Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(53,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.ce (of order \(12\), degree \(4\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.6040479020157644046336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 233.4 | ||
Root | \(-1.47240 + 0.912166i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.233 |
Dual form | 630.2.ce.b.557.4 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 1.87809 | + | 1.21358i | 0.839908 | + | 0.542729i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.94831 | − | 1.79000i | −0.736392 | − | 0.676555i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.12819 | + | 0.686141i | 0.672994 | + | 0.216977i | ||||
\(11\) | 2.64338 | − | 1.52616i | 0.797010 | − | 0.460154i | −0.0454148 | − | 0.998968i | \(-0.514461\pi\) |
0.842424 | + | 0.538814i | \(0.181128\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.00000i | 0.277350 | + | 0.277350i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −2.34521 | − | 1.22474i | −0.626783 | − | 0.327327i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 1.11722 | − | 4.16954i | 0.270967 | − | 1.01126i | −0.687529 | − | 0.726157i | \(-0.741305\pi\) |
0.958496 | − | 0.285105i | \(-0.0920286\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.47036 | + | 3.15831i | 1.25499 | + | 0.724567i | 0.972095 | − | 0.234586i | \(-0.0753733\pi\) |
0.282891 | + | 0.959152i | \(0.408707\pi\) | |||||||
\(20\) | 2.23326 | + | 0.111944i | 0.499373 | + | 0.0250314i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.15831 | − | 2.15831i | 0.460154 | − | 0.460154i | ||||
\(23\) | −0.435690 | − | 1.62602i | −0.0908476 | − | 0.339048i | 0.905510 | − | 0.424326i | \(-0.139489\pi\) |
−0.996357 | + | 0.0852780i | \(0.972822\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.05446 | + | 4.55842i | 0.410891 | + | 0.911684i | ||||
\(26\) | 1.22474 | + | 0.707107i | 0.240192 | + | 0.138675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.58228 | − | 0.576028i | −0.488006 | − | 0.108859i | ||||
\(29\) | −5.88074 | −1.09203 | −0.546013 | − | 0.837777i | \(-0.683855\pi\) | ||||
−0.546013 | + | 0.837777i | \(0.683855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 2.59808i | 0.269408 | + | 0.466628i | 0.968709 | − | 0.248199i | \(-0.0798387\pi\) |
−0.699301 | + | 0.714827i | \(0.746505\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.31662i | − | 0.740295i | ||||||
\(35\) | −1.48680 | − | 5.72620i | −0.251315 | − | 0.967905i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.83013 | + | 6.83013i | 0.300871 | + | 1.12287i | 0.936442 | + | 0.350823i | \(0.114098\pi\) |
−0.635571 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(38\) | 6.10139 | + | 1.63486i | 0.989776 | + | 0.265210i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.18614 | − | 0.469882i | 0.345659 | − | 0.0742949i | ||||
\(41\) | 2.82843i | 0.441726i | 0.975305 | + | 0.220863i | \(0.0708874\pi\) | ||||
−0.975305 | + | 0.220863i | \(0.929113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.63325 | − | 7.63325i | −1.16406 | − | 1.16406i | −0.983578 | − | 0.180481i | \(-0.942234\pi\) |
−0.180481 | − | 0.983578i | \(-0.557766\pi\) | |||||||
\(44\) | 1.52616 | − | 2.64338i | 0.230077 | − | 0.398505i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.841688 | − | 1.45785i | −0.124100 | − | 0.214948i | ||||
\(47\) | −0.305836 | + | 0.0819485i | −0.0446108 | + | 0.0119534i | −0.281055 | − | 0.959692i | \(-0.590684\pi\) |
0.236445 | + | 0.971645i | \(0.424018\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.591820 | + | 6.97494i | 0.0845458 | + | 0.996420i | ||||
\(50\) | 3.16426 | + | 3.87137i | 0.447494 | + | 0.547494i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.36603 | + | 0.366025i | 0.189434 | + | 0.0507586i | ||||
\(53\) | 1.57760 | + | 0.422716i | 0.216700 | + | 0.0580645i | 0.365535 | − | 0.930797i | \(-0.380886\pi\) |
−0.148836 | + | 0.988862i | \(0.547553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.81662 | + | 0.341688i | 0.919153 | + | 0.0460731i | ||||
\(56\) | −2.64338 | + | 0.111944i | −0.353237 | + | 0.0149591i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.68036 | + | 1.52205i | −0.745868 | + | 0.199855i | ||||
\(59\) | −5.99269 | − | 10.3796i | −0.780181 | − | 1.35131i | −0.931836 | − | 0.362880i | \(-0.881794\pi\) |
0.151655 | − | 0.988434i | \(-0.451540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.15831 | + | 5.47036i | −0.404380 | + | 0.700408i | −0.994249 | − | 0.107092i | \(-0.965846\pi\) |
0.589869 | + | 0.807499i | \(0.299179\pi\) | |||||||
\(62\) | 2.12132 | + | 2.12132i | 0.269408 | + | 0.269408i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0.664513 | + | 3.09167i | 0.0824227 | + | 0.383474i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.5253 | − | 3.89204i | −1.77455 | − | 0.475488i | −0.784975 | − | 0.619528i | \(-0.787324\pi\) |
−0.989572 | + | 0.144040i | \(0.953991\pi\) | |||||||
\(68\) | −1.11722 | − | 4.16954i | −0.135483 | − | 0.505631i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.91819 | − | 5.14628i | −0.348791 | − | 0.615098i | ||||
\(71\) | 1.86199i | 0.220977i | 0.993877 | + | 0.110489i | \(0.0352416\pi\) | ||||
−0.993877 | + | 0.110489i | \(0.964758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.982183 | + | 3.66556i | −0.114956 | + | 0.429021i | −0.999284 | − | 0.0378455i | \(-0.987951\pi\) |
0.884328 | + | 0.466867i | \(0.154617\pi\) | |||||||
\(74\) | 3.53553 | + | 6.12372i | 0.410997 | + | 0.711868i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.31662 | 0.724567 | ||||||||
\(77\) | −7.88194 | − | 1.75822i | −0.898231 | − | 0.200368i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.14649 | + | 1.81662i | 0.354007 | + | 0.204386i | 0.666449 | − | 0.745551i | \(-0.267813\pi\) |
−0.312441 | + | 0.949937i | \(0.601147\pi\) | |||||||
\(80\) | 1.99004 | − | 1.01969i | 0.222493 | − | 0.114004i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.732051 | + | 2.73205i | 0.0808415 | + | 0.301705i | ||||
\(83\) | 8.67372 | − | 8.67372i | 0.952065 | − | 0.952065i | −0.0468375 | − | 0.998903i | \(-0.514914\pi\) |
0.998903 | + | 0.0468375i | \(0.0149143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.15831 | − | 6.47494i | 0.776428 | − | 0.702306i | ||||
\(86\) | −9.34878 | − | 5.39752i | −1.00811 | − | 0.582030i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.789997 | − | 2.94831i | 0.0842140 | − | 0.314291i | ||||
\(89\) | 6.32852 | − | 10.9613i | 0.670821 | − | 1.16190i | −0.306850 | − | 0.951758i | \(-0.599275\pi\) |
0.977672 | − | 0.210139i | \(-0.0673916\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.158312 | − | 3.73831i | −0.0165956 | − | 0.391881i | ||||
\(92\) | −1.19033 | − | 1.19033i | −0.124100 | − | 0.124100i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.274205 | + | 0.158312i | −0.0282821 | + | 0.0163287i | ||||
\(95\) | 6.44097 | + | 12.5703i | 0.660830 | + | 1.28969i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.84169 | + | 5.84169i | −0.593134 | + | 0.593134i | −0.938477 | − | 0.345343i | \(-0.887763\pi\) |
0.345343 | + | 0.938477i | \(0.387763\pi\) | |||||||
\(98\) | 2.37690 | + | 6.58410i | 0.240103 | + | 0.665094i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.05842 | + | 2.92048i | 0.405842 | + | 0.292048i | ||||
\(101\) | −14.6355 | + | 8.44984i | −1.45629 | + | 0.840790i | −0.998826 | − | 0.0484373i | \(-0.984576\pi\) |
−0.457465 | + | 0.889228i | \(0.651243\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.96311 | − | 1.32986i | 0.489030 | − | 0.131035i | −0.00587425 | − | 0.999983i | \(-0.501870\pi\) |
0.494904 | + | 0.868948i | \(0.335203\pi\) | |||||||
\(104\) | 1.41421 | 0.138675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.63325 | 0.158635 | ||||||||
\(107\) | −13.1687 | + | 3.52854i | −1.27307 | + | 0.341117i | −0.831205 | − | 0.555966i | \(-0.812349\pi\) |
−0.441862 | + | 0.897083i | \(0.645682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9532 | + | 8.63325i | −1.43226 | + | 0.826915i | −0.997293 | − | 0.0735313i | \(-0.976573\pi\) |
−0.434966 | + | 0.900447i | \(0.643240\pi\) | |||||||
\(110\) | 6.67279 | − | 1.43423i | 0.636225 | − | 0.136748i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.52434 | + | 0.792287i | −0.238528 | + | 0.0748641i | ||||
\(113\) | 1.41421 | − | 1.41421i | 0.133038 | − | 0.133038i | −0.637452 | − | 0.770490i | \(-0.720012\pi\) |
0.770490 | + | 0.637452i | \(0.220012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.15503 | − | 3.58255i | 0.107707 | − | 0.334074i | ||||
\(116\) | −5.09287 | + | 2.94037i | −0.472861 | + | 0.273007i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.47494 | − | 8.47494i | −0.780181 | − | 0.780181i | ||||
