − | 0.858159i | \(-0.671609\pi\) |
0.999879 | + | 0.0155250i | \(0.00494195\pi\) | |||||||
\(434\) | 6.35782 | − | 21.1940i | 0.305185 | − | 1.01735i | ||||
\(435\) | 8.05822 | + | 4.65241i | 0.386362 | + | 0.223066i | ||||
\(436\) | 21.5939i | 1.03416i | ||||||||
\(437\) | 18.6743 | + | 10.7816i | 0.893313 | + | 0.515755i | ||||
\(438\) | 5.72106 | + | 9.90917i | 0.273363 | + | 0.473478i | ||||
\(439\) | −13.9882 | + | 24.2283i | −0.667621 | + | 1.15635i | 0.310946 | + | 0.950428i | \(0.399354\pi\) |
−0.978567 | + | 0.205926i | \(0.933979\pi\) | |||||||
\(440\) | 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 | \(0.662329\pi\) | |||||||
\(444\) | − | 10.0945i | − | 0.479066i | ||||||
\(445\) | 29.8642 | 1.41570 | ||||||||
\(446\) | −3.25557 | −0.154156 | ||||||||
\(447\) | 14.9944i | 0.709211i | ||||||||
\(448\) | −10.3023 | − | 10.9319i | −0.486739 | − | 0.516484i | ||||
\(449\) | −2.50177 | − | 1.44440i | −0.118066 | − | 0.0681652i | 0.439804 | − | 0.898094i | \(-0.355048\pi\) |
−0.557870 | + | 0.829928i | \(0.688381\pi\) | |||||||
\(450\) | −1.46988 | + | 0.848638i | −0.0692910 | + | 0.0400052i | ||||
\(451\) | 5.86335 | + | 10.1556i | 0.276095 | + | 0.478210i | ||||
\(452\) | 8.40429 | 0.395305 | ||||||||
\(453\) | 7.81993 | + | 4.51484i | 0.367413 | + | 0.212126i | ||||
\(454\) | 7.13551 | 0.334886 | ||||||||
\(455\) | 10.5710 | − | 22.6270i | 0.495574 | − | 1.06077i | ||||
\(456\) | 7.91045 | 0.370441 | ||||||||
\(457\) | −28.2917 | − | 16.3342i | −1.32343 | − | 0.764083i | −0.339156 | − | 0.940730i | \(-0.610142\pi\) |
−0.984274 | + | 0.176647i | \(0.943475\pi\) | |||||||
\(458\) | −15.0287 | −0.702247 | ||||||||
\(459\) | 3.09980 | + | 5.36901i | 0.144686 | + | 0.250604i | ||||
\(460\) | −20.7885 | + | 12.0022i | −0.969268 | + | 0.559607i | ||||
\(461\) | −32.7978 | − | 18.9358i | −1.52755 | − | 0.881930i | −0.999464 | − | 0.0327376i | \(-0.989577\pi\) |
−0.528084 | − | 0.849192i | \(-0.677089\pi\) | |||||||
\(462\) | 6.00173 | − | 1.41894i | 0.279226 | − | 0.0660150i | ||||
\(463\) | − | 20.8936i | − | 0.971006i | −0.874235 | − | 0.485503i | \(-0.838636\pi\) | ||
0.874235 | − | 0.485503i | \(-0.161364\pi\) | |||||||
\(464\) | −1.15701 | −0.0537130 | ||||||||
\(465\) | −23.9190 | −1.10922 | ||||||||
\(466\) | 6.93620i | 0.321313i | ||||||||
\(467\) | −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 | ||||
\(471\) | −0.0998014 | + | 0.172861i | −0.00459860 | + | 0.00796501i | ||||
\(472\) | 3.26843 | + | 5.66109i | 0.150442 | + | 0.260573i | ||||
\(473\) | 9.31622 | + | 5.37872i | 0.428360 | + | 0.247314i | ||||
\(474\) | 1.13830i | 0.0522838i | ||||||||
\(475\) | 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 | ||||
\(478\) | 2.14502 | − | 3.71529i | 0.0981110 | − | 0.169933i | ||||
\(479\) | 10.8998i | 0.498025i | 0.968500 | + | 0.249013i | \(0.0801061\pi\) | ||||
−0.968500 | + | 0.249013i | \(0.919894\pi\) | |||||||
\(480\) | −7.18791 | + | 12.4498i | −0.328082 | + | 0.568254i | ||||
\(481\) | −19.4304 | + | 24.5653i | −0.885950 | + | 1.12008i | ||||
\(482\) | 9.81606 | 0.447109 | ||||||||
\(483\) | −20.3156 | + | 4.80305i | −0.924391 | + | 0.218546i | ||||
\(484\) | −2.62379 | − | 4.54453i | −0.119263 | − | 0.206570i | ||||
\(485\) | −4.01871 | −0.182480 | ||||||||
\(486\) | 0.792756 | + | 0.457698i | 0.0359602 | + | 0.0207616i | ||||
\(487\) | 5.32787 | − | 3.07605i | 0.241429 | − | 0.139389i | −0.374404 | − | 0.927265i | \(-0.622153\pi\) |
0.615833 | + | 0.787877i | \(0.288820\pi\) | |||||||
\(488\) | 35.8112i | 1.62110i | ||||||||
\(489\) | 7.05212i | 0.318908i | ||||||||
\(490\) | 0.993904 | − | 16.7464i | 0.0449000 | − | 0.756523i | ||||
\(491\) | 5.40015 | + | 9.35334i | 0.243705 | + | 0.422110i | 0.961767 | − | 0.273869i | \(-0.0883036\pi\) |
−0.718061 | + | 0.695980i | \(0.754970\pi\) | |||||||
\(492\) | −4.63450 | − | 2.67573i | −0.208939 | − | 0.120631i | ||||
\(493\) | −11.0171 | + | 19.0821i | −0.496183 | + | 0.859415i | ||||
\(494\) | −7.07445 | − | 5.59567i | −0.318295 | − | 0.251761i | ||||
\(495\) | −3.33331 | − | 5.77345i | −0.149821 | − | 0.259497i | ||||
\(496\) | 2.57575 | − | 1.48711i | 0.115655 | − | 0.0667733i | ||||
\(497\) | 4.55521 | + | 19.2673i | 0.204329 | + | 0.864257i | ||||
\(498\) | 0.961247 | − | 1.66493i | 0.0430745 | − | 0.0746072i | ||||
\(499\) | 1.85936 | − | 1.07350i | 0.0832362 | − | 0.0480565i | −0.457804 | − | 0.889053i | \(-0.651364\pi\) |
0.541040 | + | 0.840997i | \(0.318031\pi\) | |||||||
\(500\) | 8.28840 | − | 4.78531i | 0.370669 | − | 0.214006i | ||||
\(501\) | 1.55981 | − | 0.900559i | 0.0696874 | − | 0.0402340i | ||||
\(502\) | −9.40424 | + | 5.42954i | −0.419732 | + | 0.242332i | ||||
\(503\) | −3.07639 | + | 5.32846i | −0.137169 | + | 0.237584i | −0.926424 | − | 0.376482i | \(-0.877134\pi\) |
0.789255 | + | 0.614066i | \(0.210467\pi\) | |||||||
\(504\) | −5.57327 | + | 5.25230i | −0.248253 | + | 0.233956i | ||||
\(505\) | 1.14442 | − | 0.660732i | 0.0509261 | − | 0.0294022i | ||||
