Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + 14 x^{3} + 145 x^{2} + 33 x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.6 | ||
Root | \(-1.08347 + 1.87662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.f.501.6 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.58347 | − | 2.74265i | 0.914217 | − | 1.58347i | 0.106173 | − | 0.994348i | \(-0.466140\pi\) |
0.808044 | − | 0.589122i | \(-0.200526\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.03607 | 1.14753 | 0.573764 | − | 0.819021i | \(-0.305483\pi\) | ||||
0.573764 | + | 0.819021i | \(0.305483\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.51475 | − | 6.08773i | −1.17158 | − | 2.02924i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.71642 | 0.819031 | 0.409516 | − | 0.912303i | \(-0.365698\pi\) | ||||
0.409516 | + | 0.912303i | \(0.365698\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.95668 | + | 3.38907i | 0.542686 | + | 0.939960i | 0.998749 | + | 0.0500123i | \(0.0159261\pi\) |
−0.456062 | + | 0.889948i | \(0.650741\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.944962 | + | 1.63672i | −0.229187 | + | 0.396963i | −0.957567 | − | 0.288210i | \(-0.906940\pi\) |
0.728380 | + | 0.685173i | \(0.240273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83281 | − | 3.95485i | 0.420476 | − | 0.907304i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.80753 | − | 8.32689i | 1.04909 | − | 1.81708i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.57611 | − | 6.19400i | −0.745670 | − | 1.29154i | −0.949881 | − | 0.312611i | \(-0.898796\pi\) |
0.204211 | − | 0.978927i | \(-0.434537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12.7612 | −2.45590 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45668 | + | 2.52305i | 0.270499 | + | 0.468518i | 0.968990 | − | 0.247101i | \(-0.0794779\pi\) |
−0.698491 | + | 0.715619i | \(0.746145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.40548 | 1.33006 | 0.665032 | − | 0.746815i | \(-0.268418\pi\) | ||||
0.665032 | + | 0.746815i | \(0.268418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.30137 | − | 7.45019i | 0.748772 | − | 1.29691i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.43284 | −0.564355 | −0.282178 | − | 0.959362i | \(-0.591057\pi\) | ||||
−0.282178 | + | 0.959362i | \(0.591057\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.3934 | 1.98453 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.16090 | + | 8.93895i | −0.805998 | + | 1.39603i | 0.109618 | + | 0.993974i | \(0.465037\pi\) |
−0.915616 | + | 0.402055i | \(0.868296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.37852 | − | 9.31587i | 0.820217 | − | 1.42066i | −0.0853036 | − | 0.996355i | \(-0.527186\pi\) |
0.905521 | − | 0.424302i | \(-0.139481\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.63731 | + | 4.56795i | 0.384691 | + | 0.666304i | 0.991726 | − | 0.128371i | \(-0.0409747\pi\) |
−0.607035 | + | 0.794675i | \(0.707641\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.21774 | 0.316820 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.99264 | + | 5.18340i | 0.419053 | + | 0.725821i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.843574 | + | 1.46111i | 0.115874 | + | 0.200699i | 0.918129 | − | 0.396282i | \(-0.129700\pi\) |
−0.802255 | + | 0.596982i | \(0.796367\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.94456 | − | 11.2891i | −1.05228 | − | 1.49528i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.347967 | − | 0.602697i | 0.0453015 | − | 0.0784644i | −0.842486 | − | 0.538719i | \(-0.818908\pi\) |
0.887787 | + | 0.460254i | \(0.152242\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.28553 | − | 10.8869i | −0.804780 | − | 1.39392i | −0.916440 | − | 0.400173i | \(-0.868950\pi\) |
0.111660 | − | 0.993747i | \(-0.464383\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.6710 | − | 18.4828i | −1.34443 | − | 2.32861i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.365572 | + | 0.633189i | 0.0446617 | + | 0.0773564i | 0.887492 | − | 0.460823i | \(-0.152446\pi\) |
−0.842830 | + | 0.538179i | \(0.819112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.6506 | −2.72682 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.75274 | − | 3.03584i | 0.208012 | − | 0.360288i | −0.743076 | − | 0.669207i | \(-0.766634\pi\) |
0.951088 | + | 0.308919i | \(0.0999673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55396 | + | 9.61973i | −0.650041 | + | 1.12590i | 0.333071 | + | 0.942902i | \(0.391915\pi\) |
−0.983112 | + | 0.183003i | \(0.941418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.24725 | 0.939861 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.03374 | − | 10.4507i | 0.678849 | − | 1.17580i | −0.296479 | − | 0.955039i | \(-0.595812\pi\) |
0.975328 | − | 0.220761i | \(-0.0708542\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.66273 | + | 16.7363i | −1.07364 | + | 1.85959i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.4181 | −1.25330 | −0.626650 | − | 0.779301i | \(-0.715575\pi\) | ||||
−0.626650 | + | 0.779301i | \(0.715575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.22645 | 0.989180 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.34057 | + | 7.51809i | 0.460099 | + | 0.796916i | 0.998965 | − | 0.0454758i | \(-0.0144804\pi\) |
−0.538866 | + | 0.842392i | \(0.681147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.94063 | + | 10.2895i | 0.622747 | + | 1.07863i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.7264 | − | 20.3106i | 1.21597 | − | 2.10612i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.43468 | + | 5.94905i | −0.348739 | + | 0.604034i | −0.986026 | − | 0.166593i | \(-0.946724\pi\) |
0.637286 | + | 0.770627i | \(0.280057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.54754 | − | 16.5368i | −0.959564 | − | 1.66201i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.96831 | + | 12.0695i | 0.693373 | + | 1.20096i | 0.970726 | + | 0.240189i | \(0.0772093\pi\) |
−0.277354 | + | 0.960768i | \(0.589457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.81071 | −0.966678 | −0.483339 | − | 0.875433i | \(-0.660576\pi\) | ||||
−0.483339 | + | 0.875433i | \(0.660576\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6908 | 1.22687 | 0.613434 | − | 0.789746i | \(-0.289788\pi\) | ||||
0.613434 | + | 0.789746i | \(0.289788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.85085 | + | 6.66986i | −0.368844 | + | 0.638857i | −0.989385 | − | 0.145317i | \(-0.953580\pi\) |