\(119\) | −9.64016 | + | 6.12372i | −0.883712 | + | 0.561361i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.841688 | + | 1.45785i | −0.0765171 | + | 0.132531i | ||||
\(122\) | −1.63486 | + | 6.10139i | −0.148014 | + | 0.552394i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.59808 | + | 1.50000i | 0.233314 | + | 0.134704i | ||||
\(125\) | −1.67355 | + | 11.0544i | −0.149686 | + | 0.988734i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.79156 | + | 4.79156i | −0.425182 | + | 0.425182i | −0.886983 | − | 0.461801i | \(-0.847203\pi\) |
0.461801 | + | 0.886983i | \(0.347203\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.44205 | + | 2.81433i | 0.126476 | + | 0.246834i | ||||
\(131\) | 10.8288 | + | 6.25202i | 0.946118 | + | 0.546241i | 0.891873 | − | 0.452286i | \(-0.149392\pi\) |
0.0542449 | + | 0.998528i | \(0.482725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00458 | − | 15.9453i | −0.433952 | − | 1.38263i | ||||
\(134\) | −15.0377 | −1.29906 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.15831 | − | 3.73831i | −0.185074 | − | 0.320557i | ||||
\(137\) | −4.65874 | + | 17.3867i | −0.398023 | + | 1.48544i | 0.418546 | + | 0.908196i | \(0.362540\pi\) |
−0.816569 | + | 0.577247i | \(0.804127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.2665i | 1.12525i | 0.826712 | + | 0.562625i | \(0.190208\pi\) | ||||
−0.826712 | + | 0.562625i | \(0.809792\pi\) | |||||||
\(140\) | −4.15071 | − | 4.21564i | −0.350799 | − | 0.356286i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.481918 | + | 1.79854i | 0.0404417 | + | 0.150930i | ||||
\(143\) | 4.16954 | + | 1.11722i | 0.348674 | + | 0.0934270i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.0446 | − | 7.13674i | −0.917202 | − | 0.592674i | ||||
\(146\) | 3.79487i | 0.314065i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.00000 | + | 5.00000i | 0.410997 | + | 0.410997i | ||||
\(149\) | −3.53553 | + | 6.12372i | −0.289642 | + | 0.501675i | −0.973724 | − | 0.227730i | \(-0.926870\pi\) |
0.684082 | + | 0.729405i | \(0.260203\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.34169 | − | 14.4482i | −0.678837 | − | 1.17578i | −0.975331 | − | 0.220745i | \(-0.929151\pi\) |
0.296495 | − | 0.955035i | \(-0.404182\pi\) | |||||||
\(152\) | 6.10139 | − | 1.63486i | 0.494888 | − | 0.132605i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.06843 | + | 0.341688i | −0.650173 | + | 0.0275340i | ||||
\(155\) | −0.335831 | + | 6.69979i | −0.0269746 | + | 0.538140i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.03158 | + | 1.34821i | 0.401564 | + | 0.107599i | 0.453948 | − | 0.891028i | \(-0.350015\pi\) |
−0.0523837 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(158\) | 3.50945 | + | 0.940354i | 0.279197 | + | 0.0748106i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.65831 | − | 1.50000i | 0.131101 | − | 0.118585i | ||||
\(161\) | −2.06171 | + | 3.94786i | −0.162485 | + | 0.311135i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8597 | − | 2.90986i | 0.850600 | − | 0.227918i | 0.192919 | − | 0.981215i | \(-0.438204\pi\) |
0.657680 | + | 0.753297i | \(0.271538\pi\) | |||||||
\(164\) | 1.41421 | + | 2.44949i | 0.110432 | + | 0.191273i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.13325 | − | 10.6231i | 0.476032 | − | 0.824512i | ||||
\(167\) | 5.65685 | + | 5.65685i | 0.437741 | + | 0.437741i | 0.891251 | − | 0.453510i | \(-0.149829\pi\) |
−0.453510 | + | 0.891251i | \(0.649829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 5.23856 | − | 8.10702i | 0.401779 | − | 0.621780i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.4272 | − | 2.79396i | −0.795068 | − | 0.213038i | ||||
\(173\) | −5.15043 | − | 19.2217i | −0.391580 | − | 1.46140i | −0.827528 | − | 0.561425i | \(-0.810253\pi\) |
0.435947 | − | 0.899972i | \(-0.356413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.15685 | − | 12.5587i | 0.314228 | − | 0.949348i | ||||
\(176\) | − | 3.05231i | − | 0.230077i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.27588 | − | 12.2258i | 0.245538 | − | 0.916359i | ||||
\(179\) | 0.707107 | + | 1.22474i | 0.0528516 | + | 0.0915417i | 0.891241 | − | 0.453530i | \(-0.149836\pi\) |
−0.838389 | + | 0.545072i | \(0.816502\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6332 | 1.83098 | 0.915488 | − | 0.402346i | \(-0.131805\pi\) | ||||
0.915488 | + | 0.402346i | \(0.131805\pi\) | |||||||
\(182\) | −1.12046 | − | 3.56995i | −0.0830542 | − | 0.264623i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.45785 | − | 0.841688i | −0.107474 | − | 0.0620500i | ||||
\(185\) | −4.85175 | + | 15.0486i | −0.356708 | + | 1.10640i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.41012 | − | 12.7267i | −0.249373 | − | 0.930672i | ||||
\(188\) | −0.223888 | + | 0.223888i | −0.0163287 | + | 0.0163287i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.47494 | + | 10.4749i | 0.687384 | + | 0.759932i | ||||
\(191\) | 17.9220 | + | 10.3473i | 1.29679 | + | 0.748702i | 0.979848 | − | 0.199743i | \(-0.0640107\pi\) |
0.316942 | + | 0.948445i | \(0.397344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.73602 | + | 10.2110i | −0.196943 | + | 0.735001i | 0.794813 | + | 0.606855i | \(0.207569\pi\) |
−0.991755 | + | 0.128146i | \(0.959098\pi\) | |||||||
\(194\) | −4.13070 | + | 7.15458i | −0.296567 | + | 0.513669i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | + | 5.74456i | 0.285714 | + | 0.410326i | ||||
\(197\) | −18.3139 | − | 18.3139i | −1.30481 | − | 1.30481i | −0.925109 | − | 0.379701i | \(-0.876027\pi\) |
−0.379701 | − | 0.925109i | \(-0.623973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.01251 | − | 2.31662i | 0.284439 | − | 0.164221i | −0.350992 | − | 0.936378i | \(-0.614156\pi\) |
0.635431 | + | 0.772157i | \(0.280822\pi\) | |||||||
\(200\) | 4.67601 | + | 1.77057i | 0.330644 | + | 0.125198i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.9499 | + | 11.9499i | −0.840790 | + | 0.840790i | ||||
\(203\) | 11.4575 | + | 10.5265i | 0.804159 | + | 0.738816i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.43252 | + | 5.31205i | −0.239737 | + | 0.371009i | ||||
\(206\) | 4.44980 | − | 2.56910i | 0.310033 | − | 0.178997i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.36603 | − | 0.366025i | 0.0947168 | − | 0.0253793i | ||||
\(209\) | 19.2803 | 1.33365 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.94987 | −0.340763 | −0.170382 | − | 0.985378i | \(-0.554500\pi\) | ||||
−0.170382 | + | 0.985378i | \(0.554500\pi\) | |||||||
\(212\) | 1.57760 | − | 0.422716i | 0.108350 | − | 0.0290323i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.8067 | + | 6.81662i | −0.807092 | + | 0.465975i | ||||
\(215\) | −5.07240 | − | 23.5995i | −0.345935 | − | 1.60947i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.72808 | − | 7.74685i | 0.117310 | − | 0.525891i | ||||
\(218\) | −12.2093 | + | 12.2093i | −0.826915 | + | 0.826915i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.07421 | − | 3.11240i | 0.409523 | − | 0.209838i | ||||
\(221\) | 5.28676 | − | 3.05231i | 0.355626 | − | 0.205321i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1583 | − | 16.1583i | −1.08204 | − | 1.08204i | −0.996319 | − | 0.0857215i | \(-0.972680\pi\) |
−0.0857215 | − | 0.996319i | \(-0.527320\pi\) | |||||||
\(224\) | −2.23326 | + | 1.41864i | −0.149216 | + | 0.0947867i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.00000 | − | 1.73205i | 0.0665190 | − | 0.115214i | ||||
\(227\) | 4.31798 | − | 16.1149i | 0.286594 | − | 1.06958i | −0.661073 | − | 0.750322i | \(-0.729898\pi\) |
0.947667 | − | 0.319262i | \(-0.103435\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.5167 | + | 13.0000i | 1.48794 | + | 0.859064i | 0.999905 | − | 0.0137585i | \(-0.00437961\pi\) |
0.488037 | + | 0.872823i | \(0.337713\pi\) | |||||||
\(230\) | 0.188443 | − | 3.75942i | 0.0124256 | − | 0.247889i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.15831 | + | 4.15831i | −0.273007 | + | 0.273007i | ||||
\(233\) | −5.42223 | − | 20.2360i | −0.355222 | − | 1.32571i | −0.880205 | − | 0.474593i | \(-0.842595\pi\) |
0.524983 | − | 0.851113i | \(-0.324072\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.673839 | − | 0.217249i | −0.0439564 | − | 0.0141718i | ||||
\(236\) | −10.3796 | − | 5.99269i | −0.675657 | − | 0.390091i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.72675 | + | 8.41012i | −0.500851 | + | 0.545147i | ||||
\(239\) | 0.966438 | 0.0625137 | 0.0312569 | − | 0.999511i | \(-0.490049\pi\) | ||||
0.0312569 | + | 0.999511i | \(0.490049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.29156 | + | 5.70115i | 0.212028 | + | 0.367244i | 0.952349 | − | 0.305010i | \(-0.0986598\pi\) |
−0.740321 | + | 0.672254i | \(0.765326\pi\) | |||||||