\(506\) | 9.19599 | + | 15.9279i | 0.408812 | + | 0.708083i | ||||
\(507\) | 12.4526 | + | 3.73260i | 0.553040 | + | 0.165770i | ||||
\(508\) | 4.89302 | − | 8.47497i | 0.217093 | − | 0.376016i | ||||
\(509\) | −3.97233 | − | 2.29343i | −0.176070 | − | 0.101654i | 0.409375 | − | 0.912366i | \(-0.365747\pi\) |
−0.585445 | + | 0.810712i | \(0.699080\pi\) | |||||||
\(510\) | −7.42881 | − | 12.8671i | −0.328953 | − | 0.569764i | ||||
\(511\) | 7.60893 | + | 32.1837i | 0.336599 | + | 1.42372i | ||||
\(512\) | − | 3.67215i | − | 0.162288i | ||||||
\(513\) | − | 2.73290i | − | 0.120660i | ||||||
\(514\) | 7.41034 | − | 4.27836i | 0.326856 | − | 0.188710i | ||||
\(515\) | −12.1035 | − | 6.98795i | −0.533343 | − | 0.307926i | ||||
\(516\) | −4.90914 | −0.216113 | ||||||||
\(517\) | −2.25895 | − | 3.91262i | −0.0993487 | − | 0.172077i | ||||
\(518\) | −6.04510 | + | 20.1516i | −0.265607 | + | 0.885410i | ||||
\(519\) | 11.9257 | 0.523479 | ||||||||
\(520\) | 25.3941 | − | 10.0835i | 1.11361 | − | 0.442192i | ||||
\(521\) | 10.7536 | − | 18.6258i | 0.471123 | − | 0.816009i | −0.528331 | − | 0.849038i | \(-0.677182\pi\) |
0.999454 | + | 0.0330292i | \(0.0105154\pi\) | |||||||
\(522\) | 3.25343i | 0.142399i | ||||||||
\(523\) | 6.01902 | − | 10.4252i | 0.263193 | − | 0.455864i | −0.703895 | − | 0.710304i | \(-0.748558\pi\) |
0.967089 | + | 0.254439i | \(0.0818910\pi\) | |||||||
\(524\) | 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 | ||||
\(527\) | − | 56.6410i | − | 2.46732i | ||||||
\(528\) | 0.717903 | + | 0.414482i | 0.0312427 | + | 0.0180380i | ||||
\(529\) | −19.6280 | − | 33.9968i | −0.853393 | − | 1.47812i | ||||
\(530\) | 8.20298 | − | 14.2080i | 0.356315 | − | 0.617155i | ||||
\(531\) | 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 | ||||
\(535\) | 46.6308i | 2.01603i | ||||||||
\(536\) | 1.79325 | 0.0774567 | ||||||||
\(537\) | 16.3400 | 0.705123 | ||||||||
\(538\) | − | 6.94150i | − | 0.299269i | ||||||
\(539\) | 17.7936 | + | 1.05606i | 0.766423 | + | 0.0454876i | ||||
\(540\) | 2.63470 | + | 1.52115i | 0.113380 | + | 0.0654597i | ||||
\(541\) | 1.68945 | − | 0.975405i | 0.0726352 | − | 0.0419360i | −0.463243 | − | 0.886232i | \(-0.653314\pi\) |
0.535878 | + | 0.844296i | \(0.319981\pi\) | |||||||
\(542\) | −9.42411 | − | 16.3230i | −0.404800 | − | 0.701135i | ||||
\(543\) | −16.7748 | −0.719874 | ||||||||
\(544\) | −29.4816 | − | 17.0212i | −1.26401 | − | 0.729777i | ||||
\(545\) | −48.6500 | −2.08393 | ||||||||
\(546\) | 8.69964 | − | 0.754822i | 0.372310 | − | 0.0323034i | ||||
\(547\) | 4.27037 | 0.182588 | 0.0912940 | − | 0.995824i | \(-0.470900\pi\) | ||||
0.0912940 | + | 0.995824i | \(0.470900\pi\) | |||||||
\(548\) | −1.93075 | − | 1.11472i | −0.0824774 | − | 0.0476183i | ||||
\(549\) | 12.3720 | 0.528025 | ||||||||
\(550\) | 2.16098 | + | 3.74293i | 0.0921445 | + | 0.159599i | ||||
\(551\) | 8.41173 | − | 4.85652i | 0.358352 | − | 0.206895i | ||||
\(552\) | −19.7788 | − | 11.4193i | −0.841840 | − | 0.486037i | ||||
\(553\) | −0.945323 | + | 3.15127i | −0.0401992 | + | 0.134006i | ||||
\(554\) | 18.6975i | 0.794382i | ||||||||
\(555\) | 22.7425 | 0.965366 | ||||||||
\(556\) | 25.6349 | 1.08716 | ||||||||
\(557\) | 39.9834i | 1.69415i | 0.531473 | + | 0.847075i | \(0.321639\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(558\) | −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 | ||||
\(562\) | 4.97530 | − | 8.61748i | 0.209871 | − | 0.363506i | ||||
\(563\) | −16.7574 | − | 29.0246i | −0.706239 | − | 1.22324i | −0.966243 | − | 0.257634i | \(-0.917057\pi\) |
0.260004 | − | 0.965608i | \(-0.416276\pi\) | |||||||
\(564\) | 1.78552 | + | 1.03087i | 0.0751839 | + | 0.0434074i | ||||
\(565\) | 18.9345i | 0.796579i | ||||||||
\(566\) | −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 | ||||
\(569\) | 19.4418 | − | 33.6742i | 0.815043 | − | 1.41170i | −0.0942547 | − | 0.995548i | \(-0.530047\pi\) |
0.909297 | − | 0.416147i | \(-0.136620\pi\) | |||||||
\(570\) | 6.54951i | 0.274329i | ||||||||
\(571\) | 11.3324 | − | 19.6282i | 0.474245 | − | 0.821417i | −0.525320 | − | 0.850905i | \(-0.676054\pi\) |
0.999565 | + | 0.0294882i | \(0.00938774\pi\) | |||||||
\(572\) | 3.93742 | + | 9.91589i | 0.164632 | + | 0.414604i | ||||
\(573\) | −7.48391 | −0.312645 | ||||||||
\(574\) | 7.64942 | + | 8.11688i | 0.319281 | + | 0.338792i | ||||
\(575\) | −7.31482 | − | 12.6696i | −0.305049 | − | 0.528361i | ||||
\(576\) | −5.67758 | −0.236566 | ||||||||
\(577\) | −20.1472 | − | 11.6320i | −0.838740 | − | 0.484247i | 0.0180956 | − | 0.999836i | \(-0.494240\pi\) |
−0.856836 | + | 0.515589i | \(0.827573\pi\) | |||||||
\(578\) | 16.9928 | − | 9.81079i | 0.706807 | − | 0.408075i | ||||
\(579\) | − | 11.6862i | − | 0.485663i | ||||||
\(580\) | 10.8127i | 0.448972i | ||||||||
\(581\) | 4.04379 | − | 3.81090i | 0.167765 | − | 0.158103i | ||||
\(582\) | −0.702569 | − | 1.21689i | −0.0291224 | − | 0.0504416i | ||||