0.620541 | + | 0.784174i | \(0.286913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.43580 | + | 9.41507i | −0.515943 | + | 0.893639i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.8536 | −1.20917 | −0.604583 | − | 0.796542i | \(-0.706660\pi\) | ||||
−0.604583 | + | 0.796542i | \(0.706660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.7545 | − | 23.8235i | 1.27161 | − | 2.20249i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.86897 | + | 4.96921i | −0.262998 | + | 0.455526i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.62107 | −0.329188 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.3443 | + | 28.3091i | 1.47371 | + | 2.55255i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.735934 | − | 1.27468i | −0.0653036 | − | 0.113109i | 0.831525 | − | 0.555487i | \(-0.187468\pi\) |
−0.896829 | + | 0.442378i | \(0.854135\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.0335 | − | 29.5028i | −1.49971 | − | 2.59758i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.76584 | + | 15.1829i | −0.765875 | + | 1.32653i | 0.173907 | + | 0.984762i | \(0.444361\pi\) |
−0.939783 | + | 0.341773i | \(0.888973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.56455 | − | 12.0072i | 0.482507 | − | 1.04116i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.49344 | − | 6.05081i | −0.298464 | − | 0.516955i | 0.677321 | − | 0.735688i | \(-0.263141\pi\) |
−0.975785 | + | 0.218733i | \(0.929808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.52394 | + | 13.0318i | 0.638172 | + | 1.10535i | 0.985834 | + | 0.167727i | \(0.0536426\pi\) |
−0.347661 | + | 0.937620i | \(0.613024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.7044 | 1.40676 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.31517 | + | 9.20615i | 0.444477 | + | 0.769857i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.51172 | − | 6.08248i | 0.289642 | − | 0.501674i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.664435 | − | 1.15084i | 0.0544326 | − | 0.0942801i | −0.837525 | − | 0.546399i | \(-0.815998\pi\) |
0.891958 | + | 0.452119i | \(0.149332\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.88336 | −0.153266 | −0.0766328 | − | 0.997059i | \(-0.524417\pi\) | ||||
−0.0766328 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.2852 | 1.07405 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.40932 | − | 7.63717i | 0.351902 | − | 0.609512i | −0.634681 | − | 0.772775i | \(-0.718868\pi\) |
0.986583 | + | 0.163262i | \(0.0522017\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.34310 | 0.423735 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8573 | − | 18.8054i | −0.855677 | − | 1.48208i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.9424 | −1.56201 | −0.781004 | − | 0.624526i | \(-0.785292\pi\) | ||||
−0.781004 | + | 0.624526i | \(0.785292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.43395 | − | 12.8760i | −0.575256 | − | 0.996373i | −0.996014 | − | 0.0892000i | \(-0.971569\pi\) |
0.420757 | − | 0.907173i | \(-0.361764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.15722 | + | 2.00436i | −0.0890167 | + | 0.154181i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30.5179 | + | 2.74265i | −2.33376 | + | 0.209736i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.61271 | + | 9.72149i | −0.426726 | + | 0.739111i | −0.996580 | − | 0.0826348i | \(-0.973667\pi\) |
0.569854 | + | 0.821746i | \(0.307000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.10199 | − | 1.90870i | −0.0828307 | − | 0.143467i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2702 | 1.29084 | 0.645419 | − | 0.763828i | \(-0.276683\pi\) | ||||
0.645419 | + | 0.763828i | \(0.276683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.87048 | + | 15.3641i | 0.659338 | + | 1.14201i | 0.980787 | + | 0.195080i | \(0.0624965\pi\) |
−0.321450 | + | 0.946927i | \(0.604170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −39.8118 | −2.94297 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.56691 | + | 4.44602i | −0.187711 | + | 0.325125i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −38.7440 | −2.81821 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.1341 | −1.81864 | −0.909321 | − | 0.416096i | \(-0.863398\pi\) | ||||
−0.909321 | + | 0.416096i | \(0.863398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.61627 | − | 13.1918i | 0.548231 | − | 0.949564i | −0.450165 | − | 0.892945i | \(-0.648635\pi\) |
0.998396 | − | 0.0566184i | \(-0.0180318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.15878 | −0.581289 | −0.290644 | − | 0.956831i | \(-0.593870\pi\) | ||||
−0.290644 | + | 0.956831i | \(0.593870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.96105 | + | 12.0569i | 0.493456 | + | 0.854690i | 0.999972 | − | 0.00754036i | \(-0.00240020\pi\) |
−0.506516 | + | 0.862231i | \(0.669067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.31549 | 0.163322 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.42260 | + | 7.66016i | 0.310405 | + | 0.537638i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.1383 | + | 43.5408i | −1.74723 | + | 3.02629i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.97868 | − | 10.7430i | 0.344383 | − | 0.743110i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.79305 | − | 4.83770i | 0.192281 | − | 0.333041i | −0.753725 | − | 0.657190i | \(-0.771745\pi\) |
0.946006 | + | 0.324149i | \(0.105078\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.55083 | − | 9.61431i | −0.380336 | − | 0.658762i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.4836 | 1.52629 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.5890 | + | 30.4651i | 1.18856 | + | 2.05864i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.39596 | −0.497506 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.43684 | + | 4.22074i | −0.163183 | + | 0.282641i | −0.936009 | − | 0.351977i | \(-0.885509\pi\) |
0.772825 | + | 0.634619i | \(0.218843\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.7800 | −1.77745 | −0.888727 | − | 0.458438i | \(-0.848409\pi\) | ||||
−0.888727 | + | 0.458438i | \(0.848409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.4407 | 1.41684 | 0.708422 | − | 0.705789i | \(-0.249407\pi\) | ||||
0.708422 | + | 0.705789i | \(0.249407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.0593 | − | 22.6193i | 0.859237 | − | 1.48824i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.0459183 | − | 0.0795329i | 0.00300821 | − | 0.00521037i | −0.864517 | − | 0.502603i | \(-0.832376\pi\) |
