Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1121,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.l (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.3 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1121 |
Dual form | 1155.2.l.a.1121.4 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.292893 | 0.146447 | − | 0.989219i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989219i | \(0.453216\pi\) | |||||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0.414214 | − | 0.585786i | 0.169102 | − | 0.239146i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 0.414214i | 0.130986i | ||||||||
\(11\) | 1.41421 | + | 3.00000i | 0.426401 | + | 0.904534i | ||||
\(12\) | −1.82843 | + | 2.58579i | −0.527821 | + | 0.746452i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0.414214i | 0.110703i | ||||||||
\(15\) | 1.41421 | + | 1.00000i | 0.365148 | + | 0.258199i | ||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 6.82843 | 1.65614 | 0.828068 | − | 0.560627i | \(-0.189440\pi\) | ||||
0.828068 | + | 0.560627i | \(0.189440\pi\) | |||||||
\(18\) | −0.414214 | − | 1.17157i | −0.0976311 | − | 0.276142i | ||||
\(19\) | − | 0.828427i | − | 0.190054i | −0.995475 | − | 0.0950271i | \(-0.969706\pi\) | ||
0.995475 | − | 0.0950271i | \(-0.0302938\pi\) | |||||||
\(20\) | − | 1.82843i | − | 0.408849i | ||||||
\(21\) | 1.41421 | + | 1.00000i | 0.308607 | + | 0.218218i | ||||
\(22\) | 0.585786 | + | 1.24264i | 0.124890 | + | 0.264932i | ||||
\(23\) | 0.828427i | 0.172739i | 0.996263 | + | 0.0863695i | \(0.0275266\pi\) | ||||
−0.996263 | + | 0.0863695i | \(0.972473\pi\) | |||||||
\(24\) | −1.58579 | + | 2.24264i | −0.323697 | + | 0.457777i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | − | 1.82843i | − | 0.345540i | ||||||
\(29\) | 5.65685 | 1.05045 | 0.525226 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525226 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(30\) | 0.585786 | + | 0.414214i | 0.106949 | + | 0.0756247i | ||||
\(31\) | 0.828427 | 0.148790 | 0.0743950 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743950 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(32\) | 4.41421 | 0.780330 | ||||||||
\(33\) | 5.65685 | + | 1.00000i | 0.984732 | + | 0.174078i | ||||
\(34\) | 2.82843 | 0.485071 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.82843 | + | 5.17157i | 0.304738 | + | 0.861929i | ||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | − | 0.343146i | − | 0.0556656i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1.58579i | − | 0.250735i | ||||||
\(41\) | 7.65685 | 1.19580 | 0.597900 | − | 0.801571i | \(-0.296002\pi\) | ||||
0.597900 | + | 0.801571i | \(0.296002\pi\) | |||||||
\(42\) | 0.585786 | + | 0.414214i | 0.0903888 | + | 0.0639145i | ||||
\(43\) | − | 9.65685i | − | 1.47266i | −0.676625 | − | 0.736328i | \(-0.736558\pi\) | ||
0.676625 | − | 0.736328i | \(-0.263442\pi\) | |||||||
\(44\) | −2.58579 | − | 5.48528i | −0.389822 | − | 0.826937i | ||||
\(45\) | 2.82843 | − | 1.00000i | 0.421637 | − | 0.149071i | ||||
\(46\) | 0.343146i | 0.0505941i | ||||||||
\(47\) | 10.8284i | 1.57949i | 0.613436 | + | 0.789744i | \(0.289787\pi\) | ||||
−0.613436 | + | 0.789744i | \(0.710213\pi\) | |||||||
\(48\) | 3.00000 | − | 4.24264i | 0.433013 | − | 0.612372i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.414214 | −0.0585786 | ||||||||
\(51\) | 6.82843 | − | 9.65685i | 0.956171 | − | 1.35223i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.828427i | 0.113793i | 0.998380 | + | 0.0568966i | \(0.0181205\pi\) | ||||
−0.998380 | + | 0.0568966i | \(0.981879\pi\) | |||||||
\(54\) | −2.07107 | − | 0.585786i | −0.281837 | − | 0.0797154i | ||||
\(55\) | −3.00000 | + | 1.41421i | −0.404520 | + | 0.190693i | ||||
\(56\) | − | 1.58579i | − | 0.211910i | ||||||
\(57\) | −1.17157 | − | 0.828427i | −0.155179 | − | 0.109728i | ||||
\(58\) | 2.34315 | 0.307670 | ||||||||
\(59\) | − | 0.343146i | − | 0.0446738i | −0.999751 | − | 0.0223369i | \(-0.992889\pi\) | ||
0.999751 | − | 0.0223369i | \(-0.00711064\pi\) | |||||||
\(60\) | −2.58579 | − | 1.82843i | −0.333824 | − | 0.236049i | ||||
\(61\) | 5.17157i | 0.662152i | 0.943604 | + | 0.331076i | \(0.107412\pi\) | ||||
−0.943604 | + | 0.331076i | \(0.892588\pi\) | |||||||
\(62\) | 0.343146 | 0.0435796 | ||||||||
\(63\) | 2.82843 | − | 1.00000i | 0.356348 | − | 0.125988i | ||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.34315 | + | 0.414214i | 0.288421 | + | 0.0509862i | ||||
\(67\) | −6.48528 | −0.792303 | −0.396152 | − | 0.918185i | \(-0.629655\pi\) | ||||
−0.396152 | + | 0.918185i | \(0.629655\pi\) | |||||||
\(68\) | −12.4853 | −1.51406 | ||||||||
\(69\) | 1.17157 | + | 0.828427i | 0.141041 | + | 0.0997309i | ||||
\(70\) | −0.414214 | −0.0495080 | ||||||||
\(71\) | 0.343146i | 0.0407239i | 0.999793 | + | 0.0203620i | \(0.00648186\pi\) | ||||
−0.999793 | + | 0.0203620i | \(0.993518\pi\) | |||||||
\(72\) | 1.58579 | + | 4.48528i | 0.186887 | + | 0.528595i | ||||
\(73\) | − | 12.0000i | − | 1.40449i | −0.711934 | − | 0.702247i | \(-0.752180\pi\) | ||
0.711934 | − | 0.702247i | \(-0.247820\pi\) | |||||||
\(74\) | 2.48528 | 0.288908 | ||||||||
\(75\) | −1.00000 | + | 1.41421i | −0.115470 | + | 0.163299i | ||||
\(76\) | 1.51472i | 0.173750i | ||||||||
\(77\) | −3.00000 | + | 1.41421i | −0.341882 | + | 0.161165i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 3.00000i | 0.335410i | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 3.17157 | 0.350242 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | −2.58579 | − | 1.82843i | −0.282132 | − | 0.199498i | ||||
\(85\) | 6.82843i | 0.740647i | ||||||||
\(86\) | − | 4.00000i | − | 0.431331i | ||||||
\(87\) | 5.65685 | − | 8.00000i | 0.606478 | − | 0.857690i | ||||
\(88\) | −2.24264 | − | 4.75736i | −0.239066 | − | 0.507136i | ||||
\(89\) | 7.65685i | 0.811625i | 0.913956 | + | 0.405812i | \(0.133011\pi\) | ||||
−0.913956 | + | 0.405812i | \(0.866989\pi\) | |||||||
\(90\) | 1.17157 | − | 0.414214i | 0.123495 | − | 0.0436619i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1.51472i | − | 0.157920i | ||||||
\(93\) | 0.828427 | − | 1.17157i | 0.0859039 | − | 0.121486i | ||||
\(94\) | 4.48528i | 0.462621i | ||||||||
\(95\) | 0.828427 | 0.0849948 | ||||||||
\(96\) | 4.41421 | − | 6.24264i | 0.450524 | − | 0.637137i | ||||
\(97\) | −5.17157 | −0.525094 | −0.262547 | − | 0.964919i | \(-0.584562\pi\) | ||||
−0.262547 | + | 0.964919i | \(0.584562\pi\) | |||||||
\(98\) | −0.414214 | −0.0418419 | ||||||||
\(99\) | 7.07107 | − | 7.00000i | 0.710669 | − | 0.703526i | ||||
\(100\) | 1.82843 | 0.182843 | ||||||||
\(101\) | −9.31371 | −0.926749 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(102\) | 2.82843 | − | 4.00000i | 0.280056 | − | 0.396059i | ||||
\(103\) | 9.31371 | 0.917707 | 0.458853 | − | 0.888512i | \(-0.348260\pi\) | ||||
0.458853 | + | 0.888512i | \(0.348260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | + | 1.41421i | −0.0975900 | + | 0.138013i | ||||
\(106\) | 0.343146i | 0.0333293i | ||||||||
\(107\) | 9.31371 | 0.900390 | 0.450195 | − | 0.892930i | \(-0.351354\pi\) | ||||
0.450195 | + | 0.892930i | \(0.351354\pi\) | |||||||
\(108\) | 9.14214 | + | 2.58579i | 0.879702 | + | 0.248817i | ||||
\(109\) | − | 9.65685i | − | 0.924959i | −0.886630 | − | 0.462479i | \(-0.846960\pi\) | ||
0.886630 | − | 0.462479i | \(-0.153040\pi\) | |||||||
\(110\) | −1.24264 | + | 0.585786i | −0.118481 | + | 0.0558525i | ||||
\(111\) | 6.00000 | − | 8.48528i | 0.569495 | − | 0.805387i | ||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | 3.17157i | 0.298356i | 0.988810 | + | 0.149178i | \(0.0476628\pi\) | ||||
−0.988810 | + | 0.149178i | \(0.952337\pi\) | |||||||
\(114\) | −0.485281 | − | 0.343146i | −0.0454508 | − | 0.0321385i | ||||
\(115\) | −0.828427 | −0.0772512 | ||||||||
\(116\) | −10.3431 | −0.960337 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 0.142136i | − | 0.0130846i | ||||||
\(119\) | 6.82843i | 0.625961i | ||||||||
\(120\) | −2.24264 | − | 1.58579i | −0.204724 | − | 0.144762i | ||||
\(121\) | −7.00000 | + | 8.48528i | −0.636364 | + | 0.771389i | ||||
\(122\) | 2.14214i | 0.193940i | ||||||||
\(123\) | 7.65685 | − | 10.8284i | 0.690395 | − | 0.976366i | ||||
\(124\) | −1.51472 | −0.136026 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 1.17157 | − | 0.414214i | 0.104372 | − | 0.0369011i | ||||