\(583\) | 15.0965 | + | 8.71594i | 0.625231 | + | 0.360977i | ||||
\(584\) | −18.0903 | + | 31.3333i | −0.748581 | + | 1.29658i | ||||
\(585\) | −3.48365 | − | 8.77314i | −0.144031 | − | 0.362725i | ||||
\(586\) | −8.26538 | − | 14.3161i | −0.341440 | − | 0.591391i | ||||
\(587\) | −11.6230 | + | 6.71057i | −0.479734 | + | 0.276975i | −0.720306 | − | 0.693657i | \(-0.755998\pi\) |
0.240571 | + | 0.970631i | \(0.422665\pi\) | |||||||
\(588\) | −7.27314 | + | 3.64267i | −0.299939 | + | 0.150221i | ||||
\(589\) | −12.4842 | + | 21.6232i | −0.514402 | + | 0.890970i | ||||
\(590\) | −4.68714 | + | 2.70612i | −0.192967 | + | 0.111409i | ||||
\(591\) | −0.388915 | + | 0.224540i | −0.0159978 | + | 0.00923636i | ||||
\(592\) | −2.44906 | + | 1.41396i | −0.100656 | + | 0.0581136i | ||||
\(593\) | 7.76746 | − | 4.48455i | 0.318972 | − | 0.184158i | −0.331963 | − | 0.943293i | \(-0.607711\pi\) |
0.650934 | + | 0.759134i | \(0.274377\pi\) | |||||||
\(594\) | 1.16549 | − | 2.01868i | 0.0478205 | − | 0.0828276i | ||||
\(595\) | −9.88022 | − | 41.7906i | −0.405049 | − | 1.71325i | ||||
\(596\) | −15.0898 | + | 8.71212i | −0.618104 | + | 0.356862i | ||||
\(597\) | −4.91166 | − | 8.50724i | −0.201021 | − | 0.348178i | ||||
\(598\) | 9.61077 | + | 24.2035i | 0.393014 | + | 0.989756i | ||||
\(599\) | −17.2505 | + | 29.8787i | −0.704836 | + | 1.22081i | 0.261914 | + | 0.965091i | \(0.415646\pi\) |
−0.966751 | + | 0.255721i | \(0.917687\pi\) | |||||||
\(600\) | −4.64784 | − | 2.68343i | −0.189747 | − | 0.109551i | ||||
\(601\) | 10.6843 | + | 18.5058i | 0.435824 | + | 0.754869i | 0.997362 | − | 0.0725818i | \(-0.0231238\pi\) |
−0.561539 | + | 0.827450i | \(0.689791\pi\) | |||||||
\(602\) | 9.80003 | + | 2.93983i | 0.399420 | + | 0.119819i | ||||
\(603\) | − | 0.619532i | − | 0.0252293i | ||||||
\(604\) | 10.4929i | 0.426952i | ||||||||
\(605\) | 10.2386 | − | 5.91126i | 0.416259 | − | 0.240327i | ||||
\(606\) | 0.400146 | + | 0.231024i | 0.0162548 | + | 0.00938472i | ||||
\(607\) | −1.12616 | −0.0457096 | −0.0228548 | − | 0.999739i | \(-0.507276\pi\) | ||||
−0.0228548 | + | 0.999739i | \(0.507276\pi\) | |||||||
\(608\) | 7.50324 | + | 12.9960i | 0.304297 | + | 0.527057i | ||||
\(609\) | −2.70187 | + | 9.00678i | −0.109485 | + | 0.364973i | ||||
\(610\) | −29.6501 | −1.20050 | ||||||||
\(611\) | −2.36084 | − | 5.94549i | −0.0955095 | − | 0.240529i | ||||
\(612\) | −3.60212 | + | 6.23906i | −0.145607 | + | 0.252199i | ||||
\(613\) | 28.9424i | 1.16897i | 0.811404 | + | 0.584486i | \(0.198704\pi\) | ||||
−0.811404 | + | 0.584486i | \(0.801296\pi\) | |||||||
\(614\) | 4.06798 | − | 7.04595i | 0.164170 | − | 0.284351i | ||||
\(615\) | 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 | 0.426747 | − | 0.904371i | \(-0.359660\pi\) |
−0.569835 | + | 0.821759i | \(0.692993\pi\) | |||||||
\(618\) | − | 4.88666i | − | 0.196570i | ||||||
\(619\) | −9.06150 | − | 5.23166i | −0.364212 | − | 0.210278i | 0.306715 | − | 0.951802i | \(-0.400770\pi\) |
−0.670927 | + | 0.741523i | \(0.734104\pi\) | |||||||
\(620\) | −13.8975 | − | 24.0712i | −0.558139 | − | 0.966725i | ||||
\(621\) | −3.94513 | + | 6.83316i | −0.158312 | + | 0.274205i | ||||
\(622\) | 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 | ||||
\(626\) | 20.1820i | 0.806633i | ||||||||
\(627\) | −6.95908 | −0.277919 | ||||||||
\(628\) | −0.231948 | −0.00925574 | ||||||||
\(629\) | 53.8550i | 2.14734i | ||||||||
\(630\) | −4.34868 | − | 4.61443i | −0.173256 | − | 0.183843i | ||||
\(631\) | 24.3336 | + | 14.0490i | 0.968704 | + | 0.559281i | 0.898841 | − | 0.438275i | \(-0.144410\pi\) |
0.0698630 | + | 0.997557i | \(0.477744\pi\) | |||||||
\(632\) | −3.11714 | + | 1.79968i | −0.123993 | + | 0.0715874i | ||||
\(633\) | −1.80752 | − | 3.13072i | −0.0718426 | − | 0.124435i | ||||
\(634\) | −20.8802 | −0.829259 | ||||||||
\(635\) | 19.0937 | + | 11.0237i | 0.757710 | + | 0.437464i | ||||
\(636\) | −7.95501 | −0.315437 | ||||||||
\(637\) | 24.7109 | + | 5.13513i | 0.979083 | + | 0.203461i | ||||
\(638\) | 8.28456 | 0.327989 | ||||||||
\(639\) | 6.48057 | + | 3.74156i | 0.256367 | + | 0.148014i | ||||
\(640\) | −15.1451 | −0.598661 | ||||||||
\(641\) | 14.3138 | + | 24.7923i | 0.565362 | + | 0.979235i | 0.997016 | + | 0.0771962i | \(0.0245968\pi\) |
−0.431654 | + | 0.902039i | \(0.642070\pi\) | |||||||
\(642\) | −14.1201 | + | 8.15222i | −0.557274 | + | 0.321742i | ||||
\(643\) | −7.81711 | − | 4.51321i | −0.308277 | − | 0.177984i | 0.337878 | − | 0.941190i | \(-0.390291\pi\) |
−0.646155 | + | 0.763206i | \(0.723624\pi\) | |||||||
\(644\) | −16.6375 | − | 17.6542i | −0.655609 | − | 0.695673i | ||||
\(645\) | − | 11.0600i | − | 0.435489i | ||||||
\(646\) | −15.5094 | −0.610211 | ||||||||
\(647\) | −26.2048 | −1.03022 | −0.515109 | − | 0.857125i | \(-0.672249\pi\) | ||||
−0.515109 | + | 0.857125i | \(0.672249\pi\) | |||||||
\(648\) | 2.89453i | 0.113708i | ||||||||
\(649\) | −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 | ||||