0.867526 | + | 0.497393i | \(0.165709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.1085 | − | 33.0969i | −1.24123 | − | 2.14987i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.9290 | 1.35378 | 0.676892 | − | 0.736082i | \(-0.263326\pi\) | ||||
0.676892 | + | 0.736082i | \(0.263326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.937689 | + | 1.62412i | 0.0604019 | + | 0.104619i | 0.894645 | − | 0.446778i | \(-0.147428\pi\) |
−0.834243 | + | 0.551397i | \(0.814095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.4595 | + | 19.8484i | 0.735125 | + | 1.27327i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.9895 | − | 1.52685i | 1.08102 | − | 0.0971511i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.0802 | + | 31.3159i | −1.14579 | + | 1.98456i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.93088 | + | 15.4687i | 0.563712 | + | 0.976378i | 0.997168 | + | 0.0752035i | \(0.0239606\pi\) |
−0.433456 | + | 0.901175i | \(0.642706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.71421 | − | 16.8255i | −0.610727 | − | 1.05781i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0988 | + | 26.1518i | 0.941836 | + | 1.63131i | 0.761967 | + | 0.647616i | \(0.224234\pi\) |
0.179869 | + | 0.983691i | \(0.442433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.4223 | −0.647613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.2398 | − | 17.7358i | 0.633826 | − | 1.09782i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.6687 | − | 18.4788i | 0.657863 | − | 1.13945i | −0.323305 | − | 0.946295i | \(-0.604794\pi\) |
0.981168 | − | 0.193157i | \(-0.0618726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.4926 | 1.68252 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1825 | − | 26.2969i | 0.925694 | − | 1.60335i | 0.135253 | − | 0.990811i | \(-0.456815\pi\) |
0.790441 | − | 0.612538i | \(-0.209851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.20262 | − | 9.01119i | 0.316036 | − | 0.547391i | −0.663621 | − | 0.748069i | \(-0.730981\pi\) |
0.979657 | + | 0.200678i | \(0.0643145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 37.6272 | 2.27730 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5757 | 0.815683 | 0.407842 | − | 0.913053i | \(-0.366282\pi\) | ||||
0.407842 | + | 0.913053i | \(0.366282\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.0284 | − | 45.0826i | −1.55828 | − | 2.69902i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.30763 | + | 3.99693i | 0.137661 | + | 0.238437i | 0.926611 | − | 0.376021i | \(-0.122708\pi\) |
−0.788950 | + | 0.614458i | \(0.789375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.38676 | − | 12.7942i | 0.439097 | − | 0.760539i | −0.558523 | − | 0.829489i | \(-0.688632\pi\) |
0.997620 | + | 0.0689504i | \(0.0219650\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.6689 | + | 27.1393i | −0.924905 | + | 1.60198i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.71409 | + | 11.6292i | 0.394947 | + | 0.684068i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8774 | + | 18.8403i | 0.637647 | + | 1.10444i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.5565 | −0.967240 | −0.483620 | − | 0.875278i | \(-0.660678\pi\) | ||||
−0.483620 | + | 0.875278i | \(0.660678\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34.6648 | −2.01146 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.9946 | − | 24.2394i | 0.809330 | − | 1.40180i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.3296 | − | 28.2837i | 0.941222 | − | 1.63024i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 44.1364 | 2.53557 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.07134 | − | 12.2479i | 0.403583 | − | 0.699026i | −0.590573 | − | 0.806984i | \(-0.701098\pi\) |
0.994155 | + | 0.107959i | \(0.0344315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.5350 | + | 26.9074i | −0.883754 | + | 1.53071i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.1773 | 1.31427 | 0.657133 | − | 0.753775i | \(-0.271769\pi\) | ||||
0.657133 | + | 0.753775i | \(0.271769\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4209 | + | 21.5136i | 0.702068 | + | 1.21602i | 0.967739 | + | 0.251954i | \(0.0810732\pi\) |
−0.265671 | + | 0.964064i | \(0.585593\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.9737 | + | 24.2031i | 0.784840 | + | 1.35938i | 0.929095 | + | 0.369842i | \(0.120588\pi\) |
−0.144255 | + | 0.989541i | \(0.546078\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.95696 | + | 6.85366i | 0.221547 | + | 0.383731i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.0955 | − | 34.8065i | 1.12162 | − | 1.94271i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.74105 | + | 6.73698i | 0.263799 | + | 0.374856i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1954 | + | 21.1231i | 0.674407 | + | 1.16811i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00706 | + | 13.8686i | 0.441443 | + | 0.764602i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3670 | 0.844649 | 0.422324 | − | 0.906445i | \(-0.361214\pi\) | ||||
0.422324 | + | 0.906445i | \(0.361214\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0656 | + | 20.8982i | 0.661190 | + | 1.14521i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.85108 | + | 4.93822i | −0.155308 | + | 0.269002i | −0.933171 | − | 0.359432i | \(-0.882970\pi\) |
0.777863 | + | 0.628434i | \(0.216304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.3533 | + | 35.2529i | −1.10544 | + | 1.91468i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.1164 | 1.08936 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.5193 | −0.783968 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.48887 | − | 6.04290i | 0.187292 | − | 0.324400i | −0.757054 | − | 0.653352i | \(-0.773362\pi\) |
0.944347 | + | 0.328952i | \(0.106696\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.9017 | −0.904729 | −0.452364 | − | 0.891833i | \(-0.649419\pi\) | ||||
−0.452364 | + | 0.891833i | \(0.649419\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.9696 | − | 43.2487i | −1.33278 | − | 2.30844i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.5814 | −1.62768 | −0.813842 | − | 0.581086i | \(-0.802628\pi\) | ||||
−0.813842 | + | 0.581086i | \(0.802628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.08586 | + | 15.7372i | 0.480875 | + | 0.832900i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.95750 | + | 13.7828i | −0.419981 | + | 0.727428i | −0.995937 | − | 0.0900527i | \(-0.971296\pi\) |