\(127\) | 13.6569i | 1.21185i | 0.795522 | + | 0.605925i | \(0.207197\pi\) | ||||
−0.795522 | + | 0.605925i | \(0.792803\pi\) | |||||||
\(128\) | −10.5563 | −0.933058 | ||||||||
\(129\) | −13.6569 | − | 9.65685i | −1.20242 | − | 0.850239i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6569 | −1.54269 | −0.771343 | − | 0.636419i | \(-0.780415\pi\) | ||||
−0.771343 | + | 0.636419i | \(0.780415\pi\) | |||||||
\(132\) | −10.3431 | − | 1.82843i | −0.900255 | − | 0.159144i | ||||
\(133\) | 0.828427 | 0.0718337 | ||||||||
\(134\) | −2.68629 | −0.232060 | ||||||||
\(135\) | 1.41421 | − | 5.00000i | 0.121716 | − | 0.430331i | ||||
\(136\) | −10.8284 | −0.928530 | ||||||||
\(137\) | − | 12.8284i | − | 1.09601i | −0.836476 | − | 0.548003i | \(-0.815388\pi\) | ||
0.836476 | − | 0.548003i | \(-0.184612\pi\) | |||||||
\(138\) | 0.485281 | + | 0.343146i | 0.0413099 | + | 0.0292105i | ||||
\(139\) | 6.48528i | 0.550074i | 0.961434 | + | 0.275037i | \(0.0886902\pi\) | ||||
−0.961434 | + | 0.275037i | \(0.911310\pi\) | |||||||
\(140\) | 1.82843 | 0.154530 | ||||||||
\(141\) | 15.3137 | + | 10.8284i | 1.28965 | + | 0.911918i | ||||
\(142\) | 0.142136i | 0.0119278i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.00000 | − | 8.48528i | −0.250000 | − | 0.707107i | ||||
\(145\) | 5.65685i | 0.469776i | ||||||||
\(146\) | − | 4.97056i | − | 0.411367i | ||||||
\(147\) | −1.00000 | + | 1.41421i | −0.0824786 | + | 0.116642i | ||||
\(148\) | −10.9706 | −0.901775 | ||||||||
\(149\) | 7.31371 | 0.599162 | 0.299581 | − | 0.954071i | \(-0.403153\pi\) | ||||
0.299581 | + | 0.954071i | \(0.403153\pi\) | |||||||
\(150\) | −0.414214 | + | 0.585786i | −0.0338204 | + | 0.0478293i | ||||
\(151\) | − | 3.31371i | − | 0.269666i | −0.990868 | − | 0.134833i | \(-0.956950\pi\) | ||
0.990868 | − | 0.134833i | \(-0.0430498\pi\) | |||||||
\(152\) | 1.31371i | 0.106556i | ||||||||
\(153\) | −6.82843 | − | 19.3137i | −0.552046 | − | 1.56142i | ||||
\(154\) | −1.24264 | + | 0.585786i | −0.100135 | + | 0.0472040i | ||||
\(155\) | 0.828427i | 0.0665409i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.8284 | −1.50267 | −0.751336 | − | 0.659920i | \(-0.770590\pi\) | ||||
−0.751336 | + | 0.659920i | \(0.770590\pi\) | |||||||
\(158\) | 1.65685i | 0.131812i | ||||||||
\(159\) | 1.17157 | + | 0.828427i | 0.0929118 | + | 0.0656985i | ||||
\(160\) | 4.41421i | 0.348974i | ||||||||
\(161\) | −0.828427 | −0.0652892 | ||||||||
\(162\) | −2.89949 | + | 2.34315i | −0.227806 | + | 0.184095i | ||||
\(163\) | −1.51472 | −0.118642 | −0.0593210 | − | 0.998239i | \(-0.518894\pi\) | ||||
−0.0593210 | + | 0.998239i | \(0.518894\pi\) | |||||||
\(164\) | −14.0000 | −1.09322 | ||||||||
\(165\) | −1.00000 | + | 5.65685i | −0.0778499 | + | 0.440386i | ||||
\(166\) | 4.97056 | 0.385790 | ||||||||
\(167\) | −2.34315 | −0.181318 | −0.0906590 | − | 0.995882i | \(-0.528897\pi\) | ||||
−0.0906590 | + | 0.995882i | \(0.528897\pi\) | |||||||
\(168\) | −2.24264 | − | 1.58579i | −0.173023 | − | 0.122346i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 2.82843i | 0.216930i | ||||||||
\(171\) | −2.34315 | + | 0.828427i | −0.179185 | + | 0.0633514i | ||||
\(172\) | 17.6569i | 1.34632i | ||||||||
\(173\) | 10.1421 | 0.771092 | 0.385546 | − | 0.922689i | \(-0.374013\pi\) | ||||
0.385546 | + | 0.922689i | \(0.374013\pi\) | |||||||
\(174\) | 2.34315 | − | 3.31371i | 0.177633 | − | 0.251212i | ||||
\(175\) | − | 1.00000i | − | 0.0755929i | ||||||
\(176\) | 4.24264 | + | 9.00000i | 0.319801 | + | 0.678401i | ||||
\(177\) | −0.485281 | − | 0.343146i | −0.0364760 | − | 0.0257924i | ||||
\(178\) | 3.17157i | 0.237719i | ||||||||
\(179\) | − | 11.6569i | − | 0.871274i | −0.900122 | − | 0.435637i | \(-0.856523\pi\) | ||
0.900122 | − | 0.435637i | \(-0.143477\pi\) | |||||||
\(180\) | −5.17157 | + | 1.82843i | −0.385466 | + | 0.136283i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.31371 | + | 5.17157i | 0.540645 | + | 0.382294i | ||||
\(184\) | − | 1.31371i | − | 0.0968479i | ||||||
\(185\) | 6.00000i | 0.441129i | ||||||||
\(186\) | 0.343146 | − | 0.485281i | 0.0251607 | − | 0.0355826i | ||||
\(187\) | 9.65685 | + | 20.4853i | 0.706179 | + | 1.49803i | ||||
\(188\) | − | 19.7990i | − | 1.44399i | ||||||
\(189\) | 1.41421 | − | 5.00000i | 0.102869 | − | 0.363696i | ||||
\(190\) | 0.343146 | 0.0248944 | ||||||||
\(191\) | 6.00000i | 0.434145i | 0.976156 | + | 0.217072i | \(0.0696508\pi\) | ||||
−0.976156 | + | 0.217072i | \(0.930349\pi\) | |||||||
\(192\) | −4.17157 | + | 5.89949i | −0.301057 | + | 0.425759i | ||||
\(193\) | 22.4853i | 1.61853i | 0.587447 | + | 0.809263i | \(0.300133\pi\) | ||||
−0.587447 | + | 0.809263i | \(0.699867\pi\) | |||||||
\(194\) | −2.14214 | −0.153796 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.82843 | 0.130602 | ||||||||
\(197\) | 14.8284 | 1.05648 | 0.528241 | − | 0.849095i | \(-0.322852\pi\) | ||||
0.528241 | + | 0.849095i | \(0.322852\pi\) | |||||||
\(198\) | 2.92893 | − | 2.89949i | 0.208150 | − | 0.206058i | ||||
\(199\) | −14.4853 | −1.02683 | −0.513417 | − | 0.858139i | \(-0.671621\pi\) | ||||
−0.513417 | + | 0.858139i | \(0.671621\pi\) | |||||||
\(200\) | 1.58579 | 0.112132 | ||||||||
\(201\) | −6.48528 | + | 9.17157i | −0.457436 | + | 0.646913i | ||||
\(202\) | −3.85786 | −0.271438 | ||||||||
\(203\) | 5.65685i | 0.397033i | ||||||||
\(204\) | −12.4853 | + | 17.6569i | −0.874145 | + | 1.23623i | ||||
\(205\) | 7.65685i | 0.534778i | ||||||||
\(206\) | 3.85786 | 0.268790 | ||||||||
\(207\) | 2.34315 | − | 0.828427i | 0.162860 | − | 0.0575797i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.48528 | − | 1.17157i | 0.171911 | − | 0.0810394i | ||||
\(210\) | −0.414214 | + | 0.585786i | −0.0285835 | + | 0.0404231i | ||||
\(211\) | 16.9706i | 1.16830i | 0.811645 | + | 0.584151i | \(0.198572\pi\) | ||||
−0.811645 | + | 0.584151i | \(0.801428\pi\) | |||||||
\(212\) | − | 1.51472i | − | 0.104031i | ||||||
\(213\) | 0.485281 | + | 0.343146i | 0.0332509 | + | 0.0235120i | ||||
\(214\) | 3.85786 | 0.263718 | ||||||||
\(215\) | 9.65685 | 0.658592 | ||||||||
\(216\) | 7.92893 | + | 2.24264i | 0.539496 | + | 0.152592i | ||||
\(217\) | 0.828427i | 0.0562373i | ||||||||
\(218\) | − | 4.00000i | − | 0.270914i | ||||||
\(219\) | −16.9706 | − | 12.0000i | −1.14676 | − | 0.810885i | ||||
\(220\) | 5.48528 | − | 2.58579i | 0.369818 | − | 0.174334i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.48528 | − | 3.51472i | 0.166801 | − | 0.235892i | ||||
\(223\) | −14.9706 | −1.00250 | −0.501252 | − | 0.865302i | \(-0.667127\pi\) | ||||
−0.501252 | + | 0.865302i | \(0.667127\pi\) | |||||||
\(224\) | 4.41421i | 0.294937i | ||||||||
\(225\) | 1.00000 | + | 2.82843i | 0.0666667 | + | 0.188562i | ||||
\(226\) | 1.31371i | 0.0873866i | ||||||||
\(227\) | 14.3431 | 0.951988 | 0.475994 | − | 0.879449i | \(-0.342088\pi\) | ||||
0.475994 | + | 0.879449i | \(0.342088\pi\) | |||||||
\(228\) | 2.14214 | + | 1.51472i | 0.141866 | + | 0.100315i | ||||
\(229\) | −9.31371 | −0.615467 | −0.307734 | − | 0.951473i | \(-0.599571\pi\) | ||||
−0.307734 | + | 0.951473i | \(0.599571\pi\) | |||||||
\(230\) | −0.343146 | −0.0226264 | ||||||||
\(231\) | −1.00000 | + | 5.65685i | −0.0657952 | + | 0.372194i | ||||
\(232\) | −8.97056 | −0.588946 | ||||||||
\(233\) | −11.7990 | −0.772978 | −0.386489 | − | 0.922294i | \(-0.626312\pi\) | ||||
−0.386489 | + | 0.922294i | \(0.626312\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.8284 | −0.706369 | ||||||||
\(236\) | 0.627417i | 0.0408414i | ||||||||
\(237\) | 5.65685 | + | 4.00000i | 0.367452 | + | 0.259828i | ||||
\(238\) | 2.82843i | 0.183340i | ||||||||
\(239\) | −2.82843 | −0.182956 | −0.0914779 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914779 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(240\) | 4.24264 | + | 3.00000i | 0.273861 | + | 0.193649i | ||||
\(241\) | − | 22.8284i | − | 1.47051i | −0.677792 | − | 0.735254i | \(-0.737063\pi\) | ||
0.677792 | − | 0.735254i | \(-0.262937\pi\) | |||||||
\(242\) | −2.89949 | + | 3.51472i | −0.186387 | + | 0.225935i | ||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | − | 9.45584i | − | 0.605348i | ||||||
\(245\) | − | 1.00000i | − | 0.0638877i | ||||||
\(246\) | 3.17157 | − | 4.48528i | 0.202212 | − | 0.285971i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.31371 | −0.0834206 | ||||||||