\(242\) | −0.435690 | + | 1.62602i | −0.0280072 | + | 0.104524i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.31662i | 0.404380i | ||||||||
\(245\) | −7.35314 | + | 13.8178i | −0.469775 | + | 0.882786i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.31205 | + | 8.62867i | 0.147112 | + | 0.549029i | ||||
\(248\) | 2.89778 | + | 0.776457i | 0.184009 | + | 0.0493051i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.24456 | + | 11.1109i | 0.0787131 | + | 0.702712i | ||||
\(251\) | 17.1236i | 1.08083i | 0.841399 | + | 0.540415i | \(0.181733\pi\) | ||||
−0.841399 | + | 0.540415i | \(0.818267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.63325 | − | 3.63325i | −0.228420 | − | 0.228420i | ||||
\(254\) | −3.38815 | + | 5.86844i | −0.212591 | + | 0.368219i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 20.5419 | − | 5.50418i | 1.28137 | − | 0.343341i | 0.446991 | − | 0.894538i | \(-0.352496\pi\) |
0.834375 | + | 0.551197i | \(0.185829\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.66025 | − | 16.5831i | 0.538122 | − | 1.03043i | ||||
\(260\) | 2.12132 | + | 2.34521i | 0.131559 | + | 0.145444i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0780 | + | 3.23628i | 0.746179 | + | 0.199938i | ||||
\(263\) | 5.39288 | + | 1.44502i | 0.332539 | + | 0.0891037i | 0.421225 | − | 0.906956i | \(-0.361600\pi\) |
−0.0886860 | + | 0.996060i | \(0.528267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.44987 | + | 2.70844i | 0.150495 | + | 0.166378i | ||||
\(266\) | −8.96100 | − | 14.1067i | −0.549434 | − | 0.864937i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.5253 | + | 3.89204i | −0.887273 | + | 0.237744i | ||||
\(269\) | −6.73524 | − | 11.6658i | −0.410655 | − | 0.711275i | 0.584307 | − | 0.811533i | \(-0.301366\pi\) |
−0.994961 | + | 0.100258i | \(0.968033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.65831 | + | 14.9966i | −0.525955 | + | 0.910981i | 0.473588 | + | 0.880747i | \(0.342959\pi\) |
−0.999543 | + | 0.0302342i | \(0.990375\pi\) | |||||||
\(272\) | −3.05231 | − | 3.05231i | −0.185074 | − | 0.185074i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000i | 1.08742i | ||||||||
\(275\) | 12.3876 | + | 8.91423i | 0.746999 | + | 0.537548i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.1224 | + | 4.85588i | 1.08887 | + | 0.291761i | 0.758224 | − | 0.651994i | \(-0.226067\pi\) |
0.330644 | + | 0.943756i | \(0.392734\pi\) | |||||||
\(278\) | 3.43362 | + | 12.8145i | 0.205935 | + | 0.768560i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.10037 | − | 2.99771i | −0.304805 | − | 0.179147i | ||||
\(281\) | − | 19.7990i | − | 1.18111i | −0.806998 | − | 0.590554i | \(-0.798909\pi\) | ||
0.806998 | − | 0.590554i | \(-0.201091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.481918 | + | 1.79854i | −0.0286471 | + | 0.106912i | −0.978769 | − | 0.204966i | \(-0.934292\pi\) |
0.950122 | + | 0.311879i | \(0.100958\pi\) | |||||||
\(284\) | 0.930994 | + | 1.61253i | 0.0552443 | + | 0.0956860i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.31662 | 0.255247 | ||||||||
\(287\) | 5.06288 | − | 5.51065i | 0.298852 | − | 0.325283i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41444 | − | 0.816625i | −0.0832021 | − | 0.0480368i | ||||
\(290\) | −12.5154 | − | 4.03502i | −0.734927 | − | 0.236944i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.982183 | + | 3.66556i | 0.0574779 | + | 0.214511i | ||||
\(293\) | −0.707107 | + | 0.707107i | −0.0413096 | + | 0.0413096i | −0.727460 | − | 0.686150i | \(-0.759299\pi\) |
0.686150 | + | 0.727460i | \(0.259299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.34169 | − | 26.7665i | 0.0781161 | − | 1.55841i | ||||
\(296\) | 6.12372 | + | 3.53553i | 0.355934 | + | 0.205499i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.83013 | + | 6.83013i | −0.106016 | + | 0.395659i | ||||
\(299\) | 1.19033 | − | 2.06171i | 0.0688383 | − | 0.119231i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.20844 | + | 28.5354i | 0.0696532 | + | 1.64475i | ||||
\(302\) | −11.7969 | − | 11.7969i | −0.678837 | − | 0.678837i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.47036 | − | 3.15831i | 0.313747 | − | 0.181142i | ||||
\(305\) | −12.5703 | + | 6.44097i | −0.719774 | + | 0.368809i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.00000 | + | 9.00000i | −0.513657 | + | 0.513657i | −0.915645 | − | 0.401988i | \(-0.868319\pi\) |
0.401988 | + | 0.915645i | \(0.368319\pi\) | |||||||
\(308\) | −7.70507 | + | 2.41831i | −0.439037 | + | 0.137796i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.40965 | + | 6.55842i | 0.0800625 | + | 0.372493i | ||||
\(311\) | 12.6352 | − | 7.29496i | 0.716478 | − | 0.413659i | −0.0969768 | − | 0.995287i | \(-0.530917\pi\) |
0.813455 | + | 0.581628i | \(0.197584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.11288 | + | 1.63794i | −0.345520 | + | 0.0925819i | −0.427406 | − | 0.904060i | \(-0.640572\pi\) |
0.0818856 | + | 0.996642i | \(0.473906\pi\) | |||||||
\(314\) | 5.20908 | 0.293965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.63325 | 0.204386 | ||||||||
\(317\) | 3.81529 | − | 1.02230i | 0.214288 | − | 0.0574182i | −0.150078 | − | 0.988674i | \(-0.547952\pi\) |
0.364366 | + | 0.931256i | \(0.381286\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5450 | + | 8.97494i | −0.870356 | + | 0.502500i | ||||
\(320\) | 1.21358 | − | 1.87809i | 0.0678411 | − | 0.104989i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.969672 | + | 4.34695i | −0.0540377 | + | 0.242246i | ||||
\(323\) | 19.2803 | − | 19.2803i | 1.07279 | − | 1.07279i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.50397 | + | 6.61288i | −0.138895 | + | 0.366816i | ||||
\(326\) | 9.73657 | − | 5.62141i | 0.539259 | − | 0.311341i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00000 | + | 2.00000i | 0.110432 | + | 0.110432i | ||||
\(329\) | 0.742551 | + | 0.387785i | 0.0409382 | + | 0.0213793i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.68338 | − | 2.91569i | 0.0925267 | − | 0.160261i | −0.816047 | − | 0.577986i | \(-0.803839\pi\) |
0.908574 | + | 0.417725i | \(0.137172\pi\) | |||||||
\(332\) | 3.17480 | − | 11.8485i | 0.174240 | − | 0.650272i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.92820 | + | 4.00000i | 0.379094 | + | 0.218870i | ||||
\(335\) | −22.5565 | − | 24.9372i | −1.23239 | − | 1.36246i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1082 | − | 17.1082i | 0.931942 | − | 0.931942i | −0.0658849 | − | 0.997827i | \(-0.520987\pi\) |
0.997827 | + | 0.0658849i | \(0.0209870\pi\) | |||||||
\(338\) | −2.84701 | − | 10.6252i | −0.154857 | − | 0.577934i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.96181 | − | 9.18662i | 0.160627 | − | 0.498214i | ||||
\(341\) | 7.93015 | + | 4.57847i | 0.429441 | + | 0.247938i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.3321 | − | 14.6487i | 0.611874 | − | 0.790955i | ||||
\(344\) | −10.7950 | −0.582030 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.94987 | − | 17.2337i | −0.534909 | − | 0.926489i | ||||
\(347\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.00000i | − | 0.214115i | −0.994253 | − | 0.107058i | \(-0.965857\pi\) | ||
0.994253 | − | 0.107058i | \(-0.0341429\pi\) | |||||||
\(350\) | 0.764778 | − | 13.2066i | 0.0408791 | − | 0.705924i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.789997 | − | 2.94831i | −0.0421070 | − | 0.157145i | ||||
\(353\) | −15.3580 | − | 4.11516i | −0.817423 | − | 0.219028i | −0.174203 | − | 0.984710i | \(-0.555735\pi\) |
−0.643219 | + | 0.765682i | \(0.722402\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.25967 | + | 3.49699i | −0.119931 | + | 0.185601i | ||||
\(356\) | − | 12.6570i | − | 0.670821i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.00000 | + | 1.00000i | 0.0528516 | + | 0.0528516i | ||||
\(359\) | 3.27620 | − | 5.67455i | 0.172911 | − | 0.299491i | −0.766525 | − | 0.642214i | \(-0.778016\pi\) |
0.939436 | + | 0.342723i | \(0.111349\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.4499 | + | 18.0997i | 0.549993 | + | 0.952616i | ||||
\(362\) | 23.7939 | − | 6.37555i | 1.25058 | − | 0.335092i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00626 | − | 3.15831i | −0.105156 | − | 0.165541i | ||||
\(365\) | −6.29307 | + | 5.69230i | −0.329394 | + | 0.297949i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.84493 | + | 2.36999i | 0.461702 | + | 0.123713i | 0.482169 | − | 0.876078i | \(-0.339849\pi\) |
−0.0204680 | + | 0.999791i | \(0.506516\pi\) | |||||||
\(368\) | −1.62602 | − | 0.435690i | −0.0847619 | − | 0.0227119i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.791562 | + | 15.7916i | −0.0411513 | + | 0.820964i | ||||