0.575956 | + | 0.817480i | \(0.304630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2816 | − | 14.4970i | −0.646401 | − | 0.762998i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.73385 | + | 9.93132i | −0.300949 | + | 0.521259i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.91470 | + | 15.4407i | 0.465343 | + | 0.805998i | 0.999217 | − | 0.0395659i | \(-0.0125975\pi\) |
−0.533874 | + | 0.845564i | \(0.679264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 72.5572 | 3.77718 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.56115 | + | 4.43605i | 0.132968 | + | 0.230308i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3643 | 0.536645 | 0.268323 | − | 0.963329i | \(-0.413531\pi\) | ||||
0.268323 | + | 0.963329i | \(0.413531\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.70053 | + | 9.87361i | −0.293592 | + | 0.508517i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.1604 | −0.676002 | −0.338001 | − | 0.941146i | \(-0.609751\pi\) | ||||
−0.338001 | + | 0.941146i | \(0.609751\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.66132 | −0.238807 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.1227 | + | 17.5330i | −0.517244 | + | 0.895894i | 0.482555 | + | 0.875866i | \(0.339709\pi\) |
−0.999799 | + | 0.0200280i | \(0.993624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −75.6167 | −3.84381 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.347599 | − | 0.602059i | −0.0176240 | − | 0.0305256i | 0.857079 | − | 0.515185i | \(-0.172277\pi\) |
−0.874703 | + | 0.484660i | \(0.838944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5171 | 0.683591 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.7609 | + | 48.0833i | 1.40035 | + | 2.42548i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.16274 | − | 14.1383i | 0.409676 | − | 0.709580i | −0.585177 | − | 0.810906i | \(-0.698975\pi\) |
0.994853 | + | 0.101325i | \(0.0323083\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −24.1203 | − | 34.2746i | −1.20752 | − | 1.71588i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.19765 | − | 7.27055i | 0.209621 | − | 0.363074i | −0.741974 | − | 0.670428i | \(-0.766110\pi\) |
0.951595 | + | 0.307354i | \(0.0994437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4902 | + | 25.0977i | 0.721807 | + | 1.25021i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.32503 | −0.462224 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.21536 | − | 3.83711i | −0.109542 | − | 0.189733i | 0.806043 | − | 0.591858i | \(-0.201605\pi\) |
−0.915585 | + | 0.402125i | \(0.868272\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.1270 | −1.09144 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.05645 | − | 1.82983i | 0.0519847 | − | 0.0900401i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.6557 | 2.33371 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.05906 | −0.100592 | −0.0502958 | − | 0.998734i | \(-0.516016\pi\) | ||||
−0.0502958 | + | 0.998734i | \(0.516016\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.71640 | − | 11.6331i | 0.327337 | − | 0.566965i | −0.654645 | − | 0.755936i | \(-0.727182\pi\) |
0.981983 | + | 0.188971i | \(0.0605154\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.5390 | − | 32.1104i | 0.901396 | − | 1.56126i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.0833 | − | 33.0533i | −0.923507 | − | 1.59956i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.6657 | 1.62539 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.4194 | − | 33.6353i | −0.935398 | − | 1.62016i | −0.773923 | − | 0.633280i | \(-0.781708\pi\) |
−0.161475 | − | 0.986877i | \(-0.551625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.51526 | + | 2.62451i | 0.0728188 | + | 0.126126i | 0.900136 | − | 0.435610i | \(-0.143467\pi\) |
−0.827317 | + | 0.561736i | \(0.810134\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.0506 | + | 2.79053i | −1.48535 | + | 0.133489i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6233 | − | 21.8642i | 0.602477 | − | 1.04352i | −0.389968 | − | 0.920829i | \(-0.627514\pi\) |
0.992445 | − | 0.122692i | \(-0.0391529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.79480 | − | 13.5010i | −0.371181 | − | 0.642904i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7494 | + | 18.6185i | 0.510718 | + | 0.884590i | 0.999923 | + | 0.0124209i | \(0.00395381\pi\) |
−0.489205 | + | 0.872169i | \(0.662713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.10423 | − | 3.64463i | −0.0995265 | − | 0.172385i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.7928 | 1.17004 | 0.585022 | − | 0.811018i | \(-0.301086\pi\) | ||||
0.585022 | + | 0.811018i | \(0.301086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0192 | + | 24.2819i | −0.660137 | + | 1.14339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.98224 | + | 5.16539i | −0.140118 | + | 0.242691i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.55913 | −0.166489 | −0.0832444 | − | 0.996529i | \(-0.526528\pi\) | ||||
−0.0832444 | + | 0.996529i | \(0.526528\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.0589 | − | 20.8866i | 0.562859 | − | 0.974901i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.73320 | + | 8.19814i | −0.220447 | + | 0.381826i | −0.954944 | − | 0.296787i | \(-0.904085\pi\) |
0.734497 | + | 0.678612i | \(0.237418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.7465 | −0.964171 | −0.482085 | − | 0.876124i | \(-0.660121\pi\) | ||||
−0.482085 | + | 0.876124i | \(0.660121\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.36791 | 0.0632992 | 0.0316496 | − | 0.999499i | \(-0.489924\pi\) | ||||
0.0316496 | + | 0.999499i | \(0.489924\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.10990 | + | 1.92241i | 0.0512506 | + | 0.0887686i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.9641 | − | 24.1864i | −0.643430 | − | 1.11445i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.6103 | − | 25.3058i | 0.671783 | − | 1.16356i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.92991 | − | 10.2709i | 0.271512 | − | 0.470272i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.40085 | − | 4.15840i | −0.109698 | − | 0.190002i | 0.805950 | − | 0.591984i | \(-0.201655\pi\) |
−0.915648 | + | 0.401981i | \(0.868322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.71698 | − | 11.6341i | −0.306268 | − | 0.530471i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −68.7690 | −3.12910 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1236 | 0.685315 | 0.342657 | − | 0.939460i | \(-0.388673\pi\) | ||||
0.342657 | + | 0.939460i | \(0.388673\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.5781 | + | 54.6950i | −1.42801 | + | 2.47339i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0731 | + | 34.7676i | −0.905885 | + | 1.56904i | −0.0861613 | + | 0.996281i | \(0.527460\pi\) |