\(249\) | 12.0000 | − | 16.9706i | 0.760469 | − | 1.07547i | ||||
\(250\) | − | 0.414214i | − | 0.0261972i | ||||||
\(251\) | − | 20.6274i | − | 1.30199i | −0.759082 | − | 0.650996i | \(-0.774352\pi\) | ||
0.759082 | − | 0.650996i | \(-0.225648\pi\) | |||||||
\(252\) | −5.17157 | + | 1.82843i | −0.325778 | + | 0.115180i | ||||
\(253\) | −2.48528 | + | 1.17157i | −0.156248 | + | 0.0736562i | ||||
\(254\) | 5.65685i | 0.354943i | ||||||||
\(255\) | 9.65685 | + | 6.82843i | 0.604736 | + | 0.427613i | ||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | − | 13.3137i | − | 0.830486i | −0.909710 | − | 0.415243i | \(-0.863696\pi\) | ||
0.909710 | − | 0.415243i | \(-0.136304\pi\) | |||||||
\(258\) | −5.65685 | − | 4.00000i | −0.352180 | − | 0.249029i | ||||
\(259\) | 6.00000i | 0.372822i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.65685 | − | 16.0000i | −0.350150 | − | 0.990375i | ||||
\(262\) | −7.31371 | −0.451842 | ||||||||
\(263\) | −17.3137 | −1.06761 | −0.533805 | − | 0.845608i | \(-0.679238\pi\) | ||||
−0.533805 | + | 0.845608i | \(0.679238\pi\) | |||||||
\(264\) | −8.97056 | − | 1.58579i | −0.552100 | − | 0.0975984i | ||||
\(265\) | −0.828427 | −0.0508899 | ||||||||
\(266\) | 0.343146 | 0.0210396 | ||||||||
\(267\) | 10.8284 | + | 7.65685i | 0.662689 | + | 0.468592i | ||||
\(268\) | 11.8579 | 0.724334 | ||||||||
\(269\) | − | 17.3137i | − | 1.05564i | −0.849358 | − | 0.527818i | \(-0.823010\pi\) | ||
0.849358 | − | 0.527818i | \(-0.176990\pi\) | |||||||
\(270\) | 0.585786 | − | 2.07107i | 0.0356498 | − | 0.126041i | ||||
\(271\) | − | 2.48528i | − | 0.150970i | −0.997147 | − | 0.0754850i | \(-0.975949\pi\) | ||
0.997147 | − | 0.0754850i | \(-0.0240505\pi\) | |||||||
\(272\) | 20.4853 | 1.24210 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.31371i | − | 0.321013i | ||||||
\(275\) | −1.41421 | − | 3.00000i | −0.0852803 | − | 0.180907i | ||||
\(276\) | −2.14214 | − | 1.51472i | −0.128941 | − | 0.0911753i | ||||
\(277\) | 4.82843i | 0.290112i | 0.989423 | + | 0.145056i | \(0.0463362\pi\) | ||||
−0.989423 | + | 0.145056i | \(0.953664\pi\) | |||||||
\(278\) | 2.68629i | 0.161113i | ||||||||
\(279\) | −0.828427 | − | 2.34315i | −0.0495966 | − | 0.140280i | ||||
\(280\) | 1.58579 | 0.0947689 | ||||||||
\(281\) | −28.9706 | −1.72824 | −0.864119 | − | 0.503287i | \(-0.832124\pi\) | ||||
−0.864119 | + | 0.503287i | \(0.832124\pi\) | |||||||
\(282\) | 6.34315 | + | 4.48528i | 0.377729 | + | 0.267095i | ||||
\(283\) | 28.9706i | 1.72212i | 0.508502 | + | 0.861061i | \(0.330199\pi\) | ||||
−0.508502 | + | 0.861061i | \(0.669801\pi\) | |||||||
\(284\) | − | 0.627417i | − | 0.0372303i | ||||||
\(285\) | 0.828427 | − | 1.17157i | 0.0490718 | − | 0.0693980i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.65685i | 0.451970i | ||||||||
\(288\) | −4.41421 | − | 12.4853i | −0.260110 | − | 0.735702i | ||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | 2.34315i | 0.137594i | ||||||||
\(291\) | −5.17157 | + | 7.31371i | −0.303163 | + | 0.428737i | ||||
\(292\) | 21.9411i | 1.28401i | ||||||||
\(293\) | −18.8284 | −1.09997 | −0.549984 | − | 0.835175i | \(-0.685366\pi\) | ||||
−0.549984 | + | 0.835175i | \(0.685366\pi\) | |||||||
\(294\) | −0.414214 | + | 0.585786i | −0.0241574 | + | 0.0341638i | ||||
\(295\) | 0.343146 | 0.0199787 | ||||||||
\(296\) | −9.51472 | −0.553032 | ||||||||
\(297\) | −2.82843 | − | 17.0000i | −0.164122 | − | 0.986440i | ||||
\(298\) | 3.02944 | 0.175491 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.82843 | − | 2.58579i | 0.105564 | − | 0.149290i | ||||
\(301\) | 9.65685 | 0.556612 | ||||||||
\(302\) | − | 1.37258i | − | 0.0789833i | ||||||
\(303\) | −9.31371 | + | 13.1716i | −0.535059 | + | 0.756687i | ||||
\(304\) | − | 2.48528i | − | 0.142541i | ||||||
\(305\) | −5.17157 | −0.296123 | ||||||||
\(306\) | −2.82843 | − | 8.00000i | −0.161690 | − | 0.457330i | ||||
\(307\) | − | 8.97056i | − | 0.511977i | −0.966680 | − | 0.255989i | \(-0.917599\pi\) | ||
0.966680 | − | 0.255989i | \(-0.0824009\pi\) | |||||||
\(308\) | 5.48528 | − | 2.58579i | 0.312553 | − | 0.147339i | ||||
\(309\) | 9.31371 | − | 13.1716i | 0.529838 | − | 0.749305i | ||||
\(310\) | 0.343146i | 0.0194894i | ||||||||
\(311\) | − | 24.6274i | − | 1.39649i | −0.715858 | − | 0.698246i | \(-0.753964\pi\) | ||
0.715858 | − | 0.698246i | \(-0.246036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1716 | 0.744501 | 0.372251 | − | 0.928132i | \(-0.378586\pi\) | ||||
0.372251 | + | 0.928132i | \(0.378586\pi\) | |||||||
\(314\) | −7.79899 | −0.440122 | ||||||||
\(315\) | 1.00000 | + | 2.82843i | 0.0563436 | + | 0.159364i | ||||
\(316\) | − | 7.31371i | − | 0.411428i | ||||||
\(317\) | 28.8284i | 1.61917i | 0.587006 | + | 0.809583i | \(0.300307\pi\) | ||||
−0.587006 | + | 0.809583i | \(0.699693\pi\) | |||||||
\(318\) | 0.485281 | + | 0.343146i | 0.0272132 | + | 0.0192427i | ||||
\(319\) | 8.00000 | + | 16.9706i | 0.447914 | + | 0.950169i | ||||
\(320\) | − | 4.17157i | − | 0.233198i | ||||||
\(321\) | 9.31371 | − | 13.1716i | 0.519841 | − | 0.735166i | ||||
\(322\) | −0.343146 | −0.0191228 | ||||||||
\(323\) | − | 5.65685i | − | 0.314756i | ||||||
\(324\) | 12.7990 | − | 10.3431i | 0.711055 | − | 0.574619i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.627417 | −0.0347494 | ||||||||
\(327\) | −13.6569 | − | 9.65685i | −0.755226 | − | 0.534025i | ||||
\(328\) | −12.1421 | −0.670437 | ||||||||
\(329\) | −10.8284 | −0.596991 | ||||||||
\(330\) | −0.414214 | + | 2.34315i | −0.0228017 | + | 0.128986i | ||||
\(331\) | −10.3431 | −0.568511 | −0.284255 | − | 0.958749i | \(-0.591746\pi\) | ||||
−0.284255 | + | 0.958749i | \(0.591746\pi\) | |||||||
\(332\) | −21.9411 | −1.20418 | ||||||||
\(333\) | −6.00000 | − | 16.9706i | −0.328798 | − | 0.929981i | ||||
\(334\) | −0.970563 | −0.0531068 | ||||||||
\(335\) | − | 6.48528i | − | 0.354329i | ||||||
\(336\) | 4.24264 | + | 3.00000i | 0.231455 | + | 0.163663i | ||||
\(337\) | − | 2.48528i | − | 0.135382i | −0.997706 | − | 0.0676910i | \(-0.978437\pi\) | ||
0.997706 | − | 0.0676910i | \(-0.0215632\pi\) | |||||||
\(338\) | 5.38478 | 0.292893 | ||||||||
\(339\) | 4.48528 | + | 3.17157i | 0.243607 | + | 0.172256i | ||||
\(340\) | − | 12.4853i | − | 0.677109i | ||||||
\(341\) | 1.17157 | + | 2.48528i | 0.0634442 | + | 0.134586i | ||||
\(342\) | −0.970563 | + | 0.343146i | −0.0524820 | + | 0.0185552i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 15.3137i | 0.825660i | ||||||||
\(345\) | −0.828427 | + | 1.17157i | −0.0446010 | + | 0.0630754i | ||||
\(346\) | 4.20101 | 0.225848 | ||||||||
\(347\) | 12.3431 | 0.662615 | 0.331307 | − | 0.943523i | \(-0.392510\pi\) | ||||
0.331307 | + | 0.943523i | \(0.392510\pi\) | |||||||
\(348\) | −10.3431 | + | 14.6274i | −0.554451 | + | 0.784112i | ||||
\(349\) | − | 32.4853i | − | 1.73890i | −0.494023 | − | 0.869449i | \(-0.664474\pi\) | ||
0.494023 | − | 0.869449i | \(-0.335526\pi\) | |||||||
\(350\) | − | 0.414214i | − | 0.0221406i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.24264 | + | 13.2426i | 0.332734 | + | 0.705835i | ||||
\(353\) | 0.343146i | 0.0182638i | 0.999958 | + | 0.00913190i | \(0.00290682\pi\) | ||||
−0.999958 | + | 0.00913190i | \(0.997093\pi\) | |||||||
\(354\) | −0.201010 | − | 0.142136i | −0.0106836 | − | 0.00755442i | ||||
\(355\) | −0.343146 | −0.0182123 | ||||||||
\(356\) | − | 14.0000i | − | 0.741999i | ||||||
\(357\) | 9.65685 | + | 6.82843i | 0.511095 | + | 0.361399i | ||||
\(358\) | − | 4.82843i | − | 0.255190i | ||||||
\(359\) | 8.48528 | 0.447836 | 0.223918 | − | 0.974608i | \(-0.428115\pi\) | ||||
0.223918 | + | 0.974608i | \(0.428115\pi\) | |||||||
\(360\) | −4.48528 | + | 1.58579i | −0.236395 | + | 0.0835783i | ||||
\(361\) | 18.3137 | 0.963879 | ||||||||
\(362\) | −0.828427 | −0.0435412 | ||||||||
\(363\) | 5.00000 | + | 18.3848i | 0.262432 | + | 0.964951i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | 0.628109 | ||||||||
\(366\) | 3.02944 | + | 2.14214i | 0.158351 | + | 0.111971i | ||||
\(367\) | −18.0000 | −0.939592 | −0.469796 | − | 0.882775i | \(-0.655673\pi\) | ||||
−0.469796 | + | 0.882775i | \(0.655673\pi\) | |||||||
\(368\) | 2.48528i | 0.129554i | ||||||||
\(369\) | −7.65685 | − | 21.6569i | −0.398600 | − | 1.12741i | ||||
\(370\) | 2.48528i | 0.129204i | ||||||||
\(371\) | −0.828427 | −0.0430098 | ||||||||
\(372\) | −1.51472 | + | 2.14214i | −0.0785345 | + | 0.111065i | ||||