\(371\) | −2.31699 | − | 3.64748i | −0.120292 | − | 0.189368i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.2889 | − | 5.97230i | 1.15408 | − | 0.309234i | 0.369479 | − | 0.929239i | \(-0.379536\pi\) |
0.784598 | + | 0.620005i | \(0.212870\pi\) | |||||||
\(374\) | −6.58785 | − | 11.4105i | −0.340650 | − | 0.590022i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.158312 | + | 0.274205i | −0.00816434 | + | 0.0141410i | ||||
\(377\) | −5.88074 | − | 5.88074i | −0.302874 | − | 0.302874i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.6332i | − | 1.57352i | −0.617256 | − | 0.786762i | \(-0.711756\pi\) | ||
0.617256 | − | 0.786762i | \(-0.288244\pi\) | |||||||
\(380\) | 11.8632 | + | 7.66572i | 0.608569 | + | 0.393243i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.9894 | + | 5.35614i | 1.02275 | + | 0.274044i | ||||
\(383\) | 0.517638 | + | 1.93185i | 0.0264501 | + | 0.0987130i | 0.977889 | − | 0.209124i | \(-0.0670614\pi\) |
−0.951439 | + | 0.307837i | \(0.900395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.6693 | − | 12.8675i | −0.645686 | − | 0.655786i | ||||
\(386\) | 10.5712i | 0.538058i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.13821 | + | 7.97989i | −0.108551 | + | 0.405118i | ||||
\(389\) | 13.1403 | + | 22.7596i | 0.666237 | + | 1.15396i | 0.978948 | + | 0.204108i | \(0.0654295\pi\) |
−0.312711 | + | 0.949848i | \(0.601237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.26650 | −0.367483 | ||||||||
\(392\) | 5.35051 | + | 4.51355i | 0.270241 | + | 0.227968i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.4298 | − | 12.9499i | −1.13000 | − | 0.652405i | ||||
\(395\) | 3.70477 | + | 7.23030i | 0.186407 | + | 0.363796i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.92767 | + | 7.19417i | 0.0967471 | + | 0.361065i | 0.997279 | − | 0.0737258i | \(-0.0234890\pi\) |
−0.900531 | + | 0.434791i | \(0.856822\pi\) | |||||||
\(398\) | 3.27620 | − | 3.27620i | 0.164221 | − | 0.164221i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.97494 | + | 0.500000i | 0.248747 | + | 0.0250000i | ||||
\(401\) | 18.3098 | + | 10.5712i | 0.914347 | + | 0.527898i | 0.881827 | − | 0.471573i | \(-0.156314\pi\) |
0.0325197 | + | 0.999471i | \(0.489647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.09808 | + | 4.09808i | −0.0546991 | + | 0.204140i | ||||
\(404\) | −8.44984 | + | 14.6355i | −0.420395 | + | 0.728146i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.7916 | + | 7.20241i | 0.684464 | + | 0.357450i | ||||
\(407\) | 15.2616 | + | 15.2616i | 0.756488 | + | 0.756488i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.3146 | + | 16.9248i | −1.44952 | + | 0.836878i | −0.998452 | − | 0.0556140i | \(-0.982288\pi\) |
−0.451063 | + | 0.892492i | \(0.648955\pi\) | |||||||
\(410\) | −1.94070 | + | 6.01944i | −0.0958443 | + | 0.297279i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.63325 | − | 3.63325i | 0.178997 | − | 0.178997i | ||||
\(413\) | −6.90391 | + | 30.9496i | −0.339719 | + | 1.52293i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.8163 | − | 5.76381i | 1.31636 | − | 0.282934i | ||||
\(416\) | 1.22474 | − | 0.707107i | 0.0600481 | − | 0.0346688i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.6234 | − | 4.99012i | 0.910899 | − | 0.244075i | ||||
\(419\) | 6.17552 | 0.301694 | 0.150847 | − | 0.988557i | \(-0.451800\pi\) | ||||
0.150847 | + | 0.988557i | \(0.451800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.5831 | −1.53927 | −0.769634 | − | 0.638486i | \(-0.779561\pi\) | ||||
−0.769634 | + | 0.638486i | \(0.779561\pi\) | |||||||
\(422\) | −4.78121 | + | 1.28112i | −0.232746 | + | 0.0623640i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.41444 | − | 0.816625i | 0.0686911 | − | 0.0396588i | ||||
\(425\) | 21.3018 | − | 3.47335i | 1.03329 | − | 0.168482i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.9453 | − | 5.00458i | 0.771647 | − | 0.242189i | ||||
\(428\) | −9.64016 | + | 9.64016i | −0.465975 | + | 0.465975i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.0076 | − | 21.4825i | −0.530831 | − | 1.03598i | ||||
\(431\) | 11.0841 | − | 6.39941i | 0.533902 | − | 0.308249i | −0.208702 | − | 0.977979i | \(-0.566924\pi\) |
0.742604 | + | 0.669731i | \(0.233591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.05013 | − | 6.05013i | −0.290750 | − | 0.290750i | 0.546626 | − | 0.837377i | \(-0.315912\pi\) |
−0.837377 | + | 0.546626i | \(0.815912\pi\) | |||||||
\(434\) | −0.335831 | − | 7.93015i | −0.0161204 | − | 0.380659i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.63325 | + | 14.9532i | −0.413458 | + | 0.716130i | ||||
\(437\) | 2.75209 | − | 10.2709i | 0.131650 | − | 0.491325i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.96910 | + | 2.29156i | 0.189435 | + | 0.109370i | 0.591718 | − | 0.806145i | \(-0.298450\pi\) |
−0.402283 | + | 0.915515i | \(0.631783\pi\) | |||||||
\(440\) | 5.06169 | − | 4.57847i | 0.241307 | − | 0.218270i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.31662 | − | 4.31662i | 0.205321 | − | 0.205321i | ||||
\(443\) | −5.68105 | − | 21.2020i | −0.269915 | − | 1.00734i | −0.959173 | − | 0.282820i | \(-0.908730\pi\) |
0.689259 | − | 0.724515i | \(-0.257936\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.1879 | − | 12.9062i | 1.19402 | − | 0.611813i | ||||
\(446\) | −19.7898 | − | 11.4257i | −0.937075 | − | 0.541020i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.79000 | + | 1.94831i | −0.0845694 | + | 0.0920490i | ||||
\(449\) | 23.4521 | 1.10677 | 0.553386 | − | 0.832925i | \(-0.313335\pi\) | ||||
0.553386 | + | 0.832925i | \(0.313335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.31662 | + | 7.47661i | 0.203262 | + | 0.352060i | ||||
\(452\) | 0.517638 | − | 1.93185i | 0.0243476 | − | 0.0908667i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 16.6834i | − | 0.782990i | ||||||
\(455\) | 4.23940 | − | 7.21301i | 0.198746 | − | 0.338151i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.68997 | − | 32.4314i | −0.406500 | − | 1.51708i | −0.801273 | − | 0.598299i | \(-0.795844\pi\) |
0.394774 | − | 0.918778i | \(-0.370823\pi\) | |||||||
\(458\) | 25.1141 | + | 6.72930i | 1.17350 | + | 0.314439i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.790988 | − | 3.68009i | −0.0368800 | − | 0.171585i | ||||
\(461\) | 0.0708883i | 0.00330160i | 0.999999 | + | 0.00165080i | \(0.000525466\pi\) | ||||
−0.999999 | + | 0.00165080i | \(0.999475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.6332 | + | 27.6332i | 1.28423 | + | 1.28423i | 0.938239 | + | 0.345987i | \(0.112456\pi\) |
0.345987 | + | 0.938239i | \(0.387544\pi\) | |||||||
\(464\) | −2.94037 | + | 5.09287i | −0.136503 | + | 0.236431i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.4749 | − | 18.1431i | −0.485242 | − | 0.840464i | ||||
\(467\) | −37.2200 | + | 9.97307i | −1.72234 | + | 0.461499i | −0.978395 | − | 0.206745i | \(-0.933713\pi\) |
−0.743942 | + | 0.668244i | \(0.767046\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3330 | + | 33.5831i | 0.985067 | + | 1.55072i | ||||
\(470\) | −0.707107 | − | 0.0354442i | −0.0326164 | − | 0.00163492i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.5770 | − | 3.10204i | −0.532874 | − | 0.142783i | ||||
\(473\) | −31.8271 | − | 8.52806i | −1.46341 | − | 0.392120i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.15831 | + | 31.4248i | −0.144913 | + | 1.44187i | ||||
\(476\) | −5.28676 | + | 10.1234i | −0.242318 | + | 0.464004i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.933508 | − | 0.250133i | 0.0426977 | − | 0.0114408i | ||||
\(479\) | −5.17364 | − | 8.96100i | −0.236389 | − | 0.409438i | 0.723286 | − | 0.690548i | \(-0.242631\pi\) |
−0.959676 | + | 0.281110i | \(0.909297\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | + | 8.66025i | −0.227980 | + | 0.394874i | ||||
\(482\) | 4.65497 | + | 4.65497i | 0.212028 | + | 0.212028i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.68338i | 0.0765171i | ||||||||
\(485\) | −18.0606 | + | 3.88188i | −0.820088 | + | 0.176267i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.6751 | − | 4.20012i | −0.710305 | − | 0.190326i | −0.114463 | − | 0.993428i | \(-0.536515\pi\) |
−0.595842 | + | 0.803102i | \(0.703181\pi\) | |||||||
\(488\) | 1.63486 | + | 6.10139i | 0.0740068 | + | 0.276197i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.52628 | + | 15.2501i | −0.159301 | + | 0.688929i | ||||
\(491\) | 13.8474i | 0.624923i | 0.949930 | + | 0.312461i | \(0.101153\pi\) | ||||
−0.949930 | + | 0.312461i | \(0.898847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.57011 | + | 24.5200i | −0.295903 | + | 1.10432i | ||||
\(494\) | 4.46653 | + | 7.73625i | 0.200959 | + | 0.348071i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | 3.33295 | − | 3.62773i | 0.149503 | − | 0.162726i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0526 | − | 11.0000i | −0.852910 | − | 0.492428i | 0.00872186 | − | 0.999962i | \(-0.497224\pi\) |