\(653\) | −22.7395 | + | 39.3859i | −0.889864 | + | 1.54129i | −0.0498291 | + | 0.998758i | \(0.515868\pi\) |
−0.840035 | + | 0.542532i | \(0.817466\pi\) | |||||||
\(654\) | −8.50521 | − | 14.7315i | −0.332580 | − | 0.576045i | ||||
\(655\) | 37.4923 | + | 21.6462i | 1.46495 | + | 0.845787i | ||||
\(656\) | 1.49918i | 0.0585332i | ||||||||
\(657\) | 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 | −0.596720 | − | 0.802449i | \(-0.703530\pi\) |
0.993302 | + | 0.115550i | \(0.0368632\pi\) | |||||||
\(660\) | 3.87347 | − | 6.70904i | 0.150774 | − | 0.261149i | ||||
\(661\) | − | 40.1037i | − | 1.55985i | −0.625871 | − | 0.779926i | \(-0.715256\pi\) | ||
0.625871 | − | 0.779926i | \(-0.284744\pi\) | |||||||
\(662\) | 14.6535 | − | 25.3807i | 0.569526 | − | 0.986447i | ||||
\(663\) | 20.7751 | − | 8.24939i | 0.806837 | − | 0.320380i | ||||
\(664\) | 6.07902 | 0.235912 | ||||||||
\(665\) | −5.43916 | + | 18.1317i | −0.210922 | + | 0.703116i | ||||
\(666\) | 3.97595 | + | 6.88655i | 0.154065 | + | 0.266848i | ||||
\(667\) | −28.0429 | −1.08582 | ||||||||
\(668\) | 1.81258 | + | 1.04649i | 0.0701309 | + | 0.0404901i | ||||
\(669\) | −3.07998 | + | 1.77823i | −0.119079 | + | 0.0687503i | ||||
\(670\) | 1.48474i | 0.0573604i | ||||||||
\(671\) | − | 31.5043i | − | 1.21621i | ||||||
\(672\) | −13.9153 | − | 4.17435i | −0.536796 | − | 0.161029i | ||||
\(673\) | 10.2385 | + | 17.7336i | 0.394666 | + | 0.683581i | 0.993058 | − | 0.117622i | \(-0.0375270\pi\) |
−0.598393 | + | 0.801203i | \(0.704194\pi\) | |||||||
\(674\) | −3.96155 | − | 2.28720i | −0.152593 | − | 0.0880998i | ||||
\(675\) | −0.927071 | + | 1.60573i | −0.0356830 | + | 0.0618047i | ||||
\(676\) | 3.47893 | + | 14.7006i | 0.133805 | + | 0.565408i | ||||
\(677\) | 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 | ||||
\(679\) | −0.934407 | − | 3.95229i | −0.0358593 | − | 0.151675i | ||||
\(680\) | 23.4903 | − | 40.6864i | 0.900811 | − | 1.56025i | ||||
\(681\) | 6.75066 | − | 3.89750i | 0.258686 | − | 0.149352i | ||||
\(682\) | −18.4431 | + | 10.6482i | −0.706225 | + | 0.407739i | ||||
\(683\) | 5.13090 | − | 2.96232i | 0.196328 | − | 0.113350i | −0.398613 | − | 0.917119i | \(-0.630508\pi\) |
0.594942 | + | 0.803769i | \(0.297175\pi\) | |||||||
\(684\) | 2.75029 | − | 1.58788i | 0.105160 | − | 0.0607141i | ||||
\(685\) | 2.51140 | − | 4.34988i | 0.0959558 | − | 0.166200i | ||||
\(686\) | 16.7007 | − | 2.91629i | 0.637634 | − | 0.111344i | ||||
\(687\) | −14.2182 | + | 8.20887i | −0.542457 | + | 0.313188i | ||||
\(688\) | 0.687634 | + | 1.19102i | 0.0262158 | + | 0.0454071i | ||||
\(689\) | 19.3587 | + | 15.3121i | 0.737508 | + | 0.583346i | ||||
\(690\) | 9.45467 | − | 16.3760i | 0.359933 | − | 0.623423i | ||||
\(691\) | −2.64755 | − | 1.52856i | −0.100718 | − | 0.0581493i | 0.448795 | − | 0.893635i | \(-0.351853\pi\) |
−0.549513 | + | 0.835485i | \(0.685187\pi\) | |||||||
\(692\) | 6.92912 | + | 12.0016i | 0.263405 | + | 0.456232i | ||||
\(693\) | 4.90299 | − | 4.62062i | 0.186249 | − | 0.175523i | ||||
\(694\) | 31.4366i | 1.19332i | ||||||||
\(695\) | 57.7542i | 2.19074i | ||||||||
\(696\) | −8.90923 | + | 5.14375i | −0.337704 | + | 0.194973i | ||||
\(697\) | 24.7253 | + | 14.2752i | 0.936538 | + | 0.540711i | ||||
\(698\) | −9.00128 | −0.340703 | ||||||||
\(699\) | 3.78863 | + | 6.56210i | 0.143299 | + | 0.248201i | ||||
\(700\) | −3.90967 | − | 4.14859i | −0.147772 | − | 0.156802i | ||||
\(701\) | −2.81064 | −0.106156 | −0.0530782 | − | 0.998590i | \(-0.516903\pi\) | ||||
−0.0530782 | + | 0.998590i | \(0.516903\pi\) | |||||||
\(702\) | 2.04752 | − | 2.58863i | 0.0772788 | − | 0.0977015i | ||||
\(703\) | 11.8701 | − | 20.5596i | 0.447690 | − | 0.775422i | ||||
\(704\) | 14.4574i | 0.544885i | ||||||||
\(705\) | −2.32250 | + | 4.02269i | −0.0874704 | + | 0.151503i | ||||
\(706\) | −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 | ||||
\(709\) | − | 38.4283i | − | 1.44320i | −0.692308 | − | 0.721602i | \(-0.743406\pi\) | ||
0.692308 | − | 0.721602i | \(-0.256594\pi\) | |||||||
\(710\) | −15.5310 | − | 8.96681i | −0.582867 | − | 0.336518i | ||||
\(711\) | 0.621752 | + | 1.07691i | 0.0233175 | + | 0.0403872i | ||||
\(712\) | −16.5090 | + | 28.5945i | −0.618702 | + | 1.07162i | ||||
\(713\) | 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 | ||||
\(717\) | − | 4.68654i | − | 0.175022i | ||||||
\(718\) | 26.6050 | 0.992888 | ||||||||
\(719\) | −26.5885 | −0.991584 | −0.495792 | − | 0.868441i | \(-0.665122\pi\) | ||||
−0.495792 | + | 0.868441i | \(0.665122\pi\) | |||||||
\(720\) | − | 0.852282i | − | 0.0317627i | ||||||
\(721\) | 4.05822 | − | 13.5282i | 0.151136 | − | 0.503818i | ||||
\(722\) | −9.14150 | − | 5.27785i | −0.340211 | − | 0.196421i | ||||
\(723\) | 9.28664 | − | 5.36164i | 0.345374 | − | 0.199402i | ||||
\(724\) | −9.74655 | − | 16.8815i | −0.362228 | − | 0.627397i | ||||
\(725\) | −6.58984 | −0.244740 | ||||||||