−0.819724 | + | 0.572759i | \(0.805873\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.50604 | −0.247980 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.32145 | − | 9.21702i | 0.238700 | − | 0.413440i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.2320 | + | 31.5788i | −0.816178 | + | 1.41366i | 0.0923011 | + | 0.995731i | \(0.470578\pi\) |
−0.908479 | + | 0.417930i | \(0.862756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −47.0857 | −2.10364 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.09897 | − | 10.5637i | −0.271939 | − | 0.471013i | 0.697419 | − | 0.716664i | \(-0.254332\pi\) |
−0.969358 | + | 0.245651i | \(0.920998\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.66484 | + | 6.34768i | 0.162761 | + | 0.281910i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.94830 | − | 8.57071i | −0.219330 | − | 0.379890i | 0.735274 | − | 0.677770i | \(-0.237054\pi\) |
−0.954603 | + | 0.297880i | \(0.903720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.8622 | + | 29.2062i | −0.745940 | + | 1.29201i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.3889 | + | 50.4686i | −1.03264 | + | 2.22824i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.16403 | + | 12.4085i | 0.315074 | + | 0.545724i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.7751 | + | 30.7874i | 0.780240 | + | 1.35142i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.7004 | 1.65169 | 0.825843 | − | 0.563900i | \(-0.190700\pi\) | ||||
0.825843 | + | 0.563900i | \(0.190700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.49459 | + | 7.78487i | 0.196535 | + | 0.340408i | 0.947403 | − | 0.320044i | \(-0.103698\pi\) |
−0.750868 | + | 0.660453i | \(0.770364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.99790 | + | 12.1207i | −0.304833 | + | 0.527987i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0771 | + | 24.3822i | −0.612047 | + | 1.06010i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.89208 | −0.212298 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.3930 | −1.74962 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.3469 | − | 47.3662i | 1.18011 | − | 2.04400i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.02431 | 0.259485 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.49491 | + | 12.9816i | 0.322231 | + | 0.558121i | 0.980948 | − | 0.194270i | \(-0.0622338\pi\) |
−0.658717 | + | 0.752391i | \(0.728900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 56.1846 | 2.41111 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.9344 | − | 24.1350i | −0.595790 | − | 1.03194i | −0.993435 | − | 0.114400i | \(-0.963506\pi\) |
0.397644 | − | 0.917540i | \(-0.369828\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −44.1842 | + | 76.5293i | −1.88574 | + | 3.26619i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6481 | − | 1.13669i | 0.538827 | − | 0.0484245i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.3189 | − | 31.7292i | 0.778998 | − | 1.34926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.9869 | + | 20.7620i | 0.507903 | + | 0.879714i | 0.999958 | + | 0.00914996i | \(0.00291256\pi\) |
−0.492055 | + | 0.870564i | \(0.663754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.0963 | 1.78048 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.12926 | + | 14.0803i | 0.343217 | + | 0.594470i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.6346 | 1.20681 | 0.603403 | − | 0.797436i | \(-0.293811\pi\) | ||||
0.603403 | + | 0.797436i | \(0.293811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.3367 | + | 50.8127i | −1.23203 | + | 2.13393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.5588 | −0.610338 | −0.305169 | − | 0.952298i | \(-0.598713\pi\) | ||||
−0.305169 | + | 0.952298i | \(0.598713\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5089 | 0.900121 | 0.450061 | − | 0.892998i | \(-0.351402\pi\) | ||||
0.450061 | + | 0.892998i | \(0.351402\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.7991 | + | 68.9341i | −1.66263 | + | 2.87976i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.3885 | 1.76466 | 0.882329 | − | 0.470634i | \(-0.155975\pi\) | ||||
0.882329 | + | 0.470634i | \(0.155975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.1203 | − | 41.7775i | −1.00240 | − | 1.73621i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.6662 | −1.43820 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.29150 | + | 3.96900i | 0.0949042 | + | 0.164379i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.2971 | + | 24.7634i | −0.590106 | + | 1.02209i | 0.404112 | + | 0.914710i | \(0.367581\pi\) |
−0.994218 | + | 0.107384i | \(0.965753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.5728 | − | 29.2875i | 0.559259 | − | 1.20677i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9192 | + | 22.3767i | −0.531424 | + | 0.920454i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.33107 | − | 5.76958i | −0.136791 | − | 0.236928i | 0.789489 | − | 0.613764i | \(-0.210345\pi\) |
−0.926280 | + | 0.376836i | \(0.877012\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.0904 | 1.80450 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.78523 | − | 4.82416i | −0.113801 | − | 0.197110i | 0.803499 | − | 0.595307i | \(-0.202969\pi\) |
−0.917300 | + | 0.398197i | \(0.869636\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.78840 | 0.113741 | 0.0568706 | − | 0.998382i | \(-0.481888\pi\) | ||||
0.0568706 | + | 0.998382i | \(0.481888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.56979 | − | 4.45101i | 0.104650 | − | 0.181259i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.6698 | 1.28544 | 0.642718 | − | 0.766102i | \(-0.277807\pi\) | ||||
0.642718 | + | 0.766102i | \(0.277807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.0122 | 1.13511 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.3207 | + | 17.8761i | −0.417533 | + | 0.723188i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.75765 | + | 4.77639i | −0.111380 | + | 0.192916i | −0.916327 | − | 0.400431i | \(-0.868861\pi\) |
0.804947 | + | 0.593347i | \(0.202194\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.21546 | + | 5.56934i | 0.129450 | + | 0.224213i | 0.923463 | − | 0.383686i | \(-0.125346\pi\) |
−0.794014 | + | 0.607900i | \(0.792012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.7761 | −1.63893 | −0.819465 | − | 0.573130i | \(-0.805729\pi\) | ||||