−0.861632 | + | 0.507534i | \(0.830557\pi\) | |||||||
\(500\) | 4.07786 | + | 10.4101i | 0.182367 | + | 0.465556i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.43190 | + | 16.5401i | 0.197806 | + | 0.738220i | ||||
\(503\) | −12.4331 | + | 12.4331i | −0.554367 | + | 0.554367i | −0.927698 | − | 0.373331i | \(-0.878215\pi\) |
0.373331 | + | 0.927698i | \(0.378215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.7414 | − | 1.89181i | −1.67947 | − | 0.0841846i | ||||
\(506\) | −4.44980 | − | 2.56910i | −0.197818 | − | 0.114210i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.75383 | + | 6.54540i | −0.0778138 | + | 0.290405i | ||||
\(509\) | −7.40690 | + | 12.8291i | −0.328305 | + | 0.568641i | −0.982176 | − | 0.187965i | \(-0.939811\pi\) |
0.653871 | + | 0.756606i | \(0.273144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.47494 | − | 5.38354i | 0.374909 | − | 0.238154i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.4173 | − | 10.6332i | 0.812354 | − | 0.469013i | ||||
\(515\) | 10.9351 | + | 3.52552i | 0.481857 | + | 0.155353i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.683375 | + | 0.683375i | −0.0300548 | + | 0.0300548i | ||||
\(518\) | 4.07313 | − | 18.2595i | 0.178963 | − | 0.802277i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.65602 | + | 1.71626i | 0.116474 | + | 0.0752629i | ||||
\(521\) | 14.6355 | − | 8.44984i | 0.641195 | − | 0.370194i | −0.143880 | − | 0.989595i | \(-0.545958\pi\) |
0.785075 | + | 0.619401i | \(0.212625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4588 | − | 4.14217i | 0.675966 | − | 0.181125i | 0.0955252 | − | 0.995427i | \(-0.469547\pi\) |
0.580441 | + | 0.814302i | \(0.302880\pi\) | |||||||
\(524\) | 12.5040 | 0.546241 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.58312 | 0.243436 | ||||||||
\(527\) | 12.5086 | − | 3.35167i | 0.544884 | − | 0.146001i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.4645 | − | 10.0831i | 0.759325 | − | 0.438397i | ||||
\(530\) | 3.06739 | + | 1.98208i | 0.133239 | + | 0.0860959i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.3067 | − | 11.3067i | −0.533565 | − | 0.490209i | ||||
\(533\) | −2.82843 | + | 2.82843i | −0.122513 | + | 0.122513i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.0142 | − | 9.35433i | −1.25439 | − | 0.404423i | ||||
\(536\) | −13.0230 | + | 7.51884i | −0.562509 | + | 0.324765i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.52506 | − | 9.52506i | −0.410655 | − | 0.410655i | ||||
\(539\) | 12.2093 | + | 17.5342i | 0.525890 | + | 0.755252i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7916 | − | 25.6197i | 0.635939 | − | 1.10148i | −0.350376 | − | 0.936609i | \(-0.613946\pi\) |
0.986315 | − | 0.164870i | \(-0.0527203\pi\) | |||||||
\(542\) | −4.48187 | + | 16.7266i | −0.192513 | + | 0.718468i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.73831 | − | 2.15831i | −0.160279 | − | 0.0925369i | ||||
\(545\) | −38.5607 | − | 1.93288i | −1.65176 | − | 0.0827954i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.31662 | + | 3.31662i | −0.141809 | + | 0.141809i | −0.774447 | − | 0.632639i | \(-0.781972\pi\) |
0.632639 | + | 0.774447i | \(0.281972\pi\) | |||||||
\(548\) | 4.65874 | + | 17.3867i | 0.199012 | + | 0.742722i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.2727 | + | 5.40434i | 0.608588 | + | 0.230442i | ||||
\(551\) | −32.1698 | − | 18.5732i | −1.37048 | − | 0.791246i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.87858 | − | 9.17155i | −0.122410 | − | 0.390014i | ||||
\(554\) | 18.7617 | 0.797107 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.63325 | + | 11.4891i | 0.281312 | + | 0.487247i | ||||
\(557\) | −9.38646 | + | 35.0307i | −0.397717 | + | 1.48430i | 0.419386 | + | 0.907808i | \(0.362246\pi\) |
−0.817103 | + | 0.576492i | \(0.804421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.2665i | − | 0.645704i | ||||||
\(560\) | −5.70244 | − | 1.57549i | −0.240972 | − | 0.0665768i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.12436 | − | 19.1244i | −0.216158 | − | 0.806712i | ||||
\(563\) | −5.74714 | − | 1.53994i | −0.242213 | − | 0.0649008i | 0.135670 | − | 0.990754i | \(-0.456681\pi\) |
−0.377883 | + | 0.925853i | \(0.623348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.37228 | − | 0.939764i | 0.183943 | − | 0.0395362i | ||||
\(566\) | 1.86199i | 0.0782652i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.31662 | + | 1.31662i | 0.0552443 | + | 0.0552443i | ||||
\(569\) | 8.44984 | − | 14.6355i | 0.354236 | − | 0.613554i | −0.632751 | − | 0.774355i | \(-0.718074\pi\) |
0.986987 | + | 0.160801i | \(0.0514078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4248 | − | 35.3768i | −0.854752 | − | 1.48047i | −0.876875 | − | 0.480718i | \(-0.840376\pi\) |
0.0221234 | − | 0.999755i | \(-0.492957\pi\) | |||||||
\(572\) | 4.16954 | − | 1.11722i | 0.174337 | − | 0.0467135i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.46410 | − | 6.63325i | 0.144589 | − | 0.276866i | ||||
\(575\) | 6.51696 | − | 5.32663i | 0.271776 | − | 0.222136i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.08327 | − | 0.558212i | −0.0867279 | − | 0.0232387i | 0.215194 | − | 0.976571i | \(-0.430962\pi\) |
−0.301922 | + | 0.953333i | \(0.597628\pi\) | |||||||
\(578\) | −1.57760 | − | 0.422716i | −0.0656194 | − | 0.0175827i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.1332 | − | 0.658312i | −0.545329 | − | 0.0273349i | ||||
\(581\) | −32.4250 | + | 1.37316i | −1.34522 | + | 0.0569682i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.81533 | − | 1.29026i | 0.199430 | − | 0.0534372i | ||||
\(584\) | 1.89743 | + | 3.28645i | 0.0785163 | + | 0.135994i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.500000 | + | 0.866025i | −0.0206548 | + | 0.0357752i | ||||
\(587\) | 1.15488 | + | 1.15488i | 0.0476671 | + | 0.0476671i | 0.730539 | − | 0.682871i | \(-0.239269\pi\) |
−0.682871 | + | 0.730539i | \(0.739269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9499i | 0.780816i | ||||||||
\(590\) | −5.63171 | − | 26.2017i | −0.231854 | − | 1.07871i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.83013 | + | 1.83013i | 0.280716 | + | 0.0752178i | ||||
\(593\) | 7.32888 | + | 27.3518i | 0.300961 | + | 1.12320i | 0.936367 | + | 0.351024i | \(0.114166\pi\) |
−0.635406 | + | 0.772179i | \(0.719167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.5367 | − | 0.198177i | −1.04690 | − | 0.00812446i | ||||
\(596\) | 7.07107i | 0.289642i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.616158 | − | 2.29953i | 0.0251966 | − | 0.0940349i | ||||
\(599\) | −11.7615 | − | 20.3715i | −0.480561 | − | 0.832356i | 0.519190 | − | 0.854659i | \(-0.326234\pi\) |
−0.999751 | + | 0.0223024i | \(0.992900\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.3668 | 0.749195 | 0.374598 | − | 0.927187i | \(-0.377781\pi\) | ||||
0.374598 | + | 0.927187i | \(0.377781\pi\) | |||||||
\(602\) | 8.55277 | + | 27.2503i | 0.348585 | + | 1.11064i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.4482 | − | 8.34169i | −0.587890 | − | 0.339418i | ||||
\(605\) | −3.34998 | + | 1.71651i | −0.136196 | + | 0.0697862i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.96833 | − | 14.8100i | −0.161070 | − | 0.601120i | −0.998509 | − | 0.0545897i | \(-0.982615\pi\) |
0.837439 | − | 0.546530i | \(-0.184052\pi\) | |||||||
\(608\) | 4.46653 | − | 4.46653i | 0.181142 | − | 0.181142i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.4749 | + | 9.47494i | −0.424118 | + | 0.383629i | ||||
\(611\) | −0.387785 | − | 0.223888i | −0.0156881 | − | 0.00905752i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.99065 | + | 22.3574i | −0.241960 | + | 0.903007i | 0.732927 | + | 0.680307i | \(0.238154\pi\) |
−0.974887 | + | 0.222700i | \(0.928513\pi\) | |||||||
\(614\) | −6.36396 | + | 11.0227i | −0.256829 | + | 0.444840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.81662 | + | 4.33013i | −0.274650 | + | 0.174466i | ||||
\(617\) | 10.6420 | + | 10.6420i | 0.428433 | + | 0.428433i | 0.888094 | − | 0.459662i | \(-0.152029\pi\) |
−0.459662 | + | 0.888094i | \(0.652029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.83513 | − | 2.79156i | 0.194340 | − | 0.112202i | −0.399673 | − | 0.916658i | \(-0.630876\pi\) |
0.594013 | + | 0.804456i | \(0.297543\pi\) | |||||||
\(620\) | 3.05906 | + | 5.97011i | 0.122855 | + | 0.239765i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.3166 | − | 10.3166i | 0.413659 | − | 0.413659i | ||||
\(623\) | −31.9506 | + | 10.0280i | −1.28007 | + | 0.401763i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.5584 | + | 18.7302i | −0.662337 | + | 0.749206i | ||||