\(373\) | 4.14214i | 0.214472i | 0.994234 | + | 0.107236i | \(0.0342000\pi\) | ||||
−0.994234 | + | 0.107236i | \(0.965800\pi\) | |||||||
\(374\) | 4.00000 | + | 8.48528i | 0.206835 | + | 0.438763i | ||||
\(375\) | −1.41421 | − | 1.00000i | −0.0730297 | − | 0.0516398i | ||||
\(376\) | − | 17.1716i | − | 0.885556i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.585786 | − | 2.07107i | 0.0301296 | − | 0.106524i | ||||
\(379\) | −37.9411 | −1.94890 | −0.974452 | − | 0.224594i | \(-0.927894\pi\) | ||||
−0.974452 | + | 0.224594i | \(0.927894\pi\) | |||||||
\(380\) | −1.51472 | −0.0777034 | ||||||||
\(381\) | 19.3137 | + | 13.6569i | 0.989471 | + | 0.699662i | ||||
\(382\) | 2.48528i | 0.127158i | ||||||||
\(383\) | − | 23.7990i | − | 1.21607i | −0.793910 | − | 0.608036i | \(-0.791958\pi\) | ||
0.793910 | − | 0.608036i | \(-0.208042\pi\) | |||||||
\(384\) | −10.5563 | + | 14.9289i | −0.538701 | + | 0.761839i | ||||
\(385\) | −1.41421 | − | 3.00000i | −0.0720750 | − | 0.152894i | ||||
\(386\) | 9.31371i | 0.474055i | ||||||||
\(387\) | −27.3137 | + | 9.65685i | −1.38843 | + | 0.490885i | ||||
\(388\) | 9.45584 | 0.480048 | ||||||||
\(389\) | − | 10.6274i | − | 0.538831i | −0.963024 | − | 0.269416i | \(-0.913169\pi\) | ||
0.963024 | − | 0.269416i | \(-0.0868306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.65685i | 0.286079i | ||||||||
\(392\) | 1.58579 | 0.0800943 | ||||||||
\(393\) | −17.6569 | + | 24.9706i | −0.890670 | + | 1.25960i | ||||
\(394\) | 6.14214 | 0.309436 | ||||||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | −12.9289 | + | 12.7990i | −0.649703 | + | 0.643173i | ||||
\(397\) | 20.4853 | 1.02813 | 0.514063 | − | 0.857752i | \(-0.328140\pi\) | ||||
0.514063 | + | 0.857752i | \(0.328140\pi\) | |||||||
\(398\) | −6.00000 | −0.300753 | ||||||||
\(399\) | 0.828427 | − | 1.17157i | 0.0414732 | − | 0.0586520i | ||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | 4.68629i | 0.234022i | 0.993131 | + | 0.117011i | \(0.0373313\pi\) | ||||
−0.993131 | + | 0.117011i | \(0.962669\pi\) | |||||||
\(402\) | −2.68629 | + | 3.79899i | −0.133980 | + | 0.189476i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 17.0294 | 0.847246 | ||||||||
\(405\) | −5.65685 | − | 7.00000i | −0.281091 | − | 0.347833i | ||||
\(406\) | 2.34315i | 0.116288i | ||||||||
\(407\) | 8.48528 | + | 18.0000i | 0.420600 | + | 0.892227i | ||||
\(408\) | −10.8284 | + | 15.3137i | −0.536087 | + | 0.758142i | ||||
\(409\) | − | 37.4558i | − | 1.85207i | −0.377435 | − | 0.926036i | \(-0.623194\pi\) | ||
0.377435 | − | 0.926036i | \(-0.376806\pi\) | |||||||
\(410\) | 3.17157i | 0.156633i | ||||||||
\(411\) | −18.1421 | − | 12.8284i | −0.894886 | − | 0.632780i | ||||
\(412\) | −17.0294 | −0.838980 | ||||||||
\(413\) | 0.343146 | 0.0168851 | ||||||||
\(414\) | 0.970563 | − | 0.343146i | 0.0477006 | − | 0.0168647i | ||||
\(415\) | 12.0000i | 0.589057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.17157 | + | 6.48528i | 0.449134 | + | 0.317586i | ||||
\(418\) | 1.02944 | − | 0.485281i | 0.0503514 | − | 0.0237359i | ||||
\(419\) | − | 25.3137i | − | 1.23666i | −0.785920 | − | 0.618328i | \(-0.787810\pi\) | ||
0.785920 | − | 0.618328i | \(-0.212190\pi\) | |||||||
\(420\) | 1.82843 | − | 2.58579i | 0.0892181 | − | 0.126173i | ||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 7.02944i | 0.342188i | ||||||||
\(423\) | 30.6274 | − | 10.8284i | 1.48916 | − | 0.526496i | ||||
\(424\) | − | 1.31371i | − | 0.0637993i | ||||||
\(425\) | −6.82843 | −0.331227 | ||||||||
\(426\) | 0.201010 | + | 0.142136i | 0.00973897 | + | 0.00688649i | ||||
\(427\) | −5.17157 | −0.250270 | ||||||||
\(428\) | −17.0294 | −0.823149 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −18.1421 | −0.873876 | −0.436938 | − | 0.899492i | \(-0.643937\pi\) | ||||
−0.436938 | + | 0.899492i | \(0.643937\pi\) | |||||||
\(432\) | −15.0000 | − | 4.24264i | −0.721688 | − | 0.204124i | ||||
\(433\) | −34.8284 | −1.67375 | −0.836874 | − | 0.547396i | \(-0.815619\pi\) | ||||
−0.836874 | + | 0.547396i | \(0.815619\pi\) | |||||||
\(434\) | 0.343146i | 0.0164715i | ||||||||
\(435\) | 8.00000 | + | 5.65685i | 0.383571 | + | 0.271225i | ||||
\(436\) | 17.6569i | 0.845610i | ||||||||
\(437\) | 0.686292 | 0.0328298 | ||||||||
\(438\) | −7.02944 | − | 4.97056i | −0.335880 | − | 0.237503i | ||||
\(439\) | − | 19.4558i | − | 0.928577i | −0.885684 | − | 0.464288i | \(-0.846310\pi\) | ||
0.885684 | − | 0.464288i | \(-0.153690\pi\) | |||||||
\(440\) | 4.75736 | − | 2.24264i | 0.226798 | − | 0.106914i | ||||
\(441\) | 1.00000 | + | 2.82843i | 0.0476190 | + | 0.134687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.7990i | 1.79588i | 0.440114 | + | 0.897942i | \(0.354938\pi\) | ||||
−0.440114 | + | 0.897942i | \(0.645062\pi\) | |||||||
\(444\) | −10.9706 | + | 15.5147i | −0.520640 | + | 0.736296i | ||||
\(445\) | −7.65685 | −0.362970 | ||||||||
\(446\) | −6.20101 | −0.293626 | ||||||||
\(447\) | 7.31371 | − | 10.3431i | 0.345927 | − | 0.489214i | ||||
\(448\) | − | 4.17157i | − | 0.197088i | ||||||
\(449\) | 6.34315i | 0.299352i | 0.988735 | + | 0.149676i | \(0.0478230\pi\) | ||||
−0.988735 | + | 0.149676i | \(0.952177\pi\) | |||||||
\(450\) | 0.414214 | + | 1.17157i | 0.0195262 | + | 0.0552285i | ||||
\(451\) | 10.8284 | + | 22.9706i | 0.509891 | + | 1.08164i | ||||
\(452\) | − | 5.79899i | − | 0.272762i | ||||||
\(453\) | −4.68629 | − | 3.31371i | −0.220181 | − | 0.155692i | ||||
\(454\) | 5.94113 | 0.278831 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.85786 | + | 1.31371i | 0.0870025 | + | 0.0615200i | ||||
\(457\) | − | 26.4853i | − | 1.23893i | −0.785025 | − | 0.619465i | \(-0.787350\pi\) | ||
0.785025 | − | 0.619465i | \(-0.212650\pi\) | |||||||
\(458\) | −3.85786 | −0.180266 | ||||||||
\(459\) | −34.1421 | − | 9.65685i | −1.59362 | − | 0.450743i | ||||
\(460\) | 1.51472 | 0.0706241 | ||||||||
\(461\) | −12.3431 | −0.574878 | −0.287439 | − | 0.957799i | \(-0.592804\pi\) | ||||
−0.287439 | + | 0.957799i | \(0.592804\pi\) | |||||||
\(462\) | −0.414214 | + | 2.34315i | −0.0192710 | + | 0.109013i | ||||
\(463\) | −39.4558 | −1.83367 | −0.916834 | − | 0.399268i | \(-0.869264\pi\) | ||||
−0.916834 | + | 0.399268i | \(0.869264\pi\) | |||||||
\(464\) | 16.9706 | 0.787839 | ||||||||
\(465\) | 1.17157 | + | 0.828427i | 0.0543304 | + | 0.0384174i | ||||
\(466\) | −4.88730 | −0.226400 | ||||||||
\(467\) | 1.17157i | 0.0542139i | 0.999633 | + | 0.0271070i | \(0.00862947\pi\) | ||||
−0.999633 | + | 0.0271070i | \(0.991371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.48528i | − | 0.299462i | ||||||
\(470\) | −4.48528 | −0.206891 | ||||||||
\(471\) | −18.8284 | + | 26.6274i | −0.867568 | + | 1.22693i | ||||
\(472\) | 0.544156i | 0.0250468i | ||||||||
\(473\) | 28.9706 | − | 13.6569i | 1.33207 | − | 0.627943i | ||||
\(474\) | 2.34315 | + | 1.65685i | 0.107624 | + | 0.0761018i | ||||
\(475\) | 0.828427i | 0.0380108i | ||||||||
\(476\) | − | 12.4853i | − | 0.572262i | ||||||
\(477\) | 2.34315 | − | 0.828427i | 0.107285 | − | 0.0379311i | ||||
\(478\) | −1.17157 | −0.0535865 | ||||||||
\(479\) | 11.3137 | 0.516937 | 0.258468 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258468 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(480\) | 6.24264 | + | 4.41421i | 0.284936 | + | 0.201480i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 9.45584i | − | 0.430702i | ||||||
\(483\) | −0.828427 | + | 1.17157i | −0.0376947 | + | 0.0533084i | ||||
\(484\) | 12.7990 | − | 15.5147i | 0.581772 | − | 0.705214i | ||||
\(485\) | − | 5.17157i | − | 0.234829i | ||||||
\(486\) | 0.414214 | + | 6.44365i | 0.0187891 | + | 0.292290i | ||||
\(487\) | 26.4853 | 1.20016 | 0.600081 | − | 0.799939i | \(-0.295135\pi\) | ||||
0.600081 | + | 0.799939i | \(0.295135\pi\) | |||||||
\(488\) | − | 8.20101i | − | 0.371242i | ||||||
\(489\) | −1.51472 | + | 2.14214i | −0.0684979 | + | 0.0968707i | ||||
\(490\) | − | 0.414214i | − | 0.0187123i | ||||||
\(491\) | −18.1421 | −0.818743 | −0.409372 | − | 0.912368i | \(-0.634252\pi\) | ||||
−0.409372 | + | 0.912368i | \(0.634252\pi\) | |||||||
\(492\) | −14.0000 | + | 19.7990i | −0.631169 | + | 0.892607i | ||||
\(493\) | 38.6274 | 1.73969 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.00000 | + | 7.07107i | 0.314627 | + | 0.317821i | ||||
\(496\) | 2.48528 | 0.111592 | ||||||||