−0.819465 | + | 0.573130i | \(0.805729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 45.6355 | + | 79.0429i | 1.83129 | + | 3.17188i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.1783 | + | 22.8255i | 0.527977 | + | 0.914483i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.5808 | − | 30.6660i | −0.861852 | − | 1.22468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.24390 | − | 5.61860i | 0.129343 | − | 0.224028i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.83753 | + | 6.64680i | 0.152770 | + | 0.264605i | 0.932245 | − | 0.361828i | \(-0.117847\pi\) |
−0.779475 | + | 0.626433i | \(0.784514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.84541 | − | 15.3207i | −0.351574 | − | 0.608943i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.33941 | + | 7.51608i | 0.171934 | + | 0.297798i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.6418 | −0.974815 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.21362 | − | 14.2264i | 0.324419 | − | 0.561910i | −0.656976 | − | 0.753912i | \(-0.728165\pi\) |
0.981395 | + | 0.192002i | \(0.0614980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.14488 | + | 1.98298i | −0.0451495 | + | 0.0782013i | −0.887717 | − | 0.460389i | \(-0.847710\pi\) |
0.842568 | + | 0.538591i | \(0.181043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.0509 | −1.45662 | −0.728311 | − | 0.685247i | \(-0.759694\pi\) | ||||
−0.728311 | + | 0.685247i | \(0.759694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.945225 | − | 1.63718i | 0.0371033 | − | 0.0642648i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.6021 | − | 61.6646i | 1.39536 | − | 2.41683i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.6500 | −0.455900 | −0.227950 | − | 0.973673i | \(-0.573202\pi\) | ||||
−0.227950 | + | 0.973673i | \(0.573202\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 78.0832 | 3.04631 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.74906 | − | 11.6897i | −0.262906 | − | 0.455366i | 0.704107 | − | 0.710094i | \(-0.251348\pi\) |
−0.967013 | + | 0.254728i | \(0.918014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.57990 | − | 9.66468i | −0.217033 | − | 0.375912i | 0.736867 | − | 0.676038i | \(-0.236305\pi\) |
−0.953900 | + | 0.300126i | \(0.902971\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.7113 | + | 20.2845i | −0.454829 | + | 0.787786i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4185 | − | 18.0454i | 0.403406 | − | 0.698720i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.71734 | + | 13.3668i | 0.298369 | + | 0.516791i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.0741 | − | 29.5733i | −0.659140 | − | 1.14166i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4257 | 0.941541 | 0.470770 | − | 0.882256i | \(-0.343976\pi\) | ||||
0.470770 | + | 0.882256i | \(0.343976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.4552 | −1.55482 | −0.777409 | − | 0.628995i | \(-0.783466\pi\) | ||||
−0.777409 | + | 0.628995i | \(0.783466\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.4280 | + | 18.0617i | −0.400188 | + | 0.693146i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.4054 | + | 73.4483i | −1.62498 | + | 2.81454i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.7736 | 1.67495 | 0.837474 | − | 0.546477i | \(-0.184031\pi\) | ||||
0.837474 | + | 0.546477i | \(0.184031\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.9508 | − | 58.8044i | 1.29530 | − | 2.24353i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.30121 | + | 5.71787i | −0.125766 | + | 0.217833i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.3966 | −0.928091 | −0.464045 | − | 0.885811i | \(-0.653603\pi\) | ||||
−0.464045 | + | 0.885811i | \(0.653603\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −28.9870 | − | 50.2070i | −1.10113 | − | 1.90721i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.75371 | − | 16.8939i | −0.369448 | − | 0.639903i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.145421 | − | 0.251876i | −0.00550031 | − | 0.00952682i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.0204 | + | 29.4802i | −0.642853 | + | 1.11345i | 0.341940 | + | 0.939722i | \(0.388916\pi\) |
−0.984793 | + | 0.173732i | \(0.944417\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.29174 | + | 13.5763i | −0.237298 | + | 0.512042i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.1563 | + | 36.6438i | 0.795664 | + | 1.37813i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.29226 | + | 12.6306i | 0.273867 | + | 0.474351i | 0.969849 | − | 0.243708i | \(-0.0783640\pi\) |
−0.695982 | + | 0.718059i | \(0.745031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −84.8285 | −3.18132 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.4828 | − | 45.8696i | −0.991789 | − | 1.71783i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.1404 | − | 57.4009i | 1.23765 | − | 2.14368i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.8694 | − | 22.2904i | 0.479946 | − | 0.831291i | −0.519789 | − | 0.854294i | \(-0.673990\pi\) |
0.999735 | + | 0.0230037i | \(0.00732294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.7860 | −1.10929 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.93921 | 0.220882 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.54728 | + | 13.0723i | −0.279913 | + | 0.484824i | −0.971363 | − | 0.237601i | \(-0.923639\pi\) |
0.691450 | + | 0.722425i | \(0.256972\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.6065 | 0.540982 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1650 | + | 17.6063i | 0.375966 | + | 0.651192i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.3268 | −1.74806 | −0.874028 | − | 0.485875i | \(-0.838501\pi\) | ||||
−0.874028 | + | 0.485875i | \(0.838501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.993047 | + | 1.72001i | 0.0365794 | + | 0.0633573i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.80350 | + | 11.7840i | −0.250271 | + | 0.433482i | −0.963600 | − | 0.267347i | \(-0.913853\pi\) |
0.713330 | + | 0.700829i | \(0.247186\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.7147 | − | 49.0140i | 0.834447 | − | 1.80057i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.7359 | + | 32.4514i | −0.687352 | + | 1.19053i | 0.285340 | + | 0.958426i | \(0.407894\pi\) |
−0.972692 | + | 0.232102i | \(0.925440\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.1319 | + | 69.5104i | 1.46835 | + | 2.54325i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.5302 | 1.40786 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.17270 | + | 10.6914i | 0.225245 | + | 0.390136i | 0.956393 | − | 0.292083i | \(-0.0943484\pi\) |