\(626\) | −5.48066 | + | 3.16426i | −0.219051 | + | 0.126469i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.03158 | − | 1.34821i | 0.200782 | − | 0.0537994i | ||||
\(629\) | 30.5231 | 1.21704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.5330 | −1.25531 | −0.627654 | − | 0.778492i | \(-0.715985\pi\) | ||||
−0.627654 | + | 0.778492i | \(0.715985\pi\) | |||||||
\(632\) | 3.50945 | − | 0.940354i | 0.139598 | − | 0.0374053i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.42069 | − | 1.97494i | 0.135853 | − | 0.0784348i | ||||
\(635\) | −14.8139 | + | 3.18406i | −0.587873 | + | 0.126355i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.38312 | + | 7.56676i | −0.252908 | + | 0.299806i | ||||
\(638\) | −12.6925 | + | 12.6925i | −0.502500 | + | 0.502500i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.686141 | − | 2.12819i | 0.0271221 | − | 0.0841243i | ||||
\(641\) | 26.8830 | − | 15.5209i | 1.06181 | − | 0.613039i | 0.135881 | − | 0.990725i | \(-0.456614\pi\) |
0.925934 | + | 0.377686i | \(0.123280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.89975 | + | 7.89975i | 0.311536 | + | 0.311536i | 0.845504 | − | 0.533969i | \(-0.179300\pi\) |
−0.533969 | + | 0.845504i | \(0.679300\pi\) | |||||||
\(644\) | 0.188443 | + | 4.44980i | 0.00742571 | + | 0.175347i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.6332 | − | 23.6135i | 0.536393 | − | 0.929060i | ||||
\(647\) | −8.33821 | + | 31.1186i | −0.327809 | + | 1.22340i | 0.583649 | + | 0.812006i | \(0.301624\pi\) |
−0.911458 | + | 0.411393i | \(0.865042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.6819 | − | 18.2916i | −1.24362 | − | 0.718007i | ||||
\(650\) | −0.707107 | + | 7.03562i | −0.0277350 | + | 0.275960i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.94987 | − | 7.94987i | 0.311341 | − | 0.311341i | ||||
\(653\) | 5.84494 | + | 21.8136i | 0.228730 | + | 0.853633i | 0.980876 | + | 0.194636i | \(0.0623525\pi\) |
−0.752145 | + | 0.658997i | \(0.770981\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.7502 | + | 24.8835i | 0.498191 | + | 0.972278i | ||||
\(656\) | 2.44949 | + | 1.41421i | 0.0956365 | + | 0.0552158i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.817615 | + | 0.182385i | 0.0318740 | + | 0.00711010i | ||||
\(659\) | −47.5646 | −1.85285 | −0.926427 | − | 0.376475i | \(-0.877136\pi\) | ||||
−0.926427 | + | 0.376475i | \(0.877136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.1082 | − | 41.7566i | −0.937700 | − | 1.62414i | −0.769747 | − | 0.638349i | \(-0.779618\pi\) |
−0.167952 | − | 0.985795i | \(-0.553715\pi\) | |||||||
\(662\) | 0.871379 | − | 3.25203i | 0.0338671 | − | 0.126394i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 12.2665i | − | 0.476032i | ||||||
\(665\) | 9.95180 | − | 36.0202i | 0.385914 | − | 1.39680i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.56218 | + | 9.56218i | 0.0992079 | + | 0.370249i | ||||
\(668\) | 7.72741 | + | 2.07055i | 0.298982 | + | 0.0801121i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.2422 | − | 18.2494i | −1.09109 | − | 0.705036i | ||||
\(671\) | 19.2803i | 0.744309i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.7414 | + | 10.7414i | 0.414052 | + | 0.414052i | 0.883147 | − | 0.469096i | \(-0.155420\pi\) |
−0.469096 | + | 0.883147i | \(0.655420\pi\) | |||||||
\(674\) | 12.0973 | − | 20.9532i | 0.465971 | − | 0.807086i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.50000 | − | 9.52628i | −0.211538 | − | 0.366395i | ||||
\(677\) | −6.45564 | + | 1.72978i | −0.248111 | + | 0.0664810i | −0.380731 | − | 0.924686i | \(-0.624328\pi\) |
0.132620 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.8380 | − | 0.924812i | 0.838066 | − | 0.0354910i | ||||
\(680\) | 0.483219 | − | 9.64016i | 0.0185306 | − | 0.369683i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.84493 | + | 2.36999i | 0.338690 | + | 0.0907517i | ||||
\(683\) | −31.6819 | − | 8.48913i | −1.21227 | − | 0.324828i | −0.404620 | − | 0.914485i | \(-0.632596\pi\) |
−0.807654 | + | 0.589657i | \(0.799263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.8496 | + | 27.0000i | −1.14050 | + | 1.03162i | ||||
\(686\) | 7.15458 | − | 17.0825i | 0.273163 | − | 0.652213i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.4272 | + | 2.79396i | −0.397534 | + | 0.106519i | ||||
\(689\) | 1.15488 | + | 2.00031i | 0.0439975 | + | 0.0762059i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.0000 | + | 41.5692i | −0.913003 | + | 1.58137i | −0.103204 | + | 0.994660i | \(0.532909\pi\) |
−0.809799 | + | 0.586707i | \(0.800424\pi\) | |||||||
\(692\) | −14.0712 | − | 14.0712i | −0.534909 | − | 0.534909i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0999 | + | 24.9157i | −0.610705 | + | 0.945106i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.7932 | + | 3.15999i | 0.446701 | + | 0.119693i | ||||
\(698\) | −1.03528 | − | 3.86370i | −0.0391858 | − | 0.146243i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.67941 | − | 12.9546i | −0.101272 | − | 0.489637i | ||||
\(701\) | − | 29.3328i | − | 1.10789i | −0.832555 | − | 0.553943i | \(-0.813123\pi\) | ||
0.832555 | − | 0.553943i | \(-0.186877\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.5602 | + | 43.1433i | −0.436002 | + | 1.62718i | ||||
\(704\) | −1.52616 | − | 2.64338i | −0.0575192 | − | 0.0996262i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.8997 | −0.598395 | ||||||||
\(707\) | 43.6398 | + | 9.73469i | 1.64124 | + | 0.366111i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.2212 | + | 7.63325i | 0.496532 | + | 0.286673i | 0.727280 | − | 0.686341i | \(-0.240784\pi\) |
−0.230748 | + | 0.973013i | \(0.574117\pi\) | |||||||
\(710\) | −1.27759 | + | 3.96267i | −0.0479470 | + | 0.148716i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.27588 | − | 12.2258i | −0.122769 | − | 0.458180i | ||||
\(713\) | 3.57098 | − | 3.57098i | 0.133734 | − | 0.133734i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.47494 | + | 7.15831i | 0.242149 | + | 0.267706i | ||||
\(716\) | 1.22474 | + | 0.707107i | 0.0457709 | + | 0.0264258i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.69589 | − | 6.32914i | 0.0632899 | − | 0.236201i | ||||
\(719\) | −6.62329 | + | 11.4719i | −0.247007 | + | 0.427829i | −0.962694 | − | 0.270592i | \(-0.912780\pi\) |
0.715687 | + | 0.698421i | \(0.246114\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0501 | − | 6.29297i | −0.448770 | − | 0.234363i | ||||
\(722\) | 14.7784 | + | 14.7784i | 0.549993 | + | 0.549993i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.3330 | − | 12.3166i | 0.792835 | − | 0.457744i | ||||
\(725\) | −12.0817 | − | 26.8069i | −0.448704 | − | 0.995583i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.1082 | + | 31.1082i | −1.15374 | + | 1.15374i | −0.167942 | + | 0.985797i | \(0.553712\pi\) |
−0.985797 | + | 0.167942i | \(0.946288\pi\) | |||||||
\(728\) | −2.75533 | − | 2.53144i | −0.102119 | − | 0.0938213i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.60537 | + | 7.12711i | −0.170452 | + | 0.263786i | ||||
\(731\) | −40.3552 | + | 23.2991i | −1.49259 | + | 0.861748i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.83211 | − | 2.09861i | 0.289286 | − | 0.0775138i | −0.111258 | − | 0.993792i | \(-0.535488\pi\) |
0.400544 | + | 0.916278i | \(0.368821\pi\) | |||||||
\(734\) | 9.15694 | 0.337989 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.68338 | −0.0620500 | ||||||||
\(737\) | −44.3358 | + | 11.8797i | −1.63313 | + | 0.437595i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0375 | − | 6.94987i | 0.442808 | − | 0.255655i | −0.261980 | − | 0.965073i | \(-0.584375\pi\) |
0.704788 | + | 0.709418i | \(0.251042\pi\) | |||||||
\(740\) | 3.32257 | + | 15.4583i | 0.122140 | + | 0.568260i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.18208 | − | 2.92351i | −0.116818 | − | 0.107326i | ||||
\(743\) | 21.1423 | − | 21.1423i | 0.775636 | − | 0.775636i | −0.203449 | − | 0.979086i | \(-0.565215\pi\) |
0.979086 | + | 0.203449i | \(0.0652152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.0717 | + | 7.21027i | −0.515546 | + | 0.264164i | ||||
\(746\) | 19.9837 | − | 11.5376i | 0.731655 | − | 0.422421i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.31662 | − | 9.31662i | −0.340650 | − | 0.340650i | ||||
\(749\) | 31.9728 | + | 16.6973i | 1.16826 | + | 0.610104i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.500000 | + | 0.866025i | −0.0182453 | + | 0.0316017i | −0.875004 | − | 0.484116i | \(-0.839141\pi\) |
0.856759 | + | 0.515718i | \(0.172475\pi\) | |||||||
\(752\) | −0.0819485 | + | 0.305836i | −0.00298836 | + | 0.0111527i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.20241 | − | 4.15831i | −0.262296 | − | 0.151437i | ||||