\(497\) | −0.343146 | −0.0153922 | ||||||||
\(498\) | 4.97056 | − | 7.02944i | 0.222736 | − | 0.314997i | ||||
\(499\) | 36.0000 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(500\) | 1.82843i | 0.0817697i | ||||||||
\(501\) | −2.34315 | + | 3.31371i | −0.104684 | + | 0.148046i | ||||
\(502\) | − | 8.54416i | − | 0.381344i | ||||||
\(503\) | 25.6569 | 1.14398 | 0.571991 | − | 0.820260i | \(-0.306171\pi\) | ||||
0.571991 | + | 0.820260i | \(0.306171\pi\) | |||||||
\(504\) | −4.48528 | + | 1.58579i | −0.199790 | + | 0.0706365i | ||||
\(505\) | − | 9.31371i | − | 0.414455i | ||||||
\(506\) | −1.02944 | + | 0.485281i | −0.0457641 | + | 0.0215734i | ||||
\(507\) | 13.0000 | − | 18.3848i | 0.577350 | − | 0.816497i | ||||
\(508\) | − | 24.9706i | − | 1.10789i | ||||||
\(509\) | 10.9706i | 0.486262i | 0.969994 | + | 0.243131i | \(0.0781744\pi\) | ||||
−0.969994 | + | 0.243131i | \(0.921826\pi\) | |||||||
\(510\) | 4.00000 | + | 2.82843i | 0.177123 | + | 0.125245i | ||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | −1.17157 | + | 4.14214i | −0.0517262 | + | 0.182880i | ||||
\(514\) | − | 5.51472i | − | 0.243244i | ||||||
\(515\) | 9.31371i | 0.410411i | ||||||||
\(516\) | 24.9706 | + | 17.6569i | 1.09927 | + | 0.777300i | ||||
\(517\) | −32.4853 | + | 15.3137i | −1.42870 | + | 0.673496i | ||||
\(518\) | 2.48528i | 0.109197i | ||||||||
\(519\) | 10.1421 | − | 14.3431i | 0.445190 | − | 0.629594i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.31371i | − | 0.408041i | −0.978967 | − | 0.204020i | \(-0.934599\pi\) | ||
0.978967 | − | 0.204020i | \(-0.0654009\pi\) | |||||||
\(522\) | −2.34315 | − | 6.62742i | −0.102557 | − | 0.290074i | ||||
\(523\) | − | 12.9706i | − | 0.567163i | −0.958948 | − | 0.283582i | \(-0.908477\pi\) | ||
0.958948 | − | 0.283582i | \(-0.0915227\pi\) | |||||||
\(524\) | 32.2843 | 1.41034 | ||||||||
\(525\) | −1.41421 | − | 1.00000i | −0.0617213 | − | 0.0436436i | ||||
\(526\) | −7.17157 | −0.312695 | ||||||||
\(527\) | 5.65685 | 0.246416 | ||||||||
\(528\) | 16.9706 | + | 3.00000i | 0.738549 | + | 0.130558i | ||||
\(529\) | 22.3137 | 0.970161 | ||||||||
\(530\) | −0.343146 | −0.0149053 | ||||||||
\(531\) | −0.970563 | + | 0.343146i | −0.0421188 | + | 0.0148913i | ||||
\(532\) | −1.51472 | −0.0656714 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.48528 | + | 3.17157i | 0.194097 | + | 0.137247i | ||||
\(535\) | 9.31371i | 0.402667i | ||||||||
\(536\) | 10.2843 | 0.444213 | ||||||||
\(537\) | −16.4853 | − | 11.6569i | −0.711392 | − | 0.503030i | ||||
\(538\) | − | 7.17157i | − | 0.309188i | ||||||
\(539\) | −1.41421 | − | 3.00000i | −0.0609145 | − | 0.129219i | ||||
\(540\) | −2.58579 | + | 9.14214i | −0.111275 | + | 0.393415i | ||||
\(541\) | − | 28.9706i | − | 1.24554i | −0.782404 | − | 0.622771i | \(-0.786007\pi\) | ||
0.782404 | − | 0.622771i | \(-0.213993\pi\) | |||||||
\(542\) | − | 1.02944i | − | 0.0442181i | ||||||
\(543\) | −2.00000 | + | 2.82843i | −0.0858282 | + | 0.121379i | ||||
\(544\) | 30.1421 | 1.29233 | ||||||||
\(545\) | 9.65685 | 0.413654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.2843i | − | 1.38038i | −0.723630 | − | 0.690188i | \(-0.757528\pi\) | ||
0.723630 | − | 0.690188i | \(-0.242472\pi\) | |||||||
\(548\) | 23.4558i | 1.00198i | ||||||||
\(549\) | 14.6274 | − | 5.17157i | 0.624283 | − | 0.220717i | ||||
\(550\) | −0.585786 | − | 1.24264i | −0.0249780 | − | 0.0529864i | ||||
\(551\) | − | 4.68629i | − | 0.199643i | ||||||
\(552\) | −1.85786 | − | 1.31371i | −0.0790760 | − | 0.0559151i | ||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 2.00000i | 0.0849719i | ||||||||
\(555\) | 8.48528 | + | 6.00000i | 0.360180 | + | 0.254686i | ||||
\(556\) | − | 11.8579i | − | 0.502885i | ||||||
\(557\) | 44.4853 | 1.88490 | 0.942451 | − | 0.334344i | \(-0.108515\pi\) | ||||
0.942451 | + | 0.334344i | \(0.108515\pi\) | |||||||
\(558\) | −0.343146 | − | 0.970563i | −0.0145265 | − | 0.0410872i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | 38.6274 | + | 6.82843i | 1.63085 | + | 0.288296i | ||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | 7.02944 | 0.296255 | 0.148128 | − | 0.988968i | \(-0.452675\pi\) | ||||
0.148128 | + | 0.988968i | \(0.452675\pi\) | |||||||
\(564\) | −28.0000 | − | 19.7990i | −1.17901 | − | 0.833688i | ||||
\(565\) | −3.17157 | −0.133429 | ||||||||
\(566\) | 12.0000i | 0.504398i | ||||||||
\(567\) | −5.65685 | − | 7.00000i | −0.237566 | − | 0.293972i | ||||
\(568\) | − | 0.544156i | − | 0.0228323i | ||||||
\(569\) | −23.3137 | −0.977362 | −0.488681 | − | 0.872463i | \(-0.662522\pi\) | ||||
−0.488681 | + | 0.872463i | \(0.662522\pi\) | |||||||
\(570\) | 0.343146 | − | 0.485281i | 0.0143728 | − | 0.0203262i | ||||
\(571\) | − | 4.97056i | − | 0.208012i | −0.994577 | − | 0.104006i | \(-0.966834\pi\) | ||
0.994577 | − | 0.104006i | \(-0.0331660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.48528 | + | 6.00000i | 0.354478 | + | 0.250654i | ||||
\(574\) | 3.17157i | 0.132379i | ||||||||
\(575\) | − | 0.828427i | − | 0.0345478i | ||||||
\(576\) | 4.17157 | + | 11.7990i | 0.173816 | + | 0.491625i | ||||
\(577\) | −20.4853 | −0.852813 | −0.426407 | − | 0.904532i | \(-0.640221\pi\) | ||||
−0.426407 | + | 0.904532i | \(0.640221\pi\) | |||||||
\(578\) | 12.2721 | 0.510451 | ||||||||
\(579\) | 31.7990 | + | 22.4853i | 1.32152 | + | 0.934456i | ||||
\(580\) | − | 10.3431i | − | 0.429476i | ||||||
\(581\) | 12.0000i | 0.497844i | ||||||||
\(582\) | −2.14214 | + | 3.02944i | −0.0887944 | + | 0.125574i | ||||
\(583\) | −2.48528 | + | 1.17157i | −0.102930 | + | 0.0485216i | ||||
\(584\) | 19.0294i | 0.787444i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.79899 | −0.322173 | ||||||||
\(587\) | 37.4558i | 1.54597i | 0.634425 | + | 0.772984i | \(0.281237\pi\) | ||||
−0.634425 | + | 0.772984i | \(0.718763\pi\) | |||||||
\(588\) | 1.82843 | − | 2.58579i | 0.0754031 | − | 0.106636i | ||||
\(589\) | − | 0.686292i | − | 0.0282781i | ||||||
\(590\) | 0.142136 | 0.00585163 | ||||||||
\(591\) | 14.8284 | − | 20.9706i | 0.609960 | − | 0.862614i | ||||
\(592\) | 18.0000 | 0.739795 | ||||||||
\(593\) | 17.1716 | 0.705152 | 0.352576 | − | 0.935783i | \(-0.385306\pi\) | ||||
0.352576 | + | 0.935783i | \(0.385306\pi\) | |||||||
\(594\) | −1.17157 | − | 7.04163i | −0.0480702 | − | 0.288922i | ||||
\(595\) | −6.82843 | −0.279938 | ||||||||
\(596\) | −13.3726 | −0.547762 | ||||||||
\(597\) | −14.4853 | + | 20.4853i | −0.592843 | + | 0.838407i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.9411i | 1.63195i | 0.578087 | + | 0.815975i | \(0.303799\pi\) | ||||
−0.578087 | + | 0.815975i | \(0.696201\pi\) | |||||||
\(600\) | 1.58579 | − | 2.24264i | 0.0647395 | − | 0.0915554i | ||||
\(601\) | − | 5.45584i | − | 0.222549i | −0.993790 | − | 0.111274i | \(-0.964507\pi\) | ||
0.993790 | − | 0.111274i | \(-0.0354932\pi\) | |||||||
\(602\) | 4.00000 | 0.163028 | ||||||||
\(603\) | 6.48528 | + | 18.3431i | 0.264101 | + | 0.746991i | ||||
\(604\) | 6.05887i | 0.246532i | ||||||||
\(605\) | −8.48528 | − | 7.00000i | −0.344976 | − | 0.284590i | ||||
\(606\) | −3.85786 | + | 5.45584i | −0.156715 | + | 0.221629i | ||||
\(607\) | 36.0000i | 1.46119i | 0.682808 | + | 0.730597i | \(0.260758\pi\) | ||||
−0.682808 | + | 0.730597i | \(0.739242\pi\) | |||||||
\(608\) | − | 3.65685i | − | 0.148305i | ||||||
\(609\) | 8.00000 | + | 5.65685i | 0.324176 | + | 0.229227i | ||||
\(610\) | −2.14214 | −0.0867325 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 12.4853 | + | 35.3137i | 0.504688 | + | 1.42747i | ||||
\(613\) | 5.79899i | 0.234219i | 0.993119 | + | 0.117109i | \(0.0373628\pi\) | ||||
−0.993119 | + | 0.117109i | \(0.962637\pi\) | |||||||
\(614\) | − | 3.71573i | − | 0.149955i | ||||||
\(615\) | 10.8284 | + | 7.65685i | 0.436644 | + | 0.308754i | ||||
\(616\) | 4.75736 | − | 2.24264i | 0.191679 | − | 0.0903586i | ||||
\(617\) | 19.4558i | 0.783263i | 0.920122 | + | 0.391631i | \(0.128089\pi\) | ||||
−0.920122 | + | 0.391631i | \(0.871911\pi\) | |||||||
\(618\) | 3.85786 | − | 5.45584i | 0.155186 | − | 0.219466i | ||||
\(619\) | −21.7990 | −0.876175 | −0.438088 | − | 0.898932i | \(-0.644344\pi\) | ||||
−0.438088 | + | 0.898932i | \(0.644344\pi\) | |||||||
\(620\) | − | 1.51472i | − | 0.0608326i | ||||||
\(621\) | 1.17157 | − | 4.14214i | 0.0470136 | − | 0.166218i | ||||
\(622\) | − | 10.2010i | − | 0.409023i | ||||||