−0.731148 | + | 0.682219i | \(0.761015\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 56.5671 | 2.06142 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.1799 | + | 26.2923i | −0.551722 | + | 0.955610i | 0.446429 | + | 0.894819i | \(0.352696\pi\) |
−0.998151 | + | 0.0607908i | \(0.980638\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −61.5286 | −2.23335 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.80837 | 0.283053 | 0.141527 | − | 0.989934i | \(-0.454799\pi\) | ||||
0.141527 | + | 0.989934i | \(0.454799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6915 | + | 20.2502i | −0.423259 | + | 0.733106i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.72345 | 0.0983379 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.5971 | − | 37.4073i | −0.778811 | − | 1.34894i | −0.932627 | − | 0.360841i | \(-0.882490\pi\) |
0.153816 | − | 0.988099i | \(-0.450844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 95.6338 | 3.44417 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.12048 | − | 15.7971i | −0.328041 | − | 0.568183i | 0.654082 | − | 0.756423i | \(-0.273055\pi\) |
−0.982123 | + | 0.188240i | \(0.939722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.5035 | + | 28.5849i | −0.592059 | + | 1.02548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.8932 | + | 36.7940i | 0.927720 | + | 1.31828i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.76118 | − | 8.24661i | 0.170368 | − | 0.295087i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.5890 | − | 32.1972i | −0.664318 | − | 1.15063i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.8266 | −1.52660 | −0.763302 | − | 0.646042i | \(-0.776423\pi\) | ||||
−0.763302 | + | 0.646042i | \(0.776423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.7872 | − | 58.5212i | −1.20286 | − | 2.08341i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.0245 | −1.38755 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5976 | − | 42.6043i | 0.873486 | − | 1.51292i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −51.5064 | −1.82445 | −0.912225 | − | 0.409689i | \(-0.865637\pi\) | ||||
−0.912225 | + | 0.409689i | \(0.865637\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.96862 | −0.352664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.5121 | − | 52.8485i | 1.07809 | − | 1.86731i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0869 | + | 26.1312i | −0.532404 | + | 0.922151i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48.0821 | − | 83.2806i | −1.69257 | − | 2.93162i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.4328 | 0.788694 | 0.394347 | − | 0.918962i | \(-0.370971\pi\) | ||||
0.394347 | + | 0.918962i | \(0.370971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.76975 | − | 6.52940i | −0.132374 | − | 0.229278i | 0.792217 | − | 0.610239i | \(-0.208927\pi\) |
−0.924591 | + | 0.380961i | \(0.875593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.4764 | − | 28.5379i | −0.577852 | − | 1.00087i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.9850 | − | 38.3455i | −0.944087 | − | 1.34154i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.7597 | − | 72.3300i | 1.45920 | − | 2.52741i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.6808 | − | 20.2318i | −0.407664 | − | 0.706095i | 0.586964 | − | 0.809613i | \(-0.300323\pi\) |
−0.994628 | + | 0.103519i | \(0.966990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.59991 | − | 13.1634i | −0.264916 | − | 0.458848i | 0.702625 | − | 0.711560i | \(-0.252011\pi\) |
−0.967542 | + | 0.252711i | \(0.918678\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.6367 | − | 28.8156i | −0.578515 | − | 1.00202i | −0.995650 | − | 0.0931733i | \(-0.970299\pi\) |
0.417135 | − | 0.908845i | \(-0.363034\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.7210 | 0.962789 | 0.481394 | − | 0.876504i | \(-0.340130\pi\) | ||||
0.481394 | + | 0.876504i | \(0.340130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.4967 | − | 37.2333i | 0.745711 | − | 1.29161i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.09568 | + | 3.62982i | −0.0726109 | + | 0.125766i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −94.5029 | −3.26650 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.67328 | − | 15.0226i | 0.299435 | − | 0.518636i | −0.676572 | − | 0.736377i | \(-0.736535\pi\) |
0.976007 | + | 0.217740i | \(0.0698686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2561 | − | 17.7642i | 0.353660 | − | 0.612558i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.6162 | 0.503410 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9938 | −0.377752 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.3934 | − | 40.5186i | −0.802860 | − | 1.39059i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.2762 | + | 21.2630i | 0.420823 | + | 0.728886i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.51813 | − | 2.62947i | 0.0519796 | − | 0.0900314i | −0.838865 | − | 0.544340i | \(-0.816780\pi\) |
0.890844 | + | 0.454308i | \(0.150114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.9217 | − | 18.9170i | 0.373079 | − | 0.646191i | −0.616959 | − | 0.786996i | \(-0.711635\pi\) |
0.990037 | + | 0.140804i | \(0.0449688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.57180 | + | 11.3827i | 0.224227 | + | 0.388373i | 0.956087 | − | 0.293082i | \(-0.0946809\pi\) |
−0.731860 | + | 0.681455i | \(0.761348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.6224 | + | 85.9485i | 1.69113 | + | 2.92912i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5725 | 0.666255 | 0.333128 | − | 0.942882i | \(-0.391896\pi\) | ||||
0.333128 | + | 0.942882i | \(0.391896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.5263 | 1.44427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.3902 | − | 28.3886i | 0.555998 | − | 0.963017i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.43062 | + | 2.47790i | −0.0484746 | + | 0.0839605i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.2883 | 1.63431 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.7783 | + | 22.1326i | −0.431491 | + | 0.747365i | −0.997002 | − | 0.0773760i | \(-0.975346\pi\) |
0.565511 | + | 0.824741i | \(0.308679\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.2167 | + | 45.4086i | −0.884267 | + | 1.53159i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.49566 | −0.252535 | −0.126268 | − | 0.991996i | \(-0.540300\pi\) | ||||