\(726\) | 3.57992 | + | 2.06687i | 0.132863 | + | 0.0767087i | ||||
\(727\) | −26.5203 | −0.983583 | −0.491792 | − | 0.870713i | \(-0.663658\pi\) | ||||
−0.491792 | + | 0.870713i | \(0.663658\pi\) | |||||||
\(728\) | 15.8214 | + | 22.6298i | 0.586379 | + | 0.838717i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −25.9426 | − | 14.9780i | −0.960179 | − | 0.554360i | ||||
\(731\) | 26.1905 | 0.968692 | ||||||||
\(732\) | 7.18845 | + | 12.4508i | 0.265693 | + | 0.460193i | ||||
\(733\) | 22.0215 | − | 12.7141i | 0.813384 | − | 0.469607i | −0.0347458 | − | 0.999396i | \(-0.511062\pi\) |
0.848130 | + | 0.529789i | \(0.177729\pi\) | |||||||
\(734\) | −14.5091 | − | 8.37684i | −0.535541 | − | 0.309195i | ||||
\(735\) | −8.20675 | − | 16.3860i | −0.302711 | − | 0.604408i | ||||
\(736\) | − | 43.3258i | − | 1.59701i | ||||||
\(737\) | −1.57758 | −0.0581110 | ||||||||
\(738\) | 4.21557 | 0.155177 | ||||||||
\(739\) | 29.2795i | 1.07706i | 0.842606 | + | 0.538531i | \(0.181021\pi\) | ||||
−0.842606 | + | 0.538531i | \(0.818979\pi\) | |||||||
\(740\) | 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 | −0.265272 | − | 0.964174i | \(-0.585462\pi\) |
0.702363 | + | 0.711819i | \(0.252129\pi\) | |||||||
\(744\) | 13.2225 | − | 22.9021i | 0.484762 | − | 0.839632i | ||||
\(745\) | −19.6280 | − | 33.9967i | −0.719114 | − | 1.24554i | ||||
\(746\) | −10.1992 | − | 5.88850i | −0.373419 | − | 0.215593i | ||||
\(747\) | − | 2.10018i | − | 0.0768414i | ||||||
\(748\) | 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 | ||||
\(751\) | −15.7344 | + | 27.2528i | −0.574156 | + | 0.994468i | 0.421976 | + | 0.906607i | \(0.361337\pi\) |
−0.996133 | + | 0.0878612i | \(0.971997\pi\) | |||||||
\(752\) | − | 0.577585i | − | 0.0210623i | ||||||
\(753\) | −5.93135 | + | 10.2734i | −0.216151 | + | 0.374384i | ||||
\(754\) | 11.6063 | + | 1.70204i | 0.422675 | + | 0.0619848i | ||||
\(755\) | −23.6401 | −0.860351 | ||||||||
\(756\) | −0.883400 | + | 2.94485i | −0.0321289 | + | 0.107103i | ||||
\(757\) | −20.2956 | − | 35.1531i | −0.737657 | − | 1.27766i | −0.953548 | − | 0.301243i | \(-0.902599\pi\) |
0.215890 | − | 0.976418i | \(-0.430735\pi\) | |||||||
\(758\) | −24.1082 | −0.875651 | ||||||||
\(759\) | 17.4000 | + | 10.0459i | 0.631581 | + | 0.364644i | ||||
\(760\) | −17.9353 | + | 10.3549i | −0.650581 | + | 0.375613i | ||||
\(761\) | − | 40.5022i | − | 1.46821i | −0.679039 | − | 0.734103i | \(-0.737603\pi\) | ||
0.679039 | − | 0.734103i | \(-0.262397\pi\) | |||||||
\(762\) | 7.70889i | 0.279264i | ||||||||
\(763\) | −11.3118 | − | 47.8459i | −0.409515 | − | 1.73214i | ||||
\(764\) | −4.34833 | − | 7.53154i | −0.157317 | − | 0.272481i | ||||
\(765\) | −14.0563 | − | 8.11541i | −0.508207 | − | 0.293413i | ||||
\(766\) | −6.59291 | + | 11.4193i | −0.238211 | + | 0.412594i | ||||
\(767\) | −3.00504 | − | 7.56781i | −0.108506 | − | 0.273258i | ||||
\(768\) | −8.32531 | − | 14.4199i | −0.300414 | − | 0.520332i | ||||
\(769\) | 25.2026 | − | 14.5507i | 0.908828 | − | 0.524712i | 0.0287743 | − | 0.999586i | \(-0.490840\pi\) |
0.880054 | + | 0.474874i | \(0.157506\pi\) | |||||||
\(770\) | −11.7502 | + | 11.0735i | −0.423449 | + | 0.399062i | ||||
\(771\) | 4.67378 | − | 8.09523i | 0.168322 | − | 0.291542i | ||||
\(772\) | 11.7606 | − | 6.78998i | 0.423273 | − | 0.244377i | ||||
\(773\) | 8.96149 | − | 5.17392i | 0.322322 | − | 0.186093i | −0.330105 | − | 0.943944i | \(-0.607084\pi\) |
0.652427 | + | 0.757851i | \(0.273751\pi\) | |||||||
\(774\) | 3.34904 | − | 1.93357i | 0.120379 | − | 0.0695007i | ||||
\(775\) | 14.6704 | − | 8.46993i | 0.526975 | − | 0.304249i | ||||
\(776\) | 2.22156 | − | 3.84785i | 0.0797493 | − | 0.138130i | ||||
\(777\) | 5.28796 | + | 22.3666i | 0.189704 | + | 0.802398i | ||||
\(778\) | −5.24632 | + | 3.02897i | −0.188090 | + | 0.108594i | ||||
\(779\) | −6.29275 | − | 10.8994i | −0.225461 | − | 0.390510i | ||||
\(780\) | 6.80489 | − | 8.60324i | 0.243654 | − | 0.308045i | ||||
\(781\) | 9.52754 | − | 16.5022i | 0.340922 | − | 0.590495i | ||||
\(782\) | 38.7788 | + | 22.3890i | 1.38673 | + | 0.800627i | ||||
\(783\) | 1.77706 | + | 3.07796i | 0.0635069 | + | 0.109997i | ||||
\(784\) | 1.90252 | + | 1.25432i | 0.0679472 | + | 0.0447970i | ||||
\(785\) | − | 0.522568i | − | 0.0186513i | ||||||
\(786\) | 15.1372i | 0.539924i | ||||||||
\(787\) | 25.2027 | − | 14.5508i | 0.898381 | − | 0.518680i | 0.0217062 | − | 0.999764i | \(-0.493090\pi\) |
0.876674 | + | 0.481084i | \(0.159757\pi\) | |||||||
\(788\) | −0.451939 | − | 0.260927i | −0.0160997 | − | 0.00929514i | ||||
\(789\) | −0.943420 | −0.0335866 | ||||||||
\(790\) | −1.49006 | − | 2.58086i | −0.0530139 | − | 0.0918228i | ||||
\(791\) | −18.6215 | + | 4.40253i | −0.662105 | + | 0.156536i | ||||
\(792\) | 7.37066 | 0.261905 | ||||||||
\(793\) | 6.47248 | − | 44.1359i | 0.229844 | − | 1.56731i | ||||
\(794\) | −10.3603 | + | 17.9446i | −0.367674 | + | 0.636830i | ||||