\(623\) | −7.65685 | −0.306765 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.45584 | 0.218059 | ||||||||
\(627\) | 0.828427 | − | 4.68629i | 0.0330842 | − | 0.187152i | ||||
\(628\) | 34.4264 | 1.37376 | ||||||||
\(629\) | 40.9706 | 1.63360 | ||||||||
\(630\) | 0.414214 | + | 1.17157i | 0.0165027 | + | 0.0466766i | ||||
\(631\) | 32.9706 | 1.31254 | 0.656269 | − | 0.754527i | \(-0.272134\pi\) | ||||
0.656269 | + | 0.754527i | \(0.272134\pi\) | |||||||
\(632\) | − | 6.34315i | − | 0.252317i | ||||||
\(633\) | 24.0000 | + | 16.9706i | 0.953914 | + | 0.674519i | ||||
\(634\) | 11.9411i | 0.474243i | ||||||||
\(635\) | −13.6569 | −0.541956 | ||||||||
\(636\) | −2.14214 | − | 1.51472i | −0.0849412 | − | 0.0600625i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.31371 | + | 7.02944i | 0.131191 | + | 0.278298i | ||||
\(639\) | 0.970563 | − | 0.343146i | 0.0383949 | − | 0.0135746i | ||||
\(640\) | − | 10.5563i | − | 0.417276i | ||||||
\(641\) | − | 16.6863i | − | 0.659069i | −0.944144 | − | 0.329534i | \(-0.893108\pi\) | ||
0.944144 | − | 0.329534i | \(-0.106892\pi\) | |||||||
\(642\) | 3.85786 | − | 5.45584i | 0.152258 | − | 0.215325i | ||||
\(643\) | −10.9706 | −0.432637 | −0.216318 | − | 0.976323i | \(-0.569405\pi\) | ||||
−0.216318 | + | 0.976323i | \(0.569405\pi\) | |||||||
\(644\) | 1.51472 | 0.0596883 | ||||||||
\(645\) | 9.65685 | − | 13.6569i | 0.380238 | − | 0.537738i | ||||
\(646\) | − | 2.34315i | − | 0.0921898i | ||||||
\(647\) | 4.20101i | 0.165159i | 0.996584 | + | 0.0825794i | \(0.0263158\pi\) | ||||
−0.996584 | + | 0.0825794i | \(0.973684\pi\) | |||||||
\(648\) | 11.1005 | − | 8.97056i | 0.436069 | − | 0.352397i | ||||
\(649\) | 1.02944 | − | 0.485281i | 0.0404089 | − | 0.0190490i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.17157 | + | 0.828427i | 0.0459176 | + | 0.0324686i | ||||
\(652\) | 2.76955 | 0.108464 | ||||||||
\(653\) | 26.4853i | 1.03645i | 0.855245 | + | 0.518225i | \(0.173407\pi\) | ||||
−0.855245 | + | 0.518225i | \(0.826593\pi\) | |||||||
\(654\) | −5.65685 | − | 4.00000i | −0.221201 | − | 0.156412i | ||||
\(655\) | − | 17.6569i | − | 0.689910i | ||||||
\(656\) | 22.9706 | 0.896850 | ||||||||
\(657\) | −33.9411 | + | 12.0000i | −1.32417 | + | 0.468165i | ||||
\(658\) | −4.48528 | −0.174854 | ||||||||
\(659\) | −44.4853 | −1.73290 | −0.866450 | − | 0.499263i | \(-0.833604\pi\) | ||||
−0.866450 | + | 0.499263i | \(0.833604\pi\) | |||||||
\(660\) | 1.82843 | − | 10.3431i | 0.0711714 | − | 0.402606i | ||||
\(661\) | −46.9706 | −1.82694 | −0.913472 | − | 0.406903i | \(-0.866609\pi\) | ||||
−0.913472 | + | 0.406903i | \(0.866609\pi\) | |||||||
\(662\) | −4.28427 | −0.166513 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.0294 | −0.738485 | ||||||||
\(665\) | 0.828427i | 0.0321250i | ||||||||
\(666\) | −2.48528 | − | 7.02944i | −0.0963027 | − | 0.272385i | ||||
\(667\) | 4.68629i | 0.181454i | ||||||||
\(668\) | 4.28427 | 0.165763 | ||||||||
\(669\) | −14.9706 | + | 21.1716i | −0.578795 | + | 0.818540i | ||||
\(670\) | − | 2.68629i | − | 0.103780i | ||||||
\(671\) | −15.5147 | + | 7.31371i | −0.598939 | + | 0.282343i | ||||
\(672\) | 6.24264 | + | 4.41421i | 0.240815 | + | 0.170282i | ||||
\(673\) | − | 25.5147i | − | 0.983520i | −0.870731 | − | 0.491760i | \(-0.836354\pi\) | ||
0.870731 | − | 0.491760i | \(-0.163646\pi\) | |||||||
\(674\) | − | 1.02944i | − | 0.0396524i | ||||||
\(675\) | 5.00000 | + | 1.41421i | 0.192450 | + | 0.0544331i | ||||
\(676\) | −23.7696 | −0.914214 | ||||||||
\(677\) | 40.7696 | 1.56690 | 0.783451 | − | 0.621454i | \(-0.213458\pi\) | ||||
0.783451 | + | 0.621454i | \(0.213458\pi\) | |||||||
\(678\) | 1.85786 | + | 1.31371i | 0.0713509 | + | 0.0504527i | ||||
\(679\) | − | 5.17157i | − | 0.198467i | ||||||
\(680\) | − | 10.8284i | − | 0.415251i | ||||||
\(681\) | 14.3431 | − | 20.2843i | 0.549631 | − | 0.777295i | ||||
\(682\) | 0.485281 | + | 1.02944i | 0.0185824 | + | 0.0394192i | ||||
\(683\) | − | 37.7990i | − | 1.44634i | −0.690671 | − | 0.723169i | \(-0.742685\pi\) | ||
0.690671 | − | 0.723169i | \(-0.257315\pi\) | |||||||
\(684\) | 4.28427 | − | 1.51472i | 0.163813 | − | 0.0579167i | ||||
\(685\) | 12.8284 | 0.490149 | ||||||||
\(686\) | − | 0.414214i | − | 0.0158147i | ||||||
\(687\) | −9.31371 | + | 13.1716i | −0.355340 | + | 0.502527i | ||||
\(688\) | − | 28.9706i | − | 1.10449i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.343146 | + | 0.485281i | −0.0130633 | + | 0.0184743i | ||||
\(691\) | −5.51472 | −0.209790 | −0.104895 | − | 0.994483i | \(-0.533451\pi\) | ||||
−0.104895 | + | 0.994483i | \(0.533451\pi\) | |||||||
\(692\) | −18.5442 | −0.704943 | ||||||||
\(693\) | 7.00000 | + | 7.07107i | 0.265908 | + | 0.268608i | ||||
\(694\) | 5.11270 | 0.194075 | ||||||||
\(695\) | −6.48528 | −0.246001 | ||||||||
\(696\) | −8.97056 | + | 12.6863i | −0.340028 | + | 0.480873i | ||||
\(697\) | 52.2843 | 1.98041 | ||||||||
\(698\) | − | 13.4558i | − | 0.509311i | ||||||
\(699\) | −11.7990 | + | 16.6863i | −0.446279 | + | 0.631134i | ||||
\(700\) | 1.82843i | 0.0691080i | ||||||||
\(701\) | 31.5980 | 1.19344 | 0.596720 | − | 0.802450i | \(-0.296470\pi\) | ||||
0.596720 | + | 0.802450i | \(0.296470\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.97056i | − | 0.187468i | ||||||
\(704\) | −5.89949 | − | 12.5147i | −0.222346 | − | 0.471666i | ||||
\(705\) | −10.8284 | + | 15.3137i | −0.407822 | + | 0.576748i | ||||
\(706\) | 0.142136i | 0.00534934i | ||||||||
\(707\) | − | 9.31371i | − | 0.350278i | ||||||
\(708\) | 0.887302 | + | 0.627417i | 0.0333468 | + | 0.0235798i | ||||
\(709\) | 30.0000 | 1.12667 | 0.563337 | − | 0.826227i | \(-0.309517\pi\) | ||||
0.563337 | + | 0.826227i | \(0.309517\pi\) | |||||||
\(710\) | −0.142136 | −0.00533425 | ||||||||
\(711\) | 11.3137 | − | 4.00000i | 0.424297 | − | 0.150012i | ||||
\(712\) | − | 12.1421i | − | 0.455046i | ||||||
\(713\) | 0.686292i | 0.0257018i | ||||||||
\(714\) | 4.00000 | + | 2.82843i | 0.149696 | + | 0.105851i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.3137i | 0.796531i | ||||||||
\(717\) | −2.82843 | + | 4.00000i | −0.105630 | + | 0.149383i | ||||
\(718\) | 3.51472 | 0.131168 | ||||||||
\(719\) | 6.68629i | 0.249357i | 0.992197 | + | 0.124678i | \(0.0397899\pi\) | ||||
−0.992197 | + | 0.124678i | \(0.960210\pi\) | |||||||
\(720\) | 8.48528 | − | 3.00000i | 0.316228 | − | 0.111803i | ||||
\(721\) | 9.31371i | 0.346861i | ||||||||
\(722\) | 7.58579 | 0.282314 | ||||||||
\(723\) | −32.2843 | − | 22.8284i | −1.20066 | − | 0.848998i | ||||
\(724\) | 3.65685 | 0.135906 | ||||||||
\(725\) | −5.65685 | −0.210090 | ||||||||
\(726\) | 2.07107 | + | 7.61522i | 0.0768645 | + | 0.282627i | ||||
\(727\) | 42.0000 | 1.55769 | 0.778847 | − | 0.627214i | \(-0.215805\pi\) | ||||
0.778847 | + | 0.627214i | \(0.215805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 4.97056 | 0.183969 | ||||||||
\(731\) | − | 65.9411i | − | 2.43892i | ||||||
\(732\) | −13.3726 | − | 9.45584i | −0.494265 | − | 0.349498i | ||||
\(733\) | 29.9411i | 1.10590i | 0.833214 | + | 0.552950i | \(0.186498\pi\) | ||||
−0.833214 | + | 0.552950i | \(0.813502\pi\) | |||||||
\(734\) | −7.45584 | −0.275200 | ||||||||
\(735\) | −1.41421 | − | 1.00000i | −0.0521641 | − | 0.0368856i | ||||
\(736\) | 3.65685i | 0.134793i | ||||||||
\(737\) | −9.17157 | − | 19.4558i | −0.337839 | − | 0.716665i | ||||
\(738\) | −3.17157 | − | 8.97056i | −0.116747 | − | 0.330211i | ||||
\(739\) | 20.2843i | 0.746169i | 0.927797 | + | 0.373084i | \(0.121700\pi\) | ||||
−0.927797 | + | 0.373084i | \(0.878300\pi\) | |||||||
\(740\) | − | 10.9706i | − | 0.403286i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.343146 | −0.0125973 | ||||||||
\(743\) | 22.6863 | 0.832279 | 0.416140 | − | 0.909301i | \(-0.363383\pi\) | ||||
0.416140 | + | 0.909301i | \(0.363383\pi\) | |||||||
\(744\) | −1.31371 | + | 1.85786i | −0.0481629 | + | 0.0681126i | ||||
\(745\) | 7.31371i | 0.267954i | ||||||||
\(746\) | 1.71573i | 0.0628173i | ||||||||
\(747\) | −12.0000 | − | 33.9411i | −0.439057 | − | 1.24184i | ||||
\(748\) | −17.6569 | − | 37.4558i | −0.645599 | − | 1.36952i | ||||
\(749\) | 9.31371i | 0.340316i | ||||||||
\(750\) | −0.585786 | − | 0.414214i | −0.0213899 | − | 0.0151249i | ||||
\(751\) | −29.9411 | −1.09257 | −0.546284 | − | 0.837600i | \(-0.683958\pi\) | ||||
−0.546284 | + | 0.837600i | \(0.683958\pi\) | |||||||