\(755\) | 1.86760 | − | 37.2584i | 0.0679689 | − | 1.35597i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.2665 | + | 12.2665i | −0.445833 | + | 0.445833i | −0.893967 | − | 0.448133i | \(-0.852089\pi\) |
0.448133 | + | 0.893967i | \(0.352089\pi\) | |||||||
\(758\) | −7.92847 | − | 29.5894i | −0.287975 | − | 1.07474i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.4430 | + | 4.33409i | 0.487629 | + | 0.157214i | ||||
\(761\) | −2.12310 | − | 1.22577i | −0.0769622 | − | 0.0444341i | 0.461025 | − | 0.887387i | \(-0.347482\pi\) |
−0.537987 | + | 0.842953i | \(0.680815\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.5870 | + | 9.94599i | 1.61416 | + | 0.360069i | ||||
\(764\) | 20.6945 | 0.748702 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00000 | + | 1.73205i | 0.0361315 | + | 0.0625815i | ||||
\(767\) | 4.38695 | − | 16.3723i | 0.158404 | − | 0.591170i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35.6332i | − | 1.28497i | −0.766299 | − | 0.642484i | \(-0.777904\pi\) | ||
0.766299 | − | 0.642484i | \(-0.222096\pi\) | |||||||
\(770\) | −15.5679 | − | 9.14995i | −0.561029 | − | 0.329741i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.73602 | + | 10.2110i | 0.0984714 | + | 0.367500i | ||||
\(773\) | 24.4056 | + | 6.53945i | 0.877807 | + | 0.235208i | 0.669461 | − | 0.742847i | \(-0.266525\pi\) |
0.208346 | + | 0.978055i | \(0.433192\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.76144 | + | 12.1753i | −0.314720 | + | 0.437348i | ||||
\(776\) | 8.26139i | 0.296567i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.5831 | + | 18.5831i | 0.666237 | + | 0.666237i | ||||
\(779\) | −8.93306 | + | 15.4725i | −0.320060 | + | 0.554360i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.84169 | + | 4.92195i | 0.101684 | + | 0.176121i | ||||
\(782\) | −7.01890 | + | 1.88071i | −0.250995 | + | 0.0672540i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.33638 | + | 2.97494i | 0.226299 | + | 0.106248i | ||||
\(785\) | 7.81362 | + | 8.63828i | 0.278880 | + | 0.308313i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.9841 | + | 8.03421i | 1.06882 | + | 0.286389i | 0.750007 | − | 0.661430i | \(-0.230050\pi\) |
0.318810 | + | 0.947819i | \(0.396717\pi\) | |||||||
\(788\) | −25.0172 | − | 6.70335i | −0.891202 | − | 0.238797i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.44987 | + | 6.02506i | 0.193898 | + | 0.214362i | ||||
\(791\) | −5.28676 | + | 0.223888i | −0.187976 | + | 0.00796052i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.62867 | + | 2.31205i | −0.306413 | + | 0.0821031i | ||||
\(794\) | 3.72398 | + | 6.45012i | 0.132159 | + | 0.228906i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.31662 | − | 4.01251i | 0.0821106 | − | 0.142220i | ||||
\(797\) | −27.2824 | − | 27.2824i | −0.966392 | − | 0.966392i | 0.0330615 | − | 0.999453i | \(-0.489474\pi\) |
−0.999453 | + | 0.0330615i | \(0.989474\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36675i | 0.0483522i | ||||||||
\(800\) | 4.93483 | − | 0.804646i | 0.174473 | − | 0.0284485i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.4219 | + | 5.47203i | 0.721123 | + | 0.193224i | ||||
\(803\) | 2.99793 | + | 11.1884i | 0.105795 | + | 0.394831i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.66311 | + | 4.91241i | −0.305335 | + | 0.173140i | ||||
\(806\) | 4.24264i | 0.149441i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.37396 | + | 16.3238i | −0.153875 | + | 0.574270i | ||||
\(809\) | −27.3178 | − | 47.3159i | −0.960444 | − | 1.66354i | −0.721387 | − | 0.692532i | \(-0.756495\pi\) |
−0.239057 | − | 0.971006i | \(-0.576838\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.8997 | 1.75222 | 0.876109 | − | 0.482114i | \(-0.160131\pi\) | ||||
0.876109 | + | 0.482114i | \(0.160131\pi\) | |||||||
\(812\) | 15.1857 | + | 3.38747i | 0.532915 | + | 0.118877i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.6915 | + | 10.7916i | 0.655138 | + | 0.378244i | ||||
\(815\) | 23.9269 | + | 7.71416i | 0.838123 | + | 0.270215i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.6484 | − | 65.8648i | −0.617440 | − | 2.30432i | ||||
\(818\) | −23.9353 | + | 23.9353i | −0.836878 | + | 0.836878i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.316625 | + | 6.31662i | −0.0110570 | + | 0.220586i | ||||
\(821\) | −2.19421 | − | 1.26683i | −0.0765783 | − | 0.0442125i | 0.461222 | − | 0.887285i | \(-0.347411\pi\) |
−0.537800 | + | 0.843072i | \(0.680745\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.64984 | + | 28.5496i | −0.266657 | + | 0.995176i | 0.694572 | + | 0.719423i | \(0.255594\pi\) |
−0.961229 | + | 0.275753i | \(0.911073\pi\) | |||||||
\(824\) | 2.56910 | − | 4.44980i | 0.0894987 | − | 0.155016i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.34169 | + | 31.6819i | 0.0466833 | + | 1.10235i | ||||
\(827\) | 27.8011 | + | 27.8011i | 0.966737 | + | 0.966737i | 0.999464 | − | 0.0327270i | \(-0.0104192\pi\) |
−0.0327270 | + | 0.999464i | \(0.510419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.5922 | − | 8.42481i | 0.506808 | − | 0.292606i | −0.224713 | − | 0.974425i | \(-0.572144\pi\) |
0.731521 | + | 0.681819i | \(0.238811\pi\) | |||||||
\(830\) | 24.4108 | − | 12.5080i | 0.847310 | − | 0.434158i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | − | 1.00000i | 0.0346688 | − | 0.0346688i | ||||
\(833\) | 29.7435 | + | 5.32495i | 1.03055 | + | 0.184499i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.75906 | + | 17.4891i | 0.130087 | + | 0.605236i | ||||
\(836\) | 16.6973 | − | 9.64016i | 0.577487 | − | 0.333412i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.96509 | − | 1.59834i | 0.206061 | − | 0.0552138i | ||||
\(839\) | −24.3476 | −0.840573 | −0.420287 | − | 0.907391i | \(-0.638071\pi\) | ||||
−0.420287 | + | 0.907391i | \(0.638071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.58312 | 0.192522 | ||||||||
\(842\) | −30.5070 | + | 8.17431i | −1.05134 | + | 0.281705i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.28672 | + | 2.47494i | −0.147555 | + | 0.0851909i | ||||
\(845\) | 13.3494 | − | 20.6590i | 0.459232 | − | 0.710691i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.24941 | − | 1.33372i | 0.146011 | − | 0.0458270i | ||||
\(848\) | 1.15488 | − | 1.15488i | 0.0396588 | − | 0.0396588i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.6770 | − | 8.86832i | 0.674915 | − | 0.304181i | ||||
\(851\) | 10.3085 | − | 5.95163i | 0.353372 | − | 0.204019i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.6834 | + | 15.6834i | 0.536989 | + | 0.536989i | 0.922643 | − | 0.385655i | \(-0.126024\pi\) |
−0.385655 | + | 0.922643i | \(0.626024\pi\) | |||||||
\(854\) | 14.1067 | − | 8.96100i | 0.482721 | − | 0.306639i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.81662 | + | 11.8067i | −0.232987 | + | 0.403546i | ||||
\(857\) | 11.3061 | − | 42.1949i | 0.386209 | − | 1.44135i | −0.450044 | − | 0.893006i | \(-0.648592\pi\) |
0.836253 | − | 0.548344i | \(-0.184742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.1281 | − | 6.42481i | −0.379686 | − | 0.219212i | 0.297996 | − | 0.954567i | \(-0.403682\pi\) |
−0.677682 | + | 0.735355i | \(0.737015\pi\) | |||||||
\(860\) | −16.1926 | − | 17.9016i | −0.552162 | − | 0.610438i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.05013 | − | 9.05013i | 0.308249 | − | 0.308249i | ||||
\(863\) | 6.67740 | + | 24.9204i | 0.227301 | + | 0.848300i | 0.981469 | + | 0.191619i | \(0.0613737\pi\) |
−0.754168 | + | 0.656681i | \(0.771960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.6540 | − | 42.3505i | 0.464251 | − | 1.43996i | ||||
\(866\) | −7.40986 | − | 4.27808i | −0.251797 | − | 0.145375i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.37686 | − | 7.57301i | −0.0806759 | − | 0.257045i | ||||
\(869\) | 11.0898 | 0.376196 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.6332 | − | 18.4173i | −0.360294 | − | 0.624047i | ||||
\(872\) | −4.46890 | + | 16.6782i | −0.151336 | + | 0.564794i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 10.6332i | − | 0.359675i | ||||||
\(875\) | 23.0479 | − | 18.5417i | 0.779161 | − | 0.626824i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.35561 | + | 16.2554i | 0.147079 | + | 0.548904i | 0.999654 | + | 0.0263005i | \(0.00837268\pi\) |
−0.852576 | + | 0.522604i | \(0.824961\pi\) | |||||||
\(878\) | 4.42696 | + | 1.18620i | 0.149403 | + | 0.0400323i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.70422 | − | 5.73253i | 0.124869 | − | 0.193243i | ||||
\(881\) | 20.6945i | 0.697217i | 0.937268 | + | 0.348608i | \(0.113346\pi\) | ||||
−0.937268 | + | 0.348608i | \(0.886654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.68338 | + | 3.68338i | 0.123955 | + | 0.123955i | 0.766363 | − | 0.642408i | \(-0.222064\pi\) |