\(795\) | − | 17.9222i | − | 0.635637i | ||||||
\(796\) | 5.70759 | − | 9.88583i | 0.202300 | − | 0.350394i | ||||
\(797\) | −14.9812 | + | 25.9482i | −0.530661 | + | 0.919131i | 0.468699 | + | 0.883358i | \(0.344723\pi\) |
−0.999360 | + | 0.0357733i | \(0.988611\pi\) | |||||||
\(798\) | −6.44126 | + | 1.52285i | −0.228018 | + | 0.0539085i | ||||
\(799\) | −9.52584 | − | 5.49975i | −0.337000 | − | 0.194567i | ||||
\(800\) | − | 10.1812i | − | 0.359960i | ||||||
\(801\) | 9.87880 | + | 5.70353i | 0.349050 | + | 0.201524i | ||||
\(802\) | −0.206222 | − | 0.357186i | −0.00728194 | − | 0.0126127i | ||||
\(803\) | 15.9146 | − | 27.5649i | 0.561614 | − | 0.972745i | ||||
\(804\) | 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 | ||||
\(808\) | 1.46102i | 0.0513985i | ||||||||
\(809\) | −16.0767 | −0.565227 | −0.282614 | − | 0.959234i | \(-0.591201\pi\) | ||||
−0.282614 | + | 0.959234i | \(0.591201\pi\) | |||||||
\(810\) | −2.39655 | −0.0842060 | ||||||||
\(811\) | − | 41.5793i | − | 1.46005i | −0.683423 | − | 0.730023i | \(-0.739509\pi\) | ||
0.683423 | − | 0.730023i | \(-0.260491\pi\) | |||||||
\(812\) | −10.6340 | + | 2.51410i | −0.373179 | + | 0.0882276i | ||||
\(813\) | −17.8317 | − | 10.2951i | −0.625384 | − | 0.361066i | ||||
\(814\) | 17.5360 | − | 10.1244i | 0.614636 | − | 0.354860i | ||||
\(815\) | −9.23137 | − | 15.9892i | −0.323361 | − | 0.560077i | ||||
\(816\) | 2.01823 | 0.0706521 | ||||||||
\(817\) | −9.99849 | − | 5.77263i | −0.349803 | − | 0.201959i | ||||
\(818\) | 31.5460 | 1.10298 | ||||||||
\(819\) | 7.81814 | − | 5.46595i | 0.273188 | − | 0.190996i | ||||
\(820\) | 14.0103 | 0.489262 | ||||||||
\(821\) | −3.52804 | − | 2.03691i | −0.123129 | − | 0.0710888i | 0.437170 | − | 0.899379i | \(-0.355981\pi\) |
−0.560300 | + | 0.828290i | \(0.689314\pi\) | |||||||
\(822\) | 1.75622 | 0.0612552 | ||||||||
\(823\) | −21.3186 | − | 36.9248i | −0.743118 | − | 1.28712i | −0.951069 | − | 0.308979i | \(-0.900013\pi\) |
0.207951 | − | 0.978139i | \(-0.433321\pi\) | |||||||
\(824\) | 13.3817 | − | 7.72593i | 0.466174 | − | 0.269146i | ||||
\(825\) | 4.08886 | + | 2.36070i | 0.142356 | + | 0.0821892i | ||||
\(826\) | −3.75122 | − | 3.98046i | −0.130522 | − | 0.138498i | ||||
\(827\) | − | 21.7244i | − | 0.755431i | −0.925922 | − | 0.377716i | \(-0.876710\pi\) | ||
0.925922 | − | 0.377716i | \(-0.123290\pi\) | |||||||
\(828\) | −9.16886 | −0.318640 | ||||||||
\(829\) | 0.922945 | 0.0320552 | 0.0160276 | − | 0.999872i | \(-0.494898\pi\) | ||||
0.0160276 | + | 0.999872i | \(0.494898\pi\) | |||||||
\(830\) | 5.03317i | 0.174704i | ||||||||
\(831\) | 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 | ||||
\(835\) | −2.35770 | + | 4.08366i | −0.0815916 | + | 0.141321i | ||||
\(836\) | −4.04340 | − | 7.00337i | −0.139844 | − | 0.242217i | ||||
\(837\) | −7.91220 | − | 4.56811i | −0.273486 | − | 0.157897i | ||||
\(838\) | − | 0.357044i | − | 0.0123339i | ||||||
\(839\) | 10.4845 | + | 6.05325i | 0.361966 | + | 0.208981i | 0.669943 | − | 0.742413i | \(-0.266319\pi\) |
−0.307977 | + | 0.951394i | \(0.599652\pi\) | |||||||
\(840\) | 5.76085 | − | 19.2040i | 0.198768 | − | 0.662602i | ||||
\(841\) | 8.18413 | − | 14.1753i | 0.282211 | − | 0.488804i | ||||
\(842\) | −11.2362 | + | 19.4617i | −0.387225 | + | 0.670694i | ||||
\(843\) | − | 10.8703i | − | 0.374392i | ||||||
\(844\) | 2.10043 | − | 3.63805i | 0.0722998 | − | 0.125227i | ||||
\(845\) | −33.1198 | + | 7.83786i | −1.13935 | + | 0.269630i | ||||
\(846\) | −1.62412 | −0.0558384 | ||||||||
\(847\) | 8.19419 | + | 8.69493i | 0.281556 | + | 0.298761i | ||||
\(848\) | 1.11428 | + | 1.92998i | 0.0382644 | + | 0.0662758i | ||||
\(849\) | −3.82154 | −0.131155 | ||||||||
\(850\) | 9.11269 | + | 5.26121i | 0.312563 | + | 0.180458i | ||||
\(851\) | −59.3586 | + | 34.2707i | −2.03479 | + | 1.17478i | ||||
\(852\) | 8.69575i | 0.297911i | ||||||||
\(853\) | 25.9127i | 0.887233i | 0.896217 | + | 0.443616i | \(0.146305\pi\) | ||||
−0.896217 | + | 0.443616i | \(0.853695\pi\) | |||||||
\(854\) | −6.89407 | − | 29.1601i | −0.235910 | − | 0.997837i | ||||
\(855\) | 3.57742 | + | 6.19627i | 0.122345 | + | 0.211908i | ||||
\(856\) | −44.6483 | − | 25.7777i | −1.52605 | − | 0.881064i | ||||
\(857\) | −7.12117 | + | 12.3342i | −0.243255 | + | 0.421329i | −0.961639 | − | 0.274317i | \(-0.911548\pi\) |
0.718385 | + | 0.695646i | \(0.244882\pi\) | |||||||
\(858\) | −6.59171 | − | 5.21384i | −0.225037 | − | 0.177998i | ||||
\(859\) | −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 | ||||
\(861\) | 11.6704 | + | 3.50090i | 0.397726 | + | 0.119310i | ||||
\(862\) | 0.519711 | − | 0.900165i | 0.0177014 | − | 0.0306597i | ||||
\(863\) | −18.3943 | + | 10.6200i | −0.626150 | + | 0.361508i | −0.779260 | − | 0.626701i | \(-0.784405\pi\) |
0.153109 | + | 0.988209i | \(0.451071\pi\) | |||||||
\(864\) | −4.75540 | + | 2.74553i | −0.161782 | + | 0.0934048i | ||||
\(865\) | −27.0390 | + | 15.6110i | −0.919353 | + | 0.530789i | ||||