\(752\) | 32.4853i | 1.18462i | ||||||||
\(753\) | −29.1716 | − | 20.6274i | −1.06307 | − | 0.751705i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.31371 | 0.120598 | ||||||||
\(756\) | −2.58579 | + | 9.14214i | −0.0940441 | + | 0.332496i | ||||
\(757\) | 39.9411 | 1.45168 | 0.725842 | − | 0.687861i | \(-0.241450\pi\) | ||||
0.725842 | + | 0.687861i | \(0.241450\pi\) | |||||||
\(758\) | −15.7157 | −0.570821 | ||||||||
\(759\) | −0.828427 | + | 4.68629i | −0.0300700 | + | 0.170102i | ||||
\(760\) | −1.31371 | −0.0476532 | ||||||||
\(761\) | −36.3431 | −1.31744 | −0.658719 | − | 0.752389i | \(-0.728901\pi\) | ||||
−0.658719 | + | 0.752389i | \(0.728901\pi\) | |||||||
\(762\) | 8.00000 | + | 5.65685i | 0.289809 | + | 0.204926i | ||||
\(763\) | 9.65685 | 0.349602 | ||||||||
\(764\) | − | 10.9706i | − | 0.396901i | ||||||
\(765\) | 19.3137 | − | 6.82843i | 0.698289 | − | 0.246882i | ||||
\(766\) | − | 9.85786i | − | 0.356179i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.97056 | − | 5.61522i | 0.143275 | − | 0.202622i | ||||
\(769\) | − | 20.4853i | − | 0.738718i | −0.929287 | − | 0.369359i | \(-0.879577\pi\) | ||
0.929287 | − | 0.369359i | \(-0.120423\pi\) | |||||||
\(770\) | −0.585786 | − | 1.24264i | −0.0211103 | − | 0.0447817i | ||||
\(771\) | −18.8284 | − | 13.3137i | −0.678089 | − | 0.479481i | ||||
\(772\) | − | 41.1127i | − | 1.47968i | ||||||
\(773\) | 2.68629i | 0.0966192i | 0.998832 | + | 0.0483096i | \(0.0153834\pi\) | ||||
−0.998832 | + | 0.0483096i | \(0.984617\pi\) | |||||||
\(774\) | −11.3137 | + | 4.00000i | −0.406663 | + | 0.143777i | ||||
\(775\) | −0.828427 | −0.0297580 | ||||||||
\(776\) | 8.20101 | 0.294399 | ||||||||
\(777\) | 8.48528 | + | 6.00000i | 0.304408 | + | 0.215249i | ||||
\(778\) | − | 4.40202i | − | 0.157820i | ||||||
\(779\) | − | 6.34315i | − | 0.227267i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.02944 | + | 0.485281i | −0.0368362 | + | 0.0173647i | ||||
\(782\) | 2.34315i | 0.0837907i | ||||||||
\(783\) | −28.2843 | − | 8.00000i | −1.01080 | − | 0.285897i | ||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | − | 18.8284i | − | 0.672015i | ||||||
\(786\) | −7.31371 | + | 10.3431i | −0.260871 | + | 0.368928i | ||||
\(787\) | − | 37.9411i | − | 1.35246i | −0.736693 | − | 0.676228i | \(-0.763614\pi\) | ||
0.736693 | − | 0.676228i | \(-0.236386\pi\) | |||||||
\(788\) | −27.1127 | −0.965850 | ||||||||
\(789\) | −17.3137 | + | 24.4853i | −0.616384 | + | 0.871699i | ||||
\(790\) | −1.65685 | −0.0589482 | ||||||||
\(791\) | −3.17157 | −0.112768 | ||||||||
\(792\) | −11.2132 | + | 11.1005i | −0.398444 | + | 0.394439i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.48528 | 0.301131 | ||||||||
\(795\) | −0.828427 | + | 1.17157i | −0.0293813 | + | 0.0415514i | ||||
\(796\) | 26.4853 | 0.938746 | ||||||||
\(797\) | 16.6274i | 0.588973i | 0.955656 | + | 0.294487i | \(0.0951487\pi\) | ||||
−0.955656 | + | 0.294487i | \(0.904851\pi\) | |||||||
\(798\) | 0.343146 | − | 0.485281i | 0.0121472 | − | 0.0171788i | ||||
\(799\) | 73.9411i | 2.61585i | ||||||||
\(800\) | −4.41421 | −0.156066 | ||||||||
\(801\) | 21.6569 | − | 7.65685i | 0.765207 | − | 0.270542i | ||||
\(802\) | 1.94113i | 0.0685435i | ||||||||
\(803\) | 36.0000 | − | 16.9706i | 1.27041 | − | 0.598878i | ||||
\(804\) | 11.8579 | − | 16.7696i | 0.418195 | − | 0.591417i | ||||
\(805\) | − | 0.828427i | − | 0.0291982i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.4853 | − | 17.3137i | −0.861923 | − | 0.609471i | ||||
\(808\) | 14.7696 | 0.519591 | ||||||||
\(809\) | −10.6274 | −0.373640 | −0.186820 | − | 0.982394i | \(-0.559818\pi\) | ||||
−0.186820 | + | 0.982394i | \(0.559818\pi\) | |||||||
\(810\) | −2.34315 | − | 2.89949i | −0.0823297 | − | 0.101878i | ||||
\(811\) | 17.5147i | 0.615025i | 0.951544 | + | 0.307512i | \(0.0994966\pi\) | ||||
−0.951544 | + | 0.307512i | \(0.900503\pi\) | |||||||
\(812\) | − | 10.3431i | − | 0.362973i | ||||||
\(813\) | −3.51472 | − | 2.48528i | −0.123267 | − | 0.0871626i | ||||
\(814\) | 3.51472 | + | 7.45584i | 0.123191 | + | 0.261327i | ||||
\(815\) | − | 1.51472i | − | 0.0530583i | ||||||
\(816\) | 20.4853 | − | 28.9706i | 0.717128 | − | 1.01417i | ||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | − | 15.5147i | − | 0.542459i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 14.0000i | − | 0.488901i | ||||||
\(821\) | −6.62742 | −0.231298 | −0.115649 | − | 0.993290i | \(-0.536895\pi\) | ||||
−0.115649 | + | 0.993290i | \(0.536895\pi\) | |||||||
\(822\) | −7.51472 | − | 5.31371i | −0.262106 | − | 0.185337i | ||||
\(823\) | −0.142136 | −0.00495454 | −0.00247727 | − | 0.999997i | \(-0.500789\pi\) | ||||
−0.00247727 | + | 0.999997i | \(0.500789\pi\) | |||||||
\(824\) | −14.7696 | −0.514522 | ||||||||
\(825\) | −5.65685 | − | 1.00000i | −0.196946 | − | 0.0348155i | ||||
\(826\) | 0.142136 | 0.00494553 | ||||||||
\(827\) | −51.2548 | −1.78231 | −0.891153 | − | 0.453704i | \(-0.850102\pi\) | ||||
−0.891153 | + | 0.453704i | \(0.850102\pi\) | |||||||
\(828\) | −4.28427 | + | 1.51472i | −0.148889 | + | 0.0526401i | ||||
\(829\) | −50.9706 | −1.77028 | −0.885140 | − | 0.465324i | \(-0.845938\pi\) | ||||
−0.885140 | + | 0.465324i | \(0.845938\pi\) | |||||||
\(830\) | 4.97056i | 0.172531i | ||||||||
\(831\) | 6.82843 | + | 4.82843i | 0.236876 | + | 0.167496i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.82843 | −0.236591 | ||||||||
\(834\) | 3.79899 | + | 2.68629i | 0.131548 | + | 0.0930187i | ||||
\(835\) | − | 2.34315i | − | 0.0810879i | ||||||
\(836\) | −4.54416 | + | 2.14214i | −0.157163 | + | 0.0740873i | ||||
\(837\) | −4.14214 | − | 1.17157i | −0.143173 | − | 0.0404955i | ||||
\(838\) | − | 10.4853i | − | 0.362208i | ||||||
\(839\) | − | 51.6569i | − | 1.78339i | −0.452634 | − | 0.891696i | \(-0.649516\pi\) | ||
0.452634 | − | 0.891696i | \(-0.350484\pi\) | |||||||
\(840\) | 1.58579 | − | 2.24264i | 0.0547148 | − | 0.0773785i | ||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | 7.45584 | 0.256945 | ||||||||
\(843\) | −28.9706 | + | 40.9706i | −0.997799 | + | 1.41110i | ||||
\(844\) | − | 31.0294i | − | 1.06808i | ||||||
\(845\) | 13.0000i | 0.447214i | ||||||||
\(846\) | 12.6863 | − | 4.48528i | 0.436164 | − | 0.154207i | ||||
\(847\) | −8.48528 | − | 7.00000i | −0.291558 | − | 0.240523i | ||||
\(848\) | 2.48528i | 0.0853449i | ||||||||
\(849\) | 40.9706 | + | 28.9706i | 1.40611 | + | 0.994267i | ||||
\(850\) | −2.82843 | −0.0970143 | ||||||||
\(851\) | 4.97056i | 0.170389i | ||||||||
\(852\) | −0.887302 | − | 0.627417i | −0.0303985 | − | 0.0214950i | ||||
\(853\) | − | 28.9706i | − | 0.991933i | −0.868342 | − | 0.495967i | \(-0.834814\pi\) | ||
0.868342 | − | 0.495967i | \(-0.165186\pi\) | |||||||
\(854\) | −2.14214 | −0.0733024 | ||||||||
\(855\) | −0.828427 | − | 2.34315i | −0.0283316 | − | 0.0801339i | ||||
\(856\) | −14.7696 | −0.504813 | ||||||||
\(857\) | 23.1127 | 0.789515 | 0.394757 | − | 0.918785i | \(-0.370829\pi\) | ||||
0.394757 | + | 0.918785i | \(0.370829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.4558 | −1.20974 | −0.604869 | − | 0.796325i | \(-0.706774\pi\) | ||||
−0.604869 | + | 0.796325i | \(0.706774\pi\) | |||||||
\(860\) | −17.6569 | −0.602094 | ||||||||
\(861\) | 10.8284 | + | 7.65685i | 0.369032 | + | 0.260945i | ||||
\(862\) | −7.51472 | −0.255952 | ||||||||
\(863\) | 40.1421i | 1.36645i | 0.730206 | + | 0.683227i | \(0.239424\pi\) | ||||
−0.730206 | + | 0.683227i | \(0.760576\pi\) | |||||||
\(864\) | −22.0711 | − | 6.24264i | −0.750873 | − | 0.212379i | ||||
\(865\) | 10.1421i | 0.344843i | ||||||||
\(866\) | −14.4264 | −0.490229 | ||||||||
\(867\) | 29.6274 | − | 41.8995i | 1.00620 | − | 1.42298i | ||||
\(868\) | − | 1.51472i | − | 0.0514129i | ||||||
\(869\) | −12.0000 | + | 5.65685i | −0.407072 | + | 0.191896i | ||||
\(870\) | 3.31371 | + | 2.34315i | 0.112345 | + | 0.0794401i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 15.3137i | 0.518588i | ||||||||
\(873\) | 5.17157 | + | 14.6274i | 0.175031 | + | 0.495063i | ||||
\(874\) | 0.284271 | 0.00961562 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 31.0294 | + | 21.9411i | 1.04839 | + | 0.741322i | ||||
\(877\) | 29.7990i | 1.00624i | 0.864216 | + | 0.503120i | \(0.167815\pi\) | ||||
−0.864216 | + | 0.503120i | \(0.832185\pi\) | |||||||
\(878\) | − | 8.05887i | − | 0.271974i | ||||||