−0.126268 | + | 0.991996i | \(0.540300\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.4848 | − | 21.6244i | −0.420148 | − | 0.727718i | 0.575805 | − | 0.817587i | \(-0.304689\pi\) |
−0.995954 | + | 0.0898687i | \(0.971355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.530770 | + | 0.919320i | 0.0178215 | + | 0.0308677i | 0.874799 | − | 0.484487i | \(-0.160994\pi\) |
−0.856977 | + | 0.515354i | \(0.827660\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.23435 | − | 3.87001i | −0.0749377 | − | 0.129796i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.2480 | + | 45.4629i | −0.879342 | + | 1.52306i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.8992 | − | 2.05796i | 0.766293 | − | 0.0688669i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.3201 | − | 76.7647i | −1.47981 | − | 2.56310i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.7874 | + | 18.6844i | 0.359781 | + | 0.623159i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.18858 | −0.106227 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −51.7148 | − | 89.5727i | −1.72096 | − | 2.98079i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.43661 | − | 7.68443i | 0.147315 | − | 0.255157i | −0.782919 | − | 0.622123i | \(-0.786270\pi\) |
0.930234 | + | 0.366966i | \(0.119604\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.9838 | − | 84.8424i | 1.62469 | − | 2.81404i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.13587 | 0.203291 | 0.101645 | − | 0.994821i | \(-0.467589\pi\) | ||||
0.101645 | + | 0.994821i | \(0.467589\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.0164 | −1.02649 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.6137 | + | 46.0963i | −0.878863 | + | 1.52224i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0840 | −0.332640 | −0.166320 | − | 0.986072i | \(-0.553188\pi\) | ||||
−0.166320 | + | 0.986072i | \(0.553188\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.3945 | − | 38.7884i | −0.737924 | − | 1.27812i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.7182 | 0.451541 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.4822 | + | 59.7250i | 1.13255 | + | 1.96163i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.618121 | + | 1.07062i | −0.0202799 | + | 0.0351258i | −0.875987 | − | 0.482334i | \(-0.839789\pi\) |
0.855707 | + | 0.517460i | \(0.173122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.06469 | − | 8.77081i | 0.133215 | − | 0.287452i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.7006 | − | 63.5673i | 1.20152 | − | 2.08110i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.35919 | + | 16.2106i | 0.305751 | + | 0.529577i | 0.977428 | − | 0.211267i | \(-0.0677590\pi\) |
−0.671677 | + | 0.740844i | \(0.734426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 78.6722 | 2.56737 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.90050 | − | 13.6841i | −0.257549 | − | 0.446088i | 0.708036 | − | 0.706177i | \(-0.249582\pi\) |
−0.965585 | + | 0.260089i | \(0.916248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 73.8238 | 2.40403 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4891 | + | 26.8278i | −0.503327 | + | 0.871788i | 0.496666 | + | 0.867942i | \(0.334558\pi\) |
−0.999993 | + | 0.00384589i | \(0.998776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.4693 | −1.41107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 88.5076 | 2.87006 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.89629 | − | 5.01652i | 0.0938200 | − | 0.162501i | −0.815296 | − | 0.579045i | \(-0.803426\pi\) |
0.909116 | + | 0.416544i | \(0.136759\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.0629 | 0.810169 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.6063 | − | 18.3707i | −0.342496 | − | 0.593221i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.8412 | 0.769070 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.6051 | − | 77.2583i | −1.43738 | − | 2.48961i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.560463 | + | 0.970750i | −0.0180233 | + | 0.0312172i | −0.874896 | − | 0.484310i | \(-0.839071\pi\) |
0.856873 | + | 0.515527i | \(0.172404\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.9845 | − | 2.33523i | 0.834742 | − | 0.0750184i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.2567 | + | 48.9420i | −0.906800 | + | 1.57062i | −0.0883174 | + | 0.996092i | \(0.528149\pi\) |
−0.818483 | + | 0.574531i | \(0.805184\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.8432 | + | 39.5656i | 0.732321 | + | 1.26842i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.2112 | −0.454657 | −0.227328 | − | 0.973818i | \(-0.572999\pi\) | ||||
−0.227328 | + | 0.973818i | \(0.572999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.7908 | + | 20.4223i | 0.376836 | + | 0.652699i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.1391 | 1.72853 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.52459 | + | 14.7650i | −0.271892 | + | 0.470931i | −0.969346 | − | 0.245698i | \(-0.920983\pi\) |
0.697454 | + | 0.716629i | \(0.254316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 50.7157 | 1.61430 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −76.9367 | −2.44644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.4730 | − | 28.5321i | 0.523282 | − | 0.906351i | −0.476351 | − | 0.879255i | \(-0.658041\pi\) |
0.999633 | − | 0.0270956i | \(-0.00862584\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.3332 | − | 42.1464i | 0.772192 | − | 1.33748i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1143 | − | 22.7146i | −0.415333 | − | 0.719378i | 0.580130 | − | 0.814524i | \(-0.303002\pi\) |
−0.995463 | + | 0.0951458i | \(0.969668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.8072 | 1.38600 |
(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 | 1900.2.i.f.201.6 | yes | 12 | |
5.2 | odd | 4 | 1900.2.s.e.49.1 | 24 | |||
5.3 | odd | 4 | 1900.2.s.e.49.12 | 24 | |||
5.4 | even | 2 | 1900.2.i.e.201.1 | ✓ | 12 | ||
19.7 | even | 3 | inner | 1900.2.i.f.501.6 | yes | 12 | |
95.7 | odd | 12 | 1900.2.s.e.349.12 | 24 | |||
95.64 | even | 6 | 1900.2.i.e.501.1 | yes | 12 | ||
95.83 | odd | 12 | 1900.2.s.e.349.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.i.e.201.1 | ✓ | 12 | 5.4 | even | 2 | ||
1900.2.i.e.501.1 | yes | 12 | 95.64 | even | 6 | ||
1900.2.i.f.201.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1900.2.i.f.501.6 | yes | 12 | 19.7 | even | 3 | inner | |
1900.2.s.e.49.1 | 24 | 5.2 | odd | 4 | |||
1900.2.s.e.49.12 | 24 | 5.3 | odd | 4 | |||
1900.2.s.e.349.1 | 24 | 95.83 | odd | 12 | |||
1900.2.s.e.349.12 | 24 | 95.7 | odd | 12 |