\(866\) | −16.0506 | + | 9.26683i | −0.545422 | + | 0.314900i | ||||
\(867\) | 10.7175 | − | 18.5633i | 0.363986 | − | 0.630443i | ||||
\(868\) | 20.4420 | − | 19.2648i | 0.693848 | − | 0.653888i | ||||
\(869\) | 2.74225 | − | 1.58324i | 0.0930244 | − | 0.0537077i | ||||
\(870\) | −4.25880 | − | 7.37646i | −0.144387 | − | 0.250085i | ||||
\(871\) | −2.21011 | − | 0.324111i | −0.0748869 | − | 0.0109821i | ||||
\(872\) | 26.8939 | − | 46.5816i | 0.910742 | − | 1.57745i | ||||
\(873\) | −1.32935 | − | 0.767503i | −0.0449918 | − | 0.0259760i | ||||
\(874\) | −9.86945 | − | 17.0944i | −0.333839 | − | 0.578227i | ||||
\(875\) | −15.8580 | + | 14.9447i | −0.536098 | + | 0.505224i | ||||
\(876\) | 14.5252i | 0.490761i | ||||||||
\(877\) | 30.0882i | 1.01601i | 0.861355 | + | 0.508004i | \(0.169616\pi\) | ||||
−0.861355 | + | 0.508004i | \(0.830384\pi\) | |||||||
\(878\) | 22.1785 | − | 12.8048i | 0.748488 | − | 0.432140i | ||||
\(879\) | −15.6392 | − | 9.02929i | −0.527497 | − | 0.304550i | ||||
\(880\) | −2.17026 | −0.0731594 | ||||||||
\(881\) | 22.2785 | + | 38.5876i | 0.750583 | + | 1.30005i | 0.947540 | + | 0.319636i | \(0.103561\pi\) |
−0.196957 | + | 0.980412i | \(0.563106\pi\) | |||||||
\(882\) | 3.52703 | − | 5.34973i | 0.118761 | − | 0.180135i | ||||
\(883\) | −1.96438 | −0.0661066 | −0.0330533 | − | 0.999454i | \(-0.510523\pi\) | ||||
−0.0330533 | + | 0.999454i | \(0.510523\pi\) | |||||||
\(884\) | 20.3727 | + | 16.1142i | 0.685209 | + | 0.541979i | ||||
\(885\) | −2.95623 | + | 5.12034i | −0.0993726 | + | 0.172118i | ||||
\(886\) | − | 19.7198i | − | 0.662500i | ||||||
\(887\) | −2.30867 | + | 3.99873i | −0.0775175 | + | 0.134264i | −0.902178 | − | 0.431363i | \(-0.858033\pi\) |
0.824661 | + | 0.565628i | \(0.191366\pi\) | |||||||
\(888\) | −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 | ||||
\(891\) | − | 2.54641i | − | 0.0853080i | ||||||
\(892\) | −3.57909 | − | 2.06639i | −0.119837 | − | 0.0691879i | ||||
\(893\) | 2.42439 | + | 4.19916i | 0.0811290 | + | 0.140520i | ||||
\(894\) | 6.86291 | − | 11.8869i | 0.229530 | − | 0.397558i | ||||
\(895\) | −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 | ||||
\(899\) | − | 32.4712i | − | 1.08298i | ||||||
\(900\) | −2.15461 | −0.0718202 | ||||||||
\(901\) | 42.4404 | 1.41390 | ||||||||
\(902\) | − | 10.7346i | − | 0.357423i | ||||||
\(903\) | 10.8772 | − | 2.57162i | 0.361972 | − | 0.0855781i | ||||
\(904\) | −18.1295 | − | 10.4671i | −0.602977 | − | 0.348129i | ||||
\(905\) | 38.0332 | − | 21.9585i | 1.26427 | − | 0.729925i | ||||
\(906\) | −4.13287 | − | 7.15834i | −0.137305 | − | 0.237820i | ||||
\(907\) | −20.7647 | −0.689480 | −0.344740 | − | 0.938698i | \(-0.612033\pi\) | ||||
−0.344740 | + | 0.938698i | \(0.612033\pi\) | |||||||
\(908\) | 7.84461 | + | 4.52909i | 0.260332 | + | 0.150303i | ||||
\(909\) | 0.504753 | 0.0167416 | ||||||||
\(910\) | −18.7365 | + | 13.0994i | −0.621110 | + | 0.434241i | ||||
\(911\) | −49.6547 | −1.64513 | −0.822567 | − | 0.568669i | \(-0.807459\pi\) | ||||
−0.822567 | + | 0.568669i | \(0.807459\pi\) | |||||||
\(912\) | −0.770478 | − | 0.444836i | −0.0255131 | − | 0.0147300i | ||||
\(913\) | −5.34791 | −0.176990 | ||||||||
\(914\) | 14.9523 | + | 25.8981i | 0.494578 | + | 0.856634i | ||||
\(915\) | −28.0510 | + | 16.1952i | −0.927336 | + | 0.535398i | ||||
\(916\) | −16.5222 | − | 9.53911i | −0.545910 | − | 0.315181i | ||||
\(917\) | −12.5709 | + | 41.9057i | −0.415129 | + | 1.38385i | ||||
\(918\) | − | 5.67509i | − | 0.187306i | ||||||
\(919\) | 55.1462 | 1.81911 | 0.909553 | − | 0.415588i | \(-0.136424\pi\) | ||||
0.909553 | + | 0.415588i | \(0.136424\pi\) | |||||||
\(920\) | 59.7923 | 1.97129 | ||||||||
\(921\) | − | 8.88791i | − | 0.292867i | ||||||
\(922\) | 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 | ||||
\(926\) | −9.56295 | + | 16.5635i | −0.314258 | + | 0.544311i | ||||
\(927\) | −2.66915 | − | 4.62310i | −0.0876664 | − | 0.151843i | ||||
\(928\) | −16.9012 | − | 9.75793i | −0.554810 | − | 0.320320i | ||||
\(929\) | − | 4.35353i | − | 0.142835i | −0.997447 | − | 0.0714174i | \(-0.977248\pi\) | ||
0.997447 | − | 0.0714174i | \(-0.0227522\pi\) | |||||||
\(930\) | 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 | ||||
\(933\) | 8.24533 | − | 14.2813i | 0.269940 | − | 0.467550i | ||||
\(934\) | 19.9296i | 0.652118i | ||||||||
\(935\) | −20.6652 | + | 35.7931i | −0.675823 | + | 1.17056i | ||||
\(936\) | 10.3259 | + | 1.51429i | 0.337514 | + | 0.0494960i | ||||
\(937\) | 0.712633 | 0.0232807 | 0.0116404 | − | 0.999932i | \(-0.496295\pi\) | ||||
0.0116404 | + | 0.999932i | \(0.496295\pi\) | |||||||
\(938\) | −1.46020 | + | 0.345222i | −0.0476771 | + | 0.0112719i | ||||
\(939\) | 11.0236 | + | 19.0935i | 0.359742 | + | 0.623092i | ||||
\(940\) | −5.39772 | −0.176054 | ||||||||
\(941\) | 10.1930 | + | 5.88493i | 0.332282 | + | 0.191843i | 0.656854 | − | 0.754018i | \(-0.271887\pi\) |
−0.324572 | + | 0.945861i | \(0.605220\pi\) | |||||||