\(879\) | −18.8284 | + | 26.6274i | −0.635067 | + | 0.898120i | ||||
\(880\) | −9.00000 | + | 4.24264i | −0.303390 | + | 0.143019i | ||||
\(881\) | 24.3431i | 0.820141i | 0.912054 | + | 0.410071i | \(0.134496\pi\) | ||||
−0.912054 | + | 0.410071i | \(0.865504\pi\) | |||||||
\(882\) | 0.414214 | + | 1.17157i | 0.0139473 | + | 0.0394489i | ||||
\(883\) | 17.1127 | 0.575888 | 0.287944 | − | 0.957647i | \(-0.407028\pi\) | ||||
0.287944 | + | 0.957647i | \(0.407028\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.343146 | − | 0.485281i | 0.0115347 | − | 0.0163126i | ||||
\(886\) | 15.6569i | 0.526002i | ||||||||
\(887\) | −36.6863 | −1.23181 | −0.615903 | − | 0.787822i | \(-0.711209\pi\) | ||||
−0.615903 | + | 0.787822i | \(0.711209\pi\) | |||||||
\(888\) | −9.51472 | + | 13.4558i | −0.319293 | + | 0.451549i | ||||
\(889\) | −13.6569 | −0.458036 | ||||||||
\(890\) | −3.17157 | −0.106311 | ||||||||
\(891\) | −26.8701 | − | 13.0000i | −0.900181 | − | 0.435516i | ||||
\(892\) | 27.3726 | 0.916502 | ||||||||
\(893\) | 8.97056 | 0.300188 | ||||||||
\(894\) | 3.02944 | − | 4.28427i | 0.101320 | − | 0.143287i | ||||
\(895\) | 11.6569 | 0.389646 | ||||||||
\(896\) | − | 10.5563i | − | 0.352663i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.62742i | 0.0876780i | ||||||||
\(899\) | 4.68629 | 0.156297 | ||||||||
\(900\) | −1.82843 | − | 5.17157i | −0.0609476 | − | 0.172386i | ||||
\(901\) | 5.65685i | 0.188457i | ||||||||
\(902\) | 4.48528 | + | 9.51472i | 0.149344 | + | 0.316805i | ||||
\(903\) | 9.65685 | − | 13.6569i | 0.321360 | − | 0.454472i | ||||
\(904\) | − | 5.02944i | − | 0.167277i | ||||||
\(905\) | − | 2.00000i | − | 0.0664822i | ||||||
\(906\) | −1.94113 | − | 1.37258i | −0.0644896 | − | 0.0456010i | ||||
\(907\) | −12.8284 | −0.425961 | −0.212980 | − | 0.977056i | \(-0.568317\pi\) | ||||
−0.212980 | + | 0.977056i | \(0.568317\pi\) | |||||||
\(908\) | −26.2254 | −0.870320 | ||||||||
\(909\) | 9.31371 | + | 26.3431i | 0.308916 | + | 0.873747i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.6274i | 0.418365i | 0.977877 | + | 0.209182i | \(0.0670803\pi\) | ||||
−0.977877 | + | 0.209182i | \(0.932920\pi\) | |||||||
\(912\) | −3.51472 | − | 2.48528i | −0.116384 | − | 0.0822959i | ||||
\(913\) | 16.9706 | + | 36.0000i | 0.561644 | + | 1.19143i | ||||
\(914\) | − | 10.9706i | − | 0.362874i | ||||||
\(915\) | −5.17157 | + | 7.31371i | −0.170967 | + | 0.241784i | ||||
\(916\) | 17.0294 | 0.562668 | ||||||||
\(917\) | − | 17.6569i | − | 0.583081i | ||||||
\(918\) | −14.1421 | − | 4.00000i | −0.466760 | − | 0.132020i | ||||
\(919\) | 58.9117i | 1.94332i | 0.236388 | + | 0.971659i | \(0.424036\pi\) | ||||
−0.236388 | + | 0.971659i | \(0.575964\pi\) | |||||||
\(920\) | 1.31371 | 0.0433117 | ||||||||
\(921\) | −12.6863 | − | 8.97056i | −0.418028 | − | 0.295590i | ||||
\(922\) | −5.11270 | −0.168378 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.82843 | − | 10.3431i | 0.0601508 | − | 0.340265i | ||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | −16.3431 | −0.537069 | ||||||||
\(927\) | −9.31371 | − | 26.3431i | −0.305902 | − | 0.865222i | ||||
\(928\) | 24.9706 | 0.819699 | ||||||||
\(929\) | 31.6569i | 1.03863i | 0.854584 | + | 0.519314i | \(0.173812\pi\) | ||||
−0.854584 | + | 0.519314i | \(0.826188\pi\) | |||||||
\(930\) | 0.485281 | + | 0.343146i | 0.0159130 | + | 0.0112522i | ||||
\(931\) | 0.828427i | 0.0271506i | ||||||||
\(932\) | 21.5736 | 0.706667 | ||||||||
\(933\) | −34.8284 | − | 24.6274i | −1.14023 | − | 0.806265i | ||||
\(934\) | 0.485281i | 0.0158789i | ||||||||
\(935\) | −20.4853 | + | 9.65685i | −0.669940 | + | 0.315813i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.9706i | 0.423730i | 0.977299 | + | 0.211865i | \(0.0679537\pi\) | ||||
−0.977299 | + | 0.211865i | \(0.932046\pi\) | |||||||
\(938\) | − | 2.68629i | − | 0.0877105i | ||||||
\(939\) | 13.1716 | − | 18.6274i | 0.429838 | − | 0.607883i | ||||
\(940\) | 19.7990 | 0.645772 | ||||||||
\(941\) | 22.9706 | 0.748819 | 0.374409 | − | 0.927263i | \(-0.377845\pi\) | ||||
0.374409 | + | 0.927263i | \(0.377845\pi\) | |||||||
\(942\) | −7.79899 | + | 11.0294i | −0.254105 | + | 0.359358i | ||||
\(943\) | 6.34315i | 0.206561i | ||||||||
\(944\) | − | 1.02944i | − | 0.0335053i | ||||||
\(945\) | 5.00000 | + | 1.41421i | 0.162650 | + | 0.0460044i | ||||
\(946\) | 12.0000 | − | 5.65685i | 0.390154 | − | 0.183920i | ||||
\(947\) | − | 47.1716i | − | 1.53287i | −0.642322 | − | 0.766435i | \(-0.722029\pi\) | ||
0.642322 | − | 0.766435i | \(-0.277971\pi\) | |||||||
\(948\) | −10.3431 | − | 7.31371i | −0.335930 | − | 0.237538i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.343146i | 0.0111331i | ||||||||
\(951\) | 40.7696 | + | 28.8284i | 1.32204 | + | 0.934826i | ||||
\(952\) | − | 10.8284i | − | 0.350951i | ||||||
\(953\) | −37.1716 | −1.20411 | −0.602053 | − | 0.798456i | \(-0.705650\pi\) | ||||
−0.602053 | + | 0.798456i | \(0.705650\pi\) | |||||||
\(954\) | 0.970563 | − | 0.343146i | 0.0314231 | − | 0.0111098i | ||||
\(955\) | −6.00000 | −0.194155 | ||||||||
\(956\) | 5.17157 | 0.167261 | ||||||||
\(957\) | 32.0000 | + | 5.65685i | 1.03441 | + | 0.182860i | ||||
\(958\) | 4.68629 | 0.151407 | ||||||||
\(959\) | 12.8284 | 0.414252 | ||||||||
\(960\) | −5.89949 | − | 4.17157i | −0.190405 | − | 0.134637i | ||||
\(961\) | −30.3137 | −0.977862 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.31371 | − | 26.3431i | −0.300130 | − | 0.848896i | ||||
\(964\) | 41.7401i | 1.34436i | ||||||||
\(965\) | −22.4853 | −0.723827 | ||||||||
\(966\) | −0.343146 | + | 0.485281i | −0.0110405 | + | 0.0156137i | ||||
\(967\) | − | 12.2843i | − | 0.395036i | −0.980299 | − | 0.197518i | \(-0.936712\pi\) | ||
0.980299 | − | 0.197518i | \(-0.0632880\pi\) | |||||||
\(968\) | 11.1005 | − | 13.4558i | 0.356784 | − | 0.432487i | ||||
\(969\) | −8.00000 | − | 5.65685i | −0.256997 | − | 0.181724i | ||||
\(970\) | − | 2.14214i | − | 0.0687798i | ||||||
\(971\) | 30.2843i | 0.971869i | 0.873995 | + | 0.485934i | \(0.161521\pi\) | ||||
−0.873995 | + | 0.485934i | \(0.838479\pi\) | |||||||
\(972\) | −1.82843 | − | 28.4437i | −0.0586468 | − | 0.912331i | ||||
\(973\) | −6.48528 | −0.207909 | ||||||||
\(974\) | 10.9706 | 0.351520 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.5147i | 0.496614i | ||||||||
\(977\) | − | 7.17157i | − | 0.229439i | −0.993398 | − | 0.114719i | \(-0.963403\pi\) | ||
0.993398 | − | 0.114719i | \(-0.0365969\pi\) | |||||||
\(978\) | −0.627417 | + | 0.887302i | −0.0200626 | + | 0.0283728i | ||||
\(979\) | −22.9706 | + | 10.8284i | −0.734142 | + | 0.346078i | ||||
\(980\) | 1.82843i | 0.0584070i | ||||||||
\(981\) | −27.3137 | + | 9.65685i | −0.872060 | + | 0.308320i | ||||
\(982\) | −7.51472 | −0.239804 | ||||||||
\(983\) | 2.82843i | 0.0902128i | 0.998982 | + | 0.0451064i | \(0.0143627\pi\) | ||||
−0.998982 | + | 0.0451064i | \(0.985637\pi\) | |||||||
\(984\) | −12.1421 | + | 17.1716i | −0.387077 | + | 0.547410i | ||||
\(985\) | 14.8284i | 0.472473i | ||||||||
\(986\) | 16.0000 | 0.509544 | ||||||||
\(987\) | −10.8284 | + | 15.3137i | −0.344673 | + | 0.487441i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 2.89949 | + | 2.92893i | 0.0921520 | + | 0.0930876i | ||||
\(991\) | 45.6569 | 1.45034 | 0.725169 | − | 0.688571i | \(-0.241762\pi\) | ||||
0.725169 | + | 0.688571i | \(0.241762\pi\) | |||||||
\(992\) | 3.65685 | 0.116105 | ||||||||
\(993\) | −10.3431 | + | 14.6274i | −0.328230 | + | 0.464187i | ||||
\(994\) | −0.142136 | −0.00450827 | ||||||||
\(995\) | − | 14.4853i | − | 0.459214i | ||||||
\(996\) | −21.9411 | + | 31.0294i | −0.695231 | + | 0.983205i | ||||
\(997\) | − | 44.2843i | − | 1.40250i | −0.712917 | − | 0.701248i | \(-0.752626\pi\) | ||
0.712917 | − | 0.701248i | \(-0.247374\pi\) | |||||||
\(998\) | 14.9117 | 0.472021 | ||||||||
\(999\) | −30.0000 | − | 8.48528i | −0.949158 | − | 0.268462i |
(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 | 1155.2.l.a.1121.3 | ✓ | 4 | |
3.2 | odd | 2 | 1155.2.l.d.1121.2 | yes | 4 | ||
11.10 | odd | 2 | 1155.2.l.d.1121.1 | yes | 4 | ||
33.32 | even | 2 | inner | 1155.2.l.a.1121.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.l.a.1121.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1155.2.l.a.1121.4 | yes | 4 | 33.32 | even | 2 | inner | |
1155.2.l.d.1121.1 | yes | 4 | 11.10 | odd | 2 | ||
1155.2.l.d.1121.2 | yes | 4 | 3.2 | odd | 2 |