−0.642408 | + | 0.766363i | \(0.722064\pi\) | |||||||
\(884\) | 3.05231 | − | 5.28676i | 0.102660 | − | 0.177813i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9749 | − | 19.0091i | −0.368710 | − | 0.638625i | ||||
\(887\) | 0.917508 | − | 0.245846i | 0.0308069 | − | 0.00825469i | −0.243383 | − | 0.969930i | \(-0.578257\pi\) |
0.274190 | + | 0.961676i | \(0.411590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.9123 | − | 0.758564i | 0.600760 | − | 0.0254414i | ||||
\(890\) | 20.9893 | − | 18.9856i | 0.703563 | − | 0.636397i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.0727 | − | 5.91435i | −0.739047 | − | 0.198027i | ||||
\(893\) | −1.93185 | − | 0.517638i | −0.0646470 | − | 0.0173221i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.158312 | + | 3.15831i | −0.00529180 | + | 0.105571i | ||||
\(896\) | −1.22474 | + | 2.34521i | −0.0409159 | + | 0.0783479i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.6530 | − | 6.06984i | 0.755939 | − | 0.202553i | ||||
\(899\) | −8.82111 | − | 15.2786i | −0.294201 | − | 0.509570i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.52506 | − | 6.10559i | 0.117437 | − | 0.203407i | ||||
\(902\) | 6.10463 | + | 6.10463i | 0.203262 | + | 0.203262i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.00000i | − | 0.0665190i | ||||||
\(905\) | 46.2635 | + | 29.8944i | 1.53785 | + | 0.993723i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.7603 | + | 5.02681i | 0.622926 | + | 0.166912i | 0.556458 | − | 0.830876i | \(-0.312160\pi\) |
0.0664684 | + | 0.997789i | \(0.478827\pi\) | |||||||
\(908\) | −4.31798 | − | 16.1149i | −0.143297 | − | 0.534792i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.22808 | − | 8.06447i | 0.0738603 | − | 0.267334i | ||||
\(911\) | − | 6.48152i | − | 0.214742i | −0.994219 | − | 0.107371i | \(-0.965757\pi\) | ||
0.994219 | − | 0.107371i | \(-0.0342433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.69050 | − | 36.1654i | 0.320709 | − | 1.19690i | ||||
\(914\) | −16.7877 | − | 29.0772i | −0.555289 | − | 0.961788i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | −9.90678 | − | 31.5644i | −0.327151 | − | 1.04235i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.6853 | − | 9.63325i | −0.550397 | − | 0.317772i | 0.198885 | − | 0.980023i | \(-0.436268\pi\) |
−0.749282 | + | 0.662251i | \(0.769601\pi\) | |||||||
\(920\) | −1.71651 | − | 3.34998i | −0.0565918 | − | 0.110445i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.0183473 | + | 0.0684729i | 0.000604235 | + | 0.00225503i | ||||
\(923\) | −1.86199 | + | 1.86199i | −0.0612881 | + | 0.0612881i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.3747 | + | 22.3747i | −0.900074 | + | 0.735675i | ||||
\(926\) | 33.8437 | + | 19.5397i | 1.11217 | + | 0.642113i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.52205 | + | 5.68036i | −0.0499637 | + | 0.186467i | ||||
\(929\) | 14.1776 | − | 24.5563i | 0.465151 | − | 0.805666i | −0.534057 | − | 0.845448i | \(-0.679333\pi\) |
0.999208 | + | 0.0397827i | \(0.0126666\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.7916 | + | 40.0246i | −0.615869 | + | 1.31175i | ||||
\(932\) | −14.8138 | − | 14.8138i | −0.485242 | − | 0.485242i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.3706 | + | 19.2665i | −1.09192 | + | 0.630419i | ||||
\(935\) | 9.04038 | − | 28.0404i | 0.295652 | − | 0.917021i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.3747 | − | 33.3747i | 1.09030 | − | 1.09030i | 0.0948079 | − | 0.995496i | \(-0.469776\pi\) |
0.995496 | − | 0.0948079i | \(-0.0302237\pi\) | |||||||
\(938\) | 29.2981 | + | 26.9174i | 0.956616 | + | 0.878885i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.692186 | + | 0.148776i | −0.0225766 | + | 0.00485255i | ||||
\(941\) | 4.19452 | − | 2.42171i | 0.136737 | − | 0.0789454i | −0.430071 | − | 0.902795i | \(-0.641511\pi\) |
0.566808 | + | 0.823850i | \(0.308178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.59907 | − | 1.23232i | 0.149766 | − | 0.0401297i | ||||
\(944\) | −11.9854 | −0.390091 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.9499 | −1.07129 | ||||||||
\(947\) | 23.7939 | − | 6.37555i | 0.773198 | − | 0.207178i | 0.149414 | − | 0.988775i | \(-0.452261\pi\) |
0.623784 | + | 0.781597i | \(0.285595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.64774 | + | 2.68338i | −0.150872 | + | 0.0871060i | ||||
\(950\) | 5.08264 | + | 31.1715i | 0.164903 | + | 1.01134i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.48650 | + | 11.1468i | −0.0805879 | + | 0.361268i | ||||
\(953\) | −24.1237 | + | 24.1237i | −0.781445 | + | 0.781445i | −0.980075 | − | 0.198630i | \(-0.936351\pi\) |
0.198630 | + | 0.980075i | \(0.436351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.1019 | + | 41.1829i | 0.682842 | + | 1.33265i | ||||
\(956\) | 0.836960 | − | 0.483219i | 0.0270692 | − | 0.0156284i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.31662 | − | 7.31662i | −0.236389 | − | 0.236389i | ||||
\(959\) | 40.1988 | − | 25.5355i | 1.29809 | − | 0.824583i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | −2.58819 | + | 9.65926i | −0.0834466 | + | 0.311427i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.70115 | + | 3.29156i | 0.183622 | + | 0.106014i | ||||
\(965\) | −17.5303 | + | 15.8567i | −0.564320 | + | 0.510446i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6913 | − | 27.6913i | 0.890493 | − | 0.890493i | −0.104077 | − | 0.994569i | \(-0.533189\pi\) |
0.994569 | + | 0.104077i | \(0.0331888\pi\) | |||||||
\(968\) | 0.435690 | + | 1.62602i | 0.0140036 | + | 0.0522621i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.4405 | + | 8.42403i | −0.527872 | + | 0.270479i | ||||
\(971\) | 24.9538 | + | 14.4071i | 0.800805 | + | 0.462345i | 0.843753 | − | 0.536732i | \(-0.180341\pi\) |
−0.0429474 | + | 0.999077i | \(0.513675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.7470 | − | 25.8472i | 0.761294 | − | 0.828625i | ||||
\(974\) | −16.2280 | −0.519979 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.15831 | + | 5.47036i | 0.101095 | + | 0.175102i | ||||
\(977\) | 3.02388 | − | 11.2853i | 0.0967425 | − | 0.361048i | −0.900535 | − | 0.434783i | \(-0.856825\pi\) |
0.997278 | + | 0.0737348i | \(0.0234918\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 38.6332i | − | 1.23472i | ||||||
\(980\) | 0.540890 | + | 15.6431i | 0.0172781 | + | 0.499701i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.58396 | + | 13.3755i | 0.114369 | + | 0.426830i | ||||
\(983\) | −8.43591 | − | 2.26040i | −0.269064 | − | 0.0720954i | 0.121764 | − | 0.992559i | \(-0.461145\pi\) |
−0.390828 | + | 0.920464i | \(0.627811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1698 | − | 56.6205i | −0.387763 | − | 1.80408i | ||||
\(986\) | 25.3850i | 0.808422i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.31662 | + | 6.31662i | 0.200959 | + | 0.200959i | ||||
\(989\) | −9.08606 | + | 15.7375i | −0.288920 | + | 0.500424i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.65831 | − | 14.9966i | −0.275040 | − | 0.476384i | 0.695105 | − | 0.718908i | \(-0.255358\pi\) |
−0.970145 | + | 0.242524i | \(0.922025\pi\) | |||||||
\(992\) | 2.89778 | − | 0.776457i | 0.0920045 | − | 0.0246525i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.28046 | − | 4.36675i | 0.0723318 | − | 0.138505i | ||||
\(995\) | 10.3473 | + | 0.518663i | 0.328031 | + | 0.0164427i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.3607 | + | 3.04410i | 0.359798 | + | 0.0964075i | 0.434189 | − | 0.900822i | \(-0.357035\pi\) |
−0.0743918 | + | 0.997229i | \(0.523702\pi\) | |||||||
\(998\) | −21.2504 | − | 5.69402i | −0.672669 | − | 0.180241i | ||||
\(999\) | 0 | 0 |
(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 | 630.2.ce.b.233.4 | yes | 16 | |
3.2 | odd | 2 | inner | 630.2.ce.b.233.1 | yes | 16 | |
5.2 | odd | 4 | inner | 630.2.ce.b.107.4 | yes | 16 | |
7.4 | even | 3 | inner | 630.2.ce.b.53.1 | ✓ | 16 | |
15.2 | even | 4 | inner | 630.2.ce.b.107.1 | yes | 16 | |
21.11 | odd | 6 | inner | 630.2.ce.b.53.4 | yes | 16 | |
35.32 | odd | 12 | inner | 630.2.ce.b.557.1 | yes | 16 | |
105.32 | even | 12 | inner | 630.2.ce.b.557.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.ce.b.53.1 | ✓ | 16 | 7.4 | even | 3 | inner | |
630.2.ce.b.53.4 | yes | 16 | 21.11 | odd | 6 | inner | |
630.2.ce.b.107.1 | yes | 16 | 15.2 | even | 4 | inner | |
630.2.ce.b.107.4 | yes | 16 | 5.2 | odd | 4 | inner | |
630.2.ce.b.233.1 | yes | 16 | 3.2 | odd | 2 | inner | |
630.2.ce.b.233.4 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.ce.b.557.1 | yes | 16 | 35.32 | odd | 12 | inner | |
630.2.ce.b.557.4 | yes | 16 | 105.32 | even | 12 | inner |