\(942\) | 0.158236 | − | 0.0913578i | 0.00515562 | − | 0.00297660i | ||||
\(943\) | 36.3361i | 1.18327i | ||||||||
\(944\) | − | 0.735188i | − | 0.0239283i | ||||||
\(945\) | −6.63460 | − | 1.99026i | −0.215823 | − | 0.0647431i | ||||
\(946\) | −4.92366 | − | 8.52803i | −0.160082 | − | 0.277270i | ||||
\(947\) | −26.6022 | − | 15.3588i | −0.864455 | − | 0.499093i | 0.00104667 | − | 0.999999i | \(-0.499667\pi\) |
−0.865502 | + | 0.500906i | \(0.833000\pi\) | |||||||
\(948\) | −0.722507 | + | 1.25142i | −0.0234659 | + | 0.0406442i | ||||
\(949\) | 27.9587 | − | 35.3474i | 0.907579 | − | 1.14743i | ||||
\(950\) | −2.31924 | − | 4.01704i | −0.0752460 | − | 0.130330i | ||||
\(951\) | −19.7541 | + | 11.4050i | −0.640569 | + | 0.369833i | ||||
\(952\) | 45.4757 | + | 13.6419i | 1.47388 | + | 0.442136i | ||||
\(953\) | −13.0794 | + | 22.6542i | −0.423684 | + | 0.733843i | −0.996297 | − | 0.0859835i | \(-0.972597\pi\) |
0.572612 | + | 0.819826i | \(0.305930\pi\) | |||||||
\(954\) | 5.42695 | − | 3.13325i | 0.175704 | − | 0.101443i | ||||
\(955\) | 16.9682 | − | 9.79659i | 0.549078 | − | 0.317010i | ||||
\(956\) | 4.71637 | − | 2.72300i | 0.152538 | − | 0.0880680i | ||||
\(957\) | 7.83774 | − | 4.52512i | 0.253358 | − | 0.146276i | ||||
\(958\) | 4.98883 | − | 8.64090i | 0.161182 | − | 0.279175i | ||||
\(959\) | 4.86192 | + | 1.45849i | 0.157000 | + | 0.0470970i | ||||
\(960\) | 12.8727 | − | 7.43207i | 0.415465 | − | 0.239869i | ||||
\(961\) | 26.2353 | + | 45.4409i | 0.846300 | + | 1.46583i | ||||
\(962\) | 26.6471 | − | 10.5811i | 0.859136 | − | 0.341147i | ||||
\(963\) | −8.90567 | + | 15.4251i | −0.286981 | + | 0.497066i | ||||
\(964\) | 10.7915 | + | 6.23050i | 0.347572 | + | 0.200671i | ||||
\(965\) | 15.2975 | + | 26.4961i | 0.492444 | + | 0.852938i | ||||
\(966\) | 18.3037 | + | 5.49076i | 0.588911 | + | 0.176662i | ||||
\(967\) | 2.99020i | 0.0961582i | 0.998844 | + | 0.0480791i | \(0.0153100\pi\) | ||||
−0.998844 | + | 0.0480791i | \(0.984690\pi\) | |||||||
\(968\) | 13.0711i | 0.420121i | ||||||||
\(969\) | −14.6730 | + | 8.47143i | −0.471363 | + | 0.272142i | ||||
\(970\) | 3.18586 | + | 1.83936i | 0.102292 | + | 0.0590582i | ||||
\(971\) | −18.5506 | −0.595318 | −0.297659 | − | 0.954672i | \(-0.596206\pi\) | ||||
−0.297659 | + | 0.954672i | \(0.596206\pi\) | |||||||
\(972\) | 0.581025 | + | 1.00636i | 0.0186364 | + | 0.0322792i | ||||
\(973\) | −56.7997 | + | 13.4287i | −1.82091 | + | 0.430504i | ||||
\(974\) | −5.63160 | −0.180448 | ||||||||
\(975\) | 5.24329 | + | 4.14728i | 0.167920 | + | 0.132819i | ||||
\(976\) | 2.01380 | − | 3.48801i | 0.0644603 | − | 0.111649i | ||||
\(977\) | − | 3.82828i | − | 0.122477i | −0.998123 | − | 0.0612387i | \(-0.980495\pi\) | ||
0.998123 | − | 0.0612387i | \(-0.0195051\pi\) | |||||||
\(978\) | 3.22774 | − | 5.59061i | 0.103212 | − | 0.178768i | ||||
\(979\) | 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 | ||||
\(982\) | − | 9.88656i | − | 0.315493i | ||||||
\(983\) | 27.0572 | + | 15.6215i | 0.862992 | + | 0.498248i | 0.865013 | − | 0.501749i | \(-0.167310\pi\) |
−0.00202132 | + | 0.999998i | \(0.500643\pi\) | |||||||
\(984\) | 6.66493 | + | 11.5440i | 0.212470 | + | 0.368009i | ||||
\(985\) | 0.587856 | − | 1.01820i | 0.0187307 | − | 0.0324425i | ||||
\(986\) | 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 | ||||
\(990\) | 6.10259i | 0.193953i | ||||||||
\(991\) | 5.93593 | 0.188561 | 0.0942805 | − | 0.995546i | \(-0.469945\pi\) | ||||
0.0942805 | + | 0.995546i | \(0.469945\pi\) | |||||||
\(992\) | 50.1675 | 1.59282 | ||||||||
\(993\) | − | 32.0157i | − | 1.01599i | ||||||
\(994\) | 5.20744 | − | 17.3592i | 0.165170 | − | 0.550600i | ||||
\(995\) | 22.2723 | + | 12.8589i | 0.706079 | + | 0.407655i | ||||
\(996\) | 2.11354 | − | 1.22025i | 0.0669702 | − | 0.0386652i | ||||
\(997\) | 3.92320 | + | 6.79518i | 0.124249 | + | 0.215206i | 0.921439 | − | 0.388523i | \(-0.127014\pi\) |
−0.797190 | + | 0.603728i | \(0.793681\pi\) | |||||||
\(998\) | −1.96536 | −0.0622123 | ||||||||
\(999\) | 7.52303 | + | 4.34342i | 0.238018 | + | 0.137420i |
(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.bl.d.88.4 | yes | 20 | |
3.2 | odd | 2 | 819.2.do.g.361.7 | 20 | |||
7.2 | even | 3 | 273.2.t.d.205.7 | yes | 20 | ||
13.4 | even | 6 | 273.2.t.d.4.4 | ✓ | 20 | ||
21.2 | odd | 6 | 819.2.bm.g.478.4 | 20 | |||
39.17 | odd | 6 | 819.2.bm.g.550.7 | 20 | |||
91.30 | even | 6 | inner | 273.2.bl.d.121.4 | yes | 20 | |
273.212 | odd | 6 | 819.2.do.g.667.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.d.4.4 | ✓ | 20 | 13.4 | even | 6 | ||
273.2.t.d.205.7 | yes | 20 | 7.2 | even | 3 | ||
273.2.bl.d.88.4 | yes | 20 | 1.1 | even | 1 | trivial | |
273.2.bl.d.121.4 | yes | 20 | 91.30 | even | 6 | inner | |
819.2.bm.g.478.4 | 20 | 21.2 | odd | 6 | |||
819.2.bm.g.550.7 | 20 | 39.17 | odd | 6 | |||
819.2.do.g.361.7 | 20 | 3.2 | odd | 2 | |||
819.2.do.g.667.7 | 20 | 273.212 | odd | 